Finite Group Databasebeta

← #28340332

Subgroups — #28340332

Order 13696.

548 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16812099C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D107C211yesmaximal, characteristic
3#20292563C211yesmaximal, characteristic, complemented
4#20292562C211yesmaximal, characteristic, complemented
5#20292550C211yesmaximal, characteristic, complemented
6#20292549C211yesmaximal, characteristic, complemented
7#20292527C211yesmaximal, characteristic
8#20292527C211yesmaximal, characteristic
9#20292524C211yesmaximal, characteristic, complemented
10#20292522C211yesmaximal, characteristic, complemented
11#20292501C211yesmaximal, characteristic, complemented
12#20292500C211yesmaximal, characteristic, complemented
13#20292486C211yesmaximal, characteristic, complemented
14#20292478C211yesmaximal, characteristic, complemented
15#380×C107C211yesmaximal, characteristic, complemented
16C22×C22⋊D107C2211yescharacteristic
17C22×C4×D107C2211yescharacteristic
18#16812099—24no—
19C4×C22⋊D107—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×Dic107⋊C4C2211yescharacteristic
31C2×C22⋊Dic107C2211yescharacteristic
32C2×C22⋊Dic107C2211yescharacteristic
33C2×C22⋊Dic107C2211yescharacteristic
34C2×(C2×D107)⋊C4C2211yescharacteristic
35C2×(C2×D107)⋊C4C2211yescharacteristic
36C2×(C2×D107)⋊C4C2211yescharacteristic
37C2×(C2×D107)⋊C4C2211yescharacteristic
38C2×(C2×D107)⋊C4C2211yescharacteristic
39C2×C4×Dic107C2211yescharacteristic
40C2×C4×Dic107C2211yescharacteristic
41C2×C4×Dic107C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C107⋊#95C2211yescharacteristic
45C107⋊#95C2211yescharacteristic
46C23×C4×C107C2211yescharacteristic
47C2×C4⋊C4×C107C2211yescharacteristic
48C2×C4⋊C4×C107C2211yescharacteristic
49C2×C22⋊C4×C107C2211yescharacteristic
50C2×C22⋊C4×C107C2211yescharacteristic
51#95×C107C2211yescharacteristic
52#95×C107C2211yescharacteristic
53C23×D107C2311yescharacteristic
54C2×C22⋊D107—22no—
55C2×C22⋊D107—22no—
56C2×C22⋊D107Q814yes—
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—41no—
67C4⋊Dic107—22no—
68C4⋊Dic107—41no—
69Dic107⋊C4—22no—
70Dic107⋊C4—22no—
71Dic107⋊C4—22no—
72Dic107⋊C4—22no—
73Dic107⋊C4—22no—
74Dic107⋊C4—22no—
75Dic107⋊C4—41no—
76Dic107⋊C4—41no—
77Dic107⋊C4D414yes—
78C22⋊Dic107—22no—
79C22⋊Dic107—22no—
80C22⋊Dic107—41no—
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—
87C4×Dic107—22no—
88C4×Dic107—22no—
89C24×C107C2311yescharacteristic
90C22×C4×C107—22no—
91C22×C4×C107—22no—
92C22×C4×C107—41no—
93C22×C4×C107C2311yescharacteristic
94C22×C4×C107C2311yescharacteristic
95C22×C4×C107C2311yescharacteristic
96C22×C4×C107C2311yescharacteristic
97C22×C4×C107C2311yescharacteristic
98C22×C4×C107C2311yescharacteristic
99C4⋊C4×C107—22no—
100C4⋊C4×C107—41no—
101C22⋊C4×C107—41no—
102C22⋊C4×C107—41no—
103C23×C107—21no—
104C23×C107—21no—
105C23×C107—21no—
106C23×C107—21no—
107C23×C107—21no—
108C23×C107—21no—
