Finite Group Databasebeta

← #16840508

Subgroups — #16840508

Order 3904.

220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 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#14519767C211yesmaximal, characteristic, complemented
2#14519766C211yesmaximal, characteristic, complemented
3#14519763C211yesmaximal, characteristic, complemented
4#14519762C211yesmaximal, characteristic, complemented
5#14519762C211yesmaximal, characteristic, complemented
6#14519760C211yesmaximal, characteristic, complemented
7#14519759C211yesmaximal, characteristic, complemented
8#14519757C211yesmaximal, characteristic, complemented
9#14519755C211yesmaximal, characteristic, complemented
10#14519753C211yesmaximal, characteristic, complemented
11#14519752C211yesmaximal, characteristic, complemented
12#14519751C211yesmaximal, characteristic, complemented
13#14519750C211yesmaximal, characteristic, complemented
14#14519750C211yesmaximal, characteristic, complemented
15C22⋊Q8×C61C211yesmaximal, characteristic, complemented
16C2×Q8×C61C2211yescharacteristic
17C22×C4×C61C2211yescharacteristic
18C2×C22⋊D61C2211yescharacteristic
19C2×C22⋊D61C2211yescharacteristic
20C2×C22⋊D61C2211yescharacteristic
21C2×D244C2211yescharacteristic
22C2×D244C2211yescharacteristic
23C2×D244C2211yescharacteristic
24C2×C4×D61C2211yescharacteristic
25C2×C4×D61C2211yescharacteristic
26C2×C4×D61C2211yescharacteristic
27C2×Dic122C2211yescharacteristic
28C4⋊C4×C61C2211yescharacteristic
29C4⋊C4×C61C2211yescharacteristic
30C4⋊C4×C61C2211yescharacteristic
31C22⋊C4×C61C2211yescharacteristic
32C22⋊C4×C61C2211yescharacteristic
33C22⋊Dic61C2211yescharacteristic
34#11758198C2211yescharacteristic
35#11758198C2211yescharacteristic
36#11758198C2211yescharacteristic
37#11758198C2211yescharacteristic
38#11758198C2211yescharacteristic
39#11758198C2211yescharacteristic
40#11758198C2211yescharacteristic
41#11758198C2211yescharacteristic
42#11758198C2211yescharacteristic
43C4⋊Dic61C2211yescharacteristic
44C4⋊Dic61C2211yescharacteristic
45#11758196C2211yescharacteristic
46#11758196C2211yescharacteristic
47#11758196C2211yescharacteristic
48#11758196C2211yescharacteristic
49#11758196C2211yescharacteristic
50C4×Dic61C2211yescharacteristic
51C23×C61C2311yescharacteristic
52C22×D61C2311yescharacteristic
53C22×D61C2311yescharacteristic
54C22×D61C2311yescharacteristic
55Q8×C61—41no—
56C2×C4×C61—41no—
57C2×C4×C61C2311yescharacteristic
58C2×C4×C61C2311yescharacteristic
59C2×C4×C61C2311yescharacteristic
60C2×C4×C61C2311yescharacteristic
61C2×C4×C61C2311yescharacteristic
62C2×C4×C61C2311yescharacteristic
63C22⋊D61—41no—
64C22⋊D61—41no—
65C22⋊D61—41no—
66C2×Dic61C2311yescharacteristic
67C2×Dic61C2311yescharacteristic
68C2×Dic61C2311yescharacteristic
69C2×Dic61C2311yescharacteristic
70C2×Dic61C2311yescharacteristic
71D244—41no—
72D244—41no—
73D244—41no—
74C4×D61—41no—
75C4×D61—41no—
76C4×D61—41no—
77Dic122—41no—
78C22×C61—21no—
79C22×C61—21no—
80C22×C61—21no—
81C22×C61C2411yescharacteristic
82C2×D61—21no—
83C2×D61—21no—
84C2×D61—21no—
85C2×D61—21no—
86C2×D61—21no—
87C2×D61—21no—
88C2×D61—21no—
89C2×D61—21no—
90C2×D61—21no—
91C4×C61—21no—
92C4×C61—21no—
93C4×C61—21no—
94C4×C61—21no—
95C4×C61—21no—
96C4×C61—21no—
