Finite Group Databasebeta

← #11675147

Subgroups — #11675147

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×#3507C211yesmaximal, characteristic, complemented
2#86280C211yesmaximal, characteristic, complemented
3#83715C212yesmaximal, complemented
4#83713C212yesmaximal, complemented
5#83692C212yesmaximal, complemented
6#83688C212yesmaximal, complemented
7#83669C214yesmaximal, complemented
8#83667C214yesmaximal, complemented
9#83405C212yesmaximal, complemented
10#83401C212yesmaximal, complemented
11#83328C211yesmaximal, characteristic, complemented
12#83297C211yesmaximal, characteristic
13#83281C211yesmaximal, characteristic, complemented
14#82564C212yesmaximal, complemented
15#82560C212yesmaximal, complemented
16#82431C211yesmaximal, characteristic, complemented
17C2×C4×#215C211yesmaximal, characteristic, complemented
18#61326—31nomaximal, Sylow
19C3×#559C2212yescomplemented
20C3×#557C2212yescomplemented
21C3×#556—21no—
22C3×#556C2214yescomplemented
23C3×#554—21no—
24C3×#552—22no—
25C3×#539—22no—
26C3×#536C2212yes—
27C3×#533C2211yescharacteristic
28C3×#532C2211yescharacteristic
29C3×#529—22no—
30C3×#520C2212yes—
31C2×C3×C4×Q8C2211yescharacteristic
32C2×#949C2212yes—
33C22×#215C2211yescharacteristic
34#5730—21no—
35#5727—21no—
36#5690—22no—
37#5634—22no—
38D3×C22⋊Q8—22no—
39#5579C2212yes—
40#5579C2214yes—
41Q8×D12C2212yes—
42#5521C2212yes—
43#5519C2212yes—
44C2×C4×D12C2211yescharacteristic
45#5470C2211yescharacteristic
46#5233C2212yes—
47#5233C2212yes—
48#5232C2212yes—
49#5225C2212yes—
50C2×#835C2211yescharacteristic
51#5083C2212yes—
52#5083C2214yes—
53#5083C2214yes—
54#5082C2214yescomplemented
55#5079C2211yescharacteristic, complemented
56#5079C2211yescharacteristic, complemented
57#5079C2214yescomplemented
58#5072C2212yes—
59#5070C2211yescharacteristic, complemented
60#5070C2211yescharacteristic, complemented
61#5057C2214yes—
62#5057C2214yes—
63#5057C2214yes—
64#5056C2214yescomplemented
65#5056C2212yescomplemented
66#5056C2212yescomplemented
67#5055C2214yescomplemented
68#5026C2214yes—
69C4×#215C2212yes—
70C4×#215C2212yes—
71C4×#215C2214yes—
72C4×#215C2212yes—
73C4×#215C2212yes—
74#5024C2212yescomplemented
75#5024C2212yescomplemented
76Q8×C3⋊C8C2212yescomplemented
77Q8×C3⋊C8C2212yescomplemented
78#5022C2214yescomplemented
79#5022C2214yescomplemented
80#5021C2212yescomplemented
81#5020C2212yescomplemented
82#5020C2214yescomplemented
83#5014C2214yes—
84C4×#213C2214yes—
85#5009C2214yescomplemented
86#5008C2214yescomplemented
87#4999C2212yes—
88#4997C2212yes—
89C2×#809C2211yescharacteristic
90#4964C2212yes—
91C2×#808C2211yescharacteristic
92#4924C2211yescharacteristic
93C2×C4×C3⋊C8C2211yescharacteristic
94#3507D311yescharacteristic, complemented
95#3501—31no—
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—
111C2×C3×#41C2312yes—
112C22×C3×Q8C2311yescharacteristic
113C2×D3×Q8—22no—
