Finite Group Databasebeta

← C2×#83923 #11670248

Subgroups — C2×#83923 #11670248

Order 768.

2826 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#135C211yesmaximal, characteristic, complemented
2C2×#5834C211yesmaximal, characteristic, complemented
3C2×#5831C211yesmaximal, characteristic, complemented
4C22×#918C211yesmaximal, characteristic, complemented
5C2×#5239C211yesmaximal, characteristic, complemented
6C2×#5238C211yesmaximal, characteristic, complemented
7#83923C2116yesmaximal, direct product factor
8C2×#5184C211yesmaximal, characteristic, complemented
9C2×#5172C211yesmaximal, characteristic, complemented
10C2×#5170C211yesmaximal, characteristic, complemented
11C2×#5166C211yesmaximal, characteristic, complemented
12C2×#5163C211yesmaximal, characteristic, complemented
13C2×#5159C211yesmaximal, characteristic, complemented
14C2×#5154C211yesmaximal, characteristic, complemented
15C2×#5114C211yesmaximal, characteristic, complemented
16C2×#5111C211yesmaximal, characteristic, complemented
17C2×#3271—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×C3×#41C2211yescharacteristic
20C22×#239C2211yescharacteristic
21C22×D3×Q8C2211yescharacteristic
22C2×C3×#135—28no—
23C2×C3×#135C2218yescomplemented
24C22×C3×Q16C2211yescharacteristic
25C22×C3×SD16C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic
27C22×C3×D8C2211yescharacteristic
28C23×C3×C8C2211yescharacteristic
29#5834—24no—
30#5834C2218yescomplemented
31#5831—24no—
32#5831C2218yescomplemented
33C2×Q8×Dic3C2211yescharacteristic
34C2×Q8×Dic3C2211yescharacteristic
35C22×#216C2211yescharacteristic
36C22×#215C2211yescharacteristic
37C2×#940—21no—
38C2×#940C2211yescharacteristic
39C2×#938—21no—
40C2×#938—21no—
41C2×#938C2211yescharacteristic
42C2×#938C2211yescharacteristic
43C2×#936—21no—
44C2×#936C2211yescharacteristic
45C22×#214C2211yescharacteristic
46C22×#213C2211yescharacteristic
47C2×#930—21no—
48C2×#930C2211yescharacteristic
49C2×C4×#67—21no—
50C2×C4×#67—21no—
51C2×C4×#67C2211yescharacteristic
52C2×#924—21no—
53C2×#924C2211yescharacteristic
54C2×#918—28no—
55C2×#918C2218yescomplemented
56C22×#204C2211yescharacteristic
57C22×ΓL(1,𝔽25)C2211yescharacteristic
58#5239C2218yescomplemented
59#5238C2218yescomplemented
60C2×#835C2211yescharacteristic
61C2×#835C2211yescharacteristic
62C2×#832C2211yescharacteristic
63C2×#832C2211yescharacteristic
64C2×#830C2211yescharacteristic
65#5184C2218yescomplemented
66#5172C2218yescomplemented
67#5170C2218yescomplemented
68#5166C2218yescomplemented
69#5163C2218yescomplemented
70#5159C2218yescomplemented
71#5154C2218yescomplemented
72#5114C2218yescomplemented
73C2×#821C2211yescharacteristic
74#5111C2218yescomplemented
75C2×(C2×D3)⋊C8C2211yescharacteristic
76C2×#817C2211yescharacteristic
77C2×#816C2211yescharacteristic
78C2×#815C2211yescharacteristic
79C2×Dic3⋊C8C2211yescharacteristic
80C22×#137—31no—
81C22×#135D311yescharacteristic, complemented
82C2×#550—31no—
83C2×#548—31no—
84#3271—316no—
85C2×#496—31no—
86C2×#469—31no—
87C2×#465—31no—
88C2×#464—31no—
89C2×#460—31no—
90C2×#452—31no—
91C2×#449—31no—
92C2×#449—31no—
93C2×#448—31no—
94C2×#441—31no—
95C2×#435—31no—
