Finite Group Databasebeta

← #17997841

Subgroups — #17997841

Order 4736.

696 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924498C211yesmaximal, characteristic, complemented
2C2×#11924496C211yesmaximal, characteristic, complemented
3C2×#11924496C211yesmaximal, characteristic, complemented
4C2×#11924494C211yesmaximal, characteristic, complemented
5#14557466C211yesmaximal, characteristic, complemented
6#14557462C211yesmaximal, characteristic, complemented
7#14557455C211yesmaximal, characteristic, complemented
8#14557450C211yesmaximal, characteristic, complemented
9#14557449C211yesmaximal, characteristic, complemented
10#14557449C211yesmaximal, characteristic, complemented
11#14557442C211yesmaximal, characteristic
12C4⋊C4×Dic37C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic37C211yesmaximal, characteristic, complemented
14#14557380C211yesmaximal, characteristic, complemented
15C37×#396C211yesmaximal, characteristic, complemented
16C22×D148C2211yescharacteristic
17C22×C22⋊D37C2211yescharacteristic
18C22×C22⋊D37C2211yescharacteristic
19C23×Dic37C2211yescharacteristic
20C22×C4×D37C2211yescharacteristic
21C22×C4×D37C2211yescharacteristic
22#11924498—24no—
23#11924496—24no—
24#11924496—24no—
25#11924494—24no—
26C2×C4⋊Dic37C2211yescharacteristic
27C2×C4⋊Dic37C2211yescharacteristic
28C2×#10596936C2211yescharacteristic
29C2×#10596936C2211yescharacteristic
30C2×C22⋊Dic37C2211yescharacteristic
31C2×#10596938C2211yescharacteristic
32C2×#10596938C2211yescharacteristic
33C2×#10596938C2211yescharacteristic
34C2×#10596938C2211yescharacteristic
35C2×#10596938C2211yescharacteristic
36C2×#10596938C2211yescharacteristic
37C2×#10596938C2211yescharacteristic
38C2×#10596938C2211yescharacteristic
39C2×C4×Dic37C2211yescharacteristic
40C2×C4×Dic37C2211yescharacteristic
41C2×C4×Dic37C2211yescharacteristic
42C2×C4×Dic37C2211yescharacteristic
43#11924443C2211yescharacteristic
44#11924443C2211yescharacteristic
45#11924443C2211yescharacteristic
46#11924443C2211yescharacteristic
47#11924443C2211yescharacteristic
48C2×C4⋊C4×C37C2211yescharacteristic
49C2×C4⋊C4×C37C2211yescharacteristic
50C2×C4⋊C4×C37C2211yescharacteristic
51C2×C22⋊C4×C37C2211yescharacteristic
52C2×C22⋊C4×C37C2211yescharacteristic
53C2×C22⋊C4×C37C2211yescharacteristic
54#95×C37C2211yescharacteristic
55C24×C37C2311yescharacteristic
56C23×D37C2311yescharacteristic
57C23×D37C2311yescharacteristic
58C22×C4×C37C2311yescharacteristic
59C22×C4×C37C2311yescharacteristic
60C22×C4×C37C2311yescharacteristic
61C22×C4×C37C2311yescharacteristic
62C22×C4×C37C2311yescharacteristic
63C22×C4×C37C2311yescharacteristic
64C2×C22⋊D37—22no—
65C2×C22⋊D37—22no—
66C2×C22⋊D37—22no—
67C2×C22⋊D37—22no—
68C2×C22⋊D37—22no—
69C2×C22⋊D37—22no—
70C22×Dic37—22no—
71C22×Dic37—22no—
72C22×Dic37—22no—
73C22×Dic37C2311yescharacteristic
74C22×Dic37C2311yescharacteristic
75C22×Dic37C2311yescharacteristic
76C22×Dic37C2311yescharacteristic
77C22×Dic37C2311yescharacteristic
78C22×Dic37C2311yescharacteristic
79C2×D148—22no—
80C2×D148—22no—
81C2×D148—22no—
82C2×C4×D37—22no—
83C2×C4×D37—22no—
84C2×C4×D37—22no—
85C2×C4×D37—22no—
86C2×C4×D37—22no—
87C2×C4×D37D414yescomplemented
88C4⋊C4×C37—22no—
89C4⋊C4×C37—22no—
90C4⋊C4×C37—22no—
91C22⋊C4×C37—22no—
92C22⋊C4×C37—22no—
93C22⋊C4×C37—22no—
94C22⋊Dic37—22no—
95#10596938—22no—
96#10596938—22no—
97#10596938—22no—
98#10596938—22no—
99#10596938—22no—
