Finite Group Databasebeta

← #22619778

Subgroups — #22619778

Order 9344.

376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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#17989067C211yesmaximal, characteristic
2#17988891C212yesmaximal, complemented
3#17988884C212yesmaximal, complemented
4#17988879C212yesmaximal, complemented
5#17988864C212yesmaximal, complemented
6#17988630C211yesmaximal, characteristic, complemented
7C2×#14556524C211yesmaximal, characteristic, complemented
8#17988614C211yesmaximal, characteristic, complemented
9#17988586C211yesmaximal, characteristic
10#17988581C211yesmaximal, characteristic
11#544×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C2×#11924012C2211yescharacteristic
14C22×#10596831C2211yescharacteristic
15C4×Dic146C2212yes—
16C4×D292C2212yes—
17#14556551—22no—
18#14556549—21no—
19C2×C4⋊Dic73C2211yescharacteristic
20C4⋊C4×D73—21no—
21#14556524C2212yes—
22#14556524C2212yes—
23#14556524C2212yes—
24#14556522C2212yes—
25C4⋊#10596831C2212yes—
26C4⋊#10596831C2212yes—
27#14556514C2211yescharacteristic
28#14556514C2212yes—
29#14556514C2211yescharacteristic
30#14556511C2211yescharacteristic
31#14556511C2212yes—
32#14556511C2211yescharacteristic
33C4⋊Q8×C73—21no—
34C4⋊Q8×C73C2212yes—
35#125×C73—21no—
36#125×C73C2212yes—
37C22⋊Q8×C73—22no—
38#117×C73C2211yescharacteristic
39#117×C73C2211yescharacteristic
40C2×C4⋊C4×C73C2211yescharacteristic
41#11924028—22no—
42#11924028Q814yescomplemented
43C2×Dic146C2311yescharacteristic
44C2×D292C2311yescharacteristic
45C2×C22⋊D73—21no—
46C22×Dic73—21no—
47C2×C4×D73—21no—
48C2×C4×D73—22no—
49#11924012—22no—
50C2×#10596831—22no—
51C2×#10596831C2312yes—
52C2×#10596831C2311yescharacteristic
53C2×#10596831C2311yescharacteristic
54C4⋊Dic73—21no—
55C4⋊Dic73C2312yes—
56#11924007—22no—
57#11924005—22no—
58C4×Dic73—22no—
59C2×Q8×C73—22no—
60C22×C4×C73—21no—
61C22×C4×C73C2311yescharacteristic
62C4⋊C4×C73—21no—
63C4⋊C4×C73—22no—
64C4⋊C4×C73—22no—
65C4⋊C4×C73—22no—
66C4⋊C4×C73D411yescharacteristic
67C4⋊C4×C73D411yescharacteristic
68C4⋊C4×C73C2312yes—
69C4⋊C4×C73C2311yescharacteristic
70C4⋊C4×C73C2311yescharacteristic
71C22⋊C4×C73—21no—
72C22⋊C4×C73D412yes—
73C42×C73—21no—
74C42×C73C2312yes—
75C23×C73C2×D411yescharacteristic
76C22×D73—21no—
77Q8×C73—82no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—22no—
81C2×C4×C73—81no—
82C2×C4×C73C2×D412yes—
83C2×C4×C73C2×D412yes—
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×Q812yes—
86C2×C4×C73#4112yes—
87C2×C4×C73C2411yescharacteristic
88C22⋊D73—24no—
89C2×Dic73—21no—
90C2×Dic73—22no—
91C2×Dic73—81no—
92D292—21no—
93D292C2×Q812yes—
94C4×D73—24no—
95C4×D73—82no—
96Dic146—21no—
97Dic146C2×Q812yes—
98#10596831—21no—
99#10596831—21no—
100#10596831—22no—
101C22×C73—21no—
102C22×C73—21no—
103C22×C73C22⋊Q812yes—
104C22×C73C22×D411yescharacteristic
105C2×D73—22no—
106C2×D73—41no—
107C2×D73—41no—
108C4×C73—22no—
109C4×C73—22no—
110C4×C73—42no—
111C4×C73—41no—
112C4×C73—41no—
