Finite Group Databasebeta

← #21447813

Subgroups — #21447813

Order 7808.

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

normal subgroups only

This group has 246 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#16840496C211yesmaximal, characteristic, complemented
2#16839952C211yesmaximal, characteristic, complemented
3#16839930C211yesmaximal, characteristic
4#16839554C211yesmaximal, characteristic, complemented
5#16839552C211yesmaximal, characteristic, complemented
6#16839551C211yesmaximal, characteristic, complemented
7C61×#458C211yesmaximal, characteristic, complemented
8#14519802—21no—
9#14519773C2211yescharacteristic
10#14519763—21no—
11#14519763—21no—
12#14519762—21no—
13#14519758—21no—
14#14519758C2211yescharacteristic
15#14519742—21no—
16C4×C22⋊D61—21no—
17#14519737—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
34C2×C22⋊D61—21no—
35C2×C22⋊D61—21no—
36C22×Dic61D411yescharacteristic
37C2×D244D411yescharacteristic
38C2×C4×D61—21no—
39C2×Dic122—21no—
40C4⋊C4×C61—21no—
41C4⋊C4×C61—41no—
42C22⋊C4×C61—21no—
43C22⋊C4×C61—21no—
44C22⋊C4×C61—41no—
45C22⋊C4×C61D411yescharacteristic
46C22⋊Dic61—21no—
47C22⋊Dic61—21no—
48C22⋊Dic61—41no—
49C22⋊Dic61D411yescharacteristic
50#11758201—41no—
51#11758199—41no—
52#11758198—21no—
53#11758198—21no—
54#11758198—21no—
55#11758196—21no—
56#11758196—21no—
57#11758196—41no—
58C4×Dic61—21no—
59C4×Dic61—21no—
60C4×Dic61D411yescharacteristic
61#11758194—21no—
62C23×C61—21no—
63C23×C61—21no—
64C23×C61C2×D411yescharacteristic
65C23×C61C2×D411yescharacteristic
66C22×D61—21no—
67Q8×C61—21no—
68D4×C61—21no—
69D4×C61—41no—
70D4×C61—41no—
71D4×C61—41no—
72D4×C61—41no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—41no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61C2×D411yescharacteristic
81C22⋊D61—42no—
82C22⋊D61—42no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—41no—
87C2×Dic61—41no—
88D244—41no—
89C4×D61—81no—
90Dic122—42no—
91#92418—41no—
92C22×C61—21no—
93C22×C61—21no—
94C22×C61—41no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61—81no—
98C22×C61—81no—
99C22×C61#12011yescharacteristic
100C2×D61—41no—
101C2×D61—41no—
102C2×D61—41no—
103C4×C61—21no—
104C4×C61—41no—
105C4×C61—41no—
106C4×C61—41no—
107C4×C61—81no—
108Dic61—22no—
109Dic61—41no—
110Dic61—41no—
111Dic61—81no—
112#2198—611nomaximal, Sylow
113C2×C61—21no—
114C2×C61—41no—
115C2×C61—41no—
116C2×C61—81no—
117C2×C61B(4,𝔽2)11yescharacteristic
118D61—81no—
119#559—611no—
120#458—611no—
121#458D6111yescharacteristic, complemented
122#453—611no—
123#353—611no—
124#352—611no—
125#352—611no—
126C61#219811yescharacteristic, complemented, Sylow
127H(5,𝔽2)C2×D6111yescharacteristic
128AGL(1,ℤ/8)—1221no—
129#127—611no—
130#124—1221no—
131#124—1221no—
132#123—21no—
133#123—611no—
134#123—1221no—
135#123—1221no—
136#123C2×D6111yescharacteristic
137C4×Q8—1221no—
138C4×D4—1221no—
139C4×D4—1221no—
140#104—1221no—
141#100—611no—
142#99—21no—
143#99—611no—
144#99—1221no—
145#99C2×D6111yescharacteristic
146#41—21no—
147#41—41no—
148C2×Q8—1221no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—41no—
152C2×D4—611no—
153C2×D4—1221no—
154C2×D4—1221no—
155C2×D4C22×D6111yescharacteristic
156C22×C4—611no—
157C22×C4—1221no—
158C22×C4C22⋊D6111yescharacteristic
159SD16—2441no—
160D8—2441no—
161M16—1221no—
162C4⋊C4—21no—
163C4⋊C4—41no—
164C4⋊C4—1221no—
165C4⋊C4—1221no—
166C4⋊C4—2441no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—41no—
170C22⋊C4—611no—
171C22⋊C4—1221no—
172C22⋊C4—1221no—
173C22⋊C4—1221no—
174C22⋊C4—1221no—
175C22⋊C4—1221no—
176C22⋊C4—2441no—
177C22⋊C4C22⋊D6111yescharacteristic
178C42—611no—
179C42—1221no—
180C42—1221no—
181C23—21no—
182C23—21no—
183C23—1221no—
184C23D4×D6111yescharacteristic
185C23C2×C22⋊D6111yescharacteristic
186Q8—21no—
187Q8—2442no—
188D4—21no—
189D4—41no—
190D4—41no—
191D4—41no—
192D4—41no—
193D4—2441no—
194D4—2442no—
195D4—2442no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—4881no—
207C2×C4—2441no—
208C2×C4—2441no—
209C2×C4D4×D6111yescharacteristic
210C8—2441no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—81no—
217C22—81no—
218C22—2441no—
219C22—2441no—
220C22—2441no—
221C22#1451974511yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—81no—
227C4—1222no—
228C4—4881no—
229C4—2441no—
230C4—2441no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—81no—
235C2—4881no—
236C2#1683994811yescharacteristic
subgroupG/H
centerC2#16839948
commutatorC2×D4×C61C23
FrattiniC2×D4C22×D61
FittingC61×#458C2
socleC2×C61B(4,𝔽2)
hypercenter#458D61
hypocenterC61#2198
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. #16840496C2semidirect
2. #16839952C2semidirect
4. #16839554C2semidirect
5. #16839552C2semidirect
6. #16839551C2semidirect
7. C61×#458C2semidirect
121. #458D61semidirect
126. C61#2198semidirect