Finite Group Databasebeta

← #17997317

Subgroups — #17997317

Order 4736.

740 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924532C211yesmaximal, characteristic
2C2×C4×C22⋊D37C211yesmaximal, characteristic, complemented
3C2×#11924496C211yesmaximal, characteristic, complemented
4#14557433C211yesmaximal, characteristic, complemented
5#14557433C211yesmaximal, characteristic, complemented
6#14557413C211yesmaximal, characteristic, complemented
7#14557412C211yesmaximal, characteristic, complemented
8#14557411C211yesmaximal, characteristic, complemented
9#14557411C211yesmaximal, characteristic, complemented
10#14557410C211yesmaximal, characteristic, complemented
11#14557409C211yesmaximal, characteristic, complemented
12#14557409C211yesmaximal, characteristic, complemented
13#14557397C211yesmaximal, characteristic, complemented
14#14557378C211yesmaximal, characteristic, complemented
15C37×#386C211yesmaximal, characteristic, complemented
16C22×D148C2211yescharacteristic
17C22×C22⋊D37C2211yescharacteristic
18C22×C22⋊D37C2211yescharacteristic
19C22×C22⋊D37C2211yescharacteristic
20C22×C22⋊D37C2211yescharacteristic
21C23×Dic37C2211yescharacteristic
22C22×C4×D37C2211yescharacteristic
23C22×C4×D37C2211yescharacteristic
24#11924532C418yescomplemented
25C4×C22⋊D37—24no—
26#11924496—24no—
27C2×#10596936C2211yescharacteristic
28C2×#10596936C2211yescharacteristic
29C2×C22⋊Dic37C2211yescharacteristic
30C2×C22⋊Dic37C2211yescharacteristic
31C2×C22⋊Dic37C2211yescharacteristic
32C2×#10596938C2211yescharacteristic
33C2×#10596938C2211yescharacteristic
34C2×#10596938C2211yescharacteristic
35C2×#10596938C2211yescharacteristic
36C2×#10596938C2211yescharacteristic
37C2×#10596938C2211yescharacteristic
38C2×C4×Dic37C2211yescharacteristic
39C2×C4×Dic37C2211yescharacteristic
40C2×C4×Dic37C2211yescharacteristic
41#11924443C2211yescharacteristic
42#11924443C2211yescharacteristic
43#11924443C2211yescharacteristic
44#11924443C2211yescharacteristic
45#11924443C2211yescharacteristic
46#11924443C2211yescharacteristic
47C22×D4×C37C2211yescharacteristic
48C23×C4×C37C2211yescharacteristic
49C2×C22⋊C4×C37C2211yescharacteristic
50C2×C22⋊C4×C37C2211yescharacteristic
51C2×C22⋊C4×C37C2211yescharacteristic
52#95×C37C2211yescharacteristic
53#95×C37C2211yescharacteristic
54C24×C37C2311yescharacteristic
55C24×C37C2311yescharacteristic
56C23×D37C2311yescharacteristic
57C23×D37C2311yescharacteristic
58C2×D4×C37—41no—
59C2×D4×C37—41no—
60C2×D4×C37C2×C414yescomplemented
61C22×C4×C37—22no—
62C22×C4×C37—41no—
63C22×C4×C37—41no—
64C22×C4×C37C2311yescharacteristic
65C22×C4×C37C2311yescharacteristic
66C22×C4×C37C2311yescharacteristic
67C22×C4×C37C2311yescharacteristic
68C22×C4×C37C2311yescharacteristic
69C2×C22⋊D37—22no—
70C2×C22⋊D37—22no—
71C2×C22⋊D37—22no—
72C2×C22⋊D37—22no—
73C2×C22⋊D37—41no—
74C2×C22⋊D37—41no—
75C2×C22⋊D37—41no—
76C2×C22⋊D37—41no—
