Finite Group Databasebeta

← #28348306

Subgroups — #28348306

Order 13696.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293324C211yesmaximal, characteristic, complemented
2#20293274C211yesmaximal, characteristic, complemented
3#20292980C211yesmaximal, characteristic, complemented
4#20292964C211yesmaximal, characteristic, complemented
5#20292948C211yesmaximal, characteristic, complemented
6#20292930C211yesmaximal, characteristic, complemented
7#20292855C211yesmaximal, characteristic, complemented
8#20292840C211yesmaximal, characteristic, complemented
9#20292770C211yesmaximal, characteristic, complemented
10#20292759C211yesmaximal, characteristic, complemented
11#20292707C211yesmaximal, characteristic, complemented
12C8×C22⋊D107C211yesmaximal, characteristic, complemented
13#20292624C211yesmaximal, characteristic, complemented
14#102×D107C211yesmaximal, characteristic, complemented
15#466×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C2×D4×D107C2211yescharacteristic
18C2×#13133806C2211yescharacteristic, complemented
19C2×#13133803C2211yescharacteristic
20C2×C8×D107C2211yescharacteristic
21#16812102—21no—
22#16812100C2211yescharacteristic, complemented
23#16812096C2211yescharacteristic
24#16812091—21no—
25#16812090—21no—
26#16812089C2211yescharacteristic
27#16812080—21no—
28#16812080—21no—
29#16812080C2211yescharacteristic
30#16812077—21no—
31D4×Dic107C2211yescharacteristic, complemented
32#16812071C2211yescharacteristic
33C4×C22⋊D107C2211yescharacteristic
34(C22⋊D107)⋊C4—21no—
35#16812068C2211yescharacteristic, complemented
36C4⋊C4×D107C2211yescharacteristic
37C22⋊C4×D107—21no—
38#16812042C2211yescharacteristic, complemented
39#16812040C2211yescharacteristic, complemented
40Dic107⋊C8C2211yescharacteristic, complemented
41#16812034C2211yescharacteristic, complemented
42#16812034C2211yescharacteristic, complemented
43#16812032C2211yescharacteristic, complemented
44#16812031C2211yescharacteristic
45#16812031C2211yescharacteristic
46#16812030C2211yescharacteristic
47#16812030C2211yescharacteristic
48#16812029C2211yescharacteristic
49C22⋊(C107⋊C8)C2211yescharacteristic, complemented
50(C2×D107)⋊C8C2211yescharacteristic
51C8×Dic107C2211yescharacteristic, complemented
52C2×D8×C107C2211yescharacteristic
53C22×C8×C107C2211yescharacteristic, complemented
54#121×C107C2211yescharacteristic
55#121×C107C2211yescharacteristic, complemented
56#107×C107C2211yescharacteristic, complemented
57#102×C107C2211yescharacteristic
58#102×C107C2211yescharacteristic, complemented
59C23×D107—21no—
60#13133818—22no—
61#13133818—41no—
62C2×Dic214C2311yescharacteristic
63C2×D428C2311yescharacteristic
64C2×C22⋊D107—21no—
65C2×C22⋊D107—21no—
66C2×C22⋊D107—21no—
67C2×C22⋊D107D411yescharacteristic
68D4×D107—22no—
69D4×D107—41no—
70C22×Dic107—21no—
71C2×C4×D107—21no—
72C2×C4×D107—21no—
73C2×C4×D107—21no—
74C2×C4×D107C2311yescharacteristic
75#13133806—41no—
76#13133803—22no—
77C2×C107⋊C8C2311yescharacteristic
78C2×C107⋊C8C2311yescharacteristic
79C8×D107—41no—
80C4⋊Dic107—21no—
81C4⋊Dic107—21no—
82C4⋊Dic107C2311yescharacteristic
83C4⋊Dic107C2311yescharacteristic
84Dic107⋊C4—21no—
85Dic107⋊C4—21no—
86Dic107⋊C4D411yescharacteristic
87C22⋊Dic107—21no—
88C22⋊Dic107—21no—
89C22⋊Dic107—21no—
90C22⋊Dic107—21no—
91C22⋊Dic107—21no—
92C22⋊Dic107D411yescharacteristic
93(C2×D107)⋊C4—21no—
94(C2×D107)⋊C4—21no—
95(C2×D107)⋊C4D411yescharacteristic
96C4×Dic107—21no—
97C4×Dic107C2311yescharacteristic
98C2×D4×C107—21no—
