Finite Group Databasebeta

← #21456813

Subgroups — #21456813

Order 7808.

434 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 113 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#16840313C211yesmaximal, characteristic, complemented
2#16840309C211yesmaximal, characteristic, complemented
3#16840148C212yesmaximal, complemented
4#16840123C212yesmaximal, complemented
5#16839964C211yesmaximal, characteristic, complemented
6#16839958C211yesmaximal, characteristic, complemented
7#16839957C211yesmaximal, characteristic, complemented
8#16839910C212yesmaximal, complemented
9#16839906C212yesmaximal, complemented
10#16839818C211yesmaximal, characteristic, complemented
11C61×#461C211yesmaximal, characteristic, complemented
12C2×#11758226C2212yes—
13C2×#11758222—21no—
14C2×#11758201C2212yes—
15C2×D488C2212yes—
16C2×#11758199C2212yes—
17#14519776C2211yescharacteristic
18#14519774C2211yescharacteristic
19#14519773C2211yescharacteristic
20#14519766C2212yes—
21#14519763—21no—
22#14519752—21no—
23#14519752—21no—
24#14519752C2211yescharacteristic
25#14519750—21no—
26#14519748C2211yescharacteristic
27C4×D244C2211yescharacteristic
28#14519739—21no—
29#14519739—21no—
30C4×C22⋊D61—21no—
31C42×D61C2211yescharacteristic
32C4⋊#92418C2211yescharacteristic
33#14519701C2212yes—
34#14519699C2212yes—
35#14519697C2212yes—
36#14519689C2212yes—
37#14519687C2212yes—
38C2×SD16×C61C2212yes—
39C4⋊Q8×C61C2211yescharacteristic
40C4×D4×C61C2211yescharacteristic
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61C2312yes—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C2×C22⋊D61—21no—
47C2×C22⋊D61—21no—
48C2×C22⋊D61—21no—
49#11758226—42no—
50#11758226—42no—
51#11758222—44no—
52C2×D244—21no—
53C2×D244—22no—
54C2×D244—21no—
55C2×D244—21no—
56C2×D244C2312yes—
57C2×D244C2311yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61—22no—
60C2×C4×D61D411yescharacteristic
61C2×C4×D61D411yescharacteristic
62C2×C4×D61C2311yescharacteristic
63C2×Dic122—21no—
64SD16×C61—42no—
65C2×C8×C61C2312yes—
66C4⋊C4×C61—21no—
67C4⋊C4×C61—21no—
68C4⋊C4×C61C2311yescharacteristic
69C22⋊C4×C61—21no—
70C42×C61C2311yescharacteristic
71C22⋊Dic61—21no—
72#11758201—42no—
73#11758199—42no—
74#11758198—21no—
75#11758198—21no—
76#11758198—22no—
77#11758198—22no—
78C4⋊Dic61C2311yescharacteristic
79#11758196—21no—
80C4×Dic61D411yescharacteristic
81C4×Dic61D411yescharacteristic
82C4×Dic61C2311yescharacteristic
83C2×#92418C2312yes—
84D488—42no—
85C23×C61—21no—
86C22×D61—22no—
87C22×D61—21no—
88C22×D61C2×D411yescharacteristic
89Q8×C61—22no—
90Q8×C61—22no—
91D4×C61—21no—
92D4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—42no—
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2411yescharacteristic
99C22⋊D61—42no—
100C22⋊D61—42no—
101C22⋊D61—42no—
102C2×Dic61—21no—
103C2×Dic61C2×D411yescharacteristic
104C2×Dic61C2×D411yescharacteristic
105C2×Dic61C2×D411yescharacteristic
106D244—21no—
107D244—22no—
108D244—22no—
109D244—21no—
110D244—42no—
111D244—42no—
112D244—44no—
113D244—42no—
114C4×D61—22no—
115C4×D61—21no—
116C4×D61—21no—
117C4×D61—41no—
118C4×D61—44no—
119C4×D61—42no—
120Dic122—42no—
121C8×C61—22no—
122#92418—22no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61C22×D411yescharacteristic
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—21no—
130C2×D61—42no—
131C2×D61—41no—
132C2×D61—41no—
133C2×D61—42no—
134C2×D61—42no—
135C2×D61—41no—
136C4×C61—21no—
137C4×C61—42no—
138C4×C61—41no—
139C4×C61AGL(1,ℤ/8)12yes—
140C4×C61H(5,𝔽2)11yescharacteristic
