Finite Group Databasebeta

← C2×#80604 #11666396

Subgroups — C2×#80604 #11666396

Order 768.

2186 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5668C211yesmaximal, characteristic
2C2×#5578C211yesmaximal, characteristic, complemented
3C2×C3×#464C211yesmaximal, characteristic, complemented
4C2×#5187C211yesmaximal, characteristic, complemented
5C2×#5183C211yesmaximal, characteristic, complemented
6C2×#5173C211yesmaximal, characteristic, complemented
7C2×#5175C211yesmaximal, characteristic, complemented
8C2×#5054C211yesmaximal, characteristic, complemented
9C2×#5028C211yesmaximal, characteristic, complemented
10#80604C2116yesmaximal, direct product factor
11C2×#4845C211yesmaximal, characteristic, complemented
12C2×#4833C211yesmaximal, characteristic, complemented
13C2×#4808C211yesmaximal, characteristic, complemented
14C2×#4792C211yesmaximal, characteristic, complemented
15C2×#4783C211yesmaximal, characteristic, complemented
16C2×#4760C211yesmaximal, characteristic, complemented
17C2×#3210—31nomaximal, Sylow
18C22×#239C2211yescharacteristic
19C22×#237C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C2×#946C2211yescharacteristic
25C2×#944C2211yescharacteristic
26C2×#944C2211yescharacteristic
27C22×#216C2211yescharacteristic
28C22×#216C2211yescharacteristic
29C22×#215C2211yescharacteristic
30C2×#940C2211yescharacteristic
31C22×#214C2211yescharacteristic
32C22×Dic12C2211yescharacteristic
33C22×#204C2211yescharacteristic
34#5668—24no—
35#5668C2218yes—
36#5578—24no—
37#5578C2218yescomplemented
38C2×#897C2211yescharacteristic
39C2×#896—21no—
40C2×#889—21no—
41C2×#888C2211yescharacteristic
42C2×#884—21no—
43C2×#884—21no—
44C2×#67⋊C4—21no—
45C2×#67⋊C4—21no—
46C2×#875C2211yescharacteristic
47C2×#872—21no—
48C2×C42×D3C2211yescharacteristic
49C2×C4×Dic6—21no—
50C2×C4×Dic6C2211yescharacteristic
51C3×#464C2218yescomplemented
52C2×C3×C4⋊C8C2211yescharacteristic
53C2×C3×#103C2211yescharacteristic
54C2×C3×#102C2211yescharacteristic
55C2×#835C2211yescharacteristic
56C2×#832C2211yescharacteristic
57#5187C2218yescomplemented
58#5183C2218yescomplemented
59#5175C2218yescomplemented
60#5173C2218yescomplemented
61C2×#821C2211yescharacteristic
62C2×(C2×D3)⋊C8C2211yescharacteristic
63C2×(C2×D3)⋊C8C2211yescharacteristic
64C2×#816C2211yescharacteristic
65C2×C8×Dic3C2211yescharacteristic
66C2×C8×Dic3C2211yescharacteristic
67#5054C2218yescomplemented
68#5028C2218yescomplemented
69C2×#810C2211yescharacteristic
70C2×#809C2211yescharacteristic
71C2×C4⋊(C3⋊C8)C2211yescharacteristic
72#4845C2218yescomplemented
73#4833C2218yescomplemented
74#4808C2218yescomplemented
75#4792C2218yescomplemented
76#4783C2218yescomplemented
77#4760C2218yescomplemented
78C2×#533—31no—
79C2×#532—31no—
80#3210—316no—
81C2×#494—31no—
82C2×#492—31no—
83C2×#487—31no—
84C2×#486—31no—
85C2×#464—31no—
86C2×#464—31no—
87C2×#464—31no—
