Finite Group Databasebeta

← #21447038

Subgroups — #21447038

Order 7808.

278 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 69 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#16840338C211yesmaximal, characteristic
2C2×#14519703C211yesmaximal, characteristic
3#16839761C211yesmaximal, characteristic
4C2×#14519695C211yesmaximal, characteristic, complemented
5#16839667C211yesmaximal, characteristic, complemented
6#16839521C211yesmaximal, characteristic, complemented
7C61×#428C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10C2×#11758194C2211yescharacteristic
11#14519777—21no—
12#14519765—21no—
13#14519761—22no—
14#14519757—21no—
15#14519757—21no—
16C2×C4×Dic61C2211yescharacteristic
17#14519703—22no—
18#14519700—21no—
19#14519697—21no—
20#14519695—22no—
21#14519684—22no—
22C2×M16×C61C2211yescharacteristic
23#117×C61C2211yescharacteristic
24C2×C4⋊C4×C61C2211yescharacteristic
25#107×C61—21no—
26#106×C61—21no—
27C22×C4×C61—21no—
28C22×C4×C61C2311yescharacteristic
29C2×C22⋊D61—21no—
30C22×Dic61—21no—
31C22×Dic61D412yes—
32#11758222—21no—
33#11758222—21no—
34#11758222—21no—
35#11758222—21no—
36C2×D244D411yescharacteristic
37C2×C4×D61—21no—
38C2×Dic122—21no—
39C2×Dic122—21no—
40C2×Dic122—21no—
41C2×Dic122—21no—
42C2×Dic122—21no—
43C2×Dic122—21no—
44C2×Dic122D411yescharacteristic
45M16×C61—21no—
46M16×C61D412yes—
47C2×C8×C61—21no—
48C4⋊C4×C61—21no—
49C4⋊C4×C61—21no—
50C4⋊C4×C61D411yescharacteristic
51C4⋊C4×C61D411yescharacteristic
52C22⋊C4×C61—21no—
53C42×C61—21no—
54#11758198—22no—
55#11758198—22no—
56C4⋊Dic61—22no—
57C4⋊Dic61—22no—
58C4×Dic61—21no—
59C4×Dic61—21no—
60#11758194—21no—
61#11758194—21no—
62C2×#92418—21no—
63C23×C61C2×D411yescharacteristic
64C22×D61—21no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—42no—
68C2×C4×C61—41no—
69C2×C4×C61C2×D411yescharacteristic
70C2×C4×C61C2×D411yescharacteristic
71C2×C4×C61C2×D411yescharacteristic
72C2×C4×C61#4111yescharacteristic
73C2×C4×C61#4111yescharacteristic
74C2×C4×C61#4111yescharacteristic
75C22⋊D61—41no—
76C22⋊D61—41no—
77C2×Dic61—22no—
78C2×Dic61—21no—
79C2×Dic61—22no—
80C2×Dic61—22no—
81C2×Dic61—22no—
82C2×Dic61—41no—
83C2×Dic61—41no—
84D244—21no—
85D244—21no—
86C4×D61—41no—
87C4×D61—41no—
88Dic122—21no—
89Dic122—21no—
90Dic122—41no—
91Dic122—41no—
92Dic122—41no—
93Dic122—41no—
94C8×C61—22no—
95#92418—41no—
96C22×C61—21no—
97C22×C61—21no—
98C22×C61#12011yescharacteristic
99C22×C61#12111yescharacteristic
100C22×C61#12311yescharacteristic
101C2×D61—41no—
102C2×D61—41no—
103C2×D61—41no—
104C4×C61—41no—
105C4×C61—41no—
106C4×C61—81no—
107C4×C61#12111yescharacteristic
108C4×C61#12111yescharacteristic
109C4×C61#12311yescharacteristic
110C4×C61#12411yescharacteristic
111Dic61—42no—
112Dic61—41no—
113Dic61—42no—
114#2038—611nomaximal, Sylow
115C2×C61—21no—
116C2×C61—21no—
117C2×C61#39411yescharacteristic
