Finite Group Databasebeta

← #17997592

Subgroups — #17997592

Order 4736.

652 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic37C211yesmaximal, characteristic
2C2×#11924495C211yesmaximal, characteristic, complemented
3#14557432C211yesmaximal, characteristic, complemented
4#14557426C211yesmaximal, characteristic, complemented
5#14557426C211yesmaximal, characteristic, complemented
6#14557419C211yesmaximal, characteristic, complemented
7#14557419C211yesmaximal, characteristic, complemented
8#14557413C211yesmaximal, characteristic
9#14557408C211yesmaximal, characteristic, complemented
10#14557408C211yesmaximal, characteristic, complemented
11C4⋊C4×Dic37C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic37C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic37C211yesmaximal, characteristic, complemented
14C2×#11924443C211yesmaximal, characteristic, complemented
15C2×#123×C37C211yesmaximal, characteristic
16C23×Dic37C2211yescharacteristic
17C23×Dic37C2211yescharacteristic
18C23×Dic37C2211yescharacteristic
19D4×Dic37—24no—
20#11924495—24no—
21C2×C4⋊Dic37C2211yescharacteristic
22C2×C4⋊Dic37C2211yescharacteristic
23C2×C4⋊Dic37C2211yescharacteristic
24C2×C4⋊Dic37C2211yescharacteristic
25C2×C4⋊Dic37C2211yescharacteristic
26C2×C22⋊Dic37C2211yescharacteristic
27C2×C22⋊Dic37C2211yescharacteristic
28C2×C22⋊Dic37C2211yescharacteristic
29C2×C22⋊Dic37C2211yescharacteristic
30C2×C22⋊Dic37C2211yescharacteristic
31C2×C4×Dic37C2211yescharacteristic
32C2×C4×Dic37C2211yescharacteristic
33C2×C4×Dic37C2211yescharacteristic
34C2×C4×Dic37C2211yescharacteristic
35C2×C4×Dic37C2211yescharacteristic
36#11924443C2211yescharacteristic
37#11924443C2211yescharacteristic
38#11924443C2211yescharacteristic
39#11924443C2211yescharacteristic
40#11924443C2211yescharacteristic
41#11924443C2211yescharacteristic
42#11924443C2211yescharacteristic
43#11924443C2211yescharacteristic
44#11924443C2211yescharacteristic
45#11924443C2211yescharacteristic
46C22×D4×C37C2211yescharacteristic
47C23×C4×C37C2211yescharacteristic
48#123×C37C418yescomplemented
49C2×C4⋊C4×C37C2211yescharacteristic
50C2×C4⋊C4×C37C2211yescharacteristic
51C2×C22⋊C4×C37C2211yescharacteristic
52C2×C22⋊C4×C37C2211yescharacteristic
53C2×C22⋊C4×C37C2211yescharacteristic
54C24×C37C2311yescharacteristic
55C24×C37C2311yescharacteristic
56C2×D4×C37—22no—
57C2×D4×C37—22no—
58C2×D4×C37C2×C414yes—
59C22×C4×C37—22no—
60C22×C4×C37—22no—
61C22×C4×C37C2×C414yescomplemented
62C22×C4×C37C2311yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C22×Dic37—22no—
68C22×Dic37—22no—
69C22×Dic37—22no—
70C22×Dic37—22no—
71C22×Dic37—22no—
72C22×Dic37—22no—
73C22×Dic37—41no—
74C22×Dic37—41no—
75C22×Dic37—41no—
76C22×Dic37C2311yescharacteristic
77C22×Dic37C2311yescharacteristic
78C22×Dic37C2311yescharacteristic
79C22×Dic37C2311yescharacteristic
80C22×Dic37C2311yescharacteristic
81C22×Dic37C2311yescharacteristic
82C22×Dic37C2311yescharacteristic
83C22×Dic37C2311yescharacteristic
84C4⋊C4×C37C2×C414yescomplemented
85C4⋊C4×C37C2×C414yescomplemented
86C22⋊C4×C37C2×C414yescomplemented
87C22⋊C4×C37C2×C414yescomplemented
88C22⋊C4×C37C2×C414yescomplemented
89C22⋊Dic37—22no—
90C22⋊Dic37—22no—
91C22⋊Dic37—22no—
92C22⋊Dic37—41no—
93C22⋊Dic37D414yes—
94C4⋊Dic37—22no—
95C4⋊Dic37—22no—
96C4⋊Dic37—22no—
97C4⋊Dic37—22no—
98C4⋊Dic37—41no—
99C4×Dic37—22no—
