Finite Group Databasebeta

← #10801012

Subgroups — #10801012

Order 768.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5827C211yesmaximal, characteristic
2C2×C3×#452C211yesmaximal, characteristic
3C2×Dic3×Q16C211yesmaximal, characteristic, complemented
4C2×#5164C211yesmaximal, characteristic, complemented
5#82744C211yesmaximal, characteristic, complemented
6#72135C211yesmaximal, characteristic
7#72065C211yesmaximal, characteristic, complemented
8#72047C211yesmaximal, characteristic, complemented
9#71692C211yesmaximal, characteristic, complemented
10#70236C211yesmaximal, characteristic, complemented
11#70220C211yesmaximal, characteristic, complemented
12#70168C211yesmaximal, characteristic, complemented
13Dic3×#102C211yesmaximal, characteristic, complemented
14#69927C211yesmaximal, characteristic, complemented
15#69907C211yesmaximal, characteristic, complemented
16#21465—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×Q16C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic
21#5827—24no—
22#5827—24no—
23C2×Q8×Dic3C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C2×Q8×Dic3C2211yescharacteristic
26C2×D4×Dic3—21no—
27C2×D4×Dic3—21no—
28C2×D4×Dic3C2211yescharacteristic
29C2×D4×Dic3C2211yescharacteristic
30C2×#926—21no—
31C2×#926C2211yescharacteristic
32C22×C4⋊Dic3—21no—
33C22×C4⋊Dic3C2211yescharacteristic
34C3×#452C418yescomplemented
35C2×C3×#103C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38#5229C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#835C2211yescharacteristic
42C2×#835C2211yescharacteristic
43C2×#832C2211yescharacteristic
44C2×#832C2211yescharacteristic
45#5212C2211yescharacteristic
46C2×#830C2211yescharacteristic
47Dic3×Q16—24no—
48#5164—24no—
49C2×#818C2211yescharacteristic
50C2×#818C2211yescharacteristic
51C2×#815C2211yescharacteristic
52C2×C8×Dic3C2211yescharacteristic
53#4984—21no—
54#4984C2211yescharacteristic
55#4980—21no—
56Dic3×C4⋊C4C2211yescharacteristic
57#4951—21no—
58#4951—21no—
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4550C2211yescharacteristic
62#4550C2211yescharacteristic
63#4529C2211yescharacteristic
64#4529C2211yescharacteristic
65C2×#520—31no—
66C2×#452D311yescharacteristic
67C2×#440—31no—
68C2×C4×Q16—31no—
69#2323—31no—
70#1878—31no—
71#1877—31no—
72#1872—31no—
73#1863—31no—
74#1862—31no—
75#1852—31no—
76#1788—31no—
77#1763—31no—
78C4×#102—31no—
79#1750—31no—
80C2×C3×#41—22no—
81C2×C3×#41—22no—
82C2×C3×#41—22no—
83C2×C3×#41—22no—
84C2×C3×#41—22no—
85C2×C3×#41C2×C414yes—
86C22×C3×Q8C2311yescharacteristic
87C22×C3×Q8C2311yescharacteristic
88C22×C3×D4—21no—
89C22×C3×D4C2311yescharacteristic
90C23×C3×C4—21no—
91C23×C3×C4C2311yescharacteristic
92C23×Dic3—21no—
93C23×Dic3—21no—
94C23×Dic3—21no—
95C2×C3×Q16—22no—
96C2×C3×Q16—22no—
97C2×C3×Q16C2×C414yescomplemented
98C2×C3×SD16—22no—
99C2×C3×SD16—22no—
100C2×C3×SD16C2×C414yescomplemented
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8C2×C414yescomplemented
105C2×C3×C4⋊C4—21no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×#217—21no—
109C2×#217—21no—
110C2×#217—21no—
