Finite Group Databasebeta

← #28345529

Subgroups — #28345529

Order 13696.

394 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20293174C211yesmaximal, characteristic
2#20292701C211yesmaximal, characteristic, complemented
3#20292700C211yesmaximal, characteristic, complemented
4#20292699C211yesmaximal, characteristic, complemented
5#20292698C211yesmaximal, characteristic, complemented
6#20292697C211yesmaximal, characteristic, complemented
7#20292696C211yesmaximal, characteristic, complemented
8#20292695C211yesmaximal, characteristic, complemented
9#20292683C211yesmaximal, characteristic, complemented
10#20292682C211yesmaximal, characteristic, complemented
11#20292595C211yesmaximal, characteristic, complemented
12#20292593C211yesmaximal, characteristic, complemented
13#20292592C211yesmaximal, characteristic, complemented
14#20292592C211yesmaximal, characteristic, complemented
15#435×C107C211yesmaximal, characteristic, complemented
16C2×#13133818C2211yescharacteristic
17C2×#13133818C2211yescharacteristic
18C2×#13133802C2211yescharacteristic
19C2×#13133801C2211yescharacteristic
20C2×#13133801C2211yescharacteristic
21C22×C107⋊C8C2211yescharacteristic
22C2×C8×D107C2211yescharacteristic
23C2×C8×D107C2211yescharacteristic
24#16812108C411yescharacteristic
25#16812105C411yescharacteristic
26#16812095C411yescharacteristic
27#16812095C411yescharacteristic
28#16812084C411yescharacteristic
29#16812082C411yescharacteristic
30#16812082C411yescharacteristic
31#16812080C411yescharacteristic
32C4×D428C2211yescharacteristic
33C4×C22⋊D107C2211yescharacteristic
34C4×C22⋊D107C2211yescharacteristic
35C42×D107C2211yescharacteristic
36C4⋊(C107⋊C8)C2211yescharacteristic
37Dic107⋊C8C2211yescharacteristic
38Dic107⋊C8C2211yescharacteristic
39C22⋊(C107⋊C8)C2211yescharacteristic
40C22⋊(C107⋊C8)C2211yescharacteristic
41(C2×D107)⋊C8C2211yescharacteristic
42(C2×D107)⋊C8C2211yescharacteristic
43(C2×D107)⋊C8C2211yescharacteristic
44(C2×D107)⋊C8C2211yescharacteristic
45(C2×D107)⋊C8C2211yescharacteristic
46(C2×D107)⋊C8C2211yescharacteristic
47(C2×D107)⋊C8C2211yescharacteristic
48(C2×D107)⋊C8C2211yescharacteristic
49#16812020C2211yescharacteristic
50#16812019C2211yescharacteristic
51#16812019C2211yescharacteristic
52C2×M16×C107C2211yescharacteristic
53C22×C8×C107C2211yescharacteristic
54C4×D4×C107C2211yescharacteristic
55C4⋊C8×C107C2211yescharacteristic
56C22⋊C8×C107C2211yescharacteristic
57C22⋊C8×C107C2211yescharacteristic
58#97×C107C2211yescharacteristic
59#13133818—41no—
60#13133818—41no—
61#13133818—41no—
62#13133818—41no—
63C2×Dic214C2×C411yescharacteristic
64C2×Dic214C2×C411yescharacteristic
65C2×D428C2×C411yescharacteristic
66C2×D428C2×C411yescharacteristic
67C2×D428C2×C411yescharacteristic
68C2×C22⋊D107C2×C411yescharacteristic
69C2×C22⋊D107C2×C411yescharacteristic
70C2×C22⋊D107C2×C411yescharacteristic
71C2×C22⋊D107C2×C411yescharacteristic
72C2×C22⋊D107C2×C411yescharacteristic
73C2×C22⋊D107C2×C411yescharacteristic
74C2×C4×D107C2×C411yescharacteristic
75C2×C4×D107C2×C411yescharacteristic
76C2×C4×D107C2311yescharacteristic
77C2×C4×D107C2311yescharacteristic
78C2×C4×D107C2311yescharacteristic
79#13133802—41no—
80#13133801—41no—
81#13133801—41no—
82C2×C107⋊C8—41no—
83C2×C107⋊C8C2311yescharacteristic
84C2×C107⋊C8C2311yescharacteristic
85C2×C107⋊C8C2311yescharacteristic
86C2×C107⋊C8C2311yescharacteristic
87C8×D107—41no—
88C8×D107—41no—
89C4⋊Dic107C2×C411yescharacteristic
90Dic107⋊C4C2×C411yescharacteristic
91Dic107⋊C4C2×C411yescharacteristic
92C22⋊Dic107C2×C411yescharacteristic
93C22⋊Dic107C2×C411yescharacteristic
