Finite Group Databasebeta

← #37547909

Subgroups — #37547909

Order 23168.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26042027C211yesmaximal, characteristic, complemented
2#26042025C211yesmaximal, characteristic, complemented
3#26042020C211yesmaximal, characteristic, complemented
4#26042019C211yesmaximal, characteristic, complemented
5#26041982C211yesmaximal, characteristic, complemented
6#26041980C211yesmaximal, characteristic, complemented
7#26041958C211yesmaximal, characteristic, complemented
8#26041956C211yesmaximal, characteristic, complemented
9#26041925C211yesmaximal, characteristic, complemented
10#26041924C211yesmaximal, characteristic, complemented
11#26041921C211yesmaximal, characteristic, complemented
12#26041920C211yesmaximal, characteristic, complemented
13#26041920C211yesmaximal, characteristic, complemented
14#26041918C211yesmaximal, characteristic, complemented
15D4×D724C211yesmaximal, characteristic, complemented
16#26041913C211yesmaximal, characteristic, complemented
17#26041885C211yesmaximal, characteristic, complemented
18#26041881C211yesmaximal, characteristic, complemented
19#26041877C211yesmaximal, characteristic, complemented
20#26041876C211yesmaximal, characteristic, complemented
21#26041869C211yesmaximal, characteristic, complemented
22#26041868C211yesmaximal, characteristic, complemented
23#26041868C211yesmaximal, characteristic, complemented
24#26041859C211yesmaximal, characteristic, complemented
25#26041840C211yesmaximal, characteristic, complemented
26#26041840C211yesmaximal, characteristic, complemented
27#26041840C211yesmaximal, characteristic, complemented
28#26041787C211yesmaximal, characteristic, complemented
29#123×D181C211yesmaximal, characteristic, complemented
30C2×#19153791C211yesmaximal, characteristic, complemented
31#539×C181C211yesmaximal, characteristic, complemented
32C2×#15668450C2211yescharacteristic, complemented
33C2×#15668449C2211yescharacteristic, complemented
34C2×#15668448C2211yescharacteristic, complemented
35C22×D724C2211yescharacteristic, complemented
36C22×D724C2211yescharacteristic, complemented
37C22×D724C2211yescharacteristic, complemented
38C22×D724C2211yescharacteristic, complemented
39C2×D4×D181C2211yescharacteristic
40C2×D4×D181C2211yescharacteristic, complemented
41C2×D4×D181C2211yescharacteristic, complemented
42C2×D4×D181C2211yescharacteristic, complemented
43C22×C4×D181C2211yescharacteristic, complemented
44#19153813C2211yescharacteristic, complemented
45#19153812C2211yescharacteristic, complemented
46#19153811C2211yescharacteristic, complemented
47#19153811C2211yescharacteristic, complemented
48#19153811C2211yescharacteristic, complemented
49#19153811C2211yescharacteristic, complemented
50#19153811C2211yescharacteristic, complemented
51#19153810C2211yescharacteristic, complemented
52#19153806C2211yescharacteristic, complemented
53#19153806C2211yescharacteristic, complemented
54#19153805C2211yescharacteristic, complemented
55#19153805C2211yescharacteristic, complemented
56#19153804C2211yescharacteristic, complemented
57#19153804C2211yescharacteristic, complemented
58#19153802C2211yescharacteristic, complemented
59#19153802C2211yescharacteristic, complemented
60#19153801C2211yescharacteristic, complemented
61#19153801C2211yescharacteristic, complemented
62#19153801C2211yescharacteristic, complemented
63#19153801C2211yescharacteristic, complemented
64#19153801C2211yescharacteristic, complemented
65#19153801C2211yescharacteristic, complemented
66#19153801C2211yescharacteristic, complemented
67#19153801C2211yescharacteristic, complemented
68#19153801C2211yescharacteristic, complemented
69#19153801C2211yescharacteristic, complemented
70#19153801C2211yescharacteristic, complemented
71#19153801C2211yescharacteristic, complemented
72#19153801C2211yescharacteristic, complemented
73#19153801C2211yescharacteristic, complemented
74#19153801C2211yescharacteristic, complemented
