Finite Group Databasebeta

← #37583283

Subgroups — #37583283

Order 24448.

472 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27133170C211yesmaximal, characteristic, complemented
2#121×D191C211yesmaximal, characteristic, complemented
3#27132997C211yesmaximal, characteristic, complemented
4#27132988C211yesmaximal, characteristic, complemented
5#27132984C211yesmaximal, characteristic, complemented
6#27132980C211yesmaximal, characteristic, complemented
7#27132898C211yesmaximal, characteristic, complemented
8#27132896C211yesmaximal, characteristic, complemented
9#27132895C211yesmaximal, characteristic, complemented
10#27132889C211yesmaximal, characteristic, complemented
11#27132812C211yesmaximal, characteristic, complemented
12#27132808C211yesmaximal, characteristic, complemented
13#27132795C211yesmaximal, characteristic, complemented
14C22⋊C8×D191C211yesmaximal, characteristic, complemented
15#449×C191C211yesmaximal, characteristic, complemented
16C2×D4×D191—21no—
17C2×D4×D191C2211yescharacteristic
18C22×C4×D191C2211yescharacteristic
19C2×#15690274C2211yescharacteristic, complemented
20C2×#15690272C2211yescharacteristic, complemented
21C2×C8×D191C2211yescharacteristic, complemented
22C2×C8×D191C2211yescharacteristic, complemented
23#20259303—21no—
24#20259298C2211yescharacteristic
25#20259298C2211yescharacteristic, complemented
26#20259297C2211yescharacteristic
27#20259296C2211yescharacteristic
28#20259295—21no—
29#20259294—21no—
30#20259293C2211yescharacteristic
31#20259293C2211yescharacteristic
32#20259293C2211yescharacteristic, complemented
33#20259290—21no—
34C4×C22⋊D191—21no—
35C4×C22⋊D191—21no—
36#20259281C2211yescharacteristic, complemented
37C4⋊C4×D191C2211yescharacteristic
38C22⋊C4×D191—21no—
39#20259256C2211yescharacteristic, complemented
40#20259255C2211yescharacteristic, complemented
41#20259254C2211yescharacteristic, complemented
42#20259253C2211yescharacteristic, complemented
43#20259246C2211yescharacteristic, complemented
44#20259244C2211yescharacteristic, complemented
45#20259244C2211yescharacteristic, complemented
46#20259243C2211yescharacteristic, complemented
47#20259243C2211yescharacteristic, complemented
48#20259243C2211yescharacteristic, complemented
49C22⋊(C191⋊C8)C2211yescharacteristic, complemented
50(C2×D191)⋊C8C2211yescharacteristic
51(C2×D191)⋊C8C2211yescharacteristic
52C2×#41×C191C2211yescharacteristic, complemented
53C2×SD16×C191C2211yescharacteristic, complemented
54C2×D8×C191C2211yescharacteristic, complemented
55#121×C191C2211yescharacteristic
56#103×C191C2211yescharacteristic, complemented
57#102×C191C2211yescharacteristic, complemented
58C22⋊C8×C191C2211yescharacteristic, complemented
59C23×D191—21no—
60C23×D191D411yescharacteristic
61C2×D764—21no—
62C2×D764C2311yescharacteristic
63C2×C22⋊D191—21no—
64C2×C22⋊D191—21no—
65C2×C22⋊D191—21no—
66C2×C22⋊D191—21no—
