Finite Group Databasebeta

← #11664845

Subgroups — #11664845

Order 768.

1890 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#533C211yesmaximal, characteristic
2C2×#5728C211yesmaximal, characteristic
3C3×#3165C211yesmaximal, characteristic, complemented
4#83341C211yesmaximal, characteristic, complemented
5#83207C211yesmaximal, characteristic, complemented
6#81977C214yesmaximal, complemented
7#81973C214yesmaximal, complemented
8#81940C212yesmaximal, complemented
9#81938C212yesmaximal, complemented
10#81893C212yesmaximal, complemented
11#81891C212yesmaximal, complemented
12#79208C214yesmaximal
13#79204C214yesmaximal, complemented
14C4×D3×M16C211yesmaximal, characteristic
15#78506C211yesmaximal, characteristic, complemented
16#60663—31nomaximal, Sylow
17C3×#533C2211yescharacteristic
18C2×C3×C4⋊Q8C2211yescharacteristic
19C2×#946—21no—
20C2×Q8×Dic3—21no—
21C2×D3×M16C2212yes—
22#5728—21no—
23#5728—21no—
24#5728—21no—
25#5728—21no—
26#5728C2211yescharacteristic
27#5728C2211yescharacteristic
28#5728C2212yes—
29#5728C2212yes—
30#5728C2212yes—
31#5728C2212yes—
32D3×C4⋊Q8C2211yescharacteristic
33D3×C4⋊Q8C2211yescharacteristic
34#5688C2212yes—
35D3×#125C2212yes—
36D3×C22⋊Q8—21no—
37D3×C22⋊Q8—21no—
38#5622—21no—
39#5622—21no—
40#5578—21no—
41#5578—21no—
42C4×D3×Q8—21no—
43C4×D3×Q8—21no—
44D3×#117C2212yes—
45#5517C2212yes—
46C2×#897—21no—
47C2×#892C2212yes—
48C2×#890C2212yes—
49C2×#887—21no—
50C2×C42×D3C2211yescharacteristic
51#5470C2211yescharacteristic
52C2×#869C2211yescharacteristic
53C3×#501C2214yescomplemented
54C3×#500C2212yescomplemented
55C3×#498C2212yescomplemented
56C3×#428C2214yes—
57C3×C4×M16C2211yescharacteristic
58#5121C2214yes—
59Dic3×M16C2212yes—
60#5081C2214yescomplemented
61#5080C2212yescomplemented
62#5080C2212yescomplemented
63#5078C2212yescomplemented
64#5078C2212yescomplemented
65#5064C2214yescomplemented
66#4995C2214yes—
67#4964C2214yes—
68C4×#208C2211yescharacteristic
69#4881C2218yes—
70#4880C2218yes—
71#4878C2218yescomplemented
72#4876C2218yescomplemented
73#4861C2218yes—
74#4860C2218yes—
75#4858C2218yescomplemented
76#4856C2218yescomplemented
77#4707C2212yes—
78D3×#97C2212yes—
79#4702C2214yescomplemented
80C4×ΓL(1,𝔽25)C2212yes—
81C4×D3×C8C2212yes—
82#4682C2212yescomplemented
83#4680C2212yescomplemented
84C2×#533—31no—
85C2×#533—31no—
86#3166—34no—
87#3166—34no—
88#3165—32no—
89#3165—32no—
90#3165—31no—
91#3165—31no—
92#3165—31no—
93#3165D311yescharacteristic, complemented
94#3162—34no—
95#3160—32no—
96#3160—32no—
97#2911—34no—
