Finite Group Databasebeta

← #30604495

Subgroups — #30604495

Order 15616.

336 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 90 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#21462183C211yesmaximal, characteristic, complemented
2#21462020C211yesmaximal, characteristic, complemented
3#21460787C212yesmaximal, complemented
4#21460772C212yesmaximal, complemented
5#21454784C211yesmaximal, characteristic
6C2×D61⋊C16—21no—
7C4⋊#11758187C2212yes—
8#16840657—21no—
9#16840651—21no—
10#16840651—21no—
11#16840650C2212yes—
12C4×#11758226C411yescharacteristic
13#16839893C2211yescharacteristic
14#16839841C411yescharacteristic
15#16839839C2211yescharacteristic
16#16839835—21no—
17#16839832—21no—
18#16839814—21no—
19#16839814C411yescharacteristic
20#16839714—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#446C411yescharacteristic
23D61⋊C16—24no—
24C2×#11758187—22no—
25C2×#11758187—22no—
26C2×#11758226C811yescharacteristic
27C2×#11758189—21no—
28C2×#11758189—21no—
29C2×C8×D61D411yescharacteristic
30C2×C8×D61D411yescharacteristic
31Q8×Dic61C811yescharacteristic
32C4×D244—21no—
33C4×D244C2×C411yescharacteristic
34#14519739—21no—
35#14519739C811yescharacteristic
36#14519735—21no—
37#14519735C811yescharacteristic
38C42×D61—21no—
39C42×D61C2×C411yescharacteristic
40C4⋊#92418—21no—
41C4⋊#92418C2×C411yescharacteristic
42#14519689—21no—
43#14519689—21no—
44#14519689—21no—
45#14519688—21no—
46C4×#92418C2311yescharacteristic
47C8×Dic61—21no—
48C8×Dic61D411yescharacteristic
49C8×Dic61D411yescharacteristic
50C4×Q8×C61C2×C411yescharacteristic
51C4⋊C8×C61—21no—
52C4⋊C8×C61C2×C411yescharacteristic
53#97×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×Q8×C61C2×C811yescharacteristic
56#11758226—42no—
57C2×D244—21no—
58C2×D244C2×C811yescharacteristic
59C2×C4×D61—21no—
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61C22⋊C411yescharacteristic
63C2×C4×D61C2×C811yescharacteristic
64C2×C4×D61M1611yescharacteristic
65C2×C8×C61—21no—
66C2×C8×C61C22⋊C411yescharacteristic
67C2×C8×C61C22⋊C411yescharacteristic
68C4⋊C4×C61—21no—
69C4⋊C4×C61C2×C811yescharacteristic
70C42×C61—21no—
71C42×C61C22×C411yescharacteristic
72#11758198—21no—
73#11758198—21no—
74#11758198—21no—
75C4⋊Dic61—21no—
76C4⋊Dic61C2×C811yescharacteristic
77C4×Dic61—21no—
78C4×Dic61—21no—
79C4×Dic61C22⋊C411yescharacteristic
80C4×Dic61C2×C811yescharacteristic
81C4×Dic61M1611yescharacteristic
82C2×#92418—21no—
83C2×#92418C2×D411yescharacteristic
84C2×#92418C2×D411yescharacteristic
85#11758189—42no—
86#11758189—42no—
87C8×D61—22no—
88C8×D61—22no—
89#11758187—24no—
90#11758187—42no—
91C22×D61—21no—
92C22×D61C22⋊C811yescharacteristic
93Q8×C61—41no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61C2×C22⋊C411yescharacteristic
97C2×C4×C61C22×C811yescharacteristic
98C2×C4×C61C2×M1611yescharacteristic
99C2×Dic61—21no—
100C2×Dic61C22⋊C811yescharacteristic
101C2×Dic61C22⋊C811yescharacteristic
102C2×Dic61C22⋊C811yescharacteristic
103D244—41no—
104D244—42no—
105C4×D61—22no—
106C4×D61—21no—
107C4×D61—21no—
108C4×D61—41no—
109C4×D61—42no—
110C4×D61—42no—
111C4×D61—41no—
112C4×D61—41no—
113C8×C61—21no—
114C8×C61—41no—
115C8×C61#10412yes—
116#92418—21no—
117#92418—41no—
118#92418#13512yes—
119#11619—611nomaximal, Sylow
120C22×C61C2×C22⋊C811yescharacteristic
121C2×D61—21no—
122C2×D61—21no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—41no—
126C2×D61#34912yes—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—41no—
