Finite Group Databasebeta

← C2×#69530 #10794579

Subgroups — C2×#69530 #10794579

Order 768.

2066 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×#67C211yesmaximal, characteristic
2C2×C3×#380C211yesmaximal, characteristic, complemented
3C2×#5212C211yesmaximal, characteristic, complemented
4C22×#806C212yesmaximal
5C2×#4527C212yesmaximal, complemented
6#69530C218yesmaximal, direct product factor
7C2×#1799—31nomaximal, Sylow
8C24×C3×C4C2211yescharacteristic
9C23×#67C2211yescharacteristic
10C23×C4×D3C411yescharacteristic, complemented
11C22×C3×C4⋊C4—21no—
12C22×C3×C22⋊C4C2212yes—
13C22×#217C2212yes—
14C22×#217C2211yescharacteristic
15C2×C4×#67—21no—
16C2×C4×#67—21no—
17C2×C4×#67—22no—
18C2×C4×#67—21no—
19C2×C4×#67—21no—
20C2×C4×#67—22no—
21C2×C4×#67C414yescomplemented
22C2×C4×#67C2214yes—
23C22×(C2×D3)⋊C4C411yescharacteristic, complemented
24C22×C4⋊Dic3—21no—
25C22×Dic3⋊C4C411yescharacteristic, complemented
26C22×C4×Dic3C411yescharacteristic, complemented
27C3×#380—22no—
28C3×#380C2214yescomplemented
29C2×C3×#95—21no—
30#5212—22no—
31#5212C2214yescomplemented
32C2×C3⋊#95—21no—
33C2×#806—28no—
34C2×#806C2218yes—
35#4527C2218yescomplemented
36C22×C4×D4—31no—
37C22×#99—32no—
38C2×#380—31no—
39C2×#380D311yescharacteristic, complemented
40#1799—38no—
41C2×#342—32no—
42C25×C3C2311yescharacteristic
43C24×D3C2×C411yescharacteristic
44C23×C3×C4—22no—
45C23×C3×C4—44no—
46C23×C3×C4C2×C411yescharacteristic
47C23×C3×C4C2×C411yescharacteristic
48C23×C3×C4C2×C412yes—
49C23×C3×C4D411yescharacteristic
50C23×C3×C4D411yescharacteristic
51C23×C3×C4D412yes—
52C23×C3×C4D411yescharacteristic
53C23×C3×C4D411yescharacteristic
54C23×C3×C4D412yes—
55C23×C3×C4C2312yes—
56C22×#67—21no—
57C22×#67—21no—
58C22×#67—21no—
59C22×#67—21no—
60C22×#67—22no—
61C22×#67—22no—
62C22×#67C2×C412yes—
63C22×#67D414yes—
64C22×#67Q814yes—
65C22×#67C2312yes—
66C23×Dic3—22no—
67C23×Dic3C2×C411yescharacteristic
68C23×Dic3C2×C411yescharacteristic
69C23×Dic3C2×C411yescharacteristic
70C22×C4×D3—22no—
71C22×C4×D3—21no—
72C22×C4×D3—21no—
73C22×C4×D3—44no—
74C22×C4×D3C2×C414yescomplemented
75C2×C3×C4⋊C4—24no—
76C2×C3×C4⋊C4—44no—
77C2×C3×C22⋊C4—24no—
78C2×C3×C22⋊C4—24no—
79C2×C3×C22⋊C4—22no—
80C2×C3×C22⋊C4C2314yes—
81C2×#217—21no—
82C2×#217—21no—
83C2×#217—21no—
84C2×#217—21no—
85C2×#217—24no—
86C2×#217—24no—
87C2×#217—22no—
88C2×#217C2×C412yes—
89C2×#217C2314yes—
90C2×#217C2312yes—
91C4×#67—24no—
92C4×#67—24no—
93C4×#67—24no—
94C4×#67—24no—
95C4×#67—24no—
96C4×#67—24no—
97C4×#67—24no—
98C4×#67—24no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×(C2×D3)⋊C4—22no—
102C2×(C2×D3)⋊C4C2×C414yescomplemented
103C2×C4⋊Dic3—24no—
104C2×C4⋊Dic3—44no—
105C2×Dic3⋊C4—21no—
106C2×Dic3⋊C4—21no—
107C2×Dic3⋊C4—22no—
108C2×Dic3⋊C4C2×C414yescomplemented
109C2×C4×Dic3—22no—
110C2×C4×Dic3—21no—
