Finite Group Databasebeta

← #21457199

Subgroups — #21457199

Order 7808.

430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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#16840051C212yesmaximal, complemented
4#16840049C211yesmaximal, characteristic, complemented
5#16840016C212yesmaximal, complemented
6#16840014C212yesmaximal, complemented
7#16839958C211yesmaximal, characteristic, complemented
8#16839957C211yesmaximal, characteristic, complemented
9#16839956C212yesmaximal, complemented
10#16839784C211yesmaximal, characteristic, complemented
11C61×#476C211yesmaximal, characteristic, complemented
12C2×#11758226—21no—
13C2×#11758222—21no—
14C2×D488C2212yes—
15C2×#11758199C2212yes—
16C2×#11758189C2212yes—
17#14519776C2211yescharacteristic
18#14519774C2211yescharacteristic
19#14519773C2211yescharacteristic
20#14519766—21no—
21#14519763—21no—
22#14519752—21no—
23#14519752C2212yes—
24#14519752C2211yescharacteristic
25#14519750—21no—
26#14519748C2211yescharacteristic
27C4×D244C2211yescharacteristic
28#14519739—21no—
29#14519739C2212yes—
30C4×C22⋊D61—21no—
31C42×D61C2211yescharacteristic
32#14519708C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519699C2212yes—
36#14519697C2212yes—
37#14519697C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×D4×C61C2211yescharacteristic
40#106×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—
49#11758226—44no—
50#11758222—44no—
51C2×D244—21no—
52C2×D244—22no—
53C2×D244—21no—
54C2×D244—21no—
55C2×D244C2311yescharacteristic
56C2×D244C2312yes—
57C2×C4×D61—21no—
58C2×C4×D61—22no—
59C2×C4×D61D411yescharacteristic
60C2×C4×D61D411yescharacteristic
61C2×C4×D61C2311yescharacteristic
62C2×Dic122—21no—
63C2×C8×C61C2312yes—
64C4⋊C4×C61—21no—
65C4⋊C4×C61C2312yes—
66C4⋊C4×C61C2311yescharacteristic
67C22⋊C4×C61—21no—
68C42×C61C2311yescharacteristic
69C22⋊Dic61—21no—
70#11758199—42no—
71#11758198—21no—
72#11758198—21no—
73#11758198—22no—
74#11758198—22no—
75C4⋊Dic61C2311yescharacteristic
76#11758196—21no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81D488—42no—
82#11758189—42no—
83C23×C61—21no—
84C22×D61—22no—
85C22×D61—21no—
86C22×D61C2×D411yescharacteristic
87Q8×C61—42no—
88D4×C61—21no—
89D4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—42no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2×D411yescharacteristic
95C2×C4×C61C2411yescharacteristic
96C22⋊D61—42no—
97C22⋊D61—42no—
98C22⋊D61—42no—
99C2×Dic61—21no—
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102C2×Dic61C2×D411yescharacteristic
103D244—21no—
104D244—22no—
105D244—21no—
106D244—22no—
107D244—42no—
108D244—42no—
109D244—44no—
110D244—42no—
111C4×D61—22no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—22no—
115C4×D61—42no—
116C4×D61—44no—
117Dic122—42no—
118C8×C61—22no—
119#92418—22no—
120C22×C61—41no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61C22×D411yescharacteristic
124C2×D61—21no—
125C2×D61—21no—
126C2×D61—21no—
127C2×D61—41no—
128C2×D61—42no—
129C2×D61—42no—
130C2×D61—41no—
131C2×D61—42no—
132C2×D61—41no—
133C4×C61—21no—
134C4×C61—41no—
135C4×C61—42no—
136C4×C61AGL(1,ℤ/8)12yes—
137C4×C61H(5,𝔽2)11yescharacteristic
138C4×C612−1+411yescharacteristic
139Dic61—21no—
140Dic61—21no—
141Dic61—41no—
142Dic61AGL(1,ℤ/8)12yes—
143#3253—611nomaximal, Sylow
144C2×C61—81no—
145C2×C61#53711yescharacteristic
