Finite Group Databasebeta

← #37576050

Subgroups — #37576050

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×#20259294C211yesmaximal, characteristic, complemented
3C2×#20259292C211yesmaximal, characteristic, complemented
4C2×#20259290C211yesmaximal, characteristic, complemented
5C22×(C2×D191)⋊C4C211yesmaximal, characteristic, complemented
6#27132585C211yesmaximal, characteristic, complemented
7#27132580C211yesmaximal, characteristic, complemented
8#27132579C211yesmaximal, characteristic, complemented
9#27132572C211yesmaximal, characteristic, complemented
10#27132565C211yesmaximal, characteristic, complemented
11#27132554C211yesmaximal, characteristic, complemented
12#27132542C211yesmaximal, characteristic, complemented
13#27132542C211yesmaximal, characteristic, complemented
14#27132538C211yesmaximal, characteristic, complemented
15C2×C4×D4×C191C211yesmaximal, characteristic, complemented
16C24×D191C2211yescharacteristic
17C22×D764C2211yescharacteristic
18C22×D764C2211yescharacteristic
19C22×C22⋊D191C2211yescharacteristic
20C22×C22⋊D191C2211yescharacteristic
21C22×C22⋊D191C2211yescharacteristic
22C22×C22⋊D191C2211yescharacteristic, complemented
23C23×Dic191C2211yescharacteristic
24#20259296—24no—
25#20259294—24no—
26#20259292—24no—
27#20259290—24no—
28C2×C4⋊Dic191C2211yescharacteristic, complemented
29C2×C4⋊Dic191C2211yescharacteristic, complemented
30C2×Dic191⋊C4C2211yescharacteristic, complemented
31C2×C22⋊Dic191C2211yescharacteristic
32C2×C22⋊Dic191C2211yescharacteristic, complemented
33C2×(C2×D191)⋊C4—24no—
34C2×(C2×D191)⋊C4C2211yescharacteristic
35C2×(C2×D191)⋊C4C2211yescharacteristic
36C2×(C2×D191)⋊C4C2211yescharacteristic
37C2×(C2×D191)⋊C4C2211yescharacteristic
38C2×(C2×D191)⋊C4C2211yescharacteristic
39C2×(C2×D191)⋊C4C2211yescharacteristic
40C2×(C2×D191)⋊C4C2211yescharacteristic
41C2×(C2×D191)⋊C4C2211yescharacteristic
42C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D191)⋊C4C2211yescharacteristic, complemented
45C191⋊#95C2211yescharacteristic, complemented
46C191⋊#95C2211yescharacteristic, complemented
47C191⋊#95C2211yescharacteristic, complemented
48C191⋊#95C2211yescharacteristic, complemented
49C22×D4×C191C2211yescharacteristic
50C23×C4×C191C2211yescharacteristic
51C23×C4×C191C2211yescharacteristic, complemented
52C4×D4×C191—24no—
53C2×C4⋊C4×C191C2211yescharacteristic, complemented
54C2×C22⋊C4×C191C2211yescharacteristic
55C2×C22⋊C4×C191C2211yescharacteristic, complemented
56C2×C42×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
66C23×D191C2311yescharacteristic
67C2×D764—22no—
68C2×D764—22no—
69C2×D764—22no—
70C2×D764—22no—
71C2×D764—41no—
72C2×D764—41no—
73C2×C22⋊D191—22no—
74C2×C22⋊D191—22no—
75C2×C22⋊D191—22no—
76C2×C22⋊D191—22no—
77C2×C22⋊D191—22no—
78C2×C22⋊D191—22no—
79C2×C22⋊D191—22no—
80C2×C22⋊D191—22no—
81C2×C22⋊D191—22no—
82C2×C22⋊D191—41no—
83C2×C22⋊D191—41no—
84C2×C22⋊D191—41no—
85C22×Dic191—22no—
86C22×Dic191—22no—
87C22×Dic191—41no—
88C22×Dic191C2311yescharacteristic
89C22×Dic191C2311yescharacteristic
90C22×Dic191C2311yescharacteristic
91C22×Dic191C2311yescharacteristic
92C22×Dic191C2311yescharacteristic
93C4⋊Dic191—22no—
94C4⋊Dic191—41no—
95Dic191⋊C4—22no—
96C22⋊Dic191—22no—
97C22⋊Dic191—22no—
98(C2×D191)⋊C4—22no—
99(C2×D191)⋊C4—22no—
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)⋊C4—22no—
106(C2×D191)⋊C4—22no—
107(C2×D191)⋊C4—41no—
108(C2×D191)⋊C4D414yescomplemented
109C24×C191C2311yescharacteristic
110C24×C191C2311yescharacteristic
111C2×D4×C191—22no—
112C2×D4×C191—22no—
113C2×D4×C191D414yescomplemented
114C22×C4×C191—22no—
