Finite Group Databasebeta

← #37575210

Subgroups — #37575210

Order 24448.

668 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259294C211yesmaximal, characteristic
2C2×C4×C22⋊D191C211yesmaximal, characteristic, complemented
3C2×#20259278C211yesmaximal, characteristic, complemented
4#27132566C211yesmaximal, characteristic, complemented
5#27132563C211yesmaximal, characteristic, complemented
6#27132563C211yesmaximal, characteristic, complemented
7#27132560C211yesmaximal, characteristic, complemented
8#27132552C211yesmaximal, characteristic, complemented
9#27132551C211yesmaximal, characteristic, complemented
10#27132539C211yesmaximal, characteristic, complemented
11#27132537C211yesmaximal, characteristic, complemented
12#27132536C211yesmaximal, characteristic, complemented
13#27132521C211yesmaximal, characteristic, complemented
14#27132514C211yesmaximal, characteristic, complemented
15#386×C191C211yesmaximal, characteristic, complemented
16C22×C22⋊D191C2211yescharacteristic
17C22×C22⋊D191C2211yescharacteristic
18C23×Dic191C2211yescharacteristic
19C22×C4×D191C2211yescharacteristic
20#20259294C418yescomplemented
21C4×C22⋊D191—24no—
22#20259278—24no—
23C2×C4⋊Dic191C2211yescharacteristic
24C2×Dic191⋊C4C2211yescharacteristic
25C2×Dic191⋊C4C2211yescharacteristic
26C2×Dic191⋊C4C2211yescharacteristic
27C2×Dic191⋊C4C2211yescharacteristic
28C2×Dic191⋊C4C2211yescharacteristic
29C2×Dic191⋊C4C2211yescharacteristic
30C2×C22⋊Dic191C2211yescharacteristic
31C2×C22⋊Dic191C2211yescharacteristic
32C2×C22⋊Dic191C2211yescharacteristic
33C2×C22⋊Dic191C2211yescharacteristic
34C2×C22⋊Dic191C2211yescharacteristic
35C2×(C2×D191)⋊C4C2211yescharacteristic
36C2×(C2×D191)⋊C4C2211yescharacteristic
37C2×(C2×D191)⋊C4C2211yescharacteristic
38C2×(C2×D191)⋊C4C2211yescharacteristic
39C2×C4×Dic191C2211yescharacteristic
40C2×C4×Dic191C2211yescharacteristic
41C2×C4×Dic191C2211yescharacteristic
42C2×C4×Dic191C2211yescharacteristic
43C191⋊#95C2211yescharacteristic
44C191⋊#95C2211yescharacteristic
45C191⋊#95C2211yescharacteristic
46C191⋊#95C2211yescharacteristic
47C22×D4×C191C2211yescharacteristic
48C23×C4×C191C2211yescharacteristic
49C2×C22⋊C4×C191C2211yescharacteristic
50C2×C22⋊C4×C191C2211yescharacteristic
51C2×C22⋊C4×C191C2211yescharacteristic
52#95×C191C2211yescharacteristic
53#95×C191C2211yescharacteristic
54C23×D191C2311yescharacteristic
55C2×C22⋊D191—22no—
56C2×C22⋊D191—22no—
57C2×C22⋊D191—41no—
58C2×C22⋊D191—41no—
59C2×C22⋊D191C2×C414yes—
60C2×C22⋊D191C2×C414yescomplemented
61C22×Dic191—22no—
62C22×Dic191—22no—
63C22×Dic191C2×C414yescomplemented
64C22×Dic191C2311yescharacteristic
65C22×Dic191C2311yescharacteristic
66C22×Dic191C2311yescharacteristic
67C22×Dic191C2311yescharacteristic
68C22×Dic191C2311yescharacteristic
69C22×Dic191C2311yescharacteristic
70C22×Dic191C2311yescharacteristic
71C2×C4×D191—22no—
72C2×C4×D191—41no—
73C2×C4×D191—41no—
74C4⋊Dic191—41no—
75Dic191⋊C4—22no—
76Dic191⋊C4—22no—
77Dic191⋊C4—22no—
78Dic191⋊C4—22no—
79Dic191⋊C4—41no—
80Dic191⋊C4C2×C414yescomplemented
81C22⋊Dic191—22no—
82C22⋊Dic191—22no—
83C22⋊Dic191—41no—
84C22⋊Dic191—41no—
85C22⋊Dic191C2×C414yescomplemented
86(C2×D191)⋊C4—22no—
87(C2×D191)⋊C4—41no—
88(C2×D191)⋊C4—41no—
89(C2×D191)⋊C4C2×C414yescomplemented
90C4×Dic191—22no—
91C4×Dic191—41no—
92C4×Dic191—41no—
93C4×Dic191D414yescomplemented
94C24×C191C2311yescharacteristic
95C24×C191C2311yescharacteristic
96C2×D4×C191—41no—
97C2×D4×C191—41no—
98C2×D4×C191C2×C414yescomplemented
99C22×C4×C191—22no—
100C22×C4×C191—41no—
101C22×C4×C191—41no—
102C22×C4×C191C2311yescharacteristic
103C22×C4×C191C2311yescharacteristic
