Finite Group Databasebeta

← #22619620

Subgroups — #22619620

Order 9344.

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

normal subgroups only

This group has 472 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
1C2×#14556622C211yesmaximal, characteristic, complemented
2C2×#14556597C211yesmaximal, characteristic, complemented
3#17989168C211yesmaximal, characteristic
4#17989161C211yesmaximal, characteristic, complemented
5#17988844C212yesmaximal, complemented
6#17988836C212yesmaximal, complemented
7#17988827C212yesmaximal, complemented
8#17988819C212yesmaximal, complemented
9#17988627C211yesmaximal, characteristic, complemented
10#17988584C211yesmaximal, characteristic, complemented
11C2×#103×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C2×#11924028C2211yescharacteristic
14#14556622—24no—
15C2×#11924018C2212yes—
16C2×#11924015C2212yes—
17#14556597—24no—
18C2×#11924012C2211yescharacteristic
19C2×#11924011C2212yes—
20C2×C8×D73C2212yes—
21#14556589—21no—
22#14556580—21no—
23#14556574—22no—
24#14556571—21no—
25#14556571C2212yes—
26#14556567C2212yes—
27#14556567C2212yes—
28#14556566—21no—
29#14556566C2212yes—
30#14556565—22no—
31#14556550C2211yescharacteristic
32#14556524C2212yes—
33#14556522C2212yes—
34#14556516C2211yescharacteristic
35#14556516C2211yescharacteristic
36#14556513C2211yescharacteristic
37#14556513C2211yescharacteristic
38C22×Q8×C73C2211yescharacteristic
39C22×C8×C73C2211yescharacteristic
40C2×C4⋊C4×C73C2211yescharacteristic
41#103×C73C2212yes—
42#103×C73C2212yes—
43#11924028—22no—
44#11924028—22no—
45#11924028—22no—
46#11924028—22no—
47C2×Dic146D411yescharacteristic
48C2×Dic146C2311yescharacteristic
49C2×D292—22no—
50C2×D292D411yescharacteristic
51C2×D292C2311yescharacteristic
52C2×C22⋊D73—21no—
53C2×C22⋊D73D412yes—
54C2×C4×D73—21no—
55C2×C4×D73C2312yes—
56#11924018—24no—
57#11924015—24no—
58#11924012D414yescomplemented
59#11924011—24no—
60C2×#10596831C2312yes—
61C8×D73—24no—
62C4⋊Dic73—22no—
63C4⋊Dic73C2311yescharacteristic
64C4⋊Dic73C2311yescharacteristic
65#11924007—22no—
66#11924007—22no—
67C22⋊Dic73—21no—
68#11924005—22no—
69#11924005—22no—
70#11924005—22no—
71#11924005—22no—
72C4×Dic73—21no—
73C2×Q8×C73—21no—
74C2×Q8×C73—22no—
75C2×Q8×C73—22no—
76C2×Q8×C73C2312yes—
77C22×C4×C73—21no—
78C22×C4×C73—21no—
79C22×C4×C73C2311yescharacteristic
80C2×C8×C73—22no—
81C2×C8×C73C2311yescharacteristic
82C2×C8×C73C2311yescharacteristic
83C4⋊C4×C73—21no—
84C4⋊C4×C73C2312yes—
85C23×C73C2×D411yescharacteristic
86C22×D73—21no—
87C22×D73C2×D412yes—
88Q8×C73—22no—
89Q8×C73—22no—
90Q8×C73—42no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—42no—
94C2×C4×C73—81no—
95C2×C4×C73C2×D411yescharacteristic
96C2×C4×C73C2×D412yes—
97C2×C4×C73#4112yes—
98C2×C4×C73C2411yescharacteristic
99C22⋊D73—24no—
100C22⋊D73—42no—
101C2×Dic73—21no—
102C2×Dic73—21no—
103C2×Dic73—21no—
104C2×Dic73C2×D412yes—
105D292—22no—
106D292—21no—
107D292—21no—
108D292—82no—
109C4×D73—22no—
110C4×D73—22no—
111C4×D73—42no—
112Dic146—22no—
113Dic146—21no—
114Dic146—21no—
115C8×C73—21no—
116C8×C73—21no—
117#10596831C2×D414yes—
118C22×C73—21no—
119C22×C73—21no—
120C22×C73#12112yes—
121C22×C73C22×D411yescharacteristic
122C2×D73—22no—
123C2×D73—22no—
124C2×D73—22no—
125C2×D73—41no—
126C2×D73—41no—
127C2×D73—41no—
128C4×C73—42no—
129C4×C73—42no—
130C4×C73#12112yes—
131C4×C73C22×D411yescharacteristic
132C4×C73C2×#4111yescharacteristic
