Finite Group Databasebeta

← #21456939

Subgroups — #21456939

Order 7808.

404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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#16840309C211yesmaximal, characteristic
2C4⋊Q8×D61C211yesmaximal, characteristic, complemented
3#16840166C212yesmaximal, complemented
4#16840107C212yesmaximal, complemented
5#16840077C212yesmaximal, complemented
6#16840074C212yesmaximal, complemented
7#16840043C211yesmaximal, characteristic, complemented
8#16840042C211yesmaximal, characteristic, complemented
9#16840039C211yesmaximal, characteristic, complemented
10#16839814C211yesmaximal, characteristic, complemented
11C61×#474C211yesmaximal, characteristic, complemented
12C2×#11758222—21no—
13C2×Q8×D61—21no—
14#14519777C2211yescharacteristic
15#14519776—21no—
16#14519776C2212yes—
17#14519776C2211yescharacteristic
18#14519775—21no—
19#14519773C2211yescharacteristic
20#14519763—21no—
21#14519752C2211yescharacteristic
22#14519750—21no—
23#14519748C2211yescharacteristic
24C4×D244C2211yescharacteristic
25C4×C22⋊D61—21no—
26C4⋊C4×D61—21no—
27C4⋊C4×D61C2212yes—
28C42×D61C2211yescharacteristic
29#14519711C2212yes—
30#14519710C2212yes—
31#14519710C2212yes—
32C4⋊#92418C2211yescharacteristic
33#14519699C2212yes—
34#14519698C2212yes—
35#14519697C2212yes—
36#14519689C2212yes—
37C8×Dic61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×D4×C61C2211yescharacteristic
40#107×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#102×C61C2212yes—
43C2×Q8×C61—21no—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C2×C22⋊D61—21no—
47C2×C22⋊D61—21no—
48C2×C22⋊D61—21no—
49Q8×D61—44no—
50#11758222—44no—
51C2×D244—21no—
52C2×D244C2311yescharacteristic
53C2×C4×D61—22no—
54C2×C4×D61—21no—
55C2×C4×D61D411yescharacteristic
56C2×C4×D61D411yescharacteristic
57C2×C4×D61C2311yescharacteristic
58C2×Dic122—21no—
59C2×Dic122—22no—
60C2×Dic122—21no—
61C2×C8×C61C2312yes—
62C4⋊C4×C61—21no—
63C4⋊C4×C61C2312yes—
64C4⋊C4×C61C2311yescharacteristic
65C22⋊C4×C61—21no—
66C42×C61C2311yescharacteristic
67C22⋊Dic61—21no—
68#11758198—21no—
69#11758198—21no—
70C4⋊Dic61—21no—
71C4⋊Dic61C2312yes—
72C4⋊Dic61C2311yescharacteristic
73#11758196—22no—
74#11758196—22no—
75#11758196—21no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80C23×C61—21no—
81C22×D61—21no—
82C22×D61C2×D411yescharacteristic
83Q8×C61—42no—
84D4×C61—21no—
85D4×C61—21no—
86C2×C4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—42no—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2411yescharacteristic
92C22⋊D61—42no—
93C22⋊D61—42no—
94C22⋊D61—42no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97C2×Dic61C2×D411yescharacteristic
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100D244—21no—
101D244—21no—
102D244—42no—
103C4×D61—21no—
104C4×D61—21no—
105C4×D61—22no—
106C4×D61—44no—
107C4×D61—42no—
108C4×D61D814yes—
109Dic122—42no—
110Dic122—42no—
111Dic122—44no—
112C8×C61—22no—
113#92418—22no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61C22×D411yescharacteristic
118C2×D61—21no—
119C2×D61—21no—
120C2×D61—41no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61C2×D812yes—
124C4×C61—21no—
125C4×C61—42no—
126C4×C61—41no—
127C4×C61C2×D812yes—
128C4×C612−1+411yescharacteristic
129C4×C612−1+411yescharacteristic
130Dic61—21no—
131Dic61—42no—
