Finite Group Databasebeta

← #21456875

Subgroups — #21456875

Order 7808.

388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 109 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#16840366C211yesmaximal, characteristic, complemented
2#16840332C211yesmaximal, characteristic, complemented
3#16840134C211yesmaximal, characteristic, complemented
4#16840131C211yesmaximal, characteristic, complemented
5#16840116C211yesmaximal, characteristic, complemented
6#16839975C212yesmaximal, complemented
7#16839965C212yesmaximal, complemented
8#16839904C212yesmaximal, complemented
9#16839899C212yesmaximal, complemented
10#16839824C211yesmaximal, characteristic, complemented
11C61×#496C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic
13C2×Q8×D61C2211yescharacteristic
14C2×#11758200C2212yes—
15C2×#11758200C2212yes—
16#14519777C2211yescharacteristic
17#14519775C2211yescharacteristic
18#14519769C2211yescharacteristic
19#14519764C2211yescharacteristic
20#14519759—22no—
21#14519758—22no—
22#14519754—22no—
23#14519749—22no—
24#14519748C2212yes—
25D4×Dic61C2212yes—
26#14519734C2211yescharacteristic
27#14519706C2212yes—
28#14519702C2212yes—
29#14519702C2212yes—
30#14519701C2212yes—
31#14519698C2212yes—
32#14519689C2212yes—
33C4×#92418C2211yescharacteristic
34C2×SD16×C61C2212yes—
35C2×D8×C61C2212yes—
36#127×C61C2211yescharacteristic
37#124×C61C2211yescharacteristic
38#97×C61C2211yescharacteristic
39C2×Q8×C61C2311yescharacteristic
40C2×D4×C61—22no—
41C2×D4×C61C2311yescharacteristic
42C2×D4×C61C2312yes—
43C2×C22⋊D61—21no—
44C2×C22⋊D61—22no—
45C22×Dic61—21no—
46C22×Dic61—22no—
47Q8×D61—42no—
48#11758224—42no—
49C2×C4×D61—21no—
50C2×C4×D61C2311yescharacteristic
51C2×Dic122—21no—
52C2×Dic122C2311yescharacteristic
53C2×Dic122C2311yescharacteristic
54SD16×C61—42no—
55D8×C61—42no—
56C2×C8×C61C2312yes—
57C22⋊C4×C61—22no—
58C42×C61C2311yescharacteristic
59C22⋊Dic61—22no—
60C22⋊Dic61—22no—
61C22⋊Dic61—22no—
62#11758200—42no—
63#11758200—42no—
64#11758198D412yes—
65C4⋊Dic61—22no—
66C4⋊Dic61C2312yes—
67#11758196—22no—
68#11758196—22no—
69#11758196D412yes—
70C4×Dic61C2311yescharacteristic
71C2×#92418C2312yes—
72C23×C61—21no—
73C23×C61—22no—
74C22×D61C2×D411yescharacteristic
75Q8×C61—22no—
76D4×C61—22no—
77D4×C61—22no—
78D4×C61—22no—
79D4×C61—82no—
80C2×C4×C61—21no—
81C2×C4×C61C2×D412yes—
82C2×C4×C61C2411yescharacteristic
83C22⋊D61—42no—
84C22⋊D61—82no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—21no—
88C2×Dic61—42no—
89C2×Dic61—82no—
90C2×Dic61C2×D412yes—
91C2×Dic61C2×D411yescharacteristic
92C4×D61—22no—
93C4×D61—42no—
94Dic122—22no—
95Dic122—22no—
96Dic122—42no—
97C8×C61—22no—
98#92418—22no—
99C22×C61—41no—
100C22×C61—42no—
101C22×C61—42no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61C22×D411yescharacteristic
105C2×D61—21no—
106C2×D61—22no—
107C4×C61—22no—
