Finite Group Databasebeta

← #10702248

Subgroups — #10702248

Order 768.

1066 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#389C211yesmaximal, characteristic
2C22×#810C211yesmaximal, characteristic
3C22×#810C211yesmaximal, characteristic
4C2×#4929C211yesmaximal, characteristic
5C2×#4529C211yesmaximal, characteristic
6C2×#4529C211yesmaximal, characteristic
7C2×#4524C211yesmaximal, characteristic
8#11067—31nomaximal, Sylow
9C23×Dic6C2211yescharacteristic
10C22×C3×C4⋊C4—21no—
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C22×C3×C42C2211yescharacteristic
14C22×C4⋊Dic3C2211yescharacteristic
15C23×C3⋊C8C2211yescharacteristic
16C23×C3⋊C8C2211yescharacteristic
17C3×#389—22no—
18C3×#389—22no—
19C2×C3×#95—21no—
20C2×C3⋊#95—21no—
21C2×C3⋊#95—21no—
22C2×#810—22no—
23C2×#810—22no—
24C2×#810—22no—
25C2×#810—22no—
26C2×#810—22no—
27C2×#810C414yescomplemented
28#4929—22no—
29#4929—22no—
30#4529—22no—
31#4529—22no—
32#4524—22no—
33C22×#103—31no—
34C22×#103—31no—
35C2×#391—31no—
36C2×#389D311yescharacteristic
37C2×#340—31no—
38C2×#340—31no—
39C2×#336—31no—
40C23×C3×C4—21no—
41C23×C3×C4—21no—
42C23×C3×C4D411yescharacteristic
43C23×C3×C4D411yescharacteristic
44C23×C3×C4C2311yescharacteristic
45C23×Dic3—21no—
46C23×Dic3—21no—
47C22×Dic6—21no—
48C22×Dic6—21no—
49C22×Dic6—21no—
50C22×Dic6—21no—
51C22×Dic6—21no—
52C22×Dic6—21no—
53C22×Dic6—21no—
54C22×Dic6—21no—
55C22×Dic6—21no—
56C22×Dic6—21no—
57C22×Dic6—21no—
58C22×Dic6C2×C412yes—
59C22×Dic6D412yes—
60C22×Dic6Q812yes—
61C2×C3×C4⋊C4—21no—
62C2×C3×C4⋊C4—21no—
63C2×C3×C4⋊C4—21no—
64C2×C3×C4⋊C4—21no—
65C2×C3×C4⋊C4—21no—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4—21no—
68C2×C3×C4⋊C4—24no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—42no—
71C2×C3×C4⋊C4—42no—
72C2×C3×C4⋊C4C2×C412yes—
73C2×C3×C4⋊C4D412yes—
74C2×C3×C4⋊C4D412yes—
75C2×C3×C4⋊C4D412yes—
76C2×C3×C42—21no—
77C2×C3×C42—21no—
78C2×C3×C42—21no—
79C2×C3×C42—21no—
80C2×C3×C42—21no—
81C2×C3×C42—21no—
82C2×C4⋊Dic3—21no—
83C2×C4⋊Dic3—21no—
84C2×C4⋊Dic3—21no—
85C2×C4⋊Dic3—21no—
86C2×C4⋊Dic3—21no—
87C2×C4⋊Dic3D412yes—
88C22×C3⋊C8—21no—
89C22×C3⋊C8—21no—
90C22×C3⋊C8—21no—
91C22×C3⋊C8—21no—
92C22×C3⋊C8—21no—
93C22×C3⋊C8—21no—
94C22×C3⋊C8—21no—
95C22×C3⋊C8—21no—
96C22×C3⋊C8—21no—
97C22×C3⋊C8—21no—
98C22×C3⋊C8—21no—
99C22×C3⋊C8—21no—
100C22×C3⋊C8C2×C412yes—
101C22×C3⋊C8D412yes—
102C3×#95—24no—
103C3⋊#95—24no—
104C3⋊#95—24no—
105#810—28no—
106#810—28no—
107C23×Q8—31no—
108C23×C8—31no—
109C23×C8—31no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—31no—
112C22×C4⋊C4C2×D311yescharacteristic
113C22×C4⋊C4C2×D311yescharacteristic
114C22×C42C2×D311yescharacteristic
115C2×#103—34no—
116C2×#103—62no—
117C2×#103—62no—
118C2×#103—62no—
119C2×#103—62no—
120C2×#103—62no—
121#391—62no—
