Finite Group Databasebeta

← #11870368

Subgroups — #11870368

Order 1152.

875 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595043C211yesmaximal, characteristic
2#10594986C211yesmaximal, characteristic, complemented
3#10592812C211yesmaximal, characteristic, complemented
4C3×#5110C211yesmaximal, characteristic, complemented
5C2×C3×#817C211yesmaximal, characteristic, complemented
6#10591130C211yesmaximal, characteristic, complemented
7#10591106C211yesmaximal, characteristic, complemented
8#10590709C212yesmaximal, complemented
9#10590704C212yesmaximal, complemented
10#10590677C212yesmaximal, complemented
11#10590674C212yesmaximal, complemented
12#79112—31nomaximal
13#78654—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C32×C8C2211yescharacteristic
17#64135C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63978—22no—
22Dic3×#67—22no—
23#63916—21no—
24#63909C2212yes—
25#63898—21no—
26D3×C4⋊Dic3C2212yes—
27#63871—21no—
28#63857C2212yes—
29#63843—21no—
30#63841C2212yes—
31#63648C2211yescharacteristic
32#63648C2211yescharacteristic
33#63643C2211yescharacteristic
34#63643C2211yescharacteristic
35C3×(C2×D3)⋊C8C2212yes—
36C3×(C2×D3)⋊C8C2212yes—
37C3×#817C2212yes—
38C3×#817C2212yes—
39#63575C2212yes—
40#63573C2212yes—
41#63567C2212yes—
42#63564C2212yes—
43#5833—31no—
44#5827—31no—
45#5510—31no—
46#5504—31no—
47C2×C3×#106—31no—
48C3×#408—31no—
49#5133—31no—
50#5121—31no—
51#5113—31no—
52#5113—31no—
53#5113—61no—
54#5110D311yescharacteristic, complemented
55C2×#817D311yescharacteristic, complemented
56#4966—31no—
57#4964—31no—
58#4868—32no—
59#4866—32no—
60#4863—32no—
61#4862—32no—
62#4737—32no—
63#4735—32no—
64#4723—32no—
65#4721—32no—
66C22×C32×C4C2311yescharacteristic
67C2×#638—21no—
68#3828—22no—
69#3828—22no—
70C2×C4⋊(C3⋊D3)C2311yescharacteristic
71C2×C4×C3⋊D3—21no—
72C2×#634C2311yescharacteristic
73C2×C3×#67D412yes—
74C22×C3×Dic3—21no—
75C22×C3×Dic3—21no—
76C3×#235—22no—
77C3×#235—22no—
78C2×C3×D12D411yescharacteristic
79C2×C3×C4×D3C2312yes—
80C2×C3×Dic6D411yescharacteristic
81C2×#626—22no—
82C2×D3×Dic3—22no—
83C2×C32×C8—22no—
84C2×C32×C8C2311yescharacteristic
85C2×C32×C8C2311yescharacteristic
86#3757—21no—
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C4×C3⋊Dic3—21no—
90C3×C4⋊Dic3—21no—
91C3×C4⋊Dic3—21no—
92C3×C4⋊Dic3C2312yes—
93C3×C4⋊Dic3C2312yes—
94C3×#208—22no—
95C2×C3×C3⋊C8C2312yes—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98#3722—22no—
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101Dic32—22no—
102#3099—91noSylow
103C2×C3×#41—31no—
104C2×#235—31no—
105C2×#235—31no—
106C2×#235—61no—
107C2×#235C2×D311yescharacteristic
108C2×C3×M16—31no—
109C22×C3×C8—21no—
110C22×C3×C8C2×D311yescharacteristic
111C22×C3×C8C2×D311yescharacteristic
112C2×C3×C4⋊C4—31no—
113C2×C3×C4⋊C4—31no—
114#946—61no—
115Q8×Dic3—61no—
116#939—62no—
117#938—61no—
118D4×Dic3—61no—
119D4×Dic3—62no—
120#930—32no—
121#930—62no—
122C4×#67—62no—
123#926—31no—
124#926—31no—
125#926—32no—
126#926—61no—
127C2×C4⋊Dic3—32no—
128C2×C4⋊Dic3C2×D311yescharacteristic
