Finite Group Databasebeta

← #37576056

Subgroups — #37576056

Order 24448.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259296C211yesmaximal, characteristic, complemented
2C2×#20259295C211yesmaximal, characteristic, complemented
3C2×#20259291C211yesmaximal, characteristic, complemented
4C2×#20259291C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊D191C211yesmaximal, characteristic, complemented
6#27132586C211yesmaximal, characteristic, complemented
7#27132578C211yesmaximal, characteristic, complemented
8#27132578C211yesmaximal, characteristic, complemented
9#27132572C211yesmaximal, characteristic, complemented
10#27132563C211yesmaximal, characteristic, complemented
11#27132556C211yesmaximal, characteristic, complemented
12#27132542C211yesmaximal, characteristic, complemented
13#27132539C211yesmaximal, characteristic, complemented
14#27132536C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×C191C211yesmaximal, characteristic, complemented
16C22×D764C2211yescharacteristic, complemented
17C22×C22⋊D191C2211yescharacteristic
18C22×C22⋊D191C2211yescharacteristic
19C22×C22⋊D191C2211yescharacteristic
20C22×C22⋊D191C2211yescharacteristic
21C22×C22⋊D191C2211yescharacteristic
22C22×C22⋊D191C2211yescharacteristic
23C22×C4×D191C2211yescharacteristic, complemented
24#20259296—24no—
25#20259295—24no—
26#20259291—24no—
27#20259291—24no—
28C4×C22⋊D191—24no—
29C2×C4⋊Dic191C2211yescharacteristic, complemented
30C2×Dic191⋊C4C2211yescharacteristic, complemented
31C2×Dic191⋊C4C2211yescharacteristic, complemented
32C2×Dic191⋊C4C2211yescharacteristic, complemented
33C2×C22⋊Dic191C2211yescharacteristic
34C2×C22⋊Dic191C2211yescharacteristic
35C2×C22⋊Dic191C2211yescharacteristic
36C2×C22⋊Dic191C2211yescharacteristic
37C2×C22⋊Dic191C2211yescharacteristic
38C2×C22⋊Dic191C2211yescharacteristic
39C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
44C2×C4×Dic191C2211yescharacteristic, complemented
45C191⋊#95C2211yescharacteristic, complemented
46C191⋊#95C2211yescharacteristic, complemented
47C191⋊#95C2211yescharacteristic, complemented
48C191⋊#95C2211yescharacteristic, complemented
49C25×C191C2211yescharacteristic
50C23×C4×C191C2211yescharacteristic
51C23×C4×C191C2211yescharacteristic
52C2×C22⋊C4×C191—24no—
53C2×C22⋊C4×C191C2211yescharacteristic
54C2×C22⋊C4×C191C2211yescharacteristic
55C2×C22⋊C4×C191C2211yescharacteristic
56C2×C22⋊C4×C191C2211yescharacteristic
57C23×D191C2311yescharacteristic
58C23×D191C2311yescharacteristic
59C2×D764—22no—
60C2×D764—22no—
61C2×D764—41no—
62C2×C22⋊D191—22no—
63C2×C22⋊D191—22no—
64C2×C22⋊D191—22no—
65C2×C22⋊D191—22no—
66C2×C22⋊D191—22no—
67C2×C22⋊D191—22no—
68C2×C22⋊D191—22no—