122#391—62no—
123#389—22no—
124#389—22no—
125C2×#95—21no—
126C2×#95—61no—
127C2×#95—61no—
128#340—62no—
129#340—62no—
130#336—62no—
131C24×C3C2×D411yescharacteristic
132C22×C3×C4—22no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—21no—
136C22×C3×C4—22no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—22no—
141C22×C3×C4—21no—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4—21no—
145C22×C3×C4—21no—
146C22×C3×C4—21no—
147C22×C3×C4—22no—
148C22×C3×C4—41no—
149C22×C3×C4—41no—
150C22×C3×C4—41no—
151C22×C3×C4—41no—
152C22×C3×C4—41no—
153C22×C3×C4—41no—
154C22×C3×C4—41no—
155C22×C3×C4—41no—
156C22×C3×C4—41no—
157C22×C3×C4—41no—
158C22×C3×C4SD1612yes—
159C22×C3×C4Q1612yes—
160C22×C3×C4C22×C411yescharacteristic
161C22×C3×C4C2×D411yescharacteristic
162C22×C3×C4C2×D411yescharacteristic
163C22×C3×C4C2×D411yescharacteristic
164C22×C3×C4C2×D411yescharacteristic
165C22×C3×C4C2×D411yescharacteristic
166C22×C3×C4C2×D411yescharacteristic
167C22×C3×C4C2×Q811yescharacteristic
168C22×C3×C4#4111yescharacteristic
169C22×C3×C4#4111yescharacteristic
170C22×C3×C4#4111yescharacteristic
171C22×C3×C4#4111yescharacteristic
172C22×C3×C4#4111yescharacteristic
173C22×C3×C4#4111yescharacteristic
174C22×Dic3—22no—
175C22×Dic3—22no—
176C22×Dic3—22no—
177C22×Dic3—22no—
178C22×Dic3—41no—
179C22×Dic3—41no—
180C22×Dic3—41no—
181C22×Dic3—41no—
182C22×Dic3—41no—
183C22×Dic3—41no—
184C22×Dic3—41no—
185C22×Dic3—41no—
186C22×Dic3—41no—
187C22×Dic3—41no—
188C2×Dic6—22no—
189C2×Dic6—22no—
190C2×Dic6—22no—
191C2×Dic6—22no—
192C2×Dic6—22no—
193C2×Dic6—22no—
194C2×Dic6—22no—
195C2×Dic6—22no—
196C2×Dic6—22no—
197C2×Dic6—22no—
198C2×Dic6—22no—
199C2×Dic6—22no—
200C2×Dic6—22no—
201C2×Dic6—22no—
202C2×Dic6—22no—
203C2×Dic6—41no—
204C2×Dic6—41no—
205C2×Dic6—41no—
206C2×Dic6—41no—
207C2×Dic6—41no—
208C2×Dic6—41no—
209C2×Dic6—41no—
210C2×Dic6—41no—
211C2×Dic6—41no—
212C2×Dic6—41no—
213C2×Dic6—41no—
214C2×Dic6—41no—
215C2×Dic6C4⋊C414yescomplemented
216C3×C4⋊C4—22no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—22no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—48no—
222C3×C4⋊C4—41no—
223C3×C4⋊C4—41no—
224C3×C4⋊C4C22⋊C414yes—
225C3×C42—41no—
226C3×C42—41no—
227C3×C42—41no—
228C3×C42—41no—
229C4⋊Dic3—22no—
230C4⋊Dic3—22no—
231C4⋊Dic3—41no—
232C4⋊Dic3—41no—
233C2×C3⋊C8—22no—
234C2×C3⋊C8—22no—
235C2×C3⋊C8—22no—
236C2×C3⋊C8—22no—
237C2×C3⋊C8—22no—
238C2×C3⋊C8—22no—
239C2×C3⋊C8—41no—
240C2×C3⋊C8—41no—
241C2×C3⋊C8—41no—
242C2×C3⋊C8—41no—
243C2×C3⋊C8—41no—
244C2×C3⋊C8—41no—
245C2×C3⋊C8—41no—
246C2×C3⋊C8—41no—
247C22×Q8—32no—
248C22×Q8—32no—
249C22×Q8—32no—
250C22×Q8—61no—
251C22×Q8—61no—
252C22×Q8—61no—
253C22×Q8—61no—
254C22×Q8—61no—
255C22×Q8—61no—
256C22×Q8—61no—
257C22×Q8—61no—
258C22×Q8—61no—
259C22×Q8—61no—
