Finite Group Databasebeta

← #22620770

Subgroups — #22620770

Order 9344.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989097C211yesmaximal, characteristic, complemented
2#17989094C211yesmaximal, characteristic, complemented
3#17988929C211yesmaximal, characteristic, complemented
4#17988926C211yesmaximal, characteristic, complemented
5#17988909C211yesmaximal, characteristic, complemented
6#17988908C211yesmaximal, characteristic, complemented
7#17988844C211yesmaximal, characteristic, complemented
8#17988837C211yesmaximal, characteristic, complemented
9#17988832C211yesmaximal, characteristic, complemented
10#17988830C211yesmaximal, characteristic, complemented
11#17988749C211yesmaximal, characteristic, complemented
12#17988746C211yesmaximal, characteristic, complemented
13#17988729C211yesmaximal, characteristic, complemented
14#17988549C211yesmaximal, characteristic, complemented
15#449×C73C211yesmaximal, characteristic, complemented
16C2×#11924027C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18C2×#11924018C2211yescharacteristic, complemented
19C2×#11924016C2211yescharacteristic, complemented
20C2×#11924011C2211yescharacteristic
21C2×#11924011C2211yescharacteristic
22#14556573—21no—
23#14556572—21no—
24#14556571C2211yescharacteristic
25#14556570C2211yescharacteristic
26#14556567C2211yescharacteristic
27#14556567C2211yescharacteristic
28#14556562C2211yescharacteristic
29#14556562C2211yescharacteristic
30#14556562C2211yescharacteristic
31#14556559—21no—
32#14556559—21no—
33D4×Dic73—21no—
34C4×C22⋊D73—21no—
35C4×C22⋊D73—21no—
36#14556551—21no—
37#14556550C2211yescharacteristic
38#14556549C2211yescharacteristic
39#14556525C2211yescharacteristic, complemented
40#14556524C2211yescharacteristic, complemented
41#14556523C2211yescharacteristic, complemented
42#14556522C2211yescharacteristic, complemented
43#14556516C2211yescharacteristic, complemented
44#14556516C2211yescharacteristic, complemented
45#14556515C2211yescharacteristic, complemented
46#14556512C2211yescharacteristic, complemented
47#14556512C2211yescharacteristic, complemented
48#14556512C2211yescharacteristic, complemented
49C22⋊#10596831C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556503C2211yescharacteristic
52C2×#41×C73C2211yescharacteristic
53C2×SD16×C73C2211yescharacteristic, complemented
54C2×D8×C73C2211yescharacteristic, complemented
55#121×C73C2211yescharacteristic
56#103×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic, complemented
58C22⋊C8×C73C2211yescharacteristic
59C23×D73D411yescharacteristic
60#11924027—41no—
61#11924027—41no—
62C2×Dic146C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67C22×Dic73—21no—
68C22×Dic73D411yescharacteristic
69C2×C4×D73—41no—
70C2×C4×D73—41no—
71C2×C4×D73D411yescharacteristic
72C2×C4×D73D411yescharacteristic
73C2×C4×D73C2311yescharacteristic
74C2×C4×D73C2311yescharacteristic
75#11924018—41no—
76#11924016—41no—
77#11924011—41no—
78#11924011—41no—
79C2×#10596831C2311yescharacteristic
80C2×#10596831C2311yescharacteristic
81C4⋊Dic73—21no—
82C4⋊Dic73C2311yescharacteristic
83C4⋊Dic73C2311yescharacteristic
84C4⋊Dic73C2311yescharacteristic
85#11924007—21no—
86#11924007—21no—
87#11924007—21no—
88C22⋊Dic73—21no—
89C22⋊Dic73—21no—
90C22⋊Dic73—21no—
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93#11924005—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97C4×Dic73—21no—
