Finite Group Databasebeta

← #10823486

Subgroups — #10823486

Order 768.

1178 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5534C211yesmaximal, characteristic, complemented
2C3×#2324C211yesmaximal, characteristic, complemented
3C2×#5018C211yesmaximal, characteristic, complemented
4C2×C4×#213C211yesmaximal, characteristic, complemented
5#71685C211yesmaximal, characteristic, complemented
6#71684C211yesmaximal, characteristic
7#71582C211yesmaximal, characteristic, complemented
8#69659C211yesmaximal, characteristic, complemented
9#69638C211yesmaximal, characteristic, complemented
10#69628C211yesmaximal, characteristic, complemented
11#69604C211yesmaximal, characteristic, complemented
12#69527C211yesmaximal, characteristic, complemented
13#69523C211yesmaximal, characteristic, complemented
14#69474C211yesmaximal, characteristic, complemented
15C4×#810C211yesmaximal, characteristic, complemented
16#23579—31nomaximal, Sylow
17C2×C3×#121C2211yescharacteristic
18C2×C3×C4×D4C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic
20C22×#214C2211yescharacteristic
21C22×#213C2211yescharacteristic
22C2×#930C2211yescharacteristic
23C2×#924C2211yescharacteristic
24#5534—24no—
25#5534—24no—
26C2×#898—21no—
27C2×#896—21no—
28C2×#885—21no—
29C2×#883—21no—
30C2×#875C2211yescharacteristic
31C2×C4×D12C2211yescharacteristic
32C2×#869C2211yescharacteristic
33C2×C4×Dic6C2211yescharacteristic
34C3×#390—21no—
35C3×#390C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C3×#388—21no—
38C3×#386—21no—
39C3×#385—21no—
40C3×#380C2211yescharacteristic
41C3×C4×C4⋊C4C2211yescharacteristic
42C2×#832C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#830C2211yescharacteristic
45C2×#830C2211yescharacteristic
46#5018—24no—
47C4×#213—24no—
48C2×#810C2211yescharacteristic
49C2×#810C2211yescharacteristic
50C2×#810C2211yescharacteristic
51C2×#809C2211yescharacteristic
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#807C2211yescharacteristic
55C2×#807C2211yescharacteristic
56C2×#803C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#542—31no—
65C2×#440—31no—
66C2×C4×D8—31no—
67#2324D311yescharacteristic, complemented
68#2057—31no—
69#2042—31no—
70#2036—31no—
71#2033—31no—
72#2023—31no—
73#2012—31no—
74#2000—31no—
75#1999—31no—
76#1762—31no—
77C4×#103—31no—
78#1750—31no—
79C22×C3×D4—21no—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4C2311yescharacteristic
83C22×#67—21no—
84C22×D12C2311yescharacteristic
85C22×C4×D3—21no—
86C22×Dic6—21no—
87C22×Dic6C2311yescharacteristic
88C3×#121—22no—
89C3×#121—22no—
90C3×C4×D4—22no—
91C3×C4×D4—22no—
92C3×#117—22no—
93C3×#117—22no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4D411yescharacteristic
96C2×C3×C4⋊C4D411yescharacteristic
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C4⋊C4C2311yescharacteristic
99C2×C3×C4⋊C4C2311yescharacteristic
100C2×C3×C22⋊C4—21no—
101C2×C3×C22⋊C4—21no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—21no—
104C2×C3×C22⋊C4—21no—
105C2×C3×C22⋊C4D411yescharacteristic
106C2×C3×C22⋊C4D411yescharacteristic
107C2×C3×C42—21no—
108C2×C3×C42C2311yescharacteristic
109C2×C3×C42C2311yescharacteristic
110C2×#217—21no—
111C2×#214—22no—
112C2×#214—22no—
113C2×#214—22no—
114C2×#213—22no—
115C2×#213—22no—
116C2×#213—22no—
117#930—22no—
118#930—22no—
119C2×(C2×D3)⋊C4—21no—
120C2×(C2×D3)⋊C4—21no—
121C2×(C2×D3)⋊C4—21no—
122C2×(C2×D3)⋊C4—21no—
123C2×C4⋊Dic3—21no—
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126#924—22no—
127#924—22no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×C4×Dic3—21no—
131C22×C3⋊C8C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C22×C3⋊C8C2311yescharacteristic
135#898—28no—
136#896—28no—
