Finite Group Databasebeta

← #10701900

Subgroups — #10701900

Order 768.

1558 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#947C211yesmaximal, characteristic
2C22×C3×#103C211yesmaximal, characteristic, complemented
3C22×#835C211yesmaximal, characteristic, complemented
4C22×#821C211yesmaximal, characteristic
5C22×#809C211yesmaximal, characteristic
6C2×#4550C211yesmaximal, characteristic, complemented
7#71563C211yesmaximal, characteristic, complemented
8#11009—31nomaximal, Sylow
9C23×C3×Q8C2211yescharacteristic
10C23×D12C2211yescharacteristic
11C23×C3×C8C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C2×#947—22no—
14C2×#947—22no—
15C2×#947—22no—
16C2×#947—22no—
17C2×#947—22no—
18C2×#947C414yescomplemented
19C22×(C2×D3)⋊C4—22no—
20C22×C4⋊Dic3C2211yescharacteristic
21C22×C4×Dic3C2211yescharacteristic
22C23×C3⋊C8C2211yescharacteristic
23C2×C3×#103—22no—
24C2×C3×#103—22no—
25C2×C3×#103—22no—
26C2×#835—22no—
27C2×#835—22no—
28C2×#835—22no—
29C2×C3⋊#95—22no—
30C2×#821—22no—
31C2×#821—22no—
32C2×#821—22no—
33C2×#809—22no—
34C2×#809—22no—
35C2×#809—22no—
36#4550—22no—
37C22×#124—31no—
38C22×#103—31no—
39C22×#103D311yescharacteristic, complemented
40C22×#102—31no—
41C22×#102—31no—
42C2×#336—31no—
43C4⋊#95—31no—
44C24×D3—21no—
45C22×C3×Q8—21no—
46C22×C3×Q8—21no—
47C22×C3×Q8—21no—
48C22×C3×Q8—21no—
49C22×C3×Q8—21no—
50C22×C3×Q8—21no—
51C22×C3×Q8—21no—
52C22×C3×Q8—21no—
53C22×C3×Q8—21no—
54C22×C3×Q8—21no—
55C22×C3×Q8—21no—
56C22×C3×Q8C2×C412yes—
57C22×C3×Q8D412yes—
58C22×C3×Q8D412yes—
59C23×C3×C4—21no—
60C23×C3×C4—21no—
61C23×C3×C4C2311yescharacteristic
62C23×Dic3—21no—
63C23×Dic3D412yes—
64C22×D12—21no—
65C22×D12—21no—
66C22×D12—21no—
67C22×D12—21no—
68C22×D12—21no—
69C22×D12—21no—
70C22×D12—21no—
71C22×D12—21no—
72C22×D12—21no—
73C22×D12—21no—
74C22×D12—21no—
75C22×D12C2×C412yes—
76C22×D12D412yes—
77C22×D12D412yes—
78C22×C3×C8—21no—
79C22×C3×C8—21no—
80C22×C3×C8—21no—
81C22×C3×C8—21no—
82C22×C3×C8—21no—
83C22×C3×C8—21no—
84C22×C3×C8D412yes—
85C2×C3×C4⋊C4—21no—
86C2×C3×C4⋊C4—21no—
87C2×C3×C4⋊C4—21no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4D412yes—
91#947—28no—
92#947—28no—
93#947—28no—
94#947—28no—
95C2×(C2×D3)⋊C4—28no—
96C2×(C2×D3)⋊C4—28no—
97C2×(C2×D3)⋊C4—28no—
98C2×C4⋊Dic3—21no—
99C2×C4⋊Dic3—21no—
100C2×C4⋊Dic3—21no—
101C2×C4⋊Dic3—21no—
102C2×C4⋊Dic3—21no—
103C2×C4⋊Dic3D412yes—
104C2×C4×Dic3—21no—
105C2×C4×Dic3—21no—
106C2×C4×Dic3—21no—
107C2×C4×Dic3—21no—
108C2×C4×Dic3C2×C412yes—
109C2×C4×Dic3D412yes—
110C22×C3⋊C8—21no—
111C22×C3⋊C8—21no—
112C22×C3⋊C8—21no—
113C22×C3⋊C8—21no—
114C22×C3⋊C8—21no—
115C22×C3⋊C8—21no—
116C22×C3⋊C8D412yes—
117C3×#103—28no—
118#835—28no—
119C3⋊#95—44no—
120#821—28no—
121#809—28no—
122C23×Q8C2×D311yescharacteristic
123C23×D4—31no—
124C23×C8—31no—
125C23×C8C2×D311yescharacteristic
