Finite Group Databasebeta

← #10701905

Subgroups — #10701905

Order 768.

1430 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#944C211yesmaximal, characteristic
2C22×C3×#103C211yesmaximal, characteristic
3C22×#835C211yesmaximal, characteristic
4C22×#816C211yesmaximal, characteristic
5C22×#810C211yesmaximal, characteristic
6C2×#4550C211yesmaximal, characteristic
7#71563C211yesmaximal, characteristic
8#11010—31nomaximal, Sylow
9C23×C3×Q8C2211yescharacteristic
10C23×Dic6C2211yescharacteristic
11C23×C3×C8C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C2×#944—22no—
14C2×#944—22no—
15C2×#944—22no—
16C2×#944—22no—
17C2×#944—22no—
18C2×#944C414yescomplemented
19C22×C4⋊Dic3C2211yescharacteristic
20C22×Dic3⋊C4—22no—
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×#816—22no—
31C2×#816—22no—
32C2×#816—22no—
33C2×#810—22no—
34C2×#810—22no—
35C2×#810—22no—
36#4550—22no—
37C22×C4⋊Q8—31no—
38C22×#103—31no—
39C22×#103—31no—
40C22×#103—31no—
41C22×#103D311yescharacteristic
42C2×#336—31no—
43C4⋊#95—31no—
44C22×C3×Q8—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×Q8C2×C412yes—
56C22×C3×Q8D412yes—
57C22×C3×Q8D412yes—
58C23×C3×C4—21no—
59C23×C3×C4—21no—
60C23×C3×C4C2311yescharacteristic
61C23×Dic3—21no—
62C23×Dic3—21no—
63C23×Dic3D412yes—
64C22×Dic6—21no—
65C22×Dic6—21no—
66C22×Dic6—21no—
67C22×Dic6—21no—
68C22×Dic6—21no—
69C22×Dic6—21no—
70C22×Dic6—21no—
71C22×Dic6—21no—
72C22×Dic6—21no—
73C22×Dic6—21no—
74C22×Dic6—21no—
75C22×Dic6C2×C412yes—
76C22×Dic6D412yes—
77C22×Dic6D412yes—
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#944—28no—
92#944—28no—
93#944—28no—
94#944—28no—
95C2×C4⋊Dic3—21no—
96C2×C4⋊Dic3—21no—
97C2×C4⋊Dic3—21no—
98C2×C4⋊Dic3—21no—
99C2×C4⋊Dic3—21no—
100C2×C4⋊Dic3D412yes—
101C2×Dic3⋊C4—28no—
102C2×Dic3⋊C4—28no—
103C2×Dic3⋊C4—28no—
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#816—28no—
121#810—28no—
122C23×Q8—31no—
123C23×Q8C2×D311yescharacteristic
124C23×C8—31no—
125C23×C8C2×D311yescharacteristic
126C2×C4⋊Q8—34no—
127C2×C4⋊Q8—62no—
128C2×C4⋊Q8—62no—
129C2×C4⋊Q8—62no—
130C2×C4⋊Q8—62no—
131C2×C4⋊Q8—62no—
132C22×C4⋊C4—31no—
133C22×C4⋊C4—62no—
134C22×C4⋊C4C2×D311yescharacteristic
135C22×C42—31no—
136C2×#103—22no—
137C2×#103—22no—
138C2×#103—22no—
139C2×#103—62no—
140C2×#103—62no—
141C2×#103—62no—
142C2×#103—62no—
143C2×#103—62no—
144C2×#103—62no—
145C2×#103—62no—
146C2×#103—62no—
147C2×#103—62no—
148C2×#95—62no—
149#336—62no—
150C24×C3C2×D411yescharacteristic
151C2×C3×Q8—22no—
152C2×C3×Q8—22no—
153C2×C3×Q8—22no—
154C2×C3×Q8—22no—
155C2×C3×Q8—22no—
156C2×C3×Q8—22no—
157C2×C3×Q8—22no—
158C2×C3×Q8—22no—
159C2×C3×Q8—22no—
160C2×C3×Q8—22no—
161C2×C3×Q8—22no—
162C2×C3×Q8—22no—
163C2×C3×Q8—22no—
164C2×C3×Q8—22no—
165C2×C3×Q8—22no—
166C2×C3×Q8—41no—
167C2×C3×Q8—41no—
168C2×C3×Q8—41no—
169C2×C3×Q8—41no—
170C2×C3×Q8—41no—
171C2×C3×Q8—41no—
172C2×C3×Q8—41no—
173C2×C3×Q8—41no—
174C2×C3×Q8—41no—
175C2×C3×Q8—41no—
176C2×C3×Q8—41no—
177C2×C3×Q8—41no—
178C2×C3×Q8C22⋊C414yes—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C22×C3×C4—22no—