69C2×C22⋊D191—22no—
70C2×C22⋊D191—22no—
71C2×C22⋊D191—22no—
72C2×C22⋊D191—22no—
73C2×C22⋊D191—22no—
74C2×C22⋊D191—22no—
75C2×C22⋊D191—41no—
76C2×C22⋊D191—41no—
77C2×C22⋊D191—41no—
78C2×C22⋊D191—41no—
79C2×C22⋊D191D414yescomplemented
80C22×Dic191C2311yescharacteristic
81C22×Dic191C2311yescharacteristic
82C22×Dic191C2311yescharacteristic
83C22×Dic191C2311yescharacteristic
84C22×Dic191C2311yescharacteristic
85C22×Dic191C2311yescharacteristic
86C2×C4×D191—22no—
87C2×C4×D191—22no—
88C2×C4×D191—41no—
89C4⋊Dic191—22no—
90Dic191⋊C4—22no—
91Dic191⋊C4—22no—
92Dic191⋊C4—41no—
93C22⋊Dic191—22no—
94C22⋊Dic191—22no—
95C22⋊Dic191—22no—
96C22⋊Dic191—22no—
97C22⋊Dic191—22no—
98C22⋊Dic191D414yescomplemented
99(C2×D191)⋊C4—22no—
100(C2×D191)⋊C4—22no—
101(C2×D191)⋊C4—22no—
102(C2×D191)⋊C4—22no—
103(C2×D191)⋊C4—41no—
104C4×Dic191—22no—
105C24×C191—22no—
106C24×C191—22no—
107C24×C191—22no—
108C24×C191—22no—
109C24×C191—22no—
110C24×C191—41no—
111C24×C191—41no—
112C24×C191C2311yescharacteristic
113C24×C191C2311yescharacteristic
114C24×C191C2311yescharacteristic
115C22×C4×C191—22no—
116C22×C4×C191—22no—
117C22×C4×C191—22no—
118C22×C4×C191—22no—
119C22×C4×C191—41no—
120C22×C4×C191—41no—
121C22×C4×C191C2311yescharacteristic
122C22×C4×C191C2311yescharacteristic
123C22×C4×C191C2311yescharacteristic
124C22×C4×C191C2311yescharacteristic
125C22⋊C4×C191—22no—
126C22⋊C4×C191—22no—
127C22⋊C4×C191—22no—
128C22⋊C4×C191D414yescomplemented
129C22×D191—21no—
130C22×D191—21no—
131C22×D191—21no—
132C22×D191—21no—
133C22×D191—21no—
134C22×D191—21no—
135C22×D191—21no—
136C22×D191—21no—
137C22×D191—21no—
138C22×D191—21no—
139C22×D191—21no—
140C22×D191—21no—
141C22×D191—21no—
142C22×D191C2×D412yes—
143D764—44no—
144C22⋊D191—28no—
145C22⋊D191—44no—
146C22⋊D191—44no—
147C22⋊D191—44no—
148C22⋊D191—44no—
149C22⋊D191—44no—
150C2×Dic191—21no—
151C2×Dic191—21no—
152C2×Dic191—21no—
153C2×Dic191—21no—
154C2×Dic191—21no—
155C2×Dic191—21no—
156C2×Dic191—21no—
157C2×Dic191—21no—
158C2×Dic191—21no—
159C2×Dic191—21no—
160C2×Dic191—21no—
161C2×Dic191—21no—
162C2×Dic191—21no—
163C2×Dic191—21no—
164C2×Dic191—21no—
165C2×Dic191C2×D412yes—
166C2×Dic191C2×D412yes—
167C2×Dic191C2×D412yes—
168C4×D191—44no—
169C23×C191—21no—
170C23×C191—21no—
171C23×C191—21no—
172C23×C191—21no—
173C23×C191—28no—
174C23×C191—21no—
175C23×C191—21no—
176C23×C191—21no—
177C23×C191—21no—
178C23×C191—21no—
179C23×C191—21no—
180C23×C191—21no—
181C23×C191—21no—
182C23×C191—21no—
183C23×C191—21no—
184C23×C191—21no—
185C23×C191—21no—
186C23×C191—44no—
187C23×C191—44no—
188C23×C191—44no—
189C23×C191—44no—
190C23×C191—44no—
191C23×C191—44no—
192C23×C191C2×D412yes—
193C23×C191C2×D412yes—
194C23×C191C2×D412yes—
