Finite Group Databasebeta

← #21447838

Subgroups — #21447838

Order 7808.

216 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 41 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#16840511C211yesmaximal, characteristic, complemented
2#16839945C211yesmaximal, characteristic, complemented
3#16839935C211yesmaximal, characteristic
4#16839561C211yesmaximal, characteristic, complemented
5#16839560C211yesmaximal, characteristic, complemented
6#16839558C211yesmaximal, characteristic, complemented
7C61×#456C211yesmaximal, characteristic, complemented
8#14519807—21no—
9#14519802—21no—
10#14519775C2211yescharacteristic
11#14519772—21no—
12#14519771—21no—
13#14519767—21no—
14#14519766C2211yescharacteristic
15#14519762—21no—
16#14519755—21no—
17#14519753—21no—
18#14519704—21no—
19#14519704—21no—
20#14519696C2211yescharacteristic
21#14519696C2211yescharacteristic
222−1+4×C61C2211yescharacteristic
23#137×C61—21no—
24C4⋊Q8×C61C2211yescharacteristic
25#104×C61—21no—
26#101×C61C2211yescharacteristic
27#41×C61—21no—
28#41×C61—21no—
29#41×C61—21no—
30#41×C61—41no—
31C2×Q8×C61—41no—
32C2×Q8×C61D411yescharacteristic
33C2×Q8×C61C2311yescharacteristic
34C2×D244D411yescharacteristic
35C2×C4×D61—21no—
36C2×Dic122D411yescharacteristic
37Q16×C61—41no—
38SD16×C61—41no—
39M16×C61—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—21no—
42C42×C61D411yescharacteristic
43#11758202—41no—
44#11758201—41no—
45#11758200—41no—
46#11758199—41no—
47#11758198—21no—
48#11758198—21no—
49#11758198—21no—
50#11758198—21no—
51#11758198—21no—
52C4⋊Dic61—21no—
53#11758196—21no—
54#11758196—21no—
55#11758196—21no—
56#11758196—21no—
57#11758196—21no—
58C4×Dic61D411yescharacteristic
59C4×Dic61D411yescharacteristic
60#11758194—21no—
61#11758194—21no—
62C22×D61—21no—
63Q8×C61—21no—
64Q8×C61—21no—
65Q8×C61—21no—
66Q8×C61—41no—
67Q8×C61—41no—
68D4×C61—21no—
69D4×C61—21no—
70D4×C61—21no—
71D4×C61—41no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—41no—
75C2×C4×C61—41no—
76C2×C4×C61—41no—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83D244—41no—
84C4×D61—81no—
85Dic122—41no—
86C8×C61—41no—
87#92418—41no—
88#92418—41no—
89C22×C61—41no—
90C22×C61#12011yescharacteristic
91C2×D61—42no—
92C2×D61—41no—
93C4×C61—21no—
94C4×C61—21no—
95C4×C61—21no—
96C4×C61—41no—
97C4×C61—41no—
98C4×C61—41no—
99Dic61—41no—
100Dic61—41no—
101Dic61—41no—
102#2203—611nomaximal, Sylow
103C2×C61—21no—
104C2×C61—81no—
105C2×C61B(4,𝔽2)11yescharacteristic
106D61—81no—
107#563—611no—
108#456—611no—
109#456D6111yescharacteristic, complemented
110#454—611no—
111#356—611no—
112#356—611no—
113#355—611no—
114C61#220311yescharacteristic, complemented, Sylow
1152−1+4C2×D6111yescharacteristic
116#137—21no—
117#137—1221no—
118AGL(1,ℤ/8)—1221no—
119C4⋊Q8—611no—
120C4⋊Q8C2×D6111yescharacteristic
121#126—1221no—
122#126—1221no—
123#125—1221no—
124#124—611no—
125#123—1221no—
126C22⋊Q8—1221no—
127C22⋊Q8—1221no—
128#104—21no—
129#104—1221no—
130#104—1221no—
131#101—611no—
132#101—611no—
133#101C2×D6111yescharacteristic
134#41—21no—
135#41—21no—
136#41—21no—
137#41—41no—
138C2×Q8—41no—
139C2×Q8—611no—
140C2×Q8C22⋊D6111yescharacteristic
141C2×Q8C22×D6111yescharacteristic
142C2×D4—611no—
143C22×C4—1221no—
144Q16—41no—
145Q16—2441no—
146SD16—41no—
147SD16—2441no—
148SD16—2441no—
149D8—2441no—
150M16—21no—
151M16—1221no—
152M16—1221no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—1221no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4—1221no—
159C4⋊C4—1221no—
160C4⋊C4—1221no—
161C22⋊C4—1221no—
162C22⋊C4—1221no—
163C22⋊C4—1221no—
164C22⋊C4—1221no—
165C22⋊C4—1221no—
166C42—611no—
167C42—611no—
168C42C22⋊D6111yescharacteristic
169C23—1221no—
170Q8—21no—
171Q8—21no—
172Q8—21no—
173Q8—41no—
174Q8—41no—
175Q8—2441no—
176D4—21no—
177D4—21no—
178D4—21no—
179D4—41no—
180D4—2441no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—1221no—
187C2×C4—1221no—
188C2×C4—1221no—
189C2×C4—4881no—
190C2×C4D4×D6111yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C2×C4C2×C22⋊D6111yescharacteristic
193C8—41no—
194C8—2441no—
195C8—2441no—
196C22—41no—
197C22—2442no—
198C22—2441no—
199C22#1451974511yescharacteristic
200C4—21no—
201C4—21no—
202C4—21no—
203C4—41no—
204C4—41no—
205C4—41no—
206C4—2441no—
207C4—2441no—
208C4—2441no—
209C2—21no—
210C2—81no—
211C2—4881no—
212C2#1683994811yescharacteristic
subgroupG/H
centerC2#16839948
commutatorC2×Q8×C61C23
FrattiniC2×Q8C22×D61
FittingC61×#456C2
socleC2×C61B(4,𝔽2)
hypercenter#456D61
hypocenterC61#2203
LCSG ▷ C2×Q8×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #16840511C2semidirect
2. #16839945C2semidirect
4. #16839561C2semidirect
5. #16839560C2semidirect
6. #16839558C2semidirect
7. C61×#456C2semidirect
109. #456D61semidirect
114. C61#2203semidirect