Finite Group Databasebeta

← #22619554

Subgroups — #22619554

Order 9344.

496 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556620C211yesmaximal, characteristic, complemented
2C22×#11924011C211yesmaximal, characteristic, complemented
3#17989097C211yesmaximal, characteristic
4C22⋊Q8×D73C211yesmaximal, characteristic, complemented
5#17988846C211yesmaximal, characteristic, complemented
6#17988844C211yesmaximal, characteristic, complemented
7#17988832C211yesmaximal, characteristic, complemented
8#17988830C211yesmaximal, characteristic, complemented
9#17988828C211yesmaximal, characteristic, complemented
10#17988826C211yesmaximal, characteristic, complemented
11#17988814C211yesmaximal, characteristic, complemented
12#17988626C211yesmaximal, characteristic, complemented
13#17988594C211yesmaximal, characteristic, complemented
14#17988585C211yesmaximal, characteristic, complemented
15#465×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C2×Q8×D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19#14556620—24no—
20C2×Dic292C2211yescharacteristic, complemented
21C2×#11924018C2211yescharacteristic, complemented
22C2×#11924016C2211yescharacteristic, complemented
23C2×#11924011—24no—
24C2×#11924011C2211yescharacteristic
25C2×#11924011C2211yescharacteristic
26C2×#11924011C2211yescharacteristic
27C2×#11924011C2211yescharacteristic
28C22×#10596831C2211yescharacteristic
29#14556573—21no—
30#14556571C2211yescharacteristic
31#14556571C2211yescharacteristic
32#14556570C2211yescharacteristic
33#14556570C2211yescharacteristic
34#14556569—21no—
35#14556568—21no—
36#14556567C2211yescharacteristic
37#14556562C2211yescharacteristic
38#14556559—21no—
39D4×Dic73—21no—
40#14556551—21no—
41#14556549C2211yescharacteristic
42C4⋊C4×D73—21no—
43C4⋊C4×D73C2211yescharacteristic
44C22⋊C4×D73—21no—
45#14556525C2211yescharacteristic, complemented
46#14556524C2211yescharacteristic, complemented
47#14556522C2211yescharacteristic, complemented
48#14556516C2211yescharacteristic, complemented
49#14556516C2211yescharacteristic, complemented
50#14556515C2211yescharacteristic, complemented
51#14556514C2211yescharacteristic, complemented
52#14556514C2211yescharacteristic, complemented
53#14556512C2211yescharacteristic, complemented
54C2×SD16×C73C2211yescharacteristic, complemented
55C22×C8×C73C2211yescharacteristic
56C22⋊Q8×C73C2211yescharacteristic
57#121×C73C2211yescharacteristic
58#106×C73C2211yescharacteristic, complemented
59#103×C73C2211yescharacteristic, complemented
60#102×C73C2211yescharacteristic, complemented
61C23×D73D411yescharacteristic
62#11924027—22no—
63#11924027—22no—
64C2×Dic146—21no—
65C2×Dic146C2311yescharacteristic
66C2×Dic146C2311yescharacteristic
67Q8×D73—22no—
68Q8×D73—22no—
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C22×Dic73—21no—
72C22×Dic73D411yescharacteristic
73C2×C4×D73—22no—
74C2×C4×D73—22no—
75C2×C4×D73—21no—
76C2×C4×D73—21no—
77C2×C4×D73D411yescharacteristic
78C2×C4×D73D411yescharacteristic
79C2×C4×D73C2311yescharacteristic
80C2×C4×D73C2311yescharacteristic
81Dic292—22no—
82#11924018—22no—
83#11924016—22no—
84#11924011—22no—
85#11924011—22no—
86#11924011—22no—
87#11924011D414yescomplemented
88C2×#10596831—22no—
89C2×#10596831C2311yescharacteristic
90C2×#10596831C2311yescharacteristic
91C4⋊Dic73—21no—
92C4⋊Dic73—21no—
93C4⋊Dic73C2311yescharacteristic
94C4⋊Dic73C2311yescharacteristic
95#11924007—21no—
96#11924007—21no—
97#11924007—21no—
98#11924007—21no—
99C22⋊Dic73—21no—
100C22⋊Dic73—21no—
