Finite Group Databasebeta

← #11675155

Subgroups — #11675155

Order 768.

1806 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3501C211yesmaximal, characteristic, complemented
2#86260C211yesmaximal, characteristic, complemented
3#83645C214yesmaximal, complemented
4#83644C212yesmaximal, complemented
5#83643C212yesmaximal, complemented
6#83637C214yesmaximal, complemented
7#83569C212yesmaximal, complemented
8#83568C212yesmaximal, complemented
9#83476C212yesmaximal, complemented
10#83471C212yesmaximal, complemented
11#83367C211yesmaximal, characteristic, complemented
12#83334C211yesmaximal, characteristic, complemented
13#83328C211yesmaximal, characteristic, complemented
14#82544C212yesmaximal, complemented
15#82537C212yesmaximal, complemented
16C2×C4×#214C211yesmaximal, characteristic, complemented
17#82307C211yesmaximal, characteristic
18#61326—31nomaximal, Sylow
19C3×#554—21no—
20C3×#554—22no—
21C3×#554C2214yes—
22C3×#554C2212yes—
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×#214C2211yescharacteristic
33C2×#932C2212yes—
34#5732—21no—
35#5730—21no—
36#5694—22no—
37#5645—22no—
38#5624—22no—
39#5585C2212yescomplemented
40#5584C2214yescomplemented
41#5570C2212yescomplemented
42#5526C2212yes—
43#5523C2212yes—
44#5477C2211yescharacteristic
45C2×C4×Dic6C2211yescharacteristic
46C2×#832C2211yescharacteristic
47#5094C2214yescomplemented
48#5094C2212yescomplemented
49#5093C2214yescomplemented
50#5093C2211yescharacteristic, complemented
51#5093C2211yescharacteristic, complemented
52#5091C2212yescomplemented
53#5089C2214yescomplemented
54#5088C2211yescharacteristic, complemented
55#5088C2211yescharacteristic, complemented
56#5084C2214yescomplemented
57#5069C2214yescomplemented
58#5068C2214yescomplemented
59#5068C2212yescomplemented
60#5068C2212yescomplemented
61#5066C2214yescomplemented
62#5063C2214yescomplemented
63#5063C2214yescomplemented
64#5024C2212yescomplemented
65#5024C2212yescomplemented
66Q8×C3⋊C8C2212yescomplemented
67Q8×C3⋊C8C2212yescomplemented
68#5019C2214yes—
69#5019C2214yes—
70#5019C2212yes—
71#5018C2214yes—
72C4×#214C2214yes—
73C4×#214C2212yes—
74C4×#214C2212yes—
75C4×#214C2212yes—
76C4×#214C2212yes—
77#5016C2214yes—
78#5016C2214yes—
79#5016C2214yes—
80#5015C2212yes—
81#5014C2214yes—
82C4×#213C2214yes—
83#5004C2212yes—
84#5002C2212yes—
85#5002C2212yes—
86#4999C2212yes—
87#4997C2212yes—
88#4995C2212yes—
89C2×#810C2211yescharacteristic
90#4966C2212yes—
91C2×#808C2211yescharacteristic
92#4924C2211yescharacteristic
93C2×C4×C3⋊C8C2211yescharacteristic
94#3507—31no—
95#3501D311yescharacteristic, complemented
96#3376—34no—
97#3373—32no—
98#3372—32no—
99#3361—32no—
100#3360—34no—
101#3359—32no—
102#3137—32no—
103#3131—31no—
104#3084—32no—
105#3078—31no—
106#3042—32no—
107#3036—31no—
108#2960—31no—
109#2946—32no—
110C2×C4×SD16—31no—
111C22×C3×Q8—22no—
112C22×C3×D4C2311yescharacteristic
113C23×C3×C4—21no—
114C2×#235C2312yes—
115C22×Dic6C2311yescharacteristic
116C3×C4⋊Q8—22no—
117C3×C4⋊Q8D411yescharacteristic
118C3×C4⋊Q8D411yescharacteristic
119C3×C4⋊Q8C2314yes—
120C3×C4⋊Q8C2311yescharacteristic
121C3×C4⋊Q8C2311yescharacteristic
122C3×#125—22no—
123C3×#125D412yes—
