Finite Group Databasebeta

← #28348365

Subgroups — #28348365

Order 13696.

398 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#20293323C211yesmaximal, characteristic, complemented
2#20293286C211yesmaximal, characteristic, complemented
3#20292982C211yesmaximal, characteristic, complemented
4#20292969C211yesmaximal, characteristic, complemented
5#20292946C211yesmaximal, characteristic, complemented
6#20292935C211yesmaximal, characteristic, complemented
7#20292863C211yesmaximal, characteristic, complemented
8#20292856C211yesmaximal, characteristic, complemented
9#20292843C211yesmaximal, characteristic, complemented
10#20292774C211yesmaximal, characteristic, complemented
11#20292768C211yesmaximal, characteristic, complemented
12C4×#13133807C211yesmaximal, characteristic, complemented
13#20292624C211yesmaximal, characteristic, complemented
14C2×#16812034C211yesmaximal, characteristic, complemented
15C8×D4×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C22×Dic214C2211yescharacteristic
18C2×#13133807C2211yescharacteristic
19C2×#13133807C2211yescharacteristic
20C2×D856C2211yescharacteristic
21#16812104—21no—
22#16812101C2211yescharacteristic
23#16812097C2211yescharacteristic
24#16812095—21no—
25#16812091—21no—
26#16812088C2211yescharacteristic
27#16812087—21no—
28#16812083C2211yescharacteristic
29#16812083C2211yescharacteristic
30#16812083C2211yescharacteristic
31#16812081—21no—
32#16812081—21no—
33C4×Dic214C2211yescharacteristic
34C4×D428C2211yescharacteristic
35(C22⋊D107)⋊C4—21no—
36(C22⋊D107)⋊C4—21no—
37#16812068C2211yescharacteristic
38C2×C4⋊Dic107C2211yescharacteristic
39#16812043C2211yescharacteristic
40#16812041C2211yescharacteristic
41#16812041C2211yescharacteristic
42#16812034C2211yescharacteristic
43#16812034C2211yescharacteristic
44#16812034C2211yescharacteristic
45#16812034C2211yescharacteristic
46#16812034C2211yescharacteristic
47#16812034C2211yescharacteristic
48#16812031C2211yescharacteristic
49#16812031C2211yescharacteristic
50#16812031C2211yescharacteristic
51#16812031C2211yescharacteristic
52C22×C8×C107C2211yescharacteristic
53C22×C8×C107C2211yescharacteristic
54C4×D4×C107C2211yescharacteristic
55C4⋊C8×C107C2211yescharacteristic
56C22⋊C8×C107C2211yescharacteristic
57C22⋊C8×C107C2211yescharacteristic
58C4×C8×C107C2211yescharacteristic
59#13133818—22no—
60#13133818—41no—
61C2×Dic214—22no—
62C2×Dic214—21no—
63C2×Dic214—41no—
64C2×Dic214C2311yescharacteristic
65C2×Dic214C2311yescharacteristic
66C2×D428C2311yescharacteristic
67C2×D428C2311yescharacteristic
68C2×C22⋊D107—21no—
69C2×C22⋊D107—21no—
70C2×C22⋊D107—21no—
71C2×C22⋊D107—21no—
72C22×Dic107—21no—
73C22×Dic107—21no—
74C2×C4×D107—21no—
75C2×C4×D107—21no—
76#13133807—22no—
77#13133807—41no—
78D856—41no—
79C4⋊Dic107—21no—
80C4⋊Dic107C2311yescharacteristic
81C4⋊Dic107C2311yescharacteristic
82C4⋊Dic107C2311yescharacteristic
83C4⋊Dic107C2311yescharacteristic
84Dic107⋊C4—21no—
85Dic107⋊C4—21no—
86Dic107⋊C4—21no—
87Dic107⋊C4—21no—
88C22⋊Dic107—21no—
89C22⋊Dic107—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4—21no—
93(C2×D107)⋊C4—21no—
94(C2×D107)⋊C4—21no—
95(C2×D107)⋊C4—21no—
96C4×Dic107—21no—
97C4×Dic107—21no—