101C22⋊Dic73—21no—
102#11924005—21no—
103#11924005—21no—
104#11924005—21no—
105#11924005—21no—
106C4×Dic73—21no—
107C2×Q8×C73C2311yescharacteristic
108C2×D4×C73—21no—
109C2×D4×C73C2311yescharacteristic
110C22×C4×C73C2311yescharacteristic
111SD16×C73—22no—
112C2×C8×C73—22no—
113C2×C8×C73C2311yescharacteristic
114C2×C8×C73C2311yescharacteristic
115C4⋊C4×C73—21no—
116C4⋊C4×C73C2311yescharacteristic
117C4⋊C4×C73C2311yescharacteristic
118C22⋊C4×C73—21no—
119C22⋊C4×C73—21no—
120C23×C73—21no—
121C23×C73C2×D411yescharacteristic
122C22×D73—22no—
123C22×D73—22no—
124C22×D73—41no—
125C22×D73C2×D411yescharacteristic
126C22×D73C2×D411yescharacteristic
127Q8×C73—21no—
128Q8×C73—21no—
129D4×C73—21no—
130D4×C73—21no—
131D4×C73—42no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—21no—
136C2×C4×C73—21no—
137C2×C4×C73C2×D411yescharacteristic
138C2×C4×C73C2411yescharacteristic
139C22⋊D73—42no—
140C22⋊D73—42no—
141C2×Dic73—22no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—21no—
146C2×Dic73—42no—
147C2×Dic73C2×D411yescharacteristic
148C2×Dic73C2×D411yescharacteristic
149C4×D73—22no—
150C4×D73—21no—
151C4×D73—21no—
152C4×D73—22no—
153C4×D73—42no—
154C4×D73—42no—
155C4×D73C2×D412yes—
156C4×D73#4112yes—
157Dic146—21no—
158Dic146—21no—
159Dic146—21no—
160Dic146—21no—
161Dic146—42no—
162C8×C73—21no—
163C8×C73C2×D412yes—
164#10596831—21no—
165#10596831C2×D412yes—
166C22×C73—21no—
167C22×C73—21no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73—41no—
171C22×C73#13712yescomplemented
172C22×C73C22×D411yescharacteristic
173C2×D73—21no—
174C2×D73—21no—
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—21no—
178C2×D73—44no—
179C2×D73#12112yes—
180C4×C73—21no—
181C4×C73—41no—
182C4×C73—41no—
183C4×C73—41no—
184C4×C73C22×D411yescharacteristic
185C4×C73C2×#4111yescharacteristic
186Dic73—21no—
187Dic73—41no—
188Dic73—41no—
189Dic73—41no—
190Dic73—41no—
191Dic73#12112yes—
192C2×C73—22no—
193C2×C73—81no—
194C2×C73C2×#12111yescharacteristic
195C2×C73C2×#13711yescharacteristic
196C2×C73#57511yescharacteristic
197D73—22no—
198D73—41no—
199#3056—731nomaximal, Sylow
200C73#305611yescharacteristic, complemented, Sylow
201C2×#137—731no—
202C22×M16—731no—
203#525—731no—
204C2×C22⋊Q8—731no—
205#470—731no—
206#470—731no—
207#468—731no—
208#468—731no—
209#467—731no—
210#467—731no—
211#465—731no—
212#465D7311yescharacteristic, complemented
213#428—731no—
214#419—731no—
215#417—731no—
216C2×#41—731no—
217C22×Q8—731no—
218C23×C4—731no—
219#137—1464no—
220C2×Q16—731no—
221C2×Q16—731no—
222C2×SD16—731no—
223C2×SD16C2×D7311yescharacteristic, complemented
224C2×M16—731no—
225C2×M16—731no—
226C2×M16—731no—
227C2×M16—731no—
228C2×M16—1464no—
229C22×C8—731no—
230C22×C8C2×D7311yescharacteristic
231#123—1461no—
232C22⋊Q8—731no—
233C22⋊Q8—731no—
234C22⋊Q8—731no—
235C22⋊Q8—731no—
236C22⋊Q8—731no—
237C22⋊Q8—1461no—
238C22⋊Q8—1461no—
239C22⋊Q8C2×D7311yescharacteristic
240#121—731no—
241#121C2×D7311yescharacteristic
242#120—1461no—
243C4×D4—1461no—
244C4×D4—1461no—
245#117—731no—
246C2×C4⋊C4—731no—
247C2×C4⋊C4—1461no—
248C2×C22⋊C4—1461no—
249#107—731no—
250#107—731no—
251#106—731no—
252#106C2×D7311yescharacteristic, complemented
253#103—731no—
254#103—731no—
255#103—731no—
256#103—731no—
257#103—731no—
258#103C2×D7311yescharacteristic, complemented
259#102—731no—
260#102C2×D7311yescharacteristic, complemented
261C24—731no—
262#41—1462no—
263#41—1462no—
264C2×Q8—731no—
265C2×Q8—731no—
266C2×Q8—1461no—
267C2×Q8—1462no—
