Finite Group Databasebeta

← #21446289

Subgroups — #21446289

Order 7808.

304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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#16840528C211yesmaximal, characteristic
3#16839780C211yesmaximal, characteristic
4C2×#14519696C211yesmaximal, characteristic, complemented
5#16839532C211yesmaximal, characteristic, complemented
6#16839520C211yesmaximal, characteristic, complemented
7C61×#419C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—22no—
10#14519808—22no—
11C2×#11758202C412yescomplemented
12C2×#11758201C412yescomplemented
13#14519785—22no—
14#14519783—22no—
15C2×#11758194C2211yescharacteristic
16C2×#11758194C2211yescharacteristic
17C2×#11758194C2211yescharacteristic
18M16×D61—22no—
19#14519705—22no—
20#14519696—22no—
21C22×Q8×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23#117×C61C2211yescharacteristic
24#103×C61—22no—
25C2×Q8×C61—21no—
26C2×Q8×C61—21no—
27C2×Q8×C61—21no—
28C2×Q8×C61—21no—
29C2×Q8×C61—21no—
30C2×Q8×C61C2×C412yes—
31C22×C4×C61—21no—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—21no—
34#11758222—21no—
35#11758222—21no—
36#11758222D412yes—
37#11758222D412yes—
38C2×D244C2×C411yescharacteristic
39C2×C4×D61—21no—
40C2×Dic122C2×C411yescharacteristic
41M16×C61—21no—
42M16×C61—21no—
43C2×C8×C61D412yes—
44C4⋊C4×C61—21no—
45C22⋊C4×C61—21no—
46C42×C61—21no—
47#11758202—24no—
48#11758201—24no—
49#11758194—21no—
50#11758194—21no—
51#11758194—21no—
52#11758194—21no—
53#11758194—21no—
54#11758194D412yes—
55C2×#92418—21no—
56C2×#92418—21no—
57C2×#92418C2×C412yes—
58#11758189—24no—
59C8×D61—24no—
60C23×C61#4111yescharacteristic
61C22×D61—21no—
62Q8×C61—22no—
63Q8×C61—22no—
64Q8×C61—41no—
65Q8×C61—41no—
66C2×C4×C61—22no—
67C2×C4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61—41no—
70C2×C4×C61C22×C411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61C2×D411yescharacteristic
74C2×C4×C61C2×D411yescharacteristic
75C2×C4×C61#4111yescharacteristic
76C22⋊D61—22no—
77C22⋊D61—22no—
78C2×Dic61—21no—
79D244—21no—
80D244C22⋊C412yes—
81C4×D61—22no—
82C4×D61—22no—
83Dic122—21no—
84Dic122C22⋊C412yes—
85C8×C61—22no—
86#92418—22no—
87#92418—22no—
88#92418—41no—
89C22×C61—41no—
90C22×C61C4×D411yescharacteristic
91C22×C61#12111yescharacteristic
92C22×C61#12311yescharacteristic
93C2×D61—22no—
94C2×D61—81no—
95C4×C61—42no—
96C4×C61—81no—
97C4×C61C2×C22⋊C411yescharacteristic
98C4×C61C4×D411yescharacteristic
99C4×C61#12011yescharacteristic
100C4×C61#12111yescharacteristic
101Dic61—22no—
102#1902—611nomaximal, Sylow
103C2×C61—21no—
104C2×C61—21no—
105C2×C61—21no—
106C2×C61#38611yescharacteristic
107D61—42no—
108C2×#137—611no—
109#568—611no—
110#421—611no—
111#419D6111yescharacteristic, complemented
112C2×#101—611no—
113#344—611no—
114#338—611no—
115C61#190211yescharacteristic, complemented, Sylow
116C2×#41—611no—
117C22×Q8C2×D6111yescharacteristic
118#137—1222no—
119#137—1222no—
120C2×Q16—612no—
121C2×SD16—612no—
122#131—1222no—
123#131—1222no—
124C2×M16—611no—
125C2×M16—611no—
126C2×M16—611no—
127C2×M16—1222no—
128C2×M16C2×D6111yescharacteristic
129#117C2×D6111yescharacteristic
130#104—1222no—
131#103—22no—
132#101—1222no—
133#41—612no—
134#41—612no—
135#41—1221no—
136#41—1221no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—21no—
142C2×Q8—611no—
143C2×Q8C4×D6112yes—
144C2×D4—611no—
145C2×D4—1221no—
146C22×C4—21no—
147C22×C4—1221no—
148C22×C4C22×D6111yescharacteristic
149Q16—1224no—
150SD16—1224no—
151M16—21no—
152M16—21no—
153M16—612no—
154M16—1224no—
155M16—1221no—
156M16—1221no—
157M16—1221no—
158M16—1221no—
159M16—1221no—
160C2×C8—612no—
161C2×C8—1224no—
162C2×C8—1221no—
163C2×C8—1221no—
164C2×C8C22⋊D6112yes—
165C4⋊C4—21no—
166C22⋊C4—21no—
167C42—21no—
168C23—1221no—
169C23#1175822411yescharacteristic
170Q8—22no—
171Q8—22no—
172Q8—41no—
173Q8—41no—
174Q8—612no—
175Q8—1221no—
176D4—612no—
177D4—1222no—
178D4—1222no—
179D4—1221no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—1221no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4C2×C4×D6111yescharacteristic
188C2×C4#1175822211yescharacteristic
189C2×C4D4×D6111yescharacteristic
190C2×C4D4×D6111yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C2×C4C2×C22⋊D6111yescharacteristic
193C8—22no—
194C8—1222no—
195C8—1222no—
196C8—2441no—
197C22—41no—
198C22—1222no—
199C22—4881no—
200C22#1451973711yescharacteristic
201C22#1451974811yescharacteristic
202C22#1451975911yescharacteristic
203C4—42no—
204C4—81no—
205C4—1222no—
206C4C22⋊C4×D6111yescharacteristic
207C4C4×C22⋊D6111yescharacteristic
208C4#1451974511yescharacteristic
209C4#1451975011yescharacteristic
210C2—21no—
211C2—21no—
212C2—21no—
213C2—2442no—
214C2#1683963811yescharacteristic
subgroupG/H
centerC2#16839638
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#419C2
socleC2×C61#386
hypercenter#419D61
hypocenterC61#1902
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
4. C2×#14519696C2semidirect
5. #16839532C2semidirect
6. #16839520C2semidirect
7. C61×#419C2semidirect
11. C2×#11758202C4semidirect
12. C2×#11758201C4semidirect
111. #419D61semidirect
115. C61#1902semidirect