Finite Group Databasebeta

← #10701979

Subgroups — #10701979

Order 768.

1278 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#137C211yesmaximal, characteristic
2C2×#5234C211yesmaximal, characteristic
3C2×#5232C211yesmaximal, characteristic
4C22×#836C211yesmaximal, characteristic, complemented
5C22×#835C211yesmaximal, characteristic, complemented
6C2×#4558C211yesmaximal, characteristic, complemented
7C2×#4554C211yesmaximal, characteristic, complemented
8#11021—31nomaximal, Sylow
9C22×C3×#41C2211yescharacteristic
10C23×C3×Q8C2211yescharacteristic
11C2×C3×#137—22no—
12C2×C3×#137—22no—
13C2×C3×#137—22no—
14C2×C3×#137—22no—
15C2×C3×#137—22no—
16C2×C3×#137C414yescomplemented
17C22×C3×Q16—21no—
18C22×C3×SD16—21no—
19C22×C3×M16C2211yescharacteristic
20C22×C4⋊Dic3C2211yescharacteristic
21C22×#208C2211yescharacteristic
22C22×#208C2211yescharacteristic
23C23×C3⋊C8C2211yescharacteristic
24#5234—22no—
25#5234—22no—
26#5232—22no—
27#5232—22no—
28C2×#836—22no—
29C2×#836—22no—
30C2×#836—22no—
31C2×#835—22no—
32C2×#835—21no—
33C2×#835—22no—
34C2×#835—22no—
35C2×#832—21no—
36C2×#830—22no—
37#4558—22no—
38#4554—22no—
39C22×#137D311yescharacteristic
40C2×#417—31no—
41C22×#103—31no—
42C22×#101—31no—
43C2×#408—31no—
44C2×#343—31no—
45C2×#341—31no—
46C2×C3×#41—21no—
47C2×C3×#41—21no—
48C2×C3×#41—21no—
49C2×C3×#41—21no—
50C2×C3×#41—21no—
51C2×C3×#41—21no—
52C2×C3×#41—21no—
53C2×C3×#41—21no—
54C2×C3×#41—21no—
55C2×C3×#41—21no—
56C2×C3×#41C2×C412yes—
57C2×C3×#41D412yes—
58C22×C3×Q8—21no—
59C22×C3×Q8—21no—
60C22×C3×Q8—21no—
61C22×C3×Q8—21no—
62C22×C3×Q8—21no—
63C22×C3×Q8—21no—
64C22×C3×Q8—21no—
65C22×C3×Q8—21no—
66C22×C3×Q8—21no—
67C22×C3×Q8—21no—
68C22×C3×Q8—21no—
69C22×C3×Q8C2×C412yes—
70C22×C3×Q8D411yescharacteristic
71C22×C3×Q8D412yes—
72C22×C3×Q8D412yes—
73C22×C3×D4—21no—
74C22×C3×D4D411yescharacteristic
75C23×C3×C4—21no—
76C23×C3×C4—21no—
77C23×C3×C4C2311yescharacteristic
78C23×Dic3—21no—
79C3×#137—28no—
80C3×#137—28no—
81C3×#137—28no—
82C3×#137—28no—
83C2×C3×Q16—24no—
84C2×C3×Q16—24no—
85C2×C3×Q16—24no—
86C2×C3×SD16—24no—
87C2×C3×SD16—24no—
88C2×C3×SD16—24no—
89C2×C3×M16—21no—
90C2×C3×M16—21no—
91C2×C3×M16—21no—
92C2×C3×M16C2×C412yes—
93C2×C3×M16D412yes—
94C2×C3×M16D412yes—
95C22×C3×C8—21no—
96C2×C4⋊Dic3—21no—
97C2×C4⋊Dic3—21no—
98C2×C4⋊Dic3—21no—
99C2×C4⋊Dic3—21no—
100C2×C4⋊Dic3—21no—
101C2×C4⋊Dic3D412yes—
102C2×#208—21no—
103C2×#208—21no—
104C2×#208—21no—
105C2×#208—21no—
106C2×#208—21no—
107C2×#208—21no—
108C2×#208—21no—
109C2×#208—21no—
110C2×#208—21no—
111C2×#208—21no—
112C2×#208D412yes—
113C2×#208D412yes—
114C22×C3⋊C8—21no—
115C22×C3⋊C8—21no—
116C22×C3⋊C8—21no—
117C22×C3⋊C8—21no—
118C22×C3⋊C8—21no—
119C22×C3⋊C8—21no—
120C22×C3⋊C8—21no—
121C22×C3⋊C8—21no—
122C22×C3⋊C8D412yes—
123#836—28no—
124#835—28no—
125#835—24no—
126#832—24no—
127#830—28no—
128C22×#41C2×D311yescharacteristic
129C23×Q8C2×D311yescharacteristic
130C2×#137—22no—
131C2×#137—22no—
132C2×#137—22no—
133C2×#137—22no—