183C22×C3×C4—41no—
184C22×C3×C4—41no—
185C22×C3×C4—41no—
186C22×C3×C4—41no—
187C22×C3×C4—41no—
188C22×C3×C4—41no—
189C22×C3×C4—42no—
190C22×C3×C4—42no—
191C22×C3×C4C22×C411yescharacteristic
192C22×C3×C4C2×D411yescharacteristic
193C22×C3×C4C2×D411yescharacteristic
194C22×C3×C4C2×D411yescharacteristic
195C22×C3×C4C2×D411yescharacteristic
196C22×C3×C4C2×D411yescharacteristic
197C22×C3×C4C2×D411yescharacteristic
198C22×C3×C4C2×D411yescharacteristic
199C22×C3×C4C2×D411yescharacteristic
200C22×C3×C4C2×D411yescharacteristic
201C22×C3×C4#4111yescharacteristic
202C22×C3×C4#4111yescharacteristic
203C22×C3×C4#4111yescharacteristic
204C22×C3×C4#4111yescharacteristic
205C22×Dic3—22no—
206C22×Dic3—22no—
207C22×Dic3—22no—
208C22×Dic3—22no—
209C22×Dic3—22no—
210C22×Dic3—22no—
211C22×Dic3—22no—
212C22×Dic3—22no—
213C22×Dic3—41no—
214C22×Dic3—41no—
215C22×Dic3—41no—
216C22×Dic3—41no—
217C22×Dic3—41no—
218C22×Dic3—41no—
219C22×Dic3—42no—
220C22×Dic3—42no—
221C22×Dic3C22⋊C414yes—
222C22×Dic3SD1614yes—
223C22×Dic3Q1614yes—
224C2×Dic6—22no—
225C2×Dic6—22no—
226C2×Dic6—22no—
227C2×Dic6—22no—
228C2×Dic6—22no—
229C2×Dic6—22no—
230C2×Dic6—22no—
231C2×Dic6—22no—
232C2×Dic6—22no—
233C2×Dic6—22no—
234C2×Dic6—22no—
235C2×Dic6—22no—
236C2×Dic6—22no—
237C2×Dic6—22no—
238C2×Dic6—22no—
239C2×Dic6—41no—
240C2×Dic6—41no—
241C2×Dic6—41no—
242C2×Dic6—41no—
243C2×Dic6—41no—
244C2×Dic6—41no—
245C2×Dic6—41no—
246C2×Dic6—41no—
247C2×Dic6—41no—
248C2×Dic6—41no—
249C2×Dic6—41no—
250C2×Dic6—41no—
251C2×Dic6C22⋊C414yes—
252C2×C3×C8—22no—
253C2×C3×C8—22no—
254C2×C3×C8—22no—
255C2×C3×C8—41no—
256C2×C3×C8—41no—
257C2×C3×C8—41no—
258C2×C3×C8—41no—
259C3×C4⋊C4—22no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—41no—
262C3×C4⋊C4—41no—
263C4⋊Dic3—22no—
264C4⋊Dic3—22no—
265C4⋊Dic3—41no—
266C4⋊Dic3—41no—
267Dic3⋊C4—232no—
268C4×Dic3—22no—
269C4×Dic3—22no—
270C4×Dic3—22no—
271C4×Dic3—22no—
272C2×C3⋊C8—22no—
273C2×C3⋊C8—22no—
274C2×C3⋊C8—22no—
275C2×C3⋊C8—41no—
276C2×C3⋊C8—41no—
277C2×C3⋊C8—41no—
278C2×C3⋊C8—41no—
279C22×Q8—21no—
280C22×Q8—21no—
281C22×Q8—21no—
282C22×Q8—21no—
283C22×Q8—21no—
284C22×Q8—21no—
285C22×Q8—21no—
286C22×Q8—21no—
287C22×Q8—21no—
288C22×Q8—21no—
289C22×Q8—21no—
290C22×Q8—32no—
291C22×Q8—32no—
292C22×Q8—32no—
293C22×Q8—61no—
294C22×Q8—61no—
295C22×Q8—61no—
296C22×Q8—61no—
297C22×Q8—61no—
298C22×Q8—61no—
299C22×Q8—61no—
300C22×Q8—61no—
301C22×Q8—61no—
302C22×Q8—61no—
303C22×Q8—61no—
304C22×Q8C4×D312yes—
305C22×Q8D1212yes—
306C22×Q8#6712yes—
307C23×C4—21no—
308C23×C4—21no—
309C23×C4—32no—
310C23×C4—61no—
311C23×C4—61no—
312C23×C4C22×D311yescharacteristic
313C22×C8—21no—
314C22×C8—21no—
315C22×C8—21no—
316C22×C8—21no—
317C22×C8—21no—
318C22×C8—21no—
319C22×C8—32no—
320C22×C8—61no—
321C22×C8—61no—
322C22×C8—61no—
323C22×C8—61no—
324C22×C8—61no—
325C22×C8—61no—
326C22×C8#6712yes—
327C4⋊Q8—68no—
328C4⋊Q8—68no—
329C4⋊Q8—68no—
330C4⋊Q8—68no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—32no—
337C2×C4⋊C4—68no—
338C2×C4⋊C4—68no—
339C2×C4⋊C4—68no—
340C2×C4⋊C4—61no—
341C2×C4⋊C4—61no—
