Finite Group Databasebeta

← #37583933

Subgroups — #37583933

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#27133284C211yesmaximal, characteristic, complemented
2#27133268C211yesmaximal, characteristic, complemented
3#27132971C211yesmaximal, characteristic, complemented
4#27132964C211yesmaximal, characteristic, complemented
5#27132954C211yesmaximal, characteristic, complemented
6#27132944C211yesmaximal, characteristic, complemented
7#27132916C211yesmaximal, characteristic, complemented
8#27132909C211yesmaximal, characteristic, complemented
9#27132899C211yesmaximal, characteristic, complemented
10#27132892C211yesmaximal, characteristic, complemented
11#27132879C211yesmaximal, characteristic, complemented
12#27132879C211yesmaximal, characteristic, complemented
13#27132864C211yesmaximal, characteristic, complemented
14#27132859C211yesmaximal, characteristic, complemented
15#424×C191C211yesmaximal, characteristic, complemented
16C2×#15690276C2211yescharacteristic
17C2×#15690276C2211yescharacteristic
18C2×D1528C2211yescharacteristic
19C2×D1528C2211yescharacteristic
20#20259322C2211yescharacteristic
21#20259319C2211yescharacteristic
22#20259317—21no—
23#20259314C2211yescharacteristic
24#20259310C2211yescharacteristic
25#20259308—21no—
26#20259307—21no—
27#20259307—21no—
28#20259304—21no—
29#20259301C2211yescharacteristic
30#20259300—21no—
31#20259296C2211yescharacteristic
32#20259296C2211yescharacteristic
33#20259296C2211yescharacteristic
34#20259295—21no—
35#20259295—21no—
36C4×Dic382C2211yescharacteristic
37C4×D764C2211yescharacteristic
38C4×D764C2211yescharacteristic
39C4×D764C2211yescharacteristic
40#20259256C2211yescharacteristic
41#20259256C2211yescharacteristic
42#20259254C2211yescharacteristic
43#20259254C2211yescharacteristic
44#20259247C2211yescharacteristic
45#20259247C2211yescharacteristic
46#20259244C2211yescharacteristic
47#20259244C2211yescharacteristic
48#20259244C2211yescharacteristic
49#20259244C2211yescharacteristic
50#20259244C2211yescharacteristic
51#20259244C2211yescharacteristic
52C2×M16×C191C2211yescharacteristic
53C22×C8×C191C2211yescharacteristic
54#117×C191C2211yescharacteristic
55C4⋊C8×C191C2211yescharacteristic
56C4⋊C8×C191C2211yescharacteristic
57C4⋊C8×C191C2211yescharacteristic
58C4⋊C8×C191C2211yescharacteristic
59C2×Dic382—21no—
60C2×Dic382C2311yescharacteristic
61C2×D764—21no—
62C2×D764—21no—
63C2×D764C2311yescharacteristic
64C2×D764C2311yescharacteristic
65C2×D764C2311yescharacteristic
66C2×C22⋊D191—21no—
67C2×C22⋊D191—21no—
68C2×C22⋊D191—21no—
69C2×C4×D191—21no—
70C2×C4×D191—21no—
71C2×C4×D191—21no—
72#15690276—41no—
73#15690276—41no—
74D1528—41no—
75D1528—41no—
76C4⋊Dic191—21no—
77C4⋊Dic191C2311yescharacteristic
78C4⋊Dic191C2311yescharacteristic
79C4⋊Dic191C2311yescharacteristic
80C4⋊Dic191C2311yescharacteristic
81Dic191⋊C4—21no—
82Dic191⋊C4—21no—
83Dic191⋊C4—21no—
84Dic191⋊C4—21no—
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)⋊C4—21no—
94C4×Dic191—21no—
95C22×C4×C191C2311yescharacteristic
96M16×C191—41no—
97C2×C8×C191—41no—
98C2×C8×C191C2311yescharacteristic
99C2×C8×C191C2311yescharacteristic
100C2×C8×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C4⋊C4×C191D411yescharacteristic
103C4⋊C4×C191D411yescharacteristic
104C22⋊C4×C191D411yescharacteristic
105C22⋊C4×C191D411yescharacteristic
106C42×C191C2311yescharacteristic
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109C22×D191—21no—
110C22×D191—21no—
111Dic382—21no—
112Dic382—21no—
113Dic382—81no—
114D764—21no—
115D764—21no—
116D764—21no—
117D764—21no—
118D764—21no—
119D764—21no—
120D764—81no—
121D764—81no—
122C22⋊D191—81no—
123C22⋊D191—81no—
124C22⋊D191—81no—
125C2×Dic191—21no—
126C2×Dic191—21no—
127C2×Dic191—21no—
128C2×Dic191—21no—
129C2×Dic191—21no—
130C4×D191—81no—
131C4×D191—81no—
132C4×D191—81no—
133C23×C191C2×D411yescharacteristic
134C2×C4×C191—21no—
135C2×C4×C191—21no—
136C2×C4×C191C2×D411yescharacteristic
137C2×C4×C191C2×D411yescharacteristic
138C2×C4×C191C2×D411yescharacteristic
139C2×C4×C191C2×D411yescharacteristic
