Finite Group Databasebeta

← #21446855

Subgroups — #21446855

Order 7808.

362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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
2#16840336C211yesmaximal, characteristic
3C2×#14519705C211yesmaximal, characteristic
4#16839771C211yesmaximal, characteristic, complemented
5C2×#14519696C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C2×C4⋊Q8×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—22no—
10#14519808—22no—
11C2×#11758202—21no—
12C2×#11758201—21no—
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15#14519775—21no—
16#14519766—21no—
17#14519760—22no—
18#14519753—22no—
19#14519736C2211yescharacteristic
20#14519705—22no—
21#14519701—22no—
22#14519696—22no—
23C22×Q8×C61C2211yescharacteristic
24C22×Q8×C61C2211yescharacteristic
25C4⋊Q8×C61—22no—
26C4⋊Q8×C61—22no—
27C2×C4⋊C4×C61—22no—
28C2×C42×C61C2211yescharacteristic
29C2×Q8×C61—21no—
30C2×Q8×C61—21no—
31C2×Q8×C61—21no—
32C2×Q8×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61—21no—
35C2×Q8×C61—21no—
36C2×Q8×C61—21no—
37C2×Q8×C61—21no—
38C2×Q8×C61—21no—
39C2×Q8×C61—21no—
40C2×Q8×C61D412yes—
41C22×C4×C61—21no—
42C22×C4×C61—21no—
43C22×C4×C61D412yes—
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—21no—
46#11758222—21no—
47#11758222—21no—
48#11758222—21no—
49#11758222—21no—
50C2×D244D411yescharacteristic
51C2×C4×D61—21no—
52C2×Dic122D411yescharacteristic
53C4⋊C4×C61—28no—
54C42×C61—21no—
55C42×C61D412yes—
56C22⋊Dic61—21no—
57#11758202—24no—
58#11758201—24no—
59#11758198—24no—
60C4⋊Dic61D412yes—
61#11758196—24no—
62C4×Dic61—21no—
63#11758194—21no—
64#11758194—21no—
65#11758194—21no—
66#11758194D412yes—
67C2×#92418—21no—
68C2×#92418—21no—
69C23×C61C2×D411yescharacteristic
70C22×D61—21no—
71Q8×C61—22no—
72Q8×C61—22no—
73Q8×C61—41no—
74Q8×C61—41no—
75Q8×C61—41no—
76Q8×C61—41no—
77Q8×C61—41no—
78Q8×C61—41no—
79C2×C4×C61—24no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61#4111yescharacteristic
93C22⋊D61—41no—
94C22⋊D61—41no—
95C2×Dic61—22no—
96C2×Dic61—21no—
97D244—21no—
98D244—21no—
99C4×D61—41no—
100C4×D61—41no—
101Dic122—21no—
102Dic122—21no—
103#92418—22no—
104#92418—41no—
105C22×C61—22no—
106C22×C61#12011yescharacteristic
107C22×C61#12011yescharacteristic
108C22×C61#12111yescharacteristic
109C2×D61—41no—
110C2×D61—42no—
111C4×C61—24no—
112C4×C61—42no—
113C4×C61—42no—
114C4×C61#12011yescharacteristic
115C4×C61#12111yescharacteristic
116C4×C61#12111yescharacteristic
117C4×C61#12711yescharacteristic
118Dic61—41no—
119Dic61—42no—
120#2005—611nomaximal, Sylow
121C2×C61—21no—
122C2×C61—21no—
123C2×C61#39211yescharacteristic
124C2×C61#45612yes—
125D61—81no—
126C2×#137—611no—
127#536—611no—
128C2×C4⋊Q8D6111yescharacteristic, complemented
129C2×#104—611no—
130#419—611no—
131C2×#101—611no—
132#339—611no—
133C61#200511yescharacteristic, complemented, Sylow
134C2×#41—611no—
135C22×Q8C2×D6111yescharacteristic
136C22×Q8C2×D6111yescharacteristic
137#137—1222no—
138#137—1222no—
139C2×Q16—1221no—
140C2×SD16—1221no—
141C2×M16—611no—
142C2×M16—611no—
143C4⋊Q8—22no—
144C4⋊Q8—22no—
145C4⋊Q8—1221no—
146#124—1221no—
147#123—1222no—
148C22⋊Q8—1222no—
149#117—611no—
150C2×C4⋊C4—22no—
151C2×C42C2×D6111yescharacteristic
152#104—1222no—
153#103—1222no—
154#101—1222no—
155#41—1221no—
156#41—1221no—
157#41—1221no—
158#41—1221no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—21no—
168C2×Q8—21no—
169C2×Q8—21no—
170C2×Q8—611no—
171C2×Q8C22⋊D6112yes—
172C2×D4—611no—
173C2×D4—1221no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—1221no—
177C22×C4C22⋊D6112yes—
178C22×C4C22×D6111yescharacteristic
179Q16—1224no—
180SD16—1224no—
181M16—612no—
182M16—1221no—
183M16—1221no—
184M16—1221no—
185C2×C8—1221no—
186C2×C8—1221no—
187C4⋊C4—28no—
188C4⋊C4—612no—
189C4⋊C4—1224no—
190C22⋊C4—1224no—
191C22⋊C4—1221no—
192C42—21no—
193C42—1221no—
194C42C22⋊D6112yes—
195C23—1221no—
196C23C2×C22⋊D6111yescharacteristic
197Q8—22no—
198Q8—22no—
199Q8—41no—
200Q8—41no—
201Q8—41no—
202Q8—41no—
203Q8—41no—
204Q8—41no—
205Q8—1221no—
206Q8—1221no—
207D4—1221no—
208D4—1221no—
209D4—2441no—
210D4—2441no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—41no—
219C2×C4—1222no—
220C2×C4—1221no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4D4×D6111yescharacteristic
224C2×C4D4×D6111yescharacteristic
225C2×C4D4×D6111yescharacteristic
226C2×C4#1175822411yescharacteristic
227C2×C4C2×C22⋊D6111yescharacteristic
228C2×C4C2×C22⋊D6111yescharacteristic
229C8—1222no—
230C8—2441no—
231C22—22no—
232C22—2442no—
233C22—2441no—
234C22#1451974511yescharacteristic
235C22#1451974611yescharacteristic
236C22#1451974911yescharacteristic
237C4—24no—
238C4—42no—
239C4—42no—
240C4—2442no—
241C4—2441no—
242C4#1451974511yescharacteristic
243C4#1451974811yescharacteristic
244C4#1451974911yescharacteristic
245C4#1451977311yescharacteristic
246C2—21no—
247C2—21no—
248C2—4881no—
249C2#1683967011yescharacteristic
250C2#1683994412yes—
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×C4⋊Q8×C61C2
socleC22×C61#120
hypercenterC2×C4⋊Q8D61
hypocenterC61#2005
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #16839771C2semidirect
5. C2×#14519696C2semidirect
6. #16839522C2semidirect
7. C2×C4⋊Q8×C61C2semidirect
128. C2×C4⋊Q8D61semidirect
133. C61#2005semidirect