75#19153800C2211yescharacteristic, complemented
76#19153800C2211yescharacteristic, complemented
77#19153799C2211yescharacteristic, complemented
78#19153799C2211yescharacteristic, complemented
79#19153799C2211yescharacteristic, complemented
80#19153798C2211yescharacteristic, complemented
81#19153798C2211yescharacteristic, complemented
82#19153798C2211yescharacteristic, complemented
83#19153797C2211yescharacteristic, complemented
84#19153796C2211yescharacteristic, complemented
85#19153795C2211yescharacteristic, complemented
86#19153794C2211yescharacteristic, complemented
87#19153794C2211yescharacteristic, complemented
88#19153794C2211yescharacteristic, complemented
89#19153794C2211yescharacteristic, complemented
90#19153794C2211yescharacteristic, complemented
91#19153794C2211yescharacteristic, complemented
92#19153792C2211yescharacteristic, complemented
93#19153791C2211yescharacteristic
94#19153791C2211yescharacteristic, complemented
95#19153791C2211yescharacteristic, complemented
96#19153791C2211yescharacteristic, complemented
97#19153791C2211yescharacteristic, complemented
98#19153791C2211yescharacteristic, complemented
99#19153791C2211yescharacteristic, complemented
100#19153791C2211yescharacteristic, complemented
101#19153791C2211yescharacteristic, complemented
102#19153791C2211yescharacteristic, complemented
103#19153791C2211yescharacteristic, complemented
104#19153791C2211yescharacteristic, complemented
105#19153791C2211yescharacteristic, complemented
106#19153791C2211yescharacteristic, complemented
107#19153791C2211yescharacteristic, complemented
108#19153791C2211yescharacteristic, complemented
109#19153791C2211yescharacteristic, complemented
110#19153791C2211yescharacteristic, complemented
111#19153791C2211yescharacteristic, complemented
112#19153790C2211yescharacteristic
113#19153790C2211yescharacteristic, complemented
114#19153790C2211yescharacteristic, complemented
115#19153790C2211yescharacteristic, complemented
116#19153789C2211yescharacteristic, complemented
117#19153789C2211yescharacteristic, complemented
118#19153789C2211yescharacteristic, complemented
119#19153789C2211yescharacteristic, complemented
120#19153789C2211yescharacteristic, complemented
121#19153789C2211yescharacteristic, complemented
122#19153789C2211yescharacteristic, complemented
123#19153789C2211yescharacteristic, complemented
124#19153789C2211yescharacteristic, complemented
125#19153789C2211yescharacteristic, complemented
126#19153789C2211yescharacteristic, complemented
127#19153788C2211yescharacteristic, complemented
128#19153786C2211yescharacteristic
129#19153786C2211yescharacteristic, complemented
130#19153786C2211yescharacteristic, complemented
131#19153786C2211yescharacteristic, complemented
132#19153786C2211yescharacteristic, complemented
133#19153786C2211yescharacteristic, complemented
134#19153786C2211yescharacteristic, complemented
135#19153786C2211yescharacteristic, complemented
136#19153786C2211yescharacteristic, complemented
137#19153786C2211yescharacteristic, complemented
138#19153786C2211yescharacteristic, complemented
139#19153786C2211yescharacteristic, complemented
140#19153784C2211yescharacteristic
141#19153784C2211yescharacteristic, complemented
142#19153784C2211yescharacteristic, complemented
143#19153784C2211yescharacteristic, complemented
144C4×D724C2211yescharacteristic, complemented
145C4×D724C2211yescharacteristic, complemented
146C4×D724C2211yescharacteristic, complemented
147#19153778C2211yescharacteristic, complemented
148#19153778C2211yescharacteristic, complemented
149#19153778C2211yescharacteristic, complemented
150#19153778C2211yescharacteristic, complemented
151#19153778C2211yescharacteristic, complemented
152C4×C22⋊D181C2211yescharacteristic, complemented
153C4×C22⋊D181C2211yescharacteristic, complemented
154C4×C22⋊D181C2211yescharacteristic, complemented
155#19153776C2211yescharacteristic, complemented
156#19153776C2211yescharacteristic, complemented
