Finite Group Databasebeta

← #49170596

Subgroups — #49170596

Order 37504.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036780C211yesmaximal, characteristic, complemented
2#34036763C211yesmaximal, characteristic, complemented
3#34036474C211yesmaximal, characteristic, complemented
4#34036444C211yesmaximal, characteristic, complemented
5#34036408C211yesmaximal, characteristic, complemented
6#34036366C211yesmaximal, characteristic, complemented
7#34036363C211yesmaximal, characteristic, complemented
8#34036323C211yesmaximal, characteristic, complemented
9#34036265C211yesmaximal, characteristic, complemented
10#34036264C211yesmaximal, characteristic, complemented
11#34036211C211yesmaximal, characteristic, complemented
12#34036192C211yesmaximal, characteristic, complemented
13C2×#22627544C211yesmaximal, characteristic, complemented
14#102×D293C211yesmaximal, characteristic, complemented
15#480×C293C211yesmaximal, characteristic, complemented
16C2×#17989802—21no—
17C22×D1172C2211yescharacteristic
18C2×D4×D293—21no—
19C2×D4×D293C2211yescharacteristic
20C2×D2344C2211yescharacteristic
21C2×D2344C2211yescharacteristic, complemented
22C2×#17989787C2211yescharacteristic, complemented
23C22×#14556873C2211yescharacteristic, complemented
24C2×C8×D293C2211yescharacteristic, complemented
25#22627623C2211yescharacteristic, complemented
26#22627620C2211yescharacteristic
27#22627609—21no—
28#22627607—21no—
29#22627602—21no—
30#22627599C2211yescharacteristic
31#22627599C2211yescharacteristic, complemented
32#22627598C2211yescharacteristic, complemented
33#22627597—21no—
34#22627594—21no—
35#22627592—21no—
36#22627586C2211yescharacteristic
37#22627586C2211yescharacteristic, complemented
38C4×C22⋊D293C2211yescharacteristic
39C4⋊C4×D293C2211yescharacteristic, complemented
40#22627557C2211yescharacteristic, complemented
41#22627553C2211yescharacteristic, complemented
42#22627546C2211yescharacteristic
43#22627546C2211yescharacteristic, complemented
44#22627545C2211yescharacteristic, complemented
45#22627544C2211yescharacteristic
46#22627544C2211yescharacteristic
47#22627544C2211yescharacteristic, complemented
48#22627544C2211yescharacteristic, complemented
49#22627544C2211yescharacteristic, complemented
50#22627536C2211yescharacteristic, complemented
51C8×Dic293C2211yescharacteristic, complemented
52#121×C293C2211yescharacteristic
53C2×C4⋊C4×C293C2211yescharacteristic, complemented
54#107×C293C2211yescharacteristic, complemented
55#107×C293C2211yescharacteristic, complemented
56#102×C293C2211yescharacteristic, complemented
57#102×C293C2211yescharacteristic, complemented
58C22⋊C8×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60C23×D293—21no—
61#17989802—44no—
62C2×Dic586—21no—
63C2×D1172—22no—
64C2×D1172—21no—
65C2×D1172—21no—
66C2×D1172—21no—
67C2×D1172—41no—
68C2×D1172C2311yescharacteristic
69C2×D1172C2311yescharacteristic
70C2×D1172C2311yescharacteristic
71C2×C22⋊D293—21no—
72C2×C22⋊D293—21no—
73C2×C22⋊D293—21no—
74C2×C22⋊D293—21no—
75C2×C22⋊D293D411yescharacteristic
76D4×D293—22no—
77D4×D293—41no—
78D4×D293—44no—
79C2×C4×D293—21no—
80C2×C4×D293—21no—
81C2×C4×D293—21no—
82C2×C4×D293C2311yescharacteristic
83D2344—22no—
84D2344—41no—
85#17989787—41no—
86C2×#14556873—41no—
87C2×#14556873C2311yescharacteristic
88C2×#14556873C2311yescharacteristic
89C8×D293—41no—
90C4⋊Dic293C2311yescharacteristic
91#17989781—21no—
92#17989781—21no—
93#17989781D411yescharacteristic
94C22⋊Dic293D411yescharacteristic
95#17989779—21no—
96#17989779—21no—
97#17989779—21no—
98#17989779—21no—
99#17989779—21no—
100#17989779D411yescharacteristic
101C4×Dic293C2311yescharacteristic
102C2×D4×C293—21no—
103C2×D4×C293C2311yescharacteristic
104C22×C4×C293—21no—
105C22×C4×C293C2311yescharacteristic
106C2×C8×C293C2311yescharacteristic
