Finite Group Databasebeta

← #17997294

Subgroups — #17997294

Order 4736.

696 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924508C211yesmaximal, characteristic
2C2×C4×C22⋊D37C211yesmaximal, characteristic, complemented
3#14557424C211yesmaximal, characteristic, complemented
4#14557421C211yesmaximal, characteristic, complemented
5#14557417C211yesmaximal, characteristic, complemented
6#14557414C211yesmaximal, characteristic, complemented
7#14557413C211yesmaximal, characteristic, complemented
8#14557412C211yesmaximal, characteristic, complemented
9#14557410C211yesmaximal, characteristic, complemented
10#14557409C211yesmaximal, characteristic, complemented
11#14557406C211yesmaximal, characteristic, complemented
12#14557404C211yesmaximal, characteristic, complemented
13#14557391C211yesmaximal, characteristic, complemented
14C2×#11924443C211yesmaximal, characteristic, complemented
15C2×C4×D4×C37C211yesmaximal, characteristic, complemented
16C22×C22⋊D37C2211yescharacteristic
17C22×C22⋊D37C2211yescharacteristic
18C23×Dic37C2211yescharacteristic
19C23×Dic37C2211yescharacteristic
20C22×C4×D37C2211yescharacteristic
21#11924508C418yescomplemented
22C4×C22⋊D37—24no—
23C2×#10596936C2211yescharacteristic
24C2×#10596936C2211yescharacteristic
25C2×#10596936C2211yescharacteristic
26C2×#10596936C2211yescharacteristic
27C2×C22⋊Dic37C2211yescharacteristic
28C2×C22⋊Dic37C2211yescharacteristic
29C2×C22⋊Dic37C2211yescharacteristic
30C2×C22⋊Dic37C2211yescharacteristic
31C2×#10596938C2211yescharacteristic
32C2×#10596938C2211yescharacteristic
33C2×#10596938C2211yescharacteristic
34C2×#10596938C2211yescharacteristic
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
48C23×C4×C37C2211yescharacteristic
49C4×D4×C37—24no—
50C2×C4⋊C4×C37C2211yescharacteristic
51C2×C22⋊C4×C37C2211yescharacteristic
52C2×C22⋊C4×C37C2211yescharacteristic
53C2×C42×C37C2211yescharacteristic
54C24×C37C2311yescharacteristic
55C24×C37C2311yescharacteristic
56C23×D37C2311yescharacteristic
57C2×D4×C37—22no—
58C2×D4×C37—22no—
59C2×D4×C37C2×C414yescomplemented
60C22×C4×C37—22no—
61C22×C4×C37—41no—
62C22×C4×C37—41no—
63C22×C4×C37—41no—
64C22×C4×C37—41no—
65C22×C4×C37D414yescomplemented
66C22×C4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C22×C4×C37C2311yescharacteristic
69C22×C4×C37C2311yescharacteristic
70C22×C4×C37C2311yescharacteristic
71C2×C22⋊D37—22no—
72C2×C22⋊D37—22no—
73C2×C22⋊D37—41no—
74C2×C22⋊D37—41no—
75C2×C22⋊D37C2×C414yescomplemented
76C2×C22⋊D37C2×C414yescomplemented
77C22×Dic37—22no—
78C22×Dic37—41no—
79C22×Dic37—41no—
80C22×Dic37—41no—
81C22×Dic37—41no—
82C22×Dic37C2×C414yescomplemented
83C22×Dic37C2311yescharacteristic
84C22×Dic37C2311yescharacteristic
85C22×Dic37C2311yescharacteristic
86C22×Dic37C2311yescharacteristic
87C22×Dic37C2311yescharacteristic
88C22×Dic37C2311yescharacteristic
89C22×Dic37C2311yescharacteristic
90C2×C4×D37—22no—
91C2×C4×D37—41no—
92C2×C4×D37—41no—
93C4⋊C4×C37—22no—
94C22⋊C4×C37—22no—
95C22⋊C4×C37—22no—
96C42×C37—22no—
97C22⋊Dic37—22no—
98C22⋊Dic37—41no—
99C22⋊Dic37—41no—
100C22⋊Dic37C2×C414yescomplemented
101#10596938—22no—
102#10596938—41no—
103#10596938—41no—
104#10596938C2×C414yescomplemented
105#10596936—22no—
106#10596936—41no—
107#10596936—41no—
108#10596936C2×C414yescomplemented
109C4×Dic37—22no—
110C23×C37—21no—
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—21no—
114C23×C37—21no—
115C23×C37—21no—
116C23×C37—21no—
117C23×C37—21no—
118C23×C37—21no—
119C23×C37—21no—
120C23×C37C22×C412yes—
121C23×C37C22×C412yes—
122C23×C37C2×D412yes—
123C23×C37#4112yes—
