Finite Group Databasebeta

← #28348404

Subgroups — #28348404

Order 13696.

408 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293341C211yesmaximal, characteristic, complemented
2#20293296C211yesmaximal, characteristic, complemented
3#20292972C211yesmaximal, characteristic, complemented
4#20292952C211yesmaximal, characteristic, complemented
5#20292950C211yesmaximal, characteristic, complemented
6#20292920C211yesmaximal, characteristic, complemented
7#20292861C211yesmaximal, characteristic, complemented
8#20292860C211yesmaximal, characteristic, complemented
9#20292820C211yesmaximal, characteristic, complemented
10#20292771C211yesmaximal, characteristic, complemented
11SD16×Dic107C211yesmaximal, characteristic, complemented
12(C22⋊D107)⋊C8C211yesmaximal, characteristic, complemented
13#20292623C211yesmaximal, characteristic, complemented
14#20292622C211yesmaximal, characteristic, complemented
15#449×C107C211yesmaximal, characteristic, complemented
16C2×#13133819C2211yescharacteristic
17C2×#13133803C2211yescharacteristic
18C22×C107⋊C8C2211yescharacteristic
19C2×C8×D107C2211yescharacteristic
20#16812108C2211yescharacteristic
21#16812105—21no—
22#16812105C2211yescharacteristic
23#16812096—21no—
24#16812095—21no—
25#16812083—21no—
26#16812083C2211yescharacteristic
27#16812081—21no—
28#16812080—21no—
29#16812080C2211yescharacteristic
30#16812080C2211yescharacteristic
31Q8×Dic107C2211yescharacteristic
32D4×Dic107C2211yescharacteristic
33C4×C22⋊D107—21no—
34C4×C22⋊D107C2211yescharacteristic
35#16812068C2211yescharacteristic
36#16812067C2211yescharacteristic
37#16812065—21no—
38#16812043C2211yescharacteristic
39#16812042C2211yescharacteristic
40#16812041C2211yescharacteristic
41Dic107⋊C8C2211yescharacteristic
42#16812033C2211yescharacteristic
43#16812033C2211yescharacteristic
44#16812031C2211yescharacteristic
45#16812031C2211yescharacteristic
46#16812030C2211yescharacteristic
47#16812030C2211yescharacteristic
48#16812030C2211yescharacteristic
49#16812029C2211yescharacteristic
50(C2×D107)⋊C8C2211yescharacteristic
51C8×Dic107C2211yescharacteristic
52C2×#41×C107C2211yescharacteristic
53C2×SD16×C107C2211yescharacteristic
54C2×D8×C107C2211yescharacteristic
55#121×C107C2211yescharacteristic
56#103×C107C2211yescharacteristic
57#102×C107C2211yescharacteristic
58C22⋊C8×C107C2211yescharacteristic
59#13133819—22no—
60#13133819—41no—
61C2×Dic214—21no—
62C2×D428—21no—
63C2×D428C2311yescharacteristic
64C2×C22⋊D107—21no—
65C2×C22⋊D107—21no—
66C2×C22⋊D107—21no—
67C2×C22⋊D107—21no—
68C2×C22⋊D107—21no—
69C2×C22⋊D107D411yescharacteristic
70C22×Dic107—21no—
71C2×C4×D107—21no—
72C2×C4×D107C2311yescharacteristic
73#13133803—41no—
74C2×C107⋊C8—41no—
75C2×C107⋊C8C2311yescharacteristic
76C2×C107⋊C8C2311yescharacteristic
77C8×D107—41no—
78C4⋊Dic107—21no—
79C4⋊Dic107C2311yescharacteristic
80C4⋊Dic107C2311yescharacteristic
81C4⋊Dic107C2311yescharacteristic
82Dic107⋊C4—21no—
83Dic107⋊C4D411yescharacteristic
84C22⋊Dic107—21no—
85C22⋊Dic107—21no—
86C22⋊Dic107—21no—
87C22⋊Dic107—21no—
88C22⋊Dic107D411yescharacteristic
