Finite Group Databasebeta

← C2×#83456 #11664979

Subgroups — C2×#83456 #11664979

Order 768.

1970 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#542C211yesmaximal, characteristic, complemented
2C2×#5534C211yesmaximal, characteristic, complemented
3#83456C2116yesmaximal, direct product factor
4C2×#5080C211yesmaximal, characteristic, complemented
5C2×#5089C211yesmaximal, characteristic, complemented
6C2×#5059C211yesmaximal, characteristic, complemented
7C2×#5055C211yesmaximal, characteristic, complemented
8C2×#5052C211yesmaximal, characteristic, complemented
9C2×#5048C211yesmaximal, characteristic, complemented
10C2×#5039C211yesmaximal, characteristic
11C2×#5041C211yesmaximal, characteristic, complemented
12C2×#5030C211yesmaximal, characteristic, complemented
13C2×C4×#215C211yesmaximal, characteristic, complemented
14C2×C4×#214C211yesmaximal, characteristic, complemented
15C2×#5014C211yesmaximal, characteristic, complemented
16C2×#4997C211yesmaximal, characteristic, complemented
17C2×#3173—31nomaximal, Sylow
18C3×#542—24no—
19C3×#542C2218yescomplemented
20C2×C3×C4⋊Q8C2211yescharacteristic
21C2×C3×#126—21no—
22C2×C3×#124—21no—
23C2×C3×#124C2211yescharacteristic
24C2×C3×#123—21no—
25C2×C3×C22⋊Q8—21no—
26C2×C3×C22⋊Q8C2211yescharacteristic
27C2×C3×#121C2211yescharacteristic
28C2×C3×C4×Q8C2211yescharacteristic
29C2×C3×C4×D4C2211yescharacteristic
30C2×C3×#117C2211yescharacteristic
31C22×#216C2211yescharacteristic
32C22×#215C2211yescharacteristic
33C22×#214C2211yescharacteristic
34C22×#213C2211yescharacteristic
35C2×#930C2211yescharacteristic
36C2×#924C2211yescharacteristic
37C22×#208C2211yescharacteristic
38C23×C3⋊C8C2211yescharacteristic
39#5534—24no—
40#5534C2218yescomplemented
41C2×#898—21no—
42C2×#896—21no—
43C2×#885—21no—
44C2×#883—21no—
45C2×#875C2211yescharacteristic
46C2×C4×D12C2211yescharacteristic
47C2×#869C2211yescharacteristic
48C2×C4×Dic6C2211yescharacteristic
49C2×#835C2211yescharacteristic
50C2×#835C2211yescharacteristic
51C2×#832C2211yescharacteristic
52C2×#832C2211yescharacteristic
53#5089C2218yescomplemented
54#5080C2218yescomplemented
55#5059C2218yescomplemented
56#5055C2218yescomplemented
57#5052C2218yescomplemented
58#5048C2218yescomplemented
59#5041C2218yescomplemented
60#5039C2218yes—
61#5030C2218yescomplemented
62C4×#215C2218yescomplemented
63C4×#214C2218yescomplemented
64#5014C2218yescomplemented
65#4997C2218yescomplemented
66C2×#810C2211yescharacteristic
67C2×#810C2211yescharacteristic
68C2×#809C2211yescharacteristic
69C2×#809C2211yescharacteristic
70C2×#808C2211yescharacteristic
71C2×#808C2211yescharacteristic
72C2×#808C2211yescharacteristic
73C2×#808C2211yescharacteristic
74C2×#803C2211yescharacteristic
75C2×#803C2211yescharacteristic
76C2×C4×C3⋊C8C2211yescharacteristic
77C2×C4×C3⋊C8C2211yescharacteristic
78C2×#542—31no—
79C2×#542D311yescharacteristic, complemented
80#3173—316no—
81C2×#498—31no—
82C2×#495—31no—
83C2×#489—31no—
84C2×#489—31no—
85C2×#470—31no—
86C2×#469—31no—
87C2×#465—31no—
88C2×#465—31no—
89C2×#442—31no—
90C2×#441—31no—
91C2×C4×SD16—31no—
92C2×C4×SD16—31no—
93C2×#405—31no—
94C22×C3×Q8—21no—
95C22×C3×Q8C2311yescharacteristic
96C22×C3×D4—21no—
97C22×C3×D4C2311yescharacteristic
98C23×C3×C4—21no—