124C23×C37C2411yescharacteristic
125C22×D37—21no—
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—21no—
129C22×D37—21no—
130C22×D37—21no—
131C22×D37C22×C412yes—
132D4×C37—28no—
133C2×C4×C37—21no—
134C2×C4×C37—21no—
135C2×C4×C37—21no—
136C2×C4×C37—21no—
137C2×C4×C37—21no—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—21no—
142C2×C4×C37—21no—
143C2×C4×C37—21no—
144C2×C4×C37—21no—
145C2×C4×C37—44no—
146C2×C4×C37—44no—
147C2×C4×C37C22×C412yes—
148C2×C4×C37C2×D412yes—
149C2×C4×C37C2×D412yes—
150C22⋊D37—28no—
151C22⋊D37—44no—
152C2×Dic37—21no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37—21no—
156C2×Dic37—21no—
157C2×Dic37—21no—
158C2×Dic37—21no—
159C2×Dic37—21no—
160C2×Dic37—21no—
161C2×Dic37—21no—
162C2×Dic37—21no—
163C2×Dic37—21no—
164C2×Dic37—21no—
165C2×Dic37—21no—
166C2×Dic37—21no—
167C2×Dic37—21no—
168C2×Dic37—21no—
169C2×Dic37—21no—
170C2×Dic37—44no—
171C2×Dic37—44no—
172C2×Dic37C22×C412yes—
173C2×Dic37C22×C412yes—
174C2×Dic37C22×C412yes—
175C4×D37—44no—
176C22×C37—22no—
177C22×C37—22no—
178C22×C37—22no—
179C22×C37—22no—
180C22×C37—22no—
181C22×C37—22no—
182C22×C37—22no—
183C22×C37—22no—
184C22×C37—22no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37—41no—
188C22×C37—41no—
189C22×C37C4×D414yes—
190C22×C37C23×C411yescharacteristic
191C22×C37C22×D411yescharacteristic
192C22×C37C2×#4111yescharacteristic
193C22×C37H(5,𝔽2)11yescharacteristic
194C22×C37H(5,𝔽2)11yescharacteristic
195C22×C37H(5,𝔽2)11yescharacteristic
196C22×C372−1+411yescharacteristic
197C2×D37—22no—
198C2×D37—22no—
199C2×D37—22no—
200C2×D37—41no—
201C2×D37—41no—
202C2×D37—41no—
203C2×D37—41no—
204C4×C37—22no—
205C4×C37—22no—
206C4×C37—22no—
207C4×C37—41no—
208C4×C37—41no—
209Dic37—22no—
210Dic37—22no—
211Dic37—22no—
212Dic37—41no—
213Dic37—41no—
214Dic37—41no—
215Dic37—41no—
216#2325—371nomaximal, Sylow
217C2×C37—24no—
218C2×C37—42no—
219C2×C37C2×C4×D411yescharacteristic
220C2×C37#51811yescharacteristic
221C2×C37#52011yescharacteristic
222C2×C37#53411yescharacteristic
223C2×C37#53711yescharacteristic
224C2×C37#53811yescharacteristic
225C2×C37#53911yescharacteristic
226D37—42no—
227C2×#121—371no—
228C2×C4×D4—371no—
229C2×C4×D4D3711yescharacteristic, complemented
230#388—371no—
231#388—371no—
232#387—371no—
233#387—371no—
234#386—371no—
235#386—371no—
236#386—371no—
237#386—371no—
238#385—371no—
239#385—371no—
240#380—371no—
241C2×#95—371no—
242C37#232511yescharacteristic, complemented, Sylow
243C22×D4—371no—
244C22×D4—371no—
245C22×D4C2×D3711yescharacteristic
246C23×C4—371no—
247C23×C4—371no—
248C23×C4—371no—
249C23×C4C2×D3711yescharacteristic
250C23×C4C2×D3711yescharacteristic
251#121—378no—
252C4×D4—24no—
253C4×D4—744no—
254C2×C4⋊C4—371no—
255C2×C4⋊C4—371no—
256C2×C4⋊C4—371no—
257C2×C4⋊C4—371no—
258C2×C4⋊C4C2×D3711yescharacteristic
259C2×C22⋊C4—371no—
260C2×C22⋊C4—371no—
261C2×C22⋊C4—371no—
262C2×C22⋊C4—371no—
263C2×C22⋊C4—371no—
264C2×C22⋊C4—371no—
265C2×C22⋊C4—371no—
266C2×C22⋊C4—371no—
267C2×C22⋊C4C2×D3711yescharacteristic
268C2×C22⋊C4C2×D3711yescharacteristic
269C2×C42—371no—
270C2×C42C2×D3711yescharacteristic
271#95—371no—
272#95—371no—
273#95—371no—
274#95—371no—
275#95—371no—
276#95—371no—
277#95—371no—
278#95—371no—
279#95—371no—
280#95—371no—
281C24—371no—
282C24C22×D3711yescharacteristic
283C24C22×D3711yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—374no—
287C2×D4—374no—
288C2×D4—742no—
289C2×D4—742no—
290C2×D4—1481no—
291C2×D4—1481no—
292C2×D4C4×D3714yescomplemented
293C22×C4—22no—
294C22×C4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—371no—
299C22×C4—371no—
300C22×C4—371no—
