Finite Group Databasebeta

← #30604507

Subgroups — #30604507

Order 15616.

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

normal subgroups only

This group has 320 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#21462178C211yesmaximal, characteristic, complemented
2D61⋊(C4⋊C16)C211yesmaximal, characteristic, complemented
3Q8⋊#11758187C212yesmaximal, complemented
4#21460770C212yesmaximal, complemented
5#21454793C211yesmaximal, characteristic
6C2×D61⋊C16—21no—
7#16840683—21no—
8#16840683—21no—
9C4⋊#11758187C2212yes—
10#16840657—21no—
11C4×#11758187C2212yes—
12#16840299C411yescharacteristic
13Q8×#92418C2211yescharacteristic
14#16839841C411yescharacteristic
15#16839835—21no—
16#16839827—21no—
17#16839827C2211yescharacteristic
18#16839822—21no—
19#16839818C411yescharacteristic
20#16839719—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#446C411yescharacteristic
23D61⋊C16—42no—
24C2×#11758187—22no—
25C2×#11758187—22no—
26C2×#11758189—21no—
27C2×C8×D61—21no—
28C2×C8×D61D411yescharacteristic
29C2×C8×D61D411yescharacteristic
30#14519772—21no—
31#14519768C811yescharacteristic
32#14519766C811yescharacteristic
33#14519762—21no—
34#14519753C811yescharacteristic
35#14519752C811yescharacteristic
36C4×D244—21no—
37C4×D244C2×C411yescharacteristic
38#14519734—21no—
39C42×D61C2×C411yescharacteristic
40C4⋊#92418—21no—
41C4⋊#92418C2×C411yescharacteristic
42#14519689—21no—
43#14519689—21no—
44#14519689—21no—
45#14519687—21no—
46C4×#92418—21no—
47C4×#92418C2311yescharacteristic
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
56C2×D244—21no—
57C2×D244C2×C811yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61C22⋊C411yescharacteristic
60C2×C4×D61C2×C811yescharacteristic
61C2×C4×D61M1611yescharacteristic
62C2×C8×C61—21no—
63C2×C8×C61C22⋊C411yescharacteristic
64C2×C8×C61C22⋊C411yescharacteristic
65C4⋊C4×C61—21no—
66C4⋊C4×C61C2×C811yescharacteristic
67C42×C61—21no—
68C42×C61C22×C411yescharacteristic
69#11758198—21no—
70#11758198—21no—
71#11758198—21no—
72#11758198—21no—
73#11758198—21no—
74C4⋊Dic61—21no—
75C4⋊Dic61C2×C811yescharacteristic
76#11758196—21no—
77#11758196—21no—
78C4×Dic61C22⋊C411yescharacteristic
79C4×Dic61C2×C811yescharacteristic
80C4×Dic61M1611yescharacteristic
81C2×#92418—21no—
82C2×#92418C2×D411yescharacteristic
83C2×#92418C2×D411yescharacteristic
84#11758189—42no—
85C8×D61—21no—
86C8×D61—21no—
87C8×D61—41no—
88C8×D61—41no—
89C8×D61—41no—
90#11758187—42no—
91#11758187—42no—
92C22×D61—21no—
93C22×D61C22⋊C811yescharacteristic
94Q8×C61—22no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61C2×C22⋊C411yescharacteristic
98C2×C4×C61C22×C811yescharacteristic
99C2×C4×C61C2×M1611yescharacteristic
100C2×Dic61—21no—
101C2×Dic61C22⋊C811yescharacteristic
102C2×Dic61C22⋊C811yescharacteristic
103C2×Dic61C22⋊C811yescharacteristic
104D244—22no—
105D244—42no—
106C4×D61—22no—
107C4×D61—21no—
108C4×D61—21no—
109C4×D61—22no—
110C4×D61—41no—
111C4×D61—41no—
112C8×C61—21no—
113C8×C61—21no—
114C8×C61—41no—
115#92418—21no—
116#92418—41no—
117#92418AGL(1,ℤ/8)11yescharacteristic
118#92418#13711yescharacteristic
119#11622—611nomaximal, Sylow
120C22×C61C2×C22⋊C811yescharacteristic
121C2×D61—21no—
122C2×D61—21no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—41no—
126C2×D61#35012yes—
