Finite Group Databasebeta

← #22619792

Subgroups — #22619792

Order 9344.

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

normal subgroups only

This group has 376 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
1#17989215C211yesmaximal, characteristic, complemented
2#17989068C211yesmaximal, characteristic
3#17988893C212yesmaximal, complemented
4#17988890C212yesmaximal, complemented
5#17988876C212yesmaximal, complemented
6#17988871C212yesmaximal, complemented
7C2×#14556522C211yesmaximal, characteristic, complemented
8#17988615C211yesmaximal, characteristic, complemented
9#17988589C211yesmaximal, characteristic
10#17988581C211yesmaximal, characteristic
11#428×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C22×#10596831C2211yescharacteristic
14#14556591—21no—
15#14556590C2212yes—
16#14556583—21no—
17#14556582C2212yes—
18#14556568—22no—
19#14556556C2212yes—
20#14556553C2212yes—
21C4×C22⋊D73—22no—
22#14556550C2211yescharacteristic
23#14556549—21no—
24C2×C4⋊Dic73C2211yescharacteristic
25C4⋊C4×D73—21no—
26#14556522C2212yes—
27#14556522C2212yes—
28#14556520C2212yes—
29#14556520C2212yes—
30#14556516C2212yes—
31#14556514C2211yescharacteristic
32#14556514C2211yescharacteristic
33#14556513C2212yes—
34#14556511C2211yescharacteristic
35#14556511C2211yescharacteristic
36C2×M16×C73C2211yescharacteristic
37#117×C73C2211yescharacteristic
38C2×C4⋊C4×C73C2211yescharacteristic
39#107×C73C2212yes—
40#106×C73C2212yes—
41#11924028—22no—
42#11924028Q814yescomplemented
43C2×Dic146—22no—
44C2×Dic146C2311yescharacteristic
45C2×D292C2311yescharacteristic
46C2×C22⋊D73—21no—
47C22×Dic73—21no—
48C2×C4×D73—21no—
49C2×C4×D73—22no—
50C2×#10596831—22no—
51C2×#10596831C2311yescharacteristic
52C2×#10596831C2311yescharacteristic
53C4⋊Dic73—21no—
54C4⋊Dic73—22no—
55C4⋊Dic73D411yescharacteristic
56C4⋊Dic73D411yescharacteristic
57C4⋊Dic73C2312yes—
58#11924007—22no—
59#11924007—22no—
60#11924007—22no—
61C22⋊Dic73D412yes—
62#11924005—22no—
63C4×Dic73—22no—
64C4×Dic73C2312yes—
65C22×C4×C73—21no—
66C22×C4×C73C2311yescharacteristic
67M16×C73—22no—
68C2×C8×C73C2312yes—
69C4⋊C4×C73—21no—
70C4⋊C4×C73C2311yescharacteristic
71C4⋊C4×C73C2312yes—
72C4⋊C4×C73C2311yescharacteristic
73C22⋊C4×C73—21no—
74C42×C73—21no—
75C23×C73C2×D411yescharacteristic
76C22×D73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—81no—
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2×Q812yes—
83C2×C4×C73#4112yes—
84C2×C4×C73C2411yescharacteristic
85C22⋊D73—24no—
86C2×Dic73—21no—
87C2×Dic73—22no—
88C2×Dic73—81no—
89C2×Dic73C2×D412yes—
90C2×Dic73C2×D412yes—
91D292—21no—
92D292C2×Q812yes—
93C4×D73—24no—
94C4×D73—82no—
95Dic146—21no—
96Dic146—82no—
97Dic146C2×Q812yes—
98C8×C73—22no—
99#10596831—21no—
100#10596831—21no—
101C22×C73—21no—
102C22×C73—21no—
103C22×C73C22⋊Q812yes—
104C22×C73C22×D411yescharacteristic
105C2×D73—22no—
106C2×D73—41no—
107C2×D73—41no—
108C4×C73—41no—
109C4×C73—42no—
110C4×C73—41no—
111C4×C73C22⋊Q812yes—
112C4×C73C22×Q811yescharacteristic
