Finite Group Databasebeta

← #37576053

Subgroups — #37576053

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×#20259293C211yesmaximal, characteristic, complemented
2C2×#20259290C211yesmaximal, characteristic, complemented
3C2×#20259290C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D191C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D191C211yesmaximal, characteristic, complemented
6#27132585C211yesmaximal, characteristic, complemented
7#27132577C211yesmaximal, characteristic, complemented
8#27132577C211yesmaximal, characteristic, complemented
9#27132571C211yesmaximal, characteristic, complemented
10#27132563C211yesmaximal, characteristic, complemented
11#27132556C211yesmaximal, characteristic, complemented
12#27132542C211yesmaximal, characteristic, complemented
13#27132539C211yesmaximal, characteristic, complemented
14#27132534C211yesmaximal, characteristic, complemented
15C2×#121×C191C211yesmaximal, characteristic, complemented
16C24×D191C2211yescharacteristic
17C22×C22⋊D191C2211yescharacteristic
18C22×C22⋊D191C2211yescharacteristic
19C22×C22⋊D191C2211yescharacteristic
20C22×C22⋊D191C2211yescharacteristic
21C22×C4×D191C2211yescharacteristic
22C22×C4×D191C2211yescharacteristic
23#20259293—24no—
24#20259290—24no—
25#20259290—24no—
26C4×C22⋊D191—24no—
27C2×C4⋊Dic191C2211yescharacteristic, complemented
28C2×Dic191⋊C4C2211yescharacteristic, complemented
29C2×Dic191⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic191C2211yescharacteristic
31C2×C22⋊Dic191C2211yescharacteristic
32C2×C22⋊Dic191C2211yescharacteristic
33C2×C22⋊Dic191C2211yescharacteristic, complemented
34C2×C22⋊Dic191C2211yescharacteristic, complemented
35C2×C22⋊Dic191C2211yescharacteristic, complemented
36C2×C22⋊Dic191C2211yescharacteristic, complemented
37C2×(C2×D191)⋊C4C2211yescharacteristic
38C2×(C2×D191)⋊C4C2211yescharacteristic
39C2×(C2×D191)⋊C4C2211yescharacteristic
40C2×(C2×D191)⋊C4C2211yescharacteristic
41C2×(C2×D191)⋊C4C2211yescharacteristic
42C2×(C2×D191)⋊C4C2211yescharacteristic
43C22⋊C4×D191—24no—
44C2×C4×Dic191C2211yescharacteristic, complemented
45C191⋊#95C2211yescharacteristic, complemented
46C191⋊#95C2211yescharacteristic, complemented
47C191⋊#95C2211yescharacteristic, complemented
48C191⋊#95C2211yescharacteristic, complemented
49C22×D4×C191C2211yescharacteristic
50C22×D4×C191C2211yescharacteristic
51C22×D4×C191C2211yescharacteristic, complemented
52C23×C4×C191C2211yescharacteristic, complemented
53#121×C191—24no—
54C2×C4⋊C4×C191C2211yescharacteristic, complemented
55C2×C22⋊C4×C191C2211yescharacteristic
56C2×C22⋊C4×C191C2211yescharacteristic, complemented
57C23×D191—22no—
58C23×D191—22no—
59C23×D191—22no—
60C23×D191—22no—
61C23×D191—22no—
62C23×D191—41no—
63C23×D191—41no—
64C23×D191C2311yescharacteristic
65C23×D191C2311yescharacteristic
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⋊D191D414yescomplemented
78C22×Dic191C2311yescharacteristic
79C22×Dic191C2311yescharacteristic
