Finite Group Databasebeta

← #49170591

Subgroups — #49170591

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
2D4×C22⋊D293C211yesmaximal, characteristic, complemented
3#34036474C211yesmaximal, characteristic, complemented
4#34036443C211yesmaximal, characteristic, complemented
5#34036441C211yesmaximal, characteristic, complemented
6#34036407C211yesmaximal, characteristic, complemented
7#34036363C211yesmaximal, characteristic, complemented
8#34036362C211yesmaximal, characteristic, complemented
9#34036322C211yesmaximal, characteristic, complemented
10#34036261C211yesmaximal, characteristic, complemented
11D8×Dic293C211yesmaximal, characteristic, complemented
12#34036192C211yesmaximal, characteristic, complemented
13C2×#22627545C211yesmaximal, characteristic, complemented
14#102×D293C211yesmaximal, characteristic, complemented
15#447×C293C211yesmaximal, characteristic, complemented
16C2×#17989801—21no—
17C22×C22⋊D293—21no—
18C2×D4×D293C2211yescharacteristic
19C2×#17989787C2211yescharacteristic, complemented
20C22×#14556873C2211yescharacteristic, complemented
21C2×C8×D293C2211yescharacteristic, complemented
22#22627623C2211yescharacteristic, complemented
23#22627620C2211yescharacteristic
24#22627606—21no—
25#22627605—21no—
26#22627601—21no—
27#22627598C2211yescharacteristic
28#22627596—21no—
29#22627595C2211yescharacteristic
30#22627595C2211yescharacteristic, complemented
31#22627593—21no—
32#22627592—21no—
33D4×Dic293C2211yescharacteristic
34D4×Dic293C2211yescharacteristic, complemented
35C4×C22⋊D293C2211yescharacteristic
36C2×C4⋊Dic293C2211yescharacteristic, complemented
37C4⋊C4×D293C2211yescharacteristic, complemented
38#22627558C2211yescharacteristic, complemented
39#22627558C2211yescharacteristic, complemented
40#22627557C2211yescharacteristic, complemented
41#22627553C2211yescharacteristic, complemented
42#22627546C2211yescharacteristic, complemented
43#22627546C2211yescharacteristic, complemented
44#22627545C2211yescharacteristic
45#22627545C2211yescharacteristic
46#22627545C2211yescharacteristic, complemented
47#22627545C2211yescharacteristic, complemented
48#22627545C2211yescharacteristic, complemented
49#22627544C2211yescharacteristic, complemented
50#22627536C2211yescharacteristic, complemented
51C8×Dic293C2211yescharacteristic, complemented
52C22×D4×C293C2211yescharacteristic
53C2×D8×C293C2211yescharacteristic
54C2×D8×C293C2211yescharacteristic, complemented
55#121×C293C2211yescharacteristic, complemented
56#102×C293C2211yescharacteristic
57#102×C293C2211yescharacteristic, complemented
58C22⋊C8×C293C2211yescharacteristic, complemented
59C23×D293—21no—
60#17989801—44no—
61C2×Dic586—21no—
62C2×D1172C2311yescharacteristic
63C2×C22⋊D293—21no—
64C2×C22⋊D293—21no—
65C2×C22⋊D293—21no—
66C2×C22⋊D293—21no—
67C2×C22⋊D293—21no—
68C2×C22⋊D293—21no—
69C2×C22⋊D293—44no—
70C2×C22⋊D293D411yescharacteristic
71D4×D293—22no—
72D4×D293—41no—
73C22×Dic293—21no—
74C22×Dic293—21no—
75C22×Dic293—21no—
76C2×C4×D293—21no—
77C2×C4×D293C2311yescharacteristic
78#17989787—41no—
79C2×#14556873—41no—
80C2×#14556873C2311yescharacteristic
81C2×#14556873C2311yescharacteristic
82C8×D293—41no—
83C4⋊Dic293—21no—
84C4⋊Dic293C2311yescharacteristic
85C4⋊Dic293C2311yescharacteristic
86C4⋊Dic293C2311yescharacteristic
87#17989781—21no—
88#17989781—21no—
89#17989781D411yescharacteristic
90C22⋊Dic293—21no—
