Finite Group Databasebeta

← #37575566

Subgroups — #37575566

Order 24448.

716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259297C211yesmaximal, characteristic
2C2×C4×D764C211yesmaximal, characteristic, complemented
3C2×#20259284C211yesmaximal, characteristic, complemented
4#27132555C211yesmaximal, characteristic, complemented
5#27132553C211yesmaximal, characteristic, complemented
6#27132549C211yesmaximal, characteristic, complemented
7#27132541C211yesmaximal, characteristic, complemented
8#27132541C211yesmaximal, characteristic, complemented
9#27132541C211yesmaximal, characteristic, complemented
10#27132541C211yesmaximal, characteristic, complemented
11C4×(C2×D191)⋊C4C211yesmaximal, characteristic, complemented
12#27132510C211yesmaximal, characteristic, complemented
13#27132510C211yesmaximal, characteristic, complemented
14#95×D191C211yesmaximal, characteristic, complemented
15#387×C191C211yesmaximal, characteristic, complemented
16C22×D764C2211yescharacteristic
17C22×D764C2211yescharacteristic
18C22×D764C2211yescharacteristic
19C22×C4×D191C2211yescharacteristic
20C22×C4×D191C2211yescharacteristic
21C22×C4×D191C2211yescharacteristic
22C22×C4×D191C2211yescharacteristic
23C22×C4×D191C2211yescharacteristic
24#20259297C418yescomplemented
25C4×D764—24no—
26#20259284—24no—
27C2×C4⋊Dic191C2211yescharacteristic
28C2×(C2×D191)⋊C4C2211yescharacteristic
29C2×(C2×D191)⋊C4C2211yescharacteristic
30C2×(C2×D191)⋊C4C2211yescharacteristic
31C2×(C2×D191)⋊C4C2211yescharacteristic
32C2×(C2×D191)⋊C4C2211yescharacteristic
33C2×(C2×D191)⋊C4C2211yescharacteristic
34C2×(C2×D191)⋊C4C2211yescharacteristic
35C2×(C2×D191)⋊C4C2211yescharacteristic
36C2×(C2×D191)⋊C4C2211yescharacteristic
37C2×(C2×D191)⋊C4C2211yescharacteristic
38C2×C4×Dic191C2211yescharacteristic
39C2×C4×Dic191C2211yescharacteristic
40C2×C4×Dic191C2211yescharacteristic
41C191⋊#95C2211yescharacteristic
42C191⋊#95C2211yescharacteristic
43C191⋊#95C2211yescharacteristic
44C191⋊#95C2211yescharacteristic
45C191⋊#95C2211yescharacteristic
46C191⋊#95C2211yescharacteristic
47C2×C4⋊C4×C191C2211yescharacteristic
48C2×C4⋊C4×C191C2211yescharacteristic
49C2×C42×C191C2211yescharacteristic
50#95×C191C2211yescharacteristic
51#95×C191C2211yescharacteristic
52#95×C191C2211yescharacteristic
53#95×C191C2211yescharacteristic
54C23×D191C2311yescharacteristic
55C23×D191C2311yescharacteristic
56C23×D191C2311yescharacteristic
57C2×D764—22no—
58C2×D764—22no—
59C2×D764—22no—
60C2×D764—22no—
61C2×D764—41no—
62C2×D764—41no—
63C2×D764C2×C414yescomplemented
64C2×D764C2×C414yescomplemented
65C2×D764C2×C414yescomplemented
66C22×Dic191C2311yescharacteristic
67C22×Dic191C2311yescharacteristic
68C22×Dic191C2311yescharacteristic
69C22×Dic191C2311yescharacteristic
70C22×Dic191C2311yescharacteristic
71C2×C4×D191—22no—
72C2×C4×D191—22no—
73C2×C4×D191—22no—
74C2×C4×D191—22no—
75C2×C4×D191—22no—
76C2×C4×D191—22no—
