Finite Group Databasebeta

← #10823492

Subgroups — #10823492

Order 768.

1178 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5582C211yesmaximal, characteristic, complemented
2C2×#5026C211yesmaximal, characteristic, complemented
3C2×C4×D24C211yesmaximal, characteristic, complemented
4#73763C211yesmaximal, characteristic, complemented
5C3×C4×#103C211yesmaximal, characteristic, complemented
6#70277C211yesmaximal, characteristic, complemented
7#70272C211yesmaximal, characteristic, complemented
8#70245C211yesmaximal, characteristic, complemented
9#70244C211yesmaximal, characteristic, complemented
10#69753C211yesmaximal, characteristic, complemented
11#69474C211yesmaximal, characteristic, complemented
12#68898C211yesmaximal, characteristic, complemented
13#68886C211yesmaximal, characteristic
14#68826C211yesmaximal, characteristic, complemented
15#68822C211yesmaximal, characteristic, complemented
16#23579—31nomaximal, Sylow
17C2×C3×C4×Q8C2211yescharacteristic
18C2×#947C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C22×#215C2211yescharacteristic
21C22×D24C2211yescharacteristic
22#5582—24no—
23#5582—24no—
24C2×#896—21no—
25C2×#895C2211yescharacteristic
26C2×#895C2211yescharacteristic
27C2×#894—21no—
28C2×#888C2211yescharacteristic
29C2×#876—21no—
30C2×#875—21no—
31C2×C4×D12C2211yescharacteristic
32C2×C4×D12C2211yescharacteristic
33C2×#872C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×C4×C8C2211yescharacteristic
37C3×C4×C4⋊C4C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×#818C2211yescharacteristic
44#5026—24no—
45#4988C2211yescharacteristic
46#4987C2211yescharacteristic
47#4984C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#809C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4940—21no—
53#4939—21no—
54C2×#803C2211yescharacteristic
55C4×D24—24no—
56#4668—21no—
57#4665—21no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#542—31no—
65C2×#440—31no—
66C2×C4×D8—31no—
67#2324—31no—
68#2057—31no—
69#2042—31no—
70#2036—31no—
71#2033—31no—
72#2023—31no—
73#2012—31no—
74#2000—31no—
75#1999—31no—
76#1762—31no—
77C4×#103D311yescharacteristic, complemented
78#1750—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×D12—21no—
81C22×D12—21no—
82C22×D12C2311yescharacteristic
83C22×D12C2311yescharacteristic
84C22×C4×D3—21no—
85C22×C4×D3—21no—
86C22×C4×D3C2311yescharacteristic
87C22×Dic6—21no—
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×C4×Q8—22no—
91C3×C4×Q8D414yescomplemented
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C42—21no—
97C2×C3×C42—21no—
98C2×C3×C42C2311yescharacteristic
99#947—22no—
100#947—22no—
101#946—22no—
102#946—22no—
103C2×#215—22no—
104C2×#215—22no—
105C2×#215—22no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4D411yescharacteristic
117C2×(C2×D3)⋊C4D411yescharacteristic
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3C2311yescharacteristic
120C2×C4⋊Dic3C2311yescharacteristic
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4—21no—
123C2×Dic3⋊C4D411yescharacteristic
124C2×Dic3⋊C4D411yescharacteristic
125C2×C4×Dic3C2311yescharacteristic
126C22×C3⋊C8C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128C2×D24—22no—
129C2×D24—22no—
130C2×D24—22no—
131#896—28no—
132#895—22no—
133#895—22no—
134#895—22no—
135#895—22no—
136#894—28no—
137#888—22no—
138#888—22no—
139#876—28no—
140#875—28no—
141C4×D12—22no—
142C4×D12—22no—
143C4×D12—22no—
144C4×D12D414yescomplemented
145#872—22no—
146#872—22no—
147C3×#103—22no—
148C3×#103—22no—
149C3×C4×C8—22no—
150C3×#95—21no—
