Finite Group Databasebeta

← C2×#80131 #11670466

Subgroups — C2×#80131 #11670466

Order 768.

2910 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5834C211yesmaximal, characteristic, complemented
2C22×#950C211yesmaximal, characteristic, complemented
3C22×#916C211yesmaximal, characteristic, complemented
4C2×#5599C211yesmaximal, characteristic, complemented
5C2×C3×#449C211yesmaximal, characteristic, complemented
6C2×#5163C211yesmaximal, characteristic, complemented
7C2×#5158C211yesmaximal, characteristic, complemented
8C2×#5151C211yesmaximal, characteristic, complemented
9C2×#5038C211yesmaximal, characteristic, complemented
10#80131C2116yesmaximal, direct product factor
11C2×#4810C211yesmaximal, characteristic, complemented
12C2×#4790C211yesmaximal, characteristic, complemented
13C2×#4762C211yesmaximal, characteristic, complemented
14C2×#4775C211yesmaximal, characteristic, complemented
15C2×#4734C211yesmaximal, characteristic, complemented
16C2×#67⋊C8C211yesmaximal, characteristic, complemented
17C2×#3287—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×#239C2211yescharacteristic
20C22×#237C2211yescharacteristic
21C22×#235C2211yescharacteristic
22C22×C3×SD16C2211yescharacteristic
23C22×C3×D8C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25#5834—24no—
26#5834C2218yescomplemented
27C2×#950—28no—
28C2×#950C2218yescomplemented
29C2×Q8×Dic3C2211yescharacteristic
30C22×#216C2211yescharacteristic
31C22×#215C2211yescharacteristic
32C2×#940—21no—
33C2×#940—21no—
34C2×#940C2211yescharacteristic
35C2×#940C2211yescharacteristic
36C2×#939—21no—
37C2×#938—21no—
38C2×#938C2211yescharacteristic
39C22×#214C2211yescharacteristic
40C22×#213C2211yescharacteristic
41C22×#213C2211yescharacteristic
42C2×#930—21no—
43C2×#930C2211yescharacteristic
44C2×C4×#67—21no—
45C2×C4×#67C2211yescharacteristic
46C23×C3⋊C8C2211yescharacteristic
47C2×#916—28no—
48C2×#916C2218yescomplemented
49C22×D24C2211yescharacteristic
50C22×#204C2211yescharacteristic
51C22×D3×C8C2211yescharacteristic
52#5599—24no—
53#5599C2218yescomplemented
54C2×#895C2211yescharacteristic
55C2×#887C2211yescharacteristic
56C2×#884—21no—
57C2×#67⋊C4—21no—
58C3×#449C2218yescomplemented
59C2×C3×#103C2211yescharacteristic
60C2×C3×#102C2211yescharacteristic
61C2×C3×C22⋊C8C2211yescharacteristic
62C2×#832C2211yescharacteristic
63#5163C2218yescomplemented
64#5158C2218yescomplemented
65#5151C2218yescomplemented
66C2×#821C2211yescharacteristic
67C2×(C2×D3)⋊C8C2211yescharacteristic
68C2×#816C2211yescharacteristic
69C2×Dic3⋊C8C2211yescharacteristic
70C2×C8×Dic3C2211yescharacteristic
71#5038C2218yescomplemented
72C2×#809C2211yescharacteristic
73C2×#807C2211yescharacteristic
74#4810C2218yescomplemented
