Finite Group Databasebeta

← #18006349

Subgroups — #18006349

Order 4736.

504 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11924557C211yesmaximal, characteristic, complemented
2C2×#11924556C211yesmaximal, characteristic, complemented
3#14558202C211yesmaximal, characteristic, complemented
4#14558201C211yesmaximal, characteristic, complemented
5#14557908C211yesmaximal, characteristic, complemented
6#14557768C211yesmaximal, characteristic, complemented
7#14557767C211yesmaximal, characteristic, complemented
8#14557732C211yesmaximal, characteristic, complemented
9#14557731C211yesmaximal, characteristic, complemented
10#14557681C211yesmaximal, characteristic, complemented
11#14557680C211yesmaximal, characteristic, complemented
12#14557675C211yesmaximal, characteristic, complemented
13#14557625C211yesmaximal, characteristic, complemented
14#14557596C211yesmaximal, characteristic, complemented
15C37×#449C211yesmaximal, characteristic, complemented
16C2×#10596966C2211yescharacteristic
17C2×#10596962C2211yescharacteristic
18C2×#10596964C2211yescharacteristic
19#11924557—24no—
20#11924556—24no—
21C2×#10596942C2211yescharacteristic
22C2×#10596930C2211yescharacteristic
23C2×#10596940C2211yescharacteristic
24C2×#10596941C2211yescharacteristic
25C2×D296C2211yescharacteristic
26C2×#10596939C2211yescharacteristic
27C2×#10596939C2211yescharacteristic
28C22×#64436C2211yescharacteristic
29C2×C8×D37C2211yescharacteristic
30#11924532—21no—
31#11924532—21no—
32#11924532C2211yescharacteristic
33#11924532C2211yescharacteristic
34#11924511C2211yescharacteristic
35#11924510—21no—
36#11924510C2211yescharacteristic
37#11924509—21no—
38#11924508—21no—
39#11924507—21no—
40#11924507C2211yescharacteristic
41Q8×Dic37C2211yescharacteristic
42#11924501C2211yescharacteristic
43C4×C22⋊D37—21no—
44C4×C22⋊D37C2211yescharacteristic
45#11924496—21no—
46#11924469C2211yescharacteristic
47#11924465C2211yescharacteristic
48#11924461C2211yescharacteristic
49#11924458C2211yescharacteristic
50#11924457C2211yescharacteristic
51#11924456C2211yescharacteristic
52#11924448C2211yescharacteristic
53C8×Dic37C2211yescharacteristic
54C2×#41×C37C2211yescharacteristic
55C2×SD16×C37C2211yescharacteristic
56C2×D8×C37C2211yescharacteristic
57#121×C37C2211yescharacteristic
58#103×C37C2211yescharacteristic
59#102×C37C2211yescharacteristic
60C22⋊C8×C37C2211yescharacteristic
61#41×C37—22no—
62#41×C37—41no—
63C2×Q8×C37C2311yescharacteristic
64C2×D4×C37—21no—
65C2×D4×C37—21no—
66C2×D4×C37C2311yescharacteristic
67C2×D4×C37C2311yescharacteristic
68C22×C4×C37—21no—
69C22×C4×C37C2311yescharacteristic
70C2×C22⋊D37—21no—
71C2×C22⋊D37—21no—
72C2×C22⋊D37—21no—
73C2×C22⋊D37—21no—
74C2×C22⋊D37—21no—
75C2×C22⋊D37—21no—
76C2×C22⋊D37—21no—
77C2×C22⋊D37—21no—
78C2×C22⋊D37D411yescharacteristic
79C22×Dic37—21no—
80#10596966—22no—
81#10596966—41no—
82#10596964—22no—
83#10596964—41no—
84#10596962—22no—
85#10596962—41no—
86C2×D148—21no—
87C2×D148—21no—
88C2×D148C2311yescharacteristic
89C2×D148C2311yescharacteristic
90C2×C4×D37—21no—
91C2×C4×D37—21no—
92C2×C4×D37C2311yescharacteristic
93C2×Dic74C2311yescharacteristic
94SD16×C37—22no—
95D8×C37—41no—
96C2×C8×C37C2311yescharacteristic
97C2×C8×C37C2311yescharacteristic
98C4⋊C4×C37C2311yescharacteristic
99C22⋊C4×C37—21no—
100C22⋊Dic37—21no—
101C22⋊Dic37D411yescharacteristic
102#10596942D414yescomplemented
103#10596941—22no—
