Finite Group Databasebeta

← #10842607

Subgroups — #10842607

Order 768.

1078 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5187C211yesmaximal, characteristic
2C2×#5182C211yesmaximal, characteristic, complemented
3#82457C211yesmaximal, characteristic
4C2×C4×#216C211yesmaximal, characteristic, complemented
5C2×#4808C211yesmaximal, characteristic
6#76625C211yesmaximal, characteristic, complemented
7C3×#1878C211yesmaximal, characteristic, complemented
8#70282C211yesmaximal, characteristic, complemented
9#70275C211yesmaximal, characteristic, complemented
10#70237C211yesmaximal, characteristic, complemented
11#69676C211yesmaximal, characteristic, complemented
12#68901C211yesmaximal, characteristic, complemented
13#68824C211yesmaximal, characteristic, complemented
14#68686C211yesmaximal, characteristic, complemented
15#68657C211yesmaximal, characteristic, complemented
16#25151—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C2×C3×C4×Q8C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×Q8×Dic3C2211yescharacteristic
22C2×#944C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#215C2211yescharacteristic
25C22×#204C2211yescharacteristic
26C2×#897C2211yescharacteristic
27C2×C4×Dic6C2211yescharacteristic
28C2×C3×#103C2211yescharacteristic
29C2×C3×#103C2211yescharacteristic
30C3×#391C2211yescharacteristic
31C2×#835C2211yescharacteristic
32C2×#835C2211yescharacteristic
33#5187—24no—
34#5182—24no—
35C2×#821C2211yescharacteristic
36C2×(C2×D3)⋊C8C2211yescharacteristic
37C2×(C2×D3)⋊C8C2211yescharacteristic
38C2×#816C2211yescharacteristic
39C2×Dic3⋊C8C2211yescharacteristic
40C4×#216—24no—
41#4988—21no—
42#4988C2211yescharacteristic
43#4987—21no—
44#4987C2211yescharacteristic
45#4972C2211yescharacteristic
46C2×#810C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#808C2211yescharacteristic
49C2×#807C2211yescharacteristic
50#4939—21no—
51#4939C2211yescharacteristic
52C4×(C2×D3)⋊C4—21no—
53C4×(C2×D3)⋊C4C2211yescharacteristic
54C2×C4×C3⋊C8C2211yescharacteristic
55#4808—24no—
56#4676—21no—
57#4669—21no—
58#4657—21no—
59#4647—21no—
60C3×#340C2211yescharacteristic
61C3×#336C2211yescharacteristic
62#4551C2211yescharacteristic
63#4550C2211yescharacteristic
64C2×#462—31no—
65C2×#452—31no—
66C2×#452—31no—
67C2×C4×Q16—31no—
68#2429—31no—
69#2341—31no—
70#2067—31no—
71#2036—31no—
72#2035—31no—
73#2013—31no—
74#1968—31no—
75#1923—31no—
76#1880—31no—
77#1878D311yescharacteristic, complemented
78#1865—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C2×#239—22no—
82C2×#239—22no—
83C2×#239—22no—
84C2×#239—22no—
85C2×#239—41no—
86C2×#239—41no—
87C22×D12—21no—
88C22×D12C2311yescharacteristic
89C22×C4×D3—21no—
90C22×C4×D3C2311yescharacteristic
91C22×Dic6C2311yescharacteristic
92C2×C3×Q16—22no—
93C2×C3×Q16—22no—
94C2×C3×Q16—22no—
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×C4×Q8—22no—
98C3×C4×Q8—41no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C42—21no—
103C2×C3×C42C2311yescharacteristic
104#946—22no—
105#946—41no—
106Q8×Dic3—22no—
107Q8×Dic3—41no—
108#944—22no—
109#944—41no—
110C2×#216—22no—
111C2×#216—22no—
112C2×#216D414yes—
113C2×#215—22no—
114C2×#215—22no—
115C2×#215—41no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×(C2×D3)⋊C4D411yescharacteristic
124C2×(C2×D3)⋊C4D411yescharacteristic
125C2×C4⋊Dic3—21no—
126C2×C4⋊Dic3—21no—
127C2×C4⋊Dic3C2311yescharacteristic
128C2×C4⋊Dic3C2311yescharacteristic
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×Dic3⋊C4—21no—
133C2×Dic3⋊C4—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3—21no—
