Finite Group Databasebeta

← #11675394

Subgroups — #11675394

Order 768.

1792 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3501C211yesmaximal, characteristic, complemented
2#86262C211yesmaximal, characteristic, complemented
3#83645C214yesmaximal, complemented
4#83644C214yesmaximal, complemented
5#83644C212yesmaximal, complemented
6#83637C212yesmaximal, complemented
7#83568C212yesmaximal, complemented
8#83563C212yesmaximal, complemented
9#83480C212yesmaximal, complemented
10#83471C212yesmaximal, complemented
11#83349C211yesmaximal, characteristic, complemented
12#83337C211yesmaximal, characteristic, complemented
13#83330C211yesmaximal, characteristic, complemented
14#82544C212yesmaximal
15#82543C212yesmaximal, complemented
16C2×#5019C211yesmaximal, characteristic, complemented
17C4×#932C211yesmaximal, characteristic
18#61340—31nomaximal, Sylow
19C3×#554—21no—
20C3×#554—22no—
21C3×#554C2212yes—
22C3×#554C2214yes—
23C3×D4×Q8—21no—
24C3×D4×Q8C2212yes—
25C3×#544C2212yes—
26C3×#543—22no—
27C3×#533C2211yescharacteristic
28C3×#533C2211yescharacteristic
29C2×C3×C22⋊Q8—22no—
30C3×#518C2212yes—
31C2×C3×C4×D4C2211yescharacteristic
32C22×#214C2212yes—
33C2×#932C2211yescharacteristic
34#5728—21no—
35#5728—21no—
36#5698—22no—
37#5642—22no—
38#5642—22no—
39#5584C2212yescomplemented
40#5584C2212yescomplemented
41#5570C2212yescomplemented
42#5570C2212yescomplemented
43#5526C2212yes—
44#5516C2212yes—
45C4×#235C2211yescharacteristic
46C2×#869C2211yescharacteristic
47#5215C2211yescharacteristic
48#5094C2214yescomplemented
49#5094C2211yescharacteristic, complemented
50#5093C2214yescomplemented
51#5093C2212yescomplemented
52#5093C2212yescomplemented
53#5091C2214yescomplemented
54#5091C2211yescharacteristic, complemented
55#5089C2214yescomplemented
56#5087C2211yescharacteristic, complemented
57#5084C2211yescharacteristic, complemented
58#5069C2214yescomplemented
59#5069C2214yescomplemented
60#5068C2214yescomplemented
61#5066C2212yescomplemented
62#5063C2214yescomplemented
63#5063C2214yescomplemented
64#5063C2212yescomplemented
65#5024C2212yescomplemented
66#5024C2214yescomplemented
67Q8×C3⋊C8C2212yescomplemented
68#5019C2212yes—
69#5019C2214yes—
70#5019C2214yes—
71#5019C2212yes—
72#5019C2214yes—
73#5018C2214yes—
74#5018C2214yes—
75#5018C2212yes—
76C4×#214C2214yes—
77C4×#214C2214yes—
78C4×#214C2212yes—
79#5016C2214yes—
80#5016C2214yes—
81#5014C2212yes—
82C4×#213C2212yes—
83#5004C2212yes—
84#5004C2212yes—
85#5002C2212yes—
86#4999C2212yes—
87#4998C2212yes—
88#4997C2212yes—
89C2×#810C2212yes—
90#4966C2211yescharacteristic
91#4964C2211yescharacteristic
92C2×C4⋊(C3⋊C8)C2211yescharacteristic
93C4×#208C2211yescharacteristic
94#3509—31no—
95#3501D311yescharacteristic, complemented
96#3376—34no—
97#3372—32no—
98#3372—34no—
