Finite Group Databasebeta

← #10945047

Subgroups — #10945047

Order 768.

1432 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5545C211yesmaximal, characteristic
2C2×#4888C211yesmaximal, characteristic, complemented
3C2×#4776C211yesmaximal, characteristic
4#76102C211yesmaximal, characteristic, complemented
5C3×#1862C211yesmaximal, characteristic, complemented
6#71612C211yesmaximal, characteristic, complemented
7#70638C211yesmaximal, characteristic, complemented
8#70198C211yesmaximal, characteristic
9#70171C211yesmaximal, characteristic, complemented
10#70169C211yesmaximal, characteristic, complemented
11#69626C211yesmaximal, characteristic, complemented
12#68896C211yesmaximal, characteristic, complemented
13#68813C211yesmaximal, characteristic, complemented
14#68672C211yesmaximal, characteristic, complemented
15#68665C211yesmaximal, characteristic, complemented
16#33018—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×D4×Dic3C2211yescharacteristic
20C22×#214C2211yescharacteristic
21C2×C4×#67—21no—
22C22×(C2×D3)⋊C4—21no—
23C22×#204C2211yescharacteristic
24#5545—24no—
25#5545—24no—
26C2×#897C2211yescharacteristic
27C2×#893C2211yescharacteristic
28C2×#892C2211yescharacteristic
29C2×#67⋊C4—21no—
30C2×D3×C22⋊C4—21no—
31C2×C4×D12C2211yescharacteristic
32C2×#872C2211yescharacteristic
33C2×C3×#107C2211yescharacteristic, complemented
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C3×#389C2211yescharacteristic, complemented
37C2×#832C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×#816C2211yescharacteristic, complemented
42#4992—21no—
43#4987C2211yescharacteristic
44#4982—21no—
45#4973C2211yescharacteristic, complemented
46#4972C2211yescharacteristic, complemented
47C2×#810C2211yescharacteristic, complemented
48C2×#809C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#808C2211yescharacteristic, complemented
51#4929C2211yescharacteristic, complemented
52#4888—24no—
53#4776—24no—
54#4675—21no—
55#4660—21no—
56C3×#340C2211yescharacteristic, complemented
57C3×#336C2211yescharacteristic, complemented
58#4551C2211yescharacteristic, complemented
59#4550C2211yescharacteristic, complemented
60#4550C2211yescharacteristic, complemented
61#4529C2211yescharacteristic, complemented
62#4529C2211yescharacteristic, complemented
63#4524C2211yescharacteristic, complemented
64C2×#518—31no—
65C2×#485—31no—
66C2×#450—31no—
67#2625—31no—
68#1877—31no—
69#1877—31no—
70#1877—31no—
71#1877—31no—
72#1864—31no—
73#1864—31no—
74#1862—31no—
75#1862D311yescharacteristic, complemented
76#1825—31no—
77#1818—31no—
78#1786—31no—
79C24×D3—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C22×#67—21no—
83C23×Dic3—21no—
84C2×D3×D4—22no—
85C2×D3×D4—22no—
86C2×D3×D4—22no—
87C2×D3×D4—22no—
88C2×D3×D4—22no—
89C2×D3×D4D414yes—
90C22×D12C2311yescharacteristic
91C22×C4×D3—21no—
92C22×C4×D3—21no—
93C22×C4×D3C2311yescharacteristic
94C22×Dic6C2311yescharacteristic
95C22×C3×C8C2311yescharacteristic
96C22×C3×C8C2311yescharacteristic
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C22⋊C4—21no—
104C2×C3×C42C2311yescharacteristic
105C2×#217—21no—
106D4×Dic3—22no—
107D4×Dic3—22no—
108C2×#214—22no—
109C2×#214—22no—
