Finite Group Databasebeta

← #37547745

Subgroups — #37547745

Order 23168.

1252 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26041991C211yesmaximal, characteristic, complemented
2#26041983C211yesmaximal, characteristic, complemented
3#26041980C211yesmaximal, characteristic, complemented
4#26041980C211yesmaximal, characteristic, complemented
5#26041974C211yesmaximal, characteristic, complemented
6#26041972C211yesmaximal, characteristic, complemented
7#26041947C211yesmaximal, characteristic, complemented
8#26041922C211yesmaximal, characteristic, complemented
9#26041921C211yesmaximal, characteristic, complemented
10#26041920C211yesmaximal, characteristic, complemented
11#26041918C211yesmaximal, characteristic, complemented
12#26041916C211yesmaximal, characteristic, complemented
13#26041916C211yesmaximal, characteristic, complemented
14#26041913C211yesmaximal, characteristic, complemented
15#26041911C211yesmaximal, characteristic, complemented
16#26041911C211yesmaximal, characteristic, complemented
17#26041881C211yesmaximal, characteristic, complemented
18#26041879C211yesmaximal, characteristic, complemented
19#26041868C211yesmaximal, characteristic, complemented
20#26041863C211yesmaximal, characteristic, complemented
21#26041862C211yesmaximal, characteristic, complemented
22#26041828C211yesmaximal, characteristic, complemented
23#26041812C211yesmaximal, characteristic, complemented
24#26041788C211yesmaximal, characteristic, complemented
25#26041787C211yesmaximal, characteristic, complemented
26C2×#19153789C211yesmaximal, characteristic, complemented
27#121×D181C211yesmaximal, characteristic, complemented
28#26041752C211yesmaximal, characteristic, complemented
29#26041751C211yesmaximal, characteristic, complemented
30C4×D4×D181C211yesmaximal, characteristic, complemented
31#538×C181C211yesmaximal, characteristic, complemented
32C2×#15668450C2211yescharacteristic, complemented
33C2×#15668449C2211yescharacteristic, complemented
34C2×#15668448C2211yescharacteristic, complemented
35C2×#15668448C2211yescharacteristic, complemented
36C22×D724C2211yescharacteristic, complemented
37C22×C22⋊D181C2211yescharacteristic
38C22×C22⋊D181C2211yescharacteristic, complemented
39C22×C22⋊D181C2211yescharacteristic, complemented
40C2×D4×D181C2211yescharacteristic
41C2×D4×D181C2211yescharacteristic
42C2×D4×D181C2211yescharacteristic, complemented
43C2×D4×D181C2211yescharacteristic, complemented
44C2×D4×D181C2211yescharacteristic, complemented
45C22×C4×D181C2211yescharacteristic, complemented
46C22×C4×D181C2211yescharacteristic, complemented
47#19153814C2211yescharacteristic, complemented
48#19153812C2211yescharacteristic, complemented
49#19153812C2211yescharacteristic, complemented
50#19153812C2211yescharacteristic, complemented
51#19153811C2211yescharacteristic, complemented
52#19153811C2211yescharacteristic, complemented
53#19153810C2211yescharacteristic, complemented
54#19153809C2211yescharacteristic, complemented
55#19153806C2211yescharacteristic, complemented
56#19153806C2211yescharacteristic, complemented
57#19153806C2211yescharacteristic, complemented
58#19153805C2211yescharacteristic, complemented
59#19153804C2211yescharacteristic, complemented
60#19153802C2211yescharacteristic, complemented
61#19153802C2211yescharacteristic, complemented
62#19153802C2211yescharacteristic, complemented
63#19153801C2211yescharacteristic, complemented
64#19153801C2211yescharacteristic, complemented
65#19153801C2211yescharacteristic, complemented
66#19153801C2211yescharacteristic, complemented
67#19153800C2211yescharacteristic, complemented
68#19153800C2211yescharacteristic, complemented
69#19153799C2211yescharacteristic, complemented
70#19153798C2211yescharacteristic, complemented
71#19153798C2211yescharacteristic, complemented
72#19153798C2211yescharacteristic, complemented
73#19153798C2211yescharacteristic, complemented
74#19153797C2211yescharacteristic, complemented
75#19153794C2211yescharacteristic, complemented
76#19153794C2211yescharacteristic, complemented
77#19153794C2211yescharacteristic, complemented
78#19153793C2211yescharacteristic, complemented
79#19153793C2211yescharacteristic, complemented
80#19153792C2211yescharacteristic, complemented
81#19153791C2211yescharacteristic, complemented
82#19153791C2211yescharacteristic, complemented
83#19153791C2211yescharacteristic, complemented
84#19153791C2211yescharacteristic, complemented
85#19153790C2211yescharacteristic, complemented
