Finite Group Databasebeta

← #28348450

Subgroups — #28348450

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#20293283C211yesmaximal, characteristic, complemented
2#20293278C211yesmaximal, characteristic, complemented
3#20292985C211yesmaximal, characteristic, complemented
4#20292964C211yesmaximal, characteristic, complemented
5#20292921C211yesmaximal, characteristic, complemented
6#20292874C211yesmaximal, characteristic, complemented
7#20292861C211yesmaximal, characteristic, complemented
8#20292841C211yesmaximal, characteristic, complemented
9#20292773C211yesmaximal, characteristic, complemented
10#20292768C211yesmaximal, characteristic, complemented
11#20292726C211yesmaximal, characteristic, complemented
12#20292695C211yesmaximal, characteristic, complemented
13#20292625C211yesmaximal, characteristic, complemented
14C2×#16812032C211yesmaximal, characteristic, complemented
15#480×C107C211yesmaximal, characteristic, complemented
16C2×#13133818—21no—
17C2×#13133817C2211yescharacteristic
18C22×Dic214C2211yescharacteristic
19C2×#13133807C2211yescharacteristic
20C2×#13133807C2211yescharacteristic
21C2×#13133803C2211yescharacteristic
22C2×#13133801C2211yescharacteristic
23C22×C107⋊C8C2211yescharacteristic
24#16812108C2211yescharacteristic
25#16812096C2211yescharacteristic
26#16812095—21no—
27#16812094—21no—
28#16812092—21no—
29#16812089C2211yescharacteristic
30#16812087—21no—
31#16812086—21no—
32#16812084C2211yescharacteristic
33#16812083C2211yescharacteristic
34#16812081—21no—
35#16812074C2211yescharacteristic
36D4×Dic107—21no—
37#16812071C2211yescharacteristic
38C4×C22⋊D107C2211yescharacteristic
39C4⋊C4×D107C2211yescharacteristic
40#16812042C2211yescharacteristic
41Dic107⋊C8C2211yescharacteristic
42#16812034C2211yescharacteristic
43#16812034C2211yescharacteristic
44#16812032C2211yescharacteristic
45#16812032C2211yescharacteristic
46#16812032C2211yescharacteristic
47#16812032C2211yescharacteristic
48#16812030C2211yescharacteristic
49#16812029C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51#16812019C2211yescharacteristic
52#121×C107C2211yescharacteristic
53C2×C4⋊C4×C107C2211yescharacteristic
54#107×C107C2211yescharacteristic
55#107×C107C2211yescharacteristic
56#102×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic
59#13133818—44no—
60#13133817—22no—
61#13133817—41no—
62C2×Dic214—22no—
63C2×Dic214—21no—
64C2×Dic214—21no—
65C2×Dic214—41no—
66C2×Dic214C2311yescharacteristic
67C2×Dic214C2311yescharacteristic
68C2×D428—21no—
69C2×D428C2311yescharacteristic
70C2×C22⋊D107—21no—
71C2×C22⋊D107—21no—
72C2×C22⋊D107D411yescharacteristic
73C22×Dic107—21no—
74C22×Dic107—21no—
75C2×C4×D107—21no—
76C2×C4×D107—21no—
77C2×C4×D107C2311yescharacteristic
78#13133807—22no—
79#13133807—41no—
80#13133803—41no—
81#13133801—41no—
82C2×C107⋊C8—41no—
83C2×C107⋊C8C2311yescharacteristic
84C2×C107⋊C8C2311yescharacteristic
85C4⋊Dic107—21no—
86C4⋊Dic107C2311yescharacteristic
87Dic107⋊C4—21no—
88Dic107⋊C4—21no—
89Dic107⋊C4—21no—
90Dic107⋊C4D411yescharacteristic
91C22⋊Dic107—21no—