98C2×C4×M16—31no—
99C22×C3×Q8—21no—
100C2×D3×Q8—21no—
101C2×D3×Q8—21no—
102C22×C4×D3D411yescharacteristic
103C22×C4×D3D411yescharacteristic
104C22×C4×D3C2311yescharacteristic
105C22×Dic6—21no—
106C2×C3×M16C2312yes—
107C3×C4⋊Q8—21no—
108C3×C4⋊Q8—21no—
109C3×C4⋊Q8C2311yescharacteristic
110C3×C4⋊Q8C2311yescharacteristic
111C3×C4⋊Q8C2312yes—
112C3×C4⋊Q8C2312yes—
113C3×#125C2312yes—
114C3×C22⋊Q8—21no—
115C3×C22⋊Q8—21no—
116C3×C4×Q8—21no—
117C3×C4×Q8—21no—
118C3×#117C2312yes—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4C2312yes—
121C2×C3×C42C2311yescharacteristic
122#946—22no—
123#946—22no—
124#946—22no—
125#946—22no—
126#946—21no—
127#946—21no—
128Q8×Dic3—22no—
129Q8×Dic3—22no—
130Q8×Dic3—22no—
131Q8×Dic3—22no—
132Q8×Dic3—21no—
133Q8×Dic3—21no—
134#944—21no—
135#944—21no—
136C2×(C2×D3)⋊C4—22no—
137#926C2312yes—
138C2×C4⋊Dic3—21no—
139C2×C4⋊Dic3—22no—
140C2×C4⋊Dic3C2312yes—
141#924—21no—
142#924—21no—
143C2×Dic3⋊C4—22no—
144C2×C4×Dic3—22no—
145C2×C4×Dic3D411yescharacteristic
146C2×C4×Dic3D411yescharacteristic
147C2×C4×Dic3C2311yescharacteristic
148C2×#208C2312yes—
149D3×M16Q8116yescomplemented
150C2×ΓL(1,𝔽25)C2314yes—
151C2×D3×C8C2314yes—
152#897—22no—
153#897—22no—
154#897—22no—
155#897—22no—
156#897—21no—
157#897—21no—
158#896—22no—
159#896—22no—
160#892—22no—
161#892—22no—
162#892C2312yes—
163#892C2314yes—
164#892C2314yes—
165#892C2312yes—
166D3×C4⋊C4—22no—
167D3×C4⋊C4—22no—
168D3×C4⋊C4—21no—
169D3×C4⋊C4—21no—
170D3×C4⋊C4C2312yes—
171D3×C4⋊C4C2312yes—
172#890—22no—
173#890—22no—
174#890C2314yes—
175#890C2312yes—
176#890C2314yes—
177#890C2312yes—
178#889—22no—
179#889—22no—
180#888—21no—
181#888—21no—
182#888C2312yes—
183#888C2312yes—
184#887—22no—
185#887—22no—
186#887—22no—
187#887—22no—
188#887—22no—
189#887—22no—
190#887—21no—
191#887—21no—
192D3×C22⋊C4—22no—
193#878—22no—
194#878—22no—
195#877—22no—
196#872—22no—
197C42×D3—22no—
198C42×D3D411yescharacteristic
199C42×D3D411yescharacteristic
200C42×D3D411yescharacteristic
201C42×D3D411yescharacteristic
202C42×D3C2311yescharacteristic
203C42×D3C2311yescharacteristic
204C42×D3C2311yescharacteristic
205C42×D3C2311yescharacteristic
206#870C2312yes—
207#869—21no—
208#869—21no—
209#869C2311yescharacteristic
210#869C2312yes—
211#869C2311yescharacteristic
212#869C2312yes—
213C4×Dic6—21no—
214C4×Dic6—21no—
215C4×Dic6—22no—
216C4×Dic6—22no—
217C3×#107C2318yes—
218C3×#106C2318yes—
219C3×#97C2312yes—
220C3×C4×C8C2312yes—
221#818C2318yes—
222#817C2318yes—
223#815C2314yes—
224C8×Dic3C2314yes—
225#808C2318yes—
