Finite Group Databasebeta

← #10702251

Subgroups — #10702251

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
1C22×C3×#103C211yesmaximal, characteristic
2C2×#5229C211yesmaximal, characteristic
3C22×#835C211yesmaximal, characteristic
4C2×#4984C211yesmaximal, characteristic
5C2×#4551C211yesmaximal, characteristic
6C2×#4550C211yesmaximal, characteristic
7C2×#4529C211yesmaximal, characteristic
8#11067—31nomaximal, Sylow
9C23×C3×Q8C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C4⋊Dic3—21no—
13C22×C4⋊Dic3C2211yescharacteristic
14C22×C4⋊Dic3C2211yescharacteristic
15C22×C4×Dic3C2211yescharacteristic
16C23×C3⋊C8C2211yescharacteristic
17C2×C3×#103—22no—
18C2×C3×#103—22no—
19C2×C3×#103C414yescomplemented
20#5229—22no—
21#5229—22no—
22C2×#835—22no—
23C2×#835—22no—
24C2×#835—22no—
25C2×C3⋊#95—21no—
26C2×C3⋊#95—21no—
27C2×C3⋊#95—21no—
28#4984—22no—
29#4984—22no—
30#4551—22no—
31#4550—22no—
32#4529—22no—
33C22×#103—31no—
34C22×#103D311yescharacteristic
35C2×#391—31no—
36C2×#389—31no—
37C2×#340—31no—
38C2×#340—31no—
39C2×#336—31no—
40C22×C3×Q8—21no—
41C22×C3×Q8—21no—
42C22×C3×Q8—21no—
43C22×C3×Q8—21no—
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×Q8C2×C412yes—
52C22×C3×Q8D412yes—
53C22×C3×Q8Q812yes—
54C23×C3×C4—21no—
55C23×C3×C4—21no—
56C23×C3×C4C2311yescharacteristic
57C23×Dic3—21no—
58C23×Dic3—21no—
59C23×Dic3D411yescharacteristic
60C23×Dic3D411yescharacteristic
61C22×C3×C8—21no—
62C22×C3×C8—21no—
63C22×C3×C8—21no—
64C22×C3×C8—21no—
65C22×C3×C8—21no—
66C22×C3×C8—21no—
67C22×C3×C8C2×C412yes—
68C2×C3×C4⋊C4—21no—
69C2×C3×C4⋊C4—21no—
70C2×C3×C4⋊C4—21no—
71C2×C3×C4⋊C4C2×C412yes—
72C2×C3×C4⋊C4D412yes—
73C2×C3×C4⋊C4D412yes—
74C2×C4⋊Dic3—21no—
75C2×C4⋊Dic3—21no—
76C2×C4⋊Dic3—21no—
77C2×C4⋊Dic3—21no—
78C2×C4⋊Dic3—21no—
79C2×C4⋊Dic3—21no—
80C2×C4⋊Dic3—21no—
81C2×C4⋊Dic3—21no—
82C2×C4⋊Dic3—24no—
83C2×C4⋊Dic3—21no—
84C2×C4⋊Dic3—21no—
85C2×C4⋊Dic3—42no—
86C2×C4⋊Dic3—42no—
87C2×C4⋊Dic3D412yes—
88C2×C4⋊Dic3D412yes—
89C2×C4×Dic3—21no—
90C2×C4×Dic3—21no—
91C2×C4×Dic3—21no—
92C2×C4×Dic3—21no—
93C2×C4×Dic3—21no—
94C2×C4×Dic3—21no—
95C22×C3⋊C8—21no—
96C22×C3⋊C8—21no—
97C22×C3⋊C8—21no—
98C22×C3⋊C8—21no—
99C22×C3⋊C8—21no—
100C22×C3⋊C8—21no—
101C22×C3⋊C8D412yes—
102C3×#103—28no—
103#835—28no—
104C3⋊#95—24no—
105C3⋊#95—24no—
106C3⋊#95—24no—
107C23×Q8C2×D311yescharacteristic
108C23×C8—31no—
109C23×C8C2×D311yescharacteristic
110C22×C4⋊C4—31no—
111C22×C4⋊C4—31no—
112C22×C4⋊C4—61no—
113C22×C4⋊C4C2×D311yescharacteristic
114C22×C42—31no—
115C2×#103—22no—
116C2×#103—22no—
117C2×#103—62no—
118C2×#103—62no—
119C2×#103—62no—
120C2×#103Dic314yescomplemented
121#391—62no—
122#391—62no—
123#389—62no—
124#389—62no—
125C2×#95—61no—
126C2×#95—61no—
127C2×#95—61no—
128#340—62no—
129#340—62no—
130#336—62no—
131C24×C3C2×D411yescharacteristic
132C2×C3×Q8—22no—
133C2×C3×Q8—22no—
134C2×C3×Q8—22no—