75#4790C2218yescomplemented
76#4775C2218yescomplemented
77#4762C2218yescomplemented
78#4734C2218yescomplemented
79#67⋊C8C2218yescomplemented
80C22×#135—31no—
81C22×#135—31no—
82C2×#550—31no—
83C2×#550—31no—
84#3287—316no—
85C2×#493—31no—
86C2×#466—31no—
87C2×#466—31no—
88C2×#460—31no—
89C2×#460—31no—
90C2×#449—31no—
91C2×#449—31no—
92C2×#449—31no—
93C2×#449D311yescharacteristic, complemented
94C2×C4×Q16—31no—
95C2×C8×D4—31no—
96C2×C3×#41—22no—
97C2×C3×#41—24no—
98C2×C3×#41—42no—
99C2×C3×#41C2314yes—
100C22×C3×Q8C2311yescharacteristic
101C22×C3×D4—21no—
102C22×C3×D4—21no—
103C22×C3×D4C2311yescharacteristic
104C22×C3×D4C2311yescharacteristic
105C23×C3×C4—21no—
106C23×C3×C4C2311yescharacteristic
107C22×#67—21no—
108C22×#67—21no—
109C22×#67—21no—
110C22×#67—21no—
111C22×#67—21no—
112C22×#67—21no—
113C22×#67—21no—
114C22×#67—21no—
115C22×#67D411yescharacteristic
116C23×Dic3—21no—
117C2×#239—22no—
118C2×#239—24no—
119C2×#239—42no—
120C2×#239C2314yes—
121C2×#237—22no—
122C2×#237—24no—
123C2×#237—42no—
124C2×#237C2314yes—
125C2×#235—22no—
126C2×#235—24no—
127C2×#235—42no—
128C2×#235C2314yes—
129C22×D12—21no—
130C22×D12—21no—
131C22×D12C2311yescharacteristic
132C22×D12C2311yescharacteristic
133C22×C4×D3—21no—
134C22×C4×D3—21no—
135C22×C4×D3C2311yescharacteristic
136C22×Dic6C2311yescharacteristic
137C2×C3×SD16—24no—
138C2×C3×SD16C2314yes—
139C2×C3×D8—42no—
140C2×C3×D8C2314yes—
141C22×C3×C8C2311yescharacteristic
142C22×C3×C8C2311yescharacteristic
143C3×#121—22no—
144C3×#121C2314yes—
145C2×C3×C4⋊C4C2311yescharacteristic
146C2×C3×C22⋊C4—21no—
147C2×#217—21no—
148C2×#217D411yescharacteristic
149#950—232no—
150Q8×Dic3—22no—
151Q8×Dic3C2314yes—
152C2×#216D418yescomplemented
153C2×#216C2314yes—
154C2×#215—24no—
155C2×#215C2314yes—
156#940—28no—
157#940—28no—
158#940—22no—
159#940—22no—
160#940C2314yes—
161#940C2314yes—
162#939—28no—
163#938—22no—
164#938—28no—
165#938C2314yes—
166C2×#214—24no—
167C2×#214C2314yes—
168C2×#213—24no—
169C2×#213—24no—
170C2×#213C2314yes—
171C2×#213C2314yes—
172#930—22no—
173#930—28no—
174#930C2314yes—
175C4×#67—28no—
176C4×#67D414yes—
177C4×#67C2314yes—
178C2×(C2×D3)⋊C4—21no—
179C2×(C2×D3)⋊C4—21no—
180C2×(C2×D3)⋊C4D411yescharacteristic
181C2×C4⋊Dic3—21no—
182C2×C4⋊Dic3C2311yescharacteristic
183C2×Dic3⋊C4—21no—
184C2×Dic3⋊C4D411yescharacteristic
185C2×C4×Dic3—21no—
186C2×C4×Dic3—21no—
187C2×C4×Dic3C2311yescharacteristic
188C22×C3⋊C8—24no—
189C22×C3⋊C8C2311yescharacteristic
190C22×C3⋊C8C2314yes—
191C22×C3⋊C8C2311yescharacteristic
192#916—232no—
193C2×D24—42no—
194C2×D24C2314yes—
195C2×#204—24no—
196C2×#204C2314yes—
197C2×D3×C8—24no—
198C2×D3×C8C2314yes—
199#895—22no—
200#895C2314yes—
201#887—22no—
202#887C2314yes—
203#884—28no—
204#67⋊C4—28no—