94(C2×D107)⋊C4C2×C411yescharacteristic
95(C2×D107)⋊C4C2×C411yescharacteristic
96(C2×D107)⋊C4C2×C411yescharacteristic
97(C2×D107)⋊C4C2×C411yescharacteristic
98C4×Dic107C2×C411yescharacteristic
99C4×Dic107C2×C411yescharacteristic
100C4×Dic107C2311yescharacteristic
101C2×D4×C107C2×C411yescharacteristic
102C22×C4×C107C2311yescharacteristic
103C22×C4×C107C2311yescharacteristic
104M16×C107—41no—
105C2×C8×C107—41no—
106C2×C8×C107C2311yescharacteristic
107C2×C8×C107C2311yescharacteristic
108C2×C8×C107C2311yescharacteristic
109C2×C8×C107C2311yescharacteristic
110C4⋊C4×C107C2×C411yescharacteristic
111C22⋊C4×C107C2×C411yescharacteristic
112C22⋊C4×C107C2×C411yescharacteristic
113C42×C107C2311yescharacteristic
114C23×C107C22×C411yescharacteristic
115C23×C107C22×C411yescharacteristic
116C22×D107C22×C411yescharacteristic
117C22×D107C22×C411yescharacteristic
118C22×D107C22×C411yescharacteristic
119D4×C107—41no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107C22×C411yescharacteristic
125C2×C4×C107C22×C411yescharacteristic
126C2×C4×C107C22×C411yescharacteristic
127C2×C4×C107C22×C411yescharacteristic
128C2×C4×C107C2411yescharacteristic
129C22⋊D107—41no—
130C22⋊D107—41no—
131C22⋊D107—41no—
132C22⋊D107—41no—
133C22⋊D107—41no—
134C22⋊D107—41no—
135C2×Dic107C22×C411yescharacteristic
136C2×Dic107C22×C411yescharacteristic
137C2×Dic107C22×C411yescharacteristic
138C2×Dic107C22×C411yescharacteristic
139C2×Dic107C22×C411yescharacteristic
140D428—41no—
141D428—41no—
142D428—41no—
143C4×D107—21no—
144C4×D107—21no—
145C4×D107—21no—
146C4×D107—21no—
147C4×D107—21no—
148C4×D107—21no—
149C4×D107—41no—
150C4×D107—41no—
151Dic214—41no—
152Dic214—41no—
153C8×C107—21no—
154C8×C107—21no—
155C8×C107—21no—
156C8×C107—21no—
157C107⋊C8—21no—
158C107⋊C8—21no—
159C107⋊C8—21no—
160C107⋊C8—21no—
161C22×C107—21no—
162C22×C107—21no—
163C22×C107—21no—
164C22×C107—21no—
165C22×C107—21no—
166C22×C107—21no—
167C22×C107C23×C411yescharacteristic
168C2×D107—21no—
169C2×D107—21no—
170C2×D107—21no—
171C2×D107—21no—
172C2×D107—21no—
173C2×D107—21no—
174C2×D107—21no—
175C2×D107—21no—
176C2×D107—21no—
177C4×C107—21no—
178C4×C107—21no—
179C4×C107—21no—
180C4×C107—21no—
181C4×C107H(5,𝔽2)11yescharacteristic
182C4×C107H(5,𝔽2)11yescharacteristic
183Dic107—21no—
184Dic107—21no—
185Dic107—21no—
186Dic107—21no—
187Dic107—21no—
188C2×C107—41no—
189C2×C107—41no—
190C2×C107#51811yescharacteristic
191C2×C107#56811yescharacteristic
192C2×C107#56811yescharacteristic
193D107—41no—
194D107—41no—
195D107—41no—
196#2980—1071nomaximal, Sylow
197C107#298011yescharacteristic, complemented, Sylow
198#532—1071no—
199#435—1071no—
200#435—1071no—
201#435—1071no—
202#435—1071no—
203#435—1071no—
204#435—1071no—
205#435—1071no—
206#435D10711yescharacteristic, complemented
207#432—1071no—
208#432—1071no—
209#408—1071no—
210#408—1071no—
211#408—1071no—
212#408—1071no—
213C2×#41—1071no—
214C2×#41—1071no—
215C2×M16—1071no—
216C2×M16—1071no—
217C2×M16—1071no—
218C2×M16C2×D10711yescharacteristic
219C22×C8—1071no—
220C22×C8—1071no—
221C22×C8—1071no—
222C22×C8C2×D10711yescharacteristic
223C4⋊Q8—1071no—
224#127—1071no—
225#124—1071no—
226#124—1071no—
227#121—1071no—
228#121—1071no—
229#121—1071no—
230#121—1071no—
231C4×D4—1071no—
232C4×D4—1071no—
233C4×D4—1071no—
234C4×D4C2×D10711yescharacteristic
235C2×C42—1071no—
236C4⋊C8—1071no—
237C4⋊C8—1071no—
238C4⋊C8—1071no—
239C4⋊C8C2×D10711yescharacteristic
240C22⋊C8—1071no—
241C22⋊C8—1071no—
242C22⋊C8—1071no—
243C22⋊C8—1071no—
244C22⋊C8—1071no—
245C22⋊C8—1071no—
246C22⋊C8—1071no—
247C22⋊C8—1071no—
248C22⋊C8—1071no—
249C22⋊C8—1071no—
