Finite Group Databasebeta

← #11872367

Subgroups — #11872367

Order 1152.

837 conjugacy classes of subgroups.

The subgroup lattice has 767 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5574C211yesmaximal, characteristic, complemented
2#10593949C211yesmaximal, characteristic, complemented
3#10592721C211yesmaximal, characteristic, complemented
4C3×#5027C211yesmaximal, characteristic, complemented
5#10591586C211yesmaximal, characteristic, complemented
6#10591586C211yesmaximal, characteristic, complemented
7#10591566C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#10590500C211yesmaximal, characteristic, complemented
10#10590498C211yesmaximal, characteristic, complemented
11#10590455C211yesmaximal, characteristic, complemented
12#10590452C211yesmaximal, characteristic, complemented
13#10590347C211yesmaximal, characteristic, complemented
14#10590271C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#82568—31nomaximal
17#80364—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic
20#64079C2211yescharacteristic
21C3×Q8×Dic3C2211yescharacteristic
22C2×C3×#215C2211yescharacteristic
23C2×C3×#215C2211yescharacteristic
24C3×#893—21no—
25C3×#893C2211yescharacteristic
26C3×D3×C4⋊C4—21no—
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×#874C2211yescharacteristic
29C3×C4×D12—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#872—21no—
32C3×#872C2211yescharacteristic
33#63908C2211yescharacteristic
34#63908C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37#63885—21no—
38#63885—21no—
39#63884—21no—
40#63884—21no—
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63662C2211yescharacteristic
44#63662C2211yescharacteristic
45#63635C2211yescharacteristic
46#63634C2211yescharacteristic
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53#63563C2211yescharacteristic
54#63563C2211yescharacteristic
55#63562C2211yescharacteristic
56#63562C2211yescharacteristic
57(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
58(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#520—31no—
62#5719—31no—
63#5574D311yescharacteristic, complemented
64#5535—31no—
65C3×#460—31no—
66#5238—31no—
67#5238—31no—
68#5172—31no—
69#5172—31no—
70#5164—31no—
71Dic3×SD16—31no—
72#5072—31no—
73#5027D311yescharacteristic, complemented
74#5026—31no—
75C4×#215—31no—
76#5022—31no—
77#5022—31no—
78#5022—61no—
79#5015—31no—
80#5014—31no—
81C4×#213—31no—
82#5009—31no—
83#5000—31no—
84#4968—31no—
85#4967—31no—
86#4847—31no—
87#4840—31no—
88#4785—31no—
89#4777—31no—
90#4774—31no—
91#4756—31no—
92C2×C32×Q8C2311yescharacteristic
93C3×#239—22no—
94C3×#239—22no—
95C2×C3×D12—21no—
96C2×C3×D12—21no—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×#625—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C42—21no—
113C32×C42C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#215—22no—
121C3×#215—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3713—22no—
140#3713—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#239C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C3×#127—31no—
147C3×C4×Q8—21no—
148C3×C4×Q8—31no—
149C3×C4×Q8C2×D311yescharacteristic
150C3×C4×Q8C2×D311yescharacteristic
151C3×C4×D4—31no—
152C3×C4×D4—31no—
153C3×C4×D4—61no—
154C3×C4×D4—61no—
155C3×#117—31no—
156C3×#117—61no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—61no—
159Q8×Dic3C2×D311yescharacteristic
160C2×#215C2×D311yescharacteristic
161C2×#215C2×D311yescharacteristic
162#939—61no—
163#939—61no—
164#938—31no—
165#938—31no—
166#935—61no—
167#935—61no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170C2×#213—31no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—31no—
174#930—31no—
175#930—31no—
176#894—61no—
177#894—61no—
178#893—21no—
179#893C2×D311yescharacteristic
180D3×C4⋊C4—21no—
181D3×C4⋊C4C2×D311yescharacteristic
182#884—61no—
183#884—61no—
184#874C2×D311yescharacteristic
185C4×D12—21no—
186C4×D12—31no—
187C4×D12—31no—
188C4×D12C2×D311yescharacteristic
189#872—21no—
190#872C2×D311yescharacteristic
191#870—31no—
192#870—31no—
193#870—61no—
194C3×C4⋊C8—31no—
195C3×#102—31no—
196C3×#102—31no—
197#835—31no—
198#835—31no—
199#835—31no—
200#835—31no—
201#835—61no—
202#835—61no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#830—31no—
208#830—31no—
209#821—31no—
210#821—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213#818—31no—
214#817—31no—
215#815—31no—
216C8×Dic3—31no—
217#809—31no—
218#809—31no—
219#809C2×D311yescharacteristic
220#809C2×D311yescharacteristic
221#808—31no—
222#808—31no—
223#808—31no—