111C2×#217D411yescharacteristic
112C2×#217D411yescharacteristic
113Q8×Dic3—22no—
114Q8×Dic3—22no—
115Q8×Dic3—22no—
116Q8×Dic3—22no—
117Q8×Dic3—22no—
118Q8×Dic3D414yes—
119D4×Dic3—28no—
120D4×Dic3—28no—
121D4×Dic3—22no—
122D4×Dic3—22no—
123D4×Dic3—22no—
124D4×Dic3D414yes—
125#926—28no—
126#926—22no—
127#926—22no—
128C2×C4⋊Dic3—28no—
129C2×C4⋊Dic3—21no—
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3—21no—
132C2×C4⋊Dic3—22no—
133C2×C4⋊Dic3—22no—
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3—21no—
136C2×C4⋊Dic3D411yescharacteristic
137C2×C4⋊Dic3D411yescharacteristic
138C2×C4⋊Dic3C2311yescharacteristic
139C2×C4⋊Dic3C2311yescharacteristic
140C2×C4⋊Dic3C2311yescharacteristic
141C2×C4⋊Dic3C2311yescharacteristic
142C2×C4×Dic3—21no—
143C2×C4×Dic3—21no—
144C2×C4×Dic3—21no—
145C2×C4×Dic3—21no—
146C2×C4×Dic3C2311yescharacteristic
147C2×C4×Dic3C2311yescharacteristic
148C22×C3⋊C8C2311yescharacteristic
149C22×C3⋊C8C2311yescharacteristic
150C3×#103C2×C414yescomplemented
151C3×#102C2×C414yescomplemented
152C3×C22⋊C8C2×C414yescomplemented
153#835—22no—
154#835—22no—
155#835—22no—
156#835—22no—
157#832—22no—
158#832—22no—
159C3⋊#95—21no—
160C3⋊#95—21no—
161C3⋊#95—21no—
162C3⋊#95—21no—
163C3⋊#95—21no—
164#830—22no—
165#818—22no—
166#818—22no—
167#815—22no—
168C8×Dic3—22no—
169C22×#41C2×D311yescharacteristic
170C22×Q16C2×D311yescharacteristic
171C22×SD16C2×D311yescharacteristic
172C2×C22⋊Q8C2×D311yescharacteristic
173#520—64no—
174#520—64no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×Q8—31no—
178C2×C4×D4—31no—
179C2×C4×D4—31no—
180C2×C4×D4—61no—
181C2×C4×D4—61no—
182C2×#117—31no—
183C2×#117—61no—
184C22×C4⋊C4—31no—
185C22×C4⋊C4—61no—
186#452Dic318yescomplemented
187#440—64no—
188C4×Q16—64no—
189C2×#107—31no—
190C2×#107—31no—
191C2×#103—31no—
192C2×#103—31no—
193C2×#103—31no—
194C2×#103—31no—
195C2×#103C2×D311yescharacteristic
196C2×#102—31no—
197C2×#102—31no—
198C2×#102C2×D311yescharacteristic
199C2×C22⋊C8—31no—
200C2×C22⋊C8C2×D311yescharacteristic
201C2×#97—31no—
202C2×C4×C8—31no—
203#391—31no—
204#389—31no—
205#389—61no—
206#388—61no—
207#388—61no—
208#387—61no—
209#380—31no—
210C4×C4⋊C4—31no—
211#340—31no—
212#340—31no—
213#340—31no—
214#340—31no—
215#336—31no—
216#336—31no—
217C24×C3—21no—
218C24×C3C2×D411yescharacteristic
219C3×#41—28no—
220C3×#41—28no—
221C3×#41—28no—
222C3×#41—28no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—21no—
229C2×C3×Q8—21no—
230C2×C3×Q8—21no—
231C2×C3×Q8C22×C412yes—
232C2×C3×Q8C22×C412yes—
233C2×C3×Q8C2×D412yes—
234C2×C3×Q8#4112yes—
235C2×C3×D4—24no—
236C2×C3×D4—24no—
237C2×C3×D4—24no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4C22×C412yes—
242C2×C3×D4C2×D412yes—
243C2×C3×D4#4112yes—
244C22×C3×C4—24no—
245C22×C3×C4—24no—
246C22×C3×C4—21no—
247C22×C3×C4—24no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4C22×C412yes—
255C22×C3×C4C2×D411yescharacteristic
256C22×C3×C4#4112yes—
257C22×C3×C4C2411yescharacteristic
258C22×Dic3—21no—
259C22×Dic3—21no—
260C22×Dic3—24no—
261C22×Dic3—24no—
262C22×Dic3—24no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3—81no—
