Finite Group Databasebeta

← #28339093

Subgroups — #28339093

Order 13696.

568 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812071C211yesmaximal, characteristic
2#20292518C211yesmaximal, characteristic, complemented
3#20292516C211yesmaximal, characteristic, complemented
4#20292513C211yesmaximal, characteristic, complemented
5#20292505C211yesmaximal, characteristic
6#20292505C211yesmaximal, characteristic
7#20292501C211yesmaximal, characteristic, complemented
8#20292498C211yesmaximal, characteristic, complemented
9#20292494C211yesmaximal, characteristic, complemented
10#20292491C211yesmaximal, characteristic, complemented
11#20292489C211yesmaximal, characteristic, complemented
12#20292484C211yesmaximal, characteristic, complemented
13C4×(C2×D107)⋊C4C211yesmaximal, characteristic, complemented
14#95×D107C211yesmaximal, characteristic, complemented
15#387×C107C211yesmaximal, characteristic, complemented
16C22×D428C2211yescharacteristic
17C22×C4×D107C2211yescharacteristic
18C22×C4×D107C2211yescharacteristic
19C22×C4×D107C2211yescharacteristic
20C22×C4×D107C2211yescharacteristic
21#16812071C418yescomplemented
22C2×C4⋊Dic107C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊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×C4×Dic107C2211yescharacteristic
34C2×C4×Dic107C2211yescharacteristic
35C107⋊#95C2211yescharacteristic
36C107⋊#95C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C2×C4⋊C4×C107C2211yescharacteristic
46C2×C4⋊C4×C107C2211yescharacteristic
47C2×C42×C107C2211yescharacteristic
48#95×C107C2211yescharacteristic
49#95×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52C23×D107C2311yescharacteristic
53C23×D107C2311yescharacteristic
54C2×D428—22no—
55C2×D428—22no—
56C2×D428C2×C414yes—
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C22×Dic107C2311yescharacteristic
63C2×C4×D107—22no—
64C2×C4×D107—22no—
65C2×C4×D107—41no—
66C2×C4×D107—41no—
67C2×C4×D107—41no—
68C2×C4×D107—41no—
69C2×C4×D107—41no—
70C2×C4×D107—41no—
71C2×C4×D107—41no—
72C2×C4×D107—41no—
73C2×C4×D107C2×C414yes—
74C2×C4×D107C2×C414yescomplemented
75C4⋊Dic107—41no—
76Dic107⋊C4—41no—
77Dic107⋊C4—41no—
78(C2×D107)⋊C4—22no—
79(C2×D107)⋊C4—22no—
80(C2×D107)⋊C4—41no—
81(C2×D107)⋊C4—41no—
82(C2×D107)⋊C4—41no—
83(C2×D107)⋊C4—41no—
84(C2×D107)⋊C4C2×C414yes—
85(C2×D107)⋊C4C2×C414yescomplemented
86C4×Dic107—41no—
87C4×Dic107C2×C414yescomplemented
88C22×C4×C107C2311yescharacteristic
89C22×C4×C107C2311yescharacteristic
90C22×C4×C107C2311yescharacteristic
91C22×C4×C107C2311yescharacteristic
92C22×C4×C107C2311yescharacteristic
93C22×C4×C107C2311yescharacteristic
94C22×C4×C107C2311yescharacteristic
95C4⋊C4×C107—41no—
96C4⋊C4×C107C2×C414yescomplemented
97C42×C107—41no—
98C23×C107C2411yescharacteristic
99C22×D107—21no—
100C22×D107—21no—
101C22×D107—21no—
102C22×D107—21no—
103C22×D107—21no—
104C22×D107—21no—
105C22×D107—21no—
106C22×D107—21no—
107C22×D107—21no—
108C22×D107—21no—
109C22×D107C22×C412yes—
110C22×D107C22×C412yes—
111C22×D107#4112yes—
112C22×D107#4112yes—
