Finite Group Databasebeta

← #11872304

Subgroups — #11872304

Order 1152.

843 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5546C211yesmaximal, characteristic, complemented
2#10593949C211yesmaximal, characteristic, complemented
3#10592708C211yesmaximal, characteristic, complemented
4C3×#5015C211yesmaximal, characteristic, complemented
5#10591450C211yesmaximal, characteristic, complemented
6#10591450C211yesmaximal, characteristic, complemented
7#10591430C211yesmaximal, characteristic, complemented
8Dic3×#213C211yesmaximal, characteristic, complemented
9#10590500C211yesmaximal, characteristic, complemented
10#10590498C211yesmaximal, characteristic, complemented
11#10590454C211yesmaximal, characteristic, complemented
12#10590453C211yesmaximal, characteristic, complemented
13#10590364C211yesmaximal, characteristic, complemented
14#10590302C211yesmaximal, characteristic, complemented
15#10590253C211yesmaximal, characteristic, complemented
16#82568—31nomaximal
17#80316—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20#64079C2211yescharacteristic
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#213C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×Dic3⋊C4—21no—
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×#877—21no—
30C3×#874C2211yescharacteristic
31C3×#872C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63908C2211yescharacteristic
34#63908C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37#63885—21no—
38#63885—21no—
39#63884—21no—
40#63884—21no—
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic
45#63635C2211yescharacteristic
46#63634C2211yescharacteristic
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
48C3×#809C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×C4⋊(C3⋊C8)C2211yescharacteristic
51#63575C2211yescharacteristic
52#63573C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
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#5546D311yescharacteristic, complemented
64#5535—31no—
65C3×#459—31no—
66#5238—31no—
67#5238—31no—
68#5158—31no—
69#5158—31no—
70#5152—31no—
71Dic3×D8—31no—
72#5075—31no—
73#5027—31no—
74#5026—31no—
75C4×#215—31no—
76#5022—31no—
77#5015D311yescharacteristic, complemented
78#5014—31no—
79C4×#213—31no—
80#5009—31no—
81#5009—31no—
82#5009—61no—
83#5000—31no—
84#4968—31no—
85#4967—31no—
86#4840—31no—
87#4829—31no—
88#4777—31no—
89#4774—31no—
90#4758—31no—
91#4757—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C3×#67—21no—
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C3×#237—22no—
98C3×#237—22no—
99C2×C3×D12—21no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#625—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112C32×C42C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116#3750—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#213—22no—
121C3×#213—22no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
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#3715—22no—
140#3715—22no—
141#3119—91noSylow
142C2×C3×#41—31no—
143C2×#237C2×D311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×#127—31no—
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×D4—21no—
150C3×C4×D4—31no—
151C3×C4×D4—61no—
152C3×C4×D4—61no—
153C3×C4×D4C2×D311yescharacteristic
154C3×C4×D4C2×D311yescharacteristic
155C3×#117—31no—
156C3×#117—61no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—61no—
159C2×#215—31no—
160C2×#215—31no—
161#939—61no—
162#939—61no—
163#938—31no—
164#938—31no—
165#935—61no—
166#935—61no—
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3C2×D311yescharacteristic
170C2×#214—31no—
171C2×#214—31no—
172C2×#213C2×D311yescharacteristic
173C2×#213C2×D311yescharacteristic
174#930—31no—
175#930—31no—
176C4×#67—21no—
177C2×Dic3⋊C4—21no—
178#894—61no—
179#894—61no—
180D3×C4⋊C4C2×D311yescharacteristic
181#887C2×D311yescharacteristic
182#884—61no—
183#884—61no—
184#67⋊C4—21no—
185#877—21no—
186#874C2×D311yescharacteristic
187C4×D12—31no—
188C4×D12—31no—
189#872C2×D311yescharacteristic
190#870—31no—
191#870—31no—
192#870—61no—
193C4×Dic6C2×D311yescharacteristic
194C3×C4⋊C8—31no—
195C3×#102—31no—
196C3×#102—31no—
197#835—31no—
198#835—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—61no—
206#832—61no—
207#830—31no—
