Finite Group Databasebeta

← #22622249

Subgroups — #22622249

Order 9344.

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

normal subgroups only

This group has 388 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#17989297C211yesmaximal, characteristic, complemented
2#17989241C211yesmaximal, characteristic
3#17988938C211yesmaximal, characteristic, complemented
4#17988919C212yesmaximal, complemented
5#17988877C211yesmaximal, characteristic, complemented
6#17988844C212yesmaximal, complemented
7#17988797C211yesmaximal, characteristic, complemented
8#17988746C212yesmaximal, complemented
9#17988666C211yesmaximal, characteristic, complemented
10#17988585C212yesmaximal, complemented
11C4×SD16×C73C211yesmaximal, characteristic, complemented
12C2×#11924027C2212yes—
13C2×#11924018C2212yes—
14C2×#11924011C2212yes—
15#14556591C2211yescharacteristic
16#14556591C2211yescharacteristic
17#14556583—21no—
18#14556575—22no—
19#14556571C2212yes—
20#14556569—22no—
21#14556567C2212yes—
22#14556565—21no—
23C4×D292—21no—
24C4×D292C2211yescharacteristic
25C2×C4⋊Dic73—21no—
26C4⋊C4×D73C2212yes—
27#14556522C2212yes—
28C4⋊#10596831C2211yescharacteristic
29#14556516C2212yes—
30#14556516C2212yes—
31#14556514C2212yes—
32#14556512C2212yes—
33#14556503C2212yes—
34C2×SD16×C73C2211yescharacteristic
35C4×Q8×C73C2211yescharacteristic
36C4×D4×C73C2211yescharacteristic
37#106×C73C2211yescharacteristic
38#103×C73C2211yescharacteristic
39#102×C73C2211yescharacteristic
40C4×C8×C73C2211yescharacteristic
41#11924027—24no—
42#11924027—42no—
43C2×Dic146—21no—
44C2×Dic146C2312yes—
45C2×D292D411yescharacteristic
46C2×C22⋊D73—22no—
47C22×Dic73—22no—
48C2×C4×D73—22no—
49C2×C4×D73C2312yes—
50#11924018—42no—
51#11924011—42no—
52C2×#10596831C2312yes—
53C4⋊Dic73—21no—
54C4⋊Dic73—21no—
55C4⋊Dic73—21no—
56C4⋊Dic73—22no—
57C4⋊Dic73D411yescharacteristic
58C4⋊Dic73C2312yes—
59#11924007—22no—
60#11924007—22no—
61#11924005—22no—
62#11924005—22no—
63#11924005D412yes—
64C2×Q8×C73C2311yescharacteristic
65C2×D4×C73C2311yescharacteristic
66C22×C4×C73—21no—
67SD16×C73—22no—
68C2×C8×C73C2311yescharacteristic
69C2×C8×C73C2311yescharacteristic
70C4⋊C4×C73—21no—
71C4⋊C4×C73C2311yescharacteristic
72C4⋊C4×C73C2311yescharacteristic
73C22⋊C4×C73—21no—
74C42×C73—21no—
75C42×C73C2311yescharacteristic
76C23×C73—21no—
77C22×D73C2×D412yes—
78Q8×C73—21no—
79Q8×C73—21no—
80D4×C73—21no—
81D4×C73#4112yes—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—42no—
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2411yescharacteristic
89C22⋊D73—44no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—44no—
93C2×Dic73C2×D412yes—
94D292—22no—
95C4×D73—22no—
96C4×D73—22no—
97C4×D73—82no—
98Dic146—22no—
99Dic146—22no—
100Dic146—81no—
101C8×C73—21no—
102C8×C73—21no—
103#10596831—22no—
104C22×C73—22no—
105C22×C73—41no—
106C22×C73—41no—
107C22×C73C22×D411yescharacteristic
108C2×D73—22no—
109C2×D73—22no—
110C2×D73—22no—
111C4×C73—21no—
112C4×C73—41no—
113C4×C73—41no—
114C4×C73—41no—
115C4×C73#13712yes—
116C4×C73C2×#4111yescharacteristic
117C4×C73H(5,𝔽2)11yescharacteristic
118Dic73—22no—
119Dic73—42no—
120Dic73—42no—
