Finite Group Databasebeta

← #11870621

Subgroups — #11870621

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#237C211yesmaximal, characteristic, complemented
2#10593870C211yesmaximal, characteristic, complemented
3C4×#3753C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591471C211yesmaximal, characteristic, complemented
6#10591461C211yesmaximal, characteristic, complemented
7#10591452C211yesmaximal, characteristic
8#10591409C211yesmaximal, characteristic, complemented
9#10590543C211yesmaximal, characteristic, complemented
10#10590536C211yesmaximal, characteristic, complemented
11#10590521C211yesmaximal, characteristic, complemented
12#10590425C211yesmaximal, characteristic, complemented
13C4×#3718C211yesmaximal, characteristic, complemented
14C4×#3717C211yesmaximal, characteristic, complemented
15#10590261C211yesmaximal, characteristic, complemented
16#82528—31nomaximal
17#79652—31nomaximal
18C2×C3×#237C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#214C2211yescharacteristic
24C3×C4×#67—21no—
25C2×C3×C4×Dic3—21no—
26C3×#892C2211yescharacteristic
27C3×#887C2211yescharacteristic
28C3×#67⋊C4—21no—
29C3×#877—21no—
30C3×C42×D3C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33#63909C2211yescharacteristic
34C4×#626—21no—
35#63874—21no—
36#63869C2211yescharacteristic
37#63868—21no—
38#63864C2211yescharacteristic
39#63856C2211yescharacteristic
40#63850—21no—
41C2×#3718C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43#63659C2211yescharacteristic
44#63636C2211yescharacteristic
45#63634C2211yescharacteristic
46C4×C3⋊(C3⋊C8)C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×C4×C3⋊C8C2211yescharacteristic
51#63576C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×C4×#41—31no—
62#5580—31no—
63C4×#237D311yescharacteristic, complemented
64#5479—31no—
65C3×C4×SD16—31no—
66#5239—31no—
67#5238—31no—
68#5173—31no—
69#5165—31no—
70C4×#216—31no—
71C4×#216—31no—
72#5028—31no—
73C4×#215—31no—
74#5022—31no—
75C4×#214D311yescharacteristic, complemented
76#5016—31no—
77C4×#213—31no—
78C4×#213—31no—
79C4×#213—61no—
80#5009—31no—
81#5003—31no—
82#4996—31no—
83#4925—31no—
84#4866—31no—
85#4857—31no—
86#4815—31no—
87#4798—31no—
88#4781—31no—
89#4763—31no—
90C4×#204—31no—
91#4685—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C3×#67—21no—
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C3×#237—22no—
100C3×#237—22no—
101C2×C3×C4×D3D411yescharacteristic
102C2×C3×C4×D3D411yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C32×C4⋊C4C2311yescharacteristic
108C32×C22⋊C4—21no—
109C32×C42C2311yescharacteristic
110#3753—22no—
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×#217—21no—
116C3×#214—22no—
117C3×(C2×D3)⋊C4—21no—
118C3×C4⋊Dic3C2311yescharacteristic
119C3×C4⋊Dic3C2311yescharacteristic
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4—21no—
122C3×Dic3⋊C4—21no—
123C3×C4×Dic3—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3D411yescharacteristic
128C3×C4×Dic3D411yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132#3724—21no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139#3718—22no—
140#3717—22no—
141#3102—91noSylow
142C2×C3×#41—31no—
143C2×#237C2×D311yescharacteristic
144C2×C3×SD16—31no—
145C3×C4×Q8—31no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C3×C4×D4—21no—
149C3×C4×D4—31no—
150C3×C4×D4—61no—
151C3×C4×D4—61no—
152C3×C4×D4C2×D311yescharacteristic
153C3×C4×D4C2×D311yescharacteristic
154C3×#117—31no—
155C3×#117—61no—
156C2×C3×C42—31no—
157C2×C3×C42—61no—
158#947—31no—
159#946—31no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#215—31no—
163D4×Dic3C2×D311yescharacteristic
