Finite Group Databasebeta

← #22618980

Subgroups — #22618980

Order 9344.

412 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#17989096C211yesmaximal, characteristic
2#17988664C211yesmaximal, characteristic, complemented
3#17988663C211yesmaximal, characteristic, complemented
4#17988660C211yesmaximal, characteristic, complemented
5#17988658C211yesmaximal, characteristic, complemented
6#17988655C211yesmaximal, characteristic, complemented
7D4×#10596831C211yesmaximal, characteristic, complemented
8#17988650C211yesmaximal, characteristic, complemented
9#17988649C211yesmaximal, characteristic, complemented
10#17988647C211yesmaximal, characteristic, complemented
11#17988555C211yesmaximal, characteristic, complemented
12#17988552C211yesmaximal, characteristic, complemented
13#17988549C211yesmaximal, characteristic, complemented
14C2×#14556503C211yesmaximal, characteristic, complemented
15#435×C73C211yesmaximal, characteristic, complemented
16C2×#11924028C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18C2×#11924011C2211yescharacteristic
19C2×#11924011C2211yescharacteristic
20C2×#11924011C2211yescharacteristic, complemented
21C22×#10596831C2211yescharacteristic
22C22×#10596831C2211yescharacteristic, complemented
23C2×C8×D73C2211yescharacteristic, complemented
24#14556576C411yescharacteristic
25#14556573C411yescharacteristic
26#14556569C411yescharacteristic
27#14556568C411yescharacteristic
28#14556564C411yescharacteristic
29#14556563C411yescharacteristic
30#14556561C411yescharacteristic
31#14556559C411yescharacteristic
32C4×D292C2211yescharacteristic
33C4×C22⋊D73C2211yescharacteristic
34C4×C22⋊D73C2211yescharacteristic
35#14556548C2211yescharacteristic
36C4⋊#10596831C2211yescharacteristic, complemented
37#14556520C2211yescharacteristic, complemented
38#14556520C2211yescharacteristic, complemented
39C22⋊#10596831C2211yescharacteristic
40C22⋊#10596831C2211yescharacteristic, complemented
41#14556503C2211yescharacteristic
42#14556503C2211yescharacteristic
43#14556503C2211yescharacteristic
44#14556503C2211yescharacteristic
45#14556503C2211yescharacteristic
46#14556503C2211yescharacteristic
47#14556503C2211yescharacteristic, complemented
48#14556503C2211yescharacteristic, complemented
49#14556501C2211yescharacteristic, complemented
50C4×#10596831C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52C2×M16×C73C2211yescharacteristic, complemented
53C22×C8×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic
55C4⋊C8×C73C2211yescharacteristic, complemented
56C22⋊C8×C73C2211yescharacteristic
57C22⋊C8×C73C2211yescharacteristic, complemented
58#97×C73C2211yescharacteristic, complemented
59C23×D73C2×C411yescharacteristic
60#11924028—41no—
61#11924028—41no—
62C2×Dic146C2×C411yescharacteristic
63C2×D292C2×C411yescharacteristic
64C2×D292C2×C411yescharacteristic
65C2×C22⋊D73C2×C411yescharacteristic
66C2×C22⋊D73C2×C411yescharacteristic
67C2×C22⋊D73C2×C411yescharacteristic
68C2×C22⋊D73C2×C411yescharacteristic
69C22×Dic73C2×C411yescharacteristic
70C2×C4×D73—41no—
71C2×C4×D73—41no—
72C2×C4×D73C2×C411yescharacteristic
73C2×C4×D73C2×C411yescharacteristic
74C2×C4×D73C2311yescharacteristic
75C2×C4×D73C2311yescharacteristic
76C2×C4×D73C2311yescharacteristic
77#11924011—41no—
78#11924011—41no—
79#11924011—41no—
80C2×#10596831—41no—
81C2×#10596831—41no—
82C2×#10596831C2311yescharacteristic
83C2×#10596831C2311yescharacteristic
84C2×#10596831C2311yescharacteristic
85C2×#10596831C2311yescharacteristic
86C8×D73—41no—
87C4⋊Dic73C2×C411yescharacteristic
88#11924007C2×C411yescharacteristic
89#11924007C2×C411yescharacteristic
90#11924007C2×C411yescharacteristic
91#11924007C2×C411yescharacteristic