86#19153789C2211yescharacteristic
87#19153789C2211yescharacteristic, complemented
88#19153789C2211yescharacteristic, complemented
89#19153789C2211yescharacteristic, complemented
90#19153789C2211yescharacteristic, complemented
91#19153789C2211yescharacteristic, complemented
92#19153789C2211yescharacteristic, complemented
93#19153789C2211yescharacteristic, complemented
94#19153789C2211yescharacteristic, complemented
95#19153789C2211yescharacteristic, complemented
96#19153789C2211yescharacteristic, complemented
97#19153789C2211yescharacteristic, complemented
98#19153789C2211yescharacteristic, complemented
99#19153789C2211yescharacteristic, complemented
100#19153789C2211yescharacteristic, complemented
101#19153789C2211yescharacteristic, complemented
102#19153788C2211yescharacteristic, complemented
103#19153788C2211yescharacteristic, complemented
104#19153788C2211yescharacteristic, complemented
105#19153788C2211yescharacteristic, complemented
106#19153788C2211yescharacteristic, complemented
107#19153788C2211yescharacteristic, complemented
108#19153788C2211yescharacteristic, complemented
109#19153788C2211yescharacteristic, complemented
110#19153788C2211yescharacteristic, complemented
111#19153787C2211yescharacteristic, complemented
112#19153787C2211yescharacteristic, complemented
113#19153786C2211yescharacteristic, complemented
114#19153786C2211yescharacteristic, complemented
115#19153786C2211yescharacteristic, complemented
116#19153786C2211yescharacteristic, complemented
117#19153786C2211yescharacteristic, complemented
118#19153786C2211yescharacteristic, complemented
119#19153784C2211yescharacteristic, complemented
120#19153784C2211yescharacteristic, complemented
121#19153784C2211yescharacteristic, complemented
122#19153784C2211yescharacteristic, complemented
123#19153781C2211yescharacteristic, complemented
124C4×D724C2211yescharacteristic, complemented
125C4×D724C2211yescharacteristic, complemented
126C4×D724C2211yescharacteristic, complemented
127D4×Dic181C2211yescharacteristic, complemented
128D4×Dic181C2211yescharacteristic, complemented
129#19153778C2211yescharacteristic, complemented
130#19153778C2211yescharacteristic, complemented
131#19153778C2211yescharacteristic, complemented
132#19153778C2211yescharacteristic, complemented
133C4×C22⋊D181C2211yescharacteristic
134C4×C22⋊D181C2211yescharacteristic
135C4×C22⋊D181C2211yescharacteristic, complemented
136C4×C22⋊D181C2211yescharacteristic, complemented
137C4×C22⋊D181C2211yescharacteristic, complemented
138C4×C22⋊D181C2211yescharacteristic, complemented
139C4×C22⋊D181C2211yescharacteristic, complemented
140#19153776C2211yescharacteristic
141#19153776C2211yescharacteristic
142#19153776C2211yescharacteristic, complemented
143#19153776C2211yescharacteristic, complemented
144#19153776C2211yescharacteristic, complemented
145#19153776C2211yescharacteristic, complemented
146#19153776C2211yescharacteristic, complemented
147#19153776C2211yescharacteristic, complemented
148#19153776C2211yescharacteristic, complemented
149#19153776C2211yescharacteristic, complemented
150#19153776C2211yescharacteristic, complemented
151#19153776C2211yescharacteristic, complemented
152#19153776C2211yescharacteristic, complemented
153#19153774C2211yescharacteristic, complemented
154#19153773C2211yescharacteristic, complemented
155#19153773C2211yescharacteristic, complemented
156#19153772C2211yescharacteristic, complemented
157#19153772C2211yescharacteristic, complemented
158#19153772C2211yescharacteristic, complemented
159C2×#15668428C2211yescharacteristic, complemented
160C4⋊C4×D181C2211yescharacteristic, complemented
161C4⋊C4×D181C2211yescharacteristic, complemented
162C2×C22⋊Dic181C2211yescharacteristic, complemented
163C2×#15668426C2211yescharacteristic, complemented
164C2×#15668426C2211yescharacteristic, complemented
165C22⋊C4×D181C2211yescharacteristic, complemented
166C22⋊C4×D181C2211yescharacteristic, complemented
167C22⋊C4×D181C2211yescharacteristic, complemented
168C22⋊C4×D181C2211yescharacteristic, complemented
169C22⋊C4×D181C2211yescharacteristic, complemented
170C22⋊C4×D181C2211yescharacteristic, complemented
171C42×D181C2211yescharacteristic, complemented
172#126×C181C2211yescharacteristic, complemented
173#126×C181C2211yescharacteristic, complemented
174#124×C181C2211yescharacteristic, complemented
175#124×C181C2211yescharacteristic, complemented
176#123×C181C2211yescharacteristic, complemented
177#123×C181C2211yescharacteristic, complemented
