Finite Group Databasebeta

← #28344137

Subgroups — #28344137

Order 13696.

448 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#20292568C211yesmaximal, characteristic, complemented
2#20292567C211yesmaximal, characteristic, complemented
3#20292556C211yesmaximal, characteristic, complemented
4#20292553C211yesmaximal, characteristic, complemented
5#20292545C211yesmaximal, characteristic
6#20292517C211yesmaximal, characteristic, complemented
7#20292516C211yesmaximal, characteristic, complemented
8#20292505C211yesmaximal, characteristic
9#20292505C211yesmaximal, characteristic
10#20292501C211yesmaximal, characteristic, complemented
11#20292501C211yesmaximal, characteristic, complemented
12#20292498C211yesmaximal, characteristic, complemented
13#20292498C211yesmaximal, characteristic, complemented
14#20292491C211yesmaximal, characteristic, complemented
15#400×C107C211yesmaximal, characteristic, complemented
16C22×D428C2211yescharacteristic
17C22×C4×D107C2211yescharacteristic
18C22×C4×D107C2211yescharacteristic
19C2×C4⋊Dic107C2211yescharacteristic
20C2×Dic107⋊C4C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×(C2×D107)⋊C4C2211yescharacteristic
25C2×(C2×D107)⋊C4C2211yescharacteristic
26C2×(C2×D107)⋊C4C2211yescharacteristic
27C2×(C2×D107)⋊C4C2211yescharacteristic
28C2×(C2×D107)⋊C4C2211yescharacteristic
29C2×(C2×D107)⋊C4C2211yescharacteristic
30C2×(C2×D107)⋊C4C2211yescharacteristic
31C2×(C2×D107)⋊C4C2211yescharacteristic
32C2×(C2×D107)⋊C4C2211yescharacteristic
33C2×(C2×D107)⋊C4C2211yescharacteristic
34C2×C4×Dic107C2211yescharacteristic
35C107⋊#95C2211yescharacteristic
36C107⋊#95C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C2×C4⋊C4×C107C2211yescharacteristic
45C2×C4⋊C4×C107C2211yescharacteristic
46#95×C107C2211yescharacteristic
47#95×C107C2211yescharacteristic
48#95×C107C2211yescharacteristic
49#95×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51C23×D107C2311yescharacteristic
52C23×D107C2311yescharacteristic
53C2×D428—22no—
54C2×D428—22no—
55C2×D428—41no—
56C22×Dic107C2311yescharacteristic
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C2×C4×D107—41no—
63C2×C4×D107—41no—
64C2×C4×D107—41no—
65C2×C4×D107—41no—
66C2×C4×D107—41no—
67C2×C4×D107—41no—
68C4⋊Dic107—41no—
69Dic107⋊C4—41no—
70Dic107⋊C4—41no—
71Dic107⋊C4—41no—
72Dic107⋊C4—41no—
73(C2×D107)⋊C4—22no—
74(C2×D107)⋊C4—22no—
75(C2×D107)⋊C4—22no—
76(C2×D107)⋊C4—22no—
77(C2×D107)⋊C4—22no—
78(C2×D107)⋊C4—22no—
79(C2×D107)⋊C4—41no—
80(C2×D107)⋊C4—41no—
81(C2×D107)⋊C4—41no—
82(C2×D107)⋊C4—41no—
83C4×Dic107—22no—
84C22×C4×C107C2311yescharacteristic
85C22×C4×C107C2311yescharacteristic
86C22×C4×C107C2311yescharacteristic
87C22×C4×C107C2311yescharacteristic
88C22×C4×C107C2311yescharacteristic
89C22×C4×C107C2311yescharacteristic
90C22×C4×C107C2311yescharacteristic
91C4⋊C4×C107—41no—
92C4⋊C4×C107—41no—
93C23×C107C2411yescharacteristic
94C22×D107—21no—
95C22×D107—21no—
96C22×D107—21no—
97C22×D107—21no—
98C22×D107—21no—
99C22×D107—21no—
100C22×D107—21no—
101C22×D107—21no—