99#3367—32no—
100#3360—32no—
101#3359—32no—
102#3139—31no—
103#3137—32no—
104#3082—32no—
105#3076—31no—
106#3042—32no—
107C2×#461—31no—
108#2962—31no—
109#2949—32no—
110C4×AGL(1,ℤ/8)—31no—
111C22×C3×Q8—22no—
112C22×C3×D4C2311yescharacteristic
113C23×C3×C4—21no—
114C2×#235C2311yescharacteristic
115C22×Dic6C2312yes—
116C3×C4⋊Q8—22no—
117C3×C4⋊Q8D411yescharacteristic
118C3×C4⋊Q8D411yescharacteristic
119C3×C4⋊Q8C2311yescharacteristic
120C3×C4⋊Q8C2311yescharacteristic
121C3×C4⋊Q8C2314yes—
122C3×#125—22no—
123C3×#125D412yes—
124C3×#125C2314yes—
125C3×#125C2312yes—
126C3×C22⋊Q8—22no—
127C3×C22⋊Q8—24no—
128C3×C22⋊Q8—21no—
129C3×C22⋊Q8—21no—
130C3×C22⋊Q8—22no—
131C3×C22⋊Q8—24no—
132C3×C22⋊Q8—24no—
133C3×C22⋊Q8—24no—
134C3×C22⋊Q8—24no—
135C3×C22⋊Q8—24no—
136C3×C22⋊Q8D412yes—
137C3×C22⋊Q8D412yes—
138C3×C4×Q8—21no—
139C3×C4×Q8—21no—
140C3×C4×Q8C2312yes—
141C3×C4×Q8C2312yes—
142C3×C4×D4—22no—
143C3×C4×D4—22no—
144C3×C4×D4—21no—
145C3×C4×D4—21no—
146C3×C4×D4C2312yes—
147C3×C4×D4C2312yes—
148C3×C4×D4C2314yes—
149C3×C4×D4C2314yes—
150C3×#117C2312yes—
151C3×#117C2312yes—
152C2×C3×C4⋊C4—24no—
153C2×C3×C4⋊C4—22no—
154C2×C3×C4⋊C4C2311yescharacteristic
155C2×C3×C22⋊C4—21no—
156C2×C3×C22⋊C4—24no—
157C2×C3×C42C2311yescharacteristic
158#946—22no—
159#946—22no—
160Q8×Dic3—22no—
161Q8×Dic3—22no—
162C2×#214—28no—
163C2×#214C2314yes—
164C2×#214C2314yes—
165C2×#214C2312yes—
166#932—24no—
167C2×#213C2312yes—
168C4×#67—21no—
169C4×#67—21no—
170#926C2311yescharacteristic
171C2×C4⋊Dic3—21no—
172C2×C4⋊Dic3—21no—
173C2×#208C2311yescharacteristic
174C2×#208C2311yescharacteristic
175C22×C3⋊C8C2312yes—
176#898—24no—
177#898—24no—
178#897—22no—
179#897—22no—
180#892—22no—
181#892—22no—
182#890—24no—
183#890—24no—
184#890—22no—
185#890—22no—
186#887—22no—
187#887—22no—
188#886—24no—
189#877—24no—
190#875C2314yes—
191C4×D12C2311yescharacteristic
192C4×D12C2311yescharacteristic
193#872—21no—
194C42×D3—21no—
195#869—21no—
196#869—21no—
197#869C2312yes—
198#869C2312yes—
199#869C2314yes—
200C4×Dic6C2311yescharacteristic
201C4×Dic6C2311yescharacteristic
202C4×Dic6C2314yes—
203C4×Dic6C2314yes—
204#832C2312yes—
205#832C2312yes—
206#810C2312yes—
207#810C2314yes—
208#810C2314yes—
209#810C2312yes—
210#810C2312yes—
211#810C2314yes—
212#810C2314yes—
213#810C2314yes—
214#810C2314yes—
215#809C2312yes—
216#809C2312yes—
217#809C2312yes—
218#808C2312yes—
219#808C2312yes—
220#808C2312yes—
221#807C2312yes—
222#807C2312yes—
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×AGL(1,ℤ/8)—31no—
234C22×SD16—32no—
235#557—32no—
236#557—32no—
237#556—32no—
238#556—32no—
239#554—21no—
240#554—22no—
241#554C2×D312yes—
242#554C2×D314yes—
243#552—62no—
244#552—62no—
245D4×Q8—21no—
246D4×Q8C2×D312yes—
247#544C2×D312yes—
248#543—22no—
249#541—62no—
250#536—32no—
251#533—61no—
