Finite Group Databasebeta

← #28348454

Subgroups — #28348454

Order 13696.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293286C211yesmaximal, characteristic, complemented
2#20293281C211yesmaximal, characteristic, complemented
3#20292987C211yesmaximal, characteristic, complemented
4#20292963C211yesmaximal, characteristic, complemented
5#20292941C211yesmaximal, characteristic, complemented
6#20292923C211yesmaximal, characteristic, complemented
7#20292873C211yesmaximal, characteristic, complemented
8#20292863C211yesmaximal, characteristic, complemented
9#20292843C211yesmaximal, characteristic, complemented
10#20292774C211yesmaximal, characteristic, complemented
11#20292768C211yesmaximal, characteristic, complemented
12#20292729C211yesmaximal, characteristic, complemented
13#20292629C211yesmaximal, characteristic, complemented
14C2×#16812034C211yesmaximal, characteristic, complemented
15#435×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C2×#13133817—21no—
18C22×Dic214C2211yescharacteristic
19C2×#13133807C2211yescharacteristic
20C2×#13133807C2211yescharacteristic
21C2×D856C2211yescharacteristic
22#16812109C2211yescharacteristic
23#16812097C2211yescharacteristic
24#16812095—21no—
25#16812093—21no—
26#16812093—21no—
27#16812089—21no—
28#16812088C2211yescharacteristic
29#16812087—21no—
30#16812083C2211yescharacteristic
31#16812083C2211yescharacteristic
32#16812083C2211yescharacteristic
33#16812081—21no—
34C4×Dic214C2211yescharacteristic
35C4×D428C2211yescharacteristic
36(C22⋊D107)⋊C4—21no—
37C2×C4⋊Dic107C2211yescharacteristic
38C2×C4⋊Dic107C2211yescharacteristic
39#16812043C2211yescharacteristic
40#16812043C2211yescharacteristic
41#16812043C2211yescharacteristic
42#16812034C2211yescharacteristic
43#16812034C2211yescharacteristic
44#16812034C2211yescharacteristic
45#16812034C2211yescharacteristic
46#16812034C2211yescharacteristic
47#16812034C2211yescharacteristic
48#16812031C2211yescharacteristic
49#16812031C2211yescharacteristic
50#16812031C2211yescharacteristic
51#16812031C2211yescharacteristic
52C2×M16×C107C2211yescharacteristic
53C22×C8×C107C2211yescharacteristic
54C4×D4×C107C2211yescharacteristic
55C4⋊C8×C107C2211yescharacteristic
56C22⋊C8×C107C2211yescharacteristic
57C22⋊C8×C107C2211yescharacteristic
58#97×C107C2211yescharacteristic
59#13133818—22no—
60#13133818—41no—
61#13133817—44no—
62C2×Dic214—22no—
63C2×Dic214—21no—
64C2×Dic214—21no—
65C2×Dic214—41no—
66C2×Dic214C2311yescharacteristic
67C2×Dic214C2311yescharacteristic
68C2×D428C2311yescharacteristic
69C2×D428C2311yescharacteristic
70C2×C22⋊D107—21no—
71C2×C22⋊D107—21no—
72C2×C22⋊D107—21no—
73C2×C22⋊D107—21no—
74C22×Dic107—21no—
75C22×Dic107—21no—
76C22×Dic107—21no—
77C2×C4×D107—21no—
78C2×C4×D107—21no—
79#13133807—22no—
80#13133807—41no—
81D856—41no—
82C4⋊Dic107—21no—
83C4⋊Dic107—21no—
84C4⋊Dic107—21no—
85C4⋊Dic107C2311yescharacteristic
86C4⋊Dic107C2311yescharacteristic
87C4⋊Dic107C2311yescharacteristic
88C4⋊Dic107C2311yescharacteristic
89Dic107⋊C4—21no—
90Dic107⋊C4—21no—
91C22⋊Dic107—21no—
92(C2×D107)⋊C4—21no—
93(C2×D107)⋊C4—21no—
94(C2×D107)⋊C4—21no—
95(C2×D107)⋊C4—21no—
96(C2×D107)⋊C4—21no—
97(C2×D107)⋊C4—21no—
98C4×Dic107—21no—
99C2×D4×C107D411yescharacteristic
