Finite Group Databasebeta

← #548×D293 #49172247

Subgroups — #548×D293 #49172247

Order 37504.

1620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D293C211yesmaximal, characteristic, complemented
2C22×Q8×D293C211yesmaximal, characteristic, complemented
3#34036791C211yesmaximal, characteristic, complemented
4#34036790C211yesmaximal, characteristic, complemented
5#34036789C213yesmaximal, complemented
6#34036788C213yesmaximal, complemented
7#34036787C213yesmaximal, complemented
8#34036786C211yesmaximal, characteristic, complemented
9#34036785C213yesmaximal, complemented
10#124×D293C213yesmaximal, complemented
11C22⋊Q8×D293C213yesmaximal, complemented
12#121×D293C213yesmaximal, complemented
13C4×Q8×D293C211yesmaximal, characteristic, complemented
14C4×D4×D293C213yesmaximal, complemented
15#548×C293C211yesmaximal, characteristic, complemented
16C2×#17989803C2211yescharacteristic, complemented
17C2×#17989802C2213yescomplemented
18C2×#17989801C2213yescomplemented
19#41×D293—28no—
20C22×Dic586C2213yescomplemented
21C2×Q8×D293—28no—
22C2×Q8×D293C2213yes—
23C2×Q8×D293C2211yescharacteristic
24C2×Q8×D293C2211yescharacteristic, complemented
25C2×Q8×D293C2213yescomplemented
26C2×D4×D293C2213yes—
27C2×D4×D293C2213yes—
28C22×C4×D293C2213yes—
29C22×C4×D293C2213yes—
30#22627613C2213yescomplemented
31#22627612C2213yescomplemented
32#22627611C2213yescomplemented
33#22627610C2216yescomplemented
34#22627610C2216yescomplemented
35#22627604C2213yescomplemented
36#22627603C2213yescomplemented
37#22627602C2216yescomplemented
38#22627601C2216yescomplemented
39#22627600C2213yescomplemented
40#22627599C2213yescomplemented
41#22627598C2213yescomplemented
42#22627597C2216yescomplemented
43#22627596C2216yescomplemented
44#22627595C2213yescomplemented
45Q8×Dic293C2211yescharacteristic, complemented
46C4×Dic586C2213yescomplemented
47#22627589C2213yescomplemented
48C4×D1172C2213yescomplemented
49D4×Dic293C2213yescomplemented
50#22627586C2213yescomplemented
51C4×C22⋊D293C2213yescomplemented
52C4×C22⋊D293C2213yescomplemented
53#22627584C2213yescomplemented
54#22627584C2213yescomplemented
55C4⋊C4×D293C2213yes—
56C4⋊C4×D293C2213yes—
57C22⋊C4×D293C2211yescharacteristic
58C22⋊C4×D293C2213yes—
59C22⋊C4×D293C2216yes—
60C42×D293C2213yes—
61C2×#41×C293C2211yescharacteristic, complemented
62C22×Q8×C293C2211yescharacteristic, complemented
63#124×C293C2213yescomplemented
64C22⋊Q8×C293C2213yescomplemented
65#121×C293C2213yescomplemented
66C4×Q8×C293C2211yescharacteristic, complemented
67C4×D4×C293C2213yescomplemented
68C23×D293C2313yes—
69C23×D293C2311yescharacteristic
70#17989803—24no—
71#17989802—212no—
72#17989801—212no—
73C2×Dic586—212no—
74C2×Dic586C2316yes—
75C2×Dic586C2313yes—
76C2×Dic586C2313yes—
77Q8×D293—212no—
78Q8×D293—212no—
79Q8×D293—24no—
80Q8×D293D418yescomplemented
81C2×D1172C2313yes—
82C2×D1172C2313yes—
83C2×C22⋊D293C2313yes—
84C2×C22⋊D293C2313yes—
85C2×C22⋊D293C2316yes—
86D4×D293—212no—
87D4×D293—212no—
88C22×Dic293C2313yes—
89C22×Dic293C2313yes—
90C2×C4×D293—212no—
91C2×C4×D293—212no—
92C2×C4×D293C2313yes—
93C2×C4×D293C2313yes—
