Finite Group Databasebeta

← #49170717

Subgroups — #49170717

Order 37504.

396 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036850C211yesmaximal, characteristic, complemented
2#34036798C211yesmaximal, characteristic
3#34036474C211yesmaximal, characteristic, complemented
4#34036454C211yesmaximal, characteristic, complemented
5#34036451C211yesmaximal, characteristic, complemented
6#34036412C211yesmaximal, characteristic, complemented
7#34036360C211yesmaximal, characteristic, complemented
8#34036355C211yesmaximal, characteristic, complemented
9#34036327C211yesmaximal, characteristic, complemented
10#34036290C211yesmaximal, characteristic, complemented
11Q16×Dic293C211yesmaximal, characteristic, complemented
12#34036192C211yesmaximal, characteristic, complemented
13#34036125C211yesmaximal, characteristic, complemented
14#34036124C211yesmaximal, characteristic, complemented
15#452×C293C211yesmaximal, characteristic, complemented
16C2×#17989803C2211yescharacteristic
17C2×#17989789C2211yescharacteristic
18C22×#14556873C2211yescharacteristic
19C2×C8×D293C2211yescharacteristic
20#22627623C2211yescharacteristic
21#22627620—21no—
22#22627620C2211yescharacteristic
23#22627619—21no—
24#22627617—21no—
25#22627610—21no—
26#22627600C2211yescharacteristic
27#22627598—21no—
28#22627598C2211yescharacteristic
29#22627595—21no—
30#22627595C2211yescharacteristic
31Q8×Dic293C2211yescharacteristic
32Q8×Dic293C2211yescharacteristic
33#22627589—21no—
34C4×C22⋊D293—21no—
35C4×C22⋊D293C2211yescharacteristic
36#22627583C2211yescharacteristic
37#22627582C2211yescharacteristic
38#22627558C2211yescharacteristic
39#22627556C2211yescharacteristic
40#22627555C2211yescharacteristic
41#22627553C2211yescharacteristic
42#22627548C2211yescharacteristic
43#22627548C2211yescharacteristic
44#22627548C2211yescharacteristic
45#22627546C2211yescharacteristic
46#22627546C2211yescharacteristic
47#22627545C2211yescharacteristic
48#22627545C2211yescharacteristic
49#22627544C2211yescharacteristic
50#22627536C2211yescharacteristic
51C8×Dic293C2211yescharacteristic
52C2×#41×C293C2211yescharacteristic
53C2×Q16×C293C2211yescharacteristic
54C2×SD16×C293C2211yescharacteristic
55C22⋊Q8×C293C2211yescharacteristic
56#103×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic
58C22⋊C8×C293C2211yescharacteristic
59#17989803—22no—
60#17989803—41no—
61C2×Dic586—21no—
62C2×D1172—21no—
63C2×D1172C2311yescharacteristic
64C2×C22⋊D293—21no—
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C2×C22⋊D293—21no—
68C2×C22⋊D293D411yescharacteristic
69C2×C4×D293—21no—
70C2×C4×D293C2311yescharacteristic
71#17989789—41no—
72C2×#14556873—41no—
73C2×#14556873C2311yescharacteristic
74C2×#14556873C2311yescharacteristic
75C8×D293—41no—
76C4⋊Dic293—21no—
77C4⋊Dic293—21no—
78C4⋊Dic293C2311yescharacteristic
79C4⋊Dic293C2311yescharacteristic
80C4⋊Dic293C2311yescharacteristic
81#17989781—21no—
82#17989781—21no—
83#17989781D411yescharacteristic
84C22⋊Dic293—21no—
85C22⋊Dic293—21no—
86C22⋊Dic293D411yescharacteristic
87#17989779—21no—
88#17989779—21no—
89#17989779—21no—
90#17989779D411yescharacteristic
91C4×Dic293—21no—
92C4×Dic293—21no—
