Finite Group Databasebeta

← #21456310

Subgroups — #21456310

Order 7808.

532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#14519808C211yesmaximal, characteristic, complemented
2C2×#14519807C211yesmaximal, characteristic, complemented
3C2×#14519797C211yesmaximal, characteristic
4C22×#11758202C211yesmaximal, characteristic, complemented
5#16840338C211yesmaximal, characteristic, complemented
6#16840157C212yesmaximal, complemented
7#16840154C212yesmaximal, complemented
8#16840144C212yesmaximal, complemented
9#16840141C212yesmaximal, complemented
10#16839718C211yesmaximal, characteristic, complemented
11C61×#536C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C22×Dic122C2211yescharacteristic
14#14519808—24no—
15#14519807—24no—
16#14519797—24no—
17C2×#11758202—24no—
18C2×#11758202C2212yes—
19C2×#11758202C2212yes—
20C2×#11758202C2211yescharacteristic
21C2×#11758202C2212yes—
22C2×#11758202C2212yes—
23C2×#11758200C2211yescharacteristic
24C2×#11758200C2212yes—
25C2×#11758201C2211yescharacteristic
26C2×#11758201C2212yes—
27C2×#11758199C2211yescharacteristic
28C2×#11758194C2211yescharacteristic
29C22×#92418C2211yescharacteristic
30#14519777C2212yes—
31#14519765C2212yes—
32#14519761—22no—
33#14519757—22no—
34#14519688C2212yes—
35C4×#92418C2212yes—
36C2×#41×C61C2211yescharacteristic
37C22×Q8×C61C2211yescharacteristic
38C4⋊Q8×C61C2212yes—
39#124×C61C2212yes—
40#123×C61—22no—
41C22⋊Q8×C61—22no—
42#117×C61C2211yescharacteristic
43#41×C61—22no—
44#41×C61—22no—
45C2×Q8×C61—21no—
46C2×Q8×C61—22no—
47C2×Q8×C61—22no—
48C2×Q8×C61C2312yes—
49C2×Q8×C61C2311yescharacteristic
50C2×D4×C61—21no—
51C2×D4×C61C2311yescharacteristic
52C22×C4×C61—21no—
53C22×C4×C61—21no—
54C22×C4×C61C2311yescharacteristic
55C2×C22⋊D61—21no—
56C22×Dic61—21no—
57#11758222—22no—
58#11758222—22no—
59C2×D244C2311yescharacteristic
60C2×C4×D61—21no—
61C2×Dic122—22no—
62C2×Dic122—22no—
63C2×Dic122—21no—
64C2×Dic122C2312yes—
65C2×Dic122C2311yescharacteristic
66C4⋊C4×C61—24no—
67C4⋊C4×C61D412yes—
68C22⋊C4×C61—24no—
69C22⋊C4×C61D412yes—
70C42×C61C2312yes—
71#11758202—24no—
72#11758202—24no—
73#11758202—24no—
74#11758202—22no—
75#11758202—24no—
76#11758201—24no—
77#11758201—22no—
78#11758200—22no—
79#11758200—24no—
80#11758199—22no—
81#11758198—24no—
82C4⋊Dic61—24no—
83#11758194D414yes—
84C2×#92418D414yes—
85C2×#92418C2311yescharacteristic
86C2×#92418C2312yes—
87C2×#92418C2311yescharacteristic
88C23×C61—21no—
89C23×C61C2×D411yescharacteristic
90C22×D61—21no—
91Q8×C61—22no—
92Q8×C61—21no—
93Q8×C61—22no—
94Q8×C61—21no—
95Q8×C61—42no—
96D4×C61—21no—
97D4×C61—21no—
98D4×C61—42no—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61—42no—
102C2×C4×C61—42no—
103C2×C4×C61C2×D414yes—
104C2×C4×C61C2×D411yescharacteristic
105C2×C4×C61C2×D412yes—
106C2×C4×C61C2×D412yes—
107C2×C4×C61C2411yescharacteristic
108C22⋊D61—42no—
109C2×Dic61—21no—
110C2×Dic61—22no—
111C2×Dic61—42no—
112D244—21no—
113D244—21no—
114C4×D61—42no—
115Dic122—22no—
116Dic122—21no—
117Dic122—22no—
118Dic122—21no—
119Dic122—42no—
120#92418C2×D412yes—
121#92418C2×D412yes—
122#92418C2×D414yes—
123C22×C61—22no—
124C22×C61—41no—
125C22×C61—42no—
126C22×C61#12712yes—
127C22×C61C22×D411yescharacteristic
128C2×D61—41no—
129C2×D61—42no—
130C4×C61—24no—
131C4×C61—41no—
132C4×C61—42no—
133C4×C61#12712yes—