118C2×C61#45411yescharacteristic
119C2×C61#45611yescharacteristic
120D61—81no—
121#536—611no—
122#428D6111yescharacteristic, complemented
123C2×#104—611no—
124#417—611no—
125C2×#101—611no—
126#391—611no—
127#339—611no—
128C61#203811yescharacteristic, complemented, Sylow
129C2×#41—611no—
130C22×Q8—611no—
131C2×M16—611no—
132C2×M16C2×D6111yescharacteristic
133C4⋊Q8—1221no—
134#124—1221no—
135#123—1222no—
136C22⋊Q8—1221no—
137C22⋊Q8—1221no—
138#117C2×D6111yescharacteristic
139C2×C4⋊C4C2×D6111yescharacteristic
140C2×C42—611no—
141#107—21no—
142#106—21no—
143#104—1222no—
144#103—1221no—
145#102—1221no—
146#101—1222no—
147#95—1222no—
148#41—1221no—
149#41—1221no—
150#41—1221no—
151#41—1221no—
152C2×Q8—611no—
153C2×Q8—1221no—
154C2×Q8—1221no—
155C2×Q8—1221no—
156C2×Q8—1221no—
157C2×Q8—1221no—
158C2×Q8—1221no—
159C2×D4—611no—
160C2×D4—1221no—
161C22×C4—21no—
162C22×C4—612no—
163C22×C4—1221no—
164C22×C4—1221no—
165C22×C4C22×D6111yescharacteristic
166M16—21no—
167M16—1221no—
168M16—1221no—
169M16D24412yes—
170C2×C8—21no—
171C2×C8—1221no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—1222no—
175C4⋊C4—1222no—
176C4⋊C4C22⋊D6111yescharacteristic
177C4⋊C4C22⋊D6111yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—1222no—
180C22⋊C4—1222no—
181C42—21no—
182C42—1221no—
183C42—1221no—
184C23—1221no—
185C23D4×D6111yescharacteristic
186Q8—1221no—
187Q8—1221no—
188Q8—2441no—
189Q8—2441no—
190Q8—2441no—
191Q8—2441no—
192D4—1221no—
193D4—1221no—
194D4—2441no—
195D4—2441no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—42no—
199C2×C4—41no—
200C2×C4—1222no—
201C2×C4—1222no—
202C2×C4—1221no—
203C2×C4—1222no—
204C2×C4—1222no—
205C2×C4—2441no—
206C2×C4—2441no—
207C2×C4—2441no—
208C2×C4—2441no—
209C2×C4C2×D24411yescharacteristic
210C2×C4#1175822211yescharacteristic
211C2×C4D4×D6111yescharacteristic
212C2×C4#1175822611yescharacteristic
213C2×C4#1175822611yescharacteristic
214C2×C4C2×C22⋊D6111yescharacteristic
215C8—22no—
216C8—2441no—
217C22—21no—
218C22—21no—
219C22—2441no—
220C22—2441no—
221C22—2441no—
222C22#1451974511yescharacteristic
223C22#1451975211yescharacteristic
224C22#1451976211yescharacteristic
225C4—41no—
226C4—41no—
227C4—81no—
228C4—2442no—
229C4—2442no—
230C4—2441no—
231C4#1451975111yescharacteristic
232C4#1451975211yescharacteristic
233C4#1451976211yescharacteristic
234C4#1451976611yescharacteristic
235C2—21no—
236C2—21no—
237C2—4881no—
238C2#1683967911yescharacteristic
239C2#1683993311yescharacteristic
240C2#1683994311yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC61×#428C2
socleC22×C61#120
hypercenter#428D61
hypocenterC61#2038
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
4. C2×#14519695C2semidirect
5. #16839667C2semidirect
6. #16839521C2semidirect
7. C61×#428C2semidirect
122. #428D61semidirect
128. C61#2038semidirect