226#808C2318yes—
227#807C2318yes—
228#807C2318yes—
229#803C2312yes—
230C4×C3⋊C8C2312yes—
231C22×M16—32no—
232#533—31no—
233#533—31no—
234#533—32no—
235#533—32no—
236#533—32no—
237#533—32no—
238#533—32no—
239#533—32no—
240#533—31no—
241#533—61no—
242#533—61no—
243#533—61no—
244#533—61no—
245#533—61no—
246#533—61no—
247#533—61no—
248#533—61no—
249#533C2×D311yescharacteristic
250C2×C4⋊Q8—31no—
251C2×C4⋊Q8—31no—
252C2×C4⋊Q8—31no—
253C2×C4⋊Q8C2×D311yescharacteristic
254C2×#125—32no—
255C2×#125—32no—
256C2×C22⋊Q8—61no—
257C2×C22⋊Q8—61no—
258C2×C22⋊Q8—61no—
259C2×C22⋊Q8—61no—
260C2×C4×Q8—61no—
261C2×C4×Q8—61no—
262C2×C4×Q8—61no—
263C2×C4×Q8—61no—
264C2×#117—32no—
265C2×#117—32no—
266C22×C42—31no—
267#501—34no—
268#501—34no—
269#501—38no—
270#501—38no—
271#501—34no—
272#501C2×D314yescomplemented
273#500—32no—
274#500—32no—
275#500—32no—
276#500C2×D312yescomplemented
277#499—38no—
278#499—38no—
279#498—32no—
280#498—32no—
281#498—32no—
282#498C2×D312yescomplemented
283#428—34no—
284#428—34no—
285#428—34no—
286#428—38no—
287#428—38no—
288#428C2×D314yes—
289#427—38no—
290#427—38no—
291C4×M16—32no—
292C4×M16—31no—
293C4×M16—32no—
294C4×M16—32no—
295C4×M16C2×D311yescharacteristic
296C2×#97—32no—
297C2×C4×C8—32no—
298C23×D3C2×D411yescharacteristic
299C2×C3×Q8—21no—
300C2×C3×Q8—21no—
301C2×C3×Q8—22no—
302C2×C3×Q8—22no—
303C2×C3×Q8—44no—
304C22×C3×C4—22no—
305C22×C3×C4C2×D411yescharacteristic
306C22×C3×C4C2×D411yescharacteristic
307C22×C3×C4C2411yescharacteristic
308C22×Dic3—22no—
309C22×Dic3C2×D411yescharacteristic
310C22×Dic3C2×D411yescharacteristic
311C22×Dic3C2×D411yescharacteristic
312D3×Q8—44no—
313D3×Q8—44no—
314C2×C4×D3—22no—
315C2×C4×D3—22no—
316C2×C4×D3—42no—
317C2×C4×D3—42no—
318C2×C4×D3C2×D411yescharacteristic
319C2×C4×D3C2×D411yescharacteristic
320C2×C4×D3C2×D411yescharacteristic
321C2×C4×D3C2×D411yescharacteristic
322C2×C4×D3C2×D411yescharacteristic
323C2×C4×D3C2×D411yescharacteristic
324C2×C4×D3C2×D411yescharacteristic
325C2×C4×D3C2×D411yescharacteristic
326C2×C4×D3C2×D411yescharacteristic
327C2×C4×D3C2×D411yescharacteristic
328C2×C4×D3C2×Q818yes—
329C2×C4×D3C2411yescharacteristic
330C2×C4×D3C2411yescharacteristic
331C2×Dic6—21no—
332C2×Dic6—21no—
333C2×Dic6—22no—
334C2×Dic6—22no—
335C2×Dic6—22no—
336C2×Dic6—22no—
337C2×Dic6—44no—
338C3×M16C2×Q818yescomplemented
339C2×C3×C8C2414yes—
340C3×C4⋊C4—22no—
341C3×C4⋊C4—22no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—21no—
344C3×C4⋊C4—22no—
345C3×C4⋊C4—22no—
346C3×C4⋊C4—22no—
347C3×C4⋊C4C2412yes—