178C22⋊Q8×C181C2211yescharacteristic, complemented
179#121×C181C2211yescharacteristic, complemented
180#121×C181C2211yescharacteristic, complemented
181#121×C181C2211yescharacteristic, complemented
182#120×C181C2211yescharacteristic, complemented
183#120×C181C2211yescharacteristic, complemented
184C4×D4×C181C2211yescharacteristic, complemented
185C4×D4×C181C2211yescharacteristic, complemented
186C2×C22⋊C4×C181C2211yescharacteristic, complemented
187C23×D181C2311yescharacteristic
188C23×D181C2311yescharacteristic
189C23×D181C2311yescharacteristic
190C23×D181C2311yescharacteristic
191C23×D181C2311yescharacteristic
192#15668450—42no—
193#15668449—42no—
194#15668448—42no—
195#15668448—42no—
196C2×Dic362C2311yescharacteristic
197C2×Dic362C2311yescharacteristic
198C2×D724—42no—
199C2×D724C2311yescharacteristic
200C2×D724C2311yescharacteristic
201C2×D724C2311yescharacteristic
202C2×D724C2311yescharacteristic
203C2×D724C2311yescharacteristic
204C2×D724C2311yescharacteristic
205C2×D724C2311yescharacteristic
206C2×D724C2311yescharacteristic
207C2×D724C2311yescharacteristic
208C2×D724C2311yescharacteristic
209C2×C22⋊D181—24no—
210C2×C22⋊D181—42no—
211C2×C22⋊D181—42no—
212C2×C22⋊D181C2311yescharacteristic
213C2×C22⋊D181C2311yescharacteristic
214C2×C22⋊D181C2311yescharacteristic
215C2×C22⋊D181C2311yescharacteristic
216C2×C22⋊D181C2311yescharacteristic
217C2×C22⋊D181C2311yescharacteristic
218C2×C22⋊D181C2311yescharacteristic
219C2×C22⋊D181C2311yescharacteristic
220C2×C22⋊D181C2311yescharacteristic
221C2×C22⋊D181C2311yescharacteristic
222C2×C22⋊D181C2311yescharacteristic
223C2×C22⋊D181C2311yescharacteristic
224C2×C22⋊D181C2311yescharacteristic
225C2×C22⋊D181C2311yescharacteristic
226C2×C22⋊D181C2311yescharacteristic
227C2×C22⋊D181C2311yescharacteristic
228C2×C22⋊D181C2311yescharacteristic
229C2×C22⋊D181C2311yescharacteristic
230C2×C22⋊D181C2311yescharacteristic
231C2×C22⋊D181C2311yescharacteristic
232D4×D181—24no—
233D4×D181—24no—
234D4×D181—42no—
235D4×D181—42no—
236D4×D181—42no—
237C22×Dic181C2311yescharacteristic
238C22×Dic181C2311yescharacteristic
239C22×Dic181C2311yescharacteristic
240C22×Dic181C2311yescharacteristic
241C22×Dic181C2311yescharacteristic
242C22×Dic181C2311yescharacteristic
243C22×Dic181C2311yescharacteristic
244C2×C4×D181—42no—
245C2×C4×D181—42no—
246C2×C4×D181C2311yescharacteristic
247C2×C4×D181C2311yescharacteristic
248C2×C4×D181C2311yescharacteristic
249C2×C4×D181C2311yescharacteristic
250C2×C4×D181C2311yescharacteristic
251C2×C4×D181C2311yescharacteristic
252C2×C4×D181C2311yescharacteristic
253C2×C4×D181C2311yescharacteristic
254C2×C4×D181C2311yescharacteristic
255C2×C4×D181C2311yescharacteristic
256C2×C4×D181C2311yescharacteristic
257C2×C4×D181C2311yescharacteristic
258C2×C4×D181C2311yescharacteristic
259C2×C4×D181C2311yescharacteristic
260C2×C4×D181C2311yescharacteristic
261C2×C4×D181C2311yescharacteristic
262C4⋊Dic181C2311yescharacteristic
263C4⋊Dic181C2311yescharacteristic
264C4⋊Dic181C2311yescharacteristic
265C4⋊Dic181C2311yescharacteristic
266#15668428C2311yescharacteristic
267#15668428C2311yescharacteristic
268#15668428C2311yescharacteristic
269#15668428C2311yescharacteristic
270#15668428C2311yescharacteristic
271#15668428C2311yescharacteristic
272#15668428C2311yescharacteristic
273#15668428C2311yescharacteristic
274#15668428C2311yescharacteristic
275#15668428C2311yescharacteristic
276#15668428C2311yescharacteristic
277#15668428C2311yescharacteristic
278#15668428C2311yescharacteristic
279#15668428C2311yescharacteristic
280#15668428C2311yescharacteristic
281#15668428C2311yescharacteristic
282C22⋊Dic181C2311yescharacteristic
283C22⋊Dic181C2311yescharacteristic
284C22⋊Dic181C2311yescharacteristic
285C22⋊Dic181C2311yescharacteristic
286C22⋊Dic181C2311yescharacteristic
287C22⋊Dic181C2311yescharacteristic
288C22⋊Dic181C2311yescharacteristic
289C22⋊Dic181C2311yescharacteristic
290#15668426C2311yescharacteristic
291#15668426C2311yescharacteristic
292#15668426C2311yescharacteristic
293#15668426C2311yescharacteristic
294#15668426C2311yescharacteristic
295#15668426C2311yescharacteristic
296#15668426C2311yescharacteristic
297#15668426C2311yescharacteristic
298#15668426C2311yescharacteristic
299#15668426C2311yescharacteristic
300#15668426C2311yescharacteristic
301#15668426C2311yescharacteristic
302#15668426C2311yescharacteristic
303#15668426C2311yescharacteristic
304#15668426C2311yescharacteristic
305#15668426C2311yescharacteristic
