Finite Group Databasebeta

← #22619894

Subgroups — #22619894

Order 9344.

386 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 133 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#17989070C211yesmaximal, characteristic
2#17988925C212yesmaximal, complemented
3#17988925C212yesmaximal, complemented
4#17988920C212yesmaximal, complemented
5#17988915C212yesmaximal, complemented
6#17988630C211yesmaximal, characteristic, complemented
7#17988623C211yesmaximal, characteristic, complemented
8#17988596C211yesmaximal, characteristic, complemented
9C2×#14556515C211yesmaximal, characteristic, complemented
10#17988554C211yesmaximal, characteristic
11#536×C73C211yesmaximal, characteristic
12C2×#11924012C2211yescharacteristic
13C22×#10596831C2211yescharacteristic
14Q8×Dic73—21no—
15D4×Dic73—22no—
16D4×Dic73—21no—
17#14556550C2211yescharacteristic
18#14556550C2212yes—
19C2×C4⋊Dic73C2211yescharacteristic
20C2×C4⋊Dic73C2212yes—
21#14556524C2211yescharacteristic
22#14556524C2211yescharacteristic
23#14556524C2212yes—
24#14556522C2211yescharacteristic
25#14556522C2211yescharacteristic
26#14556522C2212yes—
27#14556515C2212yes—
28#14556515C2212yes—
29#14556515C2212yes—
30#14556515C2212yes—
31C22⋊#10596831C2212yes—
32C22⋊#10596831C2212yes—
33C2×#41×C73C2211yescharacteristic
34C22×Q8×C73C2211yescharacteristic
35C4⋊Q8×C73—21no—
36#124×C73—21no—
37#123×C73—22no—
38C22⋊Q8×C73C2212yes—
39C22⋊Q8×C73C2212yes—
40#117×C73C2211yescharacteristic
41C22×Dic73—22no—
42C22×Dic73—21no—
43#11924012—22no—
44C2×#10596831—22no—
45C2×#10596831C2311yescharacteristic
46C2×#10596831C2312yes—
47C2×#10596831C2311yescharacteristic
48C4⋊Dic73—22no—
49C4⋊Dic73—21no—
50C4⋊Dic73C2311yescharacteristic
51C4⋊Dic73C2312yes—
52C4⋊Dic73C2311yescharacteristic
53C22⋊Dic73—22no—
54C22⋊Dic73—21no—
55C4×Dic73—22no—
56C4×Dic73—21no—
57#41×C73—22no—
58#41×C73—22no—
59C2×Q8×C73—21no—
60C2×Q8×C73—22no—
61C2×Q8×C73—22no—
62C2×Q8×C73D411yescharacteristic
63C2×Q8×C73C2312yes—
64C2×D4×C73D412yes—
65C2×D4×C73D411yescharacteristic
66C22×C4×C73—21no—
67C22×C4×C73C2312yes—
68C22×C4×C73C2311yescharacteristic
69C4⋊C4×C73—22no—
70C4⋊C4×C73—22no—
71C4⋊C4×C73C2311yescharacteristic
72C4⋊C4×C73C2311yescharacteristic
73C22⋊C4×C73—21no—
74C22⋊C4×C73—22no—
75C22⋊C4×C73—22no—
76C42×C73—21no—
77C23×C73C2×D412yes—
78C23×C73C2×D411yescharacteristic
79Q8×C73—22no—
80Q8×C73—22no—
81Q8×C73—22no—
82Q8×C73—42no—
83D4×C73—24no—
84D4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—21no—
88C2×C4×C73—21no—
89C2×C4×C73—22no—
90C2×C4×C73—42no—
91C2×C4×C73C2×D412yes—
92C2×C4×C73C2×D411yescharacteristic
93C2×C4×C73#4112yes—
94C2×C4×C73#4112yes—
95C2×C4×C73C2411yescharacteristic
96C2×Dic73—21no—
97C2×Dic73—22no—
98C2×Dic73—21no—
99C2×Dic73—81no—
100C2×Dic73—82no—
101#10596831—21no—
102#10596831—21no—
103#10596831—22no—
104C22×C73—21no—
105C22×C73—21no—
106C22×C73—22no—
107C22×C73—22no—
108C22×C73—22no—
109C22×C73#12312yes—
110C22×C73C22×D411yescharacteristic
111C4×C73—22no—
112C4×C73—42no—
113C4×C73—41no—
114C4×C73—41no—
115C4×C73#12312yes—