136C2×C4×Dic3C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139C2×#204—22no—
140C2×#204—22no—
141C2×#204—41no—
142#897—22no—
143#897—41no—
144C4×Dic6—22no—
145C4×Dic6—41no—
146C3×#103—22no—
147C3×#103—41no—
148C3×#95—21no—
149C3×#95—21no—
150#835—22no—
151#835D414yes—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95D411yescharacteristic
155C3⋊#95D411yescharacteristic
156#821—22no—
157(C2×D3)⋊C8—22no—
158(C2×D3)⋊C8—22no—
159#816—22no—
160Dic3⋊C8—22no—
161#810—22no—
162#809—22no—
163#808—41no—
164#807—22no—
165C4×C3⋊C8—22no—
166C22×#41—31no—
167C22×Q16—31no—
168C22×Q16C2×D311yescharacteristic
169C22×SD16—31no—
170C22×SD16—31no—
171C2×C4⋊Q8—31no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×C4×Q8—31no—
175C2×C4×Q8—31no—
176C2×C4×Q8C2×D311yescharacteristic
177#462—64no—
178#452—64no—
179#452—64no—
180C4×Q16—64no—
181C2×#107—31no—
182C2×#106—31no—
183C2×C4⋊C8—31no—
184C2×#103—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103C2×D311yescharacteristic
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×C22⋊C8—31no—
193C2×C22⋊C8—31no—
194C2×C4×C8—31no—
195#398—61no—
196#396—61no—
197#391C2×D311yescharacteristic
198#390—31no—
199#390—31no—
200#390—61no—
201#390—61no—
202#389—31no—
203#389—61no—
204#388—61no—
205#380—31no—
206#380—61no—
207C4×C22⋊C4—31no—
208C4×C22⋊C4—61no—
209#340—31no—
210#340C2×D311yescharacteristic
211#336—31no—
212#336C2×D311yescharacteristic
213C23×D3—21no—
214C23×D3C2×D411yescharacteristic
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8C2×D412yes—
225C2×C3×Q8C2×D412yes—
226C2×C3×Q8#4112yes—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2411yescharacteristic
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3C2×D411yescharacteristic
238C22×Dic3C2×D411yescharacteristic
239C22×Dic3C2×D411yescharacteristic
240#239—44no—
241#239—44no—
242#239—44no—
243#239—44no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—24no—
249C2×D12—21no—
250C2×D12—42no—
251C2×D12—42no—
252C2×D12#4112yes—
253C2×C4×D3—24no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—42no—
261C2×C4×D3—42no—
262C2×Dic6—21no—
263C2×Dic6—21no—
264C2×Dic6—21no—
265C2×Dic6—21no—
266C2×Dic6—21no—
267C2×Dic6C2×D412yes—
268C3×Q16—44no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C2×C3×C8—21no—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4—21no—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—21no—
279C3×C4⋊C4—42no—
280C3×C42—21no—
281C3×C42—21no—
282C3×C42—42no—
283#216—28no—
284#215—44no—
285(C2×D3)⋊C4—22no—
286(C2×D3)⋊C4—22no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—42no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—81no—
292(C2×D3)⋊C4—81no—
293(C2×D3)⋊C4—81no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—42no—
298C4⋊Dic3—42no—
299C4⋊Dic3C2×D412yes—
300Dic3⋊C4—42no—
301Dic3⋊C4—42no—
302Dic3⋊C4—42no—
303Dic3⋊C4—42no—
304Dic3⋊C4—42no—
305C4×Dic3—21no—
306C4×Dic3—21no—
307C4×Dic3—42no—
308C4×Dic3—42no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8C2×D412yes—
314C2×C3⋊C8C2×D412yes—
315#204—44no—
316C2×#41—62no—
317C2×#41—62no—
318C2×#41—62no—
319C2×#41—62no—
320C2×#41—121no—
321C2×#41—121no—
322C22×Q8—31no—
323C22×Q8C22×D311yescharacteristic
324C22×Q8C22×D311yescharacteristic
325C22×D4—31no—
326C22×D4—61no—
327C23×C4—31no—
328C23×C4—61no—
329C2×Q16—22no—
330C2×Q16—22no—
331C2×Q16—22no—
332C2×Q16—34no—
333C2×Q16—62no—
334C2×Q16—62no—
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—121no—
340C2×SD16—121no—
341C22×C8—31no—
342C22×C8—31no—
343C22×C8C22×D311yescharacteristic
344C22×C8C22×D311yescharacteristic