130C4×C61—41no—
131C4×C61#41611yescharacteristic
132C4×C61C2×#10411yescharacteristic
133Dic61—21no—
134Dic61—21no—
135Dic61—21no—
136Dic61—41no—
137#2965—611no—
138#2163—611no—
139C2×#346—611no—
140#1338—612no—
141#1330—612no—
142C2×C61#147611yescharacteristic
143C2×C61C2×#34911yescharacteristic
144C2×C61#211711yescharacteristic
145D61—22no—
146D61—81no—
147C4×#41—611no—
148C22×C16—1221no—
149#446—611no—
150#446#692311yescharacteristic
151#436—611no—
152#436—611no—
153#435—1221no—
154#435—1221no—
155#431—611no—
156#431—1221no—
157C4×M16—1221no—
158C2×C4×C8—611no—
159C4⋊C16—612no—
160C22⋊C16—1221no—
161#346—612no—
162#346—1221no—
163#346—1221no—
164C61#1161911yescharacteristic, complemented, Sylow
165C2×#41—611no—
166C2×M16—1221no—
167C2×M16—1221no—
168C22×C8—611no—
169C22×C8—611no—
170C4×Q8—611no—
171C4×Q8C2×#692311yescharacteristic
172C4×D4—611no—
173C4×D4—611no—
174C4×D4—1221no—
175C4×D4—1221no—
176#117—611no—
177#117—1221no—
178C2×C42—611no—
179C2×C42—1221no—
180C2×C16—1222no—
181C2×C16—1224no—
182C2×C16—1222no—
183C4⋊C8—21no—
184C4⋊C8—611no—
185C4⋊C8—1221no—
186C4⋊C8C2×#692311yescharacteristic
187C22⋊C8—1221no—
188C22⋊C8—1221no—
189C22⋊C8—1221no—
190#97—21no—
191#97—1221no—
192C4×C8—611no—
193C4×C8—611no—
194C4×C8—611no—
195C4×C8—1221no—
196C4×C8C2×#692311yescharacteristic
197#41—2442no—
198C2×Q8D61⋊C811yescharacteristic
199C2×D4—611no—
200C2×D4—1221no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—611no—
204C22×C4—1221no—
205C22×C4—1221no—
206C22×C4—1221no—
207M16—2442no—
208M16—2442no—
209C2×C8—21no—
210C2×C8—611no—
211C2×C8—611no—
212C2×C8—1222no—
213C2×C8—1222no—
214C2×C8—1221no—
215C2×C8C22⋊#692311yescharacteristic
216C2×C8C22⋊#692311yescharacteristic
217C4⋊C4—21no—
218C4⋊C4—611no—
219C4⋊C4—1221no—
220C4⋊C4D61⋊C811yescharacteristic
221C22⋊C4—1221no—
222C22⋊C4—1221no—
223C22⋊C4—1221no—
224C42—21no—
225C42—611no—
226C42—611no—
227C42—611no—
228C42—1221no—
229C42—1221no—
230C42C22×#692311yescharacteristic
231C16—1224no—
232C16—2442no—
233C23—611no—
234C23—1221no—
235Q8—41no—
236D4—2441no—
237D4—2442no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—1222no—
244C2×C4—1221no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—2441no—
248C2×C4—2442no—
249C2×C4—2442no—
250C2×C4—2441no—
251C2×C4—2441no—
252C2×C4C2×C22⋊#692311yescharacteristic
253C2×C4C2×D61⋊C811yescharacteristic
254C2×C4D61⋊M1611yescharacteristic
255C8—21no—
256C8—41no—
257C8—612no—
258C8—1221no—
259C8—2441no—
260C8#1451984212yes—
261C22—612no—
262C22—1221no—
263C22—1221no—
264C22—2441no—
265C22—2441no—
266C22—2441no—
267C22D61⋊(C22⋊C8)11yescharacteristic
268C4—21no—
269C4—21no—
270C4—41no—
271C4—41no—
272C4—1221no—
273C4—1221no—
274C4—1221no—
275C4—2441no—
276C4#1684075211yescharacteristic
277C4C2×#1451984211yescharacteristic
278C2—1222no—
279C2—4881no—
280C2#2146111311yescharacteristic
281C2D61⋊#34911yescharacteristic
282C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC61×#446C4
socleC22×C61C2×C22⋊C8
prime radicalC2×#11758226C8
cosocleC4×#92418C23
hypercenter#446#6923
hypocenterC61#11619
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #21462183C2semidirect
2. #21462020C2semidirect
3. #21460787C2semidirect
4. #21460772C2semidirect
164. C61#11619semidirect

Maximal subgroups

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

subgroupindex
#214621832
#214620202
#214607872
#214607722
#214547842
#1161961