Finite Group Databasebeta

← #22620299

Subgroups — #22620299

Order 9344.

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

normal subgroups only

This group has 372 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#17989218C211yesmaximal, characteristic, complemented
2#17989158C211yesmaximal, characteristic
3#17988954C212yesmaximal, complemented
4#17988945C212yesmaximal, complemented
5#17988940C212yesmaximal, complemented
6#17988936C212yesmaximal, complemented
7#17988597C211yesmaximal, characteristic, complemented
8#17988583C211yesmaximal, characteristic
9C2×#14556514C211yesmaximal, characteristic, complemented
10#17988545C211yesmaximal, characteristic, complemented
11#417×C73C211yesmaximal, characteristic
12C22×Dic146C2211yescharacteristic
13C22×#10596831C2211yescharacteristic
14#14556590—21no—
15#14556590C2212yes—
16#14556589C2212yes—
17#14556582—21no—
18#14556582C2212yes—
19#14556578C2212yes—
20#14556572—22no—
21#14556570—21no—
22#14556570—21no—
23#14556570—22no—
24#14556550C2211yescharacteristic
25#14556550C2211yescharacteristic
26#14556516C2212yes—
27#14556516C2212yes—
28#14556515C2211yescharacteristic
29#14556515C2211yescharacteristic
30#14556514C2212yes—
31#14556514C2212yes—
32#14556512C2211yescharacteristic
33#14556512C2211yescharacteristic
34#14556501C2212yes—
35C8×Dic73C2212yes—
36C2×#41×C73C2211yescharacteristic
37C2×M16×C73C2211yescharacteristic
38C2×C4⋊C4×C73C2211yescharacteristic
39#103×C73C2212yes—
40#102×C73C2212yes—
41C2×Dic146—22no—
42C2×Dic146—22no—
43C2×Dic146—21no—
44C2×Dic146—22no—
45C2×Dic146C2312yes—
46C22×Dic73—21no—
47C2×#10596831—22no—
48C2×#10596831C2311yescharacteristic
49C2×#10596831C2311yescharacteristic
50C4⋊Dic73—22no—
51C4⋊Dic73D411yescharacteristic
52C4⋊Dic73D411yescharacteristic
53C4⋊Dic73C2311yescharacteristic
54C4⋊Dic73C2311yescharacteristic
55#11924007—22no—
56#11924007—22no—
57#11924007—22no—
58#11924007—22no—
59C22⋊Dic73—21no—
60C22⋊Dic73—22no—
61C22⋊Dic73—22no—
62C22⋊Dic73D412yes—
63C4×Dic73—21no—
64C4×Dic73C2312yes—
65#41×C73—22no—
66#41×C73—22no—
67C2×Q8×C73C2311yescharacteristic
68C2×D4×C73—21no—
69C2×D4×C73C2311yescharacteristic
70C22×C4×C73—21no—
71C22×C4×C73—21no—
72C22×C4×C73C2311yescharacteristic
73M16×C73—22no—
74C2×C8×C73C2312yes—
75C4⋊C4×C73—21no—
76C4⋊C4×C73C2312yes—
77C23×C73—21no—
78C23×C73C2×D411yescharacteristic
79Q8×C73—21no—
80Q8×C73—21no—
81D4×C73—21no—
82D4×C73—21no—
83D4×C73—42no—
84C2×C4×C73—22no—
85C2×C4×C73—21no—
86C2×C4×C73—42no—
87C2×C4×C73—81no—
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73#4112yes—
90C2×C4×C73#4112yes—
91C2×C4×C73C2411yescharacteristic
92C2×Dic73—21no—
93C2×Dic73—21no—
94C2×Dic73—22no—
95C2×Dic73—42no—
96C2×Dic73C2×D412yes—
97C2×Dic73C2×D412yes—
98Dic146—22no—
99Dic146—22no—
100Dic146—42no—
101Dic146—82no—
102C8×C73—22no—
103#10596831—21no—
104#10596831—21no—
105C22×C73—21no—
106C22×C73—21no—
107C22×C73—41no—
108C22×C73—41no—
109C22×C73—41no—
110C22×C73#12412yes—
