Finite Group Databasebeta

← #22619913

Subgroups — #22619913

Order 9344.

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

normal subgroups only

This group has 398 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#17989168C211yesmaximal, characteristic
2#17989067C211yesmaximal, characteristic, complemented
3#17988931C212yesmaximal, complemented
4#17988924C212yesmaximal, complemented
5#17988913C212yesmaximal, complemented
6#17988902C212yesmaximal, complemented
7C2×#14556524C211yesmaximal, characteristic, complemented
8#17988589C211yesmaximal, characteristic, complemented
9#17988581C211yesmaximal, characteristic, complemented
10#17988555C211yesmaximal, characteristic, complemented
11#428×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C2×#11924028C2211yescharacteristic
14C22×#10596831C2211yescharacteristic
15#14556571—21no—
16#14556571C2212yes—
17#14556566—21no—
18#14556566C2212yes—
19#14556565—22no—
20C4×Dic146—21no—
21C4×D292—21no—
22#14556551—22no—
23#14556549C2212yes—
24C2×C4⋊Dic73C2211yescharacteristic
25C4⋊C4×D73C2212yes—
26#14556524C2212yes—
27#14556524C2212yes—
28#14556516C2212yes—
29#14556514C2211yescharacteristic
30#14556514C2211yescharacteristic
31#14556513C2212yes—
32#14556511C2211yescharacteristic
33#14556511C2211yescharacteristic
34#14556503C2212yes—
35#14556503C2212yes—
36C2×M16×C73C2211yescharacteristic
37#117×C73C2211yescharacteristic
38C2×C4⋊C4×C73C2211yescharacteristic
39#107×C73C2212yes—
40#106×C73C2212yes—
41#11924028—22no—
42#11924028—22no—
43#11924028—22no—
44#11924028—22no—
45C2×Dic146D411yescharacteristic
46C2×Dic146C2311yescharacteristic
47C2×D292—22no—
48C2×D292D411yescharacteristic
49C2×D292C2311yescharacteristic
50C2×C22⋊D73—21no—
51C2×C22⋊D73D412yes—
52C22×Dic73—21no—
53C2×C4×D73—21no—
54C2×C4×D73—22no—
55C2×C4×D73C2312yes—
56C2×#10596831—22no—
57C2×#10596831C2311yescharacteristic
58C2×#10596831C2311yescharacteristic
59C4⋊Dic73—21no—
60C4⋊Dic73—22no—
61C4⋊Dic73C2312yes—
62#11924007—22no—
63#11924005—22no—
64#11924005—22no—
65#11924005—22no—
66C4×Dic73—22no—
67C22×C4×C73—21no—
68C22×C4×C73C2311yescharacteristic
69M16×C73—22no—
70C2×C8×C73C2312yes—
71C4⋊C4×C73—21no—
72C4⋊C4×C73C2311yescharacteristic
73C4⋊C4×C73C2312yes—
74C4⋊C4×C73C2311yescharacteristic
75C22⋊C4×C73—21no—
76C42×C73—21no—
77C23×C73C2×D411yescharacteristic
78C22×D73—21no—
79C22×D73C2×D412yes—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73—81no—
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73#4112yes—
86C2×C4×C73#4112yes—
87C2×C4×C73C2411yescharacteristic
88C22⋊D73—24no—
89C22⋊D73—42no—
90C2×Dic73—22no—
91C2×Dic73—21no—
92C2×Dic73—81no—
93C2×Dic73C2×D412yes—
94D292—22no—
95D292—21no—
96D292—21no—
97D292—82no—
98C4×D73—22no—
99C4×D73—22no—
100C4×D73—42no—
101C4×D73—82no—
102Dic146—22no—
103Dic146—21no—
104Dic146—21no—
105C8×C73—22no—
106#10596831—21no—
107#10596831—21no—
108C22×C73—21no—
109C22×C73—21no—
110C22×C73#12312yes—
111C22×C73C22×D411yescharacteristic
112C2×D73—22no—
113C2×D73—22no—
114C2×D73—22no—
115C2×D73—41no—
116C2×D73—41no—
117C2×D73—41no—
118C4×C73—41no—
119C4×C73—42no—
120C4×C73—41no—
121C4×C73#12312yes—
122C4×C73C2×#4111yescharacteristic