133Dic73—22no—
134Dic73—41no—
135Dic73—41no—
136Dic73—41no—
137C2×C73—22no—
138C2×C73C2×#12111yescharacteristic
139C2×C73#57711yescharacteristic
140C2×C73#57811yescharacteristic
141D73—42no—
142D73—81no—
143#3063—731nomaximal, Sylow
144C73#306311yescharacteristic, complemented, Sylow
145C2×#137—731no—
146C2×#131—731no—
147#537—731no—
148#536—731no—
149#470—732no—
150#468—732no—
151#467—732no—
152#465—732no—
153#428—731no—
154#416—731no—
155C2×#103D7311yescharacteristic, complemented
156C2×#41—731no—
157C2×#41—731no—
158C22×Q8C2×D7311yescharacteristic
159#137—1464no—
160C2×Q16—732no—
161C2×SD16—732no—
162#131—1464no—
163C2×M16—731no—
164C2×M16—732no—
165C22×C8—732no—
166C22×C8C2×D7311yescharacteristic
167C4⋊Q8—1461no—
168#124—1461no—
169#123—1462no—
170C22⋊Q8—732no—
171C22⋊Q8—732no—
172C22⋊Q8—732no—
173C22⋊Q8—1461no—
174#121—732no—
175#121—1461no—
176#121—1462no—
177#117—731no—
178C2×C4⋊C4C2×D7311yescharacteristic
179#107—732no—
180#106—732no—
181#103—731no—
182#103—731no—
183#103C2×D7312yes—
184#103C2×D7312yes—
185#102—731no—
186#102—731no—
187#41—1462no—
188#41—1462no—
189#41—1462no—
190#41—1462no—
191C2×Q8—21no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—731no—
195C2×Q8—731no—
196C2×Q8C22×D7312yes—
197C2×D4—732no—
198C2×D4—731no—
199C2×D4—731no—
200C2×D4—1462no—
201C2×D4—1461no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—732no—
205C22×C4—1461no—
206C22×C4C22×D7311yescharacteristic
207Q16—1464no—
208SD16—1464no—
209M16—734no—
210M16—1464no—
211C2×C8—22no—
212C2×C8—732no—
213C2×C8—1464no—
214C2×C8C22×D7311yescharacteristic
215C2×C8C22×D7311yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—731no—
218C4⋊C4—731no—
219C4⋊C4—1462no—
220C4⋊C4—1462no—
221C4⋊C4—1462no—
222C4⋊C4C22×D7312yes—
223C22⋊C4—1462no—
224C22⋊C4—1462no—
225C22⋊C4—1462no—
226C22⋊C4—1462no—
227C22⋊C4—1461no—
228C42—1461no—
229C23—732no—
230C23—1461no—
231C23D4×D7311yescharacteristic
232Q8—22no—
233Q8—22no—
234Q8—42no—
235Q8—1461no—
236Q8—1461no—
237Q8—1462no—
238D4—2922no—
239D4—5842no—
240D4—1464no—
241D4—1462no—
242D4—1461no—
243D4—1461no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—81no—
248C2×C4—2922no—
249C2×C4—732no—
250C2×C4—1461no—
251C2×C4—1461no—
252C2×C4—1461no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4D4×D7311yescharacteristic
256C2×C4D4×D7312yes—
257C2×C4#1192402812yes—
258C2×C4C23×D7311yescharacteristic
259C8—21no—
260C8—21no—
261C8—734no—
262C22—21no—
263C22—21no—
264C22—2921no—
265C22—2921no—
266C22—2921no—
267C22—1462no—
268C22—1462no—
269C22—1462no—
270C22#1455656412yes—
271C22C2×D4×D7311yescharacteristic
272C4—42no—
273C4—42no—
274C4—2921no—
275C4—2921no—
276C4—2921no—
277C4—1462no—
278C4#1455656412yes—
279C4C2×D4×D7311yescharacteristic
280C4C2×#1192402811yescharacteristic
281C2—22no—
282C2—2922no—
283C2—5841no—
284C2C2×#1455656411yescharacteristic
285C2#1798939311yescharacteristic
286C2#1798940011yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#103×C73C2
socleC22×C73C22×D4
hypercenterC2×#103D73
hypocenterC73#3063
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C2×#14556622C2semidirect
2. C2×#14556597C2semidirect
4. #17989161C2semidirect
5. #17988844C2semidirect
6. #17988836C2semidirect
7. #17988827C2semidirect
8. #17988819C2semidirect
9. #17988627C2semidirect
10. #17988584C2semidirect
11. C2×#103×C73C2semidirect
58. #11924012D4semidirect
144. C73#3063semidirect
155. C2×#103D73semidirect