Finite Group Databasebeta

← #37576137

Subgroups — #37576137

Order 24448.

952 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#15690287C211yesmaximal, characteristic, complemented
2C2×#20259318C211yesmaximal, characteristic, complemented
3C2×#20259308C211yesmaximal, characteristic, complemented
4C2×#20259295C211yesmaximal, characteristic, complemented
5#27132573C211yesmaximal, characteristic, complemented
6#27132572C211yesmaximal, characteristic, complemented
7#27132572C211yesmaximal, characteristic, complemented
8#27132571C211yesmaximal, characteristic, complemented
9#27132567C211yesmaximal, characteristic, complemented
10#27132563C211yesmaximal, characteristic, complemented
11#27132542C211yesmaximal, characteristic, complemented
12#27132541C211yesmaximal, characteristic, complemented
13#27132539C211yesmaximal, characteristic, complemented
14#27132510C211yesmaximal, characteristic, complemented
15#386×C191C211yesmaximal, characteristic, complemented
16C2×#15690287—24no—
17C2×#15690287—24no—
18C2×#15690287—24no—
19C22×Dic382C2211yescharacteristic
20C22×D764C2211yescharacteristic
21C22×D764C2211yescharacteristic
22C22×D764C2211yescharacteristic
23C22×C22⋊D191C2211yescharacteristic
24C22×C22⋊D191C2211yescharacteristic
25C22×C22⋊D191C2211yescharacteristic
26C22×C22⋊D191C2211yescharacteristic
27C22×C22⋊D191C2211yescharacteristic
28C22×C22⋊D191C2211yescharacteristic
29C22×C4×D191C2211yescharacteristic
30C22×C4×D191C2211yescharacteristic
31#20259318—24no—
32#20259308—24no—
33#20259295—24no—
34C2×Dic191⋊C4C2211yescharacteristic
35C2×C22⋊Dic191C2211yescharacteristic
36C2×C22⋊Dic191C2211yescharacteristic
37C2×(C2×D191)⋊C4C2211yescharacteristic
38C2×(C2×D191)⋊C4C2211yescharacteristic
39C2×(C2×D191)⋊C4C2211yescharacteristic
40C2×(C2×D191)⋊C4C2211yescharacteristic
41C2×(C2×D191)⋊C4C2211yescharacteristic
42C2×(C2×D191)⋊C4C2211yescharacteristic
43C2×(C2×D191)⋊C4C2211yescharacteristic
44C2×C4×Dic191C2211yescharacteristic
45C2×C4×Dic191C2211yescharacteristic
46C191⋊#95C2211yescharacteristic
47C191⋊#95C2211yescharacteristic
48C191⋊#95C2211yescharacteristic
49C191⋊#95C2211yescharacteristic
50C22×D4×C191C2211yescharacteristic
51C23×C4×C191C2211yescharacteristic
52C2×C22⋊C4×C191C2211yescharacteristic
53C2×C22⋊C4×C191C2211yescharacteristic
54C2×C22⋊C4×C191C2211yescharacteristic
55#95×C191C2211yescharacteristic
56#95×C191C2211yescharacteristic
57C23×D191C2311yescharacteristic
58C23×D191C2311yescharacteristic
59C23×D191C2311yescharacteristic
60#15690287—232no—
61C2×Dic382—22no—
62C2×Dic382—22no—
63C2×Dic382D414yescomplemented
64C2×D764—22no—
65C2×D764—22no—
66C2×D764—22no—
67C2×D764—22no—
68C2×D764—22no—
69C2×D764—22no—
70C2×D764—41no—
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—22no—
83C2×C22⋊D191—22no—
84C2×C22⋊D191—22no—
85C2×C22⋊D191—22no—
86C2×C22⋊D191—41no—
87C2×C22⋊D191—41no—
88C2×C22⋊D191—41no—
89C2×C22⋊D191—41no—
90C2×C22⋊D191D414yescomplemented
91C22×Dic191C2311yescharacteristic
92C22×Dic191C2311yescharacteristic
93C22×Dic191C2311yescharacteristic
94C22×Dic191C2311yescharacteristic
95C22×Dic191C2311yescharacteristic
96C2×C4×D191—22no—
97C2×C4×D191—22no—
98C2×C4×D191—22no—
99C2×C4×D191—22no—
100C2×C4×D191—22no—
101C2×C4×D191D414yescomplemented
102Dic191⋊C4—22no—
103C22⋊Dic191—22no—
104C22⋊Dic191—41no—
105(C2×D191)⋊C4—22no—
106(C2×D191)⋊C4—22no—
107(C2×D191)⋊C4—22no—
108(C2×D191)⋊C4—22no—
109(C2×D191)⋊C4—22no—
110(C2×D191)⋊C4—41no—
111(C2×D191)⋊C4—41no—
112C4×Dic191—22no—
113C4×Dic191—22no—
114C24×C191C2311yescharacteristic
115C24×C191C2311yescharacteristic
116C2×D4×C191—22no—
117C2×D4×C191—22no—
118C2×D4×C191—41no—
119C22×C4×C191—22no—
120C22×C4×C191—22no—
121C22×C4×C191—22no—
122C22×C4×C191C2311yescharacteristic
