Finite Group Databasebeta

← #37584065

Subgroups — #37584065

Order 24448.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 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#27133334C211yesmaximal, characteristic, complemented
4#27133309C211yesmaximal, characteristic, complemented
5#27133052C211yesmaximal, characteristic, complemented
6#27132909C211yesmaximal, characteristic, complemented
7#27132899C211yesmaximal, characteristic, complemented
8#27132886C211yesmaximal, characteristic, complemented
9#27132859C211yesmaximal, characteristic, complemented
10#27132827C211yesmaximal, characteristic, complemented
11#27132810C211yesmaximal, characteristic, complemented
12#27132810C211yesmaximal, characteristic, complemented
13#27132799C211yesmaximal, characteristic, complemented
14#27132765C211yesmaximal, 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×#15690276C2211yescharacteristic
24C2×#15690276C2211yescharacteristic
25C2×#15690276C2211yescharacteristic, complemented
26C2×#15690276C2211yescharacteristic, complemented
27C2×D1528C2211yescharacteristic
28C2×D1528C2211yescharacteristic
29C2×D1528C2211yescharacteristic
30C2×D1528C2211yescharacteristic
31#20259319C2211yescharacteristic, complemented
32#20259318—21no—
33#20259310C2211yescharacteristic
34#20259307—21no—
35#20259301C2211yescharacteristic
36#20259296C2211yescharacteristic
37#20259296C2211yescharacteristic
38#20259296C2211yescharacteristic, complemented
39#20259295—21no—
40#20259295—21no—
41#20259295—21no—
42#20259290—21no—
43C4×Dic382C2211yescharacteristic, complemented
44C4×D764C2211yescharacteristic
45#20259284—21no—
46C22⋊C4×D191—21no—
47#20259256C2211yescharacteristic, complemented
48#20259247C2211yescharacteristic, complemented
49#20259247C2211yescharacteristic, complemented
50#20259244C2211yescharacteristic
51#20259244C2211yescharacteristic
52#20259244C2211yescharacteristic, complemented
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×D764—22no—
71C2×D764—21no—
72C2×D764—21no—
73C2×D764—21no—
74C2×D764—41no—
75C2×D764C2311yescharacteristic
76C2×D764C2311yescharacteristic
77C2×D764C2311yescharacteristic
78C2×D764C2311yescharacteristic
79C2×C22⋊D191—21no—
80C2×C22⋊D191—21no—
81C2×C22⋊D191—21no—
82C2×C22⋊D191—21no—
83C2×C22⋊D191—21no—
84C2×C22⋊D191—21no—
85C2×C4×D191—21no—
86C2×C4×D191—21no—
87C2×C4×D191—21no—
88C2×C4×D191—21no—
89Dic764—22no—
90#15690276—22no—
91#15690276—22no—
92#15690276—41no—
93#15690276D414yescomplemented
94D1528—22no—
95D1528—22no—
96D1528—22no—
97D1528—41no—
98C4⋊Dic191C2311yescharacteristic
99C4⋊Dic191C2311yescharacteristic
100Dic191⋊C4—21no—
101Dic191⋊C4—21no—
102C22⋊Dic191—21no—
103(C2×D191)⋊C4—21no—
104(C2×D191)⋊C4—21no—
105(C2×D191)⋊C4—21no—
106(C2×D191)⋊C4—21no—
107(C2×D191)⋊C4—21no—
108(C2×D191)⋊C4—21no—
109C4×Dic191—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—21no—
127C22×D191—42no—
128C22×D191—42no—
129C22×D191—81no—
130Dic382—21no—
131Dic382—21no—
132Dic382—21no—
133Dic382C2×D412yes—
134D764—21no—
135D764—21no—
136D764—21no—
137D764—21no—
138D764—21no—
139D764—21no—
140D764—21no—
141D764—42no—
142D764—42no—
143D764—81no—
144D764C2×D412yes—
145C22⋊D191—42no—
146C22⋊D191—42no—
147C22⋊D191—42no—
148C22⋊D191—81no—
149C22⋊D191—81no—
150C22⋊D191—81no—
151C2×Dic191—21no—
152C2×Dic191—21no—
153C2×Dic191—21no—
154C2×Dic191—21no—
155C4×D191—42no—
