Finite Group Databasebeta

← C2×#83922 #11670200

Subgroups — C2×#83922 #11670200

Order 768.

2966 conjugacy classes of subgroups.

The subgroup lattice has 940 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×#5829C211yesmaximal, characteristic, complemented
4C22×#914C211yesmaximal, characteristic, complemented
5C2×#5238C211yesmaximal, characteristic, complemented
6C2×#5238C211yesmaximal, characteristic, complemented
7#83922C2116yesmaximal, direct product factor
8C2×#5187C211yesmaximal, characteristic, complemented
9C2×#5185C211yesmaximal, characteristic, complemented
10C2×#5174C211yesmaximal, characteristic, complemented
11C2×#5176C211yesmaximal, characteristic, complemented
12C2×#5164C211yesmaximal, characteristic, complemented
13C2×#5156C211yesmaximal, characteristic, complemented
14C2×#5150C211yesmaximal, characteristic, complemented
15C2×#5115C211yesmaximal, characteristic, complemented
16C2×#5111C211yesmaximal, characteristic, complemented
17C2×#3268—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×C3×#41C2211yescharacteristic, complemented
20C22×#239C2211yescharacteristic
21C22×D3×D4C2211yescharacteristic
22C2×C3×#135—28no—
23C2×C3×#135C2218yescomplemented
24C22×C3×Q16C2211yescharacteristic, complemented
25C22×C3×SD16C2211yescharacteristic
26C22×C3×SD16C2211yescharacteristic, complemented
27C22×C3×D8C2211yescharacteristic
28C23×C3×C8C2211yescharacteristic, complemented
29#5834—24no—
30#5834C2218yescomplemented
31#5829—24no—
32#5829C2218yescomplemented
33C2×#947C2211yescharacteristic
34C2×#946C2211yescharacteristic
35C2×Q8×Dic3C2211yescharacteristic, complemented
36C22×#215C2211yescharacteristic
37C22×#215C2211yescharacteristic, complemented
38C2×#940—21no—
39C2×#940C2211yescharacteristic, complemented
40C2×#939—21no—
41C2×#938—21no—
42C2×#938C2211yescharacteristic
43C2×#937—21no—
44C2×D4×Dic3C2211yescharacteristic
45C22×#213C2211yescharacteristic
46C22×#213C2211yescharacteristic
47C2×#930—21no—
48C2×#930C2211yescharacteristic
49C2×#930C2211yescharacteristic, complemented
50C2×#929—21no—
51C2×C4×#67—21no—
52C2×C4×#67C2211yescharacteristic
53C22×(C2×D3)⋊C4—21no—
54C2×#914—28no—
55C2×#914C2218yescomplemented
56C22×D24C2211yescharacteristic
57C22×ΓL(1,𝔽25)C2211yescharacteristic
58#5238C2218yescomplemented
59#5238C2218yescomplemented
60C2×#835C2211yescharacteristic, complemented
61C2×#835C2211yescharacteristic, complemented
62C2×#832C2211yescharacteristic
63C2×#832C2211yescharacteristic, complemented
64C2×#830C2211yescharacteristic, complemented
65#5187C2218yescomplemented
66#5185C2218yescomplemented
67#5176C2218yescomplemented
68#5174C2218yescomplemented
69#5164C2218yescomplemented
70#5156C2218yescomplemented
71#5150C2218yescomplemented
72#5115C2218yescomplemented
73C2×#821C2211yescharacteristic
74C2×#821C2211yescharacteristic, complemented
75#5111C2218yescomplemented
76C2×(C2×D3)⋊C8C2211yescharacteristic
