Finite Group Databasebeta

← #17997615

Subgroups — #17997615

Order 4736.

788 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924509C211yesmaximal, characteristic
2C2×#11924498C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D37C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D37C211yesmaximal, characteristic, complemented
5C2×C4⋊C4×D37C211yesmaximal, characteristic, complemented
6#14557433C211yesmaximal, characteristic, complemented
7#14557428C211yesmaximal, characteristic, complemented
8#14557426C211yesmaximal, characteristic, complemented
9#14557423C211yesmaximal, characteristic, complemented
10#14557411C211yesmaximal, characteristic, complemented
11#14557409C211yesmaximal, characteristic, complemented
12#14557407C211yesmaximal, characteristic, complemented
13#14557384C211yesmaximal, characteristic, complemented
14#14557380C211yesmaximal, characteristic, complemented
15C37×#385C211yesmaximal, characteristic, complemented
16C22×D148C2211yescharacteristic
17C22×C22⋊D37C2211yescharacteristic
18C22×C22⋊D37C2211yescharacteristic
19C22×C4×D37C2211yescharacteristic
20C22×C4×D37C2211yescharacteristic
21C22×C4×D37C2211yescharacteristic
22C22×C4×D37C2211yescharacteristic
23#11924509C418yescomplemented
24#11924498—24no—
25C4×C22⋊D37—24no—
26C4×C22⋊D37—24no—
27C2×C4⋊Dic37C2211yescharacteristic
28C2×#10596936C2211yescharacteristic
29C2×#10596936C2211yescharacteristic
30C2×#10596936C2211yescharacteristic
31C2×#10596936C2211yescharacteristic
32C4⋊C4×D37—24no—
33C2×C22⋊Dic37C2211yescharacteristic
34C2×C22⋊Dic37C2211yescharacteristic
35C2×#10596938C2211yescharacteristic
36C2×#10596938C2211yescharacteristic
37C2×#10596938C2211yescharacteristic
38C2×#10596938C2211yescharacteristic
39C2×#10596938C2211yescharacteristic
40C2×#10596938C2211yescharacteristic
41C2×C4×Dic37C2211yescharacteristic
42C2×C4×Dic37C2211yescharacteristic
43C2×C4×Dic37C2211yescharacteristic
44C2×C4×Dic37C2211yescharacteristic
45#11924443C2211yescharacteristic
46#11924443C2211yescharacteristic
47#11924443C2211yescharacteristic
48#11924443C2211yescharacteristic
49C23×C4×C37C2211yescharacteristic
50C2×C4⋊C4×C37C2211yescharacteristic
51C2×C4⋊C4×C37C2211yescharacteristic
52C2×C22⋊C4×C37C2211yescharacteristic
53C2×C22⋊C4×C37C2211yescharacteristic
54#95×C37C2211yescharacteristic
55#95×C37C2211yescharacteristic
56C24×C37C2311yescharacteristic
57C23×D37C2311yescharacteristic
58C23×D37C2311yescharacteristic
59C22×C4×C37—22no—
60C22×C4×C37—22no—
61C22×C4×C37—41no—
62C22×C4×C37C2311yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C22×C4×C37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C2×C22⋊D37—22no—
69C2×C22⋊D37—22no—
70C2×C22⋊D37—22no—
71C2×C22⋊D37—22no—
72C2×C22⋊D37C2×C414yescomplemented
73C2×C22⋊D37C2×C414yescomplemented
74C22×Dic37C2311yescharacteristic