301C22×C4—374no—
302C22×C4—371no—
303C22×C4—371no—
304C22×C4—371no—
305C22×C4—371no—
306C22×C4—742no—
307C22×C4—742no—
308C22×C4—1481no—
309C22×C4—1481no—
310C22×C4—1481no—
311C22×C4—1481no—
312C22×C4—1481no—
313C22×C4—1481no—
314C22×C4C22⋊D3714yescomplemented
315C22×C4C22×D3711yescharacteristic
316C22×C4C22×D3711yescharacteristic
317C22×C4C22×D3711yescharacteristic
318C22×C4C22×D3711yescharacteristic
319C22×C4C22×D3711yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—374no—
322C4⋊C4—742no—
323C4⋊C4—1481no—
324C4⋊C4—1481no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—374no—
328C22⋊C4—374no—
329C22⋊C4—742no—
330C22⋊C4—742no—
331C22⋊C4—1481no—
332C22⋊C4—1481no—
333C22⋊C4—1481no—
334C22⋊C4—1481no—
335C42—22no—
336C42—742no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—372no—
348C23—741no—
349C23—741no—
350C23—741no—
351C23—741no—
352C23—741no—
353C23—741no—
354C23C2×C4×D3712yes—
355C23C2×C4×D3712yes—
356C23#1059696212yes—
357C23C2×C22⋊D3712yes—
358C23C23×D3711yescharacteristic
359D4—28no—
360D4—748no—
361D4—1484no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—372no—
377C2×C4—372no—
378C2×C4—372no—
379C2×C4—741no—
380C2×C4—741no—
381C2×C4—741no—
382C2×C4—741no—
383C2×C4—741no—
384C2×C4—741no—
385C2×C4—741no—
386C2×C4—741no—
387C2×C4—741no—
388C2×C4—741no—
389C2×C4—741no—
390C2×C4—741no—
391C2×C4—741no—
392C2×C4—741no—
393C2×C4—741no—
394C2×C4—741no—
395C2×C4—741no—
396C2×C4—741no—
397C2×C4—1484no—
398C2×C4—1484no—
399C2×C4—1484no—
400C2×C4C2×C4×D3712yes—
401C2×C4C2×C22⋊D3712yes—
402C2×C4C2×C22⋊D3712yes—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—742no—
417C22—742no—
418C22—742no—
419C22—1481no—
420C22—1481no—
421C22—1481no—
422C22—1481no—
423C22C4×C22⋊D3714yes—
424C22C22×C4×D3711yescharacteristic
425C22C22×C22⋊D3711yescharacteristic
426C22C2×#1059696211yescharacteristic
427C22#1192458111yescharacteristic
428C22#1192458111yescharacteristic
429C22#1192458211yescharacteristic
430C22#1192458311yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—41no—
435C4—41no—
436C4—742no—
437C4—742no—
438C4—742no—
439C4—1481no—
440C4—1481no—
441C4—1481no—
442C4—1481no—
443C2—24no—
444C2—42no—
445C2—1482no—
446C2C2×C4×C22⋊D3711yescharacteristic
447C2#1455800511yescharacteristic
448C2#1455801211yescharacteristic
449C2#1455809211yescharacteristic
450C2#1455811111yescharacteristic
451C2#1455811611yescharacteristic
452C2#1455812511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC2×C4×D4×C37C2
socle, cosocleC23×C37C24
prime radicalC2×#11924508C2
hypercenterC2×C4×D4D37
hypocenterC37#2325
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D37C2semidirect
3. #14557424C2semidirect
4. #14557421C2semidirect
5. #14557417C2semidirect
6. #14557414C2semidirect
7. #14557413C2semidirect
8. #14557412C2semidirect
9. #14557410C2semidirect
10. #14557409C2semidirect
11. #14557406C2semidirect
12. #14557404C2semidirect
13. #14557391C2semidirect
14. C2×#11924443C2semidirect
15. C2×C4×D4×C37C2semidirect
21. #11924508C4semidirect
59. C2×D4×C37C2×C4semidirect
65. C22×C4×C37D4semidirect
75. C2×C22⋊D37C2×C4semidirect
76. C2×C22⋊D37C2×C4semidirect
82. C22×Dic37C2×C4semidirect
100. C22⋊Dic37C2×C4semidirect
104. #10596938C2×C4semidirect
108. #10596936C2×C4semidirect
229. C2×C4×D4D37semidirect
242. C37#2325semidirect
292. C2×D4C4×D37semidirect
314. C22×C4C22⋊D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245082
C2×C4×C22⋊D372
#145574242
#145574212
#145574172
#145574142
#145574132
#145574122
#145574102
#145574092
#145574062
#145574042
#145573912
C2×#119244432
C2×C4×D4×C372
#232537