107C2×C8×C293C2311yescharacteristic
108C4⋊C4×C293—21no—
109C4⋊C4×C293C2311yescharacteristic
110C4⋊C4×C293C2311yescharacteristic
111C4⋊C4×C293C2311yescharacteristic
112C22⋊C4×C293—21no—
113C22×D293—21no—
114C22×D293—21no—
115C22×D293—21no—
116C22×D293—42no—
117C22×D293—42no—
118C22×D293—42no—
119C22×D293—42no—
120C22×D293—81no—
121C22×D293—81no—
122C22×D293C2×D411yescharacteristic
123Dic586—42no—
124D1172—21no—
125D1172—21no—
126D1172—21no—
127D1172—21no—
128D1172—21no—
129D1172—42no—
130D1172—42no—
131D1172—42no—
132D1172#4112yescomplemented
133C22⋊D293—42no—
134C22⋊D293—42no—
135C22⋊D293—42no—
136C22⋊D293—81no—
137C22⋊D293D814yescomplemented
138C2×Dic293—21no—
139C2×Dic293C2×D411yescharacteristic
140C2×Dic293C2×D411yescharacteristic
141C2×Dic293C2×D411yescharacteristic
142C4×D293—21no—
143C4×D293—21no—
144C4×D293—42no—
145C4×D293—42no—
146C4×D293—42no—
147#14556873—21no—
148#14556873—21no—
149C23×C293—21no—
150C23×C293C2×D411yescharacteristic
151D4×C293—21no—
152D4×C293—21no—
153D4×C293—42no—
154C2×C4×C293—21no—
155C2×C4×C293—21no—
156C2×C4×C293—21no—
157C2×C4×C293—21no—
158C2×C4×C293—21no—
159C2×C4×C293—42no—
160C2×C4×C293C2×D411yescharacteristic
161C2×C4×C293C2411yescharacteristic
162C8×C293—21no—
163C8×C293—21no—
164C22×C293—21no—
165C22×C293—21no—
166C22×C293—41no—
167C22×C293—41no—
168C22×C293—41no—
169C22×C293C2×D812yes—
170C22×C293C22×D411yescharacteristic
171C2×D293—21no—
172C2×D293—21no—
173C2×D293—22no—
174C2×D293—41no—
175C2×D293—41no—
176C2×D293—41no—
177C2×D293—41no—
178C2×D293—41no—
179C2×D293—41no—
180C2×D293—41no—
181C2×D293—41no—
182C2×D293—84no—
183C2×D293—84no—
184C2×D293C2×D812yes—
185C4×C293—21no—
186C4×C293—41no—
187C4×C293—41no—
188C4×C293—41no—
189C4×C293C2×#4111yescharacteristic
190C4×C293H(5,𝔽2)11yescharacteristic
191Dic293—21no—
192Dic293—21no—
193Dic293—41no—
194Dic293C2×D812yes—
195C2×C293—22no—
196C2×C293—81no—
197C2×C293#54611yescharacteristic
198C2×C293C22×D811yescharacteristic
199C2×C293#57711yescharacteristic
200D293—22no—
201D293—42no—
202D293—81no—
203D293—81no—
204C293#329411yescharacteristic, complemented, Sylow
205#3294—2931nomaximal, Sylow
206#547—2931no—
207D42—2931no—
208#486—2931no—
209#480—2931no—
210#480D29311yescharacteristic, complemented
211#474—2931no—
212#466—2931no—
213#466—2931no—
214#459—2931no—
215#447—2931no—
216#447—2931no—
217C4×D8—2931no—
218C8×D4—2931no—
219C2×#102—2931no—
220C2×#102—2931no—
221C2×#41—5861no—
222C22×D4—2931no—
223C22×D4—2931no—
224C22×D4—5861no—
225C2×D8—2931no—
226C2×D8—2931no—
227C2×D8—2931no—
228C22×C8—2931no—
229C22×C8—2931no—
230C4⋊Q8—2931no—
231#127—2931no—
232#123—5861no—
233#123—5861no—
234C22⋊Q8—5861no—
235#121—2931no—
236#121—2931no—
237#121—2931no—
238#121—5861no—
239#121C2×D29311yescharacteristic
240#120—5861no—
241#120—5861no—
242C4×D4—2931no—
243C4×D4—2931no—
244C4×D4—2931no—
245C2×C4⋊C4—2931no—
246C2×C4⋊C4C2×D29311yescharacteristic, complemented
247#107—2931no—
248#107C2×D29311yescharacteristic, complemented
249#107C2×D29311yescharacteristic, complemented
250C4⋊C8—2931no—
251#102—2931no—
252#102—2931no—
253#102—2931no—
254#102—2931no—
255#102—2931no—
256#102—2931no—
257#102—2931no—
258#102—2931no—
259#102C2×D29311yescharacteristic, complemented
260#102C2×D29311yescharacteristic, complemented
261C22⋊C8—2931no—
262C22⋊C8C2×D29311yescharacteristic, complemented
263C4×C8—2931no—
264C24—5861no—
265C24—5861no—
266#41—11724no—
267C2×Q8—5861no—
268C2×D4—21no—
269C2×D4—2931no—
270C2×D4—2931no—
271C2×D4—2931no—
272C2×D4—2931no—
273C2×D4—5862no—
274C2×D4—5861no—
275C2×D4—5861no—
276C2×D4—5861no—
277C2×D4—5861no—
278C2×D4—5861no—
279C2×D4—5862no—
280C2×D4—5861no—
281C2×D4—5861no—
282C2×D4—11721no—
283C2×D4—11721no—
284C2×D4—11724no—
285C2×D4C22×D29311yescharacteristic
286C22×C4—21no—
287C22×C4—2931no—
288C22×C4—5861no—