164C2×#214C2×D311yescharacteristic
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—61no—
168#930—31no—
169#929—61no—
170C4×#67—21no—
171C4×#67—61no—
172#924—31no—
173C2×C4×Dic3—21no—
174C2×#204—31no—
175#898—61no—
176#895—31no—
177#894—61no—
178#892C2×D311yescharacteristic
179#890—31no—
180#887C2×D311yescharacteristic
181#67⋊C4—21no—
182#877—21no—
183#876—61no—
184#875—31no—
185C4×D12—31no—
186C4×D12—31no—
187C4×D12—61no—
188C4×D12—61no—
189#872—61no—
190#872—61no—
191C42×D3C2×D311yescharacteristic
192#870—31no—
193C4×Dic6C2×D311yescharacteristic
194C4×Dic6C2×D311yescharacteristic
195C3×#106—31no—
196C3×#103—31no—
197C3×#102—31no—
198C3×C4×C8—31no—
199#835—31no—
200#835—31no—
201#835—31no—
202#832—31no—
203#832—31no—
204#832—61no—
205#832C2×D311yescharacteristic
206#830—31no—
207#830—31no—
208#821—31no—
209(C2×D3)⋊C8—31no—
210(C2×D3)⋊C8—31no—
211#817—31no—
212#816—31no—
213Dic3⋊C8—31no—
214Dic3⋊C8—31no—
215#810—31no—
216#810—31no—
217#810C2×D311yescharacteristic
218#809—31no—
219#809—31no—
220#809—31no—
221#809—61no—
222#808—31no—
223#808C2×D311yescharacteristic
224#807—31no—
225#807—31no—
226#807—31no—
227#807—31no—
228#807—61no—
229C4⋊(C3⋊C8)—31no—
230C4⋊(C3⋊C8)—31no—
231C4×C3⋊C8—31no—
232C4×C3⋊C8—31no—
233C4×C3⋊C8—61no—
234C4×C3⋊C8C2×D311yescharacteristic
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3C2×D411yescharacteristic
238C32×D4—21no—
239C32×D4#4112yes—
240C2×C32×C4—21no—
241C2×C32×C4—42no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—21no—
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)—21no—
248C4×C3⋊D3—42no—
249C3×#67—24no—
250C2×C3×Dic3—24no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—42no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—22no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—41no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6#4112yes—
267#626—42no—
268C3⋊(C3⋊C8)—21no—
269C3⋊(C3⋊C8)—21no—
270C3×C3⋊C8—21no—
271C3×C3⋊C8—21no—
272#529—91no—
273C4×#41—31no—
274#485—91no—
275#482—91no—
276#479—91no—
277#478—91no—
278#464—91no—
279#463—91no—
280#452—91no—
281#449—91no—
282C4×Q16—91no—
283C4×SD16—31no—
284C4×SD16—91no—
285C4×D8—91no—
286#431—91no—
287C3×#41—62no—
288C3×#41—62no—
289C2×C3×Q8—31no—
290C2×C3×Q8—31no—
291C2×C3×D4—21no—
292C2×C3×D4—61no—
293C2×C3×D4C22×D311yescharacteristic
294C2×C3×D4C22×D311yescharacteristic
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—41no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C2×#67—21no—
304C2×#67—61no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307#237—22no—
308#237—22no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—61no—
312C2×D12—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—121no—
316C2×C4×D3#6711yescharacteristic
317C2×C4×D3#6711yescharacteristic
318C2×C4×D3C22×D311yescharacteristic
319C2×Dic6C22×D311yescharacteristic
320C2×Dic6C22×D311yescharacteristic
321C3×SD16—62no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4—61no—
330C3×C4⋊C4C22×D311yescharacteristic
331C3×C4⋊C4C22×D311yescharacteristic
332C3×C22⋊C4—21no—
333C3×C22⋊C4—21no—
334C3×C22⋊C4—41no—
335C3×C22⋊C4—61no—
336C3×C22⋊C4—61no—
337C3×C42—21no—
338C3×C42—31no—
339C3×C42—31no—
340C3×C42—31no—
341C3×C42—61no—
342C3×C42—61no—
343C3×C42—61no—
344C3×C42—61no—
345C3×C42C22×D311yescharacteristic
346C3×C42C22×D311yescharacteristic
347#217—21no—
348#217—61no—
349#216—62no—
350#216—62no—
351#215—62no—
352#214—22no—
353#213—64no—
354#213—62no—
355#213—62no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—121no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3C22×D311yescharacteristic
372C4⋊Dic3C22×D311yescharacteristic