77C2×C4×D191—22no—
78C2×C4×D191—22no—
79C2×C4×D191—41no—
80C2×C4×D191—41no—
81C2×C4×D191—41no—
82C2×C4×D191—41no—
83C2×C4×D191—41no—
84C2×C4×D191—41no—
85C2×C4×D191C2×C414yescomplemented
86C4⋊Dic191—22no—
87(C2×D191)⋊C4—22no—
88(C2×D191)⋊C4—22no—
89(C2×D191)⋊C4—22no—
90(C2×D191)⋊C4—22no—
91(C2×D191)⋊C4—22no—
92(C2×D191)⋊C4—41no—
93(C2×D191)⋊C4—41no—
94(C2×D191)⋊C4C2×C414yescomplemented
95(C2×D191)⋊C4C2×C414yescomplemented
96(C2×D191)⋊C4D414yescomplemented
97C4×Dic191—22no—
98C4×Dic191—41no—
99C4×Dic191—41no—
100C22×C4×C191C2311yescharacteristic
101C22×C4×C191C2311yescharacteristic
102C22×C4×C191C2311yescharacteristic
103C22×C4×C191C2311yescharacteristic
104C22×C4×C191C2311yescharacteristic
105C22×C4×C191C2311yescharacteristic
106C22×C4×C191C2311yescharacteristic
107C4⋊C4×C191—22no—
108C4⋊C4×C191C2×C414yescomplemented
109C42×C191—22no—
110C22×D191—21no—
111C22×D191—21no—
112C22×D191—21no—
113C22×D191—21no—
114C22×D191—21no—
115C22×D191—21no—
116C22×D191—21no—
117C22×D191—21no—
118C22×D191—21no—
119C22×D191—21no—
120C22×D191—21no—
121C22×D191—21no—
122C22×D191—21no—
123C22×D191—21no—
124C22×D191—21no—
125C22×D191—21no—
126C22×D191C22×C412yes—
127C22×D191C22×C412yes—
128C22×D191C22×C412yes—
129C22×D191C2×D412yes—
130C22×D191#4112yes—
131D764—28no—
132D764—28no—
133D764—44no—
134C2×Dic191—21no—
135C2×Dic191—21no—
136C2×Dic191—21no—
137C2×Dic191—21no—
138C2×Dic191—21no—
139C2×Dic191—21no—
140C2×Dic191—21no—
141C2×Dic191—21no—
142C2×Dic191—21no—
143C2×Dic191—21no—
144C2×Dic191—21no—
145C2×Dic191—21no—
146C2×Dic191C22×C412yes—
147C2×Dic191C2×D412yes—
148C2×Dic191#4112yes—
149C4×D191—44no—
150C4×D191—44no—
151C4×D191—44no—
152C4×D191—44no—
153C4×D191—44no—
154C23×C191C2411yescharacteristic
155C2×C4×C191—21no—
156C2×C4×C191—21no—
157C2×C4×C191—21no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
160C2×C4×C191—21no—
161C2×C4×C191—21no—
162C2×C4×C191—21no—
163C2×C4×C191—21no—
164C2×C4×C191—21no—
165C2×C4×C191—21no—
166C2×C4×C191—21no—
167C2×C4×C191—21no—
168C2×C4×C191—21no—
169C2×C4×C191—21no—
170C2×C4×C191—21no—
171C2×C4×C191C22×C412yes—
172C2×C4×C191C22×C412yes—
173C2×C4×C191C22×C412yes—
174C2×C4×C191C2×D412yes—
175C2×C4×C191#4112yes—
176C22×C191C23×C411yescharacteristic
177C22×C191C22×D411yescharacteristic
178C22×C191C2×#4111yescharacteristic
179C22×C191C2×#4111yescharacteristic
180C22×C191C2×#4111yescharacteristic
181C22×C191H(5,𝔽2)11yescharacteristic
182C22×C191H(5,𝔽2)11yescharacteristic
183C2×D191—22no—
184C2×D191—22no—
185C2×D191—22no—
186C2×D191—22no—
187C2×D191—22no—
188C2×D191—22no—
189C2×D191—22no—
190C2×D191—22no—
191C2×D191—22no—
192C2×D191—22no—
193C2×D191—22no—
194C2×D191—22no—
195C2×D191—41no—
196C2×D191—41no—
197C2×D191—41no—
198C2×D191—41no—
199C2×D191—41no—
200C2×D191—41no—
201C2×D191—41no—
202C2×D191—41no—
203C2×D191C4×D414yes—
204C4×C191—22no—
205C4×C191—22no—
206C4×C191—22no—
207C4×C191—22no—