94C2×C4×D293C2313yes—
95C2×C4×D293C2313yes—
96C2×C4×D293C2311yescharacteristic
97C2×C4×D293C2313yes—
98C2×C4×D293C2313yes—
99C2×C4×D293C2311yescharacteristic
100C2×C4×D293C2313yes—
101C4⋊Dic293C2313yes—
102C4⋊Dic293C2313yes—
103#17989781C2313yes—
104#17989781C2313yes—
105#17989781C2316yes—
106C22⋊Dic293C2311yescharacteristic
107C22⋊Dic293C2313yes—
108C22⋊Dic293C2316yes—
109#17989779C2311yescharacteristic
110#17989779C2313yes—
111#17989779C2311yescharacteristic
112#17989779C2313yes—
113#17989779C2316yes—
114#17989779C2316yes—
115C4×Dic293C2313yes—
116C4×Dic293C2313yes—
117C4×Dic293C2313yes—
118#41×C293—24no—
119C2×Q8×C293—24no—
120C2×Q8×C293C2313yes—
121C2×Q8×C293C2311yescharacteristic
122C2×D4×C293C2313yes—
123C2×D4×C293C2313yes—
124C22×C4×C293C2313yes—
125C22×C4×C293C2313yes—
126C4⋊C4×C293C2313yes—
127C4⋊C4×C293C2313yes—
128C22⋊C4×C293C2311yescharacteristic
129C22⋊C4×C293C2313yes—
130C22⋊C4×C293C2316yes—
131C42×C293C2313yes—
132C22×D293—22no—
133C22×D293—22no—
134C22×D293—26no—
135C22×D293—26no—
136C22×D293—26no—
137C22×D293#4114yescomplemented
138C22×D293C2413yes—
139C22×D293C2411yescharacteristic
140C22×D293C2411yescharacteristic
141Dic586—26no—
142Dic586—212no—
143Dic586C2×D4112yescomplemented
144D1172—26no—
145D1172—26no—
146C22⋊D293—26no—
147C22⋊D293—26no—
148C22⋊D293—212no—
149C2×Dic293—26no—
150C2×Dic293—26no—
151C2×Dic293C2411yescharacteristic
152C2×Dic293C2413yes—
153C2×Dic293C2413yes—
154C2×Dic293C2411yescharacteristic
155C2×Dic293C2413yes—
156C4×D293—22no—
157C4×D293—26no—
158C4×D293—26no—
159C4×D293—22no—
160C4×D293—26no—
161C4×D293—26no—
162C4×D293—26no—
163C4×D293—26no—
164C4×D293C2×D4112yes—
165C23×C293C2413yes—
166C23×C293C2411yescharacteristic
167Q8×C293—26no—
168Q8×C293C2×D414yescomplemented
169D4×C293—26no—
170D4×C293—26no—
171C2×C4×C293—26no—
172C2×C4×C293—26no—
173C2×C4×C293C2411yescharacteristic
174C2×C4×C293C2413yes—
175C2×C4×C293C2413yes—
176C2×C4×C293C2411yescharacteristic
177C2×C4×C293C2413yes—
178C22×C293—21no—
179C22×C293—21no—
180C22×C293—23no—
181C22×C293—23no—
182C22×C293—23no—
183C22×C293C2×#4112yescomplemented
184C22×C293C2511yescharacteristic
185C2×D293—21no—
186C2×D293—21no—
187C2×D293—28no—
188C2×D293—23no—
189C2×D293—23no—
190C2×D293—23no—
191C2×D293—412no—
192C2×D293C22×D412yes—
193C2×D293C2×#4112yes—
194C2×D293C2×#4112yescomplemented
195C2×D2932−1+412yes—
196C4×C293—21no—
197C4×C293—23no—
198C4×C293—23no—
199C4×C293—21no—
200C4×C293C22×D416yes—
201Dic293—21no—
202Dic293—23no—
203Dic293—23no—
204Dic293—21no—
205Dic293C22×D416yes—
206C2×C293—22no—
207C2×C293—43no—
208C2×C293C23×D411yescharacteristic
209C2×C293C22×#4111yescharacteristic
210C2×C293C2×2−1+411yescharacteristic
211D293—22no—
212D293—43no—
213D293#54814yesdirect product factor
214C293C2×#54811yescharacteristic, complemented, Sylow
215C2×#548—2931nomaximal, Sylow
216C22×#41—2931no—
217C23×Q8—2931no—
218#548—2931no—
219#548—2931no—
220#548—2933no—
221#548—2933no—
222#548—2933no—
223#548—2931no—
224#548—2933no—
225#548D29311yescharacteristic, direct product factor
226C2×#124—2933no—
227C2×C22⋊Q8—2933no—
228C2×#121—2933no—