96C2×C3×#41—22no—
97C2×C3×#41—22no—
98C2×C3×#41—24no—
99C2×C3×#41—24no—
100C2×C3×#41—42no—
101C2×C3×#41—42no—
102C2×C3×#41C2314yes—
103C2×C3×#41C2314yes—
104C22×C3×Q8C2311yescharacteristic
105C22×C3×Q8C2311yescharacteristic
106C22×C3×D4—21no—
107C22×C3×D4—21no—
108C22×C3×D4C2311yescharacteristic
109C22×C3×D4C2311yescharacteristic
110C23×C3×C4—21no—
111C23×C3×C4—21no—
112C23×C3×C4C2311yescharacteristic
113C22×#67—21no—
114C22×#67—21no—
115C22×#67—21no—
116C22×#67—21no—
117C22×#67—21no—
118C22×#67D411yescharacteristic
119C2×#239—22no—
120C2×#239—24no—
121C2×#239—42no—
122C2×#239C2314yes—
123C2×D3×Q8—22no—
124C2×D3×Q8—24no—
125C2×D3×Q8—42no—
126C2×D3×Q8C2314yes—
127C22×D12—21no—
128C22×D12C2311yescharacteristic
129C22×C4×D3—21no—
130C22×C4×D3—21no—
131C22×C4×D3C2311yescharacteristic
132C22×Dic6—21no—
133C22×Dic6C2311yescharacteristic
134C3×#135—232no—
135C2×C3×Q16D418yescomplemented
136C2×C3×Q16C2314yes—
137C2×C3×SD16—24no—
138C2×C3×SD16—24no—
139C2×C3×SD16C2314yes—
140C2×C3×SD16C2314yes—
141C2×C3×D8—24no—
142C2×C3×D8C2314yes—
143C22×C3×C8—24no—
144C22×C3×C8C2311yescharacteristic
145C22×C3×C8C2314yes—
146C22×C3×C8C2311yescharacteristic
147C2×#217—21no—
148C2×#217—21no—
149C2×#217—21no—
150C2×#217—21no—
151C2×#217—21no—
152C2×#217D411yescharacteristic
153Q8×Dic3—22no—
154Q8×Dic3—22no—
155Q8×Dic3C2314yes—
156Q8×Dic3C2314yes—
157C2×#216—24no—
158C2×#216C2314yes—
159C2×#215—24no—
160C2×#215C2314yes—
161#940—28no—
162#940—22no—
163#940C2314yes—
164#938—28no—
165#938—22no—
166#938—22no—
167#938—28no—
168#938C2314yes—
169#938C2314yes—
170#936—28no—
171#936—22no—
172#936C2314yes—
173C2×#214—42no—
174C2×#214C2314yes—
175C2×#213—42no—
176C2×#213C2314yes—
177#930—22no—
178#930—28no—
179#930C2314yes—
180C4×#67—28no—
181C4×#67—28no—
182C4×#67D414yes—
183C4×#67C2314yes—
184C2×(C2×D3)⋊C4—21no—
185C2×(C2×D3)⋊C4D411yescharacteristic
186C2×C4⋊Dic3—21no—
187C2×C4⋊Dic3—21no—
188C2×C4⋊Dic3C2311yescharacteristic
189C2×C4⋊Dic3C2311yescharacteristic
190#924—22no—
191#924—28no—
192#924C2314yes—
193C2×Dic3⋊C4—21no—
194C2×Dic3⋊C4D411yescharacteristic
195C2×C4×Dic3—21no—
196C2×C4×Dic3—21no—
197C2×C4×Dic3C2311yescharacteristic
198C22×C3⋊C8C2311yescharacteristic
199C22×C3⋊C8C2311yescharacteristic
200#918—232no—
201C2×#204—24no—
202C2×#204C2314yes—
203C2×ΓL(1,𝔽25)—24no—
204C2×ΓL(1,𝔽25)C2314yes—
205#835C2314yes—
206#835C2314yes—
207#832C2314yes—
208#832C2314yes—
209#830C2314yes—
210#821C2314yes—
211(C2×D3)⋊C8C2314yes—
212#817C2314yes—
213#816C2314yes—
214#815C2314yes—
215Dic3⋊C8C2314yes—
216C22×#41—31no—
217C22×#41C2×D311yescharacteristic
218C22×#41C2×D311yescharacteristic
219C23×Q8—31no—
220C2×#137—38no—
221C2×#137—68no—
222C2×#135—28no—
223C2×#135C2×D318yescomplemented
224C22×Q16—31no—
225C22×Q16C2×D311yescharacteristic
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16—31no—
229C22×SD16C2×D311yescharacteristic
230C22×SD16C2×D311yescharacteristic
231C22×D8—31no—
232C22×D8C2×D311yescharacteristic
233C22×M16—31no—
234C23×C8C2×D311yescharacteristic
235#550—38no—
236#550—64no—
237#548—38no—
238#548—64no—
239C2×#127—31no—
240C2×#127—61no—
241C2×#124—31no—
