Finite Group Databasebeta

← #37582499

Subgroups — #37582499

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#27133243C211yesmaximal, characteristic
2#27133144C211yesmaximal, characteristic, complemented
3#27133002C211yesmaximal, characteristic, complemented
4#27133001C211yesmaximal, characteristic, complemented
5#27132997C211yesmaximal, characteristic, complemented
6#27132990C211yesmaximal, characteristic, complemented
7#27132988C211yesmaximal, characteristic, complemented
8#27132978C211yesmaximal, characteristic, complemented
9#27132976C211yesmaximal, characteristic, complemented
10#27132704C211yesmaximal, characteristic, complemented
11#107×D191C211yesmaximal, characteristic, complemented
12#27132663C211yesmaximal, characteristic, complemented
13#27132658C211yesmaximal, characteristic, complemented
14#27132628C211yesmaximal, characteristic, complemented
15#484×C191C211yesmaximal, characteristic, complemented
16C2×#15690288C2211yescharacteristic
17C2×#15690287C2211yescharacteristic
18C2×#15690270C2211yescharacteristic
19C2×C8×D191C2211yescharacteristic
20#20259300—21no—
21#20259298C2211yescharacteristic
22#20259297—21no—
23#20259297C2211yescharacteristic
24#20259296C2211yescharacteristic
25#20259295—21no—
26#20259295—21no—
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#20259246C2211yescharacteristic
44#20259246C2211yescharacteristic
45#20259244C2211yescharacteristic
46#20259244C2211yescharacteristic
47#20259242C2211yescharacteristic
48#20259242C2211yescharacteristic
49C22⋊(C191⋊C8)C2211yescharacteristic
50(C2×D191)⋊C8C2211yescharacteristic
51(C2×D191)⋊C8C2211yescharacteristic
52C22⋊Q8×C191C2211yescharacteristic
53C2×C4⋊C4×C191C2211yescharacteristic
54#107×C191C2211yescharacteristic
55#107×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic
57#103×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic
59#15690288—22no—
60#15690288—22no—
61#15690287—22no—
62#15690287—22no—
63C2×Dic382D411yescharacteristic
64C2×D764—21no—
65C2×D764—21no—
66C2×D764D411yescharacteristic
67C2×D764C2311yescharacteristic
68C2×C22⋊D191—21no—
69C2×C22⋊D191D411yescharacteristic
70C2×C22⋊D191D411yescharacteristic
71C2×C4×D191—21no—
72C2×C4×D191—21no—
73C2×C4×D191—21no—
74C2×C4×D191—21no—
75C2×C4×D191C2311yescharacteristic
76C2×C4×D191C2311yescharacteristic
77#15690270—22no—
78C2×C191⋊C8C2311yescharacteristic
79C2×C191⋊C8C2311yescharacteristic
80C8×D191—22no—
81C4⋊Dic191C2311yescharacteristic
82C4⋊Dic191C2311yescharacteristic
83C4⋊Dic191C2311yescharacteristic
84Dic191⋊C4—21no—
85Dic191⋊C4—21no—
86Dic191⋊C4—21no—
87Dic191⋊C4—21no—
88C22⋊Dic191—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—
95C4×Dic191—21no—
96C4×Dic191—21no—
97C2×Q8×C191C2311yescharacteristic
98C22×C4×C191—21no—
99C22×C4×C191C2311yescharacteristic
100C2×C8×C191C2311yescharacteristic
101C2×C8×C191C2311yescharacteristic
102C4⋊C4×C191—21no—
103C4⋊C4×C191—21no—
104C4⋊C4×C191C2311yescharacteristic
105C4⋊C4×C191C2311yescharacteristic
106C4⋊C4×C191C2311yescharacteristic
107C22⋊C4×C191—21no—
108C22×D191—21no—
109C22×D191C2×D411yescharacteristic
110C22×D191C2×D411yescharacteristic
111Dic382—22no—
112D764—22no—
113D764—21no—
114D764—21no—
115D764—42no—
116D764—81no—
117C22⋊D191—22no—
118C22⋊D191—22no—
119C22⋊D191—81no—
120C2×Dic191—21no—
121C2×Dic191—21no—
122C2×Dic191—21no—
123C2×Dic191C2×D411yescharacteristic
124C2×Dic191C2×D411yescharacteristic
125C4×D191—21no—
126C4×D191—21no—
127C4×D191—42no—
128C4×D191—81no—
129C4×D191—81no—
