Finite Group Databasebeta

← #22619907

Subgroups — #22619907

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#17989165C211yesmaximal, characteristic
2#17989067C211yesmaximal, characteristic, complemented
3#17988927C212yesmaximal, complemented
4#17988921C212yesmaximal, complemented
5#17988909C212yesmaximal, complemented
6#17988899C212yesmaximal, complemented
7#17988630C211yesmaximal, characteristic, complemented
8C2×#14556525C211yesmaximal, characteristic, complemented
9#17988588C211yesmaximal, characteristic, complemented
10#17988553C211yesmaximal, characteristic, complemented
11#416×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C2×#11924012C2211yescharacteristic
14#14556570—21no—
15#14556567C2212yes—
16#14556565—21no—
17#14556563—22no—
18#14556562C2212yes—
19C4×Dic146—21no—
20C4×D292—21no—
21#14556551—22no—
22#14556549C2212yes—
23C2×C4⋊Dic73C2211yescharacteristic
24C2×C4⋊Dic73C2211yescharacteristic
25C4⋊C4×D73C2212yes—
26#14556525C2212yes—
27#14556525C2212yes—
28#14556524C2212yes—
29#14556522C2212yes—
30#14556515C2212yes—
31#14556512C2212yes—
32#14556503C2212yes—
33#14556503C2212yes—
34C2×#41×C73C2211yescharacteristic
35C22×C8×C73C2211yescharacteristic
36#117×C73C2211yescharacteristic
37#103×C73C2211yescharacteristic
38#103×C73C2211yescharacteristic
39#102×C73C2211yescharacteristic
40#102×C73C2211yescharacteristic
41#11924028—22no—
42#11924028—22no—
43C2×Dic146D411yescharacteristic
44C2×D292D411yescharacteristic
45C2×C22⋊D73—22no—
46C2×C22⋊D73D412yes—
47C22×Dic73—21no—
48C22×Dic73—21no—
49C2×C4×D73—22no—
50C2×C4×D73C2312yes—
51#11924012—22no—
52C2×#10596831C2312yes—
53C4⋊Dic73—21no—
54C4⋊Dic73—21no—
55C4⋊Dic73C2312yes—
56C4⋊Dic73C2312yes—
57#11924007—22no—
58#11924007—22no—
59C22⋊Dic73—22no—
60#11924005—22no—
61#11924005—22no—
62C4×Dic73—22no—
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
79C22×D73C2×D412yes—
80Q8×C73—21no—
81Q8×C73—21no—
82D4×C73—21no—
83D4×C73—21no—
84D4×C73—42no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—21no—
88C2×C4×C73—42no—
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73#4112yes—
91C2×C4×C73#4112yes—
92C2×C4×C73C2411yescharacteristic
93C22⋊D73—24no—
94C22⋊D73—82no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—81no—
98C2×Dic73—81no—
99C2×Dic73C2×D412yes—
100D292—22no—
101C4×D73—22no—
102C4×D73—22no—
103C4×D73—82no—
104Dic146—22no—
105C8×C73—21no—
106C8×C73—21no—
107#10596831—22no—
108C22×C73—21no—
109C22×C73—21no—
110C22×C73—41no—
111C22×C73—41no—
112C22×C73—41no—
113C22×C73#12312yes—
114C22×C73C22×D411yescharacteristic
115C2×D73—22no—
116C2×D73—22no—
117C2×D73—22no—
118C4×C73—41no—
119C4×C73—41no—
120C4×C73—41no—
121C4×C73#12312yes—
122C4×C73C2×#4111yescharacteristic
123C4×C73C2×#4111yescharacteristic
124Dic73—22no—
125Dic73—42no—
126Dic73—42no—
127C2×C73—22no—
128C2×C73—81no—
129C2×C73C2×#12311yescharacteristic
130C2×C73#57611yescharacteristic
131C2×C73#57811yescharacteristic
132D73—42no—
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#428—731no—
142C2×#107—731no—
143#417—731no—
144#416D7311yescharacteristic, complemented
145#408—731no—
146C2×#41—731no—
147C2×#41C2×D7311yescharacteristic
148C2×M16—731no—
149C22×C8C2×D7311yescharacteristic
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—731no—
162C2×C4⋊C4—732no—
163#107—732no—
164#107—732no—
165#107—732no—
166#106—732no—
167#103—732no—
168#103C2×D7311yescharacteristic
169#103C2×D7311yescharacteristic
170#102—732no—
171#102C2×D7311yescharacteristic
172#102C2×D7311yescharacteristic
173C22⋊C8—732no—
174C22⋊C8—732no—
175#41—22no—
176#41—22no—
177#41—1462no—
178#41—1462no—
179C2×Q8—731no—
180C2×Q8C22×D7311yescharacteristic
181C2×D4—21no—
182C2×D4—732no—
183C2×D4—731no—
184C2×D4—1462no—
185C2×D4C22×D7311yescharacteristic
186C22×C4—21no—
187C22×C4—732no—
188C22×C4—1462no—
189C22×C4—1461no—
190C22×C4—1461no—
191C22×C4C22×D7311yescharacteristic
192M16—1462no—
193C2×C8—22no—
194C2×C8—732no—
195C2×C8C22×D7311yescharacteristic
196C2×C8C22×D7311yescharacteristic
197C4⋊C4—732no—
198C4⋊C4—732no—
199C4⋊C4—1462no—
200C4⋊C4—1462no—
201C4⋊C4—1461no—
202C4⋊C4—1461no—
203C4⋊C4C22×D7311yescharacteristic
204C4⋊C4C22×D7311yescharacteristic
205C22⋊C4—21no—
206C22⋊C4—1462no—
207C22⋊C4—1462no—
208C22⋊C4—1462no—
209C42—21no—
210C42—1462no—
211C23—21no—
212C23—732no—
213C23D4×D7311yescharacteristic
214Q8—21no—
215Q8—21no—
216Q8—1462no—
217D4—21no—
218D4—21no—
219D4—42no—
220D4—5842no—
221D4—1464no—
222D4—1462no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—5842no—
228C2×C4—5841no—
229C2×C4—5841no—
230C2×C4—732no—
231C2×C4—1462no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4—1462no—
235C2×C4D4×D7311yescharacteristic
236C2×C4#1192402712yes—
237C2×C4#1192402812yes—
238C2×C4C23×D7311yescharacteristic
239C8—21no—
240C8—21no—
241C8—1462no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—1462no—
248C22—1462no—
249C22—1462no—
250C22#1455657312yes—
251C22C2×D4×D7311yescharacteristic
252C4—41no—
253C4—41no—
254C4—41no—
255C4—2922no—
256C4—2922no—
257C4—1462no—
258C4#1455657312yes—
259C4C2×#1192402711yescharacteristic
260C4C2×#1192402811yescharacteristic
261C2—22no—
262C2—81no—
263C2—2922no—
264C2C2×#1455657311yescharacteristic
265C2#1798938911yescharacteristic
266C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#416×C73C2
socleC22×C73C22×D4
hypercenter#416D73
hypocenterC73#3098
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
2. #17989067C2semidirect
3. #17988927C2semidirect
4. #17988921C2semidirect
5. #17988909C2semidirect
6. #17988899C2semidirect
7. #17988630C2semidirect
8. C2×#14556525C2semidirect
9. #17988588C2semidirect
10. #17988553C2semidirect
11. #416×C73C2semidirect
134. C73#3098semidirect
144. #416D73semidirect