Finite Group Databasebeta

← #11675545

Subgroups — #11675545

Order 768.

1782 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3503C211yesmaximal, characteristic, complemented
2#86260C211yesmaximal, characteristic, complemented
3#83708C212yesmaximal, complemented
4#83707C212yesmaximal, complemented
5#83700C214yesmaximal, complemented
6#83644C212yesmaximal, complemented
7#83643C212yesmaximal, complemented
8#83563C214yesmaximal, complemented
9#83475C212yesmaximal, complemented
10#83471C212yesmaximal, complemented
11#83330C211yesmaximal, characteristic, complemented
12C2×#5091C211yesmaximal, characteristic, complemented
13#83199C211yesmaximal, characteristic, complemented
14#82572C212yesmaximal, complemented
15#82557C212yesmaximal, complemented
16C4×#951C211yesmaximal, characteristic, complemented
17#82525C211yesmaximal, characteristic
18#61348—31nomaximal, Sylow
19C3×Q82C2212yes—
20C3×#557C2212yes—
21C3×#554—22no—
22C3×#554C2212yes—
23C3×D4×Q8—22no—
24C3×D4×Q8C2212yes—
25C3×#544—22no—
26C3×#544C2212yes—
27C3×#533—21no—
28C3×#533C2211yescharacteristic
29C2×C3×C4⋊Q8—21no—
30C2×C3×C4⋊Q8C2211yescharacteristic
31C3×#520C2212yes—
32C3×C4×#41C2211yescharacteristic
33C2×#951C2211yescharacteristic
34C2×#950C2212yes—
35#5732—21no—
36#5730—21no—
37#5694—22no—
38#5645—22no—
39#5624—22no—
40#5585C2212yes—
41#5584C2214yes—
42#5570C2212yes—
43#5526C2212yes—
44#5523C2212yes—
45#5477C2211yescharacteristic
46C2×C4×Dic6C2211yescharacteristic
47#5232C2211yescharacteristic
48#5093C2214yes—
49#5093C2212yes—
50#5091C2214yes—
51#5091C2214yes—
52#5091C2212yes—
53#5091C2212yes—
54#5089C2214yes—
55#5089C2214yes—
56#5088C2212yes—
57#5087C2214yes—
58#5069C2214yes—
59#5068C2214yes—
60#5066C2214yes—
61#5063C2214yes—
62#5031C2211yescharacteristic
63#5031C2214yes—
64#5030C2212yes—
65C4×#216C2212yes—
66C4×#216C2214yes—
67#5028C2212yes—
68#5028C2214yes—
69#5027C2211yescharacteristic
70#5026C2214yes—
71#5024C2214yes—
72#5024C2212yes—
73Q8×C3⋊C8C2212yes—
74#5019C2211yescharacteristic
75#5019C2214yes—
76#5018C2212yes—
77#5018C2214yes—
78C4×#214C2212yes—
79#5016C2212yes—
80#5016C2214yes—
81#5015C2211yescharacteristic
82C4×#213C2214yes—
83#5004C2211yescharacteristic
84#5002C2212yes—
85#4999C2212yes—
86#4997C2212yes—
87#4995C2211yescharacteristic
88C2×#810C2212yes—
89#4966C2212yes—
90#4966C2212yes—
91C2×#807C2212yes—
92C2×C4⋊(C3⋊C8)C2211yescharacteristic
93C4×#208C2211yescharacteristic
94#3507—31no—
95#3503D311yescharacteristic, complemented
96#3377—34no—
97#3375—32no—
98#3372—32no—
99#3367—34no—
100#3363—32no—
101#3361—32no—
102#3141—31no—
103#3137—32no—
104#3083—32no—
105C2×#477—31no—
106#3046—32no—
107#3035—31no—
108#2962—31no—
109#2951—32no—
110C4×#137—31no—