137#885—28no—
138#883—28no—
139#875—22no—
140#875—22no—
141C4×D12—22no—
142C4×D12D414yescomplemented
143#869—22no—
144#869—22no—
145C4×Dic6—22no—
146C4×Dic6D414yescomplemented
147C3×#95—21no—
148C3×#95—21no—
149C3×#95—21no—
150#832—22no—
151#832—22no—
152#830—22no—
153#830—22no—
154#810—22no—
155#810—22no—
156#810—22no—
157#809—22no—
158#809—22no—
159#809—22no—
160#807—22no—
161#807—22no—
162#803—22no—
163C4×C3⋊C8—22no—
164C22×SD16—31no—
165C22×D8—31no—
166#542—64no—
167#542—64no—
168C2×C4⋊Q8—31no—
169C2×#126—61no—
170C2×#124—31no—
171C2×#124—61no—
172C2×#123—61no—
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—61no—
175C2×#121—31no—
176C2×#121C2×D311yescharacteristic
177C2×C4×Q8—31no—
178C2×C4×D4—31no—
179C2×C4×D4C2×D311yescharacteristic
180C2×#117C2×D311yescharacteristic
181#440—64no—
182C4×D8—64no—
183C2×#107—31no—
184C2×#107—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#102—31no—
189C2×#102—31no—
190C2×#102—31no—
191C2×#102—31no—
192C2×#102—31no—
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×#97—31no—
196C2×C4×C8—31no—
197#390—21no—
198#390C2×D311yescharacteristic
199#389C2×D311yescharacteristic
200#388—21no—
201#386—21no—
202#385—21no—
203#380C2×D311yescharacteristic
204C4×C4⋊C4C2×D311yescharacteristic
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#336—31no—
210#336—31no—
211C24×C3—21no—
212C24×C3C2×D411yescharacteristic
213C23×D3—21no—
214C2×C3×D4—24no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—81no—
221C2×C3×D4—81no—
222C2×C3×D4#4112yes—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—42no—
233C22×C3×C4—81no—
234C22×C3×C4—81no—
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2411yescharacteristic
241C2×#67—24no—
242C2×#67—81no—
243C2×#67—81no—
244C22×Dic3—21no—
245C22×Dic3—21no—
246C22×Dic3—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12C2×D412yes—
253C2×C4×D3—24no—
254C2×C4×D3—81no—
255C2×C4×D3—81no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6—21no—
260C2×Dic6—21no—
261C2×Dic6—24no—
262C2×Dic6—81no—
263C2×Dic6—81no—
264C2×Dic6C2×D412yes—
265C3×C4⋊C4—22no—
266C3×C4⋊C4—22no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—21no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—81no—
273C3×C4⋊C4#4112yes—
274C3×C22⋊C4—24no—
275C3×C22⋊C4—22no—
276C3×C22⋊C4—22no—
277C3×C22⋊C4—42no—
278C3×C22⋊C4—81no—
279C3×C22⋊C4—81no—
280C3×C22⋊C4—81no—
281C3×C42—21no—
282C3×C42—21no—
283C3×C42—81no—
284C3×C42C2×D412yes—
285C3×C42C2×D412yes—
286#217—24no—
287#214—28no—
288#213—28no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—24no—
291(C2×D3)⋊C4—24no—
292(C2×D3)⋊C4—24no—
293C4⋊Dic3—24no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3C2×D412yes—
297C4⋊Dic3C2×D412yes—
298Dic3⋊C4—24no—
299Dic3⋊C4—24no—
300C4×Dic3—24no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C2×C3⋊C8—21no—
310C2×C3⋊C8—21no—
311C2×C3⋊C8#4112yes—
312C2×C3⋊C8#4112yes—
313C22×Q8—31no—
314C22×Q8—61no—
315C22×D4—21no—
316C22×D4—31no—
317C22×D4—61no—
318C22×D4C22×D311yescharacteristic
319C23×C4—21no—
320C23×C4—61no—
321C23×C4C22×D311yescharacteristic
322C2×SD16—62no—
323C2×SD16—62no—
324C2×SD16—62no—
325C2×D8—62no—
326C2×D8—62no—
327C2×D8—62no—
328C22×C8—31no—
329C22×C8—31no—
330C22×C8—31no—
331C22×C8—31no—
332C4⋊Q8—62no—
333C4⋊Q8—62no—
334#126—68no—
335#124—62no—
336#124—62no—
337#124—68no—
338#123—68no—
339C22⋊Q8—68no—
340C22⋊Q8—62no—
341C22⋊Q8—62no—
342#121—22no—
343#121—22no—
344#121—62no—
345#121—62no—
346C4×Q8—34no—
347C4×Q8—62no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—34no—
351C4×D4—62no—
352#117—22no—
353#117—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—31no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4#6711yescharacteristic