130C4×D191—81no—
131C4×D191#4112yes—
132C4×D191#4112yes—
133C191⋊C8—21no—
134C191⋊C8—21no—
135C23×C191C2×D411yescharacteristic
136Q8×C191—21no—
137Q8×C191—21no—
138C2×C4×C191—21no—
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×C191C22×D411yescharacteristic
153C2×D191—21no—
154C2×D191—21no—
155C2×D191—21no—
156C2×D191—21no—
157C2×D191—21no—
158C2×D191—41no—
159C2×D191—41no—
160C2×D191—41no—
161C2×D191#12312yes—
162C4×C191—21no—
163C4×C191—41no—
164C4×C191—41no—
165C4×C191—41no—
166C4×C191—41no—
167C4×C191C2×#4111yescharacteristic
168C4×C191C2×#4111yescharacteristic
169Dic191—21no—
170Dic191—41no—
171Dic191—41no—
172Dic191—41no—
173Dic191#12312yes—
174C2×C191—41no—
175C2×C191C2×#12311yescharacteristic
176C2×C191#57611yescharacteristic
177C2×C191#57811yescharacteristic
178D191—22no—
179D191—41no—
180D191—81no—
181C191#309811yescharacteristic, complemented, Sylow
182#3098—1911nomaximal, Sylow
183#537—1911no—
184#520—1911no—
185#485—1911no—
186#485—1911no—
187#484—1911no—
188#484D19111yescharacteristic, complemented
189#482—1911no—
190#482—1911no—
191#480—1911no—
192#480—1911no—
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⋊Q8C2×D19111yescharacteristic
205#121—3821no—
206#121—3821no—
207#121—3821no—
208#121—1911no—
209#121—1911no—
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#103C2×D19111yescharacteristic
232#103C2×D19111yescharacteristic
233#102—1911no—
234#102—1911no—
235#102—1911no—
236#102—1911no—
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×Q8C22×D19111yescharacteristic
247C2×D4—3821no—
248C2×D4—3821no—
249C2×D4—3821no—
250C2×D4—1911no—
251C2×D4—1911no—
252C2×D4—1911no—
253C2×D4—1911no—
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—21no—
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—3821no—
291C23—1911no—
292C23—1911no—
293C23D4×D19111yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—3822no—
297D4—3822no—
298D4—3822no—
299D4—3822no—
300D4—3821no—
301D4—3821no—
302D4—15281no—
303D4—15281no—
304D4—7642no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
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—3821no—
335C22—3821no—
336C22—3821no—
337C22—3821no—
338C22—3821no—
339C22—1912no—
340C22—7641no—
341C22—7641no—
342C22—7641no—
343C22C2×D4×D19111yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—3821no—
350C4—1912no—
351C4—7641no—
352C4—7641no—
353C4—7641no—
354C4#41×D19111yescharacteristic
355C4#41×D19111yescharacteristic
356C2—41no—
357C2—3822no—
358C2—15281no—
359C2—7641no—
360C2#123×D19111yescharacteristic
361C2#2713346711yescharacteristic
362C2#2713347611yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#484×C191C2
socleC22×C191C22×D4
prime radical#27133243C2
hypercenter#484D191
hypocenterC191#3098
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. #27133144C2semidirect
3. #27133002C2semidirect
4. #27133001C2semidirect
5. #27132997C2semidirect
6. #27132990C2semidirect
7. #27132988C2semidirect
8. #27132978C2semidirect
9. #27132976C2semidirect
10. #27132704C2semidirect
11. #107×D191C2semidirect
12. #27132663C2semidirect
13. #27132658C2semidirect
14. #27132628C2semidirect
15. #484×C191C2semidirect
181. C191#3098semidirect
188. #484D191semidirect

Maximal subgroups

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

subgroupindex
#271332432
#271331442
#271330022
#271330012
#271329972
#271329902
#271329882
#271329782
#271329762
#271327042
#107×D1912
#271326632
#271326582
#271326282
#484×C1912
#3098191