242C2×#124—61no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8—61no—
245C2×#121—31no—
246C2×#121—31no—
247C2×#121—31no—
248C2×#121—61no—
249C2×#121—61no—
250C2×#121—61no—
251C2×C4×Q8—31no—
252C2×C4×Q8—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C2×C4×D4—61no—
256#496—38no—
257#469—38no—
258#465—38no—
259#464—38no—
260#460—38no—
261#452—38no—
262#449—38no—
263#449—38no—
264#448—38no—
265#441—38no—
266#435—38no—
267C2×#106—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#103—31no—
272C2×#102—31no—
273C2×#102—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×#97—31no—
278C24×C3—21no—
279C24×C3—21no—
280C24×C3C2×D411yescharacteristic
281C23×D3—21no—
282C23×D3C2×D411yescharacteristic
283C3×#41—28no—
284C3×#41—28no—
285C3×#41—44no—
286C3×#41—44no—
287C3×#41—48no—
288C3×#41—48no—
289C2×C3×Q8—21no—
290C2×C3×Q8—21no—
291C2×C3×Q8—22no—
292C2×C3×Q8—22no—
293C2×C3×Q8C2×D414yes—
294C2×C3×Q8C2×D414yes—
295C2×C3×Q8C2412yes—
296C2×C3×Q8C2412yes—
297C2×C3×D4—24no—
298C2×C3×D4—24no—
299C2×C3×D4—22no—
300C2×C3×D4—22no—
301C2×C3×D4—21no—
302C2×C3×D4—21no—
303C2×C3×D4—22no—
304C2×C3×D4—22no—
305C2×C3×D4—44no—
306C2×C3×D4—44no—
307C2×C3×D4C2412yes—
308C2×C3×D4C2412yes—
309C22×C3×C4—21no—
310C22×C3×C4—21no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—24no—
314C22×C3×C4—24no—
315C22×C3×C4—44no—
316C22×C3×C4—44no—
317C22×C3×C4C2×D411yescharacteristic
318C22×C3×C4C2×D412yes—
319C22×C3×C4C2412yes—
320C22×C3×C4C2411yescharacteristic
321C2×#67—24no—
322C2×#67—24no—
323C2×#67—24no—
324C2×#67—24no—
325C2×#67—24no—
326C2×#67—42no—
327C2×#67—44no—
328C2×#67—44no—
329C2×#67—82no—
330C2×#67—82no—
331C2×#67—82no—
332C2×#67C2×D414yes—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3C2×D411yescharacteristic
337C22×Dic3C2×D411yescharacteristic
338C22×Dic3C2×D411yescharacteristic
339#239—28no—
340#239—44no—
341#239—48no—
342D3×Q8—28no—
343D3×Q8—44no—
344D3×Q8—48no—
345C2×D12—22no—
346C2×D12—22no—
347C2×D12—24no—
348C2×D12—21no—
349C2×D12—44no—
350C2×D12C2412yes—
351C2×C4×D3—22no—
352C2×C4×D3—22no—
353C2×C4×D3—24no—
354C2×C4×D3—24no—
355C2×C4×D3—44no—
356C2×C4×D3—44no—
357C2×C4×D3C2×D412yes—
358C2×C4×D3C2412yes—
359C2×Dic6—22no—
360C2×Dic6—22no—
361C2×Dic6—21no—
362C2×Dic6—24no—
363C2×Dic6—44no—
364C2×Dic6C2412yes—
365C3×Q16C2×D4116yescomplemented
366C3×SD16—28no—
367C3×SD16—28no—
368C3×D8—28no—
369C2×C3×C8—22no—
370C2×C3×C8—28no—
371C2×C3×C8C2×D414yes—
372C2×C3×C8C2412yes—
373C2×C3×C8C2412yes—
374#217—24no—
375#217—24no—
376#217—24no—
377#217—24no—
378#217—24no—
379#217C2×D414yes—
380#216—28no—
381#215—28no—
382#214—44no—
383#213—44no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4C2×D414yes—
386C4⋊Dic3—21no—
387C4⋊Dic3—21no—
388C4⋊Dic3—24no—
389C4⋊Dic3—24no—
390C4⋊Dic3C2412yes—
391C4⋊Dic3C2412yes—
392Dic3⋊C4—24no—
393Dic3⋊C4C2×D414yes—
394C4×Dic3—24no—
395C4×Dic3—24no—
396C4×Dic3C2×D412yes—
397C4×Dic3C2412yes—
398C2×C3⋊C8—22no—
399C2×C3⋊C8—22no—
400C2×C3⋊C8C2412yes—
401C2×C3⋊C8C2412yes—
402#204—28no—
403ΓL(1,𝔽25)—28no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—24no—
407C2×#41—24no—
408C2×#41—34no—
409C2×#41—42no—
410C2×#41—42no—
411C2×#41—62no—
412C2×#41—64no—
413C2×#41—122no—