100C22×C4×C107C2311yescharacteristic
101C22×C4×C107C2311yescharacteristic
102M16×C107—41no—
103C2×C8×C107—41no—
104C2×C8×C107C2311yescharacteristic
105C2×C8×C107C2311yescharacteristic
106C2×C8×C107C2311yescharacteristic
107C2×C8×C107C2311yescharacteristic
108C4⋊C4×C107D411yescharacteristic
109C22⋊C4×C107D411yescharacteristic
110C22⋊C4×C107D411yescharacteristic
111C42×C107C2311yescharacteristic
112C23×C107C2×D411yescharacteristic
113C23×C107C2×D411yescharacteristic
114C22×D107—21no—
115C22×D107—21no—
116D4×C107—22no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107C2×D411yescharacteristic
122C2×C4×C107C2×D411yescharacteristic
123C2×C4×C107C2×D411yescharacteristic
124C2×C4×C107C2×D411yescharacteristic
125C2×C4×C107C2411yescharacteristic
126C22⋊D107—42no—
127C22⋊D107—42no—
128C22⋊D107—42no—
129C22⋊D107—42no—
130C2×Dic107—21no—
131C2×Dic107—21no—
132C2×Dic107—21no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107—21no—
136C2×Dic107—42no—
137C2×Dic107—42no—
138C2×Dic107—42no—
139D428—21no—
140D428—21no—
141D428—21no—
142D428—21no—
143C4×D107—42no—
144C4×D107—42no—
145Dic214—21no—
146Dic214—21no—
147Dic214—21no—
148Dic214—42no—
149Dic214—42no—
150Dic214#4112yescomplemented
151C8×C107—21no—
152C8×C107—21no—
153C8×C107—21no—
154C8×C107—21no—
155C22×C107—21no—
156C22×C107—21no—
157C22×C107—21no—
158C22×C107—21no—
159C22×C107—21no—
160C22×C107AGL(1,ℤ/8)12yes—
161C22×C107C22×D411yescharacteristic
162C2×D107—41no—
163C2×D107—41no—
164C2×D107—41no—
165C2×D107—41no—
166C2×D107—41no—
167C2×D107—41no—
168C4×C107—21no—
169C4×C107—21no—
170C4×C107—21no—
171C4×C107—21no—
172C4×C107C2×#4111yescharacteristic
173C4×C107H(5,𝔽2)11yescharacteristic
174Dic107—22no—
175Dic107—41no—
176Dic107—41no—
177Dic107—41no—
178Dic107—41no—
179Dic107—41no—
180C2×C107—22no—
181C2×C107—41no—
182C2×C107#54611yescharacteristic
183C2×C107C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C107#57811yescharacteristic
185D107—81no—
186D107—81no—
187#3308—1071nomaximal, Sylow
188C107#330811yescharacteristic, complemented, Sylow
189#548—1071no—
190#547—1071no—
191#489—1071no—
192#484—1071no—
193#480—1071no—
194#477—1071no—
195#468—1071no—
196#466—1071no—
197#463—1071no—
198#449—1071no—
199#448—1071no—
200#440—1071no—
201#435D10711yescharacteristic, complemented
202#417—1071no—
203C2×#103—1071no—
204C2×#41—1071no—
205C2×#41—2141no—
206C22×Q8—1071no—
207C2×SD16—1071no—
208C2×SD16—1071no—
209C2×D8—1071no—
210C2×M16C2×D10711yescharacteristic
211C22×C8C2×D10711yescharacteristic
212C4⋊Q8—1071no—
213#124—1071no—
214#124—2141no—
215#123—2141no—
216#123—2141no—
217C22⋊Q8—1071no—
218C22⋊Q8—2141no—
219C22⋊Q8—2141no—
220#121—1071no—
221#121—1071no—
222#121—1071no—
223#121—2141no—
224C4×Q8—1071no—
225C4×D4—1071no—
226C4×D4—2141no—
227C4×D4C2×D10711yescharacteristic
228C2×C4⋊C4—1071no—
229C2×C4⋊C4—1071no—
230#107—1071no—
231#107—1071no—
232#107—1071no—
233C4⋊C8C2×D10711yescharacteristic
234#103—1071no—
235#103—1071no—
236#103—1071no—
237#103—1071no—
238#103—1071no—
239#103—1071no—
240#102—1071no—
241#102—1071no—
242#102—1071no—
243#102—1071no—
244C22⋊C8C2×D10711yescharacteristic
245C22⋊C8C2×D10711yescharacteristic
246#97C2×D10711yescharacteristic
247#41—4281no—
248#41—4284no—
249#41—2142no—