135C2×C3×Q8—22no—
136C2×C3×Q8—22no—
137C2×C3×Q8—22no—
138C2×C3×Q8—22no—
139C2×C3×Q8—22no—
140C2×C3×Q8—22no—
141C2×C3×Q8—22no—
142C2×C3×Q8—22no—
143C2×C3×Q8—22no—
144C2×C3×Q8—22no—
145C2×C3×Q8—22no—
146C2×C3×Q8—22no—
147C2×C3×Q8—41no—
148C2×C3×Q8—41no—
149C2×C3×Q8—41no—
150C2×C3×Q8—41no—
151C2×C3×Q8—41no—
152C2×C3×Q8—41no—
153C2×C3×Q8—41no—
154C2×C3×Q8—41no—
155C2×C3×Q8—41no—
156C2×C3×Q8—41no—
157C2×C3×Q8—41no—
158C2×C3×Q8—41no—
159C2×C3×Q8C4⋊C414yescomplemented
160C22×C3×C4—22no—
161C22×C3×C4—22no—
162C22×C3×C4—22no—
163C22×C3×C4—22no—
164C22×C3×C4—22no—
165C22×C3×C4—22no—
166C22×C3×C4—41no—
167C22×C3×C4—41no—
168C22×C3×C4—41no—
169C22×C3×C4—41no—
170C22×C3×C4—41no—
171C22×C3×C4—41no—
172C22×C3×C4—41no—
173C22×C3×C4—41no—
174C22×C3×C4C22×C411yescharacteristic
175C22×C3×C4C2×D411yescharacteristic
176C22×C3×C4C2×D411yescharacteristic
177C22×C3×C4C2×D411yescharacteristic
178C22×C3×C4C2×D411yescharacteristic
179C22×C3×C4C2×D411yescharacteristic
180C22×C3×C4C2×D411yescharacteristic
181C22×C3×C4C2×Q811yescharacteristic
182C22×C3×C4#4111yescharacteristic
183C22×C3×C4#4111yescharacteristic
184C22×C3×C4#4111yescharacteristic
185C22×C3×C4#4111yescharacteristic
186C22×C3×C4#4111yescharacteristic
187C22×C3×C4#4111yescharacteristic
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—21no—
191C22×Dic3—21no—
192C22×Dic3—21no—
193C22×Dic3—21no—
194C22×Dic3—21no—
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3—21no—
198C22×Dic3—21no—
199C22×Dic3—21no—
200C22×Dic3—22no—
201C22×Dic3—22no—
202C22×Dic3—41no—
203C22×Dic3—41no—
204C22×Dic3—41no—
205C22×Dic3—41no—
206C22×Dic3—41no—
207C22×Dic3—41no—
208C22×Dic3—41no—
209C22×Dic3—41no—
210C22×Dic3—41no—
211C22×Dic3—41no—
212C22×Dic3—41no—
213C22×Dic3—41no—
214C22×Dic3SD1612yes—
215C22×Dic3Q1612yes—
216C2×C3×C8—22no—
217C2×C3×C8—22no—
218C2×C3×C8—22no—
219C2×C3×C8—41no—
220C2×C3×C8—41no—
221C2×C3×C8—41no—
222C2×C3×C8—41no—
223C3×C4⋊C4—22no—
224C3×C4⋊C4—22no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4C22⋊C414yes—
227C4⋊Dic3—22no—
228C4⋊Dic3—22no—
229C4⋊Dic3—22no—
230C4⋊Dic3—22no—
231C4⋊Dic3—48no—
232C4⋊Dic3—41no—
233C4⋊Dic3—41no—
234C4⋊Dic3—41no—
235C4⋊Dic3—41no—
236C4×Dic3—41no—
237C4×Dic3—41no—
238C4×Dic3—41no—
239C4×Dic3—41no—
240C2×C3⋊C8—22no—
241C2×C3⋊C8—22no—
242C2×C3⋊C8—22no—
243C2×C3⋊C8—41no—
244C2×C3⋊C8—41no—
245C2×C3⋊C8—41no—
246C2×C3⋊C8—41no—
247C22×Q8—21no—
248C22×Q8—21no—
249C22×Q8—21no—
250C22×Q8—21no—
251C22×Q8—21no—
252C22×Q8—21no—
253C22×Q8—21no—
254C22×Q8—21no—
255C22×Q8—21no—
256C22×Q8—21no—
257C22×Q8—21no—
258C22×Q8Dic612yes—
259C22×Q8D1212yes—
260C22×Q8C2×Dic312yes—
261C23×C4—21no—
262C23×C4—21no—
263C23×C4—31no—
264C23×C4—31no—
265C23×C4—61no—
266C23×C4—61no—
267C23×C4C22×D311yescharacteristic
268C22×C8—21no—
269C22×C8—21no—
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—32no—
