Finite Group Databasebeta

← #10823391

Subgroups — #10823391

Order 768.

1188 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic
2C2×C4×#216C211yesmaximal, characteristic, complemented
3C2×C4×#214C211yesmaximal, characteristic, complemented
4C4×#924C211yesmaximal, characteristic, complemented
5#71744C211yesmaximal, characteristic, complemented
6#71739C211yesmaximal, characteristic, complemented
7#71729C211yesmaximal, characteristic, complemented
8#71722C211yesmaximal, characteristic, complemented
9#71700C211yesmaximal, characteristic, complemented
10#71694C211yesmaximal, characteristic, complemented
11#71685C211yesmaximal, characteristic
12#71679C211yesmaximal, characteristic
13C4×#835C211yesmaximal, characteristic, complemented
14C4×#832C211yesmaximal, characteristic, complemented
15C4×#830C211yesmaximal, characteristic, complemented
16#23572—31nomaximal, Sylow
17C3×#529—24no—
18C3×#529—24no—
19C2×C3×#126—21no—
20C2×C3×#125C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×C3×#123—21no—
23C2×C3×C22⋊Q8C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4—21no—
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×#117—21no—
29C22×C3×C42C2211yescharacteristic
30C22×#216C2211yescharacteristic
31C22×#214C2211yescharacteristic
32C2×#924C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40#5212C2211yescharacteristic
41#5210—21no—
42C4×#217—21no—
43C2×#830C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C4×#216—24no—
46C4×#214—24no—
47C2×#810C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#808C2211yescharacteristic
50C2×#807C2211yescharacteristic
51C4×C4⋊Dic3C2211yescharacteristic
52#4933—21no—
53C4×Dic3⋊C4—21no—
54#4929C2211yescharacteristic
55#4928C2211yescharacteristic
56C2×C4×C3⋊C8C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529D311yescharacteristic
65C2×C4×Q16—31no—
66C2×C4×SD16—31no—
67C4×C22⋊Q8—31no—
68#2059—31no—
69#2042—31no—
70#2035—31no—
71#2033—31no—
72#2026—31no—
73#2015—31no—
74#2001—31no—
75#2000—31no—
76C4×#103—31no—
77C4×#102—31no—
78C4×C22⋊C8—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4—21no—
83C23×C3×C4D411yescharacteristic
84C23×C3×C4D411yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×Dic6C2311yescharacteristic
87C3×#126—28no—
88C3×#125—22no—
89C3×#125—22no—
90C3×#124—22no—
91C3×#124—22no—
92C3×#123—28no—
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8—22no—
95C3×#121—22no—
96C3×#121—22no—
97C3×C4×Q8—22no—
98C3×C4×Q8D414yes—
99C3×C4×D4—28no—
100C3×C4×D4—22no—
101C3×C4×D4D414yes—
102C3×#117—28no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C42—21no—
115C2×C3×C42—22no—
116C2×C3×C42—22no—
117C2×C3×C42D411yescharacteristic
118C2×C3×C42D411yescharacteristic
119C2×C3×C42C2311yescharacteristic
120C2×C3×C42C2311yescharacteristic
121C2×#217—21no—
122C2×#217—21no—
123C2×#216—22no—
124C2×#216—22no—
125C2×#216—22no—
126C2×#214—22no—
127C2×#214—22no—
128C2×#214—22no—
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132#924—22no—
133#924—22no—
134C2×Dic3⋊C4—21no—
135C2×Dic3⋊C4—21no—
136C2×Dic3⋊C4—21no—
137C2×C4×Dic3—21no—
138C2×C4×Dic3—21no—
139C22×C3⋊C8C2311yescharacteristic
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C4×Dic6—22no—
144C4×Dic6—22no—
145#835—22no—
146#835—22no—
147#835—22no—
148#832—22no—
149#832—22no—
150#832—22no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#830—22no—
157#830—22no—
158#810—22no—
159#810—22no—
160#808—22no—
161#807—22no—
162C4×C3⋊C8—22no—
163C4×C3⋊C8—22no—
164C22×Q16—31no—
165C22×SD16—31no—
166#529—24no—
167#529—24no—
168C2×#126—21no—
169C2×#125C2×D311yescharacteristic
170C2×#124C2×D311yescharacteristic
171C2×#123—21no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8C2×D311yescharacteristic
174C2×#121C2×D311yescharacteristic
175C2×C4×Q8—31no—
176C2×C4×Q8C2×D311yescharacteristic
177C2×C4×D4—21no—
178C2×C4×D4C2×D311yescharacteristic
179C2×#117—21no—
180C22×C42C2×D311yescharacteristic
181C4×Q16—64no—
182C4×SD16—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C4×C8—31no—
196C2×C4×C8—31no—
197#391—31no—
198#389—31no—
199#387—61no—
200#385—61no—
201#380—31no—
202C4×C4⋊C4—31no—
203C4×C4⋊C4—61no—
204C4×C22⋊C4—61no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#336—31no—
210#336—31no—
211C24×C3—21no—
212C24×C3C2×D411yescharacteristic
