Finite Group Databasebeta

← #10702245

Subgroups — #10702245

Order 768.

1282 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#821C211yesmaximal, characteristic
2C2×#4988C211yesmaximal, characteristic
3C2×#4984C211yesmaximal, characteristic, complemented
4C22×#809C211yesmaximal, characteristic
5C2×C3×#340C211yesmaximal, characteristic, complemented
6C2×#4550C211yesmaximal, characteristic, complemented
7C2×#4529C211yesmaximal, characteristic, complemented
8#11066—31nomaximal, Sylow
9C23×D12C2211yescharacteristic
10C23×C3×C8C2211yescharacteristic
11C22×C3×C4⋊C4C2211yescharacteristic
12C22×C3×C4⋊C4C2211yescharacteristic
13C22×(C2×D3)⋊C4—21no—
14C22×(C2×D3)⋊C4—21no—
15C22×C4⋊Dic3—21no—
16C22×C4⋊Dic3C2211yescharacteristic
17C22×C4×Dic3C2211yescharacteristic
18C23×C3⋊C8C2211yescharacteristic
19C2×C3⋊#95—21no—
20C2×#821—22no—
21C2×#821—22no—
22C2×#821—22no—
23#4988—22no—
24#4988—22no—
25#4984—22no—
26#4984—22no—
27C2×#809—22no—
28C2×#809—22no—
29C2×#809C414yescomplemented
30C3×#340—22no—
31#4550—22no—
32#4529—22no—
33C22×#102—31no—
34C22×#102—31no—
35C2×#390—31no—
36C2×#389—31no—
37C2×#340—31no—
38C2×#340D311yescharacteristic, complemented
39C2×#336—31no—
40C24×D3—21no—
41C23×C3×C4—21no—
42C23×C3×C4—21no—
43C23×C3×C4C2311yescharacteristic
44C23×Dic3—21no—
45C23×Dic3D411yescharacteristic
46C23×Dic3D411yescharacteristic
47C22×D12—21no—
48C22×D12—21no—
49C22×D12—21no—
50C22×D12—21no—
51C22×D12—21no—
52C22×D12—21no—
53C22×D12—21no—
54C22×D12—21no—
55C22×D12—21no—
56C22×D12—21no—
57C22×D12—21no—
58C22×D12C2×C412yes—
59C22×D12D412yes—
60C22×D12Q812yes—
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×C8D412yes—
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⋊C4C2×C412yes—
77C2×C3×C4⋊C4D412yes—
78C2×C3×C4⋊C4D412yes—
79C2×C3×C4⋊C4D412yes—
80C2×(C2×D3)⋊C4—24no—
81C2×(C2×D3)⋊C4—24no—
82C2×(C2×D3)⋊C4—42no—
83C2×(C2×D3)⋊C4—42no—
84C2×(C2×D3)⋊C4—42no—
85C2×(C2×D3)⋊C4—42no—
86C2×C4⋊Dic3—21no—
87C2×C4⋊Dic3—21no—
88C2×C4⋊Dic3—21no—
89C2×C4⋊Dic3—21no—
90C2×C4⋊Dic3—24no—
91C2×C4⋊Dic3—21no—
92C2×C4⋊Dic3—42no—
93C2×C4⋊Dic3—42no—
94C2×C4⋊Dic3D412yes—
95C2×C4×Dic3—21no—
96C2×C4×Dic3—21no—
97C2×C4×Dic3—21no—
98C2×C4×Dic3—21no—
99C2×C4×Dic3—21no—
100C2×C4×Dic3—21no—
101C22×C3⋊C8—21no—
102C22×C3⋊C8—21no—
103C22×C3⋊C8—21no—
104C22×C3⋊C8—21no—
105C22×C3⋊C8—21no—
106C22×C3⋊C8—21no—
107C22×C3⋊C8C2×C412yes—
108C3⋊#95—24no—
109#821—28no—
110#809—28no—
111C23×D4—31no—
112C23×C8—31no—
113C23×C8C2×D311yescharacteristic
114C22×C4⋊C4—31no—
115C22×C4⋊C4—61no—
116C22×C4⋊C4C2×D311yescharacteristic
117C22×C4⋊C4C2×D311yescharacteristic
118C22×C22⋊C4—61no—
119C22×C22⋊C4—61no—
120C22×C42—31no—
121C2×#102—34no—
122C2×#102—62no—
123C2×#102—62no—
124C2×#102—62no—
125C2×#102—62no—
126C2×#102—62no—
127#390—62no—
128#390—62no—
129#389—62no—
130#389—62no—
131C2×#95—61no—
132#340—22no—
133#340—62no—
134#336—62no—
135C24×C3C2×D411yescharacteristic
136C23×D3—22no—
137C23×D3—22no—
138C23×D3—22no—
139C23×D3—41no—
140C23×D3—41no—
141C23×D3—41no—
142C23×D3—41no—
143C23×D3—41no—
144C23×D3—41no—
145C23×D3—41no—
146C23×D3—41no—
147C23×D3—41no—