111C2×C4×Dic3—21no—
112C2×C4×Dic3C2×C414yescomplemented
113C3×#95—24no—
114C3⋊#95—24no—
115#806—216no—
116C23×D4—31no—
117C24×C4—31no—
118C24×C4C2×D311yescharacteristic
119C2×C4×D4—34no—
120C2×C4×D4—34no—
121C2×C4×D4—61no—
122C2×C4×D4—61no—
123C2×C4×D4—62no—
124C2×C4×D4—61no—
125C2×C4×D4—61no—
126C2×C4×D4—62no—
127C22×C4⋊C4—21no—
128C22×C4⋊C4—31no—
129C22×C4⋊C4—61no—
130C22×C22⋊C4—31no—
131C22×C22⋊C4—31no—
132C22×C22⋊C4—32no—
133C22×C22⋊C4C2×D312yes—
134C22×C42—31no—
135C2×#99—38no—
136C2×#99—68no—
137#380—22no—
138#380—34no—
139#380—62no—
140#380C2×D314yescomplemented
141C2×#95—21no—
142C2×#95—61no—
143#342—38no—
144C24×C3—42no—
145C24×C3—42no—
146C24×C3C22×C411yescharacteristic
147C24×C3C22×C411yescharacteristic
148C24×C3C2×D411yescharacteristic
149C24×C3C2×D411yescharacteristic
150C24×C3C2×D412yes—
151C24×C3C2×D411yescharacteristic
152C24×C3C2×D411yescharacteristic
153C24×C3C2×Q812yes—
154C24×C3#4112yes—
155C24×C3#4112yes—
156C24×C3C2411yescharacteristic
157C23×D3—21no—
158C23×D3—21no—
159C23×D3—22no—
160C23×D3—42no—
161C23×D3—42no—
162C23×D3C4⋊C414yescomplemented
163C23×D3C22×C412yes—
164C22×C3×C4—24no—
165C22×C3×C4—24no—
166C22×C3×C4—24no—
167C22×C3×C4—24no—
168C22×C3×C4—44no—
169C22×C3×C4—44no—
170C22×C3×C4—44no—
171C22×C3×C4—44no—
172C22×C3×C4—42no—
173C22×C3×C4—42no—
174C22×C3×C4—42no—
175C22×C3×C4—44no—
176C22×C3×C4—44no—
177C22×C3×C4—44no—
178C22×C3×C4C22⋊C412yes—
179C22×C3×C4C22⋊C411yescharacteristic
180C22×C3×C4C22⋊C411yescharacteristic
181C22×C3×C4C22⋊C411yescharacteristic
182C22×C3×C4C22⋊C412yes—
183C22×C3×C4C22⋊C412yes—
184C22×C3×C4C22⋊C412yes—
185C22×C3×C4C22⋊C412yes—
186C22×C3×C4C22⋊C412yes—
187C22×C3×C4C22⋊C411yescharacteristic
188C22×C3×C4C22×C412yes—
189C22×C3×C4C22×C412yes—
190C22×C3×C4C2×D412yes—
191C22×C3×C4C2×D412yes—
192C22×C3×C4C2×D412yes—
193C22×C3×C4C2×D412yes—
194C2×#67—22no—
195C2×#67—22no—
196C2×#67—24no—
197C2×#67—24no—
198C2×#67—24no—
199C2×#67—24no—
200C2×#67—24no—
201C2×#67—24no—
202C2×#67—24no—
203C2×#67—24no—
204C2×#67—24no—
205C2×#67—22no—
206C2×#67—22no—
207C2×#67—22no—
208C2×#67—22no—
209C2×#67C4⋊C418yescomplemented
210C2×#67C2×D414yes—
211C2×#67C2×Q814yes—
212C22×Dic3—21no—
213C22×Dic3—21no—
214C22×Dic3—22no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—24no—
220C22×Dic3—42no—
221C22×Dic3—42no—
222C22×Dic3—44no—
223C22×Dic3—44no—
224C22×Dic3—44no—
225C22×Dic3C4⋊C414yescomplemented
226C22×Dic3C22×C412yes—
227C22×Dic3C22×C412yes—
228C22×Dic3C22×C412yes—
229C2×C4×D3—24no—
230C2×C4×D3—24no—
231C2×C4×D3—44no—
232C2×C4×D3—48no—
233C2×C4×D3—44no—
234C2×C4×D3—48no—
235C3×C4⋊C4—48no—
236C3×C22⋊C4—24no—
237C3×C22⋊C4—24no—
238C3×C22⋊C4—44no—
239#217—22no—
240#217—22no—
241#217—22no—
242#217—22no—
243#217—24no—
244#217—24no—
245#217—44no—
246(C2×D3)⋊C4—24no—
247(C2×D3)⋊C4—24no—
248C4⋊Dic3—48no—
