Finite Group Databasebeta

← #17997852

Subgroups — #17997852

Order 4736.

560 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic37C211yesmaximal, characteristic
2C2×#11924492C211yesmaximal, characteristic, complemented
3#14557475C211yesmaximal, characteristic, complemented
4#14557469C211yesmaximal, characteristic, complemented
5#14557466C211yesmaximal, characteristic, complemented
6#14557461C211yesmaximal, characteristic, complemented
7#14557461C211yesmaximal, characteristic, complemented
8#14557458C211yesmaximal, characteristic, complemented
9#14557447C211yesmaximal, characteristic
10C4⋊C4×Dic37C211yesmaximal, characteristic, complemented
11#14557384C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic37C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic37C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic37C211yesmaximal, characteristic, complemented
15C37×#394C211yesmaximal, characteristic
16C23×Dic37C2211yescharacteristic
17C23×Dic37C2211yescharacteristic
18D4×Dic37—24no—
19#11924492—24no—
20C2×C4⋊Dic37C2211yescharacteristic
21C2×C4⋊Dic37C2211yescharacteristic
22C2×#10596936C2211yescharacteristic
23C2×#10596936C2211yescharacteristic
24C2×#10596936C2211yescharacteristic
25C2×#10596936C2211yescharacteristic
26C2×C22⋊Dic37C2211yescharacteristic
27C2×C22⋊Dic37C2211yescharacteristic
28C2×C22⋊Dic37C2211yescharacteristic
29C2×C22⋊Dic37C2211yescharacteristic
30C2×C22⋊Dic37C2211yescharacteristic
31C2×C22⋊Dic37C2211yescharacteristic
32C2×C4×Dic37C2211yescharacteristic
33C2×C4×Dic37C2211yescharacteristic
34C2×C4×Dic37C2211yescharacteristic
35C2×C4×Dic37C2211yescharacteristic
36C2×C4×Dic37C2211yescharacteristic
37#11924443C2211yescharacteristic
38#11924443C2211yescharacteristic
39#11924443C2211yescharacteristic
40#11924443C2211yescharacteristic
41#11924443C2211yescharacteristic
42#11924443C2211yescharacteristic
43#11924443C2211yescharacteristic
44#11924443C2211yescharacteristic
45#11924443C2211yescharacteristic
46C22×D4×C37C2211yescharacteristic
47C2×C4⋊C4×C37C2211yescharacteristic
48C2×C22⋊C4×C37C2211yescharacteristic
49C2×C22⋊C4×C37C2211yescharacteristic
50C2×C22⋊C4×C37C2211yescharacteristic
51C2×C22⋊C4×C37C2211yescharacteristic
52#95×C37C2211yescharacteristic
53C24×C37C2311yescharacteristic
54C24×C37C2311yescharacteristic
55C2×D4×C37—22no—
56C2×D4×C37—22no—
57C2×D4×C37—22no—
58C22×C4×C37C2311yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C22×C4×C37C2311yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C22×Dic37—22no—
64C22×Dic37—22no—
65C22×Dic37—22no—
66C22×Dic37—22no—
67C22×Dic37—22no—
68C22×Dic37D414yes—
69C22×Dic37C2311yescharacteristic
70C22×Dic37C2311yescharacteristic
71C22×Dic37C2311yescharacteristic
72C22×Dic37C2311yescharacteristic
73C22×Dic37C2311yescharacteristic
74C22×Dic37C2311yescharacteristic
75C22×Dic37C2311yescharacteristic
76C22×Dic37C2311yescharacteristic
77C4⋊C4×C37—22no—
78C22⋊C4×C37—22no—
79C22⋊C4×C37—22no—
80C22⋊C4×C37—22no—
81C22⋊C4×C37—22no—
82C22⋊Dic37—22no—
83C22⋊Dic37—22no—
84C22⋊Dic37—22no—
85C22⋊Dic37—22no—
86C22⋊Dic37—22no—
87C22⋊Dic37—22no—
88C4⋊Dic37—22no—
89C4⋊Dic37—22no—
90#10596936—22no—
91#10596936—22no—