102C22×D107—21no—
103C22×D107—21no—
104C22×D107—21no—
105C22×D107—21no—
106C22×D107#4112yes—
107C22×D107#4112yes—
108C2×C4×C107—21no—
109C2×C4×C107—21no—
110C2×C4×C107—21no—
111C2×C4×C107—21no—
112C2×C4×C107—21no—
113C2×C4×C107—21no—
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—21no—
124C2×C4×C107—21no—
125C2×C4×C107—21no—
126C2×C4×C107—21no—
127C2×C4×C107—21no—
128C2×C4×C107—21no—
129C2×Dic107—21no—
130C2×Dic107—21no—
131C2×Dic107—21no—
132C2×Dic107—21no—
133C2×Dic107—21no—
134C2×Dic107—21no—
135C2×Dic107—21no—
136C2×Dic107—21no—
137C2×Dic107—21no—
138C2×Dic107—21no—
139C2×Dic107—21no—
140C2×Dic107—21no—
141C2×Dic107—21no—
142C2×Dic107—21no—
143C2×Dic107—21no—
144C2×Dic107—21no—
145C2×Dic107—21no—
146C2×Dic107#4112yes—
147D428—44no—
148C4×D107—44no—
149C4×D107—44no—
150C22×C107C2×#4111yescharacteristic
151C22×C107C2×#4111yescharacteristic
152C22×C107C2×#4111yescharacteristic
153C22×C107H(5,𝔽2)11yescharacteristic
154C22×C107H(5,𝔽2)11yescharacteristic
155C22×C107H(5,𝔽2)11yescharacteristic
156C22×C1072−1+411yescharacteristic
157C2×D107—22no—
158C2×D107—22no—
159C2×D107—22no—
160C2×D107—22no—
161C2×D107—22no—
162C2×D107—22no—
163C2×D107—41no—
164C2×D107—41no—
165C2×D107—41no—
166C2×D107—41no—
167C2×D107—41no—
168C2×D107—41no—
169C2×D107—41no—
170C2×D107—41no—
171C4×C107—41no—
172C4×C107—41no—
173C4×C107—41no—
174C4×C107—41no—
175C4×C107—41no—
176C4×C107—41no—
177C4×C107—41no—
178Dic107—22no—
179Dic107—41no—
180Dic107—41no—
181Dic107—41no—
182Dic107—41no—
183Dic107—41no—
184C2×C107#53911yescharacteristic
185C2×C107#53911yescharacteristic
186C2×C107#53911yescharacteristic
187C2×C107#55111yescharacteristic
188C2×C107#55311yescharacteristic
189C2×C107#55311yescharacteristic
190C2×C107H(3,𝔽4)11yescharacteristic
191D107—42no—
192D107—42no—
193#2782—1071nomaximal, Sylow
194C107#278211yescharacteristic, complemented, Sylow
195#400—1071no—
196#400—1071no—
197#400D10711yescharacteristic, complemented
198#397—1071no—
199#397—1071no—
200#394—1071no—
201#388—1071no—
202#388—1071no—
203#386—1071no—
204#386—1071no—
205#385—1071no—
206#385—1071no—
207#385—1071no—
208#385—1071no—
209#382—1071no—
210C22×D4—1071no—
211C23×C4—1071no—
212C23×C4—1071no—
213C2×C4⋊C4—1071no—
214C2×C4⋊C4—1071no—
215C2×C4⋊C4—1071no—
216C2×C4⋊C4—1071no—
217C2×C4⋊C4—1071no—
218C2×C4⋊C4C2×D10711yescharacteristic
219C2×C4⋊C4C2×D10711yescharacteristic
220C2×C22⋊C4—1071no—
221C2×C22⋊C4—1071no—
222C2×C22⋊C4—1071no—
223C2×C22⋊C4—1071no—
224C2×C22⋊C4—1071no—
225C2×C22⋊C4—1071no—
226C2×C22⋊C4—1071no—
227C2×C22⋊C4—1071no—
228C2×C22⋊C4—1071no—
229C2×C22⋊C4—1071no—
230C2×C42—1071no—
231#95—1071no—
232#95—1071no—
233#95—1071no—
234#95—1071no—
235#95—1071no—
236#95—1071no—
237#95—1071no—
238#95—1071no—
239#95—1071no—
240#95C2×D10711yescharacteristic
241#95C2×D10711yescharacteristic
242#95C2×D10711yescharacteristic
243#95C2×D10711yescharacteristic
244#95C2×D10711yescharacteristic
245C24—1071no—
246C24—1071no—
247C2×D4—4281no—
248C2×D4—2142no—
249C2×D4—2142no—
250C22×C4—1071no—
251C22×C4—1071no—