342C2×C4⋊C4—61no—
343C2×C4⋊C4—61no—
344C2×C4⋊C4—61no—
345C2×C4⋊C4#6712yes—
346C2×C42—32no—
347C2×C42—32no—
348C2×C42—61no—
349C2×C42—61no—
350C2×C42—61no—
351C2×C42—61no—
352#103—28no—
353#103—68no—
354#103—68no—
355#103—68no—
356#95—124no—
357C23×C3C2×C22⋊C411yescharacteristic
358C23×C3#12011yescharacteristic
359C23×C3#12011yescharacteristic
360C23×C3#12111yescharacteristic
361C23×C3#12111yescharacteristic
362C23×C3#12411yescharacteristic
363C23×C3#12711yescharacteristic
364C23×C3C2×SD1612yes—
365C23×C3C2×Q1612yes—
366C23×C3#13712yes—
367C23×C3#13712yes—
368C3×Q8—24no—
369C3×Q8—24no—
370C3×Q8—42no—
371C3×Q8—42no—
372C3×Q8—42no—
373C3×Q8—42no—
374C3×Q8—42no—
375C3×Q8—42no—
376C2×C3×C4—24no—
377C2×C3×C4—42no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—44no—
385C2×C3×C4—82no—
386C2×C3×C4—81no—
387C2×C3×C4—81no—
388C2×C3×C4C2×C22⋊C411yescharacteristic
389C2×C3×C4C2×C22⋊C411yescharacteristic
390C2×C3×C4C4×D411yescharacteristic
391C2×C3×C4C4×D411yescharacteristic
392C2×C3×C4C4×D411yescharacteristic
393C2×C3×C4C4×D411yescharacteristic
394C2×C3×C4#12011yescharacteristic
395C2×C3×C4#12011yescharacteristic
396C2×C3×C4#12011yescharacteristic
397C2×C3×C4#12011yescharacteristic
398C2×C3×C4#12011yescharacteristic
399C2×C3×C4#12011yescharacteristic
400C2×C3×C4#12111yescharacteristic
401C2×C3×C4#12111yescharacteristic
402C2×C3×C4#12111yescharacteristic
403C2×C3×C4#12111yescharacteristic
404C2×C3×C4#12111yescharacteristic
405C2×C3×C4#12111yescharacteristic
406C2×C3×C4#12111yescharacteristic
407C2×C3×C4#12111yescharacteristic
408C2×C3×C4#12111yescharacteristic
409C2×C3×C4#12111yescharacteristic
410C2×C3×C4#12311yescharacteristic
411C2×C3×C4#12311yescharacteristic
412C2×C3×C4#12311yescharacteristic
413C2×C3×C4#12311yescharacteristic
414C2×C3×C4#12411yescharacteristic
415C2×C3×C4#12711yescharacteristic
416C2×Dic3—24no—
417C2×Dic3—24no—
418C2×Dic3—24no—
419C2×Dic3—24no—
420C2×Dic3—24no—
421C2×Dic3—24no—
422C2×Dic3—24no—
423C2×Dic3—42no—
424C2×Dic3—42no—
425C2×Dic3—42no—
426C2×Dic3—42no—
427C2×Dic3—42no—
428C2×Dic3—42no—
429C2×Dic3—42no—
430C2×Dic3—44no—
431C2×Dic3—82no—
432C2×Dic3—81no—
433C2×Dic3—81no—
434C2×Dic3#10318yescomplemented
435Dic6—24no—
436Dic6—24no—
437Dic6—42no—
438Dic6—42no—
439Dic6—42no—
440Dic6—42no—
441Dic6—42no—
442Dic6—42no—
443C3×C8—42no—
444C3⋊C8—42no—
445C24D3×D411yescharacteristic
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—34no—
462C2×Q8—41no—
463C2×Q8—41no—
464C2×Q8—41no—
465C2×Q8—41no—
466C2×Q8—41no—
467C2×Q8—41no—
468C2×Q8—41no—
469C2×Q8—41no—
470C2×Q8—41no—
471C2×Q8—41no—
472C2×Q8—41no—
473C2×Q8—41no—
474C2×Q8—62no—
475C2×Q8—62no—
476C2×Q8—62no—
477C2×Q8—62no—
478C2×Q8—62no—
479C2×Q8—62no—
480C2×Q8—62no—
481C2×Q8—62no—
482C2×Q8—62no—
483C2×Q8—62no—
484C2×Q8—62no—
485C2×Q8—62no—
486C2×Q8—62no—
487C2×Q8—62no—
488C2×Q8—62no—
489C2×Q8—121no—
490C2×Q8—121no—
491C2×Q8—121no—
492C2×Q8—121no—
493C2×Q8—121no—
494C2×Q8—121no—
495C2×Q8—121no—
496C2×Q8—121no—
497C2×Q8—121no—
498C2×Q8—121no—
499C2×Q8—121no—
500C2×Q8—121no—