129C2×C4⋊Dic3C2×D311yescharacteristic
130#924—32no—
131C2×#208C2×D311yescharacteristic
132#897—32no—
133#897—61no—
134#895—32no—
135#895—61no—
136#893—61no—
137#892—32no—
138D3×C4⋊C4—32no—
139#887—61no—
140C3×#106—32no—
141C3×#106—32no—
142C3×C22⋊C8—32no—
143C3×C22⋊C8—32no—
144#821—31no—
145#821—31no—
146#821—31no—
147#821—31no—
148#821—32no—
149#821—61no—
150#821—61no—
151(C2×D3)⋊C8C2×D312yes—
152(C2×D3)⋊C8C2×D312yes—
153#818—32no—
154#817—32no—
155#817C2×D312yes—
156#817C2×D312yes—
157#816—31no—
158#816—31no—
159#816—31no—
160#816—31no—
161#816—32no—
162#816—61no—
163#816—61no—
164#810—32no—
165#809—32no—
166#808—32no—
167#807—32no—
168C23×C32C2×D411yescharacteristic
169C22×C3⋊D3—21no—
170C22×C3×D3C2×D412yes—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4#4112yes—
173C2×C32×C4#4112yes—
174C2×C32×C4C2411yescharacteristic
175#638—42no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C4⋊(C3⋊D3)—21no—
180C4⋊(C3⋊D3)—21no—
181C4×C3⋊D3—42no—
182#634—21no—
183#634—21no—
184C3×#67—24no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—81no—
188C2×C3×Dic3—81no—
189C2×C3×Dic3C2×D412yes—
190C3×D12—22no—
191C3×C4×D3—22no—
192C3×C4×D3—22no—
193C3×Dic6—22no—
194#626—82no—
195D3×Dic3—82no—
196C32×C8—21no—
197C32×C8—21no—
198C3×C3⋊C8—22no—
199#537—91no—
200#520—91no—
201#485—92no—
202#483—92no—
203#482—92no—
204#481—92no—
205#428—91no—
206C2×#106—31no—
207#417—91no—
208#416—91no—
209#408—31no—
210C3×#41—62no—
211C3×#41—62no—
212C2×C3×Q8—31no—
213C2×C3×D4—32no—
214C2×C3×D4—31no—
215C22×C3×C4—21no—
216C22×C3×C4—32no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C2×#67—62no—
222C2×#67—61no—
223C2×#67—61no—
224C2×#67—121no—
225C2×#67D1212yes—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—62no—
229#235—22no—
230#235—22no—
231#235—64no—
232#235—62no—
233#235—62no—
234#235—62no—
235#235—62no—
236#235—122no—
237C2×D12—31no—
238C2×D12—31no—
239C2×D12—61no—
240C2×D12—62no—
241C2×D12D1211yescharacteristic
242C2×C4×D3—61no—
243C2×C4×D3—61no—
244C2×C4×D3—62no—
245C2×C4×D3—121no—
246C2×C4×D3C22×D312yes—
247C2×Dic6—31no—
248C2×Dic6—31no—
249C2×Dic6—61no—
250C2×Dic6D1211yescharacteristic
251C3×M16—62no—
252C2×C3×C8—22no—
253C2×C3×C8—22no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—32no—
257C2×C3×C8—42no—
258C2×C3×C8C22×D311yescharacteristic
259C2×C3×C8C22×D311yescharacteristic
260C2×C3×C8C22×D311yescharacteristic
261C2×C3×C8C22×D311yescharacteristic
262C3×C4⋊C4—32no—
263C3×C4⋊C4—32no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4—61no—
266#217—62no—
267#217—62no—
268#217—61no—
269#217—61no—
270#217—121no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—62no—
273(C2×D3)⋊C4—62no—
274(C2×D3)⋊C4—62no—
275C4⋊Dic3—21no—
276C4⋊Dic3—21no—
277C4⋊Dic3—31no—
278C4⋊Dic3—31no—
279C4⋊Dic3—31no—
280C4⋊Dic3—31no—
281C4⋊Dic3—61no—
282C4⋊Dic3—61no—
283C4⋊Dic3—62no—
284C4⋊Dic3—62no—
285C4⋊Dic3C22×D312yes—
286C4⋊Dic3C22×D312yes—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289C4×Dic3—62no—
290C4×Dic3—61no—
291C4×Dic3—61no—
292C4×Dic3—62no—
293C4×Dic3—121no—