88C2×#464D311yescharacteristic, complemented
89C2×#452—31no—
90C2×#452—31no—
91C2×#452—31no—
92C2×#452—31no—
93C2×#431—31no—
94C22×C3×Q8C2311yescharacteristic
95C22×C3×Q8C2311yescharacteristic
96C22×C3×D4C2311yescharacteristic
97C22×#67—21no—
98C22×#67—21no—
99C22×#67—21no—
100C23×Dic3—21no—
101C2×#239—22no—
102C2×#239—42no—
103C2×#239—42no—
104C2×#239C2314yes—
105C2×#237—22no—
106C2×#237—42no—
107C2×#237—42no—
108C2×#237C2314yes—
109C22×D12—21no—
110C22×D12C2311yescharacteristic
111C22×C4×D3—21no—
112C22×C4×D3D411yescharacteristic
113C22×C4×D3D411yescharacteristic
114C22×C4×D3C2311yescharacteristic
115C22×Dic6—21no—
116C22×Dic6C2311yescharacteristic
117C22×Dic6C2311yescharacteristic
118C2×C3×Q16—42no—
119C2×C3×Q16C2314yes—
120C2×C3×SD16—42no—
121C2×C3×SD16C2314yes—
122C22×C3×C8C2311yescharacteristic
123C22×C3×C8C2311yescharacteristic
124C3×#124—22no—
125C3×#124C2314yes—
126C3×C4×Q8—22no—
127C3×C4×Q8C2314yes—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C42—21no—
133C2×C3×C42C2311yescharacteristic
134#946—22no—
135#946C2314yes—
136#944—22no—
137#944—22no—
138#944C2314yes—
139#944C2314yes—
140C2×#216—42no—
141C2×#216—42no—
142C2×#216C2314yes—
143C2×#216C2314yes—
144C2×#215—42no—
145C2×#215C2314yes—
146#940—22no—
147#940C2314yes—
148C2×#214—42no—
149C2×#214C2314yes—
150C2×(C2×D3)⋊C4—21no—
151C2×(C2×D3)⋊C4—21no—
152C2×(C2×D3)⋊C4—21no—
153C2×(C2×D3)⋊C4—21no—
154C2×C4⋊Dic3—21no—
155C2×C4⋊Dic3C2311yescharacteristic
156C2×Dic3⋊C4—21no—
157C2×Dic3⋊C4—21no—
158C2×Dic3⋊C4—21no—
159C2×Dic3⋊C4—21no—
160C2×Dic3⋊C4—21no—
161C2×Dic3⋊C4—21no—
162C2×Dic3⋊C4—21no—
163C2×C4×Dic3—21no—
164C2×C4×Dic3D411yescharacteristic
165C2×C4×Dic3D411yescharacteristic
166C2×C4×Dic3C2311yescharacteristic
167C22×C3⋊C8C2311yescharacteristic
168C22×C3⋊C8C2311yescharacteristic
169C2×Dic12—42no—
170C2×Dic12C2314yes—
171C2×#204—42no—
172C2×#204C2314yes—
173#897—22no—
174#897C2314yes—
175#896—28no—
176#889—28no—
177#888—22no—
178#888C2314yes—
179#884—28no—
180#884—28no—
181#67⋊C4—28no—
182#67⋊C4—28no—
183#875—22no—
184#875C2314yes—
185#872—28no—
186C42×D3D414yes—
187C42×D3C2314yes—
188C4×Dic6—22no—
189C4×Dic6—28no—
190C4×Dic6C2314yes—
191C3×C4⋊C8C2314yes—
192C3×#103C2314yes—
193C3×#102C2314yes—
194#835C2314yes—
195#832C2314yes—
196#821C2314yes—
197(C2×D3)⋊C8C2314yes—
198(C2×D3)⋊C8C2314yes—
199#816C2314yes—
200C8×Dic3C2314yes—
201C8×Dic3C2314yes—
202#810C2314yes—
203#809C2314yes—
204C4⋊(C3⋊C8)C2314yes—
205C22×#41—31no—
206C22×#41—31no—
207C22×Q16—31no—
208C22×Q16—31no—
209C22×Q16—31no—
210C22×Q16C2×D311yescharacteristic
211C22×SD16—31no—
212C22×SD16—31no—
213C22×SD16—31no—
214C22×SD16C2×D311yescharacteristic
215#533—38no—
216#533—64no—
217#532—38no—
218#532—64no—
219C2×C4⋊Q8—31no—
220C2×C4⋊Q8—31no—
221C2×C4⋊Q8—31no—
222C2×#127—31no—
223C2×#125—61no—
224C2×#124—31no—
225C2×#124C2×D311yescharacteristic
226C2×C22⋊Q8—31no—
227C2×C22⋊Q8—31no—