205C3×#103C2314yes—
206C3×#102C2314yes—
207C3×C22⋊C8C2314yes—
208#832C2314yes—
209#821C2314yes—
210(C2×D3)⋊C8C2314yes—
211#816C2314yes—
212Dic3⋊C8C2314yes—
213C8×Dic3C2314yes—
214#809C2314yes—
215#807C2314yes—
216C22×#41—31no—
217C22×#41—31no—
218C22×#41—31no—
219C22×#41C2×D311yescharacteristic
220C2×#135—38no—
221C2×#135—38no—
222C2×#135—68no—
223C2×#135—68no—
224C22×Q16—31no—
225C22×SD16—31no—
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16C2×D311yescharacteristic
229C22×D8—31no—
230C22×D8—31no—
231C22×D8—31no—
232C22×D8C2×D311yescharacteristic
233C23×C8—31no—
234C23×C8—31no—
235#550—38no—
236#550—38no—
237#550—64no—
238#550—64no—
239C2×#127—31no—
240C2×#127—31no—
241C2×#127—61no—
242C2×#127—61no—
243C2×#121—31no—
244C2×#121—31no—
245C2×#121—31no—
246C2×#121—61no—
247C2×#121—61no—
248C2×#121—61no—
249C2×#121—61no—
250C2×#121C2×D311yescharacteristic
251C2×C4×Q8—31no—
252C2×C4×Q8—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C2×C4×D4—61no—
256#493—38no—
257#466—38no—
258#466—38no—
259#460—38no—
260#460—38no—
261#449—38no—
262#449—38no—
263#449—38no—
264#449C2×D318yescomplemented
265C4×Q16—38no—
266C8×D4—38no—
267C2×#107—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103C2×D311yescharacteristic
271C2×#102—31no—
272C2×#102—31no—
273C2×#102—31no—
274C2×#102C2×D311yescharacteristic
275C2×C22⋊C8—31no—
276C2×C22⋊C8C2×D311yescharacteristic
277C2×C4×C8—31no—
278C24×C3—21no—
279C24×C3—21no—
280C24×C3C2×D411yescharacteristic
281C23×D3—21no—
282C23×D3—21no—
283C23×D3C2×D411yescharacteristic
284C3×#41—28no—
285C3×#41—44no—
286C3×#41—48no—
287C2×C3×Q8—21no—
288C2×C3×Q8—22no—
289C2×C3×Q8C2×D414yes—
290C2×C3×Q8C2412yes—
291C2×C3×D4—24no—
292C2×C3×D4—24no—
293C2×C3×D4—22no—
294C2×C3×D4—22no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—22no—
298C2×C3×D4—22no—
299C2×C3×D4—44no—
300C2×C3×D4—82no—
301C2×C3×D4C2412yes—
302C2×C3×D4C2412yes—
303C22×C3×C4—21no—
304C22×C3×C4—22no—
305C22×C3×C4—22no—
306C22×C3×C4—21no—
307C22×C3×C4—24no—
308C22×C3×C4—44no—
309C22×C3×C4C2×D411yescharacteristic
310C22×C3×C4C2×D412yes—
311C22×C3×C4C2412yes—
312C22×C3×C4C2411yescharacteristic
313C2×#67—24no—
314C2×#67—24no—
315C2×#67—24no—
316C2×#67—24no—
317C2×#67—24no—
318C2×#67—24no—
319C2×#67—24no—
320C2×#67—24no—
321C2×#67—24no—
322C2×#67—44no—
323C2×#67—44no—
324C2×#67—44no—
325C2×#67—44no—
326C2×#67—82no—
327C2×#67—82no—
328C2×#67—82no—
329C2×#67—82no—
330C2×#67C2×D414yes—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—24no—
334C22×Dic3—44no—
335C22×Dic3C2×D411yescharacteristic
336C22×Dic3C2×D411yescharacteristic
337C22×Dic3C2×D411yescharacteristic
338#239—28no—
339#239—44no—
340#239—48no—
341#237—28no—
342#237—44no—
343#237—48no—
344#235—28no—
345#235—44no—
