Finite Group Databasebeta

← #28339963

Subgroups — #28339963

Order 13696.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812087C211yesmaximal, characteristic
2C2×C4×Dic214C211yesmaximal, characteristic, complemented
3#20292568C211yesmaximal, characteristic, complemented
4#20292566C211yesmaximal, characteristic, complemented
5#20292556C211yesmaximal, characteristic
6#20292554C211yesmaximal, characteristic
7#20292531C211yesmaximal, characteristic, complemented
8#20292522C211yesmaximal, characteristic, complemented
9#20292518C211yesmaximal, characteristic
10#20292517C211yesmaximal, characteristic
11#20292509C211yesmaximal, characteristic, complemented
12#20292491C211yesmaximal, characteristic, complemented
13#20292486C211yesmaximal, characteristic
14#20292474C211yesmaximal, characteristic
15#387×C107C211yesmaximal, characteristic, complemented
16C22×Dic214C2211yescharacteristic
17C22×C4×D107C2211yescharacteristic
18#16812087—24no—
19C4×Dic214—24no—
20C2×C4⋊Dic107C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×Dic107⋊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
35C2×C4×Dic107C2211yescharacteristic
36C107⋊#95C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C2×C4⋊C4×C107C2211yescharacteristic
47C2×C4⋊C4×C107C2211yescharacteristic
48C2×C42×C107C2211yescharacteristic
49#95×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52#95×C107C2211yescharacteristic
53C23×D107C2311yescharacteristic
54C2×Dic214—22no—
55C2×Dic214—22no—
56C2×Dic214D414yes—
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C22×Dic107C2311yescharacteristic
63C22×Dic107C2311yescharacteristic
64C2×C4×D107—22no—
65C2×C4×D107—22no—
66C2×C4×D107—22no—
67C4⋊Dic107—22no—
68Dic107⋊C4—22no—
69Dic107⋊C4—22no—
70Dic107⋊C4—22no—
71Dic107⋊C4—22no—
72Dic107⋊C4—22no—
73Dic107⋊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—22no—
80C4×Dic107—22no—
81C4×Dic107—22no—
82C4×Dic107—22no—
83C22×C4×C107C2311yescharacteristic
84C22×C4×C107C2311yescharacteristic
85C22×C4×C107C2311yescharacteristic
86C22×C4×C107C2311yescharacteristic
87C22×C4×C107C2311yescharacteristic
88C22×C4×C107C2311yescharacteristic
89C22×C4×C107C2311yescharacteristic
90C4⋊C4×C107—22no—
91C4⋊C4×C107—22no—
92C42×C107—22no—
93C23×C107C2411yescharacteristic
94C22×D107—21no—
95C22×D107—21no—
96C22×D107—21no—
97C22×D107—21no—
98C22×D107—21no—
99C22×D107—21no—
100C22×D107#4112yes—
101C2×C4×C107—21no—
102C2×C4×C107—21no—
103C2×C4×C107—21no—
104C2×C4×C107—21no—
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×C107C2×D412yes—
121C2×C4×C107#4112yes—
122C2×Dic107—21no—
123C2×Dic107—21no—
124C2×Dic107—21no—
125C2×Dic107—21no—
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×Dic107C2×D412yes—
140C2×Dic107C2×D412yes—
141C2×Dic107#4112yes—
142C2×Dic107#4112yes—
143C4×D107—44no—
144Dic214—28no—
145C22×C107C22×D411yescharacteristic
146C22×C107C2×#4111yescharacteristic
147C22×C107C2×#4111yescharacteristic
148C22×C107C2×#4111yescharacteristic
149C22×C107C2×#4111yescharacteristic
150C22×C1072−1+411yescharacteristic
151C22×C1072−1+411yescharacteristic
152C2×D107—22no—
153C2×D107—22no—
154C2×D107—22no—
155C2×D107—41no—
156C2×D107—41no—
157C2×D107—41no—
158C2×D107—41no—
159C4×C107—22no—
160C4×C107—22no—
161C4×C107—41no—
162C4×C107—41no—
163C4×C107—41no—
164C4×C107—41no—
165C4×C107—41no—
166Dic107—22no—
167Dic107—41no—
168Dic107—41no—
169Dic107—41no—
170Dic107—41no—
171Dic107—41no—
172Dic107#12314yes—
173C2×C107C2×#12311yescharacteristic
174C2×C107#52911yescharacteristic
175C2×C107#54111yescharacteristic
176C2×C107#54811yescharacteristic
177C2×C107#54811yescharacteristic
178C2×C107#55211yescharacteristic
179C2×C107#55611yescharacteristic
