Finite Group Databasebeta

← #30604069

Subgroups — #30604069

Order 15616.

292 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 88 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#21462181C211yesmaximal, characteristic
2#21462177C211yesmaximal, characteristic
3#21460758C212yesmaximal
4#21460757C212yesmaximal
5#21454751C211yesmaximal, characteristic
6#16840683—21no—
7#16840683—21no—
8C22⋊#11758187C2212yes—
9C22⋊#11758187C2212yes—
10#16840651—21no—
11#16840648—21no—
12#16840315C411yescharacteristic
13#16839890—21no—
14#16839890—21no—
15C8×Dic122—21no—
16C8×Dic122—21no—
17#16839790C2211yescharacteristic
18#16839789C2211yescharacteristic
19#16839785C411yescharacteristic
20#16839717C411yescharacteristic
21C2×C8×Dic61C2211yescharacteristic
22C61×#405C411yescharacteristic
23C2×#11758187—22no—
24C2×#11758187—22no—
25C2×#11758194C2×C411yescharacteristic
26C22×#92418C2311yescharacteristic
27#14519776C811yescharacteristic
28#14519776C811yescharacteristic
29#14519768C811yescharacteristic
30#14519768C811yescharacteristic
31#14519754—21no—
32#14519754—21no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35#14519736C2×C411yescharacteristic
36C2×C4×Dic61C2×C411yescharacteristic
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39#14519706—21no—
40#14519706—21no—
41#14519706—21no—
42#14519706—21no—
43#14519687—21no—
44C8×Dic61—21no—
45C8×Dic61D411yescharacteristic
46C8×Dic61D411yescharacteristic
47C8×Dic61D411yescharacteristic
48C8×Dic61D411yescharacteristic
49C2×M16×C61C2×C411yescharacteristic
50C22×C8×C61C2×C411yescharacteristic
51#117×C61C2×C411yescharacteristic
52#97×C61—21no—
53C4×C8×C61—21no—
54C22×C4×C61C22×C411yescharacteristic
55C22×Dic61M1611yescharacteristic
56C22×Dic61M1611yescharacteristic
57C2×Dic122—21no—
58C2×Dic122—21no—
59M16×C61—41no—
60C2×C8×C61—22no—
61C2×C8×C61—21no—
62C2×C8×C61C22⋊C411yescharacteristic
63C2×C8×C61C22⋊C411yescharacteristic
64C4⋊C4×C61C2×C811yescharacteristic
65C4⋊C4×C61C2×C811yescharacteristic
66C22⋊C4×C61—21no—
67C42×C61—21no—
68C22⋊Dic61—21no—
69C4⋊Dic61—21no—
70C4⋊Dic61—21no—
71C4⋊Dic61C2×C811yescharacteristic
72C4⋊Dic61C2×C811yescharacteristic
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76#11758196—21no—
77C4×Dic61—21no—
78C4×Dic61C22⋊C411yescharacteristic
79C4×Dic61C22⋊C411yescharacteristic
80C4×Dic61C2×C811yescharacteristic
81C4×Dic61C2×C811yescharacteristic
82#11758194—41no—
83C2×#92418—21no—
84C2×#92418—41no—
85C2×#92418C2×D411yescharacteristic
86C2×#92418C2×D411yescharacteristic
87#11758187—42no—
88#11758187—42no—
89C23×C61C2×M1611yescharacteristic
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61C2×C22⋊C411yescharacteristic
95C2×C4×C61C22×C811yescharacteristic
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—41no—
100C2×Dic61C22⋊C811yescharacteristic
101C2×Dic61C22⋊C811yescharacteristic
102C2×Dic61C22⋊C811yescharacteristic
103C2×Dic61C22⋊C811yescharacteristic
104Dic122—42no—
105Dic122—42no—
106C8×C61—21no—
107C8×C61—41no—
108C8×C61#10112yes—
109#92418—21no—
110#92418—21no—
111#92418—41no—
112#11498—611nomaximal, Sylow
113C22×C61—21no—
114C22×C61—21no—
115C22×C61—21no—
116C22×C61C2×C22⋊C811yescharacteristic
