Finite Group Databasebeta

← #10703004

Subgroups — #10703004

Order 768.

994 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#816C211yesmaximal, characteristic
2C2×#4973C211yesmaximal, characteristic
3C22×#810C211yesmaximal, characteristic
4C2×C3×#340C211yesmaximal, characteristic
5C2×#4550C211yesmaximal, characteristic
6#71563C211yesmaximal, characteristic
7C2×#4529C211yesmaximal, characteristic
8#11190—31nomaximal, Sylow
9C23×Dic6C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic3C2211yescharacteristic
14C22×C4×Dic3C2211yescharacteristic
15C23×C3⋊C8C2211yescharacteristic
16C2×C3⋊#95—21no—
17C2×C3⋊#95—21no—
18C2×C3⋊#95—21no—
19C2×C3⋊#95—21no—
20C2×#816—22no—
21C2×#816—22no—
22C2×#816C414yescomplemented
23#4973—22no—
24#4973—22no—
25C2×#810—22no—
26C2×#810—22no—
27C2×#810—22no—
28C3×#340—22no—
29#4550—22no—
30#4529—22no—
31C22×#103—31no—
32C22×#103—31no—
33C2×#391—31no—
34C2×#340—31no—
35C2×#340D311yescharacteristic
36C2×#336—31no—
37C4⋊#95—31no—
38C23×C3×C4—21no—
39C23×C3×C4—21no—
40C23×C3×C4C2311yescharacteristic
41C23×Dic3—21no—
42C23×Dic3—21no—
43C23×Dic3D411yescharacteristic
44C23×Dic3D411yescharacteristic
45C22×Dic6—21no—
46C22×Dic6—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×Dic6C2×C412yes—
57C22×Dic6D412yes—
58C22×Dic6D412yes—
59C22×C3×C8—21no—
60C22×C3×C8—21no—
61C22×C3×C8—21no—
62C22×C3×C8—21no—
63C22×C3×C8—21no—
64C22×C3×C8—21no—
65C22×C3×C8C2×C412yes—
66C2×C3×C4⋊C4—21no—
67C2×C3×C4⋊C4—21no—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—21no—
71C2×C3×C4⋊C4—21no—
72C2×C3×C4⋊C4—21no—
73C2×C3×C4⋊C4—21no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4D412yes—
77C2×C3×C4⋊C4D412yes—
78C2×C4⋊Dic3—21no—
79C2×C4⋊Dic3—21no—
80C2×C4⋊Dic3—21no—
81C2×C4⋊Dic3—21no—
82C2×C4⋊Dic3—21no—
83C2×C4⋊Dic3C2×C412yes—
84C2×C4×Dic3—21no—
85C2×C4×Dic3—21no—
86C2×C4×Dic3—21no—
87C2×C4×Dic3—21no—
88C2×C4×Dic3—21no—
89C2×C4×Dic3—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⋊C8D412yes—
97C3⋊#95—24no—
98C3⋊#95—24no—
99C3⋊#95—42no—
100C3⋊#95—42no—
101#816—28no—
102#810—28no—
103C23×Q8—31no—
104C23×C8—31no—
105C23×C8C2×D311yescharacteristic
106C22×C4⋊C4—31no—
107C22×C4⋊C4C2×D311yescharacteristic
108C22×C4⋊C4C2×D311yescharacteristic
109C22×C42—31no—
110C2×#103—34no—
111C2×#103—62no—
112C2×#103—62no—
113C2×#103—62no—
114C2×#103—62no—
115C2×#103—62no—
116#391—62no—
117#391—62no—
118C2×#95—61no—
119C2×#95—61no—
120C2×#95—61no—
121C2×#95—61no—
122#340—22no—
123#340—62no—
124#336—62no—
125C24×C3C2×D411yescharacteristic
126C22×C3×C4—22no—
127C22×C3×C4—22no—
128C22×C3×C4—41no—
129C22×C3×C4—41no—
130C22×C3×C4—41no—
131C22×C3×C4—41no—
132C22×C3×C4—41no—
133C22×C3×C4—41no—
134C22×C3×C4—41no—
135C22×C3×C4—41no—
136C22×C3×C4—41no—
137C22×C3×C4—41no—
138C22×C3×C4—41no—
139C22×C3×C4—41no—
140C22×C3×C4C22×C411yescharacteristic
141C22×C3×C4C2×D411yescharacteristic
142C22×C3×C4C2×D411yescharacteristic
143C22×C3×C4C2×D411yescharacteristic
144C22×C3×C4C2×D411yescharacteristic
145C22×C3×C4C2×D411yescharacteristic
146C22×C3×C4#4111yescharacteristic
147C22×C3×C4#4111yescharacteristic
148C22×C3×C4#4111yescharacteristic
149C22×C3×C4#4111yescharacteristic
150C22×C3×C4#4111yescharacteristic
151C22×C3×C4#4111yescharacteristic
152C22×C3×C4#4111yescharacteristic