346#235—48no—
347C2×D12—22no—
348C2×D12—22no—
349C2×D12—22no—
350C2×D12—22no—
351C2×D12—24no—
352C2×D12—21no—
353C2×D12—21no—
354C2×D12—24no—
355C2×D12—44no—
356C2×D12—82no—
357C2×D12C2412yes—
358C2×D12C2412yes—
359C2×C4×D3—22no—
360C2×C4×D3—22no—
361C2×C4×D3—24no—
362C2×C4×D3—24no—
363C2×C4×D3—44no—
364C2×C4×D3—44no—
365C2×C4×D3C2×D412yes—
366C2×C4×D3C2412yes—
367C2×Dic6—21no—
368C2×Dic6—22no—
369C2×Dic6C2×D414yes—
370C2×Dic6C2412yes—
371C3×SD16—28no—
372C3×D8—44no—
373C2×C3×C8—22no—
374C2×C3×C8—22no—
375C2×C3×C8C2412yes—
376C2×C3×C8C2412yes—
377C3×C4⋊C4—21no—
378C3×C4⋊C4C2412yes—
379C3×C22⋊C4—24no—
380#217—24no—
381#217C2×D414yes—
382#216C2×D4116yescomplemented
383#215—28no—
384#214—28no—
385#213—28no—
386#213—28no—
387(C2×D3)⋊C4—24no—
388(C2×D3)⋊C4—24no—
389(C2×D3)⋊C4C2×D414yes—
390C4⋊Dic3—21no—
391C4⋊Dic3—24no—
392C4⋊Dic3C2412yes—
393Dic3⋊C4—24no—
394Dic3⋊C4C2×D414yes—
395C4×Dic3—24no—
396C4×Dic3—24no—
397C4×Dic3C2×D412yes—
398C4×Dic3C2412yes—
399C2×C3⋊C8—22no—
400C2×C3⋊C8—28no—
401C2×C3⋊C8C2×D414yes—
402C2×C3⋊C8C2412yes—
403C2×C3⋊C8C2412yes—
404D24—44no—
405#204—28no—
406D3×C8—28no—
407C2×#41—22no—
408C2×#41—24no—
409C2×#41—34no—
410C2×#41—34no—
411C2×#41—34no—
412C2×#41—42no—
413C2×#41—64no—
414C2×#41—62no—
415C2×#41—62no—
416C2×#41—62no—
417C2×#41—64no—
418C2×#41—64no—
419C2×#41—122no—
420C2×#41—122no—
421C2×#41—122no—
422C2×#41C22×D314yes—
423C22×Q8—31no—
424C22×Q8C22×D311yescharacteristic
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—31no—
428C22×D4—31no—
429C22×D4—31no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4—61no—
434C22×D4—61no—
435C22×D4—61no—
436C22×D4—61no—
437C22×D4—61no—
438C22×D4—61no—
439C22×D4—61no—
440C22×D4C22×D311yescharacteristic
441C22×D4C22×D311yescharacteristic
442C23×C4—21no—
443C23×C4—31no—
444C23×C4—61no—
445C23×C4—61no—
446C23×C4—61no—
447C23×C4C22×D311yescharacteristic
448#135—632no—
449#135—632no—
450C2×Q16—38no—
451C2×Q16—34no—
452C2×SD16—24no—
453C2×SD16—34no—
454C2×SD16—34no—
455C2×SD16—34no—
456C2×SD16—64no—
457C2×SD16—64no—
458C2×SD16—64no—
459C2×SD16C22×D314yes—
460C2×D8—34no—
461C2×D8—34no—
462C2×D8—34no—
463C2×D8—42no—
464C2×D8—64no—
465C2×D8—64no—
466C2×D8—122no—
467C2×D8C22×D314yes—
468C22×C8—31no—
469C22×C8—31no—
470C22×C8—34no—
471C22×C8—34no—
472C22×C8—64no—
473C22×C8—64no—
474C22×C8C22×D311yescharacteristic
475C22×C8C22×D311yescharacteristic
476#127—34no—
477#127—34no—
478#127—62no—
479#127—62no—
480#127—68no—
481#127—68no—
482#121—22no—
483#121—34no—
484#121—34no—
485#121—34no—
486#121—68no—
487#121—68no—
488#121—68no—
489#121—68no—
490#121—62no—
491#121—62no—
492#121—62no—
493#121C22×D314yes—
494C4×Q8—34no—
495C4×Q8—34no—
496C4×Q8—62no—
497C4×Q8—62no—
498C4×D4—34no—
499C4×D4—34no—