92#10596936—22no—
93#10596936—22no—
94C4×Dic37—22no—
95C4×Dic37—22no—
96C4×Dic37—22no—
97C4×Dic37—22no—
98C4×Dic37—22no—
99C23×C37—21no—
100C23×C37—21no—
101C23×C37—21no—
102C23×C37—21no—
103C23×C37—21no—
104C23×C37—21no—
105C23×C37—21no—
106C23×C37—21no—
107C23×C37—21no—
108C23×C37—21no—
109C23×C37—21no—
110C23×C37—21no—
111C23×C37C2×D412yes—
112C23×C37#4112yes—
113C23×C37C2411yescharacteristic
114D4×C37—28no—
115C2×C4×C37—21no—
116C2×C4×C37—21no—
117C2×C4×C37—21no—
118C2×C4×C37—21no—
119C2×C4×C37—21no—
120C2×C4×C37—21no—
121C2×C4×C37—21no—
122C2×C4×C37—21no—
123C2×C4×C37—21no—
124C2×C4×C37—21no—
125C2×C4×C37—21no—
126C2×C4×C37—21no—
127C2×C4×C37—21no—
128C2×C4×C37#4112yes—
129C2×C4×C37#4112yes—
130C2×Dic37—21no—
131C2×Dic37—21no—
132C2×Dic37—21no—
133C2×Dic37—21no—
134C2×Dic37—28no—
135C2×Dic37—21no—
136C2×Dic37—21no—
137C2×Dic37—21no—
138C2×Dic37—21no—
139C2×Dic37—21no—
140C2×Dic37—21no—
141C2×Dic37—21no—
142C2×Dic37—21no—
143C2×Dic37—21no—
144C2×Dic37—21no—
145C2×Dic37—21no—
146C2×Dic37—21no—
147C2×Dic37—21no—
148C2×Dic37—21no—
149C2×Dic37—21no—
150C2×Dic37—44no—
151C2×Dic37C2×D412yes—
152C2×Dic37C2×D412yes—
153C2×Dic37#4112yes—
154C2×Dic37#4112yes—
155C2×Dic37#4112yes—
156C22×C37—22no—
157C22×C37—22no—
158C22×C37—22no—
159C22×C37—22no—
160C22×C37—22no—
161C22×C37—22no—
162C22×C37—41no—
163C22×C37—41no—
164C22×C37—41no—
165C22×C37—41no—
166C22×C37—41no—
167C22×C37—41no—
168C22×C37—41no—
169C22×C37—41no—
170C22×C37C22×D411yescharacteristic
171C22×C37C2×#4111yescharacteristic
172C22×C37C2×#4111yescharacteristic
173C22×C37C2×#4111yescharacteristic
174C22×C37C2×#4111yescharacteristic
175C22×C37C2×#4111yescharacteristic
176C22×C37C2×#4111yescharacteristic
177C4×C37—22no—
178C4×C37—22no—
179C4×C37—41no—
180C4×C37—41no—
181C4×C37—41no—
182Dic37—22no—
183Dic37—22no—
184Dic37—41no—
185Dic37—41no—
186Dic37—41no—
187Dic37—41no—
188Dic37—41no—
189Dic37#12314yes—
190#2395—371nomaximal, Sylow
191C2×C37—42no—
192C2×C37—42no—
193C2×C37C2×#12311yescharacteristic
194C2×C37#52511yescharacteristic
195C2×C37#52911yescharacteristic
196C2×C37#52911yescharacteristic
197C2×C37#52911yescharacteristic
198C2×C37#52911yescharacteristic
199C2×C37#53211yescharacteristic
200C2×C4×D4—371no—
201C2×#117—371no—
202#400—371no—
203#399—371no—
204#398—371no—
205#397—371no—
206#397—371no—
207#397—371no—
208#394—371no—
209#394D3711yescharacteristic
210C4×C4⋊C4—371no—
211C4×C4⋊C4—371no—
212C4×C22⋊C4—371no—
213C4×C22⋊C4—371no—
214C4×C22⋊C4—371no—
215C37#239511yescharacteristic, complemented, Sylow
216C22×D4C2×D3711yescharacteristic
217C23×C4—371no—
218C23×C4—371no—
219C4×D4—744no—
220#117—744no—
221C2×C4⋊C4—371no—
222C2×C4⋊C4—371no—
223C2×C4⋊C4—371no—
224C2×C4⋊C4—371no—
225C2×C4⋊C4—371no—
226C2×C4⋊C4—371no—
227C2×C4⋊C4C2×D3711yescharacteristic
228C2×C22⋊C4—371no—
229C2×C22⋊C4—371no—
230C2×C22⋊C4—371no—
231C2×C22⋊C4—371no—
232C2×C22⋊C4—371no—
233C2×C22⋊C4—371no—
234C2×C22⋊C4C2×D3711yescharacteristic
235C2×C22⋊C4C2×D3711yescharacteristic
236C2×C22⋊C4C2×D3711yescharacteristic
237C2×C22⋊C4C2×D3711yescharacteristic
238C2×C42—371no—
239C2×C42—371no—
240C2×C42—371no—
241C2×C42—371no—
242C2×C42—371no—
