Finite Group Databasebeta

← #22619596

Subgroups — #22619596

Order 9344.

484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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×#14556610C211yesmaximal, characteristic, complemented
2C2×#14556597C211yesmaximal, characteristic, complemented
3#17989166C212yesmaximal, complemented
4#17988832C212yesmaximal, complemented
5#17988831C212yesmaximal, complemented
6#17988829C211yesmaximal, characteristic, complemented
7#17988828C211yesmaximal, characteristic, complemented
8#17988820C211yesmaximal, characteristic, complemented
9#107×D73C211yesmaximal, characteristic, complemented
10#17988585C212yesmaximal, complemented
11#466×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C2×#11924027C2212yes—
14#14556610—24no—
15C2×Dic292C2211yescharacteristic
16C2×#11924016C2212yes—
17#14556597—24no—
18C2×#11924012C2211yescharacteristic
19C2×#11924011C2211yescharacteristic
20C2×#11924011C2211yescharacteristic
21C2×C8×D73C2211yescharacteristic
22C2×C8×D73C2211yescharacteristic
23#14556571C2212yes—
24#14556570C2212yes—
25#14556568—22no—
26#14556564—22no—
27#14556563—22no—
28#14556562—22no—
29#14556562C2212yes—
30C4⋊C4×D73C2212yes—
31#14556525C2211yescharacteristic
32#14556524C2212yes—
33#14556516C2212yes—
34#14556514C2212yes—
35#14556512C2212yes—
36C2×D8×C73C2211yescharacteristic
37C22×C8×C73C2211yescharacteristic
38#121×C73C2212yes—
39#107×C73C2211yescharacteristic
40#102×C73C2212yes—
41#11924028—22no—
42#11924028—22no—
43#11924027—24no—
44#11924027—24no—
45C2×Dic146D411yescharacteristic
46C2×Dic146C2312yes—
47C2×D292D411yescharacteristic
48C2×C22⋊D73—22no—
49C2×C22⋊D73—22no—
50C2×C22⋊D73D411yescharacteristic
51C2×C22⋊D73D411yescharacteristic
52C22×Dic73—22no—
53C2×C4×D73—22no—
54C2×C4×D73C2311yescharacteristic
55C2×C4×D73C2311yescharacteristic
56Dic292—22no—
57#11924016—24no—
58#11924012—22no—
59#11924011—22no—
60#11924011—22no—
61C2×#10596831C2311yescharacteristic
62C2×#10596831C2311yescharacteristic
63C8×D73—22no—
64C8×D73D414yescomplemented
65C4⋊Dic73—22no—
66C4⋊Dic73C2312yes—
67#11924007—22no—
68#11924007—22no—
69C22⋊Dic73—22no—
70C22⋊Dic73—22no—
71#11924005—22no—
72C2×D4×C73—22no—
73C2×D4×C73C2312yes—
74C22×C4×C73C2311yescharacteristic
75D8×C73—22no—
76C2×C8×C73—22no—
77C2×C8×C73C2311yescharacteristic
78C2×C8×C73C2311yescharacteristic
79C4⋊C4×C73C2312yes—
80C22⋊C4×C73—22no—
81C23×C73—22no—
82C23×C73C2×D411yescharacteristic
83C22×D73C2×D411yescharacteristic
84C22×D73C2×D411yescharacteristic
85D4×C73—22no—
86D4×C73—22no—
87D4×C73—82no—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—22no—
91C2×C4×C73C2×D411yescharacteristic
92C2×C4×C73C2411yescharacteristic
93C22⋊D73—22no—
94C22⋊D73—22no—
95C22⋊D73—44no—
96C22⋊D73—82no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—44no—
100C2×Dic73C2×D411yescharacteristic
101C2×Dic73C2×D411yescharacteristic
102D292—22no—
103C4×D73—21no—
104C4×D73—21no—
105C4×D73—82no—
106C4×D73C2×D412yes—
107C4×D73#4112yes—
108Dic146—22no—
109Dic146—22no—
110Dic146—22no—
111C8×C73—21no—
112C8×C73C2×D412yes—
113#10596831—21no—
114#10596831C2×D412yes—
115C22×C73—21no—
116C22×C73—21no—
117C22×C73—21no—
118C22×C73—42no—
119C22×C73—42no—
120C22×C73—42no—
121C22×C73C22×D411yescharacteristic
122C2×D73—21no—
123C2×D73—21no—
124C2×D73—21no—
125C2×D73—21no—
126C2×D73—21no—
127C2×D73#12112yes—
128C4×C73—21no—
129C4×C73—42no—