151#835—22no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154#821—22no—
155#821—22no—
156(C2×D3)⋊C8—22no—
157(C2×D3)⋊C8—22no—
158#818—22no—
159#809—22no—
160#809—22no—
161#809—22no—
162#807—22no—
163#803—22no—
164C22×SD16—31no—
165C22×D8—31no—
166#542—64no—
167#542—64no—
168C2×C4⋊Q8—31no—
169C2×#126—61no—
170C2×#124—31no—
171C2×#124—61no—
172C2×#123—61no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—61no—
175C2×#121—31no—
176C2×#121—31no—
177C2×C4×Q8C2×D311yescharacteristic
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×#117—31no—
181#440—64no—
182C4×D8—64no—
183C2×#107—31no—
184C2×#107—31no—
185C2×#103—31no—
186C2×#103C2×D311yescharacteristic
187C2×#103C2×D311yescharacteristic
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×#97—31no—
196C2×C4×C8C2×D311yescharacteristic
197#390—31no—
198#390—61no—
199#389—31no—
200#388—61no—
201#386—61no—
202#385—61no—
203#380—31no—
204C4×C4⋊C4C2×D311yescharacteristic
205#340—31no—
206#340—31no—
207#340C2×D311yescharacteristic
208#340C2×D311yescharacteristic
209#336—31no—
210#336—31no—
211C23×D3—21no—
212C23×D3—21no—
213C23×D3C2×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—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2411yescharacteristic
227C22×Dic3—21no—
228C22×Dic3—21no—
229C22×Dic3C2×D411yescharacteristic
230C22×Dic3C2×D411yescharacteristic
231C22×Dic3C2×D411yescharacteristic
232C2×D12—21no—
233C2×D12—21no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—21no—
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—24no—
243C2×D12—24no—
244C2×D12—81no—
245C2×D12—81no—
246C2×D12—81no—
247C2×D12—81no—
248C2×D12C2×D412yes—
249C2×D12#4112yes—
250C2×C4×D3—21no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—24no—
257C2×C4×D3—42no—
258C2×C4×D3—81no—
259C2×C4×D3—81no—
260C2×C4×D3—81no—
261C2×C4×D3—81no—
262C2×Dic6—24no—
263C2×Dic6—81no—
264C2×Dic6—81no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8#4112yes—
271C3×C4⋊C4—24no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—21no—
276C3×C4⋊C4C2×D412yes—
277C3×C4⋊C4#4112yes—
278C3×C42—24no—
279C3×C42—81no—
280C3×C42C2×D412yes—
281C3×C42C2×D412yes—
282#215—28no—
283(C2×D3)⋊C4—24no—
284(C2×D3)⋊C4—24no—
285(C2×D3)⋊C4—24no—
286(C2×D3)⋊C4—24no—
287(C2×D3)⋊C4—24no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—24no—
291(C2×D3)⋊C4—42no—
292(C2×D3)⋊C4—81no—
293(C2×D3)⋊C4—81no—
294(C2×D3)⋊C4—81no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—81no—
299C4⋊Dic3C2×D412yes—
300Dic3⋊C4—24no—
301Dic3⋊C4—24no—
302Dic3⋊C4—22no—
303Dic3⋊C4—22no—
304C4×Dic3—21no—
305C4×Dic3—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8#4112yes—
312D24—28no—
313C22×Q8—61no—
314C22×Q8C22×D311yescharacteristic
315C22×D4—31no—
316C22×D4—31no—
317C22×D4—61no—
318C22×D4—61no—
319C23×C4—31no—
320C23×C4—61no—
321C23×C4—61no—
322C2×SD16—62no—
323C2×SD16—62no—
324C2×SD16—62no—
325C2×D8—62no—
326C2×D8—62no—
327C2×D8—62no—
328C22×C8—31no—
329C22×C8—31no—
330C22×C8C22×D311yescharacteristic
331C22×C8C22×D311yescharacteristic
332C4⋊Q8—62no—
333C4⋊Q8—62no—
334#126—68no—
335#124—68no—
336#124—62no—
337#124—62no—
338#123—68no—
339C22⋊Q8—68no—
340C22⋊Q8—62no—
341C22⋊Q8—62no—
342#121—62no—
343#121—62no—
344#121—62no—
345#121—62no—
346C4×Q8—22no—
347C4×Q8D1214yescomplemented
348C4×D4—34no—
349C4×D4—62no—
350C4×D4—62no—
351C4×D4—62no—
352#117—62no—
353#117—62no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4—61no—
362C2×C4⋊C4C22×D311yescharacteristic
363C2×C4⋊C4C22×D311yescharacteristic
364C2×C4⋊C4C22×D311yescharacteristic