306#15668426C2311yescharacteristic
307#15668426C2311yescharacteristic
308#15668426C2311yescharacteristic
309#15668426C2311yescharacteristic
310#15668426C2311yescharacteristic
311#15668426C2311yescharacteristic
312#15668426C2311yescharacteristic
313#15668426C2311yescharacteristic
314C4×Dic181C2311yescharacteristic
315C4×Dic181C2311yescharacteristic
316C4×Dic181C2311yescharacteristic
317C4×Dic181C2311yescharacteristic
318C4×Dic181C2311yescharacteristic
319C4×Dic181C2311yescharacteristic
320C4×Dic181C2311yescharacteristic
321C4×Dic181C2311yescharacteristic
322C24×C181C2311yescharacteristic
323C2×Q8×C181C2311yescharacteristic
324C2×D4×C181C2311yescharacteristic
325C2×D4×C181C2311yescharacteristic
326C2×D4×C181C2311yescharacteristic
327C2×D4×C181C2311yescharacteristic
328C2×D4×C181C2311yescharacteristic
329C2×D4×C181C2311yescharacteristic
330C2×D4×C181C2311yescharacteristic
331C22×C4×C181C2311yescharacteristic
332C22×C4×C181C2311yescharacteristic
333C22×C4×C181C2311yescharacteristic
334C22×C4×C181C2311yescharacteristic
335C4⋊C4×C181C2311yescharacteristic
336C4⋊C4×C181C2311yescharacteristic
337C4⋊C4×C181C2311yescharacteristic
338C4⋊C4×C181C2311yescharacteristic
339C4⋊C4×C181C2311yescharacteristic
340C4⋊C4×C181C2311yescharacteristic
341C22⋊C4×C181C2311yescharacteristic
342C22⋊C4×C181C2311yescharacteristic
343C22⋊C4×C181C2311yescharacteristic
344C22⋊C4×C181C2311yescharacteristic
345C22⋊C4×C181C2311yescharacteristic
346C22⋊C4×C181C2311yescharacteristic
347C22⋊C4×C181C2311yescharacteristic
348C22⋊C4×C181C2311yescharacteristic
349C22⋊C4×C181C2311yescharacteristic
350C22⋊C4×C181C2311yescharacteristic
351C22⋊C4×C181C2311yescharacteristic
352C22⋊C4×C181C2311yescharacteristic
353C22⋊C4×C181C2311yescharacteristic
354C22⋊C4×C181C2311yescharacteristic
355C42×C181C2311yescharacteristic
356C42×C181C2311yescharacteristic
357C22×D181—22no—
358C22×D181—22no—
359C22×D181—22no—
360C22×D181—22no—
361C22×D181—22no—
362C22×D181—22no—
363C22×D181—22no—
364C22×D181—41no—
365C22×D181—41no—
366C22×D181—41no—
367C22×D181—41no—
368C22×D181—41no—
369C22×D181—41no—
370C22×D181—41no—
371C22×D181—41no—
372C22×D181C2411yescharacteristic
373C22×D181C2411yescharacteristic
374C22×D181C2411yescharacteristic
375C22×D181C2411yescharacteristic
376C22×D181C2411yescharacteristic
377C22×D181C2411yescharacteristic
378Dic362—22no—
379Dic362—41no—
380D724—22no—
381D724—22no—
382D724—22no—
383D724—22no—
384D724—22no—
385D724—41no—
386D724—41no—
387D724—41no—
388D724—41no—
389D724—41no—
390C22⋊D181—22no—
391C22⋊D181—22no—
392C22⋊D181—22no—
393C22⋊D181—22no—
394C22⋊D181—22no—
395C22⋊D181—22no—
396C22⋊D181—22no—
397C22⋊D181—22no—
398C22⋊D181—22no—
399C22⋊D181—22no—
400C22⋊D181—22no—
401C22⋊D181—41no—
402C22⋊D181—41no—
403C22⋊D181—41no—
404C22⋊D181—41no—
405C22⋊D181—41no—
406C22⋊D181—41no—
407C22⋊D181—41no—
408C22⋊D181—41no—
409C22⋊D181#4114yescomplemented
410C2×Dic181—22no—
411C2×Dic181—22no—
412C2×Dic181—22no—
413C2×Dic181—41no—
414C2×Dic181—41no—
415C2×Dic181—41no—
416C2×Dic181—41no—
417C2×Dic181C2411yescharacteristic
418C2×Dic181C2411yescharacteristic
419C2×Dic181C2411yescharacteristic
420C2×Dic181C2411yescharacteristic
421C2×Dic181C2411yescharacteristic
422C2×Dic181C2411yescharacteristic
423C2×Dic181C2411yescharacteristic
424C2×Dic181C2411yescharacteristic
425C2×Dic181C2411yescharacteristic
426C2×Dic181C2411yescharacteristic
427C4×D181—22no—
428C4×D181—22no—
429C4×D181—22no—
430C4×D181—22no—
431C4×D181—22no—
432C4×D181—22no—
433C4×D181—41no—
434C4×D181—41no—
435C4×D181—41no—
436C4×D181—41no—
437C4×D181—41no—
438C4×D181—41no—
439C4×D181—41no—
440C4×D181—41no—
441C4×D181—41no—
442C4×D181—41no—
443C23×C181—22no—
444C23×C181—41no—
445C23×C181—41no—
446C23×C181C2411yescharacteristic
447C23×C181C2411yescharacteristic
448C23×C181C2411yescharacteristic
449C23×C181C2411yescharacteristic
450C23×C181C2411yescharacteristic
451Q8×C181—41no—
452D4×C181—22no—
453D4×C181—22no—
454D4×C181—41no—
455D4×C181—41no—
456D4×C181—41no—
457D4×C181—41no—
458D4×C181—41no—
459C2×C4×C181—41no—
460C2×C4×C181—41no—
461C2×C4×C181—41no—
462C2×C4×C181—41no—
463C2×C4×C181C2411yescharacteristic
464C2×C4×C181C2411yescharacteristic
465C2×C4×C181C2411yescharacteristic
466C2×C4×C181C2411yescharacteristic
467C2×C4×C181C2411yescharacteristic
468C2×C4×C181C2411yescharacteristic
469C2×C4×C181C2411yescharacteristic
470C2×C4×C181C2411yescharacteristic
471C2×C4×C181C2411yescharacteristic
472C2×C4×C181C2411yescharacteristic
473C22×C181—21no—
474C22×C181—21no—