153C22×C3×C4#4111yescharacteristic
154C22×Dic3—22no—
155C22×Dic3—21no—
156C22×Dic3—21no—
157C22×Dic3—22no—
158C22×Dic3—21no—
159C22×Dic3—21no—
160C22×Dic3—22no—
161C22×Dic3—21no—
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3—21no—
165C22×Dic3—21no—
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3—22no—
170C22×Dic3—41no—
171C22×Dic3—41no—
172C22×Dic3—41no—
173C22×Dic3—41no—
174C22×Dic3—41no—
175C22×Dic3—41no—
176C22×Dic3—41no—
177C22×Dic3—41no—
178C22×Dic3—41no—
179C22×Dic3—41no—
180C22×Dic3SD1612yes—
181C22×Dic3Q1612yes—
182C2×Dic6—22no—
183C2×Dic6—22no—
184C2×Dic6—22no—
185C2×Dic6—22no—
186C2×Dic6—22no—
187C2×Dic6—22no—
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—41no—
198C2×Dic6—41no—
199C2×Dic6—41no—
200C2×Dic6—41no—
201C2×Dic6—41no—
202C2×Dic6—41no—
203C2×Dic6—41no—
204C2×Dic6—41no—
205C2×Dic6—41no—
206C2×Dic6—41no—
207C2×Dic6—41no—
208C2×Dic6—41no—
209C2×Dic6C22⋊C414yes—
210C2×C3×C8—22no—
211C2×C3×C8—22no—
212C2×C3×C8—22no—
213C2×C3×C8—41no—
214C2×C3×C8—41no—
215C2×C3×C8—41no—
216C2×C3×C8—41no—
217C3×C4⋊C4—22no—
218C3×C4⋊C4—22no—
219C3×C4⋊C4—22no—
220C3×C4⋊C4—22no—
221C3×C4⋊C4—41no—
222C3×C4⋊C4—41no—
223C3×C4⋊C4—41no—
224C3×C4⋊C4—41no—
225C4⋊Dic3—22no—
226C4⋊Dic3—22no—
227C4⋊Dic3—41no—
228C4⋊Dic3—41no—
229C4×Dic3—41no—
230C4×Dic3—41no—
231C4×Dic3—41no—
232C4×Dic3—41no—
233C2×C3⋊C8—22no—
234C2×C3⋊C8—22no—
235C2×C3⋊C8—22no—
236C2×C3⋊C8—41no—
237C2×C3⋊C8—41no—
238C2×C3⋊C8—41no—
239C2×C3⋊C8—41no—
240C22×Q8—32no—
241C22×Q8—32no—
242C22×Q8—32no—
243C22×Q8—61no—
244C22×Q8—61no—
245C22×Q8—61no—
246C22×Q8—61no—
247C22×Q8—61no—
248C22×Q8—61no—
249C22×Q8—61no—
250C22×Q8—61no—
251C22×Q8—61no—
252C22×Q8—61no—
253C22×Q8—61no—
254C23×C4—21no—
255C23×C4—21no—
256C23×C4—31no—
257C23×C4—31no—
258C23×C4—61no—
259C23×C4—61no—
260C23×C4C22×D311yescharacteristic
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—32no—
268C22×C8—61no—
269C22×C8—61no—
270C22×C8—61no—
271C22×C8—61no—
272C22×C8—61no—
273C22×C8—61no—
274C22×C8C4×D312yes—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—32no—
286C2×C4⋊C4—61no—
287C2×C4⋊C4—61no—
288C2×C4⋊C4—61no—
289C2×C4⋊C4—61no—
290C2×C4⋊C4—61no—
291C2×C4⋊C4D1212yes—
292C2×C4⋊C4#6712yes—
293C2×C42—61no—
294C2×C42—61no—
295C2×C42—61no—
296C2×C42—61no—
297C2×C42—61no—
298C2×C42—61no—
299#103—68no—
300#103—68no—
301#95—64no—
302#95—64no—
303#95—122no—
304#95—122no—
305C23×C3C4×D411yescharacteristic
306C23×C3#12011yescharacteristic
307C23×C3#12111yescharacteristic
308C23×C3#12111yescharacteristic
309C23×C3#12111yescharacteristic
310C23×C3#12311yescharacteristic
311C23×C3#12411yescharacteristic
312C23×C3C2×SD1611yescharacteristic
313C23×C3C2×Q1611yescharacteristic
314C23×C3#13511yescharacteristic
315C23×C3#13511yescharacteristic
316C23×C3AGL(1,ℤ/8)11yescharacteristic
317C23×C3#13711yescharacteristic
318C23×C3#13711yescharacteristic
319C23×C3#13711yescharacteristic
320C2×C3×C4—42no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—81no—
327C2×C3×C4—81no—
328C2×C3×C4—81no—
329C2×C3×C4—81no—
330C2×C3×C4—81no—
331C2×C3×C4—81no—
332C2×C3×C4—81no—
333C2×C3×C4—81no—
334C2×C3×C4C2×C22⋊C411yescharacteristic
335C2×C3×C4#11711yescharacteristic
336C2×C3×C4#11711yescharacteristic
337C2×C3×C4C4×D411yescharacteristic