99C2×D4×C107—21no—
100C2×D4×C107C2311yescharacteristic
101C2×D4×C107C2311yescharacteristic
102C22×C4×C107C2311yescharacteristic
103D8×C107—41no—
104C2×C8×C107—41no—
105C2×C8×C107C2311yescharacteristic
106C2×C8×C107C2311yescharacteristic
107C4⋊C4×C107C2311yescharacteristic
108C4⋊C4×C107C2311yescharacteristic
109C22⋊C4×C107—21no—
110C22⋊C4×C107—21no—
111C23×C107—21no—
112C23×C107—21no—
113C23×C107C2×D411yescharacteristic
114C22×D107—21no—
115C22×D107—42no—
116C22×D107—42no—
117C22×D107—81no—
118C22×D107C2×D411yescharacteristic
119D4×C107—21no—
120D4×C107—21no—
121D4×C107—21no—
122D4×C107—21no—
123D4×C107—81no—
124D4×C107—81no—
125C2×C4×C107—21no—
126C2×C4×C107—21no—
127C2×C4×C107—21no—
128C2×C4×C107—21no—
129C2×C4×C107C2×D411yescharacteristic
130C2×C4×C107C2411yescharacteristic
131C22⋊D107—22no—
132C22⋊D107—42no—
133C22⋊D107—42no—
134C22⋊D107—42no—
135C2×Dic107—21no—
136C2×Dic107—21no—
137C2×Dic107—21no—
138C2×Dic107—81no—
139C2×Dic107C2×D411yescharacteristic
140C2×Dic107C2×D411yescharacteristic
141C2×Dic107C2×D411yescharacteristic
142D428—21no—
143D428#4112yes—
144C4×D107—21no—
145C4×D107—21no—
146C4×D107—42no—
147C4×D107—81no—
148C4×D107—81no—
149Dic214—21no—
150Dic214—21no—
151C8×C107—21no—
152C8×C107—21no—
153C107⋊C8—21no—
154C107⋊C8—21no—
155C22×C107—21no—
156C22×C107—21no—
157C22×C107—21no—
158C22×C107—41no—
159C22×C107—41no—
160C22×C107—41no—
161C22×C107—41no—
162C22×C107—41no—
163C22×C107—41no—
164C22×C107C22×D411yescharacteristic
165C2×D107—21no—
166C2×D107—21no—
167C2×D107—22no—
168C2×D107—41no—
169C2×D107—41no—
170C2×D107—84no—
171C2×D107#13512yes—
172C4×C107—21no—
173C4×C107—41no—
174C4×C107—41no—
175C4×C107C2×#4111yescharacteristic
176C4×C107H(5,𝔽2)11yescharacteristic
177Dic107—21no—
178Dic107—21no—
179Dic107—21no—
180Dic107—41no—
181Dic107—41no—
182Dic107—41no—
183C2×C107—41no—
184C2×C107—81no—
185C2×C107—81no—
186C2×C107#54611yescharacteristic
187C2×C107C2×#13511yescharacteristic
188C2×C107#57611yescharacteristic
189D107—22no—
190D107—42no—
191#3297—1071nomaximal, Sylow
192C107#329711yescharacteristic, complemented, Sylow
193#553—1071no—
194#546—1071no—
195#488—1071no—
196#484—1071no—
197#482—1071no—
198#478—1071no—
199#466D10711yescharacteristic, complemented
200#465—1071no—
201#463—1071no—
202#449—1071no—
203#447—1071no—
204C4×D8—1071no—
205C8×D4—1071no—
206#416—1071no—
207C2×#102—1071no—
208C2×#41—1071no—
209C22×D4—1071no—
210C2×SD16—1071no—
211C2×D8—1071no—
212C2×D8C2×D10711yescharacteristic
213C22×C8—1071no—
214C22×C8C2×D10711yescharacteristic, complemented
215#126—2141no—
216#125—1071no—
217#124—1071no—
218#123—2141no—
219#123—2141no—
220C22⋊Q8—1071no—
221#121—1071no—
222#121—2141no—
223#121—2141no—
224#121C2×D10711yescharacteristic
225#121C2×D10711yescharacteristic, complemented
226#120—2141no—
227C4×D4—1071no—
228C4×D4—1071no—
229C4×D4—1071no—
230C4×D4—2141no—
231#117—1071no—
232C2×C4⋊C4—1071no—
233C2×C22⋊C4—2141no—
234#107—1071no—
235#107C2×D10711yescharacteristic, complemented
236#106—1071no—
237C4⋊C8—1071no—
238#103—1071no—
239#103—1071no—
240#103—1071no—
241#102—1071no—
242#102—1071no—
243#102—1071no—
244#102—1071no—
245#102—1071no—
246#102C2×D10711yescharacteristic
247#102C2×D10711yescharacteristic, complemented
248C22⋊C8—1071no—
249C22⋊C8—1071no—
250C4×C8—1071no—
251C24—2141no—
252#41—4281no—
253#41—2142no—
254C2×Q8—1071no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—1071no—
258C2×D4—1071no—
259C2×D4—4281no—
260C2×D4—2141no—
261C2×D4—2142no—
