Finite Group Databasebeta

← #21456897

Subgroups — #21456897

Order 7808.

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

normal subgroups only

This group has 364 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#16840373C211yesmaximal, characteristic, complemented
2#16840332C211yesmaximal, characteristic
3#16840141C211yesmaximal, characteristic, complemented
4#16840131C211yesmaximal, characteristic, complemented
5#16840116C211yesmaximal, characteristic, complemented
6#16839982C212yesmaximal, complemented
7#16839970C212yesmaximal, complemented
8#16839921C212yesmaximal
9#16839916C212yesmaximal, complemented
10#16839824C211yesmaximal, characteristic, complemented
11C61×#497C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic
13C2×Q8×D61C2211yescharacteristic
14C2×#11758202C2212yes—
15C2×#11758202C2212yes—
16#14519777C2211yescharacteristic
17#14519775C2211yescharacteristic
18#14519772—22no—
19#14519769C2211yescharacteristic
20#14519767—22no—
21#14519764C2211yescharacteristic
22#14519759—22no—
23#14519754—22no—
24#14519753C2212yes—
25Q8×Dic61C2212yes—
26#14519734C2211yescharacteristic
27#14519706C2212yes—
28#14519702C2212yes—
29#14519702C2212yes—
30#14519701C2212yes—
31#14519698C2212yes—
32#14519689C2212yes—
33C4×#92418C2211yescharacteristic
34C2×Q16×C61C2212yes—
35C2×SD16×C61C2212yes—
36C4⋊Q8×C61C2211yescharacteristic
37#124×C61C2211yescharacteristic
38#97×C61C2211yescharacteristic
39C2×Q8×C61C2311yescharacteristic
40C2×Q8×C61C2312yes—
41C2×D4×C61C2311yescharacteristic
42C2×C22⋊D61—21no—
43C22×Dic61—21no—
44Q8×D61—42no—
45#11758224—42no—
46C2×C4×D61—21no—
47C2×C4×D61C2311yescharacteristic
48C2×Dic122—21no—
49C2×Dic122C2311yescharacteristic
50C2×Dic122C2311yescharacteristic
51Q16×C61—42no—
52SD16×C61—42no—
53C2×C8×C61C2312yes—
54C4⋊C4×C61—22no—
55C22⋊C4×C61—22no—
56C42×C61C2311yescharacteristic
57C22⋊Dic61—22no—
58#11758202—42no—
59#11758202—42no—
60#11758198—22no—
61#11758198D412yes—
62C4⋊Dic61—22no—
63C4⋊Dic61—22no—
64C4⋊Dic61C2312yes—
65#11758196—22no—
66#11758196—22no—
67#11758196—22no—
68#11758196D412yes—
69C4×Dic61—22no—
70C4×Dic61C2311yescharacteristic
71C2×#92418C2312yes—
72C23×C61—21no—
73C22×D61C2×D411yescharacteristic
74Q8×C61—22no—
75Q8×C61—22no—
76Q8×C61—22no—
77D4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—21no—
80C2×C4×C61C2×D412yes—
81C2×C4×C61C2411yescharacteristic
82C22⋊D61—42no—
83C2×Dic61—22no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—42no—
87C2×Dic61C2×D412yes—
88C2×Dic61C2×D411yescharacteristic
89C4×D61—22no—
90C4×D61—42no—
91Dic122—22no—
92Dic122—22no—
93Dic122—42no—
94C8×C61—22no—
95#92418—22no—
96C22×C61—41no—
97C22×C61—42no—
98C22×C61C22×D411yescharacteristic
99C2×D61—21no—
100C2×D61—22no—
101C4×C61—22no—
102C4×C61—41no—
103C4×C61—42no—
104C4×C61H(5,𝔽2)12yes—
105Dic61—21no—
106Dic61—22no—
107Dic61—41no—
108Dic61—41no—
109Dic61—42no—
110#3223—611nomaximal, Sylow
111C2×C61—81no—
112C2×C61#53511yescharacteristic
113C2×C61#57812yes—
114D61—41no—
115#541—611no—
116#536—611no—
117#497D6111yescharacteristic, complemented
118#494—611no—
119#491—611no—
120#488—611no—
121#464—612no—
122#462—612no—
123#452—612no—
124#451—612no—
125#433—611no—
126C61#322311yescharacteristic, complemented, Sylow
127C2×#41—611no—
128C22×Q8—611no—
129C2×Q16—612no—
130C2×Q16—612no—
131C2×Q16C2×D6112yes—
132C2×SD16C2×D6112yes—
133C4⋊Q8—611no—
134C4⋊Q8—611no—
135C4⋊Q8C2×D6111yescharacteristic
136#126—1222no—
137#125—611no—
138#125—1222no—
139#124—611no—
140#124C2×D6111yescharacteristic
141#123—1222no—
142C22⋊Q8—612no—
143C22⋊Q8—1222no—
144C4×Q8—612no—
145#117—611no—
146C4⋊C8—612no—
147#103—612no—
148#103—612no—
149#103—612no—
150#102—612no—
151C22⋊C8—612no—
152#97C2×D6111yescharacteristic
153C4×C8—611no—
154#41—2442no—
155C2×Q8—611no—
156C2×Q8—611no—
157C2×Q8—1221no—
158C2×Q8—2442no—
159C2×Q8C22×D6111yescharacteristic
160C2×Q8C22×D6112yes—
161C2×D4—1221no—
162C2×D4C22×D6111yescharacteristic
163C22×C4—611no—
164C22×C4—1221no—
165C22×C4—1221no—
166Q16—42no—
167Q16—2442no—
168Q16—2442no—
169SD16—42no—
170C2×C8—612no—
171C2×C8C22×D6112yes—
172C4⋊C4—22no—
173C4⋊C4—612no—
174C4⋊C4—612no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4—1222no—
180C22⋊C4—22no—
181C22⋊C4—612no—
182C22⋊C4—1222no—
183C22⋊C4—1222no—
184C42—611no—
185C42—1222no—
186C42C22×D6111yescharacteristic
187C23—21no—
188C23—611no—
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—1222no—
193Q8—1222no—
194Q8—2442no—
195D4—22no—
196D4—2442no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—612no—
200C2×C4—611no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—2442no—
206C2×C4—2442no—
207C2×C4D4×D6112yes—
208C2×C4C23×D6111yescharacteristic
209C8—22no—
210C8—1222no—
211C22—42no—
212C22—41no—
213C22—1222no—
214C22—1221no—
215C22C2×D4×D6111yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—1222no—
220C4—1221no—
221C4—2442no—
222C4—2441no—
223C4—2441no—
224C4#1451982212yes—
225C2—81no—
226C2—2441no—
227C2#1684032511yescharacteristic
228C2#1684057812yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#497C2
socleC22×C61C22×D4
hypercenter#497D61
hypocenterC61#3223
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #16840373C2semidirect
3. #16840141C2semidirect
4. #16840131C2semidirect
5. #16840116C2semidirect
6. #16839982C2semidirect
7. #16839970C2semidirect
9. #16839916C2semidirect
10. #16839824C2semidirect
11. C61×#497C2semidirect
117. #497D61semidirect
126. C61#3223semidirect