Finite Group Databasebeta

← #10702250

Subgroups — #10702250

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×#816C211yesmaximal, characteristic
2C2×#4973C211yesmaximal, characteristic
3C2×#4972C211yesmaximal, characteristic
4C22×#810C211yesmaximal, characteristic
5C2×C3×#340C211yesmaximal, characteristic
6C2×#4550C211yesmaximal, characteristic
7C2×#4529C211yesmaximal, characteristic
8#11067—31nomaximal, Sylow
9C23×Dic6C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C22×C4⋊Dic3C2211yescharacteristic
14C22×Dic3⋊C4—21no—
15C22×C4×Dic3C2211yescharacteristic
16C23×C3⋊C8C2211yescharacteristic
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—
25#4972—22no—
26#4972—22no—
27C2×#810—22no—
28C2×#810—22no—
29C2×#810—22no—
30C3×#340—22no—
31#4550—22no—
32#4529—22no—
33C22×#103—31no—
34C22×#103—31no—
35C2×#391—31no—
36C2×#389—31no—
37C2×#340—31no—
38C2×#340D311yescharacteristic
39C2×#336—31no—
40C23×C3×C4—21no—
41C23×C3×C4—21no—
42C23×C3×C4C2311yescharacteristic
43C23×Dic3—21no—
44C23×Dic3—21no—
45C23×Dic3D411yescharacteristic
46C23×Dic3D411yescharacteristic
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—
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⋊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⋊C4—21no—
77C2×C3×C4⋊C4—21no—
78C2×C3×C4⋊C4D412yes—
79C2×C3×C4⋊C4D412yes—
80C2×C4⋊Dic3—21no—
81C2×C4⋊Dic3—21no—
82C2×C4⋊Dic3—21no—
83C2×C4⋊Dic3C2×C412yes—
84C2×C4⋊Dic3D412yes—
85C2×C4⋊Dic3D412yes—
86C2×Dic3⋊C4—24no—
87C2×Dic3⋊C4—42no—
88C2×Dic3⋊C4—42no—
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⋊#95—24no—
103C3⋊#95—24no—
104C3⋊#95—24no—
105#816—28no—
106#810—28no—
107C23×Q8—31no—
108C23×C8—31no—
109C23×C8C2×D311yescharacteristic
110C22×C4⋊C4—31no—
111C22×C4⋊C4—61no—
112C22×C4⋊C4C2×D311yescharacteristic
113C22×C4⋊C4C2×D311yescharacteristic
114C22×C42—31no—
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—62no—
124#389—62no—
125C2×#95—61no—
126C2×#95—61no—
127C2×#95—61no—
128#340—22no—
129#340—62no—
130#336—62no—
131C24×C3C2×D411yescharacteristic
132C22×C3×C4—22no—
133C22×C3×C4—22no—
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×C4—41no—
141C22×C3×C4—41no—
142C22×C3×C4—41no—
143C22×C3×C4—41no—
144C22×C3×C4—41no—
145C22×C3×C4—41no—
146C22×C3×C4C22×C411yescharacteristic
147C22×C3×C4C2×D411yescharacteristic
148C22×C3×C4C2×D411yescharacteristic
149C22×C3×C4C2×D411yescharacteristic
150C22×C3×C4C2×D411yescharacteristic
151C22×C3×C4C2×D411yescharacteristic
152C22×C3×C4C2×D411yescharacteristic
153C22×C3×C4C2×Q811yescharacteristic
154C22×C3×C4#4111yescharacteristic
155C22×C3×C4#4111yescharacteristic
156C22×C3×C4#4111yescharacteristic
157C22×C3×C4#4111yescharacteristic
158C22×C3×C4#4111yescharacteristic
159C22×C3×C4#4111yescharacteristic
160C22×Dic3—22no—
161C22×Dic3—22no—
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3—21no—
165C22×Dic3—22no—
166C22×Dic3—22no—
167C22×Dic3—21no—
168C22×Dic3—21no—
169C22×Dic3—21no—
170C22×Dic3—22no—
171C22×Dic3—22no—
172C22×Dic3—21no—
173C22×Dic3—21no—
174C22×Dic3—21no—
175C22×Dic3—21no—
176C22×Dic3—21no—
177C22×Dic3—21no—
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×Dic3SD1612yes—
187C22×Dic3Q1612yes—
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
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⋊C4—22no—
227C3×C4⋊C4—41no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4—41no—
230C3×C4⋊C4—41no—
231C4⋊Dic3—22no—
232C4⋊Dic3—22no—
233C4⋊Dic3—22no—
234C4⋊Dic3C22⋊C414yes—
235Dic3⋊C4—48no—
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—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—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×C8C4×D312yes—
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—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—32no—
293C2×C4⋊C4—32no—
294C2×C4⋊C4—32no—
295C2×C4⋊C4—61no—
296C2×C4⋊C4—61no—
297C2×C4⋊C4—61no—
298C2×C4⋊C4—64no—
