Finite Group Databasebeta

← #22620171

Subgroups — #22620171

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#17989188C211yesmaximal, characteristic, complemented
2#17989059C211yesmaximal, characteristic, complemented
3#17988914C211yesmaximal, characteristic, complemented
4#17988909C211yesmaximal, characteristic, complemented
5#17988890C211yesmaximal, characteristic, complemented
6#17988885C211yesmaximal, characteristic, complemented
7#17988781C211yesmaximal, characteristic, complemented
8#17988780C211yesmaximal, characteristic, complemented
9#17988722C211yesmaximal, characteristic, complemented
10#17988719C211yesmaximal, characteristic, complemented
11#17988697C211yesmaximal, characteristic, complemented
12#17988697C211yesmaximal, characteristic, complemented
13C4×D584C211yesmaximal, characteristic, complemented
14#17988646C211yesmaximal, characteristic, complemented
15C4×D8×C73C211yesmaximal, characteristic, complemented
16C2×D4×D73C2211yescharacteristic
17C2×D584C2211yescharacteristic
18C2×#11924013C2211yescharacteristic
19C2×#11924013C2211yescharacteristic
20#14556587C2211yescharacteristic, complemented
21#14556582C2211yescharacteristic, complemented
22#14556574—21no—
23#14556573—21no—
24#14556566C2211yescharacteristic
25#14556565—21no—
26#14556564—21no—
27#14556562C2211yescharacteristic
28C4×D292C2211yescharacteristic
29C4×D292C2211yescharacteristic, complemented
30D4×Dic73C2211yescharacteristic
31#14556553C2211yescharacteristic
32C4×C22⋊D73—21no—
33#14556551—21no—
34#14556549C2211yescharacteristic
35#14556548C2211yescharacteristic
36C2×#11924005—21no—
37C22⋊C4×D73—21no—
38#14556525C2211yescharacteristic, complemented
39#14556522C2211yescharacteristic, complemented
40#14556522C2211yescharacteristic, complemented
41#14556520C2211yescharacteristic, complemented
42#14556520C2211yescharacteristic, complemented
43#14556513C2211yescharacteristic
44#14556513C2211yescharacteristic, complemented
45#14556512C2211yescharacteristic
46#14556512C2211yescharacteristic, complemented
47#14556511C2211yescharacteristic
48#14556511C2211yescharacteristic, complemented
49#14556503C2211yescharacteristic
50#14556503C2211yescharacteristic
51#14556502C2211yescharacteristic, complemented
52C2×D8×C73C2211yescharacteristic
53C4×D4×C73C2211yescharacteristic
54C4×D4×C73C2211yescharacteristic, complemented
55#107×C73C2211yescharacteristic, complemented
56#102×C73C2211yescharacteristic
57#102×C73C2211yescharacteristic, complemented
58C4×C8×C73C2211yescharacteristic, complemented
59C23×D73—21no—
60C2×D292—21no—
61C2×D292C2311yescharacteristic
62C2×D292C2311yescharacteristic
63C2×C22⋊D73—21no—
64C2×C22⋊D73—21no—
65C2×C22⋊D73—21no—
66C2×C22⋊D73—21no—
67D4×D73—22no—
68D4×D73—22no—
69C22×Dic73—21no—
70C2×C4×D73—21no—
71C2×C4×D73—21no—
72C2×C4×D73—21no—
73C2×C4×D73C2311yescharacteristic
74D584—22no—
75#11924013—22no—
76#11924013—22no—
77C2×#10596831C2311yescharacteristic
78C2×#10596831C2311yescharacteristic
79C4⋊Dic73—21no—
80C4⋊Dic73C2311yescharacteristic
81C4⋊Dic73C2311yescharacteristic
82#11924007—21no—
83#11924007D411yescharacteristic
84#11924007D411yescharacteristic
85C22⋊Dic73—21no—
86C22⋊Dic73—21no—
87#11924005—21no—
88#11924005—21no—
89#11924005—21no—
90#11924005—21no—
91#11924005—21no—
92#11924005D411yescharacteristic
93#11924005D411yescharacteristic
94C4×Dic73—21no—
95C4×Dic73C2311yescharacteristic
96C2×D4×C73C2311yescharacteristic
97C2×D4×C73C2311yescharacteristic
98C22×C4×C73—21no—
99C22×C4×C73—21no—
100D8×C73—22no—
101C2×C8×C73C2311yescharacteristic
102C2×C8×C73C2311yescharacteristic
103C4⋊C4×C73C2311yescharacteristic
104C4⋊C4×C73C2311yescharacteristic
105C22⋊C4×C73—21no—
106C22⋊C4×C73—21no—
107C42×C73C2311yescharacteristic
108C23×C73—21no—
109C23×C73—21no—
110C22×D73—21no—
111C22×D73—24no—
112C22×D73—21no—
113C22×D73—81no—
114C22×D73—81no—
115C22×D73C2×D411yescharacteristic
116D4×C73—21no—
117D4×C73—21no—
118D4×C73—21no—
119D4×C73#4112yes—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73—81no—
123C2×C4×C73—81no—
124C2×C4×C73C2×D411yescharacteristic
125C2×C4×C73C2×D411yescharacteristic
126C2×C4×C73C2411yescharacteristic
127C22⋊D73—24no—
128C22⋊D73—81no—
129C22⋊D73—81no—
130C22⋊D73—81no—
131C2×Dic73—21no—
132C2×Dic73—21no—
133C2×Dic73—81no—
134C2×Dic73C2×D411yescharacteristic
135C2×Dic73C2×D411yescharacteristic
136C2×Dic73C2×D411yescharacteristic
137D292—21no—
