Finite Group Databasebeta

← #22620122

Subgroups — #22620122

Order 9344.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989211C211yesmaximal, characteristic, complemented
2#17989059C211yesmaximal, characteristic, complemented
3#17988930C211yesmaximal, characteristic, complemented
4#17988914C211yesmaximal, characteristic, complemented
5#17988874C211yesmaximal, characteristic, complemented
6#17988803C211yesmaximal, characteristic, complemented
7#17988802C211yesmaximal, characteristic, complemented
8#17988739C211yesmaximal, characteristic, complemented
9#17988722C211yesmaximal, characteristic
10#17988696C211yesmaximal, characteristic, complemented
11#17988686C211yesmaximal, characteristic, complemented
12#17988678C211yesmaximal, characteristic, complemented
13#17988669C211yesmaximal, characteristic, complemented
14#17988647C211yesmaximal, characteristic, complemented
15#474×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73C2211yescharacteristic
17C2×#11924017C2211yescharacteristic
18C2×#11924016C2211yescharacteristic
19C2×D584C2211yescharacteristic
20C2×#11924013C2211yescharacteristic
21#14556586—21no—
22#14556580—21no—
23#14556579C2211yescharacteristic, complemented
24#14556576—21no—
25#14556571C2211yescharacteristic
26#14556567—21no—
27#14556566C2211yescharacteristic
28#14556556C2211yescharacteristic, complemented
29C4×D292C2211yescharacteristic
30D4×Dic73C2211yescharacteristic
31#14556553C2211yescharacteristic
32#14556553C2211yescharacteristic, complemented
33C4×C22⋊D73—21no—
34#14556551—21no—
35#14556549C2211yescharacteristic
36#14556548C2211yescharacteristic
37C2×#11924005—21no—
38C22⋊C4×D73—21no—
39#14556522C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41C4⋊#10596831C2211yescharacteristic, complemented
42#14556516C2211yescharacteristic, complemented
43#14556514C2211yescharacteristic, complemented
44#14556513C2211yescharacteristic, complemented
45#14556511C2211yescharacteristic
46#14556511C2211yescharacteristic
47#14556511C2211yescharacteristic, complemented
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556501C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52C4⋊Q8×C73C2211yescharacteristic, complemented
53C4×D4×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic, complemented
55#107×C73C2211yescharacteristic, complemented
56C4⋊C8×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C23×D73—21no—
60C2×Dic146C2311yescharacteristic
61C2×D292—21no—
62C2×D292C2311yescharacteristic
63C2×D292C2311yescharacteristic
64C2×C22⋊D73—21no—
65D4×D73—22no—
66D4×D73—22no—
67C22×Dic73—21no—
68C2×C4×D73—21no—
69C2×C4×D73—21no—
70C2×C4×D73—21no—
71C2×C4×D73C2311yescharacteristic
72#11924017—22no—
73#11924016—22no—
74D584—22no—
75#11924013—22no—
76C2×#10596831C2311yescharacteristic
77C2×#10596831C2311yescharacteristic
78C4⋊Dic73—21no—
79C4⋊Dic73C2311yescharacteristic
80#11924007—21no—
81#11924007D411yescharacteristic
82#11924007D411yescharacteristic
83C22⋊Dic73—21no—
84#11924005—21no—
85#11924005—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005D411yescharacteristic
93#11924005D411yescharacteristic
94C4×Dic73—21no—