208#830—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#818—31no—
212#817—31no—
213#816—31no—
214#816—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—
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3C2×D411yescharacteristic
239C32×D4—21no—
240C32×D4#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—81no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C3×#67—24no—
249C2×C3×Dic3—24no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—81no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—81no—
261C3×D12—81no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—81no—
265C3×Dic6—21no—
266C3×Dic6#4112yes—
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—91no—
282#459—31no—
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—31no—
293C2×C3×D4—21no—
294C2×C3×D4—31no—
295C2×C3×D4—31no—
296C2×C3×D4—61no—
297C2×C3×D4—61no—
298C2×C3×D4—61no—
299C2×C3×D4C22×D311yescharacteristic
300C2×C3×D4C22×D311yescharacteristic
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—41no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—21no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317#237—22no—
318#237—22no—
319C2×D12—21no—
320C2×D12—21no—
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3C22×D311yescharacteristic
327C2×Dic6C22×D311yescharacteristic
328C3×D8—62no—
329C3×D8—62no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C22⋊C4—21no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—41no—
346C3×C22⋊C4—61no—
347C3×C42—21no—
348C3×C42—31no—
349C3×C42—61no—
350C3×C42—61no—
351C3×C42C22×D311yescharacteristic
352C3×C42C22×D311yescharacteristic
353#217—21no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#215—62no—
359#215—62no—
360#214—62no—
361#214—62no—
362#213—22no—
363#213—22no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4#6711yescharacteristic
369(C2×D3)⋊C4#6711yescharacteristic
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—121no—
385Dic3⋊C4—121no—
386Dic3⋊C4#6711yescharacteristic
387Dic3⋊C4#6711yescharacteristic
388C4×Dic3—21no—
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×C32—22no—
400C22×C32—41no—
401C22×C32—41no—
402C22×C32C22×D411yescharacteristic
403C2×C3×D3—21no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
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—21no—
413C32×C4—21no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4C2×#4111yescharacteristic
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C2×#41—31no—
425C2×SD16—91no—
426C2×SD16—91no—
427C2×D8—31no—
428C2×D8—31no—
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×Q8—31no—
439C4×D4—31no—
440C4×D4—61no—
441C4×D4—61no—
442C4×D4—91no—
443C4×D4—91no—
444C4×D4D3211yescharacteristic
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—21no—
468C23×C3—21no—
469C23×C3—31no—
470C23×C3—41no—
471C23×C3—61no—
472C23×C3—61no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3C2×#6711yescharacteristic
476C3×Q8—32no—
477C3×Q8—61no—
478C3×D4—21no—
479C3×D4—21no—
480C3×D4—22no—
481C3×D4—41no—
482C3×D4—64no—
483C3×D4—61no—
484C3×D4—61no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—241no—
488C3×D4—241no—
489C3×D4#23512yes—
490C3×D4#23712yes—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—31no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—41no—
500C2×C3×C4—64no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—81no—
506C2×C3×C4—81no—
507C2×C3×C4—82no—
508C2×C3×C4—241no—
509C2×C3×C4—241no—
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C2×#6711yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—24no—
517#67—241no—
518#67—241no—
519#67—241no—
520#67—241no—
521C2×Dic3—24no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—81no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—241no—
532C2×Dic3—241no—
533C2×Dic3C2×#6711yescharacteristic
534C2×Dic3C2×#6711yescharacteristic
535C2×Dic3C2×#6711yescharacteristic
536D12—21no—
537D12—21no—
538D12—21no—
539D12—21no—
540D12—81no—
541D12—81no—
542C4×D3—21no—
543C4×D3—21no—
544C4×D3—81no—
545C4×D3—241no—
546C4×D3—241no—
547Dic6—21no—
548Dic6#23512yes—
549C3×C8—61no—
550C3×C8—61no—
551C3⋊C8—21no—
552C3⋊C8—21no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—121no—
558C3⋊C8—121no—
559C2×C32—42no—
560C2×C32#52511yescharacteristic
