Finite Group Databasebeta

← #37583937

Subgroups — #37583937

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#27133285C211yesmaximal, characteristic, complemented
2#27133269C211yesmaximal, characteristic, complemented
3#27132960C211yesmaximal, characteristic, complemented
4#27132952C211yesmaximal, characteristic, complemented
5#27132942C211yesmaximal, characteristic, complemented
6#27132917C211yesmaximal, characteristic, complemented
7#27132912C211yesmaximal, characteristic, complemented
8#27132900C211yesmaximal, characteristic, complemented
9#27132895C211yesmaximal, characteristic, complemented
10#27132881C211yesmaximal, characteristic, complemented
11#27132881C211yesmaximal, characteristic, complemented
12#27132863C211yesmaximal, characteristic, complemented
13#27132859C211yesmaximal, characteristic, complemented
14#27132688C211yesmaximal, characteristic, complemented
15#479×C191C211yesmaximal, characteristic, complemented
16C2×#15690274C2211yescharacteristic
17C2×#15690274C2211yescharacteristic
18C2×D1528C2211yescharacteristic
19C2×D1528C2211yescharacteristic
20C2×#15690270C2211yescharacteristic
21C2×C8×D191C2211yescharacteristic
22#20259321C2211yescharacteristic
23#20259319C2211yescharacteristic
24#20259316—21no—
25#20259311C2211yescharacteristic
26#20259310—21no—
27#20259307—21no—
28#20259307—21no—
29#20259307—21no—
30#20259300—21no—
31#20259298C2211yescharacteristic
32#20259297—21no—
33#20259297—21no—
34#20259297C2211yescharacteristic
35#20259297C2211yescharacteristic
36#20259297C2211yescharacteristic
37C4×D764C2211yescharacteristic
38#20259284C2211yescharacteristic
39#20259284C2211yescharacteristic
40#20259279C2211yescharacteristic
41#20259255C2211yescharacteristic
42#20259253C2211yescharacteristic
43C4⋊(C191⋊C8)C2211yescharacteristic
44Dic191⋊C8C2211yescharacteristic
45Dic191⋊C8C2211yescharacteristic
46#20259244C2211yescharacteristic
47#20259244C2211yescharacteristic
48#20259242C2211yescharacteristic
49#20259242C2211yescharacteristic
50#20259242C2211yescharacteristic
51#20259242C2211yescharacteristic
52#125×C191C2211yescharacteristic
53C4×Q8×C191C2211yescharacteristic
54#107×C191C2211yescharacteristic
55#106×C191C2211yescharacteristic
56C4⋊C8×C191C2211yescharacteristic
57#103×C191C2211yescharacteristic
58#103×C191C2211yescharacteristic
59C2×Dic382—21no—
60C2×D764—21no—
61C2×D764—21no—
62C2×D764—21no—
63C2×D764—21no—
64C2×D764—21no—
65C2×D764C2311yescharacteristic
66C2×D764C2311yescharacteristic
67C2×D764C2311yescharacteristic
68C2×C4×D191—21no—
69C2×C4×D191—21no—
70C2×C4×D191—21no—
71C2×C4×D191C2311yescharacteristic
72#15690274—41no—
73#15690274—41no—
74D1528—41no—
75D1528—41no—
76#15690270—41no—
77C2×C191⋊C8C2311yescharacteristic
78C2×C191⋊C8C2311yescharacteristic
79C8×D191—41no—
80C4⋊Dic191C2311yescharacteristic
81Dic191⋊C4—21no—
82Dic191⋊C4—21no—
83Dic191⋊C4D411yescharacteristic
84Dic191⋊C4D411yescharacteristic
85(C2×D191)⋊C4—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)⋊C4—21no—
94(C2×D191)⋊C4D411yescharacteristic
95(C2×D191)⋊C4D411yescharacteristic
96C4×Dic191C2311yescharacteristic
97C2×Q8×C191C2311yescharacteristic
98C2×C8×C191C2311yescharacteristic
99C2×C8×C191C2311yescharacteristic
100C4⋊C4×C191—21no—
101C4⋊C4×C191—21no—
102C4⋊C4×C191—21no—
103C4⋊C4×C191C2311yescharacteristic
104C4⋊C4×C191C2311yescharacteristic
105C4⋊C4×C191C2311yescharacteristic
106C42×C191—21no—
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191—21no—
110C22×D191—21no—
111C22×D191C2×D411yescharacteristic
112Dic382—81no—
113D764—21no—
114D764—21no—
115D764—21no—
116D764—21no—
117D764—21no—
118D764—21no—
119D764—81no—
120D764—81no—
121D764—81no—
122D764—81no—
123D764—81no—
124C2×Dic191—21no—
125C2×Dic191C2×D411yescharacteristic
126C2×Dic191C2×D411yescharacteristic
127C2×Dic191C2×D411yescharacteristic
128C4×D191—21no—
129C4×D191—21no—
130C4×D191—81no—
131C4×D191—81no—
132C4×D191—81no—
133C191⋊C8—21no—
134C191⋊C8—21no—
135Q8×C191—21no—