289C22×C4—5861no—
290C22×C4—5861no—
291C22×C4C22×D29311yescharacteristic
292D8—5862no—
293D8—11721no—
294D8—11721no—
295C2×C8—2931no—
296C2×C8—2931no—
297C2×C8—11721no—
298C2×C8—11721no—
299C2×C8C22×D29311yescharacteristic
300C2×C8C22×D29311yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—2931no—
303C4⋊C4—2931no—
304C4⋊C4—5861no—
305C4⋊C4—5861no—
306C4⋊C4C22×D29311yescharacteristic
307C4⋊C4C22×D29311yescharacteristic
308C4⋊C4C22×D29311yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—2931no—
311C22⋊C4—2931no—
312C22⋊C4—5861no—
313C22⋊C4—5861no—
314C22⋊C4—5861no—
315C22⋊C4—5861no—
316C22⋊C4—5861no—
317C42—2931no—
318C23—21no—
319C23—2931no—
320C23—23441no—
321C23—23441no—
322C23—5861no—
323C23—5861no—
324C23—5861no—
325C23—11722no—
326C23—11722no—
327C23—11722no—
328C23—11722no—
329C23D4×D29311yescharacteristic
330Q8—11722no—
331D4—21no—
332D4—21no—
333D4—42no—
334D4—2934no—
335D4—2932no—
336D4—23441no—
337D4—5861no—
338D4—5861no—
339D4—5861no—
340D4—5861no—
341D4—5861no—
342D4—11722no—
343D4—11722no—
344D4—11722no—
345D4—11722no—
346D4—11722no—
347D4—11722no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—42no—
354C2×C4—2931no—
355C2×C4—2931no—
356C2×C4—2931no—
357C2×C4—5861no—
358C2×C4—5861no—
359C2×C4—5861no—
360C2×C4—11722no—
361C2×C4—11722no—
362C2×C4—11722no—
363C2×C4D4×D29311yescharacteristic
364C2×C4C23×D29311yescharacteristic
365C8—21no—
366C8—21no—
367C8—5861no—
368C8—5861no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—2932no—
375C22—23444no—
376C22—23444no—
377C22—5861no—
378C22—5861no—
379C22—5862no—
380C22—11721no—
381C22—11721no—
382C22—11721no—
383C22—11721no—
384C22—11721no—
385C22—11721no—
386C22—11721no—
387C22—11721no—
388C22D8×D29312yes—
389C22C2×D4×D29311yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—2932no—
395C4—5861no—
396C4—5861no—
397C4—11721no—
398C4#41×D29311yescharacteristic
399C4#2262767011yescharacteristic
400C2—22no—
401C2—81no—
402C2—23441no—
403C2—23441no—
404C2—5862no—
405C2—11722no—
406C2#3403677111yescharacteristic
407C2C2×D8×D29311yescharacteristic
408C2#3403693811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#480×C293C2
socleC22×C293C22×D4
hypercenter#480D293
hypocenterC293#3294
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #34036780C2semidirect
2. #34036763C2semidirect
3. #34036474C2semidirect
4. #34036444C2semidirect
5. #34036408C2semidirect
6. #34036366C2semidirect
7. #34036363C2semidirect
8. #34036323C2semidirect
9. #34036265C2semidirect
10. #34036264C2semidirect
11. #34036211C2semidirect
12. #34036192C2semidirect
13. C2×#22627544C2semidirect
14. #102×D293C2semidirect
15. #480×C293C2semidirect
21. C2×D2344C22semidirect
22. C2×#17989787C22semidirect
23. C22×#14556873C22semidirect
24. C2×C8×D293C22semidirect
25. #22627623C22semidirect
31. #22627599C22semidirect
32. #22627598C22semidirect
37. #22627586C22semidirect
39. C4⋊C4×D293C22semidirect
40. #22627557C22semidirect
41. #22627553C22semidirect
43. #22627546C22semidirect
44. #22627545C22semidirect
47. #22627544C22semidirect
48. #22627544C22semidirect
49. #22627544C22semidirect
50. #22627536C22semidirect
51. C8×Dic293C22semidirect
53. C2×C4⋊C4×C293C22semidirect
54. #107×C293C22semidirect
55. #107×C293C22semidirect
56. #102×C293C22semidirect
57. #102×C293C22semidirect
58. C22⋊C8×C293C22semidirect
132. D1172#41semidirect
137. C22⋊D293D8semidirect
204. C293#3294semidirect
210. #480D293semidirect
246. C2×C4⋊C4C2×D293semidirect
248. #107C2×D293semidirect
249. #107C2×D293semidirect
259. #102C2×D293semidirect
260. #102C2×D293semidirect
262. C22⋊C8C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340367802
#340367632
#340364742
#340364442
#340364082
#340363662
#340363632
#340363232
#340362652
#340362642
#340362112
#340361922
C2×#226275442
#102×D2932
#480×C2932
#3294293