Finite Group Databasebeta

← #22620176

Subgroups — #22620176

Order 9344.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17989193C211yesmaximal, characteristic, complemented
2#17989059C211yesmaximal, characteristic, complemented
3#17988914C211yesmaximal, characteristic, complemented
4#17988913C211yesmaximal, characteristic, complemented
5#17988884C211yesmaximal, characteristic, complemented
6#17988783C211yesmaximal, characteristic, complemented
7#17988782C211yesmaximal, characteristic, complemented
8#17988722C211yesmaximal, characteristic, complemented
9#17988722C211yesmaximal, characteristic, complemented
10#17988698C211yesmaximal, characteristic, complemented
11#17988696C211yesmaximal, characteristic, complemented
12#17988669C211yesmaximal, characteristic, complemented
13#17988667C211yesmaximal, characteristic, complemented
14#17988647C211yesmaximal, characteristic, complemented
15#478×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73C2211yescharacteristic
17C2×D584C2211yescharacteristic
18C2×D584C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20C2×#11924013C2211yescharacteristic
21#14556588C2211yescharacteristic, complemented
22#14556576—21no—
23#14556576—21no—
24#14556566—21no—
25#14556566—21no—
26#14556566C2211yescharacteristic
27#14556566C2211yescharacteristic
28C4×D292C2211yescharacteristic
29D4×Dic73C2211yescharacteristic
30#14556553C2211yescharacteristic
31#14556553C2211yescharacteristic, complemented
32#14556553C2211yescharacteristic, complemented
33C4×C22⋊D73—21no—
34#14556551—21no—
35#14556549C2211yescharacteristic
36#14556548C2211yescharacteristic
37C2×#11924005—21no—
38C22⋊C4×D73—21no—
39#14556524C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41C4⋊#10596831C2211yescharacteristic, complemented
42#14556513C2211yescharacteristic, complemented
43#14556513C2211yescharacteristic, complemented
44#14556511C2211yescharacteristic
45#14556511C2211yescharacteristic
46#14556511C2211yescharacteristic, complemented
47#14556511C2211yescharacteristic, complemented
48#14556503C2211yescharacteristic
49#14556503C2211yescharacteristic
50#14556501C2211yescharacteristic, complemented
51C8×Dic73C2211yescharacteristic, complemented
52#125×C73C2211yescharacteristic, complemented
53C4×D4×C73C2211yescharacteristic
54#107×C73C2211yescharacteristic, complemented
55#106×C73C2211yescharacteristic, complemented
56C4⋊C8×C73C2211yescharacteristic, complemented
57#102×C73C2211yescharacteristic
58#102×C73C2211yescharacteristic
59C23×D73—21no—
60C2×D292—21no—
61C2×D292—21no—
62C2×D292—21no—
63C2×D292—21no—
64C2×D292C2311yescharacteristic
65C2×D292C2311yescharacteristic
66C2×D292C2311yescharacteristic
67C2×C22⋊D73—21no—
68D4×D73—22no—
69D4×D73—22no—
70C22×Dic73—21no—
71C2×C4×D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73—21no—
74C2×C4×D73—21no—
75C2×C4×D73C2311yescharacteristic
76D584—22no—
77D584—22no—
78#11924013—22no—
79#11924013—22no—
80C2×#10596831C2311yescharacteristic
81C2×#10596831C2311yescharacteristic
82C4⋊Dic73C2311yescharacteristic
83#11924007D411yescharacteristic
84#11924007D411yescharacteristic
85C22⋊Dic73—21no—
86#11924005—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005—21no—
93#11924005D411yescharacteristic
94#11924005D411yescharacteristic
95C4×Dic73—21no—
96C4×Dic73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98C22×C4×C73—21no—
99C2×C8×C73C2311yescharacteristic
100C2×C8×C73C2311yescharacteristic
101C4⋊C4×C73—21no—
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—21no—
113C22×D73—81no—
114C22×D73—81no—
115C22×D73C2×D411yescharacteristic
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—81no—
128C2×Dic73C2×D411yescharacteristic
129C2×Dic73C2×D411yescharacteristic
130C2×Dic73C2×D411yescharacteristic
131D292—21no—
132D292—21no—
133D292—21no—
134D292—21no—
135D292—21no—
136D292—81no—
137D292—81no—
138D292—81no—
139D292—81no—
140D292#4112yes—
141C4×D73—21no—
142C4×D73—21no—
143C4×D73—81no—
144C4×D73—81no—
145C4×D73—81no—
146C4×D73—81no—
147C8×C73—21no—
148C8×C73—21no—
149#10596831—21no—
150#10596831—21no—
151C22×C73—22no—
152C22×C73—41no—
153C22×C73—41no—
154C22×C73C22×D411yescharacteristic
155C2×D73—21no—
156C2×D73—22no—
157C2×D73—21no—
158C2×D73—21no—
159C2×D73—41no—
160C2×D73—41no—
161C2×D73—41no—
162C2×D73—41no—
163C2×D73—41no—
164C2×D73—41no—
165C2×D73—41no—
166C2×D73—41no—
167C2×D73—84no—
168C4×C73—21no—
169C4×C73—21no—
170C4×C73—41no—
171C4×C73—41no—
172C4×C73—41no—
173C4×C73C2×#4111yescharacteristic
174C4×C73C2×#4111yescharacteristic
175Dic73—21no—
176Dic73—21no—
177Dic73—21no—