266C22×Dic3—81no—
267C22×Dic3—81no—
268C22×Dic3—81no—
269C22×Dic3—81no—
270C22×Dic3—81no—
271C22×Dic3C2×D411yescharacteristic
272C22×Dic3C2×D411yescharacteristic
273C22×Dic3C2×D411yescharacteristic
274C22×Dic3C2×D411yescharacteristic
275C3×Q16—28no—
276C3×SD16—28no—
277C2×C3×C8—21no—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8C22×C412yes—
282C2×C3×C8C22×C412yes—
283C3×C4⋊C4—24no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4C22×C412yes—
286C3×C22⋊C4—24no—
287#217—24no—
288#217—22no—
289#217—22no—
290#217—24no—
291#217—81no—
292C4⋊Dic3—24no—
293C4⋊Dic3—24no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—22no—
297C4⋊Dic3—24no—
298C4⋊Dic3—22no—
299C4⋊Dic3—21no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—42no—
304C4⋊Dic3—81no—
305C4⋊Dic3C2×D412yes—
306C4⋊Dic3C2×D412yes—
307C4×Dic3—24no—
308C4×Dic3—21no—
309C4×Dic3—21no—
310C4×Dic3—24no—
311C4×Dic3—42no—
312C4×Dic3—81no—
313C4×Dic3C2×D412yes—
314C4×Dic3C2×D412yes—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—21no—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41—22no—
325C2×#41—22no—
326C2×#41C2×Dic314yes—
327C22×Q8C22×D311yescharacteristic
328C22×Q8C22×D311yescharacteristic
329C22×D4—21no—
330C22×D4C22×D311yescharacteristic
331C23×C4—21no—
332C23×C4—61no—
333C23×C4—61no—
334C23×C4—61no—
335C23×C4C22×D311yescharacteristic
336C2×Q16—22no—
337C2×Q16—22no—
338C2×Q16C2×Dic314yescomplemented
339C2×SD16—22no—
340C2×SD16—22no—
341C2×SD16C2×Dic314yescomplemented
342C22×C8—31no—
343C22×C8—31no—
344C22×C8C22×D311yescharacteristic
345C22×C8C22×D311yescharacteristic
346C22⋊Q8—22no—
347C22⋊Q8C2×Dic314yescomplemented
348C4×Q8—34no—
349C4×Q8—62no—
350C4×Q8—62no—
351C4×Q8—62no—
352C4×Q8—62no—
353C4×Q8—62no—
354C4×D4—34no—
355C4×D4—62no—
356C4×D4—62no—
357C4×D4—68no—
358C4×D4—68no—
359C4×D4—62no—
360#117—62no—
361#117—62no—
362#117—68no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4—62no—
371C2×C4⋊C4—62no—
372C2×C4⋊C4—61no—
373C2×C4⋊C4—61no—
374C2×C4⋊C4—68no—
375C2×C4⋊C4—61no—
376C2×C4⋊C4—61no—
377C2×C4⋊C4—61no—
378C2×C4⋊C4C22×D311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—31no—
381C2×C22⋊C4—31no—
382C2×C22⋊C4—61no—
383C2×C22⋊C4—61no—
384C2×C22⋊C4—61no—
385C2×C42—31no—
386C2×C42—31no—
387C2×C42—61no—
388C2×C42—61no—
389C2×C42—61no—
390C2×C42—61no—
391#107—62no—
392#107—62no—
393#103—62no—
394#103—62no—
395#103—62no—
396#103—62no—
397#103C2×Dic314yescomplemented
398#102—62no—
399#102—62no—
400#102C2×Dic314yescomplemented
401C22⋊C8—62no—
402C22⋊C8C2×Dic314yescomplemented
403#97—62no—
404C4×C8—62no—
405#95—61no—
406#95—61no—
407#95—61no—
408#95—61no—
409#95—61no—
410C23×C3—22no—
411C23×C3—21no—
412C23×C3—22no—
413C23×C3—21no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—41no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3C4×D412yes—
424C23×C3C22×D411yescharacteristic
425C3×Q8—22no—
426C3×Q8—22no—
427C3×Q8—22no—
428C3×Q8—22no—
429C3×Q8—22no—
430C3×Q8—41no—
431C3×Q8—41no—
432C3×Q8C4×D414yes—
433C3×D4—216no—
434C3×D4—22no—
435C3×D4—22no—
436C3×D4—22no—
437C3×D4C4×D414yes—
