Finite Group Databasebeta

← C2×#83997 #11670349

Subgroups — C2×#83997 #11670349

Order 768.

2794 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#137C211yesmaximal, characteristic, complemented
2C2×#5834C211yesmaximal, characteristic
3C2×Q8×#67C211yesmaximal, characteristic, complemented
4C22×#918C211yesmaximal, characteristic, complemented
5C2×#5239C211yesmaximal, characteristic, complemented
6C2×#5227C211yesmaximal, characteristic, complemented
7#83997C2116yesmaximal, direct product factor
8C2×#5187C211yesmaximal, characteristic, complemented
9C2×#5182C211yesmaximal, characteristic, complemented
10C2×Dic3×Q16C211yesmaximal, characteristic, complemented
11C2×#5174C211yesmaximal, characteristic, complemented
12C2×#5170C211yesmaximal, characteristic, complemented
13C2×#5175C211yesmaximal, characteristic, complemented
14C2×#5163C211yesmaximal, characteristic, complemented
15C2×#5134C211yesmaximal, characteristic, complemented
16C2×#5128C211yesmaximal, characteristic, complemented
17C2×#3278—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C22×#239C2211yescharacteristic
21C22×D3×Q8C2211yescharacteristic
22C2×C3×#137—28no—
23C2×C3×#137C2218yescomplemented
24C22×C3×Q16C2211yescharacteristic
25C22×C3×Q16C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic
27C22×C3×SD16C2211yescharacteristic
28C22×C3×M16C2211yescharacteristic
29#5834—24no—
30#5834C2218yes—
31Q8×#67—24no—
32Q8×#67C2218yescomplemented
33C2×#946—21no—
34C2×#946C2211yescharacteristic
35C2×Q8×Dic3C2211yescharacteristic
36C2×Q8×Dic3C2211yescharacteristic
37C2×#944—21no—
38C2×#944C2211yescharacteristic
39C22×#216C2211yescharacteristic
40C22×#215C2211yescharacteristic
41C22×#215C2211yescharacteristic
42C2×#940—21no—
43C2×#940C2211yescharacteristic
44C2×#938—21no—
45C2×#938C2211yescharacteristic
46C22×#214C2211yescharacteristic
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#5227C2218yescomplemented
60C2×#835C2211yescharacteristic
61C2×#835C2211yescharacteristic
62C2×#835C2211yescharacteristic
63C2×#832C2211yescharacteristic
64C2×#830C2211yescharacteristic
65#5187C2218yescomplemented
66#5182C2218yescomplemented
67Dic3×Q16C2218yescomplemented
68#5175C2218yescomplemented
69#5174C2218yescomplemented
70#5170C2218yescomplemented
71#5163C2218yescomplemented
72#5134C2218yescomplemented
73#5128C2218yescomplemented
74C2×#821C2211yescharacteristic
75C2×(C2×D3)⋊C8C2211yescharacteristic
76C2×#818C2211yescharacteristic
77C2×#816C2211yescharacteristic
78C2×Dic3⋊C8C2211yescharacteristic
79C2×C8×Dic3C2211yescharacteristic
80C22×#137—31no—
81C22×#137D311yescharacteristic, complemented
82C2×#550—31no—
83C2×D4×Q8—31no—
84#3278—316no—
85C2×#492—31no—
86C2×#468—31no—
87C2×#468—31no—
88C2×#462—31no—
89C2×#460—31no—
90C2×#452—31no—
91C2×#452—31no—
92C2×#448—31no—
93C2×#448—31no—
94C2×C4×Q16—31no—
95C2×#436—31no—
96C2×C3×#41—22no—
97C2×C3×#41—24no—
98C2×C3×#41—42no—
99C2×C3×#41C2314yes—
100C22×C3×Q8—21no—
101C22×C3×Q8—22no—
102C22×C3×Q8—24no—
