Finite Group Databasebeta

← #37583938

Subgroups — #37583938

Order 24448.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133287C211yesmaximal, characteristic, complemented
2#27133264C211yesmaximal, characteristic, complemented
3#27132969C211yesmaximal, characteristic, complemented
4#27132966C211yesmaximal, characteristic, complemented
5#27132950C211yesmaximal, characteristic, complemented
6#27132915C211yesmaximal, characteristic, complemented
7#27132910C211yesmaximal, characteristic, complemented
8#27132900C211yesmaximal, characteristic, complemented
9#27132891C211yesmaximal, characteristic, complemented
10#27132879C211yesmaximal, characteristic, complemented
11#27132878C211yesmaximal, characteristic, complemented
12#27132862C211yesmaximal, characteristic, complemented
13#27132857C211yesmaximal, characteristic, complemented
14#27132688C211yesmaximal, characteristic, complemented
15#474×C191C211yesmaximal, characteristic, complemented
16C2×#15690276C2211yescharacteristic
17C2×#15690275C2211yescharacteristic
18C2×D1528C2211yescharacteristic
19C2×#15690272C2211yescharacteristic
20C2×#15690270C2211yescharacteristic
21C2×C8×D191C2211yescharacteristic
22#20259318C2211yescharacteristic
23#20259317—21no—
24#20259313C2211yescharacteristic
25#20259311—21no—
26#20259310C2211yescharacteristic
27#20259307—21no—
28#20259305—21no—
29#20259304—21no—
30#20259302C2211yescharacteristic
31#20259298—21no—
32#20259297C2211yescharacteristic
33#20259297C2211yescharacteristic
34#20259296—21no—
35#20259295—21no—
36#20259293C2211yescharacteristic
37#20259287C2211yescharacteristic
38C4×D764C2211yescharacteristic
39#20259284C2211yescharacteristic
40#20259279C2211yescharacteristic
41#20259253C2211yescharacteristic
42#20259253C2211yescharacteristic
43C4⋊(C191⋊C8)C2211yescharacteristic
44Dic191⋊C8C2211yescharacteristic
45Dic191⋊C8C2211yescharacteristic
46#20259247C2211yescharacteristic
47#20259245C2211yescharacteristic
48#20259244C2211yescharacteristic
49#20259242C2211yescharacteristic
50#20259242C2211yescharacteristic
51#20259242C2211yescharacteristic
52C4⋊Q8×C191C2211yescharacteristic
53C4×D4×C191C2211yescharacteristic
54#107×C191C2211yescharacteristic
55#107×C191C2211yescharacteristic
56C4⋊C8×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58#102×C191C2211yescharacteristic
59C2×Dic382C2311yescharacteristic
60C2×D764—21no—
61C2×D764—21no—
62C2×D764C2311yescharacteristic
63C2×D764C2311yescharacteristic
64C2×C22⋊D191—21no—
65C2×C22⋊D191—21no—
66C2×C22⋊D191—21no—
67C2×C4×D191—21no—
68C2×C4×D191—21no—
69C2×C4×D191C2311yescharacteristic
70#15690276—41no—
71#15690275—41no—
72D1528—41no—
73#15690272—41no—
74#15690270—41no—
75C2×C191⋊C8C2311yescharacteristic
76C2×C191⋊C8C2311yescharacteristic
77C8×D191—41no—
78C4⋊Dic191—21no—
79C4⋊Dic191—21no—
80C4⋊Dic191C2311yescharacteristic
81Dic191⋊C4—21no—
82Dic191⋊C4—21no—
83Dic191⋊C4D411yescharacteristic
84Dic191⋊C4D411yescharacteristic
85C22⋊Dic191—21no—
86(C2×D191)⋊C4—21no—
87(C2×D191)⋊C4—21no—
88(C2×D191)⋊C4—21no—
89(C2×D191)⋊C4—21no—
