Finite Group Databasebeta

← #21455374

Subgroups — #21455374

Order 7808.

472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519799C211yesmaximal, characteristic
3#16840336C211yesmaximal, characteristic, complemented
4#16840243C211yesmaximal, characteristic, complemented
5#16839987C212yesmaximal, complemented
6#16839980C212yesmaximal, complemented
7#16839971C212yesmaximal, complemented
8#16839966C212yesmaximal, complemented
9#16839788C211yesmaximal, characteristic, complemented
10#16839761C211yesmaximal, characteristic, complemented
11C2×#103×C61C211yesmaximal, characteristic, complemented
12C2×#11758222C2211yescharacteristic
13C2×#11758222C2211yescharacteristic
14#14519808—24no—
15#14519799—24no—
16C2×Dic244C2211yescharacteristic
17C2×#11758202C2212yes—
18C2×#11758190C2211yescharacteristic
19C2×#11758190C2211yescharacteristic
20C2×#11758201C2212yes—
21C2×D488C2211yescharacteristic
22C2×#11758194C2211yescharacteristic
23#14519775C2212yes—
24#14519766C2212yes—
25#14519760—22no—
26#14519753—21no—
27#14519753—21no—
28#14519742C2212yes—
29#14519739C2212yes—
30C4×C22⋊D61—22no—
31#14519736C2211yescharacteristic
32#14519735—21no—
33C4⋊C4×D61—21no—
34#14519706C2212yes—
35#14519706C2212yes—
36#14519700C2212yes—
37#14519697C2212yes—
38C22×Q8×C61C2211yescharacteristic
39C22×C8×C61C2211yescharacteristic
40C2×C4⋊C4×C61C2211yescharacteristic
41#103×C61C2212yes—
42#103×C61C2212yes—
43C2×Q8×C61—21no—
44C2×Q8×C61—22no—
45C2×Q8×C61—22no—
46C2×Q8×C61C2312yes—
47C22×C4×C61—21no—
48C22×C4×C61—21no—
49C22×C4×C61C2311yescharacteristic
50C2×C22⋊D61—21no—
51C2×C22⋊D61—21no—
52#11758222—22no—
53#11758222—22no—
54#11758222—22no—
55#11758222D414yes—
56C2×D244C2311yescharacteristic
57C2×D244C2311yescharacteristic
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—22no—
61C2×Dic122C2311yescharacteristic
62C2×Dic122C2311yescharacteristic
63C2×C8×C61—22no—
64C2×C8×C61C2311yescharacteristic
65C2×C8×C61C2311yescharacteristic
66C4⋊C4×C61—21no—
67C4⋊C4×C61C2312yes—
68C22⋊Dic61D412yes—
69#11758202—24no—
70#11758201—24no—
71#11758198—22no—
72#11758198—22no—
73#11758198—22no—
74C4⋊Dic61D411yescharacteristic
75C4⋊Dic61D411yescharacteristic
76#11758196—22no—
77#11758196—22no—
78#11758196—22no—
79C4×Dic61—22no—
80C4×Dic61C2312yes—
81#11758194—22no—
82C2×#92418C2312yes—
83Dic244—22no—
84D488—22no—
85#11758190—22no—
86#11758190—22no—
87C23×C61C2×D411yescharacteristic
88C22×D61—21no—
89C22×D61—21no—
90Q8×C61—22no—
91Q8×C61—22no—
92Q8×C61—42no—
93C2×C4×C61—22no—
94C2×C4×C61—22no—
95C2×C4×C61—42no—
96C2×C4×C61—81no—
97C2×C4×C61C2×D411yescharacteristic
98C2×C4×C61C2×D412yes—
99C2×C4×C61#4112yes—
100C2×C4×C61C2411yescharacteristic
101C22⋊D61—24no—
102C22⋊D61—42no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61C2×D412yes—
106C2×Dic61C2×D412yes—
107D244—21no—
108D244—21no—
109D244—21no—
110D244C2×D412yes—
111C4×D61—24no—
112C4×D61—42no—
113C4×D61—82no—
114Dic122—21no—
115Dic122—21no—
116Dic122—21no—
117Dic122C2×D412yes—
118C8×C61—21no—
119C8×C61—21no—
120#92418—22no—
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#12112yes—
124C22×C61C22×D411yescharacteristic
125C2×D61—22no—
126C2×D61—41no—
127C2×D61—41no—
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—41no—
131C4×C61—42no—
132C4×C61—42no—
133C4×C61#12112yes—
134C4×C61C22×D411yescharacteristic
135C4×C61C2×#4111yescharacteristic
136Dic61—22no—