178Dic73—41no—
179C2×C73—42no—
180C2×C73#52511yescharacteristic
181C2×C73#57611yescharacteristic
182C2×C73#57611yescharacteristic
183D73—41no—
184D73—42no—
185D73—81no—
186D73—81no—
187#3122—731nomaximal, Sylow
188C73#312211yescharacteristic, complemented, Sylow
189#540—731no—
190#518—731no—
191#482—731no—
192#482—731no—
193#478—731no—
194#478D7311yescharacteristic, complemented
195#459—731no—
196#459—731no—
197#447—731no—
198#447—731no—
199#442—731no—
200#442—731no—
201C4×D8—731no—
202C4×D8—731no—
203#433—731no—
204C22×D4—731no—
205C2×D8—731no—
206C2×D8—731no—
207C2×D8—731no—
208C2×D8—731no—
209#127—731no—
210#125C2×D7311yescharacteristic, complemented
211#123—1461no—
212#123—1461no—
213#121—731no—
214#121—731no—
215#121—1461no—
216#121—1461no—
217C4×D4—731no—
218C4×D4—731no—
219C4×D4—731no—
220C4×D4—731no—
221C4×D4—731no—
222C4×D4—1461no—
223C4×D4—1461no—
224C4×D4C2×D7311yescharacteristic
225#117—731no—
226#117—731no—
227C2×C22⋊C4—1461no—
228C2×C22⋊C4—1461no—
229#107—731no—
230#107C2×D7311yescharacteristic, complemented
231#106—731no—
232#106C2×D7311yescharacteristic, complemented
233C4⋊C8—731no—
234C4⋊C8C2×D7311yescharacteristic, complemented
235#102—731no—
236#102—731no—
237#102—731no—
238#102—731no—
239#102—731no—
240#102—731no—
241#102C2×D7311yescharacteristic
242#102C2×D7311yescharacteristic
243C22⋊C8—731no—
244C22⋊C8—731no—
245#97—731no—
246C4×C8—731no—
247C24—1461no—
248C2×D4—731no—
249C2×D4—731no—
250C2×D4—731no—
251C2×D4—1461no—
252C2×D4—1461no—
253C2×D4—1461no—
254C2×D4—1462no—
255C2×D4—1462no—
256C2×D4—1461no—
257C2×D4—1461no—
258C2×D4C22×D7311yescharacteristic
259C22×C4—21no—
260C22×C4—731no—
261C22×C4—1461no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4—1461no—
266D8—1462no—
267D8—1462no—
268D8—1462no—
269D8—1462no—
270C2×C8—731no—
271C2×C8—731no—
272C2×C8C22×D7311yescharacteristic
273C2×C8C22×D7311yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—731no—
277C4⋊C4—731no—
278C4⋊C4—731no—
279C4⋊C4C22×D7311yescharacteristic
280C4⋊C4C22×D7311yescharacteristic
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—
295C42C22×D7311yescharacteristic
296C23—21no—
297C23—5841no—
298C23—5841no—
299C23—731no—
300C23—1464no—
301C23—1461no—
302C23—1461no—
303C23—1461no—
304D4—21no—
305D4—5841no—
306D4—5841no—
307D4—5841no—
308D4—5841no—
309D4—732no—
310D4—1464no—
311D4—1461no—
312D4—1461no—
313D4—1461no—
314D4—1461no—
315D4—1461no—
316D4#1192402912yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—5841no—
322C2×C4—5841no—
323C2×C4—5841no—
324C2×C4—5841no—
325C2×C4—5841no—
326C2×C4—731no—
327C2×C4—731no—
328C2×C4—731no—
329C2×C4—1461no—
330C2×C4—1461no—
331C2×C4—1461no—
332C2×C4D4×D7311yescharacteristic
333C2×C4D4×D7311yescharacteristic
334C2×C4C23×D7311yescharacteristic
335C8—21no—
336C8—21no—
337C8—1461no—
338C8—1461no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—2921no—
343C22—2921no—
344C22—2921no—
345C22—2921no—
346C22—2921no—
347C22—2921no—
348C22—2921no—
349C22—2921no—
350C22—5844no—
351C22—1461no—
352C22—1461no—
353C22—1461no—
354C22—1462no—
355C22C2×D4×D7311yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—2921no—
362C4—1461no—
363C4—1461no—
364C4—1461no—
365C4#41×D7311yescharacteristic
366C4C2×#1192402911yescharacteristic
367C2—42no—
368C2—2922no—
369C2—2921no—
370C2—5841no—
371C2—5841no—
372C2#1798910011yescharacteristic
373C2#1798938911yescharacteristic
374C2#1798939111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#478×C73C2
socleC22×C73C22×D4
hypercenter#478D73
hypocenterC73#3122
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #17989193C2semidirect
2. #17989059C2semidirect
3. #17988914C2semidirect
4. #17988913C2semidirect
5. #17988884C2semidirect
6. #17988783C2semidirect
7. #17988782C2semidirect
8. #17988722C2semidirect
9. #17988722C2semidirect
10. #17988698C2semidirect
11. #17988696C2semidirect
12. #17988669C2semidirect
13. #17988667C2semidirect
14. #17988647C2semidirect
15. #478×C73C2semidirect
21. #14556588C22semidirect
31. #14556553C22semidirect
32. #14556553C22semidirect
39. #14556524C22semidirect
40. #14556522C22semidirect
41. C4⋊#10596831C22semidirect
42. #14556513C22semidirect
43. #14556513C22semidirect
46. #14556511C22semidirect
47. #14556511C22semidirect
50. #14556501C22semidirect
51. C8×Dic73C22semidirect
52. #125×C73C22semidirect
54. #107×C73C22semidirect
55. #106×C73C22semidirect
56. C4⋊C8×C73C22semidirect
188. C73#3122semidirect
194. #478D73semidirect
210. #125C2×D73semidirect
230. #107C2×D73semidirect
232. #106C2×D73semidirect
234. C4⋊C8C2×D73semidirect