Finite Group Databasebeta

← #30604387

Subgroups — #30604387

Order 15616.

414 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 102 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
1#21462152C211yesmaximal, characteristic, complemented
2#21462026C211yesmaximal, characteristic, complemented
3#21460772C212yesmaximal, complemented
4#21460771C212yesmaximal, complemented
5#436×D61C211yesmaximal, characteristic
6C2×#14519852—21no—
7C2×#14519852—21no—
8#16840683—21no—
9C4⋊#11758187C2212yescomplemented
10#16840650C2212yescomplemented
11#16840648—21no—
12C2×M16×D61—21no—
13C4×D4×D61C411yescharacteristic
14#16839841C411yescharacteristic
15#16839840C2211yescharacteristic
16#16839839C2211yescharacteristic
17#16839838—21no—
18#16839837—21no—
19C4⋊C8×D61C411yescharacteristic
20C22⋊C8×D61—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#436C411yescharacteristic
23#14519852—24no—
24#14519852—42no—
25C2×#11758187—22no—
26C2×#11758187—22no—
27C2×D4×D61C811yescharacteristic
28C22×C4×D61—21no—
29C2×#11758194—21no—
30C2×#11758189—21no—
31C2×#11758189—21no—
32M16×D61—42no—
33M16×D61—42no—
34C2×C8×D61—21no—
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C4×D244C2×C411yescharacteristic
38D4×Dic61C811yescharacteristic
39#14519739C811yescharacteristic
40C4×C22⋊D61—21no—
41#14519737—21no—
42C4⋊C4×D61C811yescharacteristic
43C22⋊C4×D61—21no—
44C42×D61C2×C411yescharacteristic
45C4⋊#92418C2×C411yescharacteristic
46#14519706—21no—
47C22⋊#92418—21no—
48#14519689—21no—
49#14519689—21no—
50C4×#92418C2311yescharacteristic
51C8×Dic61D411yescharacteristic
52C8×Dic61D411yescharacteristic
53C2×M16×C61—21no—
54C4×D4×C61C2×C411yescharacteristic
55C4⋊C8×C61C2×C411yescharacteristic
56C22⋊C8×C61—21no—
57C4×C8×C61C2×C411yescharacteristic
58C23×D61—21no—
59C2×D4×C61C2×C811yescharacteristic
60C22×C4×C61—21no—
61C2×C22⋊D61—21no—
62C22×Dic61—21no—
63D4×D61—42no—
64C2×D244C2×C811yescharacteristic
65C2×C4×D61—21no—
66C2×C4×D61—21no—
67C2×C4×D61—21no—
68C2×C4×D61—42no—
69C2×C4×D61—42no—
70C2×C4×D61C22⋊C411yescharacteristic
71C2×C4×D61C2×C811yescharacteristic
72C2×C4×D61M1611yescharacteristic
73M16×C61—42no—
74C2×C8×C61—21no—
75C2×C8×C61C22⋊C411yescharacteristic
76C2×C8×C61C22⋊C411yescharacteristic
77C4⋊C4×C61C2×C811yescharacteristic
78C22⋊C4×C61—21no—
79C42×C61C22×C411yescharacteristic
80C22⋊Dic61—21no—
81#11758198—21no—
82#11758198—21no—
83C4⋊Dic61C2×C811yescharacteristic
84#11758196—21no—
85C4×Dic61C22⋊C411yescharacteristic
86C4×Dic61C2×C811yescharacteristic
87C4×Dic61M1611yescharacteristic
88#11758194—41no—
89#11758194—41no—
90C2×#92418—21no—
91C2×#92418C2×D411yescharacteristic
92C2×#92418C2×D411yescharacteristic
93#11758189—42no—
94#11758189—41no—
95#11758189—41no—
96C8×D61—22no—
97C8×D61—42no—
98C8×D61D812yes—
99C8×D61SD1612yes—
100#11758187—24no—
101#11758187—42no—
102C23×C61—21no—
103C22×D61—21no—
104C22×D61—42no—
105C22×D61—42no—
106C22×D61—42no—
107C22×D61C22⋊C811yescharacteristic
108D4×C61—41no—
109C2×C4×C61—21no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61C2×C22⋊C411yescharacteristic
113C2×C4×C61C22×C811yescharacteristic
114C2×C4×C61C2×M1611yescharacteristic
115C22⋊D61—42no—
116C2×Dic61—21no—
117C2×Dic61—42no—
118C2×Dic61C22⋊C811yescharacteristic
119C2×Dic61C22⋊C811yescharacteristic
120C2×Dic61C22⋊C811yescharacteristic
121D244—41no—
122C4×D61—22no—
123C4×D61—41no—
124C4×D61—42no—
125C4×D61—41no—
126C4×D61—41no—
127C4×D61—42no—
128C4×D61#10212yes—
129C4×D61#10412yes—
130C8×C61—21no—
131C8×C61—41no—
132C8×C61#10212yes—
133#92418—21no—
134#92418—41no—
135#92418C2×D811yescharacteristic
136#92418C2×SD1611yescharacteristic
137#11587—611nomaximal, Sylow
138C22×C61—41no—
139C22×C61—41no—
140C22×C61—41no—
141C22×C61C2×C22⋊C811yescharacteristic
142C2×D61—21no—
143C2×D61—21no—
144C2×D61—41no—
145C2×D61—41no—
146C2×D61—41no—
147C2×D61—84no—
148C2×D61D4⋊C812yes—
149C4×C61—21no—