98C2×D4×C107D411yescharacteristic
99C22×C4×C107C2311yescharacteristic
100C22×C4×C107C2311yescharacteristic
101C2×C8×C107—41no—
102C2×C8×C107—41no—
103C2×C8×C107C2311yescharacteristic
104C2×C8×C107C2311yescharacteristic
105C2×C8×C107C2311yescharacteristic
106C2×C8×C107C2311yescharacteristic
107C4⋊C4×C107D411yescharacteristic
108C22⋊C4×C107D411yescharacteristic
109C22⋊C4×C107D411yescharacteristic
110C42×C107C2311yescharacteristic
111C23×C107C2×D411yescharacteristic
112C23×C107C2×D411yescharacteristic
113C22×D107—21no—
114C22×D107—21no—
115D4×C107—22no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107C2×D411yescharacteristic
121C2×C4×C107C2×D411yescharacteristic
122C2×C4×C107C2×D411yescharacteristic
123C2×C4×C107C2×D411yescharacteristic
124C2×C4×C107C2411yescharacteristic
125C22⋊D107—42no—
126C22⋊D107—42no—
127C22⋊D107—42no—
128C22⋊D107—81no—
129C2×Dic107—21no—
130C2×Dic107—21no—
131C2×Dic107—21no—
132C2×Dic107—21no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107—42no—
136C2×Dic107—81no—
137D428—21no—
138D428—21no—
139D428—21no—
140D428—21no—
141C4×D107—42no—
142C4×D107—81no—
143Dic214—21no—
144Dic214—21no—
145Dic214—21no—
146Dic214—42no—
147Dic214#4112yes—
148C8×C107—21no—
149C8×C107—21no—
150C8×C107—21no—
151C8×C107—21no—
152C22×C107—21no—
153C22×C107—21no—
154C22×C107—21no—
155C22×C107—21no—
156C22×C107—21no—
157C22×C107#13512yes—
158C22×C107C22×D411yescharacteristic
159C2×D107—41no—
160C2×D107—41no—
161C2×D107—41no—
162C2×D107—41no—
163C2×D107—41no—
164C2×D107—41no—
165C4×C107—21no—
166C4×C107—21no—
167C4×C107—21no—
168C4×C107—21no—
169C4×C107C2×#4111yescharacteristic
170C4×C107H(5,𝔽2)11yescharacteristic
171Dic107—22no—
172Dic107—41no—
173Dic107—41no—
174Dic107—41no—
175Dic107—41no—
176Dic107—41no—
177C2×C107—22no—
178C2×C107—41no—
179C2×C107#54611yescharacteristic
180C2×C107C2×#13511yescharacteristic
181C2×C107#57711yescharacteristic
182D107—81no—
183D107—81no—
184#3301—1071nomaximal, Sylow
185C107#330111yescharacteristic, complemented, Sylow
186#553—1071no—
187#548—1071no—
188#488—1071no—
189#485—1071no—
190#481—1071no—
191#479—1071no—
192#466—1071no—
193#465—1071no—
194#463—1071no—
195#449—1071no—
196#448—1071no—
197C4×SD16—1071no—
198C8×D4D10711yescharacteristic, complemented
199#416—1071no—
200C2×#103—1071no—
201C2×#41—1071no—
202C22×Q8—1071no—
203C2×SD16—1071no—
204C2×SD16—1071no—
205C2×D8—1071no—
206C22×C8C2×D10711yescharacteristic
207C22×C8C2×D10711yescharacteristic
208#126—2141no—
209#125—1071no—
210#124—1071no—
211#124—2141no—
212#123—2141no—
213C22⋊Q8—1071no—
214C22⋊Q8—2141no—
215#121—1071no—
216#121—1071no—
217#121—1071no—
218#121—2141no—
219#121—2141no—
220C4×Q8—1071no—
221C4×D4—1071no—
222C4×D4—2141no—
223C4×D4—2141no—
224C4×D4C2×D10711yescharacteristic
225#117—1071no—
226C2×C4⋊C4—1071no—
227#107—1071no—
228#106—1071no—
229#106—1071no—
230C4⋊C8C2×D10711yescharacteristic
231#103—1071no—
232#103—1071no—
233#103—1071no—
234#103—1071no—
235#103—1071no—
236#103—1071no—
237#102—1071no—
238#102—1071no—
239#102—1071no—
240#102—1071no—
241C22⋊C8C2×D10711yescharacteristic
242C22⋊C8C2×D10711yescharacteristic
243C4×C8C2×D10711yescharacteristic
244#41—4281no—
245#41—2142no—
246C2×Q8—1071no—
