Finite Group Databasebeta

← #22626665

Subgroups — #22626665

Order 9344.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14556678C211yesmaximal, characteristic, complemented
2C2×D73⋊M16C211yesmaximal, characteristic, complemented
3#17989621C211yesmaximal, characteristic, complemented
4#17989620C211yesmaximal, characteristic, complemented
5#17989619C211yesmaximal, characteristic, complemented
6#17989617C211yesmaximal, characteristic, complemented
7#17989617C211yesmaximal, characteristic, complemented
8#17989616C211yesmaximal, characteristic, complemented
9#17989615C211yesmaximal, characteristic, complemented
10#17989614C211yesmaximal, characteristic, complemented
11#17989593C211yesmaximal, characteristic, complemented
12#17989560C211yesmaximal, characteristic, complemented
13C2×#14556648C211yesmaximal, characteristic, complemented
14#17989551C211yesmaximal, characteristic, complemented
15#17989095C211yesmaximal, characteristic
16#14556678—24no—
17C2×#11924038C2211yescharacteristic
18C2×#11924038C2211yescharacteristic
19C2×#11924038C2211yescharacteristic, complemented
20D73⋊M16—24no—
21C2×#11924037C2211yescharacteristic
22C2×#11924037C2211yescharacteristic
23C2×#11924037C2211yescharacteristic, complemented
24C2×#11924036C2211yescharacteristic
25C2×#11924036C2211yescharacteristic
26C2×#11924036C2211yescharacteristic, complemented
27C22×#10596833C2211yescharacteristic
28C22×#10596833C2211yescharacteristic
29C22×#10596833C2211yescharacteristic, complemented
30#14556658C2211yescharacteristic, complemented
31#14556658C2211yescharacteristic, complemented
32C4⋊#10596833C2211yescharacteristic, complemented
33C4⋊#10596833C2211yescharacteristic, complemented
34#14556648C2211yescharacteristic
35#14556648C2211yescharacteristic
36#14556648C2211yescharacteristic
37#14556648C2211yescharacteristic
38#14556648C2211yescharacteristic, complemented
39#14556648C2211yescharacteristic, complemented
40C22⋊#10596833C2211yescharacteristic, complemented
41C22⋊#10596833C2211yescharacteristic, complemented
42#14556646C2211yescharacteristic, complemented
43#14556646C2211yescharacteristic, complemented
44C4×#10596833C2211yescharacteristic, complemented
45C4×#10596833C2211yescharacteristic, complemented
46C2×#11924027C2211yescharacteristic
47C22×C4×D73C2211yescharacteristic
48#14556574C411yescharacteristic
49#14556569C411yescharacteristic
50#14556569C411yescharacteristic
51#14556564C411yescharacteristic
52#14556564C411yescharacteristic
53#14556561C411yescharacteristic
54#14556559C411yescharacteristic
55#14556553C2211yescharacteristic
56#14556553C2211yescharacteristic
57#14556551C2211yescharacteristic
58#14556551C2211yescharacteristic
59#14556547C2211yescharacteristic
60#123×C73C411yescharacteristic
61#11924038—22no—
62#11924038—22no—
63#11924038—22no—
64#11924037—22no—
65#11924037—22no—
66#11924037D414yescomplemented
67#11924036—22no—
68#11924036—22no—
69#11924036—22no—
70C2×#10596833—22no—
71C2×#10596833—22no—
72C2×#10596833—22no—
73C2×#10596833C2311yescharacteristic
74C2×#10596833C2311yescharacteristic
75C2×#10596833C2311yescharacteristic
76C2×#10596833C2311yescharacteristic
77C2×#10596833C2311yescharacteristic
78C2×#10596833C2311yescharacteristic
79C2×#10596833C2311yescharacteristic
80C2×#10596833C2311yescharacteristic
81C23×D73C2×C411yescharacteristic
82#11924027—22no—
83#11924027—22no—
84C2×Dic146C2×C411yescharacteristic
85C2×D292C2×C411yescharacteristic
86C2×D292C2×C411yescharacteristic
87C2×C22⋊D73C2×C411yescharacteristic
88C2×C22⋊D73C2×C411yescharacteristic
89C2×C22⋊D73C2×C411yescharacteristic
90C2×C22⋊D73C2×C411yescharacteristic
91C22×Dic73C2311yescharacteristic
92C22×Dic73C2311yescharacteristic
93C2×C4×D73—22no—
94C2×C4×D73—22no—