157#19153776C2211yescharacteristic, complemented
158#19153774C2211yescharacteristic, complemented
159#19153773C2211yescharacteristic, complemented
160#19153772C2211yescharacteristic, complemented
161C4⋊C4×D181C2211yescharacteristic, complemented
162C4⋊C4×D181C2211yescharacteristic, complemented
163C2×#15668426C2211yescharacteristic, complemented
164C2×#15668426C2211yescharacteristic, complemented
165C2×#15668426C2211yescharacteristic, complemented
166C22⋊C4×D181C2211yescharacteristic, complemented
167C22⋊C4×D181C2211yescharacteristic, complemented
168C22⋊C4×D181C2211yescharacteristic, complemented
169C22⋊C4×D181C2211yescharacteristic, complemented
170C22⋊C4×D181C2211yescharacteristic, complemented
171C22⋊C4×D181C2211yescharacteristic, complemented
172#126×C181C2211yescharacteristic, complemented
173#126×C181C2211yescharacteristic, complemented
174#125×C181C2211yescharacteristic, complemented
175#125×C181C2211yescharacteristic, complemented
176#123×C181C2211yescharacteristic, complemented
177#123×C181C2211yescharacteristic, complemented
178#123×C181C2211yescharacteristic, complemented
179#123×C181C2211yescharacteristic, complemented
180C22⋊Q8×C181C2211yescharacteristic, complemented
181C22⋊Q8×C181C2211yescharacteristic, complemented
182C22⋊Q8×C181C2211yescharacteristic, complemented
183#121×C181C2211yescharacteristic
184C4×D4×C181C2211yescharacteristic, complemented
185C4×D4×C181C2211yescharacteristic, complemented
186C2×C4⋊C4×C181C2211yescharacteristic, complemented
187C23×D181C2311yescharacteristic
188C23×D181C2311yescharacteristic
189C23×D181C2311yescharacteristic
190C23×D181C2311yescharacteristic
191C23×D181C2311yescharacteristic
192C23×D181C2311yescharacteristic
193#15668450—42no—
194#15668449—42no—
195#15668448—42no—
196C2×Dic362C2311yescharacteristic
197C2×Dic362C2311yescharacteristic
198C2×D724—42no—
199C2×D724—42no—
200C2×D724—42no—
201C2×D724—42no—
202C2×D724C2311yescharacteristic
203C2×D724C2311yescharacteristic
204C2×D724C2311yescharacteristic
205C2×D724C2311yescharacteristic
206C2×D724C2311yescharacteristic
207C2×D724C2311yescharacteristic
208C2×D724C2311yescharacteristic
209C2×D724C2311yescharacteristic
210C2×D724C2311yescharacteristic
211C2×D724C2311yescharacteristic
212C2×D724C2311yescharacteristic
213C2×D724C2311yescharacteristic
214C2×D724C2311yescharacteristic
215C2×D724C2311yescharacteristic
216C2×D724C2311yescharacteristic
217C2×D724C2311yescharacteristic
218C2×D724C2311yescharacteristic
219C2×D724C2311yescharacteristic
220C2×D724C2311yescharacteristic
221C2×D724C2311yescharacteristic
222C2×D724C2311yescharacteristic
223C2×D724C2311yescharacteristic
224C2×C22⋊D181C2311yescharacteristic
225C2×C22⋊D181C2311yescharacteristic
226C2×C22⋊D181C2311yescharacteristic
227C2×C22⋊D181C2311yescharacteristic
228C2×C22⋊D181C2311yescharacteristic
229C2×C22⋊D181C2311yescharacteristic
230C2×C22⋊D181C2311yescharacteristic
231C2×C22⋊D181C2311yescharacteristic
232C2×C22⋊D181C2311yescharacteristic
233C2×C22⋊D181C2311yescharacteristic
234C2×C22⋊D181C2311yescharacteristic
235C2×C22⋊D181C2311yescharacteristic
236D4×D181—42no—
237D4×D181—42no—
238D4×D181—42no—
239D4×D181—42no—
240C22×Dic181C2311yescharacteristic
241C22×Dic181C2311yescharacteristic
242C2×C4×D181—42no—
243C2×C4×D181C2311yescharacteristic
244C2×C4×D181C2311yescharacteristic
245C2×C4×D181C2311yescharacteristic
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
259C4⋊Dic181C2311yescharacteristic
260C4⋊Dic181C2311yescharacteristic
261C4⋊Dic181C2311yescharacteristic
262C4⋊Dic181C2311yescharacteristic
263#15668428C2311yescharacteristic
264#15668428C2311yescharacteristic
265#15668428C2311yescharacteristic
266#15668428C2311yescharacteristic
267#15668428C2311yescharacteristic
268#15668428C2311yescharacteristic
269#15668428C2311yescharacteristic
270#15668428C2311yescharacteristic
271#15668428C2311yescharacteristic
272#15668428C2311yescharacteristic
273#15668428C2311yescharacteristic