500C4×D4—68no—
501C4×D4—68no—
502C2×C4⋊C4—31no—
503C2×C4⋊C4—31no—
504C2×C4⋊C4—61no—
505C2×C4⋊C4—61no—
506C2×C4⋊C4C22×D311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—31no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—61no—
512C2×C22⋊C4—61no—
513C2×C42—31no—
514C2×C42—61no—
515C2×C42—61no—
516#107—34no—
517C4⋊C8—34no—
518#103—34no—
519#103C22×D314yes—
520#102—34no—
521#102—34no—
522#102—34no—
523#102C22×D314yes—
524C22⋊C8—34no—
525C22⋊C8C22×D314yes—
526C4×C8—34no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—42no—
533C23×C3—42no—
534C23×C3—42no—
535C23×C3—42no—
536C23×C3—42no—
537C23×C3—42no—
538C23×C3C22×D412yes—
539C23×C3C22×D411yescharacteristic
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—42no—
546C22×D3—42no—
547C22×D3—42no—
548C22×D3—42no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3C22×D412yes—
552C3×Q8—24no—
553C3×Q8—22no—
554C3×Q8C22×D414yes—
555C3×D4—22no—
556C3×D4—22no—
557C3×D4—22no—
558C3×D4—22no—
559C3×D4—48no—
560C3×D4—42no—
561C3×D4—42no—
562C3×D4—84no—
563C2×C3×C4—22no—
564C2×C3×C4—24no—
565C2×C3×C4—22no—
566C2×C3×C4—24no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—48no—
571C2×C3×C4—42no—
572C2×C3×C4C22×D412yes—
573C2×C3×C4C22×D411yescharacteristic
574C2×C3×C4C22×D412yes—
575C2×C3×C4H(5,𝔽2)12yes—
576C2×C3×C4C2511yescharacteristic
577#67—28no—
578#67—48no—
579#67—48no—
580#67—48no—
581#67—48no—
582#67—84no—
583#67—84no—
584#67—84no—
585#67—84no—
586C2×Dic3—24no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—48no—
592C2×Dic3—42no—
593C2×Dic3#13514yescomplemented
594C2×Dic3C22×D412yes—
595C2×Dic3C22×D412yes—
596C2×Dic3C22×D412yes—
597D12—22no—
598D12—22no—
599D12—22no—
600D12—22no—
601D12—48no—
602D12—42no—
603D12—42no—
604D12—84no—
605C4×D3—24no—
606C4×D3—22no—
607C4×D3—22no—
608C4×D3—48no—
609C4×D3—48no—
610Dic6—24no—
611Dic6—22no—
612Dic6C22×D414yes—
613C3×C8—22no—
614C3×C8—22no—
615C3⋊C8—22no—
616C3⋊C8C22×D414yes—
617C24—21no—
618C24—21no—
619C24—31no—
620C24—61no—
621C24—61no—
622C24D3×D411yescharacteristic
623#41—28no—
624#41—44no—
625#41—48no—
626#41—68no—
627#41—68no—
628#41—68no—
629#41—124no—
630#41—128no—
631#41—124no—
632#41—128no—
633#41—124no—
634#41—128no—
635C2×Q8—21no—
636C2×Q8—22no—
637C2×Q8—34no—
638C2×Q8—32no—
639C2×Q8—61no—
640C2×Q8—62no—
641C2×Q8D3×D414yes—
642C2×Q8C23×D312yes—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—22no—
646C2×D4—22no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—34no—
652C2×D4—32no—
653C2×D4—32no—
654C2×D4—44no—
655C2×D4—64no—
656C2×D4—64no—
657C2×D4—64no—
658C2×D4—64no—
659C2×D4—64no—
660C2×D4—64no—
661C2×D4—64no—
662C2×D4—64no—
663C2×D4—64no—
664C2×D4—64no—
665C2×D4—64no—
666C2×D4—62no—
667C2×D4—62no—
668C2×D4—61no—
669C2×D4—61no—