104C22×C4×C191C2311yescharacteristic
105C22×C4×C191C2311yescharacteristic
106C22×C4×C191C2311yescharacteristic
107C22⋊C4×C191—22no—
108C22⋊C4×C191—41no—
109C22⋊C4×C191—41no—
110C22×D191—21no—
111C22×D191—21no—
112C22×D191—21no—
113C22×D191—21no—
114C22×D191—21no—
115C22×D191—21no—
116C22×D191C22×C412yes—
117C22⋊D191—28no—
118C22⋊D191—44no—
119C2×Dic191—21no—
120C2×Dic191—21no—
121C2×Dic191—21no—
122C2×Dic191—21no—
123C2×Dic191—21no—
124C2×Dic191—21no—
125C2×Dic191—28no—
126C2×Dic191—21no—
127C2×Dic191—21no—
128C2×Dic191—21no—
129C2×Dic191—21no—
130C2×Dic191—21no—
131C2×Dic191—21no—
132C2×Dic191—21no—
133C2×Dic191—21no—
134C2×Dic191—21no—
135C2×Dic191C22×C412yes—
136C2×Dic191C22×C412yes—
137C2×Dic191C22×C412yes—
138C2×Dic191C2×D412yes—
139C2×Dic191C2×D412yes—
140C2×Dic191#4112yes—
141C4×D191—44no—
142C23×C191—21no—
143C23×C191—21no—
144C23×C191—21no—
145C23×C191—21no—
146C23×C191—21no—
147C23×C191—21no—
148C23×C191—21no—
149C23×C191—21no—
150C23×C191—21no—
151C23×C191—21no—
152C23×C191—21no—
153C23×C191—21no—
154C23×C191C22×C412yes—
155C23×C191C22×C412yes—
156C23×C191C2411yescharacteristic
157D4×C191—44no—
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×C191—44no—
172C2×C4×C191C22×C412yes—
173C2×C4×C191C2×D412yes—
174C22×C191—22no—
175C22×C191—22no—
176C22×C191—22no—
177C22×C191—22no—
178C22×C191—22no—
179C22×C191—22no—
180C22×C191—41no—
181C22×C191—41no—
182C22×C191—41no—
183C22×C191—41no—
184C22×C191—41no—
185C22×C191—41no—
186C22×C191—41no—
187C22×C191—41no—
188C22×C191C23×C411yescharacteristic
189C22×C191C22×D411yescharacteristic
190C22×C191C2×#4111yescharacteristic
191C22×C191H(5,𝔽2)11yescharacteristic
192C22×C191H(5,𝔽2)11yescharacteristic
193C22×C191H(5,𝔽2)11yescharacteristic
194C22×C1912−1+411yescharacteristic
195C2×D191—22no—
196C2×D191—22no—
197C2×D191—22no—
198C2×D191—41no—
199C2×D191—41no—
200C2×D191—41no—
201C2×D191—41no—
202C4×C191—22no—
203C4×C191—22no—
204C4×C191—41no—
205C4×C191—41no—
206C4×C191—41no—
207Dic191—22no—
208Dic191—22no—
209Dic191—22no—
210Dic191—41no—
211Dic191—41no—
212Dic191—41no—
213Dic191C4×D414yes—
214C2×C191—42no—
215C2×C191—42no—
216C2×C191C2×C4×D411yescharacteristic
217C2×C191#51811yescharacteristic
218C2×C191#52011yescharacteristic
219C2×C191#53511yescharacteristic
220C2×C191#53711yescharacteristic
221C2×C191#54011yescharacteristic
222C2×C191#54211yescharacteristic
223D191—42no—
224C191#232411yescharacteristic, complemented, Sylow
225#2324—1911nomaximal, Sylow
226C2×#121—1911no—
227C2×C4×D4—1911no—
228C2×#117—1911no—
229#390—1911no—
230#390—1911no—
231#390—1911no—
232#389—1911no—
233#388—1911no—
234#388—1911no—
235#386—1911no—
236#386D19111yescharacteristic, complemented
237#385—1911no—
238#385—1911no—
239#380—1911no—
240C4×C4⋊C4—1911no—
241C22×D4—1911no—
242C22×D4—1911no—
243C22×D4C2×D19111yescharacteristic
244C23×C4—1911no—
245C23×C4—1911no—
246C23×C4C2×D19111yescharacteristic
247#121—1918no—
248C4×D4—3824no—
249#117—3824no—
250C2×C4⋊C4—1911no—
251C2×C4⋊C4—1911no—
252C2×C4⋊C4—1911no—
253C2×C4⋊C4—1911no—
254C2×C4⋊C4—1911no—
255C2×C4⋊C4—1911no—
256C2×C4⋊C4—1911no—
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⋊C4C2×D19111yescharacteristic
267C2×C22⋊C4C2×D19111yescharacteristic
268C2×C22⋊C4C2×D19111yescharacteristic
269C2×C42—1911no—
270C2×C42—1911no—
271C2×C42—1911no—
272C2×C42—1911no—
273#95—1911no—
274#95—1911no—
275#95—1911no—
276#95—1911no—
277#95C2×D19111yescharacteristic
278#95C2×D19111yescharacteristic
279C24—1911no—
280C24C22×D19111yescharacteristic
281C24C22×D19111yescharacteristic
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—3822no—