274#15668428C2311yescharacteristic
275C22⋊Dic181C2311yescharacteristic
276C22⋊Dic181C2311yescharacteristic
277C22⋊Dic181C2311yescharacteristic
278C22⋊Dic181C2311yescharacteristic
279#15668426C2311yescharacteristic
280#15668426C2311yescharacteristic
281#15668426C2311yescharacteristic
282#15668426C2311yescharacteristic
283#15668426C2311yescharacteristic
284#15668426C2311yescharacteristic
285#15668426C2311yescharacteristic
286#15668426C2311yescharacteristic
287#15668426C2311yescharacteristic
288#15668426C2311yescharacteristic
289#15668426C2311yescharacteristic
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
314#15668426C2311yescharacteristic
315C4×Dic181C2311yescharacteristic
316C4×Dic181C2311yescharacteristic
317C4×Dic181C2311yescharacteristic
318C4×Dic181C2311yescharacteristic
319C2×Q8×C181C2311yescharacteristic
320C2×D4×C181C2311yescharacteristic
321C2×D4×C181C2311yescharacteristic
322C2×D4×C181C2311yescharacteristic
323C22×C4×C181C2311yescharacteristic
324C22×C4×C181C2311yescharacteristic
325C22×C4×C181C2311yescharacteristic
326C22×C4×C181C2311yescharacteristic
327C22×C4×C181C2311yescharacteristic
328C4⋊C4×C181C2311yescharacteristic
329C4⋊C4×C181C2311yescharacteristic
330C4⋊C4×C181C2311yescharacteristic
331C4⋊C4×C181C2311yescharacteristic
332C4⋊C4×C181C2311yescharacteristic
333C4⋊C4×C181C2311yescharacteristic
334C4⋊C4×C181C2311yescharacteristic
335C4⋊C4×C181C2311yescharacteristic
336C4⋊C4×C181C2311yescharacteristic
337C4⋊C4×C181C2311yescharacteristic
338C4⋊C4×C181C2311yescharacteristic
339C4⋊C4×C181C2311yescharacteristic
340C4⋊C4×C181C2311yescharacteristic
341C4⋊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
352C42×C181C2311yescharacteristic
353C42×C181C2311yescharacteristic
354C22×D181—22no—
355C22×D181—22no—
356C22×D181—22no—
357C22×D181—22no—
358C22×D181—22no—
359C22×D181—41no—
360C22×D181—41no—
361C22×D181—41no—
362C22×D181—41no—
363C22×D181—41no—
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
378C22×D181C2411yescharacteristic
379C22×D181C2411yescharacteristic
380Dic362—41no—
381Dic362—41no—
382D724—22no—
383D724—22no—
384D724—22no—
385D724—22no—
386D724—22no—
387D724—41no—
388D724—41no—
389D724—41no—
390D724—41no—
391D724—41no—
392D724—41no—
393D724—41no—
394D724—41no—
395D724—41no—
396D724—41no—
397D724—41no—
398D724—41no—
399D724—41no—
400D724—41no—
401D724—41no—
402D724—41no—
403D724—41no—
404C22⋊D181—22no—
405C22⋊D181—22no—
406C22⋊D181—22no—
407C22⋊D181—41no—
408C22⋊D181—41no—
409C22⋊D181—41no—
410C22⋊D181—41no—
411C22⋊D181—41no—
412C22⋊D181—41no—
413C22⋊D181—41no—
414C22⋊D181—41no—
415C22⋊D181—41no—
416C2×Dic181—22no—
417C2×Dic181—41no—
418C2×Dic181C2411yescharacteristic
419C2×Dic181C2411yescharacteristic
420C2×Dic181C2411yescharacteristic
421C2×Dic181C2411yescharacteristic
422C2×Dic181C2411yescharacteristic
423C2×Dic181C2411yescharacteristic
424C2×Dic181C2411yescharacteristic
425C2×Dic181C2411yescharacteristic
426C4×D181—22no—
427C4×D181—41no—
428C4×D181—41no—
429C4×D181—41no—
430C4×D181—41no—
431C4×D181—41no—
432C4×D181—41no—
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—
442C23×C181C2411yescharacteristic
443C23×C181C2411yescharacteristic
444C23×C181C2411yescharacteristic
445Q8×C181—41no—
446D4×C181—22no—
447D4×C181—22no—
448D4×C181—41no—
449C2×C4×C181—22no—
450C2×C4×C181—41no—
451C2×C4×C181—41no—
452C2×C4×C181—41no—
453C2×C4×C181—41no—
454C2×C4×C181C2411yescharacteristic
455C2×C4×C181C2411yescharacteristic
456C2×C4×C181C2411yescharacteristic
457C2×C4×C181C2411yescharacteristic
458C2×C4×C181C2411yescharacteristic
459C2×C4×C181C2411yescharacteristic
460C2×C4×C181C2411yescharacteristic
461C2×C4×C181C2411yescharacteristic
462C2×C4×C181C2411yescharacteristic
463C2×C4×C181C2411yescharacteristic
464C2×C4×C181C2411yescharacteristic
465C2×C4×C181C2411yescharacteristic
466C22×C181—21no—
467C22×C181—21no—
468C22×C181—21no—
469C22×C181—21no—
470C22×C181—21no—
471C22×C181—21no—
472C22×C181—21no—
473C22×C181—21no—
