Finite Group Databasebeta

← #29589364

Subgroups — #29589364

Order 15616.

292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 89 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#21454752C211yesmaximal, characteristic
2#21447619C211yesmaximal, characteristic
3#21447615C211yesmaximal, characteristic
4#21443761C211yesmaximal, characteristic
5#21443760C211yesmaximal, characteristic
6#21443760C211yesmaximal, characteristic
7C61×#1323C211yesmaximal, characteristic
8#16840315C411yescharacteristic
9#16839891—21no—
10#16839891—21no—
11#16839886—21no—
12#16839886—21no—
13#16839788C2211yescharacteristic
14#16839785C411yescharacteristic
15#16839720C411yescharacteristic
16#16839718C411yescharacteristic
17C2×C8×Dic61C2211yescharacteristic
18#16839580—21no—
19#16839580—21no—
20C22⋊#11758185C2211yescharacteristic
21C22⋊#11758185C2211yescharacteristic
22#16839537—21no—
23C16×Dic61—21no—
24C61×#424C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×C22⋊C16C2211yescharacteristic
27C2×#11758194C2×C411yescharacteristic
28C22×#92418C2×C411yescharacteristic
29#14519776C811yescharacteristic
30#14519776C811yescharacteristic
31#14519768C811yescharacteristic
32#14519768C811yescharacteristic
33#14519754—21no—
34#14519754—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37#14519736C2×C411yescharacteristic
38C2×C4×Dic61C2×C411yescharacteristic
39C2×#11758185—21no—
40C2×#11758185—21no—
41#14519706—21no—
42#14519706—21no—
43#14519706—21no—
44#14519706—21no—
45#14519688—21no—
46#14519687—21no—
47C4×#92418—21no—
48C8×Dic61—21no—
49C8×Dic61D411yescharacteristic
50C8×Dic61D411yescharacteristic
51C8×Dic61D411yescharacteristic
52C8×Dic61D411yescharacteristic
53C2×M16×C61C2×C411yescharacteristic
54C22×C8×C61C2311yescharacteristic
55#117×C61C2×C411yescharacteristic
56C2×C16×C61—21no—
57C2×C16×C61—21no—
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61M1611yescharacteristic
62C22×Dic61M1611yescharacteristic
63C2×Dic122—21no—
64C2×Dic122—21no—
65M16×C61—41no—
66C2×C8×C61—21no—
67C2×C8×C61—41no—
68C2×C8×C61C2×D411yescharacteristic
69C2×C8×C61C2×D411yescharacteristic
70C4⋊C4×C61C2×C811yescharacteristic
71C4⋊C4×C61C2×C811yescharacteristic
72C22⋊C4×C61—21no—
73C42×C61—21no—
74C22⋊Dic61—21no—
75C4⋊Dic61—21no—
76C4⋊Dic61—21no—
77C4⋊Dic61C2×C811yescharacteristic
78C4⋊Dic61C2×C811yescharacteristic
79#11758196—21no—
80#11758196—21no—
81#11758196—21no—
82#11758196—21no—
83C4×Dic61—21no—
84C4×Dic61C22⋊C411yescharacteristic
85C4×Dic61C22⋊C411yescharacteristic
86C4×Dic61C2×C811yescharacteristic
87C4×Dic61C2×C811yescharacteristic
88#11758194—41no—
89C2×#92418—22no—
90C2×#92418—21no—
91C2×#92418C22⋊C411yescharacteristic
92C2×#92418C22⋊C411yescharacteristic
93C16×C61—41no—
94C16×C61—41no—
95#11758185—41no—
96#11758185—41no—
97C23×C61C2×M1611yescharacteristic
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61C2×C22⋊C411yescharacteristic
103C2×C4×C61C22×C811yescharacteristic
104C2×Dic61—22no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—41no—
108C2×Dic61C22⋊C811yescharacteristic
109C2×Dic61C22⋊C811yescharacteristic
110C2×Dic61C22⋊C811yescharacteristic
111C2×Dic61C22⋊C811yescharacteristic
112Dic122—42no—
113Dic122—42no—
114C8×C61—21no—
115C8×C61—21no—
116C8×C61—41no—
117#92418—21no—
118#92418—41no—
119#92418#10112yes—
120#11498—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—21no—