132Dic61—41no—
133Dic61C2×D812yes—
134Dic61#13712yes—
135#3226—611nomaximal, Sylow
136C2×C61—81no—
137C2×C61#53611yescharacteristic
138C2×C61C22×D811yescharacteristic
139C2×C61C2×#13711yescharacteristic
140D61—22no—
141D61—81no—
142#532—611no—
143C2×C4⋊Q8—611no—
144#500—612no—
145#486—612no—
146#480—612no—
147#480—612no—
148#474—611no—
149#474—611no—
150#474—611no—
151#474D6111yescharacteristic, complemented
152#431—611no—
153C61#322611yescharacteristic, complemented, Sylow
154C2×#41—1221no—
155C22×Q8—1221no—
156C4⋊Q8—612no—
157C4⋊Q8—611no—
158C4⋊Q8—611no—
159C4⋊Q8—1221no—
160C4⋊Q8—1221no—
161C4⋊Q8C2×D6111yescharacteristic
162#127—611no—
163#124—1221no—
164#121—611no—
165#121—611no—
166#121—1221no—
167C4×D4—611no—
168C4×D4—1221no—
169C4×D4C2×D6111yescharacteristic
170C2×C4⋊C4—612no—
171C2×C4⋊C4—1221no—
172C2×C42—611no—
173#107—612no—
174#107—612no—
175#107—612no—
176#107C2×D6112yes—
177C4⋊C8—611no—
178C4⋊C8C2×D6111yescharacteristic
179#102—612no—
180#102—612no—
181#102—612no—
182#102C2×D6112yes—
183C22⋊C8—612no—
184C4×C8—612no—
185#41—2444no—
186C2×Q8—21no—
187C2×Q8—1221no—
188C2×Q8—1222no—
189C2×Q8—1221no—
190C2×Q8—2444no—
191C2×D4—611no—
192C2×D4—1221no—
193C2×D4—1221no—
194C2×D4—1221no—
195C2×D4—1221no—
196C2×D4C22×D6111yescharacteristic
197C22×C4—21no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—611no—
201C22×C4—1222no—
202C22×C4—1221no—
203C2×C8—612no—
204C2×C8C22×D6112yes—
205C4⋊C4—21no—
206C4⋊C4—612no—
207C4⋊C4—611no—
208C4⋊C4—1222no—
209C4⋊C4—1222no—
210C4⋊C4—1221no—
211C4⋊C4—1221no—
212C4⋊C4C22×D6112yes—
213C4⋊C4C22×D6111yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—1221no—
216C22⋊C4—1221no—
217C22⋊C4—1221no—
218C42—611no—
219C42—611no—
220C42—611no—
221C42C22×D6111yescharacteristic
222C23—21no—
223C23—611no—
224C23—1221no—
225Q8—42no—
226Q8—2444no—
227Q8—2442no—
228Q8—2442no—
229D4—21no—
230D4—21no—
231D4—1221no—
232D4—1221no—
233D4—2442no—
234D4—2442no—
235D4—2442no—
236D4—2442no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—42no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—614no—
243C2×C4—611no—
244C2×C4—1222no—
245C2×C4—1221no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1222no—
249C2×C4—2444no—
250C2×C4—2442no—
251C2×C4D4×D6111yescharacteristic
252C2×C4D4×D6111yescharacteristic
253C2×C4C23×D6111yescharacteristic
254C8—22no—
255C8—1222no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—612no—
260C22—1221no—
261C22—1221no—
262C22—2441no—
263C22—2441no—
264C22—2441no—
265C22C2×D4×D6111yescharacteristic
266C4—21no—
267C4—41no—
268C4—42no—
269C4—612no—
270C4—612no—
271C4—1221no—
272C4—2441no—
273C4—2442no—
274C4D8×D6112yes—
275C4#1451982411yescharacteristic
276C4#1451982511yescharacteristic
277C2—81no—
278C2—1222no—
279C2—4881no—
280C2#1684033511yescharacteristic
281C2C2×D8×D6111yescharacteristic
282C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#474C2
socleC22×C61C22×D4
hypercenter#474D61
hypocenterC61#3226
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. C4⋊Q8×D61C2semidirect
3. #16840166C2semidirect
4. #16840107C2semidirect
5. #16840077C2semidirect
6. #16840074C2semidirect
7. #16840043C2semidirect
8. #16840042C2semidirect
9. #16840039C2semidirect
10. #16839814C2semidirect
11. C61×#474C2semidirect
151. #474D61semidirect
153. C61#3226semidirect