Finite Group Databasebeta

← #37582493

Subgroups — #37582493

Order 24448.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133242C211yesmaximal, characteristic
2#27133144C211yesmaximal, characteristic, complemented
3#27133006C211yesmaximal, characteristic, complemented
4#27133005C211yesmaximal, characteristic, complemented
5#27133000C211yesmaximal, characteristic, complemented
6#27132998C211yesmaximal, characteristic, complemented
7#27132986C211yesmaximal, characteristic, complemented
8#27132984C211yesmaximal, characteristic, complemented
9#27132975C211yesmaximal, characteristic, complemented
10#27132704C211yesmaximal, characteristic, complemented
11#107×D191C211yesmaximal, characteristic, complemented
12#27132661C211yesmaximal, characteristic, complemented
13#27132656C211yesmaximal, characteristic, complemented
14#27132628C211yesmaximal, characteristic, complemented
15#480×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×#15690286C2211yescharacteristic
18C2×#15690270C2211yescharacteristic
19C2×C8×D191C2211yescharacteristic
20#20259302C2211yescharacteristic
21#20259301C2211yescharacteristic
22#20259299—21no—
23#20259295—21no—
24#20259294—21no—
25#20259293—21no—
26#20259293C2211yescharacteristic
27#20259287—21no—
28#20259284—21no—
29C4×C22⋊D191—21no—
30C4×C22⋊D191—21no—
31#20259281C2211yescharacteristic
32#20259280C2211yescharacteristic
33#20259280C2211yescharacteristic
34C4⋊C4×D191C2211yescharacteristic
35C4⋊C4×D191C2211yescharacteristic
36C4⋊C4×D191C2211yescharacteristic
37#20259256C2211yescharacteristic
38#20259255C2211yescharacteristic
39#20259255C2211yescharacteristic
40#20259255C2211yescharacteristic
41#20259254C2211yescharacteristic
42#20259253C2211yescharacteristic
43#20259247C2211yescharacteristic
44#20259247C2211yescharacteristic
45#20259245C2211yescharacteristic
46#20259245C2211yescharacteristic
47#20259243C2211yescharacteristic
48#20259243C2211yescharacteristic
49C22⋊(C191⋊C8)C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51(C2×D191)⋊C8C2211yescharacteristic
52#121×C191C2211yescharacteristic
53C2×C4⋊C4×C191C2211yescharacteristic
54#107×C191C2211yescharacteristic
55#107×C191C2211yescharacteristic
56#102×C191C2211yescharacteristic
57#102×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic
59#15690287—22no—
60#15690287—22no—
61#15690286—22no—
62#15690286—22no—
63C2×Dic382D411yescharacteristic
64C2×Dic382C2311yescharacteristic
65C2×D764D411yescharacteristic
66C2×C22⋊D191—21no—
67C2×C22⋊D191—21no—
68C2×C22⋊D191D411yescharacteristic
69C2×C22⋊D191D411yescharacteristic
70C22×Dic191—21no—
71C2×C4×D191—21no—
72C2×C4×D191—21no—
73C2×C4×D191—21no—
74C2×C4×D191C2311yescharacteristic
75C2×C4×D191C2311yescharacteristic
76#15690270—22no—
77C2×C191⋊C8C2311yescharacteristic
78C2×C191⋊C8C2311yescharacteristic
79C8×D191—22no—
80C4⋊Dic191—21no—
81C4⋊Dic191C2311yescharacteristic
82C4⋊Dic191C2311yescharacteristic
83C4⋊Dic191C2311yescharacteristic
84Dic191⋊C4—21no—
85Dic191⋊C4—21no—
86Dic191⋊C4—21no—
87Dic191⋊C4—21no—
88C22⋊Dic191—21no—
89C22⋊Dic191—21no—
90C22⋊Dic191—21no—
91(C2×D191)⋊C4—21no—