115C22×C4×C191—22no—
116C22×C4×C191—22no—
117C22×C4×C191—22no—
118C22×C4×C191—41no—
119C22×C4×C191—41no—
120C22×C4×C191C2311yescharacteristic
121C22×C4×C191C2311yescharacteristic
122C22×C4×C191C2311yescharacteristic
123C22×C4×C191C2311yescharacteristic
124C22×C4×C191C2311yescharacteristic
125C4⋊C4×C191—22no—
126C22⋊C4×C191—22no—
127C22⋊C4×C191D414yescomplemented
128C42×C191—22no—
129C22×D191—28no—
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×D191—21no—
143C22×D191—21no—
144C22×D191—21no—
145C22×D191—21no—
146C22×D191—21no—
147C22×D191—21no—
148C22×D191—21no—
149C22×D191—44no—
150C22×D191—44no—
151C22×D191—44no—
152C22×D191—44no—
153C22×D191—44no—
154C22×D191—44no—
155C22×D191C2×D412yes—
156C22×D191#4112yes—
157D764—44no—
158D764—44no—
159C22⋊D191—44no—
160C22⋊D191—44no—
161C22⋊D191—44no—
162C22⋊D191—44no—
163C2×Dic191—21no—
164C2×Dic191—21no—
165C2×Dic191—21no—
166C2×Dic191—21no—
167C2×Dic191—21no—
168C2×Dic191—21no—
169C2×Dic191—21no—
170C2×Dic191—21no—
171C2×Dic191—21no—
172C2×Dic191—21no—
173C2×Dic191—21no—
174C2×Dic191—21no—
175C2×Dic191—21no—
176C2×Dic191—21no—
177C2×Dic191—44no—
178C2×Dic191C2×D412yes—
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×C191C2×D412yes—
190C23×C191C2×D412yes—
191C23×C191C2×D412yes—
192C23×C191#4112yes—
193C23×C191C2411yescharacteristic
194D4×C191—28no—
195C2×C4×C191—21no—
196C2×C4×C191—21no—
197C2×C4×C191—21no—
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—44no—
207C2×C4×C191—44no—
208C2×C4×C191C2×D412yes—
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—22no—
219C22×C191—22no—
220C22×C191—22no—
221C22×C191—41no—
222C22×C191—41no—
223C22×C191—41no—
224C22×C191—41no—
225C22×C191#12114yescomplemented
226C22×C191C22×D411yescharacteristic
227C22×C191C22×D411yescharacteristic
228C22×C191C22×D411yescharacteristic
229C22×C191C2×#4111yescharacteristic
230C22×C191C2×#4111yescharacteristic
231C22×C191H(5,𝔽2)11yescharacteristic
232C22×C191H(5,𝔽2)11yescharacteristic
233C2×D191—22no—
234C2×D191—22no—
235C2×D191—22no—
236C2×D191—22no—
237C2×D191—22no—
238C2×D191—22no—
239C2×D191—416no—
240C2×D191—41no—
241C2×D191—41no—
242C2×D191—41no—
243C2×D191—41no—
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—22no—
258C4×C191—22no—
259C4×C191—41no—
260Dic191—22no—
261Dic191—41no—
262Dic191—41no—
263Dic191—41no—
264Dic191—41no—
265C2×C191—24no—
266C2×C191—42no—
267C2×C191C2×#12111yescharacteristic
268C2×C191#52511yescharacteristic
269C2×C191#53811yescharacteristic
270C2×C191D4211yescharacteristic
271C2×C191D4211yescharacteristic
272C2×C191#54611yescharacteristic
273C2×C191#54611yescharacteristic
274D191—42no—
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×D4D19111yescharacteristic, complemented
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×D4—1911no—
300C22×D4—1911no—
301C22×D4C2×D19111yescharacteristic
302C23×C4—1911no—
303C23×C4C2×D19111yescharacteristic
304C23×C4C2×D19111yescharacteristic, complemented
305#121—3824no—
306#121—3824no—
307#120—3824no—
308#120—3824no—
309C4×D4—24no—
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×C42C2×D19111yescharacteristic, complemented
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—1911no—
343C24—7641no—
344C24—7641no—
345C24C22×D19111yescharacteristic
346C24C22×D19111yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
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—7641no—
363C2×D4—7641no—
364C2×D4—7641no—
365C2×D4—7641no—
366C2×D4—7641no—
367C2×D4D76414yescomplemented
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—7641no—