249Dic3⋊C4—24no—
250Dic3⋊C4—24no—
251C4×Dic3—24no—
252C4×Dic3—24no—
253C25—31no—
254C25C22×D311yescharacteristic
255C22×D4—32no—
256C22×D4—34no—
257C22×D4—34no—
258C22×D4—32no—
259C22×D4—61no—
260C22×D4—61no—
261C22×D4—62no—
262C22×D4—62no—
263C22×D4—61no—
264C22×D4—61no—
265C23×C4—22no—
266C23×C4—31no—
267C23×C4—31no—
268C23×C4—31no—
269C23×C4—34no—
270C23×C4—44no—
271C23×C4—62no—
272C23×C4—61no—
273C23×C4—61no—
274C23×C4—62no—
275C23×C4—124no—
276C23×C4C4×D311yescharacteristic
277C23×C4C4×D311yescharacteristic
278C23×C4C4×D312yes—
279C23×C4D1211yescharacteristic
280C23×C4D1211yescharacteristic
281C23×C4D1212yes—
282C23×C4#6711yescharacteristic
283C23×C4#6711yescharacteristic
284C23×C4#6712yes—
285C23×C4C22×D312yes—
286C4×D4—64no—
287C4×D4—64no—
288C4×D4—64no—
289C4×D4—64no—
290C4×D4—64no—
291C4×D4—64no—
292C4×D4—64no—
293C4×D4—64no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—34no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—62no—
298C2×C4⋊C4—61no—
299C2×C4⋊C4—61no—
300C2×C4⋊C4—64no—
301C2×C4⋊C4—124no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—32no—
306C2×C22⋊C4—32no—
307C2×C22⋊C4—34no—
308C2×C22⋊C4—34no—
309C2×C22⋊C4—61no—
310C2×C22⋊C4—61no—
311C2×C22⋊C4—61no—
312C2×C22⋊C4—61no—
313C2×C22⋊C4—62no—
314C2×C22⋊C4—61no—
315C2×C22⋊C4—61no—
316C2×C22⋊C4—64no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—62no—
319C2×C22⋊C4C22×D314yes—
320C2×C42—34no—
321C2×C42—62no—
322C2×C42—61no—
323C2×C42—61no—
324#99—616no—
325#95—24no—
326#95—64no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—22no—
333C23×C3—41no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—44no—
340C23×C3—41no—
341C23×C3—44no—
342C23×C3—44no—
343C23×C3—44no—
344C23×C3—41no—
345C23×C3C2×C22⋊C411yescharacteristic
346C23×C3C2×C22⋊C411yescharacteristic
347C23×C3C2×C22⋊C411yescharacteristic
348C23×C3C2×C22⋊C411yescharacteristic
349C23×C3C2×C4⋊C412yes—
350C23×C3C2×C4⋊C412yes—
351C23×C3#11712yes—
352C23×C3#11712yes—
353C23×C3#12112yes—
354C23×C3#12112yes—
355C23×C3#12112yes—
356C23×C3#12112yes—
357C23×C3C22⋊Q812yes—
358C23×C3C22⋊Q812yes—
359C23×C3C22⋊Q812yes—
360C23×C3C22⋊Q812yes—
361C23×C3C23×C411yescharacteristic
362C23×C3C22×D411yescharacteristic
363C23×C3C22×D411yescharacteristic
364C23×C3C22×D411yescharacteristic
365C23×C3C22×Q811yescharacteristic
366C23×C3C2×#4111yescharacteristic
367C23×C3C2×#4111yescharacteristic
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—42no—
373C22×D3—48no—
374C22×D3—42no—
375C22×D3—42no—
376C22×D3—42no—
377C22×D3—42no—
378C22×D3—48no—
379C22×D3—42no—
380C22×D3C2×C4⋊C414yescomplemented
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—42no—
393C2×C3×C4—42no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—44no—
397C2×C3×C4—44no—
398C2×C3×C4—44no—
399C2×C3×C4—88no—
400C2×C3×C4#9914yescomplemented