361C2×C4⋊C4#6711yescharacteristic
362C2×C4⋊C4C22×D311yescharacteristic
363C2×C4⋊C4C22×D311yescharacteristic
364C2×C4⋊C4C22×D311yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—61no—
372C2×C22⋊C4—61no—
373C2×C22⋊C4—61no—
374C2×C22⋊C4—61no—
375C2×C22⋊C4#6711yescharacteristic
376C2×C22⋊C4#6711yescharacteristic
377C2×C42—21no—
378C2×C42—61no—
379C2×C42C22×D311yescharacteristic
380C2×C42C22×D311yescharacteristic
381#107—62no—
382#107—62no—
383#103—62no—
384#103—62no—
385#103—62no—
386#102—62no—
387#102—62no—
388#102—62no—
389#102—62no—
390#102—62no—
391C22⋊C8—62no—
392C22⋊C8—62no—
393#97—62no—
394C4×C8—62no—
395#95—21no—
396#95—21no—
397#95—21no—
398C23×C3—21no—
399C23×C3—22no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—41no—
407C23×C3—41no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—41no—
411C23×C3—41no—
412C23×C3C22×D411yescharacteristic
413C22×D3—22no—
414C22×D3—41no—
415C22×D3—41no—
416C22×D3—41no—
417C22×D3—41no—
418C22×D3—41no—
419C22×D3—41no—
420C3×D4—22no—
421C3×D4—22no—
422C3×D4—41no—
423C3×D4—41no—
424C3×D4—84no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—22no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—41no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—41no—
445C2×C3×C4—41no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—84no—
452C2×C3×C4#12012yes—
453C2×C3×C4#12012yes—
454C2×C3×C4C22×D411yescharacteristic
455C2×C3×C4C22×D411yescharacteristic
456C2×C3×C4C2×#4111yescharacteristic
457C2×C3×C4C2×#4111yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460#67—84no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—41no—
465C2×Dic3—41no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470D12—22no—
471D12—22no—
472D12—41no—
473D12—41no—
474C4×D3—84no—
475Dic6—22no—
476Dic6—22no—
477Dic6—41no—
478Dic6—41no—
479Dic6—84no—
480C3⋊C8—22no—
481C3⋊C8—22no—
482C3⋊C8—41no—
483C3⋊C8—41no—
484C24—21no—
485C24—61no—
486C24C2×#6711yescharacteristic
487C2×Q8—32no—
488C2×Q8—64no—
489C2×Q8—61no—
490C2×Q8—61no—
491C2×Q8—61no—
492C2×Q8—61no—
493C2×Q8—61no—
494C2×Q8—241no—
495C2×Q8—241no—
496C2×D4—24no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—32no—
503C2×D4—64no—
504C2×D4—61no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—81no—
510C2×D4—81no—
511C2×D4—241no—
512C2×D4—241no—
513C2×D4#23512yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—42no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—64no—
528C22×C4—81no—
529C22×C4—81no—
530C22×C4—241no—
531C22×C4—241no—
532C22×C4C2×#6711yescharacteristic
533C22×C4C2×#6711yescharacteristic
534C22×C4C2×#6711yescharacteristic
535C22×C4C2×#6711yescharacteristic
536C22×C4C2×#6711yescharacteristic
537C22×C4C23×D311yescharacteristic
538SD16—68no—
539D8—68no—
540C2×C8—32no—
541C2×C8—32no—
542C2×C8—61no—
543C2×C8—61no—
544C2×C8—61no—
545C2×C8—61no—
546C2×C8—61no—
547C2×C8—61no—
548C2×C8—61no—
549C2×C8—61no—
550C2×C8—61no—
551C2×C8—61no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—32no—
560C4⋊C4—32no—
561C4⋊C4—64no—
562C4⋊C4—64no—
563C4⋊C4—64no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—81no—
567C4⋊C4#23512yes—
568C22⋊C4—24no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—42no—
572C22⋊C4—64no—
573C22⋊C4—64no—
574C22⋊C4—64no—
575C22⋊C4—64no—
576C22⋊C4—64no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C42—21no—
581C42—21no—
582C42—64no—
583C42—81no—
584C42D3×D412yes—
585C42D3×D412yes—
586C22×C3—41no—
587C22×C3—42no—
588C22×C3—41no—
589C22×C3—42no—
590C22×C3—41no—
591C22×C3—42no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3—81no—
597C22×C3—81no—
598C22×C3—81no—
599C22×C3—81no—
600C22×C3C2×#12011yescharacteristic