75C22×Dic37C2311yescharacteristic
76C22×Dic37C2311yescharacteristic
77C22×Dic37C2311yescharacteristic
78C22×Dic37C2311yescharacteristic
79C22×Dic37C2311yescharacteristic
80C2×D148—22no—
81C2×D148—22no—
82C2×D148C2×C414yescomplemented
83C2×C4×D37—22no—
84C2×C4×D37—22no—
85C2×C4×D37—22no—
86C2×C4×D37—22no—
87C2×C4×D37—22no—
88C2×C4×D37—22no—
89C2×C4×D37—22no—
90C2×C4×D37—22no—
91C2×C4×D37—41no—
92C2×C4×D37—41no—
93C2×C4×D37—41no—
94C2×C4×D37C2×C414yescomplemented
95C4⋊C4×C37—22no—
96C4⋊C4×C37—22no—
97C22⋊C4×C37—41no—
98C22⋊C4×C37C2×C414yescomplemented
99C22⋊Dic37—22no—
100C22⋊Dic37—22no—
101#10596938—22no—
102#10596938—22no—
103#10596938—22no—
104#10596938—41no—
105#10596938C2×C414yescomplemented
106#10596938D414yescomplemented
107C4⋊Dic37—22no—
108#10596936—22no—
109#10596936—22no—
110#10596936C2×C414yescomplemented
111#10596936D414yescomplemented
112C4×Dic37—22no—
113C4×Dic37—22no—
114C4×Dic37—22no—
115C4×Dic37—22no—
116C23×C37—21no—
117C23×C37—21no—
118C23×C37—21no—
119C23×C37—21no—
120C23×C37—21no—
121C23×C37—21no—
122C23×C37C22×C412yes—
123C23×C37C2411yescharacteristic
124C22×D37—21no—
125C22×D37—21no—
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—21no—
129C22×D37—21no—
130C22×D37—21no—
131C22×D37—21no—
132C22×D37—21no—
133C22×D37—21no—
134C22×D37C22×C412yes—
135C22×D37C22×C412yes—
136C22×D37C2×D412yes—
137C22×D37#4112yes—
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—21no—
146C2×C4×C37—21no—
147C2×C4×C37—21no—
148C2×C4×C37—21no—
149C2×C4×C37—21no—
150C2×C4×C37—21no—
151C2×C4×C37—21no—
152C2×C4×C37—44no—
153C2×C4×C37C22×C412yes—
154C2×C4×C37C22×C412yes—
155C2×C4×C37C2×D412yes—
156C2×C4×C37C2×D412yes—
157C22⋊D37—28no—
158C22⋊D37—28no—
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—21no—
171C2×Dic37C22×C412yes—
172C2×Dic37C22×C412yes—
173C2×Dic37C2×D412yes—
174C2×Dic37C2×D412yes—
175C2×Dic37C2×D412yes—
176C2×Dic37#4112yes—
177D148—28no—
178C4×D37—28no—
179C4×D37—44no—
180C4×D37—44no—
181C4×D37—44no—
182C22×C37—22no—
183C22×C37—22no—
184C22×C37—22no—
185C22×C37—41no—
186C22×C37—41no—
187C22×C37—41no—
188C22×C37—41no—
189C22×C37C23×C411yescharacteristic
190C22×C37C22×D411yescharacteristic
191C22×C37C22×D411yescharacteristic
192C22×C37C2×#4111yescharacteristic
193C22×C37C2×#4111yescharacteristic
194C22×C37H(5,𝔽2)11yescharacteristic
195C22×C372−1+411yescharacteristic
196C2×D37—22no—
197C2×D37—22no—
198C2×D37—22no—
199C2×D37—22no—
200C2×D37—22no—
201C2×D37—22no—
202C2×D37—22no—
203C2×D37—22no—
204C2×D37—22no—
205C2×D37—41no—
206C2×D37—41no—
207C2×D37—41no—
208C2×D37—41no—
209C2×D37C4×D414yescomplemented
210C4×C37—22no—
211C4×C37—22no—
212C4×C37—22no—
213C4×C37—22no—
214C4×C37—41no—
215C4×C37—41no—
216Dic37—22no—
217Dic37—22no—
218Dic37—22no—
219Dic37—41no—
220Dic37—41no—
221Dic37C4×D414yescomplemented
222#2361—371nomaximal, Sylow