104#10596940—22no—
105#10596939—22no—
106#10596939—22no—
107#10596938—21no—
108#10596938—21no—
109#10596938D411yescharacteristic
110C4⋊Dic37—21no—
111C4⋊Dic37C2311yescharacteristic
112#10596936—21no—
113#10596936D411yescharacteristic
114C4×Dic37—21no—
115C4×Dic37—21no—
116C4×Dic37C2311yescharacteristic
117C2×#64436—22no—
118C2×#64436C2311yescharacteristic
119C2×#64436C2311yescharacteristic
120D296—41no—
121#10596930—22no—
122C8×D37—22no—
123C23×C37—21no—
124C23×C37—21no—
125C23×C37C2×D411yescharacteristic
126C22×D37—21no—
127C22×D37—21no—
128C22×D37C2×D411yescharacteristic
129Q8×C37—21no—
130Q8×C37C2×D412yes—
131D4×C37—21no—
132D4×C37—21no—
133D4×C37—21no—
134D4×C37—21no—
135D4×C37—42no—
136D4×C37—81no—
137C2×C4×C37—21no—
138C2×C4×C37—21no—
139C2×C4×C37—21no—
140C2×C4×C37—21no—
141C2×C4×C37—42no—
142C2×C4×C37C2×D411yescharacteristic
143C2×C4×C37C2411yescharacteristic
144C22⋊D37—22no—
145C22⋊D37—42no—
146C22⋊D37—42no—
147C22⋊D37—42no—
148C22⋊D37—42no—
149C22⋊D37—81no—
150C22⋊D37—81no—
151C22⋊D37—81no—
152C22⋊D37—81no—
153C2×Dic37—21no—
154C2×Dic37—21no—
155C2×Dic37—42no—
156C2×Dic37C2×D411yescharacteristic
157C2×Dic37C2×D411yescharacteristic
158C2×Dic37C2×D411yescharacteristic
159D148—21no—
160D148—21no—
161D148—21no—
162D148—21no—
163D148—42no—
164D148—81no—
165C4×D37—21no—
166C4×D37—21no—
167C4×D37—42no—
168C4×D37—42no—
169Dic74—21no—
170Dic74C2×D412yes—
171C8×C37—21no—
172C8×C37—21no—
173#64436—21no—
174#64436C2×D412yes—
175C22×C37—21no—
176C22×C37—21no—
177C22×C37—21no—
178C22×C37—41no—
179C22×C37—41no—
180C22×C37—41no—
181C22×C37—41no—
182C22×C37—41no—
183C22×C37—41no—
184C22×C37C22×D411yescharacteristic
185C2×D37—21no—
186C2×D37—21no—
187C2×D37—21no—
188C2×D37—41no—
189C2×D37—41no—
190C2×D37—41no—
191C2×D37—41no—
192C2×D37—41no—
193C2×D37—41no—
194C4×C37—21no—
195C4×C37—22no—
196C4×C37—41no—
197C4×C37C22×D411yescharacteristic
198C4×C37H(5,𝔽2)11yescharacteristic
199Dic37—22no—
200Dic37—21no—
201Dic37—21no—
202Dic37—41no—
203Dic37#13512yescomplemented
204#3287—371nomaximal, Sylow
205C2×C37—41no—
206C2×C37—81no—
207C2×C37—81no—
208C2×C37D4211yescharacteristic
209C2×C37C2×#13511yescharacteristic
210C2×C37#57611yescharacteristic
211D37—41no—
212D37—81no—
213D37—81no—
214C2×#135—371no—
215C2×#135—371no—
216#550—371no—
217#550—371no—
218#493—371no—
219#466—371no—
220#466—371no—
221#460—371no—
222#460—371no—
223#449—371no—
224#449—371no—
225#449—371no—
226#449D3711yescharacteristic, complemented
227C4×Q16—371no—
228C8×D4—371no—
229C37#328711yescharacteristic, complemented, Sylow
230C2×#41—371no—
231C2×#41—371no—
232C2×#41—371no—
233C2×#41C2×D3711yescharacteristic
234#135—744no—
235#135—744no—
236C2×Q16—371no—
237C2×SD16—371no—
238C2×SD16—371no—
239C2×SD16—371no—
240C2×SD16C2×D3711yescharacteristic
241C2×D8—371no—
242C2×D8—371no—
243C2×D8—371no—
244C2×D8C2×D3711yescharacteristic
245C22×C8—371no—
246C22×C8—371no—
247#127—371no—
248#127—371no—
249#127—741no—
250#127—741no—
251#121—371no—
252#121—371no—
253#121—371no—
254#121—741no—
255#121—741no—
256#121—741no—
257#121—741no—
258#121C2×D3711yescharacteristic
259C4×Q8—371no—
260C4×Q8—371no—
261C4×D4—371no—
262C4×D4—741no—
263C4×D4—741no—
264#107—371no—
265C4⋊C8—371no—
266#103—371no—
267#103C2×D3711yescharacteristic
268#102—371no—
269#102—371no—
270#102—371no—
271#102C2×D3711yescharacteristic
272C22⋊C8—371no—
273C22⋊C8C2×D3711yescharacteristic