475C22×C181—21no—
476C22×C181—21no—
477C22×C181—21no—
478C22×C181—21no—
479C22×C181—21no—
480C22×C181—21no—
481C22×C181—21no—
482C22×C181—21no—
483C22×C181—21no—
484C22×C181—21no—
485C22×C181—21no—
486C22×C181—21no—
487C22×C181—82no—
488C22×C181C2×#4112yes—
489C22×C181C2511yescharacteristic
490C2×D181—21no—
491C2×D181—21no—
492C2×D181—21no—
493C2×D181—21no—
494C2×D181—21no—
495C2×D181—21no—
496C2×D181—21no—
497C2×D181—21no—
498C2×D181—21no—
499C2×D181—21no—
500C2×D181—21no—
501C2×D181—21no—
502C2×D181—21no—
503C2×D181—21no—
504C2×D181—21no—
505C2×D181—21no—
506C2×D181—44no—
507C2×D181—44no—
508C2×D181—82no—
509C2×D181—82no—
510C2×D181—82no—
511C2×D181C2×#4112yes—
512C2×D181H(5,𝔽2)12yes—
513C4×C181—21no—
514C4×C181—21no—
515C4×C181—21no—
516C4×C181—21no—
517C4×C181—21no—
518C4×C181—21no—
519C4×C181—21no—
520C4×C181—21no—
521C4×C181—21no—
522C4×C181—21no—
523Dic181—21no—
524Dic181—21no—
525Dic181—21no—
526Dic181—21no—
527Dic181—21no—
528Dic181—21no—
529Dic181—21no—
530Dic181—21no—
531Dic181C2×#4112yes—
532Dic181H(5,𝔽2)12yes—
533C2×C181—22no—
534C2×C181—41no—
535C2×C181—41no—
536C2×C181—41no—
537C2×C181—41no—
538C2×C181C22×#4111yescharacteristic
539C2×C181C2×H(5,𝔽2)11yescharacteristic
540C2×C181C2×H(5,𝔽2)11yescharacteristic
541D181—22no—
542D181—22no—
543D181—41no—
544D181—41no—
545D181—41no—
546D181—41no—
547C181#351911yescharacteristic, complemented, Sylow
548#3519—1811nomaximal, Sylow
549#555—1811no—
550#554—1811no—
551#553—1811no—
552#553—1811no—
553#553—1811no—
554#553—1811no—
555#550—1811no—
556#546—1811no—
557#546—1811no—
558#546—1811no—
559#546—1811no—
560#546—1811no—
561#546—1811no—
562D42—1811no—
563D42—1811no—
564D42—1811no—
565#540—1811no—
566#540—1811no—
567#538—1811no—
568#538—1811no—
569#538—1811no—
570#538D18111yescharacteristic, complemented
571#532—1811no—
572#529—1811no—
573#525—1811no—
574#525—1811no—
575C2×#121—1811no—
576C2×#121—1811no—
577#518—1811no—
578#518—1811no—
579C2×C4×D4—1811no—
580C2×#41—1811no—
581C2×#41—1811no—
582C2×#41—1811no—
583C2×#41—1811no—
584C22×D4—1811no—
585C22×D4—1811no—
586C22×D4—1811no—
587C22×D4—1811no—
588C22×D4—1811no—
589C22×D4—1811no—
590C22×D4—1811no—
591C22×D4—1811no—
592C22×D4—1811no—
593C23×C4—1811no—
594C23×C4—1811no—
595C4⋊Q8—1811no—
596#127—1811no—
597#127—1811no—
598#127—1811no—
599#126—1811no—
600#126—1811no—
601#126—1811no—
602#126—1811no—
603#126C2×D18111yescharacteristic, complemented
604#126C2×D18111yescharacteristic, complemented
605#125—1811no—
606#125—1811no—
607#125—1811no—
608#124—1811no—
609#124—1811no—
610#124—1811no—
611#124—1811no—
612#124—1811no—
613#124C2×D18111yescharacteristic, complemented
614#124C2×D18111yescharacteristic, complemented
615#123—1811no—
616#123—1811no—
617#123—1811no—
618#123—1811no—
619#123—1811no—
620#123—1811no—
621#123—1811no—
622#123—1811no—
623#123—1811no—
624#123—1811no—
625#123—1811no—
626#123—1811no—
627#123C2×D18111yescharacteristic, complemented
628#123C2×D18111yescharacteristic, complemented
629C22⋊Q8—1811no—
630C22⋊Q8—1811no—
631C22⋊Q8—1811no—
632C22⋊Q8—1811no—
633C22⋊Q8—1811no—
634C22⋊Q8—1811no—
635C22⋊Q8C2×D18111yescharacteristic, complemented
636#121—1811no—
637#121—1811no—
638#121—1811no—
639#121—1811no—
640#121—1811no—
641#121—1811no—
642#121—1811no—
643#121—1811no—
644#121—1811no—
645#121—1811no—
646#121—1811no—
647#121—1811no—
648#121—1811no—
649#121—1811no—
650#121—1811no—
651#121—1811no—
652#121—1811no—
653#121—1811no—
654#121—1811no—
655#121—1811no—
656#121—1811no—
657#121—1811no—
658#121—1811no—
659#121—1811no—
660#121—1811no—
661#121—1811no—
662#121—1811no—
663#121—1811no—
664#121—1811no—
665#121—1811no—
666#121—1811no—
667#121—1811no—
668#121C2×D18111yescharacteristic, complemented
669#121C2×D18111yescharacteristic, complemented
670#121C2×D18111yescharacteristic, complemented
671#120—1811no—
672#120—1811no—
673#120—1811no—
674#120—1811no—
675#120—1811no—
676#120—1811no—
677#120—1811no—
678#120—1811no—
679#120—1811no—
680#120—1811no—
681#120C2×D18111yescharacteristic, complemented
682#120C2×D18111yescharacteristic, complemented
683C4×Q8—1811no—
684C4×D4—1811no—
685C4×D4—1811no—
686C4×D4—1811no—
687C4×D4—1811no—
688C4×D4—1811no—
689C4×D4—1811no—
690C4×D4—1811no—
691C4×D4—1811no—
692C4×D4—1811no—
693C4×D4—1811no—
694C4×D4—1811no—
695C4×D4—1811no—
696C4×D4—1811no—
697C4×D4—1811no—
698C4×D4—1811no—
699C4×D4—1811no—
700C4×D4—1811no—
701C4×D4—1811no—
702C4×D4—1811no—
703C4×D4—1811no—
704C4×D4—1811no—
705C4×D4—1811no—
706C4×D4—1811no—