124C3×#125C2312yes—
125C3×#125C2314yes—
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×D4C2314yes—
147C3×C4×D4C2314yes—
148C3×C4×D4C2312yes—
149C3×C4×D4C2312yes—
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#947—22no—
159#946—24no—
160Q8×Dic3—22no—
161C2×#214—24no—
162C2×#214C2312yes—
163C2×#214C2312yes—
164C2×#214C2314yes—
165#932—28no—
166C2×#213C2314yes—
167#930—21no—
168#930—21no—
169C2×C4⋊Dic3C2311yescharacteristic
170C2×Dic3⋊C4—21no—
171C2×C4×Dic3—21no—
172C2×#208C2312yes—
173C22×C3⋊C8C2311yescharacteristic
174C22×C3⋊C8C2311yescharacteristic
175#898—24no—
176#898—24no—
177#897—22no—
178#897—22no—
179#894—24no—
180#893—22no—
181#892—22no—
182#892—24no—
183D3×C4⋊C4—22no—
184#890—24no—
185#890—22no—
186#886—24no—
187#67⋊C4—24no—
188#875C2312yes—
189#875C2314yes—
190#874C2311yescharacteristic
191C4×D12—21no—
192C4×D12—21no—
193C4×D12C2314yes—
194#869C2311yescharacteristic
195#869C2314yes—
196C4×Dic6—21no—
197C4×Dic6—21no—
198C4×Dic6C2312yes—
199C4×Dic6C2312yes—
200C4×Dic6C2314yes—
201#832C2312yes—
202#832C2312yes—
203#810C2314yes—
204#810C2312yes—
205#810C2312yes—
206#810C2312yes—
207#810C2312yes—
208#810C2312yes—
209#810C2312yes—
210#810C2314yes—
211#810C2314yes—
212#809C2314yes—
213#809C2312yes—
214#809C2312yes—
215#809C2312yes—
216#809C2312yes—
217#808C2312yes—
218#808C2312yes—
219#808C2314yes—
220#807C2314yes—
221C4⋊(C3⋊C8)C2312yes—
222C4⋊(C3⋊C8)C2312yes—
223C4⋊(C3⋊C8)C2314yes—
224C4⋊(C3⋊C8)C2314yes—
225#803C2314yes—
226C4×C3⋊C8C2311yescharacteristic
227C4×C3⋊C8C2311yescharacteristic
228C4×C3⋊C8C2311yescharacteristic
229C4×C3⋊C8C2311yescharacteristic
230C4×C3⋊C8C2314yes—
231C2×AGL(1,ℤ/8)—32no—
232C22×SD16—31no—
233#559—32no—
234#557—32no—
235#556—34no—
236#556—61no—
237#554—21no—
238#554—22no—
239#554—61no—
240#554C2×D314yes—
241#554C2×D312yes—
242#552—62no—
243D4×Q8—21no—
244D4×Q8C2×D312yes—
245#544C2×D312yes—
246#543—22no—
247#539—62no—
248#536—32no—
249#533C2×D311yescharacteristic
250#533C2×D311yescharacteristic
251#532—31no—
252#529—62no—
253C2×C22⋊Q8—22no—
254#520—32no—
255#518C2×D312yes—
256C2×C4×Q8—31no—
257C2×C4×D4C2×D311yescharacteristic
258#491—34no—
259#489—34no—
260#488—32no—
261#488—34no—
262#488—32no—
263#487—31no—
264#487—34no—
265#487—31no—
266#486—31no—
267#486—31no—
268#479—34no—
269#479—34no—
270#478—34no—
271#477—32no—
272#476—34no—
273#475—32no—
274#475—34no—
275#463—34no—
276#463—34no—
277#463—34no—
278#461—32no—
279#461—34no—
280#461—34no—
281#459—32no—
282#446—32no—
283#446—32no—
284C8×Q8—32no—
285C8×Q8—32no—
286#442—34no—
287#440—34no—
288C4×SD16—34no—
289C4×SD16—32no—
290C4×SD16—32no—
291C4×SD16—32no—
292C4×SD16—32no—
293C4×D8—34no—
294#428—32no—
295C2×#106—31no—
296#424—32no—
297#423—31no—
298#419—32no—
299#417—32no—
300#416—32no—
301#416—32no—
302C2×#103—31no—
303C2×#102—31no—
304#405—32no—
305C2×C4×C8—31no—
306C24×C3—21no—
307C2×C3×Q8—21no—
308C2×C3×Q8—21no—
309C2×C3×Q8—24no—
310C2×C3×Q8—84no—
311C2×C3×Q8C2×D412yes—
312C2×C3×Q8C2×D412yes—
313C2×C3×D4—21no—
314C2×C3×D4—22no—
315C2×C3×D4#4114yes—
316C2×C3×D4C2412yes—
317C22×C3×C4—21no—
318C22×C3×C4—22no—
319C22×C3×C4—24no—
320C22×C3×C4—24no—
321C22×C3×C4—22no—
322C22×C3×C4—82no—
