Finite Group Databasebeta

← #21446623

Subgroups — #21446623

Order 7808.

436 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14519773C211yesmaximal, characteristic
2C2×#14519699C211yesmaximal, characteristic, complemented
3C2×#14519698C211yesmaximal, characteristic, complemented
4C2×#14519697C211yesmaximal, characteristic, complemented
5C2×C8×Dic61C211yesmaximal, characteristic, complemented
6#16839631C211yesmaximal, characteristic, complemented
7C2×#102×C61C211yesmaximal, characteristic, complemented
8C22×D244C2211yescharacteristic
9C22×C22⋊D61—22no—
10C22×#92418C2211yescharacteristic
11#14519773—22no—
12#14519773C414yescomplemented
13C2×C4⋊Dic61C2211yescharacteristic
14C2×#11758196—22no—
15C2×C4×Dic61C2211yescharacteristic
16#14519699—22no—
17#14519698—22no—
18#14519697—22no—
19C8×Dic61—22no—
20C22×D4×C61C2211yescharacteristic
21C22×C8×C61C2211yescharacteristic
22C2×C4⋊C4×C61C2211yescharacteristic
23#102×C61—22no—
24C24×C61—21no—
25C23×D61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61C2×C412yes—
32C22×C4×C61—21no—
33C22×C4×C61C2311yescharacteristic
34C2×C22⋊D61—28no—
35C2×C22⋊D61—44no—
36C2×C22⋊D61—44no—
37C22×Dic61—21no—
38C22×Dic61D412yes—
39C2×D244—21no—
40C2×D244—21no—
41C2×D244—21no—
42C2×D244—21no—
43C2×D244—21no—
44C2×D244C2×C412yes—
45C2×C8×C61—21no—
46C2×C8×C61—21no—
47C2×C8×C61D412yescomplemented
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50C4⋊Dic61—21no—
51C4⋊Dic61—21no—
52#11758196—44no—
53C4×Dic61C2×C412yes—
54C4×Dic61D412yes—
55C2×#92418—21no—
56C2×#92418—21no—
57C2×#92418D412yescomplemented
58C23×C61—22no—
59C23×C61—41no—
60C23×C61—41no—
61C23×C61—42no—
62C23×C61—42no—
63C23×C61C2×D411yescharacteristic
64C22×D61—22no—
65C22×D61—41no—
66C22×D61—41no—
67C22×D61—42no—
68C22×D61—42no—
69D4×C61—22no—
70D4×C61—22no—
71D4×C61—41no—
72D4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61—42no—
75C2×C4×C61C22×C411yescharacteristic
76C2×C4×C61C2×D411yescharacteristic
77C2×C4×C61C2×D411yescharacteristic
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61#4111yescharacteristic
80C2×C4×C61#4111yescharacteristic
81C22⋊D61—416no—
82C2×Dic61—41no—
83C2×Dic61—42no—
84C2×Dic61C22⋊C414yes—
85C2×Dic61D814yes—
86C2×Dic61SD1614yes—
87D244—22no—
88D244—22no—
89D244—41no—
90D244—41no—
91C8×C61—22no—
92#92418—22no—
93C22×C61—42no—
94C22×C61—44no—
95C22×C61—82no—
96C22×C61—81no—
97C22×C61—81no—
98C22×C61C2×C22⋊C411yescharacteristic
99C22×C61#12411yescharacteristic
100C22×C61#12711yescharacteristic
101C22×C61C2×D812yes—
102C22×C61C2×SD1612yes—
103C2×D61—42no—
104C2×D61—44no—
105C2×D61—82no—
106C2×D61—81no—
107C2×D61—81no—
108C4×C61—81no—
109C4×C61C4×D411yescharacteristic
110C4×C61C4×D411yescharacteristic
111C4×C61#12111yescharacteristic
112C4×C61#12111yescharacteristic
113Dic61—81no—
114Dic61#10218yescomplemented
115#1957—611nomaximal, Sylow
116C2×C61—82no—
117C2×C61#39011yescharacteristic
118C2×C61C2×#10212yes—
119C2×C61#48612yes—
120C2×C61#49211yescharacteristic