114C22×D12C2311yescharacteristic
115C22×C4×D3—21no—
116C3×C4⋊Q8D411yescharacteristic
117C3×C4⋊Q8D411yescharacteristic
118C3×C4⋊Q8C2311yescharacteristic
119C3×C4⋊Q8C2314yes—
120C3×#127C2311yescharacteristic
121C3×#126—24no—
122C3×#126—24no—
123C3×#125—22no—
124C3×#125—24no—
125C3×#125D412yes—
126C3×#124—22no—
127C3×#124C2314yes—
128C3×#124C2312yes—
129C3×#123—24no—
130C3×#123—24no—
131C3×C22⋊Q8—24no—
132C3×C22⋊Q8—22no—
133C3×C22⋊Q8—22no—
134C3×C22⋊Q8D412yes—
135C3×C22⋊Q8D412yes—
136C3×#121—21no—
137C3×#121—21no—
138C3×C4×Q8—22no—
139C3×C4×Q8—21no—
140C3×C4×Q8—21no—
141C3×C4×Q8C2312yes—
142C3×C4×Q8C2314yes—
143C3×C4×Q8C2312yes—
144C3×C4×Q8C2312yes—
145C3×C4×Q8C2312yes—
146C3×C4×D4—22no—
147C3×C4×D4—24no—
148C3×C4×D4—21no—
149C3×C4×D4—21no—
150C3×C4×D4C2314yes—
151C3×#117—22no—
152C3×#117—24no—
153C3×#117C2312yes—
154C2×C3×C4⋊C4—21no—
155C2×C3×C4⋊C4—22no—
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C42—21no—
158C2×C3×C42C2311yescharacteristic
159#949—28no—
160#946—24no—
161#946—22no—
162C2×#215—24no—
163C2×#215C2312yes—
164C2×#215C2312yes—
165C2×#215C2314yes—
166C2×#213C2314yes—
167C2×(C2×D3)⋊C4—21no—
168#926C2312yes—
169C2×C4⋊Dic3C2311yescharacteristic
170#924—21no—
171#924—21no—
172C2×#208C2312yes—
173C22×C3⋊C8C2311yescharacteristic
174C22×C3⋊C8C2311yescharacteristic
175#897—24no—
176#897—22no—
177#896—24no—
178#896—24no—
179#896—24no—
180#893—22no—
181#893—22no—
182D3×C4⋊C4—24no—
183D3×C4⋊C4—22no—
184#890—22no—
185#888—22no—
186D3×C22⋊C4—24no—
187#878—24no—
188C4×D12—21no—
189C4×D12—21no—
190C4×D12C2312yes—
191C4×D12C2312yes—
192C4×D12C2314yes—
193C4×D12C2314yes—
194#870C2312yes—
195#870C2314yes—
196#869C2311yescharacteristic
197#869C2311yescharacteristic
198#869C2314yes—
199C4×Dic6—21no—
200C4×Dic6—21no—
201#835C2312yes—
202#835C2312yes—
203#835C2314yes—
204#835C2314yes—
205#835C2314yes—
206#835C2312yes—
207#835C2312yes—
208#835C2312yes—
209#835C2312yes—
210#832C2314yes—
211#832C2312yes—
212#832C2312yes—
213#832C2312yes—
214#832C2312yes—
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#559C2×D312yescomplemented
234#557C2×D312yescomplemented
235#556—21no—
236#556C2×D314yescomplemented
237#554—21no—
238#554—34no—
239#554—32no—
240#554—61no—
241#554—62no—
242#552—22no—
243D4×Q8—32no—
244D4×Q8—61no—
245#544—32no—
246#543—62no—
247#539—22no—
248#536C2×D312yes—
249#533—31no—
250#533C2×D311yescharacteristic
251#532C2×D311yescharacteristic
252#529—22no—
253C2×C22⋊Q8—62no—
254#520C2×D312yes—
255#518—32no—
256C2×C4×Q8C2×D311yescharacteristic
257C2×C4×D4—31no—
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—
306C23×D3—21no—
307C3×#41—24no—
308C3×#41—24no—
309C2×C3×Q8—21no—
310C2×C3×Q8—22no—
311C2×C3×Q8—22no—
312C2×C3×Q8C2×D412yes—
313C2×C3×Q8C2×D412yes—
314C2×C3×Q8C2412yes—
315C2×C3×Q8C2412yes—
316C2×C3×D4—22no—
317C2×C3×D4—21no—
318C2×C3×D4—21no—
319C2×C3×D4C2412yes—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—22no—