99C23×C3×C4C2311yescharacteristic
100C22×#67—21no—
101C22×D12C2311yescharacteristic
102C22×C4×D3—21no—
103C22×Dic6—21no—
104C22×Dic6C2311yescharacteristic
105C3×C4⋊Q8—22no—
106C3×C4⋊Q8C2314yes—
107C3×#126—28no—
108C3×#124—28no—
109C3×#124—22no—
110C3×#124C2314yes—
111C3×#123—28no—
112C3×C22⋊Q8—22no—
113C3×C22⋊Q8—28no—
114C3×C22⋊Q8C2314yes—
115C3×#121—22no—
116C3×#121C2314yes—
117C3×C4×Q8—22no—
118C3×C4×Q8C2314yes—
119C3×C4×D4—22no—
120C3×C4×D4C2314yes—
121C3×#117D414yes—
122C3×#117C2314yes—
123C2×C3×C4⋊C4—21no—
124C2×C3×C4⋊C4—21no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4D411yescharacteristic
127C2×C3×C4⋊C4D411yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—21no—
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4D411yescharacteristic
136C2×C3×C22⋊C4D411yescharacteristic
137C2×C3×C42—21no—
138C2×C3×C42C2311yescharacteristic
139C2×C3×C42C2311yescharacteristic
140C2×#217—21no—
141C2×#216—24no—
142C2×#216C2314yes—
143C2×#215—24no—
144C2×#215C2314yes—
145C2×#214—24no—
146C2×#214C2314yes—
147C2×#213—24no—
148C2×#213C2314yes—
149#930—22no—
150#930C2314yes—
151C2×(C2×D3)⋊C4—21no—
152C2×(C2×D3)⋊C4—21no—
153C2×(C2×D3)⋊C4—21no—
154C2×(C2×D3)⋊C4—21no—
155C2×C4⋊Dic3—21no—
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2311yescharacteristic
158#924—22no—
159#924C2314yes—
160C2×Dic3⋊C4—21no—
161C2×Dic3⋊C4—21no—
162C2×C4×Dic3—21no—
163C2×#208—24no—
164C2×#208C2314yes—
165C22×C3⋊C8—24no—
166C22×C3⋊C8C2311yescharacteristic
167C22×C3⋊C8C2311yescharacteristic
168C22×C3⋊C8C2314yes—
169C22×C3⋊C8C2311yescharacteristic
170C22×C3⋊C8C2311yescharacteristic
171#898—28no—
172#896—28no—
173#885—28no—
174#883—28no—
175#875—22no—
176#875C2314yes—
177C4×D12—22no—
178C4×D12C2314yes—
179#869—22no—
180#869C2314yes—
181C4×Dic6—22no—
182C4×Dic6C2314yes—
183#835C2314yes—
184#835C2314yes—
185#832C2314yes—
186#832C2314yes—
187#810C2314yes—
188#810C2314yes—
189#809C2314yes—
190#809C2314yes—
191#808C2314yes—
192#808C2314yes—
193#808C2314yes—
194#808C2314yes—
195#803C2314yes—
196#803C2314yes—
197C4×C3⋊C8C2314yes—
198C4×C3⋊C8C2314yes—
199C22×Q16—31no—
200C22×SD16—31no—
201C22×SD16—31no—
202C22×D8—31no—
203C22×M16—31no—
204C23×C8—31no—
205#542—24no—
206#542—38no—
207#542—64no—
208#542C2×D318yescomplemented
209C2×C4⋊Q8—31no—
210C2×C4⋊Q8C2×D311yescharacteristic
211C2×#126—21no—
212C2×#126—61no—
213C2×#124—21no—
214C2×#124—31no—
215C2×#124—61no—
216C2×#124C2×D311yescharacteristic
217C2×#123—21no—
218C2×#123—61no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—31no—
221C2×C22⋊Q8—61no—
222C2×C22⋊Q8C2×D311yescharacteristic
223C2×#121—31no—
224C2×#121C2×D311yescharacteristic
225C2×C4×Q8—31no—
226C2×C4×Q8C2×D311yescharacteristic
227C2×C4×D4—31no—
228C2×C4×D4C2×D311yescharacteristic
229C2×#117C2×D311yescharacteristic
230#498—38no—
231#495—38no—
232#489—38no—
233#489—38no—
234#470—38no—
235#469—38no—
236#465—38no—
237#465—38no—
238#442—38no—
239#441—38no—
240C4×SD16—38no—
241C4×SD16—38no—
242C2×#106—31no—
243C2×#106—31no—
244C2×#106—31no—
245C2×#106—31no—
246C2×#103—31no—
247C2×#103—31no—
248C2×#103—31no—
249C2×#103—31no—
250C2×#102—31no—
251C2×#102—31no—
252C2×#102—31no—
253C2×#102—31no—
254#405—38no—
255C2×#97—31no—
256C2×#97—31no—
257C2×C4×C8—31no—
258C2×C4×C8—31no—