252C22×C4—1071no—
253C22×C4—1071no—
254C22×C4—1071no—
255C22×C4—1071no—
256C22×C4—4281no—
257C22×C4—4281no—
258C22×C4—4281no—
259C22×C4—4281no—
260C22×C4—4281no—
261C22×C4—4281no—
262C22×C4C22×D10711yescharacteristic
263C22×C4C22×D10711yescharacteristic
264C22×C4C22×D10711yescharacteristic
265C22×C4C22×D10711yescharacteristic
266C22×C4C22×D10711yescharacteristic
267C22×C4C22×D10711yescharacteristic
268C22×C4C22×D10711yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—4281no—
272C4⋊C4—4281no—
273C4⋊C4—4281no—
274C4⋊C4—4281no—
275C4⋊C4—4281no—
276C22⋊C4—4281no—
277C22⋊C4—4281no—
278C22⋊C4—4281no—
279C22⋊C4—4281no—
280C22⋊C4—2142no—
281C22⋊C4—2142no—
282C22⋊C4—2142no—
283C22⋊C4—2142no—
284C22⋊C4—2142no—
285C22⋊C4—2142no—
286C42—2142no—
287C23—1072no—
288C23—1072no—
289C23—2141no—
290C23—2141no—
291C23—2141no—
292C23—2141no—
293C23—2141no—
294C23—2141no—
295C23—2141no—
296C23—2141no—
297C23—2141no—
298C23—2141no—
299C23—2141no—
300C23—2141no—
301C23C23×D10711yescharacteristic
302D4—4284no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—1072no—
325C2×C4—4284no—
326C2×C4—4284no—
327C2×C4—2141no—
328C2×C4—2141no—
329C2×C4—2141no—
330C2×C4—2141no—
331C2×C4—2141no—
332C2×C4—2141no—
333C2×C4—2141no—
334C2×C4—2141no—
335C2×C4—2141no—
336C2×C4—2141no—
337C2×C4—2141no—
338C2×C4—2141no—
339C2×C4—2141no—
340C2×C4—2141no—
341C2×C4—2141no—
342C2×C4—2141no—
343C2×C4—2141no—
344C22—4281no—
345C22—4281no—
346C22—4281no—
347C22—4281no—
348C22—4281no—
349C22—4281no—
350C22—4281no—
351C22—4281no—
352C22—2142no—
353C22—2142no—
354C22—2142no—
355C22—2142no—
356C22—2142no—
357C22—2142no—
358C22#41×D10711yescharacteristic
359C22#41×D10711yescharacteristic
360C22#41×D10711yescharacteristic
361C22#1681215411yescharacteristic
362C22#1681215511yescharacteristic
363C22#1681215511yescharacteristic
364C22#1681215711yescharacteristic
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—4281no—
373C4—4281no—
374C4—4281no—
375C4—4281no—
376C4—4281no—
377C4—2142no—
378C2—4282no—
379C2—4282no—
380C2#2029322311yescharacteristic
381C2#2029322511yescharacteristic
382C2#2029322511yescharacteristic
383C2#2029330211yescharacteristic
384C2#2029332211yescharacteristic
385C2#2029332811yescharacteristic
386C2#2029336911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#400×C107C2
prime radicalC22×D428C22
hypercenter#400D107
hypocenterC107#2782
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #20292568C2semidirect
2. #20292567C2semidirect
3. #20292556C2semidirect
4. #20292553C2semidirect
6. #20292517C2semidirect
7. #20292516C2semidirect
10. #20292501C2semidirect
11. #20292501C2semidirect
12. #20292498C2semidirect
13. #20292498C2semidirect
14. #20292491C2semidirect
15. #400×C107C2semidirect
194. C107#2782semidirect
197. #400D107semidirect

Maximal subgroups

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

subgroupindex
#202925682
#202925672
#202925562
#202925532
#202925452
#202925172
#202925162
#202925052
#202925012
#202924982
#202924912
#400×C1072
#2782107