110C2×#214—22no—
111C4×#67—28no—
112C2×(C2×D3)⋊C4—28no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×(C2×D3)⋊C4D411yescharacteristic
119C2×(C2×D3)⋊C4D411yescharacteristic
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3C2311yescharacteristic
122C2×C4⋊Dic3C2311yescharacteristic
123C2×Dic3⋊C4—21no—
124C2×Dic3⋊C4D411yescharacteristic
125C2×Dic3⋊C4D411yescharacteristic
126C2×C4×Dic3—21no—
127C2×C4×Dic3C2311yescharacteristic
128C22×C3⋊C8C2311yescharacteristic
129C22×C3⋊C8C2311yescharacteristic
130C2×#204—22no—
131C2×#204—22no—
132C2×#204—22no—
133#897—22no—
134#897—22no—
135#893—22no—
136#893—22no—
137#892—22no—
138#892D414yes—
139#67⋊C4—28no—
140D3×C22⋊C4—28no—
141C4×D12—22no—
142C4×D12—22no—
143#872—22no—
144#872—22no—
145C3×#107—22no—
146C3×#102—22no—
147C3×#102—22no—
148C3×#95—21no—
149#832—22no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#821—22no—
157(C2×D3)⋊C8—22no—
158(C2×D3)⋊C8—22no—
159#816—22no—
160#810—22no—
161#809—22no—
162#809—22no—
163#808—22no—
164C23×D4—31no—
165C22×SD16—31no—
166C22×SD16—31no—
167C2×C22⋊Q8—31no—
168#518—64no—
169#518—64no—
170C2×C4×D4—31no—
171C2×C4×D4—31no—
172C2×C4×D4—31no—
173C2×C4×D4—61no—
174C2×C4×D4—61no—
175C2×C4×D4C2×D311yescharacteristic
176C2×#117—31no—
177C2×#117—31no—
178C22×C22⋊C4—61no—
179C22×C22⋊C4—61no—
180#485—64no—
181#450—64no—
182C2×#107C2×D311yescharacteristic, complemented
183C2×#106—31no—
184C2×#103—31no—
185C2×#103—31no—
186C2×#102—31no—
187C2×#102—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102C2×D311yescharacteristic
191C2×#102C2×D311yescharacteristic
192C2×C22⋊C8—31no—
193C2×C22⋊C8—31no—
194#400—61no—
195#398—61no—
196#397—61no—
197#397—61no—
198#391—31no—
199#391—31no—
200#389—31no—
201#389C2×D311yescharacteristic, complemented
202#380—31no—
203#340—31no—
204#340—31no—
205#340—31no—
206#340C2×D311yescharacteristic, complemented
207#336—31no—
208#336—31no—
209#336—31no—
210#336C2×D311yescharacteristic, complemented
211C24×C3—21no—
212C23×D3—21no—
213C23×D3—24no—
214C23×D3—24no—
215C23×D3—24no—
216C23×D3—81no—
217C23×D3—81no—
218C23×D3—81no—
219C23×D3—81no—
220C23×D3C2×D411yescharacteristic
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4C2×D412yes—
225C2×C3×D4#4112yes—
226C2×C3×D4#4112yes—
227C22×C3×C4—21no—
228C22×C3×C4—24no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—81no—
232C22×C3×C4—81no—
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2411yescharacteristic
236C2×#67—24no—
237C2×#67—24no—
238C2×#67—24no—
239C22×Dic3—21no—
240C22×Dic3—24no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—81no—
244C22×Dic3—81no—
245C22×Dic3C2×D411yescharacteristic
246C22×Dic3C2×D411yescharacteristic
247C22×Dic3C2×D411yescharacteristic
248D3×D4—28no—
249D3×D4—28no—
250D3×D4—28no—
251D3×D4—28no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12C2×D412yes—
256C2×D12#4112yes—
257C2×D12#4112yes—
258C2×C4×D3—21no—
259C2×C4×D3—21no—
260C2×C4×D3—21no—
261C2×C4×D3—21no—
262C2×C4×D3—24no—
263C2×C4×D3—24no—
264C2×C4×D3—81no—
265C2×C4×D3—81no—
266C2×C4×D3—81no—
267C2×C4×D3—81no—
268C2×C4×D3C2×D412yes—
269C2×C4×D3C2×D412yes—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—21no—
