Finite Group Databasebeta

← #28339469

Subgroups — #28339469

Order 13696.

620 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
1C2×#16812087C211yesmaximal, characteristic
2C2×C4×Dic214C211yesmaximal, characteristic, complemented
3C2×C4⋊C4×D107C211yesmaximal, characteristic
4#20292531C211yesmaximal, characteristic, complemented
5#20292526C211yesmaximal, characteristic, complemented
6#20292524C211yesmaximal, characteristic, complemented
7#20292522C211yesmaximal, characteristic, complemented
8#20292514C211yesmaximal, characteristic, complemented
9#20292501C211yesmaximal, characteristic
10#20292501C211yesmaximal, characteristic
11#20292478C211yesmaximal, characteristic, complemented
12C4×(C2×D107)⋊C4C211yesmaximal, characteristic
13#20292474C211yesmaximal, characteristic
14#20292474C211yesmaximal, characteristic
15#387×C107C211yesmaximal, characteristic, complemented
16C22×Dic214C2211yescharacteristic
17C22×C4×D107C2211yescharacteristic
18C22×C4×D107C2211yescharacteristic
19C22×C4×D107C2211yescharacteristic
20#16812087C418yescomplemented
21C4×Dic214—24no—
22C2×C4⋊Dic107C2211yescharacteristic
23C2×C4⋊Dic107C2211yescharacteristic
24C2×C4⋊Dic107C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×Dic107⋊C4C2211yescharacteristic
27C2×Dic107⋊C4C2211yescharacteristic
28C2×Dic107⋊C4C2211yescharacteristic
29C2×Dic107⋊C4C2211yescharacteristic
30C2×Dic107⋊C4C2211yescharacteristic
31C4⋊C4×D107—24no—
32C2×(C2×D107)⋊C4C2211yescharacteristic
33C2×(C2×D107)⋊C4C2211yescharacteristic
34C2×(C2×D107)⋊C4C2211yescharacteristic
35C2×(C2×D107)⋊C4C2211yescharacteristic
36C2×C4×Dic107C2211yescharacteristic
37C2×C4×Dic107C2211yescharacteristic
38C2×C4×Dic107C2211yescharacteristic
39C2×C4×Dic107C2211yescharacteristic
40C2×C4×Dic107C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C107⋊#95C2211yescharacteristic
47C2×C4⋊C4×C107C2211yescharacteristic
48C2×C4⋊C4×C107C2211yescharacteristic
49C2×C42×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52#95×C107C2211yescharacteristic
53#95×C107C2211yescharacteristic
54C23×D107C2311yescharacteristic
55C2×Dic214—22no—
56C2×Dic214—22no—
57C2×Dic214C2×C414yescomplemented
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C22×Dic107C2311yescharacteristic
63C22×Dic107C2311yescharacteristic
64C22×Dic107C2311yescharacteristic
65C2×C4×D107—22no—
66C2×C4×D107—22no—
67C2×C4×D107—22no—
68C2×C4×D107—22no—
69C2×C4×D107—22no—
70C2×C4×D107—22no—
71C2×C4×D107—41no—
72C2×C4×D107—41no—
73C2×C4×D107C2×C414yes—
74C4⋊Dic107—22no—
75C4⋊Dic107—22no—
76C4⋊Dic107—41no—
77Dic107⋊C4—22no—
78Dic107⋊C4—22no—
79Dic107⋊C4—41no—
80Dic107⋊C4C2×C414yescomplemented
81Dic107⋊C4C2×C414yescomplemented
82Dic107⋊C4D414yes—
83(C2×D107)⋊C4—22no—
84(C2×D107)⋊C4C2×C414yes—
85(C2×D107)⋊C4C2×C414yes—
86(C2×D107)⋊C4Q814yescomplemented
87C4×Dic107—22no—
88C4×Dic107—22no—
89C4×Dic107—22no—
90C4×Dic107—41no—
91C4×Dic107—41no—
92C22×C4×C107C2311yescharacteristic
93C22×C4×C107C2311yescharacteristic
94C22×C4×C107C2311yescharacteristic
95C22×C4×C107C2311yescharacteristic
96C22×C4×C107C2311yescharacteristic
