Finite Group Databasebeta

← #10823480

Subgroups — #10823480

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×C3×#542C211yesmaximal, characteristic, complemented
2C2×#5026C211yesmaximal, characteristic, complemented
3C2×C4×#213C211yesmaximal, characteristic, complemented
4#82236C211yesmaximal, characteristic, complemented
5#71792C211yesmaximal, characteristic, complemented
6#71782C211yesmaximal, characteristic, complemented
7#71728C211yesmaximal, characteristic, complemented
8#71722C211yesmaximal, characteristic, complemented
9#71699C211yesmaximal, characteristic, complemented
10#71695C211yesmaximal, characteristic, complemented
11#71684C211yesmaximal, characteristic
12#71679C211yesmaximal, characteristic, complemented
13C4×#835C211yesmaximal, characteristic, complemented
14#71609C211yesmaximal, characteristic, complemented
15#71582C211yesmaximal, characteristic, complemented
16#23579—31nomaximal, Sylow
17C3×#542—24no—
18C3×#542—24no—
19C2×C3×C4⋊Q8C2211yescharacteristic
20C2×C3×#126—21no—
21C2×C3×#124—21no—
22C2×C3×#124C2211yescharacteristic
23C2×C3×#123—21no—
24C2×C3×C22⋊Q8—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×C4×Q8C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×#117C2211yescharacteristic
30C22×#215C2211yescharacteristic
31C22×#213C2211yescharacteristic
32C2×#930C2211yescharacteristic
33C2×C4×D12C2211yescharacteristic
34C2×#835C2211yescharacteristic
35C2×#835C2211yescharacteristic
36C2×#835C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#832C2211yescharacteristic
39C2×#832C2211yescharacteristic
40#5212C2211yescharacteristic
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5026—24no—
44C4×#213—24no—
45#4990—21no—
46#4989—21no—
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#807C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4957—21no—
52#4956—21no—
53#4939C2211yescharacteristic
54C4×C4⋊Dic3C2211yescharacteristic
55#4928C2211yescharacteristic
56C2×#803C2211yescharacteristic
57C2×C4×C3⋊C8C2211yescharacteristic
58#4529C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4524C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#542D311yescharacteristic, complemented
65C2×#440—31no—
66C2×C4×D8—31no—
67#2324—31no—
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×Q8—21no—
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4—21no—
82C22×C3×D4C2311yescharacteristic
83C23×C3×C4—21no—
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×D12C2311yescharacteristic
87C22×C4×D3—21no—
88C3×C4⋊Q8—22no—
89C3×C4⋊Q8—22no—
90C3×#126—28no—
91C3×#124—28no—
92C3×#124—22no—
93C3×#124—22no—
94C3×#123—28no—
95C3×C22⋊Q8—28no—
96C3×C22⋊Q8—22no—
97C3×C22⋊Q8—22no—
98C3×#121—22no—
99C3×#121—22no—
100C3×C4×Q8—22no—
101C3×C4×Q8D414yescomplemented
102C3×C4×D4—22no—
103C3×C4×D4D414yescomplemented
104C3×#117—22no—
105C3×#117—22no—
106C2×C3×C4⋊C4—21no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C4⋊C4—21no—
109C2×C3×C4⋊C4D411yescharacteristic
110C2×C3×C4⋊C4D411yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4D411yescharacteristic
119C2×C3×C22⋊C4D411yescharacteristic
120C2×C3×C42—21no—
121C2×C3×C42C2311yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C2×#217—21no—
124C2×#215—22no—
125C2×#215—22no—
126C2×#215—22no—
127C2×#213—22no—
128C2×#213—22no—
129C2×#213—22no—
130#930—22no—
131#930—22no—
132C2×(C2×D3)⋊C4—21no—
133C2×(C2×D3)⋊C4—21no—
134C2×(C2×D3)⋊C4—21no—
135C2×(C2×D3)⋊C4—21no—
136C2×C4⋊Dic3C2311yescharacteristic
137C2×C4⋊Dic3C2311yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×Dic3⋊C4—21no—
140C2×C4×Dic3—21no—
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C4×D12—22no—
146C4×D12—22no—
147#835—22no—
148#835—22no—
149#835—22no—
150#832—22no—
151#832—22no—
152#832—22no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#830—22no—
