Finite Group Databasebeta

← #37583925

Subgroups — #37583925

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#27132967C211yesmaximal, characteristic, complemented
3#27132960C211yesmaximal, characteristic, complemented
4#27132953C211yesmaximal, characteristic, complemented
5#27132943C211yesmaximal, characteristic, complemented
6#27132914C211yesmaximal, characteristic, complemented
7#27132907C211yesmaximal, characteristic, complemented
8#27132897C211yesmaximal, characteristic, complemented
9#27132890C211yesmaximal, characteristic, complemented
10#27132878C211yesmaximal, characteristic, complemented
11#27132878C211yesmaximal, characteristic, complemented
12#27132860C211yesmaximal, characteristic, complemented
13#27132855C211yesmaximal, characteristic, complemented
14#27132690C211yesmaximal, characteristic, complemented
15#540×C191C211yesmaximal, characteristic, complemented
16C2×#15690275C2211yescharacteristic
17C2×#15690275C2211yescharacteristic
18C2×#15690272C2211yescharacteristic
19C2×#15690272C2211yescharacteristic
20C2×#15690271C2211yescharacteristic
21C22×C191⋊C8C2211yescharacteristic
22#20259322C2211yescharacteristic
23#20259317—21no—
24#20259310C2211yescharacteristic
25#20259308—21no—
26#20259304—21no—
27#20259301C2211yescharacteristic
28#20259300—21no—
29#20259296C2211yescharacteristic
30C4×Dic382C2211yescharacteristic
31C4×D764C2211yescharacteristic
32#20259255C2211yescharacteristic
33#20259255C2211yescharacteristic
34#20259253C2211yescharacteristic
35#20259253C2211yescharacteristic
36C4⋊(C191⋊C8)C2211yescharacteristic
37C4⋊(C191⋊C8)C2211yescharacteristic
38C4⋊(C191⋊C8)C2211yescharacteristic
39C4⋊(C191⋊C8)C2211yescharacteristic
40#20259245C2211yescharacteristic
41#20259245C2211yescharacteristic
42#20259243C2211yescharacteristic
43#20259243C2211yescharacteristic
44#20259243C2211yescharacteristic
45#20259243C2211yescharacteristic
46#20259242C2211yescharacteristic
47#20259242C2211yescharacteristic
48#127×C191C2211yescharacteristic
49#125×C191C2211yescharacteristic
50#123×C191—21no—
51#123×C191—21no—
52#121×C191—21no—
53#121×C191—21no—
54#121×C191C2211yescharacteristic
55#121×C191C2211yescharacteristic
56C4×D4×C191C2211yescharacteristic
57C4×D4×C191C2211yescharacteristic
58#117×C191C2211yescharacteristic
59C2×Dic382—21no—
60C2×Dic382C2311yescharacteristic
61C2×D764C2311yescharacteristic
62C2×C22⋊D191—21no—
63C2×C4×D191—21no—
64#15690275—41no—
65#15690275—41no—
66#15690272—41no—
67#15690272—41no—
68#15690271—41no—
69C2×C191⋊C8—41no—
70C2×C191⋊C8C2311yescharacteristic
71C2×C191⋊C8C2311yescharacteristic
72C2×C191⋊C8C2311yescharacteristic
73C2×C191⋊C8C2311yescharacteristic
74C4⋊Dic191—21no—
75C4⋊Dic191C2311yescharacteristic
76C4⋊Dic191C2311yescharacteristic
77Dic191⋊C4—21no—
78Dic191⋊C4—21no—
79C22⋊Dic191—21no—
80(C2×D191)⋊C4—21no—
81(C2×D191)⋊C4—21no—
82(C2×D191)⋊C4—21no—
83(C2×D191)⋊C4—21no—
84C4×Dic191—21no—
85C2×D4×C191—21no—
86C2×D4×C191—21no—
87C2×D4×C191—21no—
88C2×D4×C191—21no—
89C2×D4×C191C2311yescharacteristic
90C2×D4×C191C2311yescharacteristic
91C22×C4×C191—21no—
92C22×C4×C191—21no—
93C22×C4×C191C2311yescharacteristic
94C4⋊C4×C191—21no—
95C4⋊C4×C191—21no—
96C4⋊C4×C191D411yescharacteristic
97C4⋊C4×C191D411yescharacteristic
98C4⋊C4×C191C2311yescharacteristic
99C4⋊C4×C191C2311yescharacteristic
100C22⋊C4×C191—21no—
101C22⋊C4×C191—21no—
102C22⋊C4×C191—21no—
103C22⋊C4×C191—21no—
104C22⋊C4×C191D411yescharacteristic
105C22⋊C4×C191D411yescharacteristic
106C42×C191C2311yescharacteristic
107C42×C191C2311yescharacteristic
108C22×D191—21no—
109Dic382—21no—
110Dic382—21no—
111Dic382—81no—
112D764—21no—
113D764—21no—
114C22⋊D191—81no—
115C2×Dic191—21no—
116C2×Dic191—21no—
117C2×Dic191—21no—
118C4×D191—81no—
119C191⋊C8—21no—
120C191⋊C8—21no—
121C191⋊C8—21no—
122C191⋊C8—21no—
123C23×C191—21no—
124C23×C191—21no—
125C23×C191C2×D411yescharacteristic
126D4×C191—21no—
127D4×C191—21no—
128D4×C191—21no—
129D4×C191—21no—
130D4×C191—81no—
131D4×C191—81no—
132D4×C191—81no—
133D4×C191—81no—
134C2×C4×C191—21no—
135C2×C4×C191—21no—
136C2×C4×C191—21no—
137C2×C4×C191—21no—
138C2×C4×C191—81no—
139C2×C4×C191—81no—
140C2×C4×C191C2×D411yescharacteristic
141C2×C4×C191C2×D411yescharacteristic
142C2×C4×C191C2×D411yescharacteristic
143C2×C4×C191C2×D411yescharacteristic
144C2×C4×C191C2×D411yescharacteristic
