Finite Group Databasebeta

← #29669339

Subgroups — #29669339

Order 15616.

736 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 151 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#21456563C213yesmaximal, complemented
2#21456190C213yesmaximal
3#21445480C213yesmaximal, complemented
4#21445476C213yesmaximal, complemented
5#21445431C211yesmaximal, characteristic, complemented
6#21444121C211yesmaximal, characteristic, complemented
7C61×#1711C211yesmaximal, characteristic, complemented
8#16840317C2213yes—
9#127×D61C2211yescharacteristic
10#16840158C2213yescomplemented
11#16840141C2213yescomplemented
12#16840125—26no—
13#16840113C2213yescomplemented
14#16840110C2213yes—
15#16840109C2213yes—
16#16840108C2213yes—
17#16840019—26no—
18#16839866—26no—
19#16839765—26no—
20C4×#11758189C2213yes—
21#16839483C2213yescomplemented
22C61×#487C2213yescomplemented
23C61×#486C2213yes—
24C82×C61C2211yescharacteristic, complemented
25C2×D4×D61—23no—
26C2×#11758202—26no—
27C2×#11758189D416yes—
28#14519777C2313yes—
29#14519774C2311yescharacteristic
30#14519773—23no—
31#14519768—23no—
32#14519757—23no—
33#14519753—23no—
34Q8×Dic61—23no—
35#14519742—23no—
36#14519735—23no—
37C42×D61C2311yescharacteristic
38#14519708—26no—
39#14519702—26no—
40#14519699—26no—
41#14519698—26no—
42#14519697—26no—
43#14519687D416yes—
44C4×#92418C2313yes—
45C4⋊Q8×C61C2313yes—
46#127×C61C2311yescharacteristic
47#103×C61—26no—
48#102×C61—26no—
49C4×C8×C61C2313yes—
50C23×D61—41no—
51C2×Q8×C61—23no—
52C2×D4×C61—23no—
53C2×C22⋊D61—43no—
54D4×D61—412no—
55C2×D244—23no—
56C2×C4×D61C2×D413yes—
57C2×Dic122—23no—
58C2×C8×C61C2×D416yes—
59C4⋊C4×C61—23no—
60C4⋊C4×C61—23no—
61C42×C61C2411yescharacteristic
62#11758202—412no—
63#11758198—43no—
64C4⋊Dic61—23no—
65C4⋊Dic61—23no—
66C4⋊Dic61—43no—
67#11758196—43no—
68C4×Dic61—43no—
69C4×Dic61C2×D413yes—
70C2×#92418C2×D416yes—
71#11758189—46no—
72C23×C61—41no—
73C22×D61—41no—
74C22×D61—86no—
75C22×D61#12711yescharacteristic
76Q8×C61—46no—
77D4×C61—46no—
78C2×C4×C61—43no—
79C2×C4×C61C22×D413yes—
80C22⋊D61—86no—
81C2×Dic61—43no—
82C2×Dic61#12713yes—
83D244—46no—
84C4×D61—26no—
85Dic122—46no—
86C8×C61—26no—
87#92418—26no—
88#19753—611nomaximal, Sylow
89C22×C61—83no—
90C22×C61C2×#12711yescharacteristic
91C2×D61—23no—
92C2×D61—83no—
93C2×D61—164no—
94C4×C61—83no—
95C4×C61#57516yes—
96Dic61—23no—
97Dic61—83no—
98#3185—613no—
99#3138—613no—
100#1720—613no—
101#1720—613no—
102#1711—611no—
103#1711D6111yescharacteristic, complemented
104#1455—611no—
105C2×C61—161no—
106C2×C61#315313yes—
107D61—41no—
108D61—161no—
109#533—613no—
110C2×#127—611no—
111#498—613no—
112#494—613no—
113#490—1226no—
114#487—613no—
115#487C2×D6113yescomplemented
116#486—613no—
117#486—613no—
118#486—613no—
119#486C2×D6113yes—
120#470—1226no—
121#441—1226no—
122#418—1226no—
123C4×M16—613no—
124#322—613no—
125C82C2×D6111yescharacteristic, complemented
126C61#1975311yescharacteristic, complemented, Sylow
127C22×D4—1223no—
128C2×Q16—1226no—
129C2×M16—616no—
130C4⋊Q8—613no—
131C4⋊Q8C22×D6113yes—
132#127—611no—
133#127—1223no—
134#127C22×D6111yescharacteristic
135#125—1223no—
136C22⋊Q8—1223no—
137C22⋊Q8—1223no—
138C4×Q8—1223no—
139C4×Q8—1223no—
140#117—1223no—
141C2×C42—611no—
142#106—1226no—
143#103—26no—
144#103—1226no—
145#102—26no—
146#102—1226no—
147#102—1226no—
148#102—1226no—
149#97—616no—
150C4×C8—613no—
151C4×C8C22×D6113yes—
152C24—2441no—
153C2×Q8—23no—
154C2×Q8—1223no—
155C2×D4—23no—
156C2×D4—1223no—
157C2×D4—2443no—
158C2×D4—24412no—
159C22×C4—613no—
160Q16—24412no—
161M16—2446no—
162C2×C8—616no—
163C2×C8D4×D6116yes—
164C4⋊C4—23no—
165C4⋊C4—23no—
166C4⋊C4—1223no—
167C4⋊C4—1223no—
168C4⋊C4—2443no—
169C4⋊C4—2443no—
170C22⋊C4—2443no—
171C42—613no—
172C42—2443no—
173C42C23×D6111yescharacteristic
174C23—41no—
175C23—611no—
176C23—4886no—
177C23—2441no—
178Q8—46no—
179Q8—2446no—
180D4—46no—
181D4—4886no—
182D4—2446no—
183C2×C4—43no—
184C2×C4—613no—
185C2×C4—1226no—
186C2×C4—2443no—
187C2×C4C2×D4×D6113yes—
188C8—26no—
189C8—1226no—
190C22—83no—
191C22—1223no—
192C22—9764no—
193C22—4883no—
194C22#127×D6111yescharacteristic
195C4—83no—
196C4—1223no—
197C4—4883no—
198C4#1684055916yes—
199C2—161no—
200C2—9761no—
201C2—2441no—
202C2#2145628013yes—
subgroupG/H
centerC22#127×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1711C2
socleC22×C61C2×#127
prime radical#127×D61C22
hypercenter#1711D61
hypocenterC61#19753
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1711

Complements

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

NH ≅ G/Ntype
1. #21456563C2semidirect
3. #21445480C2semidirect
4. #21445476C2semidirect
5. #21445431C2semidirect
6. #21444121C2semidirect
7. C61×#1711C2semidirect
10. #16840158C22semidirect
11. #16840141C22semidirect
13. #16840113C22semidirect
21. #16839483C22semidirect
22. C61×#487C22semidirect
24. C82×C61C22semidirect
103. #1711D61semidirect
115. #487C2×D61semidirect
125. C82C2×D61semidirect
126. C61#19753semidirect

Maximal subgroups

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

subgroupindex
#214565632
#214561902
#214454802
#214454762
#214454312
#214441212
C61×#17112
#1975361