Finite Group Databasebeta

← #22620745

Subgroups — #22620745

Order 9344.

466 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 121 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#17989098C211yesmaximal, characteristic, complemented
2#17988917C211yesmaximal, characteristic, complemented
3#17988908C212yesmaximal, complemented
4#17988900C211yesmaximal, characteristic, complemented
5#17988838C212yesmaximal, complemented
6#17988831C212yesmaximal, complemented
7#17988738C211yesmaximal, characteristic, complemented
8#17988730C212yesmaximal, complemented
9#17988721C211yesmaximal, characteristic, complemented
10#17988551C211yesmaximal, characteristic, complemented
11C2×#121×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic, complemented
13C2×#11924016C2212yescomplemented
14C2×#11924013C2212yescomplemented
15C2×#11924012C2212yescomplemented
16#14556574—21no—
17#14556570C2211yescharacteristic
18#14556570C2211yescharacteristic, complemented
19#14556565C2211yescharacteristic
20#14556565C2211yescharacteristic, complemented
21#14556560—21no—
22C4×C22⋊D73—21no—
23C4×C22⋊D73—21no—
24#14556550C2211yescharacteristic, complemented
25#14556524C2212yescomplemented
26#14556522C2212yescomplemented
27#14556514C2212yescomplemented
28#14556512C2212yescomplemented
29#14556512C2212yescomplemented
30#14556511C2212yescomplemented
31C22⋊#10596831C2211yescharacteristic
32C22⋊#10596831C2211yescharacteristic
33C22⋊#10596831C2212yescomplemented
34C22×D4×C73—21no—
35C22×D4×C73C2211yescharacteristic
36C23×C4×C73C2211yescharacteristic
37#121×C73—21no—
38#121×C73—21no—
39#121×C73C2212yes—
40#121×C73C2212yes—
41C2×C4⋊C4×C73C2211yescharacteristic
42C2×C22⋊C4×C73—21no—
43#11924028—42no—
44C2×Dic146C2311yescharacteristic
45C2×D292C2311yescharacteristic
46C2×C22⋊D73—21no—
47C2×C22⋊D73—21no—
48C2×C22⋊D73—21no—
49C2×C4×D73—21no—
50#11924016—42no—
51#11924013—42no—
52#11924012—42no—
53C2×#10596831C2312yes—
54C2×#10596831C2312yes—
55C4⋊Dic73C2311yescharacteristic
56C4⋊Dic73C2311yescharacteristic
57#11924007—21no—
58#11924007—21no—
59C22⋊Dic73—21no—
60C22⋊Dic73—21no—
61C22⋊Dic73—21no—
62#11924005—21no—
63#11924005—21no—
64C4×Dic73—21no—
65C24×C73—21no—
66C24×C73D411yescharacteristic
67C2×D4×C73—22no—
68C2×D4×C73—22no—
69C2×D4×C73—21no—
70C2×D4×C73—42no—
71C2×D4×C73—44no—
72C2×D4×C73C2312yes—
73C22×C4×C73—21no—
74C22×C4×C73—42no—
75C22×C4×C73D411yescharacteristic
76C22×C4×C73D411yescharacteristic
77C22×C4×C73D411yescharacteristic
78C22×C4×C73C2311yescharacteristic
79C22×C4×C73C2311yescharacteristic
80C22×C4×C73C2311yescharacteristic
81C4⋊C4×C73—21no—
82C4⋊C4×C73C2312yes—
83C22⋊C4×C73—22no—
84C22⋊C4×C73—22no—
85C23×C73—22no—
86C23×C73—22no—
87C23×C73—41no—
88C23×C73—41no—
89C23×C73—42no—
90C23×C73—42no—
91C23×C73—42no—
92C23×C73C2×D411yescharacteristic
93C23×C73C2×D411yescharacteristic
94C23×C73C2×D411yescharacteristic
95C22×D73—21no—
96D4×C73—22no—
97D4×C73—22no—
98D4×C73—42no—
99D4×C73—44no—
100D4×C73—44no—
101C2×C4×C73—22no—
102C2×C4×C73—22no—
103C2×C4×C73—22no—
104C2×C4×C73—22no—
105C2×C4×C73—41no—
106C2×C4×C73—41no—
107C2×C4×C73—41no—
108C2×C4×C73—42no—
109C2×C4×C73C2×D411yescharacteristic
110C2×C4×C73C2×D411yescharacteristic
111C2×C4×C73C2×D411yescharacteristic
112C2×C4×C73C2411yescharacteristic
113C22⋊D73—42no—
114C22⋊D73—42no—
115C22⋊D73—42no—
116C2×Dic73—21no—
117C2×Dic73—21no—
118C2×Dic73—21no—
119D292—22no—
120C4×D73—42no—
121Dic146—22no—
122#10596831—22no—
123#10596831—22no—
124C22×C73—21no—
125C22×C73—21no—
126C22×C73—21no—
127C22×C73—21no—
128C22×C73—21no—
129C22×C73—21no—
130C22×C73—21no—
131C22×C73—21no—
132C22×C73—44no—
133C22×C73—42no—
134C22×C73—42no—
135C22×C73—42no—
136C22×C73—84no—
137C22×C73AGL(1,ℤ/8)12yes—
138C22×C73C22×D411yescharacteristic
139C2×D73—41no—
140C2×D73—41no—
141C2×D73—41no—
142C4×C73—21no—
143C4×C73—21no—
144C4×C73—21no—
145C4×C73—42no—
146C4×C73H(5,𝔽2)12yes—
147Dic73—41no—
148Dic73—41no—
149Dic73—41no—
