Finite Group Databasebeta

← #21444845

Subgroups — #21444845

Order 7808.

236 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 51 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#16840387C211yesmaximal, characteristic
2#16840098C211yesmaximal, characteristic, complemented
3#16840095C211yesmaximal, characteristic, complemented
4#16839699C211yesmaximal, characteristic
5#16839498C211yesmaximal, characteristic, complemented
6#16839485C211yesmaximal, characteristic
7C61×#328C211yesmaximal, characteristic, complemented
8#14519757—21no—
9#14519756C2211yescharacteristic
10#14519755—21no—
11#14519755—21no—
12#14519754—21no—
13#14519753—21no—
14C2×C4⋊Dic61—21no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758198—21no—
17C2×#11758198C2211yescharacteristic
18C22⋊C4×D61—21no—
19#14519711—21no—
20#14519710—21no—
21#14519702—21no—
22#14519701—21no—
23C22⋊#92418C2211yescharacteristic
24C22⋊Q8×C61C2211yescharacteristic
25C22⋊C8×C61C2211yescharacteristic
26#95×C61C2211yescharacteristic
27C23×D61D411yescharacteristic
28C2×Q8×C61D411yescharacteristic
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31C22×Dic61—21no—
32C22×Dic61D411yescharacteristic
33C2×C4×D61—21no—
34C2×C4×D61—21no—
35C2×Dic122—21no—
36C2×Dic122D411yescharacteristic
37C2×C8×C61—21no—
38C4⋊C4×C61—21no—
39C4⋊C4×C61D411yescharacteristic
40C22⋊C4×C61—21no—
41C22⋊Dic61—21no—
42#11758198—21no—
43#11758198—21no—
44#11758198—21no—
45#11758198—21no—
46#11758198—42no—
47C4⋊Dic61—21no—
48C4⋊Dic61—21no—
49C4⋊Dic61—21no—
50C4⋊Dic61—42no—
51C4⋊Dic61D411yescharacteristic
52#11758196—21no—
53#11758196—21no—
54#11758196—21no—
55C2×#92418—21no—
56C23×C61C2×D411yescharacteristic
57C22×D61—21no—
58C22×D61—21no—
59C22×D61—41no—
60C22×D61—41no—
61C22×D61Q1612yes—
62Q8×C61—41no—
63C2×C4×C61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78C4×D61—81no—
79C4×D61—81no—
80Dic122—41no—
81Dic122—81no—
82C8×C61—41no—
83#92418—41no—
84C22×C61—21no—
85C22×C61—21no—
86C22×C61#12011yescharacteristic
87C22×C61C2×Q1611yescharacteristic
88C22×C61#13711yescharacteristic
89C2×D61—22no—
90C2×D61—41no—
91C2×D61—41no—
92C2×D61—42no—
93C2×D61—81no—
94C4×C61—21no—
95C4×C61—21no—
96C4×C61—42no—
97C4×C61—41no—
98C4×C61—41no—
99Dic61—41no—
100Dic61—41no—
101Dic61—41no—
102Dic61—81no—
103#1614—611nomaximal, Sylow
104C2×C61—21no—
105C2×C61—21no—
106C2×C61#45111yescharacteristic
107C2×C61#45311yescharacteristic
108C2×C61#45811yescharacteristic
109D61—42no—
110#543—611no—
111#484—611no—
112#484—611no—
113#399—611no—
114#328—611no—
115#328D6111yescharacteristic, complemented
116#323—611no—
117C61#161411yescharacteristic, complemented, Sylow
118C22⋊Q8—611no—
119C22⋊Q8—1221no—
120C22⋊Q8—1221no—
121C22⋊Q8—1221no—
122C22⋊Q8—1221no—
123C22⋊Q8—1221no—
124C22⋊Q8C2×D6111yescharacteristic
125C2×C4⋊C4—611no—
126C2×C4⋊C4—1221no—
127C2×C22⋊C4—611no—
128C2×C22⋊C4—1221no—
129C2×C22⋊C4—1221no—
130#107—1221no—
131#107—1221no—
132#103—1221no—
133#103—1221no—
134C22⋊C8—611no—
135C22⋊C8C2×D6111yescharacteristic
136#95C2×D6111yescharacteristic
137C24—611no—
138C2×Q8—611no—
139C2×Q8—1221no—
140C2×Q8D24411yescharacteristic
141C22×C4—21no—
142C22×C4—611no—
143C22×C4—1221no—
144C22×C4—1221no—
145C22×C4—1221no—
146C22×C4C22×D6111yescharacteristic
147C2×C8—21no—
148C2×C8—1221no—
149C4⋊C4—21no—
150C4⋊C4—611no—
151C4⋊C4—1221no—
152C4⋊C4—1221no—
153C4⋊C4—1221no—
154C4⋊C4—1221no—
155C4⋊C4—1221no—
156C4⋊C4—1221no—
157C4⋊C4—2442no—
158C4⋊C4D24411yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—1221no—
161C22⋊C4—1221no—
162C22⋊C4—1221no—
163C22⋊C4—1221no—
164C22⋊C4—1221no—
165C22⋊C4—2442no—
166C23—612no—
167C23—1221no—
168C23—1221no—
169C23—2441no—
170C23—2441no—
171C23D4×D6111yescharacteristic
172Q8—41no—
173Q8—4881no—
174Q8—2441no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—1221no—
182C2×C4—1221no—
183C2×C4—1221no—
184C2×C4—4881no—
185C2×C4—4881no—
186C2×C4—2441no—
187C2×C4—2441no—
188C2×C4—2441no—
189C2×C4—2441no—
190C2×C4C2×D24411yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C8—41no—
193C8—2441no—
194C22—21no—
195C22—21no—
196C22—1222no—
197C22—4881no—
198C22—2442no—
199C22—2441no—
200C22—2441no—
201C22#1451974711yescharacteristic
202C22Q16×D6111yescharacteristic
203C22#1451980611yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—4881no—
210C4—2441no—
211C4—2441no—
212C4—2441no—
213C2—21no—
214C2—21no—
215C2—2442no—
216C2#1683991911yescharacteristic
217C2#1683993111yescharacteristic
218C2#1683995311yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#328C2
socleC22×C61#120
hypercenter#328D61
hypocenterC61#1614
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #16840098C2semidirect
3. #16840095C2semidirect
5. #16839498C2semidirect
7. C61×#328C2semidirect
115. #328D61semidirect
117. C61#1614semidirect