Finite Group Databasebeta

← #44510049

Subgroups — #44510049

Order 30848.

484 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
1C2×#21440598C211yesmaximal, characteristic
2#29507611C211yesmaximal, characteristic
3#29507610C211yesmaximal, characteristic
4#29507605C211yesmaximal, characteristic
5#29507604C211yesmaximal, characteristic, complemented
6#29507601C211yesmaximal, characteristic, complemented
7#29507599C211yesmaximal, characteristic, complemented
8#29507598C211yesmaximal, characteristic, complemented
9#29507586C211yesmaximal, characteristic, complemented
10#29507581C211yesmaximal, characteristic, complemented
11#29507575C211yesmaximal, characteristic
12#29507575C211yesmaximal, characteristic
13C4×#16838749C211yesmaximal, characteristic, complemented
14#29507568C211yesmaximal, characteristic, complemented
15#388×C241C211yesmaximal, characteristic
16C23×Dic241C2211yescharacteristic
17#21440598C418yescomplemented
18C2×C4⋊Dic241C2211yescharacteristic
19C2×#16838749C2211yescharacteristic
20C2×#16838749C2211yescharacteristic
21C2×#16838749C2211yescharacteristic
22C2×#16838749C2211yescharacteristic
23C2×#16838749C2211yescharacteristic
24C2×#16838749C2211yescharacteristic
25C2×#16838749C2211yescharacteristic
26C2×#16838749C2211yescharacteristic
27C2×C22⋊Dic241C2211yescharacteristic
28C2×C22⋊Dic241C2211yescharacteristic
29C2×C22⋊Dic241C2211yescharacteristic
30C2×C4×Dic241C2211yescharacteristic
31C2×C4×Dic241C2211yescharacteristic
32C2×C4×Dic241C2211yescharacteristic
33C2×C4×Dic241C2211yescharacteristic
34C2×C4×Dic241C2211yescharacteristic
35#21440549C2211yescharacteristic
36#21440549C2211yescharacteristic
37#21440549C2211yescharacteristic
38#21440549C2211yescharacteristic
39#21440549C2211yescharacteristic
40#21440549C2211yescharacteristic
41#21440549C2211yescharacteristic
42#21440549C2211yescharacteristic
43#21440549C2211yescharacteristic
44#21440549C2211yescharacteristic
45C2×C4⋊C4×C241C2211yescharacteristic
46C2×C22⋊C4×C241C2211yescharacteristic
47C2×C22⋊C4×C241C2211yescharacteristic
48C2×C22⋊C4×C241C2211yescharacteristic
49C2×C42×C241C2211yescharacteristic
50#95×C241C2211yescharacteristic
51#95×C241C2211yescharacteristic
52C22×Dic241—22no—
53C22×Dic241—22no—
54C22×Dic241C2×C414yes—
55C22×Dic241C2311yescharacteristic
56C22×Dic241C2311yescharacteristic
57C22×Dic241C2311yescharacteristic
58C22×Dic241C2311yescharacteristic
59C22×Dic241C2311yescharacteristic
60C22×Dic241C2311yescharacteristic
61C22×Dic241C2311yescharacteristic
62C22×Dic241C2311yescharacteristic
63C4⋊Dic241—41no—
64#16838749—22no—
65#16838749—22no—
66#16838749—22no—
67#16838749—22no—
68#16838749—41no—
69#16838749—41no—
70#16838749C2×C414yes—
71#16838749C2×C414yes—
72C22⋊Dic241—41no—
73C22⋊Dic241—41no—
74C22⋊Dic241C2×C414yes—
75C4×Dic241—41no—
76C4×Dic241—41no—
77C4×Dic241—41no—
78C4×Dic241C2×C414yes—
79C4×Dic241C2×C414yes—
80C24×C241C2311yescharacteristic
81C22×C4×C241C2311yescharacteristic
82C22×C4×C241C2311yescharacteristic
83C22×C4×C241C2311yescharacteristic
84C22×C4×C241C2311yescharacteristic
85C22×C4×C241C2311yescharacteristic