92C22⋊Dic107—21no—
93C22⋊Dic107D411yescharacteristic
94(C2×D107)⋊C4—21no—
95(C2×D107)⋊C4—21no—
96(C2×D107)⋊C4—21no—
97(C2×D107)⋊C4—21no—
98(C2×D107)⋊C4D411yescharacteristic
99C4×Dic107—21no—
100C4×Dic107C2311yescharacteristic
101C2×D4×C107—21no—
102C2×D4×C107C2311yescharacteristic
103C22×C4×C107—21no—
104C22×C4×C107C2311yescharacteristic
105C2×C8×C107C2311yescharacteristic
106C2×C8×C107C2311yescharacteristic
107C4⋊C4×C107—21no—
108C4⋊C4×C107C2311yescharacteristic
109C4⋊C4×C107C2311yescharacteristic
110C4⋊C4×C107C2311yescharacteristic
111C22⋊C4×C107—21no—
112C23×C107—21no—
113C23×C107C2×D411yescharacteristic
114C22×D107—21no—
115C22×D107C2×D411yescharacteristic
116D4×C107—21no—
117D4×C107—21no—
118D4×C107—42no—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—42no—
125C2×C4×C107C2×D411yescharacteristic
126C2×C4×C107C2411yescharacteristic
127C22⋊D107—22no—
128C22⋊D107—42no—
129C22⋊D107—42no—
130C2×Dic107—21no—
131C2×Dic107—21no—
132C2×Dic107—21no—
133C2×Dic107—42no—
134C2×Dic107—42no—
135C2×Dic107C2×D411yescharacteristic
136C2×Dic107C2×D411yescharacteristic
137C2×Dic107C2×D411yescharacteristic
138D428—21no—
139D428—21no—
140D428—42no—
141C4×D107—21no—
142C4×D107—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—
153C107⋊C8—21no—
154C107⋊C8—21no—
155C22×C107—21no—
156C22×C107—21no—
157C22×C107—41no—
158C22×C107—41no—
159C22×C107—41no—
160C22×C107AGL(1,ℤ/8)12yes—
161C22×C107C22×D411yescharacteristic
162C2×D107—21no—
163C2×D107—21no—
164C2×D107—21no—
165C2×D107—41no—
166C2×D107—41no—
167C2×D107—41no—
168C4×C107—21no—
169C4×C107—41no—
170C4×C107—41no—
171C4×C107—41no—
172C4×C107C2×#4111yescharacteristic
173C4×C107H(5,𝔽2)11yescharacteristic
174Dic107—22no—
175Dic107—21no—
176Dic107—21no—
177Dic107—21no—
178Dic107—41no—
179Dic107—41no—
180C2×C107—22no—
181C2×C107—81no—
182C2×C107#54611yescharacteristic
183C2×C107C2×AGL(1,ℤ/8)11yescharacteristic
184C2×C107#57811yescharacteristic
185D107—41no—
186D107—81no—
187#3308—1071nomaximal, Sylow
188C107#330811yescharacteristic, complemented, Sylow
189#548—1071no—
190#547—1071no—
191#489—1071no—
192#484—1071no—
193#480D10711yescharacteristic, complemented
194#477—1071no—
195#468—1071no—
196#466—1071no—
197#463—1071no—
198#449—1071no—
199#448—1071no—
200#440—1071no—
201#435—1071no—
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×M16—1071no—
211C22×C8—1071no—
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—2141no—
223#121C2×D10711yescharacteristic
224C4×Q8—1071no—
225C4×D4—1071no—
226C4×D4—1071no—
227C4×D4—2141no—
228C2×C4⋊C4—1071no—
229C2×C4⋊C4C2×D10711yescharacteristic
230#107—1071no—
231#107C2×D10711yescharacteristic
232#107C2×D10711yescharacteristic
233C4⋊C8—1071no—
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#102C2×D10711yescharacteristic
243#102C2×D10711yescharacteristic
244C22⋊C8—1071no—
245C22⋊C8C2×D10711yescharacteristic
246#97—1071no—
247#41—4284no—
248#41—4281no—
249#41—2142no—
250C2×Q8—1071no—
251C2×Q8—1071no—
252C2×Q8—4281no—
253C2×Q8—2141no—
254C2×Q8—2142no—
255C2×Q8—2141no—