77C2×#818C2211yescharacteristic, complemented
78C2×#815C2211yescharacteristic, complemented
79C2×Dic3⋊C8C2211yescharacteristic, complemented
80C22×AGL(1,ℤ/8)—31no—
81C22×#135D311yescharacteristic, complemented
82C2×#550—31no—
83C2×#546—31no—
84#3268—316no—
85C2×#496—31no—
86C2×#468—31no—
87C2×#466—31no—
88C2×#464—31no—
89C2×#459—31no—
90C2×#452—31no—
91C2×#449—31no—
92C2×#449—31no—
93C2×#447—31no—
94C2×#440—31no—
95C2×#435—31no—
96C24×D3—21no—
97C2×C3×#41—22no—
98C2×C3×#41—22no—
99C2×C3×#41—24no—
100C2×C3×#41—24no—
101C2×C3×#41—42no—
102C2×C3×#41—42no—
103C2×C3×#41C2314yes—
104C2×C3×#41C2314yescomplemented
105C22×C3×Q8C2311yescharacteristic
106C22×C3×Q8C2311yescharacteristic
107C22×C3×D4—21no—
108C22×C3×D4—21no—
109C22×C3×D4C2311yescharacteristic
110C22×C3×D4C2311yescharacteristic
111C23×C3×C4—21no—
112C23×C3×C4—21no—
113C23×C3×C4C2311yescharacteristic
114C22×#67—21no—
115C22×#67—21no—
116C22×#67—21no—
117C22×#67—21no—
118C22×#67—21no—
119C22×#67—21no—
120C22×#67D411yescharacteristic
121C23×Dic3—21no—
122C2×#239—22no—
123C2×#239—24no—
124C2×#239—42no—
125C2×#239C2314yes—
126C2×D3×D4—24no—
127C2×D3×D4—22no—
128C2×D3×D4—42no—
129C2×D3×D4C2314yes—
130C22×D12—21no—
131C22×D12C2311yescharacteristic
132C22×D12C2311yescharacteristic
133C22×C4×D3—21no—
134C22×C4×D3C2311yescharacteristic
135C3×#135—232no—
136C2×C3×Q16—24no—
137C2×C3×Q16C2314yescomplemented
138C2×C3×SD16—24no—
139C2×C3×SD16D418yescomplemented
140C2×C3×SD16C2314yes—
141C2×C3×SD16C2314yescomplemented
142C2×C3×D8—24no—
143C2×C3×D8C2314yes—
144C22×C3×C8—24no—
145C22×C3×C8C2311yescharacteristic
146C22×C3×C8C2311yescharacteristic
147C22×C3×C8C2314yescomplemented
148C2×#217—21no—
149C2×#217—21no—
150C2×#217D411yescharacteristic
151#947—22no—
152#947C2314yes—
153#946—22no—
154#946C2314yes—
155Q8×Dic3—22no—
156Q8×Dic3C2314yescomplemented
157C2×#215—24no—
158C2×#215—42no—
159C2×#215C2314yes—
160C2×#215C2314yescomplemented
161#940—28no—
162#940—22no—
163#940C2314yescomplemented
164#939—28no—
165#938—22no—
166#938—28no—
167#938C2314yes—
168#937—28no—
169D4×Dic3—22no—
170D4×Dic3C2314yes—
171C2×#213—24no—
172C2×#213—42no—
173C2×#213C2314yes—
174C2×#213C2314yes—
175#930—22no—
176#930—22no—
177#930—28no—
178#930C2314yes—
179#930C2314yescomplemented
180#929—28no—
181C4×#67—28no—
182C4×#67D414yes—
183C4×#67C2314yes—
184C2×(C2×D3)⋊C4—21no—
185C2×(C2×D3)⋊C4—21no—
186C2×(C2×D3)⋊C4—21no—
187C2×(C2×D3)⋊C4—21no—
188C2×(C2×D3)⋊C4—21no—
189C2×(C2×D3)⋊C4—28no—
190C2×(C2×D3)⋊C4D411yescharacteristic
191C2×C4⋊Dic3—21no—
192C2×C4⋊Dic3C2311yescharacteristic
193C2×C4⋊Dic3C2311yescharacteristic
194C2×Dic3⋊C4—21no—
195C2×Dic3⋊C4D411yescharacteristic
196C2×C4×Dic3—21no—
197C2×C4×Dic3C2311yescharacteristic
198C22×C3⋊C8C2311yescharacteristic
199C22×C3⋊C8C2311yescharacteristic
200#914—232no—
201C2×D24—24no—
202C2×D24C2314yes—
203C2×ΓL(1,𝔽25)—24no—
204C2×ΓL(1,𝔽25)C2314yes—
205#835C2314yescomplemented
206#835C2314yescomplemented
