Finite Group Databasebeta

← #44510044

Subgroups — #44510044

Order 30848.

512 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D241C211yesmaximal, characteristic
2#29507604C211yesmaximal, characteristic, complemented
3#29507603C211yesmaximal, characteristic, complemented
4#29507602C211yesmaximal, characteristic, complemented
5#29507601C211yesmaximal, characteristic, complemented
6#29507600C211yesmaximal, characteristic, complemented
7#29507599C211yesmaximal, characteristic, complemented
8#29507598C211yesmaximal, characteristic, complemented
9#29507579C211yesmaximal, characteristic
10#29507579C211yesmaximal, characteristic
11#29507576C211yesmaximal, characteristic
12#29507574C211yesmaximal, characteristic
13C4×#16838747C211yesmaximal, characteristic
14#29507564C211yesmaximal, characteristic
15#387×C241C211yesmaximal, characteristic, complemented
16C22×C4×D241C2211yescharacteristic
17C22×C4×D241C2211yescharacteristic
18C22×C4×D241C2211yescharacteristic
19C2×C4⋊Dic241C2211yescharacteristic
20C2×C4⋊Dic241C2211yescharacteristic
21C2×#16838749C2211yescharacteristic
22C2×#16838749C2211yescharacteristic
23C2×#16838749C2211yescharacteristic
24C2×#16838749C2211yescharacteristic
25C4⋊C4×D241C418yescomplemented
26C2×#16838747C2211yescharacteristic
27C2×#16838747C2211yescharacteristic
28C2×#16838747C2211yescharacteristic
29C2×#16838747C2211yescharacteristic
30C2×C4×Dic241C2211yescharacteristic
31C2×C4×Dic241C2211yescharacteristic
32C2×C4×Dic241C2211yescharacteristic
33#21440549C2211yescharacteristic
34#21440549C2211yescharacteristic
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×C4⋊C4×C241C2211yescharacteristic
47C2×C42×C241C2211yescharacteristic
48#95×C241C2211yescharacteristic
49#95×C241C2211yescharacteristic
50#95×C241C2211yescharacteristic
51#95×C241C2211yescharacteristic
52C23×D241C2311yescharacteristic
53C22×Dic241C2311yescharacteristic
54C22×Dic241C2311yescharacteristic
55C22×Dic241C2311yescharacteristic
56C22×Dic241C2311yescharacteristic
57C22×Dic241C2311yescharacteristic
58C22×Dic241C2311yescharacteristic
59C22×Dic241C2311yescharacteristic
60C2×C4×D241—22no—
61C2×C4×D241—22no—
62C2×C4×D241—41no—
63C2×C4×D241—41no—
64C2×C4×D241—41no—
65C2×C4×D241—41no—
66C2×C4×D241C2×C414yes—
67C2×C4×D241C2×C414yes—
68C2×C4×D241C2×C414yes—
69C4⋊Dic241—41no—
70C4⋊Dic241C2×C414yes—
71#16838749—41no—
72#16838749—41no—
73#16838749C2×C414yes—
74#16838749C2×C414yes—
75#16838747—22no—
76#16838747—22no—
77#16838747—22no—
78#16838747—22no—
79C4×Dic241—41no—
80C4×Dic241—41no—
81C4×Dic241—41no—
82C22×C4×C241C2311yescharacteristic
83C22×C4×C241C2311yescharacteristic
84C22×C4×C241C2311yescharacteristic
85C22×C4×C241C2311yescharacteristic
86C22×C4×C241C2311yescharacteristic
87C22×C4×C241C2311yescharacteristic
88C22×C4×C241C2311yescharacteristic
89C4⋊C4×C241—41no—
90C4⋊C4×C241C2×C414yes—
91C42×C241—41no—
92C22×D241—21no—
93C22×D241—21no—
94C22×D241—21no—
95C22×D241—21no—
96C22×D241C22×C412yes—
97C22×D241#4112yes—
98C22×D241#4112yes—
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×Dic241—21no—
112C2×Dic241—21no—
113C2×Dic241—21no—
114C2×Dic241—21no—
115C2×Dic241—21no—
116C2×Dic241—21no—
117C2×Dic241C22×C412yes—
118C2×Dic241C22×C412yes—
119C2×Dic241C22×C412yes—
120C4×D241—28no—
121C4×D241—44no—
122C4×D241—44no—
123C23×C241C2411yescharacteristic
124C2×C4×C241—21no—
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×C241—21no—
142C2×C4×C241C22×C412yes—
143C2×C4×C241C22×C412yes—
144C2×C4×C241C22×C412yes—
145C22×C241C23×C411yescharacteristic
146C22×C241C2×#4111yescharacteristic
147C22×C241C2×#4111yescharacteristic
148C22×C241H(5,𝔽2)11yescharacteristic
149C22×C241H(5,𝔽2)11yescharacteristic
150C22×C2412−1+411yescharacteristic
151C22×C2412−1+411yescharacteristic
152C2×D241—22no—
153C2×D241—22no—
154C2×D241—22no—
155C2×D241—22no—
156C2×D241—22no—
157C2×D241—22no—
158C2×D241#11714yes—
159C4×C241—22no—
160C4×C241—22no—
161C4×C241—22no—
162C4×C241—41no—
163C4×C241—41no—
164C4×C241—41no—
165C4×C241—41no—
166Dic241—22no—
167Dic241—22no—
168Dic241—22no—
169Dic241—41no—