126C2×#124—34no—
127C2×#124—62no—
128C2×#124—62no—
129C2×#124—62no—
130C2×#124—62no—
131C2×#124—62no—
132C22×C4⋊C4—31no—
133C22×C4⋊C4C2×D311yescharacteristic
134C22×C22⋊C4—62no—
135C22×C42—31no—
136C2×#103—22no—
137C2×#103—22no—
138C2×#103—22no—
139C2×#103—62no—
140C2×#103—62no—
141C2×#103—62no—
142C2×#102—62no—
143C2×#102—62no—
144C2×#102—62no—
145C2×#102—62no—
146C2×#102—62no—
147C2×#102—62no—
148C2×#95—62no—
149#336—62no—
150C24×C3C2×D411yescharacteristic
151C23×D3—22no—
152C23×D3—22no—
153C23×D3—22no—
154C23×D3—41no—
155C23×D3—41no—
156C23×D3—41no—
157C23×D3—41no—
158C23×D3—42no—
159C23×D3—42no—
160C23×D3—42no—
161C23×D3—42no—
162C2×C3×Q8—22no—
163C2×C3×Q8—22no—
164C2×C3×Q8—22no—
165C2×C3×Q8—22no—
166C2×C3×Q8—22no—
167C2×C3×Q8—22no—
168C2×C3×Q8—22no—
169C2×C3×Q8—22no—
170C2×C3×Q8—22no—
171C2×C3×Q8—22no—
172C2×C3×Q8—22no—
173C2×C3×Q8—22no—
174C2×C3×Q8—22no—
175C2×C3×Q8—22no—
176C2×C3×Q8—22no—
177C2×C3×Q8—41no—
178C2×C3×Q8—41no—
179C2×C3×Q8—41no—
180C2×C3×Q8—41no—
181C2×C3×Q8—41no—
182C2×C3×Q8—41no—
183C2×C3×Q8—41no—
184C2×C3×Q8—41no—
185C2×C3×Q8—41no—
186C2×C3×Q8—41no—
187C2×C3×Q8—41no—
188C2×C3×Q8—41no—
189C2×C3×Q8C22⋊C414yes—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—41no—
195C22×C3×C4—41no—
196C22×C3×C4—41no—
197C22×C3×C4—41no—
198C22×C3×C4—41no—
199C22×C3×C4—41no—
200C22×C3×C4—42no—
201C22×C3×C4—42no—
202C22×C3×C4C22×C411yescharacteristic
203C22×C3×C4C2×D411yescharacteristic
204C22×C3×C4C2×D411yescharacteristic
205C22×C3×C4C2×D411yescharacteristic
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2×D411yescharacteristic
209C22×C3×C4C2×D411yescharacteristic
210C22×C3×C4C2×D411yescharacteristic
211C22×C3×C4C2×D411yescharacteristic
212C22×C3×C4#4111yescharacteristic
213C22×C3×C4#4111yescharacteristic
214C22×C3×C4#4111yescharacteristic
215C22×C3×C4#4111yescharacteristic
216C22×Dic3—22no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—41no—
224C22×Dic3—41no—
225C22×Dic3—42no—
226C22×Dic3—42no—
227C22×Dic3C22⋊C414yes—
228C2×D12—22no—
229C2×D12—22no—
230C2×D12—22no—
231C2×D12—22no—
232C2×D12—22no—
233C2×D12—22no—
234C2×D12—22no—
235C2×D12—22no—
236C2×D12—22no—
237C2×D12—22no—
238C2×D12—22no—
239C2×D12—22no—
240C2×D12—22no—
241C2×D12—22no—
242C2×D12—22no—
243C2×D12—41no—
244C2×D12—41no—
245C2×D12—41no—
246C2×D12—41no—
247C2×D12—41no—
248C2×D12—41no—
249C2×D12—41no—
250C2×D12—41no—
251C2×D12—41no—
252C2×D12—41no—
253C2×D12—41no—
254C2×D12—41no—
255C2×D12C22⋊C414yes—
256C2×C3×C8—22no—
257C2×C3×C8—22no—
258C2×C3×C8—22no—
259C2×C3×C8—41no—
260C2×C3×C8—41no—
261C2×C3×C8—41no—
262C2×C3×C8—41no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4—22no—
265C3×C4⋊C4—41no—
266C3×C4⋊C4—41no—
267(C2×D3)⋊C4—232no—
268C4⋊Dic3—22no—
269C4⋊Dic3—22no—
270C4⋊Dic3—41no—
271C4⋊Dic3—41no—
272C4×Dic3—22no—
273C4×Dic3—22no—
