Finite Group Databasebeta

← #37547902

Subgroups — #37547902

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#26042026C211yesmaximal, characteristic, complemented
2#26042024C211yesmaximal, characteristic, complemented
3#26042017C211yesmaximal, characteristic, complemented
4#26041980C211yesmaximal, characteristic, complemented
5#26041976C211yesmaximal, characteristic, complemented
6#26041954C211yesmaximal, characteristic, complemented
7#26041952C211yesmaximal, characteristic, complemented
8#26041926C211yesmaximal, characteristic, complemented
9#26041921C211yesmaximal, characteristic, complemented
10#26041918C211yesmaximal, characteristic, complemented
11#26041918C211yesmaximal, characteristic, complemented
12#26041916C211yesmaximal, characteristic, complemented
13#26041916C211yesmaximal, characteristic, complemented
14#26041914C211yesmaximal, characteristic, complemented
15#26041911C211yesmaximal, characteristic, complemented
16#26041883C211yesmaximal, characteristic, complemented
17#26041882C211yesmaximal, characteristic, complemented
18#26041872C211yesmaximal, characteristic, complemented
19#26041870C211yesmaximal, characteristic, complemented
20#26041870C211yesmaximal, characteristic, complemented
21#26041866C211yesmaximal, characteristic, complemented
22#26041865C211yesmaximal, characteristic, complemented
23#26041864C211yesmaximal, characteristic, complemented
24#26041858C211yesmaximal, characteristic, complemented
25#26041839C211yesmaximal, characteristic, complemented
26#26041839C211yesmaximal, characteristic, complemented
27#26041837C211yesmaximal, characteristic, complemented
28#26041789C211yesmaximal, characteristic, complemented
29#123×D181C211yesmaximal, characteristic, complemented
30#121×D181C211yesmaximal, characteristic, complemented
31#560×C181C211yesmaximal, characteristic, complemented
32C2×#15668449C2211yescharacteristic, complemented
33C2×#15668448C2211yescharacteristic, complemented
34C2×#15668448C2211yescharacteristic, complemented
35C22×C22⋊D181C2211yescharacteristic, complemented
36C22×C22⋊D181C2211yescharacteristic, complemented
37C2×D4×D181C2211yescharacteristic
38C2×D4×D181C2211yescharacteristic, complemented
39C2×D4×D181C2211yescharacteristic, complemented
40C2×D4×D181C2211yescharacteristic, complemented
41C2×D4×D181C2211yescharacteristic, complemented
42C2×D4×D181C2211yescharacteristic, complemented
43C22×C4×D181C2211yescharacteristic, complemented
44#19153812C2211yescharacteristic, complemented
45#19153811C2211yescharacteristic, complemented
46#19153811C2211yescharacteristic, complemented
47#19153811C2211yescharacteristic, complemented
48#19153809C2211yescharacteristic, complemented
49#19153809C2211yescharacteristic, complemented
50#19153809C2211yescharacteristic, complemented
51#19153808C2211yescharacteristic, complemented
52#19153807C2211yescharacteristic, complemented
53#19153807C2211yescharacteristic, complemented
54#19153806C2211yescharacteristic, complemented
55#19153803C2211yescharacteristic, complemented
56#19153802C2211yescharacteristic, complemented
57#19153802C2211yescharacteristic, complemented
58#19153802C2211yescharacteristic, complemented
59#19153802C2211yescharacteristic, complemented
60#19153802C2211yescharacteristic, complemented
61#19153801C2211yescharacteristic, complemented
62#19153801C2211yescharacteristic, complemented
63#19153801C2211yescharacteristic, complemented
64#19153801C2211yescharacteristic, complemented
65#19153801C2211yescharacteristic, complemented
66#19153800C2211yescharacteristic, complemented
67#19153800C2211yescharacteristic, complemented
68#19153800C2211yescharacteristic, complemented
