Finite Group Databasebeta

← #37583404

Subgroups — #37583404

Order 24448.

390 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133241C211yesmaximal, characteristic
2#27133234C211yesmaximal, characteristic, complemented
3#27133005C211yesmaximal, characteristic, complemented
4#27132999C211yesmaximal, characteristic, complemented
5#27132994C211yesmaximal, characteristic, complemented
6#27132988C211yesmaximal, characteristic, complemented
7#27132921C211yesmaximal, characteristic, complemented
8#27132909C211yesmaximal, characteristic, complemented
9#27132904C211yesmaximal, characteristic, complemented
10#27132892C211yesmaximal, characteristic, complemented
11#27132827C211yesmaximal, characteristic, complemented
12#27132827C211yesmaximal, characteristic, complemented
13#27132821C211yesmaximal, characteristic, complemented
14#27132804C211yesmaximal, characteristic, complemented
15#408×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C22×Dic382C2211yescharacteristic
18C2×Dic764C2211yescharacteristic
19C2×Dic764C2211yescharacteristic
20C2×#15690276C2211yescharacteristic
21C2×#15690276C2211yescharacteristic
22#20259320—21no—
23#20259309—21no—
24#20259303—21no—
25#20259303—21no—
26#20259301C2211yescharacteristic
27#20259301C2211yescharacteristic
28#20259301C2211yescharacteristic
29#20259301C2211yescharacteristic
30#20259301C2211yescharacteristic
31#20259301C2211yescharacteristic
32#20259298—21no—
33#20259296C2211yescharacteristic
34#20259296C2211yescharacteristic
35#20259294—21no—
36#20259294—21no—
37#20259293—21no—
38#20259281C2211yescharacteristic
39C2×C4⋊Dic191C2211yescharacteristic
40#20259256C2211yescharacteristic
41#20259256C2211yescharacteristic
42#20259254C2211yescharacteristic
43#20259254C2211yescharacteristic
44#20259247C2211yescharacteristic
45#20259247C2211yescharacteristic
46#20259247C2211yescharacteristic
47#20259247C2211yescharacteristic
48#20259247C2211yescharacteristic
49#20259247C2211yescharacteristic
50#20259244C2211yescharacteristic
51#20259244C2211yescharacteristic
52C2×#41×C191C2211yescharacteristic
53C2×M16×C191C2211yescharacteristic
54C22×C8×C191C2211yescharacteristic
55C22⋊C8×C191C2211yescharacteristic
56C22⋊C8×C191C2211yescharacteristic
57C22⋊C8×C191C2211yescharacteristic
58C22⋊C8×C191C2211yescharacteristic
59#15690287—41no—
60#15690287—41no—
61C2×Dic382—21no—
62C2×Dic382—41no—
63C2×Dic382—41no—
64C2×Dic382C2311yescharacteristic
65C2×Dic382C2311yescharacteristic
66C2×Dic382C2311yescharacteristic
67C2×D764C2311yescharacteristic
68C2×C22⋊D191—21no—
69C2×C22⋊D191—21no—
70C2×C22⋊D191—21no—
71C22×Dic191—21no—
72C22×Dic191—21no—
73C2×C4×D191—21no—
74Dic764—41no—
75Dic764—41no—
76#15690276—41no—
77#15690276—41no—
78C4⋊Dic191—21no—
79C4⋊Dic191C2311yescharacteristic
80C4⋊Dic191C2311yescharacteristic
81C4⋊Dic191C2311yescharacteristic
82C4⋊Dic191C2311yescharacteristic
83Dic191⋊C4—21no—
84Dic191⋊C4—21no—
85Dic191⋊C4—21no—
86Dic191⋊C4—21no—
87Dic191⋊C4—21no—
88Dic191⋊C4—21no—
89C22⋊Dic191—21no—
90C22⋊Dic191—21no—
91C22⋊Dic191—21no—
92C22⋊Dic191—21no—
93C22⋊Dic191—21no—
94C22⋊Dic191—21no—
95C22⋊Dic191—21no—
96(C2×D191)⋊C4—21no—
97(C2×D191)⋊C4—21no—
98C4×Dic191—21no—
99#41×C191—41no—
100#41×C191—41no—
101C2×Q8×C191D411yescharacteristic