103C22×C3×Q8—42no—
104C22×C3×Q8C2311yescharacteristic
105C22×C3×Q8C2314yes—
106C22×C3×Q8C2311yescharacteristic
107C22×C3×Q8C2311yescharacteristic
108C22×C3×D4—21no—
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×#67D411yescharacteristic
118C2×#239—22no—
119C2×#239—24no—
120C2×#239—42no—
121C2×#239C2314yes—
122C2×D3×Q8—22no—
123C2×D3×Q8—24no—
124C2×D3×Q8—42no—
125C2×D3×Q8C2314yes—
126C22×D12—21no—
127C22×D12C2311yescharacteristic
128C22×C4×D3—21no—
129C22×C4×D3—21no—
130C22×C4×D3C2311yescharacteristic
131C22×Dic6—21no—
132C22×Dic6C2311yescharacteristic
133C3×#137—232no—
134C2×C3×Q16—24no—
135C2×C3×Q16D418yescomplemented
136C2×C3×Q16C2314yes—
137C2×C3×Q16C2314yes—
138C2×C3×SD16—24no—
139C2×C3×SD16—24no—
140C2×C3×SD16C2314yes—
141C2×C3×SD16C2314yes—
142C2×C3×M16—24no—
143C2×C3×M16C2314yes—
144C22×C3×C8C2311yescharacteristic
145C22×C3×C8C2311yescharacteristic
146C2×#217—21no—
147C2×#217—21no—
148C2×#217D411yescharacteristic
149#946—22no—
150#946—28no—
151#946C2314yes—
152Q8×Dic3—22no—
153Q8×Dic3—22no—
154Q8×Dic3C2314yes—
155Q8×Dic3C2314yes—
156#944—28no—
157#944—22no—
158#944C2314yes—
159C2×#216—24no—
160C2×#216C2314yes—
161C2×#215—24no—
162C2×#215—42no—
163C2×#215C2314yes—
164C2×#215C2314yes—
165#940—28no—
166#940—22no—
167#940C2314yes—
168#938—22no—
169#938—28no—
170#938C2314yes—
171C2×#214—42no—
172C2×#214C2314yes—
173#930—22no—
174#930—28no—
175#930C2314yes—
176C4×#67—28no—
177C4×#67—28no—
178C4×#67D414yes—
179C4×#67C2314yes—
180C2×(C2×D3)⋊C4—21no—
181C2×(C2×D3)⋊C4—21no—
182C2×(C2×D3)⋊C4D411yescharacteristic
183C2×C4⋊Dic3—21no—
184C2×C4⋊Dic3—21no—
185C2×C4⋊Dic3C2311yescharacteristic
186C2×C4⋊Dic3C2311yescharacteristic
187#924—22no—
188#924—28no—
189#924C2314yes—
190C2×Dic3⋊C4—21no—
191C2×Dic3⋊C4—21no—
192C2×Dic3⋊C4—21no—
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#835C2314yes—
208#832C2314yes—
209#830C2314yes—
210#821C2314yes—
211(C2×D3)⋊C8C2314yes—
212#818C2314yes—
213#816C2314yes—
214Dic3⋊C8C2314yes—
215C8×Dic3C2314yes—
216C22×#41—31no—
217C22×#41C2×D311yescharacteristic
218C23×Q8—31no—
219C23×Q8C2×D311yescharacteristic
220C2×#137—28no—
221C2×#137—38no—
222C2×#137—68no—
223C2×#137C2×D318yescomplemented
224C22×Q16—31no—
225C22×Q16C2×D311yescharacteristic
226C22×Q16C2×D311yescharacteristic
227C22×SD16—31no—
228C22×SD16—31no—
229C22×SD16—31no—
230C22×SD16—31no—
231C22×SD16C2×D311yescharacteristic
232C22×SD16C2×D311yescharacteristic
233C22×M16—31no—
234C22×M16C2×D311yescharacteristic
235#550—38no—
236#550—64no—
237D4×Q8—38no—
238D4×Q8—64no—
239C2×C4⋊Q8—31no—
240C2×C4⋊Q8—61no—
241C2×#127—31no—
242C2×#127—61no—
243C2×C22⋊Q8—31no—
244C2×C22⋊Q8—31no—
245C2×C22⋊Q8—61no—
246C2×C22⋊Q8—61no—
247C2×#121—31no—
248C2×#121—31no—
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#492—38no—
257#468—38no—
258#468—38no—
259#462—38no—
260#460—38no—
261#452—38no—
262#452—38no—
263#448—38no—
264#448—38no—
265C4×Q16—38no—
266#436—38no—
267C2×#107—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#103—31no—
