Finite Group Databasebeta

← D61×#1705 #29667648

Subgroups — D61×#1705 #29667648

Order 15616.

994 conjugacy classes of subgroups; only the 239 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 239 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#498×D61C213yesmaximal, complemented
2#492×D61C213yesmaximal
3#21445407C213yesmaximal, complemented
4#21445406C211yesmaximal, characteristic, complemented
5#21445405C213yesmaximal, complemented
6C82×D61C211yesmaximal, characteristic, complemented
7C61×#1705C211yesmaximal, characteristic, complemented
8C2×SD16×D61—26no—
9C4⋊Q8×D61C2213yes—
10#127×D61C2211yescharacteristic
11#16840160C2213yescomplemented
12#16840159—26no—
13#16840158C2216yescomplemented
14#16840136C2213yes—
15#16840135C2213yes—
16#16840134C2213yes—
17#16840133—26no—
18#106×D61—26no—
19C4×C8×D61C2213yes—
20C8×#92418C2213yescomplemented
21C61×#498C2213yescomplemented
22C61×#492C2213yes—
23C82×C61C2211yescharacteristic, complemented
24C2×Q8×D61—23no—
25C2×D4×D61—23no—
26C2×#11758190—26no—
27C2×#11758200—26no—
28C2×#11758201—26no—
29SD16×D61—424no—
30C2×C8×D61D416yes—
31#14519777C2313yes—
32#14519776—26no—
33#14519775—23no—
34#14519774C2311yescharacteristic
35#14519773—23no—
36C4⋊C4×D61—26no—
37C42×D61C2311yescharacteristic
38#14519709—26no—
39#14519708—212no—
40C4×#92418C2313yes—
41C8×Dic61D416yes—
42C2×SD16×C61—26no—
43C4⋊Q8×C61C2313yes—
44#127×C61C2311yescharacteristic
45#106×C61—26no—
46C4×C8×C61C2313yes—
47C23×D61—41no—
48C2×Q8×C61—23no—
49C2×D4×C61—23no—
50C2×C22⋊D61—43no—
51Q8×D61—412no—
52D4×D61—412no—
53C2×D244—23no—
54C2×C4×D61—43no—
55C2×C4×D61C2×D413yes—
56C2×Dic122—23no—
57C2×Dic122—43no—
58SD16×C61—412no—
59C2×C8×C61C2×D416yes—
60C4⋊C4×C61—26no—
61C42×C61C2411yescharacteristic
62#11758201—412no—
63#11758200—412no—
64C4⋊Dic61—26no—
65#11758196—46no—
66C4×Dic61C2×D413yes—
67C2×#92418C2×D416yes—
68#11758190—412no—
69C8×D61SD16124yescomplemented
70C23×C61—41no—
71C22×D61—41no—
72C22×D61—86no—
73C22×D61#12711yescharacteristic
74Q8×C61—46no—
75D4×C61—46no—
76C2×C4×C61—43no—
77C2×C4×C61C22×D413yes—
78C22⋊D61—86no—
79C2×Dic61—43no—
80C2×Dic61#12713yes—
81D244—46no—
82C4×D61—86no—
83C4×D61C2×SD16112yes—
84Dic122—46no—
85Dic122—86no—
86C8×C61C2×SD16112yescomplemented
87#92418C2×SD16112yescomplemented
88C2×#1705—611nomaximal, Sylow
89C22×C61—83no—
90C22×C61C2×#12711yescharacteristic
91C2×D61—83no—
92C2×D61—164no—
93C2×D61#49216yes—
94C4×C61—83no—
95C4×C61C22×SD1616yes—
96Dic61—83no—
97Dic61#49216yes—
98C2×#498—613no—
99C2×#492—613no—
100#1705—613no—
101#1705—613no—
102#1705—611no—
103#1705D6111yescharacteristic, direct product factor
104C2×C82—611no—
105C2×C61—161no—
106C2×C61C2×#49213yes—
107D61—161no—
108D61#170514yesdirect product factor
