Finite Group Databasebeta

← #28340171

Subgroups — #28340171

Order 13696.

492 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812099C211yesmaximal, characteristic, complemented
2C2×#16812066C211yesmaximal, characteristic
3#20292562C211yesmaximal, characteristic
4#20292562C211yesmaximal, characteristic
5#20292549C211yesmaximal, characteristic
6#20292549C211yesmaximal, characteristic
7#20292524C211yesmaximal, characteristic, complemented
8#20292522C211yesmaximal, characteristic, complemented
9#20292522C211yesmaximal, characteristic, complemented
10#20292514C211yesmaximal, characteristic, complemented
11#20292511C211yesmaximal, characteristic, complemented
12#20292496C211yesmaximal, characteristic, complemented
13#20292486C211yesmaximal, characteristic
14#20292474C211yesmaximal, characteristic
15#389×C107C211yesmaximal, characteristic, complemented
16C22×C4×D107C2211yescharacteristic
17#16812099—24no—
18#16812066—24no—
19C2×C4⋊Dic107C2211yescharacteristic
20C2×C4⋊Dic107C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×Dic107⋊C4C2211yescharacteristic
27C2×Dic107⋊C4C2211yescharacteristic
28C2×Dic107⋊C4C2211yescharacteristic
29C2×Dic107⋊C4C2211yescharacteristic
30C2×Dic107⋊C4C2211yescharacteristic
31C2×(C2×D107)⋊C4C2211yescharacteristic
32C2×(C2×D107)⋊C4C2211yescharacteristic
33C2×(C2×D107)⋊C4C2211yescharacteristic
34C2×(C2×D107)⋊C4C2211yescharacteristic
35C2×(C2×D107)⋊C4C2211yescharacteristic
36C2×(C2×D107)⋊C4C2211yescharacteristic
37C2×C4×Dic107C2211yescharacteristic
38C2×C4×Dic107C2211yescharacteristic
39C2×C4×Dic107C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C2×C4⋊C4×C107C2211yescharacteristic
47C2×C4⋊C4×C107C2211yescharacteristic
48C2×C4⋊C4×C107C2211yescharacteristic
49C2×C4⋊C4×C107C2211yescharacteristic
50C2×C42×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52#95×C107C2211yescharacteristic
53C23×D107C2311yescharacteristic
54C22×Dic107C2311yescharacteristic
55C22×Dic107C2311yescharacteristic
56C22×Dic107C2311yescharacteristic
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C2×C4×D107—22no—
62C2×C4×D107—22no—
63C2×C4×D107Q814yes—
64C4⋊Dic107—22no—
65C4⋊Dic107—41no—
66Dic107⋊C4—22no—
67Dic107⋊C4—22no—
68Dic107⋊C4—22no—
69Dic107⋊C4—22no—
70Dic107⋊C4—22no—
71Dic107⋊C4—22no—
72Dic107⋊C4—22no—
73Dic107⋊C4—22no—
74Dic107⋊C4—41no—
75Dic107⋊C4D414yes—
76(C2×D107)⋊C4—22no—
77(C2×D107)⋊C4—22no—
78(C2×D107)⋊C4—22no—
79(C2×D107)⋊C4—22no—
80(C2×D107)⋊C4—41no—
81(C2×D107)⋊C4—41no—
82C4×Dic107—22no—
83C4×Dic107—22no—
84C4×Dic107—22no—
85C22×C4×C107C2311yescharacteristic
86C22×C4×C107C2311yescharacteristic
87C22×C4×C107C2311yescharacteristic
88C22×C4×C107C2311yescharacteristic
89C22×C4×C107C2311yescharacteristic
90C22×C4×C107C2311yescharacteristic
91C22×C4×C107C2311yescharacteristic
92C4⋊C4×C107—22no—
93C4⋊C4×C107—22no—
94C4⋊C4×C107—41no—
95C4⋊C4×C107—41no—
96C42×C107—22no—
97C23×C107C2411yescharacteristic
98C22×D107—21no—
99C22×D107—21no—
100C22×D107—21no—
101C22×D107—21no—
102C22×D107—21no—
103C22×D107—21no—
104C22×D107C2×Q812yes—
105C2×C4×C107—21no—
106C2×C4×C107—21no—
107C2×C4×C107—21no—
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×C107C2×D412yes—
124C2×C4×C107C2×Q812yes—
125C2×C4×C107#4112yes—
126C2×Dic107—21no—
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×Dic107C2×D412yes—
143C2×Dic107C2×D412yes—
144C2×Dic107C2×Q812yes—
145C2×Dic107#4112yes—
146C2×Dic107#4112yes—
147C4×D107—28no—
148C22×C107C22×D411yescharacteristic
149C22×C107C22×Q811yescharacteristic
150C22×C107C2×#4111yescharacteristic
151C22×C107C2×#4111yescharacteristic
152C22×C107C2×#4111yescharacteristic
153C22×C107H(5,𝔽2)11yescharacteristic
154C22×C1072−1+411yescharacteristic
155C2×D107—22no—
156C2×D107—22no—
157C2×D107—22no—
158C2×D107—41no—
159C2×D107—41no—
160C2×D107—41no—
161C2×D107—41no—
162C4×C107—22no—
163C4×C107—22no—
164C4×C107—22no—
165C4×C107—41no—
166C4×C107—41no—
167C4×C107—41no—
168C4×C107—41no—
169Dic107—22no—
170Dic107—22no—
171Dic107—41no—
172Dic107—41no—
173Dic107—41no—
174Dic107—41no—
175Dic107C22⋊Q814yes—
176C2×C107C2×C22⋊Q811yescharacteristic