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×C4×C107—21no—
130C2×C4×C107—21no—
131C2×C4×C107C22×C412yes—
132C2×C4×C107C22×C412yes—
133C2×C4×C107C22×C412yes—
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—
148C2×Dic107—21no—
149C2×Dic107—21no—
150C2×Dic107C22×C412yes—
151C2×Dic107C22×C412yes—
152D428—28no—
153C4×D107—44no—
154C4×D107—44no—
155C4×D107—44no—
156C4×D107—44no—
157C22×C107C23×C411yescharacteristic
158C22×C107C2×#4111yescharacteristic
159C22×C107C2×#4111yescharacteristic
160C22×C107H(5,𝔽2)11yescharacteristic
161C22×C107H(5,𝔽2)11yescharacteristic
162C22×C107H(5,𝔽2)11yescharacteristic
163C22×C1072−1+411yescharacteristic
164C2×D107—22no—
165C2×D107—22no—
166C2×D107—22no—
167C2×D107—22no—
168C2×D107—22no—
169C2×D107—22no—
170C2×D107—22no—
171C2×D107—22no—
172C2×D107—22no—
173C2×D107—41no—
174C2×D107—41no—
175C2×D107—41no—
176C2×D107—41no—
177C2×D107#11714yes—
178C4×C107—22no—
179C4×C107—22no—
180C4×C107—22no—
181C4×C107—41no—
182C4×C107—41no—
183C4×C107—41no—
184C4×C107—41no—
185Dic107—22no—
186Dic107—22no—
187Dic107—41no—
188Dic107—41no—
189Dic107—41no—
190Dic107—41no—
191C2×C107C2×#11711yescharacteristic
192C2×C107#51811yescharacteristic
193C2×C107#52011yescharacteristic
194C2×C107#53811yescharacteristic
195C2×C107#53811yescharacteristic
196C2×C107#53911yescharacteristic
197C2×C107#53911yescharacteristic
198D107—24no—
199D107—42no—
200#2318—1071nomaximal, Sylow
201C107#231811yescharacteristic, complemented, Sylow
202C2×C4×D4—1071no—
203#388—1071no—
204#388—1071no—
205#387—1071no—
206#387D10711yescharacteristic, complemented
207#386—1071no—
208#386—1071no—
209#385—1071no—
210#385—1071no—
211#383—1071no—
212#382—1071no—
213#381—1071no—
214#380—1071no—
215C4×C22⋊C4—1071no—
216C2×#95—1071no—
217C22×D4—1071no—
218C23×C4—1071no—
219C23×C4—1071no—
220C23×C4—1071no—
221C23×C4—1071no—
222C4×D4—1078no—
223C2×C4⋊C4—1071no—
224C2×C4⋊C4—1071no—
225C2×C4⋊C4—1071no—
226C2×C4⋊C4C2×D10711yescharacteristic
227C2×C4⋊C4C2×D10711yescharacteristic
228C2×C22⋊C4—1071no—
229C2×C22⋊C4—1071no—
230C2×C22⋊C4—1071no—
231C2×C22⋊C4—1071no—
232C2×C22⋊C4—1071no—
233C2×C22⋊C4—1071no—
234C2×C22⋊C4—1071no—
235C2×C22⋊C4—1071no—
236C2×C42—1071no—
237C2×C42—1071no—
238C2×C42C2×D10711yescharacteristic
239#95—1071no—
240#95—1071no—
241#95—1071no—
242#95—1071no—
243#95—1071no—
244#95—1071no—
245#95—1071no—
246#95—1071no—
247#95—1071no—
248#95—1071no—
249#95C2×D10711yescharacteristic
250#95C2×D10711yescharacteristic
251#95C2×D10711yescharacteristic
252#95C2×D10711yescharacteristic
253C24—1071no—
254C24—1071no—
255C2×D4—1074no—
256C2×D4—2142no—
257C2×D4—2142no—
258C22×C4—1071no—
259C22×C4—1071no—
260C22×C4—1074no—
261C22×C4—1074no—
262C22×C4—1071no—
263C22×C4—1071no—
264C22×C4—1071no—
265C22×C4—1071no—
266C22×C4—4281no—
267C22×C4—4281no—
268C22×C4—4281no—
269C22×C4—4281no—
270C22×C4—4281no—
271C22×C4—4281no—
272C22×C4—4281no—
273C22×C4—4281no—
274C22×C4—2142no—
275C22×C4—2142no—
276C22×C4C22×D10711yescharacteristic
277C22×C4C22×D10711yescharacteristic
278C22×C4C22×D10711yescharacteristic
