Finite Group Databasebeta

← #18005348

Subgroups — #18005348

Order 4736.

468 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D37C211yesmaximal, characteristic, complemented
2#121×D37C211yesmaximal, characteristic
3#14557865C211yesmaximal, characteristic, complemented
4#14557862C211yesmaximal, characteristic, complemented
5#14557853C211yesmaximal, characteristic, complemented
6#14557850C211yesmaximal, characteristic, complemented
7#14557764C211yesmaximal, characteristic, complemented
8#14557762C211yesmaximal, characteristic, complemented
9#14557760C211yesmaximal, characteristic, complemented
10#14557685C211yesmaximal, characteristic, complemented
11#14557682C211yesmaximal, characteristic, complemented
12#14557673C211yesmaximal, characteristic, complemented
13#14557670C211yesmaximal, characteristic, complemented
14C2×#11924448C211yesmaximal, characteristic, complemented
15C37×#465C211yesmaximal, characteristic, complemented
16C2×Q8×D37C2211yescharacteristic, complemented
17C2×D4×D37—21no—
18C2×D4×D37C2211yescharacteristic
19C22×C4×D37C2211yescharacteristic
20C2×#10596930C2211yescharacteristic, complemented
21C2×#10596940C2211yescharacteristic, complemented
22C2×#10596941C2211yescharacteristic, complemented
23C22×#64436C2211yescharacteristic, complemented
24#11924516C2211yescharacteristic
25#11924515C2211yescharacteristic, complemented
26#11924514—21no—
27#11924513—21no—
28#11924512C2211yescharacteristic
29#11924511C2211yescharacteristic
30#11924510C2211yescharacteristic
31#11924509—21no—
32#11924508—21no—
33#11924507C2211yescharacteristic
34C4⋊C4×D37—21no—
35C4⋊C4×D37C2211yescharacteristic
36C4⋊C4×D37C2211yescharacteristic, complemented
37C22⋊C4×D37—21no—
38C22⋊C4×D37—21no—
39#11924468C2211yescharacteristic, complemented
40#11924467C2211yescharacteristic, complemented
41#11924467C2211yescharacteristic, complemented
42#11924461C2211yescharacteristic, complemented
43#11924460C2211yescharacteristic, complemented
44#11924459C2211yescharacteristic, complemented
45#11924458C2211yescharacteristic, complemented
46#11924457C2211yescharacteristic, complemented
47#11924456C2211yescharacteristic, complemented
48#11924448C2211yescharacteristic
49#11924448C2211yescharacteristic
50#11924448C2211yescharacteristic, complemented
51#11924448C2211yescharacteristic, complemented
52C2×SD16×C37C2211yescharacteristic, complemented
53C22×C8×C37C2211yescharacteristic, complemented
54C22⋊Q8×C37C2211yescharacteristic, complemented
55#121×C37C2211yescharacteristic
56#106×C37C2211yescharacteristic, complemented
57#103×C37C2211yescharacteristic, complemented
58#102×C37C2211yescharacteristic, complemented
59C23×D37—21no—
60C23×D37D411yescharacteristic
61C2×Q8×C37C2311yescharacteristic
62C2×D4×C37—21no—
63C2×D4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C2×C22⋊D37—21no—
68C22×Dic37D411yescharacteristic
69Q8×D37—41no—
70Q8×D37—41no—
71D4×D37—41no—
72D4×D37—41no—
73D4×D37—44no—
74C2×D148—21no—
75C2×D148C2311yescharacteristic
76C2×C4×D37—21no—
77C2×C4×D37—21no—
78C2×C4×D37—21no—
79C2×C4×D37—41no—
80C2×C4×D37—41no—
81C2×C4×D37D411yescharacteristic
82C2×C4×D37D411yescharacteristic
83C2×C4×D37C2311yescharacteristic
84C2×C4×D37C2311yescharacteristic
85C2×Dic74—21no—
86C2×Dic74C2311yescharacteristic
87SD16×C37—41no—
88C2×C8×C37—41no—
89C2×C8×C37C2311yescharacteristic
90C2×C8×C37C2311yescharacteristic
91C4⋊C4×C37—21no—
92C4⋊C4×C37C2311yescharacteristic
93C4⋊C4×C37C2311yescharacteristic
94C22⋊C4×C37—21no—
95C22⋊C4×C37—21no—
96C22⋊Dic37—21no—
97C22⋊Dic37—21no—
98#10596941—41no—
99#10596940—41no—
100#10596938—21no—
101#10596938—21no—
102#10596938—21no—
103#10596938—21no—
104C4⋊Dic37—21no—