274C4×Dic3—22no—
275C4×Dic3—22no—
276C2×C3⋊C8—22no—
277C2×C3⋊C8—22no—
278C2×C3⋊C8—22no—
279C2×C3⋊C8—41no—
280C2×C3⋊C8—41no—
281C2×C3⋊C8—41no—
282C2×C3⋊C8—41no—
283C25—61no—
284C22×Q8—21no—
285C22×Q8—21no—
286C22×Q8—21no—
287C22×Q8—21no—
288C22×Q8—21no—
289C22×Q8—21no—
290C22×Q8—21no—
291C22×Q8—21no—
292C22×Q8—21no—
293C22×Q8—21no—
294C22×Q8—21no—
295C22×Q8C4×D312yes—
296C22×Q8D1212yes—
297C22×Q8#6712yes—
298C22×D4—32no—
299C22×D4—32no—
300C22×D4—32no—
301C22×D4—61no—
302C22×D4—61no—
303C22×D4—61no—
304C22×D4—61no—
305C22×D4—61no—
306C22×D4—61no—
307C22×D4—61no—
308C22×D4—61no—
309C22×D4—61no—
310C22×D4—61no—
311C22×D4—61no—
312C23×C4—21no—
313C23×C4—21no—
314C23×C4—32no—
315C23×C4—61no—
316C23×C4C22×D311yescharacteristic
317C22×C8—21no—
318C22×C8—21no—
319C22×C8—21no—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—21no—
323C22×C8—32no—
324C22×C8—61no—
325C22×C8—61no—
326C22×C8—61no—
327C22×C8—61no—
328C22×C8—61no—
329C22×C8—61no—
330C22×C8#6712yes—
331#124—68no—
332#124—68no—
333#124—68no—
334#124—68no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—32no—
341C2×C4⋊C4—61no—
342C2×C4⋊C4—61no—
343C2×C4⋊C4—61no—
344C2×C4⋊C4—61no—
345C2×C4⋊C4—61no—
346C2×C4⋊C4#6712yes—
347C2×C22⋊C4—68no—
348C2×C22⋊C4—68no—
349C2×C22⋊C4—68no—
350C2×C42—32no—
351C2×C42—32no—
352C2×C42—61no—
353C2×C42—61no—
354C2×C42—61no—
355C2×C42—61no—
356#103—28no—
357#103—68no—
358#102—68no—
359#102—68no—
360#95—124no—
361C23×C3C2×C22⋊C411yescharacteristic
362C23×C3#12011yescharacteristic
363C23×C3#12011yescharacteristic
364C23×C3#12111yescharacteristic
365C23×C3#12111yescharacteristic
366C23×C3#12411yescharacteristic
367C23×C3#12711yescharacteristic
368C23×C3#13512yes—
369C23×C3#13512yes—
370C23×C3AGL(1,ℤ/8)12yes—
371C23×C3#13712yes—
372C22×D3—24no—
373C22×D3—42no—
374C22×D3—42no—
375C22×D3—42no—
376C22×D3—42no—
377C22×D3—42no—
378C22×D3—42no—
379C22×D3—44no—
380C22×D3—44no—
381C22×D3—44no—
382C22×D3—44no—
383C22×D3—44no—
384C22×D3—44no—
385C22×D3—82no—
386C22×D3—82no—
387C22×D3—82no—
388C22×D3—82no—
389C22×D3—82no—
390C22×D3—82no—
391C22×D3—81no—
392C22×D3—81no—
393C22×D3—81no—
394C22×D3—81no—
395C3×Q8—24no—
396C3×Q8—24no—
397C3×Q8—42no—
398C3×Q8—42no—
399C3×Q8—42no—
400C3×Q8—42no—
401C3×Q8—42no—
402C3×Q8—42no—
403C2×C3×C4—24no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—42no—
411C2×C3×C4—44no—
412C2×C3×C4—82no—
413C2×C3×C4—81no—
414C2×C3×C4—81no—
415C2×C3×C4C2×C22⋊C411yescharacteristic
416C2×C3×C4C2×C22⋊C411yescharacteristic
417C2×C3×C4C4×D411yescharacteristic
418C2×C3×C4C4×D411yescharacteristic
419C2×C3×C4C4×D411yescharacteristic
420C2×C3×C4C4×D411yescharacteristic
421C2×C3×C4#12011yescharacteristic
422C2×C3×C4#12011yescharacteristic
423C2×C3×C4#12011yescharacteristic
424C2×C3×C4#12011yescharacteristic
425C2×C3×C4#12011yescharacteristic