323C22×C3×C4—24no—
324C22×C3×C4C2×D411yescharacteristic
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2411yescharacteristic
327C22×Dic3—21no—
328D3×Q8—84no—
329C2×D12—21no—
330C2×D12—22no—
331C2×D12#4114yes—
332C2×D12C2412yes—
333C2×C4×D3—22no—
334C2×C4×D3—22no—
335C2×C4×D3—24no—
336C2×C4×D3—24no—
337C2×C4×D3—82no—
338C2×Dic6—21no—
339C2×Dic6—21no—
340C2×Dic6—24no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—24no—
343C3×C4⋊C4—22no—
344C3×C4⋊C4—22no—
345C3×C4⋊C4—24no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—24no—
349C3×C4⋊C4C2×D412yes—
350C3×C4⋊C4C2×D412yes—
351C3×C4⋊C4C2×D414yes—
352C3×C4⋊C4C2×D412yes—
353C3×C4⋊C4C2×D412yes—
354C3×C4⋊C4C2×D414yes—
355C3×C4⋊C4C2412yes—
356C3×C22⋊C4—22no—
357C3×C22⋊C4—24no—
358C3×C22⋊C4—24no—
359C3×C22⋊C4—22no—
360C3×C22⋊C4—24no—
361C3×C22⋊C4C2×D414yes—
362C3×C42—22no—
363C3×C42—22no—
364C3×C42—24no—
365C3×C42C2×D411yescharacteristic
366C3×C42C2×D411yescharacteristic
367C3×C42C2411yescharacteristic
368C3×C42C2411yescharacteristic
369C3×C42C2414yes—
370#217—22no—
371#215—24no—
372#215—24no—
373#215—28no—
374#213—28no—
375(C2×D3)⋊C4—22no—
376(C2×D3)⋊C4—22no—
377(C2×D3)⋊C4—24no—
378(C2×D3)⋊C4—24no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3—24no—
382C4⋊Dic3—21no—
383C4⋊Dic3C2412yes—
384C4⋊Dic3C2412yes—
385C4⋊Dic3C2412yes—
386Dic3⋊C4—22no—
387Dic3⋊C4—22no—
388Dic3⋊C4—24no—
389Dic3⋊C4—24no—
390C4×Dic3—22no—
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×#41C22×D312yes—
400C22×Q8—62no—
401C22×Q8C22×D311yescharacteristic
402C22×D4—31no—
403C23×C4—61no—
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—31no—
414C4⋊Q8—31no—
415C4⋊Q8—34no—
416C4⋊Q8—62no—
417C4⋊Q8#6711yescharacteristic
418C4⋊Q8#6711yescharacteristic
419C4⋊Q8C22×D311yescharacteristic
420C4⋊Q8C22×D314yes—
421#127C22×D311yescharacteristic
422#126—24no—
423#126—24no—
424#125—22no—
425#125—24no—
426#125—32no—
427#125—34no—
428#125—62no—
429#125#6712yes—
430#124—22no—
431#124C22×D312yes—
432#124C22×D314yes—
433#123—24no—
434#123—24no—
435C22⋊Q8—24no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8—62no—
439C22⋊Q8—64no—
440C22⋊Q8—61no—
441C22⋊Q8—61no—
442C22⋊Q8—62no—
443C22⋊Q8—64no—
444C22⋊Q8—64no—
445C22⋊Q8—64no—
446C22⋊Q8—64no—
447C22⋊Q8—64no—
448C22⋊Q8#6712yes—
449C22⋊Q8#6712yes—
450#121—21no—
451#121—21no—
452C4×Q8—22no—
453C4×Q8—21no—
454C4×Q8—21no—
455C4×Q8—61no—
456C4×Q8—61no—
457C4×Q8C22×D312yes—
458C4×Q8C22×D312yes—
459C4×Q8C22×D314yes—
460C4×Q8C22×D312yes—
461C4×Q8C22×D312yes—
462C4×D4—22no—
463C4×D4—24no—
464C4×D4—21no—
465C4×D4—21no—
466C4×D4—32no—
467C4×D4—32no—
468C4×D4—34no—
469C4×D4—34no—
470C4×D4—62no—
471C4×D4—62no—
472C4×D4—61no—
473C4×D4—61no—
474C4×D4C22×D314yes—
475#117—22no—
476#117—24no—
477#117—32no—
478#117C22×D312yes—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—31no—
482C2×C4⋊C4—64no—
483C2×C4⋊C4—62no—