414C2×#41C22×D314yes—
415C2×#41C22×D314yes—
416C22×Q8—34no—
417C22×Q8—31no—
418C22×Q8—61no—
419C22×Q8—62no—
420C22×Q8—64no—
421C22×Q8—122no—
422C22×Q8C22×D311yescharacteristic
423C22×Q8C22×D311yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—31no—
427C22×D4—31no—
428C22×D4—61no—
429C22×D4—61no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4—61no—
434C22×D4C22×D311yescharacteristic
435C22×D4C22×D311yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—31no—
439C23×C4—61no—
440C23×C4—61no—
441C23×C4C22×D311yescharacteristic
442#137—632no—
443#135—232no—
444C2×Q16—34no—
445C2×Q16—64no—
446C2×Q16#6718yescomplemented
447C2×Q16C22×D314yes—
448C2×SD16—24no—
449C2×SD16—24no—
450C2×SD16—34no—
451C2×SD16—34no—
452C2×SD16—34no—
453C2×SD16—64no—
454C2×SD16—64no—
455C2×SD16—122no—
456C2×SD16C22×D314yes—
457C2×SD16C22×D314yes—
458C2×D8—24no—
459C2×D8—34no—
460C2×D8—122no—
461C2×D8C22×D314yes—
462C2×M16—34no—
463C2×M16—64no—
464C22×C8—24no—
465C22×C8—31no—
466C22×C8—31no—
467C22×C8C22×D311yescharacteristic
468C22×C8C22×D314yes—
469C22×C8C22×D311yescharacteristic
470#127—34no—
471#127—62no—
472#127—68no—
473#124—34no—
474#124—62no—
475#124—68no—
476C22⋊Q8—34no—
477C22⋊Q8—68no—
478C22⋊Q8—62no—
479#121—34no—
480#121—34no—
481#121—34no—
482#121—68no—
483#121—68no—
484#121—62no—
485#121—62no—
486#121—68no—
487#121—62no—
488C4×Q8—34no—
489C4×Q8—34no—
490C4×Q8—62no—
491C4×Q8—62no—
492C4×D4—34no—
493C4×D4—34no—
494C4×D4—68no—
495C4×D4—68no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—31no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4—61no—
501C2×C4⋊C4—61no—
502C2×C22⋊C4—31no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—61no—
505C2×C22⋊C4—61no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C42—31no—
511C2×C42—61no—
512C2×C42—61no—
513#106—34no—
514C4⋊C8—34no—
515#103—34no—
516#103—34no—
517#103—34no—
518#102—34no—
519#102—34no—
520#102—34no—
521C22⋊C8—34no—
522C22⋊C8—34no—
523#97—34no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—42no—
530C23×C3—42no—
531C23×C3—42no—
532C23×C3—42no—
533C23×C3—42no—
534C23×C3—42no—
535C23×C3C22×D412yes—
536C23×C3C22×D411yescharacteristic
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—22no—
540C22×D3—22no—
541C22×D3—42no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3C22×D412yes—
545C3×Q8—24no—
546C3×Q8—24no—
547C3×Q8—22no—
548C3×Q8—22no—
549C3×Q8C22×D414yes—
550C3×Q8C22×D414yes—
551C3×D4—22no—
552C3×D4—22no—
553C3×D4—22no—
554C3×D4—22no—
555C3×D4—48no—
556C3×D4—48no—
557C3×D4—42no—
558C3×D4—42no—
559C2×C3×C4—24no—
560C2×C3×C4—24no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—24no—
565C2×C3×C4—22no—
566C2×C3×C4—22no—
567C2×C3×C4—48no—
568C2×C3×C4—48no—
569C2×C3×C4C22×D412yes—
570C2×C3×C4C22×D411yescharacteristic
571C2×C3×C4C22×D412yes—
572C2×C3×C4H(5,𝔽2)12yes—
573C2×C3×C4C2511yescharacteristic
574#67—44no—
575#67—48no—
576#67—48no—
577#67—84no—
578#67—84no—
579#67—84no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—42no—
587C2×Dic3—42no—
588C2×Dic3—42no—
589C2×Dic3C22×D412yes—
590C2×Dic3C22×D412yes—
591C2×Dic3C22×D412yes—
592D12—22no—
593D12—22no—
594D12—48no—
595D12—42no—
