Finite Group Databasebeta

← #10829203

Subgroups — #10829203

Order 768.

1152 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5530C211yesmaximal, characteristic
2#82777C211yesmaximal, characteristic, complemented
3C2×#4799C211yesmaximal, characteristic, complemented
4C2×#4788C211yesmaximal, characteristic, complemented
5C3×#1873C211yesmaximal, characteristic, complemented
6#71699C211yesmaximal, characteristic, complemented
7#71576C211yesmaximal, characteristic, complemented
8#70272C211yesmaximal, characteristic, complemented
9#70268C211yesmaximal, characteristic, complemented
10#69935C211yesmaximal, characteristic, complemented
11#69916C211yesmaximal, characteristic, complemented
12#68893C211yesmaximal, characteristic, complemented
13#68875C211yesmaximal, characteristic, complemented
14#68822C211yesmaximal, characteristic, complemented
15#68804C211yesmaximal, characteristic, complemented
16#24126—31nomaximal, Sylow
17C2×C3×C22⋊Q8C2211yescharacteristic
18C2×C3×#117C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C2×Q8×Dic3C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×C4×#67C2211yescharacteristic
24#5530—24no—
25#5530—24no—
26C2×#895C2211yescharacteristic
27C2×#893C2211yescharacteristic
28C2×D3×C4⋊C4C2211yescharacteristic
29C2×#890C2211yescharacteristic
30C2×#884—21no—
31C2×#883—21no—
32C2×#876—21no—
33C2×C4×D12—21no—
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×#835C2211yescharacteristic
38#5212C2211yescharacteristic
39C2×#830C2211yescharacteristic
40C2×#821C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#817C2211yescharacteristic
45C2×Dic3⋊C8C2211yescharacteristic
46C2×C8×Dic3C2211yescharacteristic
47#4990—21no—
48#4987C2211yescharacteristic
49#4982—21no—
50#4977C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#808C2211yescharacteristic
53C2×#807C2211yescharacteristic
54#4961—21no—
55#4945—21no—
56#4799—24no—
57#4788—24no—
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#553—31no—
65C2×#479—31no—
66C2×C4×SD16—31no—
67#2536—31no—
68#2034—31no—
69#2033—31no—
70#2000—31no—
71#2000—31no—
72#1991—31no—
73#1954—31no—
74#1873D311yescharacteristic, complemented
75#1872—31no—
76#1854—31no—
77#1853—31no—
78#1804—31no—
79C22×C3×Q8C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C22×#67—21no—
82C22×#67D411yescharacteristic
83C22×D12—21no—
84C22×D12C2311yescharacteristic
85C22×C4×D3—21no—
86C22×C4×D3—21no—
87C22×C4×D3C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8—41no—
92C3×#117—22no—
93C3×#117—22no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C42—21no—
101C2×#217—21no—
102C2×#217D411yescharacteristic
103#946—22no—
104#946—41no—
105Q8×Dic3—22no—
106Q8×Dic3—22no—
107C2×#215—22no—
108C2×#215—22no—
109C2×#215—22no—
110#930—22no—
111#930—22no—
112C4×#67—22no—
113C4×#67—22no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4—21no—
119C2×(C2×D3)⋊C4D411yescharacteristic
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4D411yescharacteristic
129C2×C4×Dic3—21no—
130C2×C4×Dic3C2311yescharacteristic
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133#895—22no—
134#895—22no—
135#893—22no—
136#893D414yes—
137D3×C4⋊C4—22no—
138D3×C4⋊C4—22no—
139#890—22no—
140#890D414yes—
141#884—28no—
142#883—28no—
143#876—28no—
144C4×D12—28no—
145C3×#103—22no—
146C3×#103—22no—
147C3×C22⋊C8—41no—
148#835—22no—
149C3⋊#95—21no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153#830—22no—