438C2×C3×C4—216no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4C4×D412yes—
455C2×C3×C4C23×C411yescharacteristic
456C2×C3×C4C22×D411yescharacteristic
457C2×C3×C4C22×D411yescharacteristic
458C2×C3×C4C2×#4111yescharacteristic
459C2×C3×C4C2×#4111yescharacteristic
460C2×C3×C4C2×#4111yescharacteristic
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—21no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—21no—
470C2×Dic3—21no—
471C2×Dic3—21no—
472C2×Dic3—21no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—84no—
484C2×Dic3—84no—
485C2×Dic3—84no—
486C2×Dic3#12012yes—
487C2×Dic3#12012yes—
488C3×C8—22no—
489C3×C8—22no—
490C3⋊C8—41no—
491C3⋊C8—41no—
492C24—21no—
493C24D3×D411yescharacteristic
494#41—28no—
495#41—28no—
496#41—28no—
497#41—28no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8D3×D412yes—
507C2×Q8#23712yes—
508C2×Q8C22×Dic312yes—
509C2×Q8C22×Dic312yes—
510C2×D4—24no—
511C2×D4—24no—
512C2×D4—24no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4D3×D412yes—
517C2×D4#23712yes—
518C2×D4C22×Dic312yes—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—64no—
534C22×C4—61no—
535C22×C4—61no—
536C22×C4—64no—
537C22×C4—64no—
538C22×C4—61no—
539C22×C4—61no—
540C22×C4—241no—
541C22×C4—241no—
542C22×C4—241no—
543C22×C4—241no—
544C22×C4—241no—
545C22×C4—241no—
546C22×C4D3×D411yescharacteristic
547C22×C4#23712yes—
548C22×C4C22×Dic312yes—
549C22×C4C23×D311yescharacteristic
550Q16—28no—
551SD16—28no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—61no—
557C2×C8—61no—
558C2×C8—61no—
559C2×C8—61no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8C22×Dic312yes—
563C2×C8C22×Dic312yes—
564C4⋊C4—24no—
565C4⋊C4—21no—
566C4⋊C4—32no—
567C4⋊C4—32no—
568C4⋊C4—62no—
569C4⋊C4—62no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—64no—
573C4⋊C4—61no—
574C4⋊C4—61no—
575C4⋊C4—61no—
576C4⋊C4—61no—
577C4⋊C4—61no—
578C4⋊C4—61no—
579C4⋊C4—122no—
580C4⋊C4—241no—
581C4⋊C4C22×Dic312yes—
582C22⋊C4—24no—
583C22⋊C4—62no—
584C22⋊C4—62no—
585C22⋊C4—64no—
586C22⋊C4—64no—
587C22⋊C4—241no—
588C42—32no—
589C42—32no—
590C42—64no—
591C42—64no—
592C42—61no—
593C42—61no—
594C42—122no—
595C42—241no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—24no—
600C22×C3—41no—
601C22×C3—42no—
602C22×C3—41no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—41no—
607C22×C3—42no—
608C22×C3—41no—
609C22×C3—42no—
610C22×C3C2×C4×D411yescharacteristic
611C22×C3C2×#12011yescharacteristic
612C22×C3#52511yescharacteristic
613C22×C3#57611yescharacteristic
614C22×C3#57711yescharacteristic
615C22×C3#57811yescharacteristic
616C22×C3#57811yescharacteristic
617C3×C4—22no—
618C3×C4—24no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4C2×C4×D411yescharacteristic
622C3×C4C2×C4×D411yescharacteristic
623C3×C4#52511yescharacteristic
624C3×C4#52511yescharacteristic
625Dic3—22no—
626Dic3—22no—
627Dic3—41no—
628Dic3—41no—
629Dic3—42no—
630Dic3—42no—
631Dic3—81no—
632Dic3—81no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—22no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23D4×Dic312yes—
647C23C2×D3×D411yescharacteristic
