Finite Group Databasebeta

← #49170593

Subgroups — #49170593

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#34036779C211yesmaximal, characteristic, complemented
2#34036763C211yesmaximal, characteristic, complemented
3#34036474C211yesmaximal, characteristic, complemented
4#34036444C211yesmaximal, characteristic, complemented
5#34036440C211yesmaximal, characteristic, complemented
6#34036408C211yesmaximal, characteristic, complemented
7#34036364C211yesmaximal, characteristic, complemented
8#34036322C211yesmaximal, characteristic, complemented
9#34036262C211yesmaximal, characteristic, complemented
10#34036261C211yesmaximal, characteristic, complemented
11#34036209C211yesmaximal, characteristic, complemented
12C8×C22⋊D293C211yesmaximal, characteristic, complemented
13C2×#22627546C211yesmaximal, characteristic, complemented
14#102×D293C211yesmaximal, characteristic, complemented
15#466×C293C211yesmaximal, characteristic, complemented
16C2×#17989801—21no—
17C22×D1172C2211yescharacteristic
18C2×D4×D293—21no—
19C2×D4×D293C2211yescharacteristic
20C2×#17989787C2211yescharacteristic
21C2×#17989787C2211yescharacteristic, complemented
22C2×C8×D293C2211yescharacteristic, complemented
23#22627623C2211yescharacteristic, complemented
24#22627620C2211yescharacteristic
25#22627606—21no—
26#22627605—21no—
27#22627601—21no—
28#22627599C2211yescharacteristic
29#22627597—21no—
30#22627595C2211yescharacteristic, complemented
31#22627594—21no—
32#22627592—21no—
33D4×Dic293C2211yescharacteristic, complemented
34#22627586C2211yescharacteristic
35C4×C22⋊D293C2211yescharacteristic
36C2×C4⋊Dic293C2211yescharacteristic, complemented
37C4⋊C4×D293C2211yescharacteristic, complemented
38#22627557C2211yescharacteristic, complemented
39#22627557C2211yescharacteristic, complemented
40#22627553C2211yescharacteristic, complemented
41#22627546C2211yescharacteristic
42#22627546C2211yescharacteristic
43#22627546C2211yescharacteristic, complemented
44#22627546C2211yescharacteristic, complemented
45#22627545C2211yescharacteristic, complemented
46#22627545C2211yescharacteristic, complemented
47#22627544C2211yescharacteristic
48#22627544C2211yescharacteristic, complemented
49C22⋊#14556873C2211yescharacteristic, complemented
50#22627536C2211yescharacteristic, complemented
51C8×Dic293C2211yescharacteristic, complemented
52C2×D8×C293C2211yescharacteristic, complemented
53C22×C8×C293C2211yescharacteristic, complemented
54#121×C293C2211yescharacteristic
55#121×C293C2211yescharacteristic, complemented
56#107×C293C2211yescharacteristic, complemented
57#102×C293C2211yescharacteristic, complemented
58#102×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60C23×D293—21no—
61#17989801—44no—
62C2×Dic586—21no—
63C2×D1172—22no—
64C2×D1172—21no—
65C2×D1172—21no—
66C2×D1172—41no—
67C2×D1172C2311yescharacteristic
68C2×D1172C2311yescharacteristic
69C2×C22⋊D293—21no—
70C2×C22⋊D293—21no—
71C2×C22⋊D293—21no—
72C2×C22⋊D293—21no—
73C2×C22⋊D293D411yescharacteristic
74D4×D293—22no—
75D4×D293—41no—
76D4×D293—44no—
77C22×Dic293—21no—
78C22×Dic293—21no—
79C2×C4×D293—21no—
80C2×C4×D293—21no—
81C2×C4×D293C2311yescharacteristic
82#17989787—22no—
83#17989787—41no—
84C2×#14556873C2311yescharacteristic
85C2×#14556873C2311yescharacteristic
86C8×D293—41no—
87C4⋊Dic293—21no—
88C4⋊Dic293C2311yescharacteristic
89C4⋊Dic293C2311yescharacteristic
90#17989781—21no—
91#17989781—21no—
92#17989781D411yescharacteristic
93C22⋊Dic293—21no—
94C22⋊Dic293—21no—