91C22⋊Dic293—21no—
92C22⋊Dic293—21no—
93C22⋊Dic293—21no—
94C22⋊Dic293D411yescharacteristic
95#17989779—21no—
96#17989779D411yescharacteristic
97C4×Dic293C2311yescharacteristic
98C24×C293—21no—
99C2×D4×C293—22no—
100C2×D4×C293—21no—
101C2×D4×C293—21no—
102C2×D4×C293—41no—
103C2×D4×C293C2311yescharacteristic
104C2×D4×C293C2311yescharacteristic
105C2×D4×C293C2311yescharacteristic
106C22×C4×C293C2311yescharacteristic
107D8×C293—22no—
108D8×C293—41no—
109C2×C8×C293C2311yescharacteristic
110C2×C8×C293C2311yescharacteristic
111C4⋊C4×C293C2311yescharacteristic
112C22⋊C4×C293—21no—
113C22×D293—21no—
114C22×D293—42no—
115C22×D293—42no—
116C22×D293—81no—
117C22×D293C2×D411yescharacteristic
118Dic586—42no—
119D1172—21no—
120D1172—21no—
121C22⋊D293—42no—
122C22⋊D293—42no—
123C22⋊D293—42no—
124C22⋊D293—42no—
125C22⋊D293—42no—
126C22⋊D293—81no—
127C22⋊D293D814yescomplemented
128C2×Dic293—21no—
129C2×Dic293—21no—
130C2×Dic293—21no—
131C2×Dic293—42no—
132C2×Dic293—42no—
133C2×Dic293—42no—
134C2×Dic293C2×D411yescharacteristic
135C2×Dic293C2×D411yescharacteristic
136C2×Dic293C2×D411yescharacteristic
137C4×D293—21no—
138C4×D293—21no—
139C4×D293—42no—
140#14556873—21no—
141#14556873—21no—
142C23×C293—21no—
143C23×C293—21no—
144C23×C293—21no—
145C23×C293—42no—
146C23×C293—42no—
147C23×C293—81no—
148C23×C293C2×D411yescharacteristic
149D4×C293—21no—
150D4×C293—21no—
151D4×C293—21no—
152D4×C293—21no—
153D4×C293—21no—
154D4×C293—42no—
155D4×C293—42no—
156D4×C293#4112yescomplemented
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—22no—
167C22×C293—41no—
168C22×C293—41no—
169C22×C293—41no—
170C22×C293—41no—
171C22×C293—41no—
172C22×C293—41no—
173C22×C293—41no—
174C22×C293—41no—
175C22×C293—84no—
176C22×C293C2×D812yes—
177C22×C293C22×D411yescharacteristic
178C2×D293—21no—
179C2×D293—21no—
180C2×D293—41no—
181C2×D293—41no—
182C2×D293—41no—
183C2×D293—84no—
184C2×D293C2×D812yes—
185C4×C293—21no—
186C4×C293—41no—
187C4×C293C2×#4111yescharacteristic
188C4×C293H(5,𝔽2)11yescharacteristic
189Dic293—21no—
190Dic293—21no—
191Dic293—41no—
192Dic293—41no—
193Dic293—41no—
194Dic293C2×D812yes—
195C2×C293—22no—
196C2×C293—42no—
197C2×C293—81no—
198C2×C293—81no—
199C2×C293#54611yescharacteristic
200C2×C293C22×D811yescharacteristic
201C2×C293#57711yescharacteristic
202D293—22no—
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#466—2931no—
214#459—2931no—
215#447—2931no—
216#447D29311yescharacteristic, complemented
217C4×D8—2931no—
218C8×D4—2931no—
219C2×#102—2931no—
220C2×#102—2931no—
221C2×#41—5861no—
222C22×D4—2931no—
223C22×D4—5861no—
224C22×D4C2×D29311yescharacteristic
225C2×D8—2931no—
226C2×D8C2×D29311yescharacteristic
227C2×D8C2×D29311yescharacteristic, complemented
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, 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#107—2931no—
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
260#102C2×D29311yescharacteristic, complemented
261C22⋊C8—2931no—
262C22⋊C8C2×D29311yescharacteristic, complemented
263C4×C8—2931no—
264C24—21no—
265C24—5861no—
266#41—11724no—
267C2×Q8—5861no—
268C2×D4—22no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—2931no—
273C2×D4—2931no—
274C2×D4—5861no—
275C2×D4—5861no—
276C2×D4—5861no—
277C2×D4—5862no—
278C2×D4—5861no—
279C2×D4—5861no—
280C2×D4—5861no—
281C2×D4—11721no—
282C2×D4—11724no—
283C2×D4C22×D29311yescharacteristic