80C22×Dic191C2311yescharacteristic
81C22×Dic191C2311yescharacteristic
82C22×Dic191C2311yescharacteristic
83C22×Dic191C2311yescharacteristic
84C2×C4×D191—22no—
85C2×C4×D191—22no—
86C2×C4×D191—22no—
87C2×C4×D191—22no—
88C2×C4×D191—41no—
89C2×C4×D191—41no—
90C4⋊Dic191—22no—
91Dic191⋊C4—22no—
92Dic191⋊C4—41no—
93C22⋊Dic191—22no—
94C22⋊Dic191—22no—
95C22⋊Dic191—22no—
96C22⋊Dic191—22no—
97C22⋊Dic191—22no—
98C22⋊Dic191—22no—
99C22⋊Dic191—41no—
100(C2×D191)⋊C4—22no—
101(C2×D191)⋊C4—22no—
102(C2×D191)⋊C4—22no—
103(C2×D191)⋊C4—22no—
104(C2×D191)⋊C4—22no—
105(C2×D191)⋊C4D414yescomplemented
106C4×Dic191—22no—
107C24×C191C2311yescharacteristic
108C24×C191C2311yescharacteristic
109C24×C191C2311yescharacteristic
110C2×D4×C191—22no—
111C2×D4×C191—22no—
112C2×D4×C191—22no—
113C2×D4×C191—22no—
114C2×D4×C191—22no—
115C2×D4×C191—22no—
116C2×D4×C191—41no—
117C2×D4×C191—41no—
118C2×D4×C191—41no—
119C22×C4×C191—22no—
120C22×C4×C191—22no—
121C22×C4×C191—41no—
122C22×C4×C191C2311yescharacteristic
123C22×C4×C191C2311yescharacteristic
124C22×C4×C191C2311yescharacteristic
125C22×C4×C191C2311yescharacteristic
126C4⋊C4×C191—22no—
127C22⋊C4×C191—22no—
128C22⋊C4×C191D414yescomplemented
129C22×D191—21no—
130C22×D191—21no—
131C22×D191—21no—
132C22×D191—21no—
133C22×D191—28no—
134C22×D191—21no—
135C22×D191—21no—
136C22×D191—21no—
137C22×D191—21no—
138C22×D191—21no—
139C22×D191—21no—
140C22×D191—44no—
141C22×D191—44no—
142C22×D191—44no—
143C22×D191—44no—
144C22×D191—44no—
145C22×D191—44no—
146C22×D191C2×D412yes—
147C22×D191C2×D412yes—
148C22×D191#4112yes—
149C22×D191#4112yes—
150C22⋊D191—28no—
151C22⋊D191—44no—
152C22⋊D191—44no—
153C22⋊D191—44no—
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×Dic191—21no—
166C2×Dic191—21no—
167C2×Dic191—21no—
168C2×Dic191—21no—
169C2×Dic191—21no—
170C2×Dic191C2×D412yes—
171C2×Dic191C2×D412yes—
172C4×D191—44no—
173C4×D191—44no—
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—21no—
187C23×C191—21no—
188C23×C191—21no—
189C23×C191—21no—
190C23×C191—21no—
191C23×C191—21no—
192C23×C191—21no—
193C23×C191C2×D412yes—
194C23×C191C2×D412yes—
195C23×C191C2411yescharacteristic
196D4×C191—44no—
197D4×C191—44no—
198D4×C191—44no—
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×C191C2×D412yes—
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—41no—
219C22×C191—41no—
220C22×C191—41no—
221C22×C191—41no—
222C22×C191—41no—
223C22×C191—41no—
224C22×C191—41no—
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×C191C22×D411yescharacteristic
234C22×C191C22×D411yescharacteristic
235C22×C191C22×D411yescharacteristic
236C22×C191C2×#4111yescharacteristic
237C22×C191C2×#4111yescharacteristic
238C22×C191H(5,𝔽2)11yescharacteristic
239C22×C191H(5,𝔽2)11yescharacteristic
240C2×D191—22no—
241C2×D191—22no—
242C2×D191—22no—
243C2×D191—22no—
244C2×D191—22no—
245C2×D191—22no—
246C2×D191—22no—
247C2×D191—22no—
248C2×D191—22no—
249C2×D191—416no—
250C2×D191—41no—
251C2×D191—41no—