109C23×C107C2×Q812yes—
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×C107C2×D412yes—
136C2×C4×C107#4112yes—
137C22⋊D107—28no—
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×Dic107—21no—
151C2×Dic107—21no—
152C2×Dic107—21no—
153C2×Dic107—21no—
154C2×Dic107C2×D412yes—
155C2×Dic107C2×D412yes—
156C2×Dic107C2×Q812yes—
157C2×Dic107#4112yes—
158C2×Dic107#4112yes—
159C4×D107—44no—
160C22×C107—22no—
161C22×C107—22no—
162C22×C107—22no—
163C22×C107—41no—
164C22×C107—41no—
165C22×C107—41no—
166C22×C107—41no—
167C22×C107C22×D411yescharacteristic
168C22×C107C22×Q811yescharacteristic
169C22×C107C2×#4111yescharacteristic
170C22×C107C2×#4111yescharacteristic
171C22×C107C2×#4111yescharacteristic
172C22×C107H(5,𝔽2)11yescharacteristic
173C22×C107H(5,𝔽2)11yescharacteristic
174C2×D107—22no—
175C2×D107—22no—
176C2×D107—22no—
177C2×D107—41no—
178C2×D107—41no—
179C2×D107—41no—
180C2×D107—41no—
181C4×C107—22no—
182C4×C107—22no—
183C4×C107—41no—
184C4×C107—41no—
185C4×C107—41no—
186C4×C107—41no—
187Dic107—22no—
188Dic107—22no—
189Dic107—41no—
190Dic107—41no—
191Dic107—41no—
192Dic107—41no—
193Dic107C22⋊Q814yes—
194C2×C107—42no—
195C2×C107C2×C22⋊Q811yescharacteristic
196C2×C107#52911yescharacteristic
197C2×C107#54011yescharacteristic
198C2×C107#54611yescharacteristic
199C2×C107#55011yescharacteristic
200C2×C107#55411yescharacteristic
201C2×C107#55411yescharacteristic
202D107—42no—
203#2454—1071nomaximal, Sylow
204C107#245411yescharacteristic, complemented, Sylow
205C2×#125—1071no—
206C2×C4×D4—1071no—
207#399—1071no—
208#399—1071no—
209#396—1071no—
210#396—1071no—
211#390—1071no—
212#390—1071no—
213#389—1071no—
214#389—1071no—
215#385—1071no—
216#385—1071no—
217#380—1071no—
218#380D10711yescharacteristic, complemented
219C4×C4⋊C4—1071no—
220C22×D4—1071no—
221C23×C4—1071no—
222C23×C4C2×D10711yescharacteristic
223#125—2144no—
224C4×D4—2144no—
225C2×C4⋊C4—1071no—
226C2×C4⋊C4—1071no—
227C2×C4⋊C4—1071no—
228C2×C4⋊C4—1071no—
229C2×C4⋊C4—1071no—
230C2×C4⋊C4—1071no—
231C2×C4⋊C4—1071no—
232C2×C4⋊C4—1071no—
233C2×C4⋊C4—1071no—
234C2×C4⋊C4—1071no—
235C2×C4⋊C4—1071no—
236C2×C4⋊C4C2×D10711yescharacteristic
237C2×C4⋊C4C2×D10711yescharacteristic
238C2×C22⋊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⋊C4C2×D10711yescharacteristic
247C2×C22⋊C4C2×D10711yescharacteristic
248C2×C42—1071no—
249C2×C42—1071no—
250C2×C42—1071no—
251#95—1071no—
252#95—1071no—
253#95—1071no—
254#95—1071no—
255#95C2×D10711yescharacteristic
256#95C2×D10711yescharacteristic
257C24—1071no—
258C24C22×D10711yescharacteristic
259C2×D4—1074no—
260C2×D4—2142no—
261C2×D4—2142no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—41no—
265C22×C4—1071no—
266C22×C4—1071no—
267C22×C4—1071no—
268C22×C4—1071no—
269C22×C4—1071no—
270C22×C4—1071no—
271C22×C4—1071no—
272C22×C4—4281no—
273C22×C4—2142no—
274C22×C4—2142no—
275C22×C4C22×D10711yescharacteristic
276C22×C4C22×D10711yescharacteristic
