Finite Group Databasebeta

← #49169022

Subgroups — #49169022

Order 37504.

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#34036732C211yesmaximal, characteristic, complemented
2#34036604C211yesmaximal, characteristic, complemented
3#34036454C211yesmaximal, characteristic, complemented
4#34036450C211yesmaximal, characteristic, complemented
5#34036431C211yesmaximal, characteristic, complemented
6#34036427C211yesmaximal, characteristic, complemented
7#34036322C211yesmaximal, characteristic, complemented
8#34036322C211yesmaximal, characteristic, complemented
9#34036263C211yesmaximal, characteristic, complemented
10#34036241C211yesmaximal, characteristic, complemented
11#34036238C211yesmaximal, characteristic, complemented
12D8×Dic293C211yesmaximal, characteristic, complemented
13#34036209C211yesmaximal, characteristic, complemented
14#34036187C211yesmaximal, characteristic, complemented
15#447×C293C211yesmaximal, characteristic, complemented
16C2×#17989787C2211yescharacteristic
17C2×#17989787C2211yescharacteristic
18#22627620C2211yescharacteristic, complemented
19#22627615C2211yescharacteristic, complemented
20#22627608—21no—
21#22627606—21no—
22#22627598C2211yescharacteristic
23#22627596—21no—
24#22627595—21no—
25D4×Dic293—21no—
26D4×Dic293—21no—
27D4×Dic293C2211yescharacteristic
28D4×Dic293C2211yescharacteristic
29D4×Dic293C2211yescharacteristic
30D4×Dic293C2211yescharacteristic
31D4×Dic293C2211yescharacteristic, complemented
32#22627586C2211yescharacteristic, complemented
33#22627583C2211yescharacteristic
34#22627583C2211yescharacteristic
35C2×C22⋊Dic293—21no—
36C2×C22⋊Dic293—21no—
37#22627558C2211yescharacteristic, complemented
38#22627557C2211yescharacteristic, complemented
39#22627556C2211yescharacteristic, complemented
40#22627555C2211yescharacteristic, complemented
41#22627553C2211yescharacteristic, complemented
42#22627553C2211yescharacteristic, complemented
43#22627546C2211yescharacteristic, complemented
44#22627546C2211yescharacteristic, complemented
45#22627545C2211yescharacteristic
46#22627545C2211yescharacteristic
47#22627545C2211yescharacteristic, complemented
48#22627545C2211yescharacteristic, complemented
49C22⋊#14556873C2211yescharacteristic
50#22627534C2211yescharacteristic, complemented
51C8×Dic293C2211yescharacteristic, complemented
52C22×D4×C293C2211yescharacteristic
53C2×D8×C293C2211yescharacteristic
54C2×D8×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59C2×D1172C2311yescharacteristic
60C2×C22⋊D293—21no—
61C2×C22⋊D293—21no—
62C2×C22⋊D293—21no—
63C22×Dic293—21no—
64C22×Dic293—21no—
65C22×Dic293—21no—
66C22×Dic293—21no—
67C22×Dic293—21no—
68C2×C4×D293—21no—
69#17989787—22no—
70#17989787—22no—
71C2×#14556873C2311yescharacteristic
72C2×#14556873C2311yescharacteristic
73C4⋊Dic293—21no—
74C4⋊Dic293D411yescharacteristic
75C4⋊Dic293D411yescharacteristic
76C4⋊Dic293C2311yescharacteristic
77C4⋊Dic293C2311yescharacteristic
78C4⋊Dic293C2311yescharacteristic
79#17989781—21no—
80C22⋊Dic293—21no—
81C22⋊Dic293—21no—
82C22⋊Dic293—21no—
83C22⋊Dic293—21no—
84C22⋊Dic293—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293D411yescharacteristic
87C22⋊Dic293D411yescharacteristic
88#17989779—21no—
89#17989779—21no—
90C4×Dic293—21no—
91C4×Dic293C2311yescharacteristic
92C4×Dic293C2311yescharacteristic
93C24×C293—21no—
94C2×D4×C293—22no—
95C2×D4×C293—22no—
