Finite Group Databasebeta

← C2×#83547 #11670249

Subgroups — C2×#83547 #11670249

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
1C2×C3×#548C211yesmaximal, characteristic, complemented
2C22×#950C211yesmaximal, characteristic, complemented
3C22×#942C211yesmaximal, characteristic, complemented
4C2×#5553C211yesmaximal, characteristic, complemented
5C2×#5238C211yesmaximal, characteristic, complemented
6C2×#5227C211yesmaximal, characteristic, complemented
7#83547C2116yesmaximal, direct product factor
8C2×#5054C211yesmaximal, characteristic, complemented
9C2×#5058C211yesmaximal, characteristic, complemented
10C2×#5047C211yesmaximal, characteristic, complemented
11C2×#5048C211yesmaximal, characteristic, complemented
12C2×#5037C211yesmaximal, characteristic, complemented
13C2×#5039C211yesmaximal, characteristic, complemented
14C2×#5027C211yesmaximal, characteristic, complemented
15C2×#5030C211yesmaximal, characteristic, complemented
16C2×#5011C211yesmaximal, characteristic, complemented
17C2×#3271—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C22×#235C2211yescharacteristic
22C3×#548—24no—
23C3×#548C2218yescomplemented
24C2×C3×#124—21no—
25C2×C3×#124C2211yescharacteristic
26C2×C3×C22⋊Q8—21no—
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×#121—21no—
29C2×C3×#121C2211yescharacteristic
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4—21no—
32C2×C3×C4×D4C2211yescharacteristic
33C2×#950—28no—
34C2×#950C2218yescomplemented
35C22×#216C2211yescharacteristic
36C22×#216C2211yescharacteristic
37C2×#942—28no—
38C2×#942C2218yescomplemented
39C22×#215C2211yescharacteristic
40C22×#215C2211yescharacteristic
41C22×#215C2211yescharacteristic
42C22×#215C2211yescharacteristic
43C2×#940—21no—
44C22×#214C2211yescharacteristic
45C22×#213C2211yescharacteristic
46C22×#213C2211yescharacteristic
47C2×#930C2211yescharacteristic
48C2×#930C2211yescharacteristic
49C22×#208C2211yescharacteristic
50C23×C3⋊C8C2211yescharacteristic
51#5553—24no—
52#5553C2218yescomplemented
53C2×#893—21no—
54C2×#884—21no—
55C2×#884—21no—
56C2×#874C2211yescharacteristic
57C2×C4×Dic6C2211yescharacteristic
58#5238C2218yescomplemented
59#5227C2218yescomplemented
60C2×#835C2211yescharacteristic
61C2×#835C2211yescharacteristic
62C2×#832C2211yescharacteristic
63C2×#830C2211yescharacteristic
64C2×#830C2211yescharacteristic
65#5058C2218yescomplemented
66#5054C2218yescomplemented
67#5048C2218yescomplemented
68#5047C2218yescomplemented
69#5039C2218yescomplemented
70#5037C2218yescomplemented
71#5030C2218yescomplemented
72#5027C2218yescomplemented
73#5011C2218yescomplemented
74C2×#810C2211yescharacteristic
75C2×#809C2211yescharacteristic
76C2×#809C2211yescharacteristic
77C2×#808C2211yescharacteristic
78C2×C4⋊(C3⋊C8)C2211yescharacteristic
79C2×#803C2211yescharacteristic
80C22×#137—31no—
81C22×#135—31no—
82C2×#550—31no—
83C2×#548D311yescharacteristic, complemented
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—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×D4—21no—