484C2×C4⋊C4C22×D311yescharacteristic
485C2×C22⋊C4—61no—
486C2×C22⋊C4—64no—
487C2×C42—21no—
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—34no—
511#102—32no—
512#102—32no—
513#97—34no—
514C4×C8—31no—
515C4×C8—31no—
516C4×C8—31no—
517C4×C8—31no—
518C4×C8—34no—
519C23×C3—22no—
520C23×C3C22×D411yescharacteristic
521C22×D3—22no—
522C22×D3—24no—
523C22×D3—81no—
524C22×D3—81no—
525C3×Q8—24no—
526C3×Q8—22no—
527C3×Q8—22no—
528C3×Q8—22no—
529C3×Q8—22no—
530C3×Q8—42no—
531C3×Q8—42no—
532C3×D4—22no—
533C3×D4—22no—
534C3×D4—44no—
535C3×D4—42no—
536C3×D4—81no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—41no—
542C2×C3×C4—42no—
543C2×C3×C4—44no—
544C2×C3×C4—84no—
545C2×C3×C4—81no—
546C2×C3×C4C22×D411yescharacteristic
547C2×C3×C4C22×D411yescharacteristic
548C2×C3×C4C22×D414yes—
549C2×C3×C4C22×D414yes—
550C2×C3×C4C22×D411yescharacteristic
551C2×C3×C4C22×D411yescharacteristic
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4C2×#4112yes—
554C2×C3×C42−1+412yes—
555C2×C3×C4C2511yescharacteristic
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—81no—
560D12—24no—
561D12—22no—
562D12C2×#4114yes—
563C4×D3—44no—
564C4×D3—84no—
565C4×D3—82no—
566C4×D3—84no—
567Dic6—42no—
568Dic6—81no—
569Dic6—84no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—24no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C24—61no—
576#41—24no—
577#41—24no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—61no—
582C2×Q8—61no—
583C2×Q8—64no—
584C2×Q8—244no—
585C2×Q8C2×#6712yes—
586C2×Q8C2×#6712yes—
587C2×Q8C23×D312yes—
588C2×Q8C23×D312yes—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—34no—
593C2×D4—32no—
594C2×D4—62no—
595C2×D4—61no—
596C2×D4C23×D312yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—24no—
601C22×C4—61no—
602C22×C4—62no—
603C22×C4—64no—
604C22×C4—64no—
605C22×C4—62no—
606C22×C4—242no—
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—21no—
623C4⋊C4—24no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—24no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—24no—
630C4⋊C4—32no—
631C4⋊C4—32no—
632C4⋊C4—32no—
633C4⋊C4—61no—
634C4⋊C4—62no—
635C4⋊C4—61no—
636C4⋊C4—64no—
637C4⋊C4—64no—
638C4⋊C4—64no—
639C4⋊C4—62no—
640C4⋊C4—61no—
641C4⋊C4C2×#6712yes—
642C4⋊C4C2×#6714yes—
643C4⋊C4C2×#6712yes—
644C4⋊C4C2×#6712yes—
645C4⋊C4C2×#6714yes—
646C4⋊C4C2×#6712yes—
647C4⋊C4C23×D312yes—
648C22⋊C4—22no—
649C22⋊C4—24no—
650C22⋊C4—24no—
651C22⋊C4—22no—
652C22⋊C4—24no—
653C22⋊C4—62no—
654C22⋊C4—64no—
655C22⋊C4—64no—
656C22⋊C4—62no—
657C22⋊C4—62no—
658C22⋊C4C2×#6714yes—
659C42—22no—
660C42—22no—
661C42—24no—
662C42—62no—
663C42C2×#6711yescharacteristic
664C42C2×#6711yescharacteristic
665C42C23×D311yescharacteristic
666C42C23×D311yescharacteristic
667C42C23×D314yes—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—42no—
671C22×C3—42no—
672C22×C3—42no—
673C22×C3#54812yes—
674C22×C3C23×D411yescharacteristic
