Finite Group Databasebeta

← #18004066

Subgroups — #18004066

Order 4736.

484 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924568C211yesmaximal, characteristic, complemented
2C2×#11924565C211yesmaximal, characteristic, complemented
3#14558082C211yesmaximal, characteristic
4C4×Q8×D37C211yesmaximal, characteristic, complemented
5#14557756C211yesmaximal, characteristic, complemented
6#14557755C211yesmaximal, characteristic, complemented
7#14557752C211yesmaximal, characteristic, complemented
8#14557742C211yesmaximal, characteristic, complemented
9#14557741C211yesmaximal, characteristic, complemented
10#14557732C211yesmaximal, characteristic, complemented
11#14557731C211yesmaximal, characteristic, complemented
12#14557555C211yesmaximal, characteristic, complemented
13#14557533C211yesmaximal, characteristic, complemented
14#14557531C211yesmaximal, characteristic, complemented
15C37×#464C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596964C2211yescharacteristic
18C2×Q8×D37C2211yescharacteristic
19#11924568—24no—
20#11924565—24no—
21C2×Dic148C2211yescharacteristic
22C2×#10596942C2211yescharacteristic
23C2×#10596942C2211yescharacteristic
24C2×#10596930C2211yescharacteristic
25C2×#10596940C2211yescharacteristic
26C2×#10596941C2211yescharacteristic
27C2×#10596929C2211yescharacteristic
28C2×#10596929C2211yescharacteristic
29#11924534C2211yescharacteristic
30#11924532C2211yescharacteristic
31#11924524C2211yescharacteristic
32#11924509—21no—
33#11924509—21no—
34Q8×Dic37C2211yescharacteristic
35C4×Dic74—21no—
36C4×Dic74C2211yescharacteristic
37#11924501—21no—
38#11924501C2211yescharacteristic
39#11924496—21no—
40#11924496—21no—
41C4⋊C4×D37—21no—
42C4⋊C4×D37C2211yescharacteristic
43C42×D37—21no—
44C42×D37C2211yescharacteristic
45C4⋊#64436C2211yescharacteristic
46#11924465C2211yescharacteristic
47#11924465C2211yescharacteristic
48#11924461C2211yescharacteristic
49#11924460C2211yescharacteristic
50#11924459C2211yescharacteristic
51#11924458C2211yescharacteristic
52#11924457C2211yescharacteristic
53#11924456C2211yescharacteristic
54C2×Q16×C37C2211yescharacteristic
55C2×SD16×C37C2211yescharacteristic
56#124×C37C2211yescharacteristic
57C4×Q8×C37C2211yescharacteristic
58C4⋊C8×C37C2211yescharacteristic
59#103×C37C2211yescharacteristic
60#102×C37C2211yescharacteristic
61C2×Q8×C37C2311yescharacteristic
62C2×Q8×C37C2311yescharacteristic
63C2×D4×C37C2311yescharacteristic
64C2×C22⋊D37—21no—
65C2×C22⋊D37—21no—
66C2×C22⋊D37—21no—
67C22×Dic37—21no—
68#10596966—22no—
69#10596966—22no—
70Q8×D37—22no—
71Q8×D37D414yescomplemented
72#10596964—22no—
73#10596964—22no—
74C2×D148—21no—
75C2×D148C2311yescharacteristic
76C2×C4×D37—21no—
77C2×C4×D37—21no—
78C2×C4×D37—21no—
79C2×C4×D37D411yescharacteristic
80C2×C4×D37D411yescharacteristic
81C2×C4×D37C2311yescharacteristic
82C2×Dic74—21no—
83C2×Dic74C2311yescharacteristic
84C2×Dic74C2311yescharacteristic
85Q16×C37—22no—
86SD16×C37—22no—
87C2×C8×C37C2311yescharacteristic
88C2×C8×C37C2311yescharacteristic
89C4⋊C4×C37—21no—
90C4⋊C4×C37C2311yescharacteristic
91C22⋊C4×C37—21no—
92C22⋊C4×C37—21no—
93C42×C37—21no—
94C42×C37C2311yescharacteristic
95#10596942—22no—
96#10596942—22no—
97#10596941—22no—
