Finite Group Databasebeta

← #21447808

Subgroups — #21447808

Order 7808.

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

normal subgroups only

This group has 258 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#16840442C211yesmaximal, characteristic, complemented
2#16839952C211yesmaximal, characteristic, complemented
3#16839949C211yesmaximal, characteristic
4#16839557C211yesmaximal, characteristic, complemented
5#16839553C211yesmaximal, characteristic, complemented
6#16839550C211yesmaximal, characteristic, complemented
7C61×#455C211yesmaximal, characteristic, complemented
8#14519770—21no—
9#14519759—21no—
10#14519758—21no—
11#14519758C2211yescharacteristic
12#14519753—21no—
13#14519745—21no—
14#14519745C2211yescharacteristic
15#14519737—21no—
16#14519734—21no—
17C22⋊C4×D61—21no—
18#14519692—21no—
19#14519692—21no—
20#14519692C2211yescharacteristic
21#14519692C2211yescharacteristic
22H(5,𝔽2)×C61C2211yescharacteristic
23#137×C61—21no—
24#124×C61C2211yescharacteristic
25#104×C61—21no—
26#100×C61C2211yescharacteristic
27C23×D61D411yescharacteristic
28#41×C61—21no—
29#41×C61—41no—
30C2×Q8×C61D411yescharacteristic, complemented
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—41no—
34C2×D4×C61C2311yescharacteristic
35C2×C22⋊D61—21no—
36C2×C22⋊D61—41no—
37C22×Dic61D411yescharacteristic, complemented
38C2×C4×D61—21no—
39C2×C4×D61—21no—
40Q16×C61—41no—
41SD16×C61—41no—
42M16×C61—21no—
43C22⋊C4×C61—21no—
44C22⋊C4×C61—21no—
45C42×C61D411yescharacteristic, complemented
46C22⋊Dic61—21no—
47C22⋊Dic61—21no—
48C22⋊Dic61—21no—
49C22⋊Dic61—41no—
50C22⋊Dic61D411yescharacteristic
51C22⋊Dic61D411yescharacteristic, complemented
52#11758198—21no—
53#11758198—21no—
54#11758198—21no—
55#11758198—41no—
56C4⋊Dic61—21no—
57#11758196—21no—
58#11758196—21no—
59#11758196—21no—
60#11758196—41no—
61C4×Dic61—21no—
62C23×C61—21no—
63C23×C61—21no—
64C23×C61C2×D411yescharacteristic
65C23×C61C2×D411yescharacteristic
66C22×D61—21no—
67C22×D61—42no—
68C22×D61—41no—
69Q8×C61—21no—
70Q8×C61—41no—
71D4×C61—21no—
72D4×C61—41no—
73D4×C61—41no—
74D4×C61—41no—
75D4×C61—41no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—41no—
81C2×C4×C61C2×D411yescharacteristic
82C22⋊D61—42no—
83C22⋊D61—82no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—41no—
88C2×Dic61—41no—
89C2×Dic61—41no—
90C4×D61—42no—
91C4×D61—81no—
92C8×C61—41no—
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—41no—
96C22×C61—41no—
97C22×C61—41no—
98C22×C61—81no—
99C22×C61—81no—
100C22×C61#12011yescharacteristic
101C2×D61—22no—
102C2×D61—41no—
103C2×D61—41no—
104C2×D61—42no—
105C2×D61—81no—
106C4×C61—21no—
107C4×C61—41no—
108C4×C61—41no—
109C4×C61—41no—
110Dic61—41no—
111Dic61—41no—
112Dic61—41no—
113Dic61—81no—
114Dic61—81no—
115#2197—611nomaximal, Sylow
116C2×C61—21no—
117C2×C61—41no—
118C2×C61—41no—
119C2×C61—81no—
120C2×C61B(4,𝔽2)11yescharacteristic
121D61—42no—
122#551—611no—
123#458—611no—
124B(4,𝔽2)—611no—
125#455D6111yescharacteristic, complemented
126#354—611no—
127#352—611no—
128AΣL(1,𝔽16)—611no—
129C61#219711yescharacteristic, complemented, Sylow
130H(5,𝔽2)C2×D6111yescharacteristic
131#137—21no—
132#126—1221no—
133#124C2×D6111yescharacteristic
134#123—611no—
135#123—1221no—
136#123—1221no—
137C22⋊Q8—1221no—
138#120—611no—
139#120—1221no—
140C4×D4—1221no—
141#117—1221no—
142C2×C22⋊C4—1221no—
143#104—21no—
144#100C2×D6111yescharacteristic
145#99—611no—
146#99—611no—
147#99—1221no—
148#99—1221no—
149C24—611no—
150#41—21no—
151#41—41no—
152C2×Q8C22⋊D6111yescharacteristic, complemented
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—41no—
156C2×D4—1221no—
157C2×D4—2441no—
158C2×D4C22×D6111yescharacteristic
159C22×C4—611no—
160C22×C4—1221no—
161C22×C4—1221no—
162Q16—41no—
163SD16—41no—
164M16—21no—
165C4⋊C4—1221no—
166C4⋊C4—1221no—
167C4⋊C4—1221no—
168C4⋊C4—1221no—
169C4⋊C4—2441no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—611no—
173C22⋊C4—611no—
174C22⋊C4—1221no—
175C22⋊C4—1221no—
176C22⋊C4—1221no—
177C22⋊C4—1221no—
178C22⋊C4—1221no—
179C22⋊C4—1221no—
180C22⋊C4—2441no—
181C22⋊C4—2441no—
182C42—1221no—
183C42C22⋊D6111yescharacteristic, complemented
184C23—21no—
185C23—21no—
186C23—1221no—
187C23—2441no—
188C23—2442no—
189C23D4×D6111yescharacteristic
190C23D4×D6111yescharacteristic
191Q8—21no—
192Q8—41no—
193D4—21no—
194D4—41no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—4882no—
199D4—2442no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—4881no—
209C2×C4—2442no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4—2441no—
213C2×C4C2×C22⋊D6111yescharacteristic
214C8—41no—
215C22—21no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22—81no—
222C22—1222no—
223C22—4881no—
224C22—2441no—
225C22—2442no—
226C22—2441no—
227C22#1451974511yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—4881no—
233C4—4881no—
234C4—2441no—
235C4—2441no—
236C4—2441no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—81no—
241C2—2442no—
242C2#1683994811yescharacteristic
subgroupG/H
centerC2#16839948
commutatorC2×D4×C61C23
FrattiniC2×D4C22×D61
FittingC61×#455C2
socleC2×C61B(4,𝔽2)
hypercenter#455D61
hypocenterC61#2197
LCSG ▷ C2×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #16840442C2semidirect
2. #16839952C2semidirect
4. #16839557C2semidirect
5. #16839553C2semidirect
6. #16839550C2semidirect
7. C61×#455C2semidirect
30. C2×Q8×C61D4semidirect
37. C22×Dic61D4semidirect
45. C42×C61D4semidirect
51. C22⋊Dic61D4semidirect
125. #455D61semidirect
129. C61#2197semidirect
152. C2×Q8C22⋊D61semidirect
183. C42C22⋊D61semidirect