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—22no—
293D8—41no—
294D8—11721no—
295C2×C8—2931no—
296C2×C8—2931no—
297C2×C8—11721no—
298C2×C8—11721no—
299C2×C8C22×D29311yescharacteristic
300C2×C8C22×D29311yescharacteristic
301C4⋊C4—2931no—
302C4⋊C4—2931no—
303C4⋊C4—2931no—
304C4⋊C4—2931no—
305C4⋊C4—5861no—
306C4⋊C4—5861no—
307C4⋊C4—5861no—
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—21no—
320C23—21no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—2931no—
325C23—23441no—
326C23—5861no—
327C23—11722no—
328C23—11722no—
329C23D4×D29311yescharacteristic
330Q8—11722no—
331D4—21no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—42no—
337D4—42no—
338D4—2934no—
339D4—23441no—
340D4—5861no—
341D4—5861no—
342D4—11722no—
343D4—11722no—
344D4—11722no—
345D4—11722no—
346D4—11722no—
347D4#1798980112yescomplemented
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—2931no—
352C2×C4—2931no—
353C2×C4—2931no—
354C2×C4—5861no—
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—22no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—84no—
381C22—2932no—
382C22—23444no—
383C22—5861no—
384C22—5861no—
385C22—11721no—
386C22—11721no—
387C22—11721no—
388C22D8×D29312yes—
389C22C2×D4×D29311yescharacteristic
390C4—21no—
391C4—41no—
392C4—2932no—
393C4—5861no—
394C4—5861no—
395C4—11721no—
396C4—11721no—
397C4—11721no—
398C4C2×#1798980111yescharacteristic
399C4#2262766911yescharacteristic
400C2—22no—
401C2—42no—
402C2—81no—
403C2—81no—
404C2—23441no—
405C2—5862no—
406C2#3403676611yescharacteristic
407C2C2×D8×D29311yescharacteristic
408C2#3403693911yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#447×C293C2
socleC22×C293C22×D4
hypercenter#447D293
hypocenterC293#3294
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. #34036779C2semidirect
2. D4×C22⋊D293C2semidirect
3. #34036474C2semidirect
4. #34036443C2semidirect
5. #34036441C2semidirect
6. #34036407C2semidirect
7. #34036363C2semidirect
8. #34036362C2semidirect
9. #34036322C2semidirect
10. #34036261C2semidirect
11. D8×Dic293C2semidirect
12. #34036192C2semidirect
13. C2×#22627545C2semidirect
14. #102×D293C2semidirect
15. #447×C293C2semidirect
19. C2×#17989787C22semidirect
20. C22×#14556873C22semidirect
21. C2×C8×D293C22semidirect
22. #22627623C22semidirect
30. #22627595C22semidirect
34. D4×Dic293C22semidirect
36. C2×C4⋊Dic293C22semidirect
37. C4⋊C4×D293C22semidirect
38. #22627558C22semidirect
39. #22627558C22semidirect
40. #22627557C22semidirect
41. #22627553C22semidirect
42. #22627546C22semidirect
43. #22627546C22semidirect
46. #22627545C22semidirect
47. #22627545C22semidirect
48. #22627545C22semidirect
49. #22627544C22semidirect
50. #22627536C22semidirect
51. C8×Dic293C22semidirect
54. C2×D8×C293C22semidirect
55. #121×C293C22semidirect
57. #102×C293C22semidirect
58. C22⋊C8×C293C22semidirect
127. C22⋊D293D8semidirect
156. D4×C293#41semidirect
204. C293#3294semidirect
216. #447D293semidirect
227. C2×D8C2×D293semidirect
239. #121C2×D293semidirect
260. #102C2×D293semidirect
262. C22⋊C8C2×D293semidirect
347. D4#17989801semidirect

Maximal subgroups

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

subgroupindex
#340367792
D4×C22⋊D2932
#340364742
#340364432
#340364412
#340364072
#340363632
#340363622
#340363222
#340362612
D8×Dic2932
#340361922
C2×#226275452
#102×D2932
#447×C2932
#3294293