Finite Group Databasebeta

← #22620300

Subgroups — #22620300

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#17989215C211yesmaximal, characteristic, complemented
2#17989158C211yesmaximal, characteristic
3#17988954C212yesmaximal, complemented
4#17988945C212yesmaximal, complemented
5#17988940C212yesmaximal, complemented
6#17988936C212yesmaximal, complemented
7#17988595C211yesmaximal, characteristic, complemented
8#17988588C211yesmaximal, characteristic
9C2×#14556516C211yesmaximal, characteristic, complemented
10#17988542C211yesmaximal, characteristic, complemented
11#416×C73C211yesmaximal, characteristic
12C22×Dic146C2211yescharacteristic
13C2×#11924012C2211yescharacteristic
14#14556591—21no—
15#14556590C2212yes—
16#14556589C2212yes—
17#14556583—21no—
18#14556582C2212yes—
19#14556578C2212yes—
20#14556572—22no—
21#14556570—21no—
22#14556570—21no—
23#14556568—22no—
24#14556550C2211yescharacteristic
25C2×C4⋊Dic73C2211yescharacteristic
26#14556516C2212yes—
27#14556516C2212yes—
28#14556515C2212yes—
29#14556514C2212yes—
30#14556514C2212yes—
31#14556512C2212yes—
32#14556501C2212yes—
33C8×Dic73C2212yes—
34C2×#41×C73C2211yescharacteristic
35C22×C8×C73C2211yescharacteristic
36#117×C73C2211yescharacteristic
37#103×C73C2211yescharacteristic
38#103×C73C2211yescharacteristic
39#102×C73C2211yescharacteristic
40#102×C73C2211yescharacteristic
41C2×Dic146—22no—
42C2×Dic146—22no—
43C2×Dic146—21no—
44C2×Dic146—22no—
45C2×Dic146C2312yes—
46C22×Dic73—21no—
47C22×Dic73—21no—
48#11924012—22no—
49C2×#10596831C2312yes—
50C4⋊Dic73—21no—
51C4⋊Dic73—22no—
52C4⋊Dic73D411yescharacteristic
53C4⋊Dic73D411yescharacteristic
54C4⋊Dic73C2312yes—
55#11924007—22no—
56#11924007—22no—
57#11924007—22no—
58#11924007—22no—
59C22⋊Dic73—22no—
60C22⋊Dic73—22no—
61C22⋊Dic73D412yes—
62C4×Dic73C2312yes—
63#41×C73—22no—
64#41×C73—22no—
65C2×Q8×C73C2311yescharacteristic
66C2×D4×C73—21no—
67C2×D4×C73C2311yescharacteristic
68C22×C4×C73—21no—
69C22×C4×C73C2311yescharacteristic
70C2×C8×C73—22no—
71C2×C8×C73C2311yescharacteristic
72C2×C8×C73C2311yescharacteristic
73C4⋊C4×C73C2311yescharacteristic
74C4⋊C4×C73C2311yescharacteristic
75C22⋊C4×C73—21no—
76C42×C73—21no—
77C23×C73—21no—
78C23×C73C2×D411yescharacteristic
79Q8×C73—21no—
80Q8×C73—21no—
81D4×C73—21no—
82D4×C73—21no—
83D4×C73—42no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—42no—
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73#4112yes—
90C2×C4×C73#4112yes—
91C2×C4×C73C2411yescharacteristic
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—42no—
95C2×Dic73—81no—
96C2×Dic73C2×D412yes—
97C2×Dic73C2×D412yes—
98Dic146—22no—
99Dic146—22no—
100Dic146—42no—
101Dic146—82no—
102C8×C73—21no—
103C8×C73—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—41no—
113C4×C73—41no—
114C4×C73—41no—
115C4×C73#12412yes—
116C4×C73C2×#4111yescharacteristic
117C4×C73C2×#4111yescharacteristic
118Dic73—22no—
119Dic73—22no—
120Dic73—42no—
121Dic73—42no—
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#417—731no—
137#416D7311yescharacteristic
138C2×#103—731no—
139#405—731no—
140C2×#41C2×D7311yescharacteristic
141C22×Q8—731no—
142C2×M16—731no—
143C22×C8C2×D7311yescharacteristic
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#117C2×D7311yescharacteristic
156C2×C4⋊C4—731no—
157#103—732no—
158#103—732no—
159#103—732no—
160#103—732no—
161#103—732no—
162#103C2×D7311yescharacteristic
163#103C2×D7311yescharacteristic
164#102—732no—
165#102C2×D7311yescharacteristic
166#102C2×D7311yescharacteristic
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—1461no—
181C22×C4—1461no—
182C22×C4C22×D7311yescharacteristic
183M16—1462no—
184C2×C8—22no—
185C2×C8—732no—
186C2×C8C22×D7311yescharacteristic
187C2×C8C22×D7311yescharacteristic
188C4⋊C4—731no—
189C4⋊C4—731no—
190C4⋊C4—732no—
191C4⋊C4—1462no—
192C4⋊C4—1462no—
193C4⋊C4—1462no—
194C4⋊C4—1462no—
195C4⋊C4—1462no—
196C4⋊C4—1461no—
197C4⋊C4C22×D7311yescharacteristic
198C4⋊C4C22×D7311yescharacteristic
199C22⋊C4—21no—
200C22⋊C4—732no—
201C22⋊C4—1462no—
202C22⋊C4—1462no—
203C42—21no—
204C42—732no—
205C23—21no—
206C23D4×D7311yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—2922no—
210Q8—5842no—
211Q8—1462no—
212Q8—1462no—
213D4—21no—
214D4—21no—
215D4—42no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—2922no—
221C2×C4—5841no—
222C2×C4—732no—
223C2×C4—732no—
224C2×C4—1462no—
225C2×C4—1462no—
226C2×C4D4×D7311yescharacteristic
227C2×C4#1192402712yes—
228C2×C4#1192402812yes—
229C2×C4C23×D7311yescharacteristic
230C8—21no—
231C8—21no—
232C8—1462no—
233C22—21no—
234C22—21no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22#1455657712yes—
239C22C2×D4×D7311yescharacteristic
240C4—41no—
241C4—41no—
242C4—41no—
243C4—2922no—
244C4—2922no—
245C4—1462no—
246C4—1462no—
247C4#1455657712yes—
248C4C2×#1192402711yescharacteristic
249C4C2×#1192402811yescharacteristic
250C2—22no—
251C2—81no—
252C2C2×#1455657711yescharacteristic
253C2#1798939411yescharacteristic
254C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#416×C73C2
socleC22×C73C22×D4
hypercenter#416D73
hypocenterC73#3137
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #17989215C2semidirect
3. #17988954C2semidirect
4. #17988945C2semidirect
5. #17988940C2semidirect
6. #17988936C2semidirect
7. #17988595C2semidirect
9. C2×#14556516C2semidirect
10. #17988542C2semidirect
128. C73#3137semidirect