89(C2×D107)⋊C4—21no—
90(C2×D107)⋊C4—21no—
91(C2×D107)⋊C4D411yescharacteristic
92C4×Dic107—21no—
93C4×Dic107—21no—
94C4×Dic107—21no—
95C4×Dic107C2311yescharacteristic
96#41×C107—22no—
97#41×C107—41no—
98C2×Q8×C107C2311yescharacteristic
99C2×D4×C107—21no—
100C2×D4×C107—21no—
101C2×D4×C107C2311yescharacteristic
102C2×D4×C107C2311yescharacteristic
103C22×C4×C107—21no—
104C22×C4×C107C2311yescharacteristic
105SD16×C107—22no—
106D8×C107—41no—
107C2×C8×C107C2311yescharacteristic
108C2×C8×C107C2311yescharacteristic
109C4⋊C4×C107C2311yescharacteristic
110C22⋊C4×C107—21no—
111C23×C107—21no—
112C23×C107—21no—
113C23×C107C2×D411yescharacteristic
114C22×D107—21no—
115C22×D107C2×D411yescharacteristic
116Q8×C107—21no—
117Q8×C107#4112yes—
118D4×C107—21no—
119D4×C107—21no—
120D4×C107—21no—
121D4×C107—21no—
122D4×C107—42no—
123D4×C107—81no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107—21no—
127C2×C4×C107—21no—
128C2×C4×C107—42no—
129C2×C4×C107C2×D411yescharacteristic
130C2×C4×C107C2411yescharacteristic
131C22⋊D107—22no—
132C22⋊D107—42no—
133C22⋊D107—81no—
134C22⋊D107—81no—
135C22⋊D107—81no—
136C22⋊D107—81no—
137C2×Dic107—21no—
138C2×Dic107—21no—
139C2×Dic107—21no—
140C2×Dic107—42no—
141C2×Dic107C2×D411yescharacteristic
142C2×Dic107C2×D411yescharacteristic
143C2×Dic107C2×D411yescharacteristic
144D428—21no—
145D428—21no—
146D428—42no—
147C4×D107—21no—
148C4×D107—21no—
149C4×D107—42no—
150Dic214—81no—
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—21no—
168C2×D107—41no—
169C2×D107—41no—
170C2×D107—41no—
171C4×C107—22no—
172C4×C107—21no—
173C4×C107—41no—
174C4×C107C2×#4111yescharacteristic
175C4×C107H(5,𝔽2)11yescharacteristic
176Dic107—21no—
177Dic107—21no—
178Dic107—41no—
179Dic107—41no—
180Dic107—41no—
181Dic107#13512yes—
182C2×C107—41no—
183C2×C107—81no—
184C2×C107—81no—
185C2×C107#54611yescharacteristic
186C2×C107C2×#13511yescharacteristic
187C2×C107#57611yescharacteristic
188D107—41no—
189D107—81no—
190#3305—1071nomaximal, Sylow
191C107#330511yescharacteristic, complemented, Sylow
192#555—1071no—
193#550—1071no—
194#486—1071no—
195#482—1071no—
196#482—1071no—
197#477—1071no—
198#466—1071no—
199#466—1071no—
200#459—1071no—
201#449—1071no—
202#449D10711yescharacteristic, complemented
203C4×SD16—1071no—
204C8×D4—1071no—
205#416—1071no—
206#416—1071no—
207C2×#41—1071no—
208C2×#41C2×D10711yescharacteristic
209C2×SD16C2×D10711yescharacteristic
210C2×D8—1071no—
211C2×D8C2×D10711yescharacteristic
212C22×C8—1071no—
213C22×C8—1071no—
214C4⋊Q8—1071no—
215#127—1071no—
216#127—2141no—
217#124—2141no—
218#124—2141no—
219#121—1071no—
220#121—1071no—
221#121—1071no—
222#121—2141no—
223#121—2141no—
224#121—2141no—
225#121C2×D10711yescharacteristic
226C4×Q8—1071no—
227C4×D4—1071no—
228C4×D4—1071no—
229C4×D4—2141no—
230#117—1071no—
231#117—1071no—
232#117—2141no—
233#107—1071no—
234#107—1071no—
235#106—1071no—
236C4⋊C8—1071no—
237#103—1071no—
238#103—1071no—
239#103C2×D10711yescharacteristic
240#102—1071no—
241#102—1071no—
242#102—1071no—
243#102—1071no—
244#102—1071no—
245#102—1071no—
