Finite Group Databasebeta

← #21450306

Subgroups — #21450306

Order 7808.

596 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14519750C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3#16839689C211yesmaximal, characteristic, complemented
4#16839688C211yesmaximal, characteristic, complemented
5#16839687C211yesmaximal, characteristic, complemented
6#16839662C212yesmaximal, complemented
7#16839640C212yesmaximal, complemented
8#16839638C212yesmaximal, complemented
9#16839626C212yesmaximal, complemented
10#16839609C211yesmaximal, characteristic, complemented
11C61×#397C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61C2211yescharacteristic
14C22×C22⋊D61C2211yescharacteristic
15C22×C4×D61C2211yescharacteristic
16C22×C4×D61C2212yes—
17#14519750—24no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C4⋊C4×D61—24no—
22C2×C22⋊Dic61C2212yes—
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×C4×Dic61C2212yes—
28#14519684C2211yescharacteristic
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C22⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C23×D61C2311yescharacteristic
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C2×C22⋊D61—22no—
45C2×C22⋊D61—24no—
46C2×C22⋊D61—22no—
47C2×C22⋊D61—24no—
48C22×Dic61C2312yes—
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C2×D244—22no—
53C2×D244—24no—
54C2×C4×D61—24no—
55C2×C4×D61—24no—
56C2×C4×D61—42no—
57C2×C4×D61—42no—
58C2×C4×D61D414yes—
59C4⋊C4×C61—22no—
60C22⋊C4×C61—22no—
61C22⋊C4×C61—42no—
62C22⋊Dic61—42no—
63#11758198—24no—
64#11758198—22no—
65#11758198—42no—
66#11758198—42no—
67C4⋊Dic61—22no—
68#11758196—24no—
69#11758196—22no—
70C4×Dic61—24no—
71C23×C61—21no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61C2411yescharacteristic
77C22×D61—22no—
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—22no—
82C22×D61—22no—
83C22×D61—21no—
84C22×D61—21no—
85C22×D61C2×D412yes—
86C22×D61#4114yes—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61C2×D412yes—
97C22⋊D61—44no—
98C22⋊D61—44no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61C2×D412yes—
108C2×Dic61#4114yes—
109D244—44no—
110C4×D61—28no—
111C4×D61—48no—
112C22×C61—41no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61C22×D411yescharacteristic
118C22×C61C2×#4112yes—
119C22×C61C2×#4112yes—
120C22×C61H(5,𝔽2)11yescharacteristic
121C22×C61H(5,𝔽2)11yescharacteristic
122C2×D61—22no—
123C2×D61—22no—
124C2×D61—24no—
125C2×D61—24no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—42no—
130C2×D61—42no—
131C2×D61#12414yes—
132C4×C61—22no—
133C4×C61—41no—
134C4×C61—42no—
135C4×C61—42no—
136Dic61—41no—
137Dic61—42no—
138Dic61—42no—
139Dic61#12314yes—
140#2504—611nomaximal, Sylow
141C2×C61—81no—
142C2×C61C2×#12311yescharacteristic
143C2×C61C2×#12411yescharacteristic
144C2×C61#53511yescharacteristic
145C2×C61#55312yes—
146C2×C61#55312yes—
147D61—24no—
148D61—81no—
149C2×#121—611no—
150C22×C4⋊C4—611no—
151#397—611no—
152#397—611no—
153#397—611no—
154#397D6111yescharacteristic, complemented
155#390—612no—
156#386—612no—
157#386—612no—
158#382—612no—
159C4×C22⋊C4—611no—
160C61#250411yescharacteristic, complemented, Sylow
161C22×D4—611no—
162C22×D4—611no—
163C22×D4—611no—
164C23×C4—611no—
165C23×C4—612no—
166#121—1224no—
167C2×C4⋊C4—612no—
168C2×C4⋊C4—611no—
169C2×C4⋊C4—611no—
170C2×C4⋊C4—1224no—
171C2×C4⋊C4C2×D6111yescharacteristic
172C2×C22⋊C4—611no—
173C2×C22⋊C4—612no—
174C2×C22⋊C4—612no—
175C2×C22⋊C4—612no—
176C2×C22⋊C4—612no—
177C2×C22⋊C4C2×D6111yescharacteristic
178C2×C22⋊C4C2×D6112yes—
179C2×C42—612no—
180#95—611no—
181#95—612no—
182#95—612no—
183#95—612no—
184#95C2×D6111yescharacteristic
185#95C2×D6112yes—
186C24—611no—
187C24—611no—
188C24C22×D6111yescharacteristic
189C2×D4—1222no—
190C2×D4—1224no—
191C2×D4—1222no—
192C2×D4—1224no—
193C2×D4—1222no—
194C2×D4—1224no—
195C22×C4—611no—
196C22×C4—614no—
197C22×C4—611no—
198C22×C4—612no—
199C22×C4—612no—
200C22×C4—1224no—
201C22×C4—1224no—
202C22×C4—2442no—
203C22×C4—2442no—
204C22×C4C22×D6111yescharacteristic
205C22×C4C22×D6112yes—
206C22×C4C22×D6112yes—
207C22×C4C22×D6111yescharacteristic
208C4⋊C4—22no—
209C4⋊C4—1224no—
210C4⋊C4—1222no—
211C4⋊C4—1222no—
212C22⋊C4—22no—
213C22⋊C4—42no—
214C22⋊C4—1224no—
215C22⋊C4—1222no—
216C22⋊C4—2442no—
217C22⋊C4—2442no—
218C22⋊C4—2442no—
219C42—1224no—
220C23—21no—
221C23—22no—
222C23—22no—
223C23—21no—
224C23—21no—
225C23—612no—
226C23—614no—
227C23—1222no—
228C23—1221no—
229C23—1221no—
230C23—1221no—
231C23—1222no—
232C23—1222no—
233C23—1221no—
234C23—1221no—
235C23C23×D6111yescharacteristic
236D4—2444no—
237D4—2444no—
238D4—2444no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—612no—
249C2×C4—614no—
250C2×C4—1228no—
251C2×C4—1221no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1222no—
255C2×C4—1222no—
256C2×C4—1222no—
257C2×C4—1222no—
258C2×C4—1222no—
259C2×C4—2448no—
260C2×C4D4×D6112yes—
261C22—42no—
262C22—42no—
263C22—41no—
264C22—41no—
265C22—41no—
266C22—614no—
267C22—1224no—
268C22—1224no—
269C22—1222no—
270C22—1222no—
271C22—2442no—
272C22—2442no—
273C22—2441no—
274C22—2441no—
275C22—2441no—
276C22C2×D4×D6111yescharacteristic
277C22#41×D6112yes—
278C22#41×D6112yes—
279C22#1451982211yescharacteristic
280C22#1451982311yescharacteristic
281C4—22no—
282C4—42no—
283C4—41no—
284C4—42no—
285C4—614no—
286C4—2442no—
287C4—2441no—
288C4—2442no—
289C2—81no—
290C2—1224no—
291C2—4881no—
292C2#123×D6111yescharacteristic
293C2#124×D6111yescharacteristic
294C2#1684032811yescharacteristic
295C2#1684045712yes—
296C2#1684046312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#397C2
hypercenter#397D61
hypocenterC61#2504
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D61C2semidirect
3. #16839689C2semidirect
4. #16839688C2semidirect
5. #16839687C2semidirect
6. #16839662C2semidirect
7. #16839640C2semidirect
8. #16839638C2semidirect
9. #16839626C2semidirect
10. #16839609C2semidirect
11. C61×#397C2semidirect
154. #397D61semidirect
160. C61#2504semidirect