Finite Group Databasebeta

← #28344593

Subgroups — #28344593

Order 13696.

450 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20292563C211yesmaximal, characteristic, complemented
2#20292561C211yesmaximal, characteristic, complemented
3#20292555C211yesmaximal, characteristic, complemented
4#20292555C211yesmaximal, characteristic, complemented
5#20292550C211yesmaximal, characteristic, complemented
6#20292550C211yesmaximal, characteristic, complemented
7#20292541C211yesmaximal, characteristic, complemented
8#20292541C211yesmaximal, characteristic, complemented
9#20292541C211yesmaximal, characteristic, complemented
10#20292541C211yesmaximal, characteristic, complemented
11#20292541C211yesmaximal, characteristic, complemented
12#20292530C211yesmaximal, characteristic, complemented
13#20292520C211yesmaximal, characteristic, complemented
14#20292509C211yesmaximal, characteristic, complemented
15#392×C107C211yesmaximal, characteristic
16C2×C4⋊Dic107C2211yescharacteristic
17C2×C4⋊Dic107C2211yescharacteristic
18C2×Dic107⋊C4C2211yescharacteristic
19C2×Dic107⋊C4C2211yescharacteristic
20C2×Dic107⋊C4C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×C22⋊Dic107C2211yescharacteristic
25C2×C22⋊Dic107C2211yescharacteristic
26C2×C22⋊Dic107C2211yescharacteristic
27C2×C22⋊Dic107C2211yescharacteristic
28C2×C22⋊Dic107C2211yescharacteristic
29C2×C22⋊Dic107C2211yescharacteristic
30C2×C22⋊Dic107C2211yescharacteristic
31C2×C22⋊Dic107C2211yescharacteristic
32C2×C22⋊Dic107C2211yescharacteristic
33C2×C22⋊Dic107C2211yescharacteristic
34C2×C22⋊Dic107C2211yescharacteristic
35C2×C22⋊Dic107C2211yescharacteristic
36C2×C4×Dic107C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C22×D4×C107C2211yescharacteristic
45C22×D4×C107C2211yescharacteristic
46C22×D4×C107C2211yescharacteristic
47C2×C22⋊C4×C107C2211yescharacteristic
48C2×C22⋊C4×C107C2211yescharacteristic
49C2×C22⋊C4×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51C22×Dic107C2311yescharacteristic
52C22×Dic107C2311yescharacteristic
53C22×Dic107C2311yescharacteristic
54C22×Dic107C2311yescharacteristic
55C22×Dic107C2311yescharacteristic
56C22×Dic107C2311yescharacteristic
57C22×Dic107C2311yescharacteristic
58C22×Dic107C2311yescharacteristic
59C4⋊Dic107—41no—
60C4⋊Dic107—41no—
61Dic107⋊C4—22no—
62Dic107⋊C4—41no—
63Dic107⋊C4—41no—
64Dic107⋊C4—41no—
65Dic107⋊C4—41no—
66Dic107⋊C4—41no—
67C22⋊Dic107—41no—
68C22⋊Dic107—41no—
69C22⋊Dic107—41no—
70C22⋊Dic107—41no—
71C22⋊Dic107—41no—
72C22⋊Dic107—41no—
73C22⋊Dic107—41no—
74C22⋊Dic107—41no—
75C22⋊Dic107—41no—
76C22⋊Dic107—41no—
77C22⋊Dic107—41no—
78C22⋊Dic107—41no—
79C4×Dic107—41no—
80C24×C107C2311yescharacteristic
81C24×C107C2311yescharacteristic
82C24×C107C2311yescharacteristic
83C2×D4×C107—22no—
84C2×D4×C107—41no—
85C2×D4×C107—41no—
86C2×D4×C107—41no—
87C2×D4×C107—41no—
88C2×D4×C107—41no—
89C2×D4×C107—41no—
90C2×D4×C107—41no—
91C2×D4×C107—41no—
92C22×C4×C107C2311yescharacteristic
93C22×C4×C107C2311yescharacteristic
94C22×C4×C107C2311yescharacteristic
95C22×C4×C107C2311yescharacteristic
96C22⋊C4×C107—22no—
97C22⋊C4×C107—41no—
98C22⋊C4×C107—41no—
99C23×C107—21no—
100C23×C107—21no—
101C23×C107—21no—
102C23×C107—21no—
103C23×C107—21no—
104C23×C107—21no—
105C23×C107—21no—
106C23×C107—21no—
107C23×C107—21no—
108C23×C107—21no—
109C23×C107—21no—
110C23×C107—21no—
111C23×C107—21no—
112C23×C107—21no—
113C23×C107—21no—
114C23×C107—21no—
115C23×C107—21no—
116C23×C107—21no—
117C23×C107—21no—
118C23×C107—21no—
119C23×C107—21no—
120C23×C107C2411yescharacteristic
121D4×C107—44no—
122D4×C107—44no—
123D4×C107—44no—
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—21no—
135C2×C4×C107#4112yes—
136C2×Dic107—21no—
137C2×Dic107—21no—
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×Dic107—21no—
155C2×Dic107—21no—
156C2×Dic107—21no—
157C2×Dic107—21no—
158C2×Dic107—21no—
159C2×Dic107—21no—
160C22×C107—41no—
161C22×C107—41no—
162C22×C107—41no—
163C22×C107—41no—
164C22×C107—41no—
165C22×C107—41no—
166C22×C107—41no—
167C22×C107—41no—
168C22×C107—41no—
169C22×C107—41no—
170C22×C107—41no—
171C22×C107—41no—
172C22×C107—41no—
173C22×C107—41no—
174C22×C107—41no—
175C22×C107—41no—
176C22×C107—41no—
177C22×C107—41no—
178C22×C107—41no—
179C22×C107—41no—
180C22×C107—41no—
181C22×C107C2×#4111yescharacteristic
182C22×C107H(5,𝔽2)11yescharacteristic
183C22×C107H(5,𝔽2)11yescharacteristic