426C2×C3×C4#12011yescharacteristic
427C2×C3×C4#12111yescharacteristic
428C2×C3×C4#12111yescharacteristic
429C2×C3×C4#12111yescharacteristic
430C2×C3×C4#12111yescharacteristic
431C2×C3×C4#12111yescharacteristic
432C2×C3×C4#12111yescharacteristic
433C2×C3×C4#12111yescharacteristic
434C2×C3×C4#12111yescharacteristic
435C2×C3×C4#12111yescharacteristic
436C2×C3×C4#12111yescharacteristic
437C2×C3×C4#12311yescharacteristic
438C2×C3×C4#12311yescharacteristic
439C2×C3×C4#12311yescharacteristic
440C2×C3×C4#12311yescharacteristic
441C2×C3×C4#12411yescharacteristic
442C2×C3×C4#12711yescharacteristic
443C2×Dic3—24no—
444C2×Dic3—24no—
445C2×Dic3—24no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—42no—
449C2×Dic3—42no—
450C2×Dic3—42no—
451C2×Dic3—44no—
452C2×Dic3—82no—
453C2×Dic3—81no—
454C2×Dic3—81no—
455D12—24no—
456D12—24no—
457D12—42no—
458D12—42no—
459D12—42no—
460D12—42no—
461D12—42no—
462D12—42no—
463C3×C8—42no—
464C3⋊C8—42no—
465C24—62no—
466C24—62no—
467C24—62no—
468C24—121no—
469C24—121no—
470C24—122no—
471C24—122no—
472C24—122no—
473C24—122no—
474C24—121no—
475C24—121no—
476C24D3×D411yescharacteristic
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—22no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—41no—
495C2×Q8—41no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8—41no—
499C2×Q8—41no—
500C2×Q8—41no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—41no—
504C2×Q8(C2×D3)⋊C414yes—
505C2×D4—34no—
506C2×D4—62no—
507C2×D4—62no—
508C2×D4—62no—
509C2×D4—62no—
510C2×D4—62no—
511C2×D4—62no—
512C2×D4—62no—
513C2×D4—62no—
514C2×D4—62no—
515C2×D4—62no—
516C2×D4—62no—
517C2×D4—62no—
518C2×D4—62no—
519C2×D4—62no—
520C2×D4—62no—
521C2×D4—121no—
522C2×D4—121no—
523C2×D4—121no—
524C2×D4—121no—
525C2×D4—121no—
526C2×D4—121no—
527C2×D4—121no—
528C2×D4—121no—
529C2×D4—121no—
530C2×D4—121no—
531C2×D4—121no—
532C2×D4—121no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—34no—
538C22×C4—41no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—121no—
554C22×C4—122no—
555C22×C4—122no—
556C22×C4—121no—
557C22×C4C2×C4×D311yescharacteristic
558C22×C4C2×D1211yescharacteristic
559C22×C4#23511yescharacteristic
560C22×C4#23511yescharacteristic
561C22×C4D3×D411yescharacteristic
562C22×C4D3×D411yescharacteristic
563C22×C4D3×D411yescharacteristic
564C22×C4D3×D411yescharacteristic
565C22×C4D3×D411yescharacteristic
566C22×C4#23711yescharacteristic
567C22×C4#23711yescharacteristic
568C22×C4C2×#6711yescharacteristic
569C22×C4C2×#6711yescharacteristic
570C22×C4C2×#6711yescharacteristic
571C2×C8—22no—
572C2×C8—22no—
573C2×C8—22no—
574C2×C8—41no—
575C2×C8—41no—
576C2×C8—41no—
577C2×C8—41no—
578C2×C8—62no—
579C2×C8—62no—
580C2×C8—62no—
581C2×C8—121no—
582C2×C8—121no—
583C2×C8—121no—
584C2×C8—121no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—62no—