252#533—61no—
253#533C2×D311yescharacteristic
254#533C2×D311yescharacteristic
255C2×C4⋊Q8—31no—
256C2×C22⋊Q8—22no—
257#519—32no—
258#518C2×D312yes—
259C4×#41—31no—
260C2×C4×D4C2×D311yescharacteristic
261#491—34no—
262#491—34no—
263#489—34no—
264#488—34no—
265#487—32no—
266#487—34no—
267#487—32no—
268#479—32no—
269#479—34no—
270#479—34no—
271#478—32no—
272#477—31no—
273#477—34no—
274#476—31no—
275#475—31no—
276#475—34no—
277#474—31no—
278#463—34no—
279#463—34no—
280#461—32no—
281#461—34no—
282#461—32no—
283#461—34no—
284#461—34no—
285#446—32no—
286#446—34no—
287C8×Q8—32no—
288#442—32no—
289#440—34no—
290#440—32no—
291#440—34no—
292C4×SD16—32no—
293C4×SD16—34no—
294C4×SD16—34no—
295C4×D8—32no—
296#428—31no—
297#427—32no—
298#424—32no—
299C2×C4⋊C8—31no—
300#419—32no—
301#419—32no—
302#418—31no—
303#417—31no—
304#416—32no—
305C2×#103—32no—
306#405—32no—
307C4×M16—31no—
308C24×C3—21no—
309C2×C3×Q8—21no—
310C2×C3×Q8—21no—
311C2×C3×Q8—24no—
312C2×C3×Q8—84no—
313C2×C3×Q8C2×D412yes—
314C2×C3×Q8C2×D412yes—
315C2×C3×D4—21no—
316C2×C3×D4—22no—
317C2×C3×D4#4114yes—
318C2×C3×D4C2412yes—
319C22×C3×C4—21no—
320C22×C3×C4—22no—
321C22×C3×C4—24no—
322C22×C3×C4—24no—
323C22×C3×C4—22no—
324C22×C3×C4—82no—
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2×D411yescharacteristic
327C22×C3×C4C2411yescharacteristic
328C2×#67—21no—
329C22×Dic3—22no—
330#235—22no—
331#235—22no—
332C2×D12C2411yescharacteristic
333C2×C4×D3—21no—
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×Dic6—24no—
337C2×Dic6—24no—
338C2×Dic6—22no—
339C2×Dic6C2411yescharacteristic
340C2×Dic6C2414yes—
341C3×C4⋊C4—22no—
342C3×C4⋊C4—21no—
343C3×C4⋊C4—24no—
344C3×C4⋊C4—24no—
345C3×C4⋊C4—24no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—22no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4C2×D412yes—
350C3×C4⋊C4C2×D412yes—
351C3×C4⋊C4C2×D412yes—
352C3×C4⋊C4C2×D412yes—
353C3×C4⋊C4C2×D414yes—
354C3×C4⋊C4C2×D414yes—
355C3×C4⋊C4C2412yes—
356C3×C4⋊C4C2412yes—
357C3×C4⋊C4C2412yes—
358C3×C22⋊C4—22no—
359C3×C22⋊C4—24no—
360C3×C22⋊C4—24no—
361C3×C22⋊C4—22no—
362C3×C22⋊C4—22no—
363C3×C22⋊C4C2×D414yes—
364C3×C42—22no—
365C3×C42C2×D411yescharacteristic
366C3×C42C2×D411yescharacteristic
367C3×C42C2411yescharacteristic
368C3×C42C2414yes—
369C3×C42C2411yescharacteristic
370#217—21no—
371#214—24no—
372#214—28no—
373#214—28no—
374#213—24no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379C4⋊Dic3—22no—
380C4⋊Dic3—22no—
381C4⋊Dic3—22no—
382C4⋊Dic3—22no—
383C4⋊Dic3—24no—
384C4⋊Dic3—24no—
385C4⋊Dic3C2411yescharacteristic
386C4⋊Dic3C2411yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—24no—
390Dic3⋊C4—24no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—24no—
394C4×Dic3—24no—
395C4×Dic3—21no—
396#208—22no—
397#208—22no—
398C2×C3⋊C8—24no—
399C2×C3⋊C8C2412yes—