121C2×C61#49311yescharacteristic
122D61—82no—
123C2×#127—611no—
124C2×#102—611no—
125C2×#102—611no—
126C2×#102—611no—
127C2×#102D6111yescharacteristic, complemented
128C2×C4×C8—611no—
129#384—611no—
130C61#195711yescharacteristic, complemented, Sylow
131C22×D4—611no—
132C22×D4—1222no—
133C22×D4C2×D6111yescharacteristic
134C22×C8—611no—
135C22×C8C2×D6111yescharacteristic
136#127—614no—
137#127—1222no—
138C2×C4⋊C4—611no—
139C2×C4⋊C4—1222no—
140C2×C4⋊C4C2×D6111yescharacteristic
141C2×C42—611no—
142#102—22no—
143#102—1222no—
144#102—1222no—
145#102—1222no—
146C4×C8—1222no—
147C24—21no—
148C24—1221no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4—612no—
155C2×D4—1228no—
156C2×D4—1221no—
157C2×D4—1221no—
158C2×D4—1221no—
159C2×D4—1221no—
160C2×D4—1221no—
161C2×D4—2444no—
162C2×D4—2444no—
163C2×D4C4×D6112yes—
164C22×C4—21no—
165C22×C4—612no—
166C22×C4—1221no—
167C22×C4C22×D6111yescharacteristic
168C2×C8—21no—
169C2×C8—21no—
170C2×C8—612no—
171C2×C8—1221no—
172C2×C8—1221no—
173C2×C8C22⋊D6112yescomplemented
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—1221no—
177C4⋊C4—1221no—
178C4⋊C4—2444no—
179C42—612no—
180C42—612no—
181C23—22no—
182C23—41no—
183C23—41no—
184C23—42no—
185C23—42no—
186C23—1222no—
187C23—2441no—
188C23—2441no—
189C23—2442no—
190C23—2442no—
191C23D4×D6111yescharacteristic
192D4—22no—
193D4—22no—
194D4—41no—
195D4—41no—
196D4—1222no—
197D4—1222no—
198D4—24416no—
199D4—2441no—
200D4—2441no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4—614no—
204C2×C4—614no—
205C2×C4—614no—
206C2×C4—2441no—
207C2×C4—2442no—
208C2×C4C2×C4×D6111yescharacteristic
209C2×C4#1175822211yescharacteristic
210C2×C4D4×D6111yescharacteristic
211C2×C4D4×D6111yescharacteristic
212C2×C4#1175822411yescharacteristic
213C2×C4C2×C22⋊D6111yescharacteristic
214C8—22no—
215C8—1222no—
216C22—44no—
217C22—42no—
218C22—82no—
219C22—81no—
220C22—81no—
221C22—4882no—
222C22—4881no—
223C22—4881no—
224C22—2444no—
225C22—2442no—
226C22C22⋊C4×D6111yescharacteristic
227C22#1451976311yescharacteristic
228C22#1451977311yescharacteristic
229C22D8×D6112yes—
230C22SD16×D6112yes—
231C4—81no—
232C4—618no—
233C4—4881no—
234C4#1451973711yescharacteristic
235C4C4×C22⋊D6111yescharacteristic
236C4#1451974911yescharacteristic
237C4#1451975011yescharacteristic
238C2—82no—
239C2—4882no—
240C2#1683966211yescharacteristic
241C2#102×D6112yes—
242C2#1684010712yes—
243C2#1684013311yescharacteristic
244C2#1684013711yescharacteristic
subgroupG/H
centerC23D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#102×C61C2
socleC23×C61C2×D4
hypercenterC2×#102D61
hypocenterC61#1957
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14519699C2semidirect
3. C2×#14519698C2semidirect
4. C2×#14519697C2semidirect
5. C2×C8×Dic61C2semidirect
6. #16839631C2semidirect
7. C2×#102×C61C2semidirect
12. #14519773C4semidirect
47. C2×C8×C61D4semidirect
57. C2×#92418D4semidirect
114. Dic61#102semidirect
127. C2×#102D61semidirect
130. C61#1957semidirect
173. C2×C8C22⋊D61semidirect