Finite Group Databasebeta

← #22620550

Subgroups — #22620550

Order 9344.

362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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#17989211C212yesmaximal, complemented
2#17988971C211yesmaximal, characteristic, complemented
3#17988949C212yesmaximal, complemented
4#17988846C211yesmaximal, characteristic, complemented
5#17988841C211yesmaximal, characteristic
6#17988817C212yesmaximal, complemented
7#17988698C211yesmaximal, characteristic, complemented
8#17988693C211yesmaximal, characteristic, complemented
9#17988674C212yesmaximal, complemented
10#17988541C211yesmaximal, characteristic, complemented
11#498×C73C211yesmaximal, characteristic, complemented
12C2×Dic292C2211yescharacteristic
13C2×#11924017C2212yes—
14C2×D584C2211yescharacteristic
15C2×#11924011C2211yescharacteristic
16C2×C8×D73C2211yescharacteristic
17#14556586—22no—
18#14556580—22no—
19#14556579C2212yes—
20#14556576—22no—
21#14556571C2212yes—
22#14556567—22no—
23#14556566C2212yes—
24#14556556C2212yes—
25#14556553C2212yes—
26#14556548C2211yescharacteristic
27#14556514C2212yes—
28#14556514C2212yes—
29#14556511C2212yes—
30#14556511C2212yes—
31#14556502C2211yescharacteristic
32#14556501C2211yescharacteristic
33C8×Dic73C2211yescharacteristic
34C4⋊Q8×C73C2212yes—
35#106×C73C2212yes—
36#106×C73C2211yescharacteristic
37#106×C73C2211yescharacteristic
38C4×C8×C73C2211yescharacteristic
39C2×Dic146C2312yes—
40C2×D292—22no—
41C2×D292C2312yes—
42C2×C4×D73—22no—
43C2×C4×D73C2311yescharacteristic
44Dic292—22no—
45#11924017—24no—
46D584—22no—
47#11924011—22no—
48C2×#10596831C2311yescharacteristic
49C2×#10596831C2311yescharacteristic
50C8×D73—22no—
51C4⋊Dic73—22no—
52#11924007—22no—
53#11924007D412yes—
54#11924005—22no—
55#11924005—22no—
56#11924005—22no—
57#11924005—22no—
58#11924005—22no—
59#11924005D412yes—
60C4×Dic73—22no—
61C4×Dic73C2311yescharacteristic
62C2×Q8×C73—22no—
63C2×C8×C73C2311yescharacteristic
64C2×C8×C73C2311yescharacteristic
65C4⋊C4×C73—22no—
66C4⋊C4×C73C2312yes—
67C4⋊C4×C73C2312yes—
68C42×C73C2311yescharacteristic
69C22×D73—22no—
70C22×D73C2×D411yescharacteristic
71Q8×C73—82no—
72C2×C4×C73—22no—
73C2×C4×C73—22no—
74C2×C4×C73C2×D412yes—
75C2×C4×C73C2411yescharacteristic
76C2×Dic73—22no—
77C2×Dic73C2×D412yes—
78C2×Dic73C2×D411yescharacteristic
79D292—22no—
80D292—22no—
81D292—82no—
82C4×D73—21no—
83C4×D73—21no—
84C4×D73—82no—
85Dic146—22no—
86Dic146—22no—
87C8×C73#4112yes—
88C8×C73#4112yes—
89#10596831—21no—
90#10596831—21no—
91C22×C73C22×D411yescharacteristic
92C2×D73—21no—
93C2×D73—22no—
94C2×D73—42no—
95C2×D73—42no—
96C2×D73—42no—
97C4×C73—22no—
98C4×C73—42no—
99C4×C73—42no—
100C4×C73C2×#4111yescharacteristic
101C4×C73C2×#4111yescharacteristic
102Dic73—21no—
103Dic73—22no—
104Dic73—42no—
105C2×C73#53211yescharacteristic
106C2×C73#57712yes—
107D73—41no—
108D73—82no—
109#3173—731nomaximal, Sylow
110C73#317311yescharacteristic, complemented, Sylow
111#542—732no—
112#498D7311yescharacteristic, complemented
113#495—731no—
114#489—732no—
115#470—731no—
116#469—731no—
117#465—732no—
118#442—731no—
119#441—731no—
120C4×SD16—732no—
121#405—731no—
122C2×Q16—731no—
123C2×SD16—732no—
124C2×D8—731no—
125C2×M16—731no—
126C22×C8—731no—
127C4⋊Q8C2×D7312yes—
128#126—1462no—
129#124—732no—
130#124—1462no—
131#123—1462no—
132C22⋊Q8—732no—
133C22⋊Q8—1462no—
134#121—732no—
135C4×Q8—732no—
136C4×D4—732no—
137#117—731no—
138#106C2×D7312yes—
139#106C2×D7311yescharacteristic
140#106C2×D7311yescharacteristic
141#103—732no—
142#103—732no—
143#102—732no—
144#102—732no—
145#97—731no—
146#97—731no—
147C4×C8—731no—
148C4×C8C2×D7311yescharacteristic
149C2×Q8—22no—
150C2×Q8—732no—
151C2×D4—732no—
152C2×D4—1462no—
153C22×C4—731no—
154C22×C4—1462no—
155Q16—1462no—
156SD16—1464no—
157D8—1462no—
158M16—1462no—
159C2×C8—731no—
160C2×C8—731no—
161C2×C8—1462no—
162C2×C8C22×D7311yescharacteristic
163C2×C8C22×D7311yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—732no—
166C4⋊C4—1462no—
167C4⋊C4—1462no—
168C4⋊C4C22×D7312yes—
169C4⋊C4C22×D7312yes—
170C22⋊C4—732no—
171C22⋊C4—1462no—
172C22⋊C4—1462no—
173C22⋊C4—1462no—
174C22⋊C4—1462no—
175C22⋊C4—1462no—
176C42—731no—
177C42—1462no—
178C42C22×D7311yescharacteristic
179C23—731no—
180C23—1462no—
181Q8—82no—
182Q8—1462no—
183Q8—1462no—
184D4—5842no—
185D4—1462no—
186D4—1462no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—5842no—
190C2×C4—732no—
191C2×C4—731no—
192C2×C4—1462no—
193C2×C4—1461no—
194C2×C4—1461no—
195C2×C4D4×D7312yes—
196C2×C4C23×D7311yescharacteristic
197C8—1461no—
198C8—1461no—
199C8#1192402912yes—
200C8#1192402912yes—
201C22—2922no—
202C22—2922no—
203C22—2922no—
204C22—1462no—
205C22—1461no—
206C22C2×D4×D7311yescharacteristic
207C4—22no—
208C4—42no—
209C4—42no—
210C4—2922no—
211C4—1462no—
212C4—1461no—
213C4C2×#1192402911yescharacteristic
214C4C2×#1192402911yescharacteristic
215C2—2921no—
216C2—5842no—
217C2#1798913811yescharacteristic
218C2#1798939312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#498×C73C2
socleC22×C73C22×D4
hypercenter#498D73
hypocenterC73#3173
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #17989211C2semidirect
2. #17988971C2semidirect
3. #17988949C2semidirect
4. #17988846C2semidirect
6. #17988817C2semidirect
7. #17988698C2semidirect
8. #17988693C2semidirect
9. #17988674C2semidirect
10. #17988541C2semidirect
11. #498×C73C2semidirect
110. C73#3173semidirect
112. #498D73semidirect