77C2×C22⋊D37C2×C414yescomplemented
78C2×C22⋊D37C2×C414yescomplemented
79C2×C22⋊D37C2×C414yescomplemented
80C2×C22⋊D37C2×C414yescomplemented
81C22×Dic37—22no—
82C22×Dic37—41no—
83C22×Dic37—41no—
84C22×Dic37C2311yescharacteristic
85C22×Dic37C2311yescharacteristic
86C22×Dic37C2311yescharacteristic
87C22×Dic37C2311yescharacteristic
88C22×Dic37C2311yescharacteristic
89C22×Dic37C2311yescharacteristic
90C2×D148—41no—
91C2×D148—41no—
92C2×D148C2×C414yescomplemented
93C2×C4×D37—22no—
94C2×C4×D37—22no—
95C2×C4×D37—41no—
96C2×C4×D37—41no—
97C2×C4×D37—41no—
98C2×C4×D37—41no—
99C22⋊C4×C37—22no—
100C22⋊C4×C37—41no—
101C22⋊C4×C37—41no—
102C22⋊Dic37—22no—
103C22⋊Dic37—41no—
104C22⋊Dic37—41no—
105#10596938—22no—
106#10596938—22no—
107#10596938—41no—
108#10596938—41no—
109#10596938—41no—
110#10596938—41no—
111#10596936—22no—
112#10596936—22no—
113C4×Dic37—22no—
114C4×Dic37C2×C414yescomplemented
115C4×Dic37D414yescomplemented
116C23×C37—21no—
117C23×C37—21no—
118C23×C37—21no—
119C23×C37—21no—
120C23×C37—21no—
121C23×C37—21no—
122C23×C37—21no—
123C23×C37—21no—
124C23×C37—21no—
125C23×C37—21no—
126C23×C37—21no—
127C23×C37—21no—
128C23×C37C22×C412yes—
129C23×C37C22×C412yes—
130C23×C37C2411yescharacteristic
131C22×D37—21no—
132C22×D37—21no—
133C22×D37—21no—
134C22×D37—21no—
135C22×D37—21no—
136C22×D37—21no—
137C22×D37—21no—
138C22×D37—21no—
139C22×D37—21no—
140C22×D37—21no—
141C22×D37—21no—
142C22×D37—21no—
143C22×D37C22×C412yes—
144C22×D37C22×C412yes—
145D4×C37—44no—
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—21no—
153C2×C4×C37—21no—
154C2×C4×C37—21no—
155C2×C4×C37—21no—
156C2×C4×C37—21no—
157C2×C4×C37—21no—
158C2×C4×C37—21no—
159C2×C4×C37—44no—
160C2×C4×C37C22×C412yes—
161C2×C4×C37C2×D412yes—
162C22⋊D37—28no—
163C22⋊D37—28no—
164C22⋊D37—44no—
165C22⋊D37—44no—
166C2×Dic37—21no—
167C2×Dic37—21no—
168C2×Dic37—21no—
169C2×Dic37—21no—
170C2×Dic37—21no—
171C2×Dic37—21no—
172C2×Dic37—21no—
173C2×Dic37—21no—
174C2×Dic37—21no—
175C2×Dic37—21no—
176C2×Dic37—21no—
177C2×Dic37—21no—
178C2×Dic37—21no—
179C2×Dic37—44no—
180C2×Dic37C22×C412yes—
181C2×Dic37C22×C412yes—
182C2×Dic37C2×D412yes—
183C2×Dic37C2×D412yes—
184C2×Dic37#4112yes—
185D148—44no—
186C4×D37—44no—
187C4×D37—44no—
188C22×C37—22no—
189C22×C37—22no—
190C22×C37—22no—
191C22×C37—22no—
192C22×C37—22no—
193C22×C37—22no—
194C22×C37—41no—
195C22×C37—41no—
196C22×C37—41no—
197C22×C37—41no—
198C22×C37—41no—
199C22×C37—41no—
200C22×C37—41no—
201C22×C37—41no—
202C22×C37C23×C411yescharacteristic
203C22×C37C22×D411yescharacteristic
204C22×C37C2×#4111yescharacteristic
205C22×C37H(5,𝔽2)11yescharacteristic
206C22×C37H(5,𝔽2)11yescharacteristic
207C22×C37H(5,𝔽2)11yescharacteristic
208C22×C37H(5,𝔽2)11yescharacteristic
209C2×D37—22no—
210C2×D37—22no—
211C2×D37—22no—
212C2×D37—22no—
213C2×D37—22no—
214C2×D37—22no—
215C2×D37—41no—
216C2×D37—41no—
217C2×D37—41no—
218C2×D37—41no—
219C2×D37—41no—