154#821—22no—
155#821—41no—
156(C2×D3)⋊C8—22no—
157(C2×D3)⋊C8—41no—
158#817—22no—
159Dic3⋊C8—22no—
160C8×Dic3—22no—
161#809—41no—
162#808—22no—
163#807—22no—
164C22×SD16—31no—
165#553—64no—
166#553—64no—
167C2×#126—61no—
168C2×#125—31no—
169C2×#123—61no—
170C2×C22⋊Q8—31no—
171C2×C22⋊Q8C2×D311yescharacteristic
172C2×#121—31no—
173C2×#121—31no—
174C2×#121—61no—
175C2×C4×Q8—31no—
176C2×C4×D4—31no—
177C2×C4×D4—31no—
178C2×C4×D4—61no—
179C2×#117C2×D311yescharacteristic
180C22×C4⋊C4—31no—
181#479—64no—
182C4×SD16—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×#106—31no—
186C2×C4⋊C8—31no—
187C2×#103—31no—
188C2×#103C2×D311yescharacteristic
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C22⋊C8—31no—
196C2×C22⋊C8C2×D311yescharacteristic
197C2×C4×C8—31no—
198#398—61no—
199#394—61no—
200#388—61no—
201#388—61no—
202#382—31no—
203#380—31no—
204#380—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#340C2×D311yescharacteristic
210#340C2×D311yescharacteristic
211C24×C3C2×D411yescharacteristic
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×Q8#4112yes—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2411yescharacteristic
232C2×#67—22no—
233C2×#67—24no—
234C2×#67—22no—
235C2×#67—41no—
236C2×#67—81no—
237C2×#67—81no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3C2×D411yescharacteristic
242C22×Dic3C2×D411yescharacteristic
243C22×Dic3C2×D411yescharacteristic
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×D12C2×D412yes—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×C4×D3—21no—
259C2×C4×D3—24no—
260C2×C4×D3—24no—
261C2×C4×D3—81no—
262C2×C4×D3—81no—
263C2×C4×D3—81no—
264C2×C4×D3—81no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8—21no—
269C2×C3×C8—21no—
270C2×C3×C8—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—21no—
273C3×C4⋊C4—21no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—42no—
276C3×C4⋊C4C2×D412yes—
277C3×C4⋊C4C2×D412yes—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—42no—
280C3×C42—24no—
281#217—22no—
282#217—42no—
283#215—28no—
284(C2×D3)⋊C4—24no—
285(C2×D3)⋊C4—24no—
286(C2×D3)⋊C4—22no—
287(C2×D3)⋊C4—24no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4—42no—
290C4⋊Dic3—21no—
291C4⋊Dic3—24no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—42no—
297C4⋊Dic3C2×D412yes—
298Dic3⋊C4—24no—
299Dic3⋊C4—22no—
300Dic3⋊C4—24no—
301Dic3⋊C4—42no—
302C4×Dic3—42no—
303C4×Dic3C2×D412yes—
304C4×Dic3C2×D412yes—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8#4112yes—
311C22×Q8C22×D311yescharacteristic
312C22×D4—31no—
313C22×D4—31no—
314C22×D4—61no—
315C22×D4—61no—
316C23×C4—31no—
317C23×C4—61no—
318C23×C4—61no—
319C23×C4C22×D311yescharacteristic
320C2×SD16—62no—
321C2×SD16—62no—
322C2×SD16—62no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8C22×D311yescharacteristic
326C22×C8C22×D311yescharacteristic
327#126—68no—
328#125—34no—
329#125—62no—
330#123—68no—
331C22⋊Q8—22no—
332C22⋊Q8—41no—
333C22⋊Q8—62no—
334C22⋊Q8—121no—
335#121—68no—
336#121—62no—
337#121—62no—
338#121—62no—
339#121—62no—
340C4×Q8—62no—
341C4×Q8—62no—
342C4×D4—34no—
343C4×D4—68no—
344C4×D4—62no—
345C4×D4—62no—
346C4×D4—62no—
347#117—22no—
348#117—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—31no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—62no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—62no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4C22×D311yescharacteristic