96C2×D4×C293—21no—
97C2×D4×C293—21no—
98C2×D4×C293C2311yescharacteristic
99C2×D4×C293C2311yescharacteristic
100C2×D4×C293C2311yescharacteristic
101C22×C4×C293C2311yescharacteristic
102D8×C293—22no—
103D8×C293—22no—
104C2×C8×C293C2311yescharacteristic
105C2×C8×C293C2311yescharacteristic
106C4⋊C4×C293C2311yescharacteristic
107C22⋊C4×C293—21no—
108C22×D293—21no—
109D1172—21no—
110D1172—21no—
111C22⋊D293—81no—
112C22⋊D293—81no—
113C22⋊D293—81no—
114C2×Dic293—21no—
115C2×Dic293—21no—
116C2×Dic293—21no—
117C2×Dic293—81no—
118C2×Dic293—81no—
119C2×Dic293—81no—
120C2×Dic293—81no—
121C2×Dic293—81no—
122C2×Dic293C2×D411yescharacteristic
123C2×Dic293C2×D411yescharacteristic
124C2×Dic293C2×D411yescharacteristic
125C2×Dic293C2×D411yescharacteristic
126C4×D293—81no—
127#14556873—21no—
128#14556873—21no—
129C23×C293—24no—
130C23×C293—21no—
131C23×C293—21no—
132C23×C293—21no—
133C23×C293—81no—
134C23×C293—81no—
135C23×C293C2×D411yescharacteristic
136D4×C293—24no—
137D4×C293—21no—
138D4×C293—21no—
139D4×C293—21no—
140D4×C293—21no—
141D4×C293—81no—
142D4×C293#4112yes—
143D4×C293#4112yes—
144C2×C4×C293—21no—
145C2×C4×C293—21no—
146C2×C4×C293—21no—
147C2×C4×C293C2×D411yescharacteristic
148C2×C4×C293C2411yescharacteristic
149C8×C293—21no—
150C8×C293—21no—
151C22×C293—21no—
152C22×C293—22no—
153C22×C293—22no—
154C22×C293—21no—
155C22×C293—21no—
156C22×C293—41no—
157C22×C293—41no—
158C22×C293—41no—
159C22×C293—41no—
160C22×C293—41no—
161C22×C293—41no—
162C22×C293—41no—
163C22×C293—84no—
164C22×C293C22×D411yescharacteristic
165C2×D293—41no—
166C2×D293—41no—
167C2×D293—41no—
168C4×C293—21no—
169C4×C293—41no—
170C4×C293C2×#4111yescharacteristic
171C4×C293C2×#4111yescharacteristic
172Dic293—21no—
173Dic293—21no—
174Dic293—21no—
175Dic293—21no—
176Dic293—41no—
177Dic293—41no—
178Dic293—41no—
179C2×C293—41no—
180C2×C293—42no—
181C2×C293—42no—
182C2×C293—81no—
183C2×C293#52511yescharacteristic
184C2×C293#57611yescharacteristic
185C2×C293#57611yescharacteristic
186D293—81no—
187C293#312211yescharacteristic, complemented, Sylow
188#3122—2931nomaximal, Sylow
189#540—2931no—
190#518—2931no—
191#482—2931no—
192#482—2931no—
193#478—2931no—
194#478—2931no—
195#459—2931no—
196#459—2931no—
197#447—2931no—
198#447D29311yescharacteristic, complemented
199#442—2931no—
200#442—2931no—
201C4×D8—2931no—
202C4×D8—2931no—
203#433—2931no—
204C22×D4C2×D29311yescharacteristic
205C2×D8—2931no—
206C2×D8—2931no—
207C2×D8C2×D29311yescharacteristic
208C2×D8C2×D29311yescharacteristic
209#127—2931no—
210#125—2931no—
211#123—5861no—
212#123—5861no—
213#121—2931no—
214#121—5861no—
215#121—5861no—
216#121C2×D29311yescharacteristic
217C4×D4—2931no—
218C4×D4—2931no—
219C4×D4—2931no—
220C4×D4—2931no—
221C4×D4—2931no—
222C4×D4—2931no—
223C4×D4—5861no—
224C4×D4—5861no—
225#117—2931no—
226#117—2931no—
227C2×C22⋊C4—5861no—
228C2×C22⋊C4—5861no—
229#107—2931no—
230#107—2931no—
231#106—2931no—
232#106—2931no—
233C4⋊C8—2931no—
234C4⋊C8—2931no—
235#102—2931no—
236#102—2931no—
237#102—2931no—
238#102—2931no—
239#102—2931no—
240#102—2931no—
241#102C2×D29311yescharacteristic
242#102C2×D29311yescharacteristic
243C22⋊C8—2931no—
244C22⋊C8C2×D29311yescharacteristic
245#97—2931no—
246C4×C8—2931no—
247C24—21no—
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—2931no—
253C2×D4—5861no—
254C2×D4—5861no—
255C2×D4—5861no—
