Finite Group Databasebeta

← C4×#4960 #10716973

Subgroups — C4×#4960 #10716973

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×C4×#67C212yesmaximal, complemented
2C22×C4×D12C211yesmaximal, characteristic, complemented
3C2×C3×C4×C22⋊C4C211yesmaximal, characteristic, complemented
4C2×#4960C211yesmaximal, characteristic
5C2×C4×(C2×D3)⋊C4C212yesmaximal, complemented
6#71550C212yesmaximal, complemented
7#71546C211yesmaximal, characteristic, complemented
8C4×C3⋊#95C211yesmaximal, characteristic, complemented
9#69428C212yesmaximal, complemented
10#69426C211yesmaximal, characteristic, complemented
11#69420C211yesmaximal, characteristic, complemented
12C4×#392—31nomaximal, Sylow
13C24×C3×C4C2211yescharacteristic
14C23×#67C2212yes—
15C23×D12C2211yescharacteristic
16C23×C4×D3C2212yes—
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C42C2211yescharacteristic
20C22×C3×C42C2211yescharacteristic
21C22×#217C2212yes—
22C2×C4×#67—28no—
23C2×C4×#67—28no—
24C2×C4×#67—28no—
25C22×(C2×D3)⋊C4C2212yes—
26C22×(C2×D3)⋊C4C2212yes—
27C22×(C2×D3)⋊C4C2212yes—
28C22×(C2×D3)⋊C4C2212yes—
29C22×C4⋊Dic3C2211yescharacteristic
30C22×Dic3⋊C4C2212yes—
31C22×C4×Dic3C2212yes—
32C2×C4×D12—28no—
33C2×C4×D12—24no—
34C3×C4×C22⋊C4—24no—
35C2×C3×#95C2211yescharacteristic
36C2×C3×#95C2211yescharacteristic
37C2×C3⋊#95C2212yes—
38C2×C3⋊#95C2211yescharacteristic
39C2×C3⋊#95C2212yes—
40C2×C3⋊#95C2212yes—
41C2×C3⋊#95C2211yescharacteristic
42#4960C418yesdirect product factor
43C4×(C2×D3)⋊C4—28no—
44C22×C4×D4—31no—
45C22×C4×D4—32no—
46C2×#392—31no—
47C2×C4×C22⋊C4—32no—
48C2×C4×C22⋊C4D311yescharacteristic, complemented
49#1444—31no—
50#1439—32no—
51#1439—31no—
52#1438—31no—
53#1438—32no—
54C4×#95—31no—
55C25×C3C2311yescharacteristic
56C24×D3C2312yes—
57C23×C3×C4—22no—
58C23×C3×C4—24no—
59C23×C3×C4—24no—
60C23×C3×C4—22no—
61C23×C3×C4D414yescomplemented
62C23×C3×C4C2311yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C23×C3×C4C2311yescharacteristic
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2311yescharacteristic
67C23×C3×C4C2311yescharacteristic
68C22×#67—24no—
69C22×#67—24no—
70C22×#67—24no—
71C22×#67—24no—
72C22×#67—24no—
73C22×#67—24no—
74C22×#67C2×C418yescomplemented
75C23×Dic3C2312yes—
76C23×Dic3C2312yes—
77C23×Dic3C2312yes—
78C22×D12—24no—
79C22×D12—24no—
80C22×D12—22no—
81C22×D12—22no—
82C22×D12C2×C414yescomplemented
83C22×C4×D3—24no—
84C22×C4×D3—24no—
85C22×C4×D3—24no—
86C22×C4×D3—24no—
87C22×C4×D3—24no—
88C22×C4×D3—24no—
89C22×C4×D3D418yescomplemented
90C2×C3×C22⋊C4—22no—
91C2×C3×C22⋊C4—22no—
92C2×C3×C22⋊C4—22no—
93C2×C3×C22⋊C4—22no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4C2×C414yescomplemented
96C2×C3×C42—24no—
97C2×C3×C42—24no—
98C2×C3×C42—22no—
99C2×C3×C42D414yescomplemented
100C2×#217—24no—
101C2×#217—24no—
102C2×#217—24no—
103C4×#67—264no—
104C2×(C2×D3)⋊C4—24no—