382C22×C4C22×D19111yescharacteristic
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—22no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—3828no—
418C23—3821no—
419C23—3821no—
420C23—3821no—
421C23—3821no—
422C23—3821no—
423C23—3821no—
424C23—3821no—
425C23—3821no—
426C23—3821no—
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—7644no—
440C23—7644no—
441C23—7644no—
442C23—7644no—
443C23—7644no—
444C23—7644no—
445C23C2×C22⋊D19112yes—
446C23C2×D76412yes—
447C23C2×D76412yes—
448C23#1569028712yes—
449C23C23×D19111yescharacteristic
450D4—28no—
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—21no—
468C2×C4—44no—
469C2×C4—44no—
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—7644no—
486C2×C4D4×D19112yes—
487C2×C4C2×C22⋊D19112yes—
488C2×C4C2×C22⋊D19112yes—
489C2×C4C2×D76412yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—3822no—
504C22—3822no—
505C22—3822no—
506C22—3822no—
507C22—3822no—
508C22—3822no—
509C22—76416no—
510C22—7641no—
511C22—7641no—
512C22—7641no—
513C22—7641no—
514C22—7641no—
515C22—7641no—
516C22—7641no—
517C22—7641no—
518C22—7641no—
519C22—7641no—
520C22—7641no—
521C22—7641no—
522C22—7641no—
523C22—7641no—
524C22—7641no—
525C22#2025929614yescomplemented
526C22C2×D4×D19111yescharacteristic
527C22C22×C22⋊D19111yescharacteristic
528C22C22×D76411yescharacteristic
529C22#41×D19111yescharacteristic
530C22C2×#1569028711yescharacteristic
531C22#2025936711yescharacteristic
532C22#2025936811yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—3822no—
539C4—7641no—
540C4—7641no—
541C4—7641no—
542C4—7641no—
543C2—24no—
544C2—42no—
545C2—15281no—
546C2—7642no—
547C2—7642no—
548C2C2×#2025929611yescharacteristic
549C2#2713317211yescharacteristic
550C2#2713324611yescharacteristic
551C2D4×C22⋊D19111yescharacteristic
552C2D4×D76411yescharacteristic
553C2#2713330111yescharacteristic
554C2#2713330811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
FittingC2×C4×D4×C191C2
hypercenterC2×C4×D4D191
hypocenterC191#2424
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#20259296C2semidirect
2. C2×#20259294C2semidirect
3. C2×#20259292C2semidirect
4. C2×#20259290C2semidirect
5. C22×(C2×D191)⋊C4C2semidirect
6. #27132585C2semidirect
7. #27132580C2semidirect
8. #27132579C2semidirect
9. #27132572C2semidirect
10. #27132565C2semidirect
11. #27132554C2semidirect
12. #27132542C2semidirect
13. #27132542C2semidirect
14. #27132538C2semidirect
15. C2×C4×D4×C191C2semidirect
22. C22×C22⋊D191C22semidirect
28. C2×C4⋊Dic191C22semidirect
29. C2×C4⋊Dic191C22semidirect
30. C2×Dic191⋊C4C22semidirect
32. C2×C22⋊Dic191C22semidirect
42. C2×(C2×D191)⋊C4C22semidirect
43. C2×(C2×D191)⋊C4C22semidirect
44. C2×(C2×D191)⋊C4C22semidirect
45. C191⋊#95C22semidirect
46. C191⋊#95C22semidirect
47. C191⋊#95C22semidirect
48. C191⋊#95C22semidirect
51. C23×C4×C191C22semidirect
53. C2×C4⋊C4×C191C22semidirect
55. C2×C22⋊C4×C191C22semidirect
56. C2×C42×C191C22semidirect
108. (C2×D191)⋊C4D4semidirect
113. C2×D4×C191D4semidirect
127. C22⋊C4×C191D4semidirect
225. C22×C191#121semidirect
277. C191#2424semidirect
283. C2×C4×D4D191semidirect
304. C23×C4C2×D191semidirect
313. C2×C4⋊C4C2×D191semidirect
329. C2×C22⋊C4C2×D191semidirect
330. C2×C42C2×D191semidirect
367. C2×D4D764semidirect
405. C22⋊C4C22⋊D191semidirect
525. C22#20259296semidirect

Maximal subgroups

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

subgroupindex
C2×#202592962
C2×#202592942
C2×#202592922
C2×#202592902
C22×(C2×D191)⋊C42
#271325852
#271325802
#271325792
#271325722
#271325652
#271325542
#271325422
#271325382
C2×C4×D4×C1912
#2424191