Finite Group Databasebeta

← C4×#5223 #10716971

Subgroups — C4×#5223 #10716971

Order 768.

3502 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic, complemented
2C22×C4×#67C212yesmaximal, complemented
3C2×#5223C211yesmaximal, characteristic
4C2×C4×#217C212yesmaximal, complemented
5C2×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#72131C211yesmaximal, characteristic, complemented
7#71570C211yesmaximal, characteristic, complemented
8#71568C211yesmaximal, characteristic, complemented
9#71550C212yesmaximal, complemented
10#71547C212yesmaximal, complemented
11C4×C3⋊#95C211yesmaximal, characteristic, complemented
12C4×#392—31nomaximal, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4C2212yes—
15C23×#67C2212yes—
16C23×C4×D3C2211yescharacteristic
17C2×C3×C4×D4—28no—
18C2×C3×C4×D4—24no—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2212yes—
21C22×C3×C42C2211yescharacteristic
22C22×#217C2212yes—
23C22×#217C2212yes—
24C22×#217C2212yes—
25C2×C4×#67—28no—
26C2×C4×#67—28no—
27C2×C4×#67—28no—
28C22×(C2×D3)⋊C4C2211yescharacteristic
29C22×(C2×D3)⋊C4C2212yes—
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×Dic3⋊C4C2212yes—
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2212yes—
34#5223C418yesdirect product factor
35C4×#217—28no—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2212yes—
39C2×C3⋊#95C2211yescharacteristic
40C2×C3⋊#95C2211yescharacteristic
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C4×(C2×D3)⋊C4—24no—
44C22×C4×D4—32no—
45C22×C4×D4D311yescharacteristic, complemented
46C2×#392—31no—
47C2×C4×C22⋊C4—31no—
48C2×C4×C22⋊C4—32no—
49#1444—31no—
50#1439—31no—
51#1439—32no—
52#1438—31no—
53#1438—32no—
54C4×#95—31no—
55C25×C3C2312yes—
56C24×D3C2311yescharacteristic
57C22×C3×D4—24no—
58C22×C3×D4—24no—
59C22×C3×D4—22no—
60C22×C3×D4—22no—
61C22×C3×D4C2×C414yescomplemented
62C23×C3×C4—24no—
63C23×C3×C4—24no—
64C23×C3×C4—24no—
65C23×C3×C4—24no—
66C23×C3×C4—24no—
67C23×C3×C4—24no—
68C23×C3×C4D418yescomplemented
69C23×C3×C4C2312yes—
70C23×C3×C4C2311yescharacteristic
71C23×C3×C4C2311yescharacteristic
72C23×C3×C4C2311yescharacteristic
73C22×#67—24no—
74C22×#67—24no—
75C22×#67—24no—
76C22×#67—24no—
77C22×#67—24no—
78C22×#67—24no—
79C22×#67C2×C418yescomplemented
80C23×Dic3C2311yescharacteristic
81C23×Dic3C2311yescharacteristic
82C23×Dic3C2312yes—
83C23×Dic3C2311yescharacteristic
84C23×Dic3C2312yes—
85C22×C4×D3—22no—
86C22×C4×D3—24no—
87C22×C4×D3—24no—
88C22×C4×D3—22no—
89C22×C4×D3D414yescomplemented
90C3×C4×D4—232no—
91C2×C3×C4⋊C4—24no—
92C2×C3×C4⋊C4—22no—
93C2×C3×C22⋊C4—24no—
94C2×C3×C22⋊C4—24no—
95C2×C3×C22⋊C4—24no—
96C2×C3×C42—24no—
97C2×C3×C42D414yescomplemented
98C2×#217—24no—
99C2×#217—24no—
100C2×#217—24no—
101C2×#217—24no—
102C2×#217—24no—
103C2×#217—24no—
104C2×#217—24no—
105C2×#217—24no—
106C2×#217C2×C418yescomplemented
107C4×#67—264no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—22no—
110C2×(C2×D3)⋊C4—22no—
111C2×(C2×D3)⋊C4—22no—
112C2×(C2×D3)⋊C4—24no—
113C2×(C2×D3)⋊C4—22no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4—22no—
116C2×(C2×D3)⋊C4C2×C414yescomplemented
117C2×Dic3⋊C4—24no—
118C2×Dic3⋊C4—24no—
119C2×Dic3⋊C4—24no—
120C2×C4×Dic3—24no—
121C2×C4×Dic3—24no—
122C2×C4×Dic3—22no—
123C2×C4×Dic3—24no—