134C2×#137—22no—
135C2×#137Dic314yescomplemented
136C22×Q16—21no—
137C22×SD16—21no—
138C22×M16—31no—
139C22×M16—31no—
140C22×M16C2×D311yescharacteristic
141C23×C8—31no—
142C22×C4⋊C4—31no—
143#417—62no—
144#417—62no—
145C2×#103—62no—
146C2×#103—62no—
147C2×#103—62no—
148C2×#103—61no—
149C2×#102—61no—
150C2×#101—62no—
151C2×#101—62no—
152C2×#101—62no—
153#408—62no—
154#408—62no—
155C2×C22⋊C8—62no—
156#343—62no—
157#341—62no—
158C24×C3—21no—
159C24×C3#4111yescharacteristic
160C3×#41—22no—
161C3×#41—22no—
162C3×#41—22no—
163C3×#41—22no—
164C3×#41—22no—
165C3×#41—22no—
166C3×#41—22no—
167C3×#41—22no—
168C3×#41—41no—
169C3×#41—41no—
170C3×#41—41no—
171C3×#41—41no—
172C3×#41—41no—
173C3×#41—41no—
174C3×#41—41no—
175C3×#41—41no—
176C2×C3×Q8—22no—
177C2×C3×Q8—22no—
178C2×C3×Q8—22no—
179C2×C3×Q8—21no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—22no—
185C2×C3×Q8—21no—
186C2×C3×Q8—22no—
187C2×C3×Q8—22no—
188C2×C3×Q8—21no—
189C2×C3×Q8—21no—
190C2×C3×Q8—22no—
191C2×C3×Q8—22no—
192C2×C3×Q8—22no—
193C2×C3×Q8—22no—
194C2×C3×Q8—22no—
195C2×C3×Q8—21no—
196C2×C3×Q8—41no—
197C2×C3×Q8—41no—
198C2×C3×Q8—41no—
199C2×C3×Q8—41no—
200C2×C3×Q8—41no—
201C2×C3×Q8—41no—
202C2×C3×Q8—41no—
203C2×C3×Q8—41no—
204C2×C3×Q8—41no—
205C2×C3×Q8—41no—
206C2×C3×Q8—41no—
207C2×C3×Q8—41no—
208C2×C3×Q8C22⋊C412yes—
209C2×C3×Q8C22⋊C414yes—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—41no—
218C2×C3×D4—41no—
219C2×C3×D4—41no—
220C2×C3×D4—41no—
221C2×C3×D4C22⋊C412yes—
222C22×C3×C4—22no—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—41no—
229C22×C3×C4—41no—
230C22×C3×C4—41no—
231C22×C3×C4—41no—
232C22×C3×C4—41no—
233C22×C3×C4—41no—
234C22×C3×C4—41no—
235C22×C3×C4—41no—
236C22×C3×C4C22×C411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D411yescharacteristic
241C22×C3×C4C2×D411yescharacteristic
242C22×C3×C4C2×D411yescharacteristic
243C22×C3×C4C2×D411yescharacteristic
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4#4111yescharacteristic
248C22×C3×C4#4111yescharacteristic
249C22×C3×C4#4111yescharacteristic
250C22×Dic3—22no—
251C22×Dic3—41no—
252C22×Dic3—41no—
253C22×Dic3—82no—
254C3×Q16—216no—
255C3×SD16—216no—
256C3×M16—22no—
257C3×M16—22no—
258C3×M16—22no—
259C3×M16C22⋊C414yes—
260C2×C3×C8—22no—
261C2×C3×C8—22no—
262C2×C3×C8—22no—
263C4⋊Dic3—22no—
264C4⋊Dic3—22no—
265C4⋊Dic3—41no—
266C4⋊Dic3—41no—
267#208—22no—
268#208—22no—
269#208—22no—
270#208—22no—
271#208—41no—
272#208—41no—
273#208—41no—
274#208—41no—
275C2×C3⋊C8—22no—
276C2×C3⋊C8—22no—
277C2×C3⋊C8—22no—
278C2×C3⋊C8—22no—
279C2×C3⋊C8—22no—
280C2×C3⋊C8—41no—
281C2×C3⋊C8—41no—
282C2×C3⋊C8—41no—
283C2×C3⋊C8—41no—
284C2×C3⋊C8—41no—
285C2×C3⋊C8—41no—
286C2×C3⋊C8—41no—
287C2×C3⋊C8—41no—
288C2×#41—21no—
289C2×#41—21no—
290C2×#41—21no—
291C2×#41—21no—
292C2×#41—21no—
293C2×#41—21no—
294C2×#41—21no—
295C2×#41—21no—
296C2×#41—21no—
297C2×#41—21no—
298C2×#41C2×Dic312yes—
299C2×#41#6712yes—
300C22×Q8—21no—
301C22×Q8—21no—
302C22×Q8—21no—
303C22×Q8—21no—
