Finite Group Databasebeta

← #28346459

Subgroups — #28346459

Order 13696.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293174C211yesmaximal, characteristic, complemented
2C4×D4×D107C211yesmaximal, characteristic, complemented
3#20292942C211yesmaximal, characteristic, complemented
4#20292939C211yesmaximal, characteristic, complemented
5#20292906C211yesmaximal, characteristic, complemented
6#20292905C211yesmaximal, characteristic, complemented
7#20292821C211yesmaximal, characteristic, complemented
8#20292820C211yesmaximal, characteristic, complemented
9#20292762C211yesmaximal, characteristic, complemented
10#20292759C211yesmaximal, characteristic, complemented
11C4×D856C211yesmaximal, characteristic, complemented
12C4×#13133803C211yesmaximal, characteristic, complemented
13C4×#13133803C211yesmaximal, characteristic, complemented
14#20292678C211yesmaximal, characteristic, complemented
15C4×D8×C107C211yesmaximal, characteristic, complemented
16C2×#13133818—21no—
17C2×D4×D107C2211yescharacteristic
18C22×C4×D107—21no—
19C2×D856C2211yescharacteristic
20C2×#13133803C2211yescharacteristic
21C2×#13133803C2211yescharacteristic
22#16812108C2211yescharacteristic, complemented
23#16812105C2211yescharacteristic, complemented
24#16812095—21no—
25#16812084C2211yescharacteristic
26#16812082—21no—
27#16812080C2211yescharacteristic
28C4×D428C2211yescharacteristic
29C4×D428C2211yescharacteristic, complemented
30D4×Dic107C2211yescharacteristic
31#16812071C2211yescharacteristic
32C4×C22⋊D107—21no—
33C4×C22⋊D107—21no—
34(C22⋊D107)⋊C4—21no—
35C4⋊C4×D107C2211yescharacteristic
36C22⋊C4×D107—21no—
37C42×D107C2211yescharacteristic
38#16812043C2211yescharacteristic, complemented
39#16812042C2211yescharacteristic, complemented
40#16812042C2211yescharacteristic, complemented
41Dic107⋊C8C2211yescharacteristic, complemented
42Dic107⋊C8C2211yescharacteristic, complemented
43#16812031C2211yescharacteristic
44#16812031C2211yescharacteristic, complemented
45#16812030C2211yescharacteristic
46#16812030C2211yescharacteristic, complemented
47#16812029C2211yescharacteristic
48#16812029C2211yescharacteristic, complemented
49(C2×D107)⋊C8C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51C4×C107⋊C8C2211yescharacteristic, complemented
52C2×D8×C107C2211yescharacteristic
53C4×D4×C107C2211yescharacteristic
54C4×D4×C107C2211yescharacteristic, complemented
55#107×C107C2211yescharacteristic, complemented
56#102×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic, complemented
58C4×C8×C107C2211yescharacteristic, complemented
59C23×D107—21no—
60#13133818—44no—
61C2×Dic214—21no—
62C2×D428—21no—
63C2×D428C2311yescharacteristic
64C2×D428C2311yescharacteristic
65C2×C22⋊D107—21no—
66C2×C22⋊D107—21no—
67C2×C22⋊D107—21no—
68C2×C22⋊D107—21no—
69D4×D107—22no—
70D4×D107—22no—
71C22×Dic107—21no—
72C2×C4×D107—21no—
73C2×C4×D107—21no—
74C2×C4×D107—21no—
75C2×C4×D107—21no—
76C2×C4×D107—44no—
77C2×C4×D107D411yescharacteristic
78C2×C4×D107D411yescharacteristic
79C2×C4×D107C2311yescharacteristic
80D856—22no—
81#13133803—22no—
82#13133803—22no—
83C2×C107⋊C8C2311yescharacteristic
84C2×C107⋊C8C2311yescharacteristic
85C4⋊Dic107C2311yescharacteristic
86C4⋊Dic107C2311yescharacteristic
87Dic107⋊C4—21no—
88Dic107⋊C4—21no—
89C22⋊Dic107—21no—
90C22⋊Dic107—21no—
91(C2×D107)⋊C4—21no—
92(C2×D107)⋊C4—21no—
93(C2×D107)⋊C4—21no—
94(C2×D107)⋊C4—21no—
95C4×Dic107D411yescharacteristic
96C4×Dic107D411yescharacteristic
97C4×Dic107C2311yescharacteristic
98C2×D4×C107C2311yescharacteristic
99C2×D4×C107C2311yescharacteristic
100C22×C4×C107—21no—
101C22×C4×C107—21no—