127C4×C61—21no—
128C4×C61—41no—
129C4×C61—41no—
130C4×C61#41711yescharacteristic
131C4×C61#42111yescharacteristic
132C4×C61#50412yes—
133Dic61—21no—
134Dic61—21no—
135Dic61—21no—
136Dic61—41no—
137#2966—611no—
138#2162—611no—
139C2×C4⋊C16—611no—
140Q8⋊C16—612no—
141D4⋊C16—612no—
142C2×C61#147711yescharacteristic
143C2×C61#211311yescharacteristic
144C2×C61C2×#35011yescharacteristic
145D61—22no—
146D61—81no—
147#529—611no—
148C22×C16—1221no—
149#446#692311yescharacteristic
150C8×Q8—611no—
151#436—611no—
152#435—1221no—
153C8×D4—611no—
154C8×D4—1221no—
155#433—1221no—
156#432—611no—
157#405—1221no—
158C2×C4×C8—611no—
159C4⋊C16—612no—
160C4⋊C16—1221no—
161C4⋊C16—1221no—
162C22⋊C16—1221no—
163C4×C16—612no—
164C61#1162211yescharacteristic, complemented, Sylow
165C2×M16—1221no—
166C22×C8—611no—
167C22×C8—611no—
168C22×C8—1221no—
169#126—1221no—
170#125—611no—
171#124—611no—
172#123—1221no—
173C22⋊Q8—611no—
174#121—611no—
175C4×Q8C2×#692311yescharacteristic
176C4×D4—611no—
177C4×D4—1221no—
178#117—1221no—
179C2×C42—611no—
180C2×C16—1222no—
181C2×C16—1222no—
182C2×C16—2442no—
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
197C2×Q8D61⋊C811yescharacteristic
198C2×D4—611no—
199C2×D4—1221no—
200C22×C4—611no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—1221no—
204M16—2442no—
205C2×C8—21no—
206C2×C8—611no—
207C2×C8—611no—
208C2×C8—1221no—
209C2×C8—1221no—
210C2×C8—1221no—
211C2×C8—2441no—
212C2×C8—2441no—
213C2×C8—2441no—
214C2×C8C22⋊#692311yescharacteristic
215C2×C8C22⋊#692311yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—611no—
218C4⋊C4—1221no—
219C4⋊C4—1221no—
220C4⋊C4—1221no—
221C4⋊C4D61⋊C811yescharacteristic
222C22⋊C4—1221no—
223C22⋊C4—1221no—
224C22⋊C4—1221no—
225C22⋊C4—1221no—
226C22⋊C4—1221no—
227C42—21no—
228C42—611no—
229C42—611no—
230C42—611no—
231C42C22×#692311yescharacteristic
232C16—2442no—
233C16—2442no—
234C23—611no—
235C23—1221no—
236Q8—22no—
237D4—1222no—
238D4—2442no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—1222no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1222no—
248C2×C4—1221no—
249C2×C4—2441no—
250C2×C4—2441no—
251C2×C4C2×C22⋊#692311yescharacteristic
252C2×C4C2×D61⋊C811yescharacteristic
253C2×C4D61⋊M1611yescharacteristic
254C8—21no—
255C8—21no—
256C8—41no—
257C8—611no—
258C8—611no—
259C8—1221no—
260C8—2441no—
261C22—612no—
262C22—1221no—
263C22—1221no—
264C22—2441no—
265C22—2441no—
266C22—2441no—
267C22D61⋊(C22⋊C8)11yescharacteristic
268C4—21no—
269C4—41no—
270C4—41no—
271C4—1221no—
272C4—1221no—
273C4—1221no—
274C4—2441no—
275C4#1684075311yescharacteristic
276C4#1684076111yescharacteristic
277C4#1684082112yes—
278C2—1222no—
279C2—4881no—
280C2#2146111711yescharacteristic
281C2#2146205011yescharacteristic
282C2D61⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC61×#446C4
socleC22×C61C2×C22⋊C8
prime radical#14519752C8
cosocleC4×#92418C23
hypercenter#446#6923
hypocenterC61#11622
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #21462178C2semidirect
2. D61⋊(C4⋊C16)C2semidirect
3. Q8⋊#11758187C2semidirect
4. #21460770C2semidirect
164. C61#11622semidirect

Maximal subgroups

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

subgroupindex
#214621782
D61⋊(C4⋊C16)2
Q8⋊#117581872
#214607702
#214547932
#1162261