348C3×C4⋊C4C2414yes—
349C3×C4⋊C4C2412yes—
350C3×C22⋊C4—22no—
351C3×C42—22no—
352C3×C42C2×D411yescharacteristic
353C3×C42C2×D411yescharacteristic
354C3×C42C2411yescharacteristic
355C3×C42C2411yescharacteristic
356#217—22no—
357(C2×D3)⋊C4—22no—
358(C2×D3)⋊C4—22no—
359(C2×D3)⋊C4—24no—
360(C2×D3)⋊C4—24no—
361C4⋊Dic3—21no—
362C4⋊Dic3—21no—
363C4⋊Dic3—22no—
364C4⋊Dic3—22no—
365C4⋊Dic3—22no—
366C4⋊Dic3—22no—
367C4⋊Dic3—22no—
368C4⋊Dic3—24no—
369C4⋊Dic3—24no—
370C4⋊Dic3C2412yes—
371C4⋊Dic3C2414yes—
372C4⋊Dic3C2412yes—
373Dic3⋊C4—22no—
374Dic3⋊C4—22no—
375Dic3⋊C4—22no—
376Dic3⋊C4—22no—
377Dic3⋊C4—22no—
378Dic3⋊C4—22no—
379Dic3⋊C4—22no—
380Dic3⋊C4—22no—
381Dic3⋊C4—24no—
382Dic3⋊C4—24no—
383C4×Dic3—22no—
384C4×Dic3—22no—
385C4×Dic3—22no—
386C4×Dic3—24no—
387C4×Dic3—24no—
388C4×Dic3C2×D411yescharacteristic
389C4×Dic3C2×D411yescharacteristic
390C4×Dic3C2×D411yescharacteristic
391C4×Dic3C2×D411yescharacteristic
392C4×Dic3C2×D411yescharacteristic
393C4×Dic3C2×D411yescharacteristic
394C4×Dic3C2×D411yescharacteristic
395C4×Dic3C2×D411yescharacteristic
396C4×Dic3C2×D411yescharacteristic
397C4×Dic3C2×D411yescharacteristic
398C4×Dic3C2411yescharacteristic
399C4×Dic3C2411yescharacteristic
400#208C2×Q818yescomplemented
401C2×C3⋊C8C2414yes—
402ΓL(1,𝔽25)C2×Q8116yescomplemented
403D3×C8C2×Q8116yescomplemented
404C22×Q8—21no—
405C22×Q8—61no—
406C22×Q8—61no—
407C22×Q8—61no—
408C23×C4—31no—
409C23×C4—31no—
410C23×C4—31no—
411C2×M16—32no—
412C2×M16—316no—
413C2×M16—34no—
414C2×M16C22×D312yes—
415C22×C8—34no—
416C4⋊Q8—21no—
417C4⋊Q8—21no—
418C4⋊Q8—32no—
419C4⋊Q8—32no—
420C4⋊Q8—31no—
421C4⋊Q8—31no—
422C4⋊Q8—32no—
423C4⋊Q8—32no—
424C4⋊Q8—61no—
425C4⋊Q8—61no—
426C4⋊Q8—61no—
427C4⋊Q8—61no—
428C4⋊Q8—61no—
429C4⋊Q8—61no—
430C4⋊Q8C22×D311yescharacteristic
431C4⋊Q8C22×D311yescharacteristic
432C4⋊Q8C22×D312yes—
433C4⋊Q8C22×D312yes—
434#125—32no—
435#125—34no—
436#125—32no—
437#125—34no—
438#125—32no—
439#125—62no—
440#125—62no—
441#125—62no—
442#125—62no—
443#125C22×D312yes—
444C22⋊Q8—21no—
445C22⋊Q8—21no—
446C22⋊Q8—62no—
447C22⋊Q8—62no—
448C22⋊Q8—62no—
449C22⋊Q8—62no—
450C22⋊Q8—62no—
451C22⋊Q8—62no—
452C22⋊Q8—62no—
453C22⋊Q8—62no—
454C22⋊Q8—61no—
455C22⋊Q8—61no—
456C22⋊Q8—62no—
457C22⋊Q8—61no—
458C22⋊Q8—61no—
459C22⋊Q8—62no—
460C22⋊Q8—62no—
461C22⋊Q8—62no—
462C22⋊Q8—61no—
463C22⋊Q8—61no—
464C4×Q8—21no—
465C4×Q8—21no—
466C4×Q8—62no—
467C4×Q8—62no—
468C4×Q8—62no—
469C4×Q8—62no—
470C4×Q8—62no—
471C4×Q8—62no—
472C4×Q8—61no—
473C4×Q8—61no—
474C4×Q8—62no—
475C4×Q8—62no—
476C4×Q8—61no—
477C4×Q8—61no—