275C2×Dic6—21no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—81no—
288C3×C4⋊C4C2×D412yes—
289C3×C22⋊C4—24no—
290C3×C42—21no—
291C3×C42—21no—
292#217—24no—
293#214—44no—
294(C2×D3)⋊C4—24no—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—42no—
300(C2×D3)⋊C4—81no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—42no—
305C4⋊Dic3C2×D412yes—
306Dic3⋊C4—22no—
307Dic3⋊C4—22no—
308Dic3⋊C4—81no—
309C4×Dic3—21no—
310C4×Dic3—21no—
311C4×Dic3—24no—
312C2×C3⋊C8—21no—
313C2×C3⋊C8—21no—
314C2×C3⋊C8—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318#204—44no—
319C25—61no—
320C22×Q8—31no—
321C22×D4—34no—
322C22×D4—31no—
323C22×D4—62no—
324C22×D4—61no—
325C22×D4—62no—
326C22×D4—62no—
327C22×D4—62no—
328C22×D4—62no—
329C22×D4C22×D311yescharacteristic
330C23×C4—21no—
331C23×C4—31no—
332C23×C4—61no—
333C23×C4—61no—
334C23×C4—61no—
335C2×SD16—62no—
336C2×SD16—62no—
337C2×SD16—62no—
338C2×SD16—62no—
339C2×SD16—62no—
340C2×SD16—62no—
341C22×C8—31no—
342C22×C8—31no—
343C22×C8C22×D311yescharacteristic
344C22×C8C22×D311yescharacteristic
345C22⋊Q8—62no—
346C22⋊Q8—62no—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—62no—
350C4×D4—62no—
351C4×D4—68no—
352C4×D4—62no—
353C4×D4—62no—
354C4×D4—68no—
355C4×D4—62no—
356C4×D4—62no—
357#117—34no—
358#117—62no—
359#117—62no—
360#117—62no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4—61no—
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C4⋊C4C22×D311yescharacteristic
370C2×C4⋊C4C22×D311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—31no—
373C2×C22⋊C4—31no—
374C2×C22⋊C4—68no—
375C2×C22⋊C4—61no—
376C2×C22⋊C4—61no—
377C2×C22⋊C4—68no—
378C2×C22⋊C4—61no—
379C2×C22⋊C4—61no—
380C2×C22⋊C4—61no—
381C2×C22⋊C4—61no—
382C2×C42—31no—
383C2×C42—61no—
384C2×C42C22×D311yescharacteristic
385#107—22no—
386#106—62no—
387#103—62no—
388#103—62no—
389#102—22no—
390#102—22no—
391#102—62no—
392#102—62no—
393#102—62no—
394#102—62no—
395C22⋊C8—62no—
396C22⋊C8—62no—
397#95—21no—
398#95—61no—
399#95—61no—
400#95—61no—
401#95—61no—
402#95—61no—
403#95—61no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—22no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3C22×D411yescharacteristic
412C22×D3—22no—
413C22×D3—21no—
414C22×D3—21no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—21no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—21no—
421C22×D3—216no—
422C22×D3—41no—
423C22×D3—41no—
424C22×D3—41no—
425C22×D3—41no—
426C22×D3—84no—
427C22×D3—84no—
428C22×D3—84no—
429C22×D3—84no—
430C22×D3—84no—
431C22×D3—84no—
432C22×D3#12012yes—
433C3×D4—22no—
434C3×D4—22no—
435C3×D4—22no—
436C3×D4#12314yes—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—84no—
453C2×C3×C4C22×D411yescharacteristic
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C2×#4111yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459#67—216no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—22no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—21no—
468C2×Dic3—21no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—84no—
478C2×Dic3#12012yes—
479D12—22no—
480D12—22no—
481D12—22no—
482D12#12314yes—
483C4×D3—22no—
484C4×D3—22no—
485C4×D3—22no—
486C4×D3—22no—
487C4×D3—84no—
488C4×D3—84no—