95C22⋊Dic293D411yescharacteristic
96#17989779—21no—
97#17989779—21no—
98#17989779D411yescharacteristic
99C4×Dic293C2311yescharacteristic
100C2×D4×C293—21no—
101C2×D4×C293—21no—
102C2×D4×C293C2311yescharacteristic
103C2×D4×C293C2311yescharacteristic
104C22×C4×C293C2311yescharacteristic
105D8×C293—41no—
106C2×C8×C293—41no—
107C2×C8×C293C2311yescharacteristic
108C2×C8×C293C2311yescharacteristic
109C4⋊C4×C293C2311yescharacteristic
110C4⋊C4×C293C2311yescharacteristic
111C22⋊C4×C293—21no—
112C22⋊C4×C293—21no—
113C22×D293—21no—
114C22×D293—21no—
115C22×D293—42no—
116C22×D293—42no—
117C22×D293—42no—
118C22×D293—42no—
119C22×D293—81no—
120C22×D293—81no—
121C22×D293C2×D411yescharacteristic
122Dic586—42no—
123D1172—21no—
124D1172—21no—
125D1172—21no—
126D1172—42no—
127D1172—42no—
128D1172#4112yescomplemented
129C22⋊D293—42no—
130C22⋊D293—42no—
131C22⋊D293—42no—
132C22⋊D293—81no—
133C22⋊D293D814yescomplemented
134C2×Dic293—21no—
135C2×Dic293—21no—
136C2×Dic293—42no—
137C2×Dic293—42no—
138C2×Dic293C2×D411yescharacteristic
139C2×Dic293C2×D411yescharacteristic
140C2×Dic293C2×D411yescharacteristic
141C4×D293—21no—
142C4×D293—21no—
143C4×D293—42no—
144C4×D293—42no—
145#14556873—21no—
146#14556873—21no—
147C23×C293—21no—
148C23×C293—21no—
149C23×C293C2×D411yescharacteristic
150D4×C293—21no—
151D4×C293—21no—
152D4×C293—21no—
153D4×C293—21no—
154D4×C293—42no—
155D4×C293—42no—
156C2×C4×C293—21no—
157C2×C4×C293—21no—
158C2×C4×C293—21no—
159C2×C4×C293—21no—
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×C293—41no—
170C22×C293—41no—
171C22×C293—41no—
172C22×C293C2×D812yes—
173C22×C293C22×D411yescharacteristic
174C2×D293—21no—
175C2×D293—21no—
176C2×D293—22no—
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×C293C2×#4111yescharacteristic
189C4×C293H(5,𝔽2)11yescharacteristic
190Dic293—21no—
191Dic293—21no—
192Dic293—41no—
193Dic293—41no—
194Dic293C2×D812yes—
195C2×C293—22no—
196C2×C293—81no—
197C2×C293—81no—
198C2×C293#54611yescharacteristic
199C2×C293C22×D811yescharacteristic
200C2×C293#57711yescharacteristic
201D293—22no—
202D293—42no—
203D293—81no—
204C293#329411yescharacteristic, complemented, Sylow
205#3294—2931nomaximal, Sylow
206#547—2931no—
207D42—2931no—
208#486—2931no—
209#480—2931no—
210#480—2931no—
211#474—2931no—
212#466—2931no—
213#466D29311yescharacteristic, complemented
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×D8C2×D29311yescharacteristic, complemented
228C22×C8—2931no—
229C22×C8C2×D29311yescharacteristic, complemented
230C4⋊Q8—2931no—
231#127—2931no—
232#123—5861no—
233#123—5861no—
234C22⋊Q8—5861no—
235#121—2931no—
236#121—2931no—
237#121—5861no—
238#121C2×D29311yescharacteristic
239#121C2×D29311yescharacteristic, complemented
240#120—5861no—
241#120—5861no—
242C4×D4—2931no—
243C4×D4—2931no—
244C4×D4—2931no—
245C2×C4⋊C4—2931no—
246C2×C4⋊C4—2931no—
247#107—2931no—
248#107—2931no—
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⋊C8—2931no—
263C4×C8—2931no—
264C24—5861no—
265C24—5861no—
266#41—11724no—
267C2×Q8—5861no—
268C2×D4—21no—
269C2×D4—21no—
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—5862no—
279C2×D4—5861no—
280C2×D4—5861no—
281C2×D4—11721no—
282C2×D4—11721no—
283C2×D4—11724no—
284C2×D4C22×D29311yescharacteristic
285C2×D4C22×D29311yescharacteristic
286C22×C4—2931no—
287C22×C4—5861no—
288C22×C4—5861no—
289C22×C4—5861no—
290C22×C4—5861no—
291C22×C4C22×D29311yescharacteristic
292D8—41no—
293D8—5862no—
294D8—11721no—
295C2×C8—41no—