478C4×Q8—62no—
479C4×Q8—62no—
480C4×Q8—62no—
481C4×Q8—62no—
482C4×Q8—61no—
483C4×Q8—61no—
484#117—32no—
485#117—32no—
486#117—34no—
487#117—32no—
488#117—34no—
489#117—62no—
490#117—62no—
491#117—62no—
492#117—62no—
493#117C22×D312yes—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—32no—
496C2×C4⋊C4—32no—
497C2×C4⋊C4—32no—
498C2×C4⋊C4—62no—
499C2×C4⋊C4—62no—
500C2×C4⋊C4—61no—
501C2×C4⋊C4—61no—
502C2×C4⋊C4—62no—
503C2×C4⋊C4—62no—
504C2×C4⋊C4—61no—
505C2×C4⋊C4C22×D312yes—
506C2×C22⋊C4—62no—
507C2×C22⋊C4—62no—
508C2×C42—31no—
509C2×C42—31no—
510C2×C42—31no—
511C2×C42—31no—
512C2×C42—31no—
513C2×C42—31no—
514C2×C42—31no—
515C2×C42—31no—
516C2×C42—31no—
517C2×C42—31no—
518C2×C42—31no—
519C2×C42—62no—
520C2×C42—62no—
521C2×C42C22×D311yescharacteristic
522#107—38no—
523#107—38no—
524#107—38no—
525#107C22×D318yes—
526#106—38no—
527#106—38no—
528#106—38no—
529#106C22×D318yes—
530#97—34no—
531#97—32no—
532#97C22×D312yes—
533C4×C8—34no—
534C4×C8—32no—
535C4×C8C22×D312yes—
536C23×C3C22×D411yescharacteristic
537C22×D3—41no—
538C22×D3—41no—
539C22×D3C4⋊Q814yes—
540C22×D3C22×D411yescharacteristic
541C22×D3C22×D411yescharacteristic
542C3×Q8—44no—
543C3×Q8—42no—
544C3×Q8—42no—
545C3×Q8—44no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—24no—
549C2×C3×C4—22no—
550C2×C3×C4—22no—
551C2×C3×C4—44no—
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4C22×D411yescharacteristic
554C2×C3×C4C22×D411yescharacteristic
555C2×C3×C4C22×D411yescharacteristic
556C2×C3×C4C22×D411yescharacteristic
557C2×C3×C4C22×Q814yes—
558C2×C3×C4C2511yescharacteristic
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—24no—
562C2×Dic3—41no—
563C2×Dic3—41no—
564C2×Dic3—44no—
565C2×Dic3C4⋊Q814yes—
566C2×Dic3C22×D411yescharacteristic
567C2×Dic3C22×D411yescharacteristic
568C2×Dic3C22×D411yescharacteristic
569C2×Dic3C22×D411yescharacteristic
570C2×Dic3C22×D411yescharacteristic
571C2×Dic3C22×D411yescharacteristic
572C4×D3—22no—
573C4×D3—22no—
574C4×D3—22no—
575C4×D3—22no—
576C4×D3—41no—
577C4×D3—41no—
578C4×D3—41no—
579C4×D3—41no—
580C4×D3—44no—
581C4×D3—44no—
582C4×D3C4⋊Q814yes—
583C4×D3C4⋊Q814yes—
584C4×D3C22×Q814yes—
585C4×D3C22×Q814yes—
586Dic6—44no—
587Dic6—44no—
588Dic6—44no—
589Dic6—44no—
590Dic6—42no—
591Dic6—42no—
592C3×C8C22×Q818yes—
593C3⋊C8C22×Q818yes—
594C24—31no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—22no—
598C2×Q8—22no—
599C2×Q8—44no—
600C2×Q8—62no—
601C2×Q8—62no—
602C2×Q8—62no—
603C2×Q8—61no—
604C2×Q8—62no—
605C2×Q8—61no—
606C2×Q8—124no—
607C2×Q8—124no—