250C2×Q8—1071no—
251C2×Q8—1071no—
252C2×Q8—4281no—
253C2×Q8—2142no—
254C2×Q8—2141no—
255C2×Q8—2141no—
256C2×D4—1071no—
257C2×D4—1071no—
258C2×D4—2141no—
259C2×D4—2141no—
260C2×D4—2141no—
261C2×D4—2141no—
262C2×D4D42811yescharacteristic
263C22×C4—2141no—
264C22×C4—2141no—
265C22×C4—2141no—
266C22×C4—2141no—
267C22×C4—2141no—
268C22×C4C22×D10711yescharacteristic
269C22×C4C22×D10711yescharacteristic
270SD16—4281no—
271SD16—2142no—
272D8—4281no—
273M16—41no—
274C2×C8—41no—
275C2×C8C22×D10711yescharacteristic
276C2×C8C22×D10711yescharacteristic
277C2×C8C22×D10711yescharacteristic
278C2×C8C22×D10711yescharacteristic
279C4⋊C4—1071no—
280C4⋊C4—1071no—
281C4⋊C4—1071no—
282C4⋊C4—1071no—
283C4⋊C4—2141no—
284C4⋊C4—2141no—
285C4⋊C4—2141no—
286C4⋊C4—2141no—
287C4⋊C4—2141no—
288C4⋊C4D42811yescharacteristic
289C22⋊C4—2141no—
290C22⋊C4—2141no—
291C22⋊C4—2141no—
292C22⋊C4—2141no—
293C22⋊C4—2141no—
294C22⋊C4—2141no—
295C22⋊C4—2141no—
296C22⋊C4D42811yescharacteristic
297C22⋊C4D42811yescharacteristic
298C42—2141no—
299C42C22×D10711yescharacteristic
300C23—2141no—
301C23—2141no—
302C23C2×D42811yescharacteristic
303C23C2×D42811yescharacteristic
304Q8—1072no—
305Q8—4282no—
306Q8—4282no—
307Q8—2141no—
308Q8—2141no—
309Q8—2141no—
310D4—22no—
311D4—4282no—
312D4—4282no—
313D4—4282no—
314D4—4282no—
315D4—2141no—
316D4—2141no—
317D4—2141no—
318D4—2141no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—4282no—
324C2×C4—4282no—
325C2×C4—4282no—
326C2×C4—4282no—
327C2×C4—4282no—
328C2×C4—2141no—
329C2×C4—2141no—
330C2×C4—2141no—
331C2×C4—2141no—
332C2×C4—2141no—
333C2×C4—2141no—
334C2×C4C2×D42811yescharacteristic
335C2×C4C2×D42811yescharacteristic
336C2×C4C2×D42811yescharacteristic
337C2×C4C2×D42811yescharacteristic
338C2×C4C23×D10711yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—4281no—
349C22—4281no—
350C22—4281no—
351C22—4281no—
352C22—4281no—
353C22—4281no—
354C22#1681213712yes—
355C22C22×D42811yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—4281no—
361C4—4281no—
362C4—4281no—
363C4—4281no—
364C4—4281no—
365C4—2142no—
366C4#41×D10711yescharacteristic
367C4#1681215411yescharacteristic
368C2—22no—
369C2—41no—
370C2—8561no—
371C2—8561no—
372C2#2029327211yescharacteristic
373C2C2×#1681213711yescharacteristic
374C2#2029344411yescharacteristic
subgroupG/H
centerC22C22×D428
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#435×C107C2
socleC22×C107C22×D4
hypercenter#435D107
hypocenterC107#3308
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #20293286C2semidirect
2. #20293281C2semidirect
3. #20292987C2semidirect
4. #20292963C2semidirect
5. #20292941C2semidirect
6. #20292923C2semidirect
7. #20292873C2semidirect
8. #20292863C2semidirect
9. #20292843C2semidirect
10. #20292774C2semidirect
11. #20292768C2semidirect
12. #20292729C2semidirect
13. #20292629C2semidirect
14. C2×#16812034C2semidirect
15. #435×C107C2semidirect
150. Dic214#41semidirect
188. C107#3308semidirect
201. #435D107semidirect

Maximal subgroups

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

subgroupindex
#202932862
#202932812
#202929872
#202929632
#202929412
#202929232
#202928732
#202928632
#202928432
#202927742
#202927682
#202927292
#202926292
C2×#168120342
#435×C1072
#3308107