Finite Group Databasebeta

← #21456275

Subgroups — #21456275

Order 7808.

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

normal subgroups only

This group has 552 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×#14519809C212yesmaximal, complemented
2C2×#14519806C212yesmaximal, complemented
3#16840311C211yesmaximal, characteristic
4C4⋊Q8×D61C211yesmaximal, characteristic, complemented
5#16840157C211yesmaximal, characteristic, complemented
6#16840156C211yesmaximal, characteristic, complemented
7#16840154C211yesmaximal, characteristic, complemented
8#16840140C212yesmaximal, complemented
9#16840133C212yesmaximal, complemented
10#16839714C211yesmaximal, characteristic, complemented
11C61×#497C211yesmaximal, characteristic, complemented
12C2×#11758226C2211yescharacteristic
13C2×#11758224C2211yescharacteristic
14C2×Q8×D61C2212yes—
15#14519809—28no—
16#14519806—28no—
17C2×Dic244C2212yes—
18C2×#11758202C2212yes—
19C2×#11758202C2212yes—
20C2×#11758190C2212yes—
21C2×#11758200C2212yes—
22C2×#11758201C2212yes—
23C2×#11758189C2212yes—
24#14519777C2211yescharacteristic
25#14519776—22no—
26#14519775C2212yes—
27#14519775C2211yescharacteristic
28#14519773C2211yescharacteristic
29#14519765C2211yescharacteristic
30#14519750—22no—
31#14519737—22no—
32C4⋊C4×D61—22no—
33C42×D61C2211yescharacteristic
34#14519688C2211yescharacteristic
35C8×Dic61C2212yes—
36C2×Q16×C61C2212yes—
37C2×SD16×C61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39#124×C61C2211yescharacteristic
40#97×C61C2211yescharacteristic
41C2×Q8×C61C2312yes—
42C2×Q8×C61C2311yescharacteristic
43C2×D4×C61C2311yescharacteristic
44C2×C22⋊D61—21no—
45C2×C22⋊D61—22no—
46C22×Dic61—21no—
47#11758226—24no—
48Q8×D61—24no—
49Q8×D61—24no—
50#11758224—24no—
51C2×D244—21no—
52C2×D244C2311yescharacteristic
53C2×C4×D61—22no—
54C2×C4×D61—21no—
55C2×C4×D61D412yes—
56C2×C4×D61C2311yescharacteristic
57C2×Dic122—22no—
58C2×Dic122C2312yes—
59C2×Dic122C2311yescharacteristic
60Q16×C61—24no—
61SD16×C61—24no—
62C2×C8×C61C2312yes—
63C4⋊C4×C61—22no—
64C22⋊C4×C61—22no—
65C42×C61C2311yescharacteristic
66#11758202—24no—
67#11758202—24no—
68#11758201—24no—
69#11758200—24no—
70#11758198—22no—
71C4⋊Dic61—22no—
72#11758196—24no—
73#11758196—22no—
74C4×Dic61D412yes—
75C4×Dic61C2311yescharacteristic
76C2×#92418C2312yes—
77Dic244—24no—
78#11758190—24no—
79#11758189D418yescomplemented
80C23×C61—21no—
81C22×D61—21no—
82C22×D61C2×D411yescharacteristic
83Q8×C61—22no—
84Q8×C61—22no—
85Q8×C61—22no—
86D4×C61—22no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61C2×D412yes—
90C2×C4×C61C2411yescharacteristic
91C22⋊D61—42no—
92C22⋊D61—44no—
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—42no—
96C2×Dic61C2×D411yescharacteristic
97C2×Dic61C2×D412yes—
98D244—22no—
99D244—42no—
100C4×D61—24no—
101C4×D61—44no—
102C4×D61—42no—
103C4×D61C2×D414yes—
104Dic122—22no—
105Dic122—22no—
106Dic122—22no—
107Dic122—44no—
108C8×C61C2×D414yes—
109#92418C2×D414yes—
110C22×C61—41no—
111C22×C61—42no—
112C22×C61C22×D411yescharacteristic
113C2×D61—22no—
114C2×D61—41no—
115C2×D61—42no—
116C2×D61#12712yes—
117C4×C61—22no—