67C2×C22⋊D191—21no—
68D4×D191—41no—
69D4×D191—41no—
70D4×D191—44no—
71C22×Dic191D411yescharacteristic
72C2×C4×D191—21no—
73C2×C4×D191—41no—
74C2×C4×D191—41no—
75C2×C4×D191D411yescharacteristic
76C2×C4×D191D411yescharacteristic
77C2×C4×D191C2311yescharacteristic
78C2×C4×D191C2311yescharacteristic
79#15690274—41no—
80#15690272—41no—
81C2×C191⋊C8C2311yescharacteristic
82C2×C191⋊C8C2311yescharacteristic
83C8×D191—41no—
84C8×D191—41no—
85C4⋊Dic191C2311yescharacteristic
86C4⋊Dic191C2311yescharacteristic
87C4⋊Dic191C2311yescharacteristic
88Dic191⋊C4—21no—
89Dic191⋊C4—21no—
90Dic191⋊C4—21no—
91C22⋊Dic191—21no—
92C22⋊Dic191—21no—
93C22⋊Dic191—21no—
94C22⋊Dic191—21no—
95(C2×D191)⋊C4—21no—
96(C2×D191)⋊C4—21no—
97(C2×D191)⋊C4—21no—
98(C2×D191)⋊C4—21no—
99C4×Dic191—21no—
100#41×C191—41no—
101#41×C191—41no—
102C2×Q8×C191C2311yescharacteristic
103C2×D4×C191—21no—
104C2×D4×C191—21no—
105C2×D4×C191C2311yescharacteristic
106C2×D4×C191C2311yescharacteristic
107C22×C4×C191—21no—
108C22×C4×C191C2311yescharacteristic
109SD16×C191—41no—
110D8×C191—41no—
111C2×C8×C191C2311yescharacteristic
112C2×C8×C191C2311yescharacteristic
113C4⋊C4×C191C2311yescharacteristic
114C22⋊C4×C191—21no—
115C22×D191—22no—
116C22×D191—22no—
117C22×D191—21no—
118C22×D191—41no—
119C22×D191—42no—
120C22×D191—42no—
121C22×D191—42no—
122C22×D191C2×D411yescharacteristic
123C22×D191C2×D411yescharacteristic
124D764—21no—
125D764—21no—
126D764—42no—
127C22⋊D191—42no—
128C22⋊D191—42no—
129C22⋊D191—42no—
130C22⋊D191—42no—
131C22⋊D191—42no—
132C2×Dic191—21no—
133C2×Dic191—21no—
134C2×Dic191—21no—
135C2×Dic191—41no—
136C2×Dic191C2×D411yescharacteristic
137C2×Dic191C2×D411yescharacteristic
138C4×D191—21no—
139C4×D191—21no—
140C4×D191—21no—
141C4×D191—21no—
142C4×D191—41no—
143C4×D191—41no—
144C4×D191—42no—
145C191⋊C8—21no—
146C191⋊C8—21no—
147C23×C191—21no—
148C23×C191—21no—
149C23×C191C2×D411yescharacteristic
150Q8×C191—21no—
151Q8×C191—21no—
152D4×C191—21no—
153D4×C191—21no—
154D4×C191—21no—
155D4×C191—21no—
156D4×C191—42no—
157D4×C191—42no—
158C2×C4×C191—21no—
159C2×C4×C191—21no—
160C2×C4×C191—21no—
161C2×C4×C191—21no—
162C2×C4×C191—42no—
163C2×C4×C191C2×D411yescharacteristic
164C2×C4×C191C2411yescharacteristic
165C8×C191—21no—
166C8×C191—21no—
167C22×C191—21no—
168C22×C191—21no—
169C22×C191—21no—
170C22×C191—41no—
171C22×C191—41no—
172C22×C191—41no—
173C22×C191—41no—
174C22×C191—41no—
175C22×C191—41no—
176C22×C191C22×D411yescharacteristic
177C2×D191—21no—
178C2×D191—21no—
179C2×D191—21no—
180C2×D191—21no—
181C2×D191—44no—
182C2×D191—41no—
183C2×D191—41no—
184C2×D191—41no—
185C2×D191—84no—
186C2×D191#13512yes—
187C2×D191AGL(1,ℤ/8)12yes—
188C4×C191—21no—
189C4×C191—41no—
190C4×C191—41no—
191C4×C191H(5,𝔽2)11yescharacteristic
192C4×C191H(5,𝔽2)11yescharacteristic
193Dic191—21no—
194Dic191—21no—
195Dic191—41no—
196Dic191—41no—
197Dic191—41no—
198C2×C191—41no—