262C2×D4—2141no—
263C2×D4—2141no—
264C2×D4C22×D10711yescharacteristic
265C2×D4C22×D10711yescharacteristic
266C22×C4—1071no—
267C22×C4—2141no—
268C22×C4—2141no—
269C22×C4—2141no—
270C22×C4—2141no—
271C22×C4C22×D10711yescharacteristic
272SD16—4281no—
273D8—41no—
274D8—2142no—
275C2×C8—41no—
276C2×C8—1071no—
277C2×C8—1071no—
278C2×C8—4281no—
279C2×C8C22×D10711yescharacteristic
280C2×C8C22×D10711yescharacteristic
281C4⋊C4—1071no—
282C4⋊C4—1071no—
283C4⋊C4—1071no—
284C4⋊C4—2141no—
285C4⋊C4—2141no—
286C4⋊C4—2141no—
287C4⋊C4—2141no—
288C4⋊C4C22×D10711yescharacteristic
289C4⋊C4C22×D10711yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—1071no—
293C22⋊C4—1071no—
294C22⋊C4—2141no—
295C22⋊C4—2141no—
296C22⋊C4—2141no—
297C22⋊C4—2141no—
298C22⋊C4—2141no—
299C22⋊C4—2141no—
300C22⋊C4—2141no—
301C42—1071no—
302C42—2141no—
303C23—21no—
304C23—21no—
305C23—8561no—
306C23—1071no—
307C23—4282no—
308C23—4282no—
309C23—2141no—
310C23D4×D10711yescharacteristic
311Q8—2141no—
312Q8—2141no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—81no—
318D4—81no—
319D4—1072no—
320D4—4282no—
321D4—4282no—
322D4—4282no—
323D4—2142no—
324D4—2141no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—8561no—
330C2×C4—8561no—
331C2×C4—8561no—
332C2×C4—1071no—
333C2×C4—1071no—
334C2×C4—1071no—
335C2×C4—4282no—
336C2×C4—2141no—
337C2×C4—2141no—
338C2×C4—2141no—
339C2×C4—2141no—
340C2×C4—2141no—
341C2×C4D4×D10711yescharacteristic
342C2×C4C23×D10711yescharacteristic
343C8—21no—
344C8—21no—
345C8—2141no—
346C8—2141no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—8564no—
357C22—1072no—
358C22—4281no—
359C22—4281no—
360C22—2142no—
361C22—2141no—
362C22—2141no—
363C22C2×D4×D10711yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—4281no—
368C4—4281no—
369C4—4281no—
370C4—2141no—
371C4—2141no—
372C4—2141no—
373C4#41×D10711yescharacteristic
374C4#1681215411yescharacteristic
375C2—41no—
376C2—81no—
377C2—81no—
378C2—4282no—
379C2—2142no—
380C2#2029326611yescharacteristic
381C2#135×D10711yescharacteristic
382C2#2029342811yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#466×C107C2
socleC22×C107C22×D4
hypercenter#466D107
hypocenterC107#3297
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #20293324C2semidirect
2. #20293274C2semidirect
3. #20292980C2semidirect
4. #20292964C2semidirect
5. #20292948C2semidirect
6. #20292930C2semidirect
7. #20292855C2semidirect
8. #20292840C2semidirect
9. #20292770C2semidirect
10. #20292759C2semidirect
11. #20292707C2semidirect
12. C8×C22⋊D107C2semidirect
13. #20292624C2semidirect
14. #102×D107C2semidirect
15. #466×C107C2semidirect
18. C2×#13133806C22semidirect
22. #16812100C22semidirect
31. D4×Dic107C22semidirect
35. #16812068C22semidirect
38. #16812042C22semidirect
39. #16812040C22semidirect
40. Dic107⋊C8C22semidirect
41. #16812034C22semidirect
42. #16812034C22semidirect
43. #16812032C22semidirect
49. C22⋊(C107⋊C8)C22semidirect
51. C8×Dic107C22semidirect
53. C22×C8×C107C22semidirect
55. #121×C107C22semidirect
56. #107×C107C22semidirect
58. #102×C107C22semidirect
192. C107#3297semidirect
199. #466D107semidirect
214. C22×C8C2×D107semidirect
225. #121C2×D107semidirect
235. #107C2×D107semidirect
247. #102C2×D107semidirect

Maximal subgroups

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

subgroupindex
#202933242
#202932742
#202929802
#202929642
#202929482
#202929302
#202928552
#202928402
#202927702
#202927592
#202927072
C8×C22⋊D1072
#202926242
#102×D1072
#466×C1072
#3297107