Finite Group Databasebeta

← C2×#80077 #11666404

Subgroups — C2×#80077 #11666404

Order 768.

2218 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5832C211yesmaximal, characteristic, complemented
2C2×#5600C211yesmaximal, characteristic, complemented
3C2×C3×#449C211yesmaximal, characteristic, complemented
4C2×#5239C211yesmaximal, characteristic, complemented
5C2×#5168C211yesmaximal, characteristic, complemented
6C2×#5162C211yesmaximal, characteristic, complemented
7C2×#5155C211yesmaximal, characteristic, complemented
8C2×#5150C211yesmaximal, characteristic, complemented
9C2×#5037C211yesmaximal, characteristic, complemented
10#80077C2116yesmaximal, direct product factor
11C2×#4795C211yesmaximal, characteristic, complemented
12C2×#4800C211yesmaximal, characteristic, complemented
13C2×#4762C211yesmaximal, characteristic, complemented
14C2×#4768C211yesmaximal, characteristic, complemented
15C2×#4733C211yesmaximal, characteristic, complemented
16C2×#4718C211yesmaximal, characteristic, complemented
17C2×#3212—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×#235C2211yescharacteristic
20C22×C3×SD16C2211yescharacteristic
21C22×C3×D8C2211yescharacteristic
22C2×C3×#121C2211yescharacteristic
23#5832—24no—
24#5832C2218yescomplemented
25C2×#947C2211yescharacteristic
26C2×#944C2211yescharacteristic
27C22×#216C2211yescharacteristic
28C2×#940C2211yescharacteristic
29C2×#939—21no—
30C2×#939—21no—
31C2×#936C2211yescharacteristic
32C2×#936C2211yescharacteristic
33C2×#935—21no—
34C2×D4×Dic3—21no—
35C2×D4×Dic3C2211yescharacteristic
36C22×#214C2211yescharacteristic
37C22×#214C2211yescharacteristic
38C22×#213C2211yescharacteristic
39C2×C4×#67—21no—
40C2×C4×#67—21no—
41C2×#924C2211yescharacteristic
42C22×C4×Dic3C2211yescharacteristic
43C22×Dic12C2211yescharacteristic
44C22×#204C2211yescharacteristic
45#5600—24no—
46#5600C2218yescomplemented
47C2×#890C2211yescharacteristic
48C2×#887C2211yescharacteristic
49C2×#879—21no—
50C2×#877—21no—
51C3×#449C2218yescomplemented
52C2×C3×#103C2211yescharacteristic
53C2×C3×#102C2211yescharacteristic
54C2×C3×C22⋊C8C2211yescharacteristic
55#5239C2218yescomplemented
56C2×#835C2211yescharacteristic
57C2×#832C2211yescharacteristic
58C2×#830C2211yescharacteristic
59#5168C2218yescomplemented
60#5162C2218yescomplemented
61#5155C2218yescomplemented
62#5150C2218yescomplemented
63C2×#821C2211yescharacteristic
64C2×#816C2211yescharacteristic
65C2×Dic3⋊C8C2211yescharacteristic
66C2×Dic3⋊C8C2211yescharacteristic
67C2×C8×Dic3C2211yescharacteristic
68C2×C8×Dic3C2211yescharacteristic
69#5037C2218yescomplemented
70C2×#810C2211yescharacteristic
71C2×#809C2211yescharacteristic
72#4800C2218yescomplemented
73#4795C2218yescomplemented
74#4768C2218yescomplemented
75#4762C2218yescomplemented
76#4733C2218yescomplemented
77#4718C2218yescomplemented
78C2×#532—31no—
79C2×#529—31no—