648Q8—22no—
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8—22no—
653Q8—41no—
654Q8—41no—
655Q8D4×Dic314yes—
656D4—216no—
657D4—22no—
658D4—22no—
659D4—22no—
660D4D4×Dic314yes—
661C2×C4—216no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—32no—
674C2×C4—32no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—62no—
689C2×C4—62no—
690C2×C4—61no—
691C2×C4—121no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C4—244no—
702C2×C4—244no—
703C2×C4—244no—
704C2×C4D4×Dic312yes—
705C2×C4C2×D3×D411yescharacteristic
706C2×C4C2×D3×D411yescharacteristic
707C2×C4C2×#23711yescharacteristic
708C2×C4C2×#23711yescharacteristic
709C2×C4C2×#23711yescharacteristic
710C2×C4C23×Dic311yescharacteristic
711C8—22no—
712C8—22no—
713C8—121no—
714C8—121no—
715C2×C3—42no—
716C2×C3—44no—
717C2×C3C4×#12011yescharacteristic
718C2×C3#294711yescharacteristic
719C2×C3#295111yescharacteristic
720C2×C3#301111yescharacteristic
721C2×C3#301211yescharacteristic
722C2×C3#312011yescharacteristic
723C2×C3#312411yescharacteristic
724C22—22no—
725C22—24no—
726C22—22no—
727C22—22no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22#558611yescharacteristic
739C22D3×#12011yescharacteristic
740C22#576911yescharacteristic
741C22#577111yescharacteristic
742C22#577811yescharacteristic
743C22#577911yescharacteristic
744C22C2×D4×Dic311yescharacteristic
745C4—22no—
746C4—24no—
747C4—42no—
748C4—42no—
749C4—62no—
750C4—62no—
751C4—121no—
752C4—121no—
753C4—122no—
754C4—122no—
755C4—241no—
756C4—241no—
757C4#558611yescharacteristic
758C4#558611yescharacteristic
759C4C2×D4×Dic311yescharacteristic
760C4C2×D4×Dic311yescharacteristic
761C3#2146511yescharacteristic, complemented, Sylow
762C2—42no—
763C2—44no—
764C2#8021711yescharacteristic
765C2#8021811yescharacteristic
766C2#8023011yescharacteristic
767C2#8023111yescharacteristic
768C2Dic3×#12011yescharacteristic
769C2#8389811yescharacteristic
770C2#8396511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC2×C3×#452C2
socleC23×C3C22×D4
prime radicalC22×C3×#41C22
cosocleC22×C3×C4C24
hypercenterC2×#452D3
hypocenterC3#21465
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
3. C2×Dic3×Q16C2semidirect
4. C2×#5164C2semidirect
5. #82744C2semidirect
7. #72065C2semidirect
8. #72047C2semidirect
9. #71692C2semidirect
10. #70236C2semidirect
11. #70220C2semidirect
12. #70168C2semidirect
13. Dic3×#102C2semidirect
14. #69927C2semidirect
15. #69907C2semidirect
34. C3×#452C4semidirect
97. C2×C3×Q16C2×C4semidirect
100. C2×C3×SD16C2×C4semidirect
104. C3×C22⋊Q8C2×C4semidirect
150. C3×#103C2×C4semidirect
151. C3×#102C2×C4semidirect
152. C3×C22⋊C8C2×C4semidirect
186. #452Dic3semidirect
338. C2×Q16C2×Dic3semidirect
341. C2×SD16C2×Dic3semidirect
347. C22⋊Q8C2×Dic3semidirect
397. #103C2×Dic3semidirect
400. #102C2×Dic3semidirect
402. C22⋊C8C2×Dic3semidirect
761. C3#21465semidirect

Maximal subgroups

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

subgroupindex
C2×#58272
C2×C3×#4522
C2×Dic3×Q162
C2×#51642
#827442
#721352
#720652
#720472
#716922
#702362
#702202
#701682
Dic3×#1022
#699272
#699072
#214653