140C2×C4×C191C2×D411yescharacteristic
141C2×C4×C191C2411yescharacteristic
142C8×C191—21no—
143C8×C191—21no—
144C8×C191—21no—
145C8×C191—21no—
146C22×C191—21no—
147C22×C191—21no—
148C22×C191—21no—
149C22×C191C22×D411yescharacteristic
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—21no—
162C4×C191—21no—
163C4×C191—21no—
164C4×C191H(5,𝔽2)11yescharacteristic
165C4×C1912−1+411yescharacteristic
166Dic191—41no—
167Dic191—41no—
168Dic191—41no—
169Dic191—41no—
170Dic191—41no—
171C2×C191—41no—
172C2×C191#53711yescharacteristic
173C2×C191#57611yescharacteristic
174C2×C191#57711yescharacteristic
175D191—81no—
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#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#424D19111yescharacteristic, complemented
195C2×SD16—1911no—
196C2×SD16—1911no—
197C2×D8—1911no—
198C2×D8—1911no—
199C2×M16C2×D19111yescharacteristic
200C22×C8C2×D19111yescharacteristic
201C4⋊Q8—1911no—
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×D4—1911no—
221#117C2×D19111yescharacteristic
222#107—1911no—
223#107—1911no—
224#106—1911no—
225#106—1911no—
226C4⋊C8C2×D19111yescharacteristic
227C4⋊C8C2×D19111yescharacteristic
228C4⋊C8C2×D19111yescharacteristic
229C4⋊C8C2×D19111yescharacteristic
230#103—1911no—
231#103—1911no—
232#102—1911no—
233#102—1911no—
234#102—1911no—
235#102—1911no—
236#102—1911no—
237#102—1911no—
238C2×Q8—3821no—
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×C4C22×D19111yescharacteristic
252SD16—7641no—
253SD16—7641no—
254D8—7641no—
255D8—7641no—
256M16—41no—
257C2×C8—41no—
258C2×C8C22×D19111yescharacteristic
259C2×C8C22×D19111yescharacteristic
260C2×C8C22×D19111yescharacteristic
261C2×C8C22×D19111yescharacteristic
262C4⋊C4—3821no—
263C4⋊C4—3821no—
264C4⋊C4—3821no—
265C4⋊C4—3821no—
266C4⋊C4—3821no—
267C4⋊C4—1911no—
268C4⋊C4—1911no—
269C4⋊C4—1911no—
270C4⋊C4—1911no—
271C4⋊C4D76411yescharacteristic
272C4⋊C4D76411yescharacteristic
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⋊C4D76411yescharacteristic
283C22⋊C4D76411yescharacteristic
284C42—3821no—
285C42C22×D19111yescharacteristic
286C42C22×D19111yescharacteristic
287C23—3821no—
288C23—3821no—
289C23—3821no—
290C23C2×D76411yescharacteristic
291Q8—3821no—
292Q8—3821no—
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—3821no—
308C2×C4—3821no—
309C2×C4—3821no—
310C2×C4—3821no—
311C2×C4—3821no—
312C2×C4—15281no—
313C2×C4—15281no—
314C2×C4—15281no—
315C2×C4C2×D76411yescharacteristic
316C2×C4C2×D76411yescharacteristic
317C2×C4C2×D76411yescharacteristic
318C2×C4C2×D76411yescharacteristic
319C2×C4C2×D76411yescharacteristic
320C2×C4C23×D19111yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—7641no—
329C22—7641no—
330C22—7641no—
331C22—7641no—
332C22—7641no—
333C22—7641no—
334C22—7641no—
335C22—7641no—
336C22—7641no—
337C22C22×D76411yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—7641no—
344C4—7641no—
345C4—7641no—
346C4—7641no—
347C4—7641no—
348C4#2025936711yescharacteristic
349C4#2025937011yescharacteristic
350C2—41no—
351C2—15281no—
352C2—15281no—
353C2—15281no—
354C2#2713324411yescharacteristic
355C2#2713346811yescharacteristic
356C2#2713347511yescharacteristic
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#424×C191C2
socleC22×C191C22×D4
hypercenter#424D191
hypocenterC191#3257
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #27133284C2semidirect
2. #27133268C2semidirect
3. #27132971C2semidirect
4. #27132964C2semidirect
5. #27132954C2semidirect
6. #27132944C2semidirect
7. #27132916C2semidirect
8. #27132909C2semidirect
9. #27132899C2semidirect
10. #27132892C2semidirect
11. #27132879C2semidirect
12. #27132879C2semidirect
13. #27132864C2semidirect
14. #27132859C2semidirect
15. #424×C191C2semidirect
178. C191#3257semidirect
194. #424D191semidirect

Maximal subgroups

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

subgroupindex
#271332842
#271332682
#271329712
#271329642
#271329542
#271329442
#271329162
#271329092
#271328992
#271328922
#271328792
#271328642
#271328592
#424×C1912
#3257191