80#3212—316no—
81C2×#495—31no—
82C2×#495—31no—
83C2×#488—31no—
84C2×#488—31no—
85C2×#462—31no—
86C2×#460—31no—
87C2×#461—31no—
88C2×#459—31no—
89C2×#452—31no—
90C2×#452—31no—
91C2×#449—31no—
92C2×#449D311yescharacteristic, complemented
93C2×#431—31no—
94C2×C3×#41—22no—
95C2×C3×#41—42no—
96C2×C3×#41—42no—
97C2×C3×#41C2314yes—
98C22×C3×Q8C2311yescharacteristic
99C22×C3×D4—21no—
100C22×C3×D4—21no—
101C22×C3×D4C2311yescharacteristic
102C22×C3×D4C2311yescharacteristic
103C23×C3×C4—21no—
104C23×C3×C4C2311yescharacteristic
105C22×#67—21no—
106C22×#67—21no—
107C22×#67—21no—
108C23×Dic3—21no—
109C23×Dic3D411yescharacteristic
110C23×Dic3D411yescharacteristic
111C2×#235—22no—
112C2×#235—42no—
113C2×#235—42no—
114C2×#235C2314yes—
115C22×D12C2311yescharacteristic
116C22×C4×D3—21no—
117C22×Dic6C2311yescharacteristic
118C22×Dic6C2311yescharacteristic
119C2×C3×SD16—42no—
120C2×C3×SD16C2314yes—
121C2×C3×D8—42no—
122C2×C3×D8C2314yes—
123C22×C3×C8C2311yescharacteristic
124C22×C3×C8C2311yescharacteristic
125C3×#121—22no—
126C3×#121C2314yes—
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C22⋊C4—21no—
129C2×#217—21no—
130C2×#217—21no—
131C2×#217—21no—
132C2×#217—21no—
133C2×#217—21no—
134C2×#217—21no—
135#947—22no—
136#947C2314yes—
137#944—22no—
138#944C2314yes—
139C2×#216—42no—
140C2×#216C2314yes—
141#940—22no—
142#940C2314yes—
143#939—28no—
144#939—28no—
145#936—22no—
146#936—22no—
147#936C2314yes—
148#936C2314yes—
149#935—28no—
150D4×Dic3—28no—
151D4×Dic3—22no—
152D4×Dic3C2314yes—
153C2×#214—42no—
154C2×#214—42no—
155C2×#214C2314yes—
156C2×#214C2314yes—
157C2×#213—42no—
158C2×#213C2314yes—
159C4×#67—28no—
160C4×#67—28no—
161C2×(C2×D3)⋊C4—21no—
162C2×(C2×D3)⋊C4—21no—
163C2×C4⋊Dic3—21no—
164C2×C4⋊Dic3C2311yescharacteristic
165#924—22no—
166#924C2314yes—
167C2×Dic3⋊C4—21no—
168C2×Dic3⋊C4—21no—
169C2×Dic3⋊C4—21no—
170C2×Dic3⋊C4—21no—
171C2×Dic3⋊C4—21no—
172C2×C4×Dic3—21no—
173C2×C4×Dic3D411yescharacteristic
174C2×C4×Dic3D411yescharacteristic
175C2×C4×Dic3D414yes—
176C2×C4×Dic3C2314yes—
177C2×C4×Dic3C2311yescharacteristic
178C2×C4×Dic3C2311yescharacteristic
179C22×C3⋊C8C2311yescharacteristic
180C22×C3⋊C8C2311yescharacteristic
181C2×Dic12—42no—
182C2×Dic12C2314yes—
183C2×#204—42no—
184C2×#204C2314yes—
185#890—22no—
186#890C2314yes—
187#887—22no—
188#887C2314yes—
189#879—28no—
190#877—28no—
191C3×#103C2314yes—
192C3×#102C2314yes—
193C3×C22⋊C8C2314yes—
194#835C2314yes—
195#832C2314yes—
196#830C2314yes—
197#821C2314yes—
198#816C2314yes—
199Dic3⋊C8C2314yes—
200Dic3⋊C8C2314yes—
201C8×Dic3C2314yes—
202C8×Dic3C2314yes—
203#810C2314yes—
204#809C2314yes—
205C22×#41—31no—
206C22×#41C2×D311yescharacteristic
207C22×Q16—31no—
208C22×Q16—31no—
209C22×SD16—31no—
210C22×SD16—31no—
211C22×SD16—31no—
212C22×SD16C2×D311yescharacteristic
213C22×D8—31no—
214C22×D8C2×D311yescharacteristic
215#532—38no—
216#532—64no—