95C2×C4×D73C2×C411yescharacteristic
96C2×C4×D73C2×C411yescharacteristic
97C2×C4×D73C2311yescharacteristic
98C2×C4×D73C2311yescharacteristic
99C2×C4×D73C2311yescharacteristic
100#11924007C2×C411yescharacteristic
101#11924007C2×C411yescharacteristic
102#11924007C2×C411yescharacteristic
103#11924007C2×C411yescharacteristic
104C22⋊Dic73C2×C411yescharacteristic
105#11924005C2×C411yescharacteristic
106#11924005C2×C411yescharacteristic
107#11924005C2×C411yescharacteristic
108#11924005C2×C411yescharacteristic
109#11924005C2×C411yescharacteristic
110#11924005C2×C411yescharacteristic
111C4×Dic73C2311yescharacteristic
112C4×Dic73C2311yescharacteristic
113C2×D4×C73C2×C411yescharacteristic
114C22×C4×C73C2×C411yescharacteristic
115C4⋊C4×C73C2×C411yescharacteristic
116C4⋊C4×C73C2×C411yescharacteristic
117C22⋊C4×C73C2×C411yescharacteristic
118C22⋊C4×C73C2×C411yescharacteristic
119C22⋊C4×C73C2×C411yescharacteristic
120C23×C73C22×C411yescharacteristic
121C23×C73C22×C411yescharacteristic
122C22×D73—22no—
123C22×D73—22no—
124C22×D73—41no—
125C22×D73C22×C411yescharacteristic
126C22×D73C22×C411yescharacteristic
127C22×D73C22×C411yescharacteristic
128D4×C73—22no—
129C2×C4×C73—22no—
130C2×C4×C73C22×C411yescharacteristic
131C2×C4×C73C22×C411yescharacteristic
132C2×C4×C73C22×C411yescharacteristic
133C2×C4×C73C22×C411yescharacteristic
134C2×C4×C73C22×C411yescharacteristic
135C22⋊D73—22no—
136C22⋊D73—22no—
137C22⋊D73—22no—
138C22⋊D73—41no—
139C2×Dic73—21no—
140C2×Dic73—21no—
141C2×Dic73C22×C411yescharacteristic
142C2×Dic73C22×C411yescharacteristic
143C2×Dic73C22×C411yescharacteristic
144C2×Dic73C22×C411yescharacteristic
145C2×Dic73C2×D412yes—
146C2×Dic73#4112yes—
147C2×Dic73C2411yescharacteristic
148D292—22no—
149D292—41no—
150C4×D73—22no—
151C4×D73—22no—
152C4×D73—21no—
153C4×D73—21no—
154C4×D73—21no—
155C4×D73—21no—
156C4×D73—21no—
157C4×D73—21no—
158Dic146—22no—
159#10596833—21no—
160#10596833—21no—
161#10596833—21no—
162#10596833—21no—
163#10596833—21no—
164#10596833—21no—
165#10596833C2×D412yes—
166#10596833C2×D412yes—
167C22×C73—21no—
168C22×C73—21no—
169C22×C73—21no—
170C22×C73—21no—
171C22×C73—21no—
172C22×C73C4×D412yes—
173C22×C73C23×C411yescharacteristic
174C2×D73—21no—
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—21no—
178C2×D73—21no—
179C2×D73—21no—
180C2×D73—21no—
181C2×D73—21no—
182C2×D73—44no—
183C2×D73#13112yescomplemented
184C4×C73—21no—
185C4×C73—21no—
186C4×C73—21no—
187C4×C73—21no—
188C4×C73—21no—
189Dic73—21no—
190Dic73—21no—
191Dic73—21no—
192Dic73C4×D412yes—
193Dic73C22×D411yescharacteristic
194Dic73C2×#4111yescharacteristic
195C2×C73—22no—
196C2×C73—41no—
197C2×C73C2×C4×D411yescharacteristic
198C2×C73C2×#13111yescharacteristic
199C2×C73#56811yescharacteristic
200D73—22no—
201D73—41no—
202D73—41no—
203#2933—731nomaximal, Sylow
204C73#293311yescharacteristic, complemented, Sylow
205C2×#131—731no—
206C22×M16—731no—
207#525—731no—
208#436—731no—
209#436—731no—
210#435—731no—
211#435—731no—
212#435—731no—
213#435—731no—
214C8×D4—731no—
215C8×D4—731no—
216#424—731no—
217#408—731no—
218C2×C22⋊C8—731no—
219#405—731no—
220C2×#41—731no—
221C23×C4—731no—
222#131—1464no—
223C2×M16—731no—
224C2×M16—731no—
225C2×M16—731no—
226C2×M16—731no—
227C2×M16—731no—
228C2×M16—731no—
229C2×M16—1464no—
230C22×C8—731no—
231C22×C8—731no—
232C22×C8—731no—
233C22×C8—731no—
234C22×C8—731no—
235C22×C8—731no—
236#123—731no—
237#123#6440811yescharacteristic
238C22⋊Q8—731no—
239C22⋊Q8—731no—
240#121—731no—
241#121—731no—
242#120—731no—
243#120—731no—
244C4×D4—731no—
245C4×D4—731no—
246C4×D4—731no—
247C4×D4—731no—
248#117—731no—
249C4⋊C8—731no—
250C4⋊C8—731no—
251C4⋊C8—731no—
252C4⋊C8—731no—
253C22⋊C8—731no—
254C22⋊C8—731no—