561C2×C32#57611yescharacteristic
562C2×C32#57711yescharacteristic
563C3×D3—41no—
564C3×D3—81no—
565C3×D3—81no—
566#41—62no—
567#41—62no—
568C2×Q8—31no—
569C2×D4—31no—
570C2×D4—31no—
571C2×D4—61no—
572C2×D4—61no—
573C2×D4—61no—
574C2×D4—181no—
575C2×D4—181no—
576C2×D4C2×D3211yescharacteristic
577C22×C4—21no—
578C22×C4—31no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—61no—
582C22×C4—181no—
583C22×C4—181no—
584SD16—182no—
585SD16—182no—
586D8—62no—
587D8—62no—
588C2×C8—31no—
589C2×C8—31no—
590C2×C8—91no—
591C2×C8—91no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4C2×D3211yescharacteristic
603C22⋊C4—21no—
604C22⋊C4—31no—
605C22⋊C4—31no—
606C22⋊C4—61no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C42—31no—
612C42—61no—
613C42—61no—
614C42C2×D3211yescharacteristic
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—21no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—61no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3—81no—
627C22×C3—81no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—121no—
633C22×C3—121no—
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C22×#6711yescharacteristic
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C2×D3—41no—
640C2×D3—41no—
641C2×D3—41no—
642C2×D3—41no—
643C2×D3—41no—
644C2×D3—41no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—61no—
658C3×C4—62no—
659C3×C4—81no—
660C3×C4—121no—
661C3×C4C2×#23511yescharacteristic
662C3×C4C2×#23511yescharacteristic
663C3×C4C2×#23711yescharacteristic
664C3×C4D3×#4111yescharacteristic
665Dic3—22no—
666Dic3—21no—
667Dic3—21no—
668Dic3—21no—
669Dic3—41no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—121no—
674Dic3—241no—
675Dic3—241no—
676C32#311911yescharacteristic, complemented, Sylow
677C23—21no—
678C23—31no—
679C23—61no—
680C23—61no—
681Q8—32no—
682Q8—61no—
683D4—21no—
684D4—64no—
685D4—61no—
686D4—61no—
687D4—61no—
688D4—61no—
689D4—241no—
690D4—241no—
691D4—721no—
692D4—721no—
693D4#379512yes—
694C2×C4—21no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—31no—
698C2×C4—64no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—81no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—241no—
707C2×C4—241no—
708C2×C4—721no—
709C2×C4—721no—
710C2×C4D3×#6711yescharacteristic
711C2×C4D3×#6711yescharacteristic
712C2×C4C22×D3211yescharacteristic
713C8—61no—
714C8—61no—
715C8—181no—
716C8—181no—
717C2×C3—21no—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—42no—
721C2×C3—42no—
722C2×C3—82no—
723C2×C3—121no—
724C2×C3—241no—
725C2×C3—241no—
726C2×C3#560611yescharacteristic
727C2×C3#575711yescharacteristic
728C2×C3#577511yescharacteristic
729C2×C3#579111yescharacteristic
730C2×C3#583511yescharacteristic
731C2×C3#583711yescharacteristic
732D3—41no—
733D3—81no—
734D3—81no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—121no—
742C22—121no—
743C22—121no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22C2×D3×#6711yescharacteristic
748C4—21no—
749C4—21no—
750C4—41no—
751C4—61no—
752C4—61no—
753C4—62no—
754C4—61no—
755C4—121no—
756C4—361no—
757C4—361no—
758C4C2×#379511yescharacteristic
759C4D3×#23511yescharacteristic
760C3—21no—
761C3#8031611yescharacteristic, complemented
762C3#8256811yescharacteristic, complemented
763C2—42no—
764C2—121no—
765C2—241no—
766C2—241no—
767C2#1059489211yescharacteristic
768C2#1059509611yescharacteristic
769C2#1059545511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3119
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×#5546C2semidirect
2. #10593949C2semidirect
3. #10592708C2semidirect
4. C3×#5015C2semidirect
5. #10591450C2semidirect
6. #10591450C2semidirect
7. #10591430C2semidirect
8. Dic3×#213C2semidirect
9. #10590500C2semidirect
10. #10590498C2semidirect
11. #10590454C2semidirect
12. #10590453C2semidirect
13. #10590364C2semidirect
14. #10590302C2semidirect
15. #10590253C2semidirect
63. #5546D3semidirect
77. #5015D3semidirect
676. C32#3119semidirect
761. C3#80316semidirect
762. C3#82568semidirect

Maximal subgroups

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

subgroupindex
C3×#55462
#105939492
#105927082
C3×#50152
#105914502
#105914302
Dic3×#2132
#105905002
#105904982
#105904542
#105904532
#105903642
#105903022
#105902532
#825683
#803163