246#102C2×D10711yescharacteristic
247C22⋊C8—1071no—
248C22⋊C8C2×D10711yescharacteristic
249C4×C8—1071no—
250#41—22no—
251#41—41no—
252#41—4281no—
253#41—2142no—
254C2×Q8—2141no—
255C2×Q8C22×D10711yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—1071no—
259C2×D4—1071no—
260C2×D4—2141no—
261C2×D4—2141no—
262C2×D4—2141no—
263C2×D4—2141no—
264C2×D4—2141no—
265C2×D4—2141no—
266C2×D4C22×D10711yescharacteristic
267C2×D4C22×D10711yescharacteristic
268C22×C4—21no—
269C22×C4—1071no—
270C22×C4—2141no—
271C22×C4—2141no—
272C22×C4C22×D10711yescharacteristic
273SD16—22no—
274D8—41no—
275D8—4281no—
276C2×C8—1071no—
277C2×C8—1071no—
278C2×C8—4281no—
279C2×C8—4281no—
280C2×C8C22×D10711yescharacteristic
281C2×C8C22×D10711yescharacteristic
282C4⋊C4—1071no—
283C4⋊C4—1071no—
284C4⋊C4—1071no—
285C4⋊C4—1071no—
286C4⋊C4—2141no—
287C4⋊C4—2141no—
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—
300C42—2141no—
301C42—2141no—
302C23—21no—
303C23—21no—
304C23—1071no—
305C23—2141no—
306C23D4×D10711yescharacteristic
307Q8—21no—
308Q8—8561no—
309Q8#1313381712yes—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—81no—
316D4—8561no—
317D4—8561no—
318D4—8561no—
319D4—8561no—
320D4—4282no—
321D4—4282no—
322D4—2142no—
323D4—2141no—
324D4—2141no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—1071no—
331C2×C4—1071no—
332C2×C4—1071no—
333C2×C4—4282no—
334C2×C4—4282no—
335C2×C4—2141no—
336C2×C4—2141no—
337C2×C4—2141no—
338C2×C4—2141no—
339C2×C4—2141no—
340C2×C4D4×D10711yescharacteristic
341C2×C4C23×D10711yescharacteristic
342C8—21no—
343C8—21no—
344C8—2141no—
345C8—2141no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—4281no—
356C22—4281no—
357C22—4281no—
358C22—2141no—
359C22—2141no—
360C22—2141no—
361C22C2×D4×D10711yescharacteristic
362C4—21no—
363C4—22no—
364C4—41no—
365C4—1072no—
366C4—4281no—
367C4—4281no—
368C4—4281no—
369C4—2141no—
370C4—2141no—
371C4C2×#1313381711yescharacteristic
372C4#1681215411yescharacteristic
373C2—41no—
374C2—81no—
375C2—81no—
376C2—8561no—
377C2—4281no—
378C2#2029326411yescharacteristic
379C2#135×D10711yescharacteristic
380C2#2029343111yescharacteristic
subgroupG/H
centerC22C2×D4×D107
commutator, cosocleC2×C4×C107C24
FrattiniC2×C4C23×D107
Fitting#449×C107C2
socleC22×C107C22×D4
hypercenter#449D107
hypocenterC107#3305
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #20293341C2semidirect
2. #20293296C2semidirect
3. #20292972C2semidirect
4. #20292952C2semidirect
5. #20292950C2semidirect
6. #20292920C2semidirect
7. #20292861C2semidirect
8. #20292860C2semidirect
9. #20292820C2semidirect
10. #20292771C2semidirect
11. SD16×Dic107C2semidirect
12. (C22⋊D107)⋊C8C2semidirect
13. #20292623C2semidirect
14. #20292622C2semidirect
15. #449×C107C2semidirect
191. C107#3305semidirect
202. #449D107semidirect

Maximal subgroups

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

subgroupindex
#202933412
#202932962
#202929722
#202929522
#202929502
#202929202
#202928612
#202928602
#202928202
#202927712
SD16×Dic1072
(C22⋊D107)⋊C82
#202926232
#202926222
#449×C1072
#3305107