123C22×C4×C191C2311yescharacteristic
124C22×C4×C191C2311yescharacteristic
125C22×C4×C191C2311yescharacteristic
126C22×C4×C191C2311yescharacteristic
127C22⋊C4×C191—22no—
128C22⋊C4×C191—22no—
129C22⋊C4×C191—41no—
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×D191C2×D412yes—
150C22×D191C2×D412yes—
151Dic382—28no—
152D764—28no—
153D764—44no—
154D764—44no—
155C22⋊D191—28no—
156C22⋊D191—28no—
157C22⋊D191—44no—
158C22⋊D191—44no—
159C22⋊D191—44no—
160C22⋊D191—44no—
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×Dic191—21no—
171C2×Dic191C2×D412yes—
172C2×Dic191C2×D412yes—
173C2×Dic191C2×D412yes—
174C2×Dic191C2×D412yes—
175C2×Dic191#4112yescomplemented
176C4×D191—28no—
177C4×D191—28no—
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×C191C2×D412yes—
192C23×C191C2411yescharacteristic
193D4×C191—44no—
194C2×C4×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—21no—
207C2×C4×C191C2×D412yes—
208C2×C4×C191C2×D412yes—
209C2×C4×C191#4112yescomplemented
210C22×C191—22no—
211C22×C191—22no—
212C22×C191—22no—
213C22×C191—41no—
214C22×C191—41no—
215C22×C191—41no—
216C22×C191—41no—
217C22×C191—41no—
218C22×C191—41no—
219C22×C191—41no—
220C22×C191—41no—
221C22×C191—41no—
222C22×C191—41no—
223C22×C191—41no—
224C22×C191C22×D411yescharacteristic
225C22×C191C22×D411yescharacteristic
226C22×C191C22×D411yescharacteristic
227C22×C191C2×#4111yescharacteristic
228C22×C191C2×#4111yescharacteristic
229C22×C191H(5,𝔽2)11yescharacteristic
230C22×C191H(5,𝔽2)11yescharacteristic
231C2×D191—22no—
232C2×D191—22no—
233C2×D191—22no—
234C2×D191—22no—
235C2×D191—22no—
236C2×D191—22no—
237C2×D191—41no—
238C2×D191—41no—
239C2×D191—41no—
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—
252C4×C191—22no—
253C4×C191—22no—
254C4×C191—22no—
255C4×C191—41no—
256C4×C191—41no—
257Dic191—22no—
258Dic191—22no—
259Dic191—41no—
260Dic191—41no—
261Dic191#12014yes—
262C2×C191—42no—
263C2×C191—81no—
264C2×C191C2×#12011yescharacteristic
265C2×C191#53211yescharacteristic
266C2×C191#53511yescharacteristic
267C2×C191#54611yescharacteristic
268C2×C191#54611yescharacteristic
269C2×C191#55011yescharacteristic
270C2×C191#55011yescharacteristic
271D191—42no—
272D191—42no—
273D191—81no—
274C191#243111yescharacteristic, complemented, Sylow
275#2431—1911nomaximal, Sylow
276C22×#41—1911no—
277C2×#127—1911no—
278C2×#124—1911no—
279C2×#121—1911no—
280#392—1911no—
281#392—1911no—
282#392—1911no—
283#392—1911no—
284#391—1911no—
285#390—1911no—
286#386—1911no—
287#386—1911no—
288#386—1911no—
289#386D19111yescharacteristic, complemented
290C4×C22⋊C4—1911no—
291C2×#41—3824no—
292C2×#41—3824no—
293C2×#41—3824no—
294C22×Q8—1911no—
295C22×D4—1911no—
296C22×D4—1911no—
297C22×D4—1911no—
298C22×D4—1911no—
299C22×D4—1911no—
300C22×D4—1911no—
301C22×D4—1911no—
302C22×D4—1911no—
303C22×D4—1911no—
304C22×D4C2×D19111yescharacteristic
305C23×C4—1911no—
306C23×C4—1911no—
307C23×C4C2×D19111yescharacteristic
308#127—3824no—
309#124—3824no—
310#121—3824no—
311C2×C4⋊C4—1911no—
312C2×C22⋊C4—1911no—
313C2×C22⋊C4—1911no—
314C2×C22⋊C4—1911no—
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⋊C4C2×D19111yescharacteristic
322C2×C22⋊C4C2×D19111yescharacteristic
323C2×C22⋊C4C2×D19111yescharacteristic
324C2×C42—1911no—
325C2×C42—1911no—
326#95—1911no—
327#95—1911no—
328#95—1911no—
329#95—1911no—
330#95C2×D19111yescharacteristic
331#95C2×D19111yescharacteristic
332C24—1911no—
333C24—1911no—
334C24—1911no—
335C24C22×D19111yescharacteristic
336C24C22×D19111yescharacteristic
337#41—38232no—
338C2×Q8—3822no—
339C2×Q8—3822no—
340C2×Q8—1914no—
341C2×D4—22no—
342C2×D4—22no—
343C2×D4—41no—
344C2×D4—3822no—
345C2×D4—3822no—
346C2×D4—3822no—