362C2×C4⋊C4C22×D311yescharacteristic
363C2×C4⋊C4C22×D311yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—31no—
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×C42—21no—
375C2×C42—31no—
376C2×C42—61no—
377#107—62no—
378#106—62no—
379#106—62no—
380C4⋊C8—62no—
381#103—22no—
382#103—22no—
383#103—62no—
384#102—62no—
385#102—121no—
386#102—121no—
387C22⋊C8—41no—
388C22⋊C8—62no—
389C22⋊C8—62no—
390C22⋊C8—121no—
391C4×C8—62no—
392#95—61no—
393#95—61no—
394#95—61no—
395#95—61no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3C22×D411yescharacteristic
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—21no—
410C22×D3—22no—
411C22×D3—41no—
412C22×D3—41no—
413C22×D3—41no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3#13512yes—
418C3×Q8—22no—
419C3×Q8—22no—
420C3×Q8—41no—
421C3×Q8—41no—
422C2×C3×C4—22no—
423C2×C3×C4—21no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
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×C4—41no—
441C2×C3×C4C22×D411yescharacteristic
442C2×C3×C4C22×D411yescharacteristic
443C2×C3×C4C2×#4111yescharacteristic
444C2×C3×C4C2×#4111yescharacteristic
445C2×C3×C4H(5,𝔽2)11yescharacteristic
446C2×C3×C42−1+411yescharacteristic
447#67—44no—
448#67—84no—
449C2×Dic3—21no—
450C2×Dic3—21no—
451C2×Dic3—21no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—22no—
455C2×Dic3—21no—
456C2×Dic3—21no—
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#12012yes—
466C2×Dic3#12012yes—
467D12—22no—
468D12—22no—
469D12—48no—
470D12—41no—
471D12—41no—
472C4×D3—41no—
473C4×D3—41no—
474C4×D3—41no—
475C4×D3—41no—
476C4×D3—84no—
477C4×D3—84no—
478C3×C8—41no—
479C3×C8—41no—
480C3⋊C8—22no—
481C3⋊C8—41no—
482C24—31no—
483C24—61no—
484C24D3×D411yescharacteristic
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8#23512yes—
491C2×D4—32no—
492C2×D4—64no—
493C2×D4—62no—
494C2×D4—62no—
495C2×D4—64no—
496C2×D4—61no—
497C2×D4—61no—
498C2×D4—61no—
499C2×D4—61no—
500C2×D4—61no—
501C2×D4—122no—
502C2×D4—122no—
503C2×D4—121no—
504C2×D4—241no—
505C2×D4—241no—
506C22×C4—21no—
507C22×C4—21no—
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—31no—
517C22×C4—31no—
518C22×C4—31no—
519C22×C4—64no—
520C22×C4—64no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—241no—
531C22×C4—241no—
532C22×C4—241no—
533C22×C4—241no—
534C22×C4D3×D411yescharacteristic
535C22×C4C23×D311yescharacteristic
536SD16—68no—
537C2×C8—21no—
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—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—32no—
554C4⋊C4—42no—
555C4⋊C4—62no—
556C4⋊C4—64no—
557C4⋊C4—64no—
558C4⋊C4—64no—
559C4⋊C4—61no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—122no—
565C4⋊C4—122no—
566C4⋊C4D3×D412yes—
567C4⋊C4D3×D412yes—
568C22⋊C4—24no—
569C22⋊C4—42no—
570C22⋊C4—62no—
571C22⋊C4—64no—
572C22⋊C4—64no—
573C22⋊C4—64no—
574C22⋊C4—62no—
575C22⋊C4—122no—
576C22⋊C4—122no—
577C22⋊C4—122no—
578C42—24no—
579C42—32no—
580C42—32no—
581C42—122no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3C2×#12011yescharacteristic
590C22×C3#54611yescharacteristic
591C22×C3#54711yescharacteristic
592C22×C3C2×#13511yescharacteristic
593C22×C3#57511yescharacteristic
594C22×C3#57711yescharacteristic
595C22×C3#57711yescharacteristic
596C2×D3—22no—
597C2×D3—22no—
598C2×D3—22no—
599C2×D3—41no—
600C2×D3—41no—
601C2×D3—41no—
602C2×D3—41no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C2×D3—81no—
