Finite Group Databasebeta

← #28371287

Subgroups — #28371287

Order 13952.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20294968C211yesmaximal, characteristic, complemented
2#20294965C211yesmaximal, characteristic, complemented
3#20294962C211yesmaximal, characteristic
4#20294960C211yesmaximal, characteristic, complemented
5#20294959C211yesmaximal, characteristic, complemented
6#20294959C211yesmaximal, characteristic, complemented
7#20294958C211yesmaximal, characteristic, complemented
8#20294949C211yesmaximal, characteristic
9#20294949C211yesmaximal, characteristic
10#20294947C211yesmaximal, characteristic, complemented
11#20294946C211yesmaximal, characteristic, complemented
12#20294938C211yesmaximal, characteristic
13#20294889C211yesmaximal, characteristic
14#20294886C211yesmaximal, characteristic
15#380×C109C211yesmaximal, characteristic
16C22×Dic218C2211yescharacteristic
17C2×C4⋊Dic109C2211yescharacteristic
18C2×C4⋊Dic109C2211yescharacteristic
19C2×C4⋊Dic109C2211yescharacteristic
20C2×C4⋊Dic109C2211yescharacteristic
21C2×C4⋊Dic109C2211yescharacteristic
22C2×#13182008C2211yescharacteristic
23C2×#13182008C2211yescharacteristic
24C2×#13182008C2211yescharacteristic
25C2×#13182008C2211yescharacteristic
26C2×#13182008C2211yescharacteristic
27C2×#13182008C2211yescharacteristic
28C2×C22⋊Dic109C2211yescharacteristic
29C2×C22⋊Dic109C2211yescharacteristic
30C2×C22⋊Dic109C2211yescharacteristic
31C2×C22⋊Dic109C2211yescharacteristic
32#16812606C2211yescharacteristic
33#16812606C2211yescharacteristic
34#16812606C2211yescharacteristic
35#16812606C2211yescharacteristic
36#16812606C2211yescharacteristic
37#16812606C2211yescharacteristic
38#16812606C2211yescharacteristic
39#16812606C2211yescharacteristic
40#16812606C2211yescharacteristic
41#16812606C2211yescharacteristic
42#16812606C2211yescharacteristic
43#16812606C2211yescharacteristic
44C23×C4×C109C2211yescharacteristic
45C2×C4⋊C4×C109C2211yescharacteristic
46C2×C4⋊C4×C109C2211yescharacteristic
47C2×C22⋊C4×C109C2211yescharacteristic
48C2×C22⋊C4×C109C2211yescharacteristic
49#95×C109C2211yescharacteristic
50#95×C109C2211yescharacteristic
51C2×Dic218—41no—
52C2×Dic218—41no—
53C2×Dic218—41no—
54C22×Dic109C2311yescharacteristic
55C22×Dic109C2311yescharacteristic
56C22×Dic109C2311yescharacteristic
57C22×Dic109C2311yescharacteristic
58C22×Dic109C2311yescharacteristic
59C22×Dic109C2311yescharacteristic
60C22×Dic109C2311yescharacteristic
61C22×Dic109C2311yescharacteristic
62C4⋊Dic109—41no—
63C4⋊Dic109—41no—
64C4⋊Dic109—41no—
65C4⋊Dic109—41no—
66C4⋊Dic109—41no—
67#13182008—41no—
68#13182008—41no—
69#13182008—41no—
70#13182008—41no—
71#13182008—41no—
72#13182008—41no—
73C22⋊Dic109—41no—
74C22⋊Dic109—41no—
75C22⋊Dic109—41no—
76C22⋊Dic109—41no—
77C24×C109C2311yescharacteristic
78C22×C4×C109—41no—
79C22×C4×C109—41no—
80C22×C4×C109Q814yescomplemented
81C22×C4×C109C2311yescharacteristic
82C22×C4×C109C2311yescharacteristic
83C22×C4×C109C2311yescharacteristic
84C22×C4×C109C2311yescharacteristic
85C22×C4×C109C2311yescharacteristic