105C2×(C2×D3)⋊C4—24no—
106C2×(C2×D3)⋊C4—24no—
107C2×(C2×D3)⋊C4—24no—
108C2×(C2×D3)⋊C4—24no—
109C2×(C2×D3)⋊C4—24no—
110C2×(C2×D3)⋊C4—24no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4—24no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—24no—
115C2×(C2×D3)⋊C4C2×C418yescomplemented
116C2×C4⋊Dic3—22no—
117C2×C4⋊Dic3—24no—
118C2×Dic3⋊C4—24no—
119C2×Dic3⋊C4—24no—
120C2×Dic3⋊C4—24no—
121C2×C4×Dic3—24no—
122C2×C4×Dic3—24no—
123C2×C4×Dic3D418yescomplemented
124C4×D12—232no—
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×D4—31no—
134C24×C4—32no—
135C24×C4C2×D311yescharacteristic
136C2×C4×D4—68no—
137C2×C4×D4—68no—
138C2×C4×D4—68no—
139C2×C4×D4—68no—
140C2×C4×D4—64no—
141C22×C4⋊C4—32no—
142C22×C4⋊C4—31no—
143C22×C22⋊C4—32no—
144C22×C22⋊C4—32no—
145C22×C22⋊C4—32no—
146C22×C22⋊C4—32no—
147C22×C22⋊C4—32no—
148C22×C22⋊C4C2×D311yescharacteristic
149C22×C22⋊C4C2×D311yescharacteristic
150C22×C42—32no—
151C22×C42C2×D311yescharacteristic
152C22×C42C2×D311yescharacteristic
153#392—38no—
154C4×C22⋊C4—24no—
155C4×C22⋊C4—68no—
156C2×#95—31no—
157C2×#95—32no—
158C2×#95—31no—
159C2×#95—32no—
160C2×#95—32no—
161C2×#95C2×D311yescharacteristic
162C2×#95C2×D311yescharacteristic
163C24×C3—22no—
164C24×C3—22no—
165C24×C3—21no—
166C24×C3—21no—
167C24×C3—21no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—21no—
171C24×C3C22×C412yes—
172C24×C3C2×D412yes—
173C24×C3#4112yes—
174C24×C3C2411yescharacteristic
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3—22no—
179C23×D3—22no—
180C23×D3—22no—
181C23×D3—22no—
182C23×D3—22no—
183C23×D3—22no—
184C23×D3—22no—
185C23×D3—22no—
186C23×D3—22no—
187C23×D3C22×C414yes—
188C23×D3C2×D414yes—
189C23×D3#4114yes—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
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—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—216no—
209C22×C3×C4—28no—
210C22×C3×C4—44no—
211C22×C3×C4—48no—
212C22×C3×C4—44no—
213C22×C3×C4C22×C412yes—
214C22×C3×C4C22×C412yes—
215C22×C3×C4C2×D412yes—
216C22×C3×C4C2×D412yes—
217C22×C3×C4C2×D414yes—
218C22×C3×C4C2×D414yes—
219C22×C3×C4C2×D412yes—
220C22×C3×C4C2×D412yes—
221C22×C3×C4C2×D412yes—
222C22×C3×C4#4112yes—
223C22×C3×C4#4112yes—
224C22×C3×C4#4112yes—
225C2×#67—216no—
226C2×#67—216no—
227C2×#67—216no—
228C2×#67—216no—
229C2×#67—216no—
230C2×#67—216no—
231C2×#67—216no—
232C22×Dic3—22no—
233C22×Dic3—22no—
234C22×Dic3—22no—
235C22×Dic3—22no—
236C22×Dic3—22no—
237C22×Dic3—22no—
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—22no—
247C22×Dic3—22no—
248C22×Dic3C22×C414yes—
249C22×Dic3C2×D414yes—
250C22×Dic3C2×D414yes—
251C22×Dic3C2×D414yes—
252C22×Dic3#4114yes—
253C2×D12—28no—
254C2×D12—28no—
255C2×D12—216no—
256C2×D12—216no—
257C2×D12—28no—
258C2×C4×D3—216no—
259C2×C4×D3—216no—
260C2×C4×D3—216no—
261C2×C4×D3—48no—
262C2×C4×D3—48no—
263C2×C4×D3—48no—