272C2×#103—31no—
273C2×#102—31no—
274C2×#102—31no—
275C2×C22⋊C8—31no—
276C2×C22⋊C8—31no—
277C2×C4×C8—31no—
278C24×C3—21no—
279C24×C3C2×D411yescharacteristic
280C23×D3—21no—
281C23×D3C2×D411yescharacteristic
282C3×#41—28no—
283C3×#41—44no—
284C3×#41—48no—
285C2×C3×Q8—21no—
286C2×C3×Q8—21no—
287C2×C3×Q8—24no—
288C2×C3×Q8—21no—
289C2×C3×Q8—22no—
290C2×C3×Q8—22no—
291C2×C3×Q8—28no—
292C2×C3×Q8—22no—
293C2×C3×Q8—22no—
294C2×C3×Q8—44no—
295C2×C3×Q8—44no—
296C2×C3×Q8—48no—
297C2×C3×Q8C2×D414yes—
298C2×C3×Q8C2×D414yes—
299C2×C3×Q8C2412yes—
300C2×C3×Q8C2412yes—
301C2×C3×Q8C2412yes—
302C2×C3×D4—24no—
303C2×C3×D4—22no—
304C2×C3×D4—21no—
305C2×C3×D4—22no—
306C2×C3×D4—44no—
307C2×C3×D4C2412yes—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—21no—
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—44no—
327C2×#67—82no—
328C2×#67—82no—
329C2×#67—82no—
330C2×#67C2×D414yes—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3C2×D411yescharacteristic
335C22×Dic3C2×D411yescharacteristic
336C22×Dic3C2×D411yescharacteristic
337#239—28no—
338#239—44no—
339#239—48no—
340D3×Q8—28no—
341D3×Q8—44no—
342D3×Q8—48no—
343C2×D12—22no—
344C2×D12—22no—
345C2×D12—24no—
346C2×D12—21no—
347C2×D12—44no—
348C2×D12C2412yes—
349C2×C4×D3—22no—
350C2×C4×D3—22no—
351C2×C4×D3—24no—
352C2×C4×D3—24no—
353C2×C4×D3—44no—
354C2×C4×D3—44no—
355C2×C4×D3C2×D412yes—
356C2×C4×D3C2412yes—
357C2×Dic6—22no—
358C2×Dic6—22no—
359C2×Dic6—21no—
360C2×Dic6—24no—
361C2×Dic6—44no—
362C2×Dic6C2412yes—
363C3×Q16—28no—
364C3×Q16C2×D4116yescomplemented
365C3×SD16—28no—
366C3×SD16—28no—
367C3×M16—28no—
368C2×C3×C8—22no—
369C2×C3×C8C2×D414yes—
370C2×C3×C8C2412yes—
371C2×C3×C8C2412yes—
372#217—24no—
373#217—24no—
374#217C2×D414yes—
375#216—28no—
376#215—28no—
377#215—44no—
378#214—44no—
379(C2×D3)⋊C4—24no—
380(C2×D3)⋊C4—24no—
381(C2×D3)⋊C4C2×D414yes—
382C4⋊Dic3—21no—
383C4⋊Dic3—21no—
384C4⋊Dic3—24no—
385C4⋊Dic3—24no—
386C4⋊Dic3C2412yes—
387C4⋊Dic3C2412yes—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390Dic3⋊C4—24no—
391Dic3⋊C4—24no—
392Dic3⋊C4C2×D414yes—
393C4×Dic3—24no—
394C4×Dic3—24no—
395C4×Dic3C2×D412yes—
396C4×Dic3C2412yes—
397C2×C3⋊C8—22no—
398C2×C3⋊C8—22no—
399C2×C3⋊C8C2412yes—
400C2×C3⋊C8C2412yes—
401#204—28no—
402ΓL(1,𝔽25)—28no—
403C2×#41—22no—
404C2×#41—24no—
405C2×#41—34no—
406C2×#41—42no—
407C2×#41—62no—
408C2×#41—64no—
409C2×#41—122no—
410C2×#41C22×D314yes—
411C22×Q8—21no—
412C22×Q8—22no—
413C22×Q8—24no—
414C22×Q8—34no—
415C22×Q8—31no—
416C22×Q8—42no—
417C22×Q8—61no—
418C22×Q8—62no—
419C22×Q8—64no—
420C22×Q8—122no—
421C22×Q8C22×D311yescharacteristic
422C22×Q8C22×D314yes—
423C22×Q8C22×D311yescharacteristic
424C22×Q8C22×D311yescharacteristic
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×D4C22×D311yescharacteristic
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—31no—
437C23×C4—61no—
438C23×C4—61no—
439C23×C4C22×D311yescharacteristic
440#137—232no—
441#137—632no—
442C2×Q16—24no—
443C2×Q16—34no—
444C2×Q16—64no—