97C22×C4×C107C2311yescharacteristic
98C22×C4×C107C2311yescharacteristic
99C4⋊C4×C107—22no—
100C4⋊C4×C107C2×C414yescomplemented
101C42×C107—22no—
102C23×C107C2411yescharacteristic
103C22×D107—21no—
104C22×D107—21no—
105C22×D107—21no—
106C22×D107—21no—
107C22×D107C22×C412yes—
108C22×D107C2×Q812yes—
109C22×D107#4112yes—
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×C107C22×C412yes—
127C2×C4×C107C22×C412yes—
128C2×C4×C107C22×C412yes—
129C2×C4×C107C2×D412yes—
130C2×C4×C107C2×Q812yes—
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×Dic107C22×C412yes—
146C2×Dic107C22×C412yes—
147C2×Dic107C22×C412yes—
148C2×Dic107C2×D412yes—
149C2×Dic107C2×D412yes—
150C2×Dic107C2×Q812yes—
151C2×Dic107#4112yes—
152C4×D107—28no—
153C4×D107—44no—
154C4×D107—44no—
155Dic214—28no—
156C22×C107C23×C411yescharacteristic
157C22×C107C22×D411yescharacteristic
158C22×C107C22×Q811yescharacteristic
159C22×C107C2×#4111yescharacteristic
160C22×C107C2×#4111yescharacteristic
161C22×C107H(5,𝔽2)11yescharacteristic
162C22×C1072−1+411yescharacteristic
163C2×D107—22no—
164C2×D107—22no—
165C2×D107—22no—
166C2×D107—22no—
167C2×D107—22no—
168C2×D107—22no—
169C2×D107C4×Q814yescomplemented
170C4×C107—22no—
171C4×C107—22no—
172C4×C107—22no—
173C4×C107—22no—
174C4×C107—22no—
175C4×C107—41no—
176C4×C107—41no—
177Dic107—22no—
178Dic107—22no—
179Dic107—22no—
180Dic107—22no—
181Dic107—41no—
182Dic107—41no—
183Dic107C4×D414yes—
184C2×C107C2×C4×D411yescharacteristic
185C2×C107C2×C4×Q811yescharacteristic
186C2×C107#52011yescharacteristic
187C2×C107#54611yescharacteristic
188C2×C107D4×Q811yescharacteristic
189C2×C107#55211yescharacteristic
190C2×C107#55411yescharacteristic
191D107—24no—
192#2360—1071nomaximal, Sylow
193C107#236011yescharacteristic, complemented, Sylow
194C2×C22⋊Q8—1071no—
195C2×C4×Q8—1071no—
196C22×C4⋊C4—1071no—
197#391—1071no—
198#389—1071no—
199#389—1071no—
200#389—1071no—
201#387—1071no—
202#387D10711yescharacteristic, complemented
203#385—1071no—
204#385—1071no—
205C4×C4⋊C4—1071no—
206C4×C22⋊C4—1071no—
207C4×C22⋊C4—1071no—
208C4×C22⋊C4—1071no—
209C22×Q8—1071no—
210C23×C4—1071no—
211C23×C4—1071no—
212C23×C4—1071no—
213C22⋊Q8—1078no—
214C4×Q8—2144no—
215C2×C4⋊C4—1071no—
216C2×C4⋊C4—1071no—
217C2×C4⋊C4—1071no—
218C2×C4⋊C4—1071no—
219C2×C4⋊C4—1071no—
220C2×C4⋊C4—1071no—
221C2×C4⋊C4—1071no—
222C2×C4⋊C4—1071no—
223C2×C4⋊C4—1071no—
224C2×C4⋊C4—2144no—
225C2×C4⋊C4C2×D10711yescharacteristic
226C2×C4⋊C4C2×D10711yescharacteristic
227C2×C22⋊C4—1071no—
228C2×C22⋊C4—1071no—
229C2×C22⋊C4—1071no—
230C2×C22⋊C4—1071no—
231C2×C42—1071no—
232C2×C42—1071no—
233C2×C42—1071no—
234C2×C42—1071no—
235C2×C42—1071no—
236C2×C42C2×D10711yescharacteristic
237#95—1071no—
238#95—1071no—
239#95—1071no—
240#95—1071no—
241#95—1071no—
242#95—1071no—
243#95C2×D10711yescharacteristic
244#95C2×D10711yescharacteristic
245#95C2×D10711yescharacteristic
246#95C2×D10711yescharacteristic
247C24—1071no—
248C2×Q8—1074no—
249C2×Q8—2142no—
250C2×Q8—2142no—
251C22×C4—1071no—
252C22×C4—1071no—
253C22×C4—1071no—
254C22×C4—1071no—
255C22×C4—1071no—