157#830—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—24no—
167#542—24no—
168C2×C4⋊Q8C2×D311yescharacteristic
169C2×#126—21no—
170C2×#124—21no—
171C2×#124C2×D311yescharacteristic
172C2×#123—21no—
173C2×C22⋊Q8—21no—
174C2×C22⋊Q8C2×D311yescharacteristic
175C2×#121—31no—
176C2×#121C2×D311yescharacteristic
177C2×C4×Q8C2×D311yescharacteristic
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—31no—
198#390—61no—
199#389—31no—
200#388—61no—
201#386—61no—
202#385—61no—
203#380—31no—
204C4×C4⋊C4—31no—
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×Q8—24no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—81no—
221C2×C3×Q8—81no—
222C2×C3×Q8C2×D412yes—
223C2×C3×D4—24no—
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—81no—
230C2×C3×D4—81no—
231C2×C3×D4C2×D412yes—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—24no—
242C22×C3×C4—81no—
243C22×C3×C4—81no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2×D411yescharacteristic
249C22×C3×C4C2411yescharacteristic
250C2×#67—24no—
251C2×#67—81no—
252C2×#67—81no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255C22×Dic3—21no—
256C2×D12—21no—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12—21no—
260C2×D12—21no—
261C2×D12#4112yes—
262C2×C4×D3—42no—
263C2×C4×D3—81no—
264C2×C4×D3—81no—
265C3×C4⋊C4—24no—
266C3×C4⋊C4—24no—
267C3×C4⋊C4—24no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4C2×D412yes—
273C3×C4⋊C4C2×D412yes—
274C3×C22⋊C4—24no—
275C3×C22⋊C4—24no—
276C3×C22⋊C4—24no—
277C3×C22⋊C4—24no—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—22no—
280C3×C22⋊C4—22no—
281C3×C42—24no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42C2×D412yes—
285C3×C42C2×D412yes—
286#217—81no—
287#215—28no—
288#213—28no—
289(C2×D3)⋊C4—24no—
290(C2×D3)⋊C4—42no—
291(C2×D3)⋊C4—81no—
292(C2×D3)⋊C4—81no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3#4112yes—
299Dic3⋊C4—81no—
300C4×Dic3—81no—
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—21no—
314C22×Q8C22×D311yescharacteristic
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—22no—
333C4⋊Q8—22no—
334#126—28no—
335#124—28no—
336#124—22no—
337#124—22no—
338#123—28no—
339C22⋊Q8—28no—
340C22⋊Q8—22no—
341C22⋊Q8—22no—
342#121—22no—
343#121—22no—
344#121—62no—
345#121—62no—
346C4×Q8—22no—
347C4×Q8#6714yescomplemented
348C4×D4—22no—
349C4×D4—62no—
350C4×D4—62no—
351C4×D4#6714yescomplemented
352#117—22no—
353#117—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—31no—
358C2×C4⋊C4—31no—
359C2×C4⋊C4—31no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4#6711yescharacteristic
362C2×C4⋊C4#6711yescharacteristic
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—61no—
396#95—61no—
397#95—61no—
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×Q8—22no—
421C3×Q8—22no—
422C3×Q8—41no—
423C3×Q8—41no—
424C3×Q8—84no—
425C3×D4—22no—
426C3×D4—22no—
427C3×D4—41no—
428C3×D4—41no—
429C3×D4—84no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—22no—
436C2×C3×C4—21no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—41no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—84no—
457C2×C3×C4#12012yes—
458C2×C3×C4#12012yes—
459C2×C3×C4C22×D411yescharacteristic
460C2×C3×C4C22×D411yescharacteristic
461C2×C3×C4C2×#4111yescharacteristic
462C2×C3×C4C2×#4111yescharacteristic
463C2×C3×C4C2×#4111yescharacteristic
464C2×C3×C4C2×#4111yescharacteristic
465#67—84no—
466C2×Dic3—22no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475D12—22no—
476D12—22no—
477D12—41no—
478D12—41no—
479C4×D3—84no—
480C3⋊C8—22no—
481C3⋊C8—22no—
482C3⋊C8—41no—
483C3⋊C8—41no—
484C24—21no—
485C24—61no—
486C24C2×#6711yescharacteristic
487C2×Q8—24no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—81no—
494C2×Q8—81no—
495C2×Q8C2×#6712yes—
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×D4C2×#6712yes—