445C2×Q16#6718yescomplemented
446C2×Q16C22×D314yes—
447C2×Q16C22×D314yes—
448C2×SD16—24no—
449C2×SD16—24no—
450C2×SD16—34no—
451C2×SD16—34no—
452C2×SD16—34no—
453C2×SD16—34no—
454C2×SD16—64no—
455C2×SD16—64no—
456C2×SD16—122no—
457C2×SD16—122no—
458C2×SD16C22×D314yes—
459C2×SD16C22×D314yes—
460C2×M16—24no—
461C2×M16—34no—
462C2×M16—64no—
463C2×M16C22×D314yes—
464C22×C8—31no—
465C22×C8—31no—
466C22×C8C22×D311yescharacteristic
467C22×C8C22×D311yescharacteristic
468C4⋊Q8—34no—
469C4⋊Q8—62no—
470C4⋊Q8—68no—
471#127—34no—
472#127—62no—
473#127—68no—
474C22⋊Q8—34no—
475C22⋊Q8—34no—
476C22⋊Q8—68no—
477C22⋊Q8—68no—
478C22⋊Q8—62no—
479C22⋊Q8—62no—
480#121—34no—
481#121—34no—
482#121—68no—
483#121—68no—
484#121—62no—
485#121—62no—
486C4×Q8—34no—
487C4×Q8—34no—
488C4×Q8—62no—
489C4×Q8—62no—
490C4×D4—34no—
491C4×D4—34no—
492C4×D4—68no—
493C4×D4—68no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—31no—
497C2×C4⋊C4—61no—
498C2×C4⋊C4—61no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4—61no—
501C2×C4⋊C4—61no—
502C2×C4⋊C4—61no—
503C2×C22⋊C4—31no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—61no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C42—31no—
510C2×C42—61no—
511C2×C42—61no—
512#107—34no—
513C4⋊C8—34no—
514#103—34no—
515#103—34no—
516#103—34no—
517#103—34no—
518#102—34no—
519#102—34no—
520C22⋊C8—34no—
521C22⋊C8—34no—
522C4×C8—34no—
523C23×C3—22no—
524C23×C3—22no—
525C23×C3—22no—
526C23×C3—22no—
527C23×C3—42no—
528C23×C3—42no—
529C23×C3—42no—
530C23×C3C22×D412yes—
531C23×C3C22×D411yescharacteristic
532C22×D3—22no—
533C22×D3—22no—
534C22×D3—22no—
535C22×D3—22no—
536C22×D3—42no—
537C22×D3—42no—
538C22×D3—42no—
539C22×D3C22×D412yes—
540C3×Q8—24no—
541C3×Q8—24no—
542C3×Q8—22no—
543C3×Q8—22no—
544C3×Q8—22no—
545C3×Q8—22no—
546C3×Q8—48no—
547C3×Q8—42no—
548C3×Q8C22×D414yes—
549C3×Q8C22×D414yes—
550C3×D4—22no—
551C3×D4—22no—
552C3×D4—48no—
553C3×D4—42no—
554C2×C3×C4—24no—
555C2×C3×C4—24no—
556C2×C3×C4—22no—
557C2×C3×C4—22no—
558C2×C3×C4—22no—
559C2×C3×C4—24no—
560C2×C3×C4—22no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—48no—
564C2×C3×C4—48no—
565C2×C3×C4—42no—
566C2×C3×C4C22×D412yes—
567C2×C3×C4C22×D411yescharacteristic
568C2×C3×C4C22×D412yes—
569C2×C3×C4H(5,𝔽2)12yes—
570C2×C3×C4C2511yescharacteristic
571#67—28no—
572#67—48no—
573#67—84no—
574#67—84no—
575#67—84no—
576C2×Dic3—22no—
577C2×Dic3—22no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—42no—
582C2×Dic3—42no—
583C2×Dic3—42no—
584C2×Dic3#13714yescomplemented
585C2×Dic3C22×D412yes—
586C2×Dic3C22×D412yes—
587C2×Dic3C22×D412yes—
588D12—22no—
589D12—22no—
590D12—48no—
591D12—42no—
592C4×D3—24no—
593C4×D3—22no—
594C4×D3—22no—
595C4×D3—48no—
596C4×D3—48no—
597Dic6—22no—
598Dic6—22no—
599Dic6—48no—
600Dic6—42no—
601C3×C8—22no—
602C3×C8C22×D414yes—
603C3⋊C8—22no—
604C3⋊C8—22no—
605C24—21no—
606C24—31no—
607C24—61no—
608C24D3×D411yescharacteristic
609#41—28no—
610#41—44no—
611#41—48no—
612#41—68no—
613#41—124no—