596C4×D3—24no—
597C4×D3—22no—
598C4×D3—22no—
599C4×D3—48no—
600C4×D3—48no—
601Dic6—22no—
602Dic6—22no—
603Dic6—48no—
604Dic6—42no—
605C3×C8—22no—
606C3×C8C22×D414yes—
607C3⋊C8—22no—
608C3⋊C8—22no—
609C24—21no—
610C24—21no—
611C24—31no—
612C24—61no—
613C24D3×D411yescharacteristic
614#41—28no—
615#41—28no—
616#41—44no—
617#41—44no—
618#41—48no—
619#41—48no—
620#41—68no—
621#41—124no—
622#41—128no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—32no—
628C2×Q8—64no—
629C2×Q8—61no—
630C2×Q8—68no—
631C2×Q8—62no—
632C2×Q8—62no—
633C2×Q8—124no—
634C2×Q8—124no—
635C2×Q8—128no—
636C2×Q8C2×#6714yes—
637C2×Q8C2×#6714yes—
638C2×Q8C23×D312yes—
639C2×Q8C23×D312yes—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—34no—
649C2×D4—32no—
650C2×D4—44no—
651C2×D4—44no—
652C2×D4—64no—
653C2×D4—64no—
654C2×D4—64no—
655C2×D4—64no—
656C2×D4—64no—
657C2×D4—64no—
658C2×D4—61no—
659C2×D4—62no—
660C2×D4—62no—
661C2×D4—124no—
662C2×D4—122no—
663C2×D4—124no—
664C2×D4—124no—
665C2×D4—242no—
666C2×D4—242no—
667C2×D4—242no—
668C2×D4C23×D312yes—
669C2×D4C23×D312yes—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—31no—
677C22×C4—31no—
678C22×C4—31no—
679C22×C4—32no—
680C22×C4—32no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—64no—
684C22×C4—64no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—61no—
688C22×C4—61no—
689C22×C4—61no—
690C22×C4—124no—
691C22×C4—124no—
692C22×C4D3×D412yes—
693C22×C4D3×D411yescharacteristic
694C22×C4C23×D312yes—
695C22×C4C23×D311yescharacteristic
696Q16—68no—
697Q16C2×#67116yescomplemented
698SD16—28no—
699SD16—28no—
700SD16—68no—
701SD16—68no—
702SD16—124no—
703D8—28no—
704D8—124no—
705M16—68no—
706C2×C8—22no—
707C2×C8—28no—
708C2×C8—32no—
709C2×C8—32no—
710C2×C8—62no—
711C2×C8—62no—
712C2×C8C2×#6714yes—
713C2×C8C23×D312yes—
714C2×C8C23×D312yes—
715C4⋊C4—34no—
716C4⋊C4—32no—
717C4⋊C4—32no—
718C4⋊C4—64no—
719C4⋊C4—64no—
720C4⋊C4—61no—
721C4⋊C4—61no—
722C4⋊C4—64no—
723C22⋊C4—34no—
724C22⋊C4—34no—
725C22⋊C4—64no—
726C22⋊C4—64no—
727C22⋊C4—64no—
728C22⋊C4—64no—
729C22⋊C4—64no—
730C22⋊C4—64no—
731C42—32no—
732C42—32no—
733C42—64no—
734C42—64no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—44no—
739C22×C3—42no—
740C22×C3—42no—
741C22×C3—42no—
742C22×C3—42no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—84no—
746C22×C3—84no—
747C22×C3D4212yes—
748C22×C3#57512yes—
749C22×C3#57712yes—
750C22×C3C23×D411yescharacteristic
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—44no—
755C2×D3—42no—
756C2×D3—42no—
757C2×D3—42no—
758C2×D3—84no—
759C3×C4—24no—
760C3×C4—24no—
761C3×C4—22no—
762C3×C4D4212yes—
763C3×C4C23×D411yescharacteristic
764C3×C4C2×H(5,𝔽2)11yescharacteristic
765Dic3—22no—
766Dic3—22no—
767Dic3—22no—
768Dic3—42no—
769Dic3—42no—
770Dic3—42no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—32no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—122no—
788C23—122no—
789C23—122no—
790C23C2×D3×D412yes—
791C23C2×D3×D411yescharacteristic
792Q8—22no—
793Q8—22no—
794Q8—24no—
795Q8—24no—
796Q8—62no—
797Q8—62no—
798Q8—128no—
799Q8—122no—
800Q8C22×#6714yes—
801Q8C22×#6714yes—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—48no—