156C4×D191—42no—
157C4×D191—42no—
158C4×D191—81no—
159C23×C191C2×D411yescharacteristic
160C23×C191C2×D411yescharacteristic
161D4×C191—41no—
162C2×C4×C191—21no—
163C2×C4×C191—21no—
164C2×C4×C191—21no—
165C2×C4×C191—21no—
166C2×C4×C191C2×D411yescharacteristic
167C2×C4×C191C2×D411yescharacteristic
168C2×C4×C191C2×D411yescharacteristic
169C2×C4×C191C2×D411yescharacteristic
170C2×C4×C191C2411yescharacteristic
171C8×C191—21no—
172C8×C191—21no—
173C8×C191—21no—
174C8×C191C2×D412yes—
175C22×C191—21no—
176C22×C191—21no—
177C22×C191—21no—
178C22×C191—21no—
179C22×C191—21no—
180C22×C191—21no—
181C22×C191C22×D411yescharacteristic
182C2×D191—22no—
183C2×D191—41no—
184C2×D191—41no—
185C2×D191—41no—
186C2×D191—41no—
187C2×D191—41no—
188C2×D191—41no—
189C2×D191—41no—
190C2×D191—41no—
191C2×D191—41no—
192C2×D191—41no—
193C2×D191—41no—
194C2×D191—84no—
195C4×C191—21no—
196C4×C191—21no—
197C4×C191—21no—
198C4×C191—21no—
199C4×C191C22×D411yescharacteristic
200C4×C191H(5,𝔽2)11yescharacteristic
201Dic191—22no—
202Dic191—41no—
203Dic191—41no—
204Dic191—41no—
205C2×C191—41no—
206C2×C191—41no—
207C2×C191D4211yescharacteristic
208C2×C191#57511yescharacteristic
209C2×C191#57611yescharacteristic
210D191—42no—
211D191—81no—
212D191—81no—
213D191—81no—
214C191#326811yescharacteristic, complemented, Sylow
215#3268—1911nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1911no—
217C2×#135—1911no—
218#550—1911no—
219#546—1911no—
220#496—1911no—
221#468—1911no—
222#466—1911no—
223#464—1911no—
224#459—1911no—
225#452—1911no—
226#449—1911no—
227#449—1911no—
228#447—1911no—
229#440—1911no—
230#435D19111yescharacteristic, complemented
231C2×#41—1911no—
232C2×#41—1911no—
233C2×#41—1911no—
234C22×D4—1911no—
235AGL(1,ℤ/8)—3824no—
236#135—3824no—
237C2×Q16—1911no—
238C2×SD16—1911no—
239C2×SD16—1911no—
240C2×SD16—1911no—
241C2×SD16—1911no—
242C2×D8—1911no—
243C2×D8—1911no—
244C2×D8—1911no—
245C2×D8—1911no—
246C2×M16C2×D19111yescharacteristic
247C22×C8C2×D19111yescharacteristic, complemented
248#127—3821no—
249#127—1911no—
250#124—1911no—
251#123—3821no—
252C22⋊Q8—1911no—
253#121—3821no—
254#121—3821no—
255#121—3821no—
256#121—1911no—
257#121—1911no—
258#121—1911no—
259#120—3821no—
260C4×Q8—1911no—
261C4×D4—3821no—
262C4×D4—1911no—
263C4×D4C2×D19111yescharacteristic
264C2×C22⋊C4—3821no—
265#107—1911no—
266C4⋊C8C2×D19111yescharacteristic, complemented
267#103—1911no—
268#103—1911no—
269#102—1911no—
270#102—1911no—
271#102—1911no—
272#102—1911no—
273C22⋊C8C2×D19111yescharacteristic
274C22⋊C8C2×D19111yescharacteristic, complemented
275#97C2×D19111yescharacteristic, complemented
276C24—3821no—
277#41—3822no—
278#41—3822no—
279#41—3822no—
280#41—7641no—
281#41—7641no—
282#41—7641no—
283C2×Q8—1911no—
284C2×Q8—1911no—
285C2×D4—3822no—
286C2×D4—3821no—
287C2×D4—3821no—
288C2×D4—3821no—
289C2×D4—3821no—
290C2×D4—3821no—
291C2×D4—3821no—
292C2×D4—3821no—
293C2×D4—3821no—
294C2×D4—3821no—
295C2×D4—1911no—
296C2×D4—1911no—
297C2×D4—1911no—
298C2×D4—1911no—
299C2×D4—7641no—
300C2×D4D76411yescharacteristic
301C22×C4—3821no—
302C22×C4—3821no—
303C22×C4—3821no—
304C22×C4—3821no—
305C22×C4C22×D19111yescharacteristic
306C22×C4C22×D19111yescharacteristic
307Q16—3822no—
308SD16—3822no—
309SD16—3822no—
310SD16—1914no—
311SD16—7641no—
312D8—3822no—
313D8—3822no—
314D8—3822no—
315D8—7641no—
316M16—22no—
317C2×C8—22no—