285C2×D4—3822no—
286C2×D4—1914no—
287C2×D4—1914no—
288C2×D4—7641no—
289C2×D4—7641no—
290C2×D4C4×D19114yescomplemented
291C22×C4—22no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4—3822no—
295C22×C4—3822no—
296C22×C4—3822no—
297C22×C4—1911no—
298C22×C4—1911no—
299C22×C4—1911no—
300C22×C4—1914no—
301C22×C4—1911no—
302C22×C4—1911no—
303C22×C4—1911no—
304C22×C4—1911no—
305C22×C4—7641no—
306C22×C4—7641no—
307C22×C4C22×D19111yescharacteristic
308C22×C4C22×D19111yescharacteristic
309C22×C4C22×D19111yescharacteristic
310C22×C4C22×D19111yescharacteristic
311C22×C4C22×D19111yescharacteristic
312C4⋊C4—3822no—
313C4⋊C4—3822no—
314C4⋊C4—3822no—
315C4⋊C4—3822no—
316C4⋊C4—1914no—
317C4⋊C4—7641no—
318C4⋊C4—7641no—
319C22⋊C4—22no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—3822no—
323C22⋊C4—3822no—
324C22⋊C4—3822no—
325C22⋊C4—1914no—
326C22⋊C4—1914no—
327C22⋊C4—7641no—
328C22⋊C4—7641no—
329C22⋊C4—7641no—
330C22⋊C4—7641no—
331C42—3822no—
332C42—1914no—
333C42—7641no—
334C42—7641no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—3821no—
348C23—3821no—
349C23—3821no—
350C23—3821no—
351C23—3821no—
352C23—3821no—
353C23—1912no—
354C23C2×C4×D19112yes—
355C23C2×C4×D19112yes—
356C23C23×D19111yescharacteristic
357D4—44no—
358D4—3828no—
359D4—7644no—
360C2×C4—21no—
361C2×C4—21no—
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—44no—
374C2×C4—3821no—
375C2×C4—3821no—
376C2×C4—3821no—
377C2×C4—3821no—
378C2×C4—3821no—
379C2×C4—3821no—
380C2×C4—3828no—
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—1912no—
394C2×C4—1912no—
395C2×C4—1912no—
396C2×C4—7644no—
397C2×C4C2×C4×D19112yes—
398C2×C4D4×D19112yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—3822no—
414C22—3822no—
415C22—3822no—
416C22—7641no—
417C22—7641no—
418C22—7641no—
419C22—7641no—
420C22C22×C4×D19111yescharacteristic
421C22C2×D4×D19111yescharacteristic
422C22#41×D19111yescharacteristic
423C22#2025936711yescharacteristic
424C22#2025936711yescharacteristic
425C22#2025936711yescharacteristic
426C22#2025936911yescharacteristic
427C4—22no—
428C4—22no—
429C4—41no—
430C4—41no—
431C4—41no—
432C4—3822no—
433C4—3822no—
434C4—3822no—
435C4—1914no—
436C4—7641no—
437C4—7641no—
438C4—7641no—
439C2—42no—
440C2—42no—
441C2—7642no—
442C2C4×D4×D19111yescharacteristic
443C2#2713313611yescharacteristic
444C2#2713314211yescharacteristic
445C2#2713322811yescharacteristic
446C2#2713324211yescharacteristic
447C2#2713326311yescharacteristic
448C2#2713328111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
Fitting#386×C191C2
socle, cosocleC23×C191C24
prime radicalC2×#20259294C2
hypercenter#386D191
hypocenterC191#2324
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D191C2semidirect
3. C2×#20259278C2semidirect
4. #27132566C2semidirect
5. #27132563C2semidirect
6. #27132563C2semidirect
7. #27132560C2semidirect
8. #27132552C2semidirect
9. #27132551C2semidirect
10. #27132539C2semidirect
11. #27132537C2semidirect
12. #27132536C2semidirect
13. #27132521C2semidirect
14. #27132514C2semidirect
15. #386×C191C2semidirect
20. #20259294C4semidirect
60. C2×C22⋊D191C2×C4semidirect
63. C22×Dic191C2×C4semidirect
80. Dic191⋊C4C2×C4semidirect
85. C22⋊Dic191C2×C4semidirect
89. (C2×D191)⋊C4C2×C4semidirect
93. C4×Dic191D4semidirect
98. C2×D4×C191C2×C4semidirect
224. C191#2324semidirect
236. #386D191semidirect
290. C2×D4C4×D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202592942
C2×C4×C22⋊D1912
C2×#202592782
#271325662
#271325632
#271325602
#271325522
#271325512
#271325392
#271325372
#271325362
#271325212
#271325142
#386×C1912
#2324191