275C22×C8—61no—
276C22×C8—61no—
277C22×C8—61no—
278C22×C8—61no—
279C22×C8—61no—
280C22×C8—61no—
281C22×C8C2×Dic312yes—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—32no—
286C2×C4⋊C4—32no—
287C2×C4⋊C4—61no—
288C2×C4⋊C4—61no—
289C2×C4⋊C4—61no—
290C2×C4⋊C4—61no—
291C2×C4⋊C4—61no—
292C2×C4⋊C4—61no—
293C2×C4⋊C4—61no—
294C2×C4⋊C4—61no—
295C2×C4⋊C4—64no—
296C2×C4⋊C4—61no—
297C2×C4⋊C4—61no—
298C2×C4⋊C4—122no—
299C2×C4⋊C4—122no—
300C2×C4⋊C4C2×Dic312yes—
301C2×C4⋊C4#6712yes—
302C2×C4⋊C4#6712yes—
303C2×C42—61no—
304C2×C42—61no—
305C2×C42—61no—
306C2×C42—61no—
307C2×C42—61no—
308C2×C42—61no—
309#103—28no—
310#103—68no—
311#95—64no—
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
329C3×Q8—24no—
330C3×Q8—24no—
331C3×Q8—42no—
332C3×Q8—42no—
333C3×Q8—42no—
334C3×Q8—42no—
335C3×Q8—42no—
336C3×Q8—42no—
337C2×C3×C4—24no—
338C2×C3×C4—24no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4C2×C22⋊C411yescharacteristic
352C2×C3×C4C2×C4⋊C411yescharacteristic
353C2×C3×C4#11711yescharacteristic
354C2×C3×C4C4×D411yescharacteristic
355C2×C3×C4C4×D411yescharacteristic
356C2×C3×C4C4×D411yescharacteristic
357C2×C3×C4#12011yescharacteristic
358C2×C3×C4#12111yescharacteristic
359C2×C3×C4#12111yescharacteristic
360C2×C3×C4#12111yescharacteristic
361C2×C3×C4#12111yescharacteristic
362C2×C3×C4#12111yescharacteristic
363C2×C3×C4#12111yescharacteristic
364C2×C3×C4C22⋊Q811yescharacteristic
365C2×C3×C4C22⋊Q811yescharacteristic
366C2×C3×C4C22⋊Q811yescharacteristic
367C2×C3×C4C22⋊Q811yescharacteristic
368C2×C3×C4C22⋊Q811yescharacteristic
369C2×C3×C4#12311yescharacteristic
370C2×C3×C4#12311yescharacteristic
371C2×C3×C4#12311yescharacteristic
372C2×C3×C4#12311yescharacteristic
373C2×C3×C4#12311yescharacteristic
374C2×C3×C4#12411yescharacteristic
375C2×C3×C4#12411yescharacteristic
376C2×C3×C4#12611yescharacteristic
377C2×C3×C4#12611yescharacteristic
378C2×C3×C4#12711yescharacteristic
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—41no—
386C2×Dic3—41no—
387C2×Dic3—41no—
388C2×Dic3—41no—
389C2×Dic3—41no—
390C2×Dic3—41no—
391C2×Dic3—41no—
392C2×Dic3—41no—
393C2×Dic3—42no—
394C2×Dic3—42no—
395C2×Dic3—42no—
396C2×Dic3—42no—
397C2×Dic3—42no—
398C2×Dic3—42no—
399C2×Dic3—81no—
400C2×Dic3—81no—
401C2×Dic3—81no—
402C2×Dic3—81no—
403C2×Dic3—81no—
404C2×Dic3—81no—
405C2×Dic3—81no—
406C2×Dic3—81no—
407C3×C8—42no—
408C3⋊C8—42no—
409C24D3×D411yescharacteristic
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—41no—
426C2×Q8—41no—
427C2×Q8—41no—
428C2×Q8—41no—
429C2×Q8—41no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—41no—
434C2×Q8—41no—
435C2×Q8—41no—
436C2×Q8—41no—
437C2×Q8C4⋊Dic314yescomplemented
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—61no—
460C22×C4—61no—
461C22×C4—61no—
462C22×C4—61no—
463C22×C4—61no—
464C22×C4—61no—
465C22×C4—61no—