113C4×C73C2×#4111yescharacteristic
114Dic73—22no—
115Dic73—22no—
116Dic73—22no—
117Dic73—42no—
118C2×C73—22no—
119C2×C73C2×C22⋊Q811yescharacteristic
120C2×C73#57711yescharacteristic
121C2×C73#57711yescharacteristic
122D73—42no—
123#3084—731nomaximal, Sylow
124C73#308411yescharacteristic, complemented, Sylow
125#544—731no—
126#520—731no—
127#479—732no—
128#478—732no—
129#476—732no—
130#475—732no—
131#428D7311yescharacteristic, complemented
132C2×#106—731no—
133#424—731no—
134#417—731no—
135#416—731no—
136C2×#41—731no—
137C2×M16C2×D7311yescharacteristic
138C22×C8—731no—
139C4⋊Q8—732no—
140C4⋊Q8—1461no—
141#125—732no—
142#125—1461no—
143C22⋊Q8—1462no—
144C4×Q8—732no—
145C4×D4—732no—
146C4×D4—1462no—
147#117—731no—
148#117—1461no—
149#117C2×D7311yescharacteristic
150C2×C4⋊C4—731no—
151C2×C4⋊C4—1461no—
152C2×C4⋊C4C2×D7311yescharacteristic
153#107C2×D7312yes—
154#106—732no—
155#106—732no—
156#106C2×D7312yes—
157C4⋊C8—732no—
158C4⋊C8—732no—
159#103—732no—
160#103—731no—
161#103—731no—
162#102—732no—
163#102—731no—
164#102—731no—
165#41—734no—
166#41—1462no—
167C2×Q8—731no—
168C2×Q8—1462no—
169C2×D4—731no—
170C2×D4—1461no—
171C22×C4—21no—
172C22×C4—1462no—
173C22×C4—1461no—
174C22×C4—1461no—
175C22×C4C22×D7311yescharacteristic
176M16—22no—
177C2×C8—731no—
178C2×C8—731no—
179C2×C8—1462no—
180C2×C8C22×D7312yes—
181C4⋊C4—21no—
182C4⋊C4—731no—
183C4⋊C4—731no—
184C4⋊C4—732no—
185C4⋊C4—1462no—
186C4⋊C4—1462no—
187C4⋊C4—1462no—
188C4⋊C4—1462no—
189C4⋊C4—1461no—
190C4⋊C4C22×D7311yescharacteristic
191C4⋊C4C22×D7311yescharacteristic
192C4⋊C4C22×D7312yes—
193C22⋊C4—21no—
194C22⋊C4—732no—
195C22⋊C4—1462no—
196C42—21no—
197C42—732no—
198C42—1462no—
199C23—1461no—
200C23D4×D7311yescharacteristic
201Q8—5842no—
202Q8—732no—
203Q8—1461no—
204D4—732no—
205D4—1464no—
206D4—1461no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—81no—
211C2×C4—5842no—
212C2×C4—5841no—
213C2×C4—732no—
214C2×C4—732no—
215C2×C4—1462no—
216C2×C4—1461no—
217C2×C4—1464no—
218C2×C4D4×D7311yescharacteristic
219C2×C4Q8×D7312yes—
220C2×C4#1192402812yes—
221C2×C4C23×D7311yescharacteristic
222C8—22no—
223C8—1461no—
224C8—1461no—
225C22—21no—
226C22—21no—
227C22—2921no—
228C22—2921no—
229C22—1462no—
230C22#1455656912yes—
231C22C2×D4×D7311yescharacteristic
232C4—41no—
233C4—42no—
234C4—41no—
235C4—2922no—
236C4—1462no—
237C4—1462no—
238C4—1462no—
239C4#1455656912yes—
240C4C2×Q8×D7311yescharacteristic
241C4C2×#1192402811yescharacteristic
242C2—22no—
243C2—2922no—
244C2C2×#1455656911yescharacteristic
245C2#1798939611yescharacteristic
246C2#1798939711yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#428×C73C2
socleC22×C73C22×D4
hypercenter#428D73
hypocenterC73#3084
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #17989215C2semidirect
3. #17988893C2semidirect
4. #17988890C2semidirect
5. #17988876C2semidirect
6. #17988871C2semidirect
7. C2×#14556522C2semidirect
8. #17988615C2semidirect
11. #428×C73C2semidirect
42. #11924028Q8semidirect
124. C73#3084semidirect
131. #428D73semidirect