489Dic6—41no—
490Dic6—41no—
491Dic6—41no—
492Dic6—41no—
493C3×C8—41no—
494C3×C8—41no—
495C3⋊C8—41no—
496C3⋊C8—41no—
497C24—21no—
498C24—31no—
499C24—64no—
500C24—64no—
501C24—64no—
502C24—61no—
503C24—241no—
504C24—241no—
505C24—241no—
506C24—241no—
507C2×Q8—61no—
508C2×Q8—61no—
509C2×Q8—61no—
510C2×Q8—61no—
511C2×Q8—61no—
512C2×Q8—61no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—32no—
517C2×D4—32no—
518C2×D4—32no—
519C2×D4—64no—
520C2×D4—68no—
521C2×D4—68no—
522C2×D4—68no—
523C2×D4—64no—
524C2×D4—64no—
525C2×D4—68no—
526C2×D4—61no—
527C2×D4—61no—
528C2×D4—61no—
529C2×D4#23512yes—
530C2×D4D3×D412yes—
531C2×D4#23912yes—
532C22×C4—21no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—31no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—31no—
540C22×C4—31no—
541C22×C4—64no—
542C22×C4—64no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—61no—
547C22×C4—61no—
548C22×C4—64no—
549C22×C4—61no—
550C22×C4—61no—
551C22×C4—81no—
552C22×C4—81no—
553C22×C4—241no—
554C22×C4—241no—
555C22×C4—241no—
556C22×C4—241no—
557C22×C4—241no—
558C22×C4—241no—
559C22×C4D3×D411yescharacteristic
560C22×C4D3×D411yescharacteristic
561C22×C4C23×D311yescharacteristic
562SD16—124no—
563SD16—124no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—61no—
571C2×C8—61no—
572C2×C8—61no—
573C2×C8—61no—
574C2×C8—61no—
575C2×C8—61no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—32no—
582C4⋊C4—62no—
583C4⋊C4—62no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—81no—
588C4⋊C4—122no—
589C4⋊C4—241no—
590C4⋊C4D3×D412yes—
591C22⋊C4—24no—
592C22⋊C4—62no—
593C22⋊C4—62no—
594C22⋊C4—64no—
595C22⋊C4—64no—
596C22⋊C4—64no—
597C22⋊C4—64no—
598C22⋊C4—122no—
599C22⋊C4—241no—
600C42—21no—
601C42—21no—
602C42—64no—
603C42—61no—
604C42—61no—
605C22×C3—24no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—42no—
609C22×C3—42no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3C2×#12011yescharacteristic
613C22×C3#52511yescharacteristic
614C22×C3#52511yescharacteristic
615C22×C3#57611yescharacteristic
616C22×C3#57711yescharacteristic
617C22×C3#57711yescharacteristic
618C22×C3#57711yescharacteristic
619C2×D3—22no—
620C2×D3—24no—
621C2×D3—22no—
622C2×D3—22no—
623C2×D3—41no—
624C2×D3—41no—
625C2×D3—42no—
626C2×D3—42no—
627C2×D3—41no—
628C2×D3—41no—
629C2×D3—42no—
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—816no—
634C3×C4—41no—
635C3×C4—42no—
636C3×C4—41no—
637C3×C4—81no—
638C3×C4—81no—
639C3×C4C2×#12311yescharacteristic
640C3×C4C2×#12311yescharacteristic
641C3×C4#52511yescharacteristic
642C3×C4#52511yescharacteristic
643Dic3—22no—
644Dic3—42no—
645Dic3—41no—
646Dic3—41no—
647Dic3—81no—
648Dic3—81no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—32no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—616no—
658C23—61no—
659C23—61no—
660C23—61no—
661C23—61no—
662C23—61no—
663C23—62no—
664C23—62no—
665C23—61no—
666C23—62no—
667C23—121no—
668C23—121no—
669C23—121no—
670C23—121no—
671C23—244no—
672C23—244no—
673C23—244no—
674C23—244no—
675C23—244no—
676C23—244no—
677C23C2×D3×D411yescharacteristic
678Q8—121no—
679Q8—121no—
680Q8—121no—
681Q8—121no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—34no—