675C2×D3—24no—
676C2×D3—42no—
677C2×D3—42no—
678C2×D3—84no—
679C3×C4—21no—
680C3×C4—24no—
681C3×C4—21no—
682C3×C4—24no—
683C3×C4—21no—
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—62no—
696C23—64no—
697C23—241no—
698C23—241no—
699C23C22×#6711yescharacteristic
700Q8—24no—
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—42no—
706Q8—42no—
707Q8—122no—
708Q8—244no—
709Q8—241no—
710D4—22no—
711D4—22no—
712D4—34no—
713D4—44no—
714D4—42no—
715D4—62no—
716D4—64no—
717D4—81no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—84no—
729C2×C4—81no—
730C2×C4—124no—
731C2×C4—242no—
732C2×C4—244no—
733C2×C4—244no—
734C2×C4—241no—
735C2×C4D3×#4112yes—
736C2×C4#101012yes—
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—82no—
752C2×C3C2×#54811yescharacteristic
753C2×C3C2×#57711yescharacteristic
754C2×C3#358411yescharacteristic
755D3—44no—
756C22—21no—
757C22—21no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—64no—
762C22—122no—
763C22—122no—
764C22—244no—
765C22#583112yes—
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#583112yes—
779C4#583712yes—
780C4C2×D3×#4111yescharacteristic
781C4C2×#101011yescharacteristic
782C3#6132611yescharacteristic, complemented, Sylow
783C2—22no—
784C2—82no—
785C2—124no—
786C2C2×#583111yescharacteristic
787C2C2×#583711yescharacteristic
788C2#8729711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3507C2
socleC22×C3C23×D4
prime radical#83297C2
hypercenter#3507D3
hypocenterC3#61326
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #533 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. C3×#3507C2semidirect
2. #86280C2semidirect
3. #83715C2semidirect
4. #83713C2semidirect
5. #83692C2semidirect
6. #83688C2semidirect
7. #83669C2semidirect
8. #83667C2semidirect
9. #83405C2semidirect
10. #83401C2semidirect
11. #83328C2semidirect
13. #83281C2semidirect
14. #82564C2semidirect
15. #82560C2semidirect
16. #82431C2semidirect
17. C2×C4×#215C2semidirect
19. C3×#559C22semidirect
20. C3×#557C22semidirect
22. C3×#556C22semidirect
54. #5082C22semidirect
55. #5079C22semidirect
56. #5079C22semidirect
57. #5079C22semidirect
59. #5070C22semidirect
60. #5070C22semidirect
64. #5056C22semidirect
65. #5056C22semidirect
66. #5056C22semidirect
67. #5055C22semidirect
74. #5024C22semidirect
75. #5024C22semidirect
76. Q8×C3⋊C8C22semidirect
77. Q8×C3⋊C8C22semidirect
78. #5022C22semidirect
79. #5022C22semidirect
80. #5021C22semidirect
81. #5020C22semidirect
82. #5020C22semidirect
85. #5009C22semidirect
86. #5008C22semidirect
94. #3507D3semidirect
233. #559C2×D3semidirect
234. #557C2×D3semidirect
236. #556C2×D3semidirect
782. C3#61326semidirect

Maximal subgroups

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

subgroupindex
C3×#35072
#862802
#837152
#837132
#836922
#836882
#836692
#836672
#834052
#834012
#833282
#832972
#832812
#825642
#825602
#824312
C2×C4×#2152
#613263