252C2×D191—41no—
253C2×D191—41no—
254C2×D191#12114yescomplemented
255C4×C191—22no—
256C4×C191—22no—
257C4×C191—22no—
258C4×C191—41no—
259Dic191—22no—
260Dic191—22no—
261Dic191—41no—
262Dic191—41no—
263Dic191—41no—
264Dic191—41no—
265C2×C191—42no—
266C2×C191—42no—
267C2×C191—81no—
268C2×C191C2×#12111yescharacteristic
269C2×C191#52511yescharacteristic
270C2×C191#53811yescharacteristic
271C2×C191D4211yescharacteristic
272C2×C191D4211yescharacteristic
273C2×C191#54611yescharacteristic
274C2×C191#54611yescharacteristic
275D191—24no—
276D191—42no—
277C191#242411yescharacteristic, complemented, Sylow
278#2424—1911nomaximal, Sylow
279C2×#121—1911no—
280C2×#121D19111yescharacteristic, complemented
281C2×#120—1911no—
282C2×#120—1911no—
283C2×C4×D4—1911no—
284C22×C22⋊C4—1911no—
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—
294C25—1911no—
295C22×D4—1911no—
296C22×D4—1911no—
297C22×D4—1911no—
298C22×D4—1911no—
299C22×D4C2×D19111yescharacteristic
300C22×D4C2×D19111yescharacteristic
301C22×D4C2×D19111yescharacteristic, complemented
302C23×C4—1911no—
303C23×C4—1911no—
304C23×C4C2×D19111yescharacteristic, complemented
305#121—24no—
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⋊C4C2×D19111yescharacteristic, complemented
314C2×C22⋊C4—3824no—
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⋊C4—1911no—
327C2×C22⋊C4—1911no—
328C2×C22⋊C4C2×D19111yescharacteristic
329C2×C22⋊C4C2×D19111yescharacteristic, complemented
330C2×C42—1911no—
331#95—1911no—
332#95—1911no—
333#95—1911no—
334#95—1911no—
335C24—3822no—
336C24—3822no—
337C24—3822no—
338C24—3822no—
339C24—3822no—
340C24—1911no—
341C24—1911no—
342C24—7641no—
343C24—7641no—
344C24C22×D19111yescharacteristic
345C24C22×D19111yescharacteristic
346C24C22×D19111yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—3822no—
357C2×D4—3822no—
358C2×D4—3822no—
359C2×D4—3822no—
360C2×D4—3822no—
361C2×D4—3822no—
362C2×D4—3822no—
363C2×D4—3822no—
364C2×D4—3822no—
365C2×D4—1914no—
366C2×D4—7641no—
367C2×D4—7641no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—41no—
371C22×C4—3822no—
372C22×C4—3822no—
373C22×C4—3822no—
374C22×C4—3822no—
375C22×C4—1911no—
376C22×C4—1911no—
377C22×C4—1911no—
378C22×C4—1911no—
379C22×C4—1911no—
380C22×C4—1911no—
381C22×C4—7641no—
382C22×C4—7641no—
383C22×C4C22×D19111yescharacteristic
384C22×C4C22×D19111yescharacteristic
385C22×C4C22×D19111yescharacteristic
386C22×C4C22×D19111yescharacteristic
387C4⋊C4—22no—
388C4⋊C4—3822no—
389C4⋊C4—3822no—
390C4⋊C4—7641no—
391C22⋊C4—22no—
392C22⋊C4—3822no—
393C22⋊C4—3822no—
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—21no—
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—21no—
425C23—21no—
426C23—3828no—
427C23—3821no—
428C23—3821no—
429C23—3821no—
430C23—3821no—
431C23—3821no—
432C23—3821no—
433C23—3821no—
434C23—3821no—
435C23—3821no—
436C23—3821no—
437C23—1912no—
438C23—1912no—
439C23—1912no—
440C23—1912no—
441C23—7644no—
442C23—7644no—
443C23—7644no—