148C23×D3—41no—
149C23×D3—41no—
150C23×D3—41no—
151C22×C3×C4—22no—
152C22×C3×C4—22no—
153C22×C3×C4—22no—
154C22×C3×C4—22no—
155C22×C3×C4—41no—
156C22×C3×C4—41no—
157C22×C3×C4—41no—
158C22×C3×C4—41no—
159C22×C3×C4—41no—
160C22×C3×C4—41no—
161C22×C3×C4—41no—
162C22×C3×C4—41no—
163C22×C3×C4—41no—
164C22×C3×C4—41no—
165C22×C3×C4C22×C411yescharacteristic
166C22×C3×C4C2×D411yescharacteristic
167C22×C3×C4C2×D411yescharacteristic
168C22×C3×C4C2×D411yescharacteristic
169C22×C3×C4C2×D411yescharacteristic
170C22×C3×C4C2×D411yescharacteristic
171C22×C3×C4C2×D411yescharacteristic
172C22×C3×C4C2×Q811yescharacteristic
173C22×C3×C4#4111yescharacteristic
174C22×C3×C4#4111yescharacteristic
175C22×C3×C4#4111yescharacteristic
176C22×C3×C4#4111yescharacteristic
177C22×C3×C4#4111yescharacteristic
178C22×C3×C4#4111yescharacteristic
179C22×Dic3—21no—
180C22×Dic3—21no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3—21no—
184C22×Dic3—21no—
185C22×Dic3—21no—
186C22×Dic3—21no—
187C22×Dic3—21no—
188C22×Dic3—21no—
189C22×Dic3—21no—
190C22×Dic3—21no—
191C22×Dic3—22no—
192C22×Dic3—41no—
193C22×Dic3—41no—
194C22×Dic3—41no—
195C22×Dic3—41no—
196C22×Dic3—41no—
197C22×Dic3—41no—
198C22×Dic3D812yes—
199C22×Dic3SD1612yes—
200C2×D12—22no—
201C2×D12—22no—
202C2×D12—22no—
203C2×D12—22no—
204C2×D12—22no—
205C2×D12—22no—
206C2×D12—22no—
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—22no—
210C2×D12—22no—
211C2×D12—22no—
212C2×D12—22no—
213C2×D12—22no—
214C2×D12—22no—
215C2×D12—41no—
216C2×D12—41no—
217C2×D12—41no—
218C2×D12—41no—
219C2×D12—41no—
220C2×D12—41no—
221C2×D12—41no—
222C2×D12—41no—
223C2×D12—41no—
224C2×D12—41no—
225C2×D12—41no—
226C2×D12—41no—
227C2×D12C4⋊C414yescomplemented
228C2×C3×C8—22no—
229C2×C3×C8—22no—
230C2×C3×C8—22no—
231C2×C3×C8—41no—
232C2×C3×C8—41no—
233C2×C3×C8—41no—
234C2×C3×C8—41no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—41no—
241C3×C4⋊C4—41no—
242C3×C4⋊C4C22⋊C414yescomplemented
243(C2×D3)⋊C4—48no—
244(C2×D3)⋊C4—48no—
245C4⋊Dic3—22no—
246C4⋊Dic3—22no—
247C4⋊Dic3—48no—
248C4⋊Dic3—41no—
249C4⋊Dic3—41no—
250C4×Dic3—41no—
251C4×Dic3—41no—
252C4×Dic3—41no—
253C4×Dic3—41no—
254C2×C3⋊C8—22no—
255C2×C3⋊C8—22no—
256C2×C3⋊C8—22no—
257C2×C3⋊C8—41no—
258C2×C3⋊C8—41no—
259C2×C3⋊C8—41no—
260C2×C3⋊C8—41no—
261C25—61no—
262C22×D4—32no—
263C22×D4—32no—
264C22×D4—32no—
265C22×D4—61no—
266C22×D4—61no—
267C22×D4—61no—
268C22×D4—61no—
269C22×D4—61no—
270C22×D4—61no—
271C22×D4—61no—
272C22×D4—61no—
273C22×D4—61no—
274C22×D4—61no—
275C22×D4—61no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—31no—
279C23×C4—31no—
280C23×C4—61no—
281C23×C4C22×D311yescharacteristic
282C22×C8—21no—
283C22×C8—21no—
284C22×C8—21no—
285C22×C8—21no—
286C22×C8—21no—
287C22×C8—21no—
288C22×C8—32no—
289C22×C8—61no—
290C22×C8—61no—
291C22×C8—61no—
292C22×C8—61no—
293C22×C8—61no—
294C22×C8—61no—
295C22×C8D1212yes—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—32no—
305C2×C4⋊C4—61no—
306C2×C4⋊C4—61no—
307C2×C4⋊C4—61no—
308C2×C4⋊C4—61no—
309C2×C4⋊C4—64no—
310C2×C4⋊C4—61no—
311C2×C4⋊C4—122no—
312C2×C4⋊C4—122no—
