Finite Group Databasebeta

← #30599410

Subgroups — #30599410

Order 15616.

446 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C4×#14519837C211yesmaximal, characteristic
2#21461078C211yesmaximal, characteristic
3#21460707C212yesmaximal, complemented
4#21460678C212yesmaximal, complemented
5#21448762C211yesmaximal, characteristic
6#16840783C2212yes—
7C2×#14519837—21no—
8C4×#11758217C2212yes—
9#16840642—21no—
10#16840606—21no—
11#16840605—21no—
12C2×C4×C22⋊D61C2211yescharacteristic
13#16839650—21no—
14#16839646—21no—
15#16839638—21no—
16#16839629C2211yescharacteristic
17#16839625C411yescharacteristic
18#16839621C411yescharacteristic
19C4×#11758198—21no—
20#16839607C2211yescharacteristic
21#95×D61C411yescharacteristic
22C4×C22⋊C4×C61C411yescharacteristic
23C2×#11758217—22no—
24C4⋊#92420—22no—
25#14519837—24no—
26C22⋊#92420—22no—
27#14519832—22no—
28#14519832—22no—
29C4×#92420—22no—
30C22×C22⋊D61D411yescharacteristic
31C22×C4×D61—21no—
32C22×C4×D61C2×C411yescharacteristic
33C4×C22⋊D61—22no—
34C4×C22⋊D61—22no—
35C2×#11758196—21no—
36C2×#11758196D411yescharacteristic
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61D411yescharacteristic
39C2×#11758198—21no—
40C2×#11758198D411yescharacteristic
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2311yescharacteristic
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684C2×C411yescharacteristic
49#14519684C2×C411yescharacteristic
50C23×C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61—21no—
52C2×C42×C61—21no—
53#95×C61C2×C411yescharacteristic
54#95×C61C2×C411yescharacteristic
55C24×C61C22⋊C411yescharacteristic
56C23×D61C22⋊C411yescharacteristic
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—81no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C2×C22⋊D61—22no—
65C2×C22⋊D61—22no—
66C2×C22⋊D61—41no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61C22⋊C411yescharacteristic
70C22×Dic61C2×D411yescharacteristic
71C22×Dic61C2×D411yescharacteristic
72C2×C4×D61—21no—
73C2×C4×D61—21no—
74C2×C4×D61—42no—
75C2×C4×D61—42no—
76C2×C4×D61—81no—
77C2×C4×D61—81no—
78#11758217—24no—
79#11758217—42no—
80C2×#92420—42no—
81C2×#92420—42no—
82C22⋊C4×C61—42no—
83C42×C61—81no—
84C22⋊Dic61—22no—
85C22⋊Dic61—81no—
86#11758198—22no—
87#11758198—42no—
88#11758196—22no—
89#11758196—81no—
90C4×Dic61—42no—
91C4×Dic61#4112yes—
92C4×Dic61#4112yes—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—41no—
97C23×C61—41no—
98C23×C61C2×C22⋊C411yescharacteristic
99C22×D61—21no—
100C22×D61—21no—
101C22×D61—41no—
102C22×D61—41no—
103C22×D61#10412yes—
104C2×C4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—81no—
114C2×C4×C61—81no—
115C2×C4×C61#11711yescharacteristic
116C2×C4×C61#11711yescharacteristic
117C22⋊D61—44no—
118C2×Dic61—21no—
119C2×Dic61—21no—
120C2×Dic61—21no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61#12312yes—
130C2×Dic61#12312yes—
131C4×D61—81no—
132C4×D61—81no—
133C4×D61—84no—
134#92420—44no—
135#92420—82no—
136#8772—611nomaximal, Sylow
137C22×C61—21no—
138C22×C61—21no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61—41no—
142C22×C61—81no—
143C22×C61—81no—
144C22×C61#38111yescharacteristic
145C22×C61C2×#10411yescharacteristic
146C22×C61#42111yescharacteristic
147C2×D61—22no—
148C2×D61—42no—
149C2×D61—41no—
150C2×D61—41no—
151C2×D61—42no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—42no—
155C4×C61—41no—
156C4×C61—81no—
157Dic61—22no—
158Dic61—22no—
159Dic61—41no—
160Dic61—81no—
161Dic61—81no—