707C4×D4—1811no—
708C4×D4—1811no—
709C4×D4—1811no—
710C4×D4—1811no—
711C4×D4—1811no—
712C4×D4—1811no—
713C4×D4C2×D18111yescharacteristic, complemented
714C4×D4C2×D18111yescharacteristic, complemented
715#117—1811no—
716#117—1811no—
717#117—1811no—
718#117—1811no—
719#117—1811no—
720#117—1811no—
721C2×C4⋊C4—1811no—
722C2×C4⋊C4—1811no—
723C2×C4⋊C4—1811no—
724C2×C22⋊C4—1811no—
725C2×C22⋊C4—1811no—
726C2×C22⋊C4—1811no—
727C2×C22⋊C4—1811no—
728C2×C22⋊C4—1811no—
729C2×C22⋊C4—1811no—
730C2×C22⋊C4—1811no—
731C2×C22⋊C4—1811no—
732C2×C22⋊C4—1811no—
733C2×C22⋊C4C2×D18111yescharacteristic, complemented
734C2×C42—1811no—
735C24—1811no—
736C24—1811no—
737C24—1811no—
738C24—1811no—
739C24—1811no—
740C24C22×D18111yescharacteristic
741#41—7242no—
742#41—7242no—
743#41—7242no—
744#41—7242no—
745C2×Q8—1811no—
746C2×Q8—1811no—
747C2×Q8C22×D18111yescharacteristic
748C2×D4—3624no—
749C2×D4—3624no—
750C2×D4—3624no—
751C2×D4—1811no—
752C2×D4—1811no—
753C2×D4—1811no—
754C2×D4—1811no—
755C2×D4—1811no—
756C2×D4—1811no—
757C2×D4—1811no—
758C2×D4—1811no—
759C2×D4—1811no—
760C2×D4—1811no—
761C2×D4—1811no—
762C2×D4—1811no—
763C2×D4—1811no—
764C2×D4—1811no—
765C2×D4—1811no—
766C2×D4—1811no—
767C2×D4—1811no—
768C2×D4—1811no—
769C2×D4—1811no—
770C2×D4—1811no—
771C2×D4—1811no—
772C2×D4—1811no—
773C2×D4—1811no—
774C2×D4—1811no—
775C2×D4—1811no—
776C2×D4—1811no—
777C2×D4—1811no—
778C2×D4—1811no—
779C2×D4—1811no—
780C2×D4—1811no—
781C2×D4—7242no—
782C2×D4—7242no—
783C2×D4—7242no—
784C2×D4—7242no—
785C2×D4—7242no—
786C2×D4—7242no—
787C2×D4C22×D18111yescharacteristic
788C2×D4C22×D18111yescharacteristic
789C2×D4C22×D18111yescharacteristic
790C2×D4C22×D18111yescharacteristic
791C2×D4C22×D18111yescharacteristic
792C2×D4C22×D18111yescharacteristic
793C2×D4C22×D18111yescharacteristic
794C22×C4—1811no—
795C22×C4—1811no—
796C22×C4—1811no—
797C22×C4—1811no—
798C22×C4—1811no—
799C22×C4—1811no—
800C22×C4—1811no—
801C22×C4—1811no—
802C22×C4—1811no—
803C22×C4—1811no—
804C22×C4—1811no—
805C22×C4—1811no—
806C22×C4—1811no—
807C22×C4—1811no—
808C22×C4—1811no—
809C22×C4—1811no—
810C22×C4—1811no—
811C22×C4—1811no—
812C22×C4—1811no—
813C22×C4—1811no—
814C22×C4—1811no—
815C22×C4—1811no—
816C22×C4—1811no—
817C22×C4—7242no—
818C22×C4—7242no—
819C22×C4C22×D18111yescharacteristic
820C22×C4C22×D18111yescharacteristic
821C22×C4C22×D18111yescharacteristic
822C22×C4C22×D18111yescharacteristic
823C4⋊C4—1811no—
824C4⋊C4—1811no—
825C4⋊C4—1811no—
826C4⋊C4—1811no—
827C4⋊C4—1811no—
828C4⋊C4—1811no—
829C4⋊C4—1811no—
830C4⋊C4—1811no—
831C4⋊C4—1811no—
832C4⋊C4—1811no—
833C4⋊C4—1811no—
834C4⋊C4—1811no—
835C4⋊C4—1811no—
836C4⋊C4—1811no—
837C4⋊C4—1811no—
838C4⋊C4—1811no—
839C4⋊C4—1811no—
840C4⋊C4—1811no—
841C4⋊C4—1811no—
842C4⋊C4—1811no—
843C4⋊C4C22×D18111yescharacteristic
844C4⋊C4C22×D18111yescharacteristic
845C4⋊C4C22×D18111yescharacteristic
846C4⋊C4C22×D18111yescharacteristic
847C4⋊C4C22×D18111yescharacteristic
848C4⋊C4C22×D18111yescharacteristic
849C22⋊C4—1811no—
850C22⋊C4—1811no—
851C22⋊C4—1811no—
852C22⋊C4—1811no—
853C22⋊C4—1811no—
854C22⋊C4—1811no—
855C22⋊C4—1811no—
856C22⋊C4—1811no—
857C22⋊C4—1811no—
858C22⋊C4—1811no—
859C22⋊C4—1811no—
860C22⋊C4—1811no—
861C22⋊C4—1811no—
862C22⋊C4—1811no—
863C22⋊C4—1811no—
864C22⋊C4—1811no—
865C22⋊C4—1811no—
866C22⋊C4—1811no—
867C22⋊C4—1811no—
868C22⋊C4—1811no—
869C22⋊C4—1811no—
870C22⋊C4—1811no—
871C22⋊C4—1811no—
872C22⋊C4—1811no—
873C22⋊C4—1811no—
874C22⋊C4—1811no—
875C22⋊C4—1811no—
876C22⋊C4—1811no—
877C22⋊C4—1811no—
878C22⋊C4—1811no—
879C22⋊C4—1811no—
880C22⋊C4—1811no—
881C22⋊C4C22×D18111yescharacteristic
882C22⋊C4C22×D18111yescharacteristic
883C22⋊C4C22×D18111yescharacteristic
884C22⋊C4C22×D18111yescharacteristic
885C22⋊C4C22×D18111yescharacteristic
886C22⋊C4C22×D18111yescharacteristic
887C22⋊C4C22×D18111yescharacteristic
888C22⋊C4C22×D18111yescharacteristic
889C22⋊C4C22×D18111yescharacteristic
890C22⋊C4C22×D18111yescharacteristic
891C22⋊C4C22×D18111yescharacteristic
892C22⋊C4C22×D18111yescharacteristic
893C22⋊C4C22×D18111yescharacteristic
894C22⋊C4C22×D18111yescharacteristic
895C42—1811no—
896C42—1811no—
897C42—1811no—
898C42—1811no—
899C42—1811no—
900C42—1811no—
901C42—1811no—
902C42—1811no—
903C42C22×D18111yescharacteristic
904C42C22×D18111yescharacteristic
905C23—22no—
906C23—41no—
907C23—41no—
908C23—3622no—
909C23—3622no—
910C23—3622no—
911C23—3622no—
912C23—3622no—
913C23—3622no—
914C23—3622no—
915C23—1811no—
916C23—1811no—
917C23—1811no—
918C23—1811no—
919C23—1811no—
920C23—1811no—