501C2×Q8(C2×D3)⋊C414yes—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—34no—
507C22×C4—34no—
508C22×C4—34no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—62no—
518C22×C4—62no—
519C22×C4—62no—
520C22×C4—62no—
521C22×C4—62no—
522C22×C4—62no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—121no—
526C22×C4—121no—
527C22×C4—121no—
528C22×C4—121no—
529C22×C4—121no—
530C22×C4—122no—
531C22×C4—122no—
532C22×C4—121no—
533C22×C4C2×C4×D311yescharacteristic
534C22×C4C2×D1211yescharacteristic
535C22×C4#23511yescharacteristic
536C22×C4#23511yescharacteristic
537C22×C4D3×D411yescharacteristic
538C22×C4D3×D411yescharacteristic
539C22×C4D3×D411yescharacteristic
540C22×C4D3×D411yescharacteristic
541C22×C4D3×D411yescharacteristic
542C22×C4#23711yescharacteristic
543C22×C4#23711yescharacteristic
544C22×C4C2×#6711yescharacteristic
545C22×C4C2×#6711yescharacteristic
546C22×C4C2×#6711yescharacteristic
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—62no—
555C2×C8—62no—
556C2×C8—62no—
557C2×C8—121no—
558C2×C8—121no—
559C2×C8—121no—
560C2×C8—121no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—632no—
566C4⋊C4—62no—
567C4⋊C4—62no—
568C4⋊C4—121no—
569C4⋊C4—121no—
570C42—62no—
571C42—62no—
572C42—62no—
573C42—62no—
574C22×C3#37911yescharacteristic
575C22×C3#39011yescharacteristic
576C22×C3#39011yescharacteristic
577C22×C3#39211yescharacteristic
578C22×C3#39211yescharacteristic
579C22×C3#39411yescharacteristic
580C22×C3#39411yescharacteristic
581C22×C3C2×#10312yes—
582C22×C3#41912yes—
583C22×C3#44812yes—
584C22×C3#44812yes—
585C22×C3#45112yes—
586C22×C3#45112yes—
587C22×C3#46112yes—
588C22×C3#46112yes—
589C22×C3#46212yes—
590C22×C3#46212yes—
591C22×C3#48712yes—
592C22×C3#49112yes—
593C22×C3#49211yescharacteristic
594C22×C3#49411yescharacteristic
595C22×C3#49711yescharacteristic
596C22×C3#49711yescharacteristic
597C3×C4—44no—
598C3×C4—82no—
599C3×C4#38611yescharacteristic
600C3×C4#38611yescharacteristic
601C3×C4#38611yescharacteristic
602C3×C4#38611yescharacteristic
603C3×C4#39211yescharacteristic
604C3×C4#39211yescharacteristic
605C3×C4#39411yescharacteristic
606C3×C4#39411yescharacteristic
607Dic3—28no—
608Dic3—44no—
609Dic3—82no—
610C23D3×C22⋊C411yescharacteristic
611C23#88211yescharacteristic
612C23#88411yescharacteristic
613C23#88511yescharacteristic
614C23D3×SD1612yes—
615C23#91512yes—
616C23D3×Q1612yes—
617C23#91812yes—
618C23#93711yescharacteristic
619C23#93911yescharacteristic
620C23#94011yescharacteristic
621Q8—24no—
622Q8—24no—
623Q8—42no—
624Q8—42no—
625Q8—42no—
626Q8—42no—
627Q8—42no—
628Q8—42no—
629Q8—64no—
630Q8—64no—
631Q8—122no—
632Q8—122no—
633Q8—122no—
634Q8—122no—
635Q8—122no—
636Q8—122no—
637C2×C4—24no—
638C2×C4—38no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—44no—
646C2×C4—42no—
647C2×C4—64no—
648C2×C4—64no—
649C2×C4—64no—
650C2×C4—64no—
651C2×C4—64no—
652C2×C4—64no—
653C2×C4—64no—
654C2×C4—81no—
655C2×C4—82no—
656C2×C4—81no—
657C2×C4—122no—
658C2×C4—122no—
659C2×C4—122no—
660C2×C4—122no—
661C2×C4—122no—
662C2×C4—122no—
663C2×C4—122no—
