Finite Group Databasebeta

← #28339335

Subgroups — #28339335

Order 13696.

548 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D107C211yesmaximal, characteristic
2#20292524C211yesmaximal, characteristic, complemented
3#20292522C211yesmaximal, characteristic, complemented
4#20292513C211yesmaximal, characteristic, complemented
5#20292512C211yesmaximal, characteristic, complemented
6#20292510C211yesmaximal, characteristic, complemented
7#20292486C211yesmaximal, characteristic
8#20292486C211yesmaximal, characteristic
9#20292484C211yesmaximal, characteristic
10C4×Dic107⋊C4C211yesmaximal, characteristic, complemented
11#20292478C211yesmaximal, characteristic, complemented
12C4×(C2×D107)⋊C4C211yesmaximal, characteristic
13#20292474C211yesmaximal, characteristic
14#20292474C211yesmaximal, characteristic
15#387×C107C211yesmaximal, characteristic, complemented
16C22×C4×D107C2211yescharacteristic
17C22×C4×D107C2211yescharacteristic
18C22×C4×D107C2211yescharacteristic
19C2×C4⋊Dic107C2211yescharacteristic
20C2×C4⋊Dic107C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×Dic107⋊C4C2211yescharacteristic
26C2×Dic107⋊C4C2211yescharacteristic
27C4⋊C4×D107C418yescomplemented
28C2×(C2×D107)⋊C4C2211yescharacteristic
29C2×(C2×D107)⋊C4C2211yescharacteristic
30C2×(C2×D107)⋊C4C2211yescharacteristic
31C2×(C2×D107)⋊C4C2211yescharacteristic
32C2×C4×Dic107C2211yescharacteristic
33C2×C4×Dic107C2211yescharacteristic
34C2×C4×Dic107C2211yescharacteristic
35C2×C4×Dic107C2211yescharacteristic
36C2×C4×Dic107C2211yescharacteristic
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
53C22×Dic107C2311yescharacteristic
54C22×Dic107C2311yescharacteristic
55C22×Dic107C2311yescharacteristic
56C22×Dic107C2311yescharacteristic
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C2×C4×D107—22no—
61C2×C4×D107—22no—
62C2×C4×D107—41no—
63C2×C4×D107—41no—
64C2×C4×D107—41no—
65C2×C4×D107—41no—
66C2×C4×D107C2×C414yes—
67C2×C4×D107C2×C414yes—
68C2×C4×D107C2×C414yes—
69C4⋊Dic107—41no—
70C4⋊Dic107C2×C414yes—
71Dic107⋊C4—22no—
72Dic107⋊C4—22no—
73Dic107⋊C4—41no—
74Dic107⋊C4—41no—
75Dic107⋊C4C2×C414yes—
76Dic107⋊C4C2×C414yes—
77(C2×D107)⋊C4—22no—
78(C2×D107)⋊C4—22no—
79(C2×D107)⋊C4—22no—
80(C2×D107)⋊C4Q814yes—
81C4×Dic107—22no—
82C4×Dic107—22no—
83C4×Dic107—41no—
84C4×Dic107—41no—
85C4×Dic107—41no—
86C22×C4×C107C2311yescharacteristic
87C22×C4×C107C2311yescharacteristic
88C22×C4×C107C2311yescharacteristic
89C22×C4×C107C2311yescharacteristic
90C22×C4×C107C2311yescharacteristic
91C22×C4×C107C2311yescharacteristic
92C22×C4×C107C2311yescharacteristic
93C4⋊C4×C107—41no—
94C4⋊C4×C107C2×C414yes—
95C42×C107—41no—
96C23×C107C2411yescharacteristic
97C22×D107—21no—
98C22×D107—21no—
99C22×D107—21no—
100C22×D107—21no—
101C22×D107C22×C412yes—
102C22×D107C2×Q812yes—
103C22×D107#4112yes—
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×C107—21no—
121C2×C4×C107C22×C412yes—
122C2×C4×C107C22×C412yes—
123C2×C4×C107C22×C412yes—
124C2×C4×C107C2×Q812yes—
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×Dic107—21no—
140C2×Dic107C22×C412yes—
141C2×Dic107C22×C412yes—
142C2×Dic107C22×C412yes—
143C2×Dic107C2×Q812yes—
144C2×Dic107#4112yes—
145C2×Dic107#4112yes—
146C4×D107—28no—
147C4×D107—44no—
148C4×D107—44no—
149C22×C107C23×C411yescharacteristic
150C22×C107C22×Q811yescharacteristic
151C22×C107C2×#4111yescharacteristic
152C22×C107C2×#4111yescharacteristic
153C22×C107C2×#4111yescharacteristic
154C22×C107H(5,𝔽2)11yescharacteristic
155C22×C107H(5,𝔽2)11yescharacteristic
156C2×D107—22no—
157C2×D107—22no—
158C2×D107—22no—
159C2×D107—22no—
160C2×D107—22no—
161C2×D107—22no—
162C2×D107C4×Q814yes—
163C4×C107—22no—
164C4×C107—22no—
165C4×C107—22no—
166C4×C107—22no—
167C4×C107—41no—
168C4×C107—41no—
169C4×C107—41no—
170Dic107—22no—
171Dic107—22no—
172Dic107—22no—
173Dic107—41no—
174Dic107—41no—
175Dic107—41no—
176Dic107#11714yes—
177C2×C107C2×#11711yescharacteristic
178C2×C107C2×C4×Q811yescharacteristic
179C2×C107#51811yescharacteristic
180C2×C107#55311yescharacteristic
181C2×C107#55311yescharacteristic