109C22×SD16—1226no—
110C2×C4⋊Q8—613no—
111C2×#127—611no—
112#498—616no—
113#498—613no—
114#498—1226no—
115#498C2×D6113yescomplemented
116#492—613no—
117#492—613no—
118#492—613no—
119#492—1226no—
120#492C2×D6113yes—
121C2×#106—1226no—
122C2×C4×C8—613no—
123C82—613no—
124C82C2×D6111yescharacteristic, complemented
125C61C2×#170511yescharacteristic, complemented, Sylow
126C22×Q8—1223no—
127C22×D4—1223no—
128C2×SD16—26no—
129C2×SD16—1226no—
130C2×SD16—1226no—
131C2×SD16—1226no—
132C2×SD16—24424no—
133C22×C8—616no—
134C4⋊Q8—613no—
135C4⋊Q8—1226no—
136C4⋊Q8—1223no—
137C4⋊Q8C22×D6113yes—
138#127—611no—
139#127—1223no—
140#127C22×D6111yescharacteristic
141C2×C4⋊C4—1226no—
142C2×C42—611no—
143#106—26no—
144#106—12212no—
145#106—1226no—
146C4×C8—616no—
147C4×C8—613no—
148C4×C8C22×D6113yes—
149C24—2441no—
150C2×Q8—23no—
151C2×Q8—1223no—
152C2×Q8—2443no—
153C2×Q8—24412no—
154C2×D4—23no—
155C2×D4—1223no—
156C2×D4—24412no—
157C2×D4—2443no—
158C22×C4—613no—
159C22×C4—2443no—
160SD16—412no—
161SD16—24412no—
162SD16—24412no—
163SD16—24412no—
164C2×C8—616no—
165C2×C8—6124no—
166C2×C8D4×D6116yes—
167C4⋊C4—26no—
168C4⋊C4—1226no—
169C4⋊C4—2446no—
170C42—613no—
171C42C23×D6111yescharacteristic
172C23—41no—
173C23—611no—
174C23—4886no—
175C23—2441no—
176Q8—46no—
177Q8—4886no—
178Q8—2446no—
179D4—46no—
180D4—4886no—
181D4—2446no—
182C2×C4—43no—
183C2×C4—613no—
184C2×C4—6112no—
185C2×C4—4886no—
186C2×C4—2443no—
187C2×C4C2×D4×D6113yes—
188C8—6112no—
189C8SD16×D61112yescomplemented
190C22—83no—
191C22—616no—
192C22—9764no—
193C22—4883no—
194C22#127×D6111yescharacteristic
195C4—83no—
196C4—616no—
197C4—4883no—
198C4C2×SD16×D6116yes—
199C2—161no—
200C2—614no—
201C2—9761no—
202C2#492×D6113yes—
subgroupG/H
centerC22#127×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1705C2
socleC22×C61C2×#127
prime radical#127×D61C22
hypercenter#1705D61
hypocenterC61C2×#1705
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1705

Complements

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

NH ≅ G/Ntype
1. #498×D61C2semidirect
3. #21445407C2semidirect
4. #21445406C2semidirect
5. #21445405C2semidirect
6. C82×D61C2semidirect
7. C61×#1705C2semidirect
11. #16840160C22semidirect
13. #16840158C22semidirect
20. C8×#92418C22semidirect
21. C61×#498C22semidirect
23. C82×C61C22semidirect
69. C8×D61SD16semidirect
86. C8×C61C2×SD16semidirect
87. #92418C2×SD16semidirect
103. #1705D61direct (N × H)
108. D61#1705direct (N × H)
115. #498C2×D61semidirect
124. C82C2×D61semidirect
125. C61C2×#1705semidirect
189. C8SD16×D61semidirect

Maximal subgroups

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

subgroupindex
#498×D612
#492×D612
#214454072
#214454062
#214454052
C82×D612
C61×#17052
C2×#170561