105C4⋊Dic37C2311yescharacteristic
106C4⋊Dic37C2311yescharacteristic
107#10596936—21no—
108#10596936—21no—
109#10596936—21no—
110#10596936—21no—
111C2×#64436—41no—
112C2×#64436C2311yescharacteristic
113C2×#64436C2311yescharacteristic
114#10596930—41no—
115C23×C37—21no—
116C23×C37C2×D411yescharacteristic
117C22×D37—21no—
118C22×D37—41no—
119C22×D37—41no—
120C22×D37—42no—
121C22×D37—42no—
122C22×D37—42no—
123C22×D37SD1614yescomplemented
124C22×D37C2×D411yescharacteristic
125C22×D37C2×D411yescharacteristic
126Q8×C37—21no—
127Q8×C37—21no—
128D4×C37—21no—
129D4×C37—21no—
130D4×C37—42no—
131C2×C4×C37—21no—
132C2×C4×C37—21no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37C2×D411yescharacteristic
137C2×C4×C37C2411yescharacteristic
138C22⋊D37—42no—
139C22⋊D37—42no—
140C22⋊D37—42no—
141C2×Dic37—21no—
142C2×Dic37—21no—
143C2×Dic37—21no—
144C2×Dic37—41no—
145C2×Dic37C2×D411yescharacteristic
146C2×Dic37C2×D411yescharacteristic
147D148—21no—
148D148—21no—
149D148—42no—
150C4×D37—21no—
151C4×D37—21no—
152C4×D37—21no—
153C4×D37—21no—
154C4×D37—41no—
155C4×D37—41no—
156C4×D37—42no—
157C4×D37—42no—
158C4×D37—42no—
159Dic74—21no—
160Dic74—21no—
161Dic74—42no—
162C8×C37—21no—
163C8×C37—21no—
164#64436—21no—
165#64436—21no—
166C22×C37—21no—
167C22×C37—21no—
168C22×C37—41no—
169C22×C37—41no—
170C22×C37—41no—
171C22×C37C2×SD1612yes—
172C22×C37C22×D411yescharacteristic
173C2×D37—21no—
174C2×D37—21no—
175C2×D37—21no—
176C2×D37—21no—
177C2×D37—44no—
178C2×D37—41no—
179C2×D37—41no—
180C2×D37—41no—
181C2×D37—84no—
182C2×D37C2×SD1612yes—
183C2×D37C2×SD1612yes—
184C4×C37—21no—
185C4×C37—41no—
186C4×C37—41no—
187C4×C37—41no—
188C4×C37H(5,𝔽2)11yescharacteristic
189C4×C37H(5,𝔽2)11yescharacteristic
190Dic37—21no—
191Dic37—21no—
192Dic37—41no—
193Dic37—41no—
194Dic37—41no—
195#3187—371nomaximal, Sylow
196C2×C37—22no—
197C2×C37—81no—
198C2×C37#53411yescharacteristic
199C2×C37C22×SD1611yescharacteristic
200C2×C37#57511yescharacteristic
201D37—22no—
202D37—22no—
203D37—81no—
204C2×C22⋊Q8—371no—
205C2×#121—371no—
206#483—371no—
207#483—371no—
208#481—371no—
209#481—371no—
210#465—371no—
211#465—371no—
212#465—371no—
213#465D3711yescharacteristic, complemented
214#450—371no—
215#450—371no—
216#448—371no—
217#448—371no—
218C2×C22⋊C8—371no—
219C37#318711yescharacteristic, complemented, Sylow
220C22×Q8—371no—
221C22×D4—371no—
222C22×D4—741no—
223C23×C4—371no—
224C2×SD16—371no—
225C2×SD16—371no—
226C2×SD16—371no—
227C2×SD16C2×D3711yescharacteristic, complemented
228C22×C8—371no—
229C22×C8C2×D3711yescharacteristic, complemented
230C22⋊Q8—371no—
231C22⋊Q8—371no—
232C22⋊Q8—371no—
233C22⋊Q8—741no—
234C22⋊Q8—741no—
235C22⋊Q8C2×D3711yescharacteristic, complemented
236#121—371no—
237#121—371no—
238#121—371no—
239#121—741no—
240#121—741no—
241#121C2×D3711yescharacteristic
242C2×C4⋊C4—371no—
243C2×C4⋊C4—371no—
244C2×C4⋊C4—741no—
245C2×C22⋊C4—741no—
246C2×C22⋊C4—741no—
247#106—371no—
248#106—371no—
249#106—371no—
250#106C2×D3711yescharacteristic, complemented
251#103—371no—
252#103—371no—
253#103—371no—
254#103C2×D3711yescharacteristic, complemented
255#102—371no—
256#102—371no—
257#102—371no—
258#102C2×D3711yescharacteristic, complemented
259C22⋊C8—371no—
260C22⋊C8—371no—
261C22⋊C8—371no—
262C22⋊C8—371no—
263C24—371no—
264C24—741no—
265C2×Q8—371no—
266C2×Q8—741no—
267C2×Q8—1481no—
268C2×Q8—1481no—
269C2×Q8C22×D3711yescharacteristic
270C2×D4—21no—
271C2×D4—371no—
272C2×D4—741no—
273C2×D4—741no—
274C2×D4—741no—
275C2×D4—741no—
276C2×D4—1481no—
277C2×D4—1481no—
278C2×D4—1484no—
279C2×D4C22×D3711yescharacteristic
280C22×C4—371no—
281C22×C4—371no—
282C22×C4—371no—
283C22×C4—371no—
284C22×C4—371no—
285C22×C4—741no—
286C22×C4—741no—
