Finite Group Databasebeta

← #21458699

Subgroups — #21458699

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#16840473C211yesmaximal, characteristic
3#16840162C212yesmaximal, complemented
4#16840072C212yesmaximal, complemented
5#16840061C212yesmaximal
6#16840054C211yesmaximal, characteristic, complemented
7#16840039C211yesmaximal, characteristic
8C8×Dic122C211yesmaximal, characteristic, complemented
9C4×#11758190C211yesmaximal, characteristic
10#16839849C212yesmaximal
11C61×#498C211yesmaximal, characteristic, complemented
12C2×#11758190C2211yescharacteristic
13#14519775—21no—
14#14519768C2212yes—
15#14519768C2212yes—
16#14519767—22no—
17#14519757—21no—
18#14519753—22no—
19Q8×Dic61—21no—
20C4×Dic122C2211yescharacteristic
21C4×Dic122C2211yescharacteristic
22#14519742C2212yes—
23C4×D244C2211yescharacteristic
24#14519739C2212yes—
25C4⋊C4×D61—21no—
26#14519710C2212yes—
27#14519710C2212yes—
28#14519709C2211yescharacteristic
29C4⋊#92418C2211yescharacteristic
30#14519706C2212yes—
31#14519702C2211yescharacteristic
32#14519700C2212yes—
33#14519699C2211yescharacteristic
34#14519697C2212yes—
35C8×Dic61C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37C4⋊Q8×C61C2211yescharacteristic
38#106×C61C2212yes—
39#106×C61C2212yes—
40C4×C8×C61C2211yescharacteristic
41C2×Q8×C61—21no—
42C2×Q8×C61—21no—
43C2×D244C2311yescharacteristic
44C2×C4×D61—21no—
45C2×C4×D61—22no—
46C2×Dic122D411yescharacteristic
47C2×Dic122C2311yescharacteristic
48C2×C8×C61C2311yescharacteristic
49C2×C8×C61C2311yescharacteristic
50C4⋊C4×C61—21no—
51C4⋊C4×C61—21no—
52C4⋊C4×C61C2312yes—
53C4⋊C4×C61C2312yes—
54C42×C61C2311yescharacteristic
55#11758198—21no—
56#11758198—22no—
57C4⋊Dic61—22no—
58C4⋊Dic61—22no—
59C4⋊Dic61D411yescharacteristic
60C4⋊Dic61C2311yescharacteristic
61C4⋊Dic61C2311yescharacteristic
62#11758196—21no—
63#11758196—22no—
64#11758196—22no—
65#11758196—22no—
66#11758196D412yes—
67C4×Dic61—21no—
68C4×Dic61—22no—
69C4×Dic61C2312yes—
70C2×#92418C2312yes—
71#11758190Q814yescomplemented
72C22×D61—21no—
73Q8×C61—42no—
74Q8×C61—81no—
75C2×C4×C61—22no—
76C2×C4×C61—22no—
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2411yescharacteristic
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61C2×D412yes—
84C2×Dic61C2×D412yes—
85D244—21no—
86D244C2×Q812yes—
87C4×D61—42no—
88C4×D61—82no—
89Dic122—22no—
90Dic122—21no—
91Dic122C2×Q812yes—
92C8×C61—21no—
93C8×C61C2×Q812yes—
94#92418—22no—
95C22×C61C22×D411yescharacteristic
96C2×D61—22no—
97C2×D61—41no—
98C2×D61—41no—
99C4×C61—21no—
100C4×C61—42no—
101C4×C61—42no—
102C4×C61#13512yes—
103C4×C61C22×Q811yescharacteristic
104C4×C612−1+411yescharacteristic
105Dic61—22no—
106Dic61—22no—
107Dic61—22no—
108Dic61—41no—
109Dic61—41no—
110#3381—611nomaximal, Sylow
111C2×C61D4×Q811yescharacteristic
112C2×C61C2×#13511yescharacteristic
113C2×C61#57711yescharacteristic
114D61—42no—
115#557—611no—
116#554—611no—
117#499—612no—
118#498D6111yescharacteristic, complemented
119#479—612no—
120#478—612no—
121#477—611no—
122#474—611no—
123C8×Q8—611no—
124C4×SD16—612no—
125C4×SD16—611no—
126C61#338111yescharacteristic, complemented, Sylow
127C2×SD16—611no—
128C4⋊Q8—1221no—
129C4⋊Q8C2×D6111yescharacteristic
130C4⋊Q8C2×D6111yescharacteristic
131#125—612no—
132#125—612no—
133#125—1222no—
134C22⋊Q8—1221no—
135C22⋊Q8—1222no—
136C4×Q8—611no—
137C4×Q8—612no—
138C4×Q8—611no—
139C4×Q8—1221no—
140C4×D4—612no—
141C4×D4—611no—
142C2×C4⋊C4—1221no—
143#107—612no—
144#107—612no—
145#106—611no—
146#106C2×D6112yes—
147#106C2×D6112yes—
148C4⋊C8—612no—
149C4⋊C8—611no—
150#103—611no—
151#103—612no—
152#102—611no—
153#102—612no—
154C4×C8—612no—
155C4×C8C2×D6111yescharacteristic
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—611no—
159C2×Q8—611no—
160C2×D4—611no—
161C22×C4—1222no—
162C22×C4—1221no—
163SD16—614no—
164C2×C8—612no—
165C2×C8C22×D6111yescharacteristic
166C2×C8C22×D6111yescharacteristic
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—611no—
170C4⋊C4—612no—
171C4⋊C4—611no—
172C4⋊C4—611no—
173C4⋊C4—1222no—
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1221no—
179C4⋊C4C22×D6112yes—
180C4⋊C4C22×D6112yes—
181C22⋊C4—1222no—
182C22⋊C4—1221no—
183C42—612no—
184C42—1222no—
185C42—1221no—
186C42C22×D6111yescharacteristic
187C23—1221no—
188Q8—42no—
189Q8—81no—
190Q8—612no—
191Q8—1221no—
192Q8—1222no—
193D4—612no—
194D4—1221no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—612no—
198C2×C4—612no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—4882no—
203C2×C4—2442no—
204C2×C4D4×D6111yescharacteristic
205C2×C4D4×D6111yescharacteristic
206C2×C4C23×D6111yescharacteristic
207C8—21no—
208C8—1222no—
209C8Q8×D6112yes—
210C22—1222no—
211C22—2441no—
212C22—2441no—
213C22C2×D4×D6111yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—1222no—
218C4—1222no—
219C4—1222no—
220C4—2441no—
221C4—2441no—
222C4#1451979812yes—
223C4C2×Q8×D6111yescharacteristic
224C4#1451982511yescharacteristic
225C2—2442no—
226C2#1684042711yescharacteristic
227C2C2×#1451979811yescharacteristic
228C2#1684056811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#498C2
socleC22×C61C22×D4
hypercenter#498D61
hypocenterC61#3381
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #16840487C2semidirect
3. #16840162C2semidirect
4. #16840072C2semidirect
6. #16840054C2semidirect
8. C8×Dic122C2semidirect
11. C61×#498C2semidirect
71. #11758190Q8semidirect
118. #498D61semidirect
126. C61#3381semidirect