229C2×C4×Q8—2931no—
230C2×C4×D4—2933no—
231C2×#41—2931no—
232C2×#41—2933no—
233C2×#41—2933no—
234C2×#41—5868no—
235C2×#41C2×D29311yescharacteristic, complemented
236C22×Q8—2931no—
237C22×Q8—2933no—
238C22×Q8—2933no—
239C22×Q8—2931no—
240C22×Q8—2933no—
241C22×Q8—5868no—
242C22×Q8C2×D29311yescharacteristic, complemented
243C22×D4—2933no—
244C22×D4—2933no—
245C23×C4—2933no—
246C23×C4—2933no—
247#124—2933no—
248#124—2933no—
249#124—2936no—
250#124—2936no—
251#124—2933no—
252#124C2×D29313yescomplemented
253C22⋊Q8—2933no—
254C22⋊Q8—2933no—
255C22⋊Q8—2936no—
256C22⋊Q8—2933no—
257C22⋊Q8—2936no—
258C22⋊Q8C2×D29313yescomplemented
259#121—2933no—
260#121—2936no—
261#121—2933no—
262#121—2933no—
263#121—2936no—
264#121C2×D29313yescomplemented
265C4×Q8—2931no—
266C4×Q8—2933no—
267C4×Q8—2933no—
268C4×Q8C2×D29311yescharacteristic, complemented
269C4×D4—2933no—
270C4×D4—2933no—
271C4×D4—2933no—
272C4×D4—2933no—
273C4×D4—2933no—
274C4×D4—2933no—
275C4×D4—2933no—
276C4×D4C2×D29313yescomplemented
277C2×C4⋊C4—2933no—
278C2×C4⋊C4—2933no—
279C2×C22⋊C4—2931no—
280C2×C22⋊C4—2933no—
281C2×C22⋊C4—2936no—
282C2×C42—2933no—
283C24—2931no—
284C24—2933no—
285#41—24no—
286#41—58612no—
287#41—58612no—
288#41—5864no—
289C2×Q8—24no—
290C2×Q8—2938no—
291C2×Q8—2933no—
292C2×Q8—2936no—
293C2×Q8—2933no—
294C2×Q8—58612no—
295C2×Q8—58612no—
296C2×Q8—58612no—
297C2×Q8—5864no—
298C2×Q8C22×D29313yes—
299C2×Q8C22×D29311yescharacteristic
300C2×D4—2933no—
301C2×D4—2933no—
302C2×D4—2936no—
303C2×D4—2933no—
304C2×D4—2933no—
305C2×D4—58612no—
306C2×D4—58612no—
307C2×D4C22×D29313yes—
308C2×D4C22×D29313yes—
309C22×C4—2933no—
310C22×C4—2933no—
311C22×C4—2933no—
312C22×C4—2931no—
313C22×C4—2933no—
314C22×C4—2933no—
315C22×C4—2931no—
316C22×C4—2933no—
317C22×C4—2933no—
318C22×C4—2933no—
319C22×C4—2933no—
320C22×C4—58612no—
321C22×C4—58612no—
322C22×C4C22×D29313yes—
323C22×C4C22×D29313yes—
324C4⋊C4—2933no—
325C4⋊C4—2933no—
326C4⋊C4—2933no—
327C4⋊C4—2936no—
328C4⋊C4—2933no—
329C4⋊C4C22×D29313yes—
330C4⋊C4C22×D29313yes—
331C22⋊C4—2931no—
332C22⋊C4—2933no—
333C22⋊C4—2936no—
334C22⋊C4—2931no—
335C22⋊C4—2931no—
336C22⋊C4—2933no—
337C22⋊C4—2933no—
338C22⋊C4—2936no—
339C22⋊C4—2936no—
340C22⋊C4C22×D29311yescharacteristic
341C22⋊C4C22×D29313yes—
342C22⋊C4C22×D29316yes—
343C42—2933no—
344C42—2933no—
345C42—2933no—
346C42C22×D29313yes—
347C23—2931no—
348C23—2934no—
349C23—2931no—
350C23—2933no—
351C23—5862no—
352C23—5862no—
353C23—5866no—
354C23—5866no—
355C23—5866no—
356C23C23×D29313yes—
357C23C23×D29311yescharacteristic
358Q8—26no—
359Q8—29312no—
360Q8—58612no—
361Q8—5866no—
362Q8D4×D29314yescomplemented
363D4—26no—
364D4—26no—
365D4—5866no—
366D4—58612no—
367D4—5866no—
368D4—5866no—
369D4—5866no—
370C2×C4—26no—
371C2×C4—26no—
372C2×C4—2933no—
373C2×C4—29312no—
374C2×C4—2931no—
375C2×C4—2933no—
376C2×C4—2933no—
377C2×C4—2931no—
378C2×C4—5866no—
379C2×C4—5866no—
380C2×C4—5862no—
381C2×C4—5866no—
382C2×C4—5866no—
383C2×C4—5862no—
384C2×C4—5866no—
385C2×C4—5866no—
386C2×C4—5866no—
387C2×C4—5866no—
388C2×C4C23×D29311yescharacteristic
389C2×C4C23×D29313yes—
390C2×C4C23×D29313yes—