313C2×C4⋊C4C4×D312yes—
314C2×C4⋊C4D1212yes—
315C2×C4⋊C4D1212yes—
316C2×C4⋊C4#6712yes—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—64no—
319C2×C22⋊C4—122no—
320C2×C22⋊C4—122no—
321C2×C22⋊C4—122no—
322C2×C22⋊C4—122no—
323C2×C42—61no—
324C2×C42—61no—
325C2×C42—61no—
326C2×C42—61no—
327C2×C42—61no—
328C2×C42—61no—
329#102—68no—
330#102—68no—
331#95—64no—
332C23×C3C4×D411yescharacteristic
333C23×C3#12011yescharacteristic
334C23×C3#12011yescharacteristic
335C23×C3#12111yescharacteristic
336C23×C3#12111yescharacteristic
337C23×C3C22⋊Q811yescharacteristic
338C23×C3#12411yescharacteristic
339C23×C3C2×D811yescharacteristic
340C23×C3C2×SD1611yescharacteristic
341C23×C3#13511yescharacteristic
342C23×C3#13511yescharacteristic
343C23×C3AGL(1,ℤ/8)11yescharacteristic
344C23×C3AGL(1,ℤ/8)11yescharacteristic
345C23×C3AGL(1,ℤ/8)11yescharacteristic
346C23×C3#13711yescharacteristic
347C22×D3—24no—
348C22×D3—42no—
349C22×D3—42no—
350C22×D3—42no—
351C22×D3—42no—
352C22×D3—42no—
353C22×D3—42no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—42no—
357C22×D3—42no—
358C22×D3—42no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—42no—
364C22×D3—42no—
365C22×D3—42no—
366C22×D3—81no—
367C22×D3—81no—
368C22×D3—81no—
369C22×D3—81no—
370C22×D3—81no—
371C22×D3—81no—
372C22×D3—81no—
373C22×D3—81no—
374C22×D3—81no—
375C22×D3—81no—
376C22×D3—81no—
377C22×D3—81no—
378C22×D3—81no—
379C22×D3—81no—
380C22×D3—81no—
381C22×D3—81no—
382C2×C3×C4—24no—
383C2×C3×C4—42no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—42no—
387C2×C3×C4—42no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—81no—
393C2×C3×C4—81no—
394C2×C3×C4—81no—
395C2×C3×C4—81no—
396C2×C3×C4C2×C22⋊C411yescharacteristic
397C2×C3×C4C2×C4⋊C411yescharacteristic
398C2×C3×C4#11711yescharacteristic
399C2×C3×C4C4×D411yescharacteristic
400C2×C3×C4C4×D411yescharacteristic
401C2×C3×C4C4×D411yescharacteristic
402C2×C3×C4#12011yescharacteristic
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×C4C22⋊Q811yescharacteristic
410C2×C3×C4C22⋊Q811yescharacteristic
411C2×C3×C4C22⋊Q811yescharacteristic
412C2×C3×C4C22⋊Q811yescharacteristic
413C2×C3×C4C22⋊Q811yescharacteristic
414C2×C3×C4#12311yescharacteristic
415C2×C3×C4#12311yescharacteristic
416C2×C3×C4#12311yescharacteristic
417C2×C3×C4#12311yescharacteristic
418C2×C3×C4#12311yescharacteristic
419C2×C3×C4#12411yescharacteristic
420C2×C3×C4#12411yescharacteristic
421C2×C3×C4#12611yescharacteristic
422C2×C3×C4#12611yescharacteristic
423C2×C3×C4#12711yescharacteristic
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—41no—
431C2×Dic3—41no—
432C2×Dic3—41no—
433C2×Dic3—41no—
434C2×Dic3—41no—
435C2×Dic3—41no—
436C2×Dic3—41no—
437C2×Dic3—41no—
438C2×Dic3—42no—
439C2×Dic3—42no—
440C2×Dic3—42no—
441C2×Dic3—81no—
442C2×Dic3—81no—
443C2×Dic3—81no—
444C2×Dic3—81no—
445D12—24no—
446D12—24no—
447D12—42no—
448D12—42no—
449D12—42no—
450D12—42no—
451D12—42no—
452D12—42no—
453C3×C8—42no—
454C3⋊C8—42no—
455C24—62no—
456C24—62no—
457C24—62no—
458C24—121no—
459C24—121no—
460C24—121no—
461C24—121no—
462C24—121no—
463C24—121no—
464C24—121no—