69#19153800C2211yescharacteristic, complemented
70#19153800C2211yescharacteristic, complemented
71#19153799C2211yescharacteristic, complemented
72#19153798C2211yescharacteristic, complemented
73#19153798C2211yescharacteristic, complemented
74#19153798C2211yescharacteristic, complemented
75#19153798C2211yescharacteristic, complemented
76#19153798C2211yescharacteristic, complemented
77#19153798C2211yescharacteristic, complemented
78#19153798C2211yescharacteristic, complemented
79#19153798C2211yescharacteristic, complemented
80#19153798C2211yescharacteristic, complemented
81#19153797C2211yescharacteristic, complemented
82#19153797C2211yescharacteristic, complemented
83#19153797C2211yescharacteristic, complemented
84#19153797C2211yescharacteristic, complemented
85#19153797C2211yescharacteristic, complemented
86#19153796C2211yescharacteristic, complemented
87#19153796C2211yescharacteristic, complemented
88#19153796C2211yescharacteristic, complemented
89#19153795C2211yescharacteristic, complemented
90#19153795C2211yescharacteristic, complemented
91#19153794C2211yescharacteristic, complemented
92#19153794C2211yescharacteristic, complemented
93#19153794C2211yescharacteristic, complemented
94#19153793C2211yescharacteristic, complemented
95#19153793C2211yescharacteristic, complemented
96#19153793C2211yescharacteristic, complemented
97#19153793C2211yescharacteristic, complemented
98#19153791C2211yescharacteristic, complemented
99#19153790C2211yescharacteristic, complemented
100#19153790C2211yescharacteristic, complemented
101#19153789C2211yescharacteristic
102#19153789C2211yescharacteristic
103#19153789C2211yescharacteristic, complemented
104#19153789C2211yescharacteristic, complemented
105#19153789C2211yescharacteristic, complemented
106#19153789C2211yescharacteristic, complemented
107#19153789C2211yescharacteristic, complemented
108#19153788C2211yescharacteristic, complemented
109#19153788C2211yescharacteristic, complemented
110#19153788C2211yescharacteristic, complemented
111#19153788C2211yescharacteristic, complemented
112#19153788C2211yescharacteristic, complemented
113#19153788C2211yescharacteristic, complemented
114#19153788C2211yescharacteristic, complemented
115#19153788C2211yescharacteristic, complemented
116#19153788C2211yescharacteristic, complemented
117#19153788C2211yescharacteristic, complemented
118#19153787C2211yescharacteristic
119#19153787C2211yescharacteristic, complemented
120#19153787C2211yescharacteristic, complemented
121#19153787C2211yescharacteristic, complemented
122#19153787C2211yescharacteristic, complemented
123#19153787C2211yescharacteristic, complemented
124#19153787C2211yescharacteristic, complemented
125#19153787C2211yescharacteristic, complemented
126#19153787C2211yescharacteristic, complemented
127#19153787C2211yescharacteristic, complemented
128#19153786C2211yescharacteristic
129#19153786C2211yescharacteristic, complemented
130#19153786C2211yescharacteristic, complemented
131#19153785C2211yescharacteristic, complemented
132#19153784C2211yescharacteristic
133#19153784C2211yescharacteristic, complemented
134#19153784C2211yescharacteristic, complemented
135#19153784C2211yescharacteristic, complemented
136#19153784C2211yescharacteristic, complemented
137#19153784C2211yescharacteristic, complemented
138#19153784C2211yescharacteristic, complemented
139#19153784C2211yescharacteristic, complemented
140#19153784C2211yescharacteristic, complemented
141C4×D724C2211yescharacteristic, complemented
142C4×D724C2211yescharacteristic, complemented
143D4×Dic181C2211yescharacteristic, complemented
144D4×Dic181C2211yescharacteristic, complemented
