Finite Group Databasebeta

← #28348393

Subgroups — #28348393

Order 13696.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293348C211yesmaximal, characteristic, complemented
2#20293296C211yesmaximal, characteristic
3#20292972C211yesmaximal, characteristic, complemented
4#20292952C211yesmaximal, characteristic, complemented
5#20292949C211yesmaximal, characteristic, complemented
6#20292910C211yesmaximal, characteristic, complemented
7#20292858C211yesmaximal, characteristic, complemented
8#20292853C211yesmaximal, characteristic, complemented
9#20292825C211yesmaximal, characteristic, complemented
10#20292788C211yesmaximal, characteristic, complemented
11Q16×Dic107C211yesmaximal, characteristic, complemented
12(C22⋊D107)⋊C8C211yesmaximal, characteristic, complemented
13#20292623C211yesmaximal, characteristic, complemented
14#20292622C211yesmaximal, characteristic, complemented
15#452×C107C211yesmaximal, characteristic, complemented
16C2×#13133819C2211yescharacteristic
17C2×#13133805C2211yescharacteristic
18C22×C107⋊C8C2211yescharacteristic
19C2×C8×D107C2211yescharacteristic
20#16812108C2211yescharacteristic
21#16812105—21no—
22#16812105C2211yescharacteristic
23#16812104—21no—
24#16812102—21no—
25#16812095—21no—
26#16812085C2211yescharacteristic
27#16812083—21no—
28#16812083C2211yescharacteristic
29#16812080—21no—
30#16812080C2211yescharacteristic
31Q8×Dic107C2211yescharacteristic
32Q8×Dic107C2211yescharacteristic
33#16812074—21no—
34C4×C22⋊D107—21no—
35C4×C22⋊D107C2211yescharacteristic
36#16812068C2211yescharacteristic
37#16812067C2211yescharacteristic
38#16812043C2211yescharacteristic
39#16812041C2211yescharacteristic
40#16812040C2211yescharacteristic
41Dic107⋊C8C2211yescharacteristic
42#16812033C2211yescharacteristic
43#16812033C2211yescharacteristic
44#16812033C2211yescharacteristic
45#16812031C2211yescharacteristic
46#16812031C2211yescharacteristic
47#16812030C2211yescharacteristic
48#16812030C2211yescharacteristic
49#16812029C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52C2×#41×C107C2211yescharacteristic
53C2×Q16×C107C2211yescharacteristic
54C2×SD16×C107C2211yescharacteristic
55C22⋊Q8×C107C2211yescharacteristic
56#103×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic
59#13133819—22no—
60#13133819—41no—
61C2×Dic214—21no—
62C2×D428—21no—
63C2×D428C2311yescharacteristic
64C2×C22⋊D107—21no—
65C2×C22⋊D107—21no—
66C2×C22⋊D107—21no—
67C2×C22⋊D107—21no—
68C2×C22⋊D107D411yescharacteristic
69C2×C4×D107—21no—
70C2×C4×D107C2311yescharacteristic
71#13133805—41no—
72C2×C107⋊C8—41no—
73C2×C107⋊C8C2311yescharacteristic
74C2×C107⋊C8C2311yescharacteristic
75C8×D107—41no—
76C4⋊Dic107—21no—
77C4⋊Dic107—21no—
78C4⋊Dic107C2311yescharacteristic
79C4⋊Dic107C2311yescharacteristic
80C4⋊Dic107C2311yescharacteristic
81Dic107⋊C4—21no—
82Dic107⋊C4—21no—
83Dic107⋊C4D411yescharacteristic
84C22⋊Dic107—21no—
85C22⋊Dic107—21no—
86C22⋊Dic107D411yescharacteristic
87(C2×D107)⋊C4—21no—
88(C2×D107)⋊C4—21no—
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4D411yescharacteristic
91C4×Dic107—21no—
92C4×Dic107—21no—
93C4×Dic107—21no—