199C2×C191—81no—
200C2×C191—81no—
201C2×C191#53411yescharacteristic
202C2×C191C2×#13511yescharacteristic
203C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
204D191—22no—
205D191—22no—
206D191—81no—
207C191#318811yescharacteristic, complemented, Sylow
208#3188—1911nomaximal, Sylow
209#525—1911no—
210C2×#121—1911no—
211#484—1911no—
212#482—1911no—
213#482—1911no—
214#481—1911no—
215#466—1911no—
216#466—1911no—
217#465—1911no—
218#465—1911no—
219#450—1911no—
220#449—1911no—
221#449D19111yescharacteristic, complemented
222#447—1911no—
223C2×C22⋊C8—1911no—
224C2×#41C2×D19111yescharacteristic, complemented
225C22×D4—3821no—
226C22×D4—1911no—
227C23×C4—1911no—
228C2×SD16—1911no—
229C2×SD16C2×D19111yescharacteristic, complemented
230C2×D8—1911no—
231C2×D8C2×D19111yescharacteristic, complemented
232C22×C8—1911no—
233C22×C8—1911no—
234#123—3821no—
235C22⋊Q8—1911no—
236C22⋊Q8—1911no—
237#121—3821no—
238#121—3821no—
239#121—1911no—
240#121—1911no—
241#121—1911no—
242#121—1911no—
243#121—1911no—
244#121C2×D19111yescharacteristic
245#120—3821no—
246C4×D4—3821no—
247C4×D4—3821no—
248#117—1911no—
249C2×C4⋊C4—1911no—
250C2×C22⋊C4—3821no—
251#107—1911no—
252#107—1911no—
253#106—1911no—
254#106—1911no—
255#103—1911no—
256#103C2×D19111yescharacteristic, complemented
257#102—1911no—
258#102—1911no—
259#102—1911no—
260#102—1911no—
261#102—1911no—
262#102C2×D19111yescharacteristic, complemented
263C22⋊C8—1911no—
264C22⋊C8—1911no—
265C22⋊C8—1911no—
266C22⋊C8C2×D19111yescharacteristic, complemented
267C24—3821no—
268C24—1911no—
269#41—41no—
270#41—41no—
271C2×Q8C22×D19111yescharacteristic
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—3821no—
275C2×D4—3821no—
276C2×D4—3821no—
277C2×D4—3821no—
278C2×D4—3821no—
279C2×D4—3821no—
280C2×D4—1911no—
281C2×D4—7641no—
282C2×D4—7641no—
283C2×D4—7644no—
284C2×D4C22×D19111yescharacteristic
285C2×D4C22×D19111yescharacteristic
286C22×C4—21no—
287C22×C4—3821no—
288C22×C4—1911no—
289C22×C4—1911no—
290C22×C4—1911no—
291C22×C4—1911no—
292C22×C4—1911no—
293C22×C4—7641no—
294C22×C4—7641no—
295C22×C4C22×D19111yescharacteristic
296SD16—41no—
297SD16—7641no—
298D8—41no—
299D8—7641no—
300C2×C8—1911no—
301C2×C8—1911no—
302C2×C8—7641no—
303C2×C8—7641no—
304C2×C8C22×D19111yescharacteristic
305C2×C8C22×D19111yescharacteristic
306C4⋊C4—3821no—
307C4⋊C4—3821no—
308C4⋊C4—3821no—
309C4⋊C4—1911no—
310C4⋊C4—1911no—
311C4⋊C4—1911no—
312C4⋊C4C22×D19111yescharacteristic
313C22⋊C4—21no—
314C22⋊C4—3821no—
315C22⋊C4—3821no—
316C22⋊C4—3821no—
317C22⋊C4—3821no—
318C22⋊C4—3821no—
319C22⋊C4—3821no—
320C22⋊C4—3821no—
321C22⋊C4—3821no—
322C42—3821no—
323C23—21no—
324C23—21no—
325C23—3822no—
326C23—3822no—
327C23—3821no—
328C23—1911no—
329C23—1911no—
330C23—7641no—
331C23—7642no—
332C23—7642no—
333C23—7642no—
334C23D4×D19111yescharacteristic
335Q8—21no—
336Q8—21no—
337D4—21no—
338D4—21no—
339D4—21no—
340D4—21no—