111C22×C73C22×D411yescharacteristic
112C4×C73—41no—
113C4×C73—42no—
114C4×C73#12412yes—
115C4×C73C2×#4111yescharacteristic
116C4×C73C2×#4111yescharacteristic
117Dic73—22no—
118Dic73—22no—
119Dic73—42no—
120Dic73—41no—
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#536—731no—
131#491—732no—
132#489—732no—
133#488—732no—
134#487—732no—
135#419—731no—
136#417D7311yescharacteristic
137#416—731no—
138C2×#103—731no—
139#405—731no—
140C2×#41C2×D7311yescharacteristic
141C22×Q8—731no—
142C2×M16C2×D7311yescharacteristic
143C22×C8—731no—
144C4⋊Q8—732no—
145C4⋊Q8—732no—
146C4⋊Q8—1461no—
147#125—732no—
148#125—1461no—
149#124—732no—
150#123—1462no—
151C22⋊Q8—1462no—
152C22⋊Q8—1461no—
153C22⋊Q8—1461no—
154#117—731no—
155#117—731no—
156C2×C4⋊C4C2×D7311yescharacteristic
157#103—731no—
158#103—731no—
159#103—732no—
160#103—732no—
161#103—732no—
162#103—732no—
163#103C2×D7312yes—
164#102—731no—
165#102—731no—
166#102C2×D7312yes—
167#97—732no—
168C4×C8—732no—
169#41—22no—
170#41—22no—
171C2×Q8—732no—
172C2×Q8—1462no—
173C2×Q8—1462no—
174C2×Q8—1462no—
175C2×Q8—1461no—
176C2×Q8C22×D7311yescharacteristic
177C2×D4—21no—
178C2×D4C22×D7311yescharacteristic
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—1461no—
182C22×C4C22×D7311yescharacteristic
183M16—22no—
184C2×C8—731no—
185C2×C8—731no—
186C2×C8—1462no—
187C2×C8C22×D7312yes—
188C4⋊C4—21no—
189C4⋊C4—731no—
190C4⋊C4—731no—
191C4⋊C4—731no—
192C4⋊C4—731no—
193C4⋊C4—1462no—
194C4⋊C4—1462no—
195C4⋊C4—1462no—
196C4⋊C4—1462no—
197C4⋊C4—1462no—
198C4⋊C4C22×D7312yes—
199C22⋊C4—732no—
200C22⋊C4—1462no—
201C22⋊C4—1462no—
202C22⋊C4—1461no—
203C42—732no—
204C42—1461no—
205C23—21no—
206C23D4×D7311yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—2922no—
210Q8—5842no—
211Q8—1462no—
212Q8—1462no—
213D4—21no—
214D4—21no—
215D4—42no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—81no—
220C2×C4—2922no—
221C2×C4—732no—
222C2×C4—732no—
223C2×C4—1461no—
224C2×C4—1461no—
225C2×C4—1462no—
226C2×C4D4×D7311yescharacteristic
227C2×C4#1192402712yes—
228C2×C4#1192402812yes—
229C2×C4C23×D7311yescharacteristic
230C8—22no—
231C8—1461no—
232C8—1461no—
233C22—21no—
234C22—21no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22#1455657712yes—
239C22C2×D4×D7311yescharacteristic
240C4—42no—
241C4—41no—
242C4—2921no—
243C4—2921no—
244C4—2922no—
245C4—1462no—
246C4—1462no—
247C4#1455657712yes—
248C4C2×#1192402711yescharacteristic
249C4C2×#1192402811yescharacteristic
250C2—22no—
251C2—81no—
252C2C2×#1455657711yescharacteristic
253C2#1798939711yescharacteristic
254C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#417×C73C2
socleC22×C73C22×D4
hypercenter#417D73
hypocenterC73#3137
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #17989218C2semidirect
3. #17988954C2semidirect
4. #17988945C2semidirect
5. #17988940C2semidirect
6. #17988936C2semidirect
7. #17988597C2semidirect
9. C2×#14556514C2semidirect
10. #17988545C2semidirect
128. C73#3137semidirect