277C22×C4C22×D10711yescharacteristic
278C22×C4C22×D10711yescharacteristic
279C22×C4C22×D10711yescharacteristic
280C22×C4C22×D10711yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—41no—
283C4⋊C4—1074no—
284C4⋊C4—4281no—
285C4⋊C4—4281no—
286C4⋊C4—4281no—
287C4⋊C4—2142no—
288C4⋊C4—2142no—
289C4⋊C4—2142no—
290C4⋊C4—2142no—
291C4⋊C4—2142no—
292C4⋊C4—2142no—
293C4⋊C4—2142no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—4281no—
297C22⋊C4—4281no—
298C22⋊C4—4281no—
299C22⋊C4—4281no—
300C22⋊C4—2142no—
301C22⋊C4—2142no—
302C22⋊C4—2142no—
303C22⋊C4—2142no—
304C42—2142no—
305C42—2142no—
306C42—2142no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—1072no—
314C23—2141no—
315C23—2141no—
316C23—2141no—
317C23—2141no—
318C23—2141no—
319C23—2141no—
320C23Q8×D10712yes—
321C23C23×D10711yescharacteristic
322D4—2148no—
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—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—44no—
340C2×C4—1072no—
341C2×C4—1072no—
342C2×C4—1072no—
343C2×C4—1072no—
344C2×C4—1072no—
345C2×C4—4284no—
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×C4—2141no—
356C2×C4—2141no—
357C2×C4—2141no—
358C2×C4—2141no—
359C2×C4—2141no—
360C2×C4—2141no—
361C2×C4—2141no—
362C2×C4D4×D10712yes—
363C2×C4#1313381812yes—
364C22—22no—
365C22—22no—
366C22—22no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—4281no—
372C22—4281no—
373C22—4281no—
374C22—4281no—
375C22—2142no—
376C22—2142no—
377C22—2142no—
378C22C2×D4×D10711yescharacteristic
379C22C2×Q8×D10711yescharacteristic
380C22#41×D10711yescharacteristic
381C22#41×D10711yescharacteristic
382C22C2×#1313381811yescharacteristic
383C22#1681215411yescharacteristic
384C22#1681215411yescharacteristic
385C4—22no—
386C4—22no—
387C4—41no—
388C4—41no—
389C4—41no—
390C4—41no—
391C4—1074no—
392C4—4281no—
393C4—4281no—
394C4—4281no—
395C4—4281no—
396C4—2142no—
397C4—2142no—
398C2—42no—
399C2—4282no—
400C2C22⋊Q8×D10711yescharacteristic
401C2#2029315511yescharacteristic
402C2#2029322711yescharacteristic
403C2#2029326711yescharacteristic
404C2#2029329511yescharacteristic
405C2#2029333111yescharacteristic
406C2#2029333211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#380×C107C2
prime radicalC22×C22⋊D107C22
hypercenter#380D107
hypocenterC107#2454
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#16812099C2semidirect
3. #20292563C2semidirect
4. #20292562C2semidirect
5. #20292550C2semidirect
6. #20292549C2semidirect
9. #20292524C2semidirect
10. #20292522C2semidirect
11. #20292501C2semidirect
12. #20292500C2semidirect
13. #20292486C2semidirect
14. #20292478C2semidirect
15. #380×C107C2semidirect
204. C107#2454semidirect
218. #380D107semidirect

Maximal subgroups

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

subgroupindex
C2×#168120992
C2×C4×C22⋊D1072
#202925632
#202925622
#202925502
#202925492
#202925272
#202925242
#202925222
#202925012
#202925002
#202924862
#202924782
#380×C1072
#2454107