323C22×C3×C4C2×D411yescharacteristic
324C22×C3×C4C2×D411yescharacteristic
325C22×C3×C4C2411yescharacteristic
326C2×#67—22no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329#235—24no—
330#235—24no—
331C2×D12—21no—
332C2×D12—21no—
333C2×D12C2412yes—
334C2×C4×D3—22no—
335C2×C4×D3—24no—
336C2×Dic6—22no—
337C2×Dic6—22no—
338C2×Dic6—21no—
339C2×Dic6C2412yes—
340C2×Dic6C2412yes—
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×D414yes—
351C3×C4⋊C4C2×D412yes—
352C3×C4⋊C4C2×D412yes—
353C3×C4⋊C4C2×D414yes—
354C3×C4⋊C4C2×D412yes—
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×C42C2411yescharacteristic
369C3×C42C2414yes—
370#214—28no—
371#214—24no—
372#214—24no—
373#213—28no—
374(C2×D3)⋊C4—22no—
375(C2×D3)⋊C4—22no—
376(C2×D3)⋊C4—24no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3—21no—
382C4⋊Dic3—24no—
383C4⋊Dic3—24no—
384C4⋊Dic3C2412yes—
385Dic3⋊C4—22no—
386Dic3⋊C4—22no—
387Dic3⋊C4—24no—
388C4×Dic3—22no—
389C4×Dic3—22no—
390C4×Dic3—24no—
391#208—24no—
392C2×C3⋊C8—22no—
393C2×C3⋊C8—22no—
394C2×C3⋊C8C2411yescharacteristic
395C2×C3⋊C8C2411yescharacteristic
396C2×C3⋊C8C2411yescharacteristic
397C2×C3⋊C8C2411yescharacteristic
398C2×C3⋊C8C2414yes—
399C2×#41—32no—
400C22×Q8—22no—
401C22×Q8—31no—
402C22×D4C22×D311yescharacteristic
403C23×C4—21no—
404AGL(1,ℤ/8)—68no—
405C2×SD16—32no—
406C2×SD16—32no—
407C2×SD16—34no—
408C2×SD16—64no—
409C2×D8—34no—
410C2×M16—32no—
411C22×C8—31no—
412C22×C8—31no—
413C4⋊Q8—22no—
414C4⋊Q8—31no—
415C4⋊Q8—34no—
416C4⋊Q8#6711yescharacteristic
417C4⋊Q8#6711yescharacteristic
418C4⋊Q8C22×D311yescharacteristic
419C4⋊Q8C22×D311yescharacteristic
420C4⋊Q8C22×D314yes—
421#127—31no—
422#126—64no—
423#126—64no—
424#125—22no—
425#125—62no—
426#125—64no—
427#125#6712yes—
428#125C22×D312yes—
429#125C22×D314yes—
430#124—32no—
431#124—34no—
432#124—62no—
433#123—64no—
434#123—64no—
435C22⋊Q8—22no—
436C22⋊Q8—24no—
437C22⋊Q8—21no—
438C22⋊Q8—21no—
439C22⋊Q8—22no—
440C22⋊Q8—24no—
441C22⋊Q8—24no—
442C22⋊Q8—24no—
443C22⋊Q8—24no—
444C22⋊Q8—24no—
445C22⋊Q8—64no—
446C22⋊Q8—62no—
447C22⋊Q8—62no—
448C22⋊Q8#6712yes—
449C22⋊Q8#6712yes—
450#121—61no—
451#121—61no—
452C4×Q8—21no—
453C4×Q8—21no—
454C4×Q8—32no—
455C4×Q8—32no—
456C4×Q8—34no—
457C4×Q8—62no—
458C4×Q8—61no—
459C4×Q8—61no—
460C4×Q8C22×D312yes—
461C4×Q8C22×D312yes—
462C4×D4—22no—
463C4×D4—22no—
464C4×D4—21no—
465C4×D4—21no—
466C4×D4—34no—
467C4×D4—62no—
468C4×D4—64no—
469C4×D4—61no—
470C4×D4—61no—
471C4×D4C22×D312yes—
472C4×D4C22×D312yes—
473C4×D4C22×D314yes—
474C4×D4C22×D314yes—
475#117—62no—
476#117—64no—
477#117C22×D312yes—
478#117C22×D312yes—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—61no—
483C2×C4⋊C4—62no—
484C2×C4⋊C4C22×D311yescharacteristic
485C2×C22⋊C4—21no—
486C2×C22⋊C4—24no—
487C2×C42—61no—
488C2×C42C22×D311yescharacteristic
489#107—34no—
490#106—32no—
491#106—32no—
492#106—34no—
493C4⋊C8—32no—
494C4⋊C8—32no—
495C4⋊C8—34no—
496C4⋊C8—34no—
497#103—32no—
498#103—32no—
499#103—32no—
500#103—32no—
501#103—32no—
502#103—32no—
503#103—34no—
504#103—34no—
505#103—34no—
506#102—32no—
507#102—32no—
508#102—32no—
509#102—32no—
510#102—32no—
511#102—32no—
512#102—34no—
513#97—34no—
514C4×C8—31no—
515C4×C8—31no—
516C4×C8—31no—
