Finite Group Databasebeta

← #21447824

Subgroups — #21447824

Order 7808.

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

normal subgroups only

This group has 260 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#16840501C211yesmaximal, characteristic, complemented
2#16839952C211yesmaximal, characteristic, complemented
3#16839930C211yesmaximal, characteristic, complemented
4#16839554C211yesmaximal, characteristic, complemented
5#16839551C211yesmaximal, characteristic, complemented
6#16839549C211yesmaximal, characteristic, complemented
7C61×B(4,𝔽2)C211yesmaximal, characteristic, complemented
8#14519802—21no—
9#14519773C2211yescharacteristic
10#14519770—21no—
11#14519759—21no—
12#14519758—21no—
13#14519758C2211yescharacteristic
14#14519750—21no—
15#14519749—21no—
16#14519748—21no—
17#14519746—21no—
18#14519704—21no—
19#14519694C2211yescharacteristic
20#14519692—21no—
21#14519692C2211yescharacteristic
22H(5,𝔽2)×C61C2211yescharacteristic
23#120×C61—21no—
24#120×C61C2211yescharacteristic
25#99×C61—21no—
26#99×C61C2211yescharacteristic
27C24×C61D411yescharacteristic
28#41×C61—21no—
29#41×C61—41no—
30C2×D4×C61—21no—
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—41no—
34C2×D4×C61—41no—
35C2×D4×C61C2311yescharacteristic
36C2×C22⋊D61—21no—
37C2×C22⋊D61—21no—
38C2×C22⋊D61—21no—
39C2×C22⋊D61—21no—
40C22×Dic61D411yescharacteristic, complemented
41C2×D244D411yescharacteristic, complemented
42C2×C4×D61—21no—
43C22⋊C4×C61—21no—
44C22⋊C4×C61—21no—
45C22⋊C4×C61—41no—
46C22⋊C4×C61D411yescharacteristic
47C22⋊Dic61—21no—
48C22⋊Dic61—21no—
49C22⋊Dic61—21no—
50C22⋊Dic61—21no—
51C22⋊Dic61—41no—
52C22⋊Dic61D411yescharacteristic, complemented
53#11758201—41no—
54#11758199—41no—
55#11758198—21no—
56C4⋊Dic61—21no—
57#11758196—21no—
58#11758196—21no—
59#11758196—41no—
60C4×Dic61D411yescharacteristic, complemented
61#11758194—21no—
62C23×C61—21no—
63C23×C61—21no—
64C23×C61—21no—
65C23×C61—41no—
66C23×C61—81no—
67C23×C61C2×D411yescharacteristic
68C23×C61C2×D411yescharacteristic
69C22×D61—21no—
70Q8×C61—21no—
71D4×C61—21no—
72D4×C61—41no—
73D4×C61—41no—
74D4×C61—41no—
75D4×C61—41no—
76D4×C61—81no—
77D4×C61—82no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61C2×D411yescharacteristic
84C22⋊D61—81no—
85C22⋊D61—81no—
86C22⋊D61—81no—
87C22⋊D61—81no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93D244—41no—
94C4×D61—81no—
95#92418—41no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—42no—
103C22×C61—41no—
104C22×C61—41no—
105C22×C61—81no—
106C22×C61—81no—
107C22×C61—81no—
108C22×C61#12011yescharacteristic
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—41no—
112C4×C61—21no—
113C4×C61—41no—
114C4×C61—41no—
115C4×C61—81no—
116Dic61—41no—
117Dic61—41no—
118Dic61—41no—
119Dic61—81no—
120#2200—611nomaximal, Sylow
121C2×C61—21no—
122C2×C61—41no—
123C2×C61—41no—
124C2×C61—81no—
125C2×C61—81no—
126C2×C61B(4,𝔽2)11yescharacteristic
127D61—81no—
128#560—611no—
129#458—611no—
130B(4,𝔽2)D6111yescharacteristic, complemented
131#453—611no—
132#353—611no—
133#352—611no—
134AΣL(1,𝔽16)—611no—
135C61#220011yescharacteristic, complemented, Sylow
136H(5,𝔽2)C2×D6111yescharacteristic
137AGL(1,ℤ/8)—1221no—
138#127—611no—
139#126—1221no—
140#123—611no—
141#123—1221no—
142#123—1221no—
143#121—1221no—
144#121—1221no—
145#121—1221no—
146#120—21no—
147#120—1221no—
148#120C2×D6111yescharacteristic
149#104—1221no—
150#100—611no—
151#99—21no—
152#99—611no—
153#99—1221no—
154#99C2×D6111yescharacteristic
155C24C22⋊D6111yescharacteristic
156#41—21no—
157#41—41no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—611no—
164C2×D4—1221no—
165C2×D4—1221no—
166C2×D4—1221no—
167C2×D4—1221no—
168C2×D4C22×D6111yescharacteristic
169C22×C4—611no—
170C22×C4—1221no—
171SD16—2441no—
172D8—2441no—
173M16—1221no—
174C4⋊C4—1221no—
175C4⋊C4—1221no—
176C4⋊C4—1221no—
177C4⋊C4—2441no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—41no—
181C22⋊C4—611no—
182C22⋊C4—1221no—
183C22⋊C4—1221no—
184C22⋊C4—1221no—
185C22⋊C4—1221no—
186C22⋊C4—1221no—
187C22⋊C4—2441no—
188C22⋊C4C22⋊D6111yescharacteristic
189C42—611no—
190C23—21no—
191C23—21no—
192C23—21no—
193C23—41no—
194C23—81no—
195C23—1221no—
196C23D4×D6111yescharacteristic
197C23C2×C22⋊D6111yescharacteristic
198Q8—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—41no—
204D4—81no—
205D4—82no—
206D4—4881no—
207D4—4881no—
208D4—4881no—
209D4—4881no—
210D4—2441no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—4881no—
220C2×C4—2441no—
221C2×C4—2441no—
222C2×C4D4×D6111yescharacteristic
223C8—2441no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—41no—
232C22—41no—
233C22—81no—
234C22—81no—
235C22—81no—
236C22—2441no—
237C22—2441no—
238C22—2441no—
239C22#1451974511yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—81no—
244C4—4881no—
245C4—2441no—
246C4—2441no—
247C4—2441no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—81no—
253C2—4881no—
254C2#1683994811yescharacteristic
subgroupG/H
centerC2#16839948
commutatorC2×D4×C61C23
FrattiniC2×D4C22×D61
FittingC61×B(4,𝔽2)C2
socleC2×C61B(4,𝔽2)
hypercenterB(4,𝔽2)D61
hypocenterC61#2200
LCSG ▷ C2×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ B(4,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #16840501C2semidirect
2. #16839952C2semidirect
3. #16839930C2semidirect
4. #16839554C2semidirect
5. #16839551C2semidirect
6. #16839549C2semidirect
7. C61×B(4,𝔽2)C2semidirect
40. C22×Dic61D4semidirect
41. C2×D244D4semidirect
52. C22⋊Dic61D4semidirect
60. C4×Dic61D4semidirect
130. B(4,𝔽2)D61semidirect
135. C61#2200semidirect