304C22×Q8—21no—
305C22×Q8—21no—
306C22×Q8—21no—
307C22×Q8—21no—
308C22×Q8—21no—
309C22×Q8—21no—
310C22×Q8—21no—
311C22×Q8C2×Dic312yes—
312C22×Q8#6711yescharacteristic
313C22×Q8#6712yes—
314C22×Q8#6712yes—
315C22×D4—21no—
316C22×D4#6711yescharacteristic
317C23×C4—21no—
318C23×C4—21no—
319C23×C4—61no—
320C23×C4C22×D311yescharacteristic
321#137—28no—
322#137—28no—
323#137—28no—
324#137—28no—
325C2×Q16—24no—
326C2×Q16—24no—
327C2×Q16—24no—
328C2×SD16—24no—
329C2×SD16—24no—
330C2×SD16—24no—
331C2×M16—21no—
332C2×M16—21no—
333C2×M16—21no—
334C2×M16—32no—
335C2×M16—32no—
336C2×M16—61no—
337C2×M16—61no—
338C2×M16—61no—
339C2×M16—61no—
340C2×M16—61no—
341C2×M16—61no—
342C2×M16—61no—
343C2×M16—61no—
344C2×M16—61no—
345C2×M16—61no—
346C2×M16C2×Dic312yes—
347C2×M16#6712yes—
348C2×M16#6712yes—
349C22×C8—21no—
350C22×C8—32no—
351C22×C8—61no—
352C22×C8—61no—
353C22×C8—61no—
354C22×C8—61no—
355C22×C8—61no—
356C22×C8—61no—
357C22×C8—61no—
358C22×C8—61no—
359C2×C4⋊C4—32no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365#103—68no—
366#103—64no—
367#102—64no—
368#101—68no—
369C22⋊C8—68no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—41no—
374C23×C3—41no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3C4×D411yescharacteristic
378C23×C3#12111yescharacteristic
379C23×C3#12111yescharacteristic
380C23×C3#12111yescharacteristic
381C23×C3#12311yescharacteristic
382C23×C3#12311yescharacteristic
383C23×C3#12411yescharacteristic
384C3×Q8—24no—
385C3×Q8—22no—
386C3×Q8—24no—
387C3×Q8—22no—
388C3×Q8—42no—
389C3×Q8—42no—
390C3×Q8—42no—
391C3×Q8—42no—
392C3×Q8—42no—
393C3×Q8—41no—
394C3×Q8—42no—
395C3×Q8—41no—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—42no—
399C3×D4—42no—
400C3×D4—42no—
401C3×D4—42no—
402C3×D4—41no—
403C3×D4—41no—
404C2×C3×C4—22no—
405C2×C3×C4—24no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—41no—
409C2×C3×C4—42no—
410C2×C3×C4—41no—
411C2×C3×C4—42no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4C2×C22⋊C411yescharacteristic
419C2×C3×C4C2×C22⋊C411yescharacteristic
420C2×C3×C4C2×C22⋊C411yescharacteristic
421C2×C3×C4C4×D411yescharacteristic
422C2×C3×C4C4×D411yescharacteristic
423C2×C3×C4C4×D411yescharacteristic
424C2×C3×C4#12011yescharacteristic
425C2×C3×C4#12011yescharacteristic
426C2×C3×C4#12011yescharacteristic
427C2×C3×C4#12011yescharacteristic
428C2×C3×C4#12011yescharacteristic
429C2×C3×C4#12011yescharacteristic
430C2×C3×C4#12011yescharacteristic
431C2×C3×C4#12011yescharacteristic
432C2×C3×C4#12111yescharacteristic
433C2×C3×C4#12111yescharacteristic
434C2×C3×C4#12111yescharacteristic
435C2×C3×C4#12111yescharacteristic
436C2×C3×C4#12111yescharacteristic
437C2×C3×C4#12111yescharacteristic
438C2×C3×C4#12111yescharacteristic
439C2×C3×C4#12111yescharacteristic
440C2×C3×C4#12111yescharacteristic
441C2×C3×C4#12311yescharacteristic
442C2×C3×C4#12311yescharacteristic
443C2×C3×C4#12411yescharacteristic
444C2×C3×C4#12711yescharacteristic