299C2×C4⋊C4—122no—
300C2×C4⋊C4—122no—
301C2×C4⋊C4D1212yes—
302C2×C4⋊C4#6712yes—
303C2×C42—61no—
304C2×C42—61no—
305C2×C42—61no—
306C2×C42—61no—
307C2×C42—61no—
308C2×C42—61no—
309#103—68no—
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
329C2×C3×C4—42no—
330C2×C3×C4—42no—
331C2×C3×C4—42no—
332C2×C3×C4—42no—
333C2×C3×C4—42no—
334C2×C3×C4—42no—
335C2×C3×C4—81no—
336C2×C3×C4—81no—
337C2×C3×C4—81no—
338C2×C3×C4—81no—
339C2×C3×C4—81no—
340C2×C3×C4—81no—
341C2×C3×C4—81no—
342C2×C3×C4—81no—
343C2×C3×C4C2×C22⋊C411yescharacteristic
344C2×C3×C4C2×C4⋊C411yescharacteristic
345C2×C3×C4#11711yescharacteristic
346C2×C3×C4C4×D411yescharacteristic
347C2×C3×C4C4×D411yescharacteristic
348C2×C3×C4C4×D411yescharacteristic
349C2×C3×C4#12011yescharacteristic
350C2×C3×C4#12111yescharacteristic
351C2×C3×C4#12111yescharacteristic
352C2×C3×C4#12111yescharacteristic
353C2×C3×C4#12111yescharacteristic
354C2×C3×C4#12111yescharacteristic
355C2×C3×C4#12111yescharacteristic
356C2×C3×C4C22⋊Q811yescharacteristic
357C2×C3×C4C22⋊Q811yescharacteristic
358C2×C3×C4C22⋊Q811yescharacteristic
359C2×C3×C4C22⋊Q811yescharacteristic
360C2×C3×C4C22⋊Q811yescharacteristic
361C2×C3×C4#12311yescharacteristic
362C2×C3×C4#12311yescharacteristic
363C2×C3×C4#12311yescharacteristic
364C2×C3×C4#12311yescharacteristic
365C2×C3×C4#12311yescharacteristic
366C2×C3×C4#12411yescharacteristic
367C2×C3×C4#12411yescharacteristic
368C2×C3×C4#12611yescharacteristic
369C2×C3×C4#12611yescharacteristic
370C2×C3×C4#12711yescharacteristic
371C2×Dic3—24no—
372C2×Dic3—24no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—42no—
380C2×Dic3—42no—
381C2×Dic3—41no—
382C2×Dic3—41no—
383C2×Dic3—42no—
384C2×Dic3—42no—
385C2×Dic3—42no—
386C2×Dic3—42no—
387C2×Dic3—42no—
388C2×Dic3—42no—
389C2×Dic3—41no—
390C2×Dic3—42no—
391C2×Dic3—41no—
392C2×Dic3—41no—
393C2×Dic3—41no—
394C2×Dic3—42no—
395C2×Dic3—42no—
396C2×Dic3—42no—
397C2×Dic3—41no—
398C2×Dic3—41no—
399Dic6—24no—
400Dic6—24no—
401Dic6—42no—
402Dic6—42no—
403Dic6—42no—
404Dic6—42no—
405Dic6—42no—
406Dic6—42no—
407C3×C8—42no—
408C3⋊C8—42no—
409C24D3×D411yescharacteristic
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—32no—
441C22×C4—32no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
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—62no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—62no—
460C22×C4—62no—
461C22×C4—62no—
462C22×C4—62no—
463C22×C4—61no—
464C22×C4—61no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—61no—
468C22×C4—61no—
469C22×C4—61no—
470C22×C4—61no—
471C22×C4—62no—
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×C4×D311yescharacteristic
481C22×C4C2×D1211yescharacteristic
482C22×C4#23511yescharacteristic
483C22×C4#23511yescharacteristic
484C22×C4#23511yescharacteristic
485C22×C4#23511yescharacteristic
486C22×C4D3×D411yescharacteristic
487C22×C4D3×D411yescharacteristic
488C22×C4D3×D411yescharacteristic
489C22×C4D3×D411yescharacteristic
490C22×C4#23711yescharacteristic
491C22×C4D3×Q811yescharacteristic
492C22×C4#23911yescharacteristic
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—22no—
512C4⋊C4—34no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—62no—
518C4⋊C4—62no—
519C4⋊C4—62no—
520C4⋊C4—128no—
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—82no—
561C3×C4—82no—
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—44no—
571Dic3—44no—
572Dic3—42no—
573Dic3—42no—
574C23#88211yescharacteristic
575C23#88411yescharacteristic
576C23#88411yescharacteristic
577C23#88511yescharacteristic
578C23#89311yescharacteristic
579C23#89611yescharacteristic
580C23#91111yescharacteristic
581C23#91211yescharacteristic
582C23D3×SD1611yescharacteristic
583C23#91511yescharacteristic
584C23#91511yescharacteristic
585C23#91611yescharacteristic
586C23D3×Q1611yescharacteristic
587C23#91811yescharacteristic
588C23#93711yescharacteristic
