Finite Group Databasebeta

← #22621971

Subgroups — #22621971

Order 9344.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989308C211yesmaximal, characteristic, complemented
2#17989225C211yesmaximal, characteristic
3#17988948C211yesmaximal, characteristic, complemented
4#17988927C211yesmaximal, characteristic, complemented
5#17988912C211yesmaximal, characteristic, complemented
6#17988875C211yesmaximal, characteristic, complemented
7#17988842C211yesmaximal, characteristic, complemented
8#17988818C211yesmaximal, characteristic, complemented
9#17988811C211yesmaximal, characteristic, complemented
10#17988736C211yesmaximal, characteristic, complemented
11#17988688C211yesmaximal, characteristic, complemented
12#17988655C211yesmaximal, characteristic, complemented
13#17988590C211yesmaximal, characteristic, complemented
14#17988583C211yesmaximal, characteristic, complemented
15#452×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73C2211yescharacteristic
17C2×#11924015C2211yescharacteristic
18C2×#11924011C2211yescharacteristic
19C22×#10596831C2211yescharacteristic, complemented
20#14556590C2211yescharacteristic, complemented
21#14556586—21no—
22#14556584—21no—
23#14556580C2211yescharacteristic
24#14556577—21no—
25#14556574—21no—
26#14556567C2211yescharacteristic
27#14556567C2211yescharacteristic
28#14556565C2211yescharacteristic
29#14556563—21no—
30#14556559—21no—
31Q8×Dic73C2211yescharacteristic, complemented
32#14556556—21no—
33D4×Dic73C2211yescharacteristic
34C4×C22⋊D73C2211yescharacteristic
35#14556550C2211yescharacteristic, complemented
36#14556549C2211yescharacteristic
37C2×#11924005—21no—
38#14556525C2211yescharacteristic, complemented
39#14556523C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41#14556520C2211yescharacteristic, complemented
42#14556515C2211yescharacteristic, complemented
43#14556515C2211yescharacteristic, complemented
44#14556515C2211yescharacteristic, complemented
45#14556513C2211yescharacteristic
46#14556513C2211yescharacteristic
47#14556512C2211yescharacteristic
48#14556512C2211yescharacteristic
49#14556511C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556501C2211yescharacteristic, complemented
52C2×#41×C73C2211yescharacteristic
53C2×Q16×C73C2211yescharacteristic, complemented
54C2×SD16×C73C2211yescharacteristic
55C22⋊Q8×C73C2211yescharacteristic, complemented
56#103×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic
58C22⋊C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C2×Dic146—21no—
61C2×D292C2311yescharacteristic
62C2×C22⋊D73—21no—
63C2×C22⋊D73—21no—
64C2×C22⋊D73D411yescharacteristic
65D4×D73—22no—
66D4×D73—41no—
67C22×Dic73—21no—
68C2×C4×D73C2311yescharacteristic
69#11924015—41no—
70#11924011—41no—
71C2×#10596831—41no—
72C2×#10596831C2311yescharacteristic
73C2×#10596831C2311yescharacteristic
74C4⋊Dic73—21no—
75C4⋊Dic73C2311yescharacteristic
76C4⋊Dic73C2311yescharacteristic
77C4⋊Dic73C2311yescharacteristic
78#11924007—21no—
79#11924007—21no—
80#11924007—21no—
81#11924007D411yescharacteristic
82C22⋊Dic73—21no—
83C22⋊Dic73—21no—
84C22⋊Dic73D411yescharacteristic
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005D411yescharacteristic
92C4×Dic73—21no—
93C4×Dic73—21no—