108C22×C3×D4—21no—
109C22×C3×D4D411yescharacteristic
110C22×C3×D4C2311yescharacteristic
111C23×C3×C4—21no—
112C23×C3×C4—21no—
113C23×C3×C4C2311yescharacteristic
114C23×C3×C4C2311yescharacteristic
115C22×#67—21no—
116C22×#67—21no—
117C22×#67—21no—
118C22×#67—21no—
119C2×#235—22no—
120C2×#235—22no—
121C2×#235—24no—
122C2×#235—24no—
123C2×#235—42no—
124C2×#235—42no—
125C2×#235C2314yes—
126C2×#235C2314yes—
127C22×D12—21no—
128C22×D12—21no—
129C22×D12C2311yescharacteristic
130C22×D12C2311yescharacteristic
131C22×C4×D3—21no—
132C22×C4×D3—21no—
133C22×Dic6C2311yescharacteristic
134C3×#124—28no—
135C3×#124—22no—
136C3×#124C2314yes—
137C3×C22⋊Q8—22no—
138C3×C22⋊Q8—28no—
139C3×C22⋊Q8C2314yes—
140C3×#121—28no—
141C3×#121—22no—
142C3×#121C2314yes—
143C3×C4×Q8—22no—
144C3×C4×Q8C2314yes—
145C3×C4×D4—28no—
146C3×C4×D4D414yes—
147C3×C4×D4C2314yes—
148C2×C3×C4⋊C4—21no—
149C2×C3×C4⋊C4—21no—
150C2×C3×C4⋊C4D411yescharacteristic
151C2×C3×C4⋊C4C2311yescharacteristic
152C2×C3×C22⋊C4—21no—
153C2×C3×C22⋊C4—21no—
154C2×C3×C22⋊C4—21no—
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4D411yescharacteristic
157C2×C3×C22⋊C4D411yescharacteristic
158C2×C3×C42—21no—
159C2×C3×C42C2311yescharacteristic
160#950—232no—
161C2×#216—24no—
162C2×#216D418yescomplemented
163C2×#216C2314yes—
164C2×#216C2314yes—
165#942—232no—
166C2×#215—24no—
167C2×#215—24no—
168C2×#215—24no—
169C2×#215—42no—
170C2×#215C2314yes—
171C2×#215C2314yes—
172C2×#215C2314yes—
173C2×#215C2314yes—
174#940—28no—
175C2×#214—24no—
176C2×#214C2314yes—
177C2×#213—24no—
178C2×#213—42no—
179C2×#213C2314yes—
180C2×#213C2314yes—
181#930—22no—
182#930—22no—
183#930C2314yes—
184#930C2314yes—
185C2×(C2×D3)⋊C4—21no—
186C2×(C2×D3)⋊C4—21no—
187C2×C4⋊Dic3C2311yescharacteristic
188C2×Dic3⋊C4—21no—
189C2×C4×Dic3—21no—
190C2×#208—24no—
191C2×#208C2314yes—
192C22×C3⋊C8—24no—
193C22×C3⋊C8C2311yescharacteristic
194C22×C3⋊C8C2311yescharacteristic
195C22×C3⋊C8C2311yescharacteristic
196C22×C3⋊C8C2314yes—
197C22×C3⋊C8C2311yescharacteristic
198#893—28no—
199#884—28no—
200#884—28no—
201#874—22no—
202#874C2314yes—
203C4×Dic6—22no—
204C4×Dic6C2314yes—
205#835C2314yes—
206#835C2314yes—
207#832C2314yes—
208#830C2314yes—
209#830C2314yes—
210#810C2314yes—
211#809C2314yes—
212#809C2314yes—
213#808C2314yes—
214C4⋊(C3⋊C8)C2314yes—
215#803C2314yes—
216C22×#41—31no—
217C22×#41—31no—
218C22×#41C2×D311yescharacteristic
219C23×Q8C2×D311yescharacteristic
220C2×#137—38no—
221C2×#137—68no—
222C2×#135—38no—
223C2×#135—68no—
224C22×Q16—31no—
225C22×Q16—31no—
226C22×SD16—31no—
227C22×SD16—31no—
228C22×SD16—31no—
229C22×SD16—31no—
230C22×SD16—31no—
231C22×D8—31no—
232C22×D8—31no—
233C22×M16—31no—
234C23×C8—31no—
235#550—38no—
236#550—64no—
237#548—24no—
238#548C2×D318yescomplemented
239C2×#127—31no—
240C2×#127—61no—
241C2×#124—21no—
242C2×#124C2×D311yescharacteristic
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8C2×D311yescharacteristic
245C2×#121—21no—
246C2×#121—31no—
247C2×#121—31no—
248C2×#121—61no—
249C2×#121—61no—