124C22×C61C2×C22⋊C811yescharacteristic
125C4×C61—21no—
126C4×C61—41no—
127C4×C61—41no—
128C4×C61#41011yescharacteristic
129C4×C61C2×#10111yescharacteristic
130Dic61—21no—
131Dic61—21no—
132Dic61—21no—
133Dic61—41no—
134Dic61—41no—
135Dic61#35012yes—
136#2960—611no—
137#2163—611no—
138#2162—611no—
139#1323—611no—
140#1323—611no—
141#1323—611no—
142#1323D6111yescharacteristic
143C2×C61—41no—
144C2×C61#146111yescharacteristic
145C2×C61C2×#35011yescharacteristic
146C2×C61#211711yescharacteristic
147#533—611no—
148#446—1221no—
149#446—1221no—
150C8×Q8—1221no—
151C8×Q8—1221no—
152#424—611no—
153#424C2×D6111yescharacteristic
154#423—611no—
155#405—611no—
156#405—611no—
157C2×C4×C8—611no—
158C4⋊C16—1221no—
159C4⋊C16—1221no—
160C22⋊C16—611no—
161C22⋊C16—611no—
162C22⋊C16C2×D6111yescharacteristic
163C22⋊C16C2×D6111yescharacteristic
164#346—1221no—
165C4×C16—1221no—
166C61#1149811yescharacteristic, complemented, Sylow
167C2×M16—611no—
168C2×M16C4×D6111yescharacteristic
169C22×C8—611no—
170C22×C8C22×D6111yescharacteristic
171C4⋊Q8—611no—
172C4⋊Q8—611no—
173#125—611no—
174#125—611no—
175C22⋊Q8—1221no—
176C22⋊Q8—1221no—
177C4×Q8—1221no—
178C4×Q8—1221no—
179#117—611no—
180#117C4×D6111yescharacteristic
181C2×C42—611no—
182C2×C16—21no—
183C2×C16—21no—
184C2×C16—1221no—
185C2×C16—1221no—
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—1221no—
189C4⋊C8—1221no—
190C4⋊C8—1221no—
191C4⋊C8—1221no—
192#97—1221no—
193#97—1221no—
194C4×C8—611no—
195C4×C8—611no—
196C4×C8—611no—
197C4×C8—611no—
198C4×C8—1221no—
199C4×C8—1221no—
200C2×Q8—1221no—
201C2×Q8—1221no—
202C22×C4—611no—
203C22×C4—611no—
204C22×C4C2×C4×D6111yescharacteristic
205M16—41no—
206M16—2441no—
207C2×C8—21no—
208C2×C8—41no—
209C2×C8—611no—
210C2×C8—611no—
211C2×C8—1222no—
212C2×C8—1221no—
213C2×C8D4×D6111yescharacteristic
214C2×C8D4×D6111yescharacteristic
215C4⋊C4—611no—
216C4⋊C4—611no—
217C4⋊C4—1221no—
218C4⋊C4—1221no—
219C4⋊C4—1221no—
220C4⋊C4—1221no—
221C4⋊C4—1221no—
222C4⋊C4—1221no—
223C4⋊C4C8×D6111yescharacteristic
224C4⋊C4C8×D6111yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—1221no—
227C42—21no—
228C42—611no—
229C42—611no—
230C42—611no—
231C42—611no—
232C42—1221no—
233C16—41no—
234C16—41no—
235C16—2441no—
236C16—2441no—
237C23M16×D6111yescharacteristic
238Q8—2442no—
239Q8—2442no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—611no—
247C2×C4—611no—
248C2×C4—1222no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—2441no—
252C2×C4C22⋊C4×D6111yescharacteristic
253C2×C4C2×C8×D6111yescharacteristic
254C8—21no—
255C8—21no—
256C8—41no—
257C8—612no—
258C8—1221no—
259C8—2441no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22C22⋊C8×D6111yescharacteristic
264C4—21no—
265C4—41no—
266C4—41no—
267C4—612no—
268C4—1221no—
269C4—1221no—
270C4—1221no—
271C4—2441no—
272C4—2441no—
273C4#1683973411yescharacteristic
274C4#101×D6111yescharacteristic
275C2—41no—
276C2#2144414111yescharacteristic
277C2#350×D6111yescharacteristic
278C2#2144744511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#1323C2
socleC22×C61C2×C22⋊C8
prime radicalC23×C61C2×M16
cosocleC22×C8×C61C23
hypercenter#1323D61
hypocenterC61#11498
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
166. C61#11498semidirect

Maximal subgroups

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

subgroupindex
#214547522
#214476192
#214476152
#214437612
#214437602
C61×#13232
#1149861