195C23×C191#4112yes—
196C23×C191#4112yes—
197C23×C191C2411yescharacteristic
198C2×C4×C191—21no—
199C2×C4×C191—21no—
200C2×C4×C191—21no—
201C2×C4×C191—21no—
202C2×C4×C191—21no—
203C2×C4×C191—21no—
204C2×C4×C191—21no—
205C2×C4×C191—21no—
206C2×C4×C191—21no—
207C2×C4×C191—21no—
208C2×C4×C191—44no—
209C2×C4×C191—44no—
210C2×C4×C191C2×D412yes—
211C2×C4×C191C2×D412yes—
212C22×C191—22no—
213C22×C191—22no—
214C22×C191—22no—
215C22×C191—22no—
216C22×C191—22no—
217C22×C191—22no—
218C22×C191—22no—
219C22×C191—22no—
220C22×C191—22no—
221C22×C191—22no—
222C22×C191—22no—
223C22×C191—22no—
224C22×C191—416no—
225C22×C191—41no—
226C22×C191—41no—
227C22×C191—41no—
228C22×C191—41no—
229C22×C191—41no—
230C22×C191—41no—
231C22×C191—41no—
232C22×C191—41no—
233C22×C191#12114yescomplemented
234C22×C191C22×D411yescharacteristic
235C22×C191C22×D411yescharacteristic
236C22×C191C22×D411yescharacteristic
237C22×C191C2×#4111yescharacteristic
238C22×C191C2×#4111yescharacteristic
239C22×C191H(5,𝔽2)11yescharacteristic
240C22×C191H(5,𝔽2)11yescharacteristic
241C2×D191—22no—
242C2×D191—22no—
243C2×D191—22no—
244C2×D191—41no—
245C2×D191—41no—
246C2×D191—41no—
247C2×D191—41no—
248C2×D191—41no—
249C2×D191—41no—
250C2×D191—41no—
251C2×D191—41no—
252C2×D191—41no—
253C2×D191—41no—
254C2×D191—41no—
255C4×C191—22no—
256C4×C191—22no—
257C4×C191—41no—
258C4×C191—41no—
259Dic191—22no—
260Dic191—22no—
261Dic191—22no—
262Dic191—41no—
263Dic191—41no—
264Dic191—41no—
265C2×C191—24no—
266C2×C191—42no—
267C2×C191—42no—
268C2×C191C2×#12111yescharacteristic
269C2×C191#52511yescharacteristic
270C2×C191#53811yescharacteristic
271C2×C191D4211yescharacteristic
272C2×C191D4211yescharacteristic
273C2×C191#54611yescharacteristic
274C2×C191#54611yescharacteristic
275D191—42no—
276D191—81no—
277C191#242411yescharacteristic, complemented, Sylow
278#2424—1911nomaximal, Sylow
279C2×#121—1911no—
280C2×#121—1911no—
281C2×#120—1911no—
282C2×#120—1911no—
283C2×C4×D4—1911no—
284C22×C22⋊C4D19111yescharacteristic, complemented
285#396—1911no—
286#394—1911no—
287#394—1911no—
288#392—1911no—
289#390—1911no—
290#388—1911no—
291#386—1911no—
292#386—1911no—
293#385—1911no—
294C25C2×D19111yescharacteristic
295C22×D4—1911no—
296C22×D4—1911no—
297C22×D4—1911no—
298C22×D4—1911no—
299C22×D4—1911no—
300C22×D4—1911no—
301C22×D4—1911no—
302C23×C4—1911no—
303C23×C4C2×D19111yescharacteristic
304C23×C4C2×D19111yescharacteristic
305#121—3824no—
306#121—3824no—
307#120—3824no—
308#120—3824no—
309C4×D4—3824no—
310C2×C4⋊C4—1911no—
311C2×C4⋊C4—1911no—
312C2×C4⋊C4—1911no—
313C2×C4⋊C4—1911no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—1911no—
316C2×C22⋊C4—1911no—
317C2×C22⋊C4—1911no—
318C2×C22⋊C4—1911no—