250C2×#121C2×D311yescharacteristic
251C2×C4×Q8—31no—
252C2×C4×Q8C2×D311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—61no—
255C2×C4×D4C2×D311yescharacteristic
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×C3C2×D411yescharacteristic
280C24×C3C2×D411yescharacteristic
281C23×D3—21no—
282C23×D3—21no—
283C3×#41—28no—
284C3×#41—44no—
285C3×#41—48no—
286C2×C3×Q8—21no—
287C2×C3×Q8—24no—
288C2×C3×Q8—21no—
289C2×C3×Q8—22no—
290C2×C3×Q8—28no—
291C2×C3×Q8—22no—
292C2×C3×Q8—22no—
293C2×C3×Q8—44no—
294C2×C3×Q8—44no—
295C2×C3×Q8—48no—
296C2×C3×Q8C2×D414yes—
297C2×C3×Q8C2412yes—
298C2×C3×Q8C2412yes—
299C2×C3×D4—24no—
300C2×C3×D4—24no—
301C2×C3×D4—22no—
302C2×C3×D4—21no—
303C2×C3×D4—22no—
304C2×C3×D4—42no—
305C2×C3×D4—44no—
306C2×C3×D4—44no—
307C2×C3×D4C2×D414yes—
308C2×C3×D4C2412yes—
309C22×C3×C4—21no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—21no—
315C22×C3×C4—21no—
316C22×C3×C4—24no—
317C22×C3×C4—24no—
318C22×C3×C4—44no—
319C22×C3×C4—44no—
320C22×C3×C4C2×D411yescharacteristic
321C22×C3×C4C2×D411yescharacteristic
322C22×C3×C4C2×D411yescharacteristic
323C22×C3×C4C2×D411yescharacteristic
324C22×C3×C4C2×D412yes—
325C22×C3×C4C2×D412yes—
326C22×C3×C4C2412yes—
327C22×C3×C4C2412yes—
328C22×C3×C4C2411yescharacteristic
329C2×#67—24no—
330C2×#67—24no—
331C2×#67—24no—
332C2×#67—24no—
333C2×#67—44no—
334C2×#67—44no—
335C2×#67—82no—
336C2×#67—82no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339#235—28no—
340#235—28no—
341#235—44no—
342#235—44no—
343#235—48no—
344#235—48no—
345C2×D12—22no—
346C2×D12—22no—
347C2×D12—22no—
348C2×D12—22no—
349C2×D12—21no—
350C2×D12—21no—
351C2×D12—24no—
352C2×D12—24no—
353C2×D12—44no—
354C2×D12—82no—
355C2×D12C2412yes—
356C2×D12C2412yes—
357C2×C4×D3—24no—
358C2×C4×D3—24no—
359C2×C4×D3—44no—
360C2×C4×D3—44no—
361C2×Dic6—21no—
362C2×Dic6—22no—
363C2×Dic6C2×D414yes—
364C2×Dic6C2412yes—
365C3×C4⋊C4—24no—
366C3×C4⋊C4—24no—
367C3×C4⋊C4—21no—
368C3×C4⋊C4C2×D414yes—
369C3×C4⋊C4C2412yes—
370C3×C22⋊C4—24no—
371C3×C22⋊C4—24no—
372C3×C22⋊C4—24no—
373C3×C22⋊C4—24no—
374C3×C22⋊C4C2×D414yes—
375C3×C22⋊C4C2×D414yes—
376C3×C42—24no—
377C3×C42C2×D412yes—
378C3×C42C2412yes—
379#216—28no—
380#216C2×D4116yescomplemented
381#215—28no—
382#215—28no—
383#215—28no—
384#215—44no—
385#214—28no—
386#213—28no—
387#213—44no—
388(C2×D3)⋊C4—24no—
389(C2×D3)⋊C4—24no—
390C4⋊Dic3—21no—
391C4⋊Dic3C2412yes—
392Dic3⋊C4—24no—
393C4×Dic3—24no—
394#208—28no—
395C2×C3⋊C8—22no—
396C2×C3⋊C8—22no—
397C2×C3⋊C8—22no—
398C2×C3⋊C8—28no—
399C2×C3⋊C8C2×D414yes—
400C2×C3⋊C8C2412yes—
401C2×C3⋊C8C2412yes—
402C2×C3⋊C8C2412yes—
403C2×C3⋊C8C2412yes—
404C2×#41—22no—
405C2×#41—24no—
406C2×#41—34no—
407C2×#41—34no—
408C2×#41—42no—
409C2×#41—64no—
410C2×#41—64no—
411C2×#41—62no—
412C2×#41—62no—
413C2×#41—122no—
414C2×#41—122no—
415C2×#41C22×D314yes—
416C22×Q8—21no—
417C22×Q8—22no—
418C22×Q8—24no—
419C22×Q8—31no—
420C22×Q8—42no—
421C22×Q8C22×D311yescharacteristic
422C22×Q8C22×D314yes—
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×D4#6711yescharacteristic
