Finite Group Databasebeta

← #37584050

Subgroups — #37584050

Order 24448.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259350C211yesmaximal, characteristic, complemented
2C2×#20259344C211yesmaximal, characteristic, complemented
3#27133318C211yesmaximal, characteristic, complemented
4#27133309C211yesmaximal, characteristic, complemented
5#27133057C211yesmaximal, characteristic, complemented
6#27132921C211yesmaximal, characteristic, complemented
7#27132892C211yesmaximal, characteristic, complemented
8#27132879C211yesmaximal, characteristic, complemented
9#27132869C211yesmaximal, characteristic, complemented
10#27132827C211yesmaximal, characteristic, complemented
11#27132827C211yesmaximal, characteristic, complemented
12#27132816C211yesmaximal, characteristic, complemented
13#27132810C211yesmaximal, characteristic, complemented
14#27132776C211yesmaximal, characteristic, complemented
15#435×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic
17C2×#15690287C2211yescharacteristic
18C2×#15690287C2211yescharacteristic, complemented
19C22×D764C2211yescharacteristic
20#20259350—24no—
21#20259344—24no—
22C2×Dic764C2211yescharacteristic, complemented
23C2×Dic764C2211yescharacteristic, complemented
24C2×#15690276C2211yescharacteristic
25C2×#15690276C2211yescharacteristic
26C2×#15690276C2211yescharacteristic
27C2×#15690276C2211yescharacteristic
28C2×#15690276C2211yescharacteristic, complemented
29C2×D1528C2211yescharacteristic
30C2×D1528C2211yescharacteristic
31#20259322C2211yescharacteristic, complemented
32#20259310C2211yescharacteristic
33#20259307—21no—
34#20259304—21no—
35#20259304—21no—
36#20259301C2211yescharacteristic
37#20259301C2211yescharacteristic
38#20259301C2211yescharacteristic, complemented
39#20259296C2211yescharacteristic
40#20259295—21no—
41#20259293—21no—
42#20259290—21no—
43C4×D764C2211yescharacteristic
44C4×D764C2211yescharacteristic, complemented
45C4⋊C4×D191—21no—
46C22⋊C4×D191—21no—
47#20259254C2211yescharacteristic, complemented
48#20259247C2211yescharacteristic, complemented
49#20259247C2211yescharacteristic, complemented
50#20259247C2211yescharacteristic, complemented
51#20259244C2211yescharacteristic
52#20259244C2211yescharacteristic
53#20259244C2211yescharacteristic, complemented
54C2×M16×C191C2211yescharacteristic
55C22×C8×C191C2211yescharacteristic, complemented
56C4×D4×C191C2211yescharacteristic
57C4⋊C8×C191C2211yescharacteristic, complemented
58C22⋊C8×C191C2211yescharacteristic
59C22⋊C8×C191C2211yescharacteristic, complemented
60#97×C191C2211yescharacteristic, complemented
61C23×D191—21no—
62#15690287—22no—
63#15690287—22no—
64#15690287—22no—
65#15690287—41no—
66#15690287—41no—
67#15690287—41no—
68C2×Dic382C2311yescharacteristic
69C2×Dic382C2311yescharacteristic
70C2×Dic382C2311yescharacteristic
