Finite Group Databasebeta

← #22611145

Subgroups — #22611145

Order 9344.

278 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 71 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#17988630C211yesmaximal, characteristic, complemented
2C2×#14556518C211yesmaximal, characteristic
3#17988588C211yesmaximal, characteristic
4C2×#14556510C211yesmaximal, characteristic, complemented
5#17988494C211yesmaximal, characteristic, complemented
6#17988346C211yesmaximal, characteristic, complemented
7#536×C73C211yesmaximal, characteristic
8C2×#11924012C2211yescharacteristic
9C2×#11924012C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×C4×Dic73C2211yescharacteristic
12#14556524—21no—
13#14556522—21no—
14#14556518—22no—
15#14556515—21no—
16#14556512—21no—
17#14556510—22no—
18#14556498—22no—
19C2×#41×C73C2211yescharacteristic
20C22×Q8×C73C2211yescharacteristic
21C4⋊Q8×C73—21no—
22#124×C73—21no—
23#123×C73—22no—
24C22⋊Q8×C73—21no—
25C22⋊Q8×C73—21no—
26#117×C73C2211yescharacteristic
27C22×Dic73—21no—
28C22×Dic73—21no—
29#11924012—21no—
30#11924012—21no—
31#11924012—21no—
32#11924012D412yes—
33C2×#10596831—21no—
34C2×#10596831—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73—21no—
37C4×Dic73—21no—
38C4×Dic73—21no—
39#41×C73—21no—
40#41×C73—21no—
41#41×C73—21no—
42#41×C73—21no—
43C2×Q8×C73—21no—
44C2×Q8×C73—21no—
45C2×Q8×C73—21no—
46C2×Q8×C73—21no—
47C2×Q8×C73—21no—
48C2×Q8×C73—21no—
49C2×Q8×C73D411yescharacteristic
50C2×D4×C73—21no—
51C2×D4×C73D411yescharacteristic
52C22×C4×C73—21no—
53C22×C4×C73D412yes—
54C22×C4×C73C2311yescharacteristic
55C4⋊C4×C73—22no—
56C4⋊C4×C73—22no—
57C4⋊C4×C73D411yescharacteristic
58C4⋊C4×C73D411yescharacteristic
59C22⋊C4×C73—22no—
60C22⋊C4×C73—22no—
61C22⋊C4×C73—21no—
62C42×C73—21no—
63C23×C73—21no—
64C23×C73C2×D411yescharacteristic
65Q8×C73—21no—
66Q8×C73—21no—
67Q8×C73—41no—
68Q8×C73—41no—
69Q8×C73—41no—
70Q8×C73—41no—
71D4×C73—21no—
72D4×C73—21no—
73D4×C73—41no—
74D4×C73—41no—
75C2×C4×C73—21no—
76C2×C4×C73—21no—
77C2×C4×C73—22no—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—41no—
82C2×C4×C73—41no—
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73#4111yescharacteristic
87C2×C4×C73#4111yescharacteristic
88C2×C4×C73#4111yescharacteristic
89C2×Dic73—22no—
90C2×Dic73—41no—
91C2×Dic73—41no—
92C2×Dic73—42no—
93C2×Dic73—41no—
94#10596831—22no—
95#10596831—41no—
96C22×C73—21no—
97C22×C73—21no—
98C22×C73—41no—
99C22×C73—41no—
100C22×C73—41no—
101C22×C73#12011yescharacteristic
102C22×C73#12111yescharacteristic
103C22×C73#12311yescharacteristic
104C4×C73—42no—
105C4×C73—41no—
106C4×C73—41no—
107C4×C73—41no—
108C4×C73#12111yescharacteristic
109C4×C73#12111yescharacteristic
110C4×C73#12311yescharacteristic
111C4×C73#12411yescharacteristic
112Dic73—42no—
113Dic73—81no—
114C2×C73—21no—
115C2×C73—21no—
116C2×C73—81no—
117C2×C73#39411yescharacteristic
118C2×C73#45411yescharacteristic
119C2×C73#45611yescharacteristic
120#2038—731nomaximal, Sylow
121C73#203811yescharacteristic, complemented, Sylow
122#536D7311yescharacteristic
123#428—731no—
124C2×#104—731no—
125#417—731no—
126C2×#101—731no—
127#391—731no—
128#339—731no—
129C2×#41C2×D7311yescharacteristic
130C22×Q8C2×D7311yescharacteristic
131C2×M16—731no—
132C2×M16—731no—
133C4⋊Q8—21no—
134#124—21no—
135#123—22no—
136C22⋊Q8—21no—
137C22⋊Q8—21no—
138#117C2×D7311yescharacteristic
139C2×C4⋊C4—731no—
140C2×C42—731no—
141#107—1461no—
142#106—1461no—
143#104—1462no—
144#103—1461no—
145#102—1461no—
146#101—1462no—
147#95—1462no—
148#41—21no—
149#41—21no—
150#41—21no—
151#41—21no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—21no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8C22⋊D7311yescharacteristic
159C2×D4—21no—
160C2×D4C22⋊D7311yescharacteristic
161C22×C4—21no—
162C22×C4—1461no—
163C22×C4—1461no—
164C22×C4C22⋊D7312yes—
165C22×C4C22×D7311yescharacteristic
166M16—732no—
167M16—1461no—
168M16—1461no—
169M16—1461no—
170C2×C8—1461no—
171C2×C8—1461no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—1461no—
175C4⋊C4—1461no—
176C4⋊C4C22⋊D7311yescharacteristic
177C4⋊C4C22⋊D7311yescharacteristic
178C22⋊C4—22no—
179C22⋊C4—22no—
180C22⋊C4—21no—
181C42—21no—
182C42—1461no—
183C42—1461no—
184C23—21no—
185C23C2×C22⋊D7311yescharacteristic
186Q8—21no—
187Q8—21no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191Q8—41no—
192D4—21no—
193D4—21no—
194D4—41no—
195D4—41no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—2921no—
205C2×C4—2921no—
206C2×C4—2922no—
207C2×C4—2921no—
208C2×C4—1462no—
209C2×C4D4×D7311yescharacteristic
210C2×C4C2×C22⋊D7311yescharacteristic
211C2×C4C2×C22⋊D7311yescharacteristic
212C2×C4#1192402711yescharacteristic
213C2×C4#1192402711yescharacteristic
214C2×C4#1192402711yescharacteristic
215C8—2921no—
216C8—1462no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22#1455656011yescharacteristic
223C22#1455656311yescharacteristic
224C22#1455657211yescharacteristic
225C4—42no—
226C4—41no—
227C4—41no—
228C4—41no—
229C4—2922no—
230C4—5841no—
231C4#1455656211yescharacteristic
232C4#1455656311yescharacteristic
233C4#1455657211yescharacteristic
234C4#1455657811yescharacteristic
235C2—21no—
236C2—21no—
237C2—81no—
238C2#1798850111yescharacteristic
239C2#1798876011yescharacteristic
240C2#1798877011yescharacteristic
subgroupG/H
centerC22#14556560
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#536×C73C2
socleC22×C73#120
hypercenter#536D73
hypocenterC73#2038
LCSG ▷ C22×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #17988630C2semidirect
4. C2×#14556510C2semidirect
5. #17988494C2semidirect
6. #17988346C2semidirect
121. C73#2038semidirect