118C4×C61—42no—
119C4×C61—41no—
120C4×C61C22×D412yes—
121Dic61—42no—
122Dic61—41no—
123Dic61#12712yes—
124Dic61#13714yescomplemented
125#3152—611nomaximal, Sylow
126C2×C61—81no—
127C2×C61C2×#12711yescharacteristic
128C2×C61C2×#13712yes—
129D61—22no—
130D61—81no—
131C2×#137—612no—
132C2×#137—612no—
133#532—611no—
134C2×C4⋊Q8—611no—
135#497—611no—
136#497—611no—
137#497—611no—
138#497D6111yescharacteristic, complemented
139#494—612no—
140#492—612no—
141C4×M16—611no—
142C61#315211yescharacteristic, complemented, Sylow
143C2×#41—611no—
144C2×#41—611no—
145C22×Q8—612no—
146#137—1228no—
147#137—1228no—
148C2×Q16—612no—
149C2×Q16—612no—
150C2×Q16—612no—
151C2×Q16C2×D6112yes—
152C2×SD16—612no—
153C2×SD16—612no—
154C2×SD16—612no—
155C2×SD16C2×D6112yes—
156C2×M16—612no—
157C4⋊Q8—612no—
158C4⋊Q8—611no—
159C4⋊Q8—611no—
160C4⋊Q8—1222no—
161C4⋊Q8C2×D6111yescharacteristic
162#127—611no—
163#124—611no—
164#124C2×D6111yescharacteristic
165#121—1222no—
166C4×D4—1222no—
167C2×C4⋊C4—1222no—
168C2×C42—611no—
169#97—611no—
170#97C2×D6111yescharacteristic
171C4×C8—612no—
172#41—1224no—
173#41—1224no—
174C2×Q8—611no—
175C2×Q8—612no—
176C2×Q8—1222no—
177C2×Q8—1224no—
178C2×Q8—1224no—
179C2×Q8C22×D6111yescharacteristic
180C2×Q8C22×D6112yes—
181C2×D4—611no—
182C2×D4—1221no—
183C2×D4—1222no—
184C2×D4—1221no—
185C2×D4C22×D6111yescharacteristic
186C22×C4—611no—
187C22×C4—612no—
188C22×C4—1221no—
189C22×C4—1222no—
190C22×C4—1221no—
191Q16—24no—
192Q16—1224no—
193Q16—1224no—
194Q16—1224no—
195SD16—24no—
196SD16—1224no—
197SD16—1224no—
198SD16—1224no—
199M16—618no—
200C2×C8—612no—
201C2×C8C22×D6112yes—
202C4⋊C4—22no—
203C4⋊C4—1224no—
204C4⋊C4—1222no—
205C4⋊C4—1222no—
206C22⋊C4—22no—
207C22⋊C4—1222no—
208C42—612no—
209C42—611no—
210C42C22×D6111yescharacteristic
211C23—21no—
212C23—611no—
213C23—1221no—
214Q8—22no—
215Q8—22no—
216Q8—22no—
217Q8—1222no—
218Q8—1222no—
219Q8—1222no—
220Q8—2444no—
221D4—22no—
222D4—1222no—
223D4—2442no—
224D4—2444no—
225D4—2442no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—612no—
229C2×C4—611no—
230C2×C4—614no—
231C2×C4—1224no—
232C2×C4—1221no—
233C2×C4—1222no—
234C2×C4—2442no—
235C2×C4—2444no—
236C2×C4—2442no—
237C2×C4D4×D6112yes—
238C2×C4C23×D6111yescharacteristic
239C8—614no—
240C8D4×D6114yes—
241C22—42no—
242C22—41no—
243C22—612no—
244C22—1222no—
245C22—2442no—
246C22—2441no—
247C22C2×D4×D6111yescharacteristic
248C4—22no—
249C4—41no—
250C4—42no—
251C4—614no—
252C4—612no—
253C4—2441no—
254C4—2442no—
255C4C2×D4×D6112yes—
256C2—81no—
257C2—1222no—
258C2—4881no—
259C2#127×D6111yescharacteristic
260C2#137×D6112yes—
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#497C2
socleC22×C61C22×D4
hypercenter#497D61
hypocenterC61#3152
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. C2×#14519809C2semidirect
2. C2×#14519806C2semidirect
4. C4⋊Q8×D61C2semidirect
5. #16840157C2semidirect
6. #16840156C2semidirect
7. #16840154C2semidirect
8. #16840140C2semidirect
9. #16840133C2semidirect
10. #16839714C2semidirect
11. C61×#497C2semidirect
79. #11758189D4semidirect
124. Dic61#137semidirect
138. #497D61semidirect
142. C61#3152semidirect