Finite Group Databasebeta

← #22621672

Subgroups — #22621672

Order 9344.

482 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556614C211yesmaximal, characteristic, complemented
2#17989248C212yesmaximal, complemented
3#17988972C211yesmaximal, characteristic, complemented
4#17988825C211yesmaximal, characteristic, complemented
5#17988823C211yesmaximal, characteristic, complemented
6#17988811C212yesmaximal, complemented
7#17988748C212yesmaximal, complemented
8#17988726C212yesmaximal, complemented
9Q16×Dic73C211yesmaximal, characteristic, complemented
10C8×C22⋊D73C211yesmaximal, characteristic, complemented
11C22×Q16×C73C211yesmaximal, characteristic, complemented
12C2×#11924029C2212yes—
13#14556614—24no—
14C2×#11924015C2212yes—
15C2×#11924015C2212yes—
16C2×D584C2211yescharacteristic
17C2×C8×D73C2211yescharacteristic
18#14556580—22no—
19#14556580C2212yes—
20#14556567—22no—
21#14556567C2212yes—
22#14556565—22no—
23#14556565C2212yes—
24Q8×Dic73C2212yes—
25C4×C22⋊D73—22no—
26C4×C22⋊D73C2211yescharacteristic
27#14556525C2211yescharacteristic
28#14556520C2211yescharacteristic
29#14556515C2212yes—
30#14556515C2212yes—
31#14556513C2212yes—
32C22⋊#10596831C2211yescharacteristic
33#14556503C2211yescharacteristic
34C8×Dic73C2211yescharacteristic
35C22×Q8×C73C2212yes—
36C2×Q16×C73—24no—
37C2×Q16×C73C2211yescharacteristic
38C2×Q16×C73C2212yes—
39C2×Q16×C73C2211yescharacteristic
40C22×C8×C73C2211yescharacteristic
41#11924029—24no—
42#11924029—42no—
43C2×D292—22no—
44C2×D292C2312yes—
45C2×C22⋊D73—22no—
46C2×C22⋊D73D411yescharacteristic
47C2×C4×D73—22no—
48C2×C4×D73C2311yescharacteristic
49#11924015—24no—
50#11924015—42no—
51D584—22no—
52C2×#10596831C2311yescharacteristic
53C2×#10596831C2311yescharacteristic
54C8×D73—22no—
55C4⋊Dic73—22no—
56C4⋊Dic73C2312yes—
57#11924007—22no—
58#11924007D411yescharacteristic
59C22⋊Dic73D411yescharacteristic
60#11924005—22no—
61#11924005—22no—
62#11924005—22no—
63#11924005—22no—
64#11924005D411yescharacteristic
65C4×Dic73—22no—
66C4×Dic73C2311yescharacteristic
67C2×Q8×C73—22no—
68C2×Q8×C73—24no—
69C2×Q8×C73—42no—
70C2×Q8×C73C2312yes—
71C2×Q8×C73C2312yes—
72C22×C4×C73—22no—
73C22×C4×C73C2311yescharacteristic
74Q16×C73—24no—
75Q16×C73—22no—
76Q16×C73D414yescomplemented
77C2×C8×C73—22no—
78C2×C8×C73C2311yescharacteristic
79C2×C8×C73C2311yescharacteristic
80C23×C73C2×D411yescharacteristic
81C22×D73—22no—
82C22×D73C2×D411yescharacteristic
83Q8×C73—22no—
84Q8×C73—22no—
85Q8×C73—22no—
86Q8×C73—44no—
87Q8×C73C2×D414yes—
88C2×C4×C73—22no—
89C2×C4×C73—21no—
90C2×C4×C73—21no—
91C2×C4×C73—22no—
92C2×C4×C73—44no—
93C2×C4×C73C2×D411yescharacteristic
94C2×C4×C73C2411yescharacteristic
95C22⋊D73—22no—
96C22⋊D73—44no—
97C2×Dic73—22no—
98C2×Dic73C2×D411yescharacteristic
99C2×Dic73C2×D411yescharacteristic
100C2×Dic73C2×D411yescharacteristic
101D292—22no—
102D292—22no—
103D292—44no—
104C4×D73—21no—
105C4×D73—21no—
106C4×D73—44no—
107C8×C73—21no—
108C8×C73C2×D412yes—
109#10596831—21no—
110#10596831—21no—
111C22×C73—21no—
112C22×C73—21no—
113C22×C73#13512yescomplemented
114C22×C73C22×D411yescharacteristic
115C2×D73—21no—
116C2×D73—21no—
117C2×D73—21no—
118C2×D73—42no—
119C2×D73—42no—
120C2×D73—42no—
121C4×C73—24no—
122C4×C73—21no—
123C4×C73—42no—
124C4×C73C22×D411yescharacteristic
125C4×C73H(5,𝔽2)11yescharacteristic
126Dic73—21no—
127Dic73—21no—