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8C2×D412yes—
219C2×C3×D4—24no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—42no—
226C2×C3×D4—42no—
227C2×C3×D4C2×D412yes—
228C22×C3×C4—22no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—24no—
235C22×C3×C4—22no—
236C22×C3×C4—22no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—41no—
244C22×C3×C4—42no—
245C22×C3×C4—42no—
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2×D411yescharacteristic
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2411yescharacteristic
252C22×Dic3—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6#4112yes—
262C3×C4⋊C4—24no—
263C3×C4⋊C4—24no—
264C3×C4⋊C4—24no—
265C3×C4⋊C4—24no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4C2×D412yes—
269C3×C4⋊C4C2×D412yes—
270C3×C22⋊C4—24no—
271C3×C22⋊C4—24no—
272C3×C22⋊C4—24no—
273C3×C22⋊C4—24no—
274C3×C22⋊C4—24no—
275C3×C42—22no—
276C3×C42—22no—
277C3×C42—24no—
278C3×C42—21no—
279C3×C42—21no—
280C3×C42C2×D412yes—
281C3×C42C2×D412yes—
282#217—24no—
283#217—42no—
284#216—28no—
285#214—28no—
286C4⋊Dic3—21no—
287C4⋊Dic3—21no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3#4112yes—
292Dic3⋊C4—24no—
293Dic3⋊C4—42no—
294Dic3⋊C4—42no—
295C4×Dic3—42no—
296C4×Dic3—42no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8#4112yes—
308C2×C3⋊C8#4112yes—
309C22×Q8—31no—
310C22×Q8C22×D311yescharacteristic
311C22×D4—21no—
312C22×D4C22×D311yescharacteristic
313C23×C4—21no—
314C23×C4#6711yescharacteristic
315C23×C4#6711yescharacteristic
316C23×C4C22×D311yescharacteristic
317C2×Q16—62no—
318C2×Q16—62no—
319C2×Q16—62no—
320C2×SD16—62no—
321C2×SD16—62no—
322C2×SD16—62no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8—31no—
326C22×C8—31no—
327#126—28no—
328#125—22no—
329#125—22no—
330#124—22no—
331#124—22no—
332#123—28no—
333C22⋊Q8—22no—
334C22⋊Q8—22no—
335C22⋊Q8—62no—
336C22⋊Q8—62no—
337#121—22no—
338#121—22no—
339C4×Q8—22no—
340C4×Q8—62no—
341C4×Q8—62no—
342C4×Q8#6714yes—
343C4×D4—28no—
344C4×D4—22no—
345C4×D4#6714yes—
346#117—28no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4C22×D311yescharacteristic
358C2×C4⋊C4C22×D311yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—61no—
365C2×C22⋊C4—61no—
366C2×C42—21no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—61no—
370C2×C42—61no—
371C2×C42#6711yescharacteristic
372C2×C42#6711yescharacteristic
373C2×C42C22×D311yescharacteristic
374C2×C42C22×D311yescharacteristic
375#107—62no—
376#106—62no—
377#103—62no—
378#103—62no—
379#103—62no—
380#103—62no—
381#103—62no—
382#102—62no—
383#102—62no—
384#102—62no—
385C22⋊C8—62no—
386C22⋊C8—62no—
387C4×C8—62no—
388C4×C8—62no—
389#95—61no—
390#95—61no—
391#95—61no—
392#95—61no—
393#95—61no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—22no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3—41no—
407C23×C3#13512yes—
408C23×C3C22×D411yescharacteristic
409C3×Q8—22no—
410C3×Q8—22no—
411C3×Q8—41no—
412C3×Q8—41no—
413C3×D4—22no—
414C3×D4—22no—
415C3×D4—48no—
416C3×D4—41no—
417C3×D4—41no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—44no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4—41no—
437C2×C3×C4—41no—
438C2×C3×C4—41no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—44no—
444C2×C3×C4—48no—
445C2×C3×C4#12012yes—
446C2×C3×C4#12012yes—
447C2×C3×C4#13512yes—
448C2×C3×C4#13712yes—
449C2×C3×C4C22×D411yescharacteristic
450C2×C3×C4C22×D411yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454C2×C3×C4C2×#4111yescharacteristic
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467Dic6—22no—
468Dic6—22no—
469Dic6—41no—
470Dic6—41no—
471C3⋊C8—22no—
472C3⋊C8—22no—
473C3⋊C8—41no—
474C3⋊C8—41no—
475C24—21no—
476C24C2×#6711yescharacteristic
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—32no—
483C2×Q8—61no—
484C2×Q8—61no—
485C2×Q8—61no—
486C2×Q8—61no—
487C2×Q8—61no—
488C2×Q8C2×#6712yes—
489C2×D4—24no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4C2×#6712yes—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—41no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4C2×#6711yescharacteristic
521C22×C4C2×#6711yescharacteristic
522C22×C4C2×#6711yescharacteristic
523C22×C4C2×#6711yescharacteristic
524C22×C4C2×#6711yescharacteristic
525C22×C4C23×D311yescharacteristic