260C22×Q8—61no—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—61no—
264C23×C4—61no—
265C23×C4#6711yescharacteristic
266C23×C4#6711yescharacteristic
267C23×C4C22×D311yescharacteristic
268C22×C8—32no—
269C22×C8—32no—
270C22×C8—61no—
271C22×C8—61no—
272C22×C8—61no—
273C22×C8—61no—
274C22×C8—61no—
275C22×C8—61no—
276C22×C8—61no—
277C22×C8—61no—
278C22×C8—61no—
279C22×C8—61no—
280C22×C8—61no—
281C22×C8—61no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—32no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—61no—
295C2×C4⋊C4—61no—
296C2×C4⋊C4—61no—
297C2×C4⋊C4—61no—
298C2×C4⋊C4—61no—
299C2×C4⋊C4C4×D312yes—
300C2×C4⋊C4D1212yes—
301C2×C4⋊C4#6712yes—
302C2×C4⋊C4#6712yes—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309#103—68no—
310#103—68no—
311#95—24no—
312#95—64no—
313#95—64no—
314C23×C3C4×D411yescharacteristic
315C23×C3#12011yescharacteristic
316C23×C3#12011yescharacteristic
317C23×C3#12111yescharacteristic
318C23×C3#12111yescharacteristic
319C23×C3C22⋊Q811yescharacteristic
320C23×C3#12411yescharacteristic
321C23×C3C2×SD1611yescharacteristic
322C23×C3C2×Q1611yescharacteristic
323C23×C3#13511yescharacteristic
324C23×C3#13511yescharacteristic
325C23×C3AGL(1,ℤ/8)11yescharacteristic
326C23×C3#13711yescharacteristic
327C23×C3#13711yescharacteristic
328C23×C3#13711yescharacteristic
329C2×C3×C4—24no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—41no—
337C2×C3×C4—41no—
338C2×C3×C4—42no—
339C2×C3×C4—42no—
340C2×C3×C4—41no—
341C2×C3×C4—42no—
342C2×C3×C4—41no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
352C2×C3×C4—42no—
353C2×C3×C4—81no—
354C2×C3×C4—81no—
355C2×C3×C4—81no—
356C2×C3×C4—81no—
357C2×C3×C4C2×C22⋊C411yescharacteristic
358C2×C3×C4C2×C4⋊C411yescharacteristic
359C2×C3×C4#11711yescharacteristic
360C2×C3×C4C4×D411yescharacteristic
361C2×C3×C4C4×D411yescharacteristic
362C2×C3×C4C4×D411yescharacteristic
363C2×C3×C4#12011yescharacteristic
364C2×C3×C4#12111yescharacteristic
365C2×C3×C4#12111yescharacteristic
366C2×C3×C4#12111yescharacteristic
367C2×C3×C4#12111yescharacteristic
368C2×C3×C4#12111yescharacteristic
369C2×C3×C4#12111yescharacteristic
370C2×C3×C4C22⋊Q811yescharacteristic
371C2×C3×C4C22⋊Q811yescharacteristic
372C2×C3×C4C22⋊Q811yescharacteristic
373C2×C3×C4C22⋊Q811yescharacteristic
374C2×C3×C4C22⋊Q811yescharacteristic
375C2×C3×C4#12311yescharacteristic
376C2×C3×C4#12311yescharacteristic
377C2×C3×C4#12311yescharacteristic
378C2×C3×C4#12311yescharacteristic
379C2×C3×C4#12311yescharacteristic
380C2×C3×C4#12411yescharacteristic
381C2×C3×C4#12411yescharacteristic
382C2×C3×C4#12611yescharacteristic
383C2×C3×C4#12611yescharacteristic
384C2×C3×C4#12711yescharacteristic
385C2×Dic3—24no—
386C2×Dic3—42no—
387C2×Dic3—42no—
388C2×Dic3—42no—
389C2×Dic3—42no—
390C2×Dic3—42no—