517C4×C8—31no—
518C4×C8—34no—
519C23×C3—22no—
520C23×C3—24no—
521C23×C3—81no—
522C23×C3—81no—
523C23×C3C22×D411yescharacteristic
524C22×D3—22no—
525C3×Q8—24no—
526C3×Q8—42no—
527C3×Q8—42no—
528C3×Q8—81no—
529C3×Q8—84no—
530C3×D4—24no—
531C3×D4—22no—
532C3×D4C2×#4114yes—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—41no—
538C2×C3×C4—44no—
539C2×C3×C4—84no—
540C2×C3×C4—82no—
541C2×C3×C4—84no—
542C2×C3×C4—81no—
543C2×C3×C4C22×D411yescharacteristic
544C2×C3×C4C22×D414yes—
545C2×C3×C4C22×D411yescharacteristic
546C2×C3×C4C22×D411yescharacteristic
547C2×C3×C4C22×D414yes—
548C2×C3×C4C22×D411yescharacteristic
549C2×C3×C4C22×D411yescharacteristic
550C2×C3×C4C2×#4112yes—
551C2×C3×C42−1+412yes—
552C2×C3×C4C2511yescharacteristic
553#67—44no—
554C2×Dic3—22no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—42no—
558C2×Dic3—81no—
559D12—22no—
560D12—22no—
561D12—42no—
562D12—81no—
563C4×D3—44no—
564C4×D3—84no—
565Dic6—22no—
566Dic6—22no—
567Dic6—22no—
568Dic6—22no—
569Dic6—42no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—24no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C24—21no—
576#41—64no—
577#41—64no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—24no—
581C2×Q8—32no—
582C2×Q8—32no—
583C2×Q8—61no—
584C2×Q8—62no—
585C2×Q8—62no—
586C2×Q8—84no—
587C2×Q8C2×#6712yes—
588C2×Q8C2×#6712yes—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—32no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4#23914yes—
596C2×D4C23×D312yes—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—24no—
600C22×C4—24no—
601C22×C4—22no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—62no—
605C22×C4—64no—
606C22×C4—82no—
607C22×C4C2×#6711yescharacteristic
608C22×C4C2×#6711yescharacteristic
609C22×C4C23×D311yescharacteristic
610SD16—64no—
611SD16—64no—
612SD16—68no—
613D8—68no—
614M16—64no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—34no—
620C2×C8—62no—
621C2×C8—62no—
622C4⋊C4—22no—
623C4⋊C4—21no—
624C4⋊C4—24no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—22no—
629C4⋊C4—21no—
630C4⋊C4—32no—
631C4⋊C4—61no—
632C4⋊C4—64no—
633C4⋊C4—62no—
634C4⋊C4—62no—
635C4⋊C4—64no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—64no—
639C4⋊C4C2×#6714yes—
640C4⋊C4C2×#6712yes—
641C4⋊C4C2×#6712yes—
642C4⋊C4C2×#6712yes—
643C4⋊C4C2×#6714yes—
644C4⋊C4C2×#6712yes—
645C4⋊C4C23×D312yes—
646C4⋊C4C23×D312yes—
647C4⋊C4C23×D312yes—
648C22⋊C4—22no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—62no—
654C22⋊C4—64no—
655C22⋊C4—64no—
656C22⋊C4—62no—
657C22⋊C4—64no—
658C22⋊C4C2×#6714yes—
659C42—22no—
660C42—62no—
661C42—62no—
662C42—64no—
663C42C2×#6711yescharacteristic
664C42C2×#6711yescharacteristic
665C42C23×D311yescharacteristic
666C42C23×D311yescharacteristic
667C42C23×D314yes—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—24no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3—84no—
674C22×C3#54812yes—
675C22×C3C23×D411yescharacteristic
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—42no—
679C3×C4—24no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—24no—
684C3×C4—42no—
685C3×C4—42no—
686C3×C4—42no—
687C3×C4#54812yes—
688C3×C4#57712yes—
689C3×C4C22×#4111yescharacteristic
