Finite Group Databasebeta

← #21446937

Subgroups — #21446937

Order 7808.

342 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 75 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
2C22×#11758202C211yesmaximal, characteristic, complemented
3C2×#14519696C211yesmaximal, characteristic, complemented
4C2×#14519695C211yesmaximal, characteristic, complemented
5#16839729C211yesmaximal, characteristic
6#16839526C211yesmaximal, characteristic, complemented
7C2×#137×C61C211yesmaximal, characteristic
8C22×Dic122C2211yescharacteristic
9#14519807—22no—
10#14519807—22no—
11C2×#11758202—22no—
12C2×#11758202—21no—
13C2×#11758202—22no—
14C2×#11758202—22no—
15C2×#11758200—21no—
16C2×#11758194C2211yescharacteristic
17C2×#11758194C2211yescharacteristic
18C22×#92418C2211yescharacteristic
19#14519696—22no—
20#14519695—22no—
21C22⋊#92418—22no—
22C2×#41×C61C2211yescharacteristic
23C22×Q8×C61C2211yescharacteristic
24#137×C61—22no—
25#137×C61—22no—
26C2×Q16×C61—21no—
27C2×SD16×C61—21no—
28C2×M16×C61C2211yescharacteristic
29#41×C61—21no—
30#41×C61—21no—
31#41×C61—21no—
32#41×C61—21no—
33C2×Q8×C61—21no—
34C2×Q8×C61—21no—
35C2×Q8×C61—21no—
36C2×Q8×C61—21no—
37C2×Q8×C61—21no—
38C2×Q8×C61D411yescharacteristic
39C2×Q8×C61D412yes—
40C2×D4×C61—21no—
41C2×D4×C61D411yescharacteristic
42C22×C4×C61—21no—
43C22×C4×C61—21no—
44C22×C4×C61C2311yescharacteristic
45C22×Dic61—21no—
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—21no—
49C2×Dic122—21no—
50C2×Dic122—21no—
51C2×Dic122D412yes—
52Q16×C61—24no—
53SD16×C61—24no—
54M16×C61—21no—
55M16×C61D412yes—
56C2×C8×C61—21no—
57#11758202—28no—
58#11758202—24no—
59#11758200—24no—
60#11758194—21no—
61#11758194—21no—
62#11758194—21no—
63#11758194D412yes—
64C2×#92418—21no—
65C2×#92418—21no—
66C2×#92418—21no—
67C2×#92418—21no—
68C2×#92418D412yes—
69C23×C61—21no—
70C23×C61#4111yescharacteristic
71Q8×C61—22no—
72Q8×C61—21no—
73Q8×C61—22no—
74Q8×C61—21no—
75Q8×C61—41no—
76Q8×C61—41no—
77D4×C61—21no—
78D4×C61—21no—
79D4×C61—41no—
80D4×C61—41no—
81C2×C4×C61—21no—
82C2×C4×C61—22no—
83C2×C4×C61—41no—
84C2×C4×C61—41no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61C2×D411yescharacteristic
88C2×C4×C61C2×D411yescharacteristic
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2×D411yescharacteristic
93C2×Dic61—22no—
94C2×Dic61—41no—
95C2×Dic61—41no—
96Dic122—22no—
97Dic122—22no—
98Dic122—41no—
99Dic122—41no—
100C8×C61—22no—
101#92418—22no—
102#92418—22no—
103#92418—41no—
104C22×C61—22no—
105C22×C61—41no—
106C22×C61—42no—
107C22×C61#12111yescharacteristic
108C22×C61#12111yescharacteristic
109C22×C61#12111yescharacteristic
110C4×C61—41no—
111C4×C61—42no—
112C4×C61#12011yescharacteristic
113C4×C61#12011yescharacteristic
114C4×C61#12011yescharacteristic
115C4×C61#12711yescharacteristic
116Dic61—42no—
117#2020—611nomaximal, Sylow
118C2×C61—21no—
119C2×C61—21no—
120C2×C61—81no—
121C2×C61#39211yescharacteristic
122C2×C61#47312yes—
123C2×#137—611no—
124C2×#137D6111yescharacteristic
125C22×Q16—611no—
126C2×#101—611no—
127C2×#101—611no—
128#408—611no—
129#341—611no—
130C61#202011yescharacteristic, complemented, Sylow
131C2×#41C2×D6111yescharacteristic
132C22×Q8—611no—
133C22×Q8C2×D6111yescharacteristic
134#137—22no—
135#137—22no—
136#137—1222no—
137#137—1222no—
138C2×Q16—21no—
139C2×Q16—1222no—
140C2×Q16—1222no—
141C2×Q16—1222no—
142C2×Q16—1221no—
143C2×SD16—21no—
144C2×SD16—1221no—
145C2×M16—611no—
146C2×M16—611no—
147C2×M16C2×D6111yescharacteristic
148C22×C8—611no—
149#101—1222no—
150#101—1222no—
151C22⋊C8—1222no—
152#41—21no—
153#41—21no—
154#41—21no—
155#41—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—612no—
162C2×Q8—1221no—
163C2×Q8—1221no—
164C2×Q8—1221no—
165C2×Q8—1221no—
166C2×Q8—1221no—
167C2×Q8C22⋊D6111yescharacteristic
168C2×Q8C22⋊D6112yes—
169C2×D4—21no—
170C2×D4C22⋊D6111yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—1221no—
174C22×C4C22×D6111yescharacteristic
175Q16—24no—
176Q16—1228no—
177Q16—1224no—
178SD16—24no—
179SD16—1224no—
180M16—21no—
181M16—612no—
182M16—1221no—
183M16—1221no—
184M16—1221no—
185M16C22⋊D6112yes—
186C2×C8—21no—
187C2×C8—612no—
188C2×C8—1221no—
189C2×C8—1221no—
190C2×C8—1221no—
191C2×C8—1221no—
192C23—21no—
193C23#1175822411yescharacteristic
194Q8—22no—
195Q8—21no—
196Q8—22no—
197Q8—21no—
198Q8—41no—
199Q8—41no—
200Q8—1222no—
201Q8—1222no—
202Q8—2441no—
203Q8—2441no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—1222no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4D4×D6111yescharacteristic
218C2×C4D4×D6111yescharacteristic
219C2×C4D4×D6111yescharacteristic
220C2×C4C2×C22⋊D6111yescharacteristic
221C2×C4C2×C22⋊D6111yescharacteristic
222C2×C4C2×C22⋊D6111yescharacteristic
223C8—22no—
224C8—1222no—
225C8—1222no—
226C8—2441no—
227C22—22no—
228C22—42no—
229C22—41no—
230C22#1451974811yescharacteristic
231C22#1451974911yescharacteristic
232C22#1451974911yescharacteristic
233C4—41no—
234C4—42no—
235C4—2442no—
236C4#1451974511yescharacteristic
237C4#1451974511yescharacteristic
238C4#1451974611yescharacteristic
239C4#1451977311yescharacteristic
240C2—21no—
241C2—21no—
242C2—81no—
243C2#1683967011yescharacteristic
244C2#1684003512yes—
subgroupG/H
centerC22#14519749
commutatorC22×C4×C61C23
FrattiniC22×C4C22×D61
FittingC2×#137×C61C2
socleC22×C61#121
hypercenterC2×#137D61
hypocenterC61#2020
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C22×#11758202C2semidirect
3. C2×#14519696C2semidirect
4. C2×#14519695C2semidirect
6. #16839526C2semidirect
130. C61#2020semidirect