207#832C2314yes—
208#832C2314yescomplemented
209#830C2314yescomplemented
210#821C2314yes—
211#821C2314yescomplemented
212(C2×D3)⋊C8C2314yes—
213#818C2314yescomplemented
214#815C2314yescomplemented
215Dic3⋊C8C2314yescomplemented
216C22×#41—31no—
217C22×#41C2×D311yescharacteristic
218C22×#41C2×D311yescharacteristic, complemented
219C23×D4—31no—
220C2×AGL(1,ℤ/8)—38no—
221C2×AGL(1,ℤ/8)—68no—
222C2×#135—28no—
223C2×#135C2×D318yescomplemented
224C22×Q16C2×D311yescharacteristic, complemented
225C22×SD16—31no—
226C22×SD16—31no—
227C22×SD16C2×D311yescharacteristic
228C22×SD16C2×D311yescharacteristic, complemented
229C22×D8—31no—
230C22×D8—31no—
231C22×D8—31no—
232C22×D8C2×D311yescharacteristic
233C22×M16—31no—
234C23×C8C2×D311yescharacteristic, complemented
235#550—38no—
236#550—64no—
237#546—38no—
238#546—64no—
239C2×#127—31no—
240C2×#127—61no—
241C2×#124—31no—
242C2×#123—61no—
243C2×C22⋊Q8—31no—
244C2×#121—31no—
245C2×#121—31no—
246C2×#121—31no—
247C2×#121—61no—
248C2×#121—61no—
249C2×#121—61no—
250C2×#120—61no—
251C2×C4×Q8—31no—
252C2×C4×D4—31no—
253C2×C4×D4—31no—
254C2×C4×D4—61no—
255C22×C22⋊C4—61no—
256#496—38no—
257#468—38no—
258#466—38no—
259#464—38no—
260#459—38no—
261#452—38no—
262#449—38no—
263#449—38no—
264#447—38no—
265#440—38no—
266#435—38no—
267C2×#107—31no—
268C2×C4⋊C8—31no—
269C2×#103—31no—
270C2×#103—31no—
271C2×#102—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×D3—21no—
283C23×D3—24no—
284C23×D3—44no—
285C23×D3—44no—
286C23×D3—82no—
287C23×D3C2×D411yescharacteristic
288C3×#41—28no—
289C3×#41—28no—
290C3×#41—44no—
291C3×#41—44no—
292C3×#41—48no—
293C3×#41—48no—
294C2×C3×Q8—21no—
295C2×C3×Q8—21no—
296C2×C3×Q8—22no—
297C2×C3×Q8—22no—
298C2×C3×Q8—22no—
299C2×C3×Q8C2×D414yes—
300C2×C3×Q8C2412yes—
301C2×C3×Q8C2412yes—
302C2×C3×D4—24no—
303C2×C3×D4—24no—
304C2×C3×D4—21no—
305C2×C3×D4—22no—
306C2×C3×D4—21no—
307C2×C3×D4—22no—
308C2×C3×D4—22no—
309C2×C3×D4—44no—
310C2×C3×D4—44no—
311C2×C3×D4C2×D414yes—
312C2×C3×D4C2412yes—
313C2×C3×D4C2412yes—
314C22×C3×C4—21no—
315C22×C3×C4—22no—
316C22×C3×C4—22no—
317C22×C3×C4—21no—
318C22×C3×C4—24no—
319C22×C3×C4—24no—
320C22×C3×C4—44no—
321C22×C3×C4—44no—
322C22×C3×C4C2×D411yescharacteristic
323C22×C3×C4C2×D412yes—
324C22×C3×C4C2412yes—
325C22×C3×C4C2411yescharacteristic
326C2×#67—24no—
327C2×#67—24no—
328C2×#67—24no—
329C2×#67—24no—
330C2×#67—24no—
331C2×#67—24no—
332C2×#67—42no—
333C2×#67—44no—
334C2×#67—44no—
335C2×#67—82no—
336C2×#67—82no—
337C2×#67—82no—
338C2×#67—82no—
339C2×#67C2×D414yes—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—24no—
343C22×Dic3—82no—
344C22×Dic3C2×D411yescharacteristic
345C22×Dic3C2×D411yescharacteristic
346C22×Dic3C2×D411yescharacteristic
347#239—28no—
348#239—44no—
349#239—48no—
350D3×D4—28no—
351D3×D4—44no—
352D3×D4—48no—
353C2×D12—22no—
354C2×D12—22no—
355C2×D12—22no—
356C2×D12—22no—
357C2×D12—24no—
358C2×D12—21no—
359C2×D12—21no—
360C2×D12—44no—
361C2×D12C2412yes—
