Finite Group Databasebeta

← #22620296

Subgroups — #22620296

Order 9344.

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

normal subgroups only

This group has 372 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#17989215C211yesmaximal, characteristic, complemented
2#17988955C212yesmaximal, complemented
3#17988946C212yesmaximal, complemented
4#17988941C212yesmaximal, complemented
5#17988937C212yesmaximal, complemented
6#17988596C211yesmaximal, characteristic, complemented
7#17988588C211yesmaximal, characteristic
8#17988583C211yesmaximal, characteristic
9C2×#14556515C211yesmaximal, characteristic, complemented
10#17988543C211yesmaximal, characteristic, complemented
11#536×C73C211yesmaximal, characteristic
12C2×#11924012C2211yescharacteristic
13C22×#10596831C2211yescharacteristic
14#14556591C2212yes—
15#14556590—21no—
16#14556583C2212yes—
17#14556582—21no—
18#14556568—22no—
19#14556550C2211yescharacteristic
20C2×C4⋊Dic73C2211yescharacteristic
21#14556515C2211yescharacteristic
22#14556515C2212yes—
23#14556515C2212yes—
24#14556515C2212yes—
25#14556515C2212yes—
26#14556515C2212yes—
27#14556515C2211yescharacteristic
28#14556512C2211yescharacteristic
29#14556512C2212yes—
30#14556512C2211yescharacteristic
31#14556502C2212yes—
32C4×#10596831C2212yes—
33C2×#41×C73C2211yescharacteristic
34C22×Q8×C73C2211yescharacteristic
35C4⋊Q8×C73C2212yes—
36#124×C73C2212yes—
37#123×C73—22no—
38C22⋊Q8×C73—21no—
39C22⋊Q8×C73—21no—
40#117×C73C2211yescharacteristic
41C2×Dic146—22no—
42C22×Dic73—21no—
43#11924012—22no—
44C2×#10596831—22no—
45C2×#10596831C2311yescharacteristic
46C2×#10596831C2312yes—
47C2×#10596831C2311yescharacteristic
48C4⋊Dic73—21no—
49C4⋊Dic73—22no—
50C4⋊Dic73C2312yes—
51C4⋊Dic73C2311yescharacteristic
52C4⋊Dic73C2311yescharacteristic
53#11924007—22no—
54#11924007—22no—
55C22⋊Dic73—21no—
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×C73C2312yes—
63C2×Q8×C73C2311yescharacteristic
64C2×D4×C73—21no—
65C2×D4×C73C2311yescharacteristic
66C22×C4×C73—21no—
67C22×C4×C73—21no—
68C22×C4×C73C2311yescharacteristic
69C4⋊C4×C73—22no—
70C4⋊C4×C73—22no—
71C4⋊C4×C73D411yescharacteristic
72C4⋊C4×C73D411yescharacteristic
73C22⋊C4×C73—22no—
74C22⋊C4×C73—22no—
75C22⋊C4×C73D412yes—
76C42×C73C2312yes—
77C23×C73—21no—
78C23×C73C2×D411yescharacteristic
79Q8×C73—22no—
80Q8×C73—22no—
81Q8×C73—21no—
82Q8×C73—21no—
83Q8×C73—42no—
84D4×C73—21no—
85D4×C73—21no—
86D4×C73—42no—
87C2×C4×C73—22no—
88C2×C4×C73—21no—
89C2×C4×C73—42no—
90C2×C4×C73—42no—
91C2×C4×C73C2×D412yes—
92C2×C4×C73C2×D412yes—
93C2×C4×C73C2×D411yescharacteristic
94C2×C4×C73#4112yes—
95C2×C4×C73#4112yes—
96C2×C4×C73C2411yescharacteristic
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—22no—
100C2×Dic73—81no—
101Dic146—82no—
102#10596831—21no—
103#10596831—21no—
104#10596831—22no—
105C22×C73—21no—
106C22×C73—21no—
107C22×C73—41no—
108C22×C73—41no—
109C22×C73—41no—
110C22×C73#12412yes—
111C22×C73C22×D411yescharacteristic
112C4×C73—22no—
113C4×C73—22no—
114C4×C73—41no—
115C4×C73—42no—
116C4×C73#12412yes—
117C4×C73C2×#4111yescharacteristic
