Finite Group Databasebeta

← #28371290

Subgroups — #28371290

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#20294965C211yesmaximal, characteristic, complemented
2#20294964C211yesmaximal, characteristic, complemented
3#20294961C211yesmaximal, characteristic
4#20294960C211yesmaximal, characteristic, complemented
5#20294960C211yesmaximal, characteristic, complemented
6#20294956C211yesmaximal, characteristic, complemented
7#20294948C211yesmaximal, characteristic
8#20294948C211yesmaximal, characteristic
9#20294947C211yesmaximal, characteristic, complemented
10#20294946C211yesmaximal, characteristic, complemented
11#20294939C211yesmaximal, characteristic
12#20294888C211yesmaximal, characteristic
13#20294885C211yesmaximal, characteristic
14#20294883C211yesmaximal, characteristic
15#398×C109C211yesmaximal, characteristic, complemented
16C22×Dic218C2211yescharacteristic
17C22×C4×D109C2211yescharacteristic
18C2×C4⋊Dic109C2211yescharacteristic
19C2×C4⋊Dic109C2211yescharacteristic
20C2×C4⋊Dic109C2211yescharacteristic
21C2×#13182008C2211yescharacteristic
22C2×#13182008C2211yescharacteristic
23C2×#13182008C2211yescharacteristic
24C2×#13182008C2211yescharacteristic
25C2×#13182008C2211yescharacteristic
26C2×#13182008C2211yescharacteristic
27C2×#13182006C2211yescharacteristic
28C2×#13182006C2211yescharacteristic
29C2×#13182006C2211yescharacteristic
30C2×#13182006C2211yescharacteristic
31C2×#13182006C2211yescharacteristic
32C2×#13182006C2211yescharacteristic
33#16812606C2211yescharacteristic
34#16812606C2211yescharacteristic
35#16812606C2211yescharacteristic
36#16812606C2211yescharacteristic
37#16812606C2211yescharacteristic
38#16812606C2211yescharacteristic
39#16812606C2211yescharacteristic
40#16812606C2211yescharacteristic
41#16812606C2211yescharacteristic
42#16812606C2211yescharacteristic
43#16812606C2211yescharacteristic
44C2×C4⋊C4×C109C2211yescharacteristic
45C2×C4⋊C4×C109C2211yescharacteristic
46C2×C4⋊C4×C109C2211yescharacteristic
47C2×C4⋊C4×C109C2211yescharacteristic
48#95×C109C2211yescharacteristic
49#95×C109C2211yescharacteristic
50#95×C109C2211yescharacteristic
51C23×D109C2311yescharacteristic
52C2×Dic218—41no—
53C2×Dic218—41no—
54C2×Dic218—41no—
55C22×Dic109C2311yescharacteristic
56C22×Dic109C2311yescharacteristic
57C22×Dic109C2311yescharacteristic
58C22×Dic109C2311yescharacteristic
59C22×Dic109C2311yescharacteristic
60C22×Dic109C2311yescharacteristic
61C22×Dic109C2311yescharacteristic
62C2×C4×D109—41no—
63C2×C4×D109—41no—
64C2×C4×D109Q814yescomplemented
65C4⋊Dic109—41no—
66C4⋊Dic109—41no—
67C4⋊Dic109—41no—
68#13182008—41no—
69#13182008—41no—
70#13182008—41no—
71#13182008—41no—
72#13182008—41no—
73#13182008—41no—
74#13182006—41no—
75#13182006—41no—
76#13182006—41no—
77#13182006—41no—
78#13182006—41no—
79#13182006—41no—
80C22×C4×C109C2311yescharacteristic
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—
89C4⋊C4×C109—41no—
90C4⋊C4×C109—41no—
91C23×C109C2411yescharacteristic
92C22×D109—21no—
93C22×D109—21no—
94C22×D109—21no—
95C22×D109—21no—
96C22×D109—21no—
97C22×D109—21no—
98C22×D109C2×Q812yes—
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—21no—
116C2×C4×C109—21no—
117C2×C4×C109—21no—
118C2×C4×C109—21no—
119C2×C4×C109C2×Q812yes—
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×Dic109C2×Q812yes—
141C4×D109—44no—
142Dic218—44no—
143C22×C109C22×Q811yescharacteristic
144C22×C109H(5,𝔽2)11yescharacteristic
145C22×C109H(5,𝔽2)11yescharacteristic
146C22×C109H(5,𝔽2)11yescharacteristic
147C22×C109H(5,𝔽2)11yescharacteristic
148C22×C1092−1+411yescharacteristic
149C22×C1092−1+411yescharacteristic