145D4×Dic181C2211yescharacteristic, complemented
146D4×Dic181C2211yescharacteristic, complemented
147#19153778C2211yescharacteristic, complemented
148#19153778C2211yescharacteristic, complemented
149C4×C22⋊D181C2211yescharacteristic, complemented
150C4×C22⋊D181C2211yescharacteristic, complemented
151#19153776C2211yescharacteristic, complemented
152#19153776C2211yescharacteristic, complemented
153#19153776C2211yescharacteristic, complemented
154#19153776C2211yescharacteristic, complemented
155#19153776C2211yescharacteristic, complemented
156#19153776C2211yescharacteristic, complemented
157#19153775C2211yescharacteristic, complemented
158#19153774C2211yescharacteristic, complemented
159#19153773C2211yescharacteristic, complemented
160C4⋊C4×D181C2211yescharacteristic, complemented
161C4⋊C4×D181C2211yescharacteristic, complemented
162C4⋊C4×D181C2211yescharacteristic, complemented
163C2×C22⋊Dic181C2211yescharacteristic, 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#127×C181C2211yescharacteristic, complemented
173#126×C181C2211yescharacteristic, complemented
174#126×C181C2211yescharacteristic, complemented
175#123×C181C2211yescharacteristic, complemented
176#123×C181C2211yescharacteristic, complemented
177#123×C181C2211yescharacteristic, complemented
178#121×C181C2211yescharacteristic, complemented
179#121×C181C2211yescharacteristic, complemented
180#121×C181C2211yescharacteristic, complemented
181#121×C181C2211yescharacteristic, complemented
182#121×C181C2211yescharacteristic, complemented
183#121×C181C2211yescharacteristic, complemented
184#120×C181C2211yescharacteristic, complemented
185#120×C181C2211yescharacteristic, complemented
186#120×C181C2211yescharacteristic, complemented
187C23×D181C2311yescharacteristic
188C23×D181C2311yescharacteristic
189C23×D181C2311yescharacteristic
190C23×D181C2311yescharacteristic
191C23×D181C2311yescharacteristic
192#15668449—42no—
193#15668448—42no—
194#15668448—42no—
195C2×Dic362C2311yescharacteristic
196C2×Dic362C2311yescharacteristic
197C2×Dic362C2311yescharacteristic
198C2×D724C2311yescharacteristic
199C2×D724C2311yescharacteristic
200C2×D724C2311yescharacteristic
201C2×D724C2311yescharacteristic
202C2×D724C2311yescharacteristic
203C2×C22⋊D181—42no—
204C2×C22⋊D181—42no—
205C2×C22⋊D181C2311yescharacteristic
206C2×C22⋊D181C2311yescharacteristic
207C2×C22⋊D181C2311yescharacteristic
208C2×C22⋊D181C2311yescharacteristic
209C2×C22⋊D181C2311yescharacteristic
210C2×C22⋊D181C2311yescharacteristic
211C2×C22⋊D181C2311yescharacteristic
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
225D4×D181—42no—
226D4×D181—42no—
227D4×D181—42no—
228D4×D181—42no—
229D4×D181—42no—
230D4×D181—42no—
231C22×Dic181C2311yescharacteristic
232C22×Dic181C2311yescharacteristic
233C22×Dic181C2311yescharacteristic
234C22×Dic181C2311yescharacteristic
235C22×Dic181C2311yescharacteristic
236C22×Dic181C2311yescharacteristic
237C22×Dic181C2311yescharacteristic
238C2×C4×D181—42no—
239C2×C4×D181C2311yescharacteristic
240C2×C4×D181C2311yescharacteristic
241C2×C4×D181C2311yescharacteristic
242C2×C4×D181C2311yescharacteristic
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
252C4⋊Dic181C2311yescharacteristic
253C4⋊Dic181C2311yescharacteristic
254C4⋊Dic181C2311yescharacteristic
255C4⋊Dic181C2311yescharacteristic
256C4⋊Dic181C2311yescharacteristic
257C4⋊Dic181C2311yescharacteristic
258C4⋊Dic181C2311yescharacteristic
259C4⋊Dic181C2311yescharacteristic
260C4⋊Dic181C2311yescharacteristic
261C4⋊Dic181C2311yescharacteristic
262#15668428C2311yescharacteristic
263#15668428C2311yescharacteristic
264#15668428C2311yescharacteristic
