Finite Group Databasebeta

← #28344596

Subgroups — #28344596

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#20292560C211yesmaximal, characteristic, complemented
3#20292555C211yesmaximal, characteristic, complemented
4#20292553C211yesmaximal, characteristic, complemented
5#20292551C211yesmaximal, characteristic, complemented
6#20292550C211yesmaximal, characteristic, complemented
7#20292543C211yesmaximal, characteristic, complemented
8#20292543C211yesmaximal, characteristic, complemented
9#20292542C211yesmaximal, characteristic, complemented
10#20292541C211yesmaximal, characteristic, complemented
11#20292535C211yesmaximal, characteristic
12#20292527C211yesmaximal, characteristic, complemented
13#20292521C211yesmaximal, characteristic, complemented
14#20292512C211yesmaximal, characteristic, complemented
15#394×C107C211yesmaximal, characteristic, complemented
16C22×C22⋊D107C2211yescharacteristic
17C22×C22⋊D107C2211yescharacteristic
18C2×C4⋊Dic107C2211yescharacteristic
19C2×C4⋊Dic107C2211yescharacteristic
20C2×Dic107⋊C4C2211yescharacteristic
21C2×Dic107⋊C4C2211yescharacteristic
22C2×Dic107⋊C4C2211yescharacteristic
23C2×Dic107⋊C4C2211yescharacteristic
24C2×Dic107⋊C4C2211yescharacteristic
25C2×C22⋊Dic107C2211yescharacteristic
26C2×C22⋊Dic107C2211yescharacteristic
27C2×C22⋊Dic107C2211yescharacteristic
28C2×C22⋊Dic107C2211yescharacteristic
29C2×C22⋊Dic107C2211yescharacteristic
30C2×C22⋊Dic107C2211yescharacteristic
31C2×(C2×D107)⋊C4C2211yescharacteristic
32C2×(C2×D107)⋊C4C2211yescharacteristic
33C2×(C2×D107)⋊C4C2211yescharacteristic
34C2×(C2×D107)⋊C4C2211yescharacteristic
35C2×(C2×D107)⋊C4C2211yescharacteristic
36C2×C4×Dic107C2211yescharacteristic
37C107⋊#95C2211yescharacteristic
38C107⋊#95C2211yescharacteristic
39C107⋊#95C2211yescharacteristic
40C107⋊#95C2211yescharacteristic
41C107⋊#95C2211yescharacteristic
42C107⋊#95C2211yescharacteristic
43C107⋊#95C2211yescharacteristic
44C22×D4×C107C2211yescharacteristic
45C2×C4⋊C4×C107C2211yescharacteristic
46C2×C22⋊C4×C107C2211yescharacteristic
47C2×C22⋊C4×C107C2211yescharacteristic
48C2×C22⋊C4×C107C2211yescharacteristic
49C2×C22⋊C4×C107C2211yescharacteristic
50#95×C107C2211yescharacteristic
51C23×D107C2311yescharacteristic
52C2×C22⋊D107—22no—
53C2×C22⋊D107—41no—
54C2×C22⋊D107—41no—
55C2×C22⋊D107—41no—
56C2×C22⋊D107—41no—
57C2×C22⋊D107—41no—
58C22×Dic107C2311yescharacteristic
59C22×Dic107C2311yescharacteristic
60C22×Dic107C2311yescharacteristic
61C22×Dic107C2311yescharacteristic
62C22×Dic107C2311yescharacteristic
63C22×Dic107C2311yescharacteristic
64C22×Dic107C2311yescharacteristic
65C4⋊Dic107—22no—
66C4⋊Dic107—41no—
67Dic107⋊C4—41no—
68Dic107⋊C4—41no—
69Dic107⋊C4—41no—
70Dic107⋊C4—41no—
71Dic107⋊C4—41no—
72C22⋊Dic107—22no—
73C22⋊Dic107—41no—
74C22⋊Dic107—41no—
75C22⋊Dic107—41no—
76C22⋊Dic107—41no—
77C22⋊Dic107—41no—
78(C2×D107)⋊C4—41no—
79(C2×D107)⋊C4—41no—
80(C2×D107)⋊C4—41no—
81(C2×D107)⋊C4—41no—
82(C2×D107)⋊C4—41no—
83C4×Dic107—41no—
84C24×C107C2311yescharacteristic
85C24×C107C2311yescharacteristic
86C2×D4×C107—41no—
87C2×D4×C107—41no—
88C2×D4×C107—41no—
89C22×C4×C107C2311yescharacteristic
90C22×C4×C107C2311yescharacteristic
91C22×C4×C107C2311yescharacteristic
92C22×C4×C107C2311yescharacteristic
93C22×C4×C107C2311yescharacteristic
94C4⋊C4×C107—41no—
95C22⋊C4×C107—41no—
96C22⋊C4×C107—41no—
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×C107C2411yescharacteristic
114C22×D107—21no—
115C22×D107—21no—
116C22×D107—21no—
117C22×D107—21no—
118C22×D107—21no—
119C22×D107—21no—
120C22×D107—21no—
121D4×C107—44no—
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—21no—
135C2×C4×C107—21no—
136C2×C4×C107—21no—
137C22⋊D107—44no—
138C22⋊D107—44no—
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#4112yes—
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×C107C2×#4111yescharacteristic
175C22×C107H(5,𝔽2)11yescharacteristic
176C22×C107H(5,𝔽2)11yescharacteristic
177C22×C107H(5,𝔽2)11yescharacteristic
178C22×C107H(5,𝔽2)11yescharacteristic
179C22×C107H(5,𝔽2)11yescharacteristic