435C22×D4C22×D311yescharacteristic
436C23×C4—21no—
437C23×C4—21no—
438C23×C4—61no—
439C23×C4—61no—
440C23×C4C22×D311yescharacteristic
441C23×C4C22×D311yescharacteristic
442#137—632no—
443#135—632no—
444C2×Q16—38no—
445C2×Q16—34no—
446C2×Q16—34no—
447C2×Q16—64no—
448C2×SD16—34no—
449C2×SD16—34no—
450C2×SD16—34no—
451C2×SD16—34no—
452C2×SD16—34no—
453C2×SD16—64no—
454C2×SD16—64no—
455C2×SD16—64no—
456C2×SD16—64no—
457C2×SD16—122no—
458C2×D8—34no—
459C2×D8—34no—
460C2×D8—64no—
461C2×D8—122no—
462C2×M16—34no—
463C2×M16—64no—
464C22×C8—31no—
465C22×C8—31no—
466C22×C8—34no—
467C22×C8—31no—
468C22×C8—31no—
469C22×C8—64no—
470#127—34no—
471#127—68no—
472#127—62no—
473#124—28no—
474#124—22no—
475#124C22×D314yes—
476C22⋊Q8—22no—
477C22⋊Q8—28no—
478C22⋊Q8C22×D314yes—
479#121—28no—
480#121—22no—
481#121—34no—
482#121—34no—
483#121—62no—
484#121—62no—
485#121—68no—
486#121—68no—
487#121C22×D314yes—
488C4×Q8—22no—
489C4×Q8—34no—
490C4×Q8—62no—
491C4×Q8C22×D314yes—
492C4×D4—28no—
493C4×D4—68no—
494C4×D4#6714yes—
495C4×D4C22×D314yes—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—31no—
499C2×C4⋊C4—61no—
500C2×C4⋊C4#6711yescharacteristic
501C2×C4⋊C4C22×D311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—61no—
507C2×C22⋊C4—61no—
508C2×C22⋊C4#6711yescharacteristic
509C2×C22⋊C4#6711yescharacteristic
510C2×C42—21no—
511C2×C42—61no—
512C2×C42C22×D311yescharacteristic
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—22no—
530C23×C3—22no—
531C23×C3—42no—
532C23×C3—42no—
533C23×C3—42no—
534C23×C3C22×D412yes—
535C23×C3C22×D412yes—
536C23×C3C22×D411yescharacteristic
537C22×D3—22no—
538C22×D3—22no—
539C22×D3—42no—
540C22×D3—42no—
541C22×D3—42no—
542C22×D3—42no—
543C22×D3—42no—
544C22×D3—42no—
545C3×Q8—24no—
546C3×Q8—22no—
547C3×Q8—22no—
548C3×Q8—22no—
549C3×Q8—48no—
550C3×Q8—42no—
551C3×Q8C22×D414yes—
552C3×D4—22no—
553C3×D4—22no—
554C3×D4—44no—
555C3×D4—48no—
556C3×D4—48no—
557C3×D4—42no—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—24no—
561C2×C3×C4—22no—
562C2×C3×C4—22no—
563C2×C3×C4—22no—
564C2×C3×C4—24no—
565C2×C3×C4—24no—
566C2×C3×C4—22no—
567C2×C3×C4—22no—
568C2×C3×C4—22no—
569C2×C3×C4—22no—
570C2×C3×C4—22no—
571C2×C3×C4—22no—
572C2×C3×C4—48no—
573C2×C3×C4—48no—
574C2×C3×C4—42no—
575C2×C3×C4—42no—
576C2×C3×C4C22×D412yes—
577C2×C3×C4C22×D412yes—
578C2×C3×C4C22×D412yes—
579C2×C3×C4C22×D412yes—
580C2×C3×C4C22×D412yes—
581C2×C3×C4C22×D411yescharacteristic
582C2×C3×C4H(5,𝔽2)12yes—
583C2×C3×C4C2511yescharacteristic
584#67—48no—
585#67—48no—
586#67—84no—
587#67—84no—
588C2×Dic3—24no—
589C2×Dic3—22no—
590C2×Dic3—22no—
591C2×Dic3—42no—
592D12—22no—
593D12—22no—
594D12—22no—
595D12—22no—
596D12—48no—
597D12—42no—
598D12—42no—
599D12—84no—
600C4×D3—48no—
601C4×D3—48no—
602Dic6—24no—
603Dic6—22no—
604Dic6C22×D414yes—
605C3⋊C8—22no—
606C3⋊C8—22no—
607C3⋊C8—22no—
608C3⋊C8C22×D414yes—
609C24—21no—
610C24—61no—
611C24—61no—
612C24C2×#6711yescharacteristic
613C24C2×#6711yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617#41—68no—