90(C2×D191)⋊C4—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4—21no—
93(C2×D191)⋊C4D411yescharacteristic
94(C2×D191)⋊C4D411yescharacteristic
95C4×Dic191—21no—
96C4×Dic191C2311yescharacteristic
97C2×Q8×C191—21no—
98C2×D4×C191C2311yescharacteristic
99C22×C4×C191—21no—
100C2×C8×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C4⋊C4×C191—21no—
103C4⋊C4×C191C2311yescharacteristic
104C4⋊C4×C191C2311yescharacteristic
105C4⋊C4×C191C2311yescharacteristic
106C22⋊C4×C191—21no—
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191—21no—
110C22×D191C2×D411yescharacteristic
111Dic382—21no—
112Dic382—21no—
113D764—21no—
114D764—21no—
115D764—21no—
116D764—21no—
117D764—81no—
118D764—81no—
119C22⋊D191—81no—
120C22⋊D191—81no—
121C22⋊D191—81no—
122C2×Dic191—21no—
123C2×Dic191—21no—
124C2×Dic191C2×D411yescharacteristic
125C2×Dic191C2×D411yescharacteristic
126C2×Dic191C2×D411yescharacteristic
127C4×D191—21no—
128C4×D191—21no—
129C4×D191—81no—
130C4×D191—81no—
131C191⋊C8—21no—
132C191⋊C8—21no—
133C23×C191—21no—
134Q8×C191—81no—
135D4×C191—21no—
136D4×C191—21no—
137C2×C4×C191—21no—
138C2×C4×C191—21no—
139C2×C4×C191—21no—
140C2×C4×C191—81no—
141C2×C4×C191C2×D411yescharacteristic
142C2×C4×C191C2×D411yescharacteristic
143C2×C4×C191C2411yescharacteristic
144C8×C191—21no—
145C8×C191—21no—
146C22×C191—41no—
147C22×C191—41no—
148C22×C191—41no—
149C22×C191C22×D411yescharacteristic
150C2×D191—21no—
151C2×D191—21no—
152C2×D191—21no—
153C2×D191—41no—
154C2×D191—41no—
155C2×D191—41no—
156C2×D191—41no—
157C2×D191—41no—
158C2×D191—41no—
159C4×C191—21no—
160C4×C191—21no—
161C4×C191—41no—
162C4×C191—41no—
163C4×C191—41no—
164C4×C191H(5,𝔽2)11yescharacteristic
165C4×C1912−1+411yescharacteristic
166Dic191—21no—
167Dic191—21no—
168Dic191—21no—
169Dic191—41no—
170Dic191—41no—
171C2×C191—81no—
172C2×C191#53711yescharacteristic
173C2×C191#57611yescharacteristic
174C2×C191#57711yescharacteristic
175D191—41no—
176D191—81no—
177D191—81no—
178C191#325711yescharacteristic, complemented, Sylow
179#3257—1911nomaximal, Sylow
180#542—1911no—
181#540—1911no—
182#479—1911no—
183#478—1911no—
184#476—1911no—
185#474D19111yescharacteristic, complemented
186#469—1911no—
187#468—1911no—
188#466—1911no—
189#465—1911no—
190#463—1911no—
191#463—1911no—
192#460—1911no—
193#459—1911no—
194#424—1911no—
195C2×SD16—1911no—
196C2×SD16—1911no—
197C2×D8—1911no—
198C2×D8—1911no—
199C2×M16—1911no—
200C22×C8—1911no—
201C4⋊Q8C2×D19111yescharacteristic
202#127—1911no—
203#126—3821no—
204#125—1911no—
205#124—3821no—
206#124—1911no—
207#123—3821no—
208#123—3821no—
209#123—3821no—
210C22⋊Q8—3821no—
211C22⋊Q8—1911no—
212#121—3821no—
213#121—3821no—
214#121—1911no—
215#121—1911no—
216#121—1911no—
217C4×Q8—1911no—
218C4×D4—1911no—
219C4×D4—1911no—
220C4×D4C2×D19111yescharacteristic
221#117—1911no—
222#107C2×D19111yescharacteristic
223#107C2×D19111yescharacteristic
224#106—1911no—
225#106—1911no—
226C4⋊C8—1911no—
227C4⋊C8—1911no—
228C4⋊C8—1911no—
229C4⋊C8C2×D19111yescharacteristic
230#103—1911no—
231#103—1911no—
232#102—1911no—
233#102—1911no—
234#102—1911no—
235#102—1911no—
236#102C2×D19111yescharacteristic