128Dic73—21no—
129Dic73—42no—
130C2×C73—22no—
131C2×C73D4211yescharacteristic
132C2×C73C2×#13511yescharacteristic
133C2×C73#57811yescharacteristic
134D73—41no—
135D73—82no—
136#3285—731nomaximal, Sylow
137C73#328511yescharacteristic, complemented, Sylow
138C2×#135—731no—
139C22×Q16D7311yescharacteristic, complemented
140#548—732no—
141#495—731no—
142#467—731no—
143#466—731no—
144#464—732no—
145#452—732no—
146#448—732no—
147C4×Q16—731no—
148C8×D4—731no—
149C2×#41—732no—
150C22×Q8C2×D7312yes—
151#135—1464no—
152C2×Q16—24no—
153C2×Q16C2×D7312yes—
154C2×Q16C2×D7311yescharacteristic
155C2×Q16C2×D7311yescharacteristic
156C2×SD16—732no—
157C2×SD16—732no—
158C2×D8—731no—
159C22×C8—731no—
160C22×C8C2×D7311yescharacteristic
161#124—732no—
162#124—1462no—
163C22⋊Q8—732no—
164C22⋊Q8—1462no—
165#121—732no—
166#121—1462no—
167C4×Q8—732no—
168C4×D4—731no—
169C4×D4—1462no—
170#107—731no—
171C4⋊C8—731no—
172#103—732no—
173#103—732no—
174#102—732no—
175C22⋊C8—731no—
176C22⋊C8—731no—
177C4×C8—731no—
178#41—2922no—
179#41—1464no—
180C2×Q8—22no—
181C2×Q8—24no—
182C2×Q8—42no—
183C2×Q8C22×D7312yes—
184C2×Q8C22×D7312yes—
185C2×D4—731no—
186C2×D4—732no—
187C2×D4—1462no—
188C2×D4—1462no—
189C22×C4—22no—
190C22×C4—731no—
191C22×C4—1462no—
192C22×C4C22×D7311yescharacteristic
193Q16—24no—
194Q16—22no—
195Q16C22⋊D7314yescomplemented
196SD16—2922no—
197SD16—1464no—
198D8—1462no—
199C2×C8—22no—
200C2×C8—731no—
201C2×C8—731no—
202C2×C8—1462no—
203C2×C8C22×D7311yescharacteristic
204C2×C8C22×D7311yescharacteristic
205C4⋊C4—731no—
206C4⋊C4—732no—
207C4⋊C4—1462no—
208C4⋊C4—1462no—
209C22⋊C4—731no—
210C22⋊C4—731no—
211C22⋊C4—1462no—
212C22⋊C4—1462no—
213C22⋊C4—1462no—
214C22⋊C4—1462no—
215C42—731no—
216C42—1462no—
217C23—731no—
218C23—1462no—
219C23D4×D7311yescharacteristic
220Q8—22no—
221Q8—22no—
222Q8—22no—
223Q8—44no—
224Q8C2×C22⋊D7314yes—
225D4—2924no—
226D4—2924no—
227D4—1462no—
228D4—1462no—
229D4—1462no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—44no—
235C2×C4—2924no—
236C2×C4—731no—
237C2×C4—731no—
238C2×C4—731no—
239C2×C4—1462no—
240C2×C4—1461no—
241C2×C4—1461no—
242C2×C4D4×D7311yescharacteristic
243C2×C4C23×D7311yescharacteristic
244C8—21no—
245C8—1461no—
246C8—1461no—
247C8C2×C22⋊D7312yes—
248C22—21no—
249C22—21no—
250C22—2922no—
251C22—2922no—
252C22—2922no—
253C22—1461no—
254C22—1461no—
255C22—1461no—
256C22#1455661412yescomplemented
257C22C2×D4×D7311yescharacteristic
258C4—21no—
259C4—24no—
260C4—42no—
261C4—2922no—
262C4—1461no—
263C4—1461no—
264C4—1461no—
265C4C22×C22⋊D7311yescharacteristic
266C4#1455663611yescharacteristic
267C2—22no—
268C2—2921no—
269C2—5842no—
270C2D4×C22⋊D7311yescharacteristic
271C2C2×#1455661411yescharacteristic
272C2#1798940011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC22×Q16×C73C2
socleC22×C73C22×D4
hypercenterC22×Q16D73
hypocenterC73#3285
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
1. C2×#14556614C2semidirect
2. #17989248C2semidirect
3. #17988972C2semidirect
4. #17988825C2semidirect
5. #17988823C2semidirect
6. #17988811C2semidirect
7. #17988748C2semidirect
8. #17988726C2semidirect
9. Q16×Dic73C2semidirect
10. C8×C22⋊D73C2semidirect
11. C22×Q16×C73C2semidirect
76. Q16×C73D4semidirect
113. C22×C73#135semidirect
137. C73#3285semidirect
139. C22×Q16D73semidirect
195. Q16C22⋊D73semidirect
256. C22#14556614semidirect