444C23—7644no—
445C23—7644no—
446C23—7644no—
447C23D4×D19112yes—
448C23C2×C22⋊D19112yes—
449C23C23×D19111yescharacteristic
450D4—44no—
451D4—44no—
452D4—44no—
453D4—3828no—
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—44no—
467C2×C4—3821no—
468C2×C4—3821no—
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—1912no—
484C2×C4—1912no—
485C2×C4—7644no—
486C2×C4—7644no—
487C2×C4D4×D19112yes—
488C2×C4C2×C22⋊D19112yes—
489C2×C4C2×C22⋊D19112yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—3822no—
512C22—3822no—
513C22—3822no—
514C22—3822no—
515C22—3822no—
516C22—3822no—
517C22—3822no—
518C22—3822no—
519C22—3822no—
520C22—1914no—
521C22—76416no—
522C22—7641no—
523C22—7641no—
524C22—7641no—
525C22—7641no—
526C22C2×D4×D19111yescharacteristic
527C22C2×D4×D19111yescharacteristic
528C22C22×C22⋊D19111yescharacteristic
529C22#41×D19111yescharacteristic
530C22#41×D19111yescharacteristic
531C22#2025936711yescharacteristic
532C22#2025936711yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—3822no—
538C4—3822no—
539C4—7641no—
540C4—7641no—
541C4—7641no—
542C4—7641no—
543C2—42no—
544C2—42no—
545C2—81no—
546C2—3824no—
547C2—7642no—
548C2#121×D19111yescharacteristic
549C2#2713317011yescharacteristic
550C2#2713324511yescharacteristic
551C2D4×C22⋊D19111yescharacteristic
552C2D4×C22⋊D19111yescharacteristic
553C2#2713330211yescharacteristic
554C2#2713331011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
FittingC2×#121×C191C2
hypercenterC2×#121D191
hypocenterC191#2424
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#20259293C2semidirect
2. C2×#20259290C2semidirect
3. C2×#20259290C2semidirect
4. C2×C4×C22⋊D191C2semidirect
5. C2×C22⋊C4×D191C2semidirect
6. #27132585C2semidirect
7. #27132577C2semidirect
8. #27132577C2semidirect
9. #27132571C2semidirect
10. #27132563C2semidirect
11. #27132556C2semidirect
12. #27132542C2semidirect
13. #27132539C2semidirect
14. #27132534C2semidirect
15. C2×#121×C191C2semidirect
27. C2×C4⋊Dic191C22semidirect
28. C2×Dic191⋊C4C22semidirect
29. C2×Dic191⋊C4C22semidirect
33. C2×C22⋊Dic191C22semidirect
34. C2×C22⋊Dic191C22semidirect
35. C2×C22⋊Dic191C22semidirect
36. C2×C22⋊Dic191C22semidirect
44. C2×C4×Dic191C22semidirect
45. C191⋊#95C22semidirect
46. C191⋊#95C22semidirect
47. C191⋊#95C22semidirect
48. C191⋊#95C22semidirect
51. C22×D4×C191C22semidirect
52. C23×C4×C191C22semidirect
54. C2×C4⋊C4×C191C22semidirect
56. C2×C22⋊C4×C191C22semidirect
77. C2×C22⋊D191D4semidirect
105. (C2×D191)⋊C4D4semidirect
128. C22⋊C4×C191D4semidirect
254. C2×D191#121semidirect
277. C191#2424semidirect
280. C2×#121D191semidirect
301. C22×D4C2×D191semidirect
304. C23×C4C2×D191semidirect
313. C2×C4⋊C4C2×D191semidirect
329. C2×C22⋊C4C2×D191semidirect
405. C22⋊C4C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202592932
C2×#202592902
C2×C4×C22⋊D1912
C2×C22⋊C4×D1912
#271325852
#271325772
#271325712
#271325632
#271325562
#271325422
#271325392
#271325342
C2×#121×C1912
#2424191