255C22⋊C8—731no—
256C22⋊C8—731no—
257C22⋊C8—731no—
258C22⋊C8—731no—
259C22⋊C8—731no—
260C22⋊C8—731no—
261#97—731no—
262#97—731no—
263C4×C8—731no—
264C4×C8—731no—
265C24—731no—
266#41—1462no—
267#41—1462no—
268C2×Q8—731no—
269C2×D4—731no—
270C2×D4—731no—
271C2×D4—731no—
272C2×D4—731no—
273C2×D4—731no—
274C2×D4—731no—
275C2×D4C2×#6440811yescharacteristic
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4—731no—
281C22×C4—731no—
282C22×C4—731no—
283C22×C4—1462no—
284C22×C4—1462no—
285C22×C4C2×#6440811yescharacteristic
286M16—734no—
287M16—1462no—
288M16—1462no—
289M16—1462no—
290M16—1462no—
291M16—1462no—
292C2×C8—731no—
293C2×C8—731no—
294C2×C8—731no—
295C2×C8—731no—
296C2×C8—731no—
297C2×C8—731no—
298C2×C8—731no—
299C2×C8—731no—
300C2×C8—1462no—
301C2×C8—1462no—
302C2×C8—1462no—
303C2×C8—1462no—
304C2×C8—1462no—
305C2×C8—1462no—
306C4⋊C4—731no—
307C4⋊C4—731no—
308C4⋊C4—731no—
309C4⋊C4—731no—
310C4⋊C4C2×#6440811yescharacteristic
311C4⋊C4C2×#6440811yescharacteristic
312C22⋊C4—731no—
313C22⋊C4—731no—
314C22⋊C4—731no—
315C22⋊C4—731no—
316C22⋊C4—731no—
317C22⋊C4—731no—
318C22⋊C4—731no—
319C22⋊C4C2×#6440811yescharacteristic
320C22⋊C4C2×#6440811yescharacteristic
321C22⋊C4C2×#6440811yescharacteristic
322C42—731no—
323C42—731no—
324C23—2921no—
325C23—731no—
326C23—731no—
327C23—731no—
328C23—1462no—
329C23—1462no—
330C23C22×#6440811yescharacteristic
331C23C22×#6440811yescharacteristic
332Q8—1462no—
333D4—22no—
334D4—2921no—
335D4—2921no—
336D4—1462no—
337D4—1462no—
338D4—1462no—
339D4—1462no—
340C2×C4—22no—
341C2×C4—731no—
342C2×C4—731no—
343C2×C4—732no—
344C2×C4—732no—
345C2×C4—731no—
346C2×C4—731no—
347C2×C4—731no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4—1462no—
354C2×C4—1462no—
355C2×C4—1461no—
356C2×C4—1461no—
357C2×C4—1461no—
358C2×C4C22×#6440811yescharacteristic
359C2×C4C22×#6440811yescharacteristic
360C2×C4C22×#6440811yescharacteristic
361C2×C4C22×#6440811yescharacteristic
362C2×C4C22×#6440811yescharacteristic
363C8—732no—
364C8—732no—
365C8—1461no—
366C8—1461no—
367C8—1461no—
368C8—1461no—
369C8—1461no—
370C8—1461no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—2924no—
377C22—732no—
378C22—1461no—
379C22—1461no—
380C22—1461no—
381C22—1461no—
382C22—1461no—
383C22—1461no—
384C22—1461no—
385C22—1461no—
386C22D4×#6440812yes—
387C22C23×#6440811yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—731no—
394C4—731no—
395C4—732no—
396C4—1461no—
397C4—1461no—
398C4—1461no—
399C2—22no—
400C2—41no—
401C2—2921no—
402C2—2921no—
403C2—1462no—
404C2C2×D4×#6440811yescharacteristic
405C2D73⋊#13111yescharacteristic
406C2#1798966611yescharacteristic
subgroupG/H
center, FrattiniC22C23×#64408
commutator, socleC22×C73C23×C4
Fitting#123×C73C4
hypercenter#123#64408
hypocenterC73#2933
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#14556678C2semidirect
2. C2×D73⋊M16C2semidirect
3. #17989621C2semidirect
4. #17989620C2semidirect
5. #17989619C2semidirect
6. #17989617C2semidirect
7. #17989617C2semidirect
8. #17989616C2semidirect
9. #17989615C2semidirect
10. #17989614C2semidirect
11. #17989593C2semidirect
12. #17989560C2semidirect
13. C2×#14556648C2semidirect
14. #17989551C2semidirect
19. C2×#11924038C22semidirect
23. C2×#11924037C22semidirect
26. C2×#11924036C22semidirect
29. C22×#10596833C22semidirect
30. #14556658C22semidirect
31. #14556658C22semidirect
32. C4⋊#10596833C22semidirect
33. C4⋊#10596833C22semidirect
38. #14556648C22semidirect
39. #14556648C22semidirect
40. C22⋊#10596833C22semidirect
41. C22⋊#10596833C22semidirect
42. #14556646C22semidirect
43. #14556646C22semidirect
44. C4×#10596833C22semidirect
45. C4×#10596833C22semidirect
66. #11924037D4semidirect
183. C2×D73#131semidirect
204. C73#2933semidirect