259C24×C3—21no—
260C24×C3C2×D411yescharacteristic
261C23×D3—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—24no—
264C2×C3×Q8—22no—
265C2×C3×Q8—22no—
266C2×C3×Q8—82no—
267C2×C3×Q8C2412yes—
268C2×C3×D4—24no—
269C2×C3×D4—21no—
270C2×C3×D4—22no—
271C2×C3×D4—22no—
272C2×C3×D4—82no—
273C2×C3×D4C2412yes—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—24no—
280C22×C3×C4—82no—
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2×D411yescharacteristic
286C22×C3×C4C2×D411yescharacteristic
287C22×C3×C4C2412yes—
288C22×C3×C4C2411yescharacteristic
289C2×#67—24no—
290C2×#67—82no—
291C22×Dic3—21no—
292C22×Dic3—21no—
293C22×Dic3—21no—
294C2×D12—22no—
295C2×D12—22no—
296C2×D12—21no—
297C2×D12C2412yes—
298C2×C4×D3—24no—
299C2×C4×D3—82no—
300C2×Dic6—22no—
301C2×Dic6—22no—
302C2×Dic6—21no—
303C2×Dic6—24no—
304C2×Dic6—82no—
305C2×Dic6C2412yes—
306C3×C4⋊C4—24no—
307C3×C4⋊C4—24no—
308C3×C4⋊C4—24no—
309C3×C4⋊C4—21no—
310C3×C4⋊C4—21no—
311C3×C4⋊C4C2×D414yes—
312C3×C4⋊C4C2×D414yes—
313C3×C4⋊C4C2412yes—
314C3×C4⋊C4C2412yes—
315C3×C22⋊C4—24no—
316C3×C22⋊C4—24no—
317C3×C22⋊C4—24no—
318C3×C22⋊C4—24no—
319C3×C22⋊C4—24no—
320C3×C22⋊C4C2×D414yes—
321C3×C22⋊C4C2×D414yes—
322C3×C42—24no—
323C3×C42C2×D412yes—
324C3×C42C2×D412yes—
325C3×C42C2412yes—
326C3×C42C2412yes—
327#217—24no—
328#216—28no—
329#215—28no—
330#214—28no—
331#213—28no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336C4⋊Dic3—21no—
337C4⋊Dic3—21no—
338C4⋊Dic3—24no—
339C4⋊Dic3C2412yes—
340C4⋊Dic3C2412yes—
341Dic3⋊C4—24no—
342Dic3⋊C4—24no—
343C4×Dic3—24no—
344#208—28no—
345C2×C3⋊C8—22no—
346C2×C3⋊C8—22no—
347C2×C3⋊C8—28no—
348C2×C3⋊C8#4114yes—
349C2×C3⋊C8#4114yes—
350C2×C3⋊C8C2412yes—
351C2×C3⋊C8C2412yes—
352C2×C3⋊C8C2412yes—
353C2×C3⋊C8C2412yes—
354C22×Q8—21no—
355C22×Q8—31no—
356C22×Q8—61no—
357C22×Q8C22×D311yescharacteristic
358C22×D4—21no—
359C22×D4—31no—
360C22×D4—61no—
361C22×D4C22×D311yescharacteristic
362C23×C4—21no—
363C23×C4—61no—
364C23×C4C22×D311yescharacteristic
365C2×Q16—34no—
366C2×Q16—64no—
367C2×SD16—34no—
368C2×SD16—34no—
369C2×SD16—64no—
370C2×SD16—64no—
371C2×D8—34no—
372C2×D8—64no—
373C2×M16—34no—
374C2×M16—64no—
375C22×C8—31no—
376C22×C8—31no—
377C22×C8—31no—
378C22×C8—34no—
379C22×C8—31no—
380C22×C8—64no—
381C4⋊Q8—22no—
382C4⋊Q8—34no—
383C4⋊Q8—62no—
384C4⋊Q8C22×D314yes—
385#126—28no—
386#126—68no—
387#124—28no—
388#124—22no—
389#124—34no—
390#124—68no—
391#124—62no—
392#124C22×D314yes—
393#123—28no—
394#123—68no—
395C22⋊Q8—22no—
396C22⋊Q8—28no—
397C22⋊Q8—34no—
398C22⋊Q8—62no—
399C22⋊Q8—68no—
400C22⋊Q8C22×D314yes—
401#121—22no—
402#121—34no—
403#121—62no—
404#121C22×D314yes—
405C4×Q8—22no—
406C4×Q8—34no—
407C4×Q8—62no—
408C4×Q8C22×D314yes—
409C4×D4—22no—
410C4×D4—34no—
411C4×D4—62no—
412C4×D4C22×D314yes—
413#117#6714yes—
414#117C22×D314yes—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—31no—
420C2×C4⋊C4—61no—
421C2×C4⋊C4—61no—
422C2×C4⋊C4—61no—
423C2×C4⋊C4#6711yescharacteristic
424C2×C4⋊C4#6711yescharacteristic
425C2×C4⋊C4C22×D311yescharacteristic
426C2×C4⋊C4C22×D311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C22⋊C4—61no—
436C2×C22⋊C4—61no—
437C2×C22⋊C4#6711yescharacteristic
438C2×C22⋊C4#6711yescharacteristic
439C2×C42—21no—
440C2×C42—61no—