614#41—128no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—24no—
618C2×Q8—21no—
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—28no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—32no—
625C2×Q8—44no—
626C2×Q8—44no—
627C2×Q8—48no—
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×Q8C23×D312yes—
641C2×D4—24no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—34no—
646C2×D4—32no—
647C2×D4—44no—
648C2×D4—64no—
649C2×D4—64no—
650C2×D4—64no—
651C2×D4—64no—
652C2×D4—64no—
653C2×D4—64no—
654C2×D4—61no—
655C2×D4—62no—
656C2×D4—62no—
657C2×D4—124no—
658C2×D4—124no—
659C2×D4—242no—
660C2×D4—242no—
661C2×D4—242no—
662C2×D4C23×D312yes—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—24no—
668C22×C4—21no—
669C22×C4—24no—
670C22×C4—31no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—32no—
674C22×C4—32no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—64no—
678C22×C4—64no—
679C22×C4—62no—
680C22×C4—62no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—61no—
684C22×C4—124no—
685C22×C4—124no—
686C22×C4D3×D412yes—
687C22×C4D3×D411yescharacteristic
688C22×C4C23×D312yes—
689C22×C4C23×D311yescharacteristic
690Q16—28no—
691Q16—68no—
692Q16C2×#67116yescomplemented
693SD16—28no—
694SD16—28no—
695SD16—68no—
696SD16—68no—
697SD16—124no—
698SD16—124no—
699M16—28no—
700M16—68no—
701C2×C8—22no—
702C2×C8—32no—
703C2×C8—32no—
704C2×C8—62no—
705C2×C8—62no—
706C2×C8C2×#6714yes—
707C2×C8C23×D312yes—
708C2×C8C23×D312yes—
709C4⋊C4—34no—
710C4⋊C4—32no—
711C4⋊C4—32no—
712C4⋊C4—64no—
713C4⋊C4—64no—
714C4⋊C4—64no—
715C4⋊C4—64no—
716C4⋊C4—64no—
717C4⋊C4—61no—
718C4⋊C4—61no—
719C4⋊C4—64no—
720C22⋊C4—34no—
721C22⋊C4—34no—
722C22⋊C4—64no—
723C22⋊C4—64no—
724C22⋊C4—64no—
725C22⋊C4—64no—
726C42—32no—
727C42—32no—
728C42—64no—
729C42—64no—
730C22×C3—22no—
731C22×C3—22no—
732C22×C3—22no—
733C22×C3—44no—
734C22×C3—42no—
735C22×C3—42no—
736C22×C3—42no—
737C22×C3—84no—
738C22×C3D4212yes—
739C22×C3C2×#13712yes—
740C22×C3#57712yes—
741C22×C3C23×D411yescharacteristic
742C2×D3—22no—
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—44no—
746C2×D3—42no—
747C2×D3—42no—
748C2×D3—42no—
749C2×D3—84no—
750C3×C4—24no—
751C3×C4—24no—
752C3×C4—22no—
753C3×C4—42no—
754C3×C4D4212yes—
755C3×C4C23×D411yescharacteristic
756C3×C4C2×H(5,𝔽2)11yescharacteristic
757Dic3—22no—
758Dic3—22no—
759Dic3—42no—
760Dic3—42no—
761Dic3—42no—
762Dic3C2×#13714yescomplemented
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—32no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—62no—
772C23—62no—
773C23—62no—
774C23—62no—
775C23—122no—
776C23—122no—
777C23—122no—
778C23C2×D3×D412yes—
779C23C2×D3×D411yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—24no—
783Q8—24no—
784Q8—22no—
785Q8—22no—
786Q8—48no—
787Q8—42no—
788Q8—62no—
789Q8—62no—
790Q8—128no—
791Q8—122no—
792Q8C22×#6714yes—
793Q8C22×#6714yes—
794D4—22no—
795D4—22no—
796D4—48no—
797D4—42no—
798D4—68no—
799D4—62no—
800D4—62no—
801D4—128no—
802D4—128no—
803D4—122no—
804D4—244no—
805D4—244no—