124C2×C4×Dic3D418yescomplemented
125C3⋊#95—22no—
126C3⋊#95—22no—
127C3⋊#95—22no—
128C3⋊#95—24no—
129C3⋊#95—24no—
130C3⋊#95—24no—
131C3⋊#95C2×C414yescomplemented
132C23×D4—32no—
133C23×D4C2×D311yescharacteristic
134C24×C4—31no—
135C24×C4C2×D312yes—
136C2×C4×D4—28no—
137C2×C4×D4—24no—
138C2×C4×D4—68no—
139C2×C4×D4—68no—
140C2×C4×D4—68no—
141C22×C4⋊C4—32no—
142C22×C4⋊C4C2×D311yescharacteristic
143C22×C22⋊C4—32no—
144C22×C22⋊C4—31no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4—31no—
149C22×C22⋊C4C2×D312yes—
150C22×C42—32no—
151C22×C42—31no—
152C22×C42C2×D311yescharacteristic
153#392—38no—
154C4×C22⋊C4—68no—
155C4×C22⋊C4—64no—
156C2×#95—31no—
157C2×#95—32no—
158C2×#95—31no—
159C2×#95—32no—
160C2×#95—31no—
161C2×#95—32no—
162C2×#95—31no—
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—22no—
171C24×C3—22no—
172C24×C3—22no—
173C24×C3—22no—
174C24×C3—22no—
175C24×C3C22×C414yes—
176C24×C3C2×D414yes—
177C24×C3#4114yes—
178C24×C3C2411yescharacteristic
179C23×D3—21no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—21no—
183C23×D3—21no—
184C23×D3—21no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3C22×C412yes—
188C23×D3C2×D412yes—
189C23×D3#4112yes—
190C2×C3×D4—28no—
191C2×C3×D4—28no—
192C2×C3×D4—216no—
193C2×C3×D4—216no—
194C2×C3×D4—28no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—22no—
207C22×C3×C4—216no—
208C22×C3×C4—216no—
209C22×C3×C4—216no—
210C22×C3×C4—48no—
211C22×C3×C4—48no—
212C22×C3×C4—48no—
213C22×C3×C4—48no—
214C22×C3×C4C22×C412yes—
215C22×C3×C4C2×D412yes—
216C22×C3×C4C2×D414yes—
217C22×C3×C4C2×D412yes—
218C22×C3×C4C2×D414yes—
219C22×C3×C4C2×D412yes—
220C22×C3×C4C2×D414yes—
221C22×C3×C4C2×D412yes—
222C22×C3×C4#4112yes—
223C22×C3×C4#4112yes—
224C2×#67—216no—
225C2×#67—216no—
226C2×#67—216no—
227C2×#67—216no—
228C2×#67—216no—
229C2×#67—216no—
230C2×#67—216no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3—21no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—22no—
244C22×Dic3—22no—
245C22×Dic3—22no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248C22×Dic3—22no—
249C22×Dic3—22no—
250C22×Dic3—22no—
251C22×Dic3—22no—
252C22×Dic3—21no—
253C22×Dic3C22×C412yes—
254C22×Dic3C22×C414yes—
255C22×Dic3C2×D414yes—
256C22×Dic3C2×D412yes—
257C22×Dic3C2×D414yes—
258C22×Dic3#4112yes—
259C22×Dic3#4114yes—
260C2×C4×D3—216no—
261C2×C4×D3—28no—
262C2×C4×D3—44no—
263C2×C4×D3—48no—
264C2×C4×D3—44no—
265C3×C4⋊C4—28no—
266C3×C22⋊C4—216no—
267C3×C42—28no—
268#217—216no—
269#217—216no—
270#217—216no—
271(C2×D3)⋊C4—28no—
272(C2×D3)⋊C4—216no—
273(C2×D3)⋊C4—28no—
274Dic3⋊C4—216no—
275C4×Dic3—216no—
276C4×Dic3—44no—
277C25—31no—
278C25C22×D312yes—
279C22×D4—24no—
280C22×D4—24no—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—38no—
284C22×D4—64no—
285C22×D4—64no—
286C22×D4—64no—
287C22×D4—64no—
288C22×D4—64no—
289C22×D4—64no—
290C22×D4C4×D314yescomplemented
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—32no—
298C23×C4—31no—
299C23×C4—32no—
300C23×C4—31no—
301C23×C4—31no—
302C23×C4—34no—
303C23×C4—64no—
304C23×C4—62no—
305C23×C4—64no—
306C23×C4—62no—
307C23×C4#6718yescomplemented
308C23×C4C22×D311yescharacteristic
309C23×C4C22×D312yes—
310C23×C4C22×D311yescharacteristic
311C23×C4C22×D311yescharacteristic
312C4×D4—232no—