100C4×Dic37—22no—
101C4×Dic37—22no—
102C4×Dic37—22no—
103C4×Dic37—41no—
104C23×C37—21no—
105C23×C37—21no—
106C23×C37—21no—
107C23×C37—21no—
108C23×C37—21no—
109C23×C37—21no—
110C23×C37—21no—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—21no—
114C23×C37C22×C412yes—
115C23×C37C22×C412yes—
116C23×C37C2×D412yes—
117C23×C37#4112yes—
118C23×C37C2411yescharacteristic
119D4×C37—28no—
120C2×C4×C37—28no—
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—21no—
129C2×C4×C37—21no—
130C2×C4×C37—21no—
131C2×C4×C37C22×C412yes—
132C2×C4×C37C22×C412yes—
133C2×C4×C37C22×C412yes—
134C2×C4×C37C22×C412yes—
135C2×C4×C37C22×C412yes—
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—21no—
151C2×Dic37—21no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37—21no—
156C2×Dic37—44no—
157C2×Dic37—44no—
158C2×Dic37—44no—
159C2×Dic37C2×D412yes—
160C2×Dic37C2×D412yes—
161C2×Dic37#4112yes—
162C2×Dic37#4112yes—
163C22×C37—22no—
164C22×C37—22no—
165C22×C37—22no—
166C22×C37—22no—
167C22×C37—22no—
168C22×C37—22no—
169C22×C37—22no—
170C22×C37—22no—
171C22×C37—22no—
172C22×C37—41no—
173C22×C37—41no—
174C22×C37—41no—
175C22×C37—41no—
176C22×C37C4×D414yes—
177C22×C37C23×C411yescharacteristic
178C22×C37C22×D411yescharacteristic
179C22×C37C2×#4111yescharacteristic
180C22×C37C2×#4111yescharacteristic
181C22×C37C2×#4111yescharacteristic
182C22×C37H(5,𝔽2)11yescharacteristic
183C22×C372−1+411yescharacteristic
184C4×C37—22no—
185C4×C37—22no—
186C4×C37—22no—
187C4×C37—22no—
188C4×C37—22no—
189Dic37—22no—
190Dic37—22no—
191Dic37—22no—
192Dic37—22no—
193Dic37—41no—
194Dic37—41no—
195Dic37—41no—
196Dic37—41no—
197#2359—371nomaximal, Sylow
198C2×C37—24no—
199C2×C37—42no—
200C2×C37C2×C4×D411yescharacteristic
201C2×C37C4×#4111yescharacteristic
202C2×C37#52011yescharacteristic
203C2×C37#54611yescharacteristic
204C2×C37#54711yescharacteristic
205C2×C37#55111yescharacteristic
206C2×C37#55211yescharacteristic
207C2×#123D3711yescharacteristic
208C2×C4×D4—371no—
209C2×#117—371no—
210#389—371no—
211#388—371no—
212#388—371no—
213#387—371no—
214#387—371no—
215#386—371no—
216#385—371no—
217#385—371no—
218C4×C4⋊C4—371no—
219C4×C22⋊C4—371no—
220C4×C22⋊C4—371no—
221C2×#95—371no—
222C37#235911yescharacteristic, complemented, Sylow
223C22×D4C2×D3711yescharacteristic
224C23×C4—371no—
225C23×C4—371no—
226C23×C4—371no—
227C23×C4C2×D3711yescharacteristic
228#123Dic3718yescomplemented
229C4×D4—744no—
230#117—744no—
231C2×C4⋊C4—371no—
232C2×C4⋊C4—371no—
233C2×C4⋊C4—371no—
234C2×C4⋊C4—371no—
235C2×C4⋊C4—371no—
236C2×C4⋊C4C2×D3711yescharacteristic
237C2×C4⋊C4C2×D3711yescharacteristic
238C2×C22⋊C4—371no—
239C2×C22⋊C4—371no—
240C2×C22⋊C4—371no—
241C2×C22⋊C4—371no—
242C2×C22⋊C4—371no—
243C2×C22⋊C4C2×D3711yescharacteristic
244C2×C22⋊C4C2×D3711yescharacteristic
245C2×C22⋊C4C2×D3711yescharacteristic
246C2×C42—371no—
247C2×C42—371no—
248C2×C42—371no—
249C2×C42—371no—
250C2×C42—371no—
251#95—371no—
252#95—371no—
253#95—371no—
254#95—371no—
255#95—371no—
256#95—371no—
257#95—371no—
258#95—371no—
259#95—371no—
260#95—371no—
261C24C22×D3711yescharacteristic
262C24C22×D3711yescharacteristic
263C2×D4—22no—
264C2×D4—22no—
265C2×D4C2×Dic3714yes—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—371no—
269C22×C4—371no—
270C22×C4—371no—
271C22×C4—371no—
272C22×C4—371no—
273C22×C4—371no—
274C22×C4—371no—
275C22×C4—371no—