111C2×C3×#41C2311yescharacteristic
112C22×C3×Q8—22no—
113C22×C3×Q8—21no—
114C2×#235C2312yes—
115C22×Dic6C2311yescharacteristic
116C3×C4⋊Q8—22no—
117C3×C4⋊Q8—22no—
118C3×C4⋊Q8—24no—
119C3×C4⋊Q8—22no—
120C3×C4⋊Q8—21no—
121C3×C4⋊Q8—21no—
122C3×C4⋊Q8D411yescharacteristic
123C3×C4⋊Q8D411yescharacteristic
124C3×C4⋊Q8C2314yes—
125C3×C4⋊Q8C2312yes—
126C3×C4⋊Q8C2312yes—
127C3×#125—22no—
128C3×#125—24no—
129C3×#125D412yes—
130C3×#125C2314yes—
131C3×C22⋊Q8—22no—
132C3×C22⋊Q8—22no—
133C3×C22⋊Q8—24no—
134C3×C22⋊Q8—24no—
135C3×C22⋊Q8—24no—
136C3×C22⋊Q8D412yes—
137C3×C22⋊Q8D412yes—
138C3×C4×Q8—22no—
139C3×C4×Q8—22no—
140C3×C4×Q8C2311yescharacteristic
141C3×C4×Q8C2314yes—
142C3×C4×Q8C2311yescharacteristic
143C3×C4×Q8C2312yes—
144C3×C4×Q8C2312yes—
145C3×C4×D4—21no—
146C3×C4×D4—21no—
147C3×C4×D4—24no—
148C3×C4×D4C2314yes—
149C3×C4×D4C2311yescharacteristic
150C3×C4×D4C2311yescharacteristic
151C3×#117—22no—
152C3×#117—21no—
153C3×#117C2311yescharacteristic
154C3×#117C2312yes—
155C2×C3×C4⋊C4—21no—
156C2×C3×C4⋊C4—22no—
157C2×C3×C4⋊C4—22no—
158C2×C3×C4⋊C4C2312yes—
159C2×C3×C42—21no—
160C2×C3×C42C2311yescharacteristic
161#951—24no—
162#950—28no—
163#947—22no—
164#946—24no—
165Q8×Dic3—22no—
166C2×#216C2312yes—
167C2×#216C2312yes—
168C2×#215C2312yes—
169C2×#214C2312yes—
170C2×#214C2312yes—
171C2×#213C2312yes—
172#930—21no—
173#930—21no—
174C2×C4⋊Dic3C2311yescharacteristic
175C2×Dic3⋊C4—21no—
176C2×C4×Dic3—21no—
177C2×#208C2311yescharacteristic
178C2×#208C2311yescharacteristic
179C22×C3⋊C8C2312yes—
180#898—24no—
181#898—24no—
182#897—22no—
183#897—22no—
184#894—24no—
185#893—22no—
186#892—22no—
187#892—24no—
188D3×C4⋊C4—22no—
189#890—24no—
190#890—22no—
191#886—24no—
192#67⋊C4—24no—
193#875C2312yes—
194#875C2314yes—
195#874C2311yescharacteristic
196C4×D12—21no—
197C4×D12—21no—
198C4×D12C2314yes—
199#869C2311yescharacteristic
200#869C2314yes—
201C4×Dic6—21no—
202C4×Dic6—21no—
203C4×Dic6C2312yes—
204C4×Dic6C2312yes—
205C4×Dic6C2314yes—
206#835C2312yes—
207#832C2312yes—
208#810C2314yes—
209#810C2314yes—
210#810C2314yes—
211#810C2314yes—
212#810C2312yes—
213#810C2312yes—
214#810C2312yes—
215#810C2312yes—
216#809C2314yes—
217#809C2314yes—
218#809C2312yes—
219#809C2312yes—
220#808C2312yes—
221#807C2314yes—
222#807C2314yes—
223#807C2312yes—
224C4⋊(C3⋊C8)C2311yescharacteristic
225C4⋊(C3⋊C8)C2312yes—
226C4⋊(C3⋊C8)C2311yescharacteristic
227C4⋊(C3⋊C8)C2314yes—
228C4⋊(C3⋊C8)C2314yes—
229#803C2312yes—
230#803C2314yes—
231C4×C3⋊C8C2312yes—
232C4×C3⋊C8C2314yes—
233C2×#137—31no—
234C2×#135—32no—
235#559—32no—
236Q82C2×D312yes—
237#557—32no—
238#557C2×D312yes—
239#556—34no—
240#556—61no—
241#554—22no—
242#554—61no—
243#554C2×D312yes—
244#552—62no—
245D4×Q8—22no—