373Dic3⋊C4—21no—
374Dic3⋊C4—21no—
375Dic3⋊C4—21no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381C4×Dic3—21no—
382C4×Dic3—21no—
383C4×Dic3—21no—
384C4×Dic3—21no—
385C4×Dic3#6711yescharacteristic
386C4×Dic3#6711yescharacteristic
387C4×Dic3C22×D311yescharacteristic
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8C22×D311yescharacteristic
395C2×C3⋊C8C22×D311yescharacteristic
396#204—62no—
397C22×C32—22no—
398C22×C32—41no—
399C22×C32—41no—
400C22×C32C22×D411yescharacteristic
401C2×C3⋊D3—41no—
402C2×C3⋊D3—41no—
403C2×C3⋊D3—41no—
404C2×C3×D3—21no—
405C2×C3×D3—21no—
406C2×C3×D3—21no—
407C32×C4—21no—
408C32×C4—41no—
409C32×C4#13512yes—
410C32×C4C2×#4111yescharacteristic
411C32×C4C2×#4111yescharacteristic
412C3⋊Dic3—41no—
413C3×Dic3—22no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C3×Dic3—41no—
420C2×#41—31no—
421C2×Q16—91no—
422C2×SD16—31no—
423C2×SD16—91no—
424C2×D8—91no—
425#126—181no—
426#125—91no—
427#124—91no—
428#123—181no—
429C22⋊Q8—91no—
430#121—91no—
431C4×Q8—31no—
432C4×Q8—31no—
433C4×Q8—31no—
434C4×D4—31no—
435C4×D4—61no—
436C4×D4—61no—
437C4×D4—91no—
438C4×D4—181no—
439C4×D4D3211yescharacteristic
440#117—31no—
441#117—61no—
442#117—181no—
443C2×C42—31no—
444C2×C42—61no—
445#107—91no—
446#107—91no—
447#106—31no—
448#106—91no—
449C4⋊C8—91no—
450C4⋊C8—91no—
451#103—31no—
452#103—91no—
453#103—91no—
454#103—91no—
455#102—31no—
456#102—91no—
457#102—91no—
458#102—91no—
459C22⋊C8—91no—
460C22⋊C8—91no—
461C4×C8—31no—
462C4×C8—91no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—31no—
466C23×C3—41no—
467C22×D3—61no—
468C22×D3—61no—
469C22×D3—121no—
470C22×D3C2×#6711yescharacteristic
471C3×Q8—32no—
472C3×Q8—61no—
473C3×Q8—61no—
474C3×Q8—61no—
475C3×D4—21no—
476C3×D4—21no—
477C3×D4—22no—
478C3×D4—41no—
479C3×D4—64no—
480C3×D4#23512yes—
481C3×D4#23512yes—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—41no—
491C2×C3×C4—42no—
492C2×C3×C4—42no—
493C2×C3×C4—64no—
494C2×C3×C4—61no—
495C2×C3×C4—62no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—82no—
502C2×C3×C4—121no—
503C2×C3×C4—122no—
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4C2×#6711yescharacteristic
507C2×C3×C4C2×#6711yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—24no—
511#67—122no—
512C2×Dic3—24no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—42no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—121no—
521C2×Dic3C2×#6711yescharacteristic
522C2×Dic3C2×#6711yescharacteristic
523C2×Dic3C2×#6711yescharacteristic
524D12—62no—
525D12—61no—
526D12—61no—
527D12—61no—
528D12—61no—
529D12—121no—
530D12—122no—
531C4×D3—22no—
532C4×D3—21no—
533C4×D3—21no—
534C4×D3—41no—
535C4×D3—122no—
536C4×D3—122no—
537C4×D3—242no—
538Dic6—21no—
539Dic6—21no—
540Dic6—21no—
541Dic6#23512yes—
542C3×C8—61no—
543C3×C8—61no—
544C3⋊C8—21no—
545C3⋊C8—21no—
546C3⋊C8—62no—
547C3⋊C8—61no—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—121no—
552C2×C32—42no—
553C2×C32#52511yescharacteristic
554C2×C32C2×#13511yescharacteristic
555C2×C32#57511yescharacteristic
556C3⋊D3—81no—
557C3×D3—41no—
558#41—62no—
559#41—62no—
560C2×Q8—31no—
561C2×Q8—31no—
562C2×D4—61no—
563C2×D4—91no—
564C2×D4—181no—
565C2×D4C2×D3211yescharacteristic
566C22×C4—21no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—181no—
573Q16—182no—
574SD16—62no—
575SD16—182no—
576D8—182no—
577C2×C8—31no—
578C2×C8—31no—
579C2×C8—91no—
580C2×C8—91no—
581C4⋊C4—31no—
582C4⋊C4—31no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—91no—
587C4⋊C4—181no—
588C4⋊C4—181no—
589C4⋊C4—181no—
590C4⋊C4C2×D3211yescharacteristic
591C22⋊C4—21no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—181no—
595C22⋊C4—181no—