134C4×C61C22×D411yescharacteristic
135C4×C61C22×D411yescharacteristic
136Dic61—42no—
137Dic61—41no—
138#3156—611nomaximal, Sylow
139C2×C61—22no—
140C2×C61—81no—
141C2×C61C2×#12711yescharacteristic
142C2×C61#57812yes—
143D61—81no—
144C2×#137—611no—
145C2×#137—611no—
146C2×#135—611no—
147C22×Q16—611no—
148#536—611no—
149#536D6111yescharacteristic, complemented
150#497—612no—
151#497—612no—
152#495—612no—
153#494—612no—
154#405—611no—
155C61#315611yescharacteristic, complemented, Sylow
156C2×#41—611no—
157C2×#41C2×D6111yescharacteristic
158C22×Q8—611no—
159C22×Q8C2×D6111yescharacteristic
160#137—1224no—
161#137—1224no—
162#135—1224no—
163C2×Q16—612no—
164C2×Q16—612no—
165C2×Q16—611no—
166C2×Q16—612no—
167C2×Q16—612no—
168C2×Q16—1224no—
169C2×SD16—611no—
170C2×SD16—612no—
171C2×SD16—611no—
172C2×SD16—612no—
173C2×D8—611no—
174C2×M16—611no—
175C22×C8—611no—
176C4⋊Q8—612no—
177C4⋊Q8C2×D6112yes—
178#124—612no—
179#124C2×D6112yes—
180#123—22no—
181#123—1222no—
182C22⋊Q8—22no—
183C22⋊Q8—1222no—
184#117C2×D6111yescharacteristic
185#97—612no—
186C4×C8—612no—
187#41—22no—
188#41—22no—
189#41—1222no—
190#41—1222no—
191C2×Q8—21no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—612no—
195C2×Q8—611no—
196C2×Q8—1221no—
197C2×Q8—1222no—
198C2×Q8—1222no—
199C2×Q8C22×D6112yes—
200C2×Q8C22×D6111yescharacteristic
201C2×D4—21no—
202C2×D4—611no—
203C2×D4—1221no—
204C2×D4C22×D6111yescharacteristic
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4C22×D6111yescharacteristic
210Q16—1224no—
211Q16—1224no—
212Q16—1222no—
213Q16—1224no—
214Q16—1224no—
215SD16—1222no—
216SD16—1224no—
217SD16—1222no—
218SD16—1224no—
219D8—1222no—
220M16—614no—
221C2×C8—614no—
222C2×C8—611no—
223C2×C8—612no—
224C2×C8—611no—
225C4⋊C4—24no—
226C4⋊C4—1224no—
227C4⋊C4C22⋊D6112yes—
228C22⋊C4—24no—
229C22⋊C4—1224no—
230C22⋊C4C22⋊D6112yes—
231C42C22×D6112yes—
232C23—21no—
233C23—1221no—
234C23C2×C22⋊D6111yescharacteristic
235Q8—22no—
236Q8—21no—
237Q8—22no—
238Q8—21no—
239Q8—42no—
240Q8—1222no—
241Q8—1221no—
242Q8—1222no—
243Q8—1221no—
244Q8—2442no—
245D4—21no—
246D4—21no—
247D4—42no—
248D4—1221no—
249D4—1221no—
250D4—2442no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—1222no—
256C2×C4—1221no—
257C2×C4—2442no—
258C2×C4—2442no—
259C2×C4D4×D6112yes—
260C2×C4D4×D6112yes—
261C2×C4C2×C22⋊D6114yes—
262C2×C4C2×C22⋊D6111yescharacteristic
263C2×C4C23×D6111yescharacteristic
264C8—612no—
265C8—612no—
266C8—614no—
267C22—22no—
268C22—41no—
269C22—42no—
270C22—2441no—
271C22—2442no—
272C22#1451977312yes—
273C22C22×C22⋊D6111yescharacteristic
274C4—24no—
275C4—41no—
276C4—42no—
277C4—2441no—
278C4—2442no—
279C4#1451977312yes—
280C4C2×D4×D6111yescharacteristic
281C4C2×D4×D6111yescharacteristic
282C2—22no—
283C2—81no—
284C2—4881no—
285C2C2×#1451977311yescharacteristic
286C2#1684057712yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#536C2
socleC22×C61C22×D4
hypercenter#536D61
hypocenterC61#3156
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. C2×#14519808C2semidirect
2. C2×#14519807C2semidirect
4. C22×#11758202C2semidirect
5. #16840338C2semidirect
6. #16840157C2semidirect
7. #16840154C2semidirect
8. #16840144C2semidirect
9. #16840141C2semidirect
10. #16839718C2semidirect
11. C61×#536C2semidirect
149. #536D61semidirect
155. C61#3156semidirect