223C2×C37—42no—
224C2×C37C2×C4×D411yescharacteristic
225C2×C37C2×C4×D411yescharacteristic
226C2×C37#52011yescharacteristic
227C2×C37D4211yescharacteristic
228C2×C37#54711yescharacteristic
229C2×C37#54811yescharacteristic
230C2×C37#55311yescharacteristic
231D37—24no—
232D37—42no—
233C2×#121—371no—
234C2×C4×D4—371no—
235C2×C4×D4—371no—
236C2×C4×D4—371no—
237C22×C4⋊C4—371no—
238#390—371no—
239#389—371no—
240#388—371no—
241#388—371no—
242#386—371no—
243#386—371no—
244#385—371no—
245#385D3711yescharacteristic, complemented
246C4×C4⋊C4—371no—
247C4×C22⋊C4—371no—
248C37#236111yescharacteristic, complemented, Sylow
249C22×D4—371no—
250C22×D4—371no—
251C22×D4—371no—
252C23×C4—371no—
253C23×C4—371no—
254C23×C4—371no—
255C23×C4—371no—
256C23×C4C2×D3711yescharacteristic
257#121—378no—
258C4×D4—744no—
259C4×D4—744no—
260C4×D4—744no—
261C2×C4⋊C4—371no—
262C2×C4⋊C4—371no—
263C2×C4⋊C4—371no—
264C2×C4⋊C4—371no—
265C2×C4⋊C4—371no—
266C2×C4⋊C4—744no—
267C2×C4⋊C4C2×D3711yescharacteristic
268C2×C4⋊C4C2×D3711yescharacteristic
269C2×C22⋊C4—371no—
270C2×C22⋊C4—371no—
271C2×C22⋊C4—371no—
272C2×C22⋊C4—371no—
273C2×C22⋊C4—371no—
274C2×C22⋊C4—371no—
275C2×C22⋊C4—371no—
276C2×C22⋊C4—371no—
277C2×C22⋊C4C2×D3711yescharacteristic
278C2×C22⋊C4C2×D3711yescharacteristic
279C2×C42—371no—
280C2×C42—371no—
281C2×C42—371no—
282C2×C42—371no—
283#95—371no—
284#95—371no—
285#95—371no—
286#95—371no—
287#95C2×D3711yescharacteristic
288#95C2×D3711yescharacteristic
289C24—371no—
290C24—371no—
291C24C22×D3711yescharacteristic
292C2×D4—374no—
293C2×D4—374no—
294C2×D4—374no—
295C2×D4—742no—
296C2×D4—742no—
297C2×D4—742no—
298C2×D4—742no—
299C2×D4—742no—
300C2×D4—742no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—41no—
304C22×C4—371no—
305C22×C4—371no—
306C22×C4—371no—
307C22×C4—371no—
308C22×C4—374no—
309C22×C4—371no—
310C22×C4—371no—
311C22×C4—742no—
312C22×C4—742no—
313C22×C4—742no—
314C22×C4—742no—
315C22×C4—742no—
316C22×C4—742no—
317C22×C4—742no—
318C22×C4—742no—
319C22×C4—1481no—
320C22×C4—1481no—
321C22×C4—1481no—
322C22×C4C22×D3711yescharacteristic
323C22×C4C22×D3711yescharacteristic
324C22×C4C22×D3711yescharacteristic
325C22×C4C22×D3711yescharacteristic
326C22×C4C22×D3711yescharacteristic
327C22×C4C22×D3711yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—374no—
331C4⋊C4—374no—
332C4⋊C4—742no—
333C4⋊C4—742no—
334C4⋊C4—742no—
335C22⋊C4—41no—
336C22⋊C4—374no—
337C22⋊C4—374no—
338C22⋊C4—742no—
339C22⋊C4—742no—
340C22⋊C4—742no—
341C22⋊C4—742no—
342C22⋊C4—742no—
343C22⋊C4—1481no—
344C22⋊C4C4×D3714yescomplemented
345C42—742no—
346C42—742no—
347C42—742no—
348C42—742no—
349C23—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—372no—
356C23—372no—
357C23—372no—
358C23—372no—
359C23—741no—
360C23—741no—
361C23—741no—
362C23—741no—
363C23—741no—
