Finite Group Databasebeta

← #21446335

Subgroups — #21446335

Order 7808.

312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#14519810C211yesmaximal, characteristic
2C2×#14519785C211yesmaximal, characteristic
3#16839761C211yesmaximal, characteristic
4C2×#14519700C211yesmaximal, characteristic, complemented
5C2×#14519695C211yesmaximal, characteristic, complemented
6#16839526C211yesmaximal, characteristic, complemented
7C61×#343C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10#14519810—22no—
11#14519810C414yescomplemented
12C2×Dic244—21no—
13C2×#11758190—21no—
14#14519785—22no—
15#14519785—22no—
16C2×#11758194C2211yescharacteristic
17C2×#11758189—21no—
18C22×#92418C2211yescharacteristic
19C2×C8×D61—21no—
20#14519700—21no—
21#14519700—21no—
22#14519700—21no—
23#14519697—21no—
24#14519695—22no—
25C2×M16×C61C2211yescharacteristic
26C2×M16×C61C2211yescharacteristic
27C2×C4⋊C4×C61C2211yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—21no—
31C22×Dic61—21no—
32#11758222—21no—
33#11758222—21no—
34#11758222C2×C412yes—
35#11758222D412yes—
36C2×D244D411yescharacteristic
37C2×C4×D61—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122—21no—
42C2×Dic122—21no—
43C2×Dic122C2×C412yes—
44C2×Dic122D411yescharacteristic
45M16×C61—21no—
46M16×C61—21no—
47M16×C61C2×C412yes—
48M16×C61D412yes—
49C2×C8×C61—21no—
50C2×C8×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61—21no—
53#11758194—21no—
54#11758194—21no—
55C2×#92418—21no—
56C2×#92418—21no—
57C2×#92418—21no—
58C2×#92418D411yescharacteristic
59C2×#92418D411yescharacteristic
60Dic244—24no—
61#11758190—24no—
62#11758189—24no—
63C8×D61—24no—
64C23×C61#4111yescharacteristic
65C22×D61—21no—
66C2×C4×C61—41no—
67C2×C4×C61—81no—
68C2×C4×C61C22×C411yescharacteristic
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C22⋊D61—22no—
75C22⋊D61—22no—
76C2×Dic61—21no—
77C2×Dic61—22no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80D244—21no—
81D244C22⋊C412yes—
82C4×D61—22no—
83C4×D61—22no—
84Dic122—21no—
85Dic122—22no—
86Dic122—22no—
87Dic122—41no—
88Dic122—41no—
89Dic122C22⋊C412yes—
90C8×C61—22no—
91C8×C61—22no—
92#92418—21no—
93#92418—21no—
94#92418—41no—
95C22×C61—21no—
96C22×C61—21no—
97C22×C61C4×D411yescharacteristic
98C22×C61#12111yescharacteristic
99C22×C61#12311yescharacteristic
100C2×D61—22no—
101C2×D61—41no—
102C2×D61—41no—
103C4×C61—81no—
104C4×C61C2×C22⋊C411yescharacteristic
105C4×C61C4×D411yescharacteristic
106C4×C61#12011yescharacteristic
107C4×C61#12111yescharacteristic
108Dic61—22no—
109Dic61—42no—
110#1908—611nomaximal, Sylow
111C2×C61—21no—
112C2×C61—21no—
113C2×C61#38611yescharacteristic
114C2×C61#47111yescharacteristic
115C2×C61#47311yescharacteristic
116D61—42no—
117C2×#137—611no—
118C2×#131—611no—
119#417—611no—
120C2×#103—611no—
121C2×#101—611no—
122#343D6111yescharacteristic, complemented
123#341—611no—
124C61#190811yescharacteristic, complemented, Sylow
125C2×#41—611no—
126C22×Q8—611no—
127#137—614no—
128#137—1222no—
129C2×Q16—1221no—
130C2×SD16—1221no—
131#131—1222no—
132#131—1222no—
133C2×M16—611no—
134C2×M16—1221no—
135C2×M16C2×D6111yescharacteristic
136C2×M16C2×D6111yescharacteristic
137C22×C8—611no—
138C22×C8—1221no—
139C2×C4⋊C4C2×D6111yescharacteristic
140#103—1221no—
141#103—1221no—
142#103—1221no—
143#102—1221no—
144#101—1222no—
145#41—612no—
146#41—612no—
147#41—1221no—
148#41—1221no—
149C2×Q8—612no—
150C2×Q8—611no—
151C2×Q8—1221no—
152C2×Q8—1221no—
153C2×Q8—1221no—
154C2×Q8—1221no—
155C2×Q8—1221no—
156C2×D4—611no—
157C2×D4—1221no—
158C22×C4—21no—
159C22×C4—1221no—
160C22×C4—1221no—
161C22×C4C22×D6111yescharacteristic
162Q16—1224no—
163SD16—1224no—
164M16—21no—
165M16—21no—
166M16—1224no—
167M16—1221no—
168M16—1221no—
169M16C4×D6112yes—
170M16D24412yes—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—611no—
174C2×C8—611no—
175C2×C8—1224no—
176C2×C8—1221no—
177C2×C8—1221no—
178C2×C8—1221no—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C23—1221no—
182C23#1175822211yescharacteristic
183Q8—612no—
184Q8—1221no—
185Q8—1222no—
186Q8—1222no—
187Q8—2441no—
188Q8—2441no—
189D4—612no—
190D4—1222no—
191D4—1222no—
192D4—1221no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—1221no—
196C2×C4—1222no—
197C2×C4—1222no—
198C2×C4—1222no—
199C2×C4—2441no—
200C2×C4—2441no—
201C2×C4C2×C4×D6111yescharacteristic
202C2×C4C2×D24411yescharacteristic
203C2×C4D4×D6111yescharacteristic
204C2×C4D4×D6111yescharacteristic
205C2×C4D4×D6111yescharacteristic
206C2×C4#1175822611yescharacteristic
207C8—22no—
208C8—22no—
209C8—1221no—
210C8—1221no—
211C8—2441no—
212C22—21no—
213C22—21no—
214C22—1222no—
215C22—2441no—
216C22—2441no—
217C22C4×D24411yescharacteristic
218C22#1451975011yescharacteristic
219C22#1451976211yescharacteristic
220C4—81no—
221C4—1222no—
222C4—2442no—
223C4C22⋊C4×D6111yescharacteristic
224C4#1451973911yescharacteristic
225C4#1451974711yescharacteristic
226C4#1451975211yescharacteristic
227C2—21no—
228C2—21no—
229C2—2442no—
230C2#1683964011yescharacteristic
231C2#1684002411yescharacteristic
232C2#1684003611yescharacteristic
subgroupG/H
centerC22#14519750
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#343C2
socleC22×C61#121
hypercenter#343D61
hypocenterC61#1908
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
4. C2×#14519700C2semidirect
5. C2×#14519695C2semidirect
6. #16839526C2semidirect
7. C61×#343C2semidirect
11. #14519810C4semidirect
122. #343D61semidirect
124. C61#1908semidirect