150C2×D109—22no—
151C2×D109—22no—
152C2×D109—22no—
153C2×D109—41no—
154C2×D109—41no—
155C2×D109—41no—
156C2×D109—41no—
157C4×C109—22no—
158C4×C109—41no—
159C4×C109—41no—
160C4×C109—41no—
161C4×C109—41no—
162C4×C109—41no—
163C4×C109—41no—
164Dic109—22no—
165Dic109—41no—
166Dic109—41no—
167Dic109—41no—
168Dic109—41no—
169Dic109—41no—
170Dic109—41no—
171C2×C109#54311yescharacteristic
172C2×C109#54411yescharacteristic
173C2×C109#54411yescharacteristic
174C2×C109#56011yescharacteristic
175C2×C109#56211yescharacteristic
176C2×C109#56211yescharacteristic
177C2×C109#56311yescharacteristic
178D109—42no—
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#398D10911yescharacteristic, complemented
188#396—1091no—
189#396—1091no—
190#395—1091no—
191#395—1091no—
192#393—1091no—
193#381—1091no—
194#380—1091no—
195#380—1091no—
196C22×Q8—1091no—
197C23×C4—1091no—
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⋊C4C2×D10911yescharacteristic
208C2×C4⋊C4C2×D10911yescharacteristic
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⋊C4—1091no—
216C2×C22⋊C4—1091no—
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#95C2×D10911yescharacteristic
229#95C2×D10911yescharacteristic
230#95C2×D10911yescharacteristic
231C24—1091no—
232C2×Q8—4361no—
233C2×Q8—4361no—
234C2×Q8—4361no—
235C22×C4—1091no—
236C22×C4—1094no—
237C22×C4—1091no—
238C22×C4—1091no—
239C22×C4—1091no—
240C22×C4—1091no—
241C22×C4—1091no—
242C22×C4—1091no—
243C22×C4—4361no—
244C22×C4—4361no—
245C22×C4C22×D10911yescharacteristic
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—41no—
255C4⋊C4—41no—
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—4361no—
266C22⋊C4—4361no—
267C22⋊C4—4361no—
268C22⋊C4—4361no—
269C22⋊C4—4361no—
270C22⋊C4—4361no—
271C23—1092no—
272C23—2181no—
273C23—2181no—
274C23—2181no—
275C23—2181no—
276C23—2181no—
277C23—2181no—
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—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—1092no—
301C2×C4—4364no—
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×C4—2181no—
322C2×C4Q8×D10912yes—
323C22—4361no—
324C22—4361no—
325C22—4361no—
326C22—4361no—
327C22—2182no—
328C22—2182no—
329C22—2182no—
330C22C2×Q8×D10911yescharacteristic
331C22#1681274411yescharacteristic
332C22#1681274411yescharacteristic
333C22#1681274511yescharacteristic
334C22#1681274511yescharacteristic
335C22#1681274611yescharacteristic
336C22#1681274711yescharacteristic
337C4—22no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—4361no—
345C4—4361no—
346C4—4361no—
347C4—4361no—
348C4—4361no—
349C4—4361no—
350C4—2182no—
351C2—4362no—
352C2#2029565111yescharacteristic
353C2#2029565311yescharacteristic
354C2#2029565611yescharacteristic
355C2#2029576611yescharacteristic
356C2#2029577111yescharacteristic
357C2#2029577211yescharacteristic
358C2#2029578011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D109
commutator, socle, cosocleC23×C109C24
Fitting#398×C109C2
prime radicalC23×D109C23
hypercenter#398D109
hypocenterC109#2841
LCSG ▷ C23×C109 ▷ C109
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. #20294965C2semidirect
2. #20294964C2semidirect
4. #20294960C2semidirect
5. #20294960C2semidirect
6. #20294956C2semidirect
9. #20294947C2semidirect
10. #20294946C2semidirect
15. #398×C109C2semidirect
64. C2×C4×D109Q8semidirect
180. C109#2841semidirect
187. #398D109semidirect

Maximal subgroups

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

subgroupindex
#202949652
#202949642
#202949612
#202949602
#202949562
#202949482
#202949472
#202949462
#202949392
#202948882
#202948852
#202948832
#398×C1092
#2841109