145C2×C4×C191C2411yescharacteristic
146C22×C191—21no—
147C22×C191—21no—
148C22×C191—21no—
149C22×C191—41no—
150C22×C191—41no—
151C22×C191—41no—
152C22×C191—41no—
153C22×C191—41no—
154C22×C191—41no—
155C22×C191C22×D411yescharacteristic
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×C191—41no—
165C4×C191—41no—
166C4×C191H(5,𝔽2)11yescharacteristic
167C4×C1912−1+411yescharacteristic
168Dic191—41no—
169Dic191—41no—
170Dic191—41no—
171C2×C191—41no—
172C2×C191—81no—
173C2×C191—81no—
174C2×C191#53711yescharacteristic
175C2×C191#57611yescharacteristic
176C2×C191#57711yescharacteristic
177D191—81no—
178C191#325711yescharacteristic, complemented, Sylow
179#3257—1911nomaximal, Sylow
180#542—1911no—
181#540D19111yescharacteristic, complemented
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#424—1911no—
195C2×SD16—1911no—
196C2×SD16—1911no—
197C2×D8—1911no—
198C2×D8—1911no—
199C2×M16—1911no—
200C22×C8—1911no—
201C4⋊Q8—1911no—
202#127C2×D19111yescharacteristic
203#126—3821no—
204#125C2×D19111yescharacteristic
205#124—3821no—
206#124—1911no—
207#123—21no—
208#123—21no—
209#123—3821no—
210C22⋊Q8—3821no—
211C22⋊Q8—1911no—
212#121—21no—
213#121—21no—
214#121—1911no—
215#121C2×D19111yescharacteristic
216#121C2×D19111yescharacteristic
217C4×Q8—1911no—
218C4×D4—1911no—
219C4×D4C2×D19111yescharacteristic
220C4×D4C2×D19111yescharacteristic
221#117C2×D19111yescharacteristic
222#107—1911no—
223#107—1911no—
224#106—1911no—
225#106—1911no—
226C4⋊C8—1911no—
227C4⋊C8—1911no—
228C4⋊C8—1911no—
229C4⋊C8—1911no—
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—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—3821no—
245C2×D4—1911no—
246C2×D4C22×D19111yescharacteristic
247C2×D4C22×D19111yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—3821no—
251C22×C4C22×D19111yescharacteristic
252SD16—7641no—
253SD16—7641no—
254D8—7641no—
255D8—7641no—
256M16—7641no—
257C2×C8—1911no—
258C2×C8—1911no—
259C2×C8—1911no—
260C2×C8—1911no—
261C2×C8—7641no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—3821no—
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—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—3821no—
278C22⋊C4—3821no—
279C22⋊C4—3821no—
280C22⋊C4—3821no—
281C22⋊C4—3821no—
282C22⋊C4C22⋊D19111yescharacteristic
283C22⋊C4C22⋊D19111yescharacteristic
284C42—3821no—
285C42C22×D19111yescharacteristic
286C42C22×D19111yescharacteristic
287C23—21no—
288C23—21no—
289C23—3821no—
290C23C2×C22⋊D19111yescharacteristic
291Q8—3821no—
292Q8—3821no—
293Q8—15281no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—81no—
299D4—81no—
300D4—81no—
301D4—81no—
302D4—3821no—
303D4—3821no—
304D4—15281no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—3821no—
312C2×C4—3821no—
313C2×C4—3821no—
314C2×C4—15281no—
315C2×C4C2×C22⋊D19111yescharacteristic
316C2×C4C2×C22⋊D19111yescharacteristic
317C2×C4C2×C22⋊D19111yescharacteristic
318C2×C4C2×C22⋊D19111yescharacteristic
319C2×C4C2×C22⋊D19111yescharacteristic
320C2×C4C23×D19111yescharacteristic
321C8—3821no—
322C8—3821no—
323C8—3821no—
324C8—3821no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—7641no—
335C22—7641no—
336C22—7641no—
337C22C22×C22⋊D19111yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—7641no—
346C4—7641no—
347C4—7641no—
348C4#2025936811yescharacteristic
349C4#2025936911yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—15281no—
354C2#2713324111yescharacteristic
355C2#2713346611yescharacteristic
356C2#2713347411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#540×C191C2
socleC22×C191C22×D4
hypercenter#540D191
hypocenterC191#3257
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #27133284C2semidirect
2. #27132967C2semidirect
3. #27132960C2semidirect
4. #27132953C2semidirect
5. #27132943C2semidirect
6. #27132914C2semidirect
7. #27132907C2semidirect
8. #27132897C2semidirect
9. #27132890C2semidirect
10. #27132878C2semidirect
11. #27132878C2semidirect
12. #27132860C2semidirect
13. #27132855C2semidirect
14. #27132690C2semidirect
15. #540×C191C2semidirect
178. C191#3257semidirect
181. #540D191semidirect

Maximal subgroups

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

subgroupindex
#271332842
#271329672
#271329602
#271329532
#271329432
#271329142
#271329072
#271328972
#271328902
#271328782
#271328602
#271328552
#271326902
#540×C1912
#3257191