Finite Group Databasebeta

← #44507746

Subgroups — #44507746

Order 30848.

376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×D241C211yesmaximal, characteristic, complemented
2#29508229C211yesmaximal, characteristic
3C2×#21440570C211yesmaximal, characteristic, complemented
4C2×#21440568C211yesmaximal, characteristic, complemented
5C4×#16838747C211yesmaximal, characteristic, complemented
6#29507476C211yesmaximal, characteristic, complemented
7#339×C241C211yesmaximal, characteristic, complemented
8C2×#16838770C2211yescharacteristic
9C22×C4×D241C2211yescharacteristic
10C2×#16838754C2211yescharacteristic
11C2×#16838753—21no—
12M16×D241—22no—
13M16×D241—22no—
14C2×C8×D241—21no—
15#21440626—21no—
16#21440622C411yescharacteristic, complemented
17#21440622C411yescharacteristic, complemented
18#21440617C411yescharacteristic, complemented
19#21440617C411yescharacteristic, complemented
20#21440612—21no—
21C4×D964—21no—
22C4×D964—21no—
23C2×#16838747—21no—
24C2×C4×Dic241C2211yescharacteristic
25#21440570—22no—
26#21440568—22no—
27#21440549—21no—
28C2×M16×C241C2211yescharacteristic
29#117×C241C2211yescharacteristic
30C2×C42×C241C2211yescharacteristic
31C23×D241D411yescharacteristic
32#16838770—21no—
33#16838770—21no—
34#16838770—21no—
35#16838770—21no—
36C2×Dic482C2×C411yescharacteristic
37C2×D964—21no—
38C2×D964—21no—
39C2×D964C2×C411yescharacteristic
40C2×C22⋊D241—21no—
41C22×Dic241—21no—
42C22×Dic241D411yescharacteristic
43C2×C4×D241—21no—
44C2×C4×D241—21no—
45C2×C4×D241—21no—
46C2×C4×D241—21no—
47C2×C4×D241—21no—
48C2×C4×D241C2×C411yescharacteristic
49C2×C4×D241C2×C411yescharacteristic
50C2×C4×D241D411yescharacteristic
51C2×C4×D241D411yescharacteristic
52#16838754—21no—
53#16838754D412yescomplemented
54#16838753—24no—
55C2×#14515349—21no—
56C8×D241—24no—
57C4⋊Dic241—21no—
58C4⋊Dic241—21no—
59#16838747—24no—
60#16838747—21no—
61#16838747—21no—
62#16838747—21no—
63#16838747—21no—
64C4×Dic241—21no—
65C4×Dic241—21no—
66C22×C4×C241—21no—
67C22×C4×C241C2311yescharacteristic
68M16×C241—21no—
69M16×C241D412yescomplemented
70C2×C8×C241—21no—
71C4⋊C4×C241C2×C411yescharacteristic
72C4⋊C4×C241C2×C411yescharacteristic
73C22⋊C4×C241—21no—
74C42×C241—21no—
75C42×C241—21no—
76C42×C241—21no—
77C22×D241—21no—
78C22×D241—21no—
79C22×D241—22no—
80C22×D241—21no—
81C22×D241—41no—
82C22×D241C22⋊C411yescharacteristic
83C22×D241C22⋊C411yescharacteristic
84Dic482—21no—
85Dic482—21no—
86D964—21no—
87D964—21no—
88D964—42no—
89D964—42no—
90C22⋊D241—41no—
91C22⋊D241—41no—
92C2×Dic241—21no—
93C2×Dic241—21no—
94C2×Dic241—22no—
95C2×Dic241—21no—
96C2×Dic241—41no—
97C2×Dic241—41no—
98C2×Dic241C22⋊C411yescharacteristic
99C2×Dic241C22⋊C411yescharacteristic
100C4×D241—21no—
101C4×D241—21no—
102C4×D241—21no—
103C4×D241—21no—
104C4×D241—21no—
105C4×D241—21no—
106C4×D241—21no—
107C4×D241—21no—
108C4×D241—41no—
109C4×D241—41no—
110#14515349—22no—
111C23×C241C2×D411yescharacteristic
112C2×C4×C241—22no—
113C2×C4×C241—21no—
114C2×C4×C241—21no—
115C2×C4×C241—41no—
116C2×C4×C241—41no—
117C2×C4×C241C22×C411yescharacteristic
118C2×C4×C241C2×D411yescharacteristic
119C2×C4×C241C2×D411yescharacteristic
120C2×C4×C241C2×D411yescharacteristic
121C2×C4×C241#4111yescharacteristic
122C2×C4×C241#4111yescharacteristic
123C8×C241—22no—
124C22×C241—21no—
125C22×C241—21no—
126C22×C241C2×C22⋊C411yescharacteristic
127C22×C241#12111yescharacteristic
128C22×C241#12111yescharacteristic
129C2×D241—21no—
130C2×D241—21no—
131C2×D241—21no—
132C2×D241—21no—
133C2×D241—21no—
134C2×D241—42no—
135C2×D241—42no—
136C2×D241—41no—
137C2×D241—41no—
138C2×D241—41no—
139C2×D241#10412yescomplemented
140C4×C241—42no—
141C4×C241—41no—
142C4×C241—41no—
143C4×C241C4×D411yescharacteristic
144C4×C241C4×D411yescharacteristic
145C4×C241#12011yescharacteristic
146C4×C241#12311yescharacteristic
147Dic241—21no—
148Dic241—21no—
149Dic241—42no—
150Dic241—41no—
151C2×C241—21no—
152C2×C241—21no—
153C2×C241#38611yescharacteristic
154C2×C241C2×#10411yescharacteristic