465C24—121no—
466C24—121no—
467C24—121no—
468C24—121no—
469C24—121no—
470C24D3×D411yescharacteristic
471C2×D4—34no—
472C2×D4—62no—
473C2×D4—62no—
474C2×D4—62no—
475C2×D4—62no—
476C2×D4—62no—
477C2×D4—62no—
478C2×D4—62no—
479C2×D4—62no—
480C2×D4—62no—
481C2×D4—62no—
482C2×D4—62no—
483C2×D4—62no—
484C2×D4—62no—
485C2×D4—62no—
486C2×D4—62no—
487C2×D4—121no—
488C2×D4—121no—
489C2×D4—121no—
490C2×D4—121no—
491C2×D4—121no—
492C2×D4—121no—
493C2×D4—121no—
494C2×D4—121no—
495C2×D4—121no—
496C2×D4—121no—
497C2×D4—121no—
498C2×D4—121no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—32no—
504C22×C4—32no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—61no—
521C22×C4—61no—
522C22×C4—61no—
523C22×C4—61no—
524C22×C4—61no—
525C22×C4—61no—
526C22×C4—61no—
527C22×C4—62no—
528C22×C4—121no—
529C22×C4—121no—
530C22×C4—121no—
531C22×C4—121no—
532C22×C4—121no—
533C22×C4—121no—
534C22×C4C2×C4×D311yescharacteristic
535C22×C4C2×D1211yescharacteristic
536C22×C4C2×D1211yescharacteristic
537C22×C4C2×D1211yescharacteristic
538C22×C4#23511yescharacteristic
539C22×C4#23511yescharacteristic
540C22×C4D3×D411yescharacteristic
541C22×C4D3×D411yescharacteristic
542C22×C4#23711yescharacteristic
543C22×C4#23711yescharacteristic
544C22×C4#23711yescharacteristic
545C22×C4D3×Q811yescharacteristic
546C22×C4#23911yescharacteristic
547C22×C4C2×#6711yescharacteristic
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—41no—
552C2×C8—41no—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—62no—
556C2×C8—62no—
557C2×C8—62no—
558C2×C8—121no—
559C2×C8—121no—
560C2×C8—121no—
561C2×C8—121no—
562C4⋊C4—22no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—62no—
570C4⋊C4—62no—
571C4⋊C4—128no—
572C4⋊C4—121no—
573C4⋊C4—121no—
574C4⋊C4(C2×D3)⋊C414yescomplemented
575C22⋊C4—128no—
576C22⋊C4—128no—
577C42—121no—
578C42—121no—
579C42—121no—
580C42—121no—
581C22×C3#38511yescharacteristic
582C22×C3#38611yescharacteristic
583C22×C3#38811yescharacteristic
584C22×C3#39211yescharacteristic
585C22×C3#39311yescharacteristic
586C22×C3#39411yescharacteristic
587C22×C3#39611yescharacteristic
588C22×C3C4×D811yescharacteristic
589C22×C3C4×SD1611yescharacteristic
590C22×C3#44011yescharacteristic
591C22×C3#44211yescharacteristic
592C22×C3#44711yescharacteristic
593C22×C3#44711yescharacteristic
594C22×C3#44811yescharacteristic
595C22×C3#44911yescharacteristic
596C22×C3#44911yescharacteristic
597C22×C3#44911yescharacteristic
598C22×C3#45011yescharacteristic
599C22×C3#45211yescharacteristic
600C22×C3#45911yescharacteristic
601C22×C3#46011yescharacteristic
602C22×C3#46311yescharacteristic
603C22×C3#46411yescharacteristic
604C22×C3#46511yescharacteristic
605C22×C3#46611yescharacteristic
606C22×C3#46811yescharacteristic
607C22×C3#46911yescharacteristic
608C22×C3#47411yescharacteristic
609C22×C3#47611yescharacteristic
610C22×C3#47811yescharacteristic
611C22×C3#47811yescharacteristic
612C22×C3#48611yescharacteristic
613C22×C3#48811yescharacteristic
614C22×C3#48911yescharacteristic
615C22×C3#49011yescharacteristic
616C2×D3—44no—
617C2×D3—44no—
618C2×D3—44no—