365C2×C22⋊C4—31no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—61no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C22⋊C4—61no—
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×C42—21no—
378C2×C42—21no—
379C2×C42—31no—
380C2×C42C22×D311yescharacteristic
381#107—62no—
382#107—62no—
383#103—22no—
384#103—22no—
385#103—62no—
386#102—62no—
387#102—62no—
388#102—62no—
389#102—62no—
390#102—62no—
391C22⋊C8—62no—
392C22⋊C8—62no—
393#97—62no—
394C4×C8—22no—
395#95—21no—
396#95—61no—
397#95—61no—
398C23×C3C22×D411yescharacteristic
399C22×D3—21no—
400C22×D3—22no—
401C22×D3—22no—
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—41no—
409C22×D3—41no—
410C22×D3—41no—
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C3×Q8—22no—
421C3×Q8—22no—
422C3×Q8—41no—
423C3×Q8—41no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
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×C4#12012yes—
441C2×C3×C4#12012yes—
442C2×C3×C4C22×D411yescharacteristic
443C2×C3×C4C22×D411yescharacteristic
444C2×C3×C4C2×#4111yescharacteristic
445C2×C3×C4C2×#4111yescharacteristic
446C2×C3×C4C2×#4111yescharacteristic
447C2×C3×C4C2×#4111yescharacteristic
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—22no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—21no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3—41no—
462C2×Dic3—41no—
463D12—22no—
464D12—22no—
465D12—22no—
466D12—22no—
467D12—41no—
468D12—41no—
469D12—41no—
470D12—41no—
471D12—84no—
472D12—84no—
473C4×D3—41no—
474C4×D3—41no—
475C4×D3—41no—
476C4×D3—41no—
477C4×D3—84no—
478C4×D3—84no—
479Dic6—84no—
480C3×C8—22no—
481C3×C8—41no—
482C3⋊C8—22no—
483C3⋊C8—41no—
484C24—31no—
485C24—61no—
486C24—61no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—64no—
493C2×Q8—241no—
494C2×Q8—241no—
495C2×Q8C2×D1212yes—
496C2×D4—32no—
497C2×D4—32no—
498C2×D4—64no—
499C2×D4—64no—
500C2×D4—61no—
501C2×D4—61no—
502C2×D4—61no—
503C2×D4—61no—
504C2×D4—61no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—241no—
511C2×D4—241no—
512C2×D4—241no—
513C2×D4—241no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—31no—
519C22×C4—31no—
520C22×C4—31no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—64no—
529C22×C4—61no—
530C22×C4—122no—
531C22×C4—241no—
532C22×C4—241no—
533C22×C4—241no—
534C22×C4—241no—
535C22×C4D3×D411yescharacteristic
536C22×C4D3×D411yescharacteristic
537C22×C4C23×D311yescharacteristic
538SD16—68no—
539D8—68no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—32no—
546C2×C8—61no—
547C2×C8—61no—
548C2×C8—61no—
549C2×C8—61no—
550C2×C8—61no—
551C2×C8#23512yes—
552C4⋊C4—24no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—32no—
558C4⋊C4—64no—
559C4⋊C4—64no—
560C4⋊C4—62no—
561C4⋊C4—62no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—241no—
566C4⋊C4C2×D1212yes—
567C4⋊C4#23512yes—
568C22⋊C4—64no—
569C22⋊C4—64no—
570C22⋊C4—64no—
571C22⋊C4—64no—
572C22⋊C4—64no—
573C22⋊C4—62no—
574C22⋊C4—62no—
575C22⋊C4—64no—
576C22⋊C4—122no—
577C22⋊C4—241no—
578C22⋊C4—241no—
579C22⋊C4—241no—
580C42—24no—
581C42—61no—
582C42—61no—
583C42—81no—
584C42C2×D1212yes—
585C42D3×D412yes—
586C22×C3C2×#12011yescharacteristic
587C22×C3#52511yescharacteristic
588C22×C3#53211yescharacteristic
589C22×C3#57611yescharacteristic
590C22×C3#57611yescharacteristic
591C22×C3#57711yescharacteristic
592C22×C3#57811yescharacteristic
593C2×D3—41no—
594C2×D3—42no—
595C2×D3—41no—
596C2×D3—42no—
597C2×D3—41no—
598C2×D3—42no—
599C2×D3—42no—
600C2×D3—41no—
601C2×D3—41no—
602C2×D3—42no—
603C2×D3—41no—
604C2×D3—41no—
605C2×D3—42no—