71C2×D764—22no—
72C2×D764—21no—
73C2×D764—41no—
74C2×D764C2311yescharacteristic
75C2×D764C2311yescharacteristic
76C2×D764C2311yescharacteristic
77C2×C22⋊D191—21no—
78C2×C22⋊D191—21no—
79C2×C22⋊D191—21no—
80C2×C22⋊D191—21no—
81C2×C4×D191—21no—
82C2×C4×D191—21no—
83C2×C4×D191—21no—
84C2×C4×D191—21no—
85C2×C4×D191—21no—
86Dic764—22no—
87Dic764—41no—
88#15690276—22no—
89#15690276—22no—
90#15690276—22no—
91#15690276—22no—
92#15690276—41no—
93D1528—22no—
94D1528D414yescomplemented
95C4⋊Dic191—21no—
96C4⋊Dic191—21no—
97C4⋊Dic191C2311yescharacteristic
98C4⋊Dic191C2311yescharacteristic
99Dic191⋊C4—21no—
100Dic191⋊C4—21no—
101Dic191⋊C4—21no—
102C22⋊Dic191—21no—
103C22⋊Dic191—21no—
104C22⋊Dic191—21no—
105(C2×D191)⋊C4—21no—
106(C2×D191)⋊C4—21no—
107(C2×D191)⋊C4—21no—
108(C2×D191)⋊C4—21no—
109(C2×D191)⋊C4—21no—
110C2×D4×C191D411yescharacteristic
111C22×C4×C191C2311yescharacteristic
112C22×C4×C191C2311yescharacteristic
113M16×C191—22no—
114C2×C8×C191—22no—
115C2×C8×C191C2311yescharacteristic
116C2×C8×C191C2311yescharacteristic
117C2×C8×C191C2311yescharacteristic
118C2×C8×C191C2311yescharacteristic
119C4⋊C4×C191D411yescharacteristic
120C22⋊C4×C191D411yescharacteristic
121C22⋊C4×C191D411yescharacteristic
122C42×C191C2311yescharacteristic
123C22×D191—21no—
124C22×D191—21no—
125C22×D191—21no—
126C22×D191—42no—
127C22×D191—42no—
128C22×D191—81no—
129Dic382—21no—
130Dic382—21no—
131Dic382—21no—
132Dic382—21no—
133Dic382—21no—
134Dic382—21no—
135D764—21no—
136D764—21no—
137D764—21no—
138D764—21no—
139D764—42no—
140D764C2×D412yes—
141D764C2×D412yes—
142C22⋊D191—42no—
143C22⋊D191—42no—
144C22⋊D191—42no—
145C22⋊D191—81no—
146C2×Dic191—21no—
147C2×Dic191—21no—
148C2×Dic191—21no—
149C2×Dic191—21no—
150C2×Dic191—21no—
151C4×D191—42no—
152C4×D191—42no—
153C4×D191—42no—
154C4×D191—42no—
155C4×D191—81no—
156C23×C191C2×D411yescharacteristic
157C23×C191C2×D411yescharacteristic
158D4×C191—41no—
159C2×C4×C191—21no—
160C2×C4×C191—21no—
161C2×C4×C191—21no—
162C2×C4×C191—21no—
163C2×C4×C191C2×D411yescharacteristic
164C2×C4×C191C2×D411yescharacteristic
165C2×C4×C191C2×D411yescharacteristic
166C2×C4×C191C2×D411yescharacteristic
167C2×C4×C191C2411yescharacteristic
168C8×C191—21no—
169C8×C191—21no—
170C8×C191—21no—
171C8×C191C2×D412yes—
172C22×C191—21no—
173C22×C191—21no—
174C22×C191—21no—
175C22×C191—21no—
176C22×C191—21no—
177C22×C191—21no—
178C22×C191C22×D411yescharacteristic
179C2×D191—22no—
180C2×D191—22no—
181C2×D191—41no—
182C2×D191—41no—
183C2×D191—41no—
184C2×D191—41no—
185C2×D191—41no—
186C2×D191—41no—
187C2×D191—41no—
188C2×D191—84no—
189C4×C191—21no—
190C4×C191—21no—
191C4×C191—21no—
192C4×C191—21no—
193C4×C191C22×D411yescharacteristic
194C4×C191H(5,𝔽2)11yescharacteristic
195Dic191—41no—
196Dic191—41no—
197Dic191—41no—
198Dic191—41no—
199Dic191—41no—