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—3822no—
363C2×D4—1914no—
364C2×D4—7641no—
365C2×D4—7641no—
366C2×D4—7641no—
367C2×D4—7641no—
368C2×D4—7641no—
369C2×D4—7641no—
370C2×D4—7641no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—3822no—
375C22×C4—3822no—
376C22×C4—3822no—
377C22×C4—3822no—
378C22×C4—3822no—
379C22×C4—1911no—
380C22×C4—1911no—
381C22×C4—1911no—
382C22×C4—1911no—
383C22×C4—1914no—
384C22×C4—1911no—
385C22×C4C22×D19111yescharacteristic
386C22×C4C22×D19111yescharacteristic
387C22×C4C22×D19111yescharacteristic
388C22×C4C22×D19111yescharacteristic
389C22×C4C22×D19111yescharacteristic
390C4⋊C4—3822no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—41no—
394C22⋊C4—3822no—
395C22⋊C4—3822no—
396C22⋊C4—3822no—
397C22⋊C4—3822no—
398C22⋊C4—3822no—
399C22⋊C4—3822no—
400C22⋊C4—7641no—
401C22⋊C4—7641no—
402C22⋊C4—7641no—
403C42—3822no—
404C42—3822no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
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—
439C23D4×D19112yes—
440C23C23×D19111yescharacteristic
441Q8—3828no—
442D4—44no—
443D4—3828no—
444D4—3828no—
445D4—3828no—
446D4—7644no—
447D4—7644no—
448D4—7644no—
449D4—7644no—
450D4—7644no—
451D4—7644no—
452C2×C4—28no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
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—3828no—
466C2×C4—3828no—
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—1912no—
478C2×C4—1912no—
479C2×C4—1912no—
480C2×C4—1912no—
481C2×C4—1912no—
482C2×C4D4×D19112yes—
483C2×C4D4×D19112yes—
484C2×C4#1569028712yescomplemented
485C22—22no—
486C22—22no—
487C22—22no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—3822no—
500C22—3822no—
501C22—3822no—
502C22—3822no—
503C22—3822no—
504C22—3822no—
505C22—7641no—
506C22—7641no—
507C22—7641no—
508C22—7641no—
509C22—7641no—
510C22—7641no—
511C22—7641no—
512C22—7641no—
513C22—7641no—
514C22—7641no—
515C22—7641no—
516C22—7641no—
517C22—7641no—
518C22—7641no—
519C22—7641no—
520C22C2×D4×D19111yescharacteristic
521C22C2×D4×D19111yescharacteristic
522C22C2×D4×D19111yescharacteristic
523C22#41×D19111yescharacteristic
524C22C2×#1569028711yescharacteristic
525C22#2025936711yescharacteristic
526C22#2025936811yescharacteristic
527C4—22no—
528C4—22no—
529C4—22no—
530C4—41no—
531C4—41no—
532C4—3822no—
533C4—3822no—
534C4—1914no—
535C4—7641no—
536C4—7641no—
537C2—42no—
538C2—81no—
539C2—15281no—
540C2—7642no—
541C2—7642no—
542C2#120×D19111yescharacteristic
543C2#2713321011yescharacteristic
544C2#2713322911yescharacteristic
545C2#2713330311yescharacteristic
546C2#2713330511yescharacteristic
547C2#2713333111yescharacteristic
548C2#2713333411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutator, socle, cosocleC23×C191C24
Fitting#386×C191C2
hypercenter#386D191
hypocenterC191#2431
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×#15690287C2semidirect
2. C2×#20259318C2semidirect
3. C2×#20259308C2semidirect
4. C2×#20259295C2semidirect
5. #27132573C2semidirect
6. #27132572C2semidirect
7. #27132572C2semidirect
8. #27132571C2semidirect
9. #27132567C2semidirect
10. #27132563C2semidirect
11. #27132542C2semidirect
12. #27132541C2semidirect
13. #27132539C2semidirect
14. #27132510C2semidirect
15. #386×C191C2semidirect
63. C2×Dic382D4semidirect
90. C2×C22⋊D191D4semidirect
101. C2×C4×D191D4semidirect
175. C2×Dic191#41semidirect
209. C2×C4×C191#41semidirect
274. C191#2431semidirect
289. #386D191semidirect
484. C2×C4#15690287semidirect

Maximal subgroups

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

subgroupindex
C22×#156902872
C2×#202593182
C2×#202593082
C2×#202592952
#271325732
#271325722
#271325712
#271325672
#271325632
#271325422
#271325412
#271325392
#271325102
#386×C1912
#2431191