100#10596938—22no—
101#10596938—22no—
102#10596938—22no—
103C4⋊Dic37—22no—
104C4⋊Dic37—22no—
105#10596936—22no—
106#10596936—22no—
107C4×Dic37—22no—
108C4×Dic37—22no—
109C4×Dic37—22no—
110C4×Dic37D414yescomplemented
111C23×C37—21no—
112C23×C37—21no—
113C23×C37—21no—
114C23×C37—21no—
115C23×C37—21no—
116C23×C37—21no—
117C23×C37#4112yes—
118C23×C37C2411yescharacteristic
119C22×D37—21no—
120C22×D37—21no—
121C22×D37—21no—
122C22×D37—21no—
123C22×D37—21no—
124C22×D37—21no—
125C22×D37—21no—
126C22×D37—21no—
127C22×D37—21no—
128C22×D37—21no—
129C22×D37—21no—
130C22×D37—21no—
131C22×D37C2×D412yes—
132C22×D37#4112yes—
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—21no—
146C2×C4×C37—21no—
147C2×C4×C37—21no—
148C2×C4×C37C2×D412yes—
149C2×C4×C37C2×D412yes—
150C2×C4×C37#4112yes—
151C22⋊D37—28no—
152C22⋊D37—28no—
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—44no—
167C2×Dic37C2×D412yes—
168C2×Dic37C2×D412yes—
169C2×Dic37C2×D412yes—
170C2×Dic37#4112yes—
171C2×Dic37#4112yes—
172D148—28no—
173C4×D37—28no—
174C4×D37—44no—
175C22×C37—22no—
176C22×C37—22no—
177C22×C37—22no—
178C22×C37—41no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37—41no—
182C22×C37C22×D411yescharacteristic
183C22×C37C22×D411yescharacteristic
184C22×C37C2×#4111yescharacteristic
185C22×C37C2×#4111yescharacteristic
186C22×C37C2×#4111yescharacteristic
187C22×C37C2×#4111yescharacteristic
188C22×C37C2×#4111yescharacteristic
189C2×D37—22no—
190C2×D37—22no—
191C2×D37—22no—
192C2×D37—22no—
193C2×D37—22no—
194C2×D37—22no—
195C2×D37—41no—
196C2×D37—41no—
197C2×D37—41no—
198C2×D37—41no—
199C2×D37—41no—
200C2×D37—41no—
201C2×D37—41no—
202C2×D37—41no—
203C4×C37—22no—
204C4×C37—22no—
205C4×C37—22no—
206C4×C37—41no—
207C4×C37—41no—
208C4×C37—41no—
209Dic37—22no—
210Dic37—22no—
211Dic37—41no—
212Dic37—41no—
213Dic37—41no—
214Dic37#12114yes—
215#2392—371nomaximal, Sylow
216C2×C37—42no—
217C2×C37C2×#12111yescharacteristic
218C2×C37#52511yescharacteristic
219C2×C37#52511yescharacteristic
220C2×C37#52511yescharacteristic
221C2×C37#52911yescharacteristic
222C2×C37#52911yescharacteristic
223C2×C37#53211yescharacteristic
224D37—42no—
225D37—42no—
226C2×C4×D4—371no—
227C2×C4×D4—371no—
228C2×C4×D4—371no—
229C2×#117—371no—
230#398—371no—
231#397—371no—
232#396—371no—
233#396D3711yescharacteristic, complemented
234#394—371no—
235#394—371no—
236#394—371no—
237#392—371no—
238C4×C4⋊C4—371no—
239C4×C22⋊C4—371no—
240C4×C22⋊C4—371no—
241C37#239211yescharacteristic, complemented, Sylow
242C22×D4—371no—
243C22×D4—371no—
244C22×D4—371no—
245C23×C4—371no—
246C23×C4—371no—
247C23×C4—371no—
248C4×D4—744no—
249C4×D4—744no—
250C4×D4—744no—
251#117—744no—
252C2×C4⋊C4—371no—
253C2×C4⋊C4—371no—
254C2×C4⋊C4—371no—
255C2×C4⋊C4—371no—
256C2×C4⋊C4C2×D3711yescharacteristic
257C2×C4⋊C4C2×D3711yescharacteristic
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⋊C4—371no—
268C2×C22⋊C4C2×D3711yescharacteristic
269C2×C22⋊C4C2×D3711yescharacteristic
270C2×C22⋊C4C2×D3711yescharacteristic
271C2×C42—371no—
272C2×C42—371no—
273C2×C42—371no—
274C2×C42—371no—
275#95—371no—
276#95—371no—
277#95—371no—
278#95—371no—
279#95—371no—
280#95C2×D3711yescharacteristic
281C24—371no—
282C24—371no—
283C24C22×D3711yescharacteristic
284C2×D4—742no—
285C2×D4—742no—
286C2×D4—742no—
287C2×D4—742no—
288C2×D4—742no—
289C2×D4—742no—
290C2×D4—742no—
291C2×D4—742no—
292C2×D4—742no—
