Finite Group Databasebeta

← #28348270

Subgroups — #28348270

Order 13696.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293278C211yesmaximal, characteristic, complemented
2D4×C22⋊D107C211yesmaximal, characteristic, complemented
3#20292972C211yesmaximal, characteristic, complemented
4#20292940C211yesmaximal, characteristic, complemented
5#20292939C211yesmaximal, characteristic, complemented
6#20292905C211yesmaximal, characteristic, complemented
7#20292863C211yesmaximal, characteristic, complemented
8#20292862C211yesmaximal, characteristic, complemented
9#20292821C211yesmaximal, characteristic, complemented
10#20292762C211yesmaximal, characteristic, complemented
11#20292761C211yesmaximal, characteristic, complemented
12#20292707C211yesmaximal, characteristic, complemented
13C8×C22⋊D107C211yesmaximal, characteristic, complemented
14#102×D107C211yesmaximal, characteristic, complemented
15C2×#102×C107C211yesmaximal, characteristic, complemented
16C2×#13133818—21no—
17C22×C22⋊D107—21no—
18C2×D4×D107C2211yescharacteristic
19C2×D856C2211yescharacteristic, complemented
20C2×#13133803C2211yescharacteristic
21C2×#13133803C2211yescharacteristic, complemented
22C2×C8×D107C2211yescharacteristic, complemented
23#16812108C2211yescharacteristic, complemented
24#16812105C2211yescharacteristic
25#16812094—21no—
26#16812092—21no—
27#16812087—21no—
28#16812084C2211yescharacteristic, complemented
29#16812083C2211yescharacteristic
30#16812083C2211yescharacteristic, complemented
31#16812081—21no—
32#16812080C2211yescharacteristic
33#16812078—21no—
34#16812077—21no—
35D4×Dic107C2211yescharacteristic
36#16812071C2211yescharacteristic, complemented
37C4×C22⋊D107C2211yescharacteristic
38C4⋊C4×D107C2211yescharacteristic, complemented
39#16812043C2211yescharacteristic, complemented
40#16812042C2211yescharacteristic, complemented
41#16812042C2211yescharacteristic, complemented
42Dic107⋊C8C2211yescharacteristic, complemented
43#16812031C2211yescharacteristic, complemented
44#16812031C2211yescharacteristic, complemented
45#16812030C2211yescharacteristic
46#16812030C2211yescharacteristic, complemented
47#16812029C2211yescharacteristic, complemented
48#16812029C2211yescharacteristic, complemented
49C22⋊(C107⋊C8)C2211yescharacteristic, complemented
50(C2×D107)⋊C8C2211yescharacteristic, complemented
51C8×Dic107C2211yescharacteristic, complemented
52C22×D4×C107C2211yescharacteristic
53C22×C8×C107C2211yescharacteristic, complemented
54C2×C4⋊C4×C107C2211yescharacteristic, complemented
55#102×C107C2211yescharacteristic
56#102×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic, complemented
58#102×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—
69C2×C22⋊D107—21no—
70C2×C22⋊D107—21no—
71C2×C22⋊D107—44no—
72C2×C22⋊D107D411yescharacteristic
73D4×D107—22no—
74D4×D107—41no—
75C22×Dic107—21no—
76C2×C4×D107—21no—
77C2×C4×D107—21no—
78C2×C4×D107C2311yescharacteristic
79D856—41no—
80#13133803—22no—
81#13133803—41no—
82C2×C107⋊C8C2311yescharacteristic
83C2×C107⋊C8C2311yescharacteristic
84C8×D107—41no—
85C4⋊Dic107C2311yescharacteristic
86C4⋊Dic107C2311yescharacteristic
87Dic107⋊C4—21no—
88Dic107⋊C4—21no—
89Dic107⋊C4D411yescharacteristic
90C22⋊Dic107—21no—
91C22⋊Dic107—21no—
92C22⋊Dic107D411yescharacteristic
93(C2×D107)⋊C4—21no—
94(C2×D107)⋊C4—21no—
95(C2×D107)⋊C4—21no—
96(C2×D107)⋊C4—21no—
97(C2×D107)⋊C4D411yescharacteristic
98C4×Dic107C2311yescharacteristic
99C24×C107—21no—
100C2×D4×C107—22no—
101C2×D4×C107—21no—
102C2×D4×C107—41no—
103C2×D4×C107C2311yescharacteristic
104C2×D4×C107C2311yescharacteristic
105C22×C4×C107—21no—
106C22×C4×C107C2311yescharacteristic
107C2×C8×C107—41no—
108C2×C8×C107C2311yescharacteristic
109C2×C8×C107C2311yescharacteristic