217C2×C4⋊Q8—31no—
218C2×#127—31no—
219#529—38no—
220#529—64no—
221C2×#126—61no—
222C2×#125—31no—
223C2×#124—31no—
224C2×#124—31no—
225C2×#124—31no—
226C2×#123—61no—
227C2×C22⋊Q8—31no—
228C2×#121—61no—
229C2×#121—61no—
230C2×#121C2×D311yescharacteristic
231C2×C4×Q8—31no—
232C2×C4×D4—31no—
233C2×C4×D4—61no—
234C2×C4×D4—61no—
235C2×C4×D4—61no—
236C2×#117—61no—
237C22×C42—31no—
238#495—38no—
239#495—38no—
240#488—38no—
241#488—38no—
242#462—38no—
243#461—38no—
244#460—38no—
245#459—38no—
246#452—38no—
247#452—38no—
248#449—38no—
249#449C2×D318yescomplemented
250#431—38no—
251C2×C4⋊C8—31no—
252C2×C4⋊C8—31no—
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⋊C8C2×D311yescharacteristic
263C2×C4×C8—31no—
264C2×C4×C8—31no—
265C24×C3—21no—
266C24×C3—21no—
267C24×C3C2×D411yescharacteristic
268C23×D3—21no—
269C3×#41—44no—
270C3×#41—44no—
271C3×#41—48no—
272C2×C3×Q8—21no—
273C2×C3×Q8—22no—
274C2×C3×Q8—22no—
275C2×C3×Q8C2412yes—
276C2×C3×D4—24no—
277C2×C3×D4—24no—
278C2×C3×D4—21no—
279C2×C3×D4—21no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4—22no—
283C2×C3×D4—22no—
284C2×C3×D4—44no—
285C2×C3×D4—44no—
286C2×C3×D4C2412yes—
287C2×C3×D4C2412yes—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—24no—
293C22×C3×C4—44no—
294C22×C3×C4C2×D411yescharacteristic
295C22×C3×C4C2×D412yes—
296C22×C3×C4C2412yes—
297C22×C3×C4C2411yescharacteristic
298C2×#67—24no—
299C2×#67—24no—
300C2×#67—24no—
301C2×#67—44no—
302C2×#67—44no—
303C2×#67—44no—
304C22×Dic3—24no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—24no—
309C22×Dic3—42no—
310C22×Dic3—44no—
311C22×Dic3C2×D411yescharacteristic
312C22×Dic3C2×D411yescharacteristic
313C22×Dic3C2×D411yescharacteristic
314C22×Dic3C2×D414yes—
315C22×Dic3C2×D414yes—
316C22×Dic3C2×D411yescharacteristic
317#235—44no—
318#235—44no—
319#235—48no—
320C2×D12—22no—
321C2×D12—22no—
322C2×D12—21no—
323C2×D12C2412yes—
324C2×C4×D3—24no—
325C2×C4×D3—44no—
326C2×Dic6—22no—
327C2×Dic6—22no—
328C2×Dic6—22no—
329C2×Dic6—22no—
330C2×Dic6—21no—
331C2×Dic6—21no—
332C2×Dic6C2412yes—
333C2×Dic6C2412yes—
334C3×SD16—44no—
335C3×D8—44no—
336C2×C3×C8—22no—
337C2×C3×C8—22no—
338C2×C3×C8C2412yes—
339C2×C3×C8C2412yes—
340C3×C4⋊C4—21no—
341C3×C4⋊C4C2412yes—
342C3×C22⋊C4—24no—
343#217—24no—
344#217—24no—
345#217—24no—
346#217—24no—
347#217—24no—
348#217—24no—
349#216—44no—
350#214—44no—
351#214—44no—
352#213—44no—
353(C2×D3)⋊C4—24no—
354(C2×D3)⋊C4—24no—
355C4⋊Dic3—21no—
356C4⋊Dic3—24no—
357C4⋊Dic3C2412yes—
358Dic3⋊C4—24no—
359Dic3⋊C4—24no—
360Dic3⋊C4—24no—
361Dic3⋊C4—24no—
362Dic3⋊C4—24no—
363C4×Dic3—24no—
364C4×Dic3C2×D414yes—
365C4×Dic3C2×D414yes—
366C4×Dic3C2×D412yes—
367C4×Dic3C2×D412yes—
368C4×Dic3C2412yes—
369C4×Dic3C2412yes—
370C2×C3⋊C8—22no—
371C2×C3⋊C8—22no—
372C2×C3⋊C8C2412yes—
373C2×C3⋊C8C2412yes—
374Dic12—44no—
375#204—44no—
376C2×#41—22no—
377C2×#41—34no—
378C2×#41—42no—