313C4×D4—664no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—64no—
317C2×C4⋊C4—64no—
318C2×C4⋊C4—64no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—38no—
323C2×C22⋊C4—34no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—62no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—62no—
328C2×C22⋊C4—64no—
329C2×C22⋊C4—64no—
330C2×C22⋊C4—64no—
331C2×C22⋊C4—64no—
332C2×C22⋊C4—64no—
333C2×C22⋊C4—64no—
334C2×C22⋊C4—64no—
335C2×C22⋊C4—64no—
336C2×C22⋊C4—62no—
337C2×C22⋊C4—64no—
338C2×C22⋊C4—62no—
339C2×C22⋊C4—62no—
340C2×C42—24no—
341C2×C42—38no—
342C2×C42—64no—
343C2×C42—64no—
344C2×C42—64no—
345C2×C42—62no—
346C2×C42#6714yescomplemented
347#95—34no—
348#95—64no—
349#95—64no—
350#95—64no—
351#95—62no—
352#95—62no—
353#95—62no—
354C23×C3—24no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—24no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—24no—
364C23×C3—24no—
365C23×C3—24no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—24no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3C4×D418yescomplemented
389C23×C3C23×C411yescharacteristic
390C23×C3C22×D411yescharacteristic
391C23×C3C22×D412yes—
392C23×C3C22×D412yes—
393C23×C3C22×D411yescharacteristic
394C23×C3C2×#4112yes—
395C23×C3C2×#4111yescharacteristic
396C23×C3C2×#4111yescharacteristic
397C23×C3C2×#4111yescharacteristic
398C23×C3C2×#4112yes—
399C23×C3C2×#4111yescharacteristic
400C22×D3—22no—
401C22×D3—24no—
402C22×D3—24no—
403C22×D3—22no—
404C22×D3—24no—
405C22×D3—22no—
406C22×D3—22no—
407C22×D3—24no—
408C22×D3—24no—
409C22×D3—24no—
410C22×D3—22no—
411C22×D3—22no—
412C22×D3—41no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—41no—
416C22×D3—42no—
417C22×D3—42no—
418C22×D3—41no—
419C22×D3—42no—
420C22×D3—41no—
421C22×D3—42no—
422C22×D3C4×D414yescomplemented
423C3×D4—232no—
424C2×C3×C4—24no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—24no—
428C2×C3×C4—24no—
429C2×C3×C4—22no—
430C2×C3×C4—24no—
431C2×C3×C4—24no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—42no—
435C2×C3×C4—42no—
436C2×C3×C4—42no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—432no—
441C2×C3×C4C4×D414yescomplemented
442C2×C3×C4#12018yes—
443C2×C3×C4#12014yes—
444C2×C3×C4#12114yes—
445C2×C3×C4#12118yes—
446C2×C3×C4#12714yes—
447#67—264no—
448C2×Dic3—24no—
449C2×Dic3—24no—
450C2×Dic3—24no—
451C2×Dic3—24no—
452C2×Dic3—24no—
453C2×Dic3—24no—
454C2×Dic3—22no—
455C2×Dic3—24no—
456C2×Dic3—24no—
457C2×Dic3—24no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—24no—
461C2×Dic3—24no—
462C2×Dic3—24no—
463C2×Dic3—41no—
464C2×Dic3—42no—
465C2×Dic3—42no—
466C2×Dic3—41no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471C2×Dic3—41no—
472C2×Dic3—42no—
473C2×Dic3—42no—
474C2×Dic3—41no—
475C2×Dic3—42no—
476C2×Dic3C4×D418yescomplemented
477C4×D3—416no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—32no—
491C24—32no—
492C24—32no—
493C24—61no—
494C24—62no—
495C24—62no—
496C24—61no—
497C24—61no—
498C24—62no—
499C24—61no—
500C24—62no—
501C24C2×C4×D314yes—
502C24#23514yes—
503C24C2×#6714yes—
504C24C23×D311yescharacteristic
505C2×D4—28no—
506C2×D4—216no—
507C2×D4—28no—
508C2×D4—216no—
509C2×D4—28no—
510C2×D4—616no—
511C2×D4—616no—
512C2×D4—616no—
513C2×D4—616no—
514C2×D4—616no—
515C2×D4—616no—