200C2×C191—41no—
201C2×C191—41no—
202C2×C191D4211yescharacteristic
203C2×C191#57511yescharacteristic
204C2×C191#57711yescharacteristic
205D191—42no—
206D191—42no—
207D191—81no—
208C191#326711yescharacteristic, complemented, Sylow
209#3267—1911nomaximal, Sylow
210C2×AGL(1,ℤ/8)—1911no—
211C2×#135—1911no—
212#547—1911no—
213#546—1911no—
214#497—1911no—
215#470—1911no—
216#465—1911no—
217#463—1911no—
218#461—1911no—
219#452—1911no—
220#452—1911no—
221#450—1911no—
222#449—1911no—
223#442—1911no—
224#435D19111yescharacteristic, complemented
225C2×#41—1911no—
226C2×#41—1911no—
227C2×#41—1911no—
228C22×D4—1911no—
229AGL(1,ℤ/8)—3824no—
230#135—3824no—
231C2×Q16—1911no—
232C2×Q16—1911no—
233C2×SD16—1911no—
234C2×SD16—1911no—
235C2×SD16—1911no—
236C2×SD16—1911no—
237C2×SD16—1911no—
238C2×D8—1911no—
239C2×D8—1911no—
240C2×M16C2×D19111yescharacteristic
241C22×C8C2×D19111yescharacteristic, complemented
242C4⋊Q8—1911no—
243#124—1911no—
244#123—3821no—
245#123—3821no—
246#123—3821no—
247C22⋊Q8—1911no—
248C22⋊Q8—1911no—
249C22⋊Q8—1911no—
250#121—3821no—
251#121—3821no—
252#121—1911no—
253#120—3821no—
254C4×D4—1911no—
255C4×D4—1911no—
256C4×D4C2×D19111yescharacteristic
257C2×C4⋊C4—3821no—
258C2×C22⋊C4—3821no—
259#106—1911no—
260C4⋊C8C2×D19111yescharacteristic, complemented
261#103—1911no—
262#103—1911no—
263#103—1911no—
264#102—1911no—
265#102—1911no—
266#102—1911no—
267C22⋊C8C2×D19111yescharacteristic
268C22⋊C8C2×D19111yescharacteristic, complemented
269#97C2×D19111yescharacteristic, complemented
270C24—3821no—
271#41—3822no—
272#41—3822no—
273#41—3822no—
274#41—7641no—
275#41—7641no—
276#41—7641no—
277C2×Q8—1911no—
278C2×Q8—1911no—
279C2×Q8—1911no—
280C2×D4—3822no—
281C2×D4—3821no—
282C2×D4—3821no—
283C2×D4—3821no—
284C2×D4—3821no—
285C2×D4—3821no—
286C2×D4—1911no—
287C2×D4—1911no—
288C2×D4—1911no—
289C2×D4—7641no—
290C2×D4D76411yescharacteristic
291C22×C4—3821no—
292C22×C4—3821no—
293C22×C4—3821no—
294C22×C4—3821no—
295C22×C4—3821no—
296C22×C4C22×D19111yescharacteristic
297C22×C4C22×D19111yescharacteristic
298Q16—3822no—
299Q16—7641no—
300SD16—3822no—
301SD16—3822no—
302SD16—3822no—
303SD16—3822no—
304SD16—7641no—
305D8—3822no—
306D8—1914no—
307M16—22no—
308C2×C8—22no—
309C2×C8C22×D19111yescharacteristic
310C2×C8C22×D19111yescharacteristic
311C2×C8C22×D19111yescharacteristic
312C2×C8C22×D19111yescharacteristic
313C4⋊C4—3821no—
314C4⋊C4—3821no—
315C4⋊C4—3821no—
316C4⋊C4—3821no—
317C4⋊C4—3821no—
318C4⋊C4—1911no—
319C4⋊C4—1911no—
320C4⋊C4D76411yescharacteristic
321C22⋊C4—3821no—
322C22⋊C4—3821no—
323C22⋊C4—3821no—
324C22⋊C4—3821no—
325C22⋊C4—3821no—
326C22⋊C4—3821no—
327C22⋊C4—3821no—
328C22⋊C4—3821no—
329C22⋊C4D76411yescharacteristic
330C22⋊C4D76411yescharacteristic
331C42C22×D19111yescharacteristic
332C23—3821no—
333C23—3821no—