265#15668428C2311yescharacteristic
266#15668428C2311yescharacteristic
267#15668428C2311yescharacteristic
268#15668428C2311yescharacteristic
269#15668428C2311yescharacteristic
270#15668428C2311yescharacteristic
271#15668428C2311yescharacteristic
272#15668428C2311yescharacteristic
273#15668428C2311yescharacteristic
274#15668428C2311yescharacteristic
275#15668428C2311yescharacteristic
276C22⋊Dic181C2311yescharacteristic
277C22⋊Dic181C2311yescharacteristic
278C22⋊Dic181C2311yescharacteristic
279C22⋊Dic181C2311yescharacteristic
280C22⋊Dic181C2311yescharacteristic
281C22⋊Dic181C2311yescharacteristic
282C22⋊Dic181C2311yescharacteristic
283C22⋊Dic181C2311yescharacteristic
284C22⋊Dic181C2311yescharacteristic
285C22⋊Dic181C2311yescharacteristic
286C22⋊Dic181C2311yescharacteristic
287C22⋊Dic181C2311yescharacteristic
288C22⋊Dic181C2311yescharacteristic
289C22⋊Dic181C2311yescharacteristic
290C22⋊Dic181C2311yescharacteristic
291C22⋊Dic181C2311yescharacteristic
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
319C24×C181C2311yescharacteristic
320C2×D4×C181C2311yescharacteristic
321C2×D4×C181C2311yescharacteristic
322C2×D4×C181C2311yescharacteristic
323C2×D4×C181C2311yescharacteristic
324C2×D4×C181C2311yescharacteristic
325C2×D4×C181C2311yescharacteristic
326C2×D4×C181C2311yescharacteristic
327C2×D4×C181C2311yescharacteristic
328C2×D4×C181C2311yescharacteristic
329C2×D4×C181C2311yescharacteristic
330C2×D4×C181C2311yescharacteristic
331C2×D4×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
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×D181C2411yescharacteristic
370C22×D181C2411yescharacteristic
371C22×D181C2411yescharacteristic
372C22×D181C2411yescharacteristic
373C22×D181C2411yescharacteristic
374Dic362—41no—
375Dic362—41no—
376Dic362—41no—
377D724—22no—
378D724—22no—
379D724—22no—
380D724—41no—
381D724—41no—
382C22⋊D181—22no—
383C22⋊D181—22no—
384C22⋊D181—22no—
385C22⋊D181—22no—
386C22⋊D181—22no—
387C22⋊D181—22no—
388C22⋊D181—22no—
389C22⋊D181—41no—
390C22⋊D181—41no—
391C22⋊D181—41no—
392C22⋊D181—41no—
393C22⋊D181—41no—
394C22⋊D181—41no—
395C22⋊D181—41no—
396C22⋊D181—41no—
397C22⋊D181—41no—
398C22⋊D181—41no—
399C22⋊D181—41no—
400C22⋊D181—41no—
401C22⋊D181—41no—
402C2×Dic181—41no—
403C2×Dic181—41no—
404C2×Dic181—41no—
405C2×Dic181—41no—
406C2×Dic181—41no—
407C2×Dic181—41no—
408C2×Dic181—41no—
409C2×Dic181C2411yescharacteristic
410C2×Dic181C2411yescharacteristic
411C2×Dic181C2411yescharacteristic
412C2×Dic181C2411yescharacteristic
413C2×Dic181C2411yescharacteristic
414C2×Dic181C2411yescharacteristic
415C2×Dic181C2411yescharacteristic
416C2×Dic181C2411yescharacteristic
417C2×Dic181C2411yescharacteristic
418C2×Dic181C2411yescharacteristic
419C2×Dic181C2411yescharacteristic
420C4×D181—22no—
421C4×D181—22no—
422C4×D181—22no—
423C4×D181—41no—
424C4×D181—41no—
425C4×D181—41no—
426C4×D181—41no—
427C4×D181—41no—
428C4×D181—41no—
429C4×D181—41no—
430C4×D181—41no—
431C4×D181—41no—
432C4×D181—41no—
433C23×C181—41no—
434C23×C181—41no—
435C23×C181—41no—
436C23×C181C2411yescharacteristic
437C23×C181C2411yescharacteristic
438C23×C181C2411yescharacteristic
439C23×C181C2411yescharacteristic
440C23×C181C2411yescharacteristic
441C23×C181C2411yescharacteristic
442D4×C181—41no—
443D4×C181—41no—
444D4×C181—41no—
445D4×C181—41no—
446D4×C181—41no—
447D4×C181—41no—
448D4×C181—41no—
449D4×C181—41no—
450D4×C181—41no—
451D4×C181—41no—
452D4×C181—41no—
453D4×C181—41no—
454C2×C4×C181—41no—
455C2×C4×C181—41no—
456C2×C4×C181—41no—
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×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—82no—
485C22×C181C2511yescharacteristic