474C22×C181H(5,𝔽2)12yes—
475C22×C181C2511yescharacteristic
476C2×D181—21no—
477C2×D181—21no—
478C2×D181—21no—
479C2×D181—21no—
480C2×D181—21no—
481C2×D181—21no—
482C2×D181—21no—
483C2×D181—21no—
484C2×D181—21no—
485C2×D181—21no—
486C2×D181—21no—
487C2×D181—21no—
488C2×D181—21no—
489C2×D181—21no—
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—44no—
500C2×D181—82no—
501C2×D181—82no—
502C2×D181—82no—
503C2×D181—82no—
504C2×D181—82no—
505C2×D181H(5,𝔽2)12yes—
506C4×C181—21no—
507C4×C181—21no—
508C4×C181—21no—
509C4×C181—21no—
510C4×C181—21no—
511C4×C181—21no—
512C4×C181—21no—
513C4×C181—21no—
514C4×C181—21no—
515C4×C181—21no—
516C4×C181—21no—
517C4×C181—21no—
518Dic181—21no—
519Dic181—21no—
520Dic181—21no—
521Dic181—21no—
522Dic181—21no—
523Dic181—21no—
524Dic181—21no—
525Dic181—21no—
526C2×C181—22no—
527C2×C181—41no—
528C2×C181—41no—
529C2×C181C2×H(5,𝔽2)11yescharacteristic
530C2×C181C2×H(5,𝔽2)11yescharacteristic
531C2×C181#58511yescharacteristic
532D181—22no—
533D181—41no—
534D181—41no—
535D181—41no—
536D181—41no—
537D181—41no—
538D181—41no—
539D181—41no—
540C181#353411yescharacteristic, complemented, Sylow
541#3534—1811nomaximal, Sylow
542#562—1811no—
543#562—1811no—
544#560—1811no—
545#560—1811no—
546#553—1811no—
547#553—1811no—
548#551—1811no—
549#551—1811no—
550#546—1811no—
551#546—1811no—
552#546—1811no—
553#546—1811no—
554#546—1811no—
555#546—1811no—
556D42—1811no—
557D42—1811no—
558#540—1811no—
559#540—1811no—
560#539—1811no—
561#539—1811no—
562#539D18111yescharacteristic, complemented
563#538—1811no—
564#538—1811no—
565#538—1811no—
566#537—1811no—
567#534—1811no—
568#534—1811no—
569#534—1811no—
570#525—1811no—
571C2×#123—1811no—
572C2×#121—1811no—
573C2×#41—1811no—
574C2×#41—1811no—
575C2×#41—1811no—
576C22×D4—1811no—
577C22×D4—1811no—
578C22×D4—1811no—
579C22×D4—1811no—
580C22×D4—1811no—
581C22×D4—1811no—
582C22×D4—1811no—
583C22×D4—1811no—
584C23×C4—1811no—
585#127—1811no—
586#127—1811no—
587#126—1811no—
588#126—1811no—
589#126—1811no—
590#126—1811no—
591#126—1811no—
592#126—1811no—
593#126C2×D18111yescharacteristic, complemented
594#126C2×D18111yescharacteristic, complemented
595#125—1811no—
596#125—1811no—
597#125C2×D18111yescharacteristic, complemented
598#125C2×D18111yescharacteristic, complemented
599#124—1811no—
600#124—1811no—
601#124—1811no—
602#124—1811no—
603#124—1811no—
604#124—1811no—
605#123—1811no—
606#123—1811no—
607#123—1811no—
608#123—1811no—
609#123—1811no—
610#123—1811no—
611#123—1811no—
612#123—1811no—
613#123—1811no—
614#123—1811no—
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#123—1811no—
628#123—1811no—
629#123C2×D18111yescharacteristic, complemented
630#123C2×D18111yescharacteristic, complemented
631#123C2×D18111yescharacteristic, complemented
632#123C2×D18111yescharacteristic, complemented
633C22⋊Q8—1811no—
634C22⋊Q8—1811no—
635C22⋊Q8—1811no—
636C22⋊Q8—1811no—
637C22⋊Q8—1811no—
638C22⋊Q8—1811no—
639C22⋊Q8—1811no—
640C22⋊Q8—1811no—
641C22⋊Q8—1811no—
642C22⋊Q8C2×D18111yescharacteristic, complemented
643C22⋊Q8C2×D18111yescharacteristic, complemented
644C22⋊Q8C2×D18111yescharacteristic, complemented
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#121—1811no—
669#121—1811no—
670#121—1811no—
671#121—1811no—
672#121—1811no—
673#121—1811no—
674#121—1811no—
675#121—1811no—
676#121—1811no—
677#121—1811no—
678#121—1811no—
679#121—1811no—
680#121C2×D18111yescharacteristic
681#120—1811no—
682#120—1811no—
683#120—1811no—
684#120—1811no—
685#120—1811no—
686#120—1811no—
687#120—1811no—
688#120—1811no—
689#120—1811no—
690#120—1811no—
691#120—1811no—
692#120—1811no—
693#120—1811no—
694#120—1811no—
695#120—1811no—
696#120—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×D4C2×D18111yescharacteristic, complemented
712C4×D4C2×D18111yescharacteristic, complemented
713#117—1811no—
714#117—1811no—
715#117—1811no—
716C2×C4⋊C4—1811no—
717C2×C4⋊C4—1811no—
718C2×C4⋊C4C2×D18111yescharacteristic, complemented