116C4×C73C2×#4111yescharacteristic
117C4×C73C2×#4111yescharacteristic
118Dic73—42no—
119Dic73—41no—
120Dic73—41no—
121C2×C73—22no—
122C2×C73—42no—
123C2×C73C2×#12311yescharacteristic
124C2×C73#57711yescharacteristic
125C2×C73#57811yescharacteristic
126#3097—731nomaximal, Sylow
127C73#309711yescharacteristic, complemented, Sylow
128#536D7311yescharacteristic
129#520—731no—
130#485—732no—
131#485—732no—
132#484—732no—
133#483—732no—
134#428—731no—
135#427—731no—
136#419—731no—
137C2×#103—731no—
138#408—731no—
139C2×#41C2×D7311yescharacteristic
140C22×Q8C2×D7311yescharacteristic
141C2×M16—731no—
142C22×C8—731no—
143C4⋊Q8—21no—
144#124—21no—
145#123—22no—
146C22⋊Q8C2×D7312yes—
147C22⋊Q8C2×D7312yes—
148C4×Q8—1461no—
149C4×D4—1462no—
150C4×D4—1461no—
151#117—731no—
152#117—732no—
153#117C2×D7311yescharacteristic
154C2×C4⋊C4—731no—
155C2×C4⋊C4—732no—
156#107—731no—
157#107—731no—
158#107—732no—
159#106—731no—
160#106—731no—
161#106—732no—
162#103—732no—
163#103—732no—
164#103—732no—
165#103—732no—
166C22⋊C8—732no—
167C22⋊C8—732no—
168#41—22no—
169#41—22no—
170C2×Q8—21no—
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8C22⋊D7311yescharacteristic
174C2×Q8C22×D7312yes—
175C2×D4C22⋊D7312yes—
176C2×D4C22⋊D7311yescharacteristic
177C22×C4—21no—
178C22×C4—1462no—
179C22×C4—1461no—
180C22×C4C22×D7312yes—
181C22×C4C22×D7311yescharacteristic
182M16—1462no—
183C2×C8—731no—
184C2×C8—732no—
185C2×C8—731no—
186C2×C8—1462no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—732no—
190C4⋊C4—731no—
191C4⋊C4—731no—
192C4⋊C4—1462no—
193C4⋊C4—1461no—
194C4⋊C4C22×D7311yescharacteristic
195C4⋊C4C22×D7311yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—22no—
198C22⋊C4—22no—
199C22⋊C4—1462no—
200C22⋊C4—1461no—
201C42—21no—
202C42—1462no—
203C42—1461no—
204C23C2×C22⋊D7312yes—
205C23C2×C22⋊D7311yescharacteristic
206Q8—22no—
207Q8—22no—
208Q8—22no—
209Q8—42no—
210D4—24no—
211D4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—5841no—
219C2×C4—5842no—
220C2×C4—1461no—
221C2×C4—1462no—
222C2×C4—1461no—
223C2×C4C2×C22⋊D7312yes—
224C2×C4C2×C22⋊D7311yescharacteristic
225C2×C4#1192402712yes—
226C2×C4#1192402712yes—
227C2×C4C23×D7311yescharacteristic
228C8—1461no—
229C8—1461no—
230C8—1462no—
231C22—21no—
232C22—21no—
233C22—22no—
234C22—22no—
235C22—22no—
236C22#1455657212yes—
237C22C22×C22⋊D7311yescharacteristic
238C4—22no—
239C4—41no—
240C4—41no—
241C4—42no—
242C4—2922no—
243C4—2921no—
244C4—2921no—
245C4#1455657212yes—
246C4C2×#1192402711yescharacteristic
247C4C2×#1192402711yescharacteristic
248C2—22no—
249C2—42no—
250C2C2×#1455657211yescharacteristic
251C2#1798939511yescharacteristic
252C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#536×C73C2
socleC22×C73C22×D4
hypercenter#536D73
hypocenterC73#3097
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #17988925C2semidirect
3. #17988925C2semidirect
4. #17988920C2semidirect
5. #17988915C2semidirect
6. #17988630C2semidirect
7. #17988623C2semidirect
8. #17988596C2semidirect
9. C2×#14556515C2semidirect
127. C73#3097semidirect