180C22×C1072−1+411yescharacteristic
181C2×D107—41no—
182C2×D107—41no—
183C2×D107—41no—
184C2×D107—41no—
185C2×D107—41no—
186C2×D107—41no—
187C2×D107—41no—
188C4×C107—41no—
189C4×C107—41no—
190C4×C107—41no—
191C4×C107—41no—
192C4×C107—41no—
193Dic107—22no—
194Dic107—41no—
195Dic107—41no—
196Dic107—41no—
197Dic107—41no—
198Dic107—41no—
199Dic107—41no—
200C2×C107—81no—
201C2×C107—81no—
202C2×C107#53811yescharacteristic
203C2×C107#54011yescharacteristic
204C2×C107#54211yescharacteristic
205C2×C107#56011yescharacteristic
206C2×C107#56011yescharacteristic
207C2×C107#56211yescharacteristic
208C2×C107#56211yescharacteristic
209D107—81no—
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#394D10711yescharacteristic, complemented
223#392—1071no—
224#390—1071no—
225#388—1071no—
226#387—1071no—
227C22×D4—1071no—
228C22×D4—1071no—
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⋊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⋊C4—1071no—
247C2×C22⋊C4—1071no—
248C2×C22⋊C4—1071no—
249C2×C22⋊C4C2×D10711yescharacteristic
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
262C24—1071no—
263C24C22×D10711yescharacteristic
264C24C22×D10711yescharacteristic
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—4281no—
269C2×D4—4281no—
270C2×D4—4281no—
271C2×D4—4281no—
272C2×D4—4281no—
273C2×D4—2142no—
274C22×C4—1071no—
275C22×C4—1071no—
276C22×C4—1071no—
277C22×C4—1071no—
278C22×C4—1071no—
279C22×C4—1071no—
280C22×C4—1071no—
281C22×C4C22×D10711yescharacteristic
282C22×C4C22×D10711yescharacteristic
283C22×C4C22×D10711yescharacteristic
284C22×C4C22×D10711yescharacteristic
285C22×C4C22×D10711yescharacteristic
286C4⋊C4—41no—
287C4⋊C4—4281no—
288C4⋊C4—4281no—
289C4⋊C4—4281no—
290C4⋊C4—4281no—
291C4⋊C4—4281no—
292C4⋊C4—4281no—
293C4⋊C4—2142no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C22⋊C4—41no—
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—2142no—
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—2141no—
325C23—2141no—
326C23—2141no—
327C23—2141no—
328C23—2141no—
329C23—2141no—
330C23—2141no—
331C23C23×D10711yescharacteristic
332D4—44no—
333D4—4284no—
334D4—4284no—
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—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—1072no—
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—2141no—
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—4281no—
386C22—4281no—
387C22—4281no—
388C22—4281no—
389C22—4281no—
390C22—4281no—
391C22—4281no—
392C22#41×D10711yescharacteristic
393C22#1681215411yescharacteristic
394C22#1681215411yescharacteristic
395C22#1681215411yescharacteristic
396C22#1681215411yescharacteristic
397C22#1681215511yescharacteristic
398C22#1681215611yescharacteristic
399C4—41no—
400C4—41no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—4281no—
405C4—4281no—
406C4—4281no—
407C4—4281no—
408C4—4281no—
409C4—4281no—
410C4—2142no—
411C2—81no—
412C2—81no—
413C2—8561no—
414C2#2029321111yescharacteristic
415C2#2029322711yescharacteristic
416C2#2029324511yescharacteristic
417C2#2029336511yescharacteristic
418C2#2029336611yescharacteristic
419C2#2029337211yescharacteristic
420C2#2029337411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D107
commutator, socle, cosocleC23×C107C24
Fitting#394×C107C2
prime radical#20292535C2
hypercenter#394D107
hypocenterC107#2829
LCSG ▷ C23×C107 ▷ C107
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #20292563C2semidirect
2. #20292560C2semidirect
3. #20292555C2semidirect
4. #20292553C2semidirect
5. #20292551C2semidirect
6. #20292550C2semidirect
7. #20292543C2semidirect
8. #20292543C2semidirect
9. #20292542C2semidirect
10. #20292541C2semidirect
12. #20292527C2semidirect
13. #20292521C2semidirect
14. #20292512C2semidirect
15. #394×C107C2semidirect
211. C107#2829semidirect
222. #394D107semidirect

Maximal subgroups

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

subgroupindex
#202925632
#202925602
#202925552
#202925532
#202925512
#202925502
#202925432
#202925422
#202925412
#202925352
#202925272
#202925212
#202925122
#394×C1072
#2829107