113C4×C73C22⋊Q812yes—
114C4×C73C22×Q811yescharacteristic
115C4×C73C2×#4111yescharacteristic
116Dic73—22no—
117Dic73—42no—
118C2×C73—22no—
119C2×C73C2×C22⋊Q811yescharacteristic
120C2×C73#57611yescharacteristic
121C2×C73#57811yescharacteristic
122D73—42no—
123#3083—731nomaximal, Sylow
124C73#308311yescharacteristic, complemented, Sylow
125#544D7311yescharacteristic, complemented
126#520—731no—
127#479—732no—
128#478—732no—
129#477—732no—
130#474—732no—
131#428—731no—
132C2×#107—731no—
133#424—731no—
134#417—731no—
135#416—731no—
136C2×#41—731no—
137C2×M16—731no—
138C22×C8—731no—
139C4⋊Q8—21no—
140C4⋊Q8C2×D7312yes—
141#125—21no—
142#125C2×D7312yes—
143C22⋊Q8—22no—
144C4×Q8—732no—
145C4×D4—732no—
146C4×D4—1462no—
147#117—1461no—
148#117C2×D7311yescharacteristic
149#117C2×D7311yescharacteristic
150C2×C4⋊C4—731no—
151C2×C4⋊C4—1461no—
152C2×C4⋊C4C2×D7311yescharacteristic
153#107—732no—
154#107—732no—
155#107—732no—
156#106—732no—
157C4⋊C8—732no—
158C4⋊C8—732no—
159#103—731no—
160#103—731no—
161#103—732no—
162#102—731no—
163#102—731no—
164#102—732no—
165#41—734no—
166#41—1462no—
167C2×Q8—22no—
168C2×Q8—731no—
169C2×D4—731no—
170C2×D4—1461no—
171C22×C4—21no—
172C22×C4—1461no—
173C22×C4—1462no—
174C22×C4—1461no—
175C22×C4C22×D7311yescharacteristic
176M16—1462no—
177C2×C8—732no—
178C2×C8—731no—
179C2×C8—731no—
180C2×C8—1462no—
181C4⋊C4—21no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—732no—
186C4⋊C4—1462no—
187C4⋊C4—1461no—
188C4⋊C4C22⋊D7311yescharacteristic
189C4⋊C4C22⋊D7311yescharacteristic
190C4⋊C4C22×D7311yescharacteristic
191C4⋊C4C22×D7312yes—
192C4⋊C4C22×D7311yescharacteristic
193C22⋊C4—21no—
194C22⋊C4—1462no—
195C22⋊C4C22⋊D7312yes—
196C42—21no—
197C42—1462no—
198C42C22×D7312yes—
199C23—1461no—
200C23C2×C22⋊D7311yescharacteristic
201Q8—82no—
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—1462no—
214C2×C4—1461no—
215C2×C4—1464no—
216C2×C4C2×C22⋊D7312yes—
217C2×C4C2×C22⋊D7312yes—
218C2×C4C2×C22⋊D7311yescharacteristic
219C2×C4Q8×D7312yes—
220C2×C4#1192402912yes—
221C2×C4C23×D7311yescharacteristic
222C8—1461no—
223C8—1461no—
224C8—1462no—
225C22—21no—
226C22—21no—
227C22—2921no—
228C22—2921no—
229C22—1462no—
230C22#1455656712yes—
231C22C22×C22⋊D7311yescharacteristic
232C4—22no—
233C4—22no—
234C4—42no—
235C4—41no—
236C4—41no—
237C4—2922no—
238C4—1462no—
239C4#1455656712yes—
240C4C2×Q8×D7311yescharacteristic
241C4C2×#1192402911yescharacteristic
242C2—22no—
243C2—2922no—
244C2C2×#1455656711yescharacteristic
245C2#1798939011yescharacteristic
246C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#544×C73C2
socleC22×C73C22×D4
hypercenter#544D73
hypocenterC73#3083
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
2. #17988891C2semidirect
3. #17988884C2semidirect
4. #17988879C2semidirect
5. #17988864C2semidirect
6. #17988630C2semidirect
7. C2×#14556524C2semidirect
8. #17988614C2semidirect
11. #544×C73C2semidirect
42. #11924028Q8semidirect
124. C73#3083semidirect
125. #544D73semidirect