Finite Group Databasebeta

← #37583421

Subgroups — #37583421

Order 24448.

402 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133243C211yesmaximal, characteristic, complemented
2#27133241C211yesmaximal, characteristic, complemented
3#27132997C211yesmaximal, characteristic, complemented
4#27132996C211yesmaximal, characteristic, complemented
5#27132977C211yesmaximal, characteristic, complemented
6#27132975C211yesmaximal, characteristic, complemented
7#27132912C211yesmaximal, characteristic, complemented
8#27132906C211yesmaximal, characteristic, complemented
9#27132901C211yesmaximal, characteristic, complemented
10#27132898C211yesmaximal, characteristic, complemented
11#27132824C211yesmaximal, characteristic, complemented
12#27132808C211yesmaximal, characteristic, complemented
13#27132807C211yesmaximal, characteristic, complemented
14#27132628C211yesmaximal, characteristic, complemented
15#452×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×#15690287C2211yescharacteristic
18C2×#15690274C2211yescharacteristic
19C2×#15690272C2211yescharacteristic
20C2×#15690270C2211yescharacteristic
21C2×C8×D191C2211yescharacteristic
22#20259301—21no—
23#20259300—21no—
24#20259298C2211yescharacteristic
25#20259298C2211yescharacteristic
26#20259298C2211yescharacteristic
27#20259297—21no—
28#20259297C2211yescharacteristic
29#20259296—21no—
30#20259296C2211yescharacteristic
31#20259295—21no—
32#20259295—21no—
33#20259294—21no—
34#20259294—21no—
35#20259293C2211yescharacteristic
36#20259293C2211yescharacteristic
37C2×C4⋊Dic191C2211yescharacteristic
38C4⋊C4×D191C2211yescharacteristic
39#20259256C2211yescharacteristic
40#20259256C2211yescharacteristic
41#20259255C2211yescharacteristic
42#20259255C2211yescharacteristic
43#20259246C2211yescharacteristic
44#20259246C2211yescharacteristic
45#20259246C2211yescharacteristic
46#20259244C2211yescharacteristic
47#20259244C2211yescharacteristic
48#20259243C2211yescharacteristic
49C22⋊(C191⋊C8)C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51(C2×D191)⋊C8C2211yescharacteristic
52C2×#41×C191C2211yescharacteristic
53C2×Q16×C191C2211yescharacteristic
54C2×SD16×C191C2211yescharacteristic
55C22⋊Q8×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic
59#15690288—41no—
60#15690288—41no—
61#15690287—41no—
62#15690287—41no—
63C2×Dic382D411yescharacteristic
64C2×D764—21no—
65C2×D764—21no—
66C2×D764D411yescharacteristic
67C2×D764C2311yescharacteristic
68C2×C22⋊D191—21no—
69C2×C22⋊D191—21no—
70C2×C22⋊D191—21no—
71C2×C22⋊D191D411yescharacteristic
72C2×C22⋊D191D411yescharacteristic
73C22×Dic191—21no—
74C2×C4×D191—21no—
75C2×C4×D191—21no—
76C2×C4×D191C2311yescharacteristic
77C2×C4×D191C2311yescharacteristic
78#15690274—41no—
79#15690272—41no—
80#15690270—41no—
81C2×C191⋊C8C2311yescharacteristic
82C2×C191⋊C8C2311yescharacteristic
83C8×D191—41no—
84C4⋊Dic191—21no—
85C4⋊Dic191C2311yescharacteristic
86C4⋊Dic191C2311yescharacteristic
87C4⋊Dic191C2311yescharacteristic
88Dic191⋊C4—21no—
89Dic191⋊C4—21no—
90Dic191⋊C4—21no—
91Dic191⋊C4—21no—
92C22⋊Dic191—21no—
93C22⋊Dic191—21no—
94(C2×D191)⋊C4—21no—
95(C2×D191)⋊C4—21no—
96(C2×D191)⋊C4—21no—
97(C2×D191)⋊C4—21no—
98(C2×D191)⋊C4—21no—
99#41×C191—41no—
100#41×C191—41no—