362C2×D12C2412yes—
363C2×C4×D3—22no—
364C2×C4×D3—22no—
365C2×C4×D3—24no—
366C2×C4×D3—44no—
367C2×C4×D3C2×D412yes—
368C2×C4×D3C2412yes—
369C3×Q16—28no—
370C3×SD16—28no—
371C3×SD16C2×D4116yescomplemented
372C3×D8—28no—
373C2×C3×C8—22no—
374C2×C3×C8—28no—
375C2×C3×C8C2×D414yes—
376C2×C3×C8C2412yes—
377C2×C3×C8C2412yes—
378#217—24no—
379#217—24no—
380#217C2×D414yes—
381#215—28no—
382#215—44no—
383#213—28no—
384#213—44no—
385(C2×D3)⋊C4—24no—
386(C2×D3)⋊C4—24no—
387(C2×D3)⋊C4—24no—
388(C2×D3)⋊C4—24no—
389(C2×D3)⋊C4—24no—
390(C2×D3)⋊C4C2×D414yes—
391C4⋊Dic3—21no—
392C4⋊Dic3—21no—
393C4⋊Dic3—24no—
394C4⋊Dic3C2412yes—
395C4⋊Dic3C2412yes—
396Dic3⋊C4—24no—
397Dic3⋊C4C2×D414yes—
398C4×Dic3—24no—
399C4×Dic3C2×D412yes—
400C4×Dic3C2412yes—
401C2×C3⋊C8—22no—
402C2×C3⋊C8—22no—
403C2×C3⋊C8C2412yes—
404C2×C3⋊C8C2412yes—
405D24—28no—
406ΓL(1,𝔽25)—28no—
407C25—61no—
408C2×#41—22no—
409C2×#41—22no—
410C2×#41—24no—
411C2×#41—24no—
412C2×#41—34no—
413C2×#41—42no—
414C2×#41—42no—
415C2×#41—62no—
416C2×#41—64no—
417C2×#41—122no—
418C2×#41C22×D314yes—
419C2×#41C22×D314yescomplemented
420C22×Q8C22×D311yescharacteristic
421C22×Q8C22×D311yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4—31no—
425C22×D4—34no—
426C22×D4—31no—
427C22×D4—31no—
428C22×D4—61no—
429C22×D4—62no—
430C22×D4—61no—
431C22×D4—61no—
432C22×D4—61no—
433C22×D4—64no—
434C22×D4—61no—
435C22×D4—61no—
436C22×D4—61no—
437C22×D4—122no—
438C22×D4C22×D311yescharacteristic
439C22×D4C22×D311yescharacteristic
440C23×C4—21no—
441C23×C4—21no—
442C23×C4—31no—
443C23×C4—61no—
444C23×C4—61no—
445C23×C4C22×D311yescharacteristic
446AGL(1,ℤ/8)—632no—
447#135—232no—
448C2×Q16—24no—
449C2×Q16C22×D314yescomplemented
450C2×SD16—24no—
451C2×SD16—34no—
452C2×SD16—34no—
453C2×SD16—64no—
454C2×SD16—122no—
455C2×SD16#6718yescomplemented
456C2×SD16C22×D314yes—
457C2×SD16C22×D314yescomplemented
458C2×D8—24no—
459C2×D8—34no—
460C2×D8—34no—
461C2×D8—34no—
462C2×D8—64no—
463C2×D8—64no—
464C2×D8—122no—
465C2×D8C22×D314yes—
466C2×M16—34no—
467C2×M16—64no—
468C22×C8—24no—
469C22×C8—31no—
470C22×C8—31no—
471C22×C8C22×D311yescharacteristic
472C22×C8C22×D311yescharacteristic
473C22×C8C22×D314yescomplemented
474#127—34no—
475#127—62no—
476#127—68no—
477#124—34no—
478#124—62no—
479#123—68no—
480C22⋊Q8—34no—
481C22⋊Q8—62no—
482#121—34no—
483#121—34no—
484#121—34no—
485#121—68no—
486#121—68no—
487#121—68no—
488#121—62no—
489#121—62no—
490#121—62no—
491#120—68no—
492C4×Q8—34no—
493C4×Q8—62no—
494C4×D4—34no—
495C4×D4—34no—
496C4×D4—34no—
497C4×D4—62no—
498C4×D4—68no—
499C2×C4⋊C4—31no—
500C2×C4⋊C4—31no—
501C2×C4⋊C4—31no—
502C2×C4⋊C4—61no—
503C2×C4⋊C4—61no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—31no—
506C2×C22⋊C4—68no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4—61no—
509C2×C22⋊C4—61no—
510C2×C22⋊C4—61no—
511C2×C22⋊C4—61no—
512C2×C22⋊C4—61no—
513C2×C22⋊C4—61no—
514C2×C42—31no—
515C2×C42—61no—
516#107—34no—