98C4×Dic73—21no—
99#41×C73—41no—
100#41×C73—41no—
101C2×Q8×C73C2311yescharacteristic
102C2×D4×C73—21no—
103C2×D4×C73—21no—
104C2×D4×C73C2311yescharacteristic
105C2×D4×C73C2311yescharacteristic
106C22×C4×C73—21no—
107C22×C4×C73C2311yescharacteristic
108SD16×C73—41no—
109D8×C73—41no—
110C2×C8×C73C2311yescharacteristic
111C2×C8×C73C2311yescharacteristic
112C4⋊C4×C73C2311yescharacteristic
113C22⋊C4×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73C2×D411yescharacteristic
117C22×D73—41no—
118C22×D73—41no—
119C22×D73—41no—
120C22×D73C2×D411yescharacteristic
121C22×D73C2×D411yescharacteristic
122Q8×C73—21no—
123Q8×C73—21no—
124D4×C73—21no—
125D4×C73—21no—
126D4×C73—21no—
127D4×C73—21no—
128D4×C73—42no—
129D4×C73—42no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—42no—
135C2×C4×C73C2×D411yescharacteristic
136C2×C4×C73C2411yescharacteristic
137C22⋊D73—42no—
138C22⋊D73—42no—
139C22⋊D73—42no—
140C22⋊D73—42no—
141C2×Dic73—21no—
142C2×Dic73—21no—
143C2×Dic73—21no—
144C2×Dic73—21no—
145C2×Dic73—41no—
146C2×Dic73—42no—
147C2×Dic73C2×D411yescharacteristic
148C2×Dic73C2×D411yescharacteristic
149C4×D73—21no—
150C4×D73—21no—
151C4×D73—21no—
152C4×D73—21no—
153C4×D73—41no—
154C4×D73—41no—
155Dic146—21no—
156Dic146—21no—
157C8×C73—21no—
158C8×C73—21no—
159#10596831—21no—
160#10596831—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73—41no—
167C22×C73—41no—
168C22×C73—41no—
169C22×C73—41no—
170C22×C73C22×D411yescharacteristic
171C2×D73—21no—
172C2×D73—21no—
173C2×D73—21no—
174C2×D73—21no—
175C2×D73—21no—
176C2×D73—21no—
177C2×D73—44no—
178C4×C73—21no—
179C4×C73—41no—
180C4×C73—41no—
181C4×C73H(5,𝔽2)11yescharacteristic
182C4×C73H(5,𝔽2)11yescharacteristic
183Dic73—21no—
184Dic73—21no—
185Dic73—41no—
186Dic73—41no—
187Dic73—41no—
188Dic73—41no—
189C2×C73—41no—
190C2×C73—81no—
191C2×C73—81no—
192C2×C73#53411yescharacteristic
193C2×C73#57511yescharacteristic
194C2×C73#57511yescharacteristic
195D73—41no—
196D73—41no—
197#3197—731nomaximal, Sylow
198C73#319711yescharacteristic, complemented, Sylow
199#525—731no—
200#525—731no—
201#485—731no—
202#485—731no—
203#482—731no—
204#482—731no—
205#470—731no—
206#469—731no—
207#468—731no—
208#468—731no—
209#452—731no—
210#452—731no—
211#449—731no—
212#449D7311yescharacteristic, complemented
213#407—731no—
214C2×#41—731no—
215C2×#41C2×D7311yescharacteristic
216C23×C4—731no—
217C2×Q16—731no—
218C2×SD16—731no—
219C2×SD16C2×D7311yescharacteristic, complemented
220C2×D8C2×D7311yescharacteristic, complemented
221C2×M16—731no—
222C2×M16—731no—
223#123—1461no—
224#123—1461no—
225C22⋊Q8—731no—
226C22⋊Q8—731no—
227C22⋊Q8—731no—
228C22⋊Q8—731no—
229#121—731no—
230#121—731no—
231#121—731no—
232#121C2×D7311yescharacteristic
233#120—1461no—
234#120—1461no—
235C4×D4—1461no—
236C4×D4—1461no—
237C4×D4—1461no—
238C4×D4—1461no—
239#117—731no—
240#117—731no—
241#107—731no—
242#107—731no—
243#106—731no—
244#106—731no—
245#103—731no—
246#103—731no—
247#103—731no—
248#103C2×D7311yescharacteristic, complemented
249#102—731no—
250#102—731no—
251#102—731no—
252#102C2×D7311yescharacteristic, complemented
253C22⋊C8—731no—
254C22⋊C8—731no—
255C22⋊C8—731no—
256C22⋊C8C2×D7311yescharacteristic
257C24—731no—
258#41—41no—
259#41—41no—
260#41—2921no—
261#41—2921no—
262C2×Q8—731no—
263C2×Q8C22×D7311yescharacteristic
