Finite Group Databasebeta

← #28340234

Subgroups — #28340234

Order 13696.

460 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812108C211yesmaximal, characteristic
2C2×C4×Dic214C211yesmaximal, characteristic
3#20292568C211yesmaximal, characteristic
4#20292567C211yesmaximal, characteristic
5#20292560C211yesmaximal, characteristic
6#20292557C211yesmaximal, characteristic
7#20292531C211yesmaximal, characteristic
8#20292531C211yesmaximal, characteristic
9#20292531C211yesmaximal, characteristic
10#20292522C211yesmaximal, characteristic
11#20292514C211yesmaximal, characteristic
12#20292511C211yesmaximal, characteristic
13#20292509C211yesmaximal, characteristic
14#20292478C211yesmaximal, characteristic
15#387×C107C211yesmaximal, characteristic
16C22×Dic214C2211yescharacteristic
17C22×Dic214C2211yescharacteristic
18#16812108—24no—
19C4×Dic214—24no—
20C2×C4⋊Dic107C2211yescharacteristic
21C2×C4⋊Dic107C2211yescharacteristic
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×C4×Dic107C2211yescharacteristic
31C2×C4×Dic107C2211yescharacteristic
32C2×C4×Dic107C2211yescharacteristic
33C2×C4×Dic107C2211yescharacteristic
34C107⋊#95C2211yescharacteristic
35C107⋊#95C2211yescharacteristic
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
53C2×Dic214—22no—
54C2×Dic214—22no—
55C2×Dic214—22no—
56C2×Dic214—22no—
57C2×Dic214—22no—
58C2×Dic214D414yes—
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C22×Dic107C2311yescharacteristic
63C22×Dic107C2311yescharacteristic
64C22×Dic107C2311yescharacteristic
65C22×Dic107C2311yescharacteristic
66C22×Dic107C2311yescharacteristic
67C4⋊Dic107—22no—
68C4⋊Dic107—22no—
69Dic107⋊C4—22no—
70Dic107⋊C4—22no—
71Dic107⋊C4—22no—
72Dic107⋊C4—22no—
73Dic107⋊C4—22no—
74Dic107⋊C4—22no—
75Dic107⋊C4—22no—
76Dic107⋊C4Q814yescomplemented
77C4×Dic107—22no—
78C4×Dic107—22no—
79C4×Dic107—22no—
80C4×Dic107—22no—
81C22×C4×C107C2311yescharacteristic
82C22×C4×C107C2311yescharacteristic
83C22×C4×C107C2311yescharacteristic
84C22×C4×C107C2311yescharacteristic
85C22×C4×C107C2311yescharacteristic
86C22×C4×C107C2311yescharacteristic
87C22×C4×C107C2311yescharacteristic
88C4⋊C4×C107—22no—
89C4⋊C4×C107—22no—
90C42×C107—22no—
91C23×C107C2411yescharacteristic
92C2×C4×C107—21no—
93C2×C4×C107—21no—
94C2×C4×C107—21no—
95C2×C4×C107—21no—
96C2×C4×C107—21no—
97C2×C4×C107—21no—
98C2×C4×C107—21no—
99C2×C4×C107—21no—
100C2×C4×C107—21no—
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×C107C2×D412yes—
111C2×C4×C107C2×Q812yes—
112C2×C4×C107#4112yes—
113C2×Dic107—21no—
114C2×Dic107—21no—
115C2×Dic107—21no—
116C2×Dic107—21no—
117C2×Dic107—21no—
118C2×Dic107—21no—
119C2×Dic107—21no—
120C2×Dic107—21no—
121C2×Dic107—21no—
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×Dic107C2×D412yes—
132C2×Dic107C2×D412yes—
133C2×Dic107C2×Q812yes—
134C2×Dic107C2×Q812yes—
135C2×Dic107#4112yes—
136C2×Dic107#4112yes—
137Dic214—28no—
138Dic214—44no—
139C22×C107C22×D411yescharacteristic
140C22×C107C22×Q811yescharacteristic
141C22×C107C2×#4111yescharacteristic
142C22×C107C2×#4111yescharacteristic
143C22×C107C2×#4111yescharacteristic
144C22×C1072−1+411yescharacteristic
145C22×C1072−1+411yescharacteristic
146C4×C107—22no—
147C4×C107—22no—
148C4×C107—22no—
149C4×C107—41no—
150C4×C107—41no—
151C4×C107—41no—
152C4×C107—41no—
153Dic107—22no—
154Dic107—22no—
155Dic107—22no—
156Dic107—41no—
157Dic107—41no—
158Dic107—41no—
159Dic107—41no—
160Dic107#12314yes—
161C2×C107C2×#12311yescharacteristic
162C2×C107#53311yescharacteristic
163C2×C107#54111yescharacteristic
164C2×C107#54811yescharacteristic
165C2×C107D4×Q811yescharacteristic
166C2×C107#55611yescharacteristic