517C4⋊C8—34no—
518#103—34no—
519#103—34no—
520#102—34no—
521#102—34no—
522#102—34no—
523#102—34no—
524C22⋊C8—34no—
525C22⋊C8—34no—
526#97—34no—
527C23×C3—24no—
528C23×C3—22no—
529C23×C3—22no—
530C23×C3—22no—
531C23×C3—22no—
532C23×C3—22no—
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—48no—
546C22×D3—48no—
547C22×D3—42no—
548C22×D3—42no—
549C22×D3—42no—
550C22×D3—42no—
551C22×D3—42no—
552C22×D3—42no—
553C22×D3—84no—
554C22×D3—816no—
555C22×D3C22×D412yes—
556C3×Q8—24no—
557C3×Q8—22no—
558C3×Q8—22no—
559C3×Q8—22no—
560C3×Q8—42no—
561C3×Q8C22×D414yes—
562C3×D4—24no—
563C3×D4—22no—
564C3×D4—22no—
565C3×D4—22no—
566C3×D4—48no—
567C3×D4—48no—
568C3×D4—42no—
569C3×D4C22×D414yes—
570C2×C3×C4—24no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—24no—
574C2×C3×C4—22no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—48no—
578C2×C3×C4—48no—
579C2×C3×C4—42no—
580C2×C3×C4C22×D412yes—
581C2×C3×C4C22×D411yescharacteristic
582C2×C3×C4C22×D412yes—
583C2×C3×C4H(5,𝔽2)12yes—
584C2×C3×C4C2511yescharacteristic
585#67—44no—
586#67—48no—
587#67—48no—
588#67—84no—
589#67—84no—
590#67—84no—
591#67—84no—
592C2×Dic3—22no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—22no—
597C2×Dic3—42no—
598C2×Dic3—42no—
599C2×Dic3—84no—
600C2×Dic3C22×D412yes—
601C2×Dic3C22×D412yes—
602C2×Dic3C22×D412yes—
603D12—22no—
604D12—22no—
605D12—22no—
606D12—22no—
607D12—48no—
608D12—42no—
609D12—42no—
610C4×D3—24no—
611C4×D3—22no—
612C4×D3—22no—
613C4×D3—48no—
614C3×C8—22no—
615C3×C8C22×D414yes—
616C3⋊C8—22no—
617C3⋊C8—22no—
618C24—21no—
619C24—21no—
620C24—31no—
621C24—64no—
622C24—61no—
623C24—61no—
624C24—124no—
625C24—124no—
626C24—242no—
627C24D3×D411yescharacteristic
628#41—28no—
629#41—28no—
630#41—44no—
631#41—44no—
632#41—48no—
633#41—48no—
634#41—68no—
635#41—124no—
636#41—128no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8C2×#6714yes—
643C2×Q8C23×D312yes—
644C2×Q8C23×D312yes—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—34no—
653C2×D4—32no—
654C2×D4—32no—
655C2×D4—44no—
656C2×D4—44no—
657C2×D4—64no—
658C2×D4—64no—
659C2×D4—64no—
660C2×D4—64no—
661C2×D4—68no—
662C2×D4—64no—
663C2×D4—64no—
664C2×D4—64no—
665C2×D4—61no—
666C2×D4—61no—
667C2×D4—62no—
668C2×D4—62no—
669C2×D4—62no—
670C2×D4—62no—
671C2×D4—124no—
672C2×D4—124no—
673C2×D4—128no—
674C2×D4—122no—
675C2×D4—124no—
676C2×D4—124no—
677C2×D4—242no—
678C2×D4—242no—
679C2×D4—242no—
680C2×D4—242no—
681C2×D4C2×#6714yes—
682C2×D4C23×D312yes—
683C2×D4C23×D312yes—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—32no—
694C22×C4—32no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—64no—
698C22×C4—64no—
699C22×C4—62no—
700C22×C4—62no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—124no—
704C22×C4—242no—
705C22×C4D3×D412yes—
706C22×C4D3×D411yescharacteristic
707C22×C4C23×D312yes—
708C22×C4C23×D311yescharacteristic
709Q16—28no—
710SD16—28no—
711SD16—68no—
712SD16—124no—
