Finite Group Databasebeta

← #22622247

Subgroups — #22622247

Order 9344.

388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989294C211yesmaximal, characteristic, complemented
2#17988937C211yesmaximal, characteristic, complemented
3#17988915C212yesmaximal, complemented
4#17988877C211yesmaximal, characteristic, complemented
5#17988843C212yesmaximal, complemented
6#17988794C211yesmaximal, characteristic, complemented
7#17988749C212yesmaximal, complemented
8C4×#11924016C211yesmaximal, characteristic, complemented
9#17988665C211yesmaximal, characteristic, complemented
10#17988588C212yesmaximal, complemented
11#547×C73C211yesmaximal, characteristic
12C2×#11924018C2212yes—
13C2×#11924016C2211yescharacteristic
14C2×#11924012C2212yes—
15#14556591C2211yescharacteristic
16#14556582—21no—
17#14556570C2212yes—
18#14556568—22no—
19C4×Dic146C2211yescharacteristic
20D4×Dic73—21no—
21C2×C4⋊Dic73C2212yes—
22#14556522C2212yes—
23#14556522C2211yescharacteristic
24C4⋊#10596831C2211yescharacteristic
25#14556515C2212yes—
26#14556515C2212yes—
27#14556515C2212yes—
28#14556514C2211yescharacteristic
29#14556512C2212yes—
30#14556512C2211yescharacteristic
31C22⋊#10596831C2212yes—
32C4×#10596831C2211yescharacteristic
33C2×#41×C73C2212yes—
34C4⋊Q8×C73C2211yescharacteristic
35#123×C73—22no—
36C22⋊Q8×C73C2212yes—
37#121×C73—21no—
38C4×D4×C73C2211yescharacteristic
39C4×D4×C73C2211yescharacteristic
40C2×C4⋊C4×C73—21no—
41C2×Dic146—21no—
42C2×Dic146C2311yescharacteristic
43C22×Dic73—22no—
44#11924018—42no—
45#11924016—22no—
46#11924012—42no—
47C2×#10596831C2311yescharacteristic
48C2×#10596831C2311yescharacteristic
49C2×#10596831C2312yes—
50C4⋊Dic73—22no—
51C4⋊Dic73—21no—
52C4⋊Dic73C2311yescharacteristic
53C4⋊Dic73C2312yes—
54#11924007—21no—
55#11924007—22no—
56C22⋊Dic73—22no—
57C4×Dic73—21no—
58#41×C73—24no—
59#41×C73—42no—
60C2×Q8×C73C2312yes—
61C2×D4×C73—22no—
62C2×D4×C73D411yescharacteristic
63C2×D4×C73C2311yescharacteristic
64C22×C4×C73—21no—
65C22×C4×C73—22no—
66C22×C4×C73C2312yes—
67C4⋊C4×C73—21no—
68C4⋊C4×C73—22no—
69C4⋊C4×C73—21no—
70C4⋊C4×C73D411yescharacteristic
71C4⋊C4×C73C2311yescharacteristic
72C22⋊C4×C73—22no—
73C22⋊C4×C73—21no—
74C22⋊C4×C73D412yes—
75C42×C73C2311yescharacteristic
76C23×C73—21no—
77C23×C73C2×D412yes—
78Q8×C73—22no—
79Q8×C73—22no—
80D4×C73—22no—
81D4×C73—21no—
82D4×C73—44no—
83D4×C73#4112yes—
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73—44no—
89C2×C4×C73—42no—
90C2×C4×C73C2×D411yescharacteristic
91C2×C4×C73C2×D412yes—
92C2×C4×C73C2×D411yescharacteristic
93C2×C4×C73C2411yescharacteristic
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—22no—
97C2×Dic73—82no—
98Dic146—21no—
99Dic146—21no—
100Dic146—81no—
101#10596831—21no—
102#10596831—21no—
103#10596831—22no—
104C22×C73—22no—
105C22×C73—22no—
106C22×C73—22no—
107C22×C73—22no—
108C22×C73—41no—
109C22×C73—41no—
110C22×C73C22×D411yescharacteristic
