Finite Group Databasebeta

← #22622241

Subgroups — #22622241

Order 9344.

388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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#17989242C211yesmaximal, characteristic
2#17988939C211yesmaximal, characteristic, complemented
3#17988917C212yesmaximal, complemented
4#17988874C211yesmaximal, characteristic, complemented
5#17988843C212yesmaximal, complemented
6#17988797C211yesmaximal, characteristic, complemented
7#17988747C212yesmaximal, complemented
8C4×#11924015C211yesmaximal, characteristic, complemented
9#17988665C211yesmaximal, characteristic, complemented
10#17988586C212yesmaximal, complemented
11#554×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2212yes—
13C2×#11924018C2212yes—
14C2×#11924015C2211yescharacteristic
15C2×#11924012C2212yes—
16#14556591C2211yescharacteristic
17#14556573—22no—
18#14556570C2212yes—
19#14556562—21no—
20C4×D292C2211yescharacteristic
21C4⋊C4×D73—21no—
22#14556522C2212yes—
23#14556522C2211yescharacteristic
24C4⋊#10596831C2211yescharacteristic
25#14556515C2211yescharacteristic
26#14556514C2212yes—
27#14556514C2212yes—
28#14556514C2212yes—
29#14556511C2212yes—
30#14556511C2211yescharacteristic
31C22⋊#10596831C2212yes—
32C4×#10596831C2211yescharacteristic
33C4⋊Q8×C73C2211yescharacteristic
34#125×C73—21no—
35C22⋊Q8×C73—22no—
36C22⋊Q8×C73C2212yes—
37C4×Q8×C73C2211yescharacteristic
38C4×D4×C73—21no—
39C4×D4×C73C2211yescharacteristic
40C2×C4⋊C4×C73C2212yes—
41#11924028—24no—
42#11924028—42no—
43C2×Dic146C2312yes—
44C2×D292C2311yescharacteristic
45C2×C22⋊D73—22no—
46C2×C4×D73—21no—
47C2×C4×D73—22no—
48#11924018—42no—
49#11924015—22no—
50#11924012—42no—
51C2×#10596831C2311yescharacteristic
52C2×#10596831C2311yescharacteristic
53C2×#10596831C2312yes—
54C4⋊Dic73—21no—
55C4⋊Dic73—21no—
56C4⋊Dic73C2311yescharacteristic
57#11924007—22no—
58C22⋊Dic73—22no—
59#11924005—21no—
60C2×Q8×C73—21no—
61C2×Q8×C73C2311yescharacteristic
62C2×D4×C73D411yescharacteristic
63C22×C4×C73—22no—
64C22×C4×C73C2312yes—
65C4⋊C4×C73—22no—
66C4⋊C4×C73—21no—
67C4⋊C4×C73—21no—
68C4⋊C4×C73—22no—
69C4⋊C4×C73D411yescharacteristic
70C4⋊C4×C73C2311yescharacteristic
71C4⋊C4×C73C2312yes—
72C22⋊C4×C73—22no—
73C22⋊C4×C73D412yes—
74C42×C73—21no—
75C42×C73C2311yescharacteristic
76C23×C73C2×D412yes—
77C22×D73—21no—
78Q8×C73—21no—
79Q8×C73—21no—
80Q8×C73—81no—
81D4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—22no—
87C2×C4×C73—82no—
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2×D412yes—
90C2×C4×C73C2×D411yescharacteristic
91C2×C4×C73C2411yescharacteristic
92C22⋊D73—44no—
93C2×Dic73—21no—
94C2×Dic73—22no—
95D292—21no—
96D292#4112yes—
97C4×D73—44no—
98C4×D73—42no—
99Dic146—22no—
100Dic146—22no—
101#10596831—21no—
102#10596831—21no—
103#10596831—22no—
104C22×C73—22no—
105C22×C73—22no—
106C22×C73—22no—
107C22×C73C22×D411yescharacteristic
108C2×D73—22no—
109C2×D73—41no—
110C2×D73—41no—
111C4×C73—22no—
112C4×C73—21no—
113C4×C73—41no—
114C4×C73—41no—
115C4×C73—42no—
116C4×C73#13712yes—
117C4×C73C2×#4111yescharacteristic