334C23—3821no—
335C23—15281no—
336C23—7642no—
337C23—7642no—
338C23C2×D76411yescharacteristic
339C23C2×D76411yescharacteristic
340Q8—3821no—
341Q8—3821no—
342Q8—3821no—
343Q8—3821no—
344Q8—3821no—
345Q8—3821no—
346D4—41no—
347D4—3821no—
348D4—3821no—
349D4—3821no—
350D4—3821no—
351D4—1912no—
352D4—1912no—
353D4—15281no—
354D4—7642no—
355D4—7642no—
356D4—7642no—
357D4—7642no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—3821no—
363C2×C4—3821no—
364C2×C4—3821no—
365C2×C4—3821no—
366C2×C4—3821no—
367C2×C4—15281no—
368C2×C4—7642no—
369C2×C4—7642no—
370C2×C4—7642no—
371C2×C4—7642no—
372C2×C4C2×D76411yescharacteristic
373C2×C4C2×D76411yescharacteristic
374C2×C4C2×D76411yescharacteristic
375C2×C4C2×D76411yescharacteristic
376C2×C4C23×D19111yescharacteristic
377C8—21no—
378C8—21no—
379C8—21no—
380C8D4×D19112yes—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—3822no—
388C22—3822no—
389C22—15284no—
390C22—7641no—
391C22—7641no—
392C22—7641no—
393C22—7641no—
394C22—7641no—
395C22—7641no—
396C22—7641no—
397C22C22×D76411yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—7641no—
403C4—7641no—
404C4—7641no—
405C4—7641no—
406C4—7641no—
407C4C2×D4×D19111yescharacteristic
408C4#2025936811yescharacteristic
409C2—41no—
410C2—41no—
411C2—15281no—
412C2—7642no—
413C2—7642no—
414C2D4×D76411yescharacteristic
415C2#2713346311yescharacteristic
416C2#2713347511yescharacteristic
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#435×C191C2
socleC22×C191C22×D4
hypercenter#435D191
hypocenterC191#3267
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#20259350C2semidirect
2. C2×#20259344C2semidirect
3. #27133318C2semidirect
4. #27133309C2semidirect
5. #27133057C2semidirect
6. #27132921C2semidirect
7. #27132892C2semidirect
8. #27132879C2semidirect
9. #27132869C2semidirect
10. #27132827C2semidirect
11. #27132827C2semidirect
12. #27132816C2semidirect
13. #27132810C2semidirect
14. #27132776C2semidirect
15. #435×C191C2semidirect
18. C2×#15690287C22semidirect
22. C2×Dic764C22semidirect
23. C2×Dic764C22semidirect
28. C2×#15690276C22semidirect
31. #20259322C22semidirect
38. #20259301C22semidirect
44. C4×D764C22semidirect
47. #20259254C22semidirect
48. #20259247C22semidirect
49. #20259247C22semidirect
50. #20259247C22semidirect
53. #20259244C22semidirect
55. C22×C8×C191C22semidirect
57. C4⋊C8×C191C22semidirect
59. C22⋊C8×C191C22semidirect
60. #97×C191C22semidirect
94. D1528D4semidirect
208. C191#3267semidirect
224. #435D191semidirect
241. C22×C8C2×D191semidirect
260. C4⋊C8C2×D191semidirect
268. C22⋊C8C2×D191semidirect
269. #97C2×D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593502
C2×#202593442
#271333182
#271333092
#271330572
#271329212
#271328922
#271328792
#271328692
#271328272
#271328162
#271328102
#271327762
#435×C1912
#3267191