94C4×Dic73—21no—
95C4×Dic73C2311yescharacteristic
96#41×C73—22no—
97#41×C73—41no—
98C2×Q8×C73C2311yescharacteristic
99C2×Q8×C73C2311yescharacteristic
100C2×D4×C73—21no—
101C2×D4×C73C2311yescharacteristic
102C22×C4×C73—21no—
103C22×C4×C73C2311yescharacteristic
104Q16×C73—41no—
105SD16×C73—22no—
106C2×C8×C73C2311yescharacteristic
107C2×C8×C73C2311yescharacteristic
108C4⋊C4×C73—21no—
109C4⋊C4×C73C2311yescharacteristic
110C22⋊C4×C73—21no—
111C23×C73—21no—
112C23×C73C2×D411yescharacteristic
113C22×D73—21no—
114C22×D73—42no—
115C22×D73—42no—
116C22×D73—81no—
117C22×D73C2×D411yescharacteristic
118Q8×C73—21no—
119Q8×C73—21no—
120Q8×C73—21no—
121Q8×C73—21no—
122D4×C73—21no—
123D4×C73—42no—
124D4×C73#4112yes—
125C2×C4×C73—21no—
126C2×C4×C73—21no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—42no—
131C2×C4×C73C2×D411yescharacteristic
132C2×C4×C73C2411yescharacteristic
133C22⋊D73—41no—
134C22⋊D73—42no—
135C22⋊D73—81no—
136C2×Dic73—21no—
137C2×Dic73—21no—
138C2×Dic73—21no—
139C2×Dic73—81no—
140C2×Dic73C2×D411yescharacteristic
141C2×Dic73C2×D411yescharacteristic
142C2×Dic73C2×D411yescharacteristic
143D292—21no—
144D292—21no—
145C4×D73—21no—
146C4×D73—21no—
147Dic146—42no—
148C8×C73—21no—
149C8×C73—21no—
150#10596831—21no—
151#10596831—21no—
152C22×C73—22no—
153C22×C73—21no—
154C22×C73—21no—
155C22×C73—21no—
156C22×C73—41no—
157C22×C73—41no—
158C22×C73C22×D411yescharacteristic
159C2×D73—21no—
160C2×D73—21no—
161C2×D73—21no—
162C2×D73—41no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—84no—
166C4×C73—21no—
167C4×C73—41no—
168C4×C73—41no—
169C4×C73—41no—
170C4×C73C2×#4111yescharacteristic
171C4×C73H(5,𝔽2)11yescharacteristic
172Dic73—21no—
173Dic73—21no—
174Dic73—21no—
175Dic73—41no—
176Dic73—41no—
177Dic73—41no—
178C2×C73—42no—
179C2×C73—41no—
180C2×C73#54611yescharacteristic
181C2×C73#57511yescharacteristic
182C2×C73#57711yescharacteristic
183D73—41no—
184D73—81no—
185#3311—731nomaximal, Sylow
186C73#331111yescharacteristic, complemented, Sylow
187#556—731no—
188#546—731no—
189#489—731no—
190#485—731no—
191#482—731no—
192#476—731no—
193#470—731no—
194#465—731no—
195#464—731no—
196#452D7311yescharacteristic, complemented
197#450—731no—
198#440—731no—
199#435—731no—
200#418—731no—
201#416—731no—
202C2×#41C2×D7311yescharacteristic
203C22×D4—731no—
204C2×Q16C2×D7311yescharacteristic, complemented
205C2×SD16—731no—
206C2×SD16C2×D7311yescharacteristic
207C2×M16—731no—
208C22×C8—731no—
209C4⋊Q8—731no—
210#126—1461no—
211#126—1461no—
212#124—731no—
213#124—1461no—
214#123—1461no—
215C22⋊Q8—731no—
216C22⋊Q8—731no—
217C22⋊Q8C2×D7311yescharacteristic, complemented
218#121—731no—
219#121—1461no—
220#120—1461no—
221C4×Q8—731no—
222C4×Q8—1461no—
223C4×D4—731no—
224C4×D4—731no—
225#117—731no—
226#117—731no—
227C2×C22⋊C4—1461no—
228#107—731no—
229#106—731no—
230#106—731no—
231C4⋊C8—731no—
232#103—731no—
233#103—731no—
234#103—731no—
235#103C2×D7311yescharacteristic, complemented
236#102—731no—
237#102—731no—
238#102—731no—
239#102—731no—
240#102—731no—
241#102C2×D7311yescharacteristic
242C22⋊C8—731no—
243C22⋊C8C2×D7311yescharacteristic, complemented
244#97—731no—
245C24—1461no—
246#41—22no—
247#41—41no—
248C2×Q8—1461no—
