Finite Group Databasebeta

← #28340285

Subgroups — #28340285

Order 13696.

584 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812088C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D107C211yesmaximal, characteristic
3#20292568C211yesmaximal, characteristic, complemented
4#20292561C211yesmaximal, characteristic, complemented
5#20292551C211yesmaximal, characteristic, complemented
6#20292540C211yesmaximal, characteristic, complemented
7#20292531C211yesmaximal, characteristic, complemented
8#20292509C211yesmaximal, characteristic, complemented
9#20292506C211yesmaximal, characteristic
10#20292506C211yesmaximal, characteristic
11#20292501C211yesmaximal, characteristic, complemented
12#20292500C211yesmaximal, characteristic, complemented
13#20292500C211yesmaximal, characteristic, complemented
14#20292486C211yesmaximal, characteristic, complemented
15C2×#95×C107C211yesmaximal, characteristic, complemented
16C22×Dic214C2211yescharacteristic
17C22×C22⋊D107C2211yescharacteristic
18C22×C4×D107C2211yescharacteristic
19#16812088—24no—
20C4×C22⋊D107—24no—
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×C22⋊Dic107C2211yescharacteristic
30C2×C22⋊Dic107C2211yescharacteristic
31C2×C22⋊Dic107C2211yescharacteristic
32C2×(C2×D107)⋊C4C2211yescharacteristic
33C2×(C2×D107)⋊C4C2211yescharacteristic
34C2×(C2×D107)⋊C4C2211yescharacteristic
35C2×(C2×D107)⋊C4C2211yescharacteristic
36C2×(C2×D107)⋊C4C2211yescharacteristic
37C2×C4×Dic107C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C23×C4×C107C2211yescharacteristic
47C23×C4×C107C2211yescharacteristic
48C23×C4×C107C2211yescharacteristic
49#95×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52#95×C107C2211yescharacteristic
53C23×D107C2311yescharacteristic
54C2×Dic214—22no—
55C2×Dic214—22no—
56C2×Dic214—41no—
57C2×C22⋊D107—22no—
58C2×C22⋊D107—22no—
59C2×C22⋊D107Q814yescomplemented
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C22×Dic107C2311yescharacteristic
63C22×Dic107C2311yescharacteristic
64C22×Dic107C2311yescharacteristic
65C22×Dic107C2311yescharacteristic
66C22×Dic107C2311yescharacteristic
67C2×C4×D107—22no—
68C2×C4×D107—22no—
69C2×C4×D107—41no—
70C4⋊Dic107—22no—
71Dic107⋊C4—22no—
72Dic107⋊C4—22no—
73Dic107⋊C4—22no—
74Dic107⋊C4—22no—
75Dic107⋊C4—41no—
76Dic107⋊C4—41no—
77Dic107⋊C4—41no—
78C22⋊Dic107—22no—
79C22⋊Dic107—22no—
80C22⋊Dic107D414yes—
81(C2×D107)⋊C4—22no—
82(C2×D107)⋊C4—22no—
83(C2×D107)⋊C4—41no—
84(C2×D107)⋊C4—41no—
85(C2×D107)⋊C4—41no—
86C4×Dic107—22no—
87C24×C107C2311yescharacteristic
88C22×C4×C107—22no—
89C22×C4×C107—22no—
90C22×C4×C107—22no—
91C22×C4×C107—22no—
92C22×C4×C107—22no—
93C22×C4×C107—41no—
94C22×C4×C107—41no—
95C22×C4×C107—41no—
96C22×C4×C107—41no—
97C22×C4×C107C2311yescharacteristic
98C22×C4×C107C2311yescharacteristic
99C22×C4×C107C2311yescharacteristic
100C22×C4×C107C2311yescharacteristic
101C22×C4×C107C2311yescharacteristic
102C22×C4×C107C2311yescharacteristic
103C23×C107—21no—
104C23×C107—21no—
105C23×C107—21no—
106C23×C107—21no—
107C23×C107C2×D412yes—
108C23×C107C2×Q812yes—
109C23×C107#4112yes—