167C2×C107#55711yescharacteristic
168#2446—1071nomaximal, Sylow
169C107#244611yescharacteristic, complemented, Sylow
170C2×C4⋊Q8—1071no—
171C2×C4×Q8—1071no—
172#400—1071no—
173#400—1071no—
174#398—1071no—
175#398—1071no—
176#391—1071no—
177#391—1071no—
178#391—1071no—
179#389—1071no—
180#387—1071no—
181#387—1071no—
182#387—1071no—
183#387D10711yescharacteristic
184C4×C4⋊C4—1071no—
185C22×Q8—1071no—
186C22×Q8—1071no—
187C4⋊Q8—2144no—
188C4×Q8—2144no—
189C2×C4⋊C4—1071no—
190C2×C4⋊C4—1071no—
191C2×C4⋊C4—1071no—
192C2×C4⋊C4—1071no—
193C2×C4⋊C4—1071no—
194C2×C4⋊C4—1071no—
195C2×C4⋊C4—1071no—
196C2×C4⋊C4—1071no—
197C2×C4⋊C4—1071no—
198C2×C4⋊C4—1071no—
199C2×C4⋊C4C2×D10711yescharacteristic
200C2×C4⋊C4C2×D10711yescharacteristic
201C2×C42—1071no—
202C2×C42—1071no—
203C2×C42—1071no—
204C2×C42—1071no—
205C2×C42C2×D10711yescharacteristic
206#95—1071no—
207#95—1071no—
208#95—1071no—
209#95—1071no—
210#95—1071no—
211#95—1071no—
212#95—1071no—
213#95—1071no—
214#95—1071no—
215#95—1071no—
216#95—1071no—
217#95—1071no—
218#95C2×D10711yescharacteristic
219#95C2×D10711yescharacteristic
220#95C2×D10711yescharacteristic
221#95C2×D10711yescharacteristic
222C2×Q8—1074no—
223C2×Q8—2142no—
224C2×Q8—2142no—
225C2×Q8—2142no—
226C2×Q8—2142no—
227C2×Q8—2142no—
228C22×C4—1071no—
229C22×C4—1071no—
230C22×C4—1071no—
231C22×C4—1071no—
232C22×C4—1071no—
233C22×C4—1071no—
234C22×C4—1071no—
235C22×C4—1071no—
236C22×C4C22×D10711yescharacteristic
237C22×C4C22×D10711yescharacteristic
238C22×C4C22×D10711yescharacteristic
239C22×C4C22×D10711yescharacteristic
240C22×C4C22×D10711yescharacteristic
241C22×C4C22×D10711yescharacteristic
242C22×C4C22×D10711yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—1074no—
246C4⋊C4—2142no—
247C4⋊C4—2142no—
248C4⋊C4—2142no—
249C4⋊C4—2142no—
250C4⋊C4—2142no—
251C4⋊C4—2142no—
252C4⋊C4—2142no—
253C4⋊C4—2142no—
254C4⋊C4—2142no—
255C42—22no—
256C42—2142no—
257C42—2142no—
258C42—2142no—
259C42—2142no—
260C23C23×D10711yescharacteristic
261Q8—4284no—
262Q8—2148no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—1072no—
282C2×C4—1072no—
283C2×C4—1072no—
284C2×C4—1072no—
285C2×C4—1072no—
286C2×C4—1072no—
287C2×C4—2141no—
288C2×C4—2141no—
289C2×C4—2141no—
290C2×C4—2141no—
291C2×C4—2141no—
292C2×C4—2141no—
293C2×C4—2141no—
294C2×C4—2141no—
295C2×C4—2141no—
296C2×C4—2141no—
297C2×C4—2141no—
298C2×C4—2141no—
299C2×C4—2141no—
300C2×C4—2141no—
301C2×C4—2141no—
302C2×C4—2141no—
303C2×C4—2141no—
304C2×C4—2141no—
305C2×C4D4×D10712yes—
306C2×C4Q8×D10712yes—
307C2×C4#1313381812yes—
308C22C2×D4×D10711yescharacteristic
309C22C2×Q8×D10711yescharacteristic
310C22#41×D10711yescharacteristic
311C22#41×D10711yescharacteristic
312C22C2×#1313381811yescharacteristic
313C22#1681215611yescharacteristic
314C22#1681215611yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—1074no—
323C4—4281no—
324C4—4281no—
325C4—4281no—
326C4—4281no—
327C4—2142no—
328C4—2142no—
329C4—2142no—
330C2#123×D10711yescharacteristic
331C2#2029318111yescharacteristic
332C2#2029323411yescharacteristic
333C2#2029328611yescharacteristic
334C2#2029329011yescharacteristic
335C2#2029334511yescharacteristic
336C2#2029335411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, prime radical, cosocleC23×C107C24
Fitting#387×C107C2
hypercenter#387D107
hypocenterC107#2446
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
76. Dic107⋊C4Q8semidirect
169. C107#2446semidirect

Maximal subgroups

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

subgroupindex
C2×#168121082
C2×C4×Dic2142
#202925682
#202925672
#202925602
#202925572
#202925312
#202925222
#202925142
#202925112
#202925092
#202924782
#387×C1072
#2446107