249C2×Q8C22×D7311yescharacteristic
250C2×Q8C22×D7311yescharacteristic
251C2×D4—21no—
252C2×D4—2921no—
253C2×D4—731no—
254C2×D4—731no—
255C2×D4—1461no—
256C2×D4—1462no—
257C2×D4—1461no—
258C2×D4C22×D7311yescharacteristic
259C22×C4—21no—
260C22×C4—731no—
261C22×C4—1461no—
262C22×C4C22×D7311yescharacteristic
263Q16—41no—
264SD16—22no—
265SD16—2921no—
266M16—2921no—
267C2×C8—2921no—
268C2×C8—731no—
269C2×C8—731no—
270C2×C8C22×D7311yescharacteristic
271C2×C8C22×D7311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—731no—
274C4⋊C4—731no—
275C4⋊C4—731no—
276C4⋊C4—731no—
277C4⋊C4—1461no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4—1461no—
281C4⋊C4C22×D7311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—731no—
284C22⋊C4—731no—
285C22⋊C4—1461no—
286C22⋊C4—1461no—
287C22⋊C4—1461no—
288C22⋊C4—1461no—
289C22⋊C4—1461no—
290C22⋊C4—1461no—
291C22⋊C4—1461no—
292C22⋊C4—1461no—
293C42—731no—
294C42—1461no—
295C42—1461no—
296C42—1461no—
297C23—21no—
298C23—2922no—
299C23—2922no—
300C23—5841no—
301C23—731no—
302C23—1461no—
303C23D4×D7311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308Q8—2922no—
309D4—21no—
310D4—42no—
311D4—2922no—
312D4—2921no—
313D4—5841no—
314D4—1461no—
315D4—1461no—
316D4#1192402712yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—42no—
323C2×C4—5841no—
324C2×C4—731no—
325C2×C4—731no—
326C2×C4—731no—
327C2×C4—1461no—
328C2×C4—1461no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4D4×D7311yescharacteristic
333C2×C4C23×D7311yescharacteristic
334C8—21no—
335C8—21no—
336C8—1461no—
337C8—1461no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—41no—
343C22—41no—
344C22—2921no—
345C22—2921no—
346C22—2921no—
347C22—5844no—
348C22—1461no—
349C22—1461no—
350C22—1461no—
351C22C2×D4×D7311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—2921no—
357C4—2921no—
358C4—2921no—
359C4—1461no—
360C4—1461no—
361C4—1461no—
362C4C2×#1192402711yescharacteristic
363C4#1455663611yescharacteristic
364C2—41no—
365C2—42no—
366C2—2921no—
367C2—5841no—
368C2#1798922411yescharacteristic
369C2#1798938411yescharacteristic
370C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#452×C73C2
socleC22×C73C22×D4
hypercenter#452D73
hypocenterC73#3311
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #17989308C2semidirect
3. #17988948C2semidirect
4. #17988927C2semidirect
5. #17988912C2semidirect
6. #17988875C2semidirect
7. #17988842C2semidirect
8. #17988818C2semidirect
9. #17988811C2semidirect
10. #17988736C2semidirect
11. #17988688C2semidirect
12. #17988655C2semidirect
13. #17988590C2semidirect
14. #17988583C2semidirect
15. #452×C73C2semidirect
19. C22×#10596831C22semidirect
20. #14556590C22semidirect
31. Q8×Dic73C22semidirect
35. #14556550C22semidirect
38. #14556525C22semidirect
39. #14556523C22semidirect
40. #14556522C22semidirect
41. #14556520C22semidirect
42. #14556515C22semidirect
43. #14556515C22semidirect
44. #14556515C22semidirect
51. #14556501C22semidirect
53. C2×Q16×C73C22semidirect
55. C22⋊Q8×C73C22semidirect
56. #103×C73C22semidirect
58. C22⋊C8×C73C22semidirect
186. C73#3311semidirect
196. #452D73semidirect
204. C2×Q16C2×D73semidirect
217. C22⋊Q8C2×D73semidirect
235. #103C2×D73semidirect
243. C22⋊C8C2×D73semidirect