276C22×C4—742no—
277C22×C4—742no—
278C22×C4—742no—
279C22×C4—742no—
280C22×C4—742no—
281C22×C4—742no—
282C22×C4—1481no—
283C22×C4—1481no—
284C22×C4—1481no—
285C22×C4C2×Dic3714yescomplemented
286C22×C4C22×D3711yescharacteristic
287C22×C4C22×D3711yescharacteristic
288C22×C4C22×D3711yescharacteristic
289C22×C4C22×D3711yescharacteristic
290C22×C4C22×D3711yescharacteristic
291C4⋊C4—742no—
292C4⋊C4—742no—
293C4⋊C4—742no—
294C4⋊C4—742no—
295C4⋊C4—1481no—
296C4⋊C4C2×Dic3714yescomplemented
297C4⋊C4C2×Dic3714yescomplemented
298C22⋊C4—374no—
299C22⋊C4—742no—
300C22⋊C4—742no—
301C22⋊C4—742no—
302C22⋊C4—1481no—
303C22⋊C4C2×Dic3714yescomplemented
304C22⋊C4C2×Dic3714yescomplemented
305C22⋊C4C2×Dic3714yescomplemented
306C42—742no—
307C42—742no—
308C42—742no—
309C42—742no—
310C42—1481no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23D4×D3712yes—
322C23#1059696412yes—
323C23C22×Dic3712yes—
324C23C22×Dic3712yes—
325C23C23×D3711yescharacteristic
326D4—28no—
327C2×C4—28no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—372no—
339C2×C4—372no—
340C2×C4—372no—
341C2×C4—372no—
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—741no—
354C2×C4—741no—
355C2×C4—741no—
356C2×C4—741no—
357C2×C4—741no—
358C2×C4—741no—
359C2×C4—741no—
360C2×C4—741no—
361C2×C4—741no—
362C2×C4—1484no—
363C2×C4—1484no—
364C2×C4—1484no—
365C2×C4C22×Dic3712yes—
366C2×C4C22×Dic3712yes—
367C2×C4C22×Dic3712yes—
368C2×C4C22×Dic3712yes—
369C2×C4C22×Dic3712yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22D4×Dic3714yes—
384C22C23×Dic3711yescharacteristic
385C22C2×D4×D3711yescharacteristic
386C22#41×D3711yescharacteristic
387C22#41×D3711yescharacteristic
388C22C2×#1059696411yescharacteristic
389C22#1192458211yescharacteristic
390C22#1192458311yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—22no—
395C4—22no—
396C4—742no—
397C4—742no—
398C4—742no—
399C4—742no—
400C4—1481no—
401C4—1481no—
402C4—1481no—
403C4—1481no—
404C2—24no—
405C2—42no—
406C2C2×D4×Dic3711yescharacteristic
407C2#41×Dic3711yescharacteristic
408C2#1455801611yescharacteristic
409C2#1455817511yescharacteristic
410C2#1455818111yescharacteristic
411C2#1455820611yescharacteristic
412C2#1455822011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC2×#123×C37C2
socle, cosocleC23×C37C24
prime radicalC22×D4×C37C22
hypercenterC2×#123D37
hypocenterC37#2359
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#11924495C2semidirect
3. #14557432C2semidirect
4. #14557426C2semidirect
5. #14557426C2semidirect
6. #14557419C2semidirect
7. #14557419C2semidirect
9. #14557408C2semidirect
10. #14557408C2semidirect
11. C4⋊C4×Dic37C2semidirect
12. C22⋊C4×Dic37C2semidirect
13. C22⋊C4×Dic37C2semidirect
14. C2×#11924443C2semidirect
48. #123×C37C4semidirect
61. C22×C4×C37C2×C4semidirect
84. C4⋊C4×C37C2×C4semidirect
85. C4⋊C4×C37C2×C4semidirect
86. C22⋊C4×C37C2×C4semidirect
87. C22⋊C4×C37C2×C4semidirect
88. C22⋊C4×C37C2×C4semidirect
222. C37#2359semidirect
228. #123Dic37semidirect
285. C22×C4C2×Dic37semidirect
296. C4⋊C4C2×Dic37semidirect
297. C4⋊C4C2×Dic37semidirect
303. C22⋊C4C2×Dic37semidirect
304. C22⋊C4C2×Dic37semidirect
305. C22⋊C4C2×Dic37semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic372
C2×#119244952
#145574322
#145574262
#145574192
#145574132
#145574082
C4⋊C4×Dic372
C22⋊C4×Dic372
C2×#119244432
C2×#123×C372
#235937