338C2×C3×C4C4×D411yescharacteristic
339C2×C3×C4C4×D411yescharacteristic
340C2×C3×C4#12011yescharacteristic
341C2×C3×C4#12111yescharacteristic
342C2×C3×C4#12111yescharacteristic
343C2×C3×C4#12111yescharacteristic
344C2×C3×C4#12111yescharacteristic
345C2×C3×C4#12111yescharacteristic
346C2×C3×C4#12311yescharacteristic
347C2×C3×C4#12311yescharacteristic
348C2×C3×C4#12311yescharacteristic
349C2×C3×C4#12311yescharacteristic
350C2×C3×C4#12311yescharacteristic
351C2×C3×C4#12311yescharacteristic
352C2×C3×C4#12311yescharacteristic
353C2×C3×C4#12311yescharacteristic
354C2×C3×C4#12311yescharacteristic
355C2×C3×C4#12411yescharacteristic
356C2×C3×C4#12411yescharacteristic
357C2×C3×C4#12411yescharacteristic
358C2×C3×C4#12611yescharacteristic
359C2×C3×C4#12611yescharacteristic
360C2×C3×C4#12611yescharacteristic
361C2×C3×C4#12611yescharacteristic
362C2×Dic3—24no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—42no—
370C2×Dic3—42no—
371C2×Dic3—41no—
372C2×Dic3—41no—
373C2×Dic3—42no—
374C2×Dic3—42no—
375C2×Dic3—42no—
376C2×Dic3—42no—
377C2×Dic3—41no—
378C2×Dic3—41no—
379C2×Dic3—41no—
380C2×Dic3—41no—
381C2×Dic3—41no—
382C2×Dic3—41no—
383C2×Dic3—42no—
384C2×Dic3—42no—
385C2×Dic3—42no—
386C2×Dic3—81no—
387C2×Dic3—81no—
388C2×Dic3—81no—
389C2×Dic3—81no—
390Dic6—24no—
391Dic6—24no—
392Dic6—42no—
393Dic6—42no—
394Dic6—42no—
395Dic6—42no—
396Dic6—42no—
397Dic6—42no—
398C3×C8—42no—
399C3⋊C8—42no—
400C24D3×D411yescharacteristic
401C2×Q8—34no—
402C2×Q8—62no—
403C2×Q8—62no—
404C2×Q8—62no—
405C2×Q8—62no—
406C2×Q8—62no—
407C2×Q8—62no—
408C2×Q8—62no—
409C2×Q8—62no—
410C2×Q8—62no—
411C2×Q8—62no—
412C2×Q8—62no—
413C2×Q8—62no—
414C2×Q8—62no—
415C2×Q8—62no—
416C2×Q8—62no—
417C2×Q8—121no—
418C2×Q8—121no—
419C2×Q8—121no—
420C2×Q8—121no—
421C2×Q8—121no—
422C2×Q8—121no—
423C2×Q8—121no—
424C2×Q8—121no—
425C2×Q8—121no—
426C2×Q8—121no—
427C2×Q8—121no—
428C2×Q8—121no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—32no—
432C22×C4—32no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—61no—
446C22×C4—61no—
447C22×C4—62no—
448C22×C4—61no—
449C22×C4—61no—
450C22×C4—62no—
451C22×C4—62no—
452C22×C4—61no—
453C22×C4—61no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—61no—
460C22×C4—62no—
461C22×C4—121no—
462C22×C4—121no—
463C22×C4—121no—
464C22×C4—121no—
465C22×C4—121no—
466C22×C4—121no—
467C22×C4—121no—
468C22×C4—121no—
469C22×C4—121no—
470C22×C4—121no—
471C22×C4C2×C4×D311yescharacteristic
472C22×C4C2×D1211yescharacteristic
473C22×C4#23511yescharacteristic
474C22×C4#23511yescharacteristic
475C22×C4#23511yescharacteristic
476C22×C4#23511yescharacteristic
477C22×C4D3×D411yescharacteristic
478C22×C4D3×D411yescharacteristic
479C22×C4D3×D411yescharacteristic
480C22×C4#23711yescharacteristic
481C22×C4#23711yescharacteristic
482C22×C4#23911yescharacteristic
483C22×C4#23911yescharacteristic
484C22×C4C2×#6711yescharacteristic
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—62no—
493C2×C8—62no—
494C2×C8—62no—
495C2×C8—121no—
496C2×C8—121no—
497C2×C8—121no—
498C2×C8—121no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—62no—
508C4⋊C4—62no—
509C4⋊C4—121no—
510C4⋊C4—121no—
511C42—121no—
512C42—121no—
513C42—121no—
514C42—121no—
515C22×C3#38611yescharacteristic
516C22×C3#38811yescharacteristic