118C4×C73C2×#4111yescharacteristic
119Dic73—41no—
120Dic73—42no—
121Dic73—41no—
122C2×C73—22no—
123C2×C73—81no—
124C2×C73C2×#12411yescharacteristic
125C2×C73#57711yescharacteristic
126C2×C73#57811yescharacteristic
127#3137—731nomaximal, Sylow
128C73#313711yescharacteristic, complemented, Sylow
129#544—731no—
130#536D7311yescharacteristic
131#491—732no—
132#489—732no—
133#488—732no—
134#487—732no—
135#419—731no—
136#417—731no—
137#416—731no—
138C2×#103—731no—
139#405—731no—
140C2×#41C2×D7311yescharacteristic
141C22×Q8C2×D7311yescharacteristic
142C2×M16—731no—
143C22×C8—731no—
144C4⋊Q8—732no—
145C4⋊Q8—1461no—
146C4⋊Q8C2×D7312yes—
147#125—732no—
148#125—1461no—
149#124C2×D7312yes—
150#123—22no—
151C22⋊Q8—21no—
152C22⋊Q8—21no—
153C22⋊Q8—1462no—
154#117—731no—
155#117C2×D7311yescharacteristic
156C2×C4⋊C4—731no—
157#103—732no—
158#103—732no—
159#103—731no—
160#103—731no—
161#103—732no—
162#103—732no—
163#103—732no—
164#102—731no—
165#102—731no—
166#102—732no—
167#97—732no—
168C4×C8—732no—
169#41—22no—
170#41—22no—
171C2×Q8—21no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—1462no—
175C2×Q8C22×D7312yes—
176C2×Q8C22×D7311yescharacteristic
177C2×D4—21no—
178C2×D4C22×D7311yescharacteristic
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—1461no—
182C22×C4C22×D7311yescharacteristic
183M16—1462no—
184C2×C8—731no—
185C2×C8—732no—
186C2×C8—731no—
187C2×C8—1462no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—732no—
191C4⋊C4—731no—
192C4⋊C4—731no—
193C4⋊C4—1462no—
194C4⋊C4—1462no—
195C4⋊C4—1461no—
196C4⋊C4—1462no—
197C4⋊C4C22⋊D7311yescharacteristic
198C4⋊C4C22⋊D7311yescharacteristic
199C22⋊C4—22no—
200C22⋊C4—22no—
201C22⋊C4—1461no—
202C22⋊C4C22⋊D7312yes—
203C42—1461no—
204C42C22×D7312yes—
205C23—21no—
206C23C2×C22⋊D7311yescharacteristic
207Q8—22no—
208Q8—22no—
209Q8—21no—
210Q8—21no—
211Q8—42no—
212Q8—5842no—
213D4—21no—
214D4—21no—
215D4—42no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—5841no—
221C2×C4—1461no—
222C2×C4—1461no—
223C2×C4—1462no—
224C2×C4C2×C22⋊D7312yes—
225C2×C4C2×C22⋊D7312yes—
226C2×C4C2×C22⋊D7311yescharacteristic
227C2×C4#1192402712yes—
228C2×C4#1192402712yes—
229C2×C4C23×D7311yescharacteristic
230C8—1461no—
231C8—1461no—
232C8—1462no—
233C22—21no—
234C22—21no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22#1455657812yes—
239C22C22×C22⋊D7311yescharacteristic
240C4—22no—
241C4—22no—
242C4—41no—
243C4—42no—
244C4—2922no—
245C4—2921no—
246C4—2921no—
247C4#1455657812yes—
248C4C2×#1192402711yescharacteristic
249C4C2×#1192402711yescharacteristic
250C2—22no—
251C2—81no—
252C2C2×#1455657811yescharacteristic
253C2#1798939511yescharacteristic
254C2#1798940211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#536×C73C2
socleC22×C73C22×D4
hypercenter#536D73
hypocenterC73#3137
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #17989215C2semidirect
2. #17988955C2semidirect
3. #17988946C2semidirect
4. #17988941C2semidirect
5. #17988937C2semidirect
6. #17988596C2semidirect
9. C2×#14556515C2semidirect
10. #17988543C2semidirect
128. C73#3137semidirect