619C2×D3—82no—
620C2×D3—82no—
621C2×D3—82no—
622C2×D3—82no—
623C2×D3—82no—
624C2×D3—82no—
625C2×D3—82no—
626C2×D3—82no—
627C2×D3—82no—
628C2×D3—82no—
629C2×D3—82no—
630C2×D3—82no—
631C3×C4—44no—
632C3×C4—82no—
633C3×C4#38011yescharacteristic
634C3×C4#38511yescharacteristic
635C3×C4#38811yescharacteristic
636C3×C4#39011yescharacteristic
637C3×C4#39411yescharacteristic
638C3×C4#39611yescharacteristic
639C3×C4#39711yescharacteristic
640C3×C4#39911yescharacteristic
641Dic3—42no—
642Dic3—42no—
643Dic3—82no—
644C23—64no—
645C23—122no—
646C23—122no—
647C23—122no—
648C23—122no—
649C23—122no—
650C23—122no—
651C23—122no—
652C23—122no—
653C23—122no—
654C23—122no—
655C23—122no—
656C23—122no—
657C23—122no—
658C23—122no—
659C23—122no—
660C23—122no—
661C23—122no—
662C23—122no—
663C23—241no—
664C23—241no—
665C23—241no—
666C23—241no—
667C23—241no—
668C23—241no—
669C23—241no—
670C23—241no—
671C23—241no—
672C23—241no—
673C23—241no—
674C23—241no—
675C23—241no—
676C23—241no—
677C23—241no—
678C23—241no—
679C23#67⋊C411yescharacteristic
680C23#88211yescharacteristic
681C23#88211yescharacteristic
682C23#88511yescharacteristic
683C23#89511yescharacteristic
684C23#89611yescharacteristic
685C23D3×D811yescharacteristic
686C23#91111yescharacteristic
687C23D3×SD1611yescharacteristic
688C23#91411yescharacteristic
689C23#91411yescharacteristic
690C23#91611yescharacteristic
691C23#91811yescharacteristic
692C23#91911yescharacteristic
693C23#93911yescharacteristic
694D4—64no—
695D4—64no—
696D4—122no—
697D4—122no—
698D4—122no—
699D4—122no—
700D4—122no—
701D4—122no—
702C2×C4—24no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—121no—
723C2×C4—121no—
724C2×C4—121no—
725C2×C4—121no—
726C2×C4—121no—
727C2×C4—121no—
728C2×C4—121no—
729C2×C4—121no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—241no—
734C2×C4—241no—
735C2×C4—241no—
736C2×C4—241no—
737C2×C4C4×D1211yescharacteristic
738C2×C4C4×D1211yescharacteristic
739C2×C4#87411yescharacteristic
740C2×C4#87511yescharacteristic
741C2×C4#67⋊C411yescharacteristic
742C2×C4#88211yescharacteristic
743C2×C4#88311yescharacteristic
744C2×C4#88311yescharacteristic
745C2×C4#88511yescharacteristic
746C2×C4#88611yescharacteristic
747C2×C4#88611yescharacteristic
748C2×C4#88611yescharacteristic
749C2×C4D3×C4⋊C411yescharacteristic
750C2×C4#89211yescharacteristic
751C2×C4#89511yescharacteristic
752C2×C4#89511yescharacteristic
753C2×C4#89611yescharacteristic
754C2×C4#89711yescharacteristic
755C2×C4#89711yescharacteristic
756C2×C4#89711yescharacteristic
757C2×C4#89811yescharacteristic
758C2×C4#89811yescharacteristic
759C2×C4C2×(C2×D3)⋊C411yescharacteristic
760C2×C4#93011yescharacteristic
761C2×C4#93011yescharacteristic
762C2×C4#93811yescharacteristic
763C2×C4#93911yescharacteristic
764C2×C4#94611yescharacteristic
765C8—42no—
766C8—122no—
767C2×C3#143911yescharacteristic
768C2×C3#186211yescharacteristic
769C2×C3#186411yescharacteristic
770C2×C3#187911yescharacteristic
771C2×C3#188011yescharacteristic
772C2×C3#193411yescharacteristic
773C2×C3#193611yescharacteristic
774C2×C3#199911yescharacteristic