228C2×C22⋊Q8—61no—
229C2×#121—61no—
230C2×#121—61no—
231C2×C4×Q8—31no—
232C2×C4×Q8—61no—
233C2×C4×Q8C2×D311yescharacteristic
234C2×C4×D4—61no—
235C2×C4×D4—61no—
236C2×#117—61no—
237C22×C42—31no—
238#494—38no—
239#492—38no—
240#487—38no—
241#486—38no—
242#464—38no—
243#464—38no—
244#464—38no—
245#464C2×D318yescomplemented
246#452—38no—
247#452—38no—
248#452—38no—
249#452—38no—
250#431—38no—
251C2×C4⋊C8—31no—
252C2×C4⋊C8C2×D311yescharacteristic
253C2×#103—31no—
254C2×#103—31no—
255C2×#103—31no—
256C2×#103C2×D311yescharacteristic
257C2×#102—31no—
258C2×#102—31no—
259C2×#102—31no—
260C2×#102C2×D311yescharacteristic
261C2×C22⋊C8—31no—
262C2×C22⋊C8—31no—
263C2×C4×C8—31no—
264C2×C4×C8—31no—
265C24×C3—21no—
266C23×D3—21no—
267C23×D3C2×D411yescharacteristic
268C2×C3×Q8—21no—
269C2×C3×Q8—21no—
270C2×C3×Q8—22no—
271C2×C3×Q8—22no—
272C2×C3×Q8—22no—
273C2×C3×Q8—22no—
274C2×C3×Q8C2412yes—
275C2×C3×Q8C2412yes—
276C2×C3×D4—21no—
277C2×C3×D4—22no—
278C2×C3×D4—22no—
279C2×C3×D4C2412yes—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2×D411yescharacteristic
285C22×C3×C4C2411yescharacteristic
286C2×#67—24no—
287C2×#67—24no—
288C2×#67—24no—
289C2×#67—44no—
290C2×#67—44no—
291C2×#67—44no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C22×Dic3—21no—
295C22×Dic3—24no—
296C22×Dic3—44no—
297C22×Dic3C2×D411yescharacteristic
298C22×Dic3C2×D411yescharacteristic
299C22×Dic3C2×D411yescharacteristic
300#239—44no—
301#239—44no—
302#239—48no—
303#237—44no—
304#237—44no—
305#237—48no—
306C2×D12—22no—
307C2×D12—22no—
308C2×D12—24no—
309C2×D12—21no—
310C2×D12—44no—
311C2×D12C2412yes—
312C2×C4×D3—22no—
313C2×C4×D3—22no—
314C2×C4×D3—24no—
315C2×C4×D3—24no—
316C2×C4×D3—24no—
317C2×C4×D3—44no—
318C2×C4×D3C2×D412yes—
319C2×C4×D3C2×D414yes—
320C2×C4×D3C2×D414yes—
321C2×C4×D3C2412yes—
322C2×Dic6—22no—
323C2×Dic6—22no—
324C2×Dic6—22no—
325C2×Dic6—22no—
326C2×Dic6—21no—
327C2×Dic6—21no—
328C2×Dic6—24no—
329C2×Dic6—44no—
330C2×Dic6C2412yes—
331C2×Dic6C2412yes—
332C3×Q16—44no—
333C3×SD16—44no—
334C2×C3×C8—22no—
335C2×C3×C8—22no—
336C2×C3×C8C2412yes—
337C2×C3×C8C2412yes—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—24no—
340C3×C4⋊C4C2412yes—
341C3×C22⋊C4—24no—
342C3×C22⋊C4—24no—
343C3×C42—24no—
344C3×C42C2×D412yes—
345C3×C42C2412yes—
346#216—44no—
347#216—44no—
348#215—44no—
349#214—44no—
350(C2×D3)⋊C4—24no—
351(C2×D3)⋊C4—24no—
352(C2×D3)⋊C4—24no—
353(C2×D3)⋊C4—24no—
354C4⋊Dic3—21no—
355C4⋊Dic3—24no—
356C4⋊Dic3C2412yes—
357Dic3⋊C4—24no—
358Dic3⋊C4—24no—
359Dic3⋊C4—24no—
360Dic3⋊C4—24no—
361Dic3⋊C4—24no—
362Dic3⋊C4—24no—
363Dic3⋊C4—24no—
364C4×Dic3—24no—
365C4×Dic3C2×D414yes—
366C4×Dic3C2×D412yes—
367C4×Dic3C2×D414yes—
368C4×Dic3C2412yes—
369C2×C3⋊C8—22no—
370C2×C3⋊C8—22no—
371C2×C3⋊C8C2412yes—
372C2×C3⋊C8C2412yes—
373Dic12—44no—
374#204—44no—
375C2×#41—34no—
376C2×#41—34no—
377C2×#41—62no—
378C2×#41—62no—
379C2×#41—122no—
380C2×#41—122no—
