Finite Group Databasebeta

← #21446317

Subgroups — #21446317

Order 7808.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#16840560C211yesmaximal, characteristic
2#16840230C211yesmaximal, characteristic, complemented
3#16839780C211yesmaximal, characteristic, complemented
4C2×#14519704C211yesmaximal, characteristic, complemented
5#16839532C211yesmaximal, characteristic, complemented
6#16839521C211yesmaximal, characteristic, complemented
7C61×#410C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808C412yescomplemented
10#14519807—21no—
11#14519803C412yescomplemented
12#14519802—21no—
13#14519797—22no—
14C2×#11758194C2211yescharacteristic
15C2×#11758194C2211yescharacteristic
16#14519742—21no—
17#14519739—21no—
18#14519737—22no—
19#14519734—21no—
20C2×C4×Dic61C2211yescharacteristic
21C42×D61—21no—
22#14519705—22no—
23#14519704—21no—
24#14519704—21no—
25C2×#41×C61C2211yescharacteristic
26#117×C61C2211yescharacteristic
27#117×C61C2211yescharacteristic
28#99×C61—22no—
29#41×C61—21no—
30#41×C61—21no—
31#41×C61—21no—
32#41×C61—21no—
33C2×Q8×C61C2×C411yescharacteristic, complemented
34C2×D4×C61—21no—
35C2×D4×C61C2×C411yescharacteristic, complemented
36C22×C4×C61—21no—
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—21no—
39C22×Dic61—21no—
40#11758222—21no—
41#11758222—21no—
42#11758222C2×C412yes—
43#11758222D412yes—
44C2×D244D411yescharacteristic
45C2×C4×D61—21no—
46C2×C4×D61—22no—
47C2×Dic122D411yescharacteristic
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50C22⋊C4×C61—21no—
51C22⋊C4×C61D412yes—
52C42×C61—21no—
53C42×C61—21no—
54#11758202—22no—
55#11758201—22no—
56#11758200—22no—
57#11758199—22no—
58#11758198—22no—
59#11758196—22no—
60C4×Dic61—22no—
61C4×Dic61—21no—
62C4×Dic61D411yescharacteristic
63C4×Dic61D411yescharacteristic
64#11758194—21no—
65#11758194—21no—
66#11758194—21no—
67#11758194C2×C412yescomplemented
68C2×#92418—21no—
69C2×#92418—21no—
70C23×C61—21no—
71C23×C61C2×D411yescharacteristic
72C22×D61—21no—
73Q8×C61—21no—
74Q8×C61—21no—
75D4×C61—21no—
76D4×C61—21no—
77D4×C61—41no—
78D4×C61—41no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61—41no—
84C2×C4×C61C22×C411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61#4111yescharacteristic
89C2×C4×C61#4111yescharacteristic
90C22⋊D61—22no—
91C22⋊D61—22no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—42no—
96D244—21no—
97D244C22⋊C412yes—
98C4×D61—22no—
99C4×D61—22no—
100C4×D61—44no—
101Dic122—21no—
102Dic122C22⋊C412yes—
103#92418—22no—
104#92418—41no—
105C22×C61—41no—
106C22×C61—41no—
107C22×C61—81no—
108C22×C61C4×D411yescharacteristic
109C22×C61#12011yescharacteristic
110C22×C61#12111yescharacteristic
111C2×D61—22no—
112C2×D61—42no—
113C4×C61—42no—
114C4×C61—41no—
115C4×C61—81no—
116C4×C61C2×C22⋊C411yescharacteristic
117C4×C61C4×D411yescharacteristic
118C4×C61#12111yescharacteristic
119C4×C61#12311yescharacteristic
120Dic61—22no—
121Dic61—22no—
122Dic61—41no—
123#1906—611nomaximal, Sylow
124C2×C61—21no—
125C2×C61—21no—
126C2×C61—21no—
127C2×C61—81no—