150C2×C73—22no—
151C2×C73—41no—
152C2×C73—41no—
153C2×C73—82no—
154C2×C73#53411yescharacteristic
155C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
156C2×C73#57511yescharacteristic
157D73—81no—
158#3194—731nomaximal, Sylow
159C73#319411yescharacteristic, complemented, Sylow
160#525—731no—
161C2×#121D7311yescharacteristic, complemented
162#483—731no—
163#482—732no—
164#480—731no—
165#469—732no—
166#468—732no—
167#450—731no—
168#449—732no—
169#447—731no—
170#407—731no—
171C2×#41—731no—
172C22×D4—21no—
173C22×D4C2×D7311yescharacteristic
174C23×C4C2×D7311yescharacteristic
175C2×SD16—732no—
176C2×D8—732no—
177C2×M16—732no—
178#123—1461no—
179C22⋊Q8—731no—
180C22⋊Q8—731no—
181#121—21no—
182#121—21no—
183#121—731no—
184#121—731no—
185#121C2×D7312yes—
186#121C2×D7312yes—
187#120—1461no—
188C4×D4—1461no—
189C4×D4—1461no—
190#117—731no—
191C2×C4⋊C4C2×D7311yescharacteristic
192C2×C22⋊C4—21no—
193#107—732no—
194#106—732no—
195#103—732no—
196#102—732no—
197#102—732no—
198#102—732no—
199C22⋊C8—731no—
200C22⋊C8—731no—
201C22⋊C8—732no—
202C24—21no—
203C24C22⋊D7311yescharacteristic
204#41—2922no—
205C2×Q8—731no—
206C2×D4—22no—
207C2×D4—22no—
208C2×D4—21no—
209C2×D4—42no—
210C2×D4—44no—
211C2×D4—731no—
212C2×D4—1461no—
213C2×D4—1461no—
214C2×D4—1461no—
215C2×D4C22×D7312yes—
216C22×C4—21no—
217C22×C4—42no—
218C22×C4—1461no—
219C22×C4C22⋊D7311yescharacteristic
220C22×C4C22⋊D7311yescharacteristic
221C22×C4C22⋊D7311yescharacteristic
222C22×C4C22×D7311yescharacteristic
223C22×C4C22×D7311yescharacteristic
224C22×C4C22×D7311yescharacteristic
225SD16—2922no—
226D8—2922no—
227M16—2922no—
228C2×C8—732no—
229C2×C8—732no—
230C4⋊C4—21no—
231C4⋊C4—731no—
232C4⋊C4—731no—
233C4⋊C4—1461no—
234C4⋊C4—1461no—
235C4⋊C4C22×D7312yes—
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—1461no—
239C22⋊C4—1461no—
240C22⋊C4—1461no—
241C22⋊C4—1461no—
242C22⋊C4—1461no—
243C42—1461no—
244C23—22no—
245C23—22no—
246C23—41no—
247C23—41no—
248C23—42no—
249C23—42no—
250C23—42no—
251C23—1461no—
252C23C2×C22⋊D7311yescharacteristic
253C23C2×C22⋊D7311yescharacteristic
254C23C2×C22⋊D7311yescharacteristic
255Q8—1462no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—44no—
260D4—44no—
261D4—2922no—
262D4—2922no—
263D4—2922no—
264D4—1462no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—2922no—
274C2×C4—1461no—
275C2×C4—1461no—
276C2×C4—1461no—
277C2×C4C2×C22⋊D7311yescharacteristic
278C2×C4C2×C22⋊D7311yescharacteristic
279C2×C4C2×C22⋊D7311yescharacteristic
280C2×C4C23×D7311yescharacteristic
281C8—1462no—
282C8—1462no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—44no—
292C22—42no—
293C22—42no—
294C22—42no—
295C22—84no—
296C22—2921no—
297C22—2921no—
298C22—2921no—
299C22#1455661712yes—
300C22C22×C22⋊D7311yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—42no—
305C4—2921no—
306C4—2921no—
307C4—2921no—
308C4#1455663612yes—
309C2—22no—
310C2—41no—
311C2—41no—
312C2—82no—
313C2—5841no—
314C2#1798914611yescharacteristic
315C2C2×#1455661711yescharacteristic
316C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×#121×C73C2
socleC22×C73C22×D4
hypercenterC2×#121D73
hypocenterC73#3194
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. #17989098C2semidirect
2. #17988917C2semidirect
3. #17988908C2semidirect
4. #17988900C2semidirect
5. #17988838C2semidirect
6. #17988831C2semidirect
7. #17988738C2semidirect
8. #17988730C2semidirect
9. #17988721C2semidirect
10. #17988551C2semidirect
11. C2×#121×C73C2semidirect
12. C2×#11924028C22semidirect
13. C2×#11924016C22semidirect
14. C2×#11924013C22semidirect
15. C2×#11924012C22semidirect
18. #14556570C22semidirect
20. #14556565C22semidirect
24. #14556550C22semidirect
25. #14556524C22semidirect
26. #14556522C22semidirect
27. #14556514C22semidirect
28. #14556512C22semidirect
29. #14556512C22semidirect
30. #14556511C22semidirect
33. C22⋊#10596831C22semidirect
159. C73#3194semidirect
161. C2×#121D73semidirect