719C2×C22⋊C4—1811no—
720C2×C22⋊C4—1811no—
721C2×C22⋊C4—1811no—
722C2×C22⋊C4—1811no—
723C2×C22⋊C4—1811no—
724C2×C22⋊C4—1811no—
725C2×C22⋊C4—1811no—
726C2×C22⋊C4—1811no—
727C2×C22⋊C4—1811no—
728C24—1811no—
729C24—1811no—
730C24—1811no—
731C24—1811no—
732C24—1811no—
733C24—1811no—
734#41—7242no—
735#41—7242no—
736#41—7242no—
737C2×Q8—1811no—
738C2×Q8—1811no—
739C2×Q8C22×D18111yescharacteristic
740C2×D4—1811no—
741C2×D4—1811no—
742C2×D4—1811no—
743C2×D4—1811no—
744C2×D4—1811no—
745C2×D4—1811no—
746C2×D4—1811no—
747C2×D4—1811no—
748C2×D4—1811no—
749C2×D4—1811no—
750C2×D4—1811no—
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—7242no—
775C2×D4—7242no—
776C2×D4—7242no—
777C2×D4—7242no—
778C2×D4—7242no—
779C2×D4—7242no—
780C2×D4—7242no—
781C2×D4—7242no—
782C2×D4C22×D18111yescharacteristic
783C2×D4C22×D18111yescharacteristic
784C2×D4C22×D18111yescharacteristic
785C22×C4—1811no—
786C22×C4—1811no—
787C22×C4—1811no—
788C22×C4—1811no—
789C22×C4—1811no—
790C22×C4—1811no—
791C22×C4—1811no—
792C22×C4—1811no—
793C22×C4—1811no—
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—7242no—
804C22×C4C22×D18111yescharacteristic
805C22×C4C22×D18111yescharacteristic
806C22×C4C22×D18111yescharacteristic
807C22×C4C22×D18111yescharacteristic
808C22×C4C22×D18111yescharacteristic
809C4⋊C4—1811no—
810C4⋊C4—1811no—
811C4⋊C4—1811no—
812C4⋊C4—1811no—
813C4⋊C4—1811no—
814C4⋊C4—1811no—
815C4⋊C4—1811no—
816C4⋊C4—1811no—
817C4⋊C4—1811no—
818C4⋊C4—1811no—
819C4⋊C4—1811no—
820C4⋊C4—1811no—
821C4⋊C4—1811no—
822C4⋊C4—1811no—
823C4⋊C4—1811no—
824C4⋊C4—1811no—
825C4⋊C4C22×D18111yescharacteristic
826C4⋊C4C22×D18111yescharacteristic
827C4⋊C4C22×D18111yescharacteristic
828C4⋊C4C22×D18111yescharacteristic
829C4⋊C4C22×D18111yescharacteristic
830C4⋊C4C22×D18111yescharacteristic
831C4⋊C4C22×D18111yescharacteristic
832C4⋊C4C22×D18111yescharacteristic
833C4⋊C4C22×D18111yescharacteristic
834C4⋊C4C22×D18111yescharacteristic
835C4⋊C4C22×D18111yescharacteristic
836C4⋊C4C22×D18111yescharacteristic
837C4⋊C4C22×D18111yescharacteristic
838C4⋊C4C22×D18111yescharacteristic
839C22⋊C4—1811no—
840C22⋊C4—1811no—
841C22⋊C4—1811no—
842C22⋊C4—1811no—
843C22⋊C4—1811no—
844C22⋊C4—1811no—
845C22⋊C4—1811no—
846C22⋊C4—1811no—
847C22⋊C4—1811no—
848C22⋊C4—1811no—
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⋊C4C22×D18111yescharacteristic
880C22⋊C4C22×D18111yescharacteristic
881C22⋊C4C22×D18111yescharacteristic
882C22⋊C4C22×D18111yescharacteristic
883C22⋊C4C22×D18111yescharacteristic
884C22⋊C4C22×D18111yescharacteristic
885C22⋊C4C22×D18111yescharacteristic
886C22⋊C4C22×D18111yescharacteristic
887C22⋊C4C22×D18111yescharacteristic
888C22⋊C4C22×D18111yescharacteristic
889C42—1811no—
890C42—1811no—
891C42—1811no—
892C42—1811no—
893C42C22×D18111yescharacteristic
894C42C22×D18111yescharacteristic
895C23—3622no—
896C23—3622no—
897C23—3622no—
898C23—3622no—
899C23—3622no—
900C23—1811no—
901C23—1811no—
902C23—1811no—
903C23—1811no—
904C23—1811no—
905C23—1811no—
906C23—1811no—
907C23—1811no—
908C23—7241no—
909C23—7241no—
910C23—7241no—
911C23—7241no—
912C23—7241no—
913C23—7241no—
914C23—7241no—
915C23—7241no—
916C23—7241no—
917C23—7241no—
918C23—7241no—
919C23—7241no—
920C23—7241no—
921C23C23×D18111yescharacteristic
922C23C23×D18111yescharacteristic
923C23C23×D18111yescharacteristic
924Q8—41no—
925Q8—7241no—
926Q8—7241no—
927D4—22no—
928D4—22no—
929D4—41no—
930D4—3622no—
931D4—3622no—
932D4—3622no—
933D4—3622no—
934D4—3622no—
935D4—3622no—
936D4—3622no—
937D4—3622no—
938D4—7241no—
939D4—7241no—
940D4—7241no—
941D4—7241no—
942D4—7241no—
943D4—7241no—
944D4—7241no—
945D4—7241no—
946D4—7241no—
947D4—7241no—
948D4—7241no—
949D4—7241no—
950D4—7241no—
951D4—7241no—
952D4—7241no—
953D4—7241no—
954D4—7241no—
955D4—7241no—
956D4—7241no—
957D4—7241no—
958D4—7241no—
959D4—7241no—
960D4—7241no—
961D4—7241no—
962D4—7241no—
963D4—7241no—
964C2×C4—22no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—3622no—
970C2×C4—3622no—
