Finite Group Databasebeta

← #22619786

Subgroups — #22619786

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#17989218C211yesmaximal, characteristic, complemented
2#17989070C211yesmaximal, characteristic
3#17988892C212yesmaximal, complemented
4#17988889C212yesmaximal, complemented
5#17988880C212yesmaximal, complemented
6#17988865C212yesmaximal, complemented
7#17988629C211yesmaximal, characteristic, complemented
8C2×#14556524C211yesmaximal, characteristic, complemented
9#17988615C211yesmaximal, characteristic, complemented
10#17988583C211yesmaximal, characteristic
11#417×C73C211yesmaximal, characteristic
12C22×#10596831C2211yescharacteristic
13#14556590—21no—
14#14556590C2212yes—
15#14556582—21no—
16#14556582C2212yes—
17#14556570—22no—
18Q8×Dic73C2212yes—
19D4×Dic73—22no—
20D4×Dic73C2212yes—
21#14556550—21no—
22#14556550C2211yescharacteristic
23#14556550C2211yescharacteristic
24C2×C4⋊Dic73—21no—
25C2×C4⋊Dic73C2211yescharacteristic
26#14556525C2212yes—
27#14556524C2212yes—
28#14556524C2212yes—
29#14556523C2212yes—
30#14556520C2212yes—
31#14556520C2212yes—
32#14556515C2211yescharacteristic
33#14556515C2211yescharacteristic
34#14556512C2211yescharacteristic
35#14556512C2211yescharacteristic
36C2×#41×C73C2211yescharacteristic
37C2×M16×C73C2211yescharacteristic
38C2×C4⋊C4×C73C2211yescharacteristic
39#103×C73C2212yes—
40#102×C73C2212yes—
41C2×Dic146—22no—
42C22×Dic73—21no—
43C22×Dic73—22no—
44C2×#10596831—22no—
45C2×#10596831C2311yescharacteristic
46C2×#10596831C2311yescharacteristic
47C4⋊Dic73—21no—
48C4⋊Dic73—22no—
49C4⋊Dic73—22no—
50C4⋊Dic73D411yescharacteristic
51C4⋊Dic73D411yescharacteristic
52C4⋊Dic73C2311yescharacteristic
53C4⋊Dic73C2311yescharacteristic
54C4⋊Dic73C2312yes—
55#11924007—22no—
56#11924007—22no—
57C22⋊Dic73—21no—
58C22⋊Dic73—22no—
59C22⋊Dic73D412yes—
60C4×Dic73—21no—
61C4×Dic73—22no—
62C4×Dic73C2312yes—
63#41×C73—22no—
64#41×C73Q814yescomplemented
65C2×Q8×C73C2311yescharacteristic
66C2×D4×C73—21no—
67C2×D4×C73C2311yescharacteristic
68C22×C4×C73—21no—
69C22×C4×C73—21no—
70C22×C4×C73C2311yescharacteristic
71M16×C73—22no—
72C2×C8×C73C2312yes—
73C4⋊C4×C73—21no—
74C4⋊C4×C73C2312yes—
75C23×C73—21no—
76C23×C73C2×D411yescharacteristic
77Q8×C73—21no—
78Q8×C73C2×Q812yes—
79D4×C73—24no—
80D4×C73—21no—
81D4×C73C2×Q812yes—
82C2×C4×C73—21no—
83C2×C4×C73—24no—
84C2×C4×C73—22no—
85C2×C4×C73—81no—
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2×Q812yes—
88C2×C4×C73#4112yes—
89C2×C4×C73C2411yescharacteristic
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—22no—
93C2×Dic73—82no—
94C2×Dic73—81no—
95C2×Dic73C2×D412yes—
96C2×Dic73C2×D412yes—
97Dic146—82no—
98C8×C73—22no—
99#10596831—21no—
100#10596831—21no—
101C22×C73—21no—
102C22×C73—21no—
103C22×C73—22no—
104C22×C73—41no—
105C22×C73—41no—
106C22×C73C22⋊Q812yes—
107C22×C73C22×D411yescharacteristic
108C4×C73—22no—
109C4×C73—42no—
110C4×C73C22⋊Q812yes—
111C4×C73C22×Q811yescharacteristic
112C4×C73C2×#4111yescharacteristic
113Dic73—22no—
114Dic73—22no—
115Dic73—41no—
116Dic73—42no—
117Dic73—41no—
118C2×C73—22no—
119C2×C73—42no—
120C2×C73C2×C22⋊Q811yescharacteristic
121C2×C73#57611yescharacteristic
122C2×C73#57811yescharacteristic
123#3083—731nomaximal, Sylow
124C73#308311yescharacteristic, complemented, Sylow
125#544—731no—
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#417D7311yescharacteristic
135#416—731no—
136C2×#41C2×D7311yescharacteristic
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—731no—
149#117—1461no—
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#103C2×D7312yes—
162#102—731no—
163#102—731no—
164#102C2×D7312yes—
165#41—22no—
166#41Dic14614yescomplemented
167C2×Q8—1462no—
168C2×Q8C22×D7311yescharacteristic
169C2×D4—21no—
170C2×D4C22×D7311yescharacteristic
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—1462no—
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—731no—
185C4⋊C4—731no—
186C4⋊C4—732no—
187C4⋊C4—1462no—
188C4⋊C4—1462no—
189C4⋊C4—1462no—
190C4⋊C4—1462no—
191C4⋊C4—1461no—
192C4⋊C4C22×D7312yes—
193C22⋊C4—732no—
194C22⋊C4—1462no—
195C22⋊C4—1461no—
196C42—732no—
197C42—1462no—
198C42—1461no—
199C23—21no—
200C23D4×D7311yescharacteristic
201Q8—21no—
202Q8—5842no—
203Q8C2×Dic14612yes—
204D4—24no—
205D4—21no—
206D4C2×Dic14612yes—
207C2×C4—21no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—81no—
211C2×C4—5841no—
212C2×C4—5842no—
213C2×C4—732no—
214C2×C4—732no—
215C2×C4—1461no—
216C2×C4—1462no—
217C2×C4—1461no—
218C2×C4D4×D7311yescharacteristic
219C2×C4C2×Dic14612yes—
220C2×C4#1192402712yes—
221C2×C4C23×D7311yescharacteristic
222C8—22no—
223C8—1461no—
224C8—1461no—
225C22—21no—
226C22—21no—
227C22—22no—
228C22—41no—
229C22—41no—
230C22#1455656812yes—
231C22C2×D4×D7311yescharacteristic
232C4—22no—
233C4—42no—
234C4—2922no—
235C4—2921no—
236C4—2921no—
237C4—1462no—
238C4—1462no—
239C4#1455656812yes—
240C4C22×Dic14611yescharacteristic
241C4C2×#1192402711yescharacteristic
242C2—22no—
243C2—42no—
244C2C2×#1455656811yescharacteristic
245C2#1798939111yescharacteristic
246C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#417×C73C2
socleC22×C73C22×D4
hypercenter#417D73
hypocenterC73#3083
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #17989218C2semidirect
3. #17988892C2semidirect
4. #17988889C2semidirect
5. #17988880C2semidirect
6. #17988865C2semidirect
7. #17988629C2semidirect
8. C2×#14556524C2semidirect
9. #17988615C2semidirect
64. #41×C73Q8semidirect
124. C73#3083semidirect
166. #41Dic146semidirect