102C2×D4×C191D411yescharacteristic
103C2×D4×C191D411yescharacteristic
104C2×D4×C191D411yescharacteristic
105C22×C4×C191C2311yescharacteristic
106C22×C4×C191C2311yescharacteristic
107C22×C4×C191C2311yescharacteristic
108M16×C191—41no—
109C2×C8×C191—41no—
110C2×C8×C191C2311yescharacteristic
111C2×C8×C191C2311yescharacteristic
112C2×C8×C191C2311yescharacteristic
113C2×C8×C191C2311yescharacteristic
114C22×D191—21no—
115Dic382—21no—
116Dic382—21no—
117Dic382—21no—
118Dic382—21no—
119Dic382—21no—
120Dic382—21no—
121Dic382—42no—
122D764—21no—
123D764—21no—
124C22⋊D191—42no—
125C22⋊D191—81no—
126C22⋊D191—81no—
127C2×Dic191—21no—
128C2×Dic191—21no—
129C2×Dic191—21no—
130C2×Dic191—21no—
131C2×Dic191—21no—
132C2×Dic191—21no—
133C2×Dic191—21no—
134C2×Dic191—42no—
135C2×Dic191—81no—
136C4×D191—42no—
137C23×C191C2×D411yescharacteristic
138C23×C191C2×D411yescharacteristic
139C23×C191C2×D411yescharacteristic
140Q8×C191—41no—
141D4×C191—41no—
142D4×C191—41no—
143D4×C191—41no—
144C2×C4×C191—21no—
145C2×C4×C191—21no—
146C2×C4×C191—21no—
147C2×C4×C191—21no—
148C2×C4×C191—21no—
149C2×C4×C191—21no—
150C2×C4×C191C2×D411yescharacteristic
151C2×C4×C191C2×D411yescharacteristic
152C2×C4×C191C2×D411yescharacteristic
153C2×C4×C191C2411yescharacteristic
154C8×C191—21no—
155C8×C191—21no—
156C8×C191—21no—
157C8×C191—21no—
158C22×C191—21no—
159C22×C191—21no—
160C22×C191—21no—
161C22×C191—21no—
162C22×C191—21no—
163C22×C191—21no—
164C22×C191—21no—
165C22×C191—21no—
166C22×C191—21no—
167C22×C191C22×D411yescharacteristic
168C2×D191—41no—
169C2×D191—41no—
170C2×D191—41no—
171C4×C191—21no—
172C4×C191—21no—
173C4×C191—21no—
174C4×C191H(5,𝔽2)11yescharacteristic
175C4×C191H(5,𝔽2)11yescharacteristic
176Dic191—41no—
177Dic191—41no—
178Dic191—41no—
179Dic191—41no—
180Dic191—41no—
181Dic191—41no—
182Dic191—41no—
183C2×C191—41no—
184C2×C191—41no—
185C2×C191—41no—
186C2×C191#53411yescharacteristic
187C2×C191#57711yescharacteristic
188C2×C191#57811yescharacteristic
189D191—81no—
190C191#320111yescharacteristic, complemented, Sylow
191#3201—1911nomaximal, Sylow
192#537—1911no—
193#536—1911no—
194#485—1911no—
195#484—1911no—
196#483—1911no—
197#482—1911no—
198#470—1911no—
199#468—1911no—
200#467—1911no—
201#465—1911no—
202#452—1911no—
203#452—1911no—
204#451—1911no—
205#448—1911no—
206#408D19111yescharacteristic, complemented
207C2×#41—1911no—
208C2×#41C2×D19111yescharacteristic
209C22×Q8—1911no—
210C2×Q16—1911no—
211C2×Q16—1911no—
212C2×SD16—1911no—
213C2×SD16—1911no—
214C2×M16C2×D19111yescharacteristic
215C22×C8C2×D19111yescharacteristic
216C4⋊Q8—3821no—
217#124—3821no—
218#123—3821no—
219#123—3821no—
220C22⋊Q8—3821no—
221C22⋊Q8—1911no—
222C22⋊Q8—1911no—
223C22⋊Q8—1911no—
224C22⋊Q8—1911no—
225C22⋊Q8—1911no—
226C22⋊Q8—1911no—
227#121—3821no—
228#121—3821no—
229#121—3821no—
230#121—1911no—
231#121—1911no—
232#117—1911no—
233C2×C4⋊C4—1911no—
234#107—1911no—
235#107—1911no—
236#106—1911no—
237#106—1911no—
238#103—1911no—
239#103—1911no—
240#103—1911no—
241#103—1911no—
242#103—1911no—
243#103—1911no—
244#102—1911no—
245#102—1911no—
246C22⋊C8C2×D19111yescharacteristic
247C22⋊C8C2×D19111yescharacteristic
248C22⋊C8C2×D19111yescharacteristic
249C22⋊C8C2×D19111yescharacteristic