364C23—741no—
365C23—741no—
366C23—741no—
367C23—741no—
368C23—741no—
369C23C2×C4×D3712yes—
370C23C23×D3711yescharacteristic
371D4—748no—
372D4—748no—
373D4—748no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—44no—
389C2×C4—372no—
390C2×C4—372no—
391C2×C4—372no—
392C2×C4—372no—
393C2×C4—372no—
394C2×C4—372no—
395C2×C4—748no—
396C2×C4—741no—
397C2×C4—741no—
398C2×C4—741no—
399C2×C4—741no—
400C2×C4—741no—
401C2×C4—741no—
402C2×C4—741no—
403C2×C4—741no—
404C2×C4—741no—
405C2×C4—741no—
406C2×C4—741no—
407C2×C4—741no—
408C2×C4—1484no—
409C2×C4—1484no—
410C2×C4—1484no—
411C2×C4C2×C4×D3712yes—
412C2×C4C2×C4×D3712yes—
413C2×C4D4×D3712yes—
414C2×C4D4×D3712yes—
415C22—22no—
416C22—22no—
417C22—22no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—374no—
423C22—742no—
424C22—742no—
425C22—742no—
426C22—742no—
427C22—742no—
428C22—742no—
429C22—742no—
430C22—742no—
431C22—742no—
432C22—1481no—
433C22—1481no—
434C22—1481no—
435C22—1481no—
436C22C22×C4×D3711yescharacteristic
437C22C2×D4×D3711yescharacteristic
438C22C2×D4×D3711yescharacteristic
439C22#41×D3711yescharacteristic
440C22#41×D3711yescharacteristic
441C22#1192458111yescharacteristic
442C22#1192458411yescharacteristic
443C4—22no—
444C4—22no—
445C4—22no—
446C4—22no—
447C4—41no—
448C4—41no—
449C4—374no—
450C4—742no—
451C4—742no—
452C4—742no—
453C4—1481no—
454C4—1481no—
455C2—42no—
456C2—744no—
457C2—1482no—
458C2C4×D4×D3711yescharacteristic
459C2C4×D4×D3711yescharacteristic
460C2#1455801411yescharacteristic
461C2#1455816511yescharacteristic
462C2#1455818511yescharacteristic
463C2#1455819311yescharacteristic
464C2#1455822811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#385C2
socle, cosocleC23×C37C24
prime radicalC2×#11924509C2
hypercenter#385D37
hypocenterC37#2361
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#11924498C2semidirect
3. C2×C4×C22⋊D37C2semidirect
4. C2×C4×C22⋊D37C2semidirect
5. C2×C4⋊C4×D37C2semidirect
6. #14557433C2semidirect
7. #14557428C2semidirect
8. #14557426C2semidirect
9. #14557423C2semidirect
10. #14557411C2semidirect
11. #14557409C2semidirect
12. #14557407C2semidirect
13. #14557384C2semidirect
14. #14557380C2semidirect
15. C37×#385C2semidirect
23. #11924509C4semidirect
72. C2×C22⋊D37C2×C4semidirect
73. C2×C22⋊D37C2×C4semidirect
82. C2×D148C2×C4semidirect
94. C2×C4×D37C2×C4semidirect
98. C22⋊C4×C37C2×C4semidirect
105. #10596938C2×C4semidirect
106. #10596938D4semidirect
110. #10596936C2×C4semidirect
111. #10596936D4semidirect
209. C2×D37C4×D4semidirect
221. Dic37C4×D4semidirect
245. #385D37semidirect
248. C37#2361semidirect
344. C22⋊C4C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245092
C2×#119244982
C2×C4×C22⋊D372
C2×C4⋊C4×D372
#145574332
#145574282
#145574262
#145574232
#145574112
#145574092
#145574072
#145573842
#145573802
C37×#3852
#236137