102D8×C107—22no—
103C2×C8×C107C2311yescharacteristic
104C2×C8×C107C2311yescharacteristic
105C4⋊C4×C107C2311yescharacteristic
106C4⋊C4×C107C2311yescharacteristic
107C22⋊C4×C107—21no—
108C22⋊C4×C107—21no—
109C42×C107C2311yescharacteristic
110C23×C107—21no—
111C23×C107—21no—
112C22×D107—24no—
113C22×D107—21no—
114C22×D107—21no—
115C22×D107—42no—
116C22×D107—42no—
117C22×D107C2×D411yescharacteristic
118D4×C107—21no—
119D4×C107—21no—
120D4×C107—21no—
121D4×C107#4112yescomplemented
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—42no—
125C2×C4×C107—42no—
126C2×C4×C107C2×D411yescharacteristic
127C2×C4×C107C2×D411yescharacteristic
128C2×C4×C107C2411yescharacteristic
129C22⋊D107—24no—
130C22⋊D107—42no—
131C22⋊D107—42no—
132C22⋊D107—42no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107—42no—
136C2×Dic107C2×D411yescharacteristic
137C2×Dic107C2×D411yescharacteristic
138C2×Dic107C2×D411yescharacteristic
139D428—21no—
140D428—21no—
141D428—21no—
142D428—42no—
143D428#4112yescomplemented
144C4×D107—21no—
145C4×D107—21no—
146C4×D107—41no—
147C4×D107—42no—
148C4×D107—42no—
149C4×D107—42no—
150C4×D107—42no—
151C4×D107D814yescomplemented
152Dic214—42no—
153C8×C107—21no—
154C8×C107—21no—
155C107⋊C8—21no—
156C107⋊C8—21no—
157C22×C107—22no—
158C22×C107—41no—
159C22×C107—41no—
160C22×C107—41no—
161C22×C107—41no—
162C22×C107—41no—
163C22×C107C22×D411yescharacteristic
164C2×D107—21no—
165C2×D107—21no—
166C2×D107—22no—
167C2×D107—48no—
168C2×D107—41no—
169C2×D107—41no—
170C2×D107—41no—
171C2×D107—41no—
172C2×D107—41no—
173C2×D107C2×D812yes—
174C4×C107—21no—
175C4×C107—41no—
176C4×C107—41no—
177C4×C107C2×D812yes—
178C4×C107C2×#4111yescharacteristic
179C4×C107C2×#4111yescharacteristic
180Dic107—21no—
181Dic107—21no—
182Dic107—41no—
183Dic107—41no—
184Dic107C2×D812yes—
185C2×C107—42no—
186C2×C107—81no—
187C2×C107#52511yescharacteristic
188C2×C107C22×D811yescharacteristic
189C2×C107#57511yescharacteristic
190D107—22no—
191D107—42no—
192D107—81no—
193#3100—1071nomaximal, Sylow
194C107#310011yescharacteristic, complemented, Sylow
195#532—1071no—
196C2×C4×D4—1071no—
197#480—1071no—
198#480—1071no—
199#474—1071no—
200#474—1071no—
201#459—1071no—
202#459—1071no—
203#447—1071no—
204#447—1071no—
205C4×D8—1071no—
206C4×D8—1071no—
207C4×D8—1071no—
208C4×D8D10711yescharacteristic, complemented
209#431—1071no—
210C2×#41—2141no—
211C22×D4—1071no—
212C23×C4—2141no—
213C2×D8—1071no—
214C2×D8—1071no—
215C2×D8—1071no—
216C2×D8C2×D10711yescharacteristic
217C4⋊Q8—1071no—
218#127—1071no—
219#124—2141no—
220#121—1071no—
221#121—1071no—
222#121—2141no—
223C4×D4—1071no—
224C4×D4—1071no—
225C4×D4—1071no—
226C4×D4—1071no—
227C4×D4—2141no—
228C4×D4—2141no—
229C4×D4—2141no—
230C4×D4C2×D10711yescharacteristic
231C4×D4C2×D10711yescharacteristic, complemented
232C2×C4⋊C4—1071no—
233C2×C22⋊C4—2141no—
234C2×C42—1071no—
235#107—1071no—
236#107—1071no—
237#107—1071no—
238#107C2×D10711yescharacteristic, complemented
239C4⋊C8—1071no—
240C4⋊C8—1071no—
241#102—1071no—
242#102—1071no—
243#102—1071no—
244#102—1071no—
245#102—1071no—
246#102—1071no—
247#102C2×D10711yescharacteristic
248#102C2×D10711yescharacteristic, complemented
249C22⋊C8—1071no—
250C22⋊C8—1071no—
251C4×C8—1071no—
252C4×C8C2×D10711yescharacteristic, complemented
253C24—2141no—
254#41—4284no—
255C2×Q8—2141no—
256C2×D4—1071no—
257C2×D4—1071no—
258C2×D4—2141no—
259C2×D4—2141no—
260C2×D4—2141no—
261C2×D4—2141no—
262C2×D4—2142no—
263C2×D4—2141no—
264C2×D4—2142no—
265C2×D4C22×D10711yescharacteristic
266C2×D4C22×D10711yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—1071no—
