Finite Group Databasebeta

← #49168972

Subgroups — #49168972

Order 37504.

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#34036752C211yesmaximal, characteristic, complemented
2#34036603C211yesmaximal, characteristic, complemented
3#34036453C211yesmaximal, characteristic, complemented
4#34036418C211yesmaximal, characteristic, complemented
5#34036408C211yesmaximal, characteristic, complemented
6#34036347C211yesmaximal, characteristic, complemented
7#34036347C211yesmaximal, characteristic, complemented
8#34036279C211yesmaximal, characteristic, complemented
9#34036265C211yesmaximal, characteristic
10#34036240C211yesmaximal, characteristic, complemented
11#34036232C211yesmaximal, characteristic, complemented
12#34036214C211yesmaximal, characteristic, complemented
13#34036211C211yesmaximal, characteristic, complemented
14#34036187C211yesmaximal, characteristic, complemented
15#485×C293C211yesmaximal, characteristic, complemented
16C22×D1172C2211yescharacteristic
17C2×#17989789C2211yescharacteristic
18C2×#17989789C2211yescharacteristic
19C2×D2344C2211yescharacteristic
20C2×D2344C2211yescharacteristic
21#22627623C2211yescharacteristic, complemented
22#22627619—21no—
23#22627613C2211yescharacteristic, complemented
24#22627610—21no—
25#22627606—21no—
26#22627604—21no—
27#22627598C2211yescharacteristic
28Q8×Dic293C2211yescharacteristic, complemented
29C4×D1172—21no—
30C4×D1172—21no—
31#22627586C2211yescharacteristic
32#22627586C2211yescharacteristic
33#22627586C2211yescharacteristic
34#22627586C2211yescharacteristic
35#22627586C2211yescharacteristic, complemented
36#22627583C2211yescharacteristic
37C22⋊C4×D293—21no—
38C22⋊C4×D293—21no—
39#22627557C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627553C2211yescharacteristic, complemented
42#22627553C2211yescharacteristic, complemented
43#22627546C2211yescharacteristic
44#22627546C2211yescharacteristic
45#22627544C2211yescharacteristic
46#22627544C2211yescharacteristic
47#22627544C2211yescharacteristic, complemented
48#22627544C2211yescharacteristic, complemented
49C22⋊#14556873C2211yescharacteristic
50#22627534C2211yescharacteristic, complemented
51C8×Dic293C2211yescharacteristic, complemented
52C22⋊Q8×C293C2211yescharacteristic
53#117×C293C2211yescharacteristic
54#107×C293C2211yescharacteristic, complemented
55#106×C293C2211yescharacteristic, complemented
56#103×C293C2211yescharacteristic, complemented
57#103×C293C2211yescharacteristic, complemented
58C22⋊C8×C293C2211yescharacteristic
59C23×D293—21no—
60C2×Dic586—21no—
61C2×D1172—22no—
62C2×D1172—22no—
63C2×D1172—21no—
64C2×D1172C2311yescharacteristic
65C2×D1172C2311yescharacteristic
66C2×D1172C2311yescharacteristic
67C2×C22⋊D293—21no—
68C2×C4×D293—21no—
69C2×C4×D293—21no—
70C2×C4×D293—21no—
71C2×C4×D293—21no—
72C2×C4×D293—21no—
73#17989789—22no—
74#17989789—22no—
75D2344—22no—
76D2344—22no—
77C2×#14556873C2311yescharacteristic
78C2×#14556873C2311yescharacteristic
79C4⋊Dic293—21no—
80C4⋊Dic293D411yescharacteristic
81C4⋊Dic293D411yescharacteristic
82C4⋊Dic293C2311yescharacteristic
83#17989781—21no—
84C22⋊Dic293D411yescharacteristic
85C22⋊Dic293D411yescharacteristic
86#17989779—21no—
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779—21no—
91#17989779—21no—
92#17989779—21no—
93#17989779—21no—
94C4×Dic293—21no—