287C22×C4—741no—
288C22×C4—1481no—
289C22×C4—1481no—
290C22×C4C22×D3711yescharacteristic
291SD16—41no—
292SD16—1481no—
293SD16—1481no—
294SD16—1481no—
295C2×C8—41no—
296C2×C8—371no—
297C2×C8—371no—
298C2×C8—1481no—
299C2×C8C22×D3711yescharacteristic
300C2×C8C22×D3711yescharacteristic
301C4⋊C4—21no—
302C4⋊C4—371no—
303C4⋊C4—371no—
304C4⋊C4—741no—
305C4⋊C4—741no—
306C4⋊C4—741no—
307C4⋊C4—741no—
308C4⋊C4—741no—
309C4⋊C4C22×D3711yescharacteristic
310C4⋊C4C22×D3711yescharacteristic
311C22⋊C4—21no—
312C22⋊C4—21no—
313C22⋊C4—741no—
314C22⋊C4—741no—
315C22⋊C4—741no—
316C22⋊C4—741no—
317C22⋊C4—741no—
318C22⋊C4—741no—
319C23—21no—
320C23—371no—
321C23—371no—
322C23—374no—
323C23—741no—
324C23—1481no—
325C23—1481no—
326C23—1482no—
327C23—1482no—
328C23—1482no—
329C23D4×D3711yescharacteristic
330Q8—21no—
331Q8—21no—
332Q8—741no—
333Q8—741no—
334Q8—1482no—
335D4—21no—
336D4—21no—
337D4—42no—
338D4—741no—
339D4—741no—
340D4—1482no—
341D4—1482no—
342D4—1482no—
343D4—1482no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—371no—
350C2×C4—371no—
351C2×C4—741no—
352C2×C4—741no—
353C2×C4—741no—
354C2×C4—741no—
355C2×C4—741no—
356C2×C4—741no—
357C2×C4—741no—
358C2×C4—1481no—
359C2×C4—1481no—
360C2×C4—1482no—
361C2×C4—1482no—
362C2×C4—1482no—
363C2×C4—1481no—
364C2×C4D4×D3711yescharacteristic
365C2×C4C23×D3711yescharacteristic
366C8—21no—
367C8—21no—
368C8—741no—
369C8—741no—
370C22—21no—
371C22—21no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—372no—
376C22—372no—
377C22—2964no—
378C22—741no—
379C22—741no—
380C22—741no—
381C22—741no—
382C22—1484no—
383C22—1481no—
384C22—1481no—
385C22—1481no—
386C22SD16×D3712yes—
387C22C2×D4×D3711yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—741no—
393C4—741no—
394C4—1481no—
395C4—1481no—
396C4—1481no—
397C4#1192458111yescharacteristic
398C4#1192458211yescharacteristic
399C2—22no—
400C2—81no—
401C2—2961no—
402C2—742no—
403C2—742no—
404C2#1455809111yescharacteristic
405C2C2×SD16×D3711yescharacteristic
406C2#1455833011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#465C2
socleC22×C37C22×D4
prime radical#121×D37C2
hypercenter#465D37
hypocenterC37#3187
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. C22⋊Q8×D37C2semidirect
3. #14557865C2semidirect
4. #14557862C2semidirect
5. #14557853C2semidirect
6. #14557850C2semidirect
7. #14557764C2semidirect
8. #14557762C2semidirect
9. #14557760C2semidirect
10. #14557685C2semidirect
11. #14557682C2semidirect
12. #14557673C2semidirect
13. #14557670C2semidirect
14. C2×#11924448C2semidirect
15. C37×#465C2semidirect
16. C2×Q8×D37C22semidirect
20. C2×#10596930C22semidirect
21. C2×#10596940C22semidirect
22. C2×#10596941C22semidirect
23. C22×#64436C22semidirect
25. #11924515C22semidirect
36. C4⋊C4×D37C22semidirect
39. #11924468C22semidirect
40. #11924467C22semidirect
41. #11924467C22semidirect
42. #11924461C22semidirect
43. #11924460C22semidirect
44. #11924459C22semidirect
45. #11924458C22semidirect
46. #11924457C22semidirect
47. #11924456C22semidirect
50. #11924448C22semidirect
51. #11924448C22semidirect
52. C2×SD16×C37C22semidirect
53. C22×C8×C37C22semidirect
54. C22⋊Q8×C37C22semidirect
56. #106×C37C22semidirect
57. #103×C37C22semidirect
58. #102×C37C22semidirect
123. C22×D37SD16semidirect
213. #465D37semidirect
219. C37#3187semidirect
227. C2×SD16C2×D37semidirect
229. C22×C8C2×D37semidirect
235. C22⋊Q8C2×D37semidirect
250. #106C2×D37semidirect
254. #103C2×D37semidirect
258. #102C2×D37semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D372
#121×D372
#145578652
#145578622
#145578532
#145578502
#145577642
#145577622
#145577602
#145576852
#145576822
#145576732
#145576702
C2×#119244482
C37×#4652
#318737