713SD16C2×#67116yescomplemented
714D8—28no—
715D8—68no—
716D8—68no—
717D8—124no—
718M16—68no—
719C2×C8—22no—
720C2×C8—28no—
721C2×C8—32no—
722C2×C8—32no—
723C2×C8—62no—
724C2×C8—62no—
725C2×C8C2×#6714yes—
726C2×C8C23×D312yes—
727C2×C8C23×D312yes—
728C4⋊C4—34no—
729C4⋊C4—32no—
730C4⋊C4—32no—
731C4⋊C4—64no—
732C4⋊C4—64no—
733C4⋊C4—61no—
734C4⋊C4—61no—
735C22⋊C4—34no—
736C22⋊C4—34no—
737C22⋊C4—64no—
738C22⋊C4—64no—
739C22⋊C4—64no—
740C22⋊C4—64no—
741C22⋊C4—64no—
742C22⋊C4—64no—
743C22⋊C4—64no—
744C42—32no—
745C42—32no—
746C42—64no—
747C22×C3—24no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—48no—
752C22×C3—44no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—42no—
756C22×C3—42no—
757C22×C3—42no—
758C22×C3—84no—
759C22×C3D4212yes—
760C22×C3#57512yes—
761C22×C3#57612yes—
762C22×C3C23×D411yescharacteristic
763C2×D3—22no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3—44no—
767C2×D3—42no—
768C2×D3—42no—
769C2×D3—42no—
770C2×D3—42no—
771C2×D3—42no—
772C2×D3—42no—
773C2×D3—816no—
774C2×D3—84no—
775C2×D3—84no—
776C3×C4—24no—
777C3×C4—22no—
778C3×C4—42no—
779C3×C4D4212yes—
780C3×C4C23×D411yescharacteristic
781C3×C4C2×H(5,𝔽2)11yescharacteristic
782Dic3—22no—
783Dic3—22no—
784Dic3—22no—
785Dic3—42no—
786Dic3—42no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—24no—
792C23—22no—
793C23—32no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—128no—
805C23—128no—
806C23—122no—
807C23—122no—
808C23—122no—
809C23—122no—
810C23—122no—
811C23—122no—
812C23—244no—
813C23—2416no—
814C23C2×D3×D412yes—
815C23C2×D3×D411yescharacteristic
816Q8—22no—
817Q8—24no—
818Q8—22no—
819Q8—22no—
820Q8—42no—
821Q8C22×#6714yes—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—24no—
826D4—48no—
827D4—48no—
828D4—42no—
829D4—62no—
830D4—62no—
831D4—62no—
832D4—62no—
833D4—128no—
834D4—124no—
835D4—128no—
836D4—128no—
837D4—122no—
838D4—122no—
839D4—244no—
840D4—244no—
841D4—244no—
842D4—244no—
843D4C22×#6714yes—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—48no—
855C2×C4—48no—
856C2×C4—42no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—64no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—128no—
866C2×C4—122no—
867C2×C4—122no—
868C2×C4—244no—
869C2×C4C2×D3×D412yes—
870C2×C4C2×D3×D411yescharacteristic
871C2×C4#100412yes—
872C2×C4C22×#6712yes—
873C2×C4C24×D311yescharacteristic
874C8—22no—
875C8—62no—
876C8—62no—
877C8C22×#6714yes—
878C2×C3—44no—
879C2×C3—42no—
880C2×C3—82no—
881C2×C3#326814yescomplemented
882C2×C3C2×D4211yescharacteristic
883C2×C3C2×#57511yescharacteristic
884C2×C3C2×#57611yescharacteristic
885D3—42no—
886D3—82no—
887D3—82no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—24no—
892C22—42no—
893C22—42no—
894C22—44no—
895C22—48no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—62no—
900C22—62no—
901C22—62no—
902C22—84no—
903C22—124no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—122no—
909C22—122no—
910C22—2416no—