589Q8—64no—
590Q8—64no—
591Q8—122no—
592Q8—122no—
593Q8—122no—
594Q8—122no—
595Q8—122no—
596Q8—122no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—62no—
604C2×C4—64no—
605C2×C4—62no—
606C2×C4—64no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—62no—
611C2×C4—81no—
612C2×C4—81no—
613C2×C4—81no—
614C2×C4—81no—
615C2×C4—81no—
616C2×C4—81no—
617C2×C4—81no—
618C2×C4—81no—
619C2×C4—122no—
620C2×C4—121no—
621C2×C4—121no—
622C2×C4—122no—
623C2×C4—122no—
624C2×C4—122no—
625C2×C4—122no—
626C2×C4—122no—
627C2×C4—121no—
628C2×C4—121no—
629C2×C4—122no—
630C2×C4—122no—
631C2×C4—121no—
632C2×C4—121no—
633C2×C4—122no—
634C2×C4—121no—
635C2×C4—122no—
636C2×C4—121no—
637C2×C4—122no—
638C2×C4—122no—
639C2×C4#87211yescharacteristic
640C2×C4C4×D1211yescharacteristic
641C2×C4#87511yescharacteristic
642C2×C4#87611yescharacteristic
643C2×C4D3×C22⋊C411yescharacteristic
644C2×C4#67⋊C411yescharacteristic
645C2×C4#88211yescharacteristic
646C2×C4#88311yescharacteristic
647C2×C4#88411yescharacteristic
648C2×C4#88411yescharacteristic
649C2×C4#88411yescharacteristic
650C2×C4#88511yescharacteristic
651C2×C4D3×C4⋊C411yescharacteristic
652C2×C4#89411yescharacteristic
653C2×C4#89411yescharacteristic
654C2×C4#89411yescharacteristic
655C2×C4#89511yescharacteristic
656C2×C4#89611yescharacteristic
657C2×C4#89611yescharacteristic
658C2×C4#89611yescharacteristic
659C2×C4#89711yescharacteristic
660C2×C4#89811yescharacteristic
661C2×C4C4×#6711yescharacteristic
662C2×C4#92911yescharacteristic
663C2×C4#93011yescharacteristic
664C2×C4#93911yescharacteristic
665C2×C4#94011yescharacteristic
666C2×C4#94611yescharacteristic
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#466511yescharacteristic
685C22#466911yescharacteristic
686C22#467311yescharacteristic
687C22#467611yescharacteristic
688C22#476511yescharacteristic
689C22#476711yescharacteristic
690C22#476811yescharacteristic
691C22#477611yescharacteristic
692C22#477811yescharacteristic
693C22#478011yescharacteristic
694C22#478311yescharacteristic
695C22#478711yescharacteristic
696C22#479211yescharacteristic
697C22#479511yescharacteristic
698C22#479711yescharacteristic
699C22#480811yescharacteristic
700C22#480911yescharacteristic
701C22#481311yescharacteristic
702C22#481611yescharacteristic
703C22#481811yescharacteristic
704C22#485211yescharacteristic
705C22#485311yescharacteristic
706C22#485411yescharacteristic
707C22#485711yescharacteristic
708C22#487311yescharacteristic
709C22#487511yescharacteristic
710C22#487711yescharacteristic
711C22#488911yescharacteristic
712C22#495911yescharacteristic
713C22#496011yescharacteristic
714C22#498911yescharacteristic
715C22#515811yescharacteristic
716C22#517011yescharacteristic
717C22#517311yescharacteristic
718C22#518611yescharacteristic
719C4—82no—
720C4—82no—
721C4—124no—
722C4—124no—
723C4—122no—
724C4—122no—
725C4#466711yescharacteristic
726C4#466811yescharacteristic
727C4#467211yescharacteristic
728C4#467511yescharacteristic
729C4#494011yescharacteristic
730C4#495711yescharacteristic
731C4#499311yescharacteristic
732C4#499411yescharacteristic
733C3#1106711yescharacteristic, complemented, Sylow
734C2#6885011yescharacteristic
735C2#6885411yescharacteristic
736C2#6889611yescharacteristic
737C2#6890811yescharacteristic
738C2#6891011yescharacteristic
739C2#6891111yescharacteristic
740C2#6891211yescharacteristic
741C2#6891311yescharacteristic
742C2#6942811yescharacteristic
743C2#7020511yescharacteristic
744C2#7021611yescharacteristic
745C2#7027311yescharacteristic
746C2#7028411yescharacteristic
747C2#7058811yescharacteristic
748C2#7064211yescharacteristic
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#11067
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
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
C22×#8162
C2×#49732
C2×#49722
C22×#8102
C2×C3×#3402
C2×#45502
C2×#45292
#110673