182C2×C107#55411yescharacteristic
183C2×C107#55411yescharacteristic
184D107—24no—
185#2345—1071nomaximal, Sylow
186C107#234511yescharacteristic, complemented, Sylow
187C22×C4⋊C4—1071no—
188#389—1071no—
189#389—1071no—
190#387—1071no—
191#387—1071no—
192#387—1071no—
193#387D10711yescharacteristic, complemented
194#380—1071no—
195#380—1071no—
196#380—1071no—
197C4×C4⋊C4—1071no—
198C4×C4⋊C4—1071no—
199C4×C22⋊C4—1071no—
200C4×C22⋊C4—1071no—
201C4×C22⋊C4—1071no—
202C23×C4—1071no—
203C23×C4—1071no—
204C23×C4—1071no—
205C2×C4⋊C4—1071no—
206C2×C4⋊C4—1071no—
207C2×C4⋊C4—1071no—
208C2×C4⋊C4—1078no—
209C2×C4⋊C4—1071no—
210C2×C4⋊C4—1071no—
211C2×C4⋊C4—1071no—
212C2×C4⋊C4—1071no—
213C2×C4⋊C4—1071no—
214C2×C4⋊C4C2×D10711yescharacteristic
215C2×C4⋊C4C2×D10711yescharacteristic
216C2×C22⋊C4—1071no—
217C2×C22⋊C4—1071no—
218C2×C22⋊C4—1071no—
219C2×C22⋊C4—1071no—
220C2×C42—1071no—
221C2×C42—1071no—
222C2×C42—1071no—
223C2×C42—1071no—
224C2×C42—1071no—
225C2×C42C2×D10711yescharacteristic
226#95—1071no—
227#95—1071no—
228#95—1071no—
229#95—1071no—
230#95—1071no—
231#95—1071no—
232#95—1071no—
233#95—1071no—
234#95C2×D10711yescharacteristic
235#95C2×D10711yescharacteristic
236#95C2×D10711yescharacteristic
237#95C2×D10711yescharacteristic
238C24—1071no—
239C22×C4—1071no—
240C22×C4—1071no—
241C22×C4—1071no—
242C22×C4—1071no—
243C22×C4—1074no—
244C22×C4—1074no—
245C22×C4—1074no—
246C22×C4—1071no—
247C22×C4—1071no—
248C22×C4—1071no—
249C22×C4—4281no—
250C22×C4—4281no—
251C22×C4—4281no—
252C22×C4—4281no—
253C22×C4—2142no—
254C22×C4—2142no—
255C22×C4C22×D10711yescharacteristic
256C22×C4C22×D10711yescharacteristic
257C22×C4C22×D10711yescharacteristic
258C22×C4C22×D10711yescharacteristic
259C22×C4C22×D10711yescharacteristic
260C22×C4C22×D10711yescharacteristic
261C22×C4C22×D10711yescharacteristic
262C4⋊C4—41no—
263C4⋊C4—1074no—
264C4⋊C4—1074no—
265C4⋊C4—1074no—
266C4⋊C4—4281no—
267C4⋊C4—4281no—
268C4⋊C4—4281no—
269C4⋊C4—2142no—
270C4⋊C4—2142no—
271C4⋊C4C4×D10714yes—
272C22⋊C4—1074no—
273C22⋊C4—2142no—
274C22⋊C4—2142no—
275C22⋊C4—2142no—
276C42—41no—
277C42—4281no—
278C42—4281no—
279C42—4281no—
280C42—2142no—
281C42—2142no—
282C23—1072no—
283C23—1072no—
284C23—1072no—
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—1072no—
308C2×C4—1072no—
309C2×C4—1072no—
310C2×C4—1072no—
311C2×C4—1072no—
312C2×C4—1072no—
313C2×C4—4284no—
314C2×C4—4284no—
315C2×C4—2148no—
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×C4—2141no—
331C2×C4C2×C4×D10712yes—
332C2×C4C2×C4×D10712yes—
333C2×C4C2×C4×D10712yes—
334C2×C4Q8×D10712yes—
335C22—1074no—
336C22—2142no—
337C22—2142no—
338C22—2142no—
339C22—2142no—
340C22—2142no—
341C22—2142no—
342C22C22×C4×D10711yescharacteristic
343C22C2×Q8×D10711yescharacteristic
344C22#41×D10711yescharacteristic
345C22#41×D10711yescharacteristic
346C22#41×D10711yescharacteristic
347C22#1681215411yescharacteristic
348C22#1681215511yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—1074no—
357C4—4281no—
358C4—4281no—
359C4—4281no—
360C4—2142no—
361C4—2142no—
362C4—2142no—
363C2—2144no—
364C2#117×D10711yescharacteristic
365C2C4×Q8×D10711yescharacteristic
366C2#2029309911yescharacteristic
367C2#2029332211yescharacteristic
368C2#2029332811yescharacteristic
369C2#2029333111yescharacteristic
370C2#2029333311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutatorC22×C107C23×C4
Fitting#387×C107C2
socle, cosocleC23×C107C24
prime radicalC23×D107C23
hypercenter#387D107
hypocenterC107#2345
LCSG ▷ C22×C107 ▷ C107
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #20292524C2semidirect
3. #20292522C2semidirect
4. #20292513C2semidirect
5. #20292512C2semidirect
6. #20292510C2semidirect
10. C4×Dic107⋊C4C2semidirect
11. #20292478C2semidirect
15. #387×C107C2semidirect
27. C4⋊C4×D107C4semidirect
186. C107#2345semidirect
193. #387D107semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D1072
#202925242
#202925222
#202925132
#202925122
#202925102
#202924862
#202924842
C4×Dic107⋊C42
#202924782
C4×(C2×D107)⋊C42
#202924742
#387×C1072
#2345107