Finite Group Databasebeta

← #21455788

Subgroups — #21455788

Order 7808.

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

normal subgroups only

This group has 386 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
1#16840333C211yesmaximal, characteristic
2#16840103C212yesmaximal, complemented
3#16840103C212yesmaximal, complemented
4#16840097C212yesmaximal, complemented
5#16840092C212yesmaximal, complemented
6#16839802C211yesmaximal, characteristic, complemented
7#16839798C211yesmaximal, characteristic, complemented
8#16839770C211yesmaximal, characteristic, complemented
9C2×#14519700C211yesmaximal, characteristic, complemented
10#16839729C211yesmaximal, characteristic
11C61×#520C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13C2×#11758194C2211yescharacteristic
14C22×#92418C2211yescharacteristic
15#14519775—21no—
16#14519764—21no—
17#14519758—22no—
18#14519756C2212yes—
19#14519756C2212yes—
20#14519736C2211yescharacteristic
21#14519710C2211yescharacteristic
22#14519710C2211yescharacteristic
23#14519710C2212yes—
24#14519708C2211yescharacteristic
25#14519708C2211yescharacteristic
26#14519708C2212yes—
27#14519700C2212yes—
28#14519700C2212yes—
29#14519700C2212yes—
30#14519700C2212yes—
31C22⋊#92418C2212yes—
32C22⋊#92418C2212yes—
33C2×#41×C61C2211yescharacteristic
34C4×Q8×C61—21no—
35C4×D4×C61—22no—
36C4×D4×C61—21no—
37#117×C61C2211yescharacteristic
38#117×C61C2212yes—
39C2×C4⋊C4×C61C2211yescharacteristic
40C2×C4⋊C4×C61C2212yes—
41#41×C61—22no—
42#41×C61—22no—
43C2×Q8×C61D411yescharacteristic
44C2×D4×C61D412yes—
45C2×D4×C61D411yescharacteristic
46C22×C4×C61—22no—
47C22×C4×C61—21no—
48C22×C4×C61C2312yes—
49C22×C4×C61C2311yescharacteristic
50C22×Dic61—21no—
51C2×Dic122—22no—
52C2×Dic122—22no—
53C2×Dic122—21no—
54C2×Dic122C2312yes—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—21no—
57C4⋊C4×C61C2312yes—
58C4⋊C4×C61C2311yescharacteristic
59C4⋊C4×C61C2311yescharacteristic
60C22⋊C4×C61—22no—
61C22⋊C4×C61—21no—
62C42×C61—22no—
63C42×C61—21no—
64C22⋊Dic61—21no—
65C22⋊Dic61—22no—
66C22⋊Dic61—22no—
67C4⋊Dic61C2311yescharacteristic
68C4⋊Dic61C2311yescharacteristic
69#11758196—22no—
70#11758196—22no—
71C4×Dic61—21no—
72#11758194—22no—
73C2×#92418—22no—
74C2×#92418C2311yescharacteristic
75C2×#92418C2312yes—
76C2×#92418C2311yescharacteristic
77C23×C61C2×D412yes—
78C23×C61C2×D411yescharacteristic
79Q8×C61—22no—
80D4×C61—24no—
81D4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—81no—
88C2×C4×C61—82no—
89C2×C4×C61C2×D412yes—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61#4112yes—
92C2×C4×C61#4112yes—
93C2×C4×C61C2411yescharacteristic
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—42no—
98Dic122—22no—
99Dic122—22no—
100Dic122—42no—
101#92418—21no—
102#92418—21no—
103#92418—22no—
104C22×C61—21no—
105C22×C61—21no—
106C22×C61—22no—
107C22×C61—22no—
108C22×C61—22no—
109C22×C61#12312yes—
110C22×C61C22×D411yescharacteristic
111C4×C61—22no—
112C4×C61—42no—
113C4×C61—41no—
114C4×C61—41no—
115C4×C61#12312yes—
116C4×C61C2×#4111yescharacteristic
117C4×C61C2×#4111yescharacteristic