319C2×C22⋊C4—1911no—
320C2×C22⋊C4—1911no—
321C2×C22⋊C4—1911no—
322C2×C22⋊C4—1911no—
323C2×C22⋊C4—1911no—
324C2×C22⋊C4—1911no—
325C2×C22⋊C4—1911no—
326C2×C22⋊C4C2×D19111yescharacteristic
327C2×C22⋊C4C2×D19111yescharacteristic
328C2×C22⋊C4C2×D19111yescharacteristic
329C2×C22⋊C4C2×D19111yescharacteristic
330C2×C42—1911no—
331#95—1911no—
332#95—1911no—
333#95—1911no—
334#95—1911no—
335C24—22no—
336C24—22no—
337C24—22no—
338C24—22no—
339C24—22no—
340C24—41no—
341C24—41no—
342C24—1911no—
343C24—1911no—
344C24C22×D19111yescharacteristic
345C24C22×D19111yescharacteristic
346C24C22×D19111yescharacteristic
347C2×D4—3822no—
348C2×D4—3822no—
349C2×D4—3822no—
350C2×D4—3822no—
351C2×D4—3822no—
352C2×D4—3822no—
353C2×D4—3822no—
354C2×D4—3822no—
355C2×D4—3822no—
356C2×D4—3822no—
357C2×D4—3822no—
358C2×D4—3822no—
359C2×D4—3822no—
360C2×D4—3822no—
361C2×D4—3822no—
362C2×D4—1914no—
363C2×D4—7641no—
364C2×D4—7641no—
365C2×D4—7641no—
366C2×D4—7641no—
367C2×D4—7641no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—3822no—
375C22×C4—3822no—
376C22×C4—1911no—
377C22×C4—1911no—
378C22×C4—1911no—
379C22×C4—1911no—
380C22×C4—1911no—
381C22×C4—1911no—
382C22×C4—7641no—
383C22×C4C22×D19111yescharacteristic
384C22×C4C22×D19111yescharacteristic
385C22×C4C22×D19111yescharacteristic
386C22×C4C22×D19111yescharacteristic
387C4⋊C4—3822no—
388C4⋊C4—3822no—
389C4⋊C4—3822no—
390C4⋊C4—7641no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—3822no—
395C22⋊C4—3822no—
396C22⋊C4—3822no—
397C22⋊C4—3822no—
398C22⋊C4—3822no—
399C22⋊C4—3822no—
400C22⋊C4—3822no—
401C22⋊C4—3822no—
402C22⋊C4—3822no—
403C22⋊C4—1914no—
404C22⋊C4—7641no—
405C22⋊C4C22⋊D19114yescomplemented
406C42—3822no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—28no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—44no—
425C23—44no—
426C23—44no—
427C23—44no—
428C23—44no—
429C23—44no—
430C23—3821no—
431C23—3821no—
432C23—3821no—
433C23—3821no—
434C23—3821no—
435C23—3821no—
436C23—3821no—
437C23—3821no—
438C23—3821no—
439C23—3821no—
440C23—3821no—
441C23—3821no—
442C23—3821no—
443C23—1912no—
444C23D4×D19112yes—
445C23D4×D19112yes—
446C23C2×C22⋊D19112yes—
447C23#1569028712yes—
448C23#1569028712yes—
449C23C23×D19111yescharacteristic
450D4—3828no—
451D4—7644no—
452D4—7644no—
453D4—7644no—
454D4—7644no—
455D4—7644no—
456D4—7644no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—44no—
468C2×C4—44no—
469C2×C4—3821no—
470C2×C4—3821no—
471C2×C4—3821no—
472C2×C4—3821no—
473C2×C4—3821no—
474C2×C4—3821no—
475C2×C4—3821no—
476C2×C4—3821no—
477C2×C4—3821no—
478C2×C4—3821no—
479C2×C4—3821no—
480C2×C4—3821no—
481C2×C4—3821no—
482C2×C4—3821no—
483C2×C4—3821no—
484C2×C4—1912no—
