Finite Group Databasebeta

← #22621024

Subgroups — #22621024

Order 9344.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989202C211yesmaximal, characteristic, complemented
2#17989155C211yesmaximal, characteristic, complemented
3#17988975C211yesmaximal, characteristic, complemented
4#17988968C211yesmaximal, characteristic, complemented
5#17988948C211yesmaximal, characteristic, complemented
6#17988932C211yesmaximal, characteristic, complemented
7#17988806C211yesmaximal, characteristic, complemented
8#17988788C211yesmaximal, characteristic, complemented
9#17988782C211yesmaximal, characteristic, complemented
10#17988752C211yesmaximal, characteristic, complemented
11#17988739C211yesmaximal, characteristic, complemented
12#17988731C211yesmaximal, characteristic, complemented
13#17988719C211yesmaximal, characteristic, complemented
14#17988647C211yesmaximal, characteristic, complemented
15#463×C73C211yesmaximal, characteristic, complemented
16C2×#11924029C2211yescharacteristic
17C2×D4×D73C2211yescharacteristic
18C2×#11924018C2211yescharacteristic, complemented
19C2×#11924017C2211yescharacteristic
20C2×#11924017C2211yescharacteristic, complemented
21C2×#11924016C2211yescharacteristic
22C2×#11924013C2211yescharacteristic
23C2×#11924013C2211yescharacteristic, complemented
24#14556590C2211yescharacteristic, complemented
25#14556588C2211yescharacteristic
26#14556587C2211yescharacteristic
27#14556584—21no—
28#14556580C2211yescharacteristic
29#14556578C2211yescharacteristic, complemented
30#14556577—21no—
31#14556574—21no—
32#14556571C2211yescharacteristic
33#14556570—21no—
34#14556564—21no—
35#14556564—21no—
36#14556562C2211yescharacteristic
37#14556561—21no—
38#14556561—21no—
39C4×Dic146C2211yescharacteristic, complemented
40#14556548C2211yescharacteristic
41C4⋊#10596831C2211yescharacteristic, complemented
42#14556515C2211yescharacteristic, complemented
43#14556513C2211yescharacteristic
44#14556513C2211yescharacteristic, complemented
45#14556512C2211yescharacteristic
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic, complemented
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556501C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52C2×SD16×C73C2211yescharacteristic, complemented
53C2×D8×C73C2211yescharacteristic
54#124×C73C2211yescharacteristic
55C4×D4×C73C2211yescharacteristic, complemented
56C4⋊C8×C73C2211yescharacteristic, complemented
57#103×C73C2211yescharacteristic, complemented
58#102×C73C2211yescharacteristic
59C23×D73—21no—
60#11924029—41no—
61#11924029—41no—
62C2×Dic146—21no—
63C2×Dic146C2311yescharacteristic
64C2×D292—21no—
65C2×D292—21no—
66C2×D292—21no—
67C2×D292C2311yescharacteristic
68C2×D292C2311yescharacteristic
69C2×C22⋊D73—21no—
70C2×C22⋊D73—21no—
71C2×C22⋊D73—21no—
72C2×C22⋊D73—21no—
73D4×D73—41no—
74D4×D73—41no—
75C2×C4×D73—21no—
76C2×C4×D73C2311yescharacteristic
77#11924018—41no—
78#11924017—41no—
79#11924017—41no—
80#11924016—41no—
81#11924013—41no—
82#11924013—41no—
83C2×#10596831C2311yescharacteristic
84C2×#10596831C2311yescharacteristic
85C4⋊Dic73—21no—
86C4⋊Dic73C2311yescharacteristic
87#11924007—21no—
88#11924007—21no—
89#11924007D411yescharacteristic
90#11924007D411yescharacteristic
91C22⋊Dic73—21no—
92C22⋊Dic73—21no—
93C22⋊Dic73—21no—
94#11924005—21no—
95#11924005—21no—
96#11924005—21no—
97#11924005D411yescharacteristic