526Q16—68no—
527SD16—68no—
528C2×C8—32no—
529C2×C8—32no—
530C2×C8—61no—
531C2×C8—61no—
532C2×C8—61no—
533C2×C8—61no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8—61no—
539C2×C8—61no—
540C4⋊C4—24no—
541C4⋊C4—24no—
542C4⋊C4—24no—
543C4⋊C4—24no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—32no—
547C4⋊C4—64no—
548C4⋊C4—61no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—122no—
554C4⋊C4—122no—
555C4⋊C4C2×#6712yes—
556C4⋊C4C2×#6712yes—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—24no—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—64no—
563C22⋊C4—122no—
564C42—22no—
565C42—22no—
566C42—24no—
567C42—21no—
568C42—21no—
569C42—122no—
570C42—122no—
571C42C2×#6712yes—
572C42C2×#6712yes—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—41no—
577C22×C3—41no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—81no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3—81no—
587C22×C3C2×#12011yescharacteristic
588C22×C3#52511yescharacteristic
589C22×C3#53211yescharacteristic
590C22×C3C2×#13511yescharacteristic
591C22×C3C2×#13511yescharacteristic
592C22×C3C2×#13711yescharacteristic
593C22×C3#57511yescharacteristic
594C3×C4—22no—
595C3×C4—41no—
596C3×C4—42no—
597C3×C4—41no—
598C3×C4—42no—
599C3×C4—41no—
600C3×C4—42no—
601C3×C4#45214yes—
602C3×C4#52511yescharacteristic
603C3×C4#52511yescharacteristic
604C3×C4#53211yescharacteristic
605C3×C4#53211yescharacteristic
606Dic3—42no—
607Dic3—42no—
608Dic3—81no—
609Dic3—81no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—22no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23#95012yes—
624C23C22×#6711yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—41no—
628Q8—41no—
629Q8—62no—
630Q8—62no—
631Q8—121no—
632Q8—121no—
633D4—22no—
634D4—22no—
635D4—48no—
636D4—41no—
637D4—41no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—44no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—44no—
660C2×C4—48no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—62no—
666C2×C4—62no—
667C2×C4—121no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4#95012yes—
678C2×C4#95112yes—
679C2×C4#95312yes—
680C2×C4#95312yes—
681C2×C4D3×#4111yescharacteristic
682C2×C4D3×#4111yescharacteristic
683C2×C4D3×#4111yescharacteristic
684C2×C4D3×#4111yescharacteristic
685C2×C4C22×#6711yescharacteristic
686C2×C4C22×#6711yescharacteristic
687C8—62no—
688C8—62no—
689C8—121no—
690C8—121no—
691C2×C3—42no—
692C2×C3—82no—
693C2×C3#238811yescharacteristic
694C2×C3C2×#45211yescharacteristic
695C2×C3#300211yescharacteristic
696C2×C3#310211yescharacteristic
697C2×C3#310811yescharacteristic
698C2×C3#316811yescharacteristic
699C2×C3#317211yescharacteristic
700C22—22no—
701C22—22no—
702C22—22no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22C2×#95011yescharacteristic
715C22C2×#95011yescharacteristic
716C22#582211yescharacteristic
717C22C2×#95111yescharacteristic
718C22#582811yescharacteristic
719C22#583211yescharacteristic
720C22C2×#95311yescharacteristic
721C4—22no—
722C4—41no—
723C4—42no—
724C4—41no—
725C4—42no—
726C4—41no—
727C4—42no—
728C4—122no—
729C4—122no—
730C4—241no—
731C4—241no—
732C4#523914yes—
733C4#582811yescharacteristic
734C4#582811yescharacteristic
735C4#583211yescharacteristic
736C4#583211yescharacteristic
737C3#2357211yescharacteristic, complemented, Sylow
738C2—42no—
739C2—82no—
740C2#8313411yescharacteristic
741C2#8313611yescharacteristic
742C2#8314011yescharacteristic
743C2#8315211yescharacteristic
744C2#8408011yescharacteristic
745C2C2×#523911yescharacteristic
746C2#8409511yescharacteristic
subgroupG/H
centerC22×C4C2×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#529C2
socleC23×C3C22×D4
prime radicalC2×C3×#121C22
hypercenterC2×#529D3
hypocenterC3#23572
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
2. C2×C4×#216C2semidirect
3. C2×C4×#214C2semidirect
4. C4×#924C2semidirect
5. #71744C2semidirect
6. #71739C2semidirect
7. #71729C2semidirect
8. #71722C2semidirect
9. #71700C2semidirect
10. #71694C2semidirect
13. C4×#835C2semidirect
14. C4×#832C2semidirect
15. C4×#830C2semidirect
737. C3#23572semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C2×C4×#2162
C2×C4×#2142
C4×#9242
#717442
#717392
#717292
#717222
#717002
#716942
#716852
#716792
C4×#8352
C4×#8322
C4×#8302
#235723