250#41—41no—
251#41—41no—
252#41—7641no—
253#41—7641no—
254C2×Q8—3821no—
255C2×Q8—1911no—
256C2×Q8—1911no—
257C2×Q8—1911no—
258C2×Q8—7641no—
259C2×Q8—7641no—
260C2×Q8D76411yescharacteristic
261C2×D4—3821no—
262C2×D4—3821no—
263C2×D4—3821no—
264C2×D4—1911no—
265C2×D4D76411yescharacteristic
266C2×D4D76411yescharacteristic
267C2×D4D76411yescharacteristic
268C22×C4—3821no—
269C22×C4—3821no—
270C22×C4—3821no—
271C22×C4C22×D19111yescharacteristic
272C22×C4C22×D19111yescharacteristic
273C22×C4C22×D19111yescharacteristic
274Q16—7641no—
275Q16—7641no—
276SD16—7641no—
277SD16—7641no—
278M16—41no—
279C2×C8—41no—
280C2×C8C22×D19111yescharacteristic
281C2×C8C22×D19111yescharacteristic
282C2×C8C22×D19111yescharacteristic
283C2×C8C22×D19111yescharacteristic
284C4⋊C4—3821no—
285C4⋊C4—3821no—
286C4⋊C4—3821no—
287C4⋊C4—3821no—
288C4⋊C4—3821no—
289C4⋊C4—3821no—
290C4⋊C4—3821no—
291C4⋊C4—1911no—
292C4⋊C4—1911no—
293C4⋊C4—1911no—
294C4⋊C4—1911no—
295C22⋊C4—3821no—
296C22⋊C4—3821no—
297C22⋊C4—3821no—
298C22⋊C4—3821no—
299C22⋊C4—3821no—
300C22⋊C4—3821no—
301C22⋊C4—3821no—
302C22⋊C4—3821no—
303C22⋊C4—3821no—
304C42—3821no—
305C23—3821no—
306C23C2×D76411yescharacteristic
307C23C2×D76411yescharacteristic
308C23C2×D76411yescharacteristic
309Q8—41no—
310Q8—3821no—
311Q8—3821no—
312Q8—3821no—
313Q8—3821no—
314Q8—3821no—
315Q8—3821no—
316Q8—7642no—
317D4—41no—
318D4—41no—
319D4—41no—
320D4—3821no—
321D4—3821no—
322D4—15281no—
323D4—15281no—
324D4—7642no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—3821no—
332C2×C4—3821no—
333C2×C4—3821no—
334C2×C4—3821no—
335C2×C4—3821no—
336C2×C4—3821no—
337C2×C4—3821no—
338C2×C4—15281no—
339C2×C4—7642no—
340C2×C4—7642no—
341C2×C4C2×D76411yescharacteristic
342C2×C4C2×D76411yescharacteristic
343C2×C4C2×D76411yescharacteristic
344C2×C4C23×D19111yescharacteristic
345C8—21no—
346C8—21no—
347C8—21no—
348C8—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—7641no—
359C22—7641no—
360C22—7641no—
361C22C22×D76411yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—7641no—
366C4—7641no—
367C4—7641no—
368C4—7641no—
369C4—7641no—
370C4—7641no—
371C4—7641no—
372C4#2025936711yescharacteristic
373C4#2025936711yescharacteristic
374C2—41no—
375C2—41no—
376C2—41no—
377C2—15281no—
378C2#2713322511yescharacteristic
379C2#2713347511yescharacteristic
380C2#2713348011yescharacteristic
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#408×C191C2
socleC22×C191C22×D4
prime radical#27133241C2
hypercenter#408D191
hypocenterC191#3201
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
2. #27133234C2semidirect
3. #27133005C2semidirect
4. #27132999C2semidirect
5. #27132994C2semidirect
6. #27132988C2semidirect
7. #27132921C2semidirect
8. #27132909C2semidirect
9. #27132904C2semidirect
10. #27132892C2semidirect
11. #27132827C2semidirect
12. #27132827C2semidirect
13. #27132821C2semidirect
14. #27132804C2semidirect
15. #408×C191C2semidirect
190. C191#3201semidirect
206. #408D191semidirect

Maximal subgroups

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

subgroupindex
#271332412
#271332342
#271330052
#271329992
#271329942
#271329882
#271329212
#271329092
#271329042
#271328922
#271328272
#271328212
#271328042
#408×C1912
#3201191