108C4×C61—41no—
109C4×C61H(5,𝔽2)12yes—
110Dic61—21no—
111Dic61—22no—
112Dic61—41no—
113Dic61—41no—
114Dic61—42no—
115#3221—611nomaximal, Sylow
116C2×C61—81no—
117C2×C61—82no—
118C2×C61#53511yescharacteristic
119C2×C61#57712yes—
120D61—41no—
121#540—611no—
122#536—611no—
123#496D6111yescharacteristic, complemented
124#492—611no—
125#491—611no—
126#488—611no—
127#463—612no—
128#461—612no—
129#449—612no—
130#448—612no—
131#433—611no—
132C61#322111yescharacteristic, complemented, Sylow
133C2×#41—611no—
134C22×Q8—611no—
135C2×SD16—612no—
136C2×SD16—612no—
137C2×SD16C2×D6112yes—
138C2×D8C2×D6112yes—
139C4⋊Q8—611no—
140C4⋊Q8—611no—
141#127C2×D6111yescharacteristic
142#125—611no—
143#124—611no—
144#124C2×D6111yescharacteristic
145#123—1222no—
146#123—1222no—
147C22⋊Q8—1222no—
148#121—612no—
149#121—1222no—
150C4×D4—612no—
151#117—611no—
152C4⋊C8—612no—
153#103—612no—
154#103—612no—
155#103—612no—
156#102—612no—
157C22⋊C8—612no—
158#97C2×D6111yescharacteristic
159C4×C8—611no—
160#41—2442no—
161C2×Q8—611no—
162C2×Q8—611no—
163C2×Q8—1221no—
164C2×Q8—2442no—
165C2×Q8C22×D6111yescharacteristic
166C2×D4—22no—
167C2×D4—1222no—
168C2×D4—1221no—
169C2×D4C22×D6111yescharacteristic
170C2×D4C22×D6112yes—
171C22×C4—611no—
172C22×C4—1221no—
173C22×C4—1222no—
174C22×C4—1221no—
175SD16—42no—
176SD16—2442no—
177SD16—2442no—
178D8—42no—
179C2×C8—612no—
180C2×C8C22×D6112yes—
181C4⋊C4—612no—
182C4⋊C4—612no—
183C4⋊C4—1222no—
184C4⋊C4—1222no—
185C4⋊C4—1222no—
186C22⋊C4—22no—
187C22⋊C4—612no—
188C22⋊C4—1222no—
189C22⋊C4—1222no—
190C22⋊C4—1222no—
191C42—611no—
192C42C22×D6111yescharacteristic
193C23—21no—
194C23—22no—
195C23—611no—
196Q8—22no—
197Q8—1222no—
198Q8—1222no—
199Q8—2442no—
200D4—22no—
201D4—22no—
202D4—22no—
203D4—82no—
204D4—4882no—
205D4—2442no—
206C2×C4—21no—
207C2×C4—612no—
208C2×C4—611no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—4882no—
214C2×C4—2442no—
215C2×C4—2442no—
216C2×C4D4×D6112yes—
217C2×C4C23×D6111yescharacteristic
218C8—22no—
219C8—1222no—
220C22—42no—
221C22—42no—
222C22—42no—
223C22—41no—
224C22—42no—
225C22—1222no—
226C22—1221no—
227C22C2×D4×D6111yescharacteristic
228C4—22no—
229C4—41no—
230C4—1222no—
231C4—1221no—
232C4—2442no—
233C4—2441no—
234C4—2441no—
235C4#1451982212yes—
236C2—82no—
237C2—81no—
238C2—2441no—
239C2#1684032511yescharacteristic
240C2#1684057212yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#496C2
socleC22×C61C22×D4
hypercenter#496D61
hypocenterC61#3221
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #16840366C2semidirect
2. #16840332C2semidirect
3. #16840134C2semidirect
4. #16840131C2semidirect
5. #16840116C2semidirect
6. #16839975C2semidirect
7. #16839965C2semidirect
8. #16839904C2semidirect
9. #16839899C2semidirect
10. #16839824C2semidirect
11. C61×#496C2semidirect
123. #496D61semidirect
132. C61#3221semidirect