220C2×D37—41no—
221C2×D37—41no—
222C2×D37—41no—
223C4×C37—22no—
224C4×C37—22no—
225C4×C37—41no—
226C4×C37—41no—
227C4×C37—41no—
228Dic37—22no—
229Dic37—22no—
230Dic37—41no—
231Dic37—41no—
232Dic37—41no—
233Dic37C4×D414yes—
234#2328—371nomaximal, Sylow
235C2×C37—42no—
236C2×C37—42no—
237C2×C37C2×C4×D411yescharacteristic
238C2×C37#51811yescharacteristic
239C2×C37#51811yescharacteristic
240C2×C37#53511yescharacteristic
241C2×C37#53511yescharacteristic
242C2×C37#54011yescharacteristic
243C2×C37#54011yescharacteristic
244D37—42no—
245D37—42no—
246C2×#127—371no—
247C2×C4×D4—371no—
248C2×C4×D4—371no—
249#390—371no—
250#390—371no—
251#386—371no—
252#386—371no—
253#386—371no—
254#386—371no—
255#386—371no—
256#386—371no—
257#386—371no—
258#386D3711yescharacteristic, complemented
259#382—371no—
260#376—371no—
261C37#232811yescharacteristic, complemented, Sylow
262C22×D4—371no—
263C22×D4—371no—
264C22×D4—371no—
265C22×D4—371no—
266C22×D4—371no—
267C22×D4C2×D3711yescharacteristic
268C23×C4—371no—
269C23×C4—371no—
270C23×C4—371no—
271C23×C4C2×D3711yescharacteristic
272#127—378no—
273C4×D4—744no—
274C4×D4—744no—
275C2×C4⋊C4—371no—
276C2×C4⋊C4—371no—
277C2×C22⋊C4—371no—
278C2×C22⋊C4—371no—
279C2×C22⋊C4—371no—
280C2×C22⋊C4—371no—
281C2×C22⋊C4—371no—
282C2×C22⋊C4—371no—
283C2×C22⋊C4—371no—
284C2×C22⋊C4—371no—
285C2×C22⋊C4—371no—
286C2×C22⋊C4C2×D3711yescharacteristic
287C2×C22⋊C4C2×D3711yescharacteristic
288C2×C22⋊C4C2×D3711yescharacteristic
289C2×C42—371no—
290C2×C42—371no—
291C2×C42—371no—
292#95—371no—
293#95—371no—
294#95—371no—
295#95—371no—
296#95—371no—
297#95—371no—
298#95C2×D3711yescharacteristic
299#95C2×D3711yescharacteristic
300C24—371no—
301C24—371no—
302C24C22×D3711yescharacteristic
303C24C22×D3711yescharacteristic
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—374no—
307C2×D4—374no—
308C2×D4—374no—
309C2×D4—374no—
310C2×D4—374no—
311C2×D4—742no—
312C2×D4—742no—
313C2×D4—742no—
314C2×D4—742no—
315C2×D4—1481no—
316C2×D4—1481no—
317C2×D4—1481no—
318C2×D4—1481no—
319C2×D4—1481no—
320C2×D4—1481no—
321C2×D4C4×D3714yescomplemented
322C22×C4—22no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—371no—
326C22×C4—371no—
327C22×C4—371no—
328C22×C4—371no—
329C22×C4—371no—
330C22×C4—371no—
331C22×C4—742no—
332C22×C4—742no—
333C22×C4—742no—
334C22×C4—1481no—
335C22×C4—1481no—
336C22×C4—1481no—
337C22×C4—1481no—
338C22×C4—1481no—
339C22×C4—1481no—
340C22×C4C22×D3711yescharacteristic
341C22×C4C22×D3711yescharacteristic
342C22×C4C22×D3711yescharacteristic
343C22×C4C22×D3711yescharacteristic
344C22×C4C22×D3711yescharacteristic
345C4⋊C4—742no—
346C4⋊C4—742no—
347C22⋊C4—22no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—742no—
351C22⋊C4—742no—
352C22⋊C4—742no—
353C22⋊C4—1481no—
354C22⋊C4—1481no—
355C22⋊C4—1481no—
356C22⋊C4—1481no—
357C22⋊C4—1481no—
358C22⋊C4—1481no—
359C42—374no—
360C42—374no—