180D107—42no—
181#2421—1071nomaximal, Sylow
182C107#242111yescharacteristic, complemented, Sylow
183C2×C22⋊Q8—1071no—
184C2×C4×Q8—1071no—
185#400—1071no—
186#400—1071no—
187#397—1071no—
188#397—1071no—
189#391—1071no—
190#389—1071no—
191#388—1071no—
192#388—1071no—
193#387—1071no—
194#387D10711yescharacteristic, complemented
195#382—1071no—
196#380—1071no—
197C4×C22⋊C4—1071no—
198C22×Q8—1071no—
199C23×C4—1071no—
200C22⋊Q8—2144no—
201C4×Q8—2144no—
202C2×C4⋊C4—1071no—
203C2×C4⋊C4—1071no—
204C2×C4⋊C4—1071no—
205C2×C4⋊C4—1071no—
206C2×C4⋊C4—1071no—
207C2×C4⋊C4—1071no—
208C2×C4⋊C4—1071no—
209C2×C4⋊C4C2×D10711yescharacteristic
210C2×C4⋊C4C2×D10711yescharacteristic
211C2×C22⋊C4—1071no—
212C2×C22⋊C4—1071no—
213C2×C22⋊C4—1071no—
214C2×C22⋊C4—1071no—
215C2×C22⋊C4—1071no—
216C2×C22⋊C4—1071no—
217C2×C42—1071no—
218C2×C42—1071no—
219C2×C42—1071no—
220C2×C42C2×D10711yescharacteristic
221#95—1071no—
222#95—1071no—
223#95—1071no—
224#95—1071no—
225#95—1071no—
226#95—1071no—
227#95—1071no—
228#95—1071no—
229#95—1071no—
230#95—1071no—
231#95C2×D10711yescharacteristic
232#95C2×D10711yescharacteristic
233#95C2×D10711yescharacteristic
234#95C2×D10711yescharacteristic
235C24—1071no—
236C2×Q8—1074no—
237C2×Q8—2142no—
238C2×Q8—2142no—
239C22×C4—1071no—
240C22×C4—1071no—
241C22×C4—1071no—
242C22×C4—1071no—
243C22×C4—1071no—
244C22×C4—1071no—
245C22×C4—1071no—
246C22×C4—2142no—
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—2142no—
259C4⋊C4—2142no—
260C4⋊C4—2142no—
261C4⋊C4—2142no—
262C4⋊C4—2142no—
263C4⋊C4—2142no—
264C4⋊C4—2142no—
265C22⋊C4—2142no—
266C22⋊C4—2142no—
267C22⋊C4—2142no—
268C22⋊C4—2142no—
269C22⋊C4—2142no—
270C22⋊C4—2142no—
271C42—22no—
272C42—2142no—
273C42—2142no—
274C42—2142no—
275C23—1072no—
276C23—2141no—
277C23—2141no—
278C23—2141no—
279C23—2141no—
280C23—2141no—
281C23—2141no—
282C23C23×D10711yescharacteristic
283Q8—2148no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
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—1072no—
304C2×C4—1072no—
305C2×C4—1072no—
306C2×C4—1072no—
307C2×C4—4284no—
308C2×C4—2141no—
309C2×C4—2141no—
310C2×C4—2141no—
311C2×C4—2141no—
312C2×C4—2141no—
313C2×C4—2141no—
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×C4D4×D10712yes—
326C2×C4#1313381812yes—
327C22—4281no—
328C22—4281no—
329C22—4281no—
330C22—4281no—
331C22—2142no—
332C22—2142no—
333C22—2142no—
334C22C2×D4×D10711yescharacteristic
335C22#41×D10711yescharacteristic
336C22#41×D10711yescharacteristic
337C22#41×D10711yescharacteristic
338C22C2×#1313381811yescharacteristic
339C22#1681215611yescharacteristic
340C22#1681215711yescharacteristic
341C4—22no—
342C4—22no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—1074no—
349C4—4281no—
350C4—4281no—
351C4—4281no—
352C4—4281no—
353C4—4281no—
354C4—2142no—
355C2—4282no—
356C2#123×D10711yescharacteristic
357C2#2029315511yescharacteristic
358C2#2029323611yescharacteristic
359C2#2029328611yescharacteristic
360C2#2029328711yescharacteristic
361C2#2029331311yescharacteristic
362C2#2029334911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#387×C107C2
prime radicalC23×D107C23
hypercenter#387D107
hypocenterC107#2421
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic214C2semidirect
3. #20292568C2semidirect
4. #20292566C2semidirect
7. #20292531C2semidirect
8. #20292522C2semidirect
11. #20292509C2semidirect
12. #20292491C2semidirect
15. #387×C107C2semidirect
182. C107#2421semidirect
194. #387D107semidirect

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
#202925682
#202925662
#202925562
#202925542
#202925312
#202925222
#202925182
#202925172
#202925092
#202924912
#202924862
#202924742
#387×C1072
#2421107