Finite Group Databasebeta

← #21458698

Subgroups — #21458698

Order 7808.

338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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#16840487C211yesmaximal, characteristic, complemented
2#16840469C211yesmaximal, characteristic
3#16840163C212yesmaximal, complemented
4#16840158C211yesmaximal, characteristic, complemented
5#16840068C212yesmaximal, complemented
6#16840060C212yesmaximal
7#16840058C211yesmaximal, characteristic, complemented
8#16839886C211yesmaximal, characteristic, complemented
9#16839853C212yesmaximal
10C4×#11758200C211yesmaximal, characteristic
11C61×#474C211yesmaximal, characteristic
12C2×#11758200C2211yescharacteristic
13#14519777C2211yescharacteristic
14#14519775—21no—
15#14519768C2212yes—
16#14519768C2212yes—
17#14519767—22no—
18#14519756—21no—
19#14519754—22no—
20Q8×Dic61—21no—
21C4×Dic122C2211yescharacteristic
22C4×Dic122C2211yescharacteristic
23#14519742C2212yes—
24D4×Dic61C2212yes—
25C2×C4⋊Dic61—21no—
26#14519711C2212yes—
27#14519708C2212yes—
28#14519708C2211yescharacteristic
29#14519708C2212yes—
30#14519706C2212yes—
31#14519702C2212yes—
32#14519700C2211yescharacteristic
33#14519698C2211yescharacteristic
34C4×#92418C2211yescharacteristic
35C8×Dic61C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37C4×D4×C61C2211yescharacteristic
38#107×C61C2212yes—
39C4⋊C8×C61C2211yescharacteristic
40#102×C61C2212yes—
41C2×Q8×C61—21no—
42C2×D4×C61C2311yescharacteristic
43C22×C4×C61—21no—
44C22×Dic61—22no—
45C2×Dic122—21no—
46C2×Dic122D411yescharacteristic
47C2×Dic122C2311yescharacteristic
48C2×C8×C61C2312yes—
49C4⋊C4×C61—21no—
50C4⋊C4×C61C2312yes—
51C4⋊C4×C61C2311yescharacteristic
52C22⋊C4×C61—21no—
53C42×C61C2311yescharacteristic
54C22⋊Dic61—22no—
55#11758200Q814yescomplemented
56C4⋊Dic61—21no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61D411yescharacteristic
60C4⋊Dic61C2311yescharacteristic
61C4⋊Dic61C2312yes—
62#11758196—21no—
63#11758196—22no—
64#11758196—22no—
65#11758196—22no—
66#11758196D412yes—
67C4×Dic61—21no—
68C4×Dic61—22no—
69C4×Dic61C2312yes—
70C2×#92418C2311yescharacteristic
71C2×#92418C2311yescharacteristic
72C23×C61—21no—
73Q8×C61—42no—
74D4×C61—21no—
75D4×C61C2×Q812yes—
76C2×C4×C61—22no—
77C2×C4×C61—21no—
78C2×C4×C61—42no—
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2411yescharacteristic
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—22no—
85C2×Dic61—82no—
86C2×Dic61C2×D412yes—
87C2×Dic61C2×D412yes—
88Dic122—22no—
89Dic122—21no—
90Dic122—81no—
91Dic122C2×Q812yes—
92C8×C61—22no—
93#92418—21no—
94#92418C2×Q812yes—
95C22×C61—22no—
96C22×C61—41no—
97C22×C61—41no—
98C22×C61C22×D411yescharacteristic
99C4×C61—21no—
100C4×C61—41no—
101C4×C61—42no—
102C4×C61#13512yes—
103C4×C61C22×Q811yescharacteristic
104C4×C612−1+411yescharacteristic
105Dic61—22no—
106Dic61—22no—
107Dic61—22no—
108Dic61—42no—
109Dic61—41no—
110#3381—611nomaximal, Sylow
111C2×C61—42no—
112C2×C61D4×Q811yescharacteristic
113C2×C61C2×#13511yescharacteristic
114C2×C61#57711yescharacteristic
115#557—611no—
116#554—611no—
117#499—612no—
118#498—611no—
119#479—612no—
120#478—612no—
121#477—611no—
122#474D6111yescharacteristic
123C8×Q8—611no—
124C4×SD16—611no—
125C4×SD16—612no—
126C61#338111yescharacteristic, complemented, Sylow
127C2×SD16—611no—
128C4⋊Q8—611no—
129C4⋊Q8—1221no—
130C4⋊Q8C2×D6111yescharacteristic
131#125—612no—
132#125—612no—
133#125—1222no—
134C22⋊Q8—1222no—
135C22⋊Q8—1221no—
136C4×Q8—611no—
137C4×Q8—612no—
138C4×Q8—611no—
139C4×Q8—1221no—
140C4×D4—612no—
141C4×D4C2×D6111yescharacteristic
142C2×C4⋊C4—1221no—
143#107—612no—
144#107C2×D6112yes—
145#106—612no—
146#106—611no—
147#106—612no—
148C4⋊C8—612no—
149C4⋊C8C2×D6111yescharacteristic
150#103—612no—
151#103—611no—
152#102—611no—
153#102C2×D6112yes—
154C4×C8—612no—
155C4×C8—611no—
156C2×Q8—21no—
157C2×Q8—611no—
158C2×Q8—611no—
159C2×Q8—1221no—
160C2×D4C22×D6111yescharacteristic
161C22×C4—21no—
162C22×C4—1222no—
163SD16—614no—
164C2×C8—611no—
165C2×C8—611no—
166C2×C8C22×D6112yes—
167C4⋊C4—21no—
168C4⋊C4—611no—
169C4⋊C4—612no—
170C4⋊C4—611no—
171C4⋊C4—612no—
172C4⋊C4—1222no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—1221no—
178C4⋊C4—1221no—
179C4⋊C4C22×D6112yes—
180C4⋊C4C22×D6111yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—1222no—
183C42—612no—
184C42—1222no—
185C42—1221no—
186C42C22×D6111yescharacteristic
187C23—21no—
188Q8—42no—
189Q8—612no—
190Q8—1221no—
191Q8—1222no—
192Q8—4881no—
193D4—21no—
194D4Q8×D6112yes—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—612no—
199C2×C4—612no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1222no—
203C2×C4—4882no—
204C2×C4D4×D6111yescharacteristic
205C2×C4D4×D6111yescharacteristic
206C2×C4C23×D6111yescharacteristic
207C8—22no—
208C8—612no—
209C8—1221no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22C2×D4×D6111yescharacteristic
214C4—21no—
215C4—41no—
216C4—42no—
217C4—1222no—
218C4—1222no—
219C4—1222no—
220C4—2441no—
221C4—2442no—
222C4#1451979612yes—
223C4C2×Q8×D6111yescharacteristic
224C4#1451982411yescharacteristic
225C2—42no—
226C2#1684042511yescharacteristic
227C2C2×#1451979611yescharacteristic
228C2#1684057111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#474C2
socleC22×C61C22×D4
hypercenter#474D61
hypocenterC61#3381
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #16840487C2semidirect
3. #16840163C2semidirect
4. #16840158C2semidirect
5. #16840068C2semidirect
7. #16840058C2semidirect
8. #16839886C2semidirect
55. #11758200Q8semidirect
126. C61#3381semidirect