118Dic61—42no—
119Dic61—41no—
120Dic61—41no—
121#3097—611nomaximal, Sylow
122C2×C61—22no—
123C2×C61—42no—
124C2×C61C2×#12311yescharacteristic
125C2×C61#57711yescharacteristic
126C2×C61#57811yescharacteristic
127#536—611no—
128#520D6111yescharacteristic
129#485—612no—
130#485—612no—
131#484—612no—
132#483—612no—
133#428—611no—
134#427—611no—
135#419—611no—
136C2×#103—611no—
137#408—611no—
138C61#309711yescharacteristic, complemented, Sylow
139C2×#41C2×D6111yescharacteristic
140C22×Q8—611no—
141C2×M16—611no—
142C22×C8—611no—
143C4⋊Q8—1221no—
144#124—1221no—
145#123—1222no—
146C22⋊Q8—612no—
147C22⋊Q8—612no—
148C4×Q8—21no—
149C4×D4—22no—
150C4×D4—21no—
151#117—611no—
152#117C2×D6111yescharacteristic
153#117C2×D6112yes—
154C2×C4⋊C4C2×D6111yescharacteristic
155C2×C4⋊C4C2×D6112yes—
156#107—611no—
157#107—611no—
158#107—612no—
159#106—611no—
160#106—611no—
161#106—612no—
162#103—612no—
163#103—612no—
164#103—612no—
165#103—612no—
166C22⋊C8—612no—
167C22⋊C8—612no—
168#41—22no—
169#41—22no—
170C2×Q8—612no—
171C2×Q8—1221no—
172C2×Q8—1222no—
173C2×Q8—1222no—
174C2×Q8C22⋊D6111yescharacteristic
175C2×D4C22⋊D6112yes—
176C2×D4C22⋊D6111yescharacteristic
177C22×C4—22no—
178C22×C4—21no—
179C22×C4—1221no—
180C22×C4C22×D6112yes—
181C22×C4C22×D6111yescharacteristic
182M16—1222no—
183C2×C8—611no—
184C2×C8—612no—
185C2×C8—611no—
186C2×C8—1222no—
187C4⋊C4—22no—
188C4⋊C4—21no—
189C4⋊C4—611no—
190C4⋊C4—611no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C4⋊C4C22×D6112yes—
194C4⋊C4C22×D6111yescharacteristic
195C4⋊C4C22×D6111yescharacteristic
196C22⋊C4—22no—
197C22⋊C4—21no—
198C22⋊C4—1221no—
199C22⋊C4—1222no—
200C22⋊C4—1222no—
201C42—22no—
202C42—21no—
203C42—1221no—
204C23C2×C22⋊D6112yes—
205C23C2×C22⋊D6111yescharacteristic
206Q8—22no—
207Q8—1222no—
208Q8—1222no—
209Q8—2442no—
210D4—24no—
211D4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—81no—
218C2×C4—82no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1222no—
222C2×C4—2442no—
223C2×C4#1175822212yes—
224C2×C4#1175822212yes—
225C2×C4C2×C22⋊D6112yes—
226C2×C4C2×C22⋊D6111yescharacteristic
227C2×C4C23×D6111yescharacteristic
228C8—1221no—
229C8—1221no—
230C8—1222no—
231C22—21no—
232C22—21no—
233C22—22no—
234C22—22no—
235C22—22no—
236C22#1451976012yes—
237C22C22×C22⋊D6111yescharacteristic
238C4—22no—
239C4—42no—
240C4—41no—
241C4—41no—
242C4—2442no—
243C4—2441no—
244C4—2441no—
245C4#1451976012yes—
246C4C2×#1175822211yescharacteristic
247C4C2×#1175822211yescharacteristic
248C2—22no—
249C2—42no—
250C2C2×#1451976011yescharacteristic
251C2#1684057311yescharacteristic
252C2#1684057711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#520C2
socleC22×C61C22×D4
hypercenter#520D61
hypocenterC61#3097
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#41 ◁ #520

Complements

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

NH ≅ G/Ntype
2. #16840103C2semidirect
3. #16840103C2semidirect
4. #16840097C2semidirect
5. #16840092C2semidirect
6. #16839802C2semidirect
7. #16839798C2semidirect
8. #16839770C2semidirect
9. C2×#14519700C2semidirect
138. C61#3097semidirect