95C4×Dic293C2311yescharacteristic
96C4×Dic293C2311yescharacteristic
97C2×Q8×C293C2311yescharacteristic
98C22×C4×C293C2311yescharacteristic
99C2×C8×C293C2311yescharacteristic
100C2×C8×C293C2311yescharacteristic
101C4⋊C4×C293—21no—
102C4⋊C4×C293C2311yescharacteristic
103C4⋊C4×C293C2311yescharacteristic
104C4⋊C4×C293C2311yescharacteristic
105C22⋊C4×C293—21no—
106C22⋊C4×C293—21no—
107C42×C293—21no—
108C22×D293—21no—
109C22×D293—21no—
110C22×D293—24no—
111C22×D293—21no—
112C22×D293—81no—
113C22×D293—81no—
114Dic586—81no—
115D1172—24no—
116D1172—21no—
117D1172—21no—
118D1172—21no—
119D1172—21no—
120D1172#4112yes—
121D1172#4112yes—
122C22⋊D293—81no—
123C2×Dic293—21no—
124C2×Dic293C2×D411yescharacteristic
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C4×D293—81no—
129C4×D293—81no—
130C4×D293—81no—
131C4×D293—81no—
132C4×D293—81no—
133#14556873—21no—
134#14556873—21no—
135C23×C293C2×D411yescharacteristic
136Q8×C293—21no—
137Q8×C293—21no—
138C2×C4×C293—21no—
139C2×C4×C293—21no—
140C2×C4×C293—21no—
141C2×C4×C293—21no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293C2×D411yescharacteristic
145C2×C4×C293C2411yescharacteristic
146C8×C293—21no—
147C8×C293—21no—
148C22×C293—21no—
149C22×C293—21no—
150C22×C293—21no—
151C22×C293C22×D411yescharacteristic
152C2×D293—22no—
153C2×D293—22no—
154C2×D293—41no—
155C2×D293—41no—
156C2×D293—41no—
157C2×D293—41no—
158C2×D293—41no—
159C2×D293—41no—
160C2×D293—41no—
161C2×D293—84no—
162C4×C293—21no—
163C4×C293—41no—
164C4×C293—41no—
165C4×C293—41no—
166C4×C293—41no—
167C4×C293C2×#4111yescharacteristic
168C4×C293C2×#4111yescharacteristic
169Dic293—21no—
170Dic293—21no—
171Dic293—21no—
172Dic293—21no—
173Dic293—41no—
174C2×C293—41no—
175C2×C293#52511yescharacteristic
176C2×C293#57611yescharacteristic
177C2×C293#57711yescharacteristic
178D293—42no—
179D293—42no—
180D293—81no—
181C293#311811yescharacteristic, complemented, Sylow
182#3118—2931nomaximal, Sylow
183#542—2931no—
184#518—2931no—
185#485D29311yescharacteristic, complemented
186#482—2931no—
187#476—2931no—
188#474—2931no—
189#463—2931no—
190#463—2931no—
191#450—2931no—
192#447—2931no—
193#442—2931no—
194#440—2931no—
195C4×SD16—2931no—
196C4×D8—2931no—
197#433—2931no—
198C22×D4—2931no—
199C2×SD16—2931no—
200C2×SD16—2931no—
201C2×D8—2931no—
202C2×D8—2931no—
203C4⋊Q8—2931no—
204#126—5861no—
205#124—2931no—
206#124—5861no—
207#123—5861no—
208C22⋊Q8—5861no—
209C22⋊Q8C2×D29311yescharacteristic
210#121—2931no—
211C4×Q8—2931no—
212C4×D4—2931no—
213C4×D4—2931no—
214C4×D4—2931no—
215C4×D4—2931no—
216C4×D4—2931no—
217C4×D4—5861no—
218C4×D4—5861no—
219#117—2931no—
220#117C2×D29311yescharacteristic
221C2×C22⋊C4—5861no—
222C2×C22⋊C4—5861no—
223#107—2931no—
224#107C2×D29311yescharacteristic, complemented
225#106—2931no—
226#106C2×D29311yescharacteristic, complemented
227C4⋊C8—2931no—
228C4⋊C8—2931no—
229#103C2×D29311yescharacteristic, complemented
230#103C2×D29311yescharacteristic, complemented
231#102—2931no—
232#102—2931no—
233#102—2931no—
234#102—2931no—
235#102—2931no—
236#102—2931no—
237C22⋊C8—2931no—
238C22⋊C8C2×D29311yescharacteristic
239#97—2931no—
240C4×C8—2931no—
241C24—5861no—
242C2×Q8—5861no—
243C2×Q8C22×D29311yescharacteristic
244C2×D4—2931no—
245C2×D4—2931no—
246C2×D4—2931no—
247C2×D4—5862no—
248C2×D4—5862no—
249C2×D4—5861no—
250C2×D4—5861no—
251C22×C4—5861no—
