Finite Group Databasebeta

← #21447825

Subgroups — #21447825

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#16840499C211yesmaximal, characteristic, complemented
2#16839952C211yesmaximal, characteristic, complemented
3#16839949C211yesmaximal, characteristic, complemented
4#16839555C211yesmaximal, characteristic, complemented
5#16839553C211yesmaximal, characteristic, complemented
6#16839550C211yesmaximal, characteristic, complemented
7C61×#453C211yesmaximal, characteristic, complemented
8#14519771—21no—
9#14519758—21no—
10#14519758—21no—
11#14519758C2211yescharacteristic
12#14519749—21no—
13#14519749—21no—
14#14519749—21no—
15#14519745—21no—
16#14519745—21no—
17#14519745C2211yescharacteristic
18#14519692—21no—
19#14519692—21no—
20#14519692C2211yescharacteristic
21#14519692C2211yescharacteristic
22H(5,𝔽2)×C61C2211yescharacteristic
23AGL(1,ℤ/8)×C61—21no—
24#127×C61C2211yescharacteristic
25#104×C61—21no—
26#100×C61C2211yescharacteristic
27C23×D61D411yescharacteristic
28#41×C61—21no—
29#41×C61—41no—
30C2×D4×C61—21no—
31C2×D4×C61—21no—
32C2×D4×C61—21no—
33C2×D4×C61—21no—
34C2×D4×C61—41no—
35C2×D4×C61D411yescharacteristic, complemented
36C2×D4×C61C2311yescharacteristic
37C2×C22⋊D61—21no—
38C2×C22⋊D61—21no—
39C2×C22⋊D61—21no—
40C2×C22⋊D61—41no—
41C22×Dic61—21no—
42C22×Dic61D411yescharacteristic, complemented
43SD16×C61—41no—
44D8×C61—41no—
45M16×C61—21no—
46C42×C61D411yescharacteristic, complemented
47C22⋊Dic61—21no—
48C22⋊Dic61—21no—
49C22⋊Dic61—21no—
50C22⋊Dic61—21no—
51C22⋊Dic61—41no—
52C22⋊Dic61D411yescharacteristic
53C22⋊Dic61D411yescharacteristic, complemented
54#11758198—21no—
55#11758198—21no—
56#11758198—21no—
57#11758198—41no—
58#11758196—21no—
59#11758196—21no—
60#11758196—21no—
61#11758196—41no—
62C23×C61—21no—
63C23×C61—21no—
64C23×C61—21no—
65C23×C61C2×D411yescharacteristic
66C23×C61C2×D411yescharacteristic
67C22×D61—21no—
68C22×D61—41no—
69C22×D61—81no—
70Q8×C61—21no—
71D4×C61—21no—
72D4×C61—41no—
73D4×C61—41no—
74D4×C61—41no—
75D4×C61—41no—
76D4×C61—41no—
77D4×C61—81no—
78D4×C61—81no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—41no—
83C2×C4×C61C2×D411yescharacteristic
84C22⋊D61—81no—
85C22⋊D61—81no—
86C22⋊D61—81no—
87C22⋊D61—82no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—41no—
92C2×Dic61—41no—
93C2×Dic61—41no—
94C2×Dic61—81no—
95C8×C61—41no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61—41no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—81no—
105C22×C61—81no—
106C22×C61#12011yescharacteristic
107C2×D61—41no—
108C2×D61—41no—
109C2×D61—42no—
110C2×D61—41no—
111C2×D61—81no—
112C4×C61—21no—
113C4×C61—41no—
114C4×C61—41no—
115Dic61—41no—
116Dic61—41no—
117Dic61—41no—
118Dic61—81no—
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)—611no—
131#453D6111yescharacteristic, complemented
132#353—611no—
133#352—611no—
134AΣL(1,𝔽16)—611no—
135C61#220011yescharacteristic, complemented, Sylow
136H(5,𝔽2)C2×D6111yescharacteristic
137AGL(1,ℤ/8)—21no—
138#127C2×D6111yescharacteristic
139#126—1221no—
140#123—611no—
141#123—1221no—
142#123—1221no—
143#121—1221no—
144#121—1221no—
145#121—1221no—
146#120—611no—
147#120—1221no—
148#120—1221no—
149#104—21no—
150#100C2×D6111yescharacteristic
151#99—611no—
152#99—611no—
153#99—1221no—
154#99—1221no—
155C24—611no—
156#41—21no—
157#41—41no—
158C2×D4—21no—
159C2×D4—21no—
160C2×D4—21no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4—1221no—
164C2×D4—1221no—
165C2×D4—1221no—
166C2×D4—2441no—
167C2×D4C22⋊D6111yescharacteristic, complemented
168C2×D4C22×D6111yescharacteristic
169C22×C4—611no—
170C22×C4—1221no—
171SD16—41no—
172D8—41no—
173M16—21no—
174C4⋊C4—1221no—
175C4⋊C4—1221no—
176C4⋊C4—1221no—
177C4⋊C4—2441no—
178C22⋊C4—611no—
179C22⋊C4—611no—
180C22⋊C4—1221no—
181C22⋊C4—1221no—
182C22⋊C4—1221no—
183C22⋊C4—1221no—
184C22⋊C4—1221no—
185C22⋊C4—1221no—
186C22⋊C4—1221no—
187C22⋊C4—2441no—
188C22⋊C4—2441no—
189C42C22⋊D6111yescharacteristic, complemented
190C23—21no—
191C23—21no—
192C23—21no—
193C23—1221no—
194C23—4881no—
195C23—2441no—
196C23D4×D6111yescharacteristic
197C23D4×D6111yescharacteristic
198Q8—21no—
199D4—21no—
200D4—41no—
201D4—41no—
202D4—41no—
203D4—41no—
204D4—41no—
205D4—81no—
206D4—81no—
207D4—4882no—
208D4—4881no—
209D4—4881no—
210D4—4881no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—4881no—
219C2×C4—2441no—
220C2×C4—2441no—
221C2×C4—2441no—
222C2×C4C2×C22⋊D6111yescharacteristic
223C8—41no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—81no—
233C22—81no—
234C22—4881no—
235C22—2441no—
236C22—2441no—
237C22—2442no—
238C22—2441no—
239C22#1451974511yescharacteristic
240C4—21no—
241C4—41no—
242C4—41no—
243C4—4881no—
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×#453C2
socleC2×C61B(4,𝔽2)
hypercenter#453D61
hypocenterC61#2200
LCSG ▷ C2×D4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #16840499C2semidirect
2. #16839952C2semidirect
3. #16839949C2semidirect
4. #16839555C2semidirect
5. #16839553C2semidirect
6. #16839550C2semidirect
7. C61×#453C2semidirect
35. C2×D4×C61D4semidirect
42. C22×Dic61D4semidirect
46. C42×C61D4semidirect
53. C22⋊Dic61D4semidirect
131. #453D61semidirect
135. C61#2200semidirect
167. C2×D4C22⋊D61semidirect
189. C42C22⋊D61semidirect