379C2×#41—42no—
380C2×#41—62no—
381C2×#41—122no—
382C2×#41—122no—
383C2×#41C22×D314yes—
384C22×Q8—31no—
385C22×Q8—31no—
386C22×Q8C22×D311yescharacteristic
387C22×D4—21no—
388C22×D4—21no—
389C22×D4—31no—
390C22×D4—61no—
391C22×D4—61no—
392C22×D4—61no—
393C22×D4C22×D311yescharacteristic
394C22×D4C22×D311yescharacteristic
395C23×C4—21no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4—61no—
399C23×C4—61no—
400C23×C4C22×D311yescharacteristic
401C2×Q16—34no—
402C2×Q16—34no—
403C2×Q16—122no—
404C2×Q16—122no—
405C2×SD16—34no—
406C2×SD16—34no—
407C2×SD16—34no—
408C2×SD16—42no—
409C2×SD16—122no—
410C2×SD16—122no—
411C2×SD16—122no—
412C2×SD16C22×D314yes—
413C2×D8—34no—
414C2×D8—42no—
415C2×D8—122no—
416C2×D8C22×D314yes—
417C22×C8—31no—
418C22×C8—31no—
419C22×C8C22×D311yescharacteristic
420C22×C8C22×D311yescharacteristic
421C4⋊Q8—34no—
422C4⋊Q8—62no—
423#127—34no—
424#127—62no—
425#126—68no—
426#125—34no—
427#125—62no—
428#124—34no—
429#124—34no—
430#124—34no—
431#124—62no—
432#124—62no—
433#124—62no—
434#123—68no—
435C22⋊Q8—34no—
436C22⋊Q8—62no—
437#121—22no—
438#121—68no—
439#121—68no—
440#121C22×D314yes—
441C4×Q8—34no—
442C4×Q8—62no—
443C4×D4—34no—
444C4×D4—68no—
445C4×D4—68no—
446C4×D4—62no—
447C4×D4—68no—
448#117—68no—
449C2×C4⋊C4—31no—
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⋊C4C22×D311yescharacteristic
457C2×C22⋊C4—21no—
458C2×C22⋊C4—61no—
459C2×C22⋊C4—61no—
460C2×C22⋊C4—61no—
461C2×C22⋊C4—61no—
462C2×C22⋊C4—61no—
463C2×C22⋊C4—61no—
464C2×C22⋊C4—61no—
465C2×C22⋊C4—61no—
466C2×C42—31no—
467C2×C42—31no—
468C2×C42—34no—
469C2×C42—31no—
470C2×C42—31no—
471C2×C42—34no—
472C2×C42—61no—
473C4⋊C8—34no—
474C4⋊C8—34no—
475#103—34no—
476#103—34no—
477#103—34no—
478#103C22×D314yes—
479#102—34no—
480#102—34no—
481#102—34no—
482#102C22×D314yes—
483C22⋊C8—34no—
484C22⋊C8C22×D314yes—
485C4×C8—34no—
486C4×C8—34no—
487C23×C3—22no—
488C23×C3—22no—
489C23×C3—22no—
490C23×C3—22no—
491C23×C3—22no—
492C23×C3—42no—
493C23×C3—42no—
494C23×C3—42no—
495C23×C3—42no—
496C23×C3—42no—
497C23×C3—42no—
498C23×C3C22×D412yes—
499C23×C3C22×D411yescharacteristic
500C22×D3—22no—
501C22×D3—42no—
502C22×D3—42no—
503C22×D3—42no—
504C3×Q8—22no—
505C3×Q8—22no—
506C3×Q8—42no—
507C3×D4—22no—
508C3×D4—22no—
509C3×D4—22no—
510C3×D4—22no—
511C3×D4—48no—
512C3×D4—48no—
513C3×D4—42no—
514C3×D4—42no—
515C2×C3×C4—22no—
516C2×C3×C4—24no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—22no—
520C2×C3×C4—22no—
521C2×C3×C4—48no—
522C2×C3×C4—42no—
523C2×C3×C4—42no—
524C2×C3×C4C22×D412yes—
525C2×C3×C4C22×D411yescharacteristic
526C2×C3×C4H(5,𝔽2)12yes—
527C2×C3×C4H(5,𝔽2)12yes—
528C2×C3×C4C2511yescharacteristic
529#67—48no—
530#67—48no—
531#67—48no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—22no—
535C2×Dic3—28no—
536C2×Dic3—22no—
537C2×Dic3—22no—
538C2×Dic3—22no—
539C2×Dic3—44no—
540C2×Dic3—42no—
541C2×Dic3—42no—