381C2×#41—122no—
382C2×#41—122no—
383C22×Q8—31no—
384C22×Q8—31no—
385C22×Q8—61no—
386C22×Q8C22×D311yescharacteristic
387C22×Q8C22×D311yescharacteristic
388C22×D4—31no—
389C22×D4—61no—
390C22×D4—61no—
391C22×D4—61no—
392C22×D4—61no—
393C22×D4C22×D311yescharacteristic
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—61no—
398C23×C4—61no—
399C2×Q16—34no—
400C2×Q16—34no—
401C2×Q16—34no—
402C2×Q16—42no—
403C2×Q16—122no—
404C2×Q16—122no—
405C2×Q16—122no—
406C2×Q16C22×D314yes—
407C2×SD16—34no—
408C2×SD16—34no—
409C2×SD16—34no—
410C2×SD16—42no—
411C2×SD16—122no—
412C2×SD16—122no—
413C2×SD16—122no—
414C2×SD16C22×D314yes—
415C22×C8—31no—
416C22×C8—31no—
417C22×C8C22×D311yescharacteristic
418C22×C8C22×D311yescharacteristic
419C4⋊Q8—34no—
420C4⋊Q8—34no—
421C4⋊Q8—34no—
422C4⋊Q8—62no—
423C4⋊Q8—62no—
424C4⋊Q8—62no—
425#127—34no—
426#127—62no—
427#125—68no—
428#124—22no—
429#124—34no—
430#124—62no—
431#124C22×D314yes—
432C22⋊Q8—34no—
433C22⋊Q8—34no—
434C22⋊Q8—62no—
435C22⋊Q8—68no—
436C22⋊Q8—62no—
437#121—68no—
438#121—68no—
439C4×Q8—22no—
440C4×Q8—34no—
441C4×Q8—68no—
442C4×Q8—62no—
443C4×Q8C22×D314yes—
444C4×D4—68no—
445C4×D4—68no—
446#117—68no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—61no—
450C2×C4⋊C4—61no—
451C2×C4⋊C4—61no—
452C2×C4⋊C4—61no—
453C2×C4⋊C4—61no—
454C2×C4⋊C4—61no—
455C2×C4⋊C4—61no—
456C2×C4⋊C4—61no—
457C2×C4⋊C4C22×D311yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—61no—
461C2×C22⋊C4—61no—
462C2×C22⋊C4—61no—
463C2×C22⋊C4—61no—
464C2×C42—21no—
465C2×C42—31no—
466C2×C42—31no—
467C2×C42—31no—
468C2×C42—34no—
469C2×C42—34no—
470C2×C42—61no—
471C2×C42C22×D311yescharacteristic
472C4⋊C8—34no—
473C4⋊C8C22×D314yes—
474#103—34no—
475#103—34no—
476#103—34no—
477#103C22×D314yes—
478#102—34no—
479#102—34no—
480#102—34no—
481#102C22×D314yes—
482C22⋊C8—34no—
483C22⋊C8—34no—
484C4×C8—34no—
485C4×C8—34no—
486C23×C3—22no—
487C23×C3—42no—
488C23×C3—42no—
489C23×C3—42no—
490C23×C3C22×D411yescharacteristic
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—42no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3C22×D412yes—
499C3×Q8—22no—
500C3×Q8—22no—
501C3×Q8—22no—
502C3×Q8—22no—
503C3×Q8—42no—
504C3×Q8—42no—
505C3×D4—22no—
506C3×D4—22no—
507C3×D4—42no—
508C2×C3×C4—22no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—42no—
514C2×C3×C4—42no—
515C2×C3×C4—42no—
516C2×C3×C4C22×D412yes—
517C2×C3×C4C22×D412yes—
518C2×C3×C4C22×D411yescharacteristic
519C2×C3×C4H(5,𝔽2)12yes—
520C2×C3×C4H(5,𝔽2)12yes—
521C2×C3×C4C2511yescharacteristic
522#67—48no—
523#67—48no—
524#67—48no—
525C2×Dic3—22no—
526C2×Dic3—22no—
527C2×Dic3—22no—
528C2×Dic3—22no—
529C2×Dic3—48no—
530C2×Dic3—42no—
531C2×Dic3—42no—
532C2×Dic3—42no—
533C2×Dic3#13514yes—
534C2×Dic3#13714yes—
535C2×Dic3C22×D412yes—
536C2×Dic3C22×D412yes—
537C2×Dic3C22×D412yes—
538D12—22no—
539D12—22no—
540D12—48no—
541D12—42no—
542C4×D3—24no—