101C2×Q8×C191C2311yescharacteristic
102C2×Q8×C191C2311yescharacteristic
103C2×D4×C191—21no—
104C2×D4×C191C2311yescharacteristic
105C22×C4×C191—21no—
106C22×C4×C191C2311yescharacteristic
107Q16×C191—41no—
108SD16×C191—41no—
109C2×C8×C191C2311yescharacteristic
110C2×C8×C191C2311yescharacteristic
111C4⋊C4×C191—21no—
112C4⋊C4×C191C2311yescharacteristic
113C22⋊C4×C191—21no—
114C22×D191—21no—
115C22×D191C2×D411yescharacteristic
116C22×D191C2×D411yescharacteristic
117Dic382—41no—
118D764—21no—
119D764—21no—
120D764—41no—
121D764—42no—
122D764—81no—
123C22⋊D191—41no—
124C22⋊D191—41no—
125C22⋊D191—81no—
126C22⋊D191—81no—
127C22⋊D191—81no—
128C2×Dic191—21no—
129C2×Dic191—21no—
130C2×Dic191—21no—
131C2×Dic191—81no—
132C2×Dic191C2×D411yescharacteristic
133C2×Dic191C2×D411yescharacteristic
134C4×D191—21no—
135C4×D191—21no—
136C4×D191—21no—
137C4×D191—21no—
138C4×D191—42no—
139C4×D191—81no—
140C191⋊C8—21no—
141C191⋊C8—21no—
142C23×C191—21no—
143C23×C191C2×D411yescharacteristic
144Q8×C191—21no—
145Q8×C191—21no—
146Q8×C191—21no—
147Q8×C191—21no—
148D4×C191—21no—
149D4×C191—21no—
150D4×C191—42no—
151C2×C4×C191—21no—
152C2×C4×C191—21no—
153C2×C4×C191—21no—
154C2×C4×C191—21no—
155C2×C4×C191—21no—
156C2×C4×C191—42no—
157C2×C4×C191C2×D411yescharacteristic
158C2×C4×C191C2411yescharacteristic
159C8×C191—21no—
160C8×C191—21no—
161C22×C191—21no—
162C22×C191—21no—
163C22×C191—21no—
164C22×C191—41no—
165C22×C191—41no—
166C22×C191—41no—
167C22×C191C22×D411yescharacteristic
168C2×D191—21no—
169C2×D191—21no—
170C2×D191—21no—
171C2×D191—21no—
172C2×D191—21no—
173C2×D191—21no—
174C2×D191—41no—
175C2×D191—41no—
176C2×D191—41no—
177C4×C191—21no—
178C4×C191—41no—
179C4×C191—41no—
180C4×C191—41no—
181C4×C191H(5,𝔽2)11yescharacteristic
182C4×C191H(5,𝔽2)11yescharacteristic
183Dic191—21no—
184Dic191—21no—
185Dic191—41no—
186Dic191—41no—
187Dic191—41no—
188C2×C191—41no—
189C2×C191—81no—
190C2×C191#53411yescharacteristic
191C2×C191#57611yescharacteristic
192C2×C191#57811yescharacteristic
193D191—41no—
194D191—41no—
195D191—81no—
196C191#320311yescharacteristic, complemented, Sylow
197#3203—1911nomaximal, Sylow
198#537—1911no—
199#537—1911no—
200#484—1911no—
201#484—1911no—
202#480—1911no—
203#480—1911no—
204#468—1911no—
205#468—1911no—
206#467—1911no—
207#466—1911no—
208#452—1911no—
209#452D19111yescharacteristic, complemented
210#449—1911no—
211#449—1911no—
212#408—1911no—
213C2×#41—1911no—
214C2×#41—1911no—
215C2×#41C2×D19111yescharacteristic
216C2×Q16C2×D19111yescharacteristic
217C2×SD16—1911no—
218C2×SD16C2×D19111yescharacteristic
219C2×D8—1911no—
220C2×M16—1911no—
221C22×C8—1911no—
222C22⋊Q8—3821no—
223C22⋊Q8—3821no—
224C22⋊Q8—1911no—
225C22⋊Q8—1911no—
226C22⋊Q8—1911no—
227C22⋊Q8C2×D19111yescharacteristic
228#121—3821no—
229#121—3821no—
230#121—3821no—
231#121—3821no—
232#121—3821no—
233#121—3821no—
234#121—1911no—
235#121—1911no—
236#121—1911no—
237#121—1911no—
238C2×C4⋊C4—1911no—
239C2×C4⋊C4—1911no—
240#107—1911no—
241#107—1911no—
242#107—1911no—
243#107—1911no—
244#103—1911no—
245#103—1911no—
246#103—1911no—
247#103C2×D19111yescharacteristic
248#102—1911no—
249#102—1911no—
250#102—1911no—
251#102C2×D19111yescharacteristic
252C22⋊C8—1911no—
253C22⋊C8—1911no—
254C22⋊C8—1911no—
255C22⋊C8C2×D19111yescharacteristic