86C22×C4×C109C2311yescharacteristic
87C4⋊C4×C109—41no—
88C4⋊C4×C109—41no—
89C22⋊C4×C109—41no—
90C22⋊C4×C109—41no—
91C23×C109—21no—
92C23×C109—21no—
93C23×C109—21no—
94C23×C109—21no—
95C23×C109—21no—
96C23×C109—21no—
97C23×C109C2×Q812yes—
98C23×C109C2411yescharacteristic
99C2×C4×C109—21no—
100C2×C4×C109—21no—
101C2×C4×C109—21no—
102C2×C4×C109—21no—
103C2×C4×C109—21no—
104C2×C4×C109—21no—
105C2×C4×C109—21no—
106C2×C4×C109—21no—
107C2×C4×C109—21no—
108C2×C4×C109—21no—
109C2×C4×C109—21no—
110C2×C4×C109—21no—
111C2×C4×C109—21no—
112C2×C4×C109—21no—
113C2×C4×C109—21no—
114C2×C4×C109—21no—
115C2×C4×C109—44no—
116C2×C4×C109C2×Q812yes—
117C2×C4×C109C2×Q812yes—
118C2×Dic109—21no—
119C2×Dic109—21no—
120C2×Dic109—21no—
121C2×Dic109—21no—
122C2×Dic109—21no—
123C2×Dic109—21no—
124C2×Dic109—21no—
125C2×Dic109—21no—
126C2×Dic109—21no—
127C2×Dic109—21no—
128C2×Dic109—21no—
129C2×Dic109—21no—
130C2×Dic109—21no—
131C2×Dic109—21no—
132C2×Dic109—21no—
133C2×Dic109—21no—
134C2×Dic109—21no—
135C2×Dic109—21no—
136C2×Dic109—21no—
137C2×Dic109—21no—
138C2×Dic109—21no—
139C2×Dic109—21no—
140C2×Dic109—21no—
141C2×Dic109—21no—
142Dic218—44no—
143C22×C109—22no—
144C22×C109—22no—
145C22×C109—22no—
146C22×C109—41no—
147C22×C109—41no—
148C22×C109—41no—
149C22×C109—41no—
150C22×C109C22×Q811yescharacteristic
151C22×C109H(5,𝔽2)11yescharacteristic
152C22×C109H(5,𝔽2)11yescharacteristic
153C22×C109H(5,𝔽2)11yescharacteristic
154C22×C109H(5,𝔽2)11yescharacteristic
155C22×C1092−1+411yescharacteristic
156C22×C1092−1+411yescharacteristic
157C4×C109—22no—
158C4×C109—22no—
159C4×C109—41no—
160C4×C109—41no—
161C4×C109—41no—
162C4×C109—41no—
163Dic109—41no—
164Dic109—41no—
165Dic109—41no—
166Dic109—41no—
167Dic109—41no—
168Dic109—41no—
169Dic109—41no—
170Dic109—41no—
171C2×C109—42no—
172C2×C109#54311yescharacteristic
173C2×C109#54411yescharacteristic
174C2×C109#54411yescharacteristic
175C2×C109#56011yescharacteristic
176C2×C109#56211yescharacteristic
177C2×C109#56211yescharacteristic
178C2×C109#56311yescharacteristic
179#2841—1091nomaximal, Sylow
180C109#284111yescharacteristic, complemented, Sylow
181#400—1091no—
182#400—1091no—
183#399—1091no—
184#398—1091no—
185#398—1091no—
186#398—1091no—
187#398—1091no—
188#396—1091no—
189#396—1091no—
190#395—1091no—
191#395—1091no—
192#393—1091no—
193#381—1091no—
194#380—1091no—
195#380D10911yescharacteristic
196C22×Q8—1091no—
197C23×C4C2×D10911yescharacteristic
198C2×C4⋊C4—1091no—
199C2×C4⋊C4—1091no—
200C2×C4⋊C4—1091no—
201C2×C4⋊C4—1091no—
202C2×C4⋊C4—1091no—
203C2×C4⋊C4—1091no—
204C2×C4⋊C4—1091no—
205C2×C4⋊C4—1091no—
206C2×C4⋊C4—1091no—
207C2×C4⋊C4—1091no—
208C2×C4⋊C4—1091no—
209C2×C4⋊C4C2×D10911yescharacteristic
210C2×C4⋊C4C2×D10911yescharacteristic
211C2×C22⋊C4—1091no—
212C2×C22⋊C4—1091no—
213C2×C22⋊C4—1091no—
214C2×C22⋊C4—1091no—
215C2×C22⋊C4C2×D10911yescharacteristic
216C2×C22⋊C4C2×D10911yescharacteristic
217#95—1091no—
218#95—1091no—
219#95—1091no—
220#95—1091no—
221#95—1091no—
222#95—1091no—
223#95—1091no—
224#95—1091no—
225#95—1091no—
226#95—1091no—