146C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
148D61—41no—
149D61—82no—
150D61—81no—
151#532—611no—
152#532—611no—
153#476—611no—
154#476—612no—
155#476D6111yescharacteristic, complemented
156#469—612no—
157#469—612no—
158#459—611no—
159#459—611no—
160#459—612no—
161#423—611no—
162C61#325311yescharacteristic, complemented, Sylow
163C2×#41—1221no—
164C2×#41—1221no—
165C2×D8—612no—
166C2×D8—612no—
167C2×M16—612no—
168C4⋊Q8—611no—
169C4⋊Q8C2×D6111yescharacteristic
170#127—611no—
171#127—611no—
172#124—1221no—
173#124—1221no—
174#121—611no—
175#121—611no—
176#121—612no—
177#121—1221no—
178#121—1221no—
179C4×D4—612no—
180C4×D4—611no—
181C4×D4—1221no—
182C4×D4—1221no—
183C4×D4C2×D6111yescharacteristic
184C2×C42—611no—
185#106—612no—
186#106C2×D6112yes—
187C4⋊C8—612no—
188C4⋊C8—611no—
189C4⋊C8C2×D6111yescharacteristic
190#102—612no—
191#102—612no—
192#102—612no—
193#102C2×D6112yes—
194#41—2444no—
195#41—2444no—
196C2×Q8—21no—
197C2×Q8—1221no—
198C2×D4—612no—
199C2×D4—611no—
200C2×D4—1221no—
201C2×D4—1222no—
202C2×D4—1221no—
203C2×D4—1221no—
204C2×D4—1221no—
205C2×D4—1221no—
206C2×D4—1221no—
207C2×D4C22×D6111yescharacteristic
208C22×C4—21no—
209C22×C4—611no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—1222no—
213C22×C4—1221no—
214D8—2442no—
215D8—2442no—
216M16—2442no—
217C2×C8—612no—
218C2×C8C22×D6112yes—
219C4⋊C4—21no—
220C4⋊C4—611no—
221C4⋊C4—1221no—
222C4⋊C4C22×D6111yescharacteristic
223C4⋊C4C22×D6112yes—
224C22⋊C4—21no—
225C22⋊C4—1222no—
226C22⋊C4—1221no—
227C22⋊C4—1222no—
228C22⋊C4—1221no—
229C22⋊C4—1221no—
230C42—611no—
231C42—611no—
232C42—611no—
233C42C22×D6111yescharacteristic
234C23—21no—
235C23—611no—
236C23—1222no—
237C23—1221no—
238Q8—42no—
239Q8—2442no—
240D4—21no—
241D4—21no—
242D4—1221no—
243D4—1222no—
244D4—1221no—
245D4—1222no—
246D4—2442no—
247D4—2444no—
248D4—2442no—
249D4—2442no—
250D4—2442no—
251D4—2442no—
252D4—2442no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—42no—
256C2×C4—611no—
257C2×C4—611no—
258C2×C4—611no—
259C2×C4—1222no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—1222no—
263C2×C4—1221no—
264C2×C4—2444no—
265C2×C4—2442no—
266C2×C4D4×D6111yescharacteristic
267C2×C4D4×D6111yescharacteristic
268C2×C4C23×D6111yescharacteristic
269C8—22no—
270C8—1222no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—1221no—
275C22—1221no—
276C22—1221no—
277C22—2442no—
278C22—2441no—
279C22—2441no—
280C22—2442no—
281C22—2442no—
282C22—2441no—
283C22C2×D4×D6111yescharacteristic
284C4—21no—
285C4—42no—
286C4—41no—
287C4—612no—
288C4—1221no—
289C4—1221no—
290C4—2441no—
291C4#1451980412yes—
292C4#1451982311yescharacteristic
293C4#1451982511yescharacteristic
294C2—81no—
295C2—4882no—
296C2—4881no—
297C2—2441no—
298C2#1684034211yescharacteristic
299C2AGL(1,ℤ/8)×D6111yescharacteristic
300C2C2×#1451980411yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#476C2
socleC22×C61C22×D4
hypercenter#476D61
hypocenterC61#3253
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16840313C2semidirect
2. #16840309C2semidirect
3. #16840051C2semidirect
4. #16840049C2semidirect
5. #16840016C2semidirect
6. #16840014C2semidirect
7. #16839958C2semidirect
8. #16839957C2semidirect
9. #16839956C2semidirect
10. #16839784C2semidirect
11. C61×#476C2semidirect
155. #476D61semidirect
162. C61#3253semidirect