252C22×C4—5861no—
253C22×C4—5861no—
254C22×C4—5861no—
255C22×C4—5861no—
256C22×C4C22×D29311yescharacteristic
257SD16—5862no—
258SD16—5862no—
259D8—5862no—
260D8—5862no—
261C2×C8—2931no—
262C2×C8—2931no—
263C2×C8C22×D29311yescharacteristic
264C2×C8C22×D29311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—2931no—
267C4⋊C4—2931no—
268C4⋊C4—2931no—
269C4⋊C4—5861no—
270C4⋊C4—5861no—
271C4⋊C4C22×D29311yescharacteristic
272C4⋊C4C22×D29311yescharacteristic
273C4⋊C4C22×D29311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—2931no—
277C22⋊C4—2931no—
278C22⋊C4—5861no—
279C22⋊C4—5861no—
280C22⋊C4—5861no—
281C22⋊C4—5861no—
282C22⋊C4—5861no—
283C22⋊C4—5861no—
284C22⋊C4—5861no—
285C22⋊C4—5861no—
286C42—21no—
287C42—2931no—
288C42—2931no—
289C42—5861no—
290C23—23441no—
291C23—23441no—
292C23—5864no—
293C23—5861no—
294C23—5861no—
295C23—5861no—
296C23D4×D29311yescharacteristic
297Q8—21no—
298Q8—21no—
299Q8—23441no—
300D4—2932no—
301D4—2932no—
302D4—23441no—
303D4—5864no—
304D4—5861no—
305D4—5861no—
306D4—5861no—
307D4—5861no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—2931no—
315C2×C4—2931no—
316C2×C4—2931no—
317C2×C4—2931no—
318C2×C4—23441no—
319C2×C4—23441no—
320C2×C4—23441no—
321C2×C4—23441no—
322C2×C4—23441no—
323C2×C4—5861no—
324C2×C4D4×D29311yescharacteristic
325C2×C4C23×D29311yescharacteristic
326C8—21no—
327C8—21no—
328C8—5861no—
329C8—5861no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—23444no—
334C22—5862no—
335C22—5862no—
336C22—11721no—
337C22—11721no—
338C22—11721no—
339C22—11721no—
340C22—11721no—
341C22—11721no—
342C22—11721no—
343C22C2×D4×D29311yescharacteristic
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—5861no—
350C4—5861no—
351C4—5861no—
352C4—5861no—
353C4—11721no—
354C4#41×D29311yescharacteristic
355C4#41×D29311yescharacteristic
356C2—41no—
357C2—23441no—
358C2—11722no—
359C2—11722no—
360C2#3403663711yescharacteristic
361C2#3403693111yescharacteristic
362C2#3403693811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#485×C293C2
socleC22×C293C22×D4
prime radical#34036265C2
hypercenter#485D293
hypocenterC293#3118
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #34036752C2semidirect
2. #34036603C2semidirect
3. #34036453C2semidirect
4. #34036418C2semidirect
5. #34036408C2semidirect
6. #34036347C2semidirect
7. #34036347C2semidirect
8. #34036279C2semidirect
10. #34036240C2semidirect
11. #34036232C2semidirect
12. #34036214C2semidirect
13. #34036211C2semidirect
14. #34036187C2semidirect
15. #485×C293C2semidirect
21. #22627623C22semidirect
23. #22627613C22semidirect
28. Q8×Dic293C22semidirect
35. #22627586C22semidirect
39. #22627557C22semidirect
40. #22627555C22semidirect
41. #22627553C22semidirect
42. #22627553C22semidirect
47. #22627544C22semidirect
48. #22627544C22semidirect
50. #22627534C22semidirect
51. C8×Dic293C22semidirect
54. #107×C293C22semidirect
55. #106×C293C22semidirect
56. #103×C293C22semidirect
57. #103×C293C22semidirect
181. C293#3118semidirect
185. #485D293semidirect
224. #107C2×D293semidirect
226. #106C2×D293semidirect
229. #103C2×D293semidirect
230. #103C2×D293semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#340367522
#340366032
#340364532
#340364182
#340364082
#340363472
#340362792
#340362652
#340362402
#340362322
#340362142
#340362112
#340361872
#485×C2932
#3118293