94C4×Dic107—21no—
95C4×Dic107C2311yescharacteristic
96#41×C107—22no—
97#41×C107—41no—
98C2×Q8×C107C2311yescharacteristic
99C2×Q8×C107C2311yescharacteristic
100C2×D4×C107—21no—
101C2×D4×C107C2311yescharacteristic
102C22×C4×C107—21no—
103C22×C4×C107C2311yescharacteristic
104Q16×C107—22no—
105SD16×C107—41no—
106C2×C8×C107C2311yescharacteristic
107C2×C8×C107C2311yescharacteristic
108C4⋊C4×C107—21no—
109C4⋊C4×C107C2311yescharacteristic
110C22⋊C4×C107—21no—
111C23×C107—21no—
112C23×C107C2×D411yescharacteristic
113C22×D107—21no—
114C22×D107C2×D411yescharacteristic
115Q8×C107—21no—
116Q8×C107—21no—
117Q8×C107—21no—
118Q8×C107#4112yes—
119D4×C107—21no—
120D4×C107—21no—
121D4×C107—42no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107—21no—
127C2×C4×C107—42no—
128C2×C4×C107C2×D411yescharacteristic
129C2×C4×C107C2411yescharacteristic
130C22⋊D107—22no—
131C22⋊D107—42no—
132C22⋊D107—81no—
133C22⋊D107—81no—
134C22⋊D107—81no—
135C2×Dic107—21no—
136C2×Dic107—21no—
137C2×Dic107—21no—
138C2×Dic107C2×D411yescharacteristic
139C2×Dic107C2×D411yescharacteristic
140C2×Dic107C2×D411yescharacteristic
141D428—21no—
142D428—21no—
143D428—42no—
144C4×D107—21no—
145C4×D107—21no—
146C4×D107—42no—
147Dic214—42no—
148C8×C107—21no—
149C8×C107—21no—
150C107⋊C8—21no—
151C107⋊C8—21no—
152C22×C107—21no—
153C22×C107—21no—
154C22×C107—21no—
155C22×C107—41no—
156C22×C107—41no—
157C22×C107—41no—
158C22×C107C22×D411yescharacteristic
159C2×D107—21no—
160C2×D107—21no—
161C2×D107—21no—
162C2×D107—41no—
163C2×D107—41no—
164C2×D107—41no—
165C4×C107—22no—
166C4×C107—21no—
167C4×C107—41no—
168C4×C107—41no—
169C4×C107C2×#4111yescharacteristic
170C4×C107H(5,𝔽2)11yescharacteristic
171Dic107—21no—
172Dic107—21no—
173Dic107—41no—
174Dic107—41no—
175Dic107—41no—
176Dic107#13512yes—
177C2×C107—41no—
178C2×C107—81no—
179C2×C107#54611yescharacteristic
180C2×C107C2×#13511yescharacteristic
181C2×C107#57711yescharacteristic
182D107—41no—
183D107—81no—
184#3304—1071nomaximal, Sylow
185C107#330411yescharacteristic, complemented, Sylow
186#556—1071no—
187#550—1071no—
188#486—1071no—
189#482—1071no—
190#482—1071no—
191#475—1071no—
192#465—1071no—
193#465—1071no—
194#460—1071no—
195#452—1071no—
196#452D10711yescharacteristic, complemented
197C4×Q16—1071no—
198C8×D4—1071no—
199#416—1071no—
200#416—1071no—
201C2×#41—1071no—
202C2×#41C2×D10711yescharacteristic
203C2×Q16C2×D10711yescharacteristic
204C2×SD16—1071no—
205C2×SD16C2×D10711yescharacteristic
206C22×C8—1071no—
207C22×C8—1071no—
208C4⋊Q8—1071no—
209#127—1071no—
210#127—2141no—
211#126—2141no—
212#126—2141no—
213#124—2141no—
214C22⋊Q8—1071no—
215C22⋊Q8C2×D10711yescharacteristic
216#121—1071no—
217#121—1071no—
218#121—2141no—
219#121—2141no—
220C4×Q8—1071no—
221C4×Q8—1071no—
222C4×Q8—2141no—
223C4×D4—1071no—
224C4×D4—2141no—
225#117—1071no—
226#117—1071no—
227#107—1071no—
228#106—1071no—
229#106—1071no—
230C4⋊C8—1071no—
231#103—1071no—
232#103—1071no—
233#103—1071no—
234#103C2×D10711yescharacteristic
235#102—1071no—
236#102—1071no—
237#102—1071no—
238#102—1071no—
239#102—1071no—
240#102C2×D10711yescharacteristic