400C2×C3⋊C8C2412yes—
401C2×C3⋊C8C2412yes—
402C2×C3⋊C8C2412yes—
403C2×#41—31no—
404C22×Q8—22no—
405C22×Q8—32no—
406C22×D4C22×D311yescharacteristic
407C23×C4—21no—
408AGL(1,ℤ/8)—64no—
409C2×SD16—34no—
410C2×SD16—34no—
411C2×SD16—32no—
412C2×SD16—68no—
413C2×D8—32no—
414C2×M16—31no—
415C2×M16—31no—
416C22×C8—32no—
417C4⋊Q8—22no—
418C4⋊Q8—32no—
419C4⋊Q8—32no—
420C4⋊Q8—34no—
421C4⋊Q8—61no—
422C4⋊Q8—61no—
423C4⋊Q8#6711yescharacteristic
424C4⋊Q8#6711yescharacteristic
425C4⋊Q8C22×D311yescharacteristic
426C4⋊Q8C22×D311yescharacteristic
427C4⋊Q8C22×D314yes—
428#126—64no—
429#126—64no—
430#125—22no—
431#125—62no—
432#125—62no—
433#125—64no—
434#125—64no—
435#125#6712yes—
436#125C22×D312yes—
437#125C22×D314yes—
438#124—34no—
439#123—64no—
440C22⋊Q8—22no—
441C22⋊Q8—24no—
442C22⋊Q8—21no—
443C22⋊Q8—21no—
444C22⋊Q8—22no—
445C22⋊Q8—24no—
446C22⋊Q8—24no—
447C22⋊Q8—24no—
448C22⋊Q8—24no—
449C22⋊Q8—24no—
450C22⋊Q8—62no—
451C22⋊Q8—62no—
452C22⋊Q8—62no—
453C22⋊Q8—62no—
454C22⋊Q8#6712yes—
455C22⋊Q8#6712yes—
456C4×Q8—21no—
457C4×Q8—21no—
458C4×Q8—31no—
459C4×Q8—31no—
460C4×Q8—34no—
461C4×Q8—34no—
462C4×Q8—62no—
463C4×Q8—62no—
464C4×Q8—62no—
465C4×Q8—62no—
466C4×Q8C22×D312yes—
467C4×Q8C22×D312yes—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—21no—
471C4×D4—21no—
472C4×D4—31no—
473C4×D4—31no—
474C4×D4—61no—
475C4×D4—61no—
476C4×D4C22×D312yes—
477C4×D4C22×D312yes—
478C4×D4C22×D314yes—
479C4×D4C22×D314yes—
480#117—31no—
481#117—62no—
482#117—62no—
483#117—64no—
484#117—61no—
485#117C22×D312yes—
486#117C22×D312yes—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—61no—
490C2×C4⋊C4—61no—
491C2×C4⋊C4C22×D311yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—24no—
494C2×C42—61no—
495C2×C42C22×D311yescharacteristic
496#107—32no—
497#107—32no—
498#107—32no—
499#106—32no—
500#106—32no—
501#106—32no—
502C4⋊C8—31no—
503C4⋊C8—31no—
504C4⋊C8—32no—
505C4⋊C8—34no—
506C4⋊C8—34no—
507#103—34no—
508#103—34no—
509#103—32no—
510#103—32no—
511#103—32no—
512#103—34no—
513#103—34no—
514#103—34no—
515#103—34no—
516#102—32no—
517#102—32no—
518#102—32no—
519#102—32no—
520#102—32no—
521#97—32no—
522#97—34no—
523C4×C8—32no—
524C4×C8—34no—
525C23×C3—22no—
526C23×C3—24no—
527C23×C3—81no—
528C23×C3—81no—
529C23×C3C22×D411yescharacteristic
530C22×D3—21no—
531C3×Q8—24no—
532C3×Q8—42no—
533C3×Q8—42no—
534C3×Q8—81no—
535C3×Q8—84no—
536C3×D4—24no—
537C3×D4—22no—
538C3×D4C2×#4114yes—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—41no—
544C2×C3×C4—44no—
545C2×C3×C4—84no—
546C2×C3×C4—82no—
547C2×C3×C4—84no—
548C2×C3×C4—81no—
549C2×C3×C4C22×D414yes—
550C2×C3×C4C22×D414yes—
551C2×C3×C4C22×D411yescharacteristic
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4C22×D411yescharacteristic
554C2×C3×C4C22×D411yescharacteristic
555C2×C3×C4C22×D411yescharacteristic
