Finite Group Databasebeta

← #21447104

Subgroups — #21447104

Order 7808.

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

normal subgroups only

This group has 266 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
1#16840560C211yesmaximal, characteristic
2#16839785C211yesmaximal, characteristic, complemented
3C2×#14519704C211yesmaximal, characteristic, complemented
4C2×#14519703C211yesmaximal, characteristic, complemented
5#16839744C211yesmaximal, characteristic, complemented
6#16839520C211yesmaximal, characteristic, complemented
7C61×#413C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9#14519808—21no—
10#14519807—21no—
11#14519803—21no—
12#14519802—21no—
13#14519797—22no—
14C2×#11758194C2211yescharacteristic
15C2×#11758194C2211yescharacteristic
16C2×C4×Dic61C2211yescharacteristic
17#14519706—22no—
18#14519704—21no—
19#14519704—21no—
20#14519703—21no—
21#14519703—21no—
22#14519695—21no—
23#14519693—21no—
24C2×#41×C61C2211yescharacteristic
25C2×M16×C61C2211yescharacteristic
26C2×M16×C61C2211yescharacteristic
27#101×C61—21no—
28#100×C61—21no—
29#41×C61—21no—
30#41×C61—21no—
31#41×C61—21no—
32#41×C61—21no—
33C2×Q8×C61D411yescharacteristic
34C2×D4×C61—21no—
35C2×D4×C61D411yescharacteristic
36C22×C4×C61—21no—
37C22×C4×C61C2311yescharacteristic
38C2×C22⋊D61—21no—
39C22×Dic61—21no—
40#11758222—21no—
41#11758222—21no—
42#11758222—21no—
43#11758222—21no—
44C2×D244D411yescharacteristic
45C2×C4×D61—21no—
46C2×Dic122D411yescharacteristic
47M16×C61—21no—
48M16×C61—21no—
49M16×C61—21no—
50M16×C61—21no—
51C2×C8×C61—21no—
52C2×C8×C61—21no—
53#11758202—22no—
54#11758201—22no—
55#11758200—22no—
56#11758199—22no—
57C4×Dic61—21no—
58C4×Dic61D411yescharacteristic
59C4×Dic61D411yescharacteristic
60#11758194—21no—
61#11758194—21no—
62#11758194—21no—
63#11758194—21no—
64C2×#92418—21no—
65C2×#92418D412yes—
66C23×C61—21no—
67C23×C61#4111yescharacteristic
68C22×D61—21no—
69Q8×C61—21no—
70Q8×C61—21no—
71D4×C61—21no—
72D4×C61—21no—
73D4×C61—41no—
74D4×C61—41no—
75C2×C4×C61—21no—
76C2×C4×C61—41no—
77C2×C4×C61—41no—
78C2×C4×C61C2×D411yescharacteristic
79C2×C4×C61C2×D411yescharacteristic
80C2×C4×C61C2×D411yescharacteristic
81C2×C4×C61C2×D411yescharacteristic
82C2×C4×C61#4111yescharacteristic
83C2×C4×C61#4111yescharacteristic
84C22⋊D61—41no—
85C22⋊D61—41no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—42no—
90D244—21no—
91D244—21no—
92C4×D61—41no—
93C4×D61—41no—
94Dic122—21no—
95Dic122—21no—
96C8×C61—41no—
97C8×C61—41no—
98#92418—22no—
99#92418—41no—
100C22×C61—41no—
101C22×C61—41no—
102C22×C61—81no—
103C22×C61#12111yescharacteristic
104C22×C61#12311yescharacteristic
105C22×C61#12311yescharacteristic
106C2×D61—41no—
107C2×D61—81no—
108C4×C61—41no—
109C4×C61#12011yescharacteristic
110C4×C61#12111yescharacteristic
111C4×C61#12111yescharacteristic
112C4×C61#12411yescharacteristic
113Dic61—22no—
114Dic61—41no—
115Dic61—41no—
116#2050—611nomaximal, Sylow
117C2×C61—21no—
118C2×C61—21no—
119C2×C61—21no—
120C2×C61—81no—
121C2×C61#39411yescharacteristic
122D61—81no—
123#575—611no—
124#423—611no—
125C2×#104—611no—
126C2×#104—611no—
127#413—611no—
128#413D6111yescharacteristic, complemented
129#338—611no—
130C61#205011yescharacteristic, complemented, Sylow
131C2×#41—611no—
132C2×#41C2×D6111yescharacteristic
133#137—1221no—
134#137—1221no—
135AGL(1,ℤ/8)—1221no—
136AGL(1,ℤ/8)—1221no—
137#135—1222no—
138C2×M16—611no—
139C2×M16—611no—
140C2×M16C2×D6111yescharacteristic
141C2×M16C2×D6111yescharacteristic
142C2×C42—611no—
143C4⋊C8—1222no—
144#104—1221no—
145#104—1221no—
146#104—1221no—
147#104—1221no—
148#101—21no—
149#101—1221no—
150#100—21no—
151#100—1221no—
152#41—21no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—1221no—
157#41—1221no—
158#41—1221no—
159#41—1221no—
160C2×Q8—611no—
161C2×Q8C22⋊D6111yescharacteristic
162C2×D4—21no—
163C2×D4—611no—
164C2×D4—1221no—
165C2×D4C22⋊D6111yescharacteristic
166C22×C4—21no—
167C22×C4—1221no—
168C22×C4—1221no—
169C22×C4C22×D6111yescharacteristic
170Q16—1222no—
171SD16—1222no—
172SD16—1222no—
173D8—1222no—
174M16—21no—
175M16—21no—
176M16—21no—
177M16—21no—
178M16—1221no—
179M16—1221no—
180M16—1221no—
181M16—1221no—
182C2×C8—21no—
183C2×C8—21no—
184C2×C8—612no—
185C2×C8—1221no—
186C42—611no—
187C42—611no—
188C42—1221no—
189C23—21no—
190C23—1221no—
191C23#1175822211yescharacteristic
192Q8—21no—
193Q8—21no—
194Q8—1221no—
195Q8—1221no—
196D4—21no—
197D4—21no—
198D4—41no—
199D4—41no—
200D4—1221no—
201D4—1221no—
202D4—2441no—
203D4—2441no—
204C2×C4—21no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—2442no—
211C2×C4—2441no—
212C2×C4—2441no—
213C2×C4#1175822211yescharacteristic
214C2×C4D4×D6111yescharacteristic
215C2×C4D4×D6111yescharacteristic
216C2×C4D4×D6111yescharacteristic
217C2×C4#1175822411yescharacteristic
218C2×C4C2×C22⋊D6111yescharacteristic
219C8—41no—
220C8—41no—
221C8—1222no—
222C8—2441no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—4881no—
227C22—2441no—
228C22#1451975011yescharacteristic
229C22#1451975911yescharacteristic
230C22#1451976011yescharacteristic
231C4—41no—
232C4—1222no—
233C4—2441no—
234C4—2441no—
235C4#1451974511yescharacteristic
236C4#1451974911yescharacteristic
237C4#1451975011yescharacteristic
238C4#1451976311yescharacteristic
239C2—21no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—4881no—
244C2#1683967711yescharacteristic
subgroupG/H
centerC4#14519763
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#413C2
socleC2×C61#394
hypercenter#413D61
hypocenterC61#2050
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #16839785C2semidirect
3. C2×#14519704C2semidirect
4. C2×#14519703C2semidirect
5. #16839744C2semidirect
6. #16839520C2semidirect
7. C61×#413C2semidirect
128. #413D61semidirect
130. C61#2050semidirect