441C2×C42C22×D311yescharacteristic
442C2×C42C22×D311yescharacteristic
443#106—34no—
444#106—34no—
445#106—34no—
446#106—34no—
447#103—34no—
448#103—34no—
449#103—34no—
450#103—34no—
451#102—34no—
452#102—34no—
453#102—34no—
454#102—34no—
455#97—34no—
456#97—34no—
457C4×C8—34no—
458C4×C8—34no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—42no—
464C23×C3—42no—
465C23×C3—42no—
466C23×C3C22×D412yes—
467C23×C3C22×D411yescharacteristic
468C22×D3—22no—
469C22×D3—42no—
470C22×D3—42no—
471C22×D3—42no—
472C3×Q8—22no—
473C3×Q8—22no—
474C3×Q8—42no—
475C3×Q8—84no—
476C3×D4—22no—
477C3×D4—22no—
478C3×D4—42no—
479C3×D4—84no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—24no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—42no—
492C2×C3×C4—42no—
493C2×C3×C4—42no—
494C2×C3×C4—84no—
495C2×C3×C4C22×D412yes—
496C2×C3×C4C22×D412yes—
497C2×C3×C4C22×D412yes—
498C2×C3×C4C22×D412yes—
499C2×C3×C4C22×D412yes—
500C2×C3×C4C22×D411yescharacteristic
501C2×C3×C4C2×#4112yes—
502C2×C3×C4C2×#4112yes—
503C2×C3×C4C2511yescharacteristic
504#67—84no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—22no—
508C2×Dic3—42no—
509C2×Dic3—42no—
510C2×Dic3—42no—
511D12—22no—
512D12—22no—
513D12—42no—
514C4×D3—84no—
515Dic6—22no—
516Dic6—22no—
517Dic6—42no—
518Dic6—84no—
519C3⋊C8—22no—
520C3⋊C8—22no—
521C3⋊C8C2×#4114yes—
522C3⋊C8C2×#4114yes—
523C24—21no—
524C24—61no—
525C24C2×#6711yescharacteristic
526C2×Q8—21no—
527C2×Q8—24no—
528C2×Q8—22no—
529C2×Q8—22no—
530C2×Q8—32no—
531C2×Q8—61no—
532C2×Q8—64no—
533C2×Q8—62no—
534C2×Q8—62no—
535C2×Q8—82no—
536C2×Q8—242no—
537C2×Q8C23×D312yes—
538C2×D4—24no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—32no—
543C2×D4—64no—
544C2×D4—62no—
545C2×D4—62no—
546C2×D4—61no—
547C2×D4—82no—
548C2×D4—242no—
549C2×D4C23×D312yes—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—24no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—64no—
560C22×C4—82no—
561C22×C4—242no—
562C22×C4C2×#6712yes—
563C22×C4C2×#6711yescharacteristic
564C22×C4C2×#6711yescharacteristic
565C22×C4C2×#6711yescharacteristic
566C22×C4C2×#6711yescharacteristic
567C22×C4C2×#6711yescharacteristic
568C22×C4C23×D312yes—
569C22×C4C23×D311yescharacteristic
570Q16—68no—
571SD16—68no—
572SD16—68no—
573D8—68no—
574M16—68no—
575C2×C8—34no—
576C2×C8—34no—
577C2×C8—32no—
578C2×C8—32no—
579C2×C8—32no—
580C2×C8—32no—
581C2×C8—68no—
582C2×C8—62no—
583C2×C8—62no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—24no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—32no—
590C4⋊C4—32no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—64no—
594C4⋊C4—64no—
595C4⋊C4—64no—
596C4⋊C4C2×#6714yes—
597C4⋊C4C2×#6714yes—
598C4⋊C4C23×D312yes—
599C4⋊C4C23×D312yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C22⋊C4—24no—
605C22⋊C4—64no—
606C22⋊C4—64no—
607C22⋊C4—64no—
608C22⋊C4—64no—
609C22⋊C4—64no—
610C22⋊C4C2×#6714yes—
611C22⋊C4C2×#6714yes—
612C42—24no—
613C42—64no—
614C42C2×#6712yes—
615C42C2×#6712yes—
616C42C23×D312yes—
617C42C23×D312yes—
618C22×C3—22no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—44no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—42no—
625C22×C3—84no—
626C22×C3#53212yes—
627C22×C3#57712yes—
628C22×C3#57712yes—
629C22×C3C23×D411yescharacteristic