921C23—7241no—
922C23—7241no—
923C23—7241no—
924C23—7241no—
925C23—7241no—
926C23—7241no—
927C23—7241no—
928C23—7241no—
929C23C23×D18111yescharacteristic
930C23C23×D18111yescharacteristic
931C23C23×D18111yescharacteristic
932C23C23×D18111yescharacteristic
933C23C23×D18111yescharacteristic
934Q8—41no—
935Q8—3622no—
936Q8—7241no—
937D4—22no—
938D4—22no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—41no—
943D4—41no—
944D4—3622no—
945D4—3622no—
946D4—3622no—
947D4—3622no—
948D4—3622no—
949D4—3622no—
950D4—3622no—
951D4—3622no—
952D4—3622no—
953D4—3622no—
954D4—3622no—
955D4—3622no—
956D4—3622no—
957D4—3622no—
958D4—3622no—
959D4—3622no—
960D4—1814no—
961D4—7241no—
962D4—7241no—
963D4—7241no—
964D4—7241no—
965D4—7241no—
966D4—7241no—
967D4—7241no—
968D4—7241no—
969D4—7241no—
970D4—7241no—
971D4—7241no—
972D4—7241no—
973D4—7241no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—3622no—
979C2×C4—3622no—
980C2×C4—3622no—
981C2×C4—3622no—
982C2×C4—3622no—
983C2×C4—3622no—
984C2×C4—3622no—
985C2×C4—3622no—
986C2×C4—3622no—
987C2×C4—1811no—
988C2×C4—1811no—
989C2×C4—1811no—
990C2×C4—1811no—
991C2×C4—1811no—
992C2×C4—1811no—
993C2×C4—1811no—
994C2×C4—1811no—
995C2×C4—1811no—
996C2×C4—1811no—
997C2×C4—7241no—
998C2×C4—7241no—
999C2×C4—7241no—
1000C2×C4—7241no—
1001C2×C4—7241no—
1002C2×C4—7241no—
1003C2×C4—7241no—
1004C2×C4—7241no—
1005C2×C4—7241no—
1006C2×C4—7241no—
1007C2×C4—7241no—
1008C2×C4—7241no—
1009C2×C4—7241no—
1010C2×C4—7241no—
1011C2×C4C23×D18111yescharacteristic
1012C2×C4C23×D18111yescharacteristic
1013C2×C4C23×D18111yescharacteristic
1014C2×C4C23×D18111yescharacteristic
1015C2×C4C23×D18111yescharacteristic
1016C2×C4C23×D18111yescharacteristic
1017C2×C4C23×D18111yescharacteristic
1018C2×C4C23×D18111yescharacteristic
1019C2×C4C23×D18111yescharacteristic
1020C2×C4C23×D18111yescharacteristic
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—82no—
1036C22—3621no—
1037C22—3621no—
1038C22—3621no—
1039C22—3621no—
1040C22—3621no—
1041C22—3621no—
1042C22—3621no—
1043C22—3621no—
1044C22—3621no—
1045C22—3621no—
1046C22—3621no—
1047C22—3621no—
1048C22—3621no—
1049C22—3621no—
1050C22—3621no—
1051C22—3621no—
1052C22—14482no—
1053C22—14482no—
1054C22—14482no—
1055C22—1812no—
1056C22—1812no—
1057C22—7244no—
1058C22—7244no—
1059C22#41×D18112yes—
1060C22C24×D18111yescharacteristic
1061C4—21no—
1062C4—21no—
1063C4—21no—
1064C4—21no—
1065C4—21no—
1066C4—21no—
1067C4—21no—
1068C4—21no—
1069C4—21no—
1070C4—21no—
1071C4—3621no—
1072C4—3621no—
1073C4—3621no—
1074C4—3621no—
1075C4—3621no—
1076C4—3621no—
1077C4—3621no—
1078C4—3621no—
1079C4—1812no—
1080C4—1812no—
1081C2—22no—
1082C2—41no—
1083C2—41no—
1084C2—41no—
1085C2—41no—
1086C2—3622no—
1087C2—3622no—
1088C2—7241no—
1089C2—7241no—
1090C2—7241no—
1091C2—7241no—
1092C2C2×#41×D18111yescharacteristic
1093C2H(5,𝔽2)×D18111yescharacteristic
1094C2H(5,𝔽2)×D18111yescharacteristic
subgroupG/H
center, FrattiniC22C24×D181
commutator, socle, cosocleC22×C181C25
Fitting#538×C181C2
hypercenter#538D181
hypocenterC181#3519
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ #538

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #26041991C2semidirect
2. #26041983C2semidirect
3. #26041980C2semidirect
4. #26041980C2semidirect
5. #26041974C2semidirect
6. #26041972C2semidirect
7. #26041947C2semidirect
8. #26041922C2semidirect
9. #26041921C2semidirect
10. #26041920C2semidirect
11. #26041918C2semidirect
12. #26041916C2semidirect
13. #26041916C2semidirect
14. #26041913C2semidirect
15. #26041911C2semidirect
16. #26041911C2semidirect
17. #26041881C2semidirect
18. #26041879C2semidirect
19. #26041868C2semidirect
20. #26041863C2semidirect
21. #26041862C2semidirect
22. #26041828C2semidirect
23. #26041812C2semidirect
24. #26041788C2semidirect
25. #26041787C2semidirect
26. C2×#19153789C2semidirect
27. #121×D181C2semidirect
28. #26041752C2semidirect
29. #26041751C2semidirect
30. C4×D4×D181C2semidirect
31. #538×C181C2semidirect
32. C2×#15668450C22semidirect
33. C2×#15668449C22semidirect
34. C2×#15668448C22semidirect
35. C2×#15668448C22semidirect
36. C22×D724C22semidirect
38. C22×C22⋊D181C22semidirect
39. C22×C22⋊D181C22semidirect
42. C2×D4×D181C22semidirect
43. C2×D4×D181C22semidirect
44. C2×D4×D181C22semidirect
45. C22×C4×D181C22semidirect
46. C22×C4×D181C22semidirect
47. #19153814C22semidirect
48. #19153812C22semidirect
49. #19153812C22semidirect
50. #19153812C22semidirect
51. #19153811C22semidirect
52. #19153811C22semidirect
53. #19153810C22semidirect