155C2×C241#42111yescharacteristic
156D241—22no—
157D241—41no—
158D241—81no—
159C241#187111yescharacteristic, complemented, Sylow
160#1871—2411nomaximal, Sylow
161C22×M16—2411no—
162#525—2411no—
163C2×#104—2411no—
164C2×#104—2411no—
165C4×C22⋊C4—2411no—
166#339—2411no—
167#339D24111yescharacteristic, complemented
168C2×#41—2411no—
169C23×C4—2411no—
170C2×M16—4821no—
171C2×M16—4822no—
172C2×M16—4822no—
173C2×M16—2411no—
174C2×M16C2×D24111yescharacteristic
175C22×C8—4821no—
176#123—4821no—
177C22⋊Q8—2411no—
178C22⋊Q8—2411no—
179#121—2411no—
180#121—2411no—
181#120—4821no—
182C4×D4—4821no—
183C4×D4—4821no—
184#117C2×D24111yescharacteristic
185C2×C22⋊C4—4821no—
186C2×C42—2411no—
187C2×C42C2×D24111yescharacteristic
188#104—4822no—
189#104—4822no—
190#95—4821no—
191C24—2411no—
192#41—4821no—
193#41—4821no—
194#41—4821no—
195#41—4821no—
196C2×Q8—2411no—
197C2×D4—4821no—
198C2×D4—4821no—
199C2×D4—4821no—
200C2×D4—2411no—
201C22×C4—21no—
202C22×C4—4821no—
203C22×C4—4821no—
204C22×C4—4821no—
205C22×C4—4821no—
206C22×C4—4821no—
207C22×C4—4821no—
208C22×C4—2411no—
209C22×C4—2411no—
210C22×C4—2411no—
211C22×C4—2411no—
212C22×C4—2411no—
213C22×C4C22×D24111yescharacteristic
214M16—21no—
215M16—4824no—
216M16—4821no—
217M16—2412no—
218M16D96412yescomplemented
219C2×C8—21no—
220C2×C8—4824no—
221C2×C8—4821no—
222C4⋊C4—4821no—
223C4⋊C4—4821no—
224C4⋊C4C4×D24111yescharacteristic
225C4⋊C4C4×D24111yescharacteristic
226C22⋊C4—21no—
227C22⋊C4—4824no—
228C22⋊C4—4821no—
229C22⋊C4—4821no—
230C22⋊C4—4821no—
231C22⋊C4—4821no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—4821no—
236C42—4821no—
237C23—9641no—
238C23—4822no—
239C23—4821no—
240C23—4821no—
241C23—4821no—
242C23—2411no—
243C23—2411no—
244C23D4×D24111yescharacteristic
245Q8—4821no—
246Q8—4821no—
247D4—9642no—
248D4—9642no—
249D4—9641no—
250D4—9641no—
251D4—4821no—
252D4—4821no—
253C2×C4—22no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—9641no—
259C2×C4—9641no—
260C2×C4—9641no—
261C2×C4—9641no—
262C2×C4—4822no—
263C2×C4—4821no—
264C2×C4—4821no—
265C2×C4—4821no—
266C2×C4—4821no—
267C2×C4—4821no—
268C2×C4—4821no—
269C2×C4—4821no—
270C2×C4—4821no—
271C2×C4—4821no—
272C2×C4—4821no—
273C2×C4—4821no—
274C2×C4—2411no—
275C2×C4—2411no—
276C2×C4C2×C4×D24111yescharacteristic
277C2×C4D4×D24111yescharacteristic
278C2×C4D4×D24111yescharacteristic
279C2×C4C2×D96411yescharacteristic
280C2×C4#1683877011yescharacteristic
281C2×C4#1683877111yescharacteristic
282C8—22no—
283C8—4822no—
284C22—21no—
285C22—21no—
286C22—9642no—
287C22—9642no—
288C22—9641no—
289C22—9641no—
290C22—9641no—
291C22—4821no—
292C22—4821no—
293C22—4821no—
294C22—4821no—
295C22—4821no—
296C22—2412no—
297C22C22⋊C4×D24111yescharacteristic
298C22#2144061511yescharacteristic
299C22#2144061711yescharacteristic
300C4—42no—
301C4—41no—
302C4—41no—
303C4—9642no—
304C4—9641no—
305C4—4821no—
306C4—4821no—
307C4#2144060411yescharacteristic
308C4C4×D96411yescharacteristic
309C4#2144061211yescharacteristic
310C4#2144062711yescharacteristic
311C2—21no—
312C2—21no—
313C2—19281no—
314C2—9641no—
315C2—4822no—
316C2#2950759511yescharacteristic
317C2#104×D24111yescharacteristic
318C2#2950773211yescharacteristic
subgroupG/H
centerC2×C4D4×D241
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
Fitting#339×C241C2
socleC22×C241C2×C22⋊C4
prime radical#29508229C2
cosocleC22×C4×C241C23
hypercenter#339D241
hypocenterC241#1871
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×M16×D241C2semidirect
3. C2×#21440570C2semidirect
4. C2×#21440568C2semidirect
5. C4×#16838747C2semidirect
6. #29507476C2semidirect
7. #339×C241C2semidirect
16. #21440622C4semidirect
17. #21440622C4semidirect
18. #21440617C4semidirect
19. #21440617C4semidirect
53. #16838754D4semidirect
69. M16×C241D4semidirect
139. C2×D241#104semidirect
159. C241#1871semidirect
167. #339D241semidirect
218. M16D964semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D2412
#295082292
C2×#214405702
C2×#214405682
C4×#168387472
#295074762
#339×C2412
#1871241