111C4×C73—22no—
112C4×C73—21no—
113C4×C73—42no—
114C4×C73—41no—
115C4×C73#13712yes—
116C4×C73C2×#4111yescharacteristic
117C4×C73H(5,𝔽2)11yescharacteristic
118Dic73—41no—
119Dic73—42no—
120Dic73—41no—
121C2×C73—42no—
122C2×C73—42no—
123C2×C73#54611yescharacteristic
124C2×C73C2×#13711yescharacteristic
125C2×C73#57711yescharacteristic
126#3331—731nomaximal, Sylow
127C73#333111yescharacteristic, complemented, Sylow
128#554—731no—
129#547D7311yescharacteristic
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×#41C2×D7312yes—
140C2×Q16—732no—
141C2×SD16—731no—
142C2×M16—732no—
143C4⋊Q8—731no—
144C4⋊Q8C2×D7311yescharacteristic
145#125—1461no—
146#123—22no—
147C22⋊Q8—732no—
148C22⋊Q8—1462no—
149C22⋊Q8C2×D7312yes—
150#121—21no—
151C4×Q8—731no—
152C4×D4—1461no—
153C4×D4C2×D7311yescharacteristic
154C4×D4C2×D7311yescharacteristic
155C2×C4⋊C4—21no—
156C2×C4⋊C4—732no—
157#106—731no—
158#106—732no—
159C4⋊C8—731no—
160#103—732no—
161#103—732no—
162#103—732no—
163#103—731no—
164#102—731no—
165#102—732no—
166C22⋊C8—732no—
167C4×C8—731no—
168#41—24no—
169#41—42no—
170C2×Q8—731no—
171C2×Q8—1461no—
172C2×Q8C22×D7312yes—
173C2×D4—22no—
174C2×D4C22⋊D7311yescharacteristic
175C2×D4C22×D7311yescharacteristic
176C22×C4—21no—
177C22×C4—22no—
178C22×C4—1462no—
179C22×C4C22×D7312yes—
180Q16—2922no—
181SD16—1462no—
182M16—2922no—
183C2×C8—731no—
184C2×C8—731no—
185C2×C8—732no—
186C4⋊C4—21no—
187C4⋊C4—22no—
188C4⋊C4—21no—
189C4⋊C4—731no—
190C4⋊C4—732no—
191C4⋊C4—1461no—
192C4⋊C4—1462no—
193C4⋊C4—1462no—
194C4⋊C4—1461no—
195C4⋊C4C22⋊D7311yescharacteristic
196C4⋊C4C22×D7311yescharacteristic
197C22⋊C4—22no—
198C22⋊C4—21no—
199C22⋊C4—1462no—
200C22⋊C4C22⋊D7312yes—
201C42—1461no—
202C42C22×D7311yescharacteristic
203C23—21no—
204C23C2×C22⋊D7312yes—
205Q8—22no—
206Q8—22no—
207Q8—5841no—
208Q8—1461no—
209Q8—1461no—
210D4—22no—
211D4—21no—
212D4—44no—
213D4#1192402712yes—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—44no—
219C2×C4—42no—
220C2×C4—5842no—
221C2×C4—1461no—
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—22no—
235C22—41no—
236C22—41no—
237C22C22×C22⋊D7311yescharacteristic
238C4—21no—
239C4—22no—
240C4—41no—
241C4—42no—
242C4—2921no—
243C4—2922no—
244C4—2921no—
245C4#1455662112yes—
246C4C2×#1192402711yescharacteristic
247C4#1455663611yescharacteristic
248C2—42no—
249C2—42no—
250C2#1798923111yescharacteristic
251C2C2×#1455662111yescharacteristic
252C2#1798939511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#547×C73C2
socleC22×C73C22×D4
hypercenter#547D73
hypocenterC73#3331
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #17989294C2semidirect
2. #17988937C2semidirect
3. #17988915C2semidirect
4. #17988877C2semidirect
5. #17988843C2semidirect
6. #17988794C2semidirect
7. #17988749C2semidirect
8. C4×#11924016C2semidirect
9. #17988665C2semidirect
10. #17988588C2semidirect
127. C73#3331semidirect