256C22×C4—1074no—
257C22×C4—1071no—
258C22×C4—1071no—
259C22×C4—4281no—
260C22×C4—4281no—
261C22×C4—2142no—
262C22×C4—2142no—
263C22×C4—2142no—
264C22×C4—2142no—
265C22×C4—2142no—
266C22×C4—2142no—
267C22×C4C22×D10711yescharacteristic
268C22×C4C22×D10711yescharacteristic
269C22×C4C22×D10711yescharacteristic
270C22×C4C22×D10711yescharacteristic
271C22×C4C22×D10711yescharacteristic
272C22×C4C22×D10711yescharacteristic
273C22×C4C22×D10711yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—1074no—
276C4⋊C4—1074no—
277C4⋊C4—1074no—
278C4⋊C4—4281no—
279C4⋊C4—4281no—
280C4⋊C4—2142no—
281C4⋊C4—2142no—
282C4⋊C4—2142no—
283C4⋊C4—2142no—
284C4⋊C4C4×D10714yescomplemented
285C22⋊C4—1074no—
286C22⋊C4—1074no—
287C22⋊C4—1074no—
288C22⋊C4—2142no—
289C42—22no—
290C42—4281no—
291C42—4281no—
292C42—2142no—
293C42—2142no—
294C42—2142no—
295C23—1072no—
296C23—1072no—
297C23—1072no—
298C23—2141no—
299C23—2141no—
300C23—2141no—
301C23—2141no—
302C23C23×D10711yescharacteristic
303Q8—2148no—
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—1072no—
321C2×C4—1072no—
322C2×C4—1072no—
323C2×C4—1072no—
324C2×C4—1072no—
325C2×C4—1072no—
326C2×C4—1072no—
327C2×C4—4284no—
328C2×C4—4284no—
329C2×C4—2148no—
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—
344C2×C4C2×C4×D10712yes—
345C2×C4C2×C4×D10712yes—
346C2×C4C2×C4×D10712yes—
347C2×C4D4×D10712yes—
348C2×C4Q8×D10712yes—
349C22—1074no—
350C22—2142no—
351C22—2142no—
352C22—2142no—
353C22—2142no—
354C22—2142no—
355C22—2142no—
356C22C22×C4×D10711yescharacteristic
357C22C2×D4×D10711yescharacteristic
358C22C2×Q8×D10711yescharacteristic
359C22#41×D10711yescharacteristic
360C22#41×D10711yescharacteristic
361C22#1681215511yescharacteristic
362C22#1681215611yescharacteristic
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—22no—
368C4—41no—
369C4—41no—
370C4—1074no—
371C4—4281no—
372C4—4281no—
373C4—2142no—
374C4—2142no—
375C4—2142no—
376C4—2142no—
377C2—2144no—
378C2C4×D4×D10711yescharacteristic
379C2C4×Q8×D10711yescharacteristic
380C2#2029310711yescharacteristic
381C2#2029326911yescharacteristic
382C2#2029329011yescharacteristic
383C2#2029331311yescharacteristic
384C2#2029333311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
Fitting#387×C107C2
socle, cosocleC23×C107C24
prime radicalC23×D107C23
hypercenter#387D107
hypocenterC107#2360
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic214C2semidirect
4. #20292531C2semidirect
5. #20292526C2semidirect
6. #20292524C2semidirect
7. #20292522C2semidirect
8. #20292514C2semidirect
11. #20292478C2semidirect
15. #387×C107C2semidirect
20. #16812087C4semidirect
57. C2×Dic214C2×C4semidirect
80. Dic107⋊C4C2×C4semidirect
81. Dic107⋊C4C2×C4semidirect
86. (C2×D107)⋊C4Q8semidirect
100. C4⋊C4×C107C2×C4semidirect
169. C2×D107C4×Q8semidirect
193. C107#2360semidirect
202. #387D107semidirect
284. C4⋊C4C4×D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120872
C2×C4×Dic2142
C2×C4⋊C4×D1072
#202925312
#202925262
#202925242
#202925222
#202925142
#202925012
#202924782
C4×(C2×D107)⋊C42
#202924742
#387×C1072
#2360107