Finite Group Databasebeta

← #21445872

Subgroups — #21445872

Order 7808.

256 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 81 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×#14519785C211yesmaximal, characteristic
2C2×#14519712C211yesmaximal, characteristic, complemented
3#16839798C211yesmaximal, characteristic, complemented
4#16839780C211yesmaximal, characteristic
5#16839778C211yesmaximal, characteristic
6#16839534C211yesmaximal, characteristic, complemented
7C61×#344C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519785—21no—
10#14519785—21no—
11#14519785C412yescomplemented
12#14519785C412yescomplemented
13C2×#11758194C2211yescharacteristic
14C2×#11758189—21no—
15C22×#92418C2211yescharacteristic
16C2×C8×D61—21no—
17#14519736C2211yescharacteristic
18#14519712—21no—
19#14519712—21no—
20#14519710—21no—
21#14519708—21no—
22#14519705—22no—
23#14519703—22no—
24C2×M16×C61C2211yescharacteristic
25C2×M16×C61C2211yescharacteristic
26#117×C61C2211yescharacteristic
27C22×C4×C61C2311yescharacteristic
28C2×C22⋊D61—21no—
29#11758222—21no—
30#11758222—21no—
31#11758222C2×C412yes—
32#11758222D412yes—
33C2×D244Q811yescharacteristic
34C2×C4×D61—21no—
35C2×Dic122Q811yescharacteristic
36M16×C61—21no—
37M16×C61—21no—
38M16×C61—21no—
39M16×C61C2×C412yes—
40C2×C8×C61—21no—
41C2×C8×C61—21no—
42C4⋊C4×C61—21no—
43C22⋊C4×C61—21no—
44C42×C61—21no—
45C22⋊Dic61—21no—
46C4⋊Dic61—21no—
47C4×Dic61—21no—
48#11758194—21no—
49#11758194—21no—
50C2×#92418—21no—
51C2×#92418C2×C411yescharacteristic
52C2×#92418C2×C411yescharacteristic
53C2×#92418D411yescharacteristic
54C2×#92418D411yescharacteristic
55C2×#92418D411yescharacteristic
56C2×#92418D411yescharacteristic
57#11758189—22no—
58#11758189—22no—
59C8×D61—22no—
60C8×D61—22no—
61C23×C61#4111yescharacteristic
62C22×D61—21no—
63C2×C4×C61—41no—
64C2×C4×C61C22×C411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61C2×Q811yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C22⋊D61—22no—
71C22⋊D61—22no—
72C2×Dic61—21no—
73C2×Dic61—41no—
74D244—21no—
75D244C4⋊C412yes—
76C4×D61—22no—
77C4×D61—22no—
78Dic122—21no—
79Dic122C4⋊C412yes—
80C8×C61—22no—
81C8×C61—41no—
82#92418—41no—
83#92418C22⋊C411yescharacteristic
84#92418C22⋊C411yescharacteristic
85#92418C22⋊C411yescharacteristic
86#92418C22⋊C411yescharacteristic
87C22×C61—41no—
88C22×C61#11711yescharacteristic
89C22×C61#12111yescharacteristic
90C22×C61C22⋊Q811yescharacteristic
91C2×D61—22no—
92C2×D61—42no—
93C4×C61—81no—
94C4×C61C2×C22⋊C411yescharacteristic
95C4×C61C2×C4⋊C411yescharacteristic
96C4×C61#12111yescharacteristic
97C4×C61C22⋊Q811yescharacteristic
98Dic61—22no—
99Dic61—81no—
100#1814—611nomaximal, Sylow
101C2×C61—21no—
102C2×C61—21no—
103C2×C61—21no—
104C2×C61#38011yescharacteristic
105D61—42no—
106C2×#131—611no—
107C2×#108—611no—
108#427—611no—
109#421—611no—
110#421—611no—
111#344—611no—
112#344D6111yescharacteristic, complemented
113C61#181411yescharacteristic, complemented, Sylow
114C2×#41—611no—
115#131—612no—
116#131—612no—
117#131—1221no—
118#131—1221no—
119C2×M16—611no—
120C2×M16—1221no—
121C2×M16C2×D6111yescharacteristic
122C2×M16C2×D6111yescharacteristic
123C22×C8—611no—
124C22×C8—1221no—
125#117—611no—
126#117C2×D6111yescharacteristic
127#108—1221no—
128#108—1221no—
129#107—1221no—
130#106—1221no—
131#104—1222no—
132#104—1222no—
133#41—612no—
134#41—612no—
135#41—1221no—
136#41—1221no—
137C2×Q8—611no—
138C2×D4—611no—
139C2×D4—1221no—
140C22×C4—1221no—
141C22×C4C22×D6111yescharacteristic
142M16—21no—
143M16—21no—
144M16—21no—
145M16—1222no—
146M16—1222no—
147M16—1221no—
148M16—1221no—
149M16C4×D6112yes—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—611no—
153C2×C8—611no—
154C2×C8—611no—
155C2×C8—611no—
156C2×C8—611no—
157C2×C8—611no—
158C2×C8—1222no—
159C2×C8—1222no—
160C2×C8—1221no—
161C4⋊C4—21no—
162C4⋊C4—1221no—
163C22⋊C4—21no—
164C22⋊C4—1221no—
165C42—21no—
166C42—1221no—
167C23—1221no—
168C23#1175822211yescharacteristic
169Q8—612no—
170Q8—1221no—
171D4—612no—
172D4—1222no—
173D4—1222no—
174D4—1221no—
175C2×C4—41no—
176C2×C4—1221no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—2441no—
180C2×C4C2×C4×D6111yescharacteristic
181C2×C4#1175822211yescharacteristic
182C2×C4D4×D6111yescharacteristic
183C2×C4D4×D6111yescharacteristic
184C2×C4D4×D6111yescharacteristic
185C2×C4Q8×D6111yescharacteristic
186C8—22no—
187C8—41no—
188C8—611no—
189C8—611no—
190C8—611no—
191C8—611no—
192C8—2441no—
193C22—41no—
194C22—1222no—
195C22—2442no—
196C22#1451973411yescharacteristic
197C22#1451975011yescharacteristic
198C22#1451975511yescharacteristic
199C4—81no—
200C4—1222no—
201C4—4881no—
202C4C22⋊C4×D6111yescharacteristic
203C4C4⋊C4×D6111yescharacteristic
204C4#1451975011yescharacteristic
205C4#1451975511yescharacteristic
206C2—21no—
207C2—21no—
208C2—21no—
209C2—2442no—
210C2#1683962111yescharacteristic
subgroupG/H
centerC4#14519750
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#344C2
socleC2×C61#380
hypercenter#344D61
hypocenterC61#1814
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
2. C2×#14519712C2semidirect
3. #16839798C2semidirect
6. #16839534C2semidirect
7. C61×#344C2semidirect
11. #14519785C4semidirect
12. #14519785C4semidirect
112. #344D61semidirect
113. C61#1814semidirect