Finite Group Databasebeta

← #21446854

Subgroups — #21446854

Order 7808.

362 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#14519807C211yesmaximal, characteristic
2#16840333C211yesmaximal, characteristic
3C2×#14519777C211yesmaximal, characteristic, complemented
4#16839772C211yesmaximal, characteristic, complemented
5C2×#14519695C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C2×#104×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9C22×Dic122C2211yescharacteristic
10#14519807—22no—
11#14519807—22no—
12C2×#11758202—21no—
13C2×#11758200—21no—
14C2×#11758194C2211yescharacteristic
15#14519777—22no—
16#14519777—22no—
17#14519775—21no—
18#14519764—21no—
19#14519758—22no—
20#14519756—22no—
21#14519736C2211yescharacteristic
22C2×C4⋊Dic61—22no—
23#14519702—22no—
24#14519695—22no—
25C2×#41×C61C2211yescharacteristic
26C2×M16×C61C2211yescharacteristic
27C2×C42×C61C2211yescharacteristic
28#104×C61—22no—
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×C61—21no—
38C22×C4×C61C2311yescharacteristic
39C22×Dic61—21no—
40C22×Dic61D412yes—
41C2×Dic122—21no—
42C2×Dic122—21no—
43C2×Dic122—21no—
44C2×Dic122—21no—
45C2×Dic122—21no—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122—21no—
51C2×Dic122—21no—
52C2×Dic122D412yes—
53M16×C61—21no—
54M16×C61—21no—
55C2×C8×C61—21no—
56C42×C61—21no—
57C42×C61D412yes—
58C22⋊Dic61—24no—
59C22⋊Dic61—21no—
60#11758202—24no—
61#11758200—24no—
62C4⋊Dic61—28no—
63C4⋊Dic61D412yes—
64#11758196—24no—
65C4×Dic61—21no—
66#11758194—21no—
67#11758194D412yes—
68C2×#92418—21no—
69C23×C61—21no—
70C23×C61C2×D411yescharacteristic
71Q8×C61—21no—
72Q8×C61—21no—
73D4×C61—21no—
74D4×C61—21no—
75D4×C61—41no—
76D4×C61—41no—
77C2×C4×C61—24no—
78C2×C4×C61—22no—
79C2×C4×C61—21no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61C2×D411yescharacteristic
83C2×C4×C61C2×D411yescharacteristic
84C2×C4×C61C2×D411yescharacteristic
85C2×C4×C61C2×D411yescharacteristic
86C2×C4×C61C2×D411yescharacteristic
87C2×C4×C61#4111yescharacteristic
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—41no—
94C2×Dic61—41no—
95Dic122—22no—
96Dic122—22no—
97Dic122—41no—
98Dic122—41no—
99Dic122—41no—
100Dic122—41no—
101Dic122—41no—
102Dic122—41no—
103C8×C61—41no—
104#92418—22no—
105C22×C61—22no—
106C22×C61—41no—
107C22×C61—42no—
108C22×C61#12011yescharacteristic
109C22×C61#12011yescharacteristic
110C22×C61#12111yescharacteristic
111C4×C61—24no—
112C4×C61—41no—
113C4×C61#12011yescharacteristic
114C4×C61#12111yescharacteristic
115C4×C61#12111yescharacteristic
116C4×C61#12711yescharacteristic
117Dic61—42no—
118Dic61—42no—
119Dic61—42no—
120#2005—611nomaximal, Sylow
121C2×C61—21no—
122C2×C61—21no—
123C2×C61—81no—
124C2×C61#39211yescharacteristic
125C2×C61#45612yes—
126C2×#137—611no—
127#536—611no—
128C2×C4⋊Q8—611no—
129C2×#104D6111yescharacteristic
130#419—611no—
131C2×#101—611no—
132#339—611no—
133C61#200511yescharacteristic, complemented, Sylow
134C2×#41C2×D6111yescharacteristic
135C22×Q8—611no—
136C22×Q8—611no—
137#137—1222no—
138#137—1222no—
139C2×Q16—1221no—
140C2×SD16—1221no—
141C2×M16—611no—
142C2×M16C2×D6111yescharacteristic
143C4⋊Q8—1222no—
144C4⋊Q8—1221no—
145C4⋊Q8—1222no—
146#124—1221no—
147#123—1222no—
148C22⋊Q8—1222no—
149#117—611no—
150C2×C4⋊C4—1222no—
151C2×C42C2×D6111yescharacteristic
152#104—22no—
153#103—1222no—
154#101—1222no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—21no—
159C2×Q8—612no—
160C2×Q8—1221no—
161C2×Q8—1221no—
162C2×Q8—1221no—
163C2×Q8—1221no—
164C2×Q8—1221no—
165C2×Q8—1221no—
166C2×Q8—1221no—
167C2×Q8—1221no—
168C2×Q8—1221no—
169C2×Q8—1221no—
170C2×Q8—1221no—
171C2×Q8D24411yescharacteristic
172C2×D4—21no—
173C2×D4D24411yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—612no—
177C22×C4—1221no—
178C22×C4C22×D6111yescharacteristic
179Q16—1224no—
180SD16—1224no—
181M16—21no—
182M16—21no—
183M16—612no—
184M16—1221no—
185C2×C8—21no—
186C2×C8—1221no—
187C4⋊C4—612no—
188C4⋊C4—1228no—
189C4⋊C4—1224no—
190C22⋊C4—1224no—
191C22⋊C4—1221no—
192C42—21no—
193C42—1221no—
194C42C22⋊D6112yes—
195C23—21no—
196C23D4×D6111yescharacteristic
197Q8—21no—
198Q8—21no—
199Q8—1222no—
200Q8—1222no—
201Q8—2441no—
202Q8—2441no—
203Q8—2441no—
204Q8—2441no—
205Q8—2441no—
206Q8—2441no—
207D4—21no—
208D4—21no—
209D4—41no—
210D4—41no—
211C2×C4—24no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—1222no—
217C2×C4—1222no—
218C2×C4—1222no—
219C2×C4—1222no—
220C2×C4—1222no—
221C2×C4—2441no—
222C2×C4—2441no—
223C2×C4C2×D24411yescharacteristic
224C2×C4#1175822211yescharacteristic
225C2×C4D4×D6111yescharacteristic
226C2×C4D4×D6111yescharacteristic
227C2×C4D4×D6111yescharacteristic
228C2×C4C2×C22⋊D6111yescharacteristic
229C8—41no—
230C8—1222no—
231C22—22no—
232C22—42no—
233C22—41no—
234C22#1451974511yescharacteristic
235C22#1451974711yescharacteristic
236C22#1451975011yescharacteristic
237C4—24no—
238C4—41no—
239C4—2442no—
240C4—2442no—
241C4—2442no—
242C4#1451974711yescharacteristic
243C4#1451975011yescharacteristic
244C4#1451975111yescharacteristic
245C4#1451977311yescharacteristic
246C2—21no—
247C2—21no—
248C2—81no—
249C2#1683967111yescharacteristic
250C2#1683994612yes—
subgroupG/H
centerC22#14519747
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#104×C61C2
socleC22×C61#120
hypercenterC2×#104D61
hypocenterC61#2005
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
3. C2×#14519777C2semidirect
4. #16839772C2semidirect
5. C2×#14519695C2semidirect
6. #16839522C2semidirect
133. C61#2005semidirect