670C2×D4—62no—
671C2×D4—62no—
672C2×D4—82no—
673C2×D4—124no—
674C2×D4—124no—
675C2×D4—124no—
676C2×D4—124no—
677C2×D4—124no—
678C2×D4—242no—
679C2×D4—242no—
680C2×D4—242no—
681C2×D4—242no—
682C2×D4—242no—
683C2×D4C23×D312yes—
684C2×D4C23×D312yes—
685C22×C4—21no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—32no—
694C22×C4—32no—
695C22×C4—44no—
696C22×C4—64no—
697C22×C4—64no—
698C22×C4—61no—
699C22×C4—62no—
700C22×C4—62no—
701C22×C4—61no—
702C22×C4—64no—
703C22×C4—124no—
704C22×C4—124no—
705C22×C4—124no—
706C22×C4D3×D412yes—
707C22×C4D3×D411yescharacteristic
708C22×C4C23×D312yes—
709C22×C4C23×D311yescharacteristic
710Q16—316no—
711SD16—28no—
712SD16—68no—
713SD16—68no—
714SD16—68no—
715D8—44no—
716D8—68no—
717D8—68no—
718D8—124no—
719C2×C8—22no—
720C2×C8—22no—
721C2×C8—34no—
722C2×C8—32no—
723C2×C8—32no—
724C2×C8—68no—
725C2×C8—68no—
726C2×C8—62no—
727C2×C8C23×D312yes—
728C2×C8C23×D312yes—
729C4⋊C4—21no—
730C4⋊C4—34no—
731C4⋊C4—32no—
732C4⋊C4—64no—
733C4⋊C4—64no—
734C4⋊C4—61no—
735C4⋊C4C23×D312yes—
736C22⋊C4—24no—
737C22⋊C4—34no—
738C22⋊C4—34no—
739C22⋊C4—64no—
740C22⋊C4—64no—
741C22⋊C4—64no—
742C42—32no—
743C42—32no—
744C42—64no—
745C42—64no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—44no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—84no—
757C22×C3—84no—
758C22×C3D4212yes—
759C22×C3C2×#13512yes—
760C22×C3#57612yes—
761C22×C3C23×D411yescharacteristic
762C2×D3—22no—
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—44no—
766C2×D3—42no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—84no—
773C2×D3—84no—
774C3×C4—22no—
775C3×C4—24no—
776C3×C4—42no—
777C3×C4D4212yes—
778C3×C4C23×D411yescharacteristic
779C3×C4C2×H(5,𝔽2)11yescharacteristic
780Dic3—24no—
781Dic3—22no—
782Dic3—22no—
783Dic3—42no—
784Dic3C2×#13514yescomplemented
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—32no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—62no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—122no—
803C23—122no—
804C23—122no—
805C23—122no—
806C23—122no—
807C23—122no—
808C23C2×D3×D412yes—
809C23C2×D3×D411yescharacteristic
810Q8—22no—
811Q8—24no—
812Q8—34no—
813Q8—62no—
814Q8—64no—
815Q8C2×D3×D414yes—
816D4—22no—
817D4—22no—
818D4—22no—
819D4—22no—
820D4—48no—
821D4—42no—
822D4—42no—
823D4—68no—
824D4—62no—
825D4—62no—
826D4—62no—
827D4—62no—
828D4—84no—
829D4—128no—
830D4—128no—
831D4—128no—
832D4—128no—
833D4—128no—
834D4—122no—
835D4—122no—
836D4—244no—
837D4—244no—
838D4—244no—
839D4—244no—
840D4—244no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—32no—
849C2×C4—34no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—48no—
853C2×C4—42no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—62no—