517C22×C3#38811yescharacteristic
518C22×C3#39411yescharacteristic
519C22×C3#39411yescharacteristic
520C22×C3#39411yescharacteristic
521C22×C3#39711yescharacteristic
522C22×C3C4×SD1611yescharacteristic
523C22×C3C4×Q1611yescharacteristic
524C22×C3#44011yescharacteristic
525C22×C3#44111yescharacteristic
526C22×C3#44811yescharacteristic
527C22×C3#44911yescharacteristic
528C22×C3#45111yescharacteristic
529C22×C3#45211yescharacteristic
530C22×C3#46011yescharacteristic
531C22×C3#46111yescharacteristic
532C22×C3#46211yescharacteristic
533C22×C3#46211yescharacteristic
534C22×C3#46311yescharacteristic
535C22×C3#46411yescharacteristic
536C22×C3#46411yescharacteristic
537C22×C3#46411yescharacteristic
538C22×C3#46511yescharacteristic
539C22×C3#46711yescharacteristic
540C22×C3#46811yescharacteristic
541C22×C3#47011yescharacteristic
542C22×C3#48311yescharacteristic
543C22×C3#48411yescharacteristic
544C22×C3#48511yescharacteristic
545C22×C3#48511yescharacteristic
546C22×C3#48711yescharacteristic
547C22×C3#48811yescharacteristic
548C22×C3#48911yescharacteristic
549C22×C3#49111yescharacteristic
550C3×C4—82no—
551C3×C4—82no—
552C3×C4#38111yescharacteristic
553C3×C4#38611yescharacteristic
554C3×C4#38811yescharacteristic
555C3×C4#38811yescharacteristic
556C3×C4#39411yescharacteristic
557C3×C4#39711yescharacteristic
558C3×C4#39711yescharacteristic
559C3×C4#39711yescharacteristic
560Dic3—44no—
561Dic3—42no—
562Dic3—42no—
563Dic3—82no—
564C23#88211yescharacteristic
565C23#88411yescharacteristic
566C23#88411yescharacteristic
567C23#88511yescharacteristic
568C23#89311yescharacteristic
569C23#89411yescharacteristic
570C23#91111yescharacteristic
571C23#91211yescharacteristic
572C23D3×SD1611yescharacteristic
573C23#91511yescharacteristic
574C23#91511yescharacteristic
575C23#91611yescharacteristic
576C23D3×Q1611yescharacteristic
577C23#91811yescharacteristic
578C23#93911yescharacteristic
579Q8—64no—
580Q8—64no—
581Q8—122no—
582Q8—122no—
583Q8—122no—
584Q8—122no—
585Q8—122no—
586Q8—122no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—62no—
594C2×C4—64no—
595C2×C4—62no—
596C2×C4—62no—
597C2×C4—62no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—81no—
601C2×C4—81no—
602C2×C4—81no—
603C2×C4—81no—
604C2×C4—81no—
605C2×C4—81no—
606C2×C4—81no—
607C2×C4—81no—
608C2×C4—121no—
609C2×C4—121no—
610C2×C4—122no—
611C2×C4—121no—
612C2×C4—121no—
613C2×C4—122no—
614C2×C4—122no—
615C2×C4—122no—
616C2×C4—122no—
617C2×C4—122no—
618C2×C4—121no—
619C2×C4—121no—
620C2×C4—121no—
621C2×C4—121no—
622C2×C4—122no—
623C2×C4—122no—
624C2×C4—122no—
625C2×C4—241no—
626C2×C4—241no—
627C2×C4—241no—
628C2×C4—241no—
629C2×C4#87211yescharacteristic
630C2×C4C4×D1211yescharacteristic
631C2×C4#87511yescharacteristic
632C2×C4#87611yescharacteristic
633C2×C4D3×C22⋊C411yescharacteristic
634C2×C4#67⋊C411yescharacteristic
635C2×C4#88311yescharacteristic
636C2×C4#88311yescharacteristic
637C2×C4#88311yescharacteristic
638C2×C4#88411yescharacteristic
639C2×C4#88511yescharacteristic
640C2×C4#88611yescharacteristic
641C2×C4#89211yescharacteristic
642C2×C4#89411yescharacteristic
643C2×C4#89411yescharacteristic
644C2×C4#89411yescharacteristic
645C2×C4#89411yescharacteristic
646C2×C4#89511yescharacteristic