86C22×C4×C241C2311yescharacteristic
87C4⋊C4×C241—41no—
88C22⋊C4×C241—41no—
89C22⋊C4×C241—41no—
90C22⋊C4×C241C2×C414yes—
91C42×C241—41no—
92C2×Dic241—21no—
93C2×Dic241—21no—
94C2×Dic241—21no—
95C2×Dic241—21no—
96C2×Dic241—21no—
97C2×Dic241—21no—
98C2×Dic241—28no—
99C2×Dic241—21no—
100C2×Dic241—21no—
101C2×Dic241—21no—
102C2×Dic241—21no—
103C2×Dic241—21no—
104C2×Dic241—21no—
105C2×Dic241—21no—
106C2×Dic241—21no—
107C2×Dic241—21no—
108C2×Dic241—21no—
109C2×Dic241—21no—
110C2×Dic241—21no—
111C2×Dic241C22×C412yes—
112C2×Dic241C22×C412yes—
113C2×Dic241C22×C412yes—
114C2×Dic241C22×C412yes—
115C2×Dic241#4112yes—
116C2×Dic241#4112yes—
117C23×C241—21no—
118C23×C241—21no—
119C23×C241—21no—
120C23×C241—21no—
121C23×C241—21no—
122C23×C241—21no—
123C23×C241C22×C412yes—
124C23×C241C2411yescharacteristic
125C2×C4×C241—21no—
126C2×C4×C241—21no—
127C2×C4×C241—21no—
128C2×C4×C241—21no—
129C2×C4×C241—21no—
130C2×C4×C241—21no—
131C2×C4×C241—21no—
132C2×C4×C241—21no—
133C2×C4×C241—21no—
134C2×C4×C241—21no—
135C2×C4×C241—21no—
136C2×C4×C241—21no—
137C2×C4×C241—21no—
138C2×C4×C241—21no—
139C2×C4×C241—21no—
140C2×C4×C241—21no—
141C2×C4×C241C22×C412yes—
142C2×C4×C241C22×C412yes—
143C22×C241—22no—
144C22×C241—22no—
145C22×C241—22no—
146C22×C241—41no—
147C22×C241—41no—
148C22×C241—41no—
149C22×C241—41no—
150C22×C241C23×C411yescharacteristic
151C22×C241C2×#4111yescharacteristic
152C22×C241C2×#4111yescharacteristic
153C22×C241H(5,𝔽2)11yescharacteristic
154C22×C241H(5,𝔽2)11yescharacteristic
155C22×C2412−1+411yescharacteristic
156C22×C2412−1+411yescharacteristic
157C4×C241—22no—
158C4×C241—22no—
159C4×C241—41no—
160C4×C241—41no—
161C4×C241—41no—
162C4×C241—41no—
163Dic241—22no—
164Dic241—22no—
165Dic241—22no—
166Dic241—41no—
167Dic241—41no—
168Dic241—41no—
169Dic241—41no—
170Dic241#11714yes—
171C2×C241—42no—
172C2×C241C2×#11711yescharacteristic
173C2×C241#52011yescharacteristic
174C2×C241#52011yescharacteristic
175C2×C241#54011yescharacteristic
176C2×C241#54111yescharacteristic
177C2×C241#54211yescharacteristic
178C2×C241#54211yescharacteristic
179C241#231411yescharacteristic, complemented, Sylow
180#2314—2411nomaximal, Sylow
181C2×#117—2411no—
182#388—2411no—
183#388—2411no—
184#388—2411no—
185#388D24111yescharacteristic
186#387—2411no—
187#387—2411no—
188#387—2411no—
189#387—2411no—
190#384—2411no—
191#382—2411no—
192#380—2411no—
193#380—2411no—
194C4×C4⋊C4—2411no—
195C4×C4⋊C4—2411no—
196C23×C4—2411no—
197#117—2418no—
198C2×C4⋊C4—2411no—
199C2×C4⋊C4—2411no—
200C2×C4⋊C4—2411no—
201C2×C4⋊C4—2411no—
202C2×C4⋊C4—2411no—
203C2×C4⋊C4—2411no—
204C2×C4⋊C4—2411no—
205C2×C4⋊C4—2411no—
206C2×C4⋊C4—2411no—
207C2×C4⋊C4C2×D24111yescharacteristic
208C2×C22⋊C4—2411no—
209C2×C22⋊C4—2411no—
210C2×C22⋊C4—2411no—
211C2×C22⋊C4C2×D24111yescharacteristic
212C2×C22⋊C4C2×D24111yescharacteristic
213C2×C22⋊C4C2×D24111yescharacteristic
214C2×C42—2411no—
215C2×C42—2411no—
216C2×C42—2411no—
217C2×C42—2411no—
218C2×C42—2411no—
219C2×C42C2×D24111yescharacteristic
220#95—2411no—
221#95—2411no—
222#95—2411no—
223#95—2411no—
224#95—2411no—