138D292—21no—
139D292—21no—
140D292—81no—
141D292#4112yes—
142C4×D73—21no—
143C4×D73—21no—
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×C73—41no—
155C22×C73—41no—
156C22×C73—41no—
157C22×C73C22×D411yescharacteristic
158C2×D73—21no—
159C2×D73—22no—
160C2×D73—21no—
161C2×D73—21no—
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×C73C2×#4111yescharacteristic
173C4×C73C2×#4111yescharacteristic
174Dic73—21no—
175Dic73—21no—
176Dic73—21no—
177Dic73—41no—
178Dic73—41no—
179C2×C73—42no—
180C2×C73—81no—
181C2×C73#52511yescharacteristic
182C2×C73#57611yescharacteristic
183C2×C73#57611yescharacteristic
184D73—41no—
185D73—42no—
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#478—731no—
195#459—731no—
196#459—731no—
197#447—731no—
198#447—731no—
199#442—731no—
200#442—731no—
201C4×D8—731no—
202C4×D8D7311yescharacteristic, complemented
203#433—731no—
204C22×D4—731no—
205C2×D8—731no—
206C2×D8—731no—
207C2×D8—731no—
208C2×D8C2×D7311yescharacteristic
209#127—731no—
210#125—731no—
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—1461no—
222C4×D4—1461no—
223C4×D4C2×D7311yescharacteristic
224C4×D4C2×D7311yescharacteristic, complemented
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#106—731no—
233C4⋊C8—731no—
234C4⋊C8—731no—
235#102—731no—
236#102—731no—
237#102—731no—
238#102—731no—
239#102—731no—
240#102—731no—
241#102C2×D7311yescharacteristic
242#102C2×D7311yescharacteristic, complemented
243C22⋊C8—731no—
244C22⋊C8—731no—
245#97—731no—
246C4×C8C2×D7311yescharacteristic, complemented
247C24—1461no—
248C2×D4—731no—
249C2×D4—731no—
250C2×D4—1461no—
251C2×D4—1461no—
252C2×D4—1461no—
253C2×D4—1461no—
254C2×D4—1462no—
255C2×D4—1461no—
256C2×D4—1462no—
257C2×D4C22×D7311yescharacteristic
258C2×D4C22×D7311yescharacteristic
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—731no—
262C22×C4—1461no—
263C22×C4—1461no—
264C22×C4—1461no—
265C22×C4—1461no—
266D8—22no—
267D8—1462no—
268D8—1462no—
269D8—1462no—
270C2×C8—731no—
271C2×C8—731no—
272C2×C8C22×D7311yescharacteristic
273C2×C8C22×D7311yescharacteristic
274C4⋊C4—731no—
275C4⋊C4—731no—
276C4⋊C4—731no—
277C4⋊C4—731no—
278C4⋊C4—1461no—
279C4⋊C4—1461no—
280C4⋊C4C22×D7311yescharacteristic
281C4⋊C4C22×D7311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—731no—
285C22⋊C4—731no—
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—21no—
298C23—5841no—
299C23—5841no—
300C23—731no—
301C23—1464no—
302C23—1461no—
303C23—1461no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—5841no—
308D4—5841no—
309D4—5841no—
310D4—5841no—
311D4—732no—
312D4—1464no—
313D4—1461no—
314D4—1461no—
315D4—1461no—
316D4#1192402812yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—5841no—
322C2×C4—5841no—
323C2×C4—5841no—
324C2×C4—5841no—
325C2×C4—731no—
326C2×C4—731no—
327C2×C4—731no—
328C2×C4—1461no—
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—41no—
343C22—41no—
344C22—41no—
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—2921no—
361C4—2921no—
362C4—1461no—
363C4—1461no—
364C4—1461no—
365C4#41×D7311yescharacteristic
366C4C2×#1192402811yescharacteristic
367C2—42no—
368C2—81no—
369C2—2922no—
370C2—2921no—
371C2—5841no—
372C2#1798909611yescharacteristic
373C2#1798938811yescharacteristic
374C2#1798938911yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×D8×C73C2
socleC22×C73C22×D4
hypercenterC4×D8D73
hypocenterC73#3122
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #17989188C2semidirect
2. #17989059C2semidirect
3. #17988914C2semidirect
4. #17988909C2semidirect
5. #17988890C2semidirect
6. #17988885C2semidirect
7. #17988781C2semidirect
8. #17988780C2semidirect
9. #17988722C2semidirect
10. #17988719C2semidirect
11. #17988697C2semidirect
12. #17988697C2semidirect
13. C4×D584C2semidirect
14. #17988646C2semidirect
15. C4×D8×C73C2semidirect
20. #14556587C22semidirect
21. #14556582C22semidirect
29. C4×D292C22semidirect
38. #14556525C22semidirect
39. #14556522C22semidirect
40. #14556522C22semidirect
41. #14556520C22semidirect
42. #14556520C22semidirect
44. #14556513C22semidirect
46. #14556512C22semidirect
48. #14556511C22semidirect
51. #14556502C22semidirect
54. C4×D4×C73C22semidirect
55. #107×C73C22semidirect
57. #102×C73C22semidirect
58. C4×C8×C73C22semidirect
188. C73#3122semidirect
202. C4×D8D73semidirect
224. C4×D4C2×D73semidirect
230. #107C2×D73semidirect
242. #102C2×D73semidirect
246. C4×C8C2×D73semidirect