606C2×D3—81no—
607C2×D3—81no—
608C2×D3—81no—
609C2×D3—81no—
610C2×D3—81no—
611C2×D3—81no—
612C2×D3—81no—
613C2×D3—81no—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—42no—
619C3×C4—81no—
620C3×C4#52511yescharacteristic
621C3×C4#52511yescharacteristic
622C3×C4#53211yescharacteristic
623C3×C4#53211yescharacteristic
624Dic3—41no—
625Dic3—41no—
626Dic3—42no—
627Dic3—41no—
628Dic3—81no—
629C23—62no—
630C23—61no—
631C23—61no—
632C23—61no—
633C23—61no—
634C23—61no—
635C23—62no—
636C23—61no—
637C23—61no—
638C23—121no—
639C23—121no—
640C23—121no—
641C23—121no—
642C23—121no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23—121no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23C2×D3×D411yescharacteristic
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655Q8—244no—
656D4—62no—
657D4—62no—
658D4—62no—
659D4—62no—
660D4—121no—
661D4—121no—
662D4—121no—
663D4—121no—
664D4—244no—
665D4—244no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—244no—
702C2×C4—244no—
703C2×C4#88212yes—
704C2×C4#88212yes—
705C2×C4C22×D1211yescharacteristic
706C2×C4C2×#23511yescharacteristic
707C2×C4C2×#23511yescharacteristic
708C2×C4C2×D3×D411yescharacteristic
709C2×C4D3×#4111yescharacteristic
710C2×C4D3×#4111yescharacteristic
711C8—22no—
712C8—41no—
713C8—62no—
714C8—121no—
715C2×C3#238811yescharacteristic
716C2×C3#300811yescharacteristic
717C2×C3#301311yescharacteristic
718C2×C3#311811yescharacteristic
719C2×C3#312411yescharacteristic
720C2×C3#317511yescharacteristic
721C2×C3#317911yescharacteristic
722D3—81no—
723D3—82no—
724D3—82no—
725C22—121no—
726C22—121no—
727C22—122no—
728C22—121no—
729C22—122no—
730C22—122no—
731C22—121no—
732C22—121no—
733C22—122no—
734C22—121no—
735C22—122no—
736C22—122no—
737C22—121no—
738C22—241no—
739C22—241no—
740C22—241no—
741C22—241no—
742C22—241no—
743C22—241no—
744C22—241no—
745C22—241no—
746C22C2×#88211yescharacteristic
747C22#554711yescharacteristic
748C22#554811yescharacteristic
749C22#576211yescharacteristic
750C22#576611yescharacteristic
751C22#576911yescharacteristic
752C22#576911yescharacteristic
753C4—22no—
754C4—22no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—81no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4—122no—
763C4—241no—
764C4#547711yescharacteristic
765C4#552411yescharacteristic
766C4#554711yescharacteristic
767C4#554811yescharacteristic
768C3#2357911yescharacteristic, complemented, Sylow
769C2—241no—
770C2—242no—
771C2—242no—
772C2#7358011yescharacteristic
773C2#7879511yescharacteristic
774C2#7883411yescharacteristic
775C2#7966911yescharacteristic
776C2#7969611yescharacteristic
777C2#7972711yescharacteristic
778C2#7974911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×C4×#103C2
socleC23×C3C22×D4
prime radical#68886C2
hypercenterC4×#103D3
hypocenterC3#23579
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
1. C2×#5582C2semidirect
2. C2×#5026C2semidirect
3. C2×C4×D24C2semidirect
4. #73763C2semidirect
5. C3×C4×#103C2semidirect
6. #70277C2semidirect
7. #70272C2semidirect
8. #70245C2semidirect
9. #70244C2semidirect
10. #69753C2semidirect
11. #69474C2semidirect
12. #68898C2semidirect
14. #68826C2semidirect
15. #68822C2semidirect
77. C4×#103D3semidirect
91. C3×C4×Q8D4semidirect
144. C4×D12D4semidirect
347. C4×Q8D12semidirect
768. C3#23579semidirect

Maximal subgroups

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

subgroupindex
C2×#55822
C2×#50262
C2×C4×D242
#737632
C3×C4×#1032
#702772
#702722
#702452
#702442
#697532
#694742
#688982
#688862
#688262
#688222
#235793