110C4⋊C4×C107—21no—
111C4⋊C4×C107C2311yescharacteristic
112C4⋊C4×C107C2311yescharacteristic
113C23×C107—21no—
114C23×C107—21no—
115C23×C107—42no—
116C23×C107—42no—
117C23×C107—81no—
118C23×C107C2×D411yescharacteristic
119C22×D107—21no—
120C22×D107—21no—
121C22×D107—42no—
122C22×D107—42no—
123C22×D107—81no—
124C22×D107C2×D411yescharacteristic
125D4×C107—21no—
126D4×C107—21no—
127D4×C107—21no—
128D4×C107—42no—
129D4×C107#4112yescomplemented
130C2×C4×C107—21no—
131C2×C4×C107—21no—
132C2×C4×C107—21no—
133C2×C4×C107—21no—
134C2×C4×C107—42no—
135C2×C4×C107C2×D411yescharacteristic
136C2×C4×C107C2411yescharacteristic
137C22⋊D107—42no—
138C22⋊D107—42no—
139C22⋊D107—42no—
140C22⋊D107—42no—
141C22⋊D107—42no—
142C22⋊D107—81no—
143C22⋊D107D814yescomplemented
144C2×Dic107—21no—
145C2×Dic107—21no—
146C2×Dic107—42no—
147C2×Dic107C2×D411yescharacteristic
148C2×Dic107C2×D411yescharacteristic
149C2×Dic107C2×D411yescharacteristic
150D428—21no—
151D428—21no—
152D428—21no—
153D428—21no—
154D428—42no—
155C4×D107—21no—
156C4×D107—21no—
157C4×D107—42no—
158C4×D107—42no—
159Dic214—42no—
160C8×C107—21no—
161C8×C107—21no—
162C107⋊C8—21no—
163C107⋊C8—21no—
164C22×C107—21no—
165C22×C107—21no—
166C22×C107—22no—
167C22×C107—41no—
168C22×C107—41no—
169C22×C107—41no—
170C22×C107—41no—
171C22×C107—41no—
172C22×C107—84no—
173C22×C107C2×D812yes—
174C22×C107C22×D411yescharacteristic
175C2×D107—21no—
176C2×D107—21no—
177C2×D107—41no—
178C2×D107—41no—
179C2×D107—41no—
180C2×D107—41no—
181C2×D107—41no—
182C2×D107—41no—
183C2×D107—84no—
184C2×D107C2×D812yes—
185C4×C107—21no—
186C4×C107—41no—
187C4×C107—41no—
188C4×C107C2×#4111yescharacteristic
189C4×C107H(5,𝔽2)11yescharacteristic
190Dic107—21no—
191Dic107—21no—
192Dic107—41no—
193Dic107—41no—
194Dic107C2×D812yes—
195C2×C107—22no—
196C2×C107—42no—
197C2×C107—81no—
198C2×C107#54611yescharacteristic
199C2×C107C22×D811yescharacteristic
200C2×C107#57711yescharacteristic
201D107—22no—
202D107—81no—
203D107—81no—
204#3294—1071nomaximal, Sylow
205C107#329411yescharacteristic, complemented, Sylow
206#547—1071no—
207D42—1071no—
208#486—1071no—
209#480—1071no—
210#480—1071no—
211#474—1071no—
212#466—1071no—
213#466—1071no—
214#459—1071no—
215#447—1071no—
216#447—1071no—
217C4×D8—1071no—
218C8×D4—1071no—
219C2×#102—1071no—
220C2×#102D10711yescharacteristic, complemented
221C2×#41—2141no—
222C22×D4—1071no—
223C22×D4—2141no—
224C22×D4C2×D10711yescharacteristic
225C2×D8—1071no—
226C2×D8—1071no—
227C2×D8—1071no—
228C22×C8—1071no—
229C22×C8C2×D10711yescharacteristic, complemented
230C4⋊Q8—1071no—
231#127—1071no—
232#123—2141no—
233#123—2141no—
234C22⋊Q8—2141no—
235#121—1071no—
236#121—1071no—
237#121—1071no—
238#121—1071no—
239#121—2141no—
240#120—2141no—
241#120—2141no—
242C4×D4—1071no—
243C4×D4—1071no—
244C4×D4—1071no—
245C2×C4⋊C4—1071no—
246C2×C4⋊C4C2×D10711yescharacteristic, complemented
247#107—1071no—
248#107—1071no—
249#107—1071no—
250C4⋊C8—1071no—
251#102—1071no—
252#102—1071no—
253#102—1071no—
254#102—1071no—
255#102—1071no—
256#102—1071no—
257#102C2×D10711yescharacteristic
258#102C2×D10711yescharacteristic
259#102C2×D10711yescharacteristic, complemented
260#102C2×D10711yescharacteristic, complemented
261C22⋊C8—1071no—
262C22⋊C8—1071no—
263C4×C8—1071no—
264C24—21no—
265C24—2141no—
266#41—4284no—
267C2×Q8—2141no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—1071no—
272C2×D4—1071no—
273C2×D4—1071no—
274C2×D4—4284no—
275C2×D4—4281no—
276C2×D4—2141no—
277C2×D4—2141no—
278C2×D4—2141no—
279C2×D4—2141no—
280C2×D4—2141no—
281C2×D4—2141no—
282C2×D4—2141no—
283C2×D4—2142no—
284C2×D4C22×D10711yescharacteristic
285C2×D4C22×D10711yescharacteristic
286C22×C4—21no—
287C22×C4—1071no—
288C22×C4—2141no—
289C22×C4—2141no—
290C22×C4—2141no—
