Finite Group Databasebeta

← #21447833

Subgroups — #21447833

Order 7808.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#16840515C211yesmaximal, characteristic, complemented
2#16839953C211yesmaximal, characteristic
3#16839951C211yesmaximal, characteristic
4#16839942C211yesmaximal, characteristic
5#16839556C211yesmaximal, characteristic, complemented
6#16839553C211yesmaximal, characteristic, complemented
7C61×#352C211yesmaximal, characteristic, complemented
8#14519822C2211yescharacteristic
9#14519810—21no—
10#14519776—21no—
11#14519770—21no—
12#14519770—21no—
13#14519767—21no—
14#14519764C2211yescharacteristic
15#14519761—21no—
16#14519760—21no—
17#14519758C2211yescharacteristic
18#14519756—21no—
19#14519754—21no—
20#14519703—21no—
21#14519692C2211yescharacteristic
22#14519691—21no—
23#14519691—21no—
24#123×C61C2211yescharacteristic
25#100×C61C2211yescharacteristic
26#99×C61C2211yescharacteristic
27C2×D4×C61C2311yescharacteristic
28C22×C4×C61D411yescharacteristic
29C2×C22⋊D61—21no—
30C2×C22⋊D61—21no—
31C22×Dic61D411yescharacteristic
32#11758224—41no—
33D4×D61—41no—
34#11758222—21no—
35C2×Dic122—21no—
36C2×Dic122D411yescharacteristic
37M16×C61—21no—
38C4⋊C4×C61—21no—
39C22⋊C4×C61—21no—
40C22⋊C4×C61—21no—
41C22⋊C4×C61D411yescharacteristic
42C22⋊Dic61—21no—
43C22⋊Dic61—21no—
44C22⋊Dic61—21no—
45C22⋊Dic61—21no—
46C22⋊Dic61D411yescharacteristic
47#11758198—41no—
48#11758198—41no—
49C4⋊Dic61—21no—
50C4⋊Dic61—21no—
51C4⋊Dic61—41no—
52#11758196—21no—
53#11758196—21no—
54#11758196—21no—
55#11758196—21no—
56#11758196—21no—
57#11758196—41no—
58C4×Dic61—21no—
59C4×Dic61D411yescharacteristic
60Dic244—41no—
61#11758190—41no—
62C23×C61C2×D411yescharacteristic
63C23×C61C2×D411yescharacteristic
64C22×D61—21no—
65C22×D61—21no—
66D4×C61—41no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—41no—
70C2×C4×C61—41no—
71C2×C4×C61C2×D411yescharacteristic
72C22⋊D61—41no—
73C22⋊D61—41no—
74C22⋊D61—41no—
75C2×Dic61—21no—
76C2×Dic61—21no—
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—41no—
82C2×Dic61—41no—
83D244—21no—
84C4×D61—41no—
85Dic122—21no—
86Dic122—41no—
87Dic122—81no—
88C8×C61—41no—
89C22×C61—21no—
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61#12011yescharacteristic
94C2×D61—41no—
95C2×D61—81no—
96C2×D61—81no—
97C4×C61—21no—
98C4×C61—41no—
99C4×C61—41no—
100C4×C61—81no—
101Dic61—41no—
102Dic61—41no—
103Dic61—41no—
104Dic61—41no—
105Dic61—41no—
106Dic61—81no—
107#2201—611nomaximal, Sylow
108C2×C61—21no—
109C2×C61—41no—
110C2×C61—41no—
111C2×C61B(4,𝔽2)11yescharacteristic
112D61—81no—
113#563—611no—
114#458—611no—
115#458—611no—
116#455—611no—
117#354—611no—
118#352—611no—
119#352D6111yescharacteristic, complemented
120C61#220111yescharacteristic, complemented, Sylow
121H(5,𝔽2)—611no—
122#137—1221no—
123C4⋊Q8—1221no—
124#126—1221no—
125#126—1221no—
126#125—1221no—
127#124—611no—
128#123—611no—
129#123—1221no—
130#123—1221no—
131#123C2×D6111yescharacteristic
132C22⋊Q8—1221no—
133C22⋊Q8—1221no—
134#104—1221no—
135#100C2×D6111yescharacteristic
136#99—611no—
137#99—1221no—
138#99—1221no—
139#99C2×D6111yescharacteristic
140#41—1221no—
141#41—2441no—
142C2×Q8—611no—
143C2×Q8—1221no—
144C2×D4—1221no—
145C2×D4—1221no—
146C2×D4—2441no—
147C2×D4C22×D6111yescharacteristic
148C22×C4—611no—
149C22×C4D24411yescharacteristic
150Q16—2441no—
151SD16—2441no—
152M16—21no—
153C4⋊C4—21no—
154C4⋊C4—1221no—
155C4⋊C4—1221no—
156C4⋊C4—1221no—
157C4⋊C4—1221no—
158C4⋊C4—1221no—
159C4⋊C4—1221no—
160C4⋊C4—1221no—
161C4⋊C4—2441no—
162C4⋊C4—2441no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—611no—
166C22⋊C4—1221no—
167C22⋊C4—1221no—
168C22⋊C4—1221no—
169C22⋊C4—1221no—
170C22⋊C4—2441no—
171C22⋊C4—2441no—
172C22⋊C4D24411yescharacteristic
173C42—611no—
174C42—1221no—
175C23—1221no—
176C23—1221no—
177C23C2×D24411yescharacteristic
178C23D4×D6111yescharacteristic
179Q8—1221no—
180Q8—4881no—
181Q8—2441no—
182D4—41no—
183D4—1221no—
184D4—2441no—
185D4—2441no—
186D4—2441no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—1221no—
196C2×C4—1221no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4—2441no—
200C2×C4D4×D6111yescharacteristic
201C8—41no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—4881no—
207C22—4881no—
208C22—2441no—
209C22#1451974711yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—81no—
214C4—4881no—
215C4—2441no—
216C4—2441no—
217C4—2441no—
218C4—2441no—
219C4—2441no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—4881no—
224C2#1683995011yescharacteristic
subgroupG/H
centerC2#16839950
commutatorC2×D4×C61C23
FrattiniC2×D4C22×D61
FittingC61×#352C2
socleC2×C61B(4,𝔽2)
hypercenter#352D61
hypocenterC61#2201
LCSG ▷ C2×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
1. #16840515C2semidirect
5. #16839556C2semidirect
6. #16839553C2semidirect
7. C61×#352C2semidirect
119. #352D61semidirect
120. C61#2201semidirect