224#808—61no—
225#807—31no—
226#807—31no—
227#807—31no—
228#807—61no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4⋊(C3⋊C8)—61no—
232C4⋊(C3⋊C8)C2×D311yescharacteristic
233#803—31no—
234C4×C3⋊C8—31no—
235C22×C3×D3—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×Q8—21no—
240C32×Q8#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×D12—24no—
253C3×D12—21no—
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—81no—
259C3×D12—81no—
260C3×D12#4112yes—
261C3×C4×D3—24no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267#625—81no—
268#625—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#540—91no—
276#520—31no—
277#481—91no—
278#480—91no—
279#479—91no—
280#478—91no—
281#460—31no—
282#459—91no—
283#449—91no—
284#449—91no—
285#442—91no—
286#440—91no—
287C4×SD16—91no—
288C4×D8—91no—
289#433—91no—
290C3×#41—62no—
291C3×#41—62no—
292C2×C3×Q8—21no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C22×C3×C4—31no—
302C22×C3×C4—61no—
303C22×C3×C4—61no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312#239—22no—
313#239—22no—
314C2×D12—21no—
315C2×D12—21no—
316C2×D12—21no—
317C2×D12C22×D311yescharacteristic
318C2×D12C22×D311yescharacteristic
319C2×D12C22×D311yescharacteristic
320C2×C4×D3—21no—
321C2×C4×D3—21no—
322C2×C4×D3—21no—
323C2×C4×D3—21no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3C22×D311yescharacteristic
327C3×SD16—62no—
328C3×SD16—62no—
329C2×C3×C8—31no—
330C2×C3×C8—31no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—41no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C22⋊C4—31no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C42—21no—
347C3×C42—21no—
348C3×C42—21no—
349C3×C42—31no—
350C3×C42—41no—
351C3×C42—61no—
352C3×C42C22×D311yescharacteristic
353C3×C42C22×D311yescharacteristic
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#215—22no—
359#215—22no—
360#213—62no—
361#213—62no—
362#213—62no—
363#213—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4#6711yescharacteristic
371(C2×D3)⋊C4#6711yescharacteristic
372C4⋊Dic3—21no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—121no—
386Dic3⋊C4—121no—
387Dic3⋊C4#6711yescharacteristic
388Dic3⋊C4#6711yescharacteristic
389C4×Dic3—21no—
390C4×Dic3C22×D311yescharacteristic
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8C22×D311yescharacteristic
398C2×C3⋊C8C22×D311yescharacteristic
399C22×C32C22×D411yescharacteristic
400C2×C3×D3—21no—
401C2×C3×D3—22no—
402C2×C3×D3—21no—
403C2×C3×D3—21no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C2×C3×D3—41no—
407C2×C3×D3—41no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C32×C4—22no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4C2×#4111yescharacteristic
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C2×#41—31no—
425C2×SD16—31no—
426C2×SD16—31no—
427C2×D8—91no—
428C2×D8—91no—
429#127—31no—
430#125—91no—
431#123—181no—
432#123—181no—
433#121—91no—
434#121—91no—
435#121—181no—
436#121—181no—
437C4×Q8—31no—
438C4×Q8D3211yescharacteristic
439C4×D4—31no—
440C4×D4—31no—
441C4×D4—61no—
442C4×D4—61no—
443C4×D4—91no—
444C4×D4—91no—
445#117—31no—
446#117—61no—
447C2×C4⋊C4—31no—
448C2×C4⋊C4—61no—
449#107—91no—
450#107—91no—
451#106—91no—
452#106—91no—
453C4⋊C8—31no—
454C4⋊C8—91no—
455#103—91no—
456#103—91no—
457#102—31no—
458#102—31no—
459#102—91no—
460#102—91no—
461#102—91no—
462#102—91no—
463C22⋊C8—91no—
464C22⋊C8—91no—
465#97—91no—
466C4×C8—91no—
467C23×C3—31no—
468C23×C3—61no—
469C23×C3—61no—
470C23×C3—61no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3C2×#6711yescharacteristic
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—22no—
478C3×Q8—41no—
479C3×Q8#23512yes—
480C3×Q8#23712yes—
481C3×D4—32no—
482C3×D4—64no—
483C3×D4—61no—
484C3×D4—61no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—61no—
488C3×D4—241no—
489C3×D4—241no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—64no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—241no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4C2×#6711yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—241no—
516#67—241no—
517#67—241no—
518#67—241no—
519C2×Dic3—21no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—241no—
527C2×Dic3—241no—
528C2×Dic3C2×#6711yescharacteristic
529C2×Dic3C2×#6711yescharacteristic
530C2×Dic3C2×#6711yescharacteristic
531D12—24no—
532D12—21no—
533D12—21no—
534D12—21no—
535D12—21no—
536D12—21no—
537D12—81no—
538D12—81no—
539D12#23512yes—
540C4×D3—24no—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—81no—
544C4×D3—81no—