911C22—244no—
912C22—244no—
913C22#576812yes—
914C22#576912yes—
915C22D4×#6712yes—
916C22C22×D3×D411yescharacteristic
917C4—22no—
918C4—24no—
919C4—42no—
920C4—62no—
921C4—62no—
922C4—62no—
923C4—122no—
924C4—122no—
925C4D4×#6712yes—
926C4C2×#100411yescharacteristic
927C4C23×#6711yescharacteristic
928C3C2×#326811yescharacteristic, complemented, Sylow
929C2—42no—
930C2—44no—
931C2—82no—
932C2—122no—
933C2—242no—
934C2—242no—
935C2#8392214yesdirect product factor
936C2C2×#576811yescharacteristic
937C2C2×#576911yescharacteristic
938C2C2×D4×#6711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC22×C3×#135C2
socleC23×C3C22×D4
hypercenterC22×#135D3
hypocenterC3C2×#3268
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×#5829C2semidirect
4. C22×#914C2semidirect
5. C2×#5238C2semidirect
6. C2×#5238C2semidirect
7. #83922C2direct (N × H)
8. C2×#5187C2semidirect
9. C2×#5185C2semidirect
10. C2×#5174C2semidirect
11. C2×#5176C2semidirect
12. C2×#5164C2semidirect
13. C2×#5156C2semidirect
14. C2×#5150C2semidirect
15. C2×#5115C2semidirect
16. C2×#5111C2semidirect
19. C22×C3×#41C22semidirect
23. C2×C3×#135C22semidirect
24. C22×C3×Q16C22semidirect
26. C22×C3×SD16C22semidirect
28. C23×C3×C8C22semidirect
30. #5834C22semidirect
32. #5829C22semidirect
35. C2×Q8×Dic3C22semidirect
37. C22×#215C22semidirect
39. C2×#940C22semidirect
49. C2×#930C22semidirect
55. C2×#914C22semidirect
58. #5238C22semidirect
59. #5238C22semidirect
60. C2×#835C22semidirect
61. C2×#835C22semidirect
63. C2×#832C22semidirect
64. C2×#830C22semidirect
65. #5187C22semidirect
66. #5185C22semidirect
67. #5176C22semidirect
68. #5174C22semidirect
69. #5164C22semidirect
70. #5156C22semidirect
71. #5150C22semidirect
72. #5115C22semidirect
74. C2×#821C22semidirect
75. #5111C22semidirect
77. C2×#818C22semidirect
78. C2×#815C22semidirect
79. C2×Dic3⋊C8C22semidirect
81. C22×#135D3semidirect
104. C2×C3×#41C23semidirect
137. C2×C3×Q16C23semidirect
139. C2×C3×SD16D4semidirect
141. C2×C3×SD16C23semidirect
147. C22×C3×C8C23semidirect
156. Q8×Dic3C23semidirect
160. C2×#215C23semidirect
163. #940C23semidirect
179. #930C23semidirect
205. #835C23semidirect
206. #835C23semidirect
208. #832C23semidirect
209. #830C23semidirect
211. #821C23semidirect
213. #818C23semidirect
214. #815C23semidirect
215. Dic3⋊C8C23semidirect
218. C22×#41C2×D3semidirect
223. C2×#135C2×D3semidirect
224. C22×Q16C2×D3semidirect
228. C22×SD16C2×D3semidirect
234. C23×C8C2×D3semidirect
371. C3×SD16C2×D4semidirect
419. C2×#41C22×D3semidirect
449. C2×Q16C22×D3semidirect
455. C2×SD16#67semidirect
457. C2×SD16C22×D3semidirect
473. C22×C8C22×D3semidirect
713. SD16C2×#67semidirect
881. C2×C3#3268semidirect
928. C3C2×#3268semidirect
935. C2#83922direct (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×#58292
C22×#9142
C2×#52382
#839222
C2×#51872
C2×#51852
C2×#51742
C2×#51762
C2×#51642
C2×#51562
C2×#51502
C2×#51152
C2×#51112
C2×#32683