250C22⋊C8C2×D10711yescharacteristic
251C22⋊C8C2×D10711yescharacteristic
252#97—1071no—
253#97—1071no—
254#97—1071no—
255#97C2×D10711yescharacteristic
256#41—4281no—
257#41—4281no—
258#41—4281no—
259#41—4281no—
260C2×Q8—1071no—
261C2×Q8—1071no—
262C2×D4—1071no—
263C2×D4—1071no—
264C2×D4—1071no—
265C2×D4—1071no—
266C2×D4—1071no—
267C2×D4—1071no—
268C2×D4—1071no—
269C2×D4—1071no—
270C2×D4—1071no—
271C2×D4C4×D10711yescharacteristic
272C22×C4—1071no—
273C22×C4—1071no—
274C22×C4—1071no—
275C22×C4—1071no—
276C22×C4—1071no—
277C22×C4C22×D10711yescharacteristic
278C22×C4C22×D10711yescharacteristic
279M16—41no—
280M16—4281no—
281M16—4281no—
282M16—4281no—
283C2×C8—41no—
284C2×C8—1071no—
285C2×C8—1071no—
286C2×C8—1071no—
287C2×C8—1071no—
288C2×C8—4281no—
289C2×C8—4281no—
290C2×C8—4281no—
291C2×C8C22×D10711yescharacteristic
292C2×C8C22×D10711yescharacteristic
293C2×C8C22×D10711yescharacteristic
294C2×C8C22×D10711yescharacteristic
295C4⋊C4—1071no—
296C4⋊C4—1071no—
297C4⋊C4—1071no—
298C4⋊C4C4×D10711yescharacteristic
299C22⋊C4—1071no—
300C22⋊C4—1071no—
301C22⋊C4—1071no—
302C22⋊C4—1071no—
303C22⋊C4—1071no—
304C22⋊C4—1071no—
305C22⋊C4C4×D10711yescharacteristic
306C22⋊C4C4×D10711yescharacteristic
307C42—1071no—
308C42—1071no—
309C42—1071no—
310C42C22×D10711yescharacteristic
311C23—1071no—
312C23—1071no—
313C23—1071no—
314C23C2×C4×D10711yescharacteristic
315C23C2×C4×D10711yescharacteristic
316Q8—4281no—
317Q8—4281no—
318D4—41no—
319D4—4281no—
320D4—4281no—
321D4—4281no—
322D4—4281no—
323D4—4281no—
324D4—4281no—
325D4—4281no—
326D4—4281no—
327D4—4281no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—1071no—
333C2×C4—1071no—
334C2×C4—1071no—
335C2×C4—1071no—
336C2×C4—1071no—
337C2×C4—4281no—
338C2×C4—4281no—
339C2×C4—2141no—
340C2×C4—2141no—
341C2×C4—2141no—
342C2×C4—2141no—
343C2×C4—2141no—
344C2×C4—2141no—
345C2×C4C2×C4×D10711yescharacteristic
346C2×C4C2×C4×D10711yescharacteristic
347C2×C4C2×C4×D10711yescharacteristic
348C2×C4C2×C4×D10711yescharacteristic
349C2×C4C23×D10711yescharacteristic
350C8—21no—
351C8—21no—
352C8—21no—
353C8—21no—
354C8—2141no—
355C8—2141no—
356C8—2141no—
357C8—2141no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—2141no—
365C22—2141no—
366C22—2141no—
367C22—2141no—
368C22—2141no—
369C22—2141no—
370C22—2141no—
371C22—2141no—
372C22—2141no—
373C22C22×C4×D10711yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—2141no—
379C4—2141no—
380C4—2141no—
381C4—2141no—
382C4—2141no—
383C4#1681215411yescharacteristic
384C4#1681215511yescharacteristic
385C2—41no—
386C2—41no—
387C2—4281no—
388C2—4281no—
389C2—4281no—
390C2#2029309911yescharacteristic
391C2#2029339211yescharacteristic
392C2#2029339311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D107
commutator, socleC22×C107C23×C4
Fitting#435×C107C2
prime radical#20293174C2
cosocleC2×C4×C107C24
hypercenter#435D107
hypocenterC107#2980
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #20292701C2semidirect
3. #20292700C2semidirect
4. #20292699C2semidirect
5. #20292698C2semidirect
6. #20292697C2semidirect
7. #20292696C2semidirect
8. #20292695C2semidirect
9. #20292683C2semidirect
10. #20292682C2semidirect
11. #20292595C2semidirect
12. #20292593C2semidirect
13. #20292592C2semidirect
14. #20292592C2semidirect
15. #435×C107C2semidirect
197. C107#2980semidirect
206. #435D107semidirect

Maximal subgroups

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

subgroupindex
#202931742
#202927012
#202927002
#202926992
#202926982
#202926972
#202926962
#202926952
#202926832
#202926822
#202925952
#202925932
#202925922
#435×C1072
#2980107