630C2×D3—42no—
631C2×D3—42no—
632C2×D3—42no—
633C2×D3—84no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—22no—
638C3×C4—22no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4—42no—
642C3×C4#53212yes—
643C3×C4C22×#4111yescharacteristic
644C3×C4C22×#4111yescharacteristic
645Dic3—42no—
646Dic3—42no—
647Dic3—42no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—62no—
656C23—122no—
657C23—122no—
658C23—122no—
659C23C22×#6712yes—
660C23C22×#6711yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—42no—
664Q8—62no—
665Q8—62no—
666Q8—84no—
667Q8—122no—
668Q8—244no—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—62no—
673D4—62no—
674D4—84no—
675D4—122no—
676D4—244no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—62no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—84no—
695C2×C4—122no—
696C2×C4—122no—
697C2×C4—122no—
698C2×C4—244no—
699C2×C4D3×#4112yes—
700C2×C4D3×#4112yes—
701C2×C4C22×#6712yes—
702C2×C4C22×#6712yes—
703C2×C4C22×#6712yes—
704C2×C4C22×#6712yes—
705C2×C4C22×#6712yes—
706C2×C4C22×#6711yescharacteristic
707C2×C4C24×D311yescharacteristic
708C8—34no—
709C8—34no—
710C8—62no—
711C8—62no—
712C2×C3—42no—
713C2×C3—82no—
714C2×C3#317314yescomplemented
715C2×C3C2×#53211yescharacteristic
716C2×C3C2×#57711yescharacteristic
717C2×C3C2×#57711yescharacteristic
718D3—82no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—44no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—84no—
727C22—122no—
728C22—122no—
729C22—122no—
730C22—244no—
731C22#583212yes—
732C22#583612yes—
733C22#583712yes—
734C22C23×#6711yescharacteristic
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—122no—
744C4—122no—
745C4—122no—
746C4#583212yes—
747C4C2×D3×#4111yescharacteristic
748C4C2×D3×#4111yescharacteristic
749C3C2×#317311yescharacteristic, complemented, Sylow
750C2—42no—
751C2—82no—
752C2—242no—
753C2#8345614yesdirect product factor
754C2C2×#583211yescharacteristic
755C2C2×#583611yescharacteristic
756C2C2×#583711yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×#542C2
socleC23×C3C22×D4
prime radicalC2×#5039C2
hypercenterC2×#542D3
hypocenterC3C2×#3173
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×C3×#542C2semidirect
2. C2×#5534C2semidirect
3. #83456C2direct (N × H)
4. C2×#5080C2semidirect
5. C2×#5089C2semidirect
6. C2×#5059C2semidirect
7. C2×#5055C2semidirect
8. C2×#5052C2semidirect
9. C2×#5048C2semidirect
11. C2×#5041C2semidirect
12. C2×#5030C2semidirect
13. C2×C4×#215C2semidirect
14. C2×C4×#214C2semidirect
15. C2×#5014C2semidirect
16. C2×#4997C2semidirect
19. C3×#542C22semidirect
40. #5534C22semidirect
53. #5089C22semidirect
54. #5080C22semidirect
55. #5059C22semidirect
56. #5055C22semidirect
57. #5052C22semidirect
58. #5048C22semidirect
59. #5041C22semidirect
61. #5030C22semidirect
62. C4×#215C22semidirect
63. C4×#214C22semidirect
64. #5014C22semidirect
65. #4997C22semidirect
79. C2×#542D3semidirect
208. #542C2×D3semidirect
714. C2×C3#3173semidirect
749. C3C2×#3173semidirect
753. C2#83456direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5422
C2×#55342
#834562
C2×#50802
C2×#50892
C2×#50592
C2×#50552
C2×#50522
C2×#50482
C2×#50392
C2×#50412
C2×#50302
C2×C4×#2152
C2×C4×#2142
C2×#50142
C2×#49972
C2×#31733