294#208—22no—
295C2×C3⋊C8C22×D312yes—
296C22×C32—21no—
297C22×C32—21no—
298C22×C32#12312yes—
299C22×C32C22×D411yescharacteristic
300C2×C3⋊D3—41no—
301C2×C3⋊D3—41no—
302C2×C3⋊D3—41no—
303C2×C3×D3—22no—
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C32×C4#12312yes—
307C32×C4C2×#4111yescharacteristic
308C32×C4C2×#4111yescharacteristic
309C3⋊Dic3—41no—
310C3⋊Dic3—41no—
311C3⋊Dic3—41no—
312C3×Dic3—22no—
313C3×Dic3—42no—
314C3×Dic3—42no—
315C2×#41—31no—
316C2×#41—91no—
317C2×M16—31no—
318C22×C8D3211yescharacteristic
319C22⋊Q8—92no—
320C22⋊Q8—181no—
321#121—92no—
322#121—181no—
323#121—182no—
324C4×Q8—181no—
325C4×D4—181no—
326C4×D4—182no—
327#117—92no—
328#117—91no—
329C2×C4⋊C4—31no—
330C2×C4⋊C4—31no—
331C2×C4⋊C4—92no—
332#107—92no—
333#106—32no—
334#106—32no—
335#106—92no—
336#103—92no—
337#103—91no—
338#103—91no—
339#102—92no—
340#102—91no—
341#102—91no—
342C22⋊C8—32no—
343C22⋊C8—32no—
344C23×C3—21no—
345C23×C3—32no—
346C23×C3C2×D1211yescharacteristic
347C23×C3D3×D411yescharacteristic
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—121no—
351C22×D3C2×D1212yes—
352C3×Q8—62no—
353C3×D4—64no—
354C3×D4—62no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—22no—
359C2×C3×C4—32no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—241no—
365C2×C3×C4—241no—
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4#23512yes—
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4#23712yes—
370C2×C3×C4#23712yes—
371C2×C3×C4#23912yes—
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—24no—
375#67—124no—
376#67—122no—
377#67—122no—
378#67—242no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—81no—
388C2×Dic3—81no—
389C2×Dic3—121no—
390C2×Dic3—121no—
391C2×Dic3—121no—
392C2×Dic3—242no—
393C2×Dic3C2×D1212yes—
394D12—22no—
395D12—62no—
396D12—61no—
397D12—61no—
398D12—61no—
399D12—61no—
400D12—121no—
401D12—242no—
402C4×D3—22no—
403C4×D3—22no—
404C4×D3—124no—
405C4×D3—122no—
406C4×D3—122no—
407C4×D3—242no—
408Dic6—22no—
409Dic6—62no—
410Dic6—61no—
411Dic6—61no—
412Dic6—61no—
413Dic6—61no—
414Dic6—121no—
415C3×C8—21no—
416C3×C8—21no—
417C3×C8—21no—
418C3×C8—21no—
419C3×C8—41no—
420C3×C8—41no—
421C3×C8—62no—
422C3⋊C8—22no—
423C2×C32—22no—
424C2×C32C2×#12311yescharacteristic
425C2×C32#57711yescharacteristic
426C2×C32#57711yescharacteristic
427C3⋊D3—81no—
428C3×D3—42no—
429#41—62no—
430#41—62no—
431#41—182no—
432#41—182no—
433C2×Q8—31no—
434C2×Q8—91no—
435C2×D4—32no—
436C2×D4—31no—
437C2×D4—91no—
438C2×D4—182no—
439C2×D4—181no—
440C22×C4—32no—
441C22×C4—61no—
442C22×C4—61no—
443C22×C4—182no—
444C22×C4—181no—
445C22×C4C2×D3211yescharacteristic
446M16—62no—
447C2×C8—22no—
448C2×C8—32no—
449C2×C8C2×D3211yescharacteristic
450C2×C8C2×D3211yescharacteristic
451C4⋊C4—32no—
452C4⋊C4—32no—
453C4⋊C4—61no—
454C4⋊C4—61no—
455C4⋊C4—91no—
456C4⋊C4—91no—
457C4⋊C4—182no—
458C4⋊C4—182no—
459C22⋊C4—182no—
460C22⋊C4—182no—
461C22⋊C4—182no—
462C22⋊C4—181no—
463C42—182no—
464C42—181no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—22no—
471C22×C3—41no—
472C22×C3—41no—
473C22×C3—62no—