807D4—48no—
808D4—42no—
809D4—42no—
810D4—62no—
811D4—62no—
812D4—128no—
813D4—124no—
814D4—128no—
815D4—128no—
816D4—122no—
817D4—244no—
818D4—244no—
819D4—244no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—24no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—32no—
831C2×C4—48no—
832C2×C4—48no—
833C2×C4—62no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—64no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—128no—
843C2×C4—128no—
844C2×C4—122no—
845C2×C4—122no—
846C2×C4—122no—
847C2×C4C2×D3×D412yes—
848C2×C4C2×D3×D411yescharacteristic
849C2×C4#100412yes—
850C2×C4C22×#6712yes—
851C2×C4C24×D311yescharacteristic
852C8—22no—
853C8—62no—
854C8—62no—
855C8C22×#6714yes—
856C2×C3—42no—
857C2×C3—82no—
858C2×C3—82no—
859C2×C3#327114yescomplemented
860C2×C3C2×D4211yescharacteristic
861C2×C3C2×#57511yescharacteristic
862C2×C3C2×#57711yescharacteristic
863D3—42no—
864D3—82no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—44no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—62no—
876C22—62no—
877C22—62no—
878C22—84no—
879C22—84no—
880C22—124no—
881C22—122no—
882C22—122no—
883C22—122no—
884C22—244no—
885C22#576812yes—
886C22#577012yes—
887C22D4×#6712yes—
888C22C22×D3×D411yescharacteristic
889C4—22no—
890C4—24no—
891C4—24no—
892C4—62no—
893C4—62no—
894C4—62no—
895C4—122no—
896C4—122no—
897C4—122no—
898C4D4×#6712yes—
899C4C2×#100411yescharacteristic
900C4C23×#6711yescharacteristic
901C3C2×#327111yescharacteristic, complemented, Sylow
902C2—42no—
903C2—82no—
904C2—82no—
905C2—122no—
906C2—242no—
907C2#8392314yesdirect product factor
908C2C2×#576811yescharacteristic
909C2C2×#577011yescharacteristic
910C2C2×D4×#6711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC22×C3×#135C2
socleC23×C3C22×D4
hypercenterC22×#135D3
hypocenterC3C2×#3271
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#135

Complements

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

NH ≅ G/Ntype
1. C22×C3×#135C2semidirect
2. C2×#5834C2semidirect
3. C2×#5831C2semidirect
4. C22×#918C2semidirect
5. C2×#5239C2semidirect
6. C2×#5238C2semidirect
7. #83923C2direct (N × H)
8. C2×#5184C2semidirect
9. C2×#5172C2semidirect
10. C2×#5170C2semidirect
11. C2×#5166C2semidirect
12. C2×#5163C2semidirect
13. C2×#5159C2semidirect
14. C2×#5154C2semidirect
15. C2×#5114C2semidirect
16. C2×#5111C2semidirect
23. C2×C3×#135C22semidirect
30. #5834C22semidirect
32. #5831C22semidirect
55. C2×#918C22semidirect
58. #5239C22semidirect
59. #5238C22semidirect
65. #5184C22semidirect
66. #5172C22semidirect
67. #5170C22semidirect
68. #5166C22semidirect
69. #5163C22semidirect
70. #5159C22semidirect
71. #5154C22semidirect
72. #5114C22semidirect
74. #5111C22semidirect
81. C22×#135D3semidirect
135. C2×C3×Q16D4semidirect
223. C2×#135C2×D3semidirect
365. C3×Q16C2×D4semidirect
446. C2×Q16#67semidirect
697. Q16C2×#67semidirect
859. C2×C3#3271semidirect
901. C3C2×#3271semidirect
907. C2#83923direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1352
C2×#58342
C2×#58312
C22×#9182
C2×#52392
C2×#52382
#839232
C2×#51842
C2×#51722
C2×#51702
C2×#51662
C2×#51632
C2×#51592
C2×#51542
C2×#51142
C2×#51112
C2×#32713