686D4—616no—
687D4—62no—
688D4—62no—
689D4—62no—
690D4#89414yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—32no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—62no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—84no—
721C2×C4—121no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—244no—
730C2×C4—244no—
731C2×C4—244no—
732C2×C4C2×#23511yescharacteristic
733C2×C4C2×D3×D411yescharacteristic
734C2×C4C2×D3×D411yescharacteristic
735C2×C4C2×#23911yescharacteristic
736C2×C4D3×#4111yescharacteristic
737C2×C4D3×#4111yescharacteristic
738C8—41no—
739C8—41no—
740C8—121no—
741C8—121no—
742C2×C3—44no—
743C2×C3#284911yescharacteristic
744C2×C3#300911yescharacteristic
745C2×C3#301211yescharacteristic
746C2×C3#311811yescharacteristic
747C2×C3#311811yescharacteristic
748C2×C3#312311yescharacteristic
749C2×C3#312311yescharacteristic
750D3—42no—
751D3—44no—
752C22—24no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—62no—
760C22—62no—
761C22—62no—
762C22—64no—
763C22—121no—
764C22—122no—
765C22—122no—
766C22—122no—
767C22—121no—
768C22—122no—
769C22—121no—
770C22—122no—
771C22—121no—
772C22—122no—
773C22—2416no—
774C22#554711yescharacteristic
775C22D3×#12011yescharacteristic
776C22#562711yescharacteristic
777C22#575711yescharacteristic
778C22#577011yescharacteristic
779C22#577511yescharacteristic
780C22#577811yescharacteristic
781C4—41no—
782C4—41no—
783C4—42no—
784C4—62no—
785C4—81no—
786C4—81no—
787C4—121no—
788C4—122no—
789C4—121no—
790C4—241no—
791C4—241no—
792C4C2×#89411yescharacteristic
793C4#554711yescharacteristic
794C4#562711yescharacteristic
795C4D3×#12311yescharacteristic
796C3#3301811yescharacteristic, complemented, Sylow
797C2—44no—
798C2—122no—
799C2—124no—
800C2#7465611yescharacteristic
801C2#7959411yescharacteristic
802C2#7978711yescharacteristic
803C2#8000511yescharacteristic
804C2#8022911yescharacteristic
805C2#8095211yescharacteristic
806C2#8114711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1862C2
socleC23×C3C22×D4
prime radicalC22×D3×D4C22
hypercenter#1862D3
hypocenterC3#33018
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. C2×#4888C2semidirect
4. #76102C2semidirect
5. C3×#1862C2semidirect
6. #71612C2semidirect
7. #70638C2semidirect
9. #70171C2semidirect
10. #70169C2semidirect
11. #69626C2semidirect
12. #68896C2semidirect
13. #68813C2semidirect
14. #68672C2semidirect
15. #68665C2semidirect
33. C2×C3×#107C22semidirect
36. C3×#389C22semidirect
41. C2×#816C22semidirect
45. #4973C22semidirect
46. #4972C22semidirect
47. C2×#810C22semidirect
50. C2×#808C22semidirect
51. #4929C22semidirect
56. C3×#340C22semidirect
57. C3×#336C22semidirect
58. #4551C22semidirect
59. #4550C22semidirect
60. #4550C22semidirect
61. #4529C22semidirect
62. #4529C22semidirect
63. #4524C22semidirect
75. #1862D3semidirect
182. C2×#107C2×D3semidirect
201. #389C2×D3semidirect
206. #340C2×D3semidirect
210. #336C2×D3semidirect
796. C3#33018semidirect

Maximal subgroups

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

subgroupindex
C2×#55452
C2×#48882
C2×#47762
#761022
C3×#18622
#716122
#706382
#701982
#701712
#701692
#696262
#688962
#688132
#686722
#686652
#330183