279C22×C4C22×D10711yescharacteristic
280C22×C4C22×D10711yescharacteristic
281C22×C4C22×D10711yescharacteristic
282C22×C4C22×D10711yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—4281no—
285C4⋊C4—4281no—
286C4⋊C4—4281no—
287C4⋊C4C4×D10714yescomplemented
288C22⋊C4—1074no—
289C22⋊C4—1074no—
290C22⋊C4—4281no—
291C22⋊C4—4281no—
292C22⋊C4—4281no—
293C22⋊C4—4281no—
294C22⋊C4—2142no—
295C22⋊C4—2142no—
296C42—41no—
297C42—1074no—
298C42—4281no—
299C23—1072no—
300C23—1072no—
301C23—1072no—
302C23—1072no—
303C23—2141no—
304C23—2141no—
305C23—2141no—
306C23—2141no—
307C23—2141no—
308C23—2141no—
309C23—2141no—
310C23—2141no—
311C23—2141no—
312C23—2141no—
313C23C23×D10711yescharacteristic
314D4—2148no—
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—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—1072no—
334C2×C4—1072no—
335C2×C4—4284no—
336C2×C4—4284no—
337C2×C4—4284no—
338C2×C4—4284no—
339C2×C4—2141no—
340C2×C4—2141no—
341C2×C4—2141no—
342C2×C4—2141no—
343C2×C4—2141no—
344C2×C4—2141no—
345C2×C4—2141no—
346C2×C4—2141no—
347C2×C4—2141no—
348C2×C4—2141no—
349C2×C4—2141no—
350C2×C4—2141no—
351C2×C4—2141no—
352C2×C4—2141no—
353C2×C4—2141no—
354C2×C4—2141no—
355C2×C4C2×C4×D10712yes—
356C2×C4C2×C4×D10712yes—
357C2×C4C2×C4×D10712yes—
358C22—1074no—
359C22—4281no—
360C22—4281no—
361C22—4281no—
362C22—4281no—
363C22—2142no—
364C22—2142no—
365C22—2142no—
366C22—2142no—
367C22—2142no—
368C22—2142no—
369C22—2142no—
370C22—2142no—
371C22—2142no—
372C22C22×C4×D10711yescharacteristic
373C22#41×D10711yescharacteristic
374C22#41×D10711yescharacteristic
375C22#1681215411yescharacteristic
376C22#1681215511yescharacteristic
377C22#1681215511yescharacteristic
378C22#1681215711yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—4281no—
387C4—4281no—
388C4—4281no—
389C4—4281no—
390C4—2142no—
391C4—2142no—
392C2—4282no—
393C2—2144no—
394C2#117×D10711yescharacteristic
395C2#2029309911yescharacteristic
396C2#2029310911yescharacteristic
397C2#2029321311yescharacteristic
398C2#2029321611yescharacteristic
399C2#2029322311yescharacteristic
400C2#2029322511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
Fitting#387×C107C2
socle, cosocleC23×C107C24
prime radicalC22×D428C22
hypercenter#387D107
hypocenterC107#2318
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #20292518C2semidirect
3. #20292516C2semidirect
4. #20292513C2semidirect
7. #20292501C2semidirect
8. #20292498C2semidirect
9. #20292494C2semidirect
10. #20292491C2semidirect
11. #20292489C2semidirect
12. #20292484C2semidirect
13. C4×(C2×D107)⋊C4C2semidirect
14. #95×D107C2semidirect
15. #387×C107C2semidirect
21. #16812071C4semidirect
74. C2×C4×D107C2×C4semidirect
85. (C2×D107)⋊C4C2×C4semidirect
87. C4×Dic107C2×C4semidirect
96. C4⋊C4×C107C2×C4semidirect
201. C107#2318semidirect
206. #387D107semidirect
287. C4⋊C4C4×D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120712
#202925182
#202925162
#202925132
#202925052
#202925012
#202924982
#202924942
#202924912
#202924892
#202924842
C4×(C2×D107)⋊C42
#95×D1072
#387×C1072
#2318107