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×D181H(5,𝔽2)12yes—
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—
515Dic181—21no—
516Dic181—21no—
517Dic181—21no—
518Dic181—21no—
519Dic181—21no—
520Dic181—21no—
521Dic181—21no—
522Dic181—21no—
523Dic181—21no—
524Dic181—21no—
525Dic181—21no—
526C2×C181—41no—
527C2×C181—41no—
528C2×C181—41no—
529C2×C181—41no—
530C2×C181—41no—
531C2×C181—41no—
532C2×C181C2×H(5,𝔽2)11yescharacteristic
533C2×C181C2×H(5,𝔽2)11yescharacteristic
534C2×C181#58511yescharacteristic
535D181—22no—
536D181—22no—
537D181—41no—
538D181—41no—
539D181—41no—
540C181#353411yescharacteristic, complemented, Sylow
541#3534—1811nomaximal, Sylow
542#562—1811no—
543#562—1811no—
544#560—1811no—
545#560D18111yescharacteristic, complemented
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#539—1811no—
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#127C2×D18111yescharacteristic, complemented
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#125—1811no—
598#125—1811no—
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#123—1811no—
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⋊Q8—1811no—
643C22⋊Q8—1811no—
644C22⋊Q8—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#121—1811no—
669#121—1811no—
670#121—1811no—
671#121—1811no—
672#121—1811no—
673#121—1811no—
674#121—1811no—
675#121C2×D18111yescharacteristic, complemented
676#121C2×D18111yescharacteristic, complemented
677#121C2×D18111yescharacteristic, complemented
678#121C2×D18111yescharacteristic, complemented
679#121C2×D18111yescharacteristic, complemented
680#121C2×D18111yescharacteristic, complemented
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#120C2×D18111yescharacteristic, complemented
695#120C2×D18111yescharacteristic, complemented
696#120C2×D18111yescharacteristic, complemented
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—
713#117—1811no—
714#117—1811no—
715#117—1811no—
716C2×C4⋊C4—1811no—
717C2×C4⋊C4—1811no—
718C2×C4⋊C4—1811no—
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—
733C24C22×D18111yescharacteristic
734#41—7242no—
735#41—7242no—
736#41—7242no—
737C2×Q8—1811no—
738C2×Q8—1811no—
739C2×Q8—1811no—
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—7242no—
766C2×D4—7242no—
767C2×D4—7242no—
768C2×D4—7242no—
769C2×D4—7242no—
770C2×D4—7242no—
771C2×D4—7242no—
772C2×D4—7242no—
773C2×D4C22×D18111yescharacteristic
774C2×D4C22×D18111yescharacteristic
775C2×D4C22×D18111yescharacteristic
776C2×D4C22×D18111yescharacteristic
777C2×D4C22×D18111yescharacteristic
778C2×D4C22×D18111yescharacteristic
779C2×D4C22×D18111yescharacteristic
780C2×D4C22×D18111yescharacteristic
781C2×D4C22×D18111yescharacteristic
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—1811no—
804C22×C4—1811no—
805C22×C4—7242no—
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⋊C4—1811no—
826C4⋊C4—1811no—
827C4⋊C4—1811no—
828C4⋊C4—1811no—
829C4⋊C4—1811no—
830C4⋊C4—1811no—
831C4⋊C4—1811no—
832C4⋊C4—1811no—
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⋊C4C22×D18111yescharacteristic
878C22⋊C4C22×D18111yescharacteristic
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—
893C42—1811no—
894C42C22×D18111yescharacteristic
895C23—41no—
896C23—41no—
897C23—41no—
898C23—3622no—
899C23—3622no—
900C23—3622no—
901C23—3622no—
902C23—3622no—
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—
918C23C23×D18111yescharacteristic
919C23C23×D18111yescharacteristic
920C23C23×D18111yescharacteristic
921C23C23×D18111yescharacteristic
922C23C23×D18111yescharacteristic
923C23C23×D18111yescharacteristic
924Q8—7241no—
925Q8—7241no—
926Q8—7241no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—3622no—