445C2×C3×C4#12711yescharacteristic
446C2×Dic3—42no—
447C2×Dic3—82no—
448C2×Dic3—82no—
449C2×Dic3—82no—
450C3×C8—24no—
451C3⋊C8—42no—
452C3⋊C8—42no—
453C3⋊C8—42no—
454C24—21no—
455C24#23711yescharacteristic
456#41—22no—
457#41—22no—
458#41—22no—
459#41—22no—
460#41—22no—
461#41—22no—
462#41—22no—
463#41—22no—
464#41—41no—
465#41—41no—
466#41—41no—
467#41—41no—
468#41—41no—
469#41—41no—
470#41—41no—
471#41—41no—
472C2×Q8—22no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—21no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—21no—
480C2×Q8—22no—
481C2×Q8—21no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8#21712yes—
505C2×Q8#21714yes—
506C2×D4—22no—
507C2×D4—22no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—41no—
514C2×D4—41no—
515C2×D4—41no—
516C2×D4—41no—
517C2×D4#21712yes—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—62no—
533C22×C4—121no—
534C22×C4—121no—
535C22×C4—242no—
536C22×C4D3×D411yescharacteristic
537C22×C4D3×D411yescharacteristic
538C22×C4D3×D411yescharacteristic
539C22×C4D3×D411yescharacteristic
540C22×C4#23711yescharacteristic
541C22×C4#23711yescharacteristic
542C22×C4#23711yescharacteristic
543C22×C4C22×Dic311yescharacteristic
544C22×C4C2×#6711yescharacteristic
545C22×C4C2×#6711yescharacteristic
546C22×C4C2×#6711yescharacteristic
547C22×C4C2×#6711yescharacteristic
548C22×C4C2×#6711yescharacteristic
549C22×C4C2×#6711yescharacteristic
550Q16—216no—
551SD16—216no—
552M16—22no—
553M16—22no—
554M16—22no—
555M16—62no—
556M16—62no—
557M16—62no—
558M16—62no—
559M16—121no—
560M16—121no—
561M16—121no—
562M16—121no—
563M16#21714yes—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—62no—
568C2×C8—62no—
569C2×C8—62no—
570C2×C8—62no—
571C2×C8—62no—
572C2×C8—121no—
573C2×C8—121no—
574C2×C8—121no—
575C2×C8—121no—
576C2×C8—121no—
577C2×C8—121no—
578C2×C8—121no—
579C2×C8—121no—
580C4⋊C4—62no—
581C4⋊C4—62no—
582C4⋊C4—121no—
583C4⋊C4—121no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—21no—
592C22×C3—44no—
593C22×C3—42no—
594C22×C3—82no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3#38611yescharacteristic
598C22×C3#38611yescharacteristic
599C22×C3#39011yescharacteristic
600C22×C3#39211yescharacteristic
601C22×C3#39411yescharacteristic
602C22×C3#39411yescharacteristic
603C22×C3#39411yescharacteristic
604C22×C3#47112yes—
605C22×C3#47312yes—
606C3×C4—42no—
607C3×C4—44no—
608C3×C4#37911yescharacteristic
609C3×C4#38611yescharacteristic
610C3×C4#38611yescharacteristic
611C3×C4#39011yescharacteristic
612C3×C4#39211yescharacteristic
613C3×C4#39211yescharacteristic
614C3×C4#39211yescharacteristic
615C3×C4#39411yescharacteristic
616Dic3—82no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—42no—
621C23—42no—
622C23—41no—
623C23—41no—
624C23D4×Dic311yescharacteristic
625C23#93511yescharacteristic
626C23#93511yescharacteristic
627C23#93611yescharacteristic
628C23#93811yescharacteristic
629C23#93911yescharacteristic
630C23#93911yescharacteristic
631Q8—24no—