162#2353—611no—
163C4×#100—611no—
164#1466—611no—
165#1300—612no—
166#1288—612no—
167C2×C61—21no—
168C2×C61—21no—
169C2×C61—81no—
170C2×C61#182611yescharacteristic
171C2×C61#182711yescharacteristic
172C2×C61#182911yescharacteristic
173D61—42no—
174C2×C4×D4—611no—
175#432—612no—
176C2×#100—1221no—
177C4×M16—612no—
178#388—1221no—
179#387—1221no—
180#386—1221no—
181#383—611no—
182#381—611no—
183#380—611no—
184C4×C22⋊C4—1221no—
185C4×C22⋊C4#692311yescharacteristic
186#376—611no—
187C2×#95—611no—
188#343—1221no—
189#323—1221no—
190#323—1221no—
191C61#877211yescharacteristic, complemented, Sylow
192C22×D4—611no—
193C23×C4—611no—
194C23×C4—1221no—
195C23×C4C2×#692311yescharacteristic
196C2×M16—1222no—
197C4×D4—1222no—
198C4×D4—1222no—
199C2×C4⋊C4—611no—
200C2×C4⋊C4—1221no—
201C2×C22⋊C4—21no—
202C2×C22⋊C4—611no—
203C2×C22⋊C4—611no—
204C2×C22⋊C4—1221no—
205C2×C22⋊C4—1221no—
206C2×C42—21no—
207C2×C42—611no—
208C2×C42—1221no—
209C4⋊C8—1222no—
210#100—1224no—
211C22⋊C8—1222no—
212#97—1222no—
213#97—1222no—
214C4×C8—1222no—
215#95—611no—
216#95—611no—
217#95—1221no—
218#95—1221no—
219#95—1221no—
220#95—1221no—
221#95—1221no—
222#95C2×#692311yescharacteristic
223#95C2×#692311yescharacteristic
224C24—611no—
225C24C22⋊#692311yescharacteristic
226C2×D4—1222no—
227C2×D4—1222no—
228C2×D4—2441no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—81no—
234C22×C4—611no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—1221no—
238C22×C4—1221no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4—4881no—
242C22×C4—4881no—
243C22×C4—2442no—
244C22×C4—2442no—
245C22×C4C22⋊#692311yescharacteristic
246C22×C4C22×#692311yescharacteristic
247M16—1224no—
248M16—2442no—
249C2×C8—2442no—
250C2×C8—2442no—
251C4⋊C4—1222no—
252C4⋊C4—4881no—
253C22⋊C4—42no—
254C22⋊C4—1222no—
255C22⋊C4—1222no—
256C22⋊C4—4881no—
257C22⋊C4—2442no—
258C42—81no—
259C42—612no—
260C42—612no—
261C42—2442no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23—612no—
268C23—1221no—
269C23—1221no—
270C23—2441no—
271C23—2441no—
272C23C2×C22⋊#692311yescharacteristic
273D4—2444no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—612no—
286C2×C4—612no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4—4881no—
291C2×C4—4881no—
292C2×C4—4884no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4—2441no—
297C2×C4—2441no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4#1451985611yescharacteristic
302C2×C4#1451985611yescharacteristic
303C8—4882no—
304C8—2444no—
305C22—21no—
306C22—21no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—81no—
311C22—81no—
312C22—1222no—
313C22—2442no—
314C22—2442no—
315C22—2441no—
316C22—2441no—
317C22#1684070511yescharacteristic
318C22D61⋊#10411yescharacteristic
319C22#1684075911yescharacteristic
320C4—21no—
321C4—21no—
322C4—42no—
323C4—41no—
324C4—81no—
325C4—1222no—
326C4—1222no—
327C4—4881no—
328C4—4881no—
329C4—2441no—
330C2—21no—
331C2—21no—
332C2—81no—
333C2—2442no—
334C2#2146172711yescharacteristic
335C2#2146172811yescharacteristic
336C2#2146173211yescharacteristic
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61#381
prime radicalC22×C22⋊D61D4
cosocleC2×C4×Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8772
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460707C2semidirect
4. #21460678C2semidirect
191. C61#8772semidirect

Maximal subgroups

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

subgroupindex
C4×#145198372
#214610782
#214607072
#214606782
#214487622
#877261