Finite Group Databasebeta

← #28344570

Subgroups — #28344570

Order 13696.

414 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20292569C211yesmaximal, characteristic, complemented
2#20292565C211yesmaximal, characteristic, complemented
3#20292563C211yesmaximal, characteristic, complemented
4#20292560C211yesmaximal, characteristic, complemented
5#20292558C211yesmaximal, characteristic, complemented
6#20292555C211yesmaximal, characteristic, complemented
7#20292553C211yesmaximal, characteristic, complemented
8#20292552C211yesmaximal, characteristic, complemented
9#20292549C211yesmaximal, characteristic, complemented
10#20292542C211yesmaximal, characteristic
11#20292542C211yesmaximal, characteristic
12#20292503C211yesmaximal, characteristic
13#20292501C211yesmaximal, characteristic, complemented
14#20292498C211yesmaximal, characteristic, complemented
15#396×C107C211yesmaximal, characteristic, complemented
16C22×C22⋊D107C2211yescharacteristic
17C22×C4×D107C2211yescharacteristic
18C2×C4⋊Dic107C2211yescharacteristic
19C2×C4⋊Dic107C2211yescharacteristic
20C2×Dic107⋊C4C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×C22⋊Dic107C2211yescharacteristic
26C2×C22⋊Dic107C2211yescharacteristic
27C2×C22⋊Dic107C2211yescharacteristic
28C2×(C2×D107)⋊C4C2211yescharacteristic
29C2×(C2×D107)⋊C4C2211yescharacteristic
30C2×(C2×D107)⋊C4C2211yescharacteristic
31C2×(C2×D107)⋊C4C2211yescharacteristic
32C2×(C2×D107)⋊C4C2211yescharacteristic
33C107⋊#95C2211yescharacteristic
34C107⋊#95C2211yescharacteristic
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
46C2×C4⋊C4×C107C2211yescharacteristic
47C2×C22⋊C4×C107C2211yescharacteristic
48C2×C22⋊C4×C107C2211yescharacteristic
49C2×C22⋊C4×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51C23×D107C2311yescharacteristic
52C2×C22⋊D107—22no—
53C2×C22⋊D107—41no—
54C2×C22⋊D107—41no—
55C22×Dic107C2311yescharacteristic
56C22×Dic107C2311yescharacteristic
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C2×C4×D107—41no—
63C2×C4×D107—41no—
64C2×C4×D107—41no—
65C4⋊Dic107—41no—
66C4⋊Dic107—41no—
67Dic107⋊C4—41no—
68Dic107⋊C4—41no—
69Dic107⋊C4—41no—
70Dic107⋊C4—41no—
71Dic107⋊C4—41no—
72C22⋊Dic107—41no—
73C22⋊Dic107—41no—
74C22⋊Dic107—41no—
75(C2×D107)⋊C4—22no—
76(C2×D107)⋊C4—22no—
77(C2×D107)⋊C4—41no—
78(C2×D107)⋊C4—41no—
79(C2×D107)⋊C4—41no—
80C24×C107C2311yescharacteristic
81C22×C4×C107C2311yescharacteristic
82C22×C4×C107C2311yescharacteristic
83C22×C4×C107C2311yescharacteristic
84C22×C4×C107C2311yescharacteristic
85C22×C4×C107C2311yescharacteristic
86C22×C4×C107C2311yescharacteristic
87C4⋊C4×C107—41no—
88C4⋊C4×C107—41no—
89C4⋊C4×C107—41no—
90C22⋊C4×C107—41no—
91C22⋊C4×C107—41no—
92C22⋊C4×C107—41no—
93C23×C107—21no—
94C23×C107—21no—
95C23×C107—21no—
96C23×C107—21no—
97C23×C107—21no—
98C23×C107—21no—
99C23×C107—21no—
100C23×C107C2411yescharacteristic
101C22×D107—21no—
102C22×D107—21no—
103C22×D107—21no—
104C22×D107—21no—
105C22×D107—21no—
106C22×D107—21no—
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—
126C22⋊D107—44no—
127C2×Dic107—21no—
128C2×Dic107—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—21no—
147C2×Dic107—21no—
148C4×D107—44no—
149C22×C107—41no—
150C22×C107—41no—
151C22×C107—41no—
152C22×C107—41no—
153C22×C107—41no—
154C22×C107—41no—
155C22×C107—41no—
156C22×C107C2×#4111yescharacteristic
157C22×C107H(5,𝔽2)11yescharacteristic
158C22×C107H(5,𝔽2)11yescharacteristic
159C22×C107H(5,𝔽2)11yescharacteristic
160C22×C107H(5,𝔽2)11yescharacteristic
161C22×C1072−1+411yescharacteristic
162C22×C1072−1+411yescharacteristic
163C2×D107—22no—
164C2×D107—22no—
165C2×D107—22no—
166C2×D107—41no—
167C2×D107—41no—
168C2×D107—41no—
169C2×D107—41no—
170C4×C107—41no—
171C4×C107—41no—
172C4×C107—41no—
173C4×C107—41no—
174C4×C107—41no—
175C4×C107—41no—
176Dic107—41no—
177Dic107—41no—
178Dic107—41no—
179Dic107—41no—
180Dic107—41no—
181Dic107—41no—