401C2×C3×C4C2×C22⋊C412yes—
402C2×C3×C4C2×C22⋊C412yes—
403C2×C3×C4C2×C22⋊C412yes—
404C2×C3×C4C2×C22⋊C412yes—
405#67—24no—
406#67—24no—
407#67—24no—
408#67—24no—
409#67—28no—
410#67—28no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—24no—
414C2×Dic3—24no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—42no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—44no—
424C2×Dic3—44no—
425C2×Dic3—44no—
426C2×Dic3—88no—
427C2×Dic3C2×C4⋊C414yescomplemented
428C4×D3—48no—
429C4×D3—48no—
430C24—34no—
431C24—32no—
432C24—42no—
433C24—42no—
434C24—62no—
435C24—61no—
436C24—61no—
437C24—122no—
438C24—122no—
439C24C2×C4×D311yescharacteristic
440C24C2×C4×D311yescharacteristic
441C24C2×D1211yescharacteristic
442C24C2×D1211yescharacteristic
443C24D3×D412yes—
444C24#23712yes—
445C24D3×Q812yes—
446C24#23912yes—
447C24C2×#6711yescharacteristic
448C24C2×#6711yescharacteristic
449C24C23×D311yescharacteristic
450C2×D4—38no—
451C2×D4—34no—
452C2×D4—34no—
453C2×D4—64no—
454C2×D4—64no—
455C2×D4—64no—
456C2×D4—64no—
457C2×D4—64no—
458C2×D4—62no—
459C2×D4—62no—
460C2×D4—64no—
461C2×D4—64no—
462C2×D4—64no—
463C2×D4—64no—
464C2×D4—62no—
465C2×D4—62no—
466C2×D4—62no—
467C2×D4—62no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—34no—
473C22×C4—32no—
474C22×C4—32no—
475C22×C4—32no—
476C22×C4—44no—
477C22×C4—44no—
478C22×C4—44no—
479C22×C4—44no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—44no—
484C22×C4—44no—
485C22×C4—44no—
486C22×C4—62no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4—61no—
490C22×C4—61no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—64no—
494C22×C4—64no—
495C22×C4—64no—
496C22×C4—124no—
497C22×C4—128no—
498C22×C4—128no—
499C22×C4—124no—
500C22×C4—122no—
501C22×C4—122no—
502C22×C4—124no—
503C22×C4—124no—
504C22×C4—124no—
505C22×C4(C2×D3)⋊C412yes—
506C22×C4(C2×D3)⋊C412yes—
507C22×C4(C2×D3)⋊C412yes—
508C22×C4(C2×D3)⋊C411yescharacteristic
509C22×C4(C2×D3)⋊C411yescharacteristic
510C22×C4(C2×D3)⋊C411yescharacteristic
511C22×C4(C2×D3)⋊C412yes—
512C22×C4(C2×D3)⋊C412yes—
513C22×C4(C2×D3)⋊C412yes—
514C22×C4(C2×D3)⋊C411yescharacteristic
515C22×C4C2×C4×D312yes—
516C22×C4C2×C4×D312yes—
517C22×C4C2×D1212yes—
518C22×C4C2×D1212yes—
519C22×C4C2×#6712yes—
520C22×C4C2×#6712yes—
521C4⋊C4—48no—
522C4⋊C4—64no—
523C4⋊C4—64no—
524C4⋊C4—128no—
525C22⋊C4—24no—
526C22⋊C4—24no—
527C22⋊C4—44no—
528C22⋊C4—62no—
529C22⋊C4—62no—
530C22⋊C4—62no—
531C22⋊C4—62no—
532C22⋊C4—64no—
533C22⋊C4—64no—
534C22⋊C4—64no—
535C22⋊C4—64no—
536C22⋊C4—124no—
537C42—64no—
538C42—64no—
539C22×C3—24no—
540C22×C3—24no—
541C22×C3—24no—
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—21no—
546C22×C3—21no—
547C22×C3—21no—
548C22×C3—21no—
549C22×C3—21no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—42no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3#38012yes—