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97C2×Q8×C73—21no—
98C2×D4×C73C2311yescharacteristic
99C22×C4×C73—21no—
100C2×C8×C73C2311yescharacteristic
101C2×C8×C73C2311yescharacteristic
102C4⋊C4×C73—21no—
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C4⋊C4×C73C2311yescharacteristic
106C22⋊C4×C73—21no—
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C22×D73—21no—
110C22×D73—24no—
111C22×D73—21no—
112C22×D73—81no—
113C22×D73—81no—
114C22×D73C2×D411yescharacteristic
115Q8×C73—81no—
116D4×C73—21no—
117D4×C73#4112yes—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—81no—
122C2×C4×C73C2×D411yescharacteristic
123C2×C4×C73C2×D411yescharacteristic
124C2×C4×C73C2411yescharacteristic
125C22⋊D73—24no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—81no—
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131C2×Dic73C2×D411yescharacteristic
132D292—21no—
133D292—21no—
134D292—21no—
135D292—81no—
136D292#4112yes—
137C4×D73—21no—
138C4×D73—21no—
139C4×D73—81no—
140C4×D73—81no—
141C4×D73—81no—
142Dic146—21no—
143Dic146—21no—
144C8×C73—21no—
145C8×C73—21no—
146#10596831—21no—
147#10596831—21no—
148C22×C73—22no—
149C22×C73—41no—
150C22×C73—41no—
151C22×C73C22×D411yescharacteristic
152C2×D73—21no—
153C2×D73—22no—
154C2×D73—21no—
155C2×D73—21no—
156C2×D73—41no—
157C2×D73—41no—
158C2×D73—41no—
159C2×D73—41no—
160C2×D73—41no—
161C2×D73—84no—
162C4×C73—21no—
163C4×C73—21no—
164C4×C73—41no—
165C4×C73—41no—
166C4×C73—41no—
167C4×C73C2×#4111yescharacteristic
168C4×C73C2×#4111yescharacteristic
169Dic73—21no—
170Dic73—21no—
171Dic73—21no—
172Dic73—41no—
173Dic73—41no—
174C2×C73—42no—
175C2×C73#52511yescharacteristic
176C2×C73#57611yescharacteristic
177C2×C73#57711yescharacteristic
178D73—41no—
179D73—42no—
180D73—81no—
181#3118—731nomaximal, Sylow
182C73#311811yescharacteristic, complemented, Sylow
183#542—731no—
184#518—731no—
185#485—731no—
186#482—731no—
187#476—731no—
188#474D7311yescharacteristic, complemented
189#463—731no—
190#463—731no—
191#450—731no—
192#447—731no—
193#442—731no—
194#440—731no—
195C4×SD16—731no—
196C4×D8—731no—
197#433—731no—
198C22×D4—731no—
199C2×SD16—731no—
200C2×SD16—731no—
201C2×D8—731no—
202C2×D8—731no—
203C4⋊Q8C2×D7311yescharacteristic, complemented
204#126—1461no—
205#124—731no—
206#124—1461no—
207#123—1461no—
208C22⋊Q8—731no—
209C22⋊Q8—1461no—
210#121—731no—
211C4×Q8—731no—
212C4×D4—731no—
213C4×D4—731no—
214C4×D4—731no—
215C4×D4—731no—
216C4×D4—1461no—
217C4×D4—1461no—
218C4×D4C2×D7311yescharacteristic
219#117—731no—
220#117—731no—
221C2×C22⋊C4—1461no—
222C2×C22⋊C4—1461no—
223#107C2×D7311yescharacteristic, complemented
224#107C2×D7311yescharacteristic, complemented
225#106—731no—
226#106—731no—
227C4⋊C8—731no—
228C4⋊C8C2×D7311yescharacteristic, complemented
229#103—731no—
230#103—731no—
231#102—731no—
232#102—731no—
233#102—731no—
234#102—731no—
235#102C2×D7311yescharacteristic
236#102C2×D7311yescharacteristic
237C22⋊C8—731no—
238C22⋊C8—731no—
239#97—731no—
240C4×C8—731no—
241C24—1461no—
242C2×Q8—21no—
243C2×Q8—731no—
244C2×D4—731no—
245C2×D4—731no—
246C2×D4—1461no—
247C2×D4—1461no—
248C2×D4—1462no—
249C2×D4—1462no—
