Finite Group Databasebeta

← #10823416

Subgroups — #10823416

Order 768.

1228 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5622C211yesmaximal, characteristic, complemented
2C2×#5164C211yesmaximal, characteristic, complemented
3Dic3×#121C211yesmaximal, characteristic
4C2×#4757C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic
6#72057C211yesmaximal, characteristic, complemented
7#71695C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic
9#70246C211yesmaximal, characteristic, complemented
10#70220C211yesmaximal, characteristic, complemented
11#70163C211yesmaximal, characteristic, complemented
12#69937C211yesmaximal, characteristic, complemented
13#69906C211yesmaximal, characteristic, complemented
14#68826C211yesmaximal, characteristic, complemented
15#68783C211yesmaximal, characteristic, complemented
16#23574—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×Q8×Dic3C2211yescharacteristic
21C2×#944C2211yescharacteristic
22C2×D4×Dic3—21no—
23C2×D4×Dic3C2211yescharacteristic
24C22×#214C2211yescharacteristic
25C2×#924C2211yescharacteristic
26C22×C4×Dic3C2211yescharacteristic
27#5622—24no—
28#5622—24no—
29C2×#889—21no—
30C2×#888C2211yescharacteristic
31C2×#887—21no—
32C2×#887C2211yescharacteristic
33C2×#878—21no—
34C2×#877—21no—
35C2×C3×#103C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40#5221C2211yescharacteristic
41#5220—21no—
42C2×#832C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45#5164—24no—
46C2×#818C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×#815C2211yescharacteristic
50C2×#815C2211yescharacteristic
51#4984C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4951—21no—
56Dic3×C22⋊C4—21no—
57#4757—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#533—31no—
65C2×#440—31no—
66C2×#440—31no—
67C4×#121—31no—
68#2057—31no—
69#2043—31no—
70#2036—31no—
71#2036—31no—
72#2023—31no—
73#2013—31no—
74#2000—31no—
75#2000D311yescharacteristic
76#1763—31no—
77#1763—31no—
78#1749—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×Dic3—21no—
84C23×Dic3D411yescharacteristic
85C23×Dic3D411yescharacteristic
86C22×Dic6—21no—
87C22×Dic6C2311yescharacteristic
88C2×C3×SD16—22no—
89C2×C3×SD16—22no—
90C2×C3×SD16—22no—
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C3×C22⋊Q8—22no—
94C3×C22⋊Q8—22no—
95C3×#121—22no—
96C3×#121—22no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—21no—
105C2×#217—21no—
106C2×#217—21no—
107Q8×Dic3—22no—
108Q8×Dic3D414yescomplemented
109#944—22no—
110#944—22no—
111D4×Dic3—22no—
112D4×Dic3—22no—
113D4×Dic3—44no—
114C2×#214—22no—
115C2×#214—22no—
116C2×#214—22no—
117C2×C4⋊Dic3—21no—
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3C2311yescharacteristic
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122#924—22no—
123#924—22no—
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×C4×Dic3—21no—
130C2×C4×Dic3—21no—
131C2×C4×Dic3—22no—
132C2×C4×Dic3—22no—
133C2×C4×Dic3—21no—
134C2×C4×Dic3D411yescharacteristic
135C2×C4×Dic3D411yescharacteristic
136C2×C4×Dic3C2311yescharacteristic
137C2×C4×Dic3C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C22×C3⋊C8C2311yescharacteristic
140#889—28no—
141#888—22no—
142#888—22no—
143#887—28no—
144#887—22no—
145#887D414yescomplemented
146#878—28no—
147#877—28no—
148C3×#103—22no—
149C3×#102—22no—
150C3×C22⋊C8—22no—
151#835—22no—
152#835—22no—
153#832—22no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157#830—22no—
158#818—22no—
159#816—22no—
160#816—22no—
161#815—22no—
162#815—22no—
163#810—22no—
164#807—22no—
165C22×SD16—31no—
166C22×SD16C2×D311yescharacteristic
167#533—64no—
168#533—64no—
169C2×C4⋊Q8—31no—
170C2×C4⋊Q8—31no—
171C2×#125—61no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—61no—
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×#121C2×D311yescharacteristic
176C2×C4×Q8—31no—
177C2×C4×Q8—31no—
178C2×C4×Q8—61no—
179C2×C4×D4—31no—
180C2×C4×D4—61no—
181C2×#117—61no—
182C22×C42—31no—
183#440—64no—
184#440—64no—
185C2×#107—31no—
186C2×#107—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103—31no—
191C2×#103—31no—
192C2×#103C2×D311yescharacteristic
193C2×#102—31no—
194C2×#102C2×D311yescharacteristic
195C2×C22⋊C8—31no—
196C2×C22⋊C8C2×D311yescharacteristic
197C2×#97—31no—
198C2×#97—31no—
199#390—31no—
200#389—31no—
201#388—61no—