556C2×C3×C4C2×#4112yes—
557C2×C3×C42−1+412yes—
558C2×C3×C4C2511yescharacteristic
559#67—42no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—24no—
564C2×Dic3—44no—
565D12—21no—
566D12—21no—
567C4×D3—42no—
568C4×D3—42no—
569C4×D3—42no—
570Dic6—24no—
571Dic6—21no—
572Dic6—24no—
573Dic6—21no—
574Dic6—44no—
575C3⋊C8—22no—
576C3⋊C8—22no—
577C3⋊C8—22no—
578C3⋊C8—22no—
579C24—21no—
580#41—62no—
581#41—62no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—24no—
585C2×Q8—34no—
586C2×Q8—31no—
587C2×Q8—62no—
588C2×Q8—64no—
589C2×Q8—64no—
590C2×Q8—84no—
591C2×Q8C2×#6712yes—
592C2×Q8C2×#6712yes—
593C2×D4—22no—
594C2×D4—21no—
595C2×D4—31no—
596C2×D4—61no—
597C2×D4#23914yes—
598C2×D4C23×D312yes—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—22no—
604C22×C4—62no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—61no—
608C22×C4—82no—
609C22×C4C2×#6711yescharacteristic
610C22×C4C2×#6711yescharacteristic
611C22×C4C23×D311yescharacteristic
612SD16—68no—
613SD16—68no—
614SD16—64no—
615D8—64no—
616M16—62no—
617M16—62no—
618C2×C8—32no—
619C2×C8—32no—
620C2×C8—32no—
621C2×C8—32no—
622C2×C8—64no—
623C4⋊C4—22no—
624C4⋊C4—21no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—21no—
629C4⋊C4—22no—
630C4⋊C4—21no—
631C4⋊C4—31no—
632C4⋊C4—31no—
633C4⋊C4—62no—
634C4⋊C4—62no—
635C4⋊C4—62no—
636C4⋊C4—62no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—64no—
640C4⋊C4—64no—
641C4⋊C4—64no—
642C4⋊C4—64no—
643C4⋊C4C2×#6712yes—
644C4⋊C4C2×#6714yes—
645C4⋊C4C2×#6712yes—
646C4⋊C4C2×#6712yes—
647C4⋊C4C2×#6712yes—
648C4⋊C4C2×#6714yes—
649C4⋊C4C23×D312yes—
650C4⋊C4C23×D312yes—
651C4⋊C4C23×D312yes—
652C22⋊C4—22no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—61no—
658C22⋊C4—61no—
659C22⋊C4—61no—
660C22⋊C4—64no—
661C22⋊C4—64no—
662C22⋊C4C2×#6714yes—
663C42—22no—
664C42—61no—
665C42—61no—
666C42—61no—
667C42—64no—
668C42—64no—
669C42C2×#6711yescharacteristic
670C42C2×#6711yescharacteristic
671C42C23×D311yescharacteristic
672C42C23×D314yes—
673C42C23×D311yescharacteristic
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—24no—
677C22×C3—42no—
678C22×C3—42no—
679C22×C3—84no—
680C22×C3#54812yes—
681C22×C3C23×D411yescharacteristic
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—24no—
688C3×C4—21no—
689C3×C4—24no—
690C3×C4—42no—
691C3×C4—42no—
692C3×C4—42no—
693C3×C4#54812yes—
694C3×C4#57712yes—
695C3×C4C22×#4111yescharacteristic
696C3×C4C2×2−1+411yescharacteristic
697Dic3—41no—
698Dic3—44no—
699Dic3—41no—
700Dic3—41no—
701C23—22no—
702C23—24no—
703C23—61no—
704C23—81no—
705C23—81no—
706C23C22×#6711yescharacteristic
707Q8—24no—
708Q8—42no—
709Q8—42no—
710Q8—64no—
711Q8—61no—
712Q8—64no—
713Q8—61no—
714Q8—84no—
715Q8—81no—
716Q8—124no—
717D4—22no—
718D4—24no—
719D4—61no—
720D4—61no—
721D4—122no—