256C2×D4—21no—
257C2×D4—1071no—
258C2×D4—1071no—
259C2×D4—2141no—
260C2×D4—2141no—
261C2×D4—2141no—
262C2×D4C22×D10711yescharacteristic
263C22×C4—21no—
264C22×C4—1071no—
265C22×C4—2141no—
266C22×C4—2141no—
267C22×C4—2141no—
268C22×C4—2141no—
269C22×C4C22×D10711yescharacteristic
270SD16—4281no—
271SD16—2142no—
272D8—4281no—
273M16—4281no—
274C2×C8—1071no—
275C2×C8—1071no—
276C2×C8—4281no—
277C2×C8C22×D10711yescharacteristic
278C2×C8C22×D10711yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—1071no—
281C4⋊C4—1071no—
282C4⋊C4—2141no—
283C4⋊C4—2141no—
284C4⋊C4—2141no—
285C4⋊C4—2141no—
286C4⋊C4C22×D10711yescharacteristic
287C4⋊C4C22×D10711yescharacteristic
288C4⋊C4C22×D10711yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—1071no—
291C22⋊C4—1071no—
292C22⋊C4—2141no—
293C22⋊C4—2141no—
294C22⋊C4—2141no—
295C22⋊C4—2141no—
296C22⋊C4—2141no—
297C22⋊C4—2141no—
298C42—1071no—
299C42—2141no—
300C23—21no—
301C23—1071no—
302C23—2141no—
303C23D4×D10711yescharacteristic
304Q8—1072no—
305Q8—4282no—
306Q8—4282no—
307Q8—2141no—
308Q8—2141no—
309Q8—2141no—
310D4—21no—
311D4—21no—
312D4—42no—
313D4—4282no—
314D4—4282no—
315D4—4282no—
316D4—2142no—
317D4—2141no—
318D4—2141no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—1071no—
326C2×C4—1071no—
327C2×C4—1071no—
328C2×C4—4282no—
329C2×C4—4282no—
330C2×C4—4282no—
331C2×C4—4282no—
332C2×C4—2141no—
333C2×C4—2141no—
334C2×C4—2141no—
335C2×C4—2141no—
336C2×C4—2141no—
337C2×C4D4×D10711yescharacteristic
338C2×C4C23×D10711yescharacteristic
339C8—21no—
340C8—21no—
341C8—2141no—
342C8—2141no—
343C22—21no—
344C22—21no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—4281no—
349C22—4281no—
350C22—4281no—
351C22—2141no—
352C22—2141no—
353C22—2141no—
354C22#1681213312yes—
355C22C2×D4×D10711yescharacteristic
356C4—21no—
357C4—41no—
358C4—41no—
359C4—41no—
360C4—4281no—
361C4—4281no—
362C4—2141no—
363C4—2141no—
364C4—2141no—
365C4—2142no—
366C4#41×D10711yescharacteristic
367C4#1681215511yescharacteristic
368C2—22no—
369C2—81no—
370C2—8561no—
371C2—4281no—
372C2#2029326911yescharacteristic
373C2C2×#1681213311yescharacteristic
374C2#2029344311yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#480×C107C2
socleC22×C107C22×D4
hypercenter#480D107
hypocenterC107#3308
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #20293283C2semidirect
2. #20293278C2semidirect
3. #20292985C2semidirect
4. #20292964C2semidirect
5. #20292921C2semidirect
6. #20292874C2semidirect
7. #20292861C2semidirect
8. #20292841C2semidirect
9. #20292773C2semidirect
10. #20292768C2semidirect
11. #20292726C2semidirect
12. #20292695C2semidirect
13. #20292625C2semidirect
14. C2×#16812032C2semidirect
15. #480×C107C2semidirect
150. Dic214#41semidirect
188. C107#3308semidirect
193. #480D107semidirect

Maximal subgroups

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

subgroupindex
#202932832
#202932782
#202929852
#202929642
#202929212
#202928742
#202928612
#202928412
#202927732
#202927682
#202927262
#202926952
#202926252
C2×#168120322
#480×C1072
#3308107