608C2×Q8—124no—
609C22×C4—22no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—38no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—31no—
621C22×C4—31no—
622C22×C4—31no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—62no—
627C22×C4—62no—
628C22×C4—62no—
629C22×C4—122no—
630C22×C4—122no—
631C22×C4D3×D411yescharacteristic
632C22×C4D3×D411yescharacteristic
633C22×C4C23×D311yescharacteristic
634M16—38no—
635M16—316no—
636M16D3×Q818yescomplemented
637C2×C8—34no—
638C2×C8—316no—
639C2×C8C23×D314yes—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—22no—
647C4⋊C4—32no—
648C4⋊C4—34no—
649C4⋊C4—32no—
650C4⋊C4—62no—
651C4⋊C4—62no—
652C4⋊C4—62no—
653C4⋊C4—62no—
654C4⋊C4—64no—
655C4⋊C4—64no—
656C4⋊C4—62no—
657C4⋊C4—62no—
658C4⋊C4—64no—
659C4⋊C4—64no—
660C4⋊C4—62no—
661C4⋊C4—62no—
662C4⋊C4—62no—
663C4⋊C4—62no—
664C4⋊C4—62no—
665C4⋊C4—62no—
666C4⋊C4—61no—
667C4⋊C4—62no—
668C4⋊C4—61no—
669C4⋊C4C23×D312yes—
670C4⋊C4C23×D314yes—
671C4⋊C4C23×D312yes—
672C22⋊C4—22no—
673C22⋊C4—62no—
674C22⋊C4—62no—
675C22⋊C4—64no—
676C22⋊C4—64no—
677C22⋊C4—62no—
678C42—22no—
679C42—31no—
680C42—31no—
681C42—31no—
682C42—31no—
683C42—31no—
684C42—31no—
685C42—31no—
686C42—31no—
687C42—31no—
688C42—31no—
689C42—31no—
690C42—31no—
691C42—62no—
692C42—62no—
693C42—64no—
694C42—64no—
695C42—62no—
696C42D3×D411yescharacteristic
697C42D3×D411yescharacteristic
698C42C23×D311yescharacteristic
699C42C23×D311yescharacteristic
700C22×C3—21no—
701C22×C3—21no—
702C22×C3C2×C4⋊Q812yes—
703C22×C3C23×D411yescharacteristic
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—21no—
708C2×D3—44no—
709C2×D3C2×C4⋊Q812yes—
710C2×D3C2×C4⋊Q812yes—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—42no—
714C3×C4—42no—
715C3×C4—44no—
716C3×C4C2×C4⋊Q812yes—
717C3×C4#57512yes—
718C3×C4#57512yes—
719C3×C4C23×Q812yes—
720Dic3—21no—
721Dic3—21no—
722Dic3—21no—
723Dic3—21no—
724Dic3—42no—
725Dic3—42no—
726Dic3—44no—
727Dic3C2×C4⋊Q812yes—
728Dic3C2×C4⋊Q812yes—
729C23—31no—
730C23—31no—
731C23—34no—
732C23—121no—
733C23—121no—
734C23C2×D3×D411yescharacteristic
735Q8—44no—
736Q8—44no—
737Q8—42no—
738Q8—42no—
739Q8—124no—
740Q8—124no—
741Q8—124no—
742Q8—122no—
743Q8—124no—
744Q8—122no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—31no—
751C2×C4—31no—
752C2×C4—34no—
753C2×C4—34no—
754C2×C4—34no—
755C2×C4—34no—
756C2×C4—34no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—31no—
760C2×C4—31no—
761C2×C4—44no—
762C2×C4—62no—
763C2×C4—62no—
764C2×C4—62no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—64no—