971C2×C4—1811no—
972C2×C4—1811no—
973C2×C4—1811no—
974C2×C4—1811no—
975C2×C4—1811no—
976C2×C4—1811no—
977C2×C4—1811no—
978C2×C4—1811no—
979C2×C4—7241no—
980C2×C4—7241no—
981C2×C4—7241no—
982C2×C4—7241no—
983C2×C4—7241no—
984C2×C4—7241no—
985C2×C4—7241no—
986C2×C4—7241no—
987C2×C4—7241no—
988C2×C4—7241no—
989C2×C4—7241no—
990C2×C4—7241no—
991C2×C4—7241no—
992C2×C4—7241no—
993C2×C4—7241no—
994C2×C4—7241no—
995C2×C4C23×D18111yescharacteristic
996C2×C4C23×D18111yescharacteristic
997C2×C4C23×D18111yescharacteristic
998C2×C4C23×D18111yescharacteristic
999C2×C4C23×D18111yescharacteristic
1000C2×C4C23×D18111yescharacteristic
1001C2×C4C23×D18111yescharacteristic
1002C2×C4C23×D18111yescharacteristic
1003C2×C4C23×D18111yescharacteristic
1004C2×C4C23×D18111yescharacteristic
1005C2×C4C23×D18111yescharacteristic
1006C2×C4C23×D18111yescharacteristic
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—3621no—
1016C22—3621no—
1017C22—3621no—
1018C22—3621no—
1019C22—3621no—
1020C22—3621no—
1021C22—3621no—
1022C22—3621no—
1023C22—3621no—
1024C22—3621no—
1025C22—3621no—
1026C22—3621no—
1027C22—3621no—
1028C22—3621no—
1029C22—3621no—
1030C22—3621no—
1031C22—3621no—
1032C22—3621no—
1033C22—3621no—
1034C22—3621no—
1035C22—3621no—
1036C22—3621no—
1037C22—3621no—
1038C22—14482no—
1039C22—14482no—
1040C22—14482no—
1041C22—14482no—
1042C22—14482no—
1043C22—1812no—
1044C22—7244no—
1045C22#1915386212yes—
1046C22C24×D18111yescharacteristic
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—21no—
1056C4—21no—
1057C4—21no—
1058C4—21no—
1059C4—3621no—
1060C4—3621no—
1061C4—3621no—
1062C4—3621no—
1063C4—3621no—
1064C4—3621no—
1065C4—3621no—
1066C4—3621no—
1067C2—22no—
1068C2—41no—
1069C2—41no—
1070C2—3622no—
1071C2—7241no—
1072C2—7241no—
1073C2—7241no—
1074C2—7241no—
1075C2—7241no—
1076C2—7241no—
1077C2—7241no—
1078C2H(5,𝔽2)×D18111yescharacteristic
1079C2C2×#1915386211yescharacteristic
1080C2#2604211611yescharacteristic
subgroupG/H
center, FrattiniC22C24×D181
commutator, socle, cosocleC22×C181C25
Fitting#539×C181C2
hypercenter#539D181
hypocenterC181#3534
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #26042027C2semidirect
2. #26042025C2semidirect
3. #26042020C2semidirect
4. #26042019C2semidirect
5. #26041982C2semidirect
6. #26041980C2semidirect
7. #26041958C2semidirect
8. #26041956C2semidirect
9. #26041925C2semidirect
10. #26041924C2semidirect
11. #26041921C2semidirect
12. #26041920C2semidirect
13. #26041920C2semidirect
14. #26041918C2semidirect
15. D4×D724C2semidirect
16. #26041913C2semidirect
17. #26041885C2semidirect
18. #26041881C2semidirect
19. #26041877C2semidirect
20. #26041876C2semidirect
21. #26041869C2semidirect
22. #26041868C2semidirect
23. #26041868C2semidirect
24. #26041859C2semidirect
25. #26041840C2semidirect
26. #26041840C2semidirect
27. #26041840C2semidirect
28. #26041787C2semidirect
29. #123×D181C2semidirect
30. C2×#19153791C2semidirect
31. #539×C181C2semidirect
32. C2×#15668450C22semidirect
33. C2×#15668449C22semidirect
34. C2×#15668448C22semidirect
35. C22×D724C22semidirect
36. C22×D724C22semidirect
37. C22×D724C22semidirect
38. C22×D724C22semidirect
40. C2×D4×D181C22semidirect
41. C2×D4×D181C22semidirect
42. C2×D4×D181C22semidirect
43. C22×C4×D181C22semidirect
44. #19153813C22semidirect
45. #19153812C22semidirect
46. #19153811C22semidirect
47. #19153811C22semidirect
48. #19153811C22semidirect
49. #19153811C22semidirect
50. #19153811C22semidirect
51. #19153810C22semidirect
52. #19153806C22semidirect
53. #19153806C22semidirect
54. #19153805C22semidirect
55. #19153805C22semidirect
56. #19153804C22semidirect
57. #19153804C22semidirect
58. #19153802C22semidirect
59. #19153802C22semidirect
60. #19153801C22semidirect
61. #19153801C22semidirect
62. #19153801C22semidirect
63. #19153801C22semidirect
64. #19153801C22semidirect
65. #19153801C22semidirect
66. #19153801C22semidirect
67. #19153801C22semidirect
68. #19153801C22semidirect
69. #19153801C22semidirect
