Finite Group Databasebeta

← #21447830

Subgroups — #21447830

Order 7808.

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

normal subgroups only

This group has 226 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#16840515C211yesmaximal, characteristic, complemented
2#16839952C211yesmaximal, characteristic
3#16839940C211yesmaximal, characteristic
4#16839556C211yesmaximal, characteristic, complemented
5#16839552C211yesmaximal, characteristic, complemented
6#16839551C211yesmaximal, characteristic, complemented
7C61×#458C211yesmaximal, characteristic
8#14519807—21no—
9#14519776—21no—
10#14519770—21no—
11#14519770—21no—
12#14519767—21no—
13#14519764C2211yescharacteristic
14#14519758—21no—
15#14519758C2211yescharacteristic
16#14519756—21no—
17#14519754—21no—
18#14519704—21no—
19#14519694C2211yescharacteristic
20#14519692—21no—
21#14519692C2211yescharacteristic
22H(5,𝔽2)×C61C2211yescharacteristic
23#123×C61—21no—
24#123×C61C2211yescharacteristic
25#99×C61—21no—
26#99×C61C2211yescharacteristic
27#41×C61—21no—
28#41×C61—41no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61—41no—
32C2×D4×C61C2311yescharacteristic
33C22×C4×C61D411yescharacteristic
34C22×Dic61D411yescharacteristic
35C2×Dic122—21no—
36C2×Dic122D411yescharacteristic
37C4⋊C4×C61—21no—
38C4⋊C4×C61—41no—
39C22⋊C4×C61—21no—
40C22⋊C4×C61—21no—
41C22⋊C4×C61—41no—
42C22⋊C4×C61D411yescharacteristic
43C22⋊Dic61—21no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46C22⋊Dic61—21no—
47C22⋊Dic61—41no—
48C22⋊Dic61D411yescharacteristic
49#11758202—41no—
50#11758200—41no—
51C4⋊Dic61—21no—
52C4⋊Dic61—21no—
53#11758196—21no—
54#11758196—21no—
55#11758196—21no—
56#11758196—21no—
57#11758196—21no—
58#11758196—41no—
59C4×Dic61—21no—
60C4×Dic61D411yescharacteristic
61#11758194—21no—
62C23×C61—21no—
63C23×C61—21no—
64C23×C61C2×D411yescharacteristic
65C23×C61C2×D411yescharacteristic
66Q8×C61—21no—
67D4×C61—21no—
68D4×C61—41no—
69D4×C61—41no—
70D4×C61—41no—
71D4×C61—41no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61C2×D411yescharacteristic
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—41no—
85C2×Dic61—41no—
86Dic122—41no—
87Dic122—81no—
88#92418—41no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—41no—
94C22×C61—81no—
95C22×C61—81no—
96C22×C61#12011yescharacteristic
97C4×C61—21no—
98C4×C61—41no—
99C4×C61—41no—
100C4×C61—41no—
101C4×C61—81no—
102Dic61—41no—
103Dic61—41no—
104Dic61—41no—
105Dic61—41no—
106Dic61—81no—
107#2201—611nomaximal, Sylow
108C2×C61—21no—
109C2×C61—41no—
110C2×C61—41no—
111C2×C61—81no—
112C2×C61B(4,𝔽2)11yescharacteristic
113#563—611no—
114#458—611no—
115#458D6111yescharacteristic
116#455—611no—
117#354—611no—
118#352—611no—
119#352—611no—
120C61#220111yescharacteristic, complemented, Sylow
121H(5,𝔽2)C2×D6111yescharacteristic
122#137—1221no—
123C4⋊Q8—1221no—
124#126—1221no—
125#126—1221no—
126#125—1221no—
127#124—611no—
128#123—21no—
129#123—611no—
130#123—1221no—
131#123C2×D6111yescharacteristic
132C22⋊Q8—1221no—
133C22⋊Q8—1221no—
134#104—1221no—
135#100—611no—
136#99—21no—
137#99—611no—
138#99—1221no—
139#99C2×D6111yescharacteristic
140#41—21no—
141#41—41no—
142C2×Q8—611no—
143C2×Q8—1221no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—41no—
147C2×D4C22×D6111yescharacteristic
148C22×C4—611no—
149C22×C4C22⋊D6111yescharacteristic
150Q16—2441no—
151SD16—2441no—
152M16—1221no—
153C4⋊C4—21no—
154C4⋊C4—41no—
155C4⋊C4—1221no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4—1221no—
159C4⋊C4—1221no—
160C4⋊C4—1221no—
161C4⋊C4—1221no—
162C4⋊C4—2441no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—41no—
166C22⋊C4—611no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C22⋊C4—1221no—
170C22⋊C4—1221no—
171C22⋊C4—2441no—
172C22⋊C4C22⋊D6111yescharacteristic
173C42—611no—
174C42—1221no—
175C23—21no—
176C23—21no—
177C23D4×D6111yescharacteristic
178C23C2×C22⋊D6111yescharacteristic
179Q8—21no—
180Q8—4881no—
181Q8—2441no—
182D4—21no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—41no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—1221no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4D4×D6111yescharacteristic
201C8—2441no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—81no—
209C22#1451974511yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—81no—
215C4—4881no—
216C4—2441no—
217C4—2441no—
218C4—2441no—
219C4—2441no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—81no—
224C2#1683994811yescharacteristic
subgroupG/H
centerC2#16839948
commutatorC2×D4×C61C23
FrattiniC2×D4C22×D61
FittingC61×#458C2
socleC2×C61B(4,𝔽2)
hypercenter#458D61
hypocenterC61#2201
LCSG ▷ C2×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #16840515C2semidirect
4. #16839556C2semidirect
5. #16839552C2semidirect
6. #16839551C2semidirect
120. C61#2201semidirect