545C4×D3—81no—
546C4×D3—241no—
547C4×D3—241no—
548C3×C8—61no—
549C3×C8—61no—
550C3⋊C8—21no—
551C3⋊C8—21no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—121no—
557C3⋊C8—121no—
558C2×C32#52511yescharacteristic
559C2×C32#57611yescharacteristic
560C2×C32#57711yescharacteristic
561C3×D3—41no—
562C3×D3—42no—
563C3×D3—81no—
564C3×D3—81no—
565#41—62no—
566#41—62no—
567C2×Q8C2×D3211yescharacteristic
568C2×D4—31no—
569C2×D4—31no—
570C2×D4—31no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—181no—
575C2×D4—181no—
576C22×C4—31no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—181no—
582C22×C4—181no—
583SD16—62no—
584SD16—62no—
585D8—182no—
586D8—182no—
587C2×C8—31no—
588C2×C8—31no—
589C2×C8—91no—
590C2×C8—91no—
591C4⋊C4—21no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—91no—
598C4⋊C4—91no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4C2×D3211yescharacteristic
602C22⋊C4—31no—
603C22⋊C4—31no—
604C22⋊C4—61no—
605C22⋊C4—61no—
606C22⋊C4—181no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C42—21no—
611C42—31no—
612C42—61no—
613C42C2×D3211yescharacteristic
614C22×C3—21no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—62no—
618C22×C3—61no—
619C22×C3—121no—
620C22×C3—121no—
621C22×C3—121no—
622C22×C3—121no—
623C22×C3—121no—
624C22×C3—121no—
625C22×C3—121no—
626C22×C3—121no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C22×#6711yescharacteristic
629C2×D3—21no—
630C2×D3—22no—
631C2×D3—21no—
632C2×D3—21no—
633C2×D3—41no—
634C2×D3—41no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—41no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—22no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—22no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—42no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—81no—
658C3×C4—121no—
659C3×C4C2×#23511yescharacteristic
660C3×C4C2×#23511yescharacteristic
661C3×C4C2×#23711yescharacteristic
662C3×C4D3×#4111yescharacteristic
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—41no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—241no—
672Dic3—241no—
673C32#311911yescharacteristic, complemented, Sylow
674C23—31no—
675C23—61no—
676C23—61no—
677C23—61no—
678Q8—21no—
679Q8#379512yes—
680D4—32no—
681D4—64no—
682D4—61no—
683D4—61no—
684D4—61no—
685D4—61no—
686D4—61no—
687D4—241no—
688D4—241no—
689D4—721no—
690D4—721no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—64no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—181no—
701C2×C4—181no—
702C2×C4—241no—
703C2×C4—241no—
704C2×C4—241no—
705C2×C4—721no—
706C2×C4—721no—
707C2×C4D3×#6711yescharacteristic
708C2×C4D3×#6711yescharacteristic
709C2×C4C22×D3211yescharacteristic
710C8—61no—
711C8—61no—
712C8—181no—
713C8—181no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—121no—
718C2×C3—122no—
719C2×C3—241no—
720C2×C3—241no—
721C2×C3#560611yescharacteristic
722C2×C3#576211yescharacteristic
723C2×C3#577411yescharacteristic
724C2×C3#579111yescharacteristic
725C2×C3#583511yescharacteristic
726C2×C3#583711yescharacteristic
727D3—41no—
728D3—42no—
729D3—81no—
730D3—81no—
731C22—62no—
732C22—61no—
733C22—61no—
734C22—61no—
735C22—121no—
736C22—121no—
737C22—121no—
738C22—121no—
739C22—121no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22C2×D3×#6711yescharacteristic
744C4—22no—
745C4—21no—
746C4—21no—
747C4—41no—
748C4—61no—
749C4—61no—
750C4—61no—
751C4—121no—
752C4—361no—
753C4—361no—
754C4C2×#379511yescharacteristic
755C4D3×#23511yescharacteristic
756C3—21no—
757C3#8036411yescharacteristic, complemented
758C3#8256811yescharacteristic, complemented
759C2—121no—
760C2—122no—
761C2—241no—
762C2—241no—
763C2#1059489211yescharacteristic
764C2#1059531811yescharacteristic
765C2#1059545411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5574C2semidirect
2. #10593949C2semidirect
3. #10592721C2semidirect
4. C3×#5027C2semidirect
5. #10591586C2semidirect
6. #10591586C2semidirect
7. #10591566C2semidirect
8. Dic3×#215C2semidirect
9. #10590500C2semidirect
10. #10590498C2semidirect
11. #10590455C2semidirect
12. #10590452C2semidirect
13. #10590347C2semidirect
14. #10590271C2semidirect
15. #10590253C2semidirect
63. #5574D3semidirect
73. #5027D3semidirect
673. C32#3119semidirect
757. C3#80364semidirect
758. C3#82568semidirect

Maximal subgroups

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

subgroupindex
C3×#55742
#105939492
#105927212
C3×#50272
#105915862
#105915662
Dic3×#2152
#105905002
#105904982
#105904552
#105904522
#105903472
#105902712
#105902532
#825683
#803643