293C22×C4—371no—
294C22×C4—371no—
295C22×C4—371no—
296C22×C4—374no—
297C22×C4—371no—
298C22×C4—371no—
299C22×C4—371no—
300C22×C4—742no—
301C22×C4—742no—
302C22×C4—742no—
303C22×C4—742no—
304C22×C4—742no—
305C22×C4—742no—
306C22×C4—742no—
307C22×C4—742no—
308C22×C4C22×D3711yescharacteristic
309C22×C4C22×D3711yescharacteristic
310C22×C4C22×D3711yescharacteristic
311C22×C4C22×D3711yescharacteristic
312C22×C4C22×D3711yescharacteristic
313C22×C4C22×D3711yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—742no—
318C4⋊C4—742no—
319C4⋊C4—742no—
320C4⋊C4—742no—
321C22⋊C4—22no—
322C22⋊C4—22no—
323C22⋊C4—22no—
324C22⋊C4—742no—
325C22⋊C4—742no—
326C22⋊C4—742no—
327C22⋊C4—742no—
328C22⋊C4—742no—
329C22⋊C4—742no—
330C22⋊C4—742no—
331C22⋊C4—742no—
332C22⋊C4—742no—
333C42—374no—
334C42—742no—
335C42—742no—
336C42—742no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—372no—
344C23—372no—
345C23—741no—
346C23—741no—
347C23—741no—
348C23—741no—
349C23—741no—
350C23—741no—
351C23—741no—
352C23—741no—
353C23—741no—
354C23—741no—
355C23—741no—
356C23—741no—
357C23#1059696612yes—
358C23C23×D3711yescharacteristic
359D4—748no—
360D4—748no—
361D4—748no—
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—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—372no—
378C2×C4—372no—
379C2×C4—372no—
380C2×C4—372no—
381C2×C4—372no—
382C2×C4—748no—
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—1484no—
397C2×C4—1484no—
398C2×C4D4×D3712yes—
399C2×C4D4×D3712yes—
400C2×C4#1059696412yes—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—742no—
409C22—742no—
410C22—742no—
411C22—742no—
412C22—742no—
413C22—742no—
414C22—1481no—
415C22—1481no—
416C22—1481no—
417C22—1481no—
418C22—1481no—
419C22—1481no—
420C22—1481no—
421C22—1481no—
422C22C2×D4×D3711yescharacteristic
423C22C2×D4×D3711yescharacteristic
424C22#41×D3711yescharacteristic
425C22#41×D3711yescharacteristic
426C22#41×D3711yescharacteristic
427C22C2×#1059696411yescharacteristic
428C22C2×#1059696611yescharacteristic
429C4—22no—
430C4—22no—
431C4—22no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—374no—
436C4—742no—
437C4—742no—
438C4—1481no—
439C4—1481no—
440C4—1481no—
441C2—42no—
442C2—1482no—
443C2—1482no—
444C2#121×D3711yescharacteristic
445C2#1455804311yescharacteristic
446C2#1455804611yescharacteristic
447C2#1455804611yescharacteristic
448C2#1455806611yescharacteristic
449C2#1455806911yescharacteristic
450C2#1455807811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutator, socle, cosocleC23×C37C24
FittingC37×#396C2
prime radical#14557442C2
hypercenter#396D37
hypocenterC37#2392
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#11924498C2semidirect
2. C2×#11924496C2semidirect
3. C2×#11924496C2semidirect
4. C2×#11924494C2semidirect
5. #14557466C2semidirect
6. #14557462C2semidirect
7. #14557455C2semidirect
8. #14557450C2semidirect
9. #14557449C2semidirect
10. #14557449C2semidirect
12. C4⋊C4×Dic37C2semidirect
13. C22⋊C4×Dic37C2semidirect
14. #14557380C2semidirect
15. C37×#396C2semidirect
87. C2×C4×D37D4semidirect
110. C4×Dic37D4semidirect
233. #396D37semidirect
241. C37#2392semidirect

Maximal subgroups

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

subgroupindex
C2×#119244982
C2×#119244962
C2×#119244942
#145574662
#145574622
#145574552
#145574502
#145574492
#145574422
C4⋊C4×Dic372
C22⋊C4×Dic372
#145573802
C37×#3962
#239237