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—121no—
479C22×C4—121no—
480C22×C4C2×Dic611yescharacteristic
481C22×C4C2×D1211yescharacteristic
482C22×C4#23511yescharacteristic
483C22×C4#23511yescharacteristic
484C22×C4D3×D411yescharacteristic
485C22×C4D3×D411yescharacteristic
486C22×C4D3×D411yescharacteristic
487C22×C4#23711yescharacteristic
488C22×C4#23711yescharacteristic
489C22×C4#23711yescharacteristic
490C22×C4#23711yescharacteristic
491C22×C4C22×Dic311yescharacteristic
492C22×C4C2×#6711yescharacteristic
493C22×C4C2×#6711yescharacteristic
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—62no—
502C2×C8—62no—
503C2×C8—62no—
504C2×C8—121no—
505C2×C8—121no—
506C2×C8—121no—
507C2×C8—121no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—62no—
512C4⋊C4—62no—
513C4⋊C4—62no—
514C4⋊C4—62no—
515C4⋊C4—128no—
516C4⋊C4—121no—
517C4⋊C4—121no—
518C4⋊C4—121no—
519C4⋊C4—121no—
520C4⋊C4#21714yes—
521C42—121no—
522C42—121no—
523C42—121no—
524C42—121no—
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—44no—
562C3×C4#38011yescharacteristic
563C3×C4#38511yescharacteristic
564C3×C4#38811yescharacteristic
565C3×C4#39011yescharacteristic
566C3×C4#39411yescharacteristic
567C3×C4#39611yescharacteristic
568C3×C4#39711yescharacteristic
569C3×C4#39911yescharacteristic
570Dic3—42no—
571Dic3—42no—
572Dic3—82no—
573Dic3—82no—
574C23#87811yescharacteristic
575C23#88211yescharacteristic
576C23#88411yescharacteristic
577C23#88511yescharacteristic
578C23D3×SD1611yescharacteristic
579C23#91411yescharacteristic
580C23#91511yescharacteristic
581C23#91611yescharacteristic
582C23D3×Q1611yescharacteristic
583C23#91811yescharacteristic
584C23#91811yescharacteristic
585C23#91911yescharacteristic
586C23D4×Dic311yescharacteristic
587C23#93711yescharacteristic
588C23#93911yescharacteristic
589Q8—24no—
590Q8—24no—
591Q8—42no—
592Q8—42no—
593Q8—42no—
594Q8—42no—
595Q8—42no—
596Q8—42no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—62no—
612C2×C4—62no—
613C2×C4—62no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—121no—
618C2×C4—121no—
619C2×C4—121no—
620C2×C4—121no—
621C2×C4—121no—
622C2×C4—121no—
623C2×C4—121no—
624C2×C4—121no—
625C2×C4—122no—
626C2×C4—122no—
627C2×C4—122no—
628C2×C4—122no—
629C2×C4—122no—
630C2×C4—122no—
631C2×C4—241no—
632C2×C4—241no—
633C2×C4—241no—
634C2×C4—241no—
635C2×C4—241no—
636C2×C4—241no—
637C2×C4—241no—
638C2×C4—241no—
639C2×C4#87811yescharacteristic
640C2×C4#87811yescharacteristic
641C2×C4#87811yescharacteristic
642C2×C4#87911yescharacteristic
643C2×C4#87911yescharacteristic
644C2×C4#88211yescharacteristic
645C2×C4#88311yescharacteristic
646C2×C4#88311yescharacteristic
647C2×C4#88411yescharacteristic
648C2×C4#88511yescharacteristic
649C2×C4#88611yescharacteristic
650C2×C4#88611yescharacteristic
651C2×C4#92411yescharacteristic
652C2×C4#92411yescharacteristic