92C22⋊Dic73C2×C411yescharacteristic
93C22⋊Dic73C2×C411yescharacteristic
94#11924005C2×C411yescharacteristic
95#11924005C2×C411yescharacteristic
96#11924005C2×C411yescharacteristic
97#11924005C2×C411yescharacteristic
98#11924005C2×C411yescharacteristic
99#11924005C2×C411yescharacteristic
100C4×Dic73C2311yescharacteristic
101C2×D4×C73C2×C411yescharacteristic
102C22×C4×C73C2311yescharacteristic
103C22×C4×C73C2311yescharacteristic
104M16×C73—41no—
105C2×C8×C73—41no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C2×C8×C73C2311yescharacteristic
109C2×C8×C73C2311yescharacteristic
110C4⋊C4×C73C2×C411yescharacteristic
111C22⋊C4×C73C2×C411yescharacteristic
112C22⋊C4×C73C2×C411yescharacteristic
113C42×C73C2311yescharacteristic
114C23×C73C22×C411yescharacteristic
115C23×C73C22×C411yescharacteristic
116C22×D73—22no—
117C22×D73—41no—
118C22×D73—41no—
119C22×D73C22×C411yescharacteristic
120C22×D73C22×C411yescharacteristic
121C22×D73C22×C411yescharacteristic
122D4×C73—22no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73C22×C411yescharacteristic
128C2×C4×C73C22×C411yescharacteristic
129C2×C4×C73C22×C411yescharacteristic
130C2×C4×C73C22×C411yescharacteristic
131C2×C4×C73C2411yescharacteristic
132C22⋊D73—22no—
133C22⋊D73—41no—
134C22⋊D73—41no—
135C22⋊D73—41no—
136C2×Dic73—41no—
137C2×Dic73C22×C411yescharacteristic
138C2×Dic73C22×C411yescharacteristic
139C2×Dic73C22×C411yescharacteristic
140C2×Dic73C22×C411yescharacteristic
141C2×Dic73C22×C411yescharacteristic
142D292—41no—
143D292—41no—
144C4×D73—21no—
145C4×D73—21no—
146C4×D73—21no—
147C4×D73—21no—
148C4×D73—21no—
149C4×D73—21no—
150C4×D73—41no—
151C4×D73—41no—
152Dic146—41no—
153C8×C73—21no—
154C8×C73—21no—
155C8×C73—21no—
156C8×C73—21no—
157#10596831—21no—
158#10596831—21no—
159#10596831—21no—
160#10596831—21no—
161C22×C73—21no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—21no—
165C22×C73—21no—
166C22×C73#13112yes—
167C22×C73C23×C411yescharacteristic
168C2×D73—21no—
169C2×D73—21no—
170C2×D73—21no—
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—21no—
180C4×C73—21no—
181C4×C73—21no—
182C4×C73H(5,𝔽2)11yescharacteristic
183C4×C73H(5,𝔽2)11yescharacteristic
184Dic73—21no—
185Dic73—21no—
186Dic73—21no—
187Dic73—21no—
188Dic73—21no—
189C2×C73—22no—
190C2×C73—41no—
191C2×C73#51811yescharacteristic
192C2×C73C2×#13111yescharacteristic
193C2×C73#56811yescharacteristic
194D73—41no—
195D73—41no—
196D73—41no—
197#2976—731nomaximal, Sylow
198C73#297611yescharacteristic, complemented, Sylow
199#525—731no—
200#436—731no—
201#436—731no—
202#435—731no—
203#435—731no—
204#435—731no—
205#435D7311yescharacteristic, complemented
206C8×D4—731no—
207C8×D4—731no—
208#433—731no—
209#433—731no—
210#408—731no—
211#408—731no—
212#407—731no—
213C2×C22⋊C8—731no—
214C2×#41—731no—
215C23×C4—731no—
216C2×M16—731no—
217C2×M16—731no—
218C2×M16—731no—
219C2×M16C2×D7311yescharacteristic, complemented
220C22×C8—731no—
221C22×C8—731no—
222C22×C8—731no—
223C22×C8C2×D7311yescharacteristic
224#123—731no—
225#123—731no—
226C22⋊Q8—731no—
227C22⋊Q8—731no—
228#121—731no—
229#121—731no—
230#120—731no—
231#120—731no—
232C4×D4—731no—
233C4×D4—731no—
234C4×D4—731no—
235C4×D4C2×D7311yescharacteristic
236#117—731no—
237C4⋊C8—731no—
238C4⋊C8—731no—
239C4⋊C8—731no—
240C4⋊C8C2×D7311yescharacteristic, complemented
241C22⋊C8—731no—
242C22⋊C8—731no—
243C22⋊C8—731no—
244C22⋊C8—731no—
245C22⋊C8—731no—
246C22⋊C8—731no—
247C22⋊C8—731no—
248C22⋊C8—731no—
249C22⋊C8—731no—
250C22⋊C8—731no—
251C22⋊C8C2×D7311yescharacteristic
252C22⋊C8C2×D7311yescharacteristic, complemented
253#97—731no—
254#97C2×D7311yescharacteristic, complemented
255C4×C8—731no—
256C4×C8—731no—
257C24—731no—
