Finite Group Databasebeta

← #37583208

Subgroups — #37583208

Order 24448.

374 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#27133269C211yesmaximal, characteristic, complemented
3#27133052C211yesmaximal, characteristic, complemented
4#27133020C211yesmaximal, characteristic, complemented
5#27133011C211yesmaximal, characteristic, complemented
6#27132917C211yesmaximal, characteristic, complemented
7#27132910C211yesmaximal, characteristic, complemented
8#27132900C211yesmaximal, characteristic, complemented
9#27132893C211yesmaximal, characteristic, complemented
10#27132774C211yesmaximal, characteristic, complemented
11#27132762C211yesmaximal, characteristic, complemented
12#27132750C211yesmaximal, characteristic, complemented
13#27132745C211yesmaximal, characteristic, complemented
14#27132620C211yesmaximal, characteristic, complemented
15#501×C191C211yesmaximal, characteristic, complemented
16C2×#15690276C2211yescharacteristic
17C2×#15690276C2211yescharacteristic
18C2×D1528C2211yescharacteristic
19C2×D1528C2211yescharacteristic
20C2×#15690270C2211yescharacteristic
21C2×C8×D191C2211yescharacteristic
22#20259319C2211yescharacteristic
23#20259317—21no—
24#20259311—21no—
25#20259310C2211yescharacteristic
26#20259307—21no—
27#20259307—21no—
28#20259307—21no—
29#20259302C2211yescharacteristic
30#20259298—21no—
31#20259297—21no—
32#20259297—21no—
33#20259297C2211yescharacteristic
34#20259297C2211yescharacteristic
35#20259297C2211yescharacteristic
36#20259287C2211yescharacteristic
37#20259284C2211yescharacteristic
38#20259284C2211yescharacteristic
39#20259284C2211yescharacteristic
40#20259279C2211yescharacteristic
41#20259245C2211yescharacteristic
42#20259245C2211yescharacteristic
43#20259242C2211yescharacteristic
44#20259242C2211yescharacteristic
45#20259242C2211yescharacteristic
46#20259242C2211yescharacteristic
47#20259242C2211yescharacteristic
48#20259242C2211yescharacteristic
49#20259232C2211yescharacteristic
50C4×C191⋊C8C2211yescharacteristic
51C8×Dic191C2211yescharacteristic
52C4⋊Q8×C191C2211yescharacteristic
53#125×C191C2211yescharacteristic
54#107×C191C2211yescharacteristic
55#107×C191C2211yescharacteristic
56#106×C191C2211yescharacteristic
57#106×C191C2211yescharacteristic
58#97×C191C2211yescharacteristic
59C2×Dic382C2311yescharacteristic
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#15690276—22no—
73#15690276—22no—
74D1528—22no—
75D1528—22no—
76#15690270—22no—
77C2×C191⋊C8C2311yescharacteristic
78C2×C191⋊C8C2311yescharacteristic
79C8×D191—22no—
80C4⋊Dic191—21no—
81Dic191⋊C4—21no—
82Dic191⋊C4D411yescharacteristic
83Dic191⋊C4D411yescharacteristic
84(C2×D191)⋊C4—21no—
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)⋊C4D411yescharacteristic
94(C2×D191)⋊C4D411yescharacteristic
95C4×Dic191—21no—
96C4×Dic191C2311yescharacteristic
97C2×Q8×C191—21no—
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
106C4⋊C4×C191C2311yescharacteristic
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191—21no—
110C22×D191—21no—
111C22×D191C2×D411yescharacteristic
112Dic382—21no—
113Dic382—21no—
114D764—21no—
115D764—21no—
116D764—21no—
117D764—21no—
118D764—21no—
119D764—21no—
120D764—81no—
121D764—81no—
122D764—81no—
123D764—81no—
124D764—81no—
125C2×Dic191—21no—
126C2×Dic191C2×D411yescharacteristic
127C2×Dic191C2×D411yescharacteristic
128C2×Dic191C2×D411yescharacteristic
129C4×D191—21no—
130C4×D191—21no—
131C4×D191—81no—
132C4×D191—81no—
133C4×D191—81no—
134C191⋊C8—21no—
135C191⋊C8—21no—
136Q8×C191—81no—
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#4112yes—
145C8×C191#4112yes—
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×C191C2×#4111yescharacteristic
166C4×C191C2×#4111yescharacteristic
167Dic191—21no—
168Dic191—21no—
169Dic191—21no—
170Dic191—41no—
171C2×C191#53211yescharacteristic
172C2×C191#57611yescharacteristic
173C2×C191#57711yescharacteristic
174D191—41no—
175D191—81no—
176D191—81no—
177D191—81no—
178C191#317911yescharacteristic, complemented, Sylow
179#3179—1911nomaximal, Sylow
180#542—1911no—
181#540—1911no—
182#501D19111yescharacteristic, complemented
183#496—1911no—
184#488—1911no—
185#486—1911no—
186#469—1911no—
187#468—1911no—
188#466—1911no—
189#465—1911no—
190#442—1911no—
191#440—1911no—
192C4×SD16—1911no—
193C4×D8—1911no—
194#405—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#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×Q8—1911no—
218C4×D4—1911no—
219C4×D4—1911no—
220C4×D4—1911no—
221#117—1911no—
222#107C2×D19111yescharacteristic
223#107C2×D19111yescharacteristic
224#106C2×D19111yescharacteristic
225#106C2×D19111yescharacteristic
226#103—1911no—
227#103—1911no—
228#102—1911no—
229#102—1911no—
230#102—1911no—
231#102—1911no—
232#102—1911no—
233#102—1911no—
234#97—1911no—
235#97C2×D19111yescharacteristic
236C4×C8—1911no—
237C4×C8—1911no—
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×D4—1911no—
248C22×C4—3821no—
249C22×C4—3821no—
250C22×C4—3821no—
251C22×C4—1911no—
252SD16—3822no—
253SD16—3822no—
254D8—3822no—
255D8—3822no—
256M16—3822no—
257C2×C8—3822no—
258C2×C8—1911no—
259C2×C8—1911no—
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⋊C4C22×D19111yescharacteristic
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—3821no—
285C42—1911no—
286C42C22×D19111yescharacteristic
287C23—3821no—
288C23—3821no—
289C23—3821no—
290C23—1911no—
291Q8—81no—
292Q8—3821no—
293Q8—3821no—
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—3821no—
322C8—3821no—
323C8#1569028812yes—
324C8#1569028812yes—
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—
348C4C2×#1569028811yescharacteristic
349C4C2×#1569028811yescharacteristic
350C2—15281no—
351C2—15281no—
352C2—15281no—
353C2—7641no—
354C2#2713321411yescharacteristic
355C2#2713346711yescharacteristic
356C2#2713347211yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#501×C191C2
socleC22×C191C22×D4
hypercenter#501D191
hypocenterC191#3179
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #27133287C2semidirect
2. #27133269C2semidirect
3. #27133052C2semidirect
4. #27133020C2semidirect
5. #27133011C2semidirect
6. #27132917C2semidirect
7. #27132910C2semidirect
8. #27132900C2semidirect
9. #27132893C2semidirect
10. #27132774C2semidirect
11. #27132762C2semidirect
12. #27132750C2semidirect
13. #27132745C2semidirect
14. #27132620C2semidirect
15. #501×C191C2semidirect
178. C191#3179semidirect
182. #501D191semidirect

Maximal subgroups

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

subgroupindex
#271332872
#271332692
#271330522
#271330202
#271330112
#271329172
#271329102
#271329002
#271328932
#271327742
#271327622
#271327502
#271327452
#271326202
#501×C1912
#3179191