118C4×C73H(5,𝔽2)11yescharacteristic
119Dic73—42no—
120Dic73—41no—
121C2×C73—42no—
122C2×C73#54611yescharacteristic
123C2×C73C2×#13711yescharacteristic
124C2×C73#57711yescharacteristic
125D73—42no—
126#3331—731nomaximal, Sylow
127C73#333111yescharacteristic, complemented, Sylow
128#554D7311yescharacteristic, complemented
129#547—731no—
130#487—731no—
131#483—732no—
132#476—731no—
133#470—732no—
134#462—731no—
135#452—732no—
136C4×SD16—731no—
137#436—731no—
138#417—732no—
139C2×#41—732no—
140C2×Q16—732no—
141C2×SD16—731no—
142C2×M16—732no—
143C4⋊Q8—731no—
144C4⋊Q8C2×D7311yescharacteristic
145#125—21no—
146#123—1462no—
147C22⋊Q8—22no—
148C22⋊Q8—732no—
149C22⋊Q8C2×D7312yes—
150#121—1461no—
151C4×Q8C2×D7311yescharacteristic
152C4×D4—21no—
153C4×D4—731no—
154C4×D4C2×D7311yescharacteristic
155C2×C4⋊C4—1461no—
156C2×C4⋊C4C2×D7312yes—
157#106—731no—
158#106—732no—
159C4⋊C8—731no—
160#103—731no—
161#103—732no—
162#103—732no—
163#103—732no—
164#102—731no—
165#102—732no—
166C22⋊C8—732no—
167C4×C8—731no—
168#41—2922no—
169#41—1464no—
170C2×Q8—21no—
171C2×Q8—732no—
172C2×Q8C22×D7311yescharacteristic
173C2×D4—731no—
174C2×D4—1462no—
175C2×D4C22⋊D7311yescharacteristic
176C22×C4—22no—
177C22×C4—1461no—
178C22×C4—1462no—
179C22×C4C22×D7312yes—
180Q16—2922no—
181SD16—1462no—
182M16—2922no—
183C2×C8—731no—
184C2×C8—731no—
185C2×C8—732no—
186C4⋊C4—22no—
187C4⋊C4—21no—
188C4⋊C4—21no—
189C4⋊C4—22no—
190C4⋊C4—731no—
191C4⋊C4—1462no—
192C4⋊C4—1461no—
193C4⋊C4—1461no—
194C4⋊C4C22⋊D7311yescharacteristic
195C4⋊C4C22×D7311yescharacteristic
196C4⋊C4C22×D7312yes—
197C22⋊C4—22no—
198C22⋊C4—1462no—
199C22⋊C4—1461no—
200C22⋊C4C22⋊D7312yes—
201C42—21no—
202C42C22×D7311yescharacteristic
203C23—1461no—
204C23C2×C22⋊D7312yes—
205Q8—21no—
206Q8—21no—
207Q8—81no—
208Q8—1462no—
209Q8—1462no—
210D4—22no—
211D4—2924no—
212D4—732no—
213D4—1461no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—82no—
220C2×C4—2924no—
221C2×C4—2922no—
222C2×C4—1461no—
223C2×C4—1462no—
224C2×C4C2×C22⋊D7311yescharacteristic
225C2×C4C2×C22⋊D7312yes—
226C2×C4C2×C22⋊D7311yescharacteristic
227C2×C4C23×D7311yescharacteristic
228C8—1461no—
229C8—1461no—
230C8—1462no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—2921no—
235C22—2921no—
236C22—1462no—
237C22C22×C22⋊D7311yescharacteristic
238C4—21no—
239C4—22no—
240C4—41no—
241C4—42no—
242C4—41no—
243C4—2921no—
244C4—2922no—
245C4#1455662212yes—
246C4#41×D7311yescharacteristic
247C4#1455663711yescharacteristic
248C2—42no—
249C2—2922no—
250C2#1798922511yescharacteristic
251C2C2×#1455662211yescharacteristic
252C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#554×C73C2
socleC22×C73C22×D4
hypercenter#554D73
hypocenterC73#3331
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
2. #17988939C2semidirect
3. #17988917C2semidirect
4. #17988874C2semidirect
5. #17988843C2semidirect
6. #17988797C2semidirect
7. #17988747C2semidirect
8. C4×#11924015C2semidirect
9. #17988665C2semidirect
10. #17988586C2semidirect
11. #554×C73C2semidirect
127. C73#3331semidirect
128. #554D73semidirect