542C2×Dic3—42no—
543C2×Dic3—48no—
544C2×Dic3#13514yes—
545C2×Dic3C22×D412yes—
546C2×Dic3C22×D412yes—
547C2×Dic3C22×D412yes—
548C2×Dic3C22×D412yes—
549D12—22no—
550D12—22no—
551D12—42no—
552C4×D3—48no—
553Dic6—22no—
554Dic6—22no—
555Dic6—22no—
556Dic6—22no—
557Dic6—42no—
558Dic6—42no—
559C3×C8—22no—
560C3×C8—22no—
561C3⋊C8—22no—
562C3⋊C8—22no—
563C24—21no—
564C24—21no—
565C24—61no—
566C24D3×D411yescharacteristic
567#41—44no—
568#41—44no—
569#41—48no—
570#41—124no—
571#41—124no—
572#41—128no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—32no—
577C2×Q8—32no—
578C2×Q8—61no—
579C2×Q8—61no—
580C2×Q8—62no—
581C2×Q8—62no—
582C2×Q8—62no—
583C2×Q8—62no—
584C2×Q8C23×D312yes—
585C2×D4—24no—
586C2×D4—24no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—32no—
594C2×D4—44no—
595C2×D4—44no—
596C2×D4—64no—
597C2×D4—64no—
598C2×D4—64no—
599C2×D4—61no—
600C2×D4—62no—
601C2×D4—62no—
602C2×D4—124no—
603C2×D4—124no—
604C2×D4—124no—
605C2×D4C23×D312yes—
606C2×D4C23×D312yes—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—31no—
613C22×C4—34no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—34no—
618C22×C4—44no—
619C22×C4—64no—
620C22×C4—64no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—64no—
625C22×C4—124no—
626C22×C4—124no—
627C22×C4—122no—
628C22×C4D3×D412yes—
629C22×C4D3×D411yescharacteristic
630C22×C4C23×D312yes—
631C22×C4C23×D311yescharacteristic
632Q16—124no—
633Q16—124no—
634SD16—44no—
635SD16—124no—
636SD16—124no—
637SD16—124no—
638D8—44no—
639D8—124no—
640C2×C8—22no—
641C2×C8—22no—
642C2×C8—32no—
643C2×C8—32no—
644C2×C8—62no—
645C2×C8—62no—
646C2×C8C23×D312yes—
647C2×C8C23×D312yes—
648C4⋊C4—21no—
649C4⋊C4—32no—
650C4⋊C4—64no—
651C4⋊C4—64no—
652C4⋊C4—64no—
653C4⋊C4—64no—
654C4⋊C4—64no—
655C4⋊C4—61no—
656C4⋊C4—64no—
657C4⋊C4C23×D312yes—
658C22⋊C4—24no—
659C22⋊C4—64no—
660C22⋊C4—64no—
661C22⋊C4—64no—
662C22⋊C4—64no—
663C22⋊C4—64no—
664C22⋊C4—64no—
665C22⋊C4—64no—
666C22⋊C4—64no—
667C42—34no—
668C42—34no—
669C42—32no—
670C42—32no—
671C42—32no—
672C42—32no—
673C42—64no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—44no—
678C22×C3—42no—
679C22×C3—42no—
680C22×C3—42no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—84no—
685C22×C3—84no—
686C22×C3#53512yes—
687C22×C3C2×#13512yes—
688C22×C3#57512yes—
689C22×C3C23×D411yescharacteristic
690C2×D3—42no—
691C2×D3—42no—
692C2×D3—42no—
693C2×D3—84no—
694C3×C4—22no—
695C3×C4—42no—
696C3×C4—42no—
697C3×C4#53512yes—
698C3×C4C2×H(5,𝔽2)11yescharacteristic
699C3×C4C2×H(5,𝔽2)11yescharacteristic
700Dic3—22no—
701Dic3—22no—
702Dic3—22no—
703Dic3—42no—
704Dic3—42no—
705Dic3—42no—
706Dic3C2×#13514yes—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—62no—
719C23—122no—
720C23—122no—
721C23—122no—
722C23C2×D3×D412yes—
723C23C2×D3×D411yescharacteristic
724Q8—22no—
725Q8—22no—
726Q8—42no—
727Q8—62no—
728Q8—62no—
729Q8—62no—
