Finite Group Databasebeta

← #22620762

Subgroups — #22620762

Order 9344.

414 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989100C211yesmaximal, characteristic
2C22⋊Q8×D73C211yesmaximal, characteristic, complemented
3#17988931C211yesmaximal, characteristic, complemented
4#17988927C211yesmaximal, characteristic, complemented
5#17988921C211yesmaximal, characteristic, complemented
6#17988907C211yesmaximal, characteristic, complemented
7#17988843C211yesmaximal, characteristic, complemented
8#17988835C211yesmaximal, characteristic, complemented
9#17988833C211yesmaximal, characteristic, complemented
10#17988752C211yesmaximal, characteristic, complemented
11#17988748C211yesmaximal, characteristic, complemented
12#17988741C211yesmaximal, characteristic, complemented
13#17988727C211yesmaximal, characteristic, complemented
14#17988550C211yesmaximal, characteristic, complemented
15#470×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×Q8×D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C2×#11924018C2211yescharacteristic, complemented
20C2×#11924017C2211yescharacteristic, complemented
21C2×#11924015C2211yescharacteristic, complemented
22C2×#11924012C2211yescharacteristic
23#14556576—21no—
24#14556571C2211yescharacteristic
25#14556570C2211yescharacteristic
26#14556569—21no—
27#14556568—21no—
28#14556567C2211yescharacteristic
29#14556567C2211yescharacteristic
30#14556566C2211yescharacteristic
31#14556565C2211yescharacteristic
32#14556561—21no—
33#14556553—21no—
34#14556551—21no—
35#14556549C2211yescharacteristic
36C4⋊C4×D73—21no—
37C4⋊C4×D73C2211yescharacteristic
38C22⋊C4×D73—21no—
39#14556525C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556522C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556515C2211yescharacteristic, complemented
44#14556515C2211yescharacteristic, complemented
45#14556514C2211yescharacteristic, complemented
46#14556513C2211yescharacteristic, complemented
47#14556511C2211yescharacteristic, complemented
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52C2×Q16×C73C2211yescharacteristic, complemented
53C2×M16×C73C2211yescharacteristic
54C22⋊Q8×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic
56#106×C73C2211yescharacteristic, complemented
57#103×C73C2211yescharacteristic, complemented
58#103×C73C2211yescharacteristic, complemented
59C23×D73D411yescharacteristic
60#11924029—41no—
61#11924029—41no—
62C2×Dic146—21no—
63C2×Dic146C2311yescharacteristic
64Q8×D73—41no—
65Q8×D73—41no—
66C2×D292—21no—
67C2×D292—21no—
68C2×D292C2311yescharacteristic
69C2×C22⋊D73—21no—
70C22×Dic73D411yescharacteristic
71C2×C4×D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74C2×C4×D73—41no—
75C2×C4×D73—41no—
76C2×C4×D73D411yescharacteristic
77C2×C4×D73D411yescharacteristic
78C2×C4×D73C2311yescharacteristic
79C2×C4×D73C2311yescharacteristic
80#11924018—41no—
81#11924017—41no—
82#11924015—41no—
83#11924012—41no—
84C2×#10596831C2311yescharacteristic
85C2×#10596831C2311yescharacteristic
86C4⋊Dic73—21no—
87C4⋊Dic73C2311yescharacteristic
88C4⋊Dic73C2311yescharacteristic
89#11924007—21no—
90#11924007—21no—
91#11924007—21no—
92#11924007—21no—
93C22⋊Dic73—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005—21no—
98#11924005—21no—