596C22⋊C4—181no—
597C22⋊C4—181no—
598C22⋊C4—181no—
599C42—31no—
600C42—31no—
601C42—31no—
602C42—61no—
603C42—61no—
604C42—61no—
605C42—61no—
606C42C2×D3211yescharacteristic
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—21no—
610C22×C3—42no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—41no—
614C22×C3—41no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3—81no—
619C22×C3—81no—
620C22×C3C2×D3×D411yescharacteristic
621C22×C3C22×#6711yescharacteristic
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—21no—
625C2×D3—122no—
626C2×D3—121no—
627C2×D3—121no—
628C2×D3—121no—
629C2×D3—121no—
630C2×D3—121no—
631C2×D3—121no—
632C2×D3—241no—
633C2×D3—241no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—22no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—61no—
643C3×C4—61no—
644C3×C4—61no—
645C3×C4—62no—
646C3×C4—81no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4#91612yes—
651C3×C4#95012yes—
652C3×C4C2×#23511yescharacteristic
653C3×C4C2×#23511yescharacteristic
654C3×C4C2×#23511yescharacteristic
655C3×C4D3×#4111yescharacteristic
656Dic3—22no—
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—121no—
664Dic3—121no—
665Dic3—241no—
666C32#310211yescharacteristic, complemented, Sylow
667C23—21no—
668C23—31no—
669C23—181no—
670Q8—32no—
671Q8—61no—
672Q8—61no—
673Q8—61no—
674D4—21no—
675D4—64no—
676D4—181no—
677D4—181no—
678D4—362no—
679D4#379812yes—
680C2×C4—21no—
681C2×C4—31no—
682C2×C4—31no—
683C2×C4—31no—
684C2×C4—42no—
685C2×C4—64no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—62no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—121no—
694C2×C4—122no—
695C2×C4—181no—
696C2×C4—362no—
697C2×C4D3×#6711yescharacteristic
698C2×C4D3×#6711yescharacteristic
699C2×C4C22×D3211yescharacteristic
700C8—61no—
701C8—61no—
702C8—181no—
703C8—181no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—42no—
708C2×C3—42no—
709C2×C3—82no—
710C2×C3—121no—
711C2×C3#554711yescharacteristic
712C2×C3C2×#91611yescharacteristic
713C2×C3#576811yescharacteristic
714C2×C3#579111yescharacteristic
715C2×C3C2×#95011yescharacteristic
716C2×C3#582211yescharacteristic
717D3—41no—
718D3—242no—
719D3—241no—
720D3—241no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—61no—
725C22—61no—
726C22—61no—
727C22—361no—
728C22—361no—
729C22—361no—
730C22C2×D3×#6711yescharacteristic
731C4—21no—
732C4—41no—
733C4—61no—
734C4—61no—
735C4—61no—
736C4—62no—
737C4—121no—
738C4—121no—
739C4—121no—
740C4—361no—
741C4#6393512yes—
742C4C2×#379811yescharacteristic
743C4D3×#23511yescharacteristic
744C3—21no—
745C3#7965211yescharacteristic, complemented
746C3#8252811yescharacteristic, complemented
747C2—42no—
748C2—121no—
749C2—721no—
750C2#1059500211yescharacteristic
751C2C2×#6393511yescharacteristic
752C2#1059545311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10591452C2
hypercenterC4×D4D32
hypocenterC32#3102
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C3×C4×#237C2semidirect
2. #10593870C2semidirect
3. C4×#3753C2semidirect
4. C3×C4×#214C2semidirect
5. #10591471C2semidirect
6. #10591461C2semidirect
8. #10591409C2semidirect
9. #10590543C2semidirect
10. #10590536C2semidirect
11. #10590521C2semidirect
12. #10590425C2semidirect
13. C4×#3718C2semidirect
14. C4×#3717C2semidirect
15. #10590261C2semidirect
63. C4×#237D3semidirect
75. C4×#214D3semidirect
666. C32#3102semidirect
745. C3#79652semidirect
746. C3#82528semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2372
#105938702
C4×#37532
C3×C4×#2142
#105914712
#105914612
#105914522
#105914092
#105905432
#105905362
#105905212
#105904252
C4×#37182
C4×#37172
#105902612
#825283
#796523