208C4×C191—22no—
209C4×C191—41no—
210C4×C191—41no—
211Dic191—22no—
212Dic191—22no—
213Dic191—22no—
214Dic191—41no—
215Dic191—41no—
216C2×C191C2×C4×D411yescharacteristic
217C2×C191C4×#4111yescharacteristic
218C2×C191#51811yescharacteristic
219C2×C191#54611yescharacteristic
220C2×C191#54611yescharacteristic
221C2×C191#55311yescharacteristic
222C2×C191#55311yescharacteristic
223D191—24no—
224D191—42no—
225D191—42no—
226C191#236411yescharacteristic, complemented, Sylow
227#2364—1911nomaximal, Sylow
228C2×#121—1911no—
229C2×C4×D4—1911no—
230C2×C4×D4—1911no—
231#388—1911no—
232#388—1911no—
233#387—1911no—
234#387D19111yescharacteristic, complemented
235#386—1911no—
236#386—1911no—
237#386—1911no—
238#386—1911no—
239C4×C22⋊C4—1911no—
240C4×C22⋊C4—1911no—
241C4×C22⋊C4—1911no—
242C2×#95—1911no—
243C22×D4—1911no—
244C22×D4—1911no—
245C22×D4—1911no—
246C23×C4—1911no—
247C23×C4—1911no—
248C23×C4—1911no—
249C23×C4—1911no—
250C23×C4—1911no—
251#121—1918no—
252C4×D4—3824no—
253C4×D4—3824no—
254C2×C4⋊C4—1911no—
255C2×C4⋊C4C2×D19111yescharacteristic
256C2×C4⋊C4C2×D19111yescharacteristic
257C2×C22⋊C4—1911no—
258C2×C22⋊C4—1911no—
259C2×C22⋊C4—1911no—
260C2×C22⋊C4—1911no—
261C2×C22⋊C4—1911no—
262C2×C22⋊C4—1911no—
263C2×C22⋊C4—1911no—
264C2×C22⋊C4—1911no—
265C2×C22⋊C4—1911no—
266C2×C22⋊C4—1911no—
267C2×C42—1911no—
268C2×C42—1911no—
269C2×C42—1911no—
270C2×C42C2×D19111yescharacteristic
271#95—1911no—
272#95—1911no—
273#95—1911no—
274#95—1911no—
275#95—1911no—
276#95—1911no—
277#95C2×D19111yescharacteristic
278#95C2×D19111yescharacteristic
279#95C2×D19111yescharacteristic
280#95C2×D19111yescharacteristic
281C24—1911no—
282C24—1911no—
283C24—1911no—
284C2×D4—3822no—
285C2×D4—3822no—
286C2×D4—3822no—
287C2×D4—3822no—
288C2×D4—1914no—
289C2×D4—1914no—
290C2×D4—1914no—
291C2×D4—7641no—
292C2×D4—7641no—
293C22×C4—3822no—
294C22×C4—3822no—
295C22×C4—3822no—
296C22×C4—3822no—
297C22×C4—3822no—
298C22×C4—3822no—
299C22×C4—3822no—
300C22×C4—3822no—
301C22×C4—1911no—
302C22×C4—1911no—
303C22×C4—1911no—
304C22×C4—1911no—
305C22×C4—1911no—
306C22×C4—1914no—
307C22×C4—7641no—
308C22×C4—7641no—
309C22×C4—7641no—
310C22×C4—7641no—
311C22×C4—7641no—
312C22×C4—7641no—
313C22×C4C22×D19111yescharacteristic
314C22×C4C22×D19111yescharacteristic
315C22×C4C22×D19111yescharacteristic
316C22×C4C22×D19111yescharacteristic
317C22×C4C22×D19111yescharacteristic
318C22×C4C22×D19111yescharacteristic
319C22×C4C22×D19111yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—3822no—
322C4⋊C4C4×D19114yescomplemented
323C22⋊C4—3822no—
324C22⋊C4—3822no—
325C22⋊C4—3822no—
326C22⋊C4—3822no—
327C22⋊C4—3822no—
328C22⋊C4—1914no—
329C22⋊C4—1914no—
330C22⋊C4—1914no—
331C22⋊C4—7641no—
332C22⋊C4—7641no—
333C42—22no—
334C42—3822no—
335C42—7641no—
336C42—7641no—
337C23—3821no—
338C23—3821no—
339C23—3821no—
340C23—3821no—
341C23—3821no—
342C23—3821no—
343C23—3821no—
344C23—3821no—