256C2×D4C22×D29311yescharacteristic
257C2×D4C22×D29311yescharacteristic
258C2×D4C22×D29311yescharacteristic
259C22×C4—5861no—
260C22×C4—5861no—
261C22×C4—5861no—
262C22×C4—5861no—
263C22×C4—5861no—
264C22×C4—5861no—
265C22×C4C22×D29311yescharacteristic
266D8—22no—
267D8—22no—
268D8—5862no—
269D8—5862no—
270C2×C8—2931no—
271C2×C8—2931no—
272C2×C8C22×D29311yescharacteristic
273C2×C8C22×D29311yescharacteristic
274C4⋊C4—2931no—
275C4⋊C4—2931no—
276C4⋊C4—2931no—
277C4⋊C4—2931no—
278C4⋊C4—2931no—
279C4⋊C4—5861no—
280C4⋊C4—5861no—
281C4⋊C4C22×D29311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—2931no—
284C22⋊C4—2931no—
285C22⋊C4—5861no—
286C22⋊C4—5861no—
287C22⋊C4—5861no—
288C22⋊C4—5861no—
289C22⋊C4—5861no—
290C22⋊C4—5861no—
291C22⋊C4—5861no—
292C22⋊C4—5861no—
293C42—2931no—
294C42—2931no—
295C42—5861no—
296C23—24no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—81no—
301C23—81no—
302C23—5861no—
303C23D4×D29311yescharacteristic
304D4—24no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—23441no—
311D4—23441no—
312D4—23441no—
313D4—5861no—
314D4—5861no—
315D4#1798980112yes—
316D4#1798980112yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—2931no—
321C2×C4—2931no—
322C2×C4—2931no—
323C2×C4—2931no—
324C2×C4—23441no—
325C2×C4—23441no—
326C2×C4—23441no—
327C2×C4—23441no—
328C2×C4—23441no—
329C2×C4—23441no—
330C2×C4—5861no—
331C2×C4—5861no—
332C2×C4—5861no—
333C2×C4D4×D29311yescharacteristic
334C2×C4C23×D29311yescharacteristic
335C8—21no—
336C8—21no—
337C8—5861no—
338C8—5861no—
339C22—21no—
340C22—22no—
341C22—22no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—84no—
352C22—11721no—
353C22—11721no—
354C22—11721no—
355C22C2×D4×D29311yescharacteristic
356C4—21no—
357C4—41no—
358C4—5861no—
359C4—5861no—
360C4—5861no—
361C4—5861no—
362C4—11721no—
363C4—11721no—
364C4—11721no—
365C4C2×#1798980111yescharacteristic
366C4C2×#1798980111yescharacteristic
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—23441no—
372C2#3403663511yescharacteristic
373C2#3403693011yescharacteristic
374C2#3403693311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#447×C293C2
socleC22×C293C22×D4
hypercenter#447D293
hypocenterC293#3122
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #34036732C2semidirect
2. #34036604C2semidirect
3. #34036454C2semidirect
4. #34036450C2semidirect
5. #34036431C2semidirect
6. #34036427C2semidirect
7. #34036322C2semidirect
8. #34036322C2semidirect
9. #34036263C2semidirect
10. #34036241C2semidirect
11. #34036238C2semidirect
12. D8×Dic293C2semidirect
13. #34036209C2semidirect
14. #34036187C2semidirect
15. #447×C293C2semidirect
18. #22627620C22semidirect
19. #22627615C22semidirect
31. D4×Dic293C22semidirect
32. #22627586C22semidirect
37. #22627558C22semidirect
38. #22627557C22semidirect
39. #22627556C22semidirect
40. #22627555C22semidirect
41. #22627553C22semidirect
42. #22627553C22semidirect
43. #22627546C22semidirect
44. #22627546C22semidirect
47. #22627545C22semidirect
48. #22627545C22semidirect
50. #22627534C22semidirect
51. C8×Dic293C22semidirect
187. C293#3122semidirect
198. #447D293semidirect

Maximal subgroups

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

subgroupindex
#340367322
#340366042
#340364542
#340364502
#340364312
#340364272
#340363222
#340362632
#340362412
#340362382
D8×Dic2932
#340362092
#340361872
#447×C2932
#3122293