Finite Group Databasebeta

← #21446181

Subgroups — #21446181

Order 7808.

310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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#16839778C211yesmaximal, characteristic, complemented
3#16839758C211yesmaximal, characteristic, complemented
4#16839730C211yesmaximal, characteristic, complemented
5#16839533C211yesmaximal, characteristic, complemented
6#16839526C211yesmaximal, characteristic, complemented
7C61×#568C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—21no—
10#14519807C412yescomplemented
11#14519803—21no—
12#14519802C412yescomplemented
13#14519797—22no—
14C2×#11758194C2211yescharacteristic
15C22×#92418C2211yescharacteristic
16#14519736C2211yescharacteristic
17#14519703—22no—
18#14519701—21no—
19#14519698—21no—
20#14519689—22no—
21C2×#41×C61C2211yescharacteristic
22#131×C61—22no—
23#131×C61—22no—
24C2×M16×C61—22no—
25C2×M16×C61C2211yescharacteristic
26C2×M16×C61C2211yescharacteristic
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
44M16×C61—24no—
45M16×C61—21no—
46M16×C61—21no—
47M16×C61—21no—
48M16×C61D412yes—
49C2×C8×C61—24no—
50C2×C8×C61—21no—
51C2×C8×C61D412yes—
52C22⋊Dic61—21no—
53#11758202—22no—
54#11758201—22no—
55#11758200—22no—
56#11758199—22no—
57C4⋊Dic61—21no—
58C4×Dic61—21no—
59#11758194—21no—
60#11758194C2×C412yes—
61C2×#92418—21no—
62C2×#92418—21no—
63C2×#92418—21no—
64C2×#92418—21no—
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×C61C22×C411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61#4111yescharacteristic
83C22⋊D61—41no—
84C22⋊D61—41no—
85C2×Dic61—21no—
86C2×Dic61—41no—
87D244—21no—
88D244—21no—
89C4×D61—41no—
90C4×D61—41no—
91Dic122—21no—
92Dic122—21no—
93C8×C61—22no—
94C8×C61—22no—
95#92418—22no—
96#92418—41no—
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×C61C2×C22⋊C411yescharacteristic
107C4×C61C4×D411yescharacteristic
108C4×C61#12011yescharacteristic
109C4×C61#12111yescharacteristic
110Dic61—41no—
111Dic61—81no—
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#568D6111yescharacteristic, complemented
121#421—611no—
122#416—611no—
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—22no—
135#131—22no—
136C2×M16—22no—
137C2×M16—611no—
138C2×M16C2×D6111yescharacteristic
139C2×M16C2×D6111yescharacteristic
140C22×C8—611no—
141#117—611no—
142#104—1222no—
143#103—1221no—
144#102—1221no—
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#41C22⋊D6112yes—
154C2×Q8—611no—
155C2×Q8D24411yescharacteristic
156C2×D4—21no—
157C2×D4—611no—
158C2×D4—1221no—
159C2×D4D24411yescharacteristic
160C22×C4—21no—
161C22×C4—1221no—
162C22×C4C22×D6111yescharacteristic
163Q16—1222no—
164SD16—1222no—
165SD16—1222no—
166D8—1222no—
167M16—24no—
168M16—21no—
169M16—21no—
170M16—21no—
171M16—612no—
172M16—1221no—
173M16C22⋊D6112yes—
174C2×C8—24no—
175C2×C8—21no—
176C2×C8—1221no—
177C2×C8—1221no—
178C2×C8—1221no—
179C2×C8—1221no—
180C2×C8C22⋊D6112yes—
181C4⋊C4—1221no—
182C22⋊C4—1221no—
183C42—1221no—
184C23—21no—
185C23—1221no—
186C23#1175822211yescharacteristic
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—1221no—
203C2×C4—2441no—
204C2×C4—2441no—
205C2×C4—2441no—
206C2×C4C2×C4×D6111yescharacteristic
207C2×C4C2×D24411yescharacteristic
208C2×C4#1175822211yescharacteristic
209C2×C4C2×C22⋊D6111yescharacteristic
210C2×C4C2×C22⋊D6111yescharacteristic
211C2×C4C2×C22⋊D6111yescharacteristic
212C8—22no—
213C8—22no—
214C8—1222no—
215C8—2441no—
216C22—22no—
217C22—41no—
218C22—81no—
219C22—2442no—
220C22—2441no—
221C22C4×C22⋊D6111yescharacteristic
222C22#1451975111yescharacteristic
223C22#1451976011yescharacteristic
224C4—22no—
225C4—4881no—
226C4—2441no—
227C4C2×#1175819811yescharacteristic
228C4C4×C22⋊D6111yescharacteristic
229C4#1451974611yescharacteristic
230C4#1451975111yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—42no—
235C2—4881no—
236C2#1683964111yescharacteristic
subgroupG/H
centerC4#14519746
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#568C2
socleC2×C61#386
hypercenter#568D61
hypocenterC61#1881
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #16839778C2semidirect
3. #16839758C2semidirect
4. #16839730C2semidirect
5. #16839533C2semidirect
6. #16839526C2semidirect
7. C61×#568C2semidirect
10. #14519807C4semidirect
12. #14519802C4semidirect
120. #568D61semidirect
126. C61#1881semidirect