Finite Group Databasebeta

← #21456902

Subgroups — #21456902

Order 7808.

364 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 117 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#16840374C211yesmaximal, characteristic, complemented
2#16840157C211yesmaximal, characteristic, complemented
3#16840141C211yesmaximal, characteristic, complemented
4#16840130C211yesmaximal, characteristic, complemented
5#16840116C211yesmaximal, characteristic, complemented
6#16839981C212yesmaximal, complemented
7#16839969C212yesmaximal, complemented
8#16839924C212yesmaximal
9#16839918C212yesmaximal, complemented
10#16839823C211yesmaximal, characteristic, complemented
11C61×#536C211yesmaximal, characteristic
12C2×#11758202C2212yes—
13C2×#11758202C2212yes—
14C2×#11758202C2212yes—
15C2×#11758200C2212yes—
16#14519777C2211yescharacteristic
17#14519770—22no—
18#14519769C2211yescharacteristic
19#14519767—22no—
20#14519756C2212yes—
21C4×Dic122C2212yes—
22C4⋊#92418C2212yes—
23#14519701C2212yes—
24#14519701C2212yes—
25#14519701C2212yes—
26#14519698C2212yes—
27C22⋊#92418C2212yes—
28#14519688C2211yescharacteristic
29C4×#92418C2211yescharacteristic
30C2×#41×C61C2211yescharacteristic
31C22×Q8×C61C2211yescharacteristic
32C4⋊Q8×C61C2211yescharacteristic
33C4⋊Q8×C61C2211yescharacteristic
34#124×C61C2211yescharacteristic
35#124×C61C2211yescharacteristic
36#123×C61—22no—
37C22⋊Q8×C61—22no—
38#117×C61C2211yescharacteristic
39#41×C61—42no—
40C2×Q8×C61—21no—
41C2×Q8×C61—42no—
42C2×Q8×C61C2311yescharacteristic
43C2×Q8×C61C2311yescharacteristic
44C2×Q8×C61C2311yescharacteristic
45C2×D4×C61—21no—
46C2×D4×C61C2311yescharacteristic
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C2311yescharacteristic
50C2×Dic122C2312yes—
51C4⋊C4×C61—22no—
52C4⋊C4×C61—22no—
53C4⋊C4×C61D412yes—
54C22⋊C4×C61—22no—
55C22⋊C4×C61—22no—
56C22⋊C4×C61D412yes—
57C42×C61C2311yescharacteristic
58C42×C61C2311yescharacteristic
59C22⋊Dic61—22no—
60#11758202—42no—
61#11758202—42no—
62#11758202—42no—
63#11758200—42no—
64C4⋊Dic61—22no—
65C4⋊Dic61C2312yes—
66#11758196—22no—
67#11758196—22no—
68#11758196—22no—
69C4×Dic61—22no—
70C2×#92418C2312yes—
71C2×#92418C2312yes—
72C23×C61—21no—
73C23×C61C2×D411yescharacteristic
74Q8×C61—22no—
75Q8×C61—22no—
76Q8×C61—22no—
77Q8×C61—42no—
78D4×C61—22no—
79D4×C61—42no—
80C2×C4×C61—22no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—42no—
85C2×C4×C61—42no—
86C2×C4×C61C2×D412yes—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D412yes—
89C2×C4×C61C2411yescharacteristic
90C2×Dic61—22no—
91C2×Dic61—22no—
92Dic122—22no—
93Dic122—22no—
94#92418—22no—
95#92418—22no—
96C22×C61—21no—
97C22×C61—22no—
98C22×C61—41no—
99C22×C61—42no—
100C22×C61C22×D411yescharacteristic
101C4×C61—21no—
102C4×C61—22no—
103C4×C61—22no—
104C4×C61—41no—
105C4×C61—41no—
106C4×C61—41no—
107C4×C61H(5,𝔽2)12yes—
108Dic61—42no—
109Dic61—42no—
110#3223—611nomaximal, Sylow
111C2×C61—41no—
112C2×C61—81no—
113C2×C61#53511yescharacteristic
114C2×C61#57812yes—
115#541—611no—
116#536D6111yescharacteristic
117#497—611no—
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×#41C2×D6111yescharacteristic
128C22×Q8C2×D6111yescharacteristic
129C2×Q16—612no—
130C2×Q16—612no—
131C2×Q16—612no—
132C2×SD16—612no—
133C4⋊Q8—611no—
134C4⋊Q8C2×D6111yescharacteristic
135C4⋊Q8C2×D6111yescharacteristic
136#126—1222no—
137#125—611no—
138#125—1222no—
139#124C2×D6111yescharacteristic
140#124C2×D6111yescharacteristic
141#123—22no—
142C22⋊Q8—22no—
143C22⋊Q8—612no—
144C4×Q8—612no—
145#117C2×D6111yescharacteristic
146C4⋊C8—612no—
147#103—612no—
148#103—612no—
149#103—612no—
150#102—612no—
151C22⋊C8—612no—
152#97—611no—
153C4×C8—611no—
154#41—42no—
155C2×Q8—21no—
156C2×Q8—42no—
157C2×Q8—612no—
158C2×Q8C22×D6111yescharacteristic
159C2×Q8C22×D6111yescharacteristic
160C2×Q8C22×D6111yescharacteristic
161C2×D4—21no—
162C2×D4C22×D6111yescharacteristic
163C22×C4—21no—
164C22×C4—21no—
165C22×C4C22×D6111yescharacteristic
166Q16—2442no—
167Q16—2442no—
168Q16—2442no—
169SD16—2442no—
170C2×C8—612no—
171C2×C8—612no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—612no—
175C4⋊C4—1222no—
176C4⋊C4—1222no—
177C4⋊C4—1222no—
178C4⋊C4—1222no—
179C4⋊C4C22⋊D6112yes—
180C22⋊C4—22no—
181C22⋊C4—22no—
182C22⋊C4—1222no—
183C22⋊C4C22⋊D6112yes—
184C42—1222no—
185C42C22×D6111yescharacteristic
186C42C22×D6111yescharacteristic
187C23—21no—
188C23C2×C22⋊D6111yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—1222no—
194Q8—1222no—
195D4—22no—
196D4—42no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4C2×C22⋊D6112yes—
206C2×C4C2×C22⋊D6112yes—
207C2×C4C2×C22⋊D6111yescharacteristic
208C2×C4C23×D6111yescharacteristic
209C8—1222no—
210C8—1222no—
211C22—22no—
212C22—21no—
213C22—42no—
214C22—41no—
215C22C22×C22⋊D6111yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—41no—
220C4—41no—
221C4—41no—
222C4—2442no—
223C4—2442no—
224C4#1451982212yes—
225C2—41no—
226C2—81no—
227C2#1684032911yescharacteristic
228C2#1684057712yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#536C2
socleC22×C61C22×D4
hypercenter#536D61
hypocenterC61#3223
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #16840374C2semidirect
2. #16840157C2semidirect
3. #16840141C2semidirect
4. #16840130C2semidirect
5. #16840116C2semidirect
6. #16839981C2semidirect
7. #16839969C2semidirect
9. #16839918C2semidirect
10. #16839823C2semidirect
126. C61#3223semidirect