Finite Group Databasebeta

← #22620566

Subgroups — #22620566

Order 9344.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#17989202C212yesmaximal, complemented
2#17988991C211yesmaximal, characteristic, complemented
3#17988970C211yesmaximal, characteristic, complemented
4#17988945C212yesmaximal, complemented
5#17988832C212yesmaximal, complemented
6#17988829C211yesmaximal, characteristic, complemented
7#17988820C211yesmaximal, characteristic
8#17988687C212yesmaximal, complemented
9C4×Dic292C211yesmaximal, characteristic, complemented
10#17988541C211yesmaximal, characteristic, complemented
11C4×D8×C73C211yesmaximal, characteristic, complemented
12C2×Dic292C2211yescharacteristic
13C2×#11924016C2212yes—
14C2×#11924011C2211yescharacteristic
15C2×C8×D73C2211yescharacteristic
16#14556590C2212yes—
17#14556584—22no—
18#14556578C2212yes—
19#14556577—22no—
20#14556574—22no—
21#14556571C2212yes—
22#14556570—22no—
23#14556562C2212yes—
24C4×Dic146C2212yes—
25#14556548C2211yescharacteristic
26#14556525C2211yescharacteristic
27#14556524C2212yes—
28#14556516C2212yes—
29#14556514C2212yes—
30#14556512C2212yes—
31#14556502C2211yescharacteristic
32#14556501C2211yescharacteristic
33C8×Dic73C2211yescharacteristic
34C2×D8×C73C2211yescharacteristic
35C4×D4×C73C2212yes—
36#107×C73C2211yescharacteristic
37#102×C73C2212yes—
38C4×C8×C73C2211yescharacteristic
39C2×Dic146—22no—
40C2×Dic146C2312yes—
41C2×C22⋊D73—22no—
42C2×C4×D73C2311yescharacteristic
43Dic292—22no—
44#11924016—24no—
45#11924011—22no—
46C2×#10596831C2311yescharacteristic
47C2×#10596831C2311yescharacteristic
48C8×D73—22no—
49C4⋊Dic73—22no—
50C4⋊Dic73C2312yes—
51#11924007—22no—
52#11924007—22no—
53#11924007D411yescharacteristic
54#11924007D411yescharacteristic
55C22⋊Dic73—22no—
56C22⋊Dic73—22no—
57C22⋊Dic73—22no—
58#11924005—22no—
59#11924005D411yescharacteristic
60#11924005D411yescharacteristic
61C4×Dic73—22no—
62C4×Dic73C2311yescharacteristic
63C2×D4×C73C2312yes—
64C22×C4×C73—22no—
65D8×C73—22no—
66C2×C8×C73C2311yescharacteristic
67C2×C8×C73C2311yescharacteristic
68C4⋊C4×C73C2312yes—
69C22⋊C4×C73—22no—
70C42×C73C2311yescharacteristic
71C23×C73—22no—
72C22×D73C2×D411yescharacteristic
73D4×C73—22no—
74D4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—82no—
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2411yescharacteristic
80C22⋊D73—82no—
81C2×Dic73—22no—
82C2×Dic73—22no—
83C2×Dic73C2×D411yescharacteristic
84C2×Dic73C2×D411yescharacteristic
85C2×Dic73C2×D411yescharacteristic
86C4×D73—21no—
87C4×D73—21no—
88Dic146—22no—
89Dic146—22no—
90Dic146—82no—
91C8×C73—21no—
92C8×C73#4112yes—
93#10596831—21no—
94#10596831#4112yes—
95C22×C73—42no—
96C22×C73—42no—
97C22×C73—42no—
98C22×C73C22×D411yescharacteristic
99C2×D73—21no—
100C2×D73—21no—
101C2×D73—21no—
102C4×C73—21no—
103C4×C73—21no—
104C4×C73—42no—
105C4×C73C2×#4111yescharacteristic
106C4×C73C2×#4111yescharacteristic