345C4⋊Q8—62no—
346C4⋊Q8—121no—
347C22⋊Q8—62no—
348C22⋊Q8—62no—
349C22⋊Q8—121no—
350C22⋊Q8—121no—
351C4×Q8—22no—
352C4×Q8—41no—
353C4×Q8—62no—
354C4×Q8—62no—
355C4×Q8—121no—
356C4×Q8—121no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4—61no—
363C2×C4⋊C4—61no—
364C2×C4⋊C4—61no—
365C2×C4⋊C4—61no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4C22×D311yescharacteristic
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C22⋊C4—31no—
370C2×C22⋊C4—31no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—61no—
378C2×C42—21no—
379C2×C42—31no—
380C2×C42—61no—
381C2×C42—61no—
382C2×C42C22×D311yescharacteristic
383#107—62no—
384#106—121no—
385C4⋊C8—62no—
386#103—22no—
387#103—34no—
388#103—41no—
389#103—62no—
390#103—62no—
391#103—62no—
392#102—62no—
393#102—62no—
394C22⋊C8—62no—
395C22⋊C8—62no—
396C4×C8—62no—
397#95—21no—
398#95—21no—
399#95—31no—
400#95—31no—
401#95—61no—
402#95—61no—
403C23×C3C22×D411yescharacteristic
404C22×D3—21no—
405C22×D3—22no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—21no—
411C22×D3—21no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C3×Q8—22no—
419C3×Q8—22no—
420C3×Q8—22no—
421C3×Q8—41no—
422C3×Q8—41no—
423C3×Q8—41no—
424C3×Q8—41no—
425C3×Q8#12114yes—
426C2×C3×C4—22no—
427C2×C3×C4—21no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
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#13712yes—
444C2×C3×C4C22×D411yescharacteristic
445C2×C3×C4C22×D411yescharacteristic
446C2×C3×C4C2×#4111yescharacteristic
447C2×C3×C4C2×#4111yescharacteristic
448C2×C3×C4H(5,𝔽2)11yescharacteristic
449C2×C3×C4H(5,𝔽2)11yescharacteristic
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—22no—
455C2×Dic3—22no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463C2×Dic3—41no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3#13512yes—
468D12—22no—
469D12—22no—
470D12—48no—
471D12—41no—
472D12—41no—
473C4×D3—48no—
474C4×D3—41no—
475C4×D3—41no—
476C4×D3—41no—
477C4×D3—41no—
478Dic6—22no—
479Dic6—22no—
480Dic6—41no—
481Dic6—41no—
482C3×C8—41no—
483C3×C8—41no—
484C3⋊C8—22no—
485C3⋊C8—22no—
486C24—31no—
487C24—61no—
488#41—124no—
489#41—124no—
490#41—124no—
491#41—124no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—32no—
502C2×Q8—61no—
503C2×Q8—61no—
504C2×Q8—61no—
505C2×Q8—61no—
506C2×Q8—61no—
507C2×Q8#23512yes—
508C2×Q8D3×D412yes—
509C2×Q8D3×D412yes—
510C2×D4—32no—
511C2×D4—64no—
512C2×D4—61no—
513C2×D4—61no—
514C2×D4—61no—
515C2×D4—61no—
516C2×D4—61no—
517C2×D4—122no—
518C2×D4—122no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—31no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—64no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—122no—
537C22×C4—122no—
538C22×C4D3×D411yescharacteristic
539C22×C4D3×D411yescharacteristic
540C22×C4C23×D311yescharacteristic
541Q16—44no—
542Q16—68no—
543SD16—124no—
544SD16—124no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—32no—
552C2×C8—32no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8—61no—
556C2×C8—61no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—32no—
562C4⋊C4—42no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—122no—
567C4⋊C4—122no—
568C4⋊C4—122no—
569C4⋊C4—122no—
570C4⋊C4—122no—
571C4⋊C4—122no—
572C4⋊C4—122no—
573C22⋊C4—62no—
574C22⋊C4—62no—
575C22⋊C4—122no—
576C22⋊C4—122no—
577C22⋊C4—122no—
578C22⋊C4—122no—
579C22⋊C4—241no—
580C22⋊C4—241no—
581C22⋊C4—241no—
582C42—21no—
583C42—21no—
584C42—42no—
585C42—61no—
586C42—61no—
587C42—122no—
588C42—122no—
589C22×C3#52511yescharacteristic
590C22×C3D4211yescharacteristic
591C22×C3D4211yescharacteristic