264C2×C4×D3—48no—
265C3×C22⋊C4—28no—
266C3×C22⋊C4—28no—
267C3×C42—28no—
268C3×C42—44no—
269#217—216no—
270(C2×D3)⋊C4—216no—
271(C2×D3)⋊C4—216no—
272(C2×D3)⋊C4—216no—
273(C2×D3)⋊C4—216no—
274C4⋊Dic3—28no—
275Dic3⋊C4—216no—
276C4×Dic3—216no—
277C25—32no—
278C25C22×D311yescharacteristic
279C22×D4—38no—
280C22×D4—34no—
281C22×D4—64no—
282C22×D4—64no—
283C22×D4—64no—
284C22×D4—64no—
285C22×D4—64no—
286C22×D4—64no—
287C22×D4—64no—
288C22×D4—64no—
289C22×D4—62no—
290C22×D4—62no—
291C23×C4—22no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—22no—
295C23×C4—32no—
296C23×C4—32no—
297C23×C4—32no—
298C23×C4—38no—
299C23×C4—64no—
300C23×C4—64no—
301C23×C4—64no—
302C23×C4—64no—
303C23×C4—64no—
304C23×C4—64no—
305C23×C4D1214yescomplemented
306C23×C4C22×D311yescharacteristic
307C23×C4C22×D311yescharacteristic
308C23×C4C22×D311yescharacteristic
309C23×C4C22×D311yescharacteristic
310C23×C4C22×D311yescharacteristic
311C23×C4C22×D311yescharacteristic
312C4×D4—632no—
313C4×D4—664no—
314C2×C4⋊C4—64no—
315C2×C4⋊C4—64no—
316C2×C4⋊C4—64no—
317C2×C4⋊C4—64no—
318C2×C4⋊C4—62no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—38no—
325C2×C22⋊C4—64no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—64no—
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—64no—
337C2×C22⋊C4—64no—
338C2×C22⋊C4—64no—
339C2×C22⋊C4C4×D314yescomplemented
340C2×C42—24no—
341C2×C42—24no—
342C2×C42—22no—
343C2×C42—38no—
344C2×C42—64no—
345C2×C42—64no—
346C2×C42#6714yescomplemented
347#95—22no—
348#95—22no—
349#95—34no—
350#95—64no—
351#95—64no—
352#95—64no—
353#95—62no—
354C23×C3—22no—
355C23×C3—24no—
356C23×C3—24no—
357C23×C3—22no—
358C23×C3—24no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—24no—
362C23×C3—24no—
363C23×C3—24no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—41no—
367C23×C3—42no—
368C23×C3—42no—
369C23×C3—42no—
370C23×C3—41no—
371C23×C3—42no—
372C23×C3—41no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—41no—
376C23×C3C4×D414yescomplemented
377C23×C3C23×C411yescharacteristic
378C23×C3C22×D411yescharacteristic
379C23×C3C22×D412yes—
380C23×C3C22×D412yes—
381C23×C3C22×D411yescharacteristic
382C23×C3C2×#4111yescharacteristic
383C23×C3C2×#4111yescharacteristic
384C23×C3C2×#4111yescharacteristic
385C23×C3C2×#4111yescharacteristic
386C23×C3C2×#4112yes—
387C23×C3C2×#4112yes—
388C22×D3—24no—
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—24no—
392C22×D3—24no—
393C22×D3—24no—
394C22×D3—24no—
395C22×D3—24no—
396C22×D3—24no—
397C22×D3—24no—
398C22×D3—24no—
399C22×D3—24no—
400C22×D3—24no—
401C22×D3—24no—
402C22×D3—24no—
403C22×D3—24no—
404C22×D3—24no—
405C22×D3—24no—
406C22×D3—42no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—42no—
410C22×D3—42no—
411C22×D3—42no—
412C22×D3—42no—
413C22×D3—42no—
414C22×D3—42no—
415C22×D3—42no—
416C22×D3—42no—
417C22×D3—42no—
418C22×D3—42no—