391C2×Dic3—42no—
392C2×Dic3—42no—
393C2×Dic3—42no—
394C2×Dic3—42no—
395C2×Dic3—81no—
396C2×Dic3—81no—
397C2×Dic3—81no—
398C2×Dic3—81no—
399Dic6—24no—
400Dic6—24no—
401Dic6—42no—
402Dic6—42no—
403Dic6—42no—
404Dic6—42no—
405Dic6—42no—
406Dic6—42no—
407C3⋊C8—42no—
408C3⋊C8—42no—
409C24C2×#6711yescharacteristic
410C2×Q8—34no—
411C2×Q8—62no—
412C2×Q8—62no—
413C2×Q8—62no—
414C2×Q8—62no—
415C2×Q8—62no—
416C2×Q8—62no—
417C2×Q8—62no—
418C2×Q8—62no—
419C2×Q8—62no—
420C2×Q8—62no—
421C2×Q8—62no—
422C2×Q8—62no—
423C2×Q8—62no—
424C2×Q8—62no—
425C2×Q8—62no—
426C2×Q8—121no—
427C2×Q8—121no—
428C2×Q8—121no—
429C2×Q8—121no—
430C2×Q8—121no—
431C2×Q8—121no—
432C2×Q8—121no—
433C2×Q8—121no—
434C2×Q8—121no—
435C2×Q8—121no—
436C2×Q8—121no—
437C2×Q8—121no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—62no—
465C22×C4—62no—
466C22×C4—62no—
467C22×C4—62no—
468C22×C4—121no—
469C22×C4—121no—
470C22×C4—121no—
471C22×C4—121no—
472C22×C4—121no—
473C22×C4—121no—
474C22×C4—121no—
475C22×C4—121no—
476C22×C4—121no—
477C22×C4—121no—
478C22×C4#21412yes—
479C22×C4#21612yes—
480C22×C4C2×C4×D311yescharacteristic
481C22×C4C2×D1211yescharacteristic
482C22×C4#23511yescharacteristic
483C22×C4#23511yescharacteristic
484C22×C4D3×D411yescharacteristic
485C22×C4D3×D411yescharacteristic
486C22×C4D3×D411yescharacteristic
487C22×C4#23711yescharacteristic
488C22×C4D3×Q811yescharacteristic
489C22×C4#23911yescharacteristic
490C22×C4#23911yescharacteristic
491C22×C4#23911yescharacteristic
492C22×C4C2×#6711yescharacteristic
493C22×C4C2×#6711yescharacteristic
494C2×C8—62no—
495C2×C8—62no—
496C2×C8—62no—
497C2×C8—62no—
498C2×C8—62no—
499C2×C8—62no—
500C2×C8—121no—
501C2×C8—121no—
502C2×C8—121no—
503C2×C8—121no—
504C2×C8—121no—
505C2×C8—121no—
506C2×C8—121no—
507C2×C8—121no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—48no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—62no—
517C4⋊C4—62no—
518C4⋊C4—121no—
519C4⋊C4—121no—
520C4⋊C4(C2×D3)⋊C414yes—
521C42—41no—
522C42—41no—
523C42—41no—
524C42—41no—
525C22×C3#38511yescharacteristic
526C22×C3#38611yescharacteristic
527C22×C3#38811yescharacteristic
528C22×C3#39211yescharacteristic
529C22×C3#39311yescharacteristic
530C22×C3#39411yescharacteristic
531C22×C3#39611yescharacteristic
532C22×C3C4×SD1611yescharacteristic
533C22×C3C4×Q1611yescharacteristic
534C22×C3#44011yescharacteristic
535C22×C3#44111yescharacteristic
536C22×C3#44811yescharacteristic
537C22×C3#44911yescharacteristic
538C22×C3#45011yescharacteristic
539C22×C3#45111yescharacteristic
540C22×C3#45111yescharacteristic
541C22×C3#45211yescharacteristic
542C22×C3#45211yescharacteristic
543C22×C3#45211yescharacteristic
544C22×C3#46111yescharacteristic
545C22×C3#46211yescharacteristic
546C22×C3#46311yescharacteristic