107Dic73—21no—
108Dic73—21no—
109Dic73—21no—
110Dic73—42no—
111Dic73—42no—
112C2×C73—82no—
113C2×C73#53211yescharacteristic
114C2×C73#57611yescharacteristic
115C2×C73#57811yescharacteristic
116D73—41no—
117#3175—731nomaximal, Sylow
118C73#317511yescharacteristic, complemented, Sylow
119#542—732no—
120#500—731no—
121#495—731no—
122#489—732no—
123#468—732no—
124#467—731no—
125#466—731no—
126#440—732no—
127C4×Q16—731no—
128C4×D8D7311yescharacteristic, complemented
129#405—731no—
130C2×Q16—731no—
131C2×SD16—732no—
132C2×D8C2×D7311yescharacteristic
133C2×M16—731no—
134C22×C8—731no—
135C4⋊Q8—732no—
136#126—1462no—
137#124—732no—
138#124—1462no—
139#123—1462no—
140C22⋊Q8—732no—
141C22⋊Q8—1462no—
142#121—732no—
143C4×Q8—732no—
144C4×D4C2×D7312yes—
145#117—731no—
146#107—731no—
147#107—732no—
148#107C2×D7311yescharacteristic
149#103—732no—
150#103—732no—
151#102—732no—
152#102C2×D7312yes—
153#97—731no—
154#97—731no—
155C4×C8—731no—
156C4×C8C2×D7311yescharacteristic
157C2×Q8—732no—
158C2×Q8—1462no—
159C2×D4—1462no—
160C2×D4C22×D7312yes—
161C22×C4—22no—
162C22×C4—731no—
163Q16—1462no—
164SD16—1464no—
165D8—22no—
166M16—1462no—
167C2×C8—731no—
168C2×C8—731no—
169C2×C8—1462no—
170C2×C8C22×D7311yescharacteristic
171C2×C8C22×D7311yescharacteristic
172C4⋊C4—731no—
173C4⋊C4—731no—
174C4⋊C4—732no—
175C4⋊C4—1462no—
176C4⋊C4—1462no—
177C4⋊C4—1462no—
178C4⋊C4C22×D7312yes—
179C22⋊C4—22no—
180C22⋊C4—731no—
181C22⋊C4—731no—
182C22⋊C4—1462no—
183C22⋊C4—1462no—
184C22⋊C4—1462no—
185C22⋊C4—1462no—
186C42—731no—
187C42—1462no—
188C42C22×D7311yescharacteristic
189C23—22no—
190C23—731no—
191Q8—5842no—
192Q8—1462no—
193Q8—1462no—
194D4—22no—
195D4—22no—
196D4—5842no—
197C2×C4—22no—
198C2×C4—82no—
199C2×C4—731no—
200C2×C4—731no—
201C2×C4—731no—
202C2×C4—1462no—
203C2×C4—1462no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4D4×D7311yescharacteristic
207C2×C4D4×D7311yescharacteristic
208C2×C4C23×D7311yescharacteristic
209C8—21no—
210C8—732no—
211C8—1461no—
212C8#1192402812yes—
213C22—42no—
214C22—42no—
215C22—42no—
216C22—1461no—
217C22—1461no—
218C22—1461no—
219C22C2×D4×D7311yescharacteristic
220C4—21no—
221C4—21no—
222C4—42no—
223C4—2922no—
224C4—2922no—
225C4—1461no—
226C4—1461no—
227C4—1461no—
228C4#41×D7311yescharacteristic
229C4C2×#1192402811yescharacteristic
230C2—82no—
231C2—2921no—
232C2#1798913411yescharacteristic
233C2#1798938811yescharacteristic
234C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×D8×C73C2
socleC22×C73C22×D4
hypercenterC4×D8D73
hypocenterC73#3175
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #17989202C2semidirect
2. #17988991C2semidirect
3. #17988970C2semidirect
4. #17988945C2semidirect
5. #17988832C2semidirect
6. #17988829C2semidirect
8. #17988687C2semidirect
9. C4×Dic292C2semidirect
10. #17988541C2semidirect
11. C4×D8×C73C2semidirect
118. C73#3175semidirect
128. C4×D8D73semidirect