543C4×D3—22no—
544C4×D3—22no—
545C4×D3—28no—
546C4×D3—28no—
547C4×D3—48no—
548Dic6—22no—
549Dic6—22no—
550Dic6—22no—
551Dic6—22no—
552Dic6—42no—
553Dic6—42no—
554Dic6—48no—
555C3×C8—22no—
556C3×C8—22no—
557C3⋊C8—22no—
558C3⋊C8—22no—
559C24—21no—
560C24—31no—
561C24—61no—
562#41—124no—
563#41—124no—
564#41—128no—
565#41—124no—
566#41—124no—
567#41—128no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—22no—
574C2×Q8—32no—
575C2×Q8—32no—
576C2×Q8—64no—
577C2×Q8—61no—
578C2×Q8—61no—
579C2×Q8—62no—
580C2×Q8—62no—
581C2×Q8—62no—
582C2×Q8—62no—
583C2×Q8—124no—
584C2×Q8C23×D312yes—
585C2×Q8C23×D312yes—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—32no—
590C2×D4—64no—
591C2×D4—64no—
592C2×D4—64no—
593C2×D4—64no—
594C2×D4—61no—
595C2×D4—62no—
596C2×D4—62no—
597C2×D4—124no—
598C2×D4—124no—
599C2×D4—124no—
600C2×D4—124no—
601C2×D4C23×D312yes—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—34no—
609C22×C4—34no—
610C22×C4—32no—
611C22×C4—32no—
612C22×C4—64no—
613C22×C4—64no—
614C22×C4—64no—
615C22×C4—64no—
616C22×C4—62no—
617C22×C4—62no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—124no—
622C22×C4—124no—
623C22×C4D3×D411yescharacteristic
624C22×C4D3×D411yescharacteristic
625C22×C4C23×D311yescharacteristic
626Q16—44no—
627Q16—124no—
628Q16—124no—
629Q16—124no—
630SD16—44no—
631SD16—124no—
632SD16—124no—
633SD16—124no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—32no—
637C2×C8—32no—
638C2×C8—62no—
639C2×C8—62no—
640C2×C8C23×D312yes—
641C2×C8C23×D312yes—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—32no—
645C4⋊C4—64no—
646C4⋊C4—64no—
647C4⋊C4—64no—
648C4⋊C4—64no—
649C4⋊C4—64no—
650C4⋊C4—64no—
651C4⋊C4—64no—
652C4⋊C4—61no—
653C4⋊C4—64no—
654C4⋊C4C23×D312yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—64no—
658C22⋊C4—64no—
659C22⋊C4—64no—
660C22⋊C4—64no—
661C42—24no—
662C42—34no—
663C42—34no—
664C42—32no—
665C42—32no—
666C42—64no—
667C42D3×D412yes—
668C42C23×D312yes—
669C22×C3—42no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—84no—
673C22×C3#53512yes—
674C22×C3C2×#13512yes—
675C22×C3C2×#13712yes—
676C22×C3C23×D411yescharacteristic
677C2×D3—22no—
678C2×D3—22no—
679C2×D3—22no—
680C2×D3—44no—
681C2×D3—42no—
682C2×D3—42no—
683C2×D3—42no—
684C2×D3—84no—
685C3×C4—22no—
686C3×C4—22no—
687C3×C4—42no—
688C3×C4—42no—
689C3×C4—42no—
690C3×C4#53512yes—
691C3×C4C2×H(5,𝔽2)11yescharacteristic
692C3×C4C2×H(5,𝔽2)11yescharacteristic
693Dic3—22no—
694Dic3—42no—
695Dic3—42no—
696Dic3—42no—
697Dic3C2×#13514yes—
698Dic3C2×#13714yes—
699C23—22no—
700C23—32no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—62no—
705C23—62no—
706C23—62no—
707C23—62no—
708C23—122no—
709C23—122no—
710C23—122no—
711C23C2×D3×D411yescharacteristic
712Q8—22no—
713Q8—22no—
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—42no—
718Q8—62no—
719Q8—62no—
720Q8—62no—
721Q8—62no—
722Q8—128no—
723Q8—122no—