722D4C2×#23914yes—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—44no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—64no—
732C2×C4—61no—
733C2×C4—82no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4—81no—
737C2×C4—122no—
738C2×C4—124no—
739C2×C4—122no—
740C2×C4—122no—
741C2×C4C2×#23912yes—
742C2×C4#100712yes—
743C2×C4C22×#6711yescharacteristic
744C2×C4C22×#6714yes—
745C2×C4C22×#6714yes—
746C2×C4C22×#6711yescharacteristic
747C2×C4C22×#6711yescharacteristic
748C2×C4C22×#6711yescharacteristic
749C2×C4C22×#6711yescharacteristic
750C2×C4C24×D311yescharacteristic
751C8—62no—
752C8—62no—
753C8—62no—
754C8—62no—
755C2×C3—22no—
756C2×C3—44no—
757C2×C3C2×#54811yescharacteristic
758C2×C3C2×#57711yescharacteristic
759C2×C3#358611yescharacteristic
760D3—81no—
761C22—21no—
762C22—21no—
763C22—24no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22#581712yes—
771C22C23×#6711yescharacteristic
772C4—21no—
773C4—21no—
774C4—24no—
775C4—21no—
776C4—24no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—121no—
781C4—121no—
782C4—124no—
783C4—121no—
784C4#581712yes—
785C4#583612yes—
786C4C22×#23911yescharacteristic
787C4C2×#100711yescharacteristic
788C3#6134011yescharacteristic, complemented, Sylow
789C2—22no—
790C2—44no—
791C2—241no—
792C2C2×#581711yescharacteristic
793C2C2×#583611yescharacteristic
794C2#8729911yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3501C2
socleC22×C3C23×D4
prime radicalC2×#932C22
hypercenter#3501D3
hypocenterC3#61340
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #533 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. C3×#3501C2semidirect
2. #86262C2semidirect
3. #83645C2semidirect
4. #83644C2semidirect
5. #83644C2semidirect
6. #83637C2semidirect
7. #83568C2semidirect
8. #83563C2semidirect
9. #83480C2semidirect
10. #83471C2semidirect
11. #83349C2semidirect
12. #83337C2semidirect
13. #83330C2semidirect
15. #82543C2semidirect
16. C2×#5019C2semidirect
39. #5584C22semidirect
40. #5584C22semidirect
41. #5570C22semidirect
42. #5570C22semidirect
48. #5094C22semidirect
49. #5094C22semidirect
50. #5093C22semidirect
51. #5093C22semidirect
52. #5093C22semidirect
53. #5091C22semidirect
54. #5091C22semidirect
55. #5089C22semidirect
56. #5087C22semidirect
57. #5084C22semidirect
58. #5069C22semidirect
59. #5069C22semidirect
60. #5068C22semidirect
61. #5066C22semidirect
62. #5063C22semidirect
63. #5063C22semidirect
64. #5063C22semidirect
65. #5024C22semidirect
66. #5024C22semidirect
67. Q8×C3⋊C8C22semidirect
95. #3501D3semidirect
788. C3#61340semidirect

Maximal subgroups

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

subgroupindex
C3×#35012
#862622
#836452
#836442
#836372
#835682
#835632
#834802
#834712
#833492
#833372
#833302
#825442
#825432
C2×#50192
C4×#9322
#613403