361C42—742no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—372no—
375C23—372no—
376C23—741no—
377C23—741no—
378C23—741no—
379C23—741no—
380C23—741no—
381C23—741no—
382C23—741no—
383C23—741no—
384C23—741no—
385C23—741no—
386C23—741no—
387C23—741no—
388C23C2×C4×D3712yes—
389C23C2×C4×D3712yes—
390C23C23×D3711yescharacteristic
391D4—44no—
392D4—748no—
393D4—748no—
394D4—1484no—
395D4—1484no—
396D4—1484no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—44no—
411C2×C4—372no—
412C2×C4—372no—
413C2×C4—372no—
414C2×C4—372no—
415C2×C4—372no—
416C2×C4—741no—
417C2×C4—741no—
418C2×C4—741no—
419C2×C4—741no—
420C2×C4—741no—
421C2×C4—741no—
422C2×C4—741no—
423C2×C4—741no—
424C2×C4—741no—
425C2×C4—741no—
426C2×C4—741no—
427C2×C4—741no—
428C2×C4—741no—
429C2×C4—1484no—
430C2×C4—1484no—
431C2×C4—1484no—
432C2×C4C2×C4×D3712yes—
433C2×C4D4×D3712yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—742no—
449C22—742no—
450C22—742no—
451C22—742no—
452C22—742no—
453C22—742no—
454C22—1481no—
455C22—1481no—
456C22—1481no—
457C22—1481no—
458C22—1481no—
459C22—1481no—
460C22—1481no—
461C22—1481no—
462C22C22×C4×D3711yescharacteristic
463C22C2×D4×D3711yescharacteristic
464C22#41×D3711yescharacteristic
465C22#1192458111yescharacteristic
466C22#1192458111yescharacteristic
467C22#1192458111yescharacteristic
468C22#1192458211yescharacteristic
469C4—22no—
470C4—22no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—374no—
475C4—742no—
476C4—742no—
477C4—1481no—
478C4—1481no—
479C4—1481no—
480C2—42no—
481C2—42no—
482C2—1482no—
483C2—1482no—
484C2C4×D4×D3711yescharacteristic
485C2#1455800511yescharacteristic
486C2#1455800611yescharacteristic
487C2#1455809811yescharacteristic
488C2#1455809911yescharacteristic
489C2#1455813311yescharacteristic
490C2#1455813511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutatorC22×C37C23×C4
FittingC37×#386C2
socle, cosocleC23×C37C24
prime radicalC2×#11924532C2
hypercenter#386D37
hypocenterC37#2328
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D37C2semidirect
3. C2×#11924496C2semidirect
4. #14557433C2semidirect
5. #14557433C2semidirect
6. #14557413C2semidirect
7. #14557412C2semidirect
8. #14557411C2semidirect
9. #14557411C2semidirect
10. #14557410C2semidirect
11. #14557409C2semidirect
12. #14557409C2semidirect
13. #14557397C2semidirect
14. #14557378C2semidirect
15. C37×#386C2semidirect
24. #11924532C4semidirect
60. C2×D4×C37C2×C4semidirect
77. C2×C22⋊D37C2×C4semidirect
78. C2×C22⋊D37C2×C4semidirect
79. C2×C22⋊D37C2×C4semidirect
80. C2×C22⋊D37C2×C4semidirect
92. C2×D148C2×C4semidirect
114. C4×Dic37C2×C4semidirect
115. C4×Dic37D4semidirect
258. #386D37semidirect
261. C37#2328semidirect
321. C2×D4C4×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245322
C2×C4×C22⋊D372
C2×#119244962
#145574332
#145574132
#145574122
#145574112
#145574102
#145574092
#145573972
#145573782
C37×#3862
#232837