117C4×C61—21no—
118C4×C61—41no—
119C4×C61—41no—
120C4×C61#41011yescharacteristic
121C4×C61C2×#10111yescharacteristic
122Dic61—21no—
123Dic61—21no—
124Dic61—21no—
125Dic61—41no—
126Dic61—41no—
127Dic61#35012yes—
128#2960—611no—
129#2163—611no—
130#2162—611no—
131#1323—612no—
132#1323—612no—
133C2×C61—41no—
134C2×C61#146111yescharacteristic
135C2×C61C2×#35011yescharacteristic
136C2×C61#211711yescharacteristic
137#533—611no—
138#446—1221no—
139#446—1221no—
140C8×Q8—1221no—
141C8×Q8—1221no—
142#424—611no—
143#424—611no—
144#423—611no—
145#405—611no—
146#405#692311yescharacteristic
147C2×C4×C8—611no—
148C4⋊C16—1221no—
149C4⋊C16—1221no—
150C22⋊C16—612no—
151C22⋊C16—612no—
152#346—1221no—
153C4×C16—1221no—
154C61#1149811yescharacteristic, complemented, Sylow
155C2×M16—611no—
156C2×M16C2×#692311yescharacteristic
157C22×C8—611no—
158C22×C8C2×#692311yescharacteristic
159C4⋊Q8—611no—
160C4⋊Q8—611no—
161#125—611no—
162#125—611no—
163C22⋊Q8—1221no—
164C22⋊Q8—1221no—
165C4×Q8—1221no—
166C4×Q8—1221no—
167#117—611no—
168#117C2×#692311yescharacteristic
169C2×C42—611no—
170C2×C16—1222no—
171C2×C16—1222no—
172C4⋊C8—1221no—
173C4⋊C8—1221no—
174C4⋊C8—1221no—
175C4⋊C8—1221no—
176C4⋊C8—1221no—
177C4⋊C8—1221no—
178#97—21no—
179#97—1221no—
180C4×C8—21no—
181C4×C8—611no—
182C4×C8—611no—
183C4×C8—611no—
184C4×C8—611no—
185C4×C8—1221no—
186C2×Q8—1221no—
187C2×Q8—1221no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4C22×#692311yescharacteristic
191M16—41no—
192M16—2441no—
193C2×C8—22no—
194C2×C8—21no—
195C2×C8—611no—
196C2×C8—611no—
197C2×C8—1221no—
198C2×C8—2441no—
199C2×C8C22⋊#692311yescharacteristic
200C2×C8C22⋊#692311yescharacteristic
201C4⋊C4—611no—
202C4⋊C4—611no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4D61⋊C811yescharacteristic
210C4⋊C4D61⋊C811yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—1221no—
213C42—21no—
214C42—611no—
215C42—611no—
216C42—611no—
217C42—611no—
218C42—1221no—
219C16—2442no—
220C16—2442no—
221C23D61⋊M1611yescharacteristic
222Q8—2442no—
223Q8—2442no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—611no—
229C2×C4—611no—
230C2×C4—611no—
231C2×C4—611no—
232C2×C4—1222no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—2441no—
236C2×C4C2×C22⋊#692311yescharacteristic
237C2×C4C2×D61⋊C811yescharacteristic
238C8—21no—
239C8—41no—
240C8—1221no—
241C8—1221no—
242C8—2441no—
243C8#1451983812yes—
244C22—21no—
245C22—21no—
246C22—21no—
247C22D61⋊(C22⋊C8)11yescharacteristic
248C4—21no—
249C4—41no—
250C4—41no—
251C4—612no—
252C4—1221no—
253C4—1221no—
254C4—1221no—
255C4—2441no—
256C4—2441no—
257C4#1684074111yescharacteristic
258C4C2×#1451983811yescharacteristic
259C2—41no—
260C2#2146106111yescharacteristic
261C2D61⋊#35011yescharacteristic
262C2#2146206211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#405C4
socleC22×C61C2×C22⋊C8
prime radicalC23×C61C2×M16
cosocleC22×#92418C23
hypercenter#405#6923
hypocenterC61#11498
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
154. C61#11498semidirect

Maximal subgroups

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

subgroupindex
#214621812
#214621772
#214607582
#214607572
#214547512
#1149861