110C23×C107C2411yescharacteristic
111C22×D107—21no—
112C22×D107—21no—
113C22×D107—21no—
114C22×D107—21no—
115C22×D107—21no—
116C22×D107—21no—
117C22×D107C2×Q812yes—
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×C107—21no—
132C2×C4×C107—21no—
133C2×C4×C107—21no—
134C2×C4×C107—44no—
135C2×C4×C107—44no—
136C2×C4×C107—44no—
137C2×C4×C107#4112yes—
138C2×C4×C107#4112yes—
139C22⋊D107—28no—
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×Dic107—21no—
151C2×Dic107—21no—
152C2×Dic107—21no—
153C2×Dic107—21no—
154C2×Dic107—21no—
155C2×Dic107—21no—
156C2×Dic107—21no—
157C2×Dic107—21no—
158C2×Dic107C2×D412yes—
159C2×Dic107C2×D412yes—
160C2×Dic107C2×Q812yes—
161C4×D107—44no—
162Dic214—44no—
163C22×C107—22no—
164C22×C107—22no—
165C22×C107—22no—
166C22×C107—22no—
167C22×C107—22no—
168C22×C107—22no—
169C22×C107C22⋊Q814yes—
170C22×C107C22×D411yescharacteristic
171C22×C107C22×Q811yescharacteristic
172C22×C107C2×#4111yescharacteristic
173C22×C107C2×#4111yescharacteristic
174C22×C107C2×#4111yescharacteristic
175C22×C107H(5,𝔽2)11yescharacteristic
176C22×C107H(5,𝔽2)11yescharacteristic
177C2×D107—22no—
178C2×D107—22no—
179C2×D107—22no—
180C2×D107—41no—
181C2×D107—41no—
182C2×D107—41no—
183C2×D107—41no—
184C4×C107—22no—
185C4×C107—22no—
186C4×C107—41no—
187C4×C107—41no—
188C4×C107—41no—
189C4×C107—41no—
190Dic107—22no—
191Dic107—22no—
192Dic107—22no—
193Dic107—41no—
194Dic107—41no—
195Dic107—41no—
196Dic107—41no—
197C2×C107—24no—
198C2×C107C2×C22⋊Q811yescharacteristic
199C2×C107#52911yescharacteristic
200C2×C107#53811yescharacteristic
201C2×C107#54611yescharacteristic
202C2×C107#54611yescharacteristic
203C2×C107#55411yescharacteristic
204C2×C107#55411yescharacteristic
205D107—42no—
206#2450—1071nomaximal, Sylow
207C107#245011yescharacteristic, complemented, Sylow
208C2×C22⋊Q8—1071no—
209C2×C4×D4—1071no—
210#400—1071no—
211#398—1071no—
212#396—1071no—
213#393—1071no—
214#391—1071no—
215#387—1071no—
216#386—1071no—
217#386—1071no—
218#385—1071no—
219#385—1071no—
220#385—1071no—
221#380—1071no—
222C2×#95D10711yescharacteristic, complemented
223C22×Q8—1071no—
224C22×D4—1071no—
225C23×C4—1071no—
226C23×C4C2×D10711yescharacteristic
227C23×C4C2×D10711yescharacteristic
228C23×C4C2×D10711yescharacteristic
229C22⋊Q8—2144no—
230C4×D4—2144no—
231C2×C4⋊C4—1071no—
232C2×C4⋊C4—1071no—
233C2×C4⋊C4—1071no—
234C2×C4⋊C4—1071no—
235C2×C4⋊C4—1071no—
236C2×C4⋊C4—1071no—
237C2×C4⋊C4—1071no—
238C2×C4⋊C4—1071no—
239C2×C22⋊C4—1071no—
240C2×C22⋊C4—1071no—
241C2×C22⋊C4—1071no—
242C2×C22⋊C4—1071no—
243C2×C22⋊C4—1071no—
244C2×C22⋊C4—1071no—
245C2×C22⋊C4—1071no—
246C2×C22⋊C4—1071no—
247C2×C42—1071no—
248#95—1071no—
249#95—1071no—
250#95—1071no—
251#95—1071no—
252#95—1071no—
253#95—1071no—
254#95—1071no—
255#95—1071no—
256#95C2×D10711yescharacteristic
257#95C2×D10711yescharacteristic
258#95C2×D10711yescharacteristic
259#95C2×D10711yescharacteristic
260C24—1071no—
261C24C22×D10711yescharacteristic
262C2×Q8—4281no—
263C2×Q8—2142no—
264C2×Q8—2142no—
265C2×D4—1074no—
266C2×D4—2142no—
267C2×D4—2142no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—1071no—