150C4×C61—21no—
151C4×C61—41no—
152C4×C61C2×#10211yescharacteristic
153C4×C61C2×#10411yescharacteristic
154Dic61—21no—
155Dic61—41no—
156Dic61D4⋊C812yes—
157Dic61#34912yes—
158C2×#436—611no—
159#2150—611no—
160C4×M32—611no—
161#1330—612no—
162#1330—612no—
163C2×C61—81no—
164C2×C61C2×D4⋊C811yescharacteristic
165C2×C61C2×#34911yescharacteristic
166C2×C61#211711yescharacteristic
167D61—22no—
168D61—81no—
169C22×M16—1221no—
170C2×C4×D4—611no—
171C2×M32—1221no—
172C2×M32—1221no—
173#436—611no—
174#436—611no—
175#436—611no—
176#436—1221no—
177#436—1221no—
178#436#692311yescharacteristic
179C2×C4⋊C8—611no—
180C2×C22⋊C8—1221no—
181C2×C4×C8—611no—
182C4⋊C16—612no—
183C4⋊C16—1221no—
184#346—612no—
185C4×C16—1221no—
186C61#1158711yescharacteristic, complemented, Sylow
187C22×D4—611no—
188C23×C4—1221no—
189C2×M16—21no—
190C2×M16—1221no—
191C2×M16—1221no—
192C2×M16—1221no—
193C2×M16—2442no—
194C2×M16—2442no—
195C22×C8—611no—
196C22×C8—611no—
197C22×C8—1221no—
198C4×D4—611no—
199C4×D4—611no—
200C4×D4—611no—
201C4×D4—1221no—
202C4×D4—1221no—
203C4×D4C2×#692311yescharacteristic
204C2×C4⋊C4—611no—
205C2×C22⋊C4—1221no—
206C2×C42—611no—
207M32—1224no—
208M32—2442no—
209C2×C16—1222no—
210C2×C16—1222no—
211C4⋊C8—611no—
212C4⋊C8—1221no—
213C4⋊C8C2×#692311yescharacteristic
214C22⋊C8—21no—
215C22⋊C8—1221no—
216C22⋊C8—1221no—
217C22⋊C8—1221no—
218C4×C8—611no—
219C4×C8—611no—
220C4×C8—611no—
221C4×C8C2×#692311yescharacteristic
222C24—1221no—
223C2×D4—611no—
224C2×D4—1221no—
225C2×D4—2442no—
226C2×D4D61⋊C811yescharacteristic
227C22×C4—21no—
228C22×C4—611no—
229C22×C4—611no—
230C22×C4—611no—
231C22×C4—1221no—
232C22×C4—1221no—
233C22×C4—1221no—
234C22×C4—1221no—
235C22×C4—2442no—
236C22×C4—2442no—
237M16—42no—
238M16—2441no—
239M16—2441no—
240M16—2441no—
241M16—2441no—
242M16—2442no—
243C2×C8—21no—
244C2×C8—611no—
245C2×C8—612no—
246C2×C8—612no—
247C2×C8—611no—
248C2×C8—1222no—
249C2×C8—1221no—
250C2×C8—2442no—
251C2×C8C22⋊#692311yescharacteristic
252C2×C8C22⋊#692311yescharacteristic
253C4⋊C4—611no—
254C4⋊C4—1221no—
255C4⋊C4D61⋊C811yescharacteristic
256C22⋊C4—21no—
257C22⋊C4—1221no—
258C22⋊C4—1221no—
259C22⋊C4—1221no—
260C42—611no—
261C42—611no—
262C42—611no—
263C42C22×#692311yescharacteristic
264C16—1224no—
265C16—2442no—
266C23—21no—
267C23—611no—
268C23—1221no—
269C23—2442no—
270C23—2442no—
271C23—2442no—
272D4—41no—
273D4—2441no—
274D4—2442no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—611no—
279C2×C4—611no—
280C2×C4—612no—
281C2×C4—612no—
282C2×C4—611no—
283C2×C4—1222no—
284C2×C4—1221no—
285C2×C4—2441no—
286C2×C4—2442no—
287C2×C4—2442no—
288C2×C4—2442no—
289C2×C4—2441no—
290C2×C4—2441no—
291C2×C4C2×C22⋊#692311yescharacteristic
292C2×C4C2×D61⋊C811yescharacteristic
293C2×C4D61⋊M1611yescharacteristic
294C8—21no—
295C8—41no—
296C8—611no—
297C8—611no—
298C8—1221no—
299C8—2441no—
300C8#1451983912yes—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—612no—
305C22—1221no—
306C22—1221no—
307C22—4884no—
308C22—2441no—
309C22—2441no—
310C22—2441no—
311C22D61⋊(C22⋊C8)11yescharacteristic
312C4—21no—
313C4—21no—
314C4—41no—
315C4—612no—
316C4—612no—
317C4—1221no—
318C4—2441no—
319C4C2×#1451983911yescharacteristic
320C4D61⋊#10411yescharacteristic
321C2—81no—
322C2—1222no—
323C2—4881no—
324C2D61⋊(D4⋊C8)11yescharacteristic
325C2D61⋊#34911yescharacteristic
326C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61C2×C22⋊C8
prime radicalC2×D4×D61C8
cosocleC4×#92418C23
hypercenter#436#6923
hypocenterC61#11587
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #21462152C2semidirect
2. #21462026C2semidirect
3. #21460772C2semidirect
4. #21460771C2semidirect
9. C4⋊#11758187C22semidirect
10. #16840650C22semidirect
186. C61#11587semidirect

Maximal subgroups

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

subgroupindex
#214621522
#214620262
#214607722
#214607712
#436×D612
#1158761