70. #19153801C22semidirect
71. #19153801C22semidirect
72. #19153801C22semidirect
73. #19153801C22semidirect
74. #19153801C22semidirect
75. #19153800C22semidirect
76. #19153800C22semidirect
77. #19153799C22semidirect
78. #19153799C22semidirect
79. #19153799C22semidirect
80. #19153798C22semidirect
81. #19153798C22semidirect
82. #19153798C22semidirect
83. #19153797C22semidirect
84. #19153796C22semidirect
85. #19153795C22semidirect
86. #19153794C22semidirect
87. #19153794C22semidirect
88. #19153794C22semidirect
89. #19153794C22semidirect
90. #19153794C22semidirect
91. #19153794C22semidirect
92. #19153792C22semidirect
94. #19153791C22semidirect
95. #19153791C22semidirect
96. #19153791C22semidirect
97. #19153791C22semidirect
98. #19153791C22semidirect
99. #19153791C22semidirect
100. #19153791C22semidirect
101. #19153791C22semidirect
102. #19153791C22semidirect
103. #19153791C22semidirect
104. #19153791C22semidirect
105. #19153791C22semidirect
106. #19153791C22semidirect
107. #19153791C22semidirect
108. #19153791C22semidirect
109. #19153791C22semidirect
110. #19153791C22semidirect
111. #19153791C22semidirect
113. #19153790C22semidirect
114. #19153790C22semidirect
115. #19153790C22semidirect
116. #19153789C22semidirect
117. #19153789C22semidirect
118. #19153789C22semidirect
119. #19153789C22semidirect
120. #19153789C22semidirect
121. #19153789C22semidirect
122. #19153789C22semidirect
123. #19153789C22semidirect
124. #19153789C22semidirect
125. #19153789C22semidirect
126. #19153789C22semidirect
127. #19153788C22semidirect
129. #19153786C22semidirect
130. #19153786C22semidirect
131. #19153786C22semidirect
132. #19153786C22semidirect
133. #19153786C22semidirect
134. #19153786C22semidirect
135. #19153786C22semidirect
136. #19153786C22semidirect
137. #19153786C22semidirect
138. #19153786C22semidirect
139. #19153786C22semidirect
141. #19153784C22semidirect
142. #19153784C22semidirect
143. #19153784C22semidirect
144. C4×D724C22semidirect
145. C4×D724C22semidirect
146. C4×D724C22semidirect
147. #19153778C22semidirect
148. #19153778C22semidirect
149. #19153778C22semidirect
150. #19153778C22semidirect
151. #19153778C22semidirect
152. C4×C22⋊D181C22semidirect
153. C4×C22⋊D181C22semidirect
154. C4×C22⋊D181C22semidirect
155. #19153776C22semidirect
156. #19153776C22semidirect
157. #19153776C22semidirect
158. #19153774C22semidirect
159. #19153773C22semidirect
160. #19153772C22semidirect
161. C4⋊C4×D181C22semidirect
162. C4⋊C4×D181C22semidirect
163. C2×#15668426C22semidirect
164. C2×#15668426C22semidirect
165. C2×#15668426C22semidirect
166. C22⋊C4×D181C22semidirect
167. C22⋊C4×D181C22semidirect
168. C22⋊C4×D181C22semidirect
169. C22⋊C4×D181C22semidirect
170. C22⋊C4×D181C22semidirect
171. C22⋊C4×D181C22semidirect
172. #126×C181C22semidirect
173. #126×C181C22semidirect
174. #125×C181C22semidirect
175. #125×C181C22semidirect
176. #123×C181C22semidirect
177. #123×C181C22semidirect
178. #123×C181C22semidirect
179. #123×C181C22semidirect
180. C22⋊Q8×C181C22semidirect
181. C22⋊Q8×C181C22semidirect
182. C22⋊Q8×C181C22semidirect
184. C4×D4×C181C22semidirect
185. C4×D4×C181C22semidirect
186. C2×C4⋊C4×C181C22semidirect
540. C181#3534semidirect
562. #539D181semidirect
593. #126C2×D181semidirect
594. #126C2×D181semidirect
597. #125C2×D181semidirect
598. #125C2×D181semidirect
629. #123C2×D181semidirect
630. #123C2×D181semidirect
631. #123C2×D181semidirect
632. #123C2×D181semidirect
642. C22⋊Q8C2×D181semidirect
643. C22⋊Q8C2×D181semidirect
644. C22⋊Q8C2×D181semidirect
711. C4×D4C2×D181semidirect
712. C4×D4C2×D181semidirect
718. C2×C4⋊C4C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260420272
#260420252
#260420202
#260420192
#260419822
#260419802
#260419582
#260419562
#260419252
#260419242
#260419212
#260419202
#260419182
D4×D7242
#260419132
#260418852
#260418812
#260418772
#260418762
#260418692
#260418682
#260418592
#260418402
#260417872
#123×D1812
C2×#191537912
#539×C1812
#3534181