940D4—3622no—
941D4—3622no—
942D4—3622no—
943D4—3622no—
944D4—3622no—
945D4—3622no—
946D4—3622no—
947D4—3622no—
948D4—3622no—
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—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—3622no—
968C2×C4—3622no—
969C2×C4—3622no—
970C2×C4—1811no—
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—1811no—
980C2×C4—1811no—
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×C4—7241no—
996C2×C4—7241no—
997C2×C4—7241no—
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—21no—
1016C22—21no—
1017C22—21no—
1018C22—21no—
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—82no—
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—3621no—
1039C22—14482no—
1040C22—14482no—
1041C22—14482no—
1042C22—14482no—
1043C22—1812no—
1044C22—1812no—
1045C22—7244no—
1046C22C24×D18111yescharacteristic
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—21no—
1055C4—21no—
1056C4—3621no—
1057C4—3621no—
1058C4—3621no—
1059C4—3621no—
1060C4—3621no—
1061C4—3621no—
1062C4—3621no—
1063C4—3621no—
1064C4—3621no—
1065C4—3621no—
1066C4—3621no—
1067C2—41no—
1068C2—41no—
1069C2—41no—
1070C2—41no—
1071C2—41no—
1072C2—41no—
1073C2—3622no—
1074C2—3622no—
1075C2—7241no—
1076C2—7241no—
1077C2—7241no—
1078C2H(5,𝔽2)×D18111yescharacteristic
1079C2H(5,𝔽2)×D18111yescharacteristic
1080C2#2604211411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D181
commutator, socle, cosocleC22×C181C25
Fitting#560×C181C2
hypercenter#560D181
hypocenterC181#3534
LCSG ▷ C22×C181 ▷ C181
UCSC1 ◁ C22 ◁ #560

Complements

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

NH ≅ G/Ntype
1. #26042026C2semidirect
2. #26042024C2semidirect
3. #26042017C2semidirect
4. #26041980C2semidirect
5. #26041976C2semidirect
6. #26041954C2semidirect
7. #26041952C2semidirect
8. #26041926C2semidirect
9. #26041921C2semidirect
10. #26041918C2semidirect
11. #26041918C2semidirect
12. #26041916C2semidirect
13. #26041916C2semidirect
14. #26041914C2semidirect
15. #26041911C2semidirect
16. #26041883C2semidirect
17. #26041882C2semidirect
18. #26041872C2semidirect
19. #26041870C2semidirect
20. #26041870C2semidirect
21. #26041866C2semidirect
22. #26041865C2semidirect
23. #26041864C2semidirect
24. #26041858C2semidirect
25. #26041839C2semidirect
26. #26041839C2semidirect
27. #26041837C2semidirect
28. #26041789C2semidirect
29. #123×D181C2semidirect
30. #121×D181C2semidirect
31. #560×C181C2semidirect
32. C2×#15668449C22semidirect
33. C2×#15668448C22semidirect
34. C2×#15668448C22semidirect
35. C22×C22⋊D181C22semidirect
36. C22×C22⋊D181C22semidirect
38. C2×D4×D181C22semidirect
39. C2×D4×D181C22semidirect
40. C2×D4×D181C22semidirect
41. C2×D4×D181C22semidirect
42. C2×D4×D181C22semidirect
43. C22×C4×D181C22semidirect
44. #19153812C22semidirect
45. #19153811C22semidirect
46. #19153811C22semidirect
47. #19153811C22semidirect
48. #19153809C22semidirect
49. #19153809C22semidirect
50. #19153809C22semidirect
51. #19153808C22semidirect
52. #19153807C22semidirect
53. #19153807C22semidirect
54. #19153806C22semidirect
55. #19153803C22semidirect
56. #19153802C22semidirect
57. #19153802C22semidirect
58. #19153802C22semidirect
59. #19153802C22semidirect
60. #19153802C22semidirect
61. #19153801C22semidirect
62. #19153801C22semidirect
63. #19153801C22semidirect
64. #19153801C22semidirect
65. #19153801C22semidirect
66. #19153800C22semidirect
67. #19153800C22semidirect
68. #19153800C22semidirect
69. #19153800C22semidirect
70. #19153800C22semidirect
71. #19153799C22semidirect
72. #19153798C22semidirect
73. #19153798C22semidirect
74. #19153798C22semidirect
75. #19153798C22semidirect