93C4×Dic293—21no—
94C4×Dic293—21no—
95C4×Dic293C2311yescharacteristic
96#41×C293—22no—
97#41×C293—41no—
98C2×Q8×C293C2311yescharacteristic
99C2×Q8×C293C2311yescharacteristic
100C2×D4×C293—21no—
101C2×D4×C293C2311yescharacteristic
102C22×C4×C293—21no—
103C22×C4×C293C2311yescharacteristic
104Q16×C293—22no—
105SD16×C293—41no—
106C2×C8×C293C2311yescharacteristic
107C2×C8×C293C2311yescharacteristic
108C4⋊C4×C293—21no—
109C4⋊C4×C293C2311yescharacteristic
110C22⋊C4×C293—21no—
111C22×D293—21no—
112C22×D293C2×D411yescharacteristic
113Dic586—42no—
114D1172—21no—
115D1172—21no—
116D1172—42no—
117C22⋊D293—22no—
118C22⋊D293—42no—
119C22⋊D293—81no—
120C22⋊D293—81no—
121C22⋊D293—81no—
122C2×Dic293—21no—
123C2×Dic293—21no—
124C2×Dic293—21no—
125C2×Dic293C2×D411yescharacteristic
126C2×Dic293C2×D411yescharacteristic
127C2×Dic293C2×D411yescharacteristic
128C4×D293—21no—
129C4×D293—21no—
130C4×D293—42no—
131#14556873—21no—
132#14556873—21no—
133C23×C293—21no—
134C23×C293C2×D411yescharacteristic
135Q8×C293—21no—
136Q8×C293—21no—
137Q8×C293—21no—
138Q8×C293#4112yes—
139D4×C293—21no—
140D4×C293—21no—
141D4×C293—42no—
142C2×C4×C293—21no—
143C2×C4×C293—21no—
144C2×C4×C293—21no—
145C2×C4×C293—21no—
146C2×C4×C293—21no—
147C2×C4×C293—42no—
148C2×C4×C293C2×D411yescharacteristic
149C2×C4×C293C2411yescharacteristic
150C8×C293—21no—
151C8×C293—21no—
152C22×C293—21no—
153C22×C293—21no—
154C22×C293—21no—
155C22×C293—41no—
156C22×C293—41no—
157C22×C293—41no—
158C22×C293C22×D411yescharacteristic
159C2×D293—21no—
160C2×D293—21no—
161C2×D293—21no—
162C2×D293—41no—
163C2×D293—41no—
164C2×D293—41no—
165C4×C293—21no—
166C4×C293—22no—
167C4×C293—41no—
168C4×C293—41no—
169C4×C293C2×#4111yescharacteristic
170C4×C293H(5,𝔽2)11yescharacteristic
171Dic293—21no—
172Dic293—21no—
173Dic293—41no—
174Dic293—41no—
175Dic293—41no—
176Dic293#13512yes—
177C2×C293—41no—
178C2×C293—81no—
179C2×C293#54611yescharacteristic
180C2×C293C2×#13511yescharacteristic
181C2×C293#57711yescharacteristic
182D293—41no—
183D293—81no—
184C293#330411yescharacteristic, complemented, Sylow
185#3304—2931nomaximal, Sylow
186#556—2931no—
187#550—2931no—
188#486—2931no—
189#482—2931no—
190#482—2931no—
191#475—2931no—
192#465—2931no—
193#465—2931no—
194#460—2931no—
195#452—2931no—
196#452D29311yescharacteristic, complemented
197C4×Q16—2931no—
198C8×D4—2931no—
199#416—2931no—
200#416—2931no—
201C2×#41—2931no—
202C2×#41C2×D29311yescharacteristic
203C2×Q16C2×D29311yescharacteristic
204C2×SD16—2931no—
205C2×SD16C2×D29311yescharacteristic
206C22×C8—2931no—
207C22×C8—2931no—
208C4⋊Q8—2931no—
209#127—2931no—
210#127—5861no—
211#126—5861no—
212#126—5861no—
213#124—5861no—
214C22⋊Q8—2931no—
215C22⋊Q8C2×D29311yescharacteristic
216#121—2931no—
217#121—2931no—
218#121—5861no—
219#121—5861no—
220C4×Q8—2931no—
221C4×Q8—2931no—
222C4×Q8—5861no—
223C4×D4—2931no—
224C4×D4—5861no—
225#117—2931no—
226#117—2931no—
227#107—2931no—
228#106—2931no—
229#106—2931no—
230C4⋊C8—2931no—
231#103—2931no—
232#103—2931no—
233#103—2931no—
234#103C2×D29311yescharacteristic
235#102—2931no—
236#102—2931no—
237#102—2931no—
238#102—2931no—
239#102—2931no—
240#102C2×D29311yescharacteristic