202#386—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205C4×C22⋊C4—61no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340C2×D311yescharacteristic
210#336—31no—
211#336—31no—
212C24×C3—21no—
213C24×C3C2×D411yescharacteristic
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8C2×D412yes—
220C2×C3×D4—24no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—42no—
227C2×C3×D4—42no—
228C2×C3×D4#4112yes—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2411yescharacteristic
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249C22×Dic3—41no—
250C22×Dic3—42no—
251C22×Dic3—42no—
252C22×Dic3—42no—
253C22×Dic3C2×D411yescharacteristic
254C22×Dic3C2×D411yescharacteristic
255C22×Dic3C2×D411yescharacteristic
256C22×Dic3C2×D411yescharacteristic
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—24no—
262C2×Dic6—21no—
263C2×Dic6—42no—
264C2×Dic6—42no—
265C2×Dic6C2×D412yes—
266C3×SD16—28no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8#4112yes—
273C3×C4⋊C4—24no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4C2×D412yes—
277C3×C4⋊C4#4112yes—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—24no—
280#217—24no—
281#217—42no—
282#217—42no—
283#217—42no—
284#217—42no—
285#214—28no—
286C4⋊Dic3—21no—
287C4⋊Dic3—24no—
288C4⋊Dic3—21no—
289C4⋊Dic3—21no—
290C4⋊Dic3—21no—
291C4⋊Dic3—21no—
292C4⋊Dic3—42no—
293C4⋊Dic3C2×D412yes—
294Dic3⋊C4—24no—
295Dic3⋊C4—24no—
296Dic3⋊C4—24no—
297Dic3⋊C4—24no—
298Dic3⋊C4—24no—
299C4×Dic3—21no—
300C4×Dic3—21no—
301C4×Dic3—24no—
302C4×Dic3—24no—
303C4×Dic3—22no—
304C4×Dic3—22no—
305C4×Dic3—42no—
306C4×Dic3C2×D412yes—
307C4×Dic3C2×D412yes—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8#4112yes—
314C22×Q8—31no—
315C22×Q8—61no—
316C22×Q8C22×D311yescharacteristic
317C22×D4—21no—
318C22×D4C22×D311yescharacteristic
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—61no—
322C23×C4C22×D311yescharacteristic
323C2×SD16—22no—
324C2×SD16—22no—
325C2×SD16—22no—
326C2×SD16—62no—
327C2×SD16—62no—
328C2×SD16—62no—
329C22×C8—31no—
330C22×C8—31no—
331C22×C8C22×D311yescharacteristic
332C22×C8C22×D311yescharacteristic
333C4⋊Q8—62no—
334C4⋊Q8—62no—
335C4⋊Q8—62no—
336C4⋊Q8—62no—
337#125—68no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—68no—
341C22⋊Q8—62no—
342C22⋊Q8—62no—
343#121—22no—
344#121—22no—
345C4×Q8—34no—
346C4×Q8—34no—
347C4×Q8—62no—
348C4×Q8—62no—
349C4×Q8—68no—
350C4×D4—62no—
351C4×D4—62no—
352C4×D4—124no—
353#117—68no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4C22×D311yescharacteristic
366C2×C4⋊C4C22×D311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C42—31no—
375C2×C42—31no—
376C2×C42—31no—
377C2×C42—31no—
378C2×C42—62no—
379C2×C42—62no—
380C2×C42—61no—
381C2×C42—61no—
382C2×C42—61no—
383#107—62no—
384#107—62no—
385#103—22no—
386#103—62no—
387#103—62no—
388#103—62no—
389#103—62no—
390#103—62no—
391#102—22no—
392#102—62no—
393C22⋊C8—22no—
394C22⋊C8—62no—
395#97—62no—
396#97—62no—
397#95—61no—
398#95—61no—
399#95—61no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3—41no—
413C23×C3#13712yes—
414C23×C3C22×D411yescharacteristic
415C3×Q8—22no—
416C3×Q8—22no—
417C3×Q8—41no—
418C3×Q8—41no—
419C3×D4—22no—
420C3×D4—22no—
421C3×D4—48no—
422C3×D4—41no—
423C3×D4—41no—
424C2×C3×C4—21no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—21no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
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×C4C22×D411yescharacteristic
441C2×C3×C4C22×D411yescharacteristic
442C2×C3×C4C2×#4111yescharacteristic
443C2×C3×C4C2×#4111yescharacteristic
444C2×C3×C4C2×#4111yescharacteristic
445C2×C3×C4C2×#4111yescharacteristic
446C2×Dic3—28no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—22no—
456C2×Dic3—22no—
457C2×Dic3—44no—
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—
467C2×Dic3—41no—
468C2×Dic3—84no—
469C2×Dic3#12012yes—
470C2×Dic3#12012yes—
471C2×Dic3AGL(1,ℤ/8)12yes—
472C2×Dic3#13712yes—
473Dic6—22no—
474Dic6—22no—
475Dic6—48no—
476Dic6—41no—
477Dic6—41no—
478C3×C8—22no—
479C3×C8—41no—
480C3⋊C8—22no—
481C3⋊C8—41no—
482C24—21no—
483C24D3×D411yescharacteristic
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—32no—
490C2×Q8—64no—
491C2×Q8—61no—
492C2×Q8—61no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—122no—
497C2×Q8—122no—
498C2×Q8D3×D412yes—