547C22×C3#46411yescharacteristic
548C22×C3#46511yescharacteristic
549C22×C3#46711yescharacteristic
550C22×C3#46811yescharacteristic
551C22×C3#47011yescharacteristic
552C22×C3#47511yescharacteristic
553C22×C3#47711yescharacteristic
554C22×C3#47911yescharacteristic
555C22×C3#47911yescharacteristic
556C22×C3#48711yescharacteristic
557C22×C3#48811yescharacteristic
558C22×C3#48911yescharacteristic
559C22×C3#49111yescharacteristic
560C3×C4—44no—
561C3×C4—42no—
562C3×C4—42no—
563C3×C4—82no—
564C3×C4#38011yescharacteristic
565C3×C4#38511yescharacteristic
566C3×C4#38811yescharacteristic
567C3×C4#39011yescharacteristic
568C3×C4#39411yescharacteristic
569C3×C4#39611yescharacteristic
570C3×C4#39711yescharacteristic
571C3×C4#39911yescharacteristic
572Dic3—44no—
573Dic3—82no—
574C23C4×#6711yescharacteristic
575C23#93011yescharacteristic
576C23#93211yescharacteristic
577C23C2×#21411yescharacteristic
578C23#93711yescharacteristic
579C23#93911yescharacteristic
580C23#94211yescharacteristic
581C23C2×#21611yescharacteristic
582C23#94611yescharacteristic
583C23#94711yescharacteristic
584C23#95011yescharacteristic
585C23#95011yescharacteristic
586C23#95111yescharacteristic
587C23#95111yescharacteristic
588C23#95311yescharacteristic
589Q8—64no—
590Q8—64no—
591Q8—122no—
592Q8—122no—
593Q8—122no—
594Q8—122no—
595Q8—122no—
596Q8—122no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—42no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—64no—
622C2×C4—81no—
623C2×C4—81no—
624C2×C4—81no—
625C2×C4—81no—
626C2×C4—122no—
627C2×C4—122no—
628C2×C4—122no—
629C2×C4—122no—
630C2×C4—122no—
631C2×C4—122no—
632C2×C4—122no—
633C2×C4—122no—
634C2×C4—122no—
635C2×C4—241no—
636C2×C4—241no—
637C2×C4—241no—
638C2×C4—241no—
639C2×C4D3×C4⋊C411yescharacteristic
640C2×C4#89211yescharacteristic
641C2×C4#89311yescharacteristic
642C2×C4#89311yescharacteristic
643C2×C4#89411yescharacteristic
644C2×C4#89411yescharacteristic
645C2×C4#89411yescharacteristic
646C2×C4#89411yescharacteristic
647C2×C4#89511yescharacteristic
648C2×C4#89511yescharacteristic
649C2×C4#89511yescharacteristic
650C2×C4#89611yescharacteristic
651C2×C4#89611yescharacteristic
652C2×C4#89711yescharacteristic
653C2×C4#89811yescharacteristic
654C2×C4#89811yescharacteristic
655C2×C4C2×(C2×D3)⋊C411yescharacteristic
656C2×C4C4×#6711yescharacteristic
657C2×C4#92911yescharacteristic
658C2×C4#93011yescharacteristic
659C2×C4#93711yescharacteristic
660C2×C4#93811yescharacteristic
661C2×C4#93911yescharacteristic
662C2×C4#94011yescharacteristic
663C2×C4#94611yescharacteristic
664C2×C4#94611yescharacteristic
665C2×C4#94711yescharacteristic
666C2×C4#94711yescharacteristic
667C8—122no—
668C8—122no—
669C2×C3#143911yescharacteristic
670C2×C3#186311yescharacteristic
671C2×C3#186511yescharacteristic