99#11924005—21no—
100C4×Dic73—21no—
101C2×Q8×C73C2311yescharacteristic
102C2×Q8×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104Q16×C73—41no—
105M16×C73—41no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73—21no—
109C4⋊C4×C73—21no—
110C4⋊C4×C73C2311yescharacteristic
111C4⋊C4×C73C2311yescharacteristic
112C22⋊C4×C73—21no—
113C22⋊C4×C73—21no—
114C23×C73C2×D411yescharacteristic
115C22×D73—22no—
116C22×D73—21no—
117C22×D73—41no—
118C22×D73—41no—
119C22×D73C2×D411yescharacteristic
120C22×D73C2×D411yescharacteristic
121Q8×C73—21no—
122Q8×C73—21no—
123Q8×C73—21no—
124Q8×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—21no—
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2411yescharacteristic
133C22⋊D73—42no—
134C2×Dic73—21no—
135C2×Dic73—21no—
136C2×Dic73—21no—
137C2×Dic73—41no—
138C2×Dic73C2×D411yescharacteristic
139C2×Dic73C2×D411yescharacteristic
140D292—21no—
141D292—21no—
142D292—42no—
143D292—42no—
144C4×D73—21no—
145C4×D73—21no—
146C4×D73—21no—
147C4×D73—21no—
148C4×D73—41no—
149C4×D73—41no—
150C4×D73—42no—
151C4×D73—42no—
152C4×D73—42no—
153Dic146—21no—
154Dic146—21no—
155Dic146—42no—
156C8×C73—21no—
157C8×C73—21no—
158#10596831—21no—
159#10596831—21no—
160C22×C73—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73C22×D411yescharacteristic
164C2×D73—21no—
165C2×D73—21no—
166C2×D73—21no—
167C2×D73—21no—
168C2×D73—21no—
169C2×D73—44no—
170C2×D73—41no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73#13712yes—
174C4×C73—21no—
175C4×C73—41no—
176C4×C73—41no—
177C4×C73—41no—
178C4×C73—41no—
179C4×C73H(5,𝔽2)11yescharacteristic
180C4×C73H(5,𝔽2)11yescharacteristic
181Dic73—21no—
182Dic73—21no—
183Dic73—41no—
184Dic73—41no—
185Dic73—41no—
186C2×C73—41no—
187C2×C73#53411yescharacteristic
188C2×C73C2×#13711yescharacteristic
189C2×C73#57511yescharacteristic
190D73—22no—
191D73—41no—
192D73—81no—
193#3196—731nomaximal, Sylow
194C73#319611yescharacteristic, complemented, Sylow
195#525—731no—
196C2×C22⋊Q8—731no—
197#485—731no—
198#485—731no—
199#484—731no—
200#481—731no—
201#470—731no—
202#470D7311yescharacteristic, complemented
203#468—731no—
204#468—731no—
205#452—731no—
206#452—731no—
207#451—731no—
208#448—731no—
209#407—731no—
210C2×#41—731no—
211C22×Q8—731no—
212C23×C4—731no—
213C2×Q16—731no—
214C2×Q16C2×D7311yescharacteristic, complemented
215C2×SD16—731no—
216C2×SD16—731no—
217C2×M16—731no—
218C2×M16C2×D7311yescharacteristic
219#123—1461no—
220C22⋊Q8—731no—
221C22⋊Q8—731no—
222C22⋊Q8—731no—
223C22⋊Q8—731no—
224C22⋊Q8—1461no—
225C22⋊Q8—1461no—
226C22⋊Q8C2×D7311yescharacteristic
227C22⋊Q8C2×D7311yescharacteristic
228#121—731no—
229#121—731no—
230#120—1461no—
231C4×D4—1461no—
232C4×D4—1461no—
233#117—731no—
234C2×C4⋊C4—731no—
235C2×C4⋊C4—1461no—
236C2×C22⋊C4—1461no—
237#107—731no—
238#107—731no—
239#106—731no—
240#106C2×D7311yescharacteristic, complemented
241#103—731no—
242#103—731no—
243#103—731no—
244#103—731no—
245#103C2×D7311yescharacteristic, complemented
246#103C2×D7311yescharacteristic, complemented
247#102—731no—
248#102—731no—
249C22⋊C8—731no—
250C22⋊C8—731no—
251C22⋊C8—731no—
252C22⋊C8—731no—
253C24—731no—
254#41—2921no—
255#41—2921no—
256C2×Q8—2921no—
257C2×Q8—2921no—
258C2×Q8—731no—
259C2×Q8—1461no—