768C2×C4—62no—
769C2×C4—121no—
770C2×C4—121no—
771C2×C4—121no—
772C2×C4—121no—
773C2×C4—124no—
774C2×C4—124no—
775C2×C4—121no—
776C2×C4—121no—
777C2×C4—124no—
778C2×C4C2×D3×D411yescharacteristic
779C2×C4C2×D3×D411yescharacteristic
780C2×C4C2×D3×D411yescharacteristic
781C2×C4C2×D3×D411yescharacteristic
782C2×C4C2×D3×D411yescharacteristic
783C2×C4C2×D3×Q814yes—
784C2×C4C24×D311yescharacteristic
785C8—38no—
786C8C2×D3×Q818yes—
787C2×C3—22no—
788C2×C3C22×C4⋊Q811yescharacteristic
789C2×C3C2×#57511yescharacteristic
790C2×C3C2×#57511yescharacteristic
791D3—22no—
792D3—22no—
793C22—21no—
794C22—21no—
795C22—32no—
796C22—32no—
797C22—61no—
798C22—61no—
799C22—61no—
800C22—61no—
801C22—124no—
802C22D3×C4⋊Q812yes—
803C22C22×D3×D411yescharacteristic
804C4—21no—
805C4—21no—
806C4—32no—
807C4—32no—
808C4—44no—
809C4—42no—
810C4—42no—
811C4—61no—
812C4—61no—
813C4—61no—
814C4—61no—
815C4—122no—
816C4—122no—
817C4—124no—
818C4D3×C4⋊Q812yes—
819C4#577312yes—
820C4#577712yes—
821C4C22×D3×Q812yes—
822C3#6066311yescharacteristic, complemented, Sylow
823C2—22no—
824C2—62no—
825C2—62no—
826C2C2×D3×C4⋊Q811yescharacteristic
827C2C2×#577311yescharacteristic
828C2C2×#577711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3165C2
socleC22×C3C23×D4
prime radicalC23×D3C2×D4
hypercenter#3165D3
hypocenterC3#60663
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
3. C3×#3165C2semidirect
4. #83341C2semidirect
5. #83207C2semidirect
6. #81977C2semidirect
7. #81973C2semidirect
8. #81940C2semidirect
9. #81938C2semidirect
10. #81893C2semidirect
11. #81891C2semidirect
13. #79204C2semidirect
15. #78506C2semidirect
53. C3×#501C22semidirect
54. C3×#500C22semidirect
55. C3×#498C22semidirect
60. #5081C22semidirect
61. #5080C22semidirect
62. #5080C22semidirect
63. #5078C22semidirect
64. #5078C22semidirect
65. #5064C22semidirect
71. #4878C22semidirect
72. #4876C22semidirect
75. #4858C22semidirect
76. #4856C22semidirect
79. #4702C22semidirect
82. #4682C22semidirect
83. #4680C22semidirect
93. #3165D3semidirect
149. D3×M16Q8semidirect
272. #501C2×D3semidirect
276. #500C2×D3semidirect
282. #498C2×D3semidirect
338. C3×M16C2×Q8semidirect
400. #208C2×Q8semidirect
402. ΓL(1,𝔽25)C2×Q8semidirect
403. D3×C8C2×Q8semidirect
636. M16D3×Q8semidirect
822. C3#60663semidirect

Maximal subgroups

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

subgroupindex
D3×#5332
C2×#57282
C3×#31652
#833412
#832072
#819772
#819732
#819402
#819382
#818932
#818912
#792082
#792042
C4×D3×M162
#785062
#606633