92(C2×D191)⋊C4—21no—
93(C2×D191)⋊C4—21no—
94C4×Dic191—21no—
95C4×Dic191—21no—
96C4×Dic191—21no—
97C2×D4×C191—21no—
98C2×D4×C191C2311yescharacteristic
99C22×C4×C191—21no—
100C22×C4×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C2×C8×C191C2311yescharacteristic
103C4⋊C4×C191—21no—
104C4⋊C4×C191C2311yescharacteristic
105C4⋊C4×C191C2311yescharacteristic
106C4⋊C4×C191C2311yescharacteristic
107C22⋊C4×C191—21no—
108C22×D191C2×D411yescharacteristic
109C22×D191C2×D411yescharacteristic
110Dic382—22no—
111Dic382—21no—
112Dic382—21no—
113D764—22no—
114C22⋊D191—22no—
115C22⋊D191—22no—
116C22⋊D191—42no—
117C22⋊D191—81no—
118C2×Dic191—21no—
119C2×Dic191—21no—
120C2×Dic191—21no—
121C2×Dic191—21no—
122C2×Dic191—42no—
123C2×Dic191C2×D411yescharacteristic
124C2×Dic191C2×D411yescharacteristic
125C4×D191—21no—
126C4×D191—21no—
127C4×D191—81no—
128C4×D191—81no—
129C4×D191—81no—
130C4×D191#4112yes—
131C4×D191#4112yes—
132C191⋊C8—21no—
133C191⋊C8—21no—
134C23×C191—21no—
135C23×C191C2×D411yescharacteristic
136D4×C191—21no—
137D4×C191—21no—
138D4×C191—81no—
139C2×C4×C191—21no—
140C2×C4×C191—21no—
141C2×C4×C191—21no—
142C2×C4×C191—21no—
143C2×C4×C191—21no—
144C2×C4×C191—81no—
145C2×C4×C191C2×D411yescharacteristic
146C2×C4×C191C2411yescharacteristic
147C8×C191—21no—
148C8×C191—21no—
149C22×C191—21no—
150C22×C191—21no—
151C22×C191—21no—
152C22×C191—41no—
153C22×C191—41no—
154C22×C191—41no—
155C22×C191C22×D411yescharacteristic
156C2×D191—21no—
157C2×D191—21no—
158C2×D191—21no—
159C2×D191—21no—
160C2×D191—21no—
161C2×D191#12312yes—
162C4×C191—21no—
163C4×C191—41no—
164C4×C191—41no—
165C4×C191—41no—
166C4×C191C2×#4111yescharacteristic
167C4×C191C2×#4111yescharacteristic
168Dic191—21no—
169Dic191—41no—
170Dic191—41no—
171Dic191—41no—
172Dic191—41no—
173Dic191#12312yes—
174C2×C191—41no—
175C2×C191—81no—
176C2×C191C2×#12311yescharacteristic
177C2×C191#57611yescharacteristic
178C2×C191#57811yescharacteristic
179D191—22no—
180D191—41no—
181C191#309811yescharacteristic, complemented, Sylow
182#3098—1911nomaximal, Sylow
183#537—1911no—
184#520—1911no—
185#485—1911no—
186#485—1911no—
187#484—1911no—
188#484—1911no—
189#482—1911no—
190#482—1911no—
191#480—1911no—
192#480D19111yescharacteristic, complemented
193#428—1911no—
194C2×#107—1911no—
195#417—1911no—
196#416—1911no—
197#408—1911no—
198C2×#41—1911no—
199C2×#41—1911no—
200C2×M16—1911no—
201C22×C8—1911no—
202C22⋊Q8—3821no—
203C22⋊Q8—1911no—
204C22⋊Q8—1911no—
205#121—3821no—
206#121—3821no—
207#121—3821no—
208#121—1911no—
209#121C2×D19111yescharacteristic
210C4×Q8—3821no—
211C4×D4—3821no—
212C4×D4—3821no—
213C4×D4—3821no—
214#117—1911no—
215#117—1911no—
216#117—1911no—
217C2×C4⋊C4—1911no—
218C2×C4⋊C4—1911no—
219C2×C4⋊C4—1911no—
220C2×C4⋊C4C2×D19111yescharacteristic
221#107—1911no—
222#107—1911no—
223#107—1911no—
224#107—1911no—
225#107C2×D19111yescharacteristic
226#107C2×D19111yescharacteristic
227#106—1911no—
228#106—1911no—
229#103—1911no—
230#103—1911no—
231#103—1911no—
232#103—1911no—
233#102—1911no—
234#102—1911no—
235#102C2×D19111yescharacteristic
236#102C2×D19111yescharacteristic
