Finite Group Databasebeta

← #21447033

Subgroups — #21447033

Order 7808.

278 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 71 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#16839805C211yesmaximal, characteristic, complemented
2C2×#14519704C211yesmaximal, characteristic
3#16839763C211yesmaximal, characteristic
4C2×#14519696C211yesmaximal, characteristic, complemented
5#16839669C211yesmaximal, characteristic, complemented
6#16839521C211yesmaximal, characteristic, complemented
7C61×#536C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C2×C4⋊Dic61C2211yescharacteristic
11C2×C4×Dic61C2211yescharacteristic
12#14519710—21no—
13#14519708—21no—
14#14519704—22no—
15#14519701—21no—
16#14519698—21no—
17#14519696—22no—
18#14519684—22no—
19C2×#41×C61C2211yescharacteristic
20C22×Q8×C61C2211yescharacteristic
21C4⋊Q8×C61—21no—
22#124×C61—21no—
23#123×C61—22no—
24C22⋊Q8×C61—21no—
25C22⋊Q8×C61—21no—
26#117×C61C2211yescharacteristic
27#41×C61—21no—
28#41×C61—21no—
29#41×C61—21no—
30#41×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61—21no—
35C2×Q8×C61—21no—
36C2×Q8×C61—21no—
37C2×Q8×C61D411yescharacteristic
38C2×D4×C61—21no—
39C2×D4×C61D411yescharacteristic
40C22×C4×C61—21no—
41C22×C4×C61D412yes—
42C22×C4×C61C2311yescharacteristic
43C22×Dic61—21no—
44C22×Dic61—21no—
45C4⋊C4×C61—22no—
46C4⋊C4×C61—22no—
47C4⋊C4×C61D411yescharacteristic
48C4⋊C4×C61D411yescharacteristic
49C22⋊C4×C61—22no—
50C22⋊C4×C61—22no—
51C22⋊C4×C61—21no—
52C42×C61—21no—
53C4⋊Dic61—21no—
54C4⋊Dic61—21no—
55C4×Dic61—21no—
56C4×Dic61—21no—
57#11758194—21no—
58#11758194—21no—
59#11758194—21no—
60#11758194D412yes—
61C2×#92418—21no—
62C2×#92418—21no—
63C23×C61—21no—
64C23×C61C2×D411yescharacteristic
65Q8×C61—21no—
66Q8×C61—21no—
67Q8×C61—41no—
68Q8×C61—41no—
69Q8×C61—41no—
70Q8×C61—41no—
71D4×C61—21no—
72D4×C61—21no—
73D4×C61—41no—
74D4×C61—41no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61#4111yescharacteristic
87C2×C4×C61#4111yescharacteristic
88C2×C4×C61#4111yescharacteristic
89C2×Dic61—22no—
90C2×Dic61—41no—
91C2×Dic61—41no—
92C2×Dic61—42no—
93C2×Dic61—41no—
94#92418—22no—
95#92418—41no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61#12011yescharacteristic
102C22×C61#12111yescharacteristic
103C22×C61#12311yescharacteristic
104C4×C61—42no—
105C4×C61—41no—
106C4×C61—41no—
107C4×C61—41no—
108C4×C61#12111yescharacteristic
109C4×C61#12111yescharacteristic
110C4×C61#12311yescharacteristic
111C4×C61#12411yescharacteristic
112Dic61—42no—
113Dic61—81no—
114#2038—611nomaximal, Sylow
115C2×C61—21no—
116C2×C61—21no—
117C2×C61—81no—
118C2×C61#39411yescharacteristic
119C2×C61#45411yescharacteristic
120C2×C61#45611yescharacteristic
121#536D6111yescharacteristic
122#428—611no—
123C2×#104—611no—
124#417—611no—
125C2×#101—611no—
126#391—611no—
127#339—611no—
128C61#203811yescharacteristic, complemented, Sylow
129C2×#41C2×D6111yescharacteristic
130C22×Q8C2×D6111yescharacteristic
131C2×M16—611no—
132C2×M16—611no—
133C4⋊Q8—21no—
134#124—21no—
135#123—22no—
136C22⋊Q8—21no—
137C22⋊Q8—21no—
138#117C2×D6111yescharacteristic
139C2×C4⋊C4—611no—
140C2×C42—611no—
141#107—1221no—
142#106—1221no—
143#104—1222no—
144#103—1221no—
145#102—1221no—
146#101—1222no—
147#95—1222no—
148#41—21no—
149#41—21no—
150#41—21no—
151#41—21no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8C22⋊D6111yescharacteristic
159C2×D4—21no—
160C2×D4C22⋊D6111yescharacteristic
161C22×C4—21no—
162C22×C4—1221no—
163C22×C4—1221no—
164C22×C4C22⋊D6112yes—
165C22×C4C22×D6111yescharacteristic
166M16—612no—
167M16—1221no—
168M16—1221no—
169M16—1221no—
170C2×C8—1221no—
171C2×C8—1221no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—1221no—
175C4⋊C4—1221no—
176C4⋊C4C22⋊D6111yescharacteristic
177C4⋊C4C22⋊D6111yescharacteristic
178C22⋊C4—22no—
179C22⋊C4—22no—
180C22⋊C4—21no—
181C42—21no—
182C42—1221no—
183C42—1221no—
184C23—21no—
185C23C2×C22⋊D6111yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—41no—
192D4—21no—
193D4—21no—
194D4—41no—
195D4—41no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—1222no—
205C2×C4—2442no—
206C2×C4—2441no—
207C2×C4—2441no—
208C2×C4—2441no—
209C2×C4D4×D6111yescharacteristic
210C2×C4#1175822411yescharacteristic
211C2×C4#1175822411yescharacteristic
212C2×C4#1175822411yescharacteristic
213C2×C4C2×C22⋊D6111yescharacteristic
214C2×C4C2×C22⋊D6111yescharacteristic
215C8—1222no—
216C8—2441no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22#1451974611yescharacteristic
223C22#1451974911yescharacteristic
224C22#1451975811yescharacteristic
225C4—41no—
226C4—42no—
227C4—41no—
228C4—41no—
229C4—4881no—
230C4—2442no—
231C4#1451974811yescharacteristic
232C4#1451974911yescharacteristic
233C4#1451975811yescharacteristic
234C4#1451976411yescharacteristic
235C2—21no—
236C2—21no—
237C2—81no—
238C2#1683967611yescharacteristic
239C2#1683993511yescharacteristic
240C2#1683994511yescharacteristic
subgroupG/H
centerC22#14519746
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#536C2
socleC22×C61#120
hypercenter#536D61
hypocenterC61#2038
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #16839805C2semidirect
4. C2×#14519696C2semidirect
5. #16839669C2semidirect
6. #16839521C2semidirect
128. C61#2038semidirect