391C2×C4C23×D29311yescharacteristic
392C2×C4C23×D29313yes—
393C22—21no—
394C22—21no—
395C22—23no—
396C22—23no—
397C22—23no—
398C22—2932no—
399C22—2932no—
400C22—2932no—
401C22—2932no—
402C22—5868no—
403C22—5861no—
404C22—5861no—
405C22—5863no—
406C22—5863no—
407C22—5863no—
408C22—117212no—
409C22#41×D29312yescomplemented
410C22C24×D29311yescharacteristic
411C4—21no—
412C4—23no—
413C4—23no—
414C4—21no—
415C4—2936no—
416C4—5861no—
417C4—5863no—
418C4—5863no—
419C4—5861no—
420C4C2×D4×D29316yes—
421C2—22no—
422C2—43no—
423C2—2934no—
424C2—5862no—
425C2—11723no—
426C2C22×D4×D29311yescharacteristic
427C2C2×#41×D29311yescharacteristic
428C22−1+4×D29311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D293
commutator, socle, cosocleC22×C293C25
Fitting#548×C293C2
hypercenter#548D293
hypocenterC293C2×#548
LCSG ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#41×D293C2semidirect
2. C22×Q8×D293C2semidirect
3. #34036791C2semidirect
4. #34036790C2semidirect
5. #34036789C2semidirect
6. #34036788C2semidirect
7. #34036787C2semidirect
8. #34036786C2semidirect
9. #34036785C2semidirect
10. #124×D293C2semidirect
11. C22⋊Q8×D293C2semidirect
12. #121×D293C2semidirect
13. C4×Q8×D293C2semidirect
14. C4×D4×D293C2semidirect
15. #548×C293C2semidirect
16. C2×#17989803C22semidirect
17. C2×#17989802C22semidirect
18. C2×#17989801C22semidirect
20. C22×Dic586C22semidirect
24. C2×Q8×D293C22semidirect
25. C2×Q8×D293C22semidirect
30. #22627613C22semidirect
31. #22627612C22semidirect
32. #22627611C22semidirect
33. #22627610C22semidirect
34. #22627610C22semidirect
35. #22627604C22semidirect
36. #22627603C22semidirect
37. #22627602C22semidirect
38. #22627601C22semidirect
39. #22627600C22semidirect
40. #22627599C22semidirect
41. #22627598C22semidirect
42. #22627597C22semidirect
43. #22627596C22semidirect
44. #22627595C22semidirect
45. Q8×Dic293C22semidirect
46. C4×Dic586C22semidirect
47. #22627589C22semidirect
48. C4×D1172C22semidirect
49. D4×Dic293C22semidirect
50. #22627586C22semidirect
51. C4×C22⋊D293C22semidirect
52. C4×C22⋊D293C22semidirect
53. #22627584C22semidirect
54. #22627584C22semidirect
61. C2×#41×C293C22semidirect
62. C22×Q8×C293C22semidirect
63. #124×C293C22semidirect
64. C22⋊Q8×C293C22semidirect
65. #121×C293C22semidirect
66. C4×Q8×C293C22semidirect
67. C4×D4×C293C22semidirect
80. Q8×D293D4semidirect
137. C22×D293#41semidirect
143. Dic586C2×D4semidirect
168. Q8×C293C2×D4semidirect
183. C22×C293C2×#41semidirect
194. C2×D293C2×#41semidirect
213. D293#548direct (N × H)
214. C293C2×#548semidirect
225. #548D293direct (N × H)
235. C2×#41C2×D293semidirect
242. C22×Q8C2×D293semidirect
252. #124C2×D293semidirect
258. C22⋊Q8C2×D293semidirect
264. #121C2×D293semidirect
268. C4×Q8C2×D293semidirect
276. C4×D4C2×D293semidirect
362. Q8D4×D293semidirect
409. C22#41×D293semidirect

Maximal subgroups

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

subgroupindex
C2×#41×D2932
C22×Q8×D2932
#340367912
#340367902
#340367892
#340367882
#340367872
#340367862
#340367852
#124×D2932
C22⋊Q8×D2932
#121×D2932
C4×Q8×D2932
C4×D4×D2932
#548×C2932
C2×#548293