98#11924005D411yescharacteristic
99C4×Dic73—21no—
100C4×Dic73C2311yescharacteristic
101C2×Q8×C73C2311yescharacteristic
102C2×D4×C73C2311yescharacteristic
103C2×D4×C73C2311yescharacteristic
104C22×C4×C73—21no—
105SD16×C73—41no—
106D8×C73—41no—
107C2×C8×C73C2311yescharacteristic
108C2×C8×C73C2311yescharacteristic
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C22⋊C4×C73—21no—
112C22⋊C4×C73—21no—
113C42×C73C2311yescharacteristic
114C23×C73—21no—
115C23×C73—21no—
116C22×D73—21no—
117C22×D73—21no—
118C22×D73—42no—
119C22×D73—81no—
120C22×D73—81no—
121C22×D73C2×D411yescharacteristic
122Q8×C73—21no—
123Q8×C73—21no—
124D4×C73—21no—
125D4×C73—21no—
126D4×C73—21no—
127D4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—81no—
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2×D411yescharacteristic
133C2×C4×C73C2411yescharacteristic
134C22⋊D73—42no—
135C22⋊D73—81no—
136C22⋊D73—81no—
137C22⋊D73—81no—
138C2×Dic73—21no—
139C2×Dic73—21no—
140C2×Dic73C2×D411yescharacteristic
141C2×Dic73C2×D411yescharacteristic
142C2×Dic73C2×D411yescharacteristic
143D292—21no—
144D292—21no—
145D292—21no—
146D292—21no—
147D292—42no—
148D292—81no—
149D292—81no—
150C4×D73—21no—
151C4×D73—21no—
152C4×D73—42no—
153Dic146—21no—
154Dic146—21no—
155Dic146—81no—
156C8×C73—21no—
157C8×C73—21no—
158#10596831—21no—
159#10596831—21no—
160C22×C73—41no—
161C22×C73—41no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73C22×D411yescharacteristic
167C2×D73—21no—
168C2×D73—21no—
169C2×D73—21no—
170C2×D73—41no—
171C2×D73—41no—
172C2×D73—41no—
173C2×D73—41no—
174C2×D73—41no—
175C2×D73—41no—
176C2×D73—84no—
177C4×C73—21no—
178C4×C73—21no—
179C4×C73—41no—
180C4×C73—41no—
181C4×C73H(5,𝔽2)11yescharacteristic
182C4×C73H(5,𝔽2)11yescharacteristic
183Dic73—21no—
184Dic73—21no—
185Dic73—21no—
186Dic73—41no—
187Dic73—41no—
188C2×C73—81no—
189C2×C73—81no—
190C2×C73#53511yescharacteristic
191C2×C73#57611yescharacteristic
192C2×C73#57711yescharacteristic
193D73—41no—
194D73—81no—
195D73—81no—
196#3224—731nomaximal, Sylow
197C73#322411yescharacteristic, complemented, Sylow
198#542—731no—
199#535—731no—
200#496—731no—
201#495—731no—
202#489—731no—
203#486—731no—
204#464—731no—
205#463D7311yescharacteristic, complemented
206#460—731no—
207#459—731no—
208#452—731no—
209#450—731no—
210#449—731no—
211#447—731no—
212#433—731no—
213C2×#41—731no—
214C22×D4—731no—
215C2×Q16—731no—
216C2×SD16—731no—
217C2×SD16—731no—
218C2×SD16—731no—
219C2×SD16C2×D7311yescharacteristic, complemented
220C2×D8—731no—
221C2×D8—731no—
222C2×D8C2×D7311yescharacteristic
223C4⋊Q8—731no—
224#127—731no—
225#127—731no—
226#126—1461no—
227#124—731no—
228#124—731no—
229#124—1461no—
230#124C2×D7311yescharacteristic
231#123—1461no—
232C22⋊Q8—731no—
233C22⋊Q8—1461no—
234#121—731no—
235#121—1461no—
236#121—1461no—
237#120—1461no—
238#120—1461no—
239C4×Q8—731no—
240C4×D4C2×D7311yescharacteristic, complemented
241#117—731no—
242C4⋊C8—731no—
243C4⋊C8C2×D7311yescharacteristic, complemented
244#103—731no—
245#103C2×D7311yescharacteristic, complemented
246#102—731no—
247#102—731no—
248#102—731no—
249#102—731no—
250#102—731no—
251#102C2×D7311yescharacteristic
252C22⋊C8—731no—
253C22⋊C8—731no—
254#97—731no—
255C4×C8—731no—
256C24—1461no—
257#41—2921no—
258#41—2921no—
259C2×Q8—731no—
260C2×Q8—1461no—
261C2×Q8C22×D7311yescharacteristic
262C2×D4—2921no—