672C2×C3#187711yescharacteristic
673C2×C3#187811yescharacteristic
674C2×C3#193311yescharacteristic
675C2×C3#193511yescharacteristic
676C2×C3#200011yescharacteristic
677C2×C3#200111yescharacteristic
678C2×C3#202411yescharacteristic
679C2×C3#202611yescharacteristic
680C2×C3#204211yescharacteristic
681C2×C3#204311yescharacteristic
682C2×C3#206611yescharacteristic
683C2×C3#206811yescharacteristic
684C22#498911yescharacteristic
685C22#499011yescharacteristic
686C22#499111yescharacteristic
687C22#499411yescharacteristic
688C22#501611yescharacteristic
689C22C4×#21411yescharacteristic
690C22#501811yescharacteristic
691C22#501911yescharacteristic
692C22#502811yescharacteristic
693C22C4×#21611yescharacteristic
694C22#503011yescharacteristic
695C22#503111yescharacteristic
696C22#503711yescharacteristic
697C22#504011yescharacteristic
698C22#504111yescharacteristic
699C22#504211yescharacteristic
700C22#504711yescharacteristic
701C22#505011yescharacteristic
702C22#505111yescharacteristic
703C22#505211yescharacteristic
704C22#506311yescharacteristic
705C22#506311yescharacteristic
706C22#506811yescharacteristic
707C22#506911yescharacteristic
708C22#508911yescharacteristic
709C22#509111yescharacteristic
710C22#509311yescharacteristic
711C22#509411yescharacteristic
712C22#521311yescharacteristic
713C22#521811yescharacteristic
714C22#522311yescharacteristic
715C22#522811yescharacteristic
716C22#523111yescharacteristic
717C22#523911yescharacteristic
718C22#523911yescharacteristic
719C4—42no—
720C4—42no—
721C4—44no—
722C4—82no—
723C4—124no—
724C4—242no—
725C4#498711yescharacteristic
726C4#498811yescharacteristic
727C4#498911yescharacteristic
728C4#499011yescharacteristic
729C4#499111yescharacteristic
730C4#499211yescharacteristic
731C4#499311yescharacteristic
732C4#499411yescharacteristic
733C3#1106711yescharacteristic, complemented, Sylow
734C2#6961411yescharacteristic
735C2#6961611yescharacteristic
736C2#6962811yescharacteristic
737C2#6963111yescharacteristic
738C2#6963211yescharacteristic
739C2#6963311yescharacteristic
740C2#6963411yescharacteristic
741C2#6963511yescharacteristic
742C2#7157011yescharacteristic
743C2#7161211yescharacteristic
744C2#7163211yescharacteristic
745C2#7168511yescharacteristic
746C2#7170011yescharacteristic
747C2#7174411yescharacteristic
748C2#7179411yescharacteristic
subgroupG/H
centerC24C2×#67
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#389C2
socle, prime radicalC24×C3C2×D4
cosocleC23×C3×C4C23
hypercenterC2×#389D3
hypocenterC3#11067
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
27. C2×#810C4semidirect
215. C2×Dic6C4⋊C4semidirect
733. C3#11067semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#3892
C22×#8102
C2×#49292
C2×#45292
C2×#45242
#110673