499C2×D4—24no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4#23712yes—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—31no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—62no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—122no—
531C22×C4—121no—
532C22×C4—122no—
533C22×C4—122no—
534C22×C4D3×D411yescharacteristic
535C22×C4C23×D311yescharacteristic
536SD16—28no—
537SD16—68no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—32no—
544C2×C8—61no—
545C2×C8—61no—
546C2×C8—61no—
547C2×C8—61no—
548C2×C8—61no—
549C2×C8#23712yes—
550C4⋊C4—24no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—32no—
554C4⋊C4—64no—
555C4⋊C4—64no—
556C4⋊C4—64no—
557C4⋊C4—64no—
558C4⋊C4—64no—
559C4⋊C4—64no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—122no—
566C4⋊C4D3×D412yes—
567C4⋊C4#23712yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—64no—
571C22⋊C4—122no—
572C22⋊C4—122no—
573C22⋊C4—122no—
574C22⋊C4—122no—
575C42—32no—
576C42—32no—
577C42—62no—
578C42—62no—
579C42—64no—
580C42—64no—
581C42—61no—
582C42—61no—
583C42—122no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—81no—
595C22×C3—81no—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3C2×#12011yescharacteristic
599C22×C3#52511yescharacteristic
600C22×C3#53211yescharacteristic
601C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
602C22×C3C2×#13711yescharacteristic
603C22×C3C2×#13711yescharacteristic
604C22×C3#57511yescharacteristic
605C3×C4—42no—
606C3×C4—41no—
607C3×C4—42no—
608C3×C4—42no—
609C3×C4#52511yescharacteristic
610C3×C4#52511yescharacteristic
611C3×C4#53211yescharacteristic
612C3×C4#53211yescharacteristic
613Dic3—22no—
614Dic3—22no—
615Dic3—22no—
616Dic3—22no—
617Dic3—42no—
618Dic3—42no—
619Dic3—81no—
620Dic3—81no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23#91512yes—
635C23C2×D3×D411yescharacteristic
636Q8—22no—
637Q8—22no—
638Q8—41no—
639Q8—41no—
640Q8—62no—
641Q8—62no—
642Q8—128no—
643Q8—121no—
644Q8—121no—
645D4—22no—
646D4—22no—
647D4—48no—
648D4—41no—
649D4—41no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—32no—
657C2×C4—32no—
658C2×C4—32no—
659C2×C4—32no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—68no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—124no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—244no—
693C2×C4C2×D3×D411yescharacteristic
694C2×C4C2×D3×D411yescharacteristic
695C2×C4C2×#23711yescharacteristic
696C2×C4C2×#23711yescharacteristic
697C2×C4C2×#23711yescharacteristic
698C2×C4D3×#4111yescharacteristic
699C8—22no—
700C8—41no—
701C8—62no—
702C8—121no—
703C2×C3—42no—
704C2×C3—82no—
705C2×C3#238811yescharacteristic
706C2×C3#300411yescharacteristic
707C2×C3#300611yescharacteristic
708C2×C3#311011yescharacteristic
709C2×C3#311611yescharacteristic
710C2×C3#318111yescharacteristic
711C2×C3#318211yescharacteristic
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22#558611yescharacteristic
727C22D3×#12011yescharacteristic
728C22#559611yescharacteristic
729C22C2×#91511yescharacteristic
730C22#576811yescharacteristic
731C22D3×AGL(1,ℤ/8)11yescharacteristic
732C22D3×#13711yescharacteristic
733C4—42no—
734C4—41no—
735C4—42no—
736C4—42no—
737C4—62no—
738C4—62no—
739C4—62no—
740C4—62no—
741C4—122no—
742C4—122no—
743C4—241no—
744C4—241no—
745C4#558611yescharacteristic
746C4#559611yescharacteristic
747C4#560611yescharacteristic
748C4#571611yescharacteristic
749C3#2357411yescharacteristic, complemented, Sylow
750C2—42no—
751C2—82no—
752C2#7666511yescharacteristic
753C2#8003911yescharacteristic
754C2#8008411yescharacteristic
755C2#8013411yescharacteristic
756C2#8021511yescharacteristic
757C2#8063911yescharacteristic
758C2#8079011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radicalC2×C3×#121C22
hypercenter#2000D3
hypocenterC3#23574
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#5622C2semidirect
2. C2×#5164C2semidirect
4. C2×#4757C2semidirect
6. #72057C2semidirect
7. #71695C2semidirect
9. #70246C2semidirect
10. #70220C2semidirect
11. #70163C2semidirect
12. #69937C2semidirect
13. #69906C2semidirect
14. #68826C2semidirect
15. #68783C2semidirect
108. Q8×Dic3D4semidirect
145. #887D4semidirect
749. C3#23574semidirect

Maximal subgroups

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

subgroupindex
C2×#56222
C2×#51642
Dic3×#1212
C2×#47572
C3×#20002
#720572
#716952
#716852
#702462
#702202
#701632
#699372
#699062
#688262
#687832
#235743