291C22×C4C22×D10711yescharacteristic
292D8—4281no—
293D8—4281no—
294D8—2142no—
295C2×C8—41no—
296C2×C8—1071no—
297C2×C8—1071no—
298C2×C8—4281no—
299C2×C8C22×D10711yescharacteristic
300C2×C8C22×D10711yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—1071no—
303C4⋊C4—1071no—
304C4⋊C4—1071no—
305C4⋊C4—2141no—
306C4⋊C4—2141no—
307C4⋊C4C22×D10711yescharacteristic
308C4⋊C4C22×D10711yescharacteristic
309C22⋊C4—1071no—
310C22⋊C4—1071no—
311C22⋊C4—2141no—
312C22⋊C4—2141no—
313C22⋊C4—2141no—
314C22⋊C4—2141no—
315C22⋊C4—2141no—
316C22⋊C4—2141no—
317C42—1071no—
318C23—21no—
319C23—21no—
320C23—42no—
321C23—42no—
322C23—81no—
323C23—8561no—
324C23—1071no—
325C23—4282no—
326C23—4282no—
327C23—2141no—
328C23—2141no—
329C23D4×D10711yescharacteristic
330Q8—4282no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—42no—
335D4—8561no—
336D4—1074no—
337D4—4282no—
338D4—4282no—
339D4—4282no—
340D4—4282no—
341D4—4282no—
342D4—4282no—
343D4—2141no—
344D4—2141no—
345D4—2141no—
346D4—2141no—
347D4#1313381812yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—1071no—
354C2×C4—1071no—
355C2×C4—1071no—
356C2×C4—4282no—
357C2×C4—4282no—
358C2×C4—4282no—
359C2×C4—2141no—
360C2×C4—2141no—
361C2×C4—2141no—
362C2×C4—2141no—
363C2×C4D4×D10711yescharacteristic
364C2×C4C23×D10711yescharacteristic
365C8—21no—
366C8—21no—
367C8—2141no—
368C8—2141no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—84no—
378C22—8564no—
379C22—1072no—
380C22—4281no—
381C22—4281no—
382C22—4281no—
383C22—4281no—
384C22—4281no—
385C22—4281no—
386C22—2141no—
387C22—2141no—
388C22D8×D10712yes—
389C22C2×D4×D10711yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—1072no—
394C4—4281no—
395C4—4281no—
396C4—2141no—
397C4—2141no—
398C4C2×#1313381811yescharacteristic
399C4#1681215411yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—8561no—
404C2—8561no—
405C2—2142no—
406C2#2029326711yescharacteristic
407C2C2×D8×D10711yescharacteristic
408C2#2029343311yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
FittingC2×#102×C107C2
socleC22×C107C22×D4
hypercenterC2×#102D107
hypocenterC107#3294
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #20293278C2semidirect
2. D4×C22⋊D107C2semidirect
3. #20292972C2semidirect
4. #20292940C2semidirect
5. #20292939C2semidirect
6. #20292905C2semidirect
7. #20292863C2semidirect
8. #20292862C2semidirect
9. #20292821C2semidirect
10. #20292762C2semidirect
11. #20292761C2semidirect
12. #20292707C2semidirect
13. C8×C22⋊D107C2semidirect
14. #102×D107C2semidirect
15. C2×#102×C107C2semidirect
19. C2×D856C22semidirect
21. C2×#13133803C22semidirect
22. C2×C8×D107C22semidirect
23. #16812108C22semidirect
28. #16812084C22semidirect
30. #16812083C22semidirect
36. #16812071C22semidirect
38. C4⋊C4×D107C22semidirect
39. #16812043C22semidirect
40. #16812042C22semidirect
41. #16812042C22semidirect
42. Dic107⋊C8C22semidirect
43. #16812031C22semidirect
44. #16812031C22semidirect
46. #16812030C22semidirect
47. #16812029C22semidirect
48. #16812029C22semidirect
49. C22⋊(C107⋊C8)C22semidirect
50. (C2×D107)⋊C8C22semidirect
51. C8×Dic107C22semidirect
53. C22×C8×C107C22semidirect
54. C2×C4⋊C4×C107C22semidirect
57. #102×C107C22semidirect
58. #102×C107C22semidirect
129. D4×C107#41semidirect
143. C22⋊D107D8semidirect
205. C107#3294semidirect
220. C2×#102D107semidirect
229. C22×C8C2×D107semidirect
246. C2×C4⋊C4C2×D107semidirect
259. #102C2×D107semidirect
260. #102C2×D107semidirect
347. D4#13133818semidirect

Maximal subgroups

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

subgroupindex
#202932782
D4×C22⋊D1072
#202929722
#202929402
#202929392
#202929052
#202928632
#202928622
#202928212
#202927622
#202927612
#202927072
C8×C22⋊D1072
#102×D1072
C2×#102×C1072
#3294107