775C2×C3#200011yescharacteristic
776C2×C3#202311yescharacteristic
777C2×C3#202511yescharacteristic
778C2×C3#204111yescharacteristic
779C2×C3#204211yescharacteristic
780C2×C3#206511yescharacteristic
781C2×C3#206711yescharacteristic
782D3—84no—
783C22—124no—
784C22—124no—
785C22—124no—
786C22—242no—
787C22—242no—
788C22—242no—
789C22—242no—
790C22—242no—
791C22—242no—
792C22—242no—
793C22—242no—
794C22—242no—
795C22—242no—
796C22—242no—
797C22—242no—
798C22#466811yescharacteristic
799C22#467011yescharacteristic
800C22#467111yescharacteristic
801C22#467311yescharacteristic
802C22#475611yescharacteristic
803C22#476011yescharacteristic
804C22#476411yescharacteristic
805C22#477311yescharacteristic
806C22#477311yescharacteristic
807C22#477611yescharacteristic
808C22#478111yescharacteristic
809C22#478511yescharacteristic
810C22#478811yescharacteristic
811C22#479411yescharacteristic
812C22#480011yescharacteristic
813C22#480611yescharacteristic
814C22#480811yescharacteristic
815C22#481011yescharacteristic
816C22#481011yescharacteristic
817C22#481711yescharacteristic
818C22#486411yescharacteristic
819C22#486511yescharacteristic
820C22#487011yescharacteristic
821C22#487111yescharacteristic
822C22#488311yescharacteristic
823C22#488611yescharacteristic
824C22#489011yescharacteristic
825C22#489111yescharacteristic
826C22#495811yescharacteristic
827C22#496111yescharacteristic
828C22#499411yescharacteristic
829C22#515011yescharacteristic
830C22#516311yescharacteristic
831C22#516511yescharacteristic
832C22#518511yescharacteristic
833C4—44no—
834C4—82no—
835C4—122no—
836C4—122no—
837C4—242no—
838C4#466811yescharacteristic
839C4#467011yescharacteristic
840C4#467411yescharacteristic
841C4#467711yescharacteristic
842C4#493911yescharacteristic
843C4#496111yescharacteristic
844C4#498711yescharacteristic
845C4#499411yescharacteristic
846C3#1106611yescharacteristic, complemented, Sylow
847C2—244no—
848C2#6885311yescharacteristic
849C2#6885711yescharacteristic
850C2#6888611yescharacteristic
851C2#6888711yescharacteristic
852C2#6889411yescharacteristic
853C2#6889511yescharacteristic
854C2#6889811yescharacteristic
855C2#6889911yescharacteristic
856C2#6942711yescharacteristic
857C2#7017211yescharacteristic
858C2#7017711yescharacteristic
859C2#7024011yescharacteristic
860C2#7024511yescharacteristic
861C2#7058511yescharacteristic
862C2#7063911yescharacteristic
subgroupG/H
centerC24D3×D4
commutatorC22×C3×C4C22×C4
FrattiniC23×C4C22×D3
FittingC2×C3×#340C2
socleC24×C3C2×D4
prime radicalC23×D12C22
cosocleC23×C3×C4C23
hypercenterC2×#340D3
hypocenterC3#11066
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
3. C2×#4984C2semidirect
5. C2×C3×#340C2semidirect
6. C2×#4550C2semidirect
7. C2×#4529C2semidirect
29. C2×#809C4semidirect
38. C2×#340D3semidirect
227. C2×D12C4⋊C4semidirect
242. C3×C4⋊C4C22⋊C4semidirect
574. C4⋊C4(C2×D3)⋊C4semidirect
846. C3#11066semidirect

Maximal subgroups

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

subgroupindex
C22×#8212
C2×#49882
C2×#49842
C22×#8092
C2×C3×#3402
C2×#45502
C2×#45292
#110663