54. #19153809C22semidirect
55. #19153806C22semidirect
56. #19153806C22semidirect
57. #19153806C22semidirect
58. #19153805C22semidirect
59. #19153804C22semidirect
60. #19153802C22semidirect
61. #19153802C22semidirect
62. #19153802C22semidirect
63. #19153801C22semidirect
64. #19153801C22semidirect
65. #19153801C22semidirect
66. #19153801C22semidirect
67. #19153800C22semidirect
68. #19153800C22semidirect
69. #19153799C22semidirect
70. #19153798C22semidirect
71. #19153798C22semidirect
72. #19153798C22semidirect
73. #19153798C22semidirect
74. #19153797C22semidirect
75. #19153794C22semidirect
76. #19153794C22semidirect
77. #19153794C22semidirect
78. #19153793C22semidirect
79. #19153793C22semidirect
80. #19153792C22semidirect
81. #19153791C22semidirect
82. #19153791C22semidirect
83. #19153791C22semidirect
84. #19153791C22semidirect
85. #19153790C22semidirect
87. #19153789C22semidirect
88. #19153789C22semidirect
89. #19153789C22semidirect
90. #19153789C22semidirect
91. #19153789C22semidirect
92. #19153789C22semidirect
93. #19153789C22semidirect
94. #19153789C22semidirect
95. #19153789C22semidirect
96. #19153789C22semidirect
97. #19153789C22semidirect
98. #19153789C22semidirect
99. #19153789C22semidirect
100. #19153789C22semidirect
101. #19153789C22semidirect
102. #19153788C22semidirect
103. #19153788C22semidirect
104. #19153788C22semidirect
105. #19153788C22semidirect
106. #19153788C22semidirect
107. #19153788C22semidirect
108. #19153788C22semidirect
109. #19153788C22semidirect
110. #19153788C22semidirect
111. #19153787C22semidirect
112. #19153787C22semidirect
113. #19153786C22semidirect
114. #19153786C22semidirect
115. #19153786C22semidirect
116. #19153786C22semidirect
117. #19153786C22semidirect
118. #19153786C22semidirect
119. #19153784C22semidirect
120. #19153784C22semidirect
121. #19153784C22semidirect
122. #19153784C22semidirect
123. #19153781C22semidirect
124. C4×D724C22semidirect
125. C4×D724C22semidirect
126. C4×D724C22semidirect
127. D4×Dic181C22semidirect
128. D4×Dic181C22semidirect
129. #19153778C22semidirect
130. #19153778C22semidirect
131. #19153778C22semidirect
132. #19153778C22semidirect
135. C4×C22⋊D181C22semidirect
136. C4×C22⋊D181C22semidirect
137. C4×C22⋊D181C22semidirect
138. C4×C22⋊D181C22semidirect
139. C4×C22⋊D181C22semidirect
142. #19153776C22semidirect
143. #19153776C22semidirect
144. #19153776C22semidirect
145. #19153776C22semidirect
146. #19153776C22semidirect
147. #19153776C22semidirect
148. #19153776C22semidirect
149. #19153776C22semidirect
150. #19153776C22semidirect
151. #19153776C22semidirect
152. #19153776C22semidirect
153. #19153774C22semidirect
154. #19153773C22semidirect
155. #19153773C22semidirect
156. #19153772C22semidirect
157. #19153772C22semidirect
158. #19153772C22semidirect
159. C2×#15668428C22semidirect
160. C4⋊C4×D181C22semidirect
161. C4⋊C4×D181C22semidirect
162. C2×C22⋊Dic181C22semidirect
163. C2×#15668426C22semidirect
164. C2×#15668426C22semidirect
165. C22⋊C4×D181C22semidirect
166. C22⋊C4×D181C22semidirect
167. C22⋊C4×D181C22semidirect
168. C22⋊C4×D181C22semidirect
169. C22⋊C4×D181C22semidirect
170. C22⋊C4×D181C22semidirect
171. C42×D181C22semidirect
172. #126×C181C22semidirect
173. #126×C181C22semidirect
174. #124×C181C22semidirect
175. #124×C181C22semidirect
176. #123×C181C22semidirect
177. #123×C181C22semidirect
178. C22⋊Q8×C181C22semidirect
179. #121×C181C22semidirect
180. #121×C181C22semidirect
181. #121×C181C22semidirect
182. #120×C181C22semidirect
183. #120×C181C22semidirect
184. C4×D4×C181C22semidirect
185. C4×D4×C181C22semidirect
186. C2×C22⋊C4×C181C22semidirect
409. C22⋊D181#41semidirect
547. C181#3519semidirect
570. #538D181semidirect
603. #126C2×D181semidirect
604. #126C2×D181semidirect
613. #124C2×D181semidirect
614. #124C2×D181semidirect
627. #123C2×D181semidirect
628. #123C2×D181semidirect
635. C22⋊Q8C2×D181semidirect
668. #121C2×D181semidirect
669. #121C2×D181semidirect
670. #121C2×D181semidirect
681. #120C2×D181semidirect
682. #120C2×D181semidirect
713. C4×D4C2×D181semidirect
714. C4×D4C2×D181semidirect
733. C2×C22⋊C4C2×D181semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#260419912
#260419832
#260419802
#260419742
#260419722
#260419472
#260419222
#260419212
#260419202
#260419182
#260419162
#260419132
#260419112
#260418812
#260418792
#260418682
#260418632
#260418622
#260418282
#260418122
#260417882
#260417872
C2×#191537892
#121×D1812
#260417522
#260417512
C4×D4×D1812
#538×C1812
#3519181