227#95—1091no—
228#95—1091no—
229#95C2×D10911yescharacteristic
230#95C2×D10911yescharacteristic
231C24C22×D10911yescharacteristic
232C2×Q8—4361no—
233C2×Q8—4361no—
234C2×Q8—4361no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—1091no—
238C22×C4—1091no—
239C22×C4—1091no—
240C22×C4—1091no—
241C22×C4—1091no—
242C22×C4—1091no—
243C22×C4—1091no—
244C22×C4—1091no—
245C22×C4Dic21814yescomplemented
246C22×C4C22×D10911yescharacteristic
247C22×C4C22×D10911yescharacteristic
248C22×C4C22×D10911yescharacteristic
249C22×C4C22×D10911yescharacteristic
250C22×C4C22×D10911yescharacteristic
251C22×C4C22×D10911yescharacteristic
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—4361no—
255C4⋊C4—4361no—
256C4⋊C4—4361no—
257C4⋊C4—4361no—
258C4⋊C4—4361no—
259C4⋊C4—4361no—
260C4⋊C4—4361no—
261C4⋊C4—4361no—
262C4⋊C4—4361no—
263C4⋊C4—4361no—
264C4⋊C4—4361no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—4361no—
268C22⋊C4—4361no—
269C22⋊C4—4361no—
270C22⋊C4—4361no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23C2×Dic21812yes—
278C23C23×D10911yescharacteristic
279Q8—4364no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—44no—
297C2×C4—2181no—
298C2×C4—2181no—
299C2×C4—2181no—
300C2×C4—2181no—
301C2×C4—2181no—
302C2×C4—2181no—
303C2×C4—2181no—
304C2×C4—2181no—
305C2×C4—2181no—
306C2×C4—2181no—
307C2×C4—2181no—
308C2×C4—2181no—
309C2×C4—2181no—
310C2×C4—2181no—
311C2×C4—2181no—
312C2×C4—2181no—
313C2×C4—2181no—
314C2×C4—2181no—
315C2×C4—2181no—
316C2×C4—2181no—
317C2×C4—2181no—
318C2×C4—2181no—
319C2×C4—2181no—
320C2×C4—2181no—
321C2×C4C2×Dic21812yes—
322C2×C4C2×Dic21812yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×Dic21811yescharacteristic
331C22#1681274411yescharacteristic
332C22#1681274411yescharacteristic
333C22#1681274411yescharacteristic
334C22#1681274511yescharacteristic
335C22#1681274611yescharacteristic
336C22#1681274711yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—4361no—
344C4—4361no—
345C4—4361no—
346C4—4361no—
347C4—4361no—
348C4—4361no—
349C4—4361no—
350C4—4361no—
351C2—42no—
352C2#2029565211yescharacteristic
353C2#2029565411yescharacteristic
354C2#2029565711yescharacteristic
355C2#2029576411yescharacteristic
356C2#2029577111yescharacteristic
357C2#2029577211yescharacteristic
358C2#2029577711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D109
commutator, socle, cosocleC23×C109C24
Fitting#380×C109C2
prime radicalC24×C109C23
hypercenter#380D109
hypocenterC109#2841
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. #20294968C2semidirect
2. #20294965C2semidirect
4. #20294960C2semidirect
5. #20294959C2semidirect
6. #20294959C2semidirect
7. #20294958C2semidirect
10. #20294947C2semidirect
11. #20294946C2semidirect
80. C22×C4×C109Q8semidirect
180. C109#2841semidirect
245. C22×C4Dic218semidirect

Maximal subgroups

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

subgroupindex
#202949682
#202949652
#202949622
#202949602
#202949592
#202949582
#202949492
#202949472
#202949462
#202949382
#202948892
#202948862
#380×C1092
#2841109