345C23—3821no—
346C23—3821no—
347C23—3821no—
348C23—3821no—
349C23—3821no—
350C23—3821no—
351C23—3821no—
352C23—3821no—
353C23—1912no—
354C23—1912no—
355C23—1912no—
356C23—1912no—
357C23—1912no—
358C23C23×D19111yescharacteristic
359D4—3828no—
360D4—3828no—
361D4—7644no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—3821no—
379C2×C4—3821no—
380C2×C4—3821no—
381C2×C4—3821no—
382C2×C4—3821no—
383C2×C4—3821no—
384C2×C4—3821no—
385C2×C4—3821no—
386C2×C4—3821no—
387C2×C4—3821no—
388C2×C4—3821no—
389C2×C4—3821no—
390C2×C4—1912no—
391C2×C4—1912no—
392C2×C4—1912no—
393C2×C4—7644no—
394C2×C4—7644no—
395C2×C4—7644no—
396C2×C4—7644no—
397C2×C4—7644no—
398C2×C4C2×C4×D19112yes—
399C2×C4C2×C4×D19112yes—
400C2×C4C2×C4×D19112yes—
401C2×C4D4×D19112yes—
402C2×C4#1569028812yes—
403C22—3822no—
404C22—3822no—
405C22—3822no—
406C22—3822no—
407C22—3822no—
408C22—3822no—
409C22—3822no—
410C22—3822no—
411C22—3822no—
412C22—3822no—
413C22—3822no—
414C22—3822no—
415C22—1914no—
416C22—7641no—
417C22—7641no—
418C22—7641no—
419C22—7641no—
420C22—7641no—
421C22—7641no—
422C22—7641no—
423C22—7641no—
424C22C22×C4×D19111yescharacteristic
425C22C2×D4×D19111yescharacteristic
426C22#41×D19111yescharacteristic
427C22#41×D19111yescharacteristic
428C22C2×#1569028811yescharacteristic
429C22#2025936811yescharacteristic
430C22#2025936811yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—22no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—3822no—
439C4—3822no—
440C4—3822no—
441C4—7641no—
442C4—7641no—
443C2—3824no—
444C2—7642no—
445C2—7642no—
446C2C4×D4×D19111yescharacteristic
447C2C4×#1569028811yescharacteristic
448C2#2713313711yescharacteristic
449C2#2713330411yescharacteristic
450C2#2713330511yescharacteristic
451C2#2713336411yescharacteristic
452C2#2713336611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
Fitting#387×C191C2
socle, cosocleC23×C191C24
prime radicalC2×#20259297C2
hypercenter#387D191
hypocenterC191#2364
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×C4×D764C2semidirect
3. C2×#20259284C2semidirect
4. #27132555C2semidirect
5. #27132553C2semidirect
6. #27132549C2semidirect
7. #27132541C2semidirect
8. #27132541C2semidirect
9. #27132541C2semidirect
10. #27132541C2semidirect
11. C4×(C2×D191)⋊C4C2semidirect
12. #27132510C2semidirect
13. #27132510C2semidirect
14. #95×D191C2semidirect
15. #387×C191C2semidirect
24. #20259297C4semidirect
63. C2×D764C2×C4semidirect
64. C2×D764C2×C4semidirect
65. C2×D764C2×C4semidirect
85. C2×C4×D191C2×C4semidirect
94. (C2×D191)⋊C4C2×C4semidirect
95. (C2×D191)⋊C4C2×C4semidirect
96. (C2×D191)⋊C4D4semidirect
108. C4⋊C4×C191C2×C4semidirect
226. C191#2364semidirect
234. #387D191semidirect
322. C4⋊C4C4×D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202592972
C2×C4×D7642
C2×#202592842
#271325552
#271325532
#271325492
#271325412
C4×(C2×D191)⋊C42
#271325102
#95×D1912
#387×C1912
#2364191