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—24no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—81no—
528C22×C4—81no—
529C22×C4—122no—
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—24no—
553C4⋊C4—24no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—32no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—241no—
566C4⋊C4C2×#6712yes—
567C4⋊C4C2×#6712yes—
568C22⋊C4—24no—
569C22⋊C4—24no—
570C22⋊C4—24no—
571C22⋊C4—24no—
572C22⋊C4—24no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—64no—
576C22⋊C4—122no—
577C22⋊C4—241no—
578C22⋊C4—241no—
579C22⋊C4—241no—
580C42—24no—
581C42—21no—
582C42—21no—
583C42—241no—
584C42C2×#6712yes—
585C42C2×#6712yes—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—41no—
589C22×C3—42no—
590C22×C3—41no—
591C22×C3—41no—
592C22×C3—42no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—42no—
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—41no—
617C3×C4—42no—
618C3×C4—41no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4#52511yescharacteristic
623C3×C4#52511yescharacteristic
624C3×C4#53211yescharacteristic
625C3×C4#53211yescharacteristic
626Dic3—42no—
627Dic3—81no—
628Dic3—81no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—22no—
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—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655Q8—84no—
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—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—22no—
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—84no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—244no—
703C2×C4#95312yes—
704C2×C4#95312yes—
705C2×C4D3×#4111yescharacteristic
706C2×C4D3×#4111yescharacteristic
707C2×C4D3×#4111yescharacteristic
708C2×C4D3×#4111yescharacteristic
709C2×C4C22×#6711yescharacteristic
710C2×C4C22×#6711yescharacteristic
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—41no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—41no—
734C22—42no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—122no—
740C22—122no—
741C22—122no—
742C22—241no—
743C22—241no—
744C22—241no—
745C22—241no—
746C22#582811yescharacteristic
747C22#583211yescharacteristic
748C22#583511yescharacteristic
749C22#583511yescharacteristic
750C22#583711yescharacteristic
751C22#583811yescharacteristic
752C22C2×#95311yescharacteristic
753C4—22no—
754C4—22no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—42no—
759C4—42no—
760C4—41no—
761C4—122no—
762C4—241no—
763C4—241no—
764C4#582811yescharacteristic
765C4#582811yescharacteristic
766C4#583211yescharacteristic
767C4#583211yescharacteristic
768C3#2357911yescharacteristic, complemented, Sylow
769C2—81no—
770C2—82no—
771C2—242no—
772C2#8345711yescharacteristic
773C2#8345911yescharacteristic
774C2#8346011yescharacteristic
775C2#8346111yescharacteristic
776C2#8409511yescharacteristic
777C2#8410111yescharacteristic
778C2#8411411yescharacteristic
subgroupG/H
centerC23C22×#67
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC2×C3×#542C2
socleC23×C3C22×D4
prime radical#71684C2
hypercenterC2×#542D3
hypocenterC3#23579
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×C3×#542C2semidirect
2. C2×#5026C2semidirect
3. C2×C4×#213C2semidirect
4. #82236C2semidirect
5. #71792C2semidirect
6. #71782C2semidirect
7. #71728C2semidirect
8. #71722C2semidirect
9. #71699C2semidirect
10. #71695C2semidirect
12. #71679C2semidirect
13. C4×#835C2semidirect
14. #71609C2semidirect
15. #71582C2semidirect
64. C2×#542D3semidirect
101. C3×C4×Q8D4semidirect
103. C3×C4×D4D4semidirect
347. C4×Q8#67semidirect
351. C4×D4#67semidirect
768. C3#23579semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5422
C2×#50262
C2×C4×#2132
#822362
#717922
#717822
#717282
#717222
#716992
#716952
#716842
#716792
C4×#8352
#716092
#715822
#235793