653C2×C4C2×C4⋊Dic311yescharacteristic
654C2×C4#92611yescharacteristic
655C2×C4#93011yescharacteristic
656C2×C4#93011yescharacteristic
657C2×C4D4×Dic311yescharacteristic
658C2×C4D4×Dic311yescharacteristic
659C2×C4D4×Dic311yescharacteristic
660C2×C4#93511yescharacteristic
661C2×C4#93611yescharacteristic
662C2×C4#93811yescharacteristic
663C2×C4#93811yescharacteristic
664C2×C4#93911yescharacteristic
665C2×C4#94011yescharacteristic
666C2×C4C2×#21711yescharacteristic
667C8—42no—
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#479111yescharacteristic
685C22#479211yescharacteristic
686C22#479311yescharacteristic
687C22#479411yescharacteristic
688C22#479611yescharacteristic
689C22#479711yescharacteristic
690C22#479911yescharacteristic
691C22#480011yescharacteristic
692C22#480611yescharacteristic
693C22#480711yescharacteristic
694C22#480811yescharacteristic
695C22#480911yescharacteristic
696C22#481011yescharacteristic
697C22#481211yescharacteristic
698C22#481311yescharacteristic
699C22#481611yescharacteristic
700C22#494711yescharacteristic
701C22#494811yescharacteristic
702C22#495011yescharacteristic
703C22#495111yescharacteristic
704C22#496011yescharacteristic
705C22#496111yescharacteristic
706C22Dic3×SD1611yescharacteristic
707C22#516211yescharacteristic
708C22#516411yescharacteristic
709C22#516511yescharacteristic
710C22#516911yescharacteristic
711C22#517311yescharacteristic
712C22Dic3×Q1611yescharacteristic
713C22#518211yescharacteristic
714C22#518411yescharacteristic
715C22#518511yescharacteristic
716C22#518611yescharacteristic
717C22#518711yescharacteristic
718C22#522011yescharacteristic
719C4—44no—
720C4—44no—
721C4—122no—
722C4—122no—
723C4—242no—
724C4—242no—
725C4#494811yescharacteristic
726C4#494911yescharacteristic
727C4#495011yescharacteristic
728C4#495111yescharacteristic
729C4#495311yescharacteristic
730C4#496111yescharacteristic
731C4#521211yescharacteristic
732C4#522111yescharacteristic
733C3#1106711yescharacteristic, complemented, Sylow
734C2#7023111yescharacteristic
735C2#7023211yescharacteristic
736C2#7023611yescharacteristic
737C2#7023811yescharacteristic
738C2#7024511yescharacteristic
739C2#7024611yescharacteristic
740C2#7025311yescharacteristic
741C2#7025511yescharacteristic
742C2#7026111yescharacteristic
743C2#7026211yescharacteristic
744C2#7027211yescharacteristic
745C2#7027311yescharacteristic
746C2#7154611yescharacteristic
747C2#7204711yescharacteristic
748C2#7206511yescharacteristic
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#11067
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
19. C2×C3×#103C4semidirect
120. C2×#103Dic3semidirect
159. C2×C3×Q8C4⋊C4semidirect
437. C2×Q8C4⋊Dic3semidirect
733. C3#11067semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1032
C2×#52292
C22×#8352
C2×#49842
C2×#45512
C2×#45502
C2×#45292
#110673