857C2×C4—64no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—64no—
861C2×C4—62no—
862C2×C4—128no—
863C2×C4—128no—
864C2×C4—128no—
865C2×C4—122no—
866C2×C4C2×D3×D412yes—
867C2×C4C2×D3×D412yes—
868C2×C4C2×D3×D411yescharacteristic
869C2×C4#100412yes—
870C2×C4C24×D311yescharacteristic
871C8—22no—
872C8—22no—
873C8—34no—
874C8—62no—
875C2×C3—42no—
876C2×C3—82no—
877C2×C3—82no—
878C2×C3#328714yescomplemented
879C2×C3C2×D4211yescharacteristic
880C2×C3C22×#13511yescharacteristic
881C2×C3C2×#57611yescharacteristic
882D3—42no—
883D3—82no—
884D3—82no—
885C22—22no—
886C22—22no—
887C22—22no—
888C22—44no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—62no—
896C22—62no—
897C22—62no—
898C22—84no—
899C22—84no—
900C22—124no—
901C22—122no—
902C22—122no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—244no—
908C22—244no—
909C22#559012yes—
910C22D3×#13512yes—
911C22#577412yes—
912C22C22×D3×D411yescharacteristic
913C4—22no—
914C4—24no—
915C4—34no—
916C4—42no—
917C4—62no—
918C4—62no—
919C4—64no—
920C4—122no—
921C4#559012yes—
922C4C22×D3×D411yescharacteristic
923C4C2×#100411yescharacteristic
924C3C2×#328711yescharacteristic, complemented, Sylow
925C2—42no—
926C2—82no—
927C2—82no—
928C2—122no—
929C2—242no—
930C2—242no—
931C2#8013114yesdirect product factor
932C2C2×#559011yescharacteristic
933C2C2×D3×#13511yescharacteristic
934C2C2×#577411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#449C2
socleC23×C3C22×D4
hypercenterC2×#449D3
hypocenterC3C2×#3287
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×#5834C2semidirect
2. C22×#950C2semidirect
3. C22×#916C2semidirect
4. C2×#5599C2semidirect
5. C2×C3×#449C2semidirect
6. C2×#5163C2semidirect
7. C2×#5158C2semidirect
8. C2×#5151C2semidirect
9. C2×#5038C2semidirect
10. #80131C2direct (N × H)
11. C2×#4810C2semidirect
12. C2×#4790C2semidirect
13. C2×#4762C2semidirect
14. C2×#4775C2semidirect
15. C2×#4734C2semidirect
16. C2×#67⋊C8C2semidirect
26. #5834C22semidirect
28. C2×#950C22semidirect
48. C2×#916C22semidirect
53. #5599C22semidirect
58. C3×#449C22semidirect
63. #5163C22semidirect
64. #5158C22semidirect
65. #5151C22semidirect
71. #5038C22semidirect
74. #4810C22semidirect
75. #4790C22semidirect
76. #4775C22semidirect
77. #4762C22semidirect
78. #4734C22semidirect
79. #67⋊C8C22semidirect
93. C2×#449D3semidirect
152. C2×#216D4semidirect
264. #449C2×D3semidirect
382. #216C2×D4semidirect
593. C2×Dic3#135semidirect
784. Dic3C2×#135semidirect
878. C2×C3#3287semidirect
924. C3C2×#3287semidirect
931. C2#80131direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#58342
C22×#9502
C22×#9162
C2×#55992
C2×C3×#4492
C2×#51632
C2×#51582
C2×#51512
C2×#50382
#801312
C2×#48102
C2×#47902
C2×#47622
C2×#47752
C2×#47342
C2×#67⋊C82
C2×#32873