690C3×C4C2×2−1+411yescharacteristic
691Dic3—42no—
692Dic3—42no—
693Dic3—42no—
694C23—22no—
695C23—24no—
696C23—62no—
697C23—81no—
698C23—81no—
699C23C22×#6711yescharacteristic
700Q8—24no—
701Q8—42no—
702Q8—42no—
703Q8—62no—
704Q8—62no—
705Q8—62no—
706Q8—62no—
707Q8—84no—
708Q8—81no—
709Q8—122no—
710D4—22no—
711D4—24no—
712D4—62no—
713D4—62no—
714D4—124no—
715D4—122no—
716D4—241no—
717D4C2×#23914yes—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—44no—
724C2×C4—62no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—82no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—81no—
731C2×C4—122no—
732C2×C4—124no—
733C2×C4—244no—
734C2×C4—241no—
735C2×C4C2×#23912yes—
736C2×C4#100712yes—
737C2×C4C22×#6711yescharacteristic
738C2×C4C22×#6714yes—
739C2×C4C22×#6711yescharacteristic
740C2×C4C22×#6711yescharacteristic
741C2×C4C22×#6714yes—
742C2×C4C22×#6711yescharacteristic
743C2×C4C22×#6711yescharacteristic
744C2×C4C24×D311yescharacteristic
745C8—61no—
746C8—61no—
747C8—64no—
748C8—61no—
749C8—61no—
750C2×C3—22no—
751C2×C3—44no—
752C2×C3C2×#54811yescharacteristic
753C2×C3C2×#57711yescharacteristic
754C2×C3#358411yescharacteristic
755D3—82no—
756C22—21no—
757C22—21no—
758C22—24no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22—122no—
763C22—122no—
764C22—122no—
765C22#581712yes—
766C22C23×#6711yescharacteristic
767C4—21no—
768C4—21no—
769C4—24no—
770C4—21no—
771C4—24no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—122no—
776C4—122no—
777C4—122no—
778C4#581712yes—
779C4#583612yes—
780C4C22×#23911yescharacteristic
781C4C2×#100711yescharacteristic
782C3#6132611yescharacteristic, complemented, Sylow
783C2—22no—
784C2—44no—
785C2—242no—
786C2C2×#581711yescharacteristic
787C2C2×#583611yescharacteristic
788C2#8729711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3501C2
socleC22×C3C23×D4
prime radical#82307C2
hypercenter#3501D3
hypocenterC3#61326
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. #86260C2semidirect
3. #83645C2semidirect
4. #83644C2semidirect
5. #83643C2semidirect
6. #83637C2semidirect
7. #83569C2semidirect
8. #83568C2semidirect
9. #83476C2semidirect
10. #83471C2semidirect
11. #83367C2semidirect
12. #83334C2semidirect
13. #83328C2semidirect
14. #82544C2semidirect
15. #82537C2semidirect
16. C2×C4×#214C2semidirect
39. #5585C22semidirect
40. #5584C22semidirect
41. #5570C22semidirect
47. #5094C22semidirect
48. #5094C22semidirect
49. #5093C22semidirect
50. #5093C22semidirect
51. #5093C22semidirect
52. #5091C22semidirect
53. #5089C22semidirect
54. #5088C22semidirect
55. #5088C22semidirect
56. #5084C22semidirect
57. #5069C22semidirect
58. #5068C22semidirect
59. #5068C22semidirect
60. #5068C22semidirect
61. #5066C22semidirect
62. #5063C22semidirect
63. #5063C22semidirect
64. #5024C22semidirect
65. #5024C22semidirect
66. Q8×C3⋊C8C22semidirect
67. Q8×C3⋊C8C22semidirect
95. #3501D3semidirect
782. C3#61326semidirect

Maximal subgroups

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

subgroupindex
C3×#35012
#862602
#836452
#836442
#836432
#836372
#835692
#835682
#834762
#834712
#833672
#833342
#833282
#825442
#825372
C2×C4×#2142
#823072
#613263