Finite Group Databasebeta

← #21446096

Subgroups — #21446096

Order 7808.

270 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 97 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×#14519784C211yesmaximal, characteristic
2C2×#14519713C211yesmaximal, characteristic, complemented
3#16839789C211yesmaximal, characteristic, complemented
4C2×#14519704C211yesmaximal, characteristic
5#16839521C211yesmaximal, characteristic, complemented
6#16839516C211yesmaximal, characteristic, complemented
7C61×#416C211yesmaximal, characteristic
8#14519784—22no—
9#14519784—22no—
10C2×#11758194—21no—
11C2×#11758194C2211yescharacteristic
12C2×#11758194C2211yescharacteristic
13C22×#92418—21no—
14C22×#92418C2211yescharacteristic
15C2×C4×Dic61C2211yescharacteristic
16#14519713—22no—
17C4⋊#92418—21no—
18C4⋊#92418—21no—
19#14519704—22no—
20C2×#41×C61C2211yescharacteristic
21C22×C8×C61C2211yescharacteristic
22#117×C61C2211yescharacteristic
23#103×C61C411yescharacteristic, complemented
24#103×C61C411yescharacteristic, complemented
25#102×C61C411yescharacteristic, complemented
26#102×C61C411yescharacteristic, complemented
27#41×C61—21no—
28#41×C61—21no—
29#41×C61D412yes—
30#41×C61Q812yes—
31C2×Q8×C61C2×C411yescharacteristic
32C2×D4×C61—21no—
33C2×D4×C61C2×C411yescharacteristic
34C22×C4×C61—21no—
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—21no—
37C2×C8×C61—21no—
38C2×C8×C61—21no—
39C2×C8×C61C2×C411yescharacteristic
40C2×C8×C61C2×C411yescharacteristic
41C4⋊C4×C61C2×C411yescharacteristic
42C4⋊C4×C61C2×C411yescharacteristic
43C22⋊C4×C61—21no—
44C42×C61—21no—
45C4×Dic61—21no—
46C4×Dic61—21no—
47#11758194—24no—
48#11758194—21no—
49#11758194—21no—
50#11758194—21no—
51#11758194D412yes—
52C2×#92418—24no—
53C2×#92418—21no—
54C2×#92418—21no—
55C2×#92418—21no—
56C2×#92418—21no—
57C2×#92418D411yescharacteristic
58C2×#92418D411yescharacteristic
59C23×C61—21no—
60C23×C61#4111yescharacteristic
61Q8×C61—21no—
62Q8×C61C4⋊C412yes—
63D4×C61—22no—
64D4×C61—22no—
65D4×C61—21no—
66D4×C61C4⋊C412yes—
67C2×C4×C61—21no—
68C2×C4×C61—22no—
69C2×C4×C61—22no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61C22×C411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61C2×D411yescharacteristic
76C2×C4×C61C2×Q811yescharacteristic
77C2×C4×C61#4111yescharacteristic
78C2×Dic61—22no—
79C2×Dic61—41no—
80C2×Dic61—41no—
81C8×C61—21no—
82C8×C61—21no—
83#92418—21no—
84#92418—22no—
85#92418—21no—
86#92418—41no—
87C22×C61—21no—
88C22×C61—21no—
89C22×C61—22no—
90C22×C61—41no—
91C22×C61—41no—
92C22×C61C4×D411yescharacteristic
93C22×C61C22⋊Q811yescharacteristic
94C22×C61#12311yescharacteristic
95C4×C61—22no—
96C4×C61—41no—
97C4×C61—41no—
98C4×C61C2×C4⋊C411yescharacteristic
99C4×C61C4×D411yescharacteristic
100C4×C61#12011yescharacteristic
101C4×C61C22⋊Q811yescharacteristic
102Dic61—42no—
103#1866—611nomaximal, Sylow
104C2×C61—21no—
105C2×C61—21no—
106C2×C61—42no—
107C2×C61#38511yescharacteristic