225#95—2411no—
226#95—2411no—
227#95—2411no—
228#95—2411no—
229#95—2411no—
230#95C2×D24111yescharacteristic
231#95C2×D24111yescharacteristic
232C24C22×D24111yescharacteristic
233C22×C4—4822no—
234C22×C4—4822no—
235C22×C4—2411no—
236C22×C4—2411no—
237C22×C4—2411no—
238C22×C4—2411no—
239C22×C4—2414no—
240C22×C4—2411no—
241C22×C4—2411no—
242C22×C4—2411no—
243C22×C4—2411no—
244C22×C4C22×D24111yescharacteristic
245C22×C4C22×D24111yescharacteristic
246C22×C4C22×D24111yescharacteristic
247C22×C4C22×D24111yescharacteristic
248C22×C4C22×D24111yescharacteristic
249C22×C4C22×D24111yescharacteristic
250C4⋊C4—41no—
251C4⋊C4—9641no—
252C4⋊C4—9641no—
253C4⋊C4—9641no—
254C4⋊C4—4822no—
255C4⋊C4—4822no—
256C4⋊C4—4822no—
257C4⋊C4—4822no—
258C4⋊C4—2414no—
259C4⋊C4—2414no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—9641no—
263C22⋊C4—9641no—
264C22⋊C4—2414no—
265C22⋊C4C4×D24114yes—
266C42—41no—
267C42—9641no—
268C42—9641no—
269C42—9641no—
270C42—2414no—
271C42—2414no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C2×C4×D24112yes—
279C23C23×D24111yescharacteristic
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—4821no—
297C2×C4—4821no—
298C2×C4—4821no—
299C2×C4—4821no—
300C2×C4—4821no—
301C2×C4—4821no—
302C2×C4—4821no—
303C2×C4—4821no—
304C2×C4—4821no—
305C2×C4—4821no—
306C2×C4—4821no—
307C2×C4—4821no—
308C2×C4—4821no—
309C2×C4—4821no—
310C2×C4—4821no—
311C2×C4—4821no—
312C2×C4—4821no—
313C2×C4—4821no—
314C2×C4—4828no—
315C2×C4—2412no—
316C2×C4—2412no—
317C2×C4—2412no—
318C2×C4—2412no—
319C2×C4—2412no—
320C2×C4—2412no—
321C2×C4C2×C4×D24112yes—
322C2×C4C2×C4×D24112yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22C22×C4×D24111yescharacteristic
331C22#41×D24111yescharacteristic
332C22#41×D24111yescharacteristic
333C22#2144068711yescharacteristic
334C22#2144068711yescharacteristic
335C22#2144068911yescharacteristic
336C22#2144068911yescharacteristic
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—9641no—
344C4—9641no—
345C4—9641no—
346C4—9641no—
347C4—4822no—
348C4—4822no—
349C4—4822no—
350C4—2414no—
351C2—42no—
352C2#117×D24111yescharacteristic
353C2#2950819611yescharacteristic
354C2#2950819611yescharacteristic
355C2#2950831711yescharacteristic
356C2#2950832411yescharacteristic
357C2#2950833111yescharacteristic
358C2#2950833511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D241
commutatorC22×C241C23×C4
Fitting#388×C241C2
socle, cosocleC23×C241C24
prime radicalC24×C241C23
hypercenter#388D241
hypocenterC241#2314
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
5. #29507604C2semidirect
6. #29507601C2semidirect
7. #29507599C2semidirect
8. #29507598C2semidirect
9. #29507586C2semidirect
10. #29507581C2semidirect
13. C4×#16838749C2semidirect
14. #29507568C2semidirect
17. #21440598C4semidirect
179. C241#2314semidirect

Maximal subgroups

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

subgroupindex
C2×#214405982
#295076112
#295076102
#295076052
#295076042
#295076012
#295075992
#295075982
#295075862
#295075812
#295075752
C4×#168387492
#295075682
#388×C2412
#2314241