243#95—371no—
244#95—371no—
245#95—371no—
246#95—371no—
247#95—371no—
248#95—371no—
249#95—371no—
250#95—371no—
251#95—371no—
252#95C2×D3711yescharacteristic
253C24C22×D3711yescharacteristic
254C24C22×D3711yescharacteristic
255C2×D4—22no—
256C2×D4—22no—
257C2×D4—22no—
258C22×C4—371no—
259C22×C4—374no—
260C22×C4—371no—
261C22×C4—371no—
262C22×C4—371no—
263C22×C4—371no—
264C22×C4—371no—
265C22×C4—371no—
266C22×C4—371no—
267C22×C4—742no—
268C22×C4—742no—
269C22×C4—742no—
270C22×C4—742no—
271C22×C4—742no—
272C22×C4C22×D3711yescharacteristic
273C22×C4C22×D3711yescharacteristic
274C22×C4C22×D3711yescharacteristic
275C22×C4C22×D3711yescharacteristic
276C22×C4C22×D3711yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—742no—
279C4⋊C4—742no—
280C4⋊C4—742no—
281C4⋊C4—742no—
282C4⋊C4—742no—
283C4⋊C4—742no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—742no—
289C22⋊C4—742no—
290C22⋊C4—742no—
291C22⋊C4—742no—
292C22⋊C4—742no—
293C22⋊C4—742no—
294C42—742no—
295C42—742no—
296C42—742no—
297C42—742no—
298C42—742no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23D4×D3712yes—
312C23#1059696412yes—
313C23C23×D3711yescharacteristic
314D4—28no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—372no—
329C2×C4—372no—
330C2×C4—372no—
331C2×C4—372no—
332C2×C4—372no—
333C2×C4—748no—
334C2×C4—741no—
335C2×C4—741no—
336C2×C4—741no—
337C2×C4—741no—
338C2×C4—741no—
339C2×C4—741no—
340C2×C4—741no—
341C2×C4—741no—
342C2×C4—741no—
343C2×C4—741no—
344C2×C4—741no—
345C2×C4—741no—
346C2×C4—741no—
347C2×C4—741no—
348C2×C4—741no—
349C2×C4—741no—
350C2×C4—741no—
351C2×C4—741no—
352C2×C4—741no—
353C2×C4—1484no—
354C2×C4#1059696412yes—
355C2×C4#1059696412yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22C2×D4×D3711yescharacteristic
371C22#41×D3711yescharacteristic
372C22#41×D3711yescharacteristic
373C22#41×D3711yescharacteristic
374C22C2×#1059696411yescharacteristic
375C22C2×#1059696411yescharacteristic
376C22C2×#1059696411yescharacteristic
377C4—22no—
378C4—22no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—374no—
383C4—742no—
384C4—742no—
385C4—1481no—
386C4—1481no—
387C4—1481no—
388C4—1481no—
389C4—1481no—
390C2—42no—
391C2—42no—
392C2#123×D3711yescharacteristic
393C2#1455803911yescharacteristic
394C2#1455806011yescharacteristic
395C2#1455806211yescharacteristic
396C2#1455806411yescharacteristic
397C2#1455806411yescharacteristic
398C2#1455807811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutator, socle, cosocleC23×C37C24
FittingC37×#394C2
prime radicalC22×D4×C37C22
hypercenter#394D37
hypocenterC37#2395
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#11924492C2semidirect
3. #14557475C2semidirect
4. #14557469C2semidirect
5. #14557466C2semidirect
6. #14557461C2semidirect
7. #14557461C2semidirect
8. #14557458C2semidirect
10. C4⋊C4×Dic37C2semidirect
11. #14557384C2semidirect
12. C22⋊C4×Dic37C2semidirect
13. C22⋊C4×Dic37C2semidirect
14. C22⋊C4×Dic37C2semidirect
215. C37#2395semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic372
C2×#119244922
#145574752
#145574692
#145574662
#145574612
#145574582
#145574472
C4⋊C4×Dic372
#145573842
C22⋊C4×Dic372
C37×#3942
#239537