Finite Group Databasebeta

← #21446179

Subgroups — #21446179

Order 7808.

310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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#16840529C211yesmaximal, characteristic, complemented
3#16839780C211yesmaximal, characteristic, complemented
4#16839728C211yesmaximal, characteristic, complemented
5#16839532C211yesmaximal, characteristic, complemented
6#16839527C211yesmaximal, characteristic, complemented
7C61×#416C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—21no—
10#14519807C412yescomplemented
11#14519803—21no—
12#14519802C412yescomplemented
13#14519797—22no—
14#14519784—22no—
15#14519784—22no—
16C2×#11758194—22no—
17C2×#11758194C2211yescharacteristic
18C2×#11758194C2211yescharacteristic
19C2×#11758194C2211yescharacteristic
20#14519705—22no—
21#14519689—22no—
22C2×#41×C61C2211yescharacteristic
23C22×C8×C61C2211yescharacteristic
24#117×C61C2211yescharacteristic
25#103×C61—21no—
26#102×C61—21no—
27#41×C61—21no—
28#41×C61—21no—
29#41×C61C2×C412yes—
30#41×C61D412yes—
31C2×Q8×C61D411yescharacteristic
32C2×D4×C61—21no—
33C2×D4×C61D411yescharacteristic
34C22×C4×C61—21no—
35C22×C4×C61C2311yescharacteristic
36C2×C22⋊D61—21no—
37#11758222—21no—
38#11758222—21no—
39#11758222—21no—
40#11758222—21no—
41C2×D244C2×C411yescharacteristic
42C2×C4×D61—21no—
43C2×Dic122C2×C411yescharacteristic
44C2×C8×C61—21no—
45C2×C8×C61—21no—
46C2×C8×C61—21no—
47C4⋊C4×C61—21no—
48C22⋊C4×C61—21no—
49C42×C61—21no—
50#11758202—22no—
51#11758201—22no—
52#11758200—22no—
53#11758199—22no—
54#11758194—24no—
55#11758194—21no—
56#11758194—21no—
57#11758194—21no—
58#11758194—21no—
59#11758194C2×C412yes—
60#11758194D412yes—
61C2×#92418—24no—
62C2×#92418—21no—
63C2×#92418—21no—
64C2×#92418D412yes—
65C23×C61—21no—
66C23×C61#4111yescharacteristic
67C22×D61—21no—
68Q8×C61—21no—
69Q8×C61C22⋊C412yes—
70D4×C61—22no—
71D4×C61—22no—
72D4×C61—21no—
73D4×C61C22⋊C412yes—
74C2×C4×C61—21no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61—41no—
78C2×C4×C61C22×C411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C22⋊D61—41no—
85C22⋊D61—41no—
86C2×Dic61—21no—
87D244—21no—
88D244—21no—
89C4×D61—41no—
90C4×D61—41no—
91Dic122—21no—
92Dic122—21no—
93C8×C61—41no—
94#92418—22no—
95#92418—22no—
96#92418—22no—
97C22×C61—22no—
98C22×C61—41no—
99C22×C61—81no—
100C22×C61C4×D411yescharacteristic
101C22×C61#12111yescharacteristic
102C22×C61#12311yescharacteristic
103C2×D61—42no—
104C2×D61—41no—
105C4×C61—22no—
106C4×C61—81no—
107C4×C61C2×C22⋊C411yescharacteristic
108C4×C61C4×D411yescharacteristic
109C4×C61#12011yescharacteristic
110C4×C61#12111yescharacteristic
111Dic61—41no—
112#1881—611nomaximal, Sylow
113C2×C61—21no—
114C2×C61—21no—
115C2×C61—21no—
116C2×C61—42no—
117C2×C61#38611yescharacteristic
118D61—81no—
119#575—611no—
120#568—611no—
121#421—611no—
122#416D6111yescharacteristic, complemented
123#408—611no—
124#344—611no—
125#341—611no—
126C61#188111yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C2×#41C2×D6111yescharacteristic
129#137—612no—
130#137—1221no—
131AGL(1,ℤ/8)—612no—
132AGL(1,ℤ/8)—1221no—
133#135—1222no—
134#131—1222no—
135#131—1222no—
136C2×M16—611no—
137C2×M16—611no—
138C2×M16—611no—
139C2×M16—1222no—
140C22×C8C2×D6111yescharacteristic
141#117C2×D6111yescharacteristic
142#104—1222no—
143#103—21no—
144#102—21no—
145C22⋊C8—1222no—
146#41—21no—
147#41—21no—
148#41—1221no—
149#41—1221no—
150#41—1221no—
151#41—1221no—
152#41C4×D6112yes—
153#41D24412yes—
154C2×Q8—611no—
155C2×Q8C22⋊D6111yescharacteristic
156C2×D4—21no—
157C2×D4—611no—
158C2×D4—1221no—
159C2×D4C22⋊D6111yescharacteristic
160C22×C4—21no—
161C22×C4—1221no—
162C22×C4C22×D6111yescharacteristic
163Q16—1222no—
164SD16—1222no—
165SD16—1222no—
166D8—1222no—
167M16—612no—
168M16—612no—
169M16—1224no—
170M16—1221no—
171M16—1221no—
172M16—1221no—
173M16—1221no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—612no—
178C2×C8—1224no—
179C2×C8—1221no—
180C2×C8—1221no—
181C4⋊C4—21no—
182C22⋊C4—21no—
183C42—21no—
184C23—21no—
185C23—1221no—
186C23#1175822411yescharacteristic
187Q8—21no—
188Q8—1221no—
189Q8—1221no—
190Q8#1175819812yes—
191D4—22no—
192D4—22no—
193D4—21no—
194D4—1221no—
195D4—1221no—
196D4—2441no—
197D4—2441no—
198D4#1175819812yes—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—1221no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4C2×C4×D6111yescharacteristic
207C2×C4C2×D24411yescharacteristic
208C2×C4D4×D6111yescharacteristic
209C2×C4D4×D6111yescharacteristic
210C2×C4#1175822411yescharacteristic
211C2×C4C2×C22⋊D6111yescharacteristic
212C8—41no—
213C8—1222no—
214C8—1222no—
215C8—1222no—
216C22—22no—
217C22—41no—
218C22—81no—
219C22—2442no—
220C22—2441no—
221C22#1451973711yescharacteristic
222C22#1451974911yescharacteristic
223C22#1451976111yescharacteristic
224C4—22no—
225C4—81no—
226C4—2441no—
227C4C2×#1175819811yescharacteristic
228C4#1451973711yescharacteristic
229C4#1451974711yescharacteristic
230C4#1451974911yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—42no—
235C2—4881no—
236C2#1683963911yescharacteristic
subgroupG/H
centerC4#14519747
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#416C2
socleC2×C61#386
hypercenter#416D61
hypocenterC61#1881
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #16840529C2semidirect
3. #16839780C2semidirect
4. #16839728C2semidirect
5. #16839532C2semidirect
6. #16839527C2semidirect
7. C61×#416C2semidirect
10. #14519807C4semidirect
12. #14519802C4semidirect
122. #416D61semidirect
126. C61#1881semidirect