246D4×Q8C2×D312yes—
247#544—22no—
248#544C2×D312yes—
249#539—62no—
250#536—32no—
251#533—21no—
252#533C2×D311yescharacteristic
253#532—31no—
254C2×C4⋊Q8—21no—
255C2×C4⋊Q8C2×D311yescharacteristic
256#529—62no—
257#520—32no—
258#520C2×D312yes—
259C4×#41C2×D311yescharacteristic
260C2×C4×Q8—31no—
261#491—34no—
262#489—34no—
263#489—34no—
264#488—34no—
265#487—34no—
266#487—32no—
267#486—32no—
268#479—34no—
269#478—34no—
270#477—32no—
271#477—34no—
272#477—32no—
273#477—34no—
274#474—34no—
275#464—34no—
276#464—32no—
277#463—34no—
278#463—32no—
279#462—31no—
280#462—34no—
281#461—34no—
282#461—31no—
283#460—31no—
284#459—31no—
285#446—34no—
286#446—32no—
287C8×Q8—32no—
288#441—32no—
289#440—34no—
290#440—32no—
291#440—34no—
292C4×Q16—32no—
293C4×Q16—34no—
294C4×SD16—32no—
295C4×D8—34no—
296#428—31no—
297C2×#107—32no—
298#424—32no—
299C2×C4⋊C8—31no—
300#419—31no—
301#417—31no—
302#417—32no—
303#417—32no—
304#416—32no—
305C2×#103—32no—
306#405—32no—
307C4×M16—31no—
308C3×#41—22no—
309C3×#41#4114yes—
310C2×C3×Q8—22no—
311C2×C3×Q8—24no—
312C2×C3×Q8—22no—
313C2×C3×Q8—82no—
314C2×C3×Q8—84no—
315C2×C3×Q8C2×D412yes—
316C2×C3×Q8C2×D412yes—
317C2×C3×Q8C2411yescharacteristic
318C2×C3×D4—21no—
319C2×C3×D4C2411yescharacteristic
320C22×C3×C4—21no—
321C22×C3×C4—22no—
322C22×C3×C4—21no—
323C22×C3×C4—21no—
324C22×C3×C4—24no—
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2×D411yescharacteristic
327C22×C3×C4C2411yescharacteristic
328C2×#67—22no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331#235—24no—
332#235—24no—
333C2×D12—21no—
334C2×D12—21no—
335C2×D12C2412yes—
336C2×C4×D3—22no—
337C2×C4×D3—24no—
338C2×Dic6—22no—
339C2×Dic6—22no—
340C2×Dic6—21no—
341C2×Dic6C2412yes—
342C2×Dic6C2412yes—
343C3×C4⋊C4—22no—
344C3×C4⋊C4—22no—
345C3×C4⋊C4—24no—
346C3×C4⋊C4—22no—
347C3×C4⋊C4—24no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—24no—
351C3×C4⋊C4—24no—
352C3×C4⋊C4C2×D412yes—
353C3×C4⋊C4C2×D414yes—
354C3×C4⋊C4C2×D412yes—
355C3×C4⋊C4C2×D412yes—
356C3×C4⋊C4C2×D414yes—
357C3×C4⋊C4C2×D412yes—
358C3×C4⋊C4C2414yes—
359C3×C4⋊C4C2411yescharacteristic
360C3×C4⋊C4C2411yescharacteristic
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—24no—
365C3×C22⋊C4C2×D414yes—
366C3×C42—21no—
367C3×C42—21no—
368C3×C42—21no—
369C3×C42—24no—
370C3×C42C2×D411yescharacteristic
371C3×C42C2×D411yescharacteristic
372C3×C42C2411yescharacteristic
373C3×C42C2414yes—
374C3×C42C2411yescharacteristic
375#216—24no—
376#216—24no—
377#215—24no—
378#214—24no—
379#214—24no—
380#213—24no—
381(C2×D3)⋊C4—22no—
382(C2×D3)⋊C4—22no—
383(C2×D3)⋊C4—24no—
384(C2×D3)⋊C4—24no—
385(C2×D3)⋊C4—24no—
386C4⋊Dic3—21no—
387C4⋊Dic3—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3—24no—