618#41—68no—
619#41—124no—
620#41—124no—
621#41—128no—
622#41—128no—
623C2×Q8—22no—
624C2×Q8—21no—
625C2×Q8—24no—
626C2×Q8—21no—
627C2×Q8—28no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—34no—
631C2×Q8—32no—
632C2×Q8—44no—
633C2×Q8—44no—
634C2×Q8—48no—
635C2×Q8—62no—
636C2×Q8—61no—
637C2×Q8D3×D414yes—
638C2×Q8C23×D312yes—
639C2×Q8C23×D312yes—
640C2×D4—24no—
641C2×D4—24no—
642C2×D4—22no—
643C2×D4—22no—
644C2×D4—21no—
645C2×D4—32no—
646C2×D4—32no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—64no—
651C2×D4—64no—
652C2×D4—64no—
653C2×D4—64no—
654C2×D4—62no—
655C2×D4—62no—
656C2×D4—62no—
657C2×D4—62no—
658C2×D4—64no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4—64no—
662C2×D4—124no—
663C2×D4—124no—
664C2×D4—124no—
665C2×D4—242no—
666C2×D4—242no—
667C2×D4—242no—
668C2×D4C2×#6714yes—
669C2×D4C23×D312yes—
670C22×C4—21no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—24no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—24no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—61no—
682C22×C4—61no—
683C22×C4—64no—
684C22×C4—64no—
685C22×C4—124no—
686C22×C4—124no—
687C22×C4C2×#6712yes—
688C22×C4C2×#6712yes—
689C22×C4C2×#6711yescharacteristic
690C22×C4C2×#6711yescharacteristic
691C22×C4C2×#6711yescharacteristic
692C22×C4C2×#6711yescharacteristic
693C22×C4C23×D312yes—
694C22×C4C23×D312yes—
695C22×C4C23×D311yescharacteristic
696Q16—316no—
697Q16—68no—
698SD16—68no—
699SD16—68no—
700SD16—68no—
701SD16—68no—
702SD16—124no—
703D8—68no—
704D8—124no—
705M16—68no—
706C2×C8—34no—
707C2×C8—32no—
708C2×C8—32no—
709C2×C8—32no—
710C2×C8—32no—
711C2×C8—68no—
712C2×C8—62no—
713C2×C8—62no—
714C2×C8—62no—
715C4⋊C4—24no—
716C4⋊C4—24no—
717C4⋊C4—21no—
718C4⋊C4—32no—
719C4⋊C4—61no—
720C4⋊C4—64no—
721C4⋊C4C2×#6714yes—
722C4⋊C4C23×D312yes—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—24no—
726C22⋊C4—24no—
727C22⋊C4—64no—
728C22⋊C4—64no—
729C22⋊C4C2×#6714yes—
730C22⋊C4C2×#6714yes—
731C42—24no—
732C42—64no—
733C42C2×#6712yes—
734C42C23×D312yes—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—44no—
742C22×C3—44no—
743C22×C3—42no—
744C22×C3—42no—
745C22×C3—42no—
746C22×C3—84no—
747C22×C3D4212yes—
748C22×C3#57512yes—
749C22×C3#57712yes—
750C22×C3C23×D411yescharacteristic
751C2×D3—42no—
752C2×D3—42no—
753C2×D3—42no—
754C2×D3—42no—
755C2×D3—42no—
756C2×D3—42no—
757C2×D3—84no—
758C2×D3—84no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—24no—
762C3×C4—22no—
763C3×C4—22no—
764C3×C4—42no—
765C3×C4—42no—
766C3×C4D4212yes—
767C3×C4C23×D411yescharacteristic
768C3×C4C2×H(5,𝔽2)11yescharacteristic
769Dic3—24no—
770Dic3—42no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—62no—
782C23—62no—
783C23—122no—
784C23—122no—
785C23—122no—
786C23—122no—
787C23—122no—
788C23—122no—
789C23C22×#6712yes—
790C23C22×#6712yes—
791C23C22×#6711yescharacteristic
792Q8—22no—
793Q8—24no—
794Q8—22no—
795Q8—22no—
796Q8—34no—
797Q8—48no—
798Q8—42no—
799Q8—62no—
800Q8—64no—
801Q8C2×D3×D414yes—
802D4—22no—
803D4—22no—