98#10596940—22no—
99#10596938—21no—
100#10596938—21no—
101C4⋊Dic37—21no—
102C4⋊Dic37C2311yescharacteristic
103#10596936—21no—
104#10596936—21no—
105#10596936—21no—
106#10596936—21no—
107#10596936—21no—
108C4×Dic37—21no—
109C4×Dic37—21no—
110C4×Dic37—21no—
111C4×Dic37D411yescharacteristic
112C4×Dic37D411yescharacteristic
113C4×Dic37C2311yescharacteristic
114C2×#64436C2311yescharacteristic
115C2×#64436C2311yescharacteristic
116Dic148—22no—
117#10596930—22no—
118#10596929—22no—
119#10596929—22no—
120C23×C37—21no—
121C22×D37—21no—
122C22×D37C2×D411yescharacteristic
123Q8×C37—21no—
124Q8×C37—21no—
125Q8×C37—21no—
126Q8×C37C2×D412yes—
127D4×C37—21no—
128D4×C37—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37—21no—
132C2×C4×C37C2×D411yescharacteristic
133C2×C4×C37C2×D411yescharacteristic
134C2×C4×C37C2411yescharacteristic
135C22⋊D37—42no—
136C22⋊D37—42no—
137C22⋊D37—42no—
138C2×Dic37—21no—
139C2×Dic37—21no—
140C2×Dic37—21no—
141C2×Dic37—42no—
142C2×Dic37C2×D411yescharacteristic
143C2×Dic37C2×D411yescharacteristic
144C2×Dic37C2×D411yescharacteristic
145D148—21no—
146D148—21no—
147D148—42no—
148C4×D37—24no—
149C4×D37—22no—
150C4×D37—41no—
151C4×D37—42no—
152C4×D37—42no—
153C4×D37C2×D412yes—
154C4×D37#4112yes—
155Dic74—21no—
156Dic74—24no—
157Dic74—21no—
158Dic74—21no—
159Dic74C2×D412yes—
160C8×C37—21no—
161C8×C37—21no—
162#64436—21no—
163#64436—21no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37—41no—
167C22×C37C22×D411yescharacteristic
168C2×D37—21no—
169C2×D37—21no—
170C2×D37—41no—
171C2×D37—41no—
172C2×D37—41no—
173C2×D37#12112yes—
174C4×C37—22no—
175C4×C37—21no—
176C4×C37—21no—
177C4×C37—41no—
178C4×C37—41no—
179C4×C37C22×D411yescharacteristic
180C4×C37C2×#4111yescharacteristic
181Dic37—22no—
182Dic37—21no—
183Dic37—41no—
184Dic37—41no—
185Dic37#12112yes—
186Dic37#13712yescomplemented
187#3037—371nomaximal, Sylow
188C2×C37—81no—
189C2×C37C2×#12111yescharacteristic
190C2×C37C2×#13711yescharacteristic
191C2×C37#57511yescharacteristic
192D37—22no—
193D37—81no—
194C2×#137—371no—
195C2×#137—371no—
196#532—371no—
197C2×C4×Q8—371no—
198#464—371no—
199#464—371no—
200#464—371no—
201#464D3711yescharacteristic, complemented
202#462—371no—
203#462—371no—
204#460—371no—
205#460—371no—
206#423—371no—
207#417—371no—
208#417—371no—
209C37#303711yescharacteristic, complemented, Sylow
210C2×#41—371no—
211C2×#41—371no—
212C22×Q8—371no—
213#137—744no—
214#137—744no—
215C2×Q16—371no—
216C2×Q16—371no—
217C2×Q16—371no—
218C2×Q16C2×D3711yescharacteristic
219C2×SD16—371no—
220C2×SD16—371no—
221C2×SD16—371no—
222C2×SD16C2×D3711yescharacteristic
223C2×M16—371no—
224C2×M16—371no—
225C4⋊Q8—371no—
226#127—371no—
227#124—371no—
228#124C2×D3711yescharacteristic
229#121—741no—
230#121—741no—
231C4×Q8—371no—
232C4×Q8—371no—
233C4×Q8—371no—
234C4×Q8—741no—
235C4×Q8—741no—
236C4×Q8C2×D3711yescharacteristic
237C4×D4—741no—
238C4×D4—741no—
239C2×C4⋊C4—371no—
240C2×C4⋊C4—741no—
241C2×C42—371no—
242C2×C42—741no—
243C4⋊C8—371no—
244C4⋊C8—371no—
245C4⋊C8—371no—
246C4⋊C8C2×D3711yescharacteristic
247#103—371no—
248#103—371no—
249#103—371no—
250#103C2×D3711yescharacteristic
251#102—371no—
252#102—371no—
253#102—371no—
254#102C2×D3711yescharacteristic