123C4×C73C2×#4111yescharacteristic
124Dic73—22no—
125Dic73—41no—
126Dic73—42no—
127C2×C73—22no—
128C2×C73C2×#12311yescharacteristic
129C2×C73#57611yescharacteristic
130C2×C73#57811yescharacteristic
131D73—42no—
132D73—81no—
133#3098—731nomaximal, Sylow
134C73#309811yescharacteristic, complemented, Sylow
135#537—731no—
136#520—731no—
137#485—732no—
138#484—732no—
139#482—732no—
140#480—732no—
141#428D7311yescharacteristic, complemented
142C2×#107—731no—
143#417—731no—
144#416—731no—
145#408—731no—
146C2×#41—731no—
147C2×#41—731no—
148C2×M16C2×D7311yescharacteristic
149C22×C8—731no—
150C22⋊Q8—732no—
151C22⋊Q8—1461no—
152#121—732no—
153#121—1461no—
154#121—1462no—
155C4×Q8—1461no—
156C4×D4—1461no—
157C4×D4—1462no—
158#117—732no—
159#117C2×D7311yescharacteristic
160C2×C4⋊C4—731no—
161C2×C4⋊C4—732no—
162C2×C4⋊C4C2×D7311yescharacteristic
163#107—732no—
164#107—732no—
165#107C2×D7312yes—
166#106C2×D7312yes—
167#103—732no—
168#103—731no—
169#103—731no—
170#102—732no—
171#102—731no—
172#102—731no—
173C22⋊C8—732no—
174C22⋊C8—732no—
175#41—1462no—
176#41—1462no—
177#41—1462no—
178#41—1462no—
179C2×Q8—731no—
180C2×Q8—731no—
181C2×D4—732no—
182C2×D4—731no—
183C2×D4—731no—
184C2×D4—1462no—
185C2×D4—1461no—
186C22×C4—21no—
187C22×C4—732no—
188C22×C4—1462no—
189C22×C4—1461no—
190C22×C4—1461no—
191C22×C4C22×D7311yescharacteristic
192M16—22no—
193C2×C8—731no—
194C2×C8—731no—
195C2×C8—1462no—
196C2×C8C22×D7312yes—
197C4⋊C4—21no—
198C4⋊C4—732no—
199C4⋊C4—1462no—
200C4⋊C4—1462no—
201C4⋊C4—1461no—
202C4⋊C4C22×D7311yescharacteristic
203C4⋊C4C22×D7311yescharacteristic
204C4⋊C4C22×D7312yes—
205C22⋊C4—21no—
206C22⋊C4—1462no—
207C22⋊C4—1462no—
208C22⋊C4—1462no—
209C42—21no—
210C42—1462no—
211C23—732no—
212C23—1461no—
213C23D4×D7311yescharacteristic
214Q8—1461no—
215Q8—1461no—
216Q8—1462no—
217D4—2922no—
218D4—5842no—
219D4—1464no—
220D4—1462no—
221D4—1461no—
222D4—1461no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—81no—
227C2×C4—2922no—
228C2×C4—5842no—
229C2×C4—5841no—
230C2×C4—732no—
231C2×C4—1462no—
232C2×C4—1461no—
233C2×C4—1462no—
234C2×C4—1462no—
235C2×C4D4×D7311yescharacteristic
236C2×C4#1192402812yes—
237C2×C4#1192402912yes—
238C2×C4C23×D7311yescharacteristic
239C8—22no—
240C8—1461no—
241C8—1461no—
242C22—21no—
243C22—21no—
244C22—2921no—
245C22—2921no—
246C22—2921no—
247C22—1462no—
248C22—1462no—
249C22—1462no—
250C22#1455657612yes—
251C22C2×D4×D7311yescharacteristic
252C4—42no—
253C4—41no—
254C4—41no—
255C4—2922no—
256C4—2921no—
257C4—1462no—
258C4#1455657612yes—
259C4C2×#1192402811yescharacteristic
260C4C2×#1192402911yescharacteristic
261C2—22no—
262C2—2922no—
263C2—5841no—
264C2C2×#1455657611yescharacteristic
265C2#1798939111yescharacteristic
266C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#428×C73C2
socleC22×C73C22×D4
hypercenter#428D73
hypocenterC73#3098
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #17989067C2semidirect
3. #17988931C2semidirect
4. #17988924C2semidirect
5. #17988913C2semidirect
6. #17988902C2semidirect
7. C2×#14556524C2semidirect
8. #17988589C2semidirect
9. #17988581C2semidirect
10. #17988555C2semidirect
11. #428×C73C2semidirect
134. C73#3098semidirect
141. #428D73semidirect