664C2×C4—124no—
665C2×C4—241no—
666C2×C4—241no—
667C2×C4—242no—
668C2×C4D3×C22⋊C411yescharacteristic
669C2×C4#67⋊C411yescharacteristic
670C2×C4#67⋊C411yescharacteristic
671C2×C4#88211yescharacteristic
672C2×C4#88211yescharacteristic
673C2×C4#88311yescharacteristic
674C2×C4#88311yescharacteristic
675C2×C4#88411yescharacteristic
676C2×C4#88411yescharacteristic
677C2×C4#88411yescharacteristic
678C2×C4#88511yescharacteristic
679C2×C4#88611yescharacteristic
680C2×C4C2×(C2×D3)⋊C411yescharacteristic
681C2×C4C4×#6711yescharacteristic
682C2×C4C4×#6711yescharacteristic
683C2×C4#92911yescharacteristic
684C2×C4#93011yescharacteristic
685C2×C4#93011yescharacteristic
686C2×C4#93711yescharacteristic
687C2×C4#93711yescharacteristic
688C2×C4#93711yescharacteristic
689C2×C4#93811yescharacteristic
690C2×C4#93811yescharacteristic
691C2×C4#93911yescharacteristic
692C2×C4#93911yescharacteristic
693C2×C4#93911yescharacteristic
694C2×C4#94011yescharacteristic
695C2×C4#95311yescharacteristic
696C8—42no—
697C8—122no—
698C2×C3#143811yescharacteristic
699C2×C3#178712yes—
700C2×C3#195611yescharacteristic
701C2×C3#196011yescharacteristic
702C2×C3#198112yes—
703C2×C3#201311yescharacteristic
704C2×C3#201311yescharacteristic
705C2×C3#201611yescharacteristic
706C2×C3#201611yescharacteristic
707C2×C3#204312yes—
708C2×C3#204312yes—
709C22#479212yes—
710C22#479512yes—
711C22#479712yes—
712C22D3×#10312yes—
713C22#480212yes—
714C22#480612yes—
715C22#480912yes—
716C22#481812yes—
717C22#495511yescharacteristic
718C22#495711yescharacteristic
719C22#495711yescharacteristic
720C22#495911yescharacteristic
721C22#496011yescharacteristic
722C22#496111yescharacteristic
723C22#516212yes—
724C22#516711yescharacteristic
725C22#517012yes—
726C22#517511yescharacteristic
727C22#518212yes—
728C22#518311yescharacteristic
729C22#518612yes—
730C22#519011yescharacteristic
731C22#522311yescharacteristic
732C4—44no—
733C4—68no—
734C4—82no—
735C4—124no—
736C4—242no—
737C4#495611yescharacteristic
738C4#495611yescharacteristic
739C4#495811yescharacteristic
740C4#495911yescharacteristic
741C4#496011yescharacteristic
742C4#496111yescharacteristic
743C4#521311yescharacteristic
744C4#522311yescharacteristic
745C3#1101011yescharacteristic, complemented, Sylow
746C2#7022511yescharacteristic
747C2#7022811yescharacteristic
748C2#7022912yes—
749C2#7024612yes—
750C2#7026612yes—
751C2#7028211yescharacteristic
752C2#7028311yescharacteristic
753C2#7028412yes—
754C2#7155011yescharacteristic
755C2#7205711yescharacteristic
756C2#7207311yescharacteristic
subgroupG/H
centerC24D3×D4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC22×C3×#103C2
socle, prime radicalC24×C3C2×D4
cosocleC23×C3×C4C23
hypercenterC22×#103D3
hypocenterC3#11010
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
18. C2×#944C4semidirect
434. C2×Dic3#103semidirect
745. C3#11010semidirect

Maximal subgroups

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

subgroupindex
C22×#9442
C22×C3×#1032
C22×#8352
C22×#8162
C22×#8102
C2×#45502
#715632
#110103