241C22⋊C8—2931no—
242C22⋊C8C2×D29311yescharacteristic
243C4×C8—2931no—
244#41—22no—
245#41—41no—
246#41—5862no—
247#41—11721no—
248C2×Q8—5861no—
249C2×Q8C22×D29311yescharacteristic
250C2×Q8C22×D29311yescharacteristic
251C2×D4—21no—
252C2×D4—2931no—
253C2×D4—2931no—
254C2×D4—5861no—
255C2×D4—5861no—
256C2×D4—5861no—
257C2×D4—5861no—
258C2×D4—5861no—
259C2×D4C22×D29311yescharacteristic
260C22×C4—21no—
261C22×C4—2931no—
262C22×C4—5861no—
263C22×C4C22×D29311yescharacteristic
264Q16—22no—
265SD16—41no—
266SD16—11721no—
267C2×C8—2931no—
268C2×C8—2931no—
269C2×C8—11721no—
270C2×C8—11721no—
271C2×C8C22×D29311yescharacteristic
272C2×C8C22×D29311yescharacteristic
273C4⋊C4—21no—
274C4⋊C4—2931no—
275C4⋊C4—2931no—
276C4⋊C4—2931no—
277C4⋊C4—2931no—
278C4⋊C4—5861no—
279C4⋊C4—5861no—
280C4⋊C4—5861no—
281C4⋊C4—5861no—
282C4⋊C4C22×D29311yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—2931no—
285C22⋊C4—2931no—
286C22⋊C4—5861no—
287C22⋊C4—5861no—
288C22⋊C4—5861no—
289C22⋊C4—5861no—
290C22⋊C4—5861no—
291C42—2931no—
292C42—5861no—
293C42—5861no—
294C42—5861no—
295C42—5861no—
296C23—21no—
297C23—2931no—
298C23—5861no—
299C23D4×D29311yescharacteristic
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—11722no—
304Q8#1798980112yes—
305D4—21no—
306D4—21no—
307D4—42no—
308D4—23441no—
309D4—23441no—
310D4—23441no—
311D4—5862no—
312D4—5861no—
313D4—5861no—
314D4—11722no—
315D4—11722no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—2931no—
323C2×C4—2931no—
324C2×C4—2931no—
325C2×C4—5861no—
326C2×C4—5861no—
327C2×C4—5861no—
328C2×C4—5861no—
329C2×C4—5861no—
330C2×C4—11722no—
331C2×C4D4×D29311yescharacteristic
332C2×C4C23×D29311yescharacteristic
333C8—21no—
334C8—21no—
335C8—5861no—
336C8—5861no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—5861no—
344C22—5861no—
345C22—5861no—
346C22—11721no—
347C22—11721no—
348C22—11721no—
349C22C2×D4×D29311yescharacteristic
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—2932no—
355C4—5861no—
356C4—5861no—
357C4—11721no—
358C4—11721no—
359C4—11721no—
360C4C2×#1798980111yescharacteristic
361C4#2262766911yescharacteristic
362C2—41no—
363C2—81no—
364C2—23441no—
365C2—11721no—
366C2#3403676611yescharacteristic
367C2#135×D29311yescharacteristic
368C2#3403693811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#452×C293C2
socleC22×C293C22×D4
prime radical#34036798C2
hypercenter#452D293
hypocenterC293#3304
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #34036850C2semidirect
3. #34036474C2semidirect
4. #34036454C2semidirect
5. #34036451C2semidirect
6. #34036412C2semidirect
7. #34036360C2semidirect
8. #34036355C2semidirect
9. #34036327C2semidirect
10. #34036290C2semidirect
11. Q16×Dic293C2semidirect
12. #34036192C2semidirect
13. #34036125C2semidirect
14. #34036124C2semidirect
15. #452×C293C2semidirect
184. C293#3304semidirect
196. #452D293semidirect

Maximal subgroups

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

subgroupindex
#340368502
#340367982
#340364742
#340364542
#340364512
#340364122
#340363602
#340363552
#340363272
#340362902
Q16×Dic2932
#340361922
#340361252
#340361242
#452×C2932
#3304293