97Dic61—21no—
98Dic61—21no—
99Dic61—21no—
100Dic61—21no—
101Dic61—21no—
102C2×C61—41no—
103C2×C61H(5,𝔽2)11yescharacteristic
104C2×C61H(5,𝔽2)11yescharacteristic
105C2×C612−1+411yescharacteristic
106D61—41no—
107D61—41no—
108D61—41no—
109#562—611nomaximal, Sylow
110C61#56211yescharacteristic, complemented, Sylow
111#125—611no—
112#124—611no—
113#124—611no—
114#123—611no—
115#123—611no—
116#123—611no—
117#123—611no—
118C22⋊Q8—611no—
119C22⋊Q8—611no—
120C22⋊Q8—611no—
121C22⋊Q8D6111yescharacteristic, complemented
122#121—611no—
123#121—611no—
124#121—611no—
125#121—611no—
126C2×Q8—611no—
127C2×Q8C2×D6111yescharacteristic
128C2×D4—611no—
129C2×D4—611no—
130C2×D4—611no—
131C2×D4—611no—
132C2×D4—611no—
133C2×D4—611no—
134C22×C4—611no—
135C22×C4—611no—
136C22×C4—611no—
137C22×C4C2×D6111yescharacteristic
138C4⋊C4—611no—
139C4⋊C4—611no—
140C4⋊C4—611no—
141C4⋊C4—611no—
142C4⋊C4—611no—
143C4⋊C4—611no—
144C4⋊C4—611no—
145C4⋊C4C2×D6111yescharacteristic
146C4⋊C4C2×D6111yescharacteristic
147C4⋊C4C2×D6111yescharacteristic
148C22⋊C4—611no—
149C22⋊C4—611no—
150C22⋊C4—611no—
151C22⋊C4—611no—
152C22⋊C4—611no—
153C22⋊C4—611no—
154C22⋊C4—611no—
155C22⋊C4—611no—
156C22⋊C4—611no—
157C22⋊C4—611no—
158C22⋊C4C2×D6111yescharacteristic
159C22⋊C4C2×D6111yescharacteristic
160C42—611no—
161C23—611no—
162C23—611no—
163C23—611no—
164C23C22×D6111yescharacteristic
165Q8—41no—
166Q8—2441no—
167D4—2441no—
168D4—2441no—
169D4—2441no—
170D4—2441no—
171D4—2441no—
172D4—2441no—
173C2×C4—41no—
174C2×C4—611no—
175C2×C4—611no—
176C2×C4—611no—
177C2×C4—611no—
178C2×C4—611no—
179C2×C4—2441no—
180C2×C4—2441no—
181C2×C4—2441no—
182C2×C4C22×D6111yescharacteristic
183C2×C4C22×D6111yescharacteristic
184C2×C4C22×D6111yescharacteristic
185C2×C4C22×D6111yescharacteristic
186C2×C4C22×D6111yescharacteristic
187C2×C4C22×D6111yescharacteristic
188C22—21no—
189C22—21no—
190C22—21no—
191C22—1221no—
192C22—1221no—
193C22—1221no—
194C22—1221no—
195C22—1221no—
196C22—1221no—
197C22—1221no—
198C22—1221no—
199C22—1221no—
200C22C23×D6111yescharacteristic
201C4—21no—
202C4—21no—
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—1221no—
208C4—1221no—
209C4—1221no—
210C4—1221no—
211C4—1221no—
212C2—41no—
213C2—2441no—
214C2—2441no—
215C2—2441no—
216C2#1451982211yescharacteristic
217C2#1451982311yescharacteristic
218C2#1451982511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D61
commutator, socle, cosocleC22×C61C24
FittingC22⋊Q8×C61C2
hypercenterC22⋊Q8D61
hypocenterC61#562
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #14519767C2semidirect
2. #14519766C2semidirect
3. #14519763C2semidirect
4. #14519762C2semidirect
5. #14519762C2semidirect
6. #14519760C2semidirect
7. #14519759C2semidirect
8. #14519757C2semidirect
9. #14519755C2semidirect
10. #14519753C2semidirect
11. #14519752C2semidirect
12. #14519751C2semidirect
13. #14519750C2semidirect
14. #14519750C2semidirect
15. C22⋊Q8×C61C2semidirect
110. C61#562semidirect
121. C22⋊Q8D61semidirect

Maximal subgroups

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

subgroupindex
#145197672
#145197662
#145197632
#145197622
#145197602
#145197592
#145197572
#145197552
#145197532
#145197522
#145197512
#145197502
C22⋊Q8×C612
#56261