136Q8×C191—21no—
137C2×C4×C191—21no—
138C2×C4×C191—21no—
139C2×C4×C191—21no—
140C2×C4×C191—21no—
141C2×C4×C191C2×D411yescharacteristic
142C2×C4×C191C2×D411yescharacteristic
143C2×C4×C191C2411yescharacteristic
144C8×C191—21no—
145C8×C191—21no—
146C22×C191C22×D411yescharacteristic
147C2×D191—21no—
148C2×D191—21no—
149C2×D191—21no—
150C2×D191—41no—
151C2×D191—41no—
152C2×D191—41no—
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×C191—41no—
165C4×C191H(5,𝔽2)11yescharacteristic
166C4×C1912−1+411yescharacteristic
167Dic191—21no—
168Dic191—21no—
169Dic191—21no—
170Dic191—41no—
171C2×C191#53711yescharacteristic
172C2×C191#57611yescharacteristic
173C2×C191#57711yescharacteristic
174D191—41no—
175D191—81no—
176D191—81no—
177D191—81no—
178C191#325711yescharacteristic, complemented, Sylow
179#3257—1911nomaximal, Sylow
180#542—1911no—
181#540—1911no—
182#479D19111yescharacteristic, complemented
183#478—1911no—
184#476—1911no—
185#474—1911no—
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⋊Q8—1911no—
202#127—1911no—
203#126—3821no—
204#125C2×D19111yescharacteristic
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×Q8C2×D19111yescharacteristic
218C4×D4—1911no—
219C4×D4—1911no—
220C4×D4—1911no—
221#117—1911no—
222#107—1911no—
223#107C2×D19111yescharacteristic
224#106—1911no—
225#106C2×D19111yescharacteristic
226C4⋊C8—1911no—
227C4⋊C8—1911no—
228C4⋊C8—1911no—
229C4⋊C8C2×D19111yescharacteristic
230#103C2×D19111yescharacteristic
231#103C2×D19111yescharacteristic
232#102—1911no—
233#102—1911no—
234#102—1911no—
235#102—1911no—
236#102—1911no—
237#102—1911no—
238C2×Q8—3821no—
239C2×Q8C22×D19111yescharacteristic
240C2×D4—3821no—
241C2×D4—3821no—
242C2×D4—3821no—
243C2×D4—3821no—
244C2×D4—3821no—
245C2×D4—1911no—
246C2×D4—1911no—
247C2×D4—1911no—
248C22×C4—3821no—
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—21no—
264C4⋊C4—21no—
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—3821no—
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—21no—
285C42—1911no—
286C42C22×D19111yescharacteristic
287C23—3821no—
288C23—3821no—
289C23—3821no—
290C23—1911no—
291Q8—21no—
292Q8—21no—
293Q8—15281no—
294D4—3821no—
295D4—3821no—
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—21no—
309C2×C4—3821no—
310C2×C4—3821no—
311C2×C4—3821no—
312C2×C4—1911no—
313C2×C4—1911no—
314C2×C4—1911no—
315C2×C4—15281no—
316C2×C4—15281no—
317C2×C4—15281no—
318C2×C4D4×D19111yescharacteristic
319C2×C4D4×D19111yescharacteristic
320C2×C4C23×D19111yescharacteristic
321C8—21no—
322C8—21no—
323C8—3821no—
324C8—3821no—
325C22—3821no—
326C22—3821no—
327C22—3821no—
328C22—7641no—
329C22—7641no—
330C22—7641no—
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—41no—
344C4—3821no—
345C4—3821no—
346C4—3821no—
347C4—7641no—
348C4#2025936811yescharacteristic
349C4#2025937011yescharacteristic
350C2—15281no—
351C2—15281no—
352C2—15281no—
353C2—7641no—
354C2#2713324311yescharacteristic
355C2#2713346511yescharacteristic
356C2#2713347211yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#479×C191C2
socleC22×C191C22×D4
hypercenter#479D191
hypocenterC191#3257
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #479

Complements

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

NH ≅ G/Ntype
1. #27133285C2semidirect
2. #27133269C2semidirect
3. #27132960C2semidirect
4. #27132952C2semidirect
5. #27132942C2semidirect
6. #27132917C2semidirect
7. #27132912C2semidirect
8. #27132900C2semidirect
9. #27132895C2semidirect
10. #27132881C2semidirect
11. #27132881C2semidirect
12. #27132863C2semidirect
13. #27132859C2semidirect
14. #27132688C2semidirect
15. #479×C191C2semidirect
178. C191#3257semidirect
182. #479D191semidirect

Maximal subgroups

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

subgroupindex
#271332852
#271332692
#271329602
#271329522
#271329422
#271329172
#271329122
#271329002
#271328952
#271328812
#271328632
#271328592
#271326882
#479×C1912
#3257191