182Dic107—41no—
183C2×C107—81no—
184C2×C107#53811yescharacteristic
185C2×C107#53911yescharacteristic
186C2×C107#53911yescharacteristic
187C2×C107#56011yescharacteristic
188C2×C107#56211yescharacteristic
189C2×C107#56211yescharacteristic
190C2×C107#56311yescharacteristic
191D107—42no—
192#2827—1071nomaximal, Sylow
193C107#282711yescharacteristic, complemented, Sylow
194#400—1071no—
195#400—1071no—
196#399—1071no—
197#398—1071no—
198#398—1071no—
199#397—1071no—
200#397—1071no—
201#397—1071no—
202#396—1071no—
203#396D10711yescharacteristic, complemented
204#394—1071no—
205#394—1071no—
206#386—1071no—
207#385—1071no—
208#385—1071no—
209C22×D4—1071no—
210C23×C4—1071no—
211C2×C4⋊C4—1071no—
212C2×C4⋊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×C4⋊C4C2×D10711yescharacteristic
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⋊C4C2×D10711yescharacteristic
230C2×C22⋊C4C2×D10711yescharacteristic
231C2×C22⋊C4C2×D10711yescharacteristic
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#95—1071no—
241#95—1071no—
242#95—1071no—
243#95C2×D10711yescharacteristic
244C24—1071no—
245C24C22×D10711yescharacteristic
246C2×D4—4281no—
247C2×D4—4281no—
248C2×D4—2142no—
249C22×C4—1071no—
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×C4C22×D10711yescharacteristic
260C22×C4C22×D10711yescharacteristic
261C22×C4C22×D10711yescharacteristic
262C22×C4C22×D10711yescharacteristic
263C22×C4C22×D10711yescharacteristic
264C22×C4C22×D10711yescharacteristic
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—4281no—
269C4⋊C4—4281no—
270C4⋊C4—4281no—
271C4⋊C4—4281no—
272C4⋊C4—4281no—
273C4⋊C4—4281no—
274C4⋊C4—4281no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—4281no—
279C22⋊C4—4281no—
280C22⋊C4—4281no—
281C22⋊C4—4281no—
282C22⋊C4—4281no—
283C22⋊C4—4281no—
284C22⋊C4—2142no—
285C22⋊C4—2142no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—1072no—
294C23—2141no—
295C23—2141no—
296C23—2141no—
297C23—2141no—
298C23—2141no—
299C23—2141no—
300C23C23×D10711yescharacteristic
301D4—4284no—
302C2×C4—21no—
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—4284no—
321C2×C4—2141no—
322C2×C4—2141no—
323C2×C4—2141no—
324C2×C4—2141no—
325C2×C4—2141no—
326C2×C4—2141no—
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—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—4281no—
350C22—4281no—
351C22—4281no—
352C22—4281no—
353C22—2142no—
354C22—2142no—
355C22—2142no—
356C22#41×D10711yescharacteristic
357C22#1681215411yescharacteristic
358C22#1681215411yescharacteristic
359C22#1681215411yescharacteristic
360C22#1681215511yescharacteristic
361C22#1681215611yescharacteristic
362C22#1681215711yescharacteristic
363C4—41no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—4281no—
370C4—4281no—
371C4—4281no—
372C4—4281no—
373C4—4281no—
374C4—4281no—
375C4—4281no—
376C2—81no—
377C2—4282no—
378C2#2029320911yescharacteristic
379C2#2029321811yescharacteristic
380C2#2029322311yescharacteristic
381C2#2029336511yescharacteristic
382C2#2029337211yescharacteristic
383C2#2029337311yescharacteristic
384C2#2029337811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#396×C107C2
prime radicalC22×C22⋊D107C22
hypercenter#396D107
hypocenterC107#2827
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #20292569C2semidirect
2. #20292565C2semidirect
3. #20292563C2semidirect
4. #20292560C2semidirect
5. #20292558C2semidirect
6. #20292555C2semidirect
7. #20292553C2semidirect
8. #20292552C2semidirect
9. #20292549C2semidirect
13. #20292501C2semidirect
14. #20292498C2semidirect
15. #396×C107C2semidirect
193. C107#2827semidirect
203. #396D107semidirect

Maximal subgroups

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

subgroupindex
#202925692
#202925652
#202925632
#202925602
#202925582
#202925552
#202925532
#202925522
#202925492
#202925422
#202925032
#202925012
#202924982
#396×C1072
#2827107