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—1461no—
267C2×D4—1461no—
268C2×D4—1461no—
269C2×D4—1461no—
270C2×D4C22×D7311yescharacteristic
271C2×D4C22×D7311yescharacteristic
272C22×C4—21no—
273C22×C4—2921no—
274C22×C4—2921no—
275C22×C4—731no—
276C22×C4—731no—
277C22×C4—731no—
278C22×C4—731no—
279C22×C4—731no—
280C22×C4—1461no—
281C22×C4C22×D7311yescharacteristic
282Q16—2921no—
283SD16—41no—
284SD16—2921no—
285D8—41no—
286M16—2921no—
287M16—2921no—
288C2×C8—731no—
289C2×C8—731no—
290C2×C8C22×D7311yescharacteristic
291C2×C8C22×D7311yescharacteristic
292C4⋊C4—731no—
293C4⋊C4—731no—
294C4⋊C4—731no—
295C4⋊C4—1461no—
296C4⋊C4—1461no—
297C4⋊C4—1461no—
298C4⋊C4—1461no—
299C4⋊C4C22×D7311yescharacteristic
300C22⋊C4—21no—
301C22⋊C4—1461no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C22⋊C4—1461no—
305C22⋊C4—1461no—
306C22⋊C4—1461no—
307C22⋊C4—1461no—
308C22⋊C4—1461no—
309C22⋊C4—1461no—
310C42—1461no—
311C42—1461no—
312C23—21no—
313C23—21no—
314C23—2921no—
315C23—2921no—
316C23—2921no—
317C23—731no—
318C23—731no—
319C23D4×D7311yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—1461no—
323Q8—1461no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—42no—
329D4—42no—
330D4—2922no—
331D4—2922no—
332D4—2922no—
333D4—2922no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—42no—
339C2×C4—2921no—
340C2×C4—2921no—
341C2×C4—2922no—
342C2×C4—2921no—
343C2×C4—731no—
344C2×C4—731no—
345C2×C4—1461no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4—1461no—
351C2×C4—1461no—
352C2×C4—1461no—
353C2×C4D4×D7311yescharacteristic
354C2×C4C23×D7311yescharacteristic
355C8—21no—
356C8—21no—
357C8—1461no—
358C8—1461no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—2924no—
369C22—1461no—
370C22—1461no—
371C22—1461no—
372C22—1461no—
373C22—1461no—
374C22—1461no—
375C22C2×D4×D7311yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—2921no—
380C4—2921no—
381C4—2921no—
382C4—2921no—
383C4—1461no—
384C4—1461no—
385C4#1455663611yescharacteristic
386C4#1455663611yescharacteristic
387C2—41no—
388C2—81no—
389C2—81no—
390C2—2921no—
391C2—2921no—
392C2#1798914711yescharacteristic
393C2#1798938311yescharacteristic
394C2#1798938411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#449×C73C2
socleC22×C73C22×D4
hypercenter#449D73
hypocenterC73#3197
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #17989097C2semidirect
2. #17989094C2semidirect
3. #17988929C2semidirect
4. #17988926C2semidirect
5. #17988909C2semidirect
6. #17988908C2semidirect
7. #17988844C2semidirect
8. #17988837C2semidirect
9. #17988832C2semidirect
10. #17988830C2semidirect
11. #17988749C2semidirect
12. #17988746C2semidirect
13. #17988729C2semidirect
14. #17988549C2semidirect
15. #449×C73C2semidirect
18. C2×#11924018C22semidirect
19. C2×#11924016C22semidirect
39. #14556525C22semidirect
40. #14556524C22semidirect
41. #14556523C22semidirect
42. #14556522C22semidirect
43. #14556516C22semidirect
44. #14556516C22semidirect
45. #14556515C22semidirect
46. #14556512C22semidirect
47. #14556512C22semidirect
48. #14556512C22semidirect
53. C2×SD16×C73C22semidirect
54. C2×D8×C73C22semidirect
56. #103×C73C22semidirect
57. #102×C73C22semidirect
198. C73#3197semidirect
212. #449D73semidirect
219. C2×SD16C2×D73semidirect
220. C2×D8C2×D73semidirect
248. #103C2×D73semidirect
252. #102C2×D73semidirect