237C22⋊C8—1911no—
238C22⋊C8—1911no—
239C22⋊C8—1911no—
240C22⋊C8C2×D19111yescharacteristic
241#41—3822no—
242#41—3822no—
243#41—3822no—
244#41—3822no—
245C2×Q8—1911no—
246C2×Q8—1911no—
247C2×D4—21no—
248C2×D4—3821no—
249C2×D4—3821no—
250C2×D4—1911no—
251C2×D4—1911no—
252C2×D4—1911no—
253C2×D4C22×D19111yescharacteristic
254C22×C4—21no—
255C22×C4—3821no—
256C22×C4—3821no—
257C22×C4—3821no—
258C22×C4—3821no—
259C22×C4—1911no—
260C22×C4—1911no—
261C22×C4C22×D19111yescharacteristic
262M16—3822no—
263C2×C8—3822no—
264C2×C8—1911no—
265C2×C8—1911no—
266C2×C8C22×D19111yescharacteristic
267C2×C8C22×D19111yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—3821no—
270C4⋊C4—3821no—
271C4⋊C4—3821no—
272C4⋊C4—3821no—
273C4⋊C4—3821no—
274C4⋊C4—1911no—
275C4⋊C4—1911no—
276C4⋊C4—1911no—
277C4⋊C4C22×D19111yescharacteristic
278C4⋊C4C22×D19111yescharacteristic
279C4⋊C4C22×D19111yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—3821no—
282C22⋊C4—3821no—
283C22⋊C4—3821no—
284C22⋊C4—3821no—
285C22⋊C4—3821no—
286C22⋊C4—3821no—
287C42—3821no—
288C42—3821no—
289C42—3821no—
290C23—21no—
291C23—1911no—
292C23—1911no—
293C23D4×D19111yescharacteristic
294Q8—3822no—
295Q8—3821no—
296Q8—3821no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—3822no—
301D4—3822no—
302D4—3822no—
303D4—15281no—
304D4—7642no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—3821no—
312C2×C4—3821no—
313C2×C4—3821no—
314C2×C4—3821no—
315C2×C4—3821no—
316C2×C4—3821no—
317C2×C4—1911no—
318C2×C4—1911no—
319C2×C4—1912no—
320C2×C4—1912no—
321C2×C4—15281no—
322C2×C4—15281no—
323C2×C4—15281no—
324C2×C4—7642no—
325C2×C4D4×D19111yescharacteristic
326C2×C4C23×D19111yescharacteristic
327C8—21no—
328C8—21no—
329C8—3821no—
330C8—3821no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—3821no—
338C22—3821no—
339C22—3821no—
340C22—3821no—
341C22—3821no—
342C22—1912no—
343C22C2×D4×D19111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—3821no—
349C4—1912no—
350C4—7641no—
351C4—7641no—
352C4—7641no—
353C4—7641no—
354C4#41×D19111yescharacteristic
355C4#41×D19111yescharacteristic
356C2—41no—
357C2—81no—
358C2—3822no—
359C2—7641no—
360C2#123×D19111yescharacteristic
361C2#2713346411yescharacteristic
362C2#2713347911yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#480×C191C2
socleC22×C191C22×D4
prime radical#27133242C2
hypercenter#480D191
hypocenterC191#3098
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. #27133144C2semidirect
3. #27133006C2semidirect
4. #27133005C2semidirect
5. #27133000C2semidirect
6. #27132998C2semidirect
7. #27132986C2semidirect
8. #27132984C2semidirect
9. #27132975C2semidirect
10. #27132704C2semidirect
11. #107×D191C2semidirect
12. #27132661C2semidirect
13. #27132656C2semidirect
14. #27132628C2semidirect
15. #480×C191C2semidirect
181. C191#3098semidirect
192. #480D191semidirect

Maximal subgroups

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

subgroupindex
#271332422
#271331442
#271330062
#271330052
#271330002
#271329982
#271329862
#271329842
#271329752
#271327042
#107×D1912
#271326612
#271326562
#271326282
#480×C1912
#3098191