804D4—44no—
805D4—48no—
806D4—48no—
807D4—42no—
808D4—62no—
809D4—62no—
810D4—62no—
811D4—62no—
812D4—128no—
813D4—128no—
814D4—128no—
815D4—122no—
816D4—122no—
817D4—244no—
818D4—244no—
819D4—244no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—24no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—48no—
835C2×C4—48no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—62no—
839C2×C4—64no—
840C2×C4—62no—
841C2×C4—128no—
842C2×C4—128no—
843C2×C4—122no—
844C2×C4C2×D3×D412yes—
845C2×C4#100412yes—
846C2×C4C22×#6712yes—
847C2×C4C22×#6712yes—
848C2×C4C22×#6712yes—
849C2×C4C22×#6712yes—
850C2×C4C22×#6711yescharacteristic
851C2×C4C24×D311yescharacteristic
852C8—34no—
853C8—62no—
854C8—62no—
855C8—62no—
856C2×C3—42no—
857C2×C3—42no—
858C2×C3—82no—
859C2×C3#327114yescomplemented
860C2×C3C2×D4211yescharacteristic
861C2×C3C2×#57511yescharacteristic
862C2×C3C2×#57711yescharacteristic
863D3—82no—
864D3—82no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—44no—
872C22—44no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—84no—
877C22—122no—
878C22—122no—
879C22—122no—
880C22—122no—
881C22—122no—
882C22—122no—
883C22—244no—
884C22—244no—
885C22D4×#6712yes—
886C22#582212yes—
887C22#583712yes—
888C22C23×#6711yescharacteristic
889C4—22no—
890C4—22no—
891C4—24no—
892C4—22no—
893C4—22no—
894C4—42no—
895C4—42no—
896C4—64no—
897C4—122no—
898C4D4×#6712yes—
899C4C22×D3×D411yescharacteristic
900C4C2×#100411yescharacteristic
901C3C2×#327111yescharacteristic, complemented, Sylow
902C2—42no—
903C2—42no—
904C2—82no—
905C2—242no—
906C2—242no—
907C2#8354714yesdirect product factor
908C2C2×D4×#6711yescharacteristic
909C2C2×#582211yescharacteristic
910C2C2×#583711yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#548C2
socleC23×C3C22×D4
hypercenterC2×#548D3
hypocenterC3C2×#3271
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×C3×#548C2semidirect
2. C22×#950C2semidirect
3. C22×#942C2semidirect
4. C2×#5553C2semidirect
5. C2×#5238C2semidirect
6. C2×#5227C2semidirect
7. #83547C2direct (N × H)
8. C2×#5054C2semidirect
9. C2×#5058C2semidirect
10. C2×#5047C2semidirect
11. C2×#5048C2semidirect
12. C2×#5037C2semidirect
13. C2×#5039C2semidirect
14. C2×#5027C2semidirect
15. C2×#5030C2semidirect
16. C2×#5011C2semidirect
23. C3×#548C22semidirect
34. C2×#950C22semidirect
38. C2×#942C22semidirect
52. #5553C22semidirect
58. #5238C22semidirect
59. #5227C22semidirect
65. #5058C22semidirect
66. #5054C22semidirect
67. #5048C22semidirect
68. #5047C22semidirect
69. #5039C22semidirect
70. #5037C22semidirect
71. #5030C22semidirect
72. #5027C22semidirect
73. #5011C22semidirect
83. C2×#548D3semidirect
162. C2×#216D4semidirect
238. #548C2×D3semidirect
380. #216C2×D4semidirect
859. C2×C3#3271semidirect
901. C3C2×#3271semidirect
907. C2#83547direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5482
C22×#9502
C22×#9422
C2×#55532
C2×#52382
C2×#52272
#835472
C2×#50542
C2×#50582
C2×#50472
C2×#50482
C2×#50372
C2×#50392
C2×#50272
C2×#50302
C2×#50112
C2×#32713