278C22×C4—1071no—
279C22×C4—1071no—
280C22×C4—1071no—
281C22×C4—1071no—
282C22×C4—1071no—
283C22×C4—1071no—
284C22×C4—4281no—
285C22×C4—2142no—
286C22×C4—2142no—
287C22×C4C22×D10711yescharacteristic
288C22×C4C22×D10711yescharacteristic
289C22×C4C22×D10711yescharacteristic
290C22×C4C22×D10711yescharacteristic
291C22×C4C22×D10711yescharacteristic
292C22×C4C22×D10711yescharacteristic
293C4⋊C4—4281no—
294C4⋊C4—4281no—
295C4⋊C4—4281no—
296C4⋊C4—2142no—
297C4⋊C4—2142no—
298C4⋊C4—2142no—
299C4⋊C4—2142no—
300C4⋊C4—2142no—
301C22⋊C4—1074no—
302C22⋊C4—4281no—
303C22⋊C4—4281no—
304C22⋊C4—4281no—
305C22⋊C4—2142no—
306C22⋊C4—2142no—
307C22⋊C4—2142no—
308C22⋊C4—2142no—
309C42—2142no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—1072no—
315C23—2141no—
316C23—2141no—
317C23—2141no—
318C23—2141no—
319C23—2141no—
320C23—2141no—
321C23D4×D10712yes—
322C23Q8×D10712yes—
323C23#1313381812yes—
324C23C23×D10711yescharacteristic
325Q8—4284no—
326D4—2148no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—1072no—
347C2×C4—1072no—
348C2×C4—1072no—
349C2×C4—4284no—
350C2×C4—2141no—
351C2×C4—2141no—
352C2×C4—2141no—
353C2×C4—2141no—
354C2×C4—2141no—
355C2×C4—2141no—
356C2×C4—2141no—
357C2×C4—2141no—
358C2×C4—2141no—
359C2×C4—2141no—
360C2×C4—2141no—
361C2×C4—2141no—
362C2×C4—2141no—
363C2×C4—2141no—
364C2×C4—2141no—
365C2×C4—2141no—
366C2×C4—2141no—
367C2×C4—2141no—
368C2×C4#1313381812yes—
369C2×C4#1313381812yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—4281no—
377C22—4281no—
378C22—4281no—
379C22—4281no—
380C22—2142no—
381C22—2142no—
382C22—2142no—
383C22#1681208714yes—
384C22C2×D4×D10711yescharacteristic
385C22C2×Q8×D10711yescharacteristic
386C22C2×#1313381811yescharacteristic
387C22C2×#1313381811yescharacteristic
388C22C2×#1313381811yescharacteristic
389C22#1681215411yescharacteristic
390C22#1681215411yescharacteristic
391C4—22no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—4281no—
398C4—4281no—
399C4—4281no—
400C4—4281no—
401C4—2142no—
402C4—2142no—
403C4—2142no—
404C2—24no—
405C2—4282no—
406C2C2×#1681208711yescharacteristic
407C2#2029316111yescharacteristic
408C2#2029321511yescharacteristic
409C2#2029326711yescharacteristic
410C2#2029326711yescharacteristic
411C2#2029333211yescharacteristic
412C2#2029333211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
FittingC2×#95×C107C2
prime radicalC22×C22⋊D107C22
hypercenterC2×#95D107
hypocenterC107#2450
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. C2×#16812088C2semidirect
3. #20292568C2semidirect
4. #20292561C2semidirect
5. #20292551C2semidirect
6. #20292540C2semidirect
7. #20292531C2semidirect
8. #20292509C2semidirect
11. #20292501C2semidirect
12. #20292500C2semidirect
13. #20292500C2semidirect
14. #20292486C2semidirect
15. C2×#95×C107C2semidirect
59. C2×C22⋊D107Q8semidirect
207. C107#2450semidirect
222. C2×#95D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120882
C2×C4×C22⋊D1072
#202925682
#202925612
#202925512
#202925402
#202925312
#202925092
#202925062
#202925012
#202925002
#202924862
C2×#95×C1072
#2450107