241C22⋊C8—1071no—
242C22⋊C8C2×D10711yescharacteristic
243C4×C8—1071no—
244#41—22no—
245#41—41no—
246#41—4281no—
247#41—2142no—
248C2×Q8—2141no—
249C2×Q8C22×D10711yescharacteristic
250C2×Q8C22×D10711yescharacteristic
251C2×D4—21no—
252C2×D4—1071no—
253C2×D4—1071no—
254C2×D4—2141no—
255C2×D4—2141no—
256C2×D4—2141no—
257C2×D4—2141no—
258C2×D4—2141no—
259C2×D4C22×D10711yescharacteristic
260C22×C4—21no—
261C22×C4—1071no—
262C22×C4—2141no—
263C22×C4C22×D10711yescharacteristic
264Q16—22no—
265SD16—41no—
266SD16—4281no—
267C2×C8—1071no—
268C2×C8—1071no—
269C2×C8—4281no—
270C2×C8—4281no—
271C2×C8C22×D10711yescharacteristic
272C2×C8C22×D10711yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—1071no—
275C4⋊C4—1071no—
276C4⋊C4—1071no—
277C4⋊C4—1071no—
278C4⋊C4—2141no—
279C4⋊C4—2141no—
280C4⋊C4—2141no—
281C4⋊C4—2141no—
282C4⋊C4C22×D10711yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—1071no—
285C22⋊C4—1071no—
286C22⋊C4—2141no—
287C22⋊C4—2141no—
288C22⋊C4—2141no—
289C22⋊C4—2141no—
290C22⋊C4—2141no—
291C42—1071no—
292C42—2141no—
293C42—2141no—
294C42—2141no—
295C42—2141no—
296C23—21no—
297C23—1071no—
298C23—2141no—
299C23D4×D10711yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—4282no—
304Q8#1313381712yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—8561no—
309D4—8561no—
310D4—8561no—
311D4—4282no—
312D4—4282no—
313D4—2142no—
314D4—2141no—
315D4—2141no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—1071no—
323C2×C4—1071no—
324C2×C4—1071no—
325C2×C4—4282no—
326C2×C4—2141no—
327C2×C4—2141no—
328C2×C4—2141no—
329C2×C4—2141no—
330C2×C4—2141no—
331C2×C4D4×D10711yescharacteristic
332C2×C4C23×D10711yescharacteristic
333C8—21no—
334C8—21no—
335C8—2141no—
336C8—2141no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—4281no—
344C22—4281no—
345C22—4281no—
346C22—2141no—
347C22—2141no—
348C22—2141no—
349C22C2×D4×D10711yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—1072no—
355C4—4281no—
356C4—4281no—
357C4—4281no—
358C4—2141no—
359C4—2141no—
360C4C2×#1313381711yescharacteristic
361C4#1681215411yescharacteristic
362C2—41no—
363C2—81no—
364C2—8561no—
365C2—4281no—
366C2#2029326411yescharacteristic
367C2#135×D10711yescharacteristic
368C2#2029343611yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#452×C107C2
socleC22×C107C22×D4
prime radical#20293296C2
hypercenter#452D107
hypocenterC107#3304
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #20293348C2semidirect
3. #20292972C2semidirect
4. #20292952C2semidirect
5. #20292949C2semidirect
6. #20292910C2semidirect
7. #20292858C2semidirect
8. #20292853C2semidirect
9. #20292825C2semidirect
10. #20292788C2semidirect
11. Q16×Dic107C2semidirect
12. (C22⋊D107)⋊C8C2semidirect
13. #20292623C2semidirect
14. #20292622C2semidirect
15. #452×C107C2semidirect
185. C107#3304semidirect
196. #452D107semidirect

Maximal subgroups

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

subgroupindex
#202933482
#202932962
#202929722
#202929522
#202929492
#202929102
#202928582
#202928532
#202928252
#202927882
Q16×Dic1072
(C22⋊D107)⋊C82
#202926232
#202926222
#452×C1072
#3304107