130C4×C73C22×D411yescharacteristic
131C4×C73C2×#4111yescharacteristic
132Dic73—21no—
133Dic73—42no—
134Dic73—42no—
135Dic73#12112yes—
136C2×C73—41no—
137C2×C73—82no—
138C2×C73C2×#12111yescharacteristic
139C2×C73#57611yescharacteristic
140C2×C73#57811yescharacteristic
141D73—22no—
142D73—41no—
143#3061—731nomaximal, Sylow
144C73#306111yescharacteristic, complemented, Sylow
145C2×#135—731no—
146C2×#131—731no—
147#537—732no—
148#468—732no—
149#468—732no—
150#467—731no—
151#467—731no—
152#466—731no—
153#466D7311yescharacteristic, complemented
154C2×#107—731no—
155#417—732no—
156C2×#41—731no—
157C2×#41—732no—
158#135—1464no—
159C2×Q16—731no—
160C2×SD16—732no—
161C2×D8C2×D7311yescharacteristic
162#131—1464no—
163C2×M16—731no—
164C2×M16—731no—
165C2×M16—731no—
166C22×C8—731no—
167C22×C8—731no—
168C22×C8C2×D7311yescharacteristic
169C22⋊Q8—732no—
170C22⋊Q8—732no—
171C22⋊Q8—1462no—
172#121—732no—
173#121—1462no—
174#121—1462no—
175#121—1462no—
176#121C2×D7312yes—
177C2×C4⋊C4—732no—
178#107—731no—
179#107—732no—
180#107C2×D7311yescharacteristic
181#103—732no—
182#103—732no—
183#102—732no—
184#102C2×D7312yes—
185#41—1462no—
186#41—1462no—
187#41—1464no—
188#41—1464no—
189C2×Q8—731no—
190C2×Q8—732no—
191C2×D4—22no—
192C2×D4—731no—
193C2×D4—731no—
194C2×D4—731no—
195C2×D4—1462no—
196C2×D4—1462no—
197C2×D4C22×D7312yes—
198C22×C4—731no—
199C22×C4—731no—
200C22×C4—1462no—
201C22×C4—1462no—
202C22×C4C22×D7311yescharacteristic
203Q16—1462no—
204SD16—1464no—
205D8—22no—
206M16—1462no—
207M16—1462no—
208M16—1462no—
209C2×C8—22no—
210C2×C8—731no—
211C2×C8—734no—
212C2×C8—731no—
213C2×C8—1462no—
214C2×C8C22×D7311yescharacteristic
215C2×C8C22×D7311yescharacteristic
216C4⋊C4—732no—
217C4⋊C4—1462no—
218C4⋊C4—1462no—
219C4⋊C4—1462no—
220C4⋊C4C22×D7312yes—
221C22⋊C4—22no—
222C22⋊C4—1462no—
223C22⋊C4—1462no—
224C22⋊C4—1462no—
225C23—22no—
226C23—731no—
227C23—731no—
228C23D4×D7311yescharacteristic
229Q8—1462no—
230Q8—1462no—
231Q8—1462no—
232D4—22no—
233D4—22no—
234D4—82no—
235D4—2924no—
236D4—5842no—
237D4—1462no—
238D4—1462no—
239D4—1462no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—2924no—
244C2×C4—5842no—
245C2×C4—731no—
246C2×C4—732no—
247C2×C4—732no—
248C2×C4—731no—
249C2×C4—1462no—
250C2×C4—1462no—
251C2×C4—1461no—
252C2×C4—1461no—
253C2×C4D4×D7311yescharacteristic
254C2×C4C23×D7311yescharacteristic
255C8—21no—
256C8—732no—
257C8—1461no—
258C8D4×D7312yes—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—732no—
266C22—1461no—
267C22—1461no—
268C22—1461no—
269C22—1461no—
270C22—1461no—
271C22C2×D4×D7311yescharacteristic
272C4—21no—
273C4—42no—
274C4—2922no—
275C4—2922no—
276C4—732no—
277C4—1461no—
278C4C2×D4×D7311yescharacteristic
279C4#41×D7311yescharacteristic
280C2—41no—
281C2—82no—
282C2—2921no—
283C2—1462no—
284C2#121×D7311yescharacteristic
285C2#1798938811yescharacteristic
286C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#466×C73C2
socleC22×C73C22×D4
hypercenter#466D73
hypocenterC73#3061
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#14556610C2semidirect
2. C2×#14556597C2semidirect
3. #17989166C2semidirect
4. #17988832C2semidirect
5. #17988831C2semidirect
6. #17988829C2semidirect
7. #17988828C2semidirect
8. #17988820C2semidirect
9. #107×D73C2semidirect
10. #17988585C2semidirect
11. #466×C73C2semidirect
64. C8×D73D4semidirect
144. C73#3061semidirect
153. #466D73semidirect