296C2×C8—2931no—
297C2×C8—2931no—
298C2×C8—11721no—
299C2×C8C22×D29311yescharacteristic
300C2×C8C22×D29311yescharacteristic
301C4⋊C4—2931no—
302C4⋊C4—2931no—
303C4⋊C4—2931no—
304C4⋊C4—5861no—
305C4⋊C4—5861no—
306C4⋊C4—5861no—
307C4⋊C4C22×D29311yescharacteristic
308C4⋊C4C22×D29311yescharacteristic
309C22⋊C4—21no—
310C22⋊C4—21no—
311C22⋊C4—2931no—
312C22⋊C4—2931no—
313C22⋊C4—5861no—
314C22⋊C4—5861no—
315C22⋊C4—5861no—
316C22⋊C4—5861no—
317C42—2931no—
318C23—21no—
319C23—21no—
320C23—2931no—
321C23—23441no—
322C23—23441no—
323C23—5861no—
324C23—5861no—
325C23—11722no—
326C23—11722no—
327C23—11722no—
328C23—11722no—
329C23D4×D29311yescharacteristic
330Q8—11722no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—42no—
336D4—42no—
337D4—2934no—
338D4—2932no—
339D4—23441no—
340D4—5861no—
341D4—5861no—
342D4—5861no—
343D4—11722no—
344D4—11722no—
345D4—11722no—
346D4—11722no—
347D4—11722no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—2931no—
353C2×C4—2931no—
354C2×C4—2931no—
355C2×C4—5861no—
356C2×C4—5861no—
357C2×C4—5861no—
358C2×C4—5861no—
359C2×C4—11722no—
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—41no—
375C22—41no—
376C22—41no—
377C22—2932no—
378C22—23444no—
379C22—23444no—
380C22—5861no—
381C22—5861no—
382C22—5862no—
383C22—11721no—
384C22—11721no—
385C22—11721no—
386C22—11721no—
387C22—11721no—
388C22D8×D29312yes—
389C22C2×D4×D29311yescharacteristic
390C4—21no—
391C4—41no—
392C4—41no—
393C4—2932no—
394C4—5861no—
395C4—5861no—
396C4—11721no—
397C4—11721no—
398C4#41×D29311yescharacteristic
399C4#2262766911yescharacteristic
400C2—22no—
401C2—81no—
402C2—81no—
403C2—23441no—
404C2—5862no—
405C2—11722no—
406C2#3403676811yescharacteristic
407C2C2×D8×D29311yescharacteristic
408C2#3403693611yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#466×C293C2
socleC22×C293C22×D4
hypercenter#466D293
hypocenterC293#3294
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #34036779C2semidirect
2. #34036763C2semidirect
3. #34036474C2semidirect
4. #34036444C2semidirect
5. #34036440C2semidirect
6. #34036408C2semidirect
7. #34036364C2semidirect
8. #34036322C2semidirect
9. #34036262C2semidirect
10. #34036261C2semidirect
11. #34036209C2semidirect
12. C8×C22⋊D293C2semidirect
13. C2×#22627546C2semidirect
14. #102×D293C2semidirect
15. #466×C293C2semidirect
21. C2×#17989787C22semidirect
22. C2×C8×D293C22semidirect
23. #22627623C22semidirect
30. #22627595C22semidirect
33. D4×Dic293C22semidirect
36. C2×C4⋊Dic293C22semidirect
37. C4⋊C4×D293C22semidirect
38. #22627557C22semidirect
39. #22627557C22semidirect
40. #22627553C22semidirect
43. #22627546C22semidirect
44. #22627546C22semidirect
45. #22627545C22semidirect
46. #22627545C22semidirect
48. #22627544C22semidirect
49. C22⋊#14556873C22semidirect
50. #22627536C22semidirect
51. C8×Dic293C22semidirect
52. C2×D8×C293C22semidirect
53. C22×C8×C293C22semidirect
55. #121×C293C22semidirect
56. #107×C293C22semidirect
57. #102×C293C22semidirect
58. #102×C293C22semidirect
128. D1172#41semidirect
133. C22⋊D293D8semidirect
204. C293#3294semidirect
213. #466D293semidirect
227. C2×D8C2×D293semidirect
229. C22×C8C2×D293semidirect
239. #121C2×D293semidirect
249. #107C2×D293semidirect
259. #102C2×D293semidirect
260. #102C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340367792
#340367632
#340364742
#340364442
#340364402
#340364082
#340363642
#340363222
#340362622
#340362612
#340362092
C8×C22⋊D2932
C2×#226275462
#102×D2932
#466×C2932
#3294293