268C2×Q8—1462no—
269C2×Q8C22×D7311yescharacteristic
270C2×D4—21no—
271C2×D4—1461no—
272C2×D4—1461no—
273C2×D4C22×D7311yescharacteristic
274C22×C4—731no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—1461no—
280C22×C4—1461no—
281C22×C4—1462no—
282C22×C4—1462no—
283C22×C4—1461no—
284C22×C4C22×D7311yescharacteristic
285Q16—1462no—
286Q16—1462no—
287SD16—22no—
288SD16—1462no—
289M16—734no—
290M16—1462no—
291M16—1462no—
292M16—1462no—
293C2×C8—22no—
294C2×C8—731no—
295C2×C8—731no—
296C2×C8—1462no—
297C2×C8C22×D7311yescharacteristic
298C2×C8C22×D7311yescharacteristic
299C4⋊C4—21no—
300C4⋊C4—731no—
301C4⋊C4—731no—
302C4⋊C4—1461no—
303C4⋊C4—1461no—
304C4⋊C4—1461no—
305C4⋊C4—1461no—
306C4⋊C4—1461no—
307C4⋊C4—1461no—
308C4⋊C4C22×D7311yescharacteristic
309C4⋊C4C22×D7311yescharacteristic
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—1461no—
313C22⋊C4—1461no—
314C22⋊C4—1461no—
315C22⋊C4—1461no—
316C22⋊C4—1461no—
317C22⋊C4—1461no—
318C22⋊C4—1461no—
319C42—1461no—
320C23—21no—
321C23—2921no—
322C23—731no—
323C23—731no—
324C23—1462no—
325C23—1462no—
326C23D4×D7311yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—2922no—
330Q8—1461no—
331Q8—1461no—
332Q8—1461no—
333Q8—1461no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—2922no—
338D4—2922no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—2922no—
345C2×C4—2922no—
346C2×C4—2922no—
347C2×C4—731no—
348C2×C4—732no—
349C2×C4—732no—
350C2×C4—731no—
351C2×C4—1462no—
352C2×C4—1462no—
353C2×C4—1461no—
354C2×C4—1461no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1462no—
358C2×C4—1461no—
359C2×C4—1461no—
360C2×C4D4×D7311yescharacteristic
361C2×C4C23×D7311yescharacteristic
362C8—21no—
363C8—732no—
364C8—1461no—
365C8D4×D7312yes—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—2924no—
372C22—732no—
373C22—1461no—
374C22—1461no—
375C22—1461no—
376C22—1461no—
377C22—1461no—
378C22#1455662012yescomplemented
379C22C2×D4×D7311yescharacteristic
380C4—21no—
381C4—41no—
382C4—41no—
383C4—41no—
384C4—2921no—
385C4—2921no—
386C4—2921no—
387C4—2921no—
388C4—732no—
389C4—1461no—
390C4C2×D4×D7311yescharacteristic
391C4#41×D7311yescharacteristic
392C2—22no—
393C2—81no—
394C2—2921no—
395C2—1462no—
396C2#121×D7311yescharacteristic
397C2C2×#1455662011yescharacteristic
398C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#465×C73C2
socleC22×C73C22×D4
hypercenter#465D73
hypocenterC73#3056
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C2×#14556620C2semidirect
2. C22×#11924011C2semidirect
4. C22⋊Q8×D73C2semidirect
5. #17988846C2semidirect
6. #17988844C2semidirect
7. #17988832C2semidirect
8. #17988830C2semidirect
9. #17988828C2semidirect
10. #17988826C2semidirect
11. #17988814C2semidirect
12. #17988626C2semidirect
13. #17988594C2semidirect
14. #17988585C2semidirect
15. #465×C73C2semidirect
20. C2×Dic292C22semidirect
21. C2×#11924018C22semidirect
22. C2×#11924016C22semidirect
45. #14556525C22semidirect
46. #14556524C22semidirect
47. #14556522C22semidirect
48. #14556516C22semidirect
49. #14556516C22semidirect
50. #14556515C22semidirect
51. #14556514C22semidirect
52. #14556514C22semidirect
53. #14556512C22semidirect
54. C2×SD16×C73C22semidirect
58. #106×C73C22semidirect
59. #103×C73C22semidirect
60. #102×C73C22semidirect
87. #11924011D4semidirect
171. C22×C73#137semidirect
200. C73#3056semidirect
212. #465D73semidirect
223. C2×SD16C2×D73semidirect
252. #106C2×D73semidirect
258. #103C2×D73semidirect
260. #102C2×D73semidirect
378. C22#14556620semidirect