474C22×C3—62no—
475C22×C3—62no—
476C22×C3#88612yes—
477C22×C3#89412yes—
478C22×C3C22×D1211yescharacteristic
479C22×C3C2×D3×D411yescharacteristic
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—22no—
483C2×D3—122no—
484C2×D3—121no—
485C2×D3—121no—
486C2×D3—121no—
487C2×D3—121no—
488C2×D3—121no—
489C2×D3—121no—
490C2×D3—241no—
491C2×D3—241no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—22no—
495C3×C4—62no—
496C3×C4—122no—
497C3×C4—122no—
498C3×C4#88612yes—
499C3×C4#89412yes—
500C3×C4C2×#23511yescharacteristic
501C3×C4C2×#23711yescharacteristic
502C3×C4C2×#23711yescharacteristic
503C3×C4C2×#23911yescharacteristic
504Dic3—22no—
505Dic3—42no—
506Dic3—42no—
507Dic3—122no—
508Dic3—121no—
509Dic3—121no—
510Dic3—121no—
511Dic3—121no—
512Dic3—121no—
513Dic3—121no—
514Dic3—241no—
515Dic3—241no—
516C32#309911yescharacteristic, complemented, Sylow
517C23—32no—
518C23—181no—
519C23D3×D1211yescharacteristic
520Q8—62no—
521Q8—181no—
522Q8—181no—
523D4—64no—
524D4—62no—
525D4—181no—
526D4—181no—
527D4—362no—
528D4—722no—
529C2×C4—32no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—241no—
538C2×C4—241no—
539C2×C4—362no—
540C2×C4—722no—
541C2×C4#379612yes—
542C2×C4D3×D1211yescharacteristic
543C2×C4#380412yes—
544C2×C4C22×D3211yescharacteristic
545C8—21no—
546C8—21no—
547C8—62no—
548C2×C3—22no—
549C2×C3—22no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—21no—
553C2×C3—42no—
554C2×C3—122no—
555C2×C3C2×#88611yescharacteristic
556C2×C3C2×#89411yescharacteristic
557C2×C3#575111yescharacteristic
558C2×C3#575111yescharacteristic
559C2×C3#576211yescharacteristic
560C2×C3#576211yescharacteristic
561D3—42no—
562D3—242no—
563D3—241no—
564D3—241no—
565C22—21no—
566C22—21no—
567C22—62no—
568C22—62no—
569C22—62no—
570C22—361no—
571C22—361no—
572C22—361no—
573C22#6389012yes—
574C22C2×D3×D1211yescharacteristic
575C4—62no—
576C4—122no—
577C4—122no—
578C4—361no—
579C4—361no—
580C4—361no—
581C4#6389012yes—
582C4C2×#379611yescharacteristic
583C4C2×#380411yescharacteristic
584C3—21no—
585C3#7865411yescharacteristic, complemented
586C3#7911211yescharacteristic, complemented
587C2—22no—
588C2—122no—
589C2—721no—
590C2#1059467711yescharacteristic
591C2#1059467711yescharacteristic
592C2C2×#6389011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595043C2
hypercenterC22×C8D32
hypocenterC32#3099
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594986C2semidirect
3. #10592812C2semidirect
4. C3×#5110C2semidirect
5. C2×C3×#817C2semidirect
6. #10591130C2semidirect
7. #10591106C2semidirect
8. #10590709C2semidirect
9. #10590704C2semidirect
10. #10590677C2semidirect
11. #10590674C2semidirect
54. #5110D3semidirect
55. C2×#817D3semidirect
516. C32#3099semidirect
585. C3#78654semidirect
586. C3#79112semidirect

Maximal subgroups

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

subgroupindex
#105950432
#105949862
#105928122
C3×#51102
C2×C3×#8172
#105911302
#105911062
#105907092
#105907042
#105906772
#105906742
#791123
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