730Q8—62no—
731Q8—122no—
732Q8—122no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—48no—
738D4—48no—
739D4—42no—
740D4—42no—
741D4—62no—
742D4—62no—
743D4—128no—
744D4—128no—
745D4—128no—
746D4—122no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—32no—
754C2×C4—34no—
755C2×C4—32no—
756C2×C4—32no—
757C2×C4—32no—
758C2×C4—48no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—68no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—62no—
768C2×C4—128no—
769C2×C4—128no—
770C2×C4—124no—
771C2×C4—122no—
772C2×C4—122no—
773C2×C4—122no—
774C2×C4C2×D3×D412yes—
775C2×C4C2×D3×D411yescharacteristic
776C2×C4#100412yes—
777C2×C4#100412yes—
778C2×C4C24×D311yescharacteristic
779C8—22no—
780C8—22no—
781C8—62no—
782C8—62no—
783C2×C3—42no—
784C2×C3—82no—
785C2×C3—82no—
786C2×C3#321214yescomplemented
787C2×C3C2×#53511yescharacteristic
788C2×C3C22×#13511yescharacteristic
789C2×C3C2×#57511yescharacteristic
790D3—82no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—44no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—84no—
802C22—84no—
803C22—122no—
804C22—122no—
805C22—122no—
806C22—244no—
807C22#559212yes—
808C22D3×#13512yes—
809C22#577312yes—
810C22C22×D3×D411yescharacteristic
811C4—22no—
812C4—34no—
813C4—42no—
814C4—42no—
815C4—62no—
816C4—62no—
817C4—62no—
818C4—122no—
819C4—122no—
820C4—122no—
821C4#559212yes—
822C4C2×#100411yescharacteristic
823C4C2×#100411yescharacteristic
824C3C2×#321211yescharacteristic, complemented, Sylow
825C2—42no—
826C2—82no—
827C2—82no—
828C2—242no—
829C2#8007714yesdirect product factor
830C2C2×#559211yescharacteristic
831C2C2×D3×#13511yescharacteristic
832C2C2×#577311yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3C2×#3212
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#5832C2semidirect
2. C2×#5600C2semidirect
3. C2×C3×#449C2semidirect
4. C2×#5239C2semidirect
5. C2×#5168C2semidirect
6. C2×#5162C2semidirect
7. C2×#5155C2semidirect
8. C2×#5150C2semidirect
9. C2×#5037C2semidirect
10. #80077C2direct (N × H)
11. C2×#4795C2semidirect
12. C2×#4800C2semidirect
13. C2×#4762C2semidirect
14. C2×#4768C2semidirect
15. C2×#4733C2semidirect
16. C2×#4718C2semidirect
24. #5832C22semidirect
46. #5600C22semidirect
51. C3×#449C22semidirect
55. #5239C22semidirect
59. #5168C22semidirect
60. #5162C22semidirect
61. #5155C22semidirect
62. #5150C22semidirect
69. #5037C22semidirect
72. #4800C22semidirect
73. #4795C22semidirect
74. #4768C22semidirect
75. #4762C22semidirect
76. #4733C22semidirect
77. #4718C22semidirect
92. C2×#449D3semidirect
249. #449C2×D3semidirect
786. C2×C3#3212semidirect
824. C3C2×#3212semidirect
829. C2#80077direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#58322
C2×#56002
C2×C3×#4492
C2×#52392
C2×#51682
C2×#51622
C2×#51552
C2×#51502
C2×#50372
#800772
C2×#47952
C2×#48002
C2×#47622
C2×#47682
C2×#47332
C2×#47182
C2×#32123