137Dic61—22no—
138Dic61—22no—
139Dic61—41no—
140#3046—611nomaximal, Sylow
141C2×C61—22no—
142C2×C61C2×#12111yescharacteristic
143C2×C61#57711yescharacteristic
144C2×C61#57811yescharacteristic
145D61—42no—
146D61—81no—
147C2×#137—611no—
148C2×#135—611no—
149#536—611no—
150#520—611no—
151#464—612no—
152#463—612no—
153#462—612no—
154#461—612no—
155#424—611no—
156#417—611no—
157C2×#103D6111yescharacteristic, complemented
158C61#304611yescharacteristic, complemented, Sylow
159C2×#41—611no—
160C2×#41—611no—
161C22×Q8C2×D6111yescharacteristic
162#137—1224no—
163#135—1224no—
164C2×Q16—612no—
165C2×Q16—611no—
166C2×SD16—612no—
167C2×SD16—611no—
168C2×SD16—611no—
169C2×D8—611no—
170C2×M16—611no—
171C22×C8C2×D6111yescharacteristic
172C4⋊Q8—612no—
173#124—612no—
174#123—1222no—
175C22⋊Q8—1221no—
176C22⋊Q8—1221no—
177C4×Q8—612no—
178C4×D4—612no—
179C4×D4—1222no—
180#117—611no—
181#117—1221no—
182C2×C4⋊C4—1221no—
183C2×C4⋊C4C2×D6111yescharacteristic
184C4⋊C8—612no—
185C4⋊C8—612no—
186#103—612no—
187#103C2×D6112yes—
188#103C2×D6112yes—
189#102—612no—
190#41—614no—
191#41—1222no—
192#41—1222no—
193#41—1222no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—611no—
198C2×Q8—611no—
199C2×Q8C22×D6112yes—
200C2×D4—611no—
201C2×D4—611no—
202C2×D4—1221no—
203C2×D4—1221no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—1222no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4C22×D6111yescharacteristic
210Q16—1222no—
211Q16—1224no—
212SD16—1222no—
213SD16—1222no—
214SD16—1224no—
215D8—1222no—
216M16—1222no—
217C2×C8—22no—
218C2×C8—612no—
219C2×C8C22×D6111yescharacteristic
220C2×C8C22×D6111yescharacteristic
221C4⋊C4—21no—
222C4⋊C4—611no—
223C4⋊C4—611no—
224C4⋊C4—1222no—
225C4⋊C4—1222no—
226C4⋊C4—1222no—
227C4⋊C4C22×D6112yes—
228C22⋊C4—612no—
229C22⋊C4—1222no—
230C22⋊C4—1222no—
231C22⋊C4—1222no—
232C42—612no—
233C42—1222no—
234C23—1221no—
235C23—1221no—
236C23D4×D6111yescharacteristic
237Q8—22no—
238Q8—22no—
239Q8—42no—
240Q8—612no—
241Q8—1221no—
242Q8—1221no—
243Q8—1221no—
244D4—612no—
245D4—1224no—
246D4—1221no—
247D4—1221no—
248D4—1221no—
249D4—2442no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—81no—
254C2×C4—612no—
255C2×C4—612no—
256C2×C4—1221no—
257C2×C4—1224no—
258C2×C4—1221no—
259C2×C4—4882no—
260C2×C4—2442no—
261C2×C4#1175822212yes—
262C2×C4D4×D6112yes—
263C2×C4D4×D6111yescharacteristic
264C2×C4C23×D6111yescharacteristic
265C8—21no—
266C8—21no—
267C8—1222no—
268C22—21no—
269C22—21no—
270C22—1222no—
271C22—2441no—
272C22—2441no—
273C22—2441no—
274C22—2441no—
275C22—2441no—
276C22#1451975012yes—
277C22C2×D4×D6111yescharacteristic
278C4—42no—
279C4—42no—
280C4—1222no—
281C4—1222no—
282C4—1222no—
283C4—2441no—
284C4#1451975012yes—
285C4C2×D4×D6111yescharacteristic
286C4C2×#1175822211yescharacteristic
287C2—22no—
288C2—4881no—
289C2—2442no—
290C2C2×#1451975011yescharacteristic
291C2#1684056811yescharacteristic
292C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#103×C61C2
socleC22×C61C22×D4
hypercenterC2×#103D61
hypocenterC61#3046
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C2×#14519808C2semidirect
3. #16840336C2semidirect
4. #16840243C2semidirect
5. #16839987C2semidirect
6. #16839980C2semidirect
7. #16839971C2semidirect
8. #16839966C2semidirect
9. #16839788C2semidirect
10. #16839761C2semidirect
11. C2×#103×C61C2semidirect
157. C2×#103D61semidirect
158. C61#3046semidirect