255#41—742no—
256#41—742no—
257#41—742no—
258#41—742no—
259C2×Q8—374no—
260C2×Q8—371no—
261C2×Q8—371no—
262C2×Q8—741no—
263C2×Q8—742no—
264C2×Q8C22×D3711yescharacteristic
265C2×Q8C22×D3711yescharacteristic
266C2×D4—371no—
267C2×D4—741no—
268C2×D4—741no—
269C2×D4—741no—
270C2×D4—741no—
271C2×D4C22×D3711yescharacteristic
272C22×C4—371no—
273C22×C4—371no—
274C22×C4—371no—
275C22×C4—741no—
276C22×C4—741no—
277C22×C4—741no—
278C22×C4—741no—
279Q16—22no—
280Q16—742no—
281Q16—742no—
282Q16—742no—
283SD16—22no—
284SD16—742no—
285SD16—742no—
286SD16—742no—
287M16—742no—
288M16—742no—
289C2×C8—371no—
290C2×C8—371no—
291C2×C8C22×D3711yescharacteristic
292C2×C8C22×D3711yescharacteristic
293C4⋊C4—21no—
294C4⋊C4—371no—
295C4⋊C4—741no—
296C4⋊C4—741no—
297C4⋊C4—741no—
298C4⋊C4—741no—
299C4⋊C4—741no—
300C4⋊C4—741no—
301C4⋊C4C22×D3711yescharacteristic
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—741no—
305C22⋊C4—741no—
306C42—21no—
307C42—371no—
308C42—371no—
309C42—371no—
310C42—741no—
311C42—741no—
312C42—741no—
313C42C22×D3711yescharacteristic
314C23—21no—
315C23—371no—
316C23—741no—
317Q8—21no—
318Q8—21no—
319Q8—21no—
320Q8—372no—
321Q8—744no—
322Q8—741no—
323Q8—741no—
324Q8—741no—
325Q8D4×D3712yes—
326D4—21no—
327D4—21no—
328D4—741no—
329D4—741no—
330D4—1482no—
331D4—1482no—
332D4—1482no—
333D4—1482no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—371no—
338C2×C4—371no—
339C2×C4—372no—
340C2×C4—372no—
341C2×C4—371no—
342C2×C4—742no—
343C2×C4—744no—
344C2×C4—741no—
345C2×C4—741no—
346C2×C4—741no—
347C2×C4—1481no—
348C2×C4—1482no—
349C2×C4—1482no—
350C2×C4—1482no—
351C2×C4D4×D3711yescharacteristic
352C2×C4D4×D3711yescharacteristic
353C2×C4C23×D3711yescharacteristic
354C8—21no—
355C8—21no—
356C8—741no—
357C8—741no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—372no—
362C22—741no—
363C22—741no—
364C22—1481no—
365C22—1481no—
366C22—1481no—
367C22C2×D4×D3711yescharacteristic
368C4—22no—
369C4—21no—
370C4—21no—
371C4—41no—
372C4—41no—
373C4—372no—
374C4—372no—
375C4—742no—
376C4—741no—
377C4—1481no—
378C4—1481no—
379C4C2×D4×D3711yescharacteristic
380C4#41×D3711yescharacteristic
381C2—81no—
382C2—2961no—
383C2—742no—
384C2#121×D3711yescharacteristic
385C2#137×D3711yescharacteristic
386C2#1455833011yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#464C2
socleC22×C37C22×D4
prime radical#14558082C2
hypercenter#464D37
hypocenterC37#3037
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#11924568C2semidirect
2. C2×#11924565C2semidirect
4. C4×Q8×D37C2semidirect
5. #14557756C2semidirect
6. #14557755C2semidirect
7. #14557752C2semidirect
8. #14557742C2semidirect
9. #14557741C2semidirect
10. #14557732C2semidirect
11. #14557731C2semidirect
12. #14557555C2semidirect
13. #14557533C2semidirect
14. #14557531C2semidirect
15. C37×#464C2semidirect
71. Q8×D37D4semidirect
186. Dic37#137semidirect
201. #464D37semidirect
209. C37#3037semidirect

Maximal subgroups

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

subgroupindex
C2×#119245682
C2×#119245652
#145580822
C4×Q8×D372
#145577562
#145577552
#145577522
#145577422
#145577412
#145577322
#145577312
#145575552
#145575332
#145575312
C37×#4642
#303737