170Dic241—41no—
171Dic241—41no—
172Dic241—41no—
173C2×C241C2×#11711yescharacteristic
174C2×C241#51811yescharacteristic
175C2×C241#51911yescharacteristic
176C2×C241#53911yescharacteristic
177C2×C241#53911yescharacteristic
178C2×C241#53911yescharacteristic
179C2×C241#53911yescharacteristic
180D241—24no—
181C241#231311yescharacteristic, complemented, Sylow
182#2313—2411nomaximal, Sylow
183C22×C4⋊C4—2411no—
184#387—2411no—
185#387—2411no—
186#387—2411no—
187#387—2411no—
188#387—2411no—
189#387—2411no—
190#387—2411no—
191#387D24111yescharacteristic, complemented
192#381—2411no—
193#381—2411no—
194#380—2411no—
195#380—2411no—
196C4×C22⋊C4—2411no—
197C4×C22⋊C4—2411no—
198C23×C4—2411no—
199C23×C4—2411no—
200C23×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⋊C4—2418no—
208C2×C4⋊C4C2×D24111yescharacteristic
209C2×C4⋊C4C2×D24111yescharacteristic
210C2×C22⋊C4—2411no—
211C2×C22⋊C4—2411no—
212C2×C22⋊C4—2411no—
213C2×C22⋊C4—2411no—
214C2×C42—2411no—
215C2×C42—2411no—
216C2×C42—2411no—
217C2×C42C2×D24111yescharacteristic
218#95—2411no—
219#95—2411no—
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
232#95C2×D24111yescharacteristic
233#95C2×D24111yescharacteristic
234C24—2411no—
235C22×C4—9641no—
236C22×C4—9641no—
237C22×C4—9641no—
238C22×C4—9641no—
239C22×C4—4822no—
240C22×C4—4822no—
241C22×C4—2414no—
242C22×C4—2414no—
243C22×C4—2411no—
244C22×C4—2411no—
245C22×C4—2411no—
246C22×C4—2411no—
247C22×C4—2411no—
248C22×C4—2411no—
249C22×C4—2411no—
250C22×C4—2414no—
251C22×C4C22×D24111yescharacteristic
252C22×C4C22×D24111yescharacteristic
253C22×C4C22×D24111yescharacteristic
254C22×C4C22×D24111yescharacteristic
255C22×C4C22×D24111yescharacteristic
256C22×C4C22×D24111yescharacteristic
257C22×C4C22×D24111yescharacteristic
258C4⋊C4—41no—
259C4⋊C4—9641no—
260C4⋊C4—9641no—
261C4⋊C4—9641no—
262C4⋊C4—2414no—
263C4⋊C4—2414no—
264C4⋊C4—2414no—
265C4⋊C4C4×D24114yes—
266C22⋊C4—4822no—
267C22⋊C4—4822no—
268C22⋊C4—4822no—
269C22⋊C4—4822no—
270C42—41no—
271C42—9641no—
272C42—9641no—
273C42—9641no—
274C23—4821no—
275C23—4821no—
276C23—4821no—
277C23—4821no—
278C23—2412no—
279C23—2412no—
280C23—2412no—
281C23C23×D24111yescharacteristic
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—9644no—
301C2×C4—9644no—
302C2×C4—4828no—
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—4821no—
315C2×C4—4821no—
316C2×C4—4821no—
317C2×C4—4821no—
318C2×C4—4821no—
319C2×C4—4821no—
320C2×C4—4821no—
321C2×C4—2412no—
322C2×C4—2412no—
323C2×C4—2412no—
324C2×C4C2×C4×D24112yes—
325C2×C4C2×C4×D24112yes—
326C2×C4C2×C4×D24112yes—
327C22—4822no—
328C22—4822no—
329C22—4822no—
330C22—4822no—
331C22—4822no—
332C22—4822no—
333C22—2414no—
334C22C22×C4×D24111yescharacteristic
335C22#41×D24111yescharacteristic
336C22#41×D24111yescharacteristic
337C22#2144068711yescharacteristic
338C22#2144068811yescharacteristic
339C22#2144068911yescharacteristic
340C22#2144069011yescharacteristic
341C4—22no—
342C4—22no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—9641no—
349C4—9641no—
350C4—9641no—
351C4—9641no—
352C4—4822no—
353C4—4822no—
354C4—4822no—
355C2—4824no—
356C2#117×D24111yescharacteristic
357C2#2950818911yescharacteristic
358C2#2950819311yescharacteristic
359C2#2950830811yescharacteristic
360C2#2950831011yescharacteristic
361C2#2950831311yescharacteristic
362C2#2950831511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D241
commutatorC22×C241C23×C4
Fitting#387×C241C2
socle, cosocleC23×C241C24
prime radicalC23×D241C23
hypercenter#387D241
hypocenterC241#2313
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #29507604C2semidirect
3. #29507603C2semidirect
4. #29507602C2semidirect
5. #29507601C2semidirect
6. #29507600C2semidirect
7. #29507599C2semidirect
8. #29507598C2semidirect
15. #387×C241C2semidirect
25. C4⋊C4×D241C4semidirect
181. C241#2313semidirect
191. #387D241semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D2412
#295076042
#295076032
#295076022
#295076012
#295076002
#295075992
#295075982
#295075792
#295075762
#295075742
C4×#168387472
#295075642
#387×C2412
#2313241