632Q8—22no—
633Q8—24no—
634Q8—22no—
635Q8—42no—
636Q8—42no—
637Q8—42no—
638Q8—41no—
639Q8—42no—
640Q8—42no—
641Q8—42no—
642Q8—41no—
643D4—22no—
644D4—22no—
645D4—42no—
646D4—42no—
647D4—42no—
648D4—42no—
649D4—41no—
650D4—41no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—122no—
666C2×C4—242no—
667C2×C4—242no—
668C2×C4—242no—
669C2×C4D4×Dic311yescharacteristic
670C2×C4D4×Dic311yescharacteristic
671C2×C4D4×Dic311yescharacteristic
672C2×C4#93511yescharacteristic
673C2×C4#93511yescharacteristic
674C2×C4#93611yescharacteristic
675C2×C4#93711yescharacteristic
676C2×C4#93711yescharacteristic
677C2×C4#93711yescharacteristic
678C2×C4#93711yescharacteristic
679C2×C4#93811yescharacteristic
680C2×C4#93811yescharacteristic
681C2×C4#93811yescharacteristic
682C2×C4#93911yescharacteristic
683C2×C4#93911yescharacteristic
684C2×C4#93911yescharacteristic
685C2×C4#93911yescharacteristic
686C2×C4#93911yescharacteristic
687C2×C4#93911yescharacteristic
688C2×C4#94011yescharacteristic
689C2×C4#94011yescharacteristic
690C2×C4C2×#21711yescharacteristic
691C2×C4C2×#21711yescharacteristic
692C2×C4C2×#21711yescharacteristic
693C2×C4#95311yescharacteristic
694C2×C4#95311yescharacteristic
695C2×C4#95311yescharacteristic
696C2×C4#95311yescharacteristic
697C8—24no—
698C8—122no—
699C8—122no—
700C8—122no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—82no—
706C2×C3#143811yescharacteristic
707C2×C3#190812yes—
708C2×C3#201911yescharacteristic
709C2×C3#202011yescharacteristic
710C2×C3#205212yes—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—44no—
720C22—42no—
721C22—82no—
722C22—81no—
723C22—81no—
724C22#520312yes—
725C22#520412yes—
726C22#522011yescharacteristic
727C22#522011yescharacteristic
728C22#522111yescharacteristic
729C22#522211yescharacteristic
730C22#522211yescharacteristic
731C22#522211yescharacteristic
732C22#522311yescharacteristic
733C4—42no—
734C4—44no—
735C4—242no—
736C4#522011yescharacteristic
737C4#522011yescharacteristic
738C4#522111yescharacteristic
739C4#522211yescharacteristic
740C4#522311yescharacteristic
741C4#522311yescharacteristic
742C4#522311yescharacteristic
743C4#524711yescharacteristic
744C3#1102111yescharacteristic, complemented, Sylow
745C2—21no—
746C2—21no—
747C2—21no—
748C2—21no—
749C2—82no—
750C2#7210312yes—
751C2#7210512yes—
752C2#7210711yescharacteristic
753C2#7210911yescharacteristic
754C2#7213111yescharacteristic
subgroupG/H
centerC23#939
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC22×C3×#137C2
socleC23×C3#121
prime radicalC22×C3×#41C22
cosocleC23×C3×C4C23
hypercenterC22×#137D3
hypocenterC3#11021
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
4. C22×#836C2semidirect
5. C22×#835C2semidirect
6. C2×#4558C2semidirect
7. C2×#4554C2semidirect
16. C2×C3×#137C4semidirect
135. C2×#137Dic3semidirect
744. C3#11021semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1372
C2×#52342
C2×#52322
C22×#8362
C22×#8352
C2×#45582
C2×#45542
#110213