390C4⋊Dic3—24no—
391C4⋊Dic3C2412yes—
392Dic3⋊C4—22no—
393Dic3⋊C4—22no—
394Dic3⋊C4—24no—
395C4×Dic3—22no—
396C4×Dic3—22no—
397C4×Dic3—24no—
398#208—22no—
399#208—22no—
400C2×C3⋊C8—24no—
401C2×C3⋊C8C2412yes—
402C2×C3⋊C8C2412yes—
403C2×C3⋊C8C2412yes—
404C2×C3⋊C8C2412yes—
405C2×#41—32no—
406C2×#41C22×D311yescharacteristic
407C22×Q8—22no—
408C22×Q8—21no—
409C22×Q8—31no—
410#137—64no—
411#135—68no—
412C2×Q16—32no—
413C2×Q16—32no—
414C2×SD16—32no—
415C2×SD16—32no—
416C2×SD16—32no—
417C2×D8—32no—
418C2×M16—31no—
419C2×M16—31no—
420C22×C8—32no—
421C4⋊Q8—22no—
422C4⋊Q8—22no—
423C4⋊Q8—22no—
424C4⋊Q8—24no—
425C4⋊Q8—21no—
426C4⋊Q8—21no—
427C4⋊Q8—31no—
428C4⋊Q8—34no—
429C4⋊Q8#6711yescharacteristic
430C4⋊Q8#6711yescharacteristic
431C4⋊Q8C22×D312yes—
432C4⋊Q8C22×D312yes—
433C4⋊Q8C22×D314yes—
434#127—31no—
435#126—64no—
436#126—64no—
437#125—22no—
438#125—24no—
439#125—62no—
440#125—64no—
441#125#6712yes—
442#125C22×D314yes—
443#124—32no—
444#124—34no—
445#124—62no—
446#123—64no—
447#123—64no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—24no—
451C22⋊Q8—24no—
452C22⋊Q8—24no—
453C22⋊Q8—64no—
454C22⋊Q8—62no—
455C22⋊Q8—62no—
456C22⋊Q8#6712yes—
457C22⋊Q8#6712yes—
458#121—61no—
459#121—61no—
460C4×Q8—22no—
461C4×Q8—22no—
462C4×Q8—32no—
463C4×Q8—32no—
464C4×Q8—34no—
465C4×Q8—62no—
466C4×Q8—61no—
467C4×Q8—61no—
468C4×Q8C22×D311yescharacteristic
469C4×Q8C22×D311yescharacteristic
470C4×Q8C22×D314yes—
471C4×Q8C22×D312yes—
472C4×Q8C22×D312yes—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—24no—
476C4×D4—34no—
477C4×D4—62no—
478C4×D4—64no—
479C4×D4—61no—
480C4×D4—61no—
481C4×D4C22×D311yescharacteristic
482C4×D4C22×D311yescharacteristic
483C4×D4C22×D314yes—
484#117—22no—
485#117—21no—
486#117—62no—
487#117—64no—
488#117C22×D311yescharacteristic
489#117C22×D312yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—61no—
495C2×C4⋊C4—62no—
496C2×C4⋊C4C22×D312yes—
497C2×C42—21no—
498C2×C42—61no—
499C2×C42C22×D311yescharacteristic
500#107—34no—
501#107—34no—
502#107—32no—
503#106—32no—
504C4⋊C8—31no—
505C4⋊C8—31no—
506C4⋊C8—32no—
507C4⋊C8—34no—
508C4⋊C8—34no—
509#103—32no—
510#103—34no—
511#103—34no—
512#103—32no—
513#103—32no—
514#103—34no—
515#103—34no—
516#103—32no—
517#103—32no—
518#102—32no—
519#102—32no—
520#102—32no—
521#102—34no—
522#102—34no—
523#97—32no—
524#97—34no—
525C4×C8—32no—
526C4×C8—34no—
527C23×C3—21no—
528C23×C3C22×D411yescharacteristic
529C22×D3—22no—
530C3×Q8—24no—
531C3×Q8—21no—
532C3×Q8—42no—
533C3×Q8—44no—
534C3×Q8—84no—
535C3×Q8—82no—
536C3×Q8C2×#4112yes—
537C3×D4—24no—
538C3×D4—21no—
539C3×D4C2×#4112yes—
540C2×C3×C4—21no—
541C2×C3×C4—24no—
542C2×C3×C4—22no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—24no—