724Q8—122no—
725D4—22no—
726D4—22no—
727D4—42no—
728D4—62no—
729D4—62no—
730D4—128no—
731D4—128no—
732D4—128no—
733D4—128no—
734D4—122no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—32no—
741C2×C4—32no—
742C2×C4—34no—
743C2×C4—34no—
744C2×C4—32no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—68no—
749C2×C4—68no—
750C2×C4—62no—
751C2×C4—62no—
752C2×C4—62no—
753C2×C4—64no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—62no—
757C2×C4—128no—
758C2×C4—128no—
759C2×C4—122no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4C2×D3×D412yes—
763C2×C4C2×D3×D412yes—
764C2×C4C2×D3×D411yescharacteristic
765C2×C4#100412yes—
766C2×C4#100912yes—
767C2×C4C24×D311yescharacteristic
768C8—22no—
769C8—22no—
770C8—62no—
771C8—62no—
772C2×C3—82no—
773C2×C3#321014yescomplemented
774C2×C3C2×#53511yescharacteristic
775C2×C3C22×#13511yescharacteristic
776C2×C3C22×#13711yescharacteristic
777D3—42no—
778D3—82no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—62no—
783C22—62no—
784C22—62no—
785C22—84no—
786C22—124no—
787C22—122no—
788C22—122no—
789C22—122no—
790C22—244no—
791C22#560712yes—
792C22D3×#13512yes—
793C22D3×#13712yes—
794C22C22×D3×D411yescharacteristic
795C4—22no—
796C4—22no—
797C4—34no—
798C4—34no—
799C4—42no—
800C4—42no—
801C4—42no—
802C4—62no—
803C4—122no—
804C4—122no—
805C4—122no—
806C4#560712yes—
807C4C2×#100411yescharacteristic
808C4C2×#100911yescharacteristic
809C3C2×#321011yescharacteristic, complemented, Sylow
810C2—82no—
811C2—122no—
812C2—242no—
813C2#8060414yesdirect product factor
814C2C2×#560711yescharacteristic
815C2C2×D3×#13511yescharacteristic
816C2C2×D3×#13711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#464C2
socleC23×C3C22×D4
prime radicalC2×#5668C2
hypercenterC2×#464D3
hypocenterC3C2×#3210
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
2. C2×#5578C2semidirect
3. C2×C3×#464C2semidirect
4. C2×#5187C2semidirect
5. C2×#5183C2semidirect
6. C2×#5173C2semidirect
7. C2×#5175C2semidirect
8. C2×#5054C2semidirect
9. C2×#5028C2semidirect
10. #80604C2direct (N × H)
11. C2×#4845C2semidirect
12. C2×#4833C2semidirect
13. C2×#4808C2semidirect
14. C2×#4792C2semidirect
15. C2×#4783C2semidirect
16. C2×#4760C2semidirect
37. #5578C22semidirect
51. C3×#464C22semidirect
57. #5187C22semidirect
58. #5183C22semidirect
59. #5175C22semidirect
60. #5173C22semidirect
67. #5054C22semidirect
68. #5028C22semidirect
72. #4845C22semidirect
73. #4833C22semidirect
74. #4808C22semidirect
75. #4792C22semidirect
76. #4783C22semidirect
77. #4760C22semidirect
88. C2×#464D3semidirect
245. #464C2×D3semidirect
773. C2×C3#3210semidirect
809. C3C2×#3210semidirect
813. C2#80604direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#56682
C2×#55782
C2×C3×#4642
C2×#51872
C2×#51832
C2×#51732
C2×#51752
C2×#50542
C2×#50282
#806042
C2×#48452
C2×#48332
C2×#48082
C2×#47922
C2×#47832
C2×#47602
C2×#32103