341D4—42no—
342D4—42no—
343D4—3821no—
344D4—3821no—
345D4—7642no—
346D4—7642no—
347D4—7642no—
348D4—7642no—
349D4—7642no—
350D4—7642no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—42no—
356C2×C4—3821no—
357C2×C4—3821no—
358C2×C4—3821no—
359C2×C4—3821no—
360C2×C4—3821no—
361C2×C4—3821no—
362C2×C4—3821no—
363C2×C4—1911no—
364C2×C4—1911no—
365C2×C4—7641no—
366C2×C4—7641no—
367C2×C4—7642no—
368C2×C4—7641no—
369C2×C4D4×D19111yescharacteristic
370C2×C4C23×D19111yescharacteristic
371C8—21no—
372C8—21no—
373C8—3821no—
374C8—3821no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—3821no—
385C22—3821no—
386C22—3821no—
387C22—3821no—
388C22—1912no—
389C22—1912no—
390C22—15284no—
391C22—7644no—
392C22—7641no—
393C22—7641no—
394C22—7641no—
395C22C2×D4×D19111yescharacteristic
396C4—21no—
397C4—41no—
398C4—41no—
399C4—3821no—
400C4—3821no—
401C4—7641no—
402C4—7641no—
403C4—7641no—
404C4#2025936711yescharacteristic
405C4#2025936711yescharacteristic
406C2—41no—
407C2—81no—
408C2—81no—
409C2—3822no—
410C2—3822no—
411C2—15281no—
412C2#2713322311yescharacteristic
413C2#135×D19111yescharacteristic
414C2AGL(1,ℤ/8)×D19111yescharacteristic
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#449×C191C2
socleC22×C191C22×D4
hypercenter#449D191
hypocenterC191#3188
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #27133170C2semidirect
2. #121×D191C2semidirect
3. #27132997C2semidirect
4. #27132988C2semidirect
5. #27132984C2semidirect
6. #27132980C2semidirect
7. #27132898C2semidirect
8. #27132896C2semidirect
9. #27132895C2semidirect
10. #27132889C2semidirect
11. #27132812C2semidirect
12. #27132808C2semidirect
13. #27132795C2semidirect
14. C22⋊C8×D191C2semidirect
15. #449×C191C2semidirect
19. C2×#15690274C22semidirect
20. C2×#15690272C22semidirect
21. C2×C8×D191C22semidirect
22. C2×C8×D191C22semidirect
25. #20259298C22semidirect
32. #20259293C22semidirect
36. #20259281C22semidirect
39. #20259256C22semidirect
40. #20259255C22semidirect
41. #20259254C22semidirect
42. #20259253C22semidirect
43. #20259246C22semidirect
44. #20259244C22semidirect
45. #20259244C22semidirect
46. #20259243C22semidirect
47. #20259243C22semidirect
48. #20259243C22semidirect
49. C22⋊(C191⋊C8)C22semidirect
52. C2×#41×C191C22semidirect
53. C2×SD16×C191C22semidirect
54. C2×D8×C191C22semidirect
56. #103×C191C22semidirect
57. #102×C191C22semidirect
58. C22⋊C8×C191C22semidirect
207. C191#3188semidirect
221. #449D191semidirect
224. C2×#41C2×D191semidirect
229. C2×SD16C2×D191semidirect
231. C2×D8C2×D191semidirect
256. #103C2×D191semidirect
262. #102C2×D191semidirect
266. C22⋊C8C2×D191semidirect

Maximal subgroups

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

subgroupindex
#271331702
#121×D1912
#271329972
#271329882
#271329842
#271329802
#271328982
#271328962
#271328952
#271328892
#271328122
#271328082
#271327952
C22⋊C8×D1912
#449×C1912
#3188191