Finite Group Databasebeta

← #21446370

Subgroups — #21446370

Order 7808.

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

normal subgroups only

This group has 308 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
1#16840528C211yesmaximal, characteristic
2#16840338C211yesmaximal, characteristic
3#16839744C211yesmaximal, characteristic
4C2×#14519695C211yesmaximal, characteristic, complemented
5C2×#14519695C211yesmaximal, characteristic, complemented
6#16839532C211yesmaximal, characteristic, complemented
7C61×#344C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10#14519785—22no—
11#14519783—22no—
12C2×#11758194C2211yescharacteristic
13C2×#11758194C2211yescharacteristic
14M16×D61—22no—
15#14519777—21no—
16#14519765—21no—
17#14519761C414yes—
18#14519757—22no—
19#14519695—21no—
20#14519695—22no—
21#14519695—22no—
22#14519693—21no—
23C2×M16×C61C2211yescharacteristic
24C2×M16×C61C2211yescharacteristic
25#117×C61C2211yescharacteristic
26C22×C4×C61C2311yescharacteristic
27C2×C22⋊D61C2×C412yes—
28C22×Dic61C2×C412yes—
29#11758222—21no—
30#11758222—21no—
31#11758222—21no—
32#11758222—21no—
33C2×D244D411yescharacteristic
34C2×C4×D61D412yes—
35C2×Dic122—21no—
36C2×Dic122—21no—
37C2×Dic122—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122D411yescharacteristic
42M16×C61—21no—
43M16×C61—21no—
44M16×C61—21no—
45M16×C61D412yes—
46C2×C8×C61—21no—
47C2×C8×C61—21no—
48C4⋊C4×C61—21no—
49C22⋊C4×C61C2×C412yes—
50C42×C61—21no—
51#11758198—24no—
52C4⋊Dic61—24no—
53#11758194—21no—
54#11758194—21no—
55#11758194—21no—
56#11758194D412yes—
57C2×#92418—21no—
58C2×#92418—21no—
59#11758189—24no—
60C8×D61—24no—
61C23×C61C22×C411yescharacteristic
62C22×D61C22⋊C412yes—
63C2×C4×C61—22no—
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2×D411yescharacteristic
67C2×C4×C61C2×D411yescharacteristic
68C2×C4×C61#4111yescharacteristic
69C2×C4×C61#4111yescharacteristic
70C22⋊D61—22no—
71C22⋊D61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61C22⋊C412yes—
76D244—21no—
77D244—21no—
78C4×D61—22no—
79C4×D61—22no—
80Dic122—21no—
81Dic122—21no—
82Dic122—41no—
83Dic122—41no—
84Dic122—41no—
85Dic122—41no—
86C8×C61—22no—
87C8×C61—41no—
88#92418—22no—
89#92418—41no—
90C22×C61—41no—
91C22×C61C2×C22⋊C411yescharacteristic
92C22×C61C4×D411yescharacteristic
93C22×C61C4×D411yescharacteristic
94C2×D61—22no—
95C2×D61—42no—
96C4×C61—42no—
97C4×C61#12011yescharacteristic
98C4×C61#12111yescharacteristic
99C4×C61#12111yescharacteristic
100C4×C61#12311yescharacteristic
101Dic61—22no—
102Dic61—42no—
103#1915—611nomaximal, Sylow
104C2×C61—21no—
105C2×C61—21no—
106C2×C61—21no—
107C2×C61#38611yescharacteristic
108D61—42no—
109#568—611no—
110#536—611no—
111#413—611no—
112C2×#101—611no—
113C2×#101—611no—
114#344—611no—
115#344D6111yescharacteristic, complemented
116C61#191511yescharacteristic, complemented, Sylow
117C2×#41—611no—
118C22×Q8—611no—
119#131—1222no—
120#131—1222no—
121C2×M16—611no—
122C2×M16—611no—
123C2×M16—1222no—
124C2×M16C2×D6111yescharacteristic
125C2×M16C2×D6111yescharacteristic
126C4⋊Q8—1221no—
127#124—1221no—
128#123—614no—
129C22⋊Q8—1222no—
130#117C2×D6111yescharacteristic
131#101—1222no—
132#101—1221no—
133#101—1222no—
134#100—1221no—
135#41—1221no—
136#41—1221no—
137#41—1221no—
138#41—1221no—
139C2×Q8—611no—
140C2×Q8—1221no—
141C2×Q8—1221no—
142C2×Q8—1221no—
143C2×Q8—1221no—
144C2×Q8—1221no—
145C2×Q8—1221no—
146C2×D4—612no—
147C2×D4—611no—
148C22×C4—612no—
149C22×C4—612no—
150C22×C4C22×D6111yescharacteristic
151M16—21no—
152M16—21no—
153M16—21no—
154M16—612no—
155M16—1224no—
156M16—1221no—
157M16—1221no—
158M16—1221no—
159M16D24412yes—
160C2×C8—21no—
161C2×C8—21no—
162C2×C8—1224no—
163C2×C8—1221no—
164C2×C8—1221no—
165C4⋊C4—21no—
166C4⋊C4—1224no—
167C22⋊C4—1224no—
168C22⋊C4C4×D6112yes—
169C42—21no—
170C23—612no—
171C23C2×C4×D6111yescharacteristic
172Q8—1221no—
173Q8—1221no—
174Q8—2441no—
175Q8—2441no—
176Q8—2441no—
177Q8—2441no—
178D4—1222no—
179D4—1222no—
180D4—1221no—
181D4—1221no—
182C2×C4—22no—
183C2×C4—612no—
184C2×C4—1222no—
185C2×C4—1222no—
186C2×C4—1222no—
187C2×C4—1222no—
188C2×C4—1222no—
189C2×C4C2×D24411yescharacteristic
190C2×C4#1175822211yescharacteristic
191C2×C4D4×D6111yescharacteristic
192C2×C4D4×D6111yescharacteristic
193C2×C4D4×D6111yescharacteristic
194C2×C4#1175822611yescharacteristic
195C8—22no—
196C8—41no—
197C8—1222no—
198C8—2441no—
199C22—41no—
200C22—1222no—
201C22—2442no—
202C22C22⋊C4×D6111yescharacteristic
203C22#1451973911yescharacteristic
204C22C4×D24411yescharacteristic
205C4—42no—
206C4—1222no—
207C4—2442no—
208C4#1451974711yescharacteristic
209C4#1451975011yescharacteristic
210C4#1451975211yescharacteristic
211C4#1451976211yescharacteristic
212C2—21no—
213C2—21no—
214C2—21no—
215C2—2442no—
216C2#1683964011yescharacteristic
subgroupG/H
centerC2#16839640
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#344C2
socleC2×C61#386
hypercenter#344D61
hypocenterC61#1915
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #344

Complements

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

NH ≅ G/Ntype
4. C2×#14519695C2semidirect
5. C2×#14519695C2semidirect
6. #16839532C2semidirect
7. C61×#344C2semidirect
115. #344D61semidirect
116. C61#1915semidirect