546C2×C3×C4—41no—
547C2×C3×C4—42no—
548C2×C3×C4—42no—
549C2×C3×C4—84no—
550C2×C3×C4—82no—
551C2×C3×C4C22×D411yescharacteristic
552C2×C3×C4C22×D414yes—
553C2×C3×C4C22×D411yescharacteristic
554C2×C3×C4C22×D411yescharacteristic
555C2×C3×C4C22×D414yes—
556C2×C3×C4C22×D411yescharacteristic
557C2×C3×C4C22×D411yescharacteristic
558C2×C3×C4C2×#4112yes—
559C2×C3×C42−1+412yes—
560C2×C3×C4C2511yescharacteristic
561#67—44no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—42no—
566C2×Dic3—81no—
567D12—22no—
568D12—22no—
569D12—42no—
570D12—81no—
571C4×D3—44no—
572C4×D3—84no—
573Dic6—22no—
574Dic6—22no—
575Dic6—22no—
576Dic6—22no—
577Dic6—42no—
578C3⋊C8—22no—
579C3⋊C8—22no—
580C3⋊C8—22no—
581C3⋊C8—22no—
582#41—22no—
583#41—64no—
584#41—64no—
585#41#23914yes—
586C2×Q8—22no—
587C2×Q8—24no—
588C2×Q8—22no—
589C2×Q8—32no—
590C2×Q8—32no—
591C2×Q8—61no—
592C2×Q8—62no—
593C2×Q8—62no—
594C2×Q8—82no—
595C2×Q8—84no—
596C2×Q8C2×#6712yes—
597C2×Q8C2×#6712yes—
598C2×Q8C23×D311yescharacteristic
599C2×D4—21no—
600C2×D4—32no—
601C2×D4—62no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4C23×D311yescharacteristic
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—62no—
613C22×C4—64no—
614C22×C4C2×#6711yescharacteristic
615C22×C4C2×#6711yescharacteristic
616C22×C4C23×D311yescharacteristic
617Q16—64no—
618Q16—64no—
619SD16—64no—
620SD16—64no—
621SD16—64no—
622D8—64no—
623M16—62no—
624M16—62no—
625C2×C8—32no—
626C2×C8—32no—
627C2×C8—32no—
628C2×C8—32no—
629C2×C8—64no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—24no—
633C4⋊C4—22no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—32no—
640C4⋊C4—61no—
641C4⋊C4—64no—
642C4⋊C4—62no—
643C4⋊C4—62no—
644C4⋊C4—64no—
645C4⋊C4—61no—
646C4⋊C4—61no—
647C4⋊C4—64no—
648C4⋊C4C2×#6712yes—
649C4⋊C4C2×#6712yes—
650C4⋊C4C2×#6712yes—
651C4⋊C4C2×#6714yes—
652C4⋊C4C2×#6712yes—
653C4⋊C4C2×#6714yes—
654C4⋊C4C23×D311yescharacteristic
655C4⋊C4C23×D314yes—
656C4⋊C4C23×D311yescharacteristic
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—24no—
661C22⋊C4—62no—
662C22⋊C4—64no—
663C22⋊C4—64no—
664C22⋊C4—62no—
665C22⋊C4—64no—
666C22⋊C4C2×#6714yes—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—24no—
671C42—62no—
672C42—62no—
673C42—64no—
674C42C2×#6711yescharacteristic
675C42C2×#6711yescharacteristic
676C42C23×D311yescharacteristic
677C42C23×D314yes—
678C42C23×D311yescharacteristic
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—22no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3#54812yes—
685C22×C3C23×D411yescharacteristic
686C2×D3—42no—
687C2×D3—42no—
688C2×D3—42no—
689C3×C4—24no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—22no—
693C3×C4—21no—
694C3×C4—24no—
695C3×C4—41no—