260C2×Q8C22×D7311yescharacteristic
261C2×Q8C22×D7311yescharacteristic
262C2×D4—731no—
263C2×D4—1461no—
264C2×D4—1461no—
265C2×D4—1461no—
266C22×C4—2921no—
267C22×C4—2921no—
268C22×C4—731no—
269C22×C4—731no—
270C22×C4—731no—
271C22×C4—731no—
272C22×C4—731no—
273C22×C4—1461no—
274C22×C4—1461no—
275C22×C4—1461no—
276C22×C4C22×D7311yescharacteristic
277Q16—41no—
278Q16—2921no—
279SD16—2921no—
280SD16—2921no—
281M16—41no—
282M16—2921no—
283C2×C8—731no—
284C2×C8—731no—
285C2×C8C22×D7311yescharacteristic
286C2×C8C22×D7311yescharacteristic
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—731no—
290C4⋊C4—731no—
291C4⋊C4—1461no—
292C4⋊C4—1461no—
293C4⋊C4—1461no—
294C4⋊C4—1461no—
295C4⋊C4—1461no—
296C4⋊C4C22×D7311yescharacteristic
297C4⋊C4C22×D7311yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—1461no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C22⋊C4—1461no—
305C22⋊C4—1461no—
306C22⋊C4—1461no—
307C42—1461no—
308C23—2921no—
309C23—2921no—
310C23—731no—
311C23—731no—
312C23—1462no—
313C23—1461no—
314C23D4×D7311yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—21no—
318Q8—21no—
319Q8—2922no—
320Q8—1461no—
321Q8—1461no—
322D4—2922no—
323D4—2922no—
324D4—2922no—
325D4—1461no—
326D4—1461no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—2921no—
334C2×C4—2921no—
335C2×C4—2922no—
336C2×C4—2922no—
337C2×C4—2922no—
338C2×C4—2921no—
339C2×C4—731no—
340C2×C4—731no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4D4×D7311yescharacteristic
349C2×C4C23×D7311yescharacteristic
350C8—21no—
351C8—21no—
352C8—1461no—
353C8—1461no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—2924no—
358C22—2921no—
359C22—2921no—
360C22—2921no—
361C22—732no—
362C22—1461no—
363C22—1461no—
364C22—1461no—
365C22—1461no—
366C22—1461no—
367C22C2×D4×D7311yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—2921no—
374C4—2921no—
375C4—2921no—
376C4—1461no—
377C4—1461no—
378C4#1455663611yescharacteristic
379C4#1455663711yescharacteristic
380C2—41no—
381C2—2921no—
382C2—5841no—
383C2—1462no—
384C2#1798914511yescharacteristic
385C2#137×D7311yescharacteristic
386C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#470×C73C2
socleC22×C73C22×D4
hypercenter#470D73
hypocenterC73#3196
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. C22⋊Q8×D73C2semidirect
3. #17988931C2semidirect
4. #17988927C2semidirect
5. #17988921C2semidirect
6. #17988907C2semidirect
7. #17988843C2semidirect
8. #17988835C2semidirect
9. #17988833C2semidirect
10. #17988752C2semidirect
11. #17988748C2semidirect
12. #17988741C2semidirect
13. #17988727C2semidirect
14. #17988550C2semidirect
15. #470×C73C2semidirect
19. C2×#11924018C22semidirect
20. C2×#11924017C22semidirect
21. C2×#11924015C22semidirect
39. #14556525C22semidirect
40. #14556524C22semidirect
41. #14556522C22semidirect
42. #14556516C22semidirect
43. #14556515C22semidirect
44. #14556515C22semidirect
45. #14556514C22semidirect
46. #14556513C22semidirect
47. #14556511C22semidirect
52. C2×Q16×C73C22semidirect
56. #106×C73C22semidirect
57. #103×C73C22semidirect
58. #103×C73C22semidirect
194. C73#3196semidirect
202. #470D73semidirect
214. C2×Q16C2×D73semidirect
240. #106C2×D73semidirect
245. #103C2×D73semidirect
246. #103C2×D73semidirect