270C22×C4—1071no—
271C22×C4—1071no—
272C22×C4—4284no—
273C22×C4—2141no—
274C22×C4—2141no—
275C22×C4—2141no—
276C22×C4—2141no—
277C22×C4—2141no—
278D8—22no—
279D8—2142no—
280D8—2142no—
281D8—2142no—
282C2×C8—1071no—
283C2×C8—1071no—
284C2×C8C22×D10711yescharacteristic
285C2×C8C22×D10711yescharacteristic
286C4⋊C4—1071no—
287C4⋊C4—1071no—
288C4⋊C4—2141no—
289C4⋊C4—2141no—
290C4⋊C4C22×D10711yescharacteristic
291C4⋊C4C22×D10711yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—2141no—
295C22⋊C4—2141no—
296C22⋊C4—2141no—
297C22⋊C4—2141no—
298C22⋊C4—2141no—
299C22⋊C4—2141no—
300C42—1071no—
301C42—1071no—
302C42—1071no—
303C42C22×D10711yescharacteristic
304C23—21no—
305C23—21no—
306C23—1071no—
307C23—4282no—
308C23—4282no—
309C23—2144no—
310C23—2141no—
311C23—2141no—
312Q8—4282no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—1072no—
317D4—4282no—
318D4—4282no—
319D4—4282no—
320D4—4282no—
321D4—2144no—
322D4—2141no—
323D4—2141no—
324D4—2141no—
325D4#1313381812yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—1071no—
331C2×C4—1074no—
332C2×C4—1071no—
333C2×C4—1071no—
334C2×C4—4281no—
335C2×C4—4282no—
336C2×C4—4282no—
337C2×C4—4282no—
338C2×C4—4282no—
339C2×C4—4282no—
340C2×C4—2141no—
341C2×C4—2141no—
342C2×C4—2141no—
343C2×C4—2141no—
344C2×C4D4×D10711yescharacteristic
345C2×C4D4×D10711yescharacteristic
346C2×C4C23×D10711yescharacteristic
347C8—21no—
348C8—21no—
349C8—2141no—
350C8—2141no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—1072no—
358C22—4288no—
359C22—4281no—
360C22—4281no—
361C22—4281no—
362C22—4281no—
363C22—4281no—
364C22—2142no—
365C22—2141no—
366C22—2141no—
367C22C2×D4×D10711yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—1072no—
372C4—4281no—
373C4—4281no—
374C4—2141no—
375C4—2141no—
376C4D8×D10712yes—
377C4#41×D10711yescharacteristic
378C4C2×#1313381811yescharacteristic
379C2—42no—
380C2—81no—
381C2—8561no—
382C2—4282no—
383C2—2142no—
384C2#2029313611yescharacteristic
385C2C2×D8×D10711yescharacteristic
386C2#2029342411yescharacteristic
subgroupG/H
centerC2×C4D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC4×D8×C107C2
socleC22×C107C22×D4
hypercenterC4×D8D107
hypocenterC107#3100
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20293174C2semidirect
2. C4×D4×D107C2semidirect
3. #20292942C2semidirect
4. #20292939C2semidirect
5. #20292906C2semidirect
6. #20292905C2semidirect
7. #20292821C2semidirect
8. #20292820C2semidirect
9. #20292762C2semidirect
10. #20292759C2semidirect
11. C4×D856C2semidirect
12. C4×#13133803C2semidirect
13. C4×#13133803C2semidirect
14. #20292678C2semidirect
15. C4×D8×C107C2semidirect
22. #16812108C22semidirect
23. #16812105C22semidirect
29. C4×D428C22semidirect
38. #16812043C22semidirect
39. #16812042C22semidirect
40. #16812042C22semidirect
41. Dic107⋊C8C22semidirect
42. Dic107⋊C8C22semidirect
44. #16812031C22semidirect
46. #16812030C22semidirect
48. #16812029C22semidirect
51. C4×C107⋊C8C22semidirect
54. C4×D4×C107C22semidirect
55. #107×C107C22semidirect
57. #102×C107C22semidirect
58. C4×C8×C107C22semidirect
121. D4×C107#41semidirect
143. D428#41semidirect
151. C4×D107D8semidirect
194. C107#3100semidirect
208. C4×D8D107semidirect
231. C4×D4C2×D107semidirect
238. #107C2×D107semidirect
248. #102C2×D107semidirect
252. C4×C8C2×D107semidirect
325. D4#13133818semidirect

Maximal subgroups

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

subgroupindex
#202931742
C4×D4×D1072
#202929422
#202929392
#202929062
#202929052
#202928212
#202928202
#202927622
#202927592
C4×D8562
C4×#131338032
#202926782
C4×D8×C1072
#3100107