Finite Group Databasebeta

← #21447090

Subgroups — #21447090

Order 7808.

274 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 63 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×#14519803C211yesmaximal, characteristic
2#16839810C211yesmaximal, characteristic, complemented
3#16839780C211yesmaximal, characteristic, complemented
4#16839744C211yesmaximal, characteristic, complemented
5C2×#14519694C211yesmaximal, characteristic, complemented
6#16839532C211yesmaximal, characteristic, complemented
7C61×#418C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519803—22no—
10#14519803—22no—
11C2×#11758200—21no—
12C2×#11758199—21no—
13C2×#11758194C2211yescharacteristic
14C2×#11758194C2211yescharacteristic
15C2×#11758194C2211yescharacteristic
16#14519712—22no—
17#14519705—22no—
18#14519695—21no—
19#14519694—22no—
20#14519693—21no—
21C22×D4×C61C2211yescharacteristic
22C2×M16×C61C2211yescharacteristic
23#117×C61C2211yescharacteristic
24#102×C61—22no—
25C24×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61—21no—
28C2×D4×C61—21no—
29C2×D4×C61—21no—
30C2×D4×C61—21no—
31C2×D4×C61D412yes—
32C22×C4×C61C2311yescharacteristic
33C2×C22⋊D61—21no—
34#11758222—21no—
35#11758222—21no—
36#11758222—21no—
37#11758222—21no—
38C2×D244D411yescharacteristic
39C2×C4×D61—21no—
40C2×Dic122D411yescharacteristic
41M16×C61—21no—
42M16×C61—21no—
43C2×C8×C61—21no—
44C4⋊C4×C61—21no—
45C22⋊C4×C61—21no—
46C42×C61—21no—
47#11758200—24no—
48#11758199—24no—
49#11758194—21no—
50#11758194—21no—
51#11758194—21no—
52#11758194—21no—
53#11758194D412yes—
54#11758194D412yes—
55C2×#92418—21no—
56C2×#92418—21no—
57C2×#92418—21no—
58C23×C61—22no—
59C23×C61—41no—
60C23×C61—41no—
61C23×C61—82no—
62C23×C61#4111yescharacteristic
63C22×D61—21no—
64D4×C61—22no—
65D4×C61—22no—
66D4×C61—41no—
67D4×C61—41no—
68C2×C4×C61—41no—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61C2×D411yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C22⋊D61—41no—
76C22⋊D61—41no—
77C2×Dic61—21no—
78D244—21no—
79D244—21no—
80C4×D61—41no—
81C4×D61—41no—
82Dic122—21no—
83Dic122—21no—
84C8×C61—41no—
85#92418—22no—
86#92418—22no—
87#92418—41no—
88C22×C61—41no—
89C22×C61—42no—
90C22×C61—82no—
91C22×C61—82no—
92C22×C61—82no—
93C22×C61#12111yescharacteristic
94C22×C61#12311yescharacteristic
95C22×C61#12411yescharacteristic
96C2×D61—41no—
97C2×D61—81no—
98C4×C61—81no—
99C4×C61#12011yescharacteristic
100C4×C61#12111yescharacteristic
101C4×C61#12111yescharacteristic
102C4×C61#12311yescharacteristic
103Dic61—41no—
104#2048—611nomaximal, Sylow
105C2×C61—21no—
106C2×C61—21no—
107C2×C61—21no—
108C2×C61—82no—
109C2×C61#39411yescharacteristic
110D61—81no—
111C2×AGL(1,ℤ/8)—611no—
112#430—611no—
113#421—611no—
114#418D6111yescharacteristic, complemented
115#413—611no—
116C2×#100—611no—
117#344—611no—
118C61#204811yescharacteristic, complemented, Sylow
119C2×#41—611no—
120C22×D4C2×D6111yescharacteristic
121AGL(1,ℤ/8)—1222no—
122AGL(1,ℤ/8)—1222no—
123C2×SD16—1221no—
124C2×D8—1221no—
125C2×M16—611no—
126C2×M16—611no—
127C2×M16—611no—
128C2×M16C2×D6111yescharacteristic
129#117C2×D6111yescharacteristic
130#108—1222no—
131#104—1222no—
132#102—22no—
133#101—1221no—
134#100—1221no—
135#100—1222no—
136C24—21no—
137#41—1221no—
138#41—1221no—
139#41—1221no—
140#41—1221no—
141C2×Q8—611no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4—611no—
148C2×D4—1221no—
149C2×D4C22⋊D6112yes—
150C22×C4—1221no—
151C22×C4C22×D6111yescharacteristic
152SD16—1224no—
153D8—1224no—
154M16—21no—
155M16—21no—
156M16—612no—
157M16—612no—
158M16—1221no—
159M16—1221no—
160M16—1221no—
161M16—1221no—
162C2×C8—21no—
163C2×C8—1221no—
164C2×C8—1221no—
165C2×C8—1221no—
166C4⋊C4—21no—
167C22⋊C4—21no—
168C42—21no—
169C23—22no—
170C23—41no—
171C23—41no—
172C23—82no—
173C23—1221no—
174C23#1175822411yescharacteristic
175Q8—1221no—
176Q8—1221no—
177D4—22no—
178D4—22no—
179D4—41no—
180D4—41no—
181D4—1221no—
182D4—1221no—
183D4—2441no—
184D4—2441no—
185C2×C4—41no—
186C2×C4—1221no—
187C2×C4—2441no—
188C2×C4—2441no—
189C2×C4#1175822211yescharacteristic
190C2×C4#1175822211yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C2×C4D4×D6111yescharacteristic
193C2×C4D4×D6111yescharacteristic
194C2×C4C2×C22⋊D6111yescharacteristic
195C8—41no—
196C8—1222no—
197C8—1222no—
198C8—2441no—
199C22—41no—
200C22—42no—
201C22—82no—
202C22—82no—
203C22—82no—
204C22—4881no—
205C22—2441no—
206C22#1451974911yescharacteristic
207C22#1451975911yescharacteristic
208C22#1451976311yescharacteristic
209C4—81no—
210C4—2441no—
211C4#1451974511yescharacteristic
212C4#1451975011yescharacteristic
213C4#1451975011yescharacteristic
214C4#1451976011yescharacteristic
215C2—21no—
216C2—21no—
217C2—21no—
218C2—82no—
219C2—4881no—
220C2#1683967711yescharacteristic
subgroupG/H
centerC2#16839677
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#418C2
socleC2×C61#394
hypercenter#418D61
hypocenterC61#2048
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
2. #16839810C2semidirect
3. #16839780C2semidirect
4. #16839744C2semidirect
5. C2×#14519694C2semidirect
6. #16839532C2semidirect
7. C61×#418C2semidirect
114. #418D61semidirect
118. C61#2048semidirect