141C4×C61H(5,𝔽2)11yescharacteristic
142Dic61—21no—
143Dic61—21no—
144Dic61—21no—
145Dic61—41no—
146#3214—611nomaximal, Sylow
147C2×C61—81no—
148C2×C61#53511yescharacteristic
149C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
150C2×C61#57511yescharacteristic
151D61—41no—
152D61—82no—
153D61—81no—
154#532—611no—
155#532—611no—
156#496—612no—
157#489—612no—
158#461—611no—
159#461D6111yescharacteristic, complemented
160#459—611no—
161#459—611no—
162#449—612no—
163#449—612no—
164#432—611no—
165C61#321411yescharacteristic, complemented, Sylow
166C2×#41—612no—
167C2×#41—1221no—
168C2×SD16—612no—
169C2×SD16C2×D6112yes—
170C2×D8—612no—
171C2×D8—612no—
172C4⋊Q8—611no—
173C4⋊Q8C2×D6111yescharacteristic
174#127—611no—
175#127—611no—
176#124—612no—
177#124—1221no—
178#121—611no—
179#121—611no—
180#121—1221no—
181#121—1221no—
182#121—1221no—
183C4×D4—611no—
184C4×D4—1221no—
185C4×D4—1221no—
186C4×D4—1221no—
187C4×D4C2×D6111yescharacteristic
188C2×C42—611no—
189C4⋊C8—611no—
190C4⋊C8C2×D6111yescharacteristic
191#103—612no—
192#103C2×D6112yes—
193#102—612no—
194#102—612no—
195C22⋊C8—612no—
196#97—612no—
197#41—2444no—
198#41—2442no—
199#41—2442no—
200C2×Q8—1221no—
201C2×Q8C22×D6112yes—
202C2×D4—612no—
203C2×D4—611no—
204C2×D4—1221no—
205C2×D4—1222no—
206C2×D4—1221no—
207C2×D4—1221no—
208C2×D4—1221no—
209C2×D4—1221no—
210C2×D4—1221no—
211C2×D4C22×D6111yescharacteristic
212C22×C4—21no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—1222no—
217C22×C4—1221no—
218SD16—42no—
219SD16—2442no—
220D8—2442no—
221D8—2442no—
222C2×C8—612no—
223C2×C8C22×D6112yes—
224C4⋊C4—21no—
225C4⋊C4—21no—
226C4⋊C4—611no—
227C4⋊C4—1221no—
228C4⋊C4C22×D6111yescharacteristic
229C22⋊C4—21no—
230C22⋊C4—1221no—
231C22⋊C4—1222no—
232C22⋊C4—1222no—
233C22⋊C4—1221no—
234C22⋊C4—1221no—
235C42—611no—
236C42—611no—
237C42—611no—
238C42C22×D6111yescharacteristic
239C23—21no—
240C23—611no—
241C23—1221no—
242C23—1222no—
243Q8—22no—
244Q8—22no—
245Q8—2442no—
246D4—21no—
247D4—21no—
248D4—1221no—
249D4—1222no—
250D4—1222no—
251D4—1221no—
252D4—2442no—
253D4—2442no—
254D4—2444no—
255D4—2442no—
256D4—2442no—
257D4—2442no—
258D4—2442no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—42no—
262C2×C4—611no—
263C2×C4—611no—
264C2×C4—611no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1222no—
268C2×C4—1221no—
269C2×C4—2441no—
270C2×C4—2444no—
271C2×C4—2442no—
272C2×C4D4×D6111yescharacteristic
273C2×C4D4×D6111yescharacteristic
274C2×C4C23×D6111yescharacteristic
275C8—22no—
276C8—1222no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—1221no—
281C22—1221no—
282C22—1221no—
283C22—2441no—
284C22—2442no—
285C22—2442no—
286C22—2441no—
287C22—2442no—
288C22—2441no—
289C22C2×D4×D6111yescharacteristic
290C4—21no—
291C4—41no—
292C4—42no—
293C4—1221no—
294C4—1221no—
295C4—1221no—
296C4—2441no—
297C4#1451980412yes—
298C4#1451982211yescharacteristic
299C4#1451982311yescharacteristic
300C2—81no—
301C2—4881no—
302C2—4882no—
303C2—2441no—
304C2#1684032811yescharacteristic
305C2C2×#1451980411yescharacteristic
306C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#461C2
socleC22×C61C22×D4
hypercenter#461D61
hypocenterC61#3214
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #16840313C2semidirect
2. #16840309C2semidirect
3. #16840148C2semidirect
4. #16840123C2semidirect
5. #16839964C2semidirect
6. #16839958C2semidirect
7. #16839957C2semidirect
8. #16839910C2semidirect
9. #16839906C2semidirect
10. #16839818C2semidirect
11. C61×#461C2semidirect
159. #461D61semidirect
165. C61#3214semidirect