256#41—41no—
257#41—41no—
258#41—7641no—
259#41—7641no—
260#41—7641no—
261#41—7641no—
262C2×Q8—1911no—
263C2×Q8C22×D19111yescharacteristic
264C2×Q8C22×D19111yescharacteristic
265C2×D4—21no—
266C2×D4—3821no—
267C2×D4—3821no—
268C2×D4—3821no—
269C2×D4—3821no—
270C2×D4—3821no—
271C2×D4—1911no—
272C2×D4—1911no—
273C2×D4—1911no—
274C2×D4—1911no—
275C2×D4C22×D19111yescharacteristic
276C22×C4—21no—
277C22×C4—3821no—
278C22×C4—3821no—
279C22×C4—3821no—
280C22×C4—1911no—
281C22×C4—1911no—
282C22×C4C22×D19111yescharacteristic
283Q16—41no—
284SD16—41no—
285SD16—7641no—
286D8—7641no—
287M16—7641no—
288C2×C8—1911no—
289C2×C8—1911no—
290C2×C8—7641no—
291C2×C8C22×D19111yescharacteristic
292C2×C8C22×D19111yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—3821no—
295C4⋊C4—3821no—
296C4⋊C4—3821no—
297C4⋊C4—3821no—
298C4⋊C4—3821no—
299C4⋊C4—1911no—
300C4⋊C4—1911no—
301C4⋊C4—1911no—
302C4⋊C4C22×D19111yescharacteristic
303C22⋊C4—21no—
304C22⋊C4—3821no—
305C22⋊C4—3821no—
306C22⋊C4—3821no—
307C22⋊C4—3821no—
308C22⋊C4—3821no—
309C22⋊C4—3821no—
310C22⋊C4—3821no—
311C23—21no—
312C23—3821no—
313C23—1911no—
314C23—1911no—
315C23D4×D19111yescharacteristic
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—7641no—
321D4—21no—
322D4—21no—
323D4—42no—
324D4—3821no—
325D4—3821no—
326D4—15281no—
327D4—15281no—
328D4—15281no—
329D4—15281no—
330D4—7641no—
331D4—7642no—
332D4—7641no—
333D4—7641no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—3821no—
341C2×C4—3821no—
342C2×C4—3821no—
343C2×C4—3821no—
344C2×C4—3821no—
345C2×C4—3821no—
346C2×C4—3821no—
347C2×C4—1911no—
348C2×C4—1911no—
349C2×C4—15281no—
350C2×C4—15281no—
351C2×C4—7642no—
352C2×C4D4×D19111yescharacteristic
353C2×C4C23×D19111yescharacteristic
354C8—21no—
355C8—21no—
356C8—3821no—
357C8—3821no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—3821no—
365C22—3821no—
366C22—3821no—
367C22—3821no—
368C22—3821no—
369C22—3821no—
370C22—7641no—
371C22—7641no—
372C22—7641no—
373C22C2×D4×D19111yescharacteristic
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—3821no—
379C4—3821no—
380C4—7641no—
381C4—7641no—
382C4—7641no—
383C4#2025936711yescharacteristic
384C4#2025936711yescharacteristic
385C2—41no—
386C2—81no—
387C2—15281no—
388C2—7641no—
389C2—7641no—
390C2#2713322311yescharacteristic
391C2#2713346511yescharacteristic
392C2#2713347911yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#452×C191C2
socleC22×C191C22×D4
hypercenter#452D191
hypocenterC191#3203
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #27133243C2semidirect
2. #27133241C2semidirect
3. #27132997C2semidirect
4. #27132996C2semidirect
5. #27132977C2semidirect
6. #27132975C2semidirect
7. #27132912C2semidirect
8. #27132906C2semidirect
9. #27132901C2semidirect
10. #27132898C2semidirect
11. #27132824C2semidirect
12. #27132808C2semidirect
13. #27132807C2semidirect
14. #27132628C2semidirect
15. #452×C191C2semidirect
196. C191#3203semidirect
209. #452D191semidirect

Maximal subgroups

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

subgroupindex
#271332432
#271332412
#271329972
#271329962
#271329772
#271329752
#271329122
#271329062
#271329012
#271328982
#271328242
#271328082
#271328072
#271326282
#452×C1912
#3203191