76. #19153798C22semidirect
77. #19153798C22semidirect
78. #19153798C22semidirect
79. #19153798C22semidirect
80. #19153798C22semidirect
81. #19153797C22semidirect
82. #19153797C22semidirect
83. #19153797C22semidirect
84. #19153797C22semidirect
85. #19153797C22semidirect
86. #19153796C22semidirect
87. #19153796C22semidirect
88. #19153796C22semidirect
89. #19153795C22semidirect
90. #19153795C22semidirect
91. #19153794C22semidirect
92. #19153794C22semidirect
93. #19153794C22semidirect
94. #19153793C22semidirect
95. #19153793C22semidirect
96. #19153793C22semidirect
97. #19153793C22semidirect
98. #19153791C22semidirect
99. #19153790C22semidirect
100. #19153790C22semidirect
103. #19153789C22semidirect
104. #19153789C22semidirect
105. #19153789C22semidirect
106. #19153789C22semidirect
107. #19153789C22semidirect
108. #19153788C22semidirect
109. #19153788C22semidirect
110. #19153788C22semidirect
111. #19153788C22semidirect
112. #19153788C22semidirect
113. #19153788C22semidirect
114. #19153788C22semidirect
115. #19153788C22semidirect
116. #19153788C22semidirect
117. #19153788C22semidirect
119. #19153787C22semidirect
120. #19153787C22semidirect
121. #19153787C22semidirect
122. #19153787C22semidirect
123. #19153787C22semidirect
124. #19153787C22semidirect
125. #19153787C22semidirect
126. #19153787C22semidirect
127. #19153787C22semidirect
129. #19153786C22semidirect
130. #19153786C22semidirect
131. #19153785C22semidirect
133. #19153784C22semidirect
134. #19153784C22semidirect
135. #19153784C22semidirect
136. #19153784C22semidirect
137. #19153784C22semidirect
138. #19153784C22semidirect
139. #19153784C22semidirect
140. #19153784C22semidirect
141. C4×D724C22semidirect
142. C4×D724C22semidirect
143. D4×Dic181C22semidirect
144. D4×Dic181C22semidirect
145. D4×Dic181C22semidirect
146. D4×Dic181C22semidirect
147. #19153778C22semidirect
148. #19153778C22semidirect
149. C4×C22⋊D181C22semidirect
150. C4×C22⋊D181C22semidirect
151. #19153776C22semidirect
152. #19153776C22semidirect
153. #19153776C22semidirect
154. #19153776C22semidirect
155. #19153776C22semidirect
156. #19153776C22semidirect
157. #19153775C22semidirect
158. #19153774C22semidirect
159. #19153773C22semidirect
160. C4⋊C4×D181C22semidirect
161. C4⋊C4×D181C22semidirect
162. C4⋊C4×D181C22semidirect
163. C2×C22⋊Dic181C22semidirect
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. #127×C181C22semidirect
173. #126×C181C22semidirect
174. #126×C181C22semidirect
175. #123×C181C22semidirect
176. #123×C181C22semidirect
177. #123×C181C22semidirect
178. #121×C181C22semidirect
179. #121×C181C22semidirect
180. #121×C181C22semidirect
181. #121×C181C22semidirect
182. #121×C181C22semidirect
183. #121×C181C22semidirect
184. #120×C181C22semidirect
185. #120×C181C22semidirect
186. #120×C181C22semidirect
540. C181#3534semidirect
545. #560D181semidirect
586. #127C2×D181semidirect
593. #126C2×D181semidirect
594. #126C2×D181semidirect
630. #123C2×D181semidirect
631. #123C2×D181semidirect
632. #123C2×D181semidirect
675. #121C2×D181semidirect
676. #121C2×D181semidirect
677. #121C2×D181semidirect
678. #121C2×D181semidirect
679. #121C2×D181semidirect
680. #121C2×D181semidirect
694. #120C2×D181semidirect
695. #120C2×D181semidirect
696. #120C2×D181semidirect

Maximal subgroups

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

subgroupindex
#260420262
#260420242
#260420172
#260419802
#260419762
#260419542
#260419522
#260419262
#260419212
#260419182
#260419162
#260419142
#260419112
#260418832
#260418822
#260418722
#260418702
#260418662
#260418652
#260418642
#260418582
#260418392
#260418372
#260417892
#123×D1812
#121×D1812
#560×C1812
#3534181