263C2×D4—2921no—
264C2×D4—731no—
265C2×D4—731no—
266C2×D4—1461no—
267C2×D4—1461no—
268C2×D4—1461no—
269C2×D4—1461no—
270C2×D4—1461no—
271C2×D4—1461no—
272C2×D4—1461no—
273C2×D4C22×D7311yescharacteristic
274C2×D4C22×D7311yescharacteristic
275C22×C4—21no—
276C22×C4—731no—
277C22×C4—1461no—
278Q16—2921no—
279SD16—41no—
280SD16—2921no—
281SD16—2921no—
282SD16—2921no—
283D8—41no—
284D8—2921no—
285D8—2921no—
286C2×C8—731no—
287C2×C8—731no—
288C2×C8C22×D7311yescharacteristic
289C2×C8C22×D7311yescharacteristic
290C4⋊C4—731no—
291C4⋊C4—731no—
292C4⋊C4—731no—
293C4⋊C4—1461no—
294C4⋊C4—1461no—
295C4⋊C4—1461no—
296C4⋊C4C22×D7311yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—731no—
301C22⋊C4—731no—
302C22⋊C4—1461no—
303C22⋊C4—1461no—
304C22⋊C4—1461no—
305C22⋊C4—1461no—
306C22⋊C4—1461no—
307C22⋊C4—1461no—
308C42—731no—
309C42—1461no—
310C42C22×D7311yescharacteristic
311C23—21no—
312C23—21no—
313C23—2922no—
314C23—5841no—
315C23—5841no—
316C23—731no—
317C23—1461no—
318C23—1461no—
319Q8—21no—
320Q8—21no—
321Q8—5841no—
322Q8—1461no—
323Q8—1461no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—2922no—
329D4—2922no—
330D4—5841no—
331D4—5841no—
332D4—5841no—
333D4—5841no—
334D4—5841no—
335D4—1461no—
336D4—1461no—
337D4—1461no—
338D4—1461no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—81no—
342C2×C4—2922no—
343C2×C4—731no—
344C2×C4—731no—
345C2×C4—731no—
346C2×C4—1461no—
347C2×C4—1461no—
348C2×C4—1461no—
349C2×C4—1461no—
350C2×C4D4×D7311yescharacteristic
351C2×C4D4×D7311yescharacteristic
352C2×C4C23×D7311yescharacteristic
353C8—21no—
354C8—21no—
355C8—1461no—
356C8—1461no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—2921no—
364C22—2921no—
365C22—2921no—
366C22—2921no—
367C22—2921no—
368C22—2921no—
369C22—5844no—
370C22—1461no—
371C22—1461no—
372C22—1461no—
373C22C2×D4×D7311yescharacteristic
374C4—21no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—2921no—
379C4—2921no—
380C4—1461no—
381C4—1461no—
382C4—1461no—
383C4#1455663611yescharacteristic
384C4#1455663711yescharacteristic
385C2—81no—
386C2—81no—
387C2—2921no—
388C2—5841no—
389C2—5841no—
390C2#1798915311yescharacteristic
391C2#1798939111yescharacteristic
392C2#1798939411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#463×C73C2
socleC22×C73C22×D4
hypercenter#463D73
hypocenterC73#3224
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #17989202C2semidirect
2. #17989155C2semidirect
3. #17988975C2semidirect
4. #17988968C2semidirect
5. #17988948C2semidirect
6. #17988932C2semidirect
7. #17988806C2semidirect
8. #17988788C2semidirect
9. #17988782C2semidirect
10. #17988752C2semidirect
11. #17988739C2semidirect
12. #17988731C2semidirect
13. #17988719C2semidirect
14. #17988647C2semidirect
15. #463×C73C2semidirect
18. C2×#11924018C22semidirect
20. C2×#11924017C22semidirect
23. C2×#11924013C22semidirect
24. #14556590C22semidirect
29. #14556578C22semidirect
39. C4×Dic146C22semidirect
41. C4⋊#10596831C22semidirect
42. #14556515C22semidirect
44. #14556513C22semidirect
47. #14556511C22semidirect
50. #14556501C22semidirect
51. C8×Dic73C22semidirect
52. C2×SD16×C73C22semidirect
55. C4×D4×C73C22semidirect
56. C4⋊C8×C73C22semidirect
57. #103×C73C22semidirect
197. C73#3224semidirect
205. #463D73semidirect
219. C2×SD16C2×D73semidirect
240. C4×D4C2×D73semidirect
243. C4⋊C8C2×D73semidirect
245. #103C2×D73semidirect