274C4×C8—371no—
275#41—22no—
276#41—41no—
277#41—742no—
278#41—742no—
279#41—742no—
280#41—1481no—
281#41—1481no—
282#41—1481no—
283C2×Q8—371no—
284C2×Q8C22×D3711yescharacteristic
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—371no—
288C2×D4—371no—
289C2×D4—371no—
290C2×D4—741no—
291C2×D4—741no—
292C2×D4—741no—
293C2×D4—741no—
294C2×D4—741no—
295C2×D4—741no—
296C2×D4—741no—
297C2×D4—741no—
298C2×D4—741no—
299C2×D4—741no—
300C2×D4C22×D3711yescharacteristic
301C2×D4C22×D3711yescharacteristic
302C22×C4—21no—
303C22×C4—371no—
304C22×C4—741no—
305C22×C4—741no—
306C22×C4—741no—
307C22×C4C22×D3711yescharacteristic
308Q16—374no—
309SD16—22no—
310SD16—742no—
311SD16—742no—
312SD16—742no—
313D8—41no—
314D8—742no—
315D8—742no—
316D8—1481no—
317C2×C8—371no—
318C2×C8—371no—
319C2×C8—742no—
320C2×C8—742no—
321C2×C8C22×D3711yescharacteristic
322C2×C8C22×D3711yescharacteristic
323C4⋊C4—371no—
324C4⋊C4—371no—
325C4⋊C4—741no—
326C4⋊C4—741no—
327C4⋊C4C22×D3711yescharacteristic
328C22⋊C4—21no—
329C22⋊C4—371no—
330C22⋊C4—371no—
331C22⋊C4—741no—
332C22⋊C4—741no—
333C22⋊C4—741no—
334C42—371no—
335C42—741no—
336C42—741no—
337C23—21no—
338C23—21no—
339C23—371no—
340C23—741no—
341C23—741no—
342C23D4×D3711yescharacteristic
343Q8—21no—
344Q8—372no—
345Q8—741no—
346Q8D4×D3712yes—
347D4—21no—
348D4—21no—
349D4—21no—
350D4—21no—
351D4—42no—
352D4—81no—
353D4—2961no—
354D4—2961no—
355D4—2961no—
356D4—2961no—
357D4—2961no—
358D4—742no—
359D4—741no—
360D4—741no—
361D4—741no—
362D4—741no—
363D4—1482no—
364D4—1482no—
365D4—1482no—
366D4—1482no—
367D4—1482no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—42no—
373C2×C4—371no—
374C2×C4—371no—
375C2×C4—371no—
376C2×C4—741no—
377C2×C4—741no—
378C2×C4—741no—
379C2×C4—741no—
380C2×C4—1482no—
381C2×C4—1482no—
382C2×C4—1482no—
383C2×C4D4×D3711yescharacteristic
384C2×C4C23×D3711yescharacteristic
385C8—21no—
386C8—21no—
387C8—372no—
388C8—741no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22—741no—
399C22—741no—
400C22—741no—
401C22—1481no—
402C22—1481no—
403C22—1481no—
404C22—1481no—
405C22—1481no—
406C22—1481no—
407C22C2×D4×D3711yescharacteristic
408C4—21no—
409C4—22no—
410C4—41no—
411C4—372no—
412C4—741no—
413C4—741no—
414C4—742no—
415C4—1481no—
416C4C2×D4×D3711yescharacteristic
417C4#1192458111yescharacteristic
418C2—41no—
419C2—81no—
420C2—81no—
421C2—2961no—
422C2—2961no—
423C2—1481no—
424C2#1455816511yescharacteristic
425C2#135×D3711yescharacteristic
426C2#1455833711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#449C2
socleC22×C37C22×D4
hypercenter#449D37
hypocenterC37#3287
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. C2×#11924557C2semidirect
2. C2×#11924556C2semidirect
3. #14558202C2semidirect
4. #14558201C2semidirect
5. #14557908C2semidirect
6. #14557768C2semidirect
7. #14557767C2semidirect
8. #14557732C2semidirect
9. #14557731C2semidirect
10. #14557681C2semidirect
11. #14557680C2semidirect
12. #14557675C2semidirect
13. #14557625C2semidirect
14. #14557596C2semidirect
15. C37×#449C2semidirect
102. #10596942D4semidirect
203. Dic37#135semidirect
226. #449D37semidirect
229. C37#3287semidirect

Maximal subgroups

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

subgroupindex
C2×#119245572
C2×#119245562
#145582022
#145582012
#145579082
#145577682
#145577672
#145577322
#145577312
#145576812
#145576802
#145576752
#145576252
#145575962
C37×#4492
#328737