128C2×C61#38611yescharacteristic
129D61—42no—
130#575—611no—
131C4×#41—611no—
132#421—611no—
133C2×#104—611no—
134#410D6111yescharacteristic, complemented
135#344—611no—
136#339—611no—
137C61#190611yescharacteristic, complemented, Sylow
138C2×#41—611no—
139C2×#41C2×D6111yescharacteristic
140#137—612no—
141#137—1221no—
142AGL(1,ℤ/8)—612no—
143AGL(1,ℤ/8)—1221no—
144#135—1222no—
145C2×M16—611no—
146C2×M16—611no—
147C4×Q8—1221no—
148C4×D4—1221no—
149C4×D4—1222no—
150#117—1221no—
151#117C2×D6111yescharacteristic
152#117C2×D6111yescharacteristic
153C2×C42—611no—
154C2×C42—1221no—
155#104—1222no—
156#104—1221no—
157#104—1221no—
158#99—22no—
159#41—21no—
160#41—21no—
161#41—21no—
162#41—21no—
163#41—612no—
164#41—612no—
165#41—1221no—
166#41—1221no—
167C2×Q8—611no—
168C2×Q8C4×D6111yescharacteristic, complemented
169C2×D4—21no—
170C2×D4—611no—
171C2×D4—1221no—
172C2×D4C4×D6111yescharacteristic, complemented
173C22×C4—21no—
174C22×C4—1222no—
175C22×C4—1221no—
176C22×C4—1221no—
177C22×C4C22×D6111yescharacteristic
178Q16—1222no—
179SD16—1222no—
180SD16—1222no—
181D8—1222no—
182M16—612no—
183M16—1221no—
184M16—1221no—
185M16—1221no—
186C2×C8—1221no—
187C2×C8—1221no—
188C4⋊C4—21no—
189C4⋊C4—21no—
190C4⋊C4—1222no—
191C22⋊C4—21no—
192C22⋊C4—1222no—
193C22⋊C4C22⋊D6112yes—
194C42—21no—
195C42—21no—
196C42—611no—
197C42—611no—
198C42—1222no—
199C42—1221no—
200C23—21no—
201C23—1221no—
202C23C2×C22⋊D6111yescharacteristic
203Q8—21no—
204Q8—21no—
205Q8—612no—
206Q8—1221no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211D4—612no—
212D4—1222no—
213D4—1222no—
214D4—1221no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1221no—
225C2×C4—2444no—
226C2×C4—2442no—
227C2×C4C2×C4×D6111yescharacteristic
228C2×C4#1175822211yescharacteristic
229C2×C4D4×D6111yescharacteristic
230C2×C4D4×D6111yescharacteristic
231C2×C4D4×D6111yescharacteristic
232C2×C4#1175822411yescharacteristic
233C8—1222no—
234C8—2441no—
235C22—41no—
236C22—41no—
237C22—81no—
238C22—1222no—
239C22—2442no—
240C22C4×C22⋊D6111yescharacteristic
241C22#1451974511yescharacteristic
242C22#1451974811yescharacteristic
243C4—42no—
244C4—41no—
245C4—81no—
246C4—1222no—
247C4—1222no—
248C4—2441no—
249C4C22⋊C4×D6111yescharacteristic
250C4#1451973711yescharacteristic
251C4#1451975011yescharacteristic
252C4#1451975911yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—81no—
257C2—2442no—
258C2#1683963811yescharacteristic
subgroupG/H
centerC4#14519750
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#410C2
socleC2×C61#386
hypercenter#410D61
hypocenterC61#1906
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #16840230C2semidirect
3. #16839780C2semidirect
4. C2×#14519704C2semidirect
5. #16839532C2semidirect
6. #16839521C2semidirect
7. C61×#410C2semidirect
9. #14519808C4semidirect
11. #14519803C4semidirect
33. C2×Q8×C61C2×C4semidirect
35. C2×D4×C61C2×C4semidirect
67. #11758194C2×C4semidirect
134. #410D61semidirect
137. C61#1906semidirect
168. C2×Q8C4×D61semidirect
172. C2×D4C4×D61semidirect