184C22×C107H(5,𝔽2)11yescharacteristic
185C22×C107H(5,𝔽2)11yescharacteristic
186C22×C107H(5,𝔽2)11yescharacteristic
187C22×C1072−1+411yescharacteristic
188C4×C107—22no—
189C4×C107—41no—
190C4×C107—41no—
191C4×C107—41no—
192Dic107—41no—
193Dic107—41no—
194Dic107—41no—
195Dic107—41no—
196Dic107—41no—
197Dic107—41no—
198Dic107—41no—
199Dic107—41no—
200C2×C107—81no—
201C2×C107—81no—
202C2×C107—81no—
203C2×C107#53811yescharacteristic
204C2×C107#54011yescharacteristic
205C2×C107#54211yescharacteristic
206C2×C107#56011yescharacteristic
207C2×C107#56011yescharacteristic
208C2×C107#56211yescharacteristic
209C2×C107#56211yescharacteristic
210#2829—1071nomaximal, Sylow
211C107#282911yescharacteristic, complemented, Sylow
212#399—1071no—
213#398—1071no—
214#397—1071no—
215#397—1071no—
216#396—1071no—
217#396—1071no—
218#394—1071no—
219#394—1071no—
220#394—1071no—
221#394—1071no—
222#394—1071no—
223#392D10711yescharacteristic
224#390—1071no—
225#388—1071no—
226#387—1071no—
227C22×D4C2×D10711yescharacteristic
228C22×D4C2×D10711yescharacteristic
229C22×D4C2×D10711yescharacteristic
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⋊C4—1071no—
237C2×C4⋊C4—1071no—
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⋊C4—1071no—
247C2×C22⋊C4—1071no—
248C2×C22⋊C4—1071no—
249C2×C22⋊C4—1071no—
250C2×C22⋊C4C2×D10711yescharacteristic
251C2×C22⋊C4C2×D10711yescharacteristic
252C2×C22⋊C4C2×D10711yescharacteristic
253C2×C42—1071no—
254#95—1071no—
255#95—1071no—
256#95—1071no—
257#95—1071no—
258#95—1071no—
259#95—1071no—
260#95—1071no—
261#95C2×D10711yescharacteristic
262C24C22×D10711yescharacteristic
263C24C22×D10711yescharacteristic
264C24C22×D10711yescharacteristic
265C2×D4—22no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C22×C4—1071no—
275C22×C4—1071no—
276C22×C4—1071no—
277C22×C4—1071no—
278C22×C4—1071no—
279C22×C4—1071no—
280C22×C4—1071no—
281C22×C4—1071no—
282C22×C4C22×D10711yescharacteristic
283C22×C4C22×D10711yescharacteristic
284C22×C4C22×D10711yescharacteristic
285C22×C4C22×D10711yescharacteristic
286C4⋊C4—4281no—
287C4⋊C4—4281no—
288C4⋊C4—4281no—
289C4⋊C4—4281no—
290C4⋊C4—4281no—
291C4⋊C4—4281no—
292C4⋊C4—4281no—
293C4⋊C4—2142no—
294C22⋊C4—22no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—4281no—
298C22⋊C4—4281no—
299C22⋊C4—4281no—
300C22⋊C4—4281no—
301C22⋊C4—4281no—
302C22⋊C4—4281no—
303C22⋊C4—4281no—
304C22⋊C4—4281no—
305C22⋊C4—4281no—
306C22⋊C4—4281no—
307C22⋊C4—4281no—
308C22⋊C4—4281no—
309C42—4281no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23C23×D10711yescharacteristic
332D4—44no—
333D4—44no—
334D4—44no—
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—21no—
344C2×C4—21no—
345C2×C4—21no—
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×C4—2141no—
363C2×C4—2141no—
364C2×C4—2141no—
365C2×C4—2141no—
366C2×C4—2141no—
367C2×C4—2141no—
368C2×C4—2141no—
369C2×C4—2141no—
370C2×C4#1313381712yes—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22C2×#1313381711yescharacteristic
393C22#1681215411yescharacteristic
394C22#1681215411yescharacteristic
395C22#1681215411yescharacteristic
396C22#1681215411yescharacteristic
397C22#1681215411yescharacteristic
398C22#1681215611yescharacteristic
399C4—22no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—4281no—
404C4—4281no—
405C4—4281no—
406C4—4281no—
407C4—4281no—
408C4—4281no—
409C4—4281no—
410C4—4281no—
411C2—81no—
412C2—81no—
413C2—81no—
414C2#2029321211yescharacteristic
415C2#2029323111yescharacteristic
416C2#2029324411yescharacteristic
417C2#2029336611yescharacteristic
418C2#2029336611yescharacteristic
419C2#2029337211yescharacteristic
420C2#2029337211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting, prime radical#392×C107C2
hypercenter#392D107
hypocenterC107#2829
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #20292563C2semidirect
2. #20292561C2semidirect
3. #20292555C2semidirect
4. #20292555C2semidirect
5. #20292550C2semidirect
6. #20292550C2semidirect
7. #20292541C2semidirect
8. #20292541C2semidirect
9. #20292541C2semidirect
10. #20292541C2semidirect
11. #20292541C2semidirect
12. #20292530C2semidirect
13. #20292520C2semidirect
14. #20292509C2semidirect
211. C107#2829semidirect

Maximal subgroups

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

subgroupindex
#202925632
#202925612
#202925552
#202925502
#202925412
#202925302
#202925202
#202925092
#392×C1072
#2829107