806D4—244no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—24no—
815C2×C4—22no—
816C2×C4—32no—
817C2×C4—34no—
818C2×C4—32no—
819C2×C4—32no—
820C2×C4—48no—
821C2×C4—48no—
822C2×C4—42no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—62no—
826C2×C4—62no—
827C2×C4—64no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—62no—
831C2×C4—128no—
832C2×C4—128no—
833C2×C4—122no—
834C2×C4—122no—
835C2×C4—122no—
836C2×C4C2×D3×D412yes—
837C2×C4C2×D3×D411yescharacteristic
838C2×C4#100412yes—
839C2×C4C22×#6712yes—
840C2×C4C24×D311yescharacteristic
841C8—22no—
842C8—62no—
843C8—62no—
844C8C22×#6714yes—
845C2×C3—42no—
846C2×C3—82no—
847C2×C3#327814yescomplemented
848C2×C3C2×D4211yescharacteristic
849C2×C3C22×#13711yescharacteristic
850C2×C3C2×#57711yescharacteristic
851D3—42no—
852D3—82no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—44no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—62no—
861C22—62no—
862C22—62no—
863C22—84no—
864C22—124no—
865C22—122no—
866C22—122no—
867C22—122no—
868C22—244no—
869C22D3×#13712yes—
870C22#577812yes—
871C22D4×#6712yes—
872C22C22×D3×D411yescharacteristic
873C4—22no—
874C4—24no—
875C4—24no—
876C4—34no—
877C4—42no—
878C4—62no—
879C4—62no—
880C4—122no—
881C4—122no—
882C4—122no—
883C4D4×#6712yes—
884C4C2×#100411yescharacteristic
885C4C23×#6711yescharacteristic
886C3C2×#327811yescharacteristic, complemented, Sylow
887C2—42no—
888C2—82no—
889C2—122no—
890C2—242no—
891C2#8399714yesdirect product factor
892C2C2×D3×#13711yescharacteristic
893C2C2×#577811yescharacteristic
894C2C2×D4×#6711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC22×C3×#137C2
socleC23×C3C22×D4
prime radicalC2×#5834C2
hypercenterC22×#137D3
hypocenterC3C2×#3278
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×C3×#137C2semidirect
3. C2×Q8×#67C2semidirect
4. C22×#918C2semidirect
5. C2×#5239C2semidirect
6. C2×#5227C2semidirect
7. #83997C2direct (N × H)
8. C2×#5187C2semidirect
9. C2×#5182C2semidirect
10. C2×Dic3×Q16C2semidirect
11. C2×#5174C2semidirect
12. C2×#5170C2semidirect
13. C2×#5175C2semidirect
14. C2×#5163C2semidirect
15. C2×#5134C2semidirect
16. C2×#5128C2semidirect
23. C2×C3×#137C22semidirect
32. Q8×#67C22semidirect
55. C2×#918C22semidirect
58. #5239C22semidirect
59. #5227C22semidirect
65. #5187C22semidirect
66. #5182C22semidirect
67. Dic3×Q16C22semidirect
68. #5175C22semidirect
69. #5174C22semidirect
70. #5170C22semidirect
71. #5163C22semidirect
72. #5134C22semidirect
73. #5128C22semidirect
81. C22×#137D3semidirect
135. C2×C3×Q16D4semidirect
223. C2×#137C2×D3semidirect
364. C3×Q16C2×D4semidirect
445. C2×Q16#67semidirect
584. C2×Dic3#137semidirect
692. Q16C2×#67semidirect
762. Dic3C2×#137semidirect
847. C2×C3#3278semidirect
886. C3C2×#3278semidirect
891. C2#83997direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1372
C2×#58342
C2×Q8×#672
C22×#9182
C2×#52392
C2×#52272
#839972
C2×#51872
C2×#51822
C2×Dic3×Q162
C2×#51742
C2×#51702
C2×#51752
C2×#51632
C2×#51342
C2×#51282
C2×#32783