592C22×C3C2×#13511yescharacteristic
593C22×C3C2×#13711yescharacteristic
594C22×C3#57711yescharacteristic
595C22×C3#57811yescharacteristic
596C2×D3—41no—
597C2×D3—42no—
598C2×D3—41no—
599C2×D3—42no—
600C2×D3—42no—
601C2×D3—41no—
602C2×D3—41no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—41no—
606C2×D3—81no—
607C2×D3—81no—
608C2×D3—81no—
609C2×D3—81no—
610C3×C4—24no—
611C3×C4—22no—
612C3×C4—41no—
613C3×C4—81no—
614C3×C4—81no—
615C3×C4—81no—
616C3×C4C2×#12111yescharacteristic
617C3×C4#53811yescharacteristic
618C3×C4#54611yescharacteristic
619C3×C4#54611yescharacteristic
620Dic3—22no—
621Dic3—42no—
622Dic3—41no—
623Dic3—41no—
624Dic3—42no—
625Dic3—81no—
626C23—61no—
627C23—61no—
628C23—61no—
629C23—61no—
630C23—62no—
631C23—61no—
632C23—61no—
633C23—61no—
634C23—121no—
635C23—121no—
636C23—121no—
637C23—121no—
638C23—121no—
639C23—121no—
640C23C2×D3×D411yescharacteristic
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—62no—
649Q8—62no—
650Q8—121no—
651Q8—121no—
652Q8#88414yes—
653D4—62no—
654D4—62no—
655D4—128no—
656D4—121no—
657D4—121no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—32no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—62no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—128no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4#91812yes—
699C2×C4C2×#23511yescharacteristic
700C2×C4C2×D3×D411yescharacteristic
701C2×C4C2×D3×D411yescharacteristic
702C2×C4#100411yescharacteristic
703C2×C4D3×#4111yescharacteristic
704C2×C4#100911yescharacteristic
705C8—41no—
706C8—41no—
707C8—62no—
708C8—62no—
709C2×C3#242411yescharacteristic
710C2×C3#310711yescharacteristic
711C2×C3#312011yescharacteristic
712C2×C3#327011yescharacteristic
713C2×C3#327811yescharacteristic
714C2×C3#328411yescharacteristic
715C2×C3#328511yescharacteristic
716D3—81no—
717D3—82no—
718C22—121no—
719C22—121no—
720C22—121no—
721C22—122no—
722C22—122no—
723C22—121no—
724C22—121no—
725C22—121no—
726C22—121no—
727C22—122no—
728C22—241no—
729C22—241no—
730C22—241no—
731C22—241no—
732C22#554711yescharacteristic
733C22#559011yescharacteristic
734C22#560911yescharacteristic
735C22C2×#91811yescharacteristic
736C22D3×#13511yescharacteristic
737C22#577811yescharacteristic
738C22#577911yescharacteristic
739C4—22no—
740C4—24no—
741C4—41no—
742C4—62no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4—121no—
747C4—121no—
748C4—122no—
749C4—122no—
750C4—241no—
751C4C2×#88411yescharacteristic
752C4#556011yescharacteristic
753C4#561011yescharacteristic
754C4#565411yescharacteristic
755C3#2515111yescharacteristic, complemented, Sylow
756C2—241no—
757C2—242no—
758C2#7489311yescharacteristic
759C2#7974711yescharacteristic
760C2#7984911yescharacteristic
761C2#8020811yescharacteristic
762C2#8027011yescharacteristic
763C2#8050311yescharacteristic
764C2#8061411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1878C2
socleC23×C3C22×D4
prime radicalC22×#239C22
hypercenter#1878D3
hypocenterC3#25151
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×#5182C2semidirect
4. C2×C4×#216C2semidirect
6. #76625C2semidirect
7. C3×#1878C2semidirect
8. #70282C2semidirect
9. #70275C2semidirect
10. #70237C2semidirect
11. #69676C2semidirect
12. #68901C2semidirect
13. #68824C2semidirect
14. #68686C2semidirect
15. #68657C2semidirect
77. #1878D3semidirect
755. C3#25151semidirect

Maximal subgroups

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

subgroupindex
C2×#51872
C2×#51822
#824572
C2×C4×#2162
C2×#48082
#766252
C3×#18782
#702822
#702752
#702372
#696762
#689012
#688242
#686862
#686572
#251513