607C2×D3—81no—
608C2×D3—81no—
609C2×D3—81no—
610C3×C4—41no—
611C3×C4—42no—
612C3×C4—42no—
613C3×C4—42no—
614C3×C4—81no—
615C3×C4#52511yescharacteristic
616C3×C4#53711yescharacteristic
617C3×C4#54811yescharacteristic
618C3×C4#55011yescharacteristic
619Dic3—22no—
620Dic3—22no—
621Dic3—41no—
622Dic3—42no—
623Dic3—81no—
624Dic3—81no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—32no—
633C23—61no—
634C23—61no—
635C23—61no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23—62no—
640C23—121no—
641C23—121no—
642C23—121no—
643C23—121no—
644C23—121no—
645C23—121no—
646C23C2×D3×D411yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—62no—
652D4—62no—
653D4—128no—
654D4—124no—
655D4—121no—
656D4—121no—
657D4—244no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—32no—
665C2×C4—32no—
666C2×C4—41no—
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—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—62no—
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—121no—
699C2×C4—244no—
700C2×C4—244no—
701C2×C4C2×#23511yescharacteristic
702C2×C4C2×D3×D411yescharacteristic
703C2×C4C2×D3×D411yescharacteristic
704C2×C4#100411yescharacteristic
705C2×C4D3×#4111yescharacteristic
706C2×C4#101011yescharacteristic
707C8—41no—
708C8—41no—
709C8—62no—
710C8—121no—
711C2×C3—81no—
712C2×C3#240711yescharacteristic
713C2×C3#300211yescharacteristic
714C2×C3#300911yescharacteristic
715C2×C3#330111yescharacteristic
716C2×C3#332611yescharacteristic
717C2×C3#333711yescharacteristic
718C2×C3#335111yescharacteristic
719D3—42no—
720D3—82no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—62no—
729C22—62no—
730C22—62no—
731C22—121no—
732C22—121no—
733C22—121no—
734C22—121no—
735C22—122no—
736C22—122no—
737C22—122no—
738C22—241no—
739C22—241no—
740C22—241no—
741C22—241no—
742C22#549011yescharacteristic
743C22D3×#12011yescharacteristic
744C22#565511yescharacteristic
745C22D3×#13511yescharacteristic
746C22#577011yescharacteristic
747C22#577711yescharacteristic
748C22#577811yescharacteristic
749C4—42no—
750C4—42no—
751C4—41no—
752C4—42no—
753C4—62no—
754C4—62no—
755C4—81no—
756C4—122no—
757C4—121no—
758C4—241no—
759C4—241no—
760C4#554711yescharacteristic
761C4#555211yescharacteristic
762C4#559911yescharacteristic
763C4#560811yescharacteristic
764C3#2412611yescharacteristic, complemented, Sylow
765C2—81no—
766C2—122no—
767C2—242no—
768C2#7468811yescharacteristic
769C2#7884811yescharacteristic
770C2#7897011yescharacteristic
771C2#8022611yescharacteristic
772C2#8022911yescharacteristic
773C2#8151011yescharacteristic
774C2#8153111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1873C2
socleC23×C3C22×D4
prime radicalC2×#5530C2
hypercenter#1873D3
hypocenterC3#24126
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. #82777C2semidirect
3. C2×#4799C2semidirect
4. C2×#4788C2semidirect
5. C3×#1873C2semidirect
6. #71699C2semidirect
7. #71576C2semidirect
8. #70272C2semidirect
9. #70268C2semidirect
10. #69935C2semidirect
11. #69916C2semidirect
12. #68893C2semidirect
13. #68875C2semidirect
14. #68822C2semidirect
15. #68804C2semidirect
74. #1873D3semidirect
764. C3#24126semidirect

Maximal subgroups

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

subgroupindex
C2×#55302
#827772
C2×#47992
C2×#47882
C3×#18732
#716992
#715762
#702722
#702682
#699352
#699162
#688932
#688752
#688222
#688042
#241263