250C2×D4C22×D7311yescharacteristic
251C22×C4—21no—
252C22×C4—731no—
253C22×C4—1461no—
254C22×C4—1461no—
255C22×C4—1461no—
256C22×C4—1461no—
257SD16—1462no—
258SD16—1462no—
259D8—1462no—
260D8—1462no—
261C2×C8—731no—
262C2×C8—731no—
263C2×C8C22×D7311yescharacteristic
264C2×C8C22×D7311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—731no—
267C4⋊C4—731no—
268C4⋊C4—731no—
269C4⋊C4—1461no—
270C4⋊C4—1461no—
271C4⋊C4C22×D7311yescharacteristic
272C4⋊C4C22×D7311yescharacteristic
273C4⋊C4C22×D7311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—731no—
276C22⋊C4—731no—
277C22⋊C4—1461no—
278C22⋊C4—1461no—
279C22⋊C4—1461no—
280C22⋊C4—1461no—
281C22⋊C4—1461no—
282C22⋊C4—1461no—
283C22⋊C4—1461no—
284C22⋊C4—1461no—
285C22⋊C4—1461no—
286C42—731no—
287C42—1461no—
288C42—1461no—
289C42C22×D7311yescharacteristic
290C23—21no—
291C23—5841no—
292C23—5841no—
293C23—731no—
294C23—1464no—
295C23—1461no—
296C23—1461no—
297Q8—81no—
298Q8—1461no—
299Q8—1461no—
300D4—21no—
301D4—5841no—
302D4—732no—
303D4—1464no—
304D4—1461no—
305D4—1461no—
306D4—1461no—
307D4#1192402912yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—5841no—
313C2×C4—5841no—
314C2×C4—5841no—
315C2×C4—5841no—
316C2×C4—731no—
317C2×C4—731no—
318C2×C4—731no—
319C2×C4—1461no—
320C2×C4—1461no—
321C2×C4—1461no—
322C2×C4—1461no—
323C2×C4D4×D7311yescharacteristic
324C2×C4D4×D7311yescharacteristic
325C2×C4C23×D7311yescharacteristic
326C8—21no—
327C8—21no—
328C8—1461no—
329C8—1461no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—2921no—
334C22—2921no—
335C22—2921no—
336C22—2921no—
337C22—2921no—
338C22—5844no—
339C22—1461no—
340C22—1461no—
341C22—1461no—
342C22—1462no—
343C22C2×D4×D7311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—2921no—
350C4—2921no—
351C4—1461no—
352C4—1461no—
353C4—1461no—
354C4#41×D7311yescharacteristic
355C4C2×#1192402911yescharacteristic
356C2—42no—
357C2—2922no—
358C2—2921no—
359C2—5841no—
360C2#1798910011yescharacteristic
361C2#1798938811yescharacteristic
362C2#1798939611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#474×C73C2
socleC22×C73C22×D4
hypercenter#474D73
hypocenterC73#3118
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #17989211C2semidirect
2. #17989059C2semidirect
3. #17988930C2semidirect
4. #17988914C2semidirect
5. #17988874C2semidirect
6. #17988803C2semidirect
7. #17988802C2semidirect
8. #17988739C2semidirect
10. #17988696C2semidirect
11. #17988686C2semidirect
12. #17988678C2semidirect
13. #17988669C2semidirect
14. #17988647C2semidirect
15. #474×C73C2semidirect
23. #14556579C22semidirect
28. #14556556C22semidirect
32. #14556553C22semidirect
39. #14556522C22semidirect
40. #14556522C22semidirect
41. C4⋊#10596831C22semidirect
42. #14556516C22semidirect
43. #14556514C22semidirect
44. #14556513C22semidirect
47. #14556511C22semidirect
50. #14556501C22semidirect
51. C8×Dic73C22semidirect
52. C4⋊Q8×C73C22semidirect
54. #107×C73C22semidirect
55. #107×C73C22semidirect
56. C4⋊C8×C73C22semidirect
182. C73#3118semidirect
188. #474D73semidirect
203. C4⋊Q8C2×D73semidirect
223. #107C2×D73semidirect
224. #107C2×D73semidirect
228. C4⋊C8C2×D73semidirect