237#102C2×D19111yescharacteristic
238C2×Q8—21no—
239C2×Q8—1911no—
240C2×D4—3821no—
241C2×D4—3821no—
242C2×D4—3821no—
243C2×D4—3821no—
244C2×D4—3821no—
245C2×D4—1911no—
246C2×D4—1911no—
247C2×D4C22×D19111yescharacteristic
248C22×C4—21no—
249C22×C4—3821no—
250C22×C4—3821no—
251C22×C4—1911no—
252SD16—7641no—
253SD16—7641no—
254D8—7641no—
255D8—7641no—
256M16—7641no—
257C2×C8—1911no—
258C2×C8—1911no—
259C2×C8—7641no—
260C2×C8C22×D19111yescharacteristic
261C2×C8C22×D19111yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—3821no—
264C4⋊C4—3821no—
265C4⋊C4—3821no—
266C4⋊C4—3821no—
267C4⋊C4—1911no—
268C4⋊C4—1911no—
269C4⋊C4—1911no—
270C4⋊C4C22×D19111yescharacteristic
271C4⋊C4C22×D19111yescharacteristic
272C4⋊C4C22×D19111yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—3821no—
275C22⋊C4—3821no—
276C22⋊C4—3821no—
277C22⋊C4—3821no—
278C22⋊C4—3821no—
279C22⋊C4—3821no—
280C22⋊C4—3821no—
281C22⋊C4—3821no—
282C22⋊C4—1911no—
283C22⋊C4—1911no—
284C42—3821no—
285C42—1911no—
286C42C22×D19111yescharacteristic
287C23—21no—
288C23—3821no—
289C23—3821no—
290C23—1911no—
291Q8—81no—
292Q8—3821no—
293Q8—3821no—
294D4—21no—
295D4—21no—
296D4—3821no—
297D4—3821no—
298D4—3821no—
299D4—3821no—
300D4—15281no—
301D4—15281no—
302D4—15281no—
303D4—15281no—
304D4—15281no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—81no—
309C2×C4—3821no—
310C2×C4—3821no—
311C2×C4—3821no—
312C2×C4—3821no—
313C2×C4—1911no—
314C2×C4—1911no—
315C2×C4—1911no—
316C2×C4—15281no—
317C2×C4—15281no—
318C2×C4D4×D19111yescharacteristic
319C2×C4D4×D19111yescharacteristic
320C2×C4C23×D19111yescharacteristic
321C8—21no—
322C8—21no—
323C8—3821no—
324C8—3821no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—3821no—
329C22—3821no—
330C22—3821no—
331C22—7641no—
332C22—7641no—
333C22—7641no—
334C22—7641no—
335C22—7641no—
336C22—7641no—
337C22C2×D4×D19111yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—3821no—
344C4—3821no—
345C4—3821no—
346C4—7641no—
347C4—7641no—
348C4#2025936811yescharacteristic
349C4#2025937011yescharacteristic
350C2—81no—
351C2—15281no—
352C2—15281no—
353C2—7641no—
354C2#2713324311yescharacteristic
355C2#2713346411yescharacteristic
356C2#2713347211yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#474×C191C2
socleC22×C191C22×D4
hypercenter#474D191
hypocenterC191#3257
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #27133287C2semidirect
2. #27133264C2semidirect
3. #27132969C2semidirect
4. #27132966C2semidirect
5. #27132950C2semidirect
6. #27132915C2semidirect
7. #27132910C2semidirect
8. #27132900C2semidirect
9. #27132891C2semidirect
10. #27132879C2semidirect
11. #27132878C2semidirect
12. #27132862C2semidirect
13. #27132857C2semidirect
14. #27132688C2semidirect
15. #474×C191C2semidirect
178. C191#3257semidirect
185. #474D191semidirect

Maximal subgroups

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

subgroupindex
#271332872
#271332642
#271329692
#271329662
#271329502
#271329152
#271329102
#271329002
#271328912
#271328792
#271328782
#271328622
#271328572
#271326882
#474×C1912
#3257191