485C2×C4—1912no—
486C2×C4—1912no—
487C2×C4—7644no—
488C2×C4C2×C22⋊D19112yes—
489C2×C4C2×C22⋊D19112yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—416no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—3822no—
512C22—3822no—
513C22—3822no—
514C22—7641no—
515C22—7641no—
516C22—7641no—
517C22—7641no—
518C22—7641no—
519C22—7641no—
520C22—7641no—
521C22—7641no—
522C22—7641no—
523C22—7641no—
524C22—7641no—
525C22#2025929514yescomplemented
526C22C2×D4×D19111yescharacteristic
527C22C2×D4×D19111yescharacteristic
528C22C22×C22⋊D19111yescharacteristic
529C22C2×#1569028711yescharacteristic
530C22C2×#1569028711yescharacteristic
531C22#2025936711yescharacteristic
532C22#2025936711yescharacteristic
533C4—22no—
534C4—22no—
535C4—41no—
536C4—41no—
537C4—3822no—
538C4—3822no—
539C4—3822no—
540C4—7641no—
541C4—7641no—
542C4—7641no—
543C2—24no—
544C2—42no—
545C2—42no—
546C2—15281no—
547C2—7642no—
548C2C2×#2025929511yescharacteristic
549C2#2713317411yescharacteristic
550C2#2713325111yescharacteristic
551C2D4×C22⋊D19111yescharacteristic
552C2D4×C22⋊D19111yescharacteristic
553C2#2713330311yescharacteristic
554C2#2713330311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
FittingC22×C22⋊C4×C191C2
hypercenterC22×C22⋊C4D191
hypocenterC191#2424
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#20259296C2semidirect
2. C2×#20259295C2semidirect
3. C2×#20259291C2semidirect
4. C2×#20259291C2semidirect
5. C2×C4×C22⋊D191C2semidirect
6. #27132586C2semidirect
7. #27132578C2semidirect
8. #27132578C2semidirect
9. #27132572C2semidirect
10. #27132563C2semidirect
11. #27132556C2semidirect
12. #27132542C2semidirect
13. #27132539C2semidirect
14. #27132536C2semidirect
15. C22×C22⋊C4×C191C2semidirect
16. C22×D764C22semidirect
23. C22×C4×D191C22semidirect
29. C2×C4⋊Dic191C22semidirect
30. C2×Dic191⋊C4C22semidirect
31. C2×Dic191⋊C4C22semidirect
32. C2×Dic191⋊C4C22semidirect
39. C2×(C2×D191)⋊C4C22semidirect
40. C2×(C2×D191)⋊C4C22semidirect
41. C2×(C2×D191)⋊C4C22semidirect
42. C2×(C2×D191)⋊C4C22semidirect
43. C2×(C2×D191)⋊C4C22semidirect
44. C2×C4×Dic191C22semidirect
45. C191⋊#95C22semidirect
46. C191⋊#95C22semidirect
47. C191⋊#95C22semidirect
48. C191⋊#95C22semidirect
79. C2×C22⋊D191D4semidirect
98. C22⋊Dic191D4semidirect
128. C22⋊C4×C191D4semidirect
233. C22×C191#121semidirect
277. C191#2424semidirect
284. C22×C22⋊C4D191semidirect
405. C22⋊C4C22⋊D191semidirect
525. C22#20259295semidirect

Maximal subgroups

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

subgroupindex
C2×#202592962
C2×#202592952
C2×#202592912
C2×C4×C22⋊D1912
#271325862
#271325782
#271325722
#271325632
#271325562
#271325422
#271325392
#271325362
C22×C22⋊C4×C1912
#2424191