Finite Group Databasebeta

← #21446027

Subgroups — #21446027

Order 7808.

324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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#16840236C211yesmaximal, characteristic
2#16839802C211yesmaximal, characteristic, complemented
3C2×#14519693C211yesmaximal, characteristic
4#16839663C211yesmaximal, characteristic
5#16839523C211yesmaximal, characteristic, complemented
6#16839521C211yesmaximal, characteristic, complemented
7C61×#428C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C2×#11758194C2211yescharacteristic
10C4×D244—21no—
11C4×D244—21no—
12#14519739—21no—
13#14519739—21no—
14#14519736C2211yescharacteristic
15C2×#11758198—22no—
16C22⋊C4×D61—22no—
17C2×C4×Dic61C2211yescharacteristic
18#14519710—21no—
19#14519708—21no—
20#14519693C414yescomplemented
21C2×M16×C61C2211yescharacteristic
22#117×C61C2211yescharacteristic
23C2×C4⋊C4×C61C2211yescharacteristic
24#107×C61—21no—
25#106×C61—21no—
26C23×D61D412yes—
27C22×C4×C61—21no—
28C22×C4×C61C2311yescharacteristic
29C22×Dic61—21no—
30C2×D244—21no—
31C2×D244—21no—
32C2×D244—21no—
33C2×D244—21no—
34C2×D244C2×C412yes—
35C2×D244Q812yes—
36C2×C4×D61—22no—
37C2×C4×D61—22no—
38M16×C61—21no—
39M16×C61C2×C412yescomplemented
40C2×C8×C61—21no—
41C4⋊C4×C61—21no—
42C4⋊C4×C61—21no—
43C4⋊C4×C61D411yescharacteristic
44C4⋊C4×C61D411yescharacteristic
45C22⋊C4×C61—21no—
46C42×C61—21no—
47C22⋊Dic61—21no—
48#11758198—22no—
49#11758198—22no—
50#11758198—44no—
51C4⋊Dic61D411yescharacteristic
52C4⋊Dic61D411yescharacteristic
53C4×Dic61—21no—
54C4×Dic61—21no—
55C4×Dic61—21no—
56#11758194—21no—
57#11758194C2×C412yescomplemented
58C2×#92418—21no—
59C23×C61C2×D411yescharacteristic
60C22×D61—22no—
61C22×D61—22no—
62C22×D61—42no—
63C22×D61—42no—
64C22×D61C4⋊C414yes—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—42no—
68C2×C4×C61—41no—
69C2×C4×C61C22×C411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×Q811yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C2×Dic61—22no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—41no—
79C2×Dic61—41no—
80D244—22no—
81D244—22no—
82D244—22no—
83D244—22no—
84C4×D61—82no—
85C4×D61—82no—
86C8×C61—22no—
87#92418—22no—
88C22×C61—21no—
89C22×C61—21no—
90C22×C61C2×C4⋊C411yescharacteristic
91C22×C61#12011yescharacteristic
92C22×C61#12311yescharacteristic
93C2×D61—24no—
94C2×D61—42no—
95C2×D61—42no—
96C2×D61—44no—
97C2×D61—82no—
98C4×C61—41no—
99C4×C61—41no—
100C4×C61—81no—
101C4×C61C4×D411yescharacteristic
102C4×C61C4×D411yescharacteristic
103C4×C61C22⋊Q811yescharacteristic
104C4×C61C22⋊Q811yescharacteristic
105Dic61—42no—
106Dic61—41no—
107Dic61—41no—
108#1856—611nomaximal, Sylow
109C2×C61—21no—
110C2×C61—21no—
111C2×C61#38511yescharacteristic
112C2×C61#45311yescharacteristic
113C2×C61#45511yescharacteristic
114D61—44no—
115#518—611no—
116#428—611no—
117#428D6111yescharacteristic, complemented
118C2×#100—611no—
119#390—611no—
120#339—611no—
121#339—611no—
122C61#185611yescharacteristic, complemented, Sylow
123C22×D4—611no—
124C2×M16—611no—
125C2×M16C2×D6111yescharacteristic
126C4×D4—1221no—
127C4×D4—1221no—
128C4×D4—1221no—
129C4×D4—1221no—
130#117—611no—
131#117C2×D6111yescharacteristic
132C2×C4⋊C4C2×D6111yescharacteristic
133C2×C22⋊C4—1222no—
134C2×C22⋊C4—1222no—
135C2×C42—611no—
136#107—21no—
137#107—1221no—
138#106—21no—
139#106—1221no—
140#100—614no—
141C24—612no—
142C2×D4—612no—
143C2×D4—612no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4—1221no—
147C2×D4—1221no—
148C22×C4—21no—
149C22×C4—1222no—
150C22×C4—1222no—
151C22×C4—1221no—
152C22×C4C22×D6111yescharacteristic
153M16—21no—
154M16—612no—
155M16—1221no—
156M16C4×D6112yescomplemented
157C2×C8—21no—
158C2×C8—1221no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—611no—
162C4⋊C4—611no—
163C4⋊C4C22⋊D6111yescharacteristic
164C4⋊C4C22⋊D6111yescharacteristic
165C22⋊C4—21no—
166C22⋊C4—1222no—
167C22⋊C4—1222no—
168C22⋊C4—1221no—
169C22⋊C4—2444no—
170C42—21no—
171C42—1221no—
172C42—1221no—
173C42—1221no—
174C23—614no—
175C23—1222no—
176C23—1222no—
177C23—2442no—
178C23—2442no—
179C23D4×D6111yescharacteristic
180D4—1222no—
181D4—1222no—
182D4—1222no—
183D4—1222no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—42no—
187C2×C4—41no—
188C2×C4—1222no—
189C2×C4—1221no—
190C2×C4—1221no—
191C2×C4—4882no—
192C2×C4—4882no—
193C2×C4—2441no—
194C2×C4—2441no—
195C2×C4C2×C4×D6111yescharacteristic
196C2×C4#1175822211yescharacteristic
197C2×C4D4×D6111yescharacteristic
198C2×C4Q8×D6111yescharacteristic
199C2×C4#1175822611yescharacteristic
200C2×C4C2×C22⋊D6111yescharacteristic
201C8—22no—
202C8—1222no—
203C22—21no—
204C22—21no—
205C22—1224no—
206C22—4882no—
207C22—2444no—
208C22—2442no—
209C22—2442no—
210C22C4⋊C4×D6111yescharacteristic
211C22#1451974511yescharacteristic
212C22#1451976211yescharacteristic
213C4—41no—
214C4—41no—
215C4—81no—
216C4—2442no—
217C4—2441no—
218C4—2441no—
219C4C4×C22⋊D6111yescharacteristic
220C4#1451973911yescharacteristic
221C4#1451975311yescharacteristic
222C4#1451975511yescharacteristic
223C2—21no—
224C2—21no—
225C2—2444no—
226C2#1683963311yescharacteristic
227C2#1683992811yescharacteristic
228C2#1683993811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#428C2
socleC22×C61#120
hypercenter#428D61
hypocenterC61#1856
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #16839802C2semidirect
5. #16839523C2semidirect
6. #16839521C2semidirect
7. C61×#428C2semidirect
20. #14519693C4semidirect
39. M16×C61C2×C4semidirect
57. #11758194C2×C4semidirect
117. #428D61semidirect
122. C61#1856semidirect
156. M16C4×D61semidirect