121C2×C73—42no—
122C2×C73#54611yescharacteristic
123C2×C73C2×#13711yescharacteristic
124C2×C73#57711yescharacteristic
125D73—42no—
126#3331—731nomaximal, Sylow
127C73#333111yescharacteristic, complemented, Sylow
128#554—731no—
129#547—731no—
130#487—731no—
131#483—732no—
132#476—731no—
133#470—732no—
134#462—731no—
135#452—732no—
136C4×SD16D7311yescharacteristic, complemented
137#436—731no—
138#417—732no—
139C2×#41—732no—
140C2×Q16—732no—
141C2×SD16C2×D7311yescharacteristic
142C2×M16—732no—
143C4⋊Q8—731no—
144C4⋊Q8—731no—
145#125—1461no—
146#123—1462no—
147C22⋊Q8—732no—
148C22⋊Q8—732no—
149C22⋊Q8—1462no—
150#121—1461no—
151C4×Q8C2×D7311yescharacteristic
152C4×D4—731no—
153C4×D4—1461no—
154C4×D4C2×D7311yescharacteristic
155C2×C4⋊C4—732no—
156C2×C4⋊C4—1461no—
157#106—732no—
158#106C2×D7311yescharacteristic
159C4⋊C8—731no—
160#103—732no—
161#103—732no—
162#103—732no—
163#103C2×D7311yescharacteristic
164#102—732no—
165#102C2×D7311yescharacteristic
166C22⋊C8—732no—
167C4×C8C2×D7311yescharacteristic
168#41—2922no—
169#41—1464no—
170C2×Q8—732no—
171C2×Q8—1461no—
172C2×Q8C22×D7311yescharacteristic
173C2×D4—731no—
174C2×D4—1462no—
175C2×D4C22×D7311yescharacteristic
176C22×C4—21no—
177C22×C4—732no—
178C22×C4—1462no—
179C22×C4—1462no—
180Q16—2922no—
181SD16—22no—
182M16—2922no—
183C2×C8—732no—
184C2×C8C22×D7311yescharacteristic
185C2×C8C22×D7311yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—731no—
188C4⋊C4—732no—
189C4⋊C4—1462no—
190C4⋊C4—1462no—
191C4⋊C4—1462no—
192C4⋊C4—1461no—
193C4⋊C4—1461no—
194C4⋊C4—1461no—
195C4⋊C4C22×D7311yescharacteristic
196C4⋊C4C22×D7311yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—732no—
199C22⋊C4—1462no—
200C22⋊C4—1462no—
201C42—21no—
202C42C22×D7311yescharacteristic
203C23—21no—
204C23—732no—
205Q8—21no—
206Q8—21no—
207Q8—5841no—
208Q8—1462no—
209Q8—1462no—
210D4—21no—
211D4—2924no—
212D4—1462no—
213D4#1192402812yes—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—42no—
218C2×C4—2924no—
219C2×C4—5842no—
220C2×C4—732no—
221C2×C4—1462no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4—1462no—
225C2×C4D4×D7311yescharacteristic
226C2×C4D4×D7311yescharacteristic
227C2×C4C23×D7311yescharacteristic
228C8—21no—
229C8—21no—
230C8—1462no—
231C22—22no—
232C22—41no—
233C22—41no—
234C22—1462no—
235C22—1462no—
236C22—1462no—
237C22C2×D4×D7311yescharacteristic
238C4—21no—
239C4—41no—
240C4—41no—
241C4—41no—
242C4—2922no—
243C4—2922no—
244C4—1462no—
245C4#1455662012yes—
246C4C2×#1192402811yescharacteristic
247C4#1455663711yescharacteristic
248C2—42no—
249C2—2922no—
250C2#1798923311yescharacteristic
251C2C2×#1455662011yescharacteristic
252C2#1798939411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×SD16×C73C2
socleC22×C73C22×D4
hypercenterC4×SD16D73
hypocenterC73#3331
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #17989297C2semidirect
3. #17988938C2semidirect
4. #17988919C2semidirect
5. #17988877C2semidirect
6. #17988844C2semidirect
7. #17988797C2semidirect
8. #17988746C2semidirect
9. #17988666C2semidirect
10. #17988585C2semidirect
11. C4×SD16×C73C2semidirect
127. C73#3331semidirect
136. C4×SD16D73semidirect