590C4⋊C4—62no—
591C4⋊C4—121no—
592C4⋊C4—121no—
593C22⋊C4—632no—
594C42—62no—
595C42—62no—
596C42—62no—
597C42—62no—
598C22×C3#37911yescharacteristic
599C22×C3#39011yescharacteristic
600C22×C3#39011yescharacteristic
601C22×C3#39211yescharacteristic
602C22×C3#39211yescharacteristic
603C22×C3#39411yescharacteristic
604C22×C3#39411yescharacteristic
605C22×C3#41612yes—
606C22×C3#41712yes—
607C22×C3#44912yes—
608C22×C3#44912yes—
609C22×C3#45212yes—
610C22×C3#45212yes—
611C22×C3#46312yes—
612C22×C3#46312yes—
613C22×C3#46412yes—
614C22×C3#46412yes—
615C22×C3#48812yes—
616C22×C3#48912yes—
617C22×C3#49511yescharacteristic
618C22×C3#49511yescharacteristic
619C22×C3#49611yescharacteristic
620C22×C3#49711yescharacteristic
621C2×D3—44no—
622C2×D3—48no—
623C2×D3—82no—
624C2×D3—82no—
625C2×D3—84no—
626C2×D3—82no—
627C2×D3—82no—
628C2×D3—82no—
629C2×D3—82no—
630C2×D3—84no—
631C2×D3—84no—
632C3×C4—44no—
633C3×C4—82no—
634C3×C4#38611yescharacteristic
635C3×C4#38611yescharacteristic
636C3×C4#38611yescharacteristic
637C3×C4#38611yescharacteristic
638C3×C4#39211yescharacteristic
639C3×C4#39211yescharacteristic
640C3×C4#39411yescharacteristic
641C3×C4#39411yescharacteristic
642Dic3—44no—
643Dic3—82no—
644C23—64no—
645C23—124no—
646C23—124no—
647C23—122no—
648C23—122no—
649C23—122no—
650C23—122no—
651C23—122no—
652C23—122no—
653C23—124no—
654C23—124no—
655C23—124no—
656C23—124no—
657C23—242no—
658C23—241no—
659C23—241no—
660C23—242no—
661C23—241no—
662C23—241no—
663C23—242no—
664C23—242no—
665C23—242no—
666C23—242no—
667C23D3×C22⋊C411yescharacteristic
668C23#88211yescharacteristic
669C23#88411yescharacteristic
670C23#88511yescharacteristic
671C23#91412yes—
672C23#91612yes—
673C23#91812yes—
674C23#91912yes—
675C23#93711yescharacteristic
676C23#93911yescharacteristic
677C23#94011yescharacteristic
678Q8—24no—
679Q8—24no—
680Q8—42no—
681Q8—42no—
682Q8—42no—
683Q8—42no—
684Q8—42no—
685Q8—42no—
686D4—64no—
687D4—64no—
688D4—122no—
689D4—122no—
690D4—122no—
691D4—122no—
692D4—122no—
693D4—122no—
694C2×C4—24no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—42no—
703C2×C4—64no—
704C2×C4—64no—
705C2×C4—64no—
706C2×C4—81no—
707C2×C4—82no—
708C2×C4—81no—
709C2×C4—122no—
710C2×C4—122no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—124no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—242no—
718C2×C4D3×C22⋊C411yescharacteristic
719C2×C4#67⋊C411yescharacteristic
720C2×C4#67⋊C411yescharacteristic
721C2×C4#88211yescharacteristic
722C2×C4#88211yescharacteristic
723C2×C4#88311yescharacteristic
724C2×C4#88311yescharacteristic
725C2×C4#88411yescharacteristic
726C2×C4#88411yescharacteristic
727C2×C4#88411yescharacteristic
728C2×C4#88511yescharacteristic
729C2×C4#88611yescharacteristic
730C2×C4C2×(C2×D3)⋊C411yescharacteristic