177C2×C107#53311yescharacteristic
178C2×C107#54411yescharacteristic
179C2×C107#54711yescharacteristic
180C2×C107#55011yescharacteristic
181C2×C107#55211yescharacteristic
182C2×C107#55311yescharacteristic
183D107—42no—
184#2441—1071nomaximal, Sylow
185C107#244111yescharacteristic, complemented, Sylow
186C2×#125—1071no—
187C2×#117—1071no—
188#399—1071no—
189#399—1071no—
190#396—1071no—
191#396—1071no—
192#389—1071no—
193#389—1071no—
194#389—1071no—
195#389D10711yescharacteristic, complemented
196#387—1071no—
197#387—1071no—
198#384—1071no—
199#380—1071no—
200C4×C22⋊C4—1071no—
201C23×C4—1071no—
202#125—2144no—
203#117—2144no—
204C2×C4⋊C4—1071no—
205C2×C4⋊C4—1071no—
206C2×C4⋊C4—1071no—
207C2×C4⋊C4—1071no—
208C2×C4⋊C4—1071no—
209C2×C4⋊C4—1071no—
210C2×C4⋊C4—1071no—
211C2×C4⋊C4—1071no—
212C2×C4⋊C4—1071no—
213C2×C4⋊C4—1071no—
214C2×C4⋊C4—1071no—
215C2×C4⋊C4—1071no—
216C2×C4⋊C4C2×D10711yescharacteristic
217C2×C4⋊C4C2×D10711yescharacteristic
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×C42—1071no—
227C2×C42—1071no—
228C2×C42—1071no—
229C2×C42C2×D10711yescharacteristic
230#95—1071no—
231#95—1071no—
232#95—1071no—
233#95—1071no—
234#95—1071no—
235#95—1071no—
236#95C2×D10711yescharacteristic
237#95C2×D10711yescharacteristic
238C24—1071no—
239C22×C4—1071no—
240C22×C4—1071no—
241C22×C4—1071no—
242C22×C4—1074no—
243C22×C4—1071no—
244C22×C4—1071no—
245C22×C4—1071no—
246C22×C4—1071no—
247C22×C4—2142no—
248C22×C4—2142no—
249C22×C4C22×D10711yescharacteristic
250C22×C4C22×D10711yescharacteristic
251C22×C4C22×D10711yescharacteristic
252C22×C4C22×D10711yescharacteristic
253C22×C4C22×D10711yescharacteristic
254C22×C4C22×D10711yescharacteristic
255C22×C4C22×D10711yescharacteristic
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—1074no—
261C4⋊C4—4281no—
262C4⋊C4—4281no—
263C4⋊C4—2142no—
264C4⋊C4—2142no—
265C4⋊C4—2142no—
266C4⋊C4—2142no—
267C4⋊C4—2142no—
268C4⋊C4—2142no—
269C4⋊C4—2142no—
270C4⋊C4—2142no—
271C4⋊C4—2142no—
272C22⋊C4—4281no—
273C22⋊C4—4281no—
274C22⋊C4—2142no—
275C22⋊C4—2142no—
276C22⋊C4—2142no—
277C22⋊C4—2142no—
278C42—22no—
279C42—2142no—
280C42—2142no—
281C42—2142no—
282C23—1072no—
283C23—2141no—
284C23—2141no—
285C23—2141no—
286C23—2141no—
287C23—2141no—
288C23—2141no—
289C23C23×D10711yescharacteristic
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—1072no—
309C2×C4—1072no—
310C2×C4—1072no—
311C2×C4—1072no—
312C2×C4—1072no—
313C2×C4—2148no—
314C2×C4—2141no—
315C2×C4—2141no—
316C2×C4—2141no—
317C2×C4—2141no—
318C2×C4—2141no—
319C2×C4—2141no—
320C2×C4—2141no—
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×C4D4×D10712yes—
331C2×C4Q8×D10712yes—
332C2×C4#1313381812yes—
333C22—4281no—
334C22—4281no—
335C22—4281no—
336C22—4281no—
337C22—2142no—
338C22—2142no—
339C22—2142no—
340C22C2×D4×D10711yescharacteristic
341C22C2×Q8×D10711yescharacteristic
342C22#41×D10711yescharacteristic
343C22#41×D10711yescharacteristic
344C22C2×#1313381811yescharacteristic
345C22#1681215411yescharacteristic
346C22#1681215711yescharacteristic
347C4—22no—
348C4—22no—
349C4—22no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—41no—
354C4—1074no—
355C4—4281no—
356C4—4281no—
357C4—4281no—
358C4—4281no—
359C4—2142no—
360C4—2142no—
361C2—4282no—
362C2C22⋊Q8×D10711yescharacteristic
363C2#2029318111yescharacteristic
364C2#2029325411yescharacteristic
365C2#2029327811yescharacteristic
366C2#2029329511yescharacteristic
367C2#2029330911yescharacteristic
368C2#2029332611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#389×C107C2
prime radicalC23×D107C23
hypercenter#389D107
hypocenterC107#2441
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#16812099C2semidirect
7. #20292524C2semidirect
8. #20292522C2semidirect
9. #20292522C2semidirect
10. #20292514C2semidirect
11. #20292511C2semidirect
12. #20292496C2semidirect
15. #389×C107C2semidirect
185. C107#2441semidirect
195. #389D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120992
C2×#168120662
#202925622
#202925492
#202925242
#202925222
#202925142
#202925112
#202924962
#202924862
#202924742
#389×C1072
#2441107