419C22×D3—42no—
420C22×D3—42no—
421C22×D3—42no—
422C22×D3C4×D418yescomplemented
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—24no—
427C2×C3×C4—24no—
428C2×C3×C4—22no—
429C2×C3×C4—24no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—24no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—41no—
437C2×C3×C4—42no—
438C2×C3×C4—42no—
439C2×C3×C4—42no—
440C2×C3×C4—41no—
441C2×C3×C4—41no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4—42no—
445C2×C3×C4—42no—
446C2×C3×C4—41no—
447C2×C3×C4—416no—
448C2×C3×C4C4×D414yescomplemented
449C2×C3×C4#12018yes—
450C2×C3×C4#12014yes—
451C2×C3×C4#12118yes—
452C2×C3×C4#12114yes—
453C2×C3×C4#12714yes—
454#67—264no—
455C2×Dic3—24no—
456C2×Dic3—24no—
457C2×Dic3—24no—
458C2×Dic3—24no—
459C2×Dic3—24no—
460C2×Dic3—24no—
461C2×Dic3—24no—
462C2×Dic3—24no—
463C2×Dic3—24no—
464C2×Dic3—24no—
465C2×Dic3—24no—
466C2×Dic3—24no—
467C2×Dic3—42no—
468C2×Dic3—42no—
469C2×Dic3—42no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—42no—
473C2×Dic3—42no—
474C2×Dic3—42no—
475C2×Dic3C4×D418yescomplemented
476D12—232no—
477C4×D3—432no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24—34no—
487C24—34no—
488C24—34no—
489C24—62no—
490C24—62no—
491C24—62no—
492C24—62no—
493C24—62no—
494C24—62no—
495C24—62no—
496C24—62no—
497C24—62no—
498C24—62no—
499C24—62no—
500C24—62no—
501C24C2×C4×D312yes—
502C24C2×D1212yes—
503C24#23512yes—
504C24C23×D311yescharacteristic
505C2×D4—616no—
506C2×D4—68no—
507C2×D4—616no—
508C2×D4—68no—
509C2×D4—616no—
510C2×D4—616no—
511C2×D4—616no—
512C2×D4—616no—
513C2×D4—616no—
514C2×D4—616no—
515C2×D4—616no—
516C2×D4—68no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—216no—
536C22×C4—28no—
537C22×C4—34no—
538C22×C4—34no—
539C22×C4—34no—
540C22×C4—34no—
541C22×C4—34no—
542C22×C4—48no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—62no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4—62no—
552C22×C4—62no—
553C22×C4—62no—
554C22×C4—62no—
555C22×C4—62no—
556C22×C4—62no—
557C22×C4—62no—
558C22×C4—62no—
559C22×C4—62no—
560C22×C4—62no—
561C22×C4—616no—
562C22×C4—616no—
563C22×C4—616no—
564C22×C4—128no—
565C22×C4—128no—
566C22×C4—128no—
567C22×C4—128no—
568C22×C4C2×C4×D312yes—
569C22×C4C2×C4×D312yes—
570C22×C4C2×D1212yes—
571C22×C4C2×D1212yes—
572C22×C4#23512yes—
573C22×C4#23512yes—
574C22×C4#23512yes—
575C22×C4D3×D414yes—
576C22×C4D3×D414yes—
577C22×C4C2×#6712yes—
578C22×C4C2×#6712yes—
579C22×C4C2×#6712yes—
580C4⋊C4—616no—
581C4⋊C4—68no—
582C22⋊C4—28no—
583C22⋊C4—28no—
584C22⋊C4—616no—
585C22⋊C4—616no—
586C22⋊C4—616no—
587C22⋊C4—616no—
588C22⋊C4—616no—
589C42—28no—
590C42—44no—
591C42—616no—
592C22×C3—28no—
593C22×C3—24no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—44no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—44no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—44no—