247C2×Q8—1071no—
248C2×Q8—4281no—
249C2×Q8—2142no—
250C2×Q8—2141no—
251C2×D4—1071no—
252C2×D4—1071no—
253C2×D4—2141no—
254C2×D4—2141no—
255C2×D4—2141no—
256C2×D4—2141no—
257C2×D4D42811yescharacteristic
258C22×C4—2141no—
259C22×C4—2141no—
260C22×C4—2141no—
261C22×C4—2141no—
262C22×C4C22×D10711yescharacteristic
263C22×C4C22×D10711yescharacteristic
264SD16—4281no—
265SD16—2142no—
266D8—4281no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8C22×D10711yescharacteristic
270C2×C8C22×D10711yescharacteristic
271C2×C8C22×D10711yescharacteristic
272C2×C8C22×D10711yescharacteristic
273C4⋊C4—1071no—
274C4⋊C4—1071no—
275C4⋊C4—1071no—
276C4⋊C4—1071no—
277C4⋊C4—2141no—
278C4⋊C4—2141no—
279C4⋊C4—2141no—
280C4⋊C4—2141no—
281C4⋊C4—2141no—
282C4⋊C4D42811yescharacteristic
283C22⋊C4—2141no—
284C22⋊C4—2141no—
285C22⋊C4—2141no—
286C22⋊C4—2141no—
287C22⋊C4—2141no—
288C22⋊C4—2141no—
289C22⋊C4—2141no—
290C22⋊C4—2141no—
291C22⋊C4D42811yescharacteristic
292C22⋊C4D42811yescharacteristic
293C42—2141no—
294C42—2141no—
295C42C22×D10711yescharacteristic
296C23—2141no—
297C23—2141no—
298C23C2×D42811yescharacteristic
299C23C2×D42811yescharacteristic
300Q8—1072no—
301Q8—4282no—
302Q8—2141no—
303Q8—2141no—
304Q8—2141no—
305D4—22no—
306D4—8561no—
307D4—4282no—
308D4—4282no—
309D4—4282no—
310D4—2141no—
311D4—2141no—
312D4—2141no—
313D4—2141no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—8561no—
319C2×C4—8561no—
320C2×C4—4282no—
321C2×C4—4282no—
322C2×C4—2141no—
323C2×C4—2141no—
324C2×C4—2141no—
325C2×C4—2141no—
326C2×C4—2141no—
327C2×C4—2141no—
328C2×C4C2×D42811yescharacteristic
329C2×C4C2×D42811yescharacteristic
330C2×C4C2×D42811yescharacteristic
331C2×C4C2×D42811yescharacteristic
332C2×C4C23×D10711yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—4281no—
343C22—4281no—
344C22—4281no—
345C22—4281no—
346C22—4281no—
347C22—4281no—
348C22#1681213112yes—
349C22C22×D42811yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—4281no—
355C4—4281no—
356C4—4281no—
357C4—4281no—
358C4—4281no—
359C4—2142no—
360C4#41×D10711yescharacteristic
361C4#1681215411yescharacteristic
362C2—22no—
363C2—41no—
364C2—8561no—
365C2—8561no—
366C2#2029327211yescharacteristic
367C2C2×#1681213111yescharacteristic
368C2#2029343911yescharacteristic
subgroupG/H
centerC22C22×D428
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC8×D4×C107C2
socleC22×C107C22×D4
hypercenterC8×D4D107
hypocenterC107#3301
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #20293323C2semidirect
2. #20293286C2semidirect
3. #20292982C2semidirect
4. #20292969C2semidirect
5. #20292946C2semidirect
6. #20292935C2semidirect
7. #20292863C2semidirect
8. #20292856C2semidirect
9. #20292843C2semidirect
10. #20292774C2semidirect
11. #20292768C2semidirect
12. C4×#13133807C2semidirect
13. #20292624C2semidirect
14. C2×#16812034C2semidirect
15. C8×D4×C107C2semidirect
185. C107#3301semidirect
198. C8×D4D107semidirect

Maximal subgroups

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

subgroupindex
#202933232
#202932862
#202929822
#202929692
#202929462
#202929352
#202928632
#202928562
#202928432
#202927742
#202927682
C4×#131338072
#202926242
C2×#168120342
C8×D4×C1072
#3301107