731C2×C4C4×#6711yescharacteristic
732C2×C4C4×#6711yescharacteristic
733C2×C4#92911yescharacteristic
734C2×C4#93011yescharacteristic
735C2×C4#93011yescharacteristic
736C2×C4#93711yescharacteristic
737C2×C4#93711yescharacteristic
738C2×C4#93711yescharacteristic
739C2×C4#93811yescharacteristic
740C2×C4#93811yescharacteristic
741C2×C4#93911yescharacteristic
742C2×C4#93911yescharacteristic
743C2×C4#93911yescharacteristic
744C2×C4#94011yescharacteristic
745C2×C4#95311yescharacteristic
746C8—42no—
747C8—122no—
748C2×C3#143811yescharacteristic
749C2×C3#178812yes—
750C2×C3#195811yescharacteristic
751C2×C3#195911yescharacteristic
752C2×C3#198312yes—
753C2×C3#201211yescharacteristic
754C2×C3#201211yescharacteristic
755C2×C3#201511yescharacteristic
756C2×C3#201511yescharacteristic
757C2×C3#204212yes—
758C2×C3#204212yes—
759D3—84no—
760C22—128no—
761C22—124no—
762C22—242no—
763C22—242no—
764C22—244no—
765C22—244no—
766C22—242no—
767C22—242no—
768C22—242no—
769C22—244no—
770C22—242no—
771C22#479412yes—
772C22#479812yes—
773C22#480012yes—
774C22#480312yes—
775C22#480412yes—
776C22#480812yes—
777C22#481012yes—
778C22#481912yes—
779C22#495511yescharacteristic
780C22#495711yescharacteristic
781C22#495711yescharacteristic
782C22#495911yescharacteristic
783C22#496011yescharacteristic
784C22#496111yescharacteristic
785C22#516512yes—
786C22#516811yescharacteristic
787C22#517212yes—
788C22#517611yescharacteristic
789C22#518512yes—
790C22#518712yes—
791C22#519011yescharacteristic
792C22#519111yescharacteristic
793C22#522311yescharacteristic
794C4—44no—
795C4—82no—
796C4—124no—
797C4—242no—
798C4#495611yescharacteristic
799C4#495611yescharacteristic
800C4#495811yescharacteristic
801C4#495911yescharacteristic
802C4#496011yescharacteristic
803C4#496111yescharacteristic
804C4#521311yescharacteristic
805C4#522311yescharacteristic
806C3#1100911yescharacteristic, complemented, Sylow
807C2—244no—
808C2#7022611yescharacteristic
809C2#7022711yescharacteristic
810C2#7023012yes—
811C2#7024512yes—
812C2#7026712yes—
813C2#7027711yescharacteristic
814C2#7027811yescharacteristic
815C2#7027912yes—
816C2#7155011yescharacteristic
817C2#7205511yescharacteristic
818C2#7207211yescharacteristic
subgroupG/H
centerC24D3×D4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC22×C3×#103C2
socleC24×C3C2×D4
prime radicalC23×D12C22
cosocleC23×C3×C4C23
hypercenterC22×#103D3
hypocenterC3#11009
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C22×C3×#103C2semidirect
3. C22×#835C2semidirect
6. C2×#4550C2semidirect
7. #71563C2semidirect
18. C2×#947C4semidirect
39. C22×#103D3semidirect
806. C3#11009semidirect

Maximal subgroups

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

subgroupindex
C22×#9472
C22×C3×#1032
C22×#8352
C22×#8212
C22×#8092
C2×#45502
#715632
#110093