516C2×D4—616no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—216no—
530C22×C4—216no—
531C22×C4—216no—
532C22×C4—34no—
533C22×C4—34no—
534C22×C4—34no—
535C22×C4—32no—
536C22×C4—34no—
537C22×C4—32no—
538C22×C4—32no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—61no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—61no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—616no—
566C22×C4—68no—
567C22×C4—128no—
568C22×C4—124no—
569C22×C4—124no—
570C22×C4C2×C4×D312yes—
571C22×C4#23512yes—
572C22×C4D3×D412yes—
573C22×C4D3×D414yes—
574C22×C4#23712yes—
575C22×C4C2×#6712yes—
576C22×C4C2×#6714yes—
577C22×C4C2×#6712yes—
578C22×C4C2×#6714yes—
579C22×C4C2×#6712yes—
580C4⋊C4—28no—
581C4⋊C4—616no—
582C22⋊C4—216no—
583C22⋊C4—616no—
584C22⋊C4—68no—
585C22⋊C4—616no—
586C22⋊C4—616no—
587C22⋊C4—616no—
588C22⋊C4—68no—
589C42—28no—
590C42—616no—
591C42—124no—
592C22×C3—28no—
593C22×C3—28no—
594C22×C3—28no—
595C22×C3—44no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3—44no—
599C22×C3—44no—
600C22×C3—44no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—44no—
606C22×C3—44no—
607C22×C3C2×C4×D411yescharacteristic
608C22×C3C2×C4×D412yes—
609C22×C3C2×C4×D412yes—
610C22×C3C2×C4×D411yescharacteristic
611C22×C3C4×#4111yescharacteristic
612C22×C3C2×#12012yes—
613C22×C3C2×#12011yescharacteristic
614C22×C3C2×#12111yescharacteristic
615C22×C3C2×#12112yes—
616C22×C3#52512yes—
617C22×C3#52511yescharacteristic
618C22×C3#52512yes—
619C22×C3#52512yes—
620C22×C3#52512yes—
621C22×C3#52512yes—
622C22×C3#52511yescharacteristic
623C22×C3#52912yes—
624C22×C3#52911yescharacteristic
625C22×C3C2×#12711yescharacteristic
626C22×C3#53212yes—
627C22×C3#53211yescharacteristic
628C22×C3#53211yescharacteristic
629C22×C3#53212yes—
630C2×D3—28no—
631C2×D3—24no—
632C2×D3—42no—
633C2×D3—42no—
634C2×D3—42no—
635C2×D3—44no—
636C2×D3—44no—
637C2×D3—42no—
638C2×D3—42no—
639C2×D3—42no—
640C2×D3—44no—
641C3×C4—24no—
642C3×C4—44no—
643C3×C4—42no—
644C3×C4#39218yescomplemented
645Dic3—28no—
646Dic3—42no—
647Dic3—42no—
648Dic3—44no—
649Dic3—42no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—34no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—62no—
686C23—64no—
687C23—62no—
688C23—64no—
689C23—64no—
690C23—62no—
691C23—64no—
692C23—64no—
693C23—62no—
694C23—62no—
695C23—62no—
696C23—64no—
697C23—122no—
698C23—121no—
699C23—122no—
700C23—122no—
701C23—122no—
702C23—121no—
703C23—122no—
704C23—122no—
705C23—121no—
706C23—121no—
707C23C4×#6718yescomplemented
708C23C22×C4×D311yescharacteristic
709C23C2×#23512yes—
710C23C2×#23511yescharacteristic
711C23C2×D3×D411yescharacteristic
712C23C2×D3×D412yes—
713C23C2×#23711yescharacteristic
714C23D3×#4111yescharacteristic
715C23D3×#4112yes—
716C23D3×#4111yescharacteristic
717C23C22×#6712yes—
718C23C22×#6711yescharacteristic
719D4—232no—
720D4—664no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—38no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—432no—
739C2×C4—64no—
740C2×C4—64no—
741C2×C4—64no—
742C2×C4—64no—
743C2×C4—64no—
744C2×C4—64no—
745C2×C4—62no—
746C2×C4—64no—
747C2×C4—64no—
748C2×C4—64no—
749C2×C4—62no—
750C2×C4—64no—
751C2×C4—64no—
752C2×C4—64no—
753C2×C4—62no—
754C2×C4—121no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4—121no—
760C2×C4—121no—
761C2×C4—121no—