108C2×C61#44311yescharacteristic
109C2×C61#44411yescharacteristic
110C2×#131—611no—
111C2×#108—611no—
112#424—611no—
113C2×#104—611no—
114#416D6111yescharacteristic
115#339—611no—
116#336—611no—
117C61#186611yescharacteristic, complemented, Sylow
118C2×#41C2×D6111yescharacteristic
119#131—1222no—
120#131—1222no—
121C2×M16—611no—
122C2×M16—611no—
123C2×M16—1221no—
124C22×C8—611no—
125C22×C8—1221no—
126C22×C8C2×D6111yescharacteristic
127#117C2×D6111yescharacteristic
128C2×C42—611no—
129#108—1222no—
130C4⋊C8—1221no—
131C4⋊C8—1221no—
132#104—1222no—
133#103Dic6111yescharacteristic, complemented
134#103Dic6111yescharacteristic, complemented
135#102Dic6111yescharacteristic, complemented
136#102Dic6111yescharacteristic, complemented
137#41—21no—
138#41—21no—
139#41Dic12212yes—
140#41D24412yes—
141C2×Q8C2×Dic6111yescharacteristic
142C2×D4—21no—
143C2×D4C2×Dic6111yescharacteristic
144C22×C4—21no—
145C22×C4—1221no—
146C22×C4C22×D6111yescharacteristic
147M16—612no—
148M16—1224no—
149M16—1221no—
150M16—1221no—
151M16—1221no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—611no—
155C2×C8—611no—
156C2×C8—1224no—
157C2×C8—1221no—
158C2×C8—1221no—
159C2×C8—1221no—
160C2×C8—1221no—
161C2×C8C2×Dic6111yescharacteristic
162C2×C8C2×Dic6111yescharacteristic
163C4⋊C4C2×Dic6111yescharacteristic
164C4⋊C4C2×Dic6111yescharacteristic
165C22⋊C4—21no—
166C42—21no—
167C42—1221no—
168C42—1221no—
169C23—21no—
170C23#1175822411yescharacteristic
171Q8—21no—
172Q8C4⋊Dic6112yes—
173D4—22no—
174D4—22no—
175D4—21no—
176D4C4⋊Dic6112yes—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—1222no—
183C2×C4—2441no—
184C2×C4—2441no—
185C2×C4C2×Dic12211yescharacteristic
186C2×C4C2×D24411yescharacteristic
187C2×C4D4×D6111yescharacteristic
188C2×C4D4×D6111yescharacteristic
189C2×C4#1175822411yescharacteristic
190C2×C4C22×Dic6111yescharacteristic
191C8—21no—
192C8—21no—
193C8—1221no—
194C8—1221no—
195C8—1222no—
196C8—2441no—
197C22—21no—
198C22—21no—
199C22—22no—
200C22—41no—
201C22—41no—
202C22D4×Dic6111yescharacteristic
203C22#1451975411yescharacteristic
204C22#1451976111yescharacteristic
205C4—22no—
206C4—41no—
207C4—41no—
208C4—2442no—
209C4C2×C4⋊Dic6111yescharacteristic
210C4D4×Dic6111yescharacteristic
211C4#1451974711yescharacteristic
212C4#1451975411yescharacteristic
213C2—21no—
214C2—21no—
215C2—42no—
216C2#1683963711yescharacteristic
217C2#1683987911yescharacteristic
218C2#1683988411yescharacteristic
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#416C2
socleC22×C61C4×D4
hypercenter#416D61
hypocenterC61#1866
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C2×#14519713C2semidirect
3. #16839789C2semidirect
5. #16839521C2semidirect
6. #16839516C2semidirect
23. #103×C61C4semidirect
24. #103×C61C4semidirect
25. #102×C61C4semidirect
26. #102×C61C4semidirect
117. C61#1866semidirect
133. #103Dic61semidirect
134. #103Dic61semidirect
135. #102Dic61semidirect
136. #102Dic61semidirect