647C2×C4#89511yescharacteristic
648C2×C4#89811yescharacteristic
649C2×C4#89811yescharacteristic
650C2×C4#89811yescharacteristic
651C2×C4C4×#6711yescharacteristic
652C2×C4#92911yescharacteristic
653C2×C4#93011yescharacteristic
654C2×C4#93711yescharacteristic
655C2×C4#93811yescharacteristic
656C2×C4#94711yescharacteristic
657C8—42no—
658C8—122no—
659C2×C3#144011yescharacteristic
660C2×C3#187811yescharacteristic
661C2×C3#188011yescharacteristic
662C2×C3#192711yescharacteristic
663C2×C3#192811yescharacteristic
664C2×C3#193311yescharacteristic
665C2×C3#193511yescharacteristic
666C2×C3#203511yescharacteristic
667C2×C3#203611yescharacteristic
668C2×C3#204211yescharacteristic
669C2×C3#204311yescharacteristic
670C2×C3#205511yescharacteristic
671C2×C3#205611yescharacteristic
672C2×C3#207211yescharacteristic
673C2×C3#207411yescharacteristic
674C22#466511yescharacteristic
675C22#466911yescharacteristic
676C22#467211yescharacteristic
677C22#467511yescharacteristic
678C22#476211yescharacteristic
679C22#476511yescharacteristic
680C22#476711yescharacteristic
681C22#476811yescharacteristic
682C22#477811yescharacteristic
683C22#478011yescharacteristic
684C22#478111yescharacteristic
685C22#478311yescharacteristic
686C22#479211yescharacteristic
687C22#479511yescharacteristic
688C22#479711yescharacteristic
689C22#479811yescharacteristic
690C22#480611yescharacteristic
691C22#480911yescharacteristic
692C22#481311yescharacteristic
693C22#481611yescharacteristic
694C22#485211yescharacteristic
695C22#485311yescharacteristic
696C22#486211yescharacteristic
697C22#486811yescharacteristic
698C22#487311yescharacteristic
699C22#488411yescharacteristic
700C22#488811yescharacteristic
701C22#488911yescharacteristic
702C22#495911yescharacteristic
703C22#496111yescharacteristic
704C22#499011yescharacteristic
705C22#515311yescharacteristic
706C22#516211yescharacteristic
707C22#516611yescharacteristic
708C22#518211yescharacteristic
709C4—82no—
710C4—82no—
711C4—124no—
712C4—122no—
713C4—122no—
714C4—242no—
715C4#466411yescharacteristic
716C4#467011yescharacteristic
717C4#467411yescharacteristic
718C4#467511yescharacteristic
719C4#494011yescharacteristic
720C4#495611yescharacteristic
721C4#499111yescharacteristic
722C4#499211yescharacteristic
723C3#1119011yescharacteristic, complemented, Sylow
724C2#6882411yescharacteristic
725C2#6882511yescharacteristic
726C2#6885011yescharacteristic
727C2#6885411yescharacteristic
728C2#6890811yescharacteristic
729C2#6890911yescharacteristic
730C2#6891411yescharacteristic
731C2#6891511yescharacteristic
732C2#6942911yescharacteristic
733C2#7017811yescharacteristic
734C2#7021711yescharacteristic
735C2#7024611yescharacteristic
736C2#7028511yescharacteristic
737C2#7057011yescharacteristic
738C2#7062411yescharacteristic
subgroupG/H
centerC24D3×D4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#340C2
socle, prime radicalC24×C3C2×D4
cosocleC23×C3×C4C23
hypercenterC2×#340D3
hypocenterC3#11190
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
22. C2×#816C4semidirect
723. C3#11190semidirect

Maximal subgroups

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

subgroupindex
C22×#8162
C2×#49732
C22×#8102
C2×C3×#3402
C2×#45502
#715632
C2×#45292
#111903