258#41—2921no—
259#41—2921no—
260C2×Q8—731no—
261C2×D4—731no—
262C2×D4—731no—
263C2×D4—731no—
264C2×D4—731no—
265C2×D4—731no—
266C2×D4—731no—
267C2×D4C4×D7311yescharacteristic
268C22×C4—2921no—
269C22×C4—2921no—
270C22×C4—731no—
271C22×C4—731no—
272C22×C4—731no—
273C22×C4—731no—
274C22×C4—731no—
275C22×C4—731no—
276C22×C4C22×D7311yescharacteristic
277C22×C4C22×D7311yescharacteristic
278M16—41no—
279M16—2921no—
280M16—2921no—
281M16—2921no—
282C2×C8—41no—
283C2×C8—2921no—
284C2×C8—2921no—
285C2×C8—2921no—
286C2×C8—731no—
287C2×C8—731no—
288C2×C8—731no—
289C2×C8—731no—
290C2×C8C22×D7311yescharacteristic
291C2×C8C22×D7311yescharacteristic
292C2×C8C22×D7311yescharacteristic
293C2×C8C22×D7311yescharacteristic
294C4⋊C4—731no—
295C4⋊C4—731no—
296C4⋊C4—731no—
297C4⋊C4—731no—
298C4⋊C4—731no—
299C4⋊C4C4×D7311yescharacteristic
300C22⋊C4—731no—
301C22⋊C4—731no—
302C22⋊C4—731no—
303C22⋊C4—731no—
304C22⋊C4—731no—
305C22⋊C4—731no—
306C22⋊C4—731no—
307C22⋊C4—731no—
308C22⋊C4C4×D7311yescharacteristic
309C22⋊C4C4×D7311yescharacteristic
310C42—731no—
311C42C22×D7311yescharacteristic
312C23—2921no—
313C23—2921no—
314C23—731no—
315C23—731no—
316C23—731no—
317C23—1462no—
318C23C2×C4×D7311yescharacteristic
319C23C2×C4×D7311yescharacteristic
320Q8—2921no—
321D4—22no—
322D4—2921no—
323D4—2921no—
324D4—2921no—
325D4—2921no—
326D4—2921no—
327D4—1462no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—2921no—
333C2×C4—2921no—
334C2×C4—2921no—
335C2×C4—731no—
336C2×C4—731no—
337C2×C4—731no—
338C2×C4—731no—
339C2×C4—731no—
340C2×C4—1461no—
341C2×C4—1461no—
342C2×C4—1461no—
343C2×C4—1461no—
344C2×C4—1461no—
345C2×C4—1461no—
346C2×C4C2×C4×D7311yescharacteristic
347C2×C4C2×C4×D7311yescharacteristic
348C2×C4C2×C4×D7311yescharacteristic
349C2×C4C2×C4×D7311yescharacteristic
350C2×C4C23×D7311yescharacteristic
351C8—21no—
352C8—21no—
353C8—21no—
354C8—21no—
355C8—1461no—
356C8—1461no—
357C8—1461no—
358C8—1461no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—2924no—
365C22—1461no—
366C22—1461no—
367C22—1461no—
368C22—1461no—
369C22—1461no—
370C22—1461no—
371C22—1461no—
372C22—1461no—
373C22—1461no—
374C22#1455659912yes—
375C22C22×C4×D7311yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—1461no—
381C4—1461no—
382C4—1461no—
383C4—1461no—
384C4—1461no—
385C4#1455663611yescharacteristic
386C4#1455663711yescharacteristic
387C2—22no—
388C2—41no—
389C2—2921no—
390C2—2921no—
391C2—2921no—
392C2#1798905911yescharacteristic
393C2C2×#1455659911yescharacteristic
394C2#1798935211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D73
commutator, socleC22×C73C23×C4
Fitting#435×C73C2
hypercenter#435D73
hypocenterC73#2976
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
2. #17988664C2semidirect
3. #17988663C2semidirect
4. #17988660C2semidirect
5. #17988658C2semidirect
6. #17988655C2semidirect
7. D4×#10596831C2semidirect
8. #17988650C2semidirect
9. #17988649C2semidirect
10. #17988647C2semidirect
11. #17988555C2semidirect
12. #17988552C2semidirect
13. #17988549C2semidirect
14. C2×#14556503C2semidirect
15. #435×C73C2semidirect
20. C2×#11924011C22semidirect
22. C22×#10596831C22semidirect
23. C2×C8×D73C22semidirect
36. C4⋊#10596831C22semidirect
37. #14556520C22semidirect
38. #14556520C22semidirect
40. C22⋊#10596831C22semidirect
47. #14556503C22semidirect
48. #14556503C22semidirect
49. #14556501C22semidirect
50. C4×#10596831C22semidirect
51. C8×Dic73C22semidirect
52. C2×M16×C73C22semidirect
55. C4⋊C8×C73C22semidirect
57. C22⋊C8×C73C22semidirect
58. #97×C73C22semidirect
198. C73#2976semidirect
205. #435D73semidirect
219. C2×M16C2×D73semidirect
240. C4⋊C8C2×D73semidirect
252. C22⋊C8C2×D73semidirect
254. #97C2×D73semidirect