318C2×C8C22×D19111yescharacteristic
319C2×C8C22×D19111yescharacteristic
320C2×C8C22×D19111yescharacteristic
321C2×C8C22×D19111yescharacteristic
322C4⋊C4—3821no—
323C4⋊C4—3821no—
324C4⋊C4—1911no—
325C4⋊C4—1911no—
326C4⋊C4D76411yescharacteristic
327C22⋊C4—3821no—
328C22⋊C4—3821no—
329C22⋊C4—3821no—
330C22⋊C4—3821no—
331C22⋊C4—3821no—
332C22⋊C4—3821no—
333C22⋊C4—3821no—
334C22⋊C4D76411yescharacteristic
335C22⋊C4D76411yescharacteristic
336C42—3821no—
337C42C22×D19111yescharacteristic
338C23—3821no—
339C23—3821no—
340C23—3821no—
341C23—3821no—
342C23—15281no—
343C23—7642no—
344C23—7642no—
345C23C2×D76411yescharacteristic
346C23C2×D76411yescharacteristic
347Q8—3821no—
348Q8—3821no—
349Q8—3821no—
350Q8—1912no—
351D4—41no—
352D4—3821no—
353D4—3821no—
354D4—3821no—
355D4—3821no—
356D4—3821no—
357D4—3821no—
358D4—3821no—
359D4—1912no—
360D4—15281no—
361D4—15281no—
362D4—15281no—
363D4—15281no—
364D4—7642no—
365D4—7642no—
366D4—7642no—
367D4—7642no—
368D4—7642no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—3821no—
374C2×C4—3821no—
375C2×C4—3821no—
376C2×C4—3821no—
377C2×C4—15281no—
378C2×C4—7642no—
379C2×C4—7642no—
380C2×C4—7642no—
381C2×C4C2×D76411yescharacteristic
382C2×C4C2×D76411yescharacteristic
383C2×C4C2×D76411yescharacteristic
384C2×C4C2×D76411yescharacteristic
385C2×C4C23×D19111yescharacteristic
386C8—21no—
387C8—21no—
388C8—21no—
389C8D4×D19112yes—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—3822no—
397C22—15284no—
398C22—7641no—
399C22—7641no—
400C22—7641no—
401C22—7641no—
402C22—7641no—
403C22—7641no—
404C22—7641no—
405C22—7641no—
406C22—7641no—
407C22—7641no—
408C22—7641no—
409C22C22×D76411yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—3822no—
415C4—7641no—
416C4—7641no—
417C4—7641no—
418C4C2×D4×D19111yescharacteristic
419C4#2025936811yescharacteristic
420C2—41no—
421C2—41no—
422C2—15281no—
423C2—15281no—
424C2—15281no—
425C2—7642no—
426C2D4×D76411yescharacteristic
427C2#2713346311yescharacteristic
428C2#2713346811yescharacteristic
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#435×C191C2
socleC22×C191C22×D4
hypercenter#435D191
hypocenterC191#3268
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. #27133334C2semidirect
4. #27133309C2semidirect
5. #27133052C2semidirect
6. #27132909C2semidirect
7. #27132899C2semidirect
8. #27132886C2semidirect
9. #27132859C2semidirect
10. #27132827C2semidirect
11. #27132810C2semidirect
12. #27132810C2semidirect
13. #27132799C2semidirect
14. #27132765C2semidirect
15. #435×C191C2semidirect
18. C2×#15690287C22semidirect
22. C2×Dic764C22semidirect
25. C2×#15690276C22semidirect
26. C2×#15690276C22semidirect
31. #20259319C22semidirect
38. #20259296C22semidirect
43. C4×Dic382C22semidirect
47. #20259256C22semidirect
48. #20259247C22semidirect
49. #20259247C22semidirect
52. #20259244C22semidirect
53. #20259244C22semidirect
55. C22×C8×C191C22semidirect
57. C4⋊C8×C191C22semidirect
59. C22⋊C8×C191C22semidirect
60. #97×C191C22semidirect
93. #15690276D4semidirect
214. C191#3268semidirect
230. #435D191semidirect
247. C22×C8C2×D191semidirect
266. C4⋊C8C2×D191semidirect
274. C22⋊C8C2×D191semidirect
275. #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
#271333342
#271333092
#271330522
#271329092
#271328992
#271328862
#271328592
#271328272
#271328102
#271327992
#271327652
#435×C1912
#3268191