603C22×C3C2×C4×D411yescharacteristic
604C22×C3C2×C4×D411yescharacteristic
605C22×C3C2×C4×D412yes—
606C22×C3C2×C4×D412yes—
607C22×C3C4×#4111yescharacteristic
608C22×C3C2×#12012yes—
609C22×C3C2×#12011yescharacteristic
610C22×C3C2×#12112yes—
611C22×C3C2×#12111yescharacteristic
612C22×C3#52512yes—
613C22×C3#52511yescharacteristic
614C22×C3#52512yes—
615C22×C3#52512yes—
616C22×C3#52512yes—
617C22×C3#52512yes—
618C22×C3#52511yescharacteristic
619C22×C3#52911yescharacteristic
620C22×C3#52912yes—
621C22×C3C2×#12711yescharacteristic
622C22×C3#53211yescharacteristic
623C22×C3#53212yes—
624C22×C3#53212yes—
625C22×C3#53211yescharacteristic
626C2×D3—28no—
627C2×D3—28no—
628C2×D3—28no—
629C2×D3—44no—
630C2×D3—44no—
631C2×D3—44no—
632C2×D3—44no—
633C2×D3—44no—
634C2×D3—44no—
635C2×D3—44no—
636C2×D3—44no—
637C2×D3—44no—
638C2×D3—44no—
639C2×D3—44no—
640C2×D3—44no—
641C3×C4—24no—
642C3×C4—42no—
643C3×C4—42no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4#39218yescomplemented
647Dic3—28no—
648Dic3—44no—
649Dic3—44no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—38no—
663C23—42no—
664C23—42no—
665C23—41no—
666C23—42no—
667C23—42no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—41no—
673C23—64no—
674C23—64no—
675C23—64no—
676C23—64no—
677C23—64no—
678C23—64no—
679C23—64no—
680C23—64no—
681C23—64no—
682C23—64no—
683C23—64no—
684C23—64no—
685C23—64no—
686C23—64no—
687C23—64no—
688C23—64no—
689C23—64no—
690C23—64no—
691C23—122no—
692C23—122no—
693C23—122no—
694C23—122no—
695C23—122no—
696C23—122no—
697C23—122no—
698C23—122no—
699C23—122no—
700C23—122no—
701C23—122no—
702C23—122no—
703C23—122no—
704C23—122no—
705C23—122no—
706C23—122no—
707C23C4×D1214yescomplemented
708C23C22×C4×D311yescharacteristic
709C23C22×D1211yescharacteristic
710C23C2×#23511yescharacteristic
711C23C2×#23511yescharacteristic
712C23C2×#23511yescharacteristic
713C23C2×#23511yescharacteristic
714C23C2×D3×D412yes—
715C23C2×D3×D412yes—
716C23D3×#4112yes—
717C23D3×#4112yes—
718C23C22×#6711yescharacteristic
719D4—632no—
720D4—664no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—38no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—416no—
747C2×C4—64no—
748C2×C4—64no—
749C2×C4—64no—
750C2×C4—64no—
751C2×C4—64no—
752C2×C4—64no—
753C2×C4—64no—
754C2×C4—64no—
755C2×C4—64no—
756C2×C4—64no—
757C2×C4—64no—
758C2×C4—64no—
759C2×C4—122no—
760C2×C4—122no—
761C2×C4—122no—
762C2×C4—122no—
763C2×C4—122no—
764C2×C4—122no—
765C2×C4—122no—
766C2×C4—122no—
767C2×C4—1232no—
768C2×C4#88218yes—
769C2×C4#88418yes—
770C2×C4C4×#6714yescomplemented
771C2×C4#93014yes—
772C2×C4#93714yes—
773C2×C4#94014yes—
774C2×C3—44no—
775C2×C3C4×#12012yes—
776C2×C3C4×#12011yescharacteristic
777C2×C3C4×#12112yes—
778C2×C3C4×#12111yescharacteristic
779C2×C3C4×#12711yescharacteristic
780C2×C3C2×#39211yescharacteristic
781C2×C3#238812yes—