762C2×C4—122no—
763C2×C4—122no—
764C2×C4—121no—
765C2×C4—122no—
766C2×C4—121no—
767C2×C4—1216no—
768C2×C4C4×#6714yescomplemented
769C2×C4#93718yes—
770C2×C4#93814yes—
771C2×C4#93918yes—
772C2×C4#94014yes—
773C2×C4#95314yes—
774C2×C3—48no—
775C2×C3C4×#12011yescharacteristic
776C2×C3C4×#12012yes—
777C2×C3C4×#12112yes—
778C2×C3C4×#12111yescharacteristic
779C2×C3C4×#12711yescharacteristic
780C2×C3C2×#39211yescharacteristic
781C2×C3#238811yescharacteristic
782C2×C3#238812yes—
783C2×C3#239212yes—
784C2×C3#239211yescharacteristic
785C2×C3#239711yescharacteristic
786D3—44no—
787C22—28no—
788C22—28no—
789C22—28no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—44no—
799C22—44no—
800C22—44no—
801C22—44no—
802C22—68no—
803C22—64no—
804C22—122no—
805C22—122no—
806C22—122no—
807C22—124no—
808C22—122no—
809C22—124no—
810C22—122no—
811C22—124no—
812C22—122no—
813C22C4×#23711yescharacteristic
814C22#553812yes—
815C22C4×D3×D412yes—
816C22C4×D3×D411yescharacteristic
817C22#554712yes—
818C22#554712yes—
819C22#554712yes—
820C22#554812yes—
821C22#554811yescharacteristic
822C22#555711yescharacteristic
823C22C2×C4×#6712yes—
824C22C2×C4×#6711yescharacteristic
825C22#579112yes—
826C22#579111yescharacteristic
827C22C2×#93712yes—
828C22C2×#93811yescharacteristic
829C22C2×#93912yes—
830C22C2×#94011yescharacteristic
831C22#582812yes—
832C22#582811yescharacteristic
833C22#583212yes—
834C22#583211yescharacteristic
835C22C2×#95311yescharacteristic
836C4—24no—
837C4—44no—
838C4—42no—
839C4—68no—
840C4—122no—
841C4—122no—
842C4—122no—
843C4—124no—
844C4#522318yesdirect product factor
845C3C4×#39211yescharacteristic, complemented, Sylow
846C2—48no—
847C2—124no—
848C2C4×#93912yes—
849C2C4×#94011yescharacteristic
850C2#8234512yes—
851C2#8234711yescharacteristic
852C2C4×#93712yes—
853C2C4×#93811yescharacteristic
854C2#8240012yes—
855C2#8240111yescharacteristic
856C2C4×#95311yescharacteristic
857C2C2×#522311yescharacteristic
858C2#8409511yescharacteristic
subgroupG/H
centerC23×C4C22×D3
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC22×C3×C4×D4C2
socle, cosocleC24×C3C24
prime radicalC2×#5223C2
hypercenterC22×C4×D4D3
hypocenterC3C4×#392
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×D4C2semidirect
2. C22×C4×#67C2semidirect
4. C2×C4×#217C2semidirect
5. C2×C4×(C2×D3)⋊C4C2semidirect
6. #72131C2semidirect
7. #71570C2semidirect
8. #71568C2semidirect
9. #71550C2semidirect
10. #71547C2semidirect
11. C4×C3⋊#95C2semidirect
34. #5223C4direct (N × H)
45. C22×C4×D4D3semidirect
61. C22×C3×D4C2×C4semidirect
68. C23×C3×C4D4semidirect
79. C22×#67C2×C4semidirect
89. C22×C4×D3D4semidirect
97. C2×C3×C42D4semidirect
106. C2×#217C2×C4semidirect
116. C2×(C2×D3)⋊C4C2×C4semidirect
124. C2×C4×Dic3D4semidirect
131. C3⋊#95C2×C4semidirect
290. C22×D4C4×D3semidirect
307. C23×C4#67semidirect
346. C2×C42#67semidirect
388. C23×C3C4×D4semidirect
422. C22×D3C4×D4semidirect
441. C2×C3×C4C4×D4semidirect
476. C2×Dic3C4×D4semidirect
644. C3×C4#392semidirect
707. C23C4×#67semidirect
768. C2×C4C4×#67semidirect
844. C4#5223direct (N × H)
845. C3C4×#392semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C22×C4×#672
C2×#52232
C2×C4×#2172
C2×C4×(C2×D3)⋊C42
#721312
#715702
#715682
#715502
#715472
C4×C3⋊#952
C4×#3923