696C3×C4—44no—
697C3×C4—41no—
698C3×C4#54812yes—
699C3×C4#57812yes—
700C3×C4C22×#4111yescharacteristic
701C3×C4C2×2−1+411yescharacteristic
702Dic3—42no—
703Dic3—42no—
704Dic3—42no—
705C23—21no—
706C23—62no—
707C23C22×#6711yescharacteristic
708Q8—21no—
709Q8—24no—
710Q8—42no—
711Q8—44no—
712Q8—62no—
713Q8—62no—
714Q8—62no—
715Q8—62no—
716Q8—82no—
717Q8—84no—
718Q8—122no—
719Q8C2×#23912yes—
720D4—24no—
721D4—21no—
722D4—62no—
723D4—62no—
724D4—124no—
725D4—122no—
726D4—241no—
727D4C2×#23912yes—
728C2×C4—21no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—24no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—84no—
741C2×C4—82no—
742C2×C4—122no—
743C2×C4—124no—
744C2×C4—244no—
745C2×C4—241no—
746C2×C4C2×#23912yes—
747C2×C4#100712yes—
748C2×C4C22×#6714yes—
749C2×C4C22×#6711yescharacteristic
750C2×C4C22×#6711yescharacteristic
751C2×C4C22×#6711yescharacteristic
752C2×C4C22×#6714yes—
753C2×C4C22×#6711yescharacteristic
754C2×C4C22×#6711yescharacteristic
755C2×C4C24×D311yescharacteristic
756C8—62no—
757C8—62no—
758C8—62no—
759C8—62no—
760C2×C3—22no—
761C2×C3—42no—
762C2×C3C2×#54811yescharacteristic
763C2×C3C2×#57811yescharacteristic
764C2×C3#358511yescharacteristic
765D3—82no—
766C22—21no—
767C22—21no—
768C22—22no—
769C22—41no—
770C22—41no—
771C22—122no—
772C22—122no—
773C22—122no—
774C22#581712yes—
775C22C23×#6711yescharacteristic
776C4—22no—
777C4—21no—
778C4—21no—
779C4—24no—
780C4—21no—
781C4—24no—
782C4—41no—
783C4—44no—
784C4—41no—
785C4—122no—
786C4—122no—
787C4—122no—
788C4#581712yes—
789C4#583812yes—
790C4C22×#23911yescharacteristic
791C4C2×#100711yescharacteristic
792C3#6134811yescharacteristic, complemented, Sylow
793C2—22no—
794C2—42no—
795C2—242no—
796C2C2×#581711yescharacteristic
797C2#8727711yescharacteristic
798C2C2×#583811yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3503C2
socleC22×C3C23×D4
prime radical#82525C2
hypercenter#3503D3
hypocenterC3#61348
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #533 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. C3×#3503C2semidirect
2. #86260C2semidirect
3. #83708C2semidirect
4. #83707C2semidirect
5. #83700C2semidirect
6. #83644C2semidirect
7. #83643C2semidirect
8. #83563C2semidirect
9. #83475C2semidirect
10. #83471C2semidirect
11. #83330C2semidirect
12. C2×#5091C2semidirect
13. #83199C2semidirect
14. #82572C2semidirect
15. #82557C2semidirect
16. C4×#951C2semidirect
95. #3503D3semidirect
792. C3#61348semidirect

Maximal subgroups

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

subgroupindex
C3×#35032
#862602
#837082
#837072
#837002
#836442
#836432
#835632
#834752
#834712
#833302
C2×#50912
#831992
#825722
#825572
C4×#9512
#825252
#613483