782C2×C3#238811yescharacteristic
783C2×C3#239211yescharacteristic
784C2×C3#239212yes—
785C2×C3#239711yescharacteristic
786D3—48no—
787C22—28no—
788C22—24no—
789C22—44no—
790C22—42no—
791C22—44no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—68no—
799C22—68no—
800C22—68no—
801C22—124no—
802C22—124no—
803C22—124no—
804C22—124no—
805C22—124no—
806C22—124no—
807C22—124no—
808C22—124no—
809C22—124no—
810C22—124no—
811C22—124no—
812C22—124no—
813C22C2×C4×D1211yescharacteristic
814C22C4×#23511yescharacteristic
815C22#547711yescharacteristic
816C22#547911yescharacteristic
817C22C2×#88212yes—
818C22C2×#88412yes—
819C22#552412yes—
820C22#552812yes—
821C22C4×D3×D412yes—
822C22C4×D3×D412yes—
823C22#554712yes—
824C22#554712yes—
825C22#554712yes—
826C22#554712yes—
827C22#554812yes—
828C22#554812yes—
829C22C2×C4×#6711yescharacteristic
830C22C2×#93011yescharacteristic
831C22#579111yescharacteristic
832C22C2×#93711yescharacteristic
833C22C2×#94011yescharacteristic
834C22#582811yescharacteristic
835C22#583211yescharacteristic
836C4—24no—
837C4—42no—
838C4—42no—
839C4—42no—
840C4—42no—
841C4—68no—
842C4—124no—
843C4—124no—
844C4#496018yesdirect product factor
845C3C4×#39211yescharacteristic, complemented, Sylow
846C2—44no—
847C2—128no—
848C2C4×#88212yes—
849C2C4×#88412yes—
850C2#7358012yes—
851C2#7358112yes—
852C2C4×#93011yescharacteristic
853C2C2×#496011yescharacteristic
854C2#8227311yescharacteristic
855C2C4×#94011yescharacteristic
856C2#8234711yescharacteristic
857C2C4×#93711yescharacteristic
858C2#8240011yescharacteristic
subgroupG/H
centerC23×C4C22×D3
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC2×C3×C4×C22⋊C4C2
socle, cosocleC24×C3C24
prime radicalC2×#4960C2
hypercenterC2×C4×C22⋊C4D3
hypocenterC3C4×#392
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×#67C2semidirect
2. C22×C4×D12C2semidirect
3. C2×C3×C4×C22⋊C4C2semidirect
5. C2×C4×(C2×D3)⋊C4C2semidirect
6. #71550C2semidirect
7. #71546C2semidirect
8. C4×C3⋊#95C2semidirect
9. #69428C2semidirect
10. #69426C2semidirect
11. #69420C2semidirect
42. #4960C4direct (N × H)
48. C2×C4×C22⋊C4D3semidirect
61. C23×C3×C4D4semidirect
74. C22×#67C2×C4semidirect
82. C22×D12C2×C4semidirect
89. C22×C4×D3D4semidirect
95. C2×C3×C22⋊C4C2×C4semidirect
99. C2×C3×C42D4semidirect
115. C2×(C2×D3)⋊C4C2×C4semidirect
123. C2×C4×Dic3D4semidirect
131. C3⋊#95C2×C4semidirect
305. C23×C4D12semidirect
339. C2×C22⋊C4C4×D3semidirect
346. C2×C42#67semidirect
376. C23×C3C4×D4semidirect
422. C22×D3C4×D4semidirect
448. C2×C3×C4C4×D4semidirect
475. C2×Dic3C4×D4semidirect
646. C3×C4#392semidirect
707. C23C4×D12semidirect
770. C2×C4C4×#67semidirect
844. C4#4960direct (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×C4×#672
C22×C4×D122
C2×C3×C4×C22⋊C42
C2×#49602
C2×C4×(C2×D3)⋊C42
#715502
#715462
C4×C3⋊#952
#694282
#694262
#694202
C4×#3923