Finite Group Databasebeta

← #22620842

Subgroups — #22620842

Order 9344.

402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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#17989166C212yesmaximal, complemented
2#17988919C212yesmaximal, complemented
3#17988904C212yesmaximal, complemented
4#17988845C211yesmaximal, characteristic, complemented
5#17988814C212yesmaximal, complemented
6#17988750C212yesmaximal, complemented
7#17988729C212yesmaximal, complemented
8#17988555C211yesmaximal, characteristic, complemented
9#469×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2211yescharacteristic
11C2×#11924027C2212yes—
12C2×Dic292C2211yescharacteristic
13C2×#11924016C2212yes—
14C22×#10596831C2211yescharacteristic
15#14556571C2212yes—
16#14556570C2212yes—
17#14556568—22no—
18#14556564—22no—
19#14556563—22no—
20#14556562—22no—
21#14556562C2212yes—
22C4⋊C4×D73C2212yes—
23#14556523C2211yescharacteristic
24#14556522C2212yes—
25#14556516C2212yes—
26#14556514C2212yes—
27#14556512C2212yes—
28#14556503C2212yes—
29#14556503C2212yes—
30C2×D8×C73C2211yescharacteristic
31C2×M16×C73C2211yescharacteristic
32#121×C73C2212yes—
33#106×C73C2211yescharacteristic
34#102×C73C2212yes—
35#11924028—41no—
36#11924028—41no—
37#11924027—42no—
38#11924027—42no—
39C2×Dic146D411yescharacteristic
40C2×Dic146C2312yes—
41C2×D292D411yescharacteristic
42C2×C22⋊D73—22no—
43C2×C22⋊D73—22no—
44C2×C22⋊D73D412yes—
45C22×Dic73—22no—
46C2×C4×D73—22no—
47C2×C4×D73C2312yes—
48Dic292—41no—
49#11924016—42no—
50C2×#10596831—41no—
51C2×#10596831C2312yes—
52C4⋊Dic73—22no—
53C4⋊Dic73C2312yes—
54#11924007—22no—
55#11924007—22no—
56C22⋊Dic73—22no—
57C22⋊Dic73—22no—
58#11924005—22no—
59C2×D4×C73—22no—
60C2×D4×C73C2312yes—
61C22×C4×C73C2311yescharacteristic
62D8×C73—41no—
63M16×C73—41no—
64C2×C8×C73C2311yescharacteristic
65C2×C8×C73C2311yescharacteristic
66C4⋊C4×C73C2312yes—
67C22⋊C4×C73—22no—
68C23×C73—22no—
69C23×C73C2×D411yescharacteristic
70C22×D73C2×D412yes—
71D4×C73—22no—
72D4×C73—22no—
73D4×C73—82no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2411yescharacteristic
79C22⋊D73—42no—
80C22⋊D73—44no—
81C22⋊D73—82no—
82C2×Dic73—22no—
83C2×Dic73—22no—
84C2×Dic73—44no—
85C2×Dic73C2×D412yes—
86D292—41no—
87C4×D73—22no—
88C4×D73—22no—
89C4×D73—82no—
90Dic146—22no—
91Dic146—22no—
92Dic146—41no—
93C8×C73—21no—
94C8×C73—21no—
95#10596831—22no—
96C22×C73—21no—
97C22×C73—22no—
98C22×C73—42no—
99C22×C73—42no—
100C22×C73—42no—
101C22×C73C22×D411yescharacteristic
102C2×D73—22no—
103C2×D73—22no—
104C2×D73—22no—
105C4×C73—21no—
106C4×C73—42no—
107C4×C73H(5,𝔽2)11yescharacteristic
108C4×C73H(5,𝔽2)11yescharacteristic
109Dic73—22no—
110Dic73—42no—
111Dic73—42no—
112C2×C73—41no—
113C2×C73—82no—
114C2×C73#53411yescharacteristic
115C2×C73#57712yes—
116D73—42no—
117#3204—731nomaximal, Sylow
118C73#320411yescharacteristic, complemented, Sylow
119#537—732no—
120#483—732no—
121#481—732no—
122#470—731no—
123#469D7311yescharacteristic, complemented
124#465—732no—
125#452—732no—
126#449—732no—
127#408—731no—
128C2×#41—731no—
129C2×#41—732no—
130C2×Q16—731no—
131C2×SD16—732no—
132C2×D8C2×D7311yescharacteristic
133C2×M16C2×D7311yescharacteristic
134C22×C8—731no—
135C22⋊Q8—732no—
136C22⋊Q8—732no—
137C22⋊Q8—1462no—
138#121—732no—
139#121—1462no—
140#121—1462no—
141#121—1462no—
142#121C2×D7312yes—
143C2×C4⋊C4—732no—
144#106—731no—
145#106—732no—
146#106C2×D7311yescharacteristic
147#103—732no—
148#103—732no—
149#102—732no—
150#102C2×D7312yes—
151C22⋊C8—732no—
152C22⋊C8—732no—
153#41—2921no—
154#41—2921no—
155#41—2922no—
156#41—2922no—
157C2×Q8—731no—
158C2×Q8—732no—
159C2×D4—22no—
160C2×D4—732no—
161C2×D4—731no—
162C2×D4—1462no—
163C2×D4—1462no—
164C2×D4C22×D7312yes—
165C22×C4—732no—
166C22×C4—1462no—
167C22×C4—1462no—
168C22×C4C22×D7311yescharacteristic
169Q16—2921no—
170SD16—2922no—
171D8—41no—
172M16—41no—
173C2×C8—2921no—
174C2×C8—732no—
175C2×C8C22×D7311yescharacteristic
176C2×C8C22×D7311yescharacteristic
177C4⋊C4—732no—
178C4⋊C4—1462no—
179C4⋊C4—1462no—
180C4⋊C4—1462no—
181C4⋊C4C22×D7312yes—
182C22⋊C4—22no—
183C22⋊C4—1462no—
184C22⋊C4—1462no—
185C22⋊C4—1462no—
186C23—22no—
187C23—732no—
188C23D4×D7311yescharacteristic
189Q8—2921no—
190Q8—1462no—
191Q8—1462no—
192D4—22no—
193D4—22no—
194D4—82no—
195D4—2921no—
196D4—2924no—
197D4—2922no—
198D4—5842no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—2924no—
203C2×C4—5842no—
204C2×C4—732no—
205C2×C4—1462no—
206C2×C4—1462no—
207C2×C4—1462no—
208C2×C4—1462no—
209C2×C4D4×D7311yescharacteristic
210C2×C4C23×D7311yescharacteristic
211C8—21no—
212C8—21no—
213C8—1462no—
214C22—22no—
215C22—21no—
216C22—42no—
217C22—42no—
218C22—42no—
219C22—1462no—
220C22—1462no—
221C22—1462no—
222C22C2×D4×D7311yescharacteristic
223C4—21no—
224C4—42no—
225C4—2922no—
226C4—2922no—
227C4—1462no—
228C4#1455663611yescharacteristic
229C4#1455663711yescharacteristic
230C2—41no—
231C2—82no—
232C2—2922no—
233C2#1798914511yescharacteristic
234C2#1798939712yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#469×C73C2
socleC22×C73C22×D4
hypercenter#469D73
hypocenterC73#3204
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #17989166C2semidirect
2. #17988919C2semidirect
3. #17988904C2semidirect
4. #17988845C2semidirect
5. #17988814C2semidirect
6. #17988750C2semidirect
7. #17988729C2semidirect
8. #17988555C2semidirect
9. #469×C73C2semidirect
118. C73#3204semidirect
123. #469D73semidirect