601C22×C3#52511yescharacteristic
602C22×C3#53211yescharacteristic
603C22×C3#57611yescharacteristic
604C22×C3#57611yescharacteristic
605C22×C3#57711yescharacteristic
606C22×C3#57811yescharacteristic
607C2×D3—42no—
608C2×D3—42no—
609C2×D3—42no—
610C2×D3—81no—
611C2×D3—81no—
612C2×D3—81no—
613C2×D3—81no—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—42no—
617C3×C4—41no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—81no—
621C3×C4—81no—
622C3×C4#52511yescharacteristic
623C3×C4#52511yescharacteristic
624C3×C4#53211yescharacteristic
625C3×C4#53211yescharacteristic
626Dic3—42no—
627Dic3—42no—
628Dic3—42no—
629C23—22no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—62no—
644C23—121no—
645C23—121no—
646C23—121no—
647C23—121no—
648C23—121no—
649C23—121no—
650C23C22×#6711yescharacteristic
651Q8—62no—
652Q8—62no—
653Q8—121no—
654Q8—121no—
655Q8—244no—
656D4—22no—
657D4—22no—
658D4—41no—
659D4—41no—
660D4—62no—
661D4—62no—
662D4—84no—
663D4—121no—
664D4—121no—
665D4—244no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—62no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—84no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—244no—
703C2×C4#93712yes—
704C2×C4#93712yes—
705C2×C4C2×#23511yescharacteristic
706C2×C4C2×#23511yescharacteristic
707C2×C4C2×D3×D411yescharacteristic
708C2×C4C2×D3×D411yescharacteristic
709C2×C4D3×#4111yescharacteristic
710C2×C4D3×#4111yescharacteristic
711C8—62no—
712C8—62no—
713C8—121no—
714C8—121no—
715C2×C3—81no—
716C2×C3—82no—
717C2×C3#238811yescharacteristic
718C2×C3#300811yescharacteristic
719C2×C3#301311yescharacteristic
720C2×C3#311811yescharacteristic
721C2×C3#312411yescharacteristic
722C2×C3#317511yescharacteristic
723C2×C3#317911yescharacteristic
724D3—82no—
725C22—41no—
726C22—41no—
727C22—42no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—41no—
732C22—42no—
733C22—41no—
734C22—41no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—122no—
740C22—122no—
741C22—122no—
742C22—241no—
743C22—241no—
744C22—241no—
745C22—241no—
746C22#579111yescharacteristic
747C22C2×#93711yescharacteristic
748C22#583211yescharacteristic
749C22#583511yescharacteristic
750C22#583511yescharacteristic
751C22#583611yescharacteristic
752C22#583811yescharacteristic
753C4—22no—
754C4—22no—
755C4—42no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—81no—
760C4—81no—
761C4—122no—
762C4—122no—
763C4—122no—
764C4#554711yescharacteristic
765C4#554711yescharacteristic
766C4#554811yescharacteristic
767C4#554811yescharacteristic
768C3#2357911yescharacteristic, complemented, Sylow
769C2—81no—
770C2—82no—
771C2—242no—
772C2#8240011yescharacteristic
773C2#8254111yescharacteristic
774C2#8256911yescharacteristic
775C2#8338311yescharacteristic
776C2#8342711yescharacteristic
777C2#8343311yescharacteristic
778C2#8345711yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2324C2
socleC23×C3C22×D4
prime radical#71684C2
hypercenter#2324D3
hypocenterC3#23579
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#5534C2semidirect
2. C3×#2324C2semidirect
3. C2×#5018C2semidirect
4. C2×C4×#213C2semidirect
5. #71685C2semidirect
7. #71582C2semidirect
8. #69659C2semidirect
9. #69638C2semidirect
10. #69628C2semidirect
11. #69604C2semidirect
12. #69527C2semidirect
13. #69523C2semidirect
14. #69474C2semidirect
15. C4×#810C2semidirect
67. #2324D3semidirect
142. C4×D12D4semidirect
146. C4×Dic6D4semidirect
768. C3#23579semidirect

Maximal subgroups

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

subgroupindex
C2×#55342
C3×#23242
C2×#50182
C2×C4×#2132
#716852
#716842
#715822
#696592
#696382
#696282
#696042
#695272
#695232
#694742
C4×#8102
#235793