568C22×C3#38012yes—
569C22×C3#38012yes—
570C22×C3#38012yes—
571C22×C3C2×#9912yes—
572C22×C3#41012yes—
573C22×C3C22×C22⋊C411yescharacteristic
574C22×C3C22×C4⋊C411yescharacteristic
575C22×C3C2×#11711yescharacteristic
576C22×C3C2×#12111yescharacteristic
577C22×C3C2×#12111yescharacteristic
578C22×C3C2×C22⋊Q811yescharacteristic
579C22×C3C2×C22⋊Q811yescharacteristic
580C2×D3—24no—
581C2×D3—44no—
582C2×D3—48no—
583C2×D3—48no—
584C2×D3—42no—
585C2×D3—42no—
586C2×D3—44no—
587C3×C4—22no—
588C3×C4—22no—
589C3×C4—22no—
590C3×C4—84no—
591C3×C4C2×#9914yescomplemented
592Dic3—24no—
593Dic3—42no—
594Dic3—42no—
595Dic3—84no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—34no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23—44no—
613C23—41no—
614C23—41no—
615C23—64no—
616C23—64no—
617C23—62no—
618C23—62no—
619C23—122no—
620C23—122no—
621C23—128no—
622C23—122no—
623C23—122no—
624C23—128no—
625C23—122no—
626C23—122no—
627C23D3×C4⋊C412yes—
628C23D3×C4⋊C412yes—
629C23#89212yes—
630C23#89212yes—
631C23#89512yes—
632C23#89512yes—
633C23#89712yes—
634C23#89712yes—
635C23C2×(C2×D3)⋊C411yescharacteristic
636C23C2×(C2×D3)⋊C411yescharacteristic
637C23C2×(C2×D3)⋊C411yescharacteristic
638C23C2×(C2×D3)⋊C411yescharacteristic
639C23#93812yes—
640C23#93812yes—
641C23#94612yes—
642C23#94612yes—
643C23C22×C4×D311yescharacteristic
644C23C22×D1211yescharacteristic
645C23C2×D3×D411yescharacteristic
646C23C2×#23711yescharacteristic
647C23C2×D3×Q811yescharacteristic
648C23C2×#23911yescharacteristic
649C23C22×#6711yescharacteristic
650D4—68no—
651D4—68no—
652D4—64no—
653D4—64no—
654D4—64no—
655D4—64no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—34no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—64no—
676C2×C4—64no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—88no—
682C2×C4—128no—
683C2×C4—122no—
684C2×C4—122no—
685C2×C4—122no—
686C2×C4—122no—
687C2×C4—128no—
688C2×C4—122no—
689C2×C4—122no—
690C2×C4—124no—
691C2×C4—124no—
692C2×C4—124no—
693C2×C4—248no—
694C2×C4#80614yescomplemented
695C2×C4C2×(C2×D3)⋊C412yes—
696C2×C4C2×(C2×D3)⋊C412yes—
697C2×C4C2×(C2×D3)⋊C412yes—
698C2×C4C2×(C2×D3)⋊C412yes—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—22no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—22no—
707C2×C3—22no—
708C2×C3#179914yescomplemented
709C2×C3C2×#38011yescharacteristic
710C2×C3C22×#9911yescharacteristic
711C2×C3C2×#41011yescharacteristic
712D3—44no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—24no—
720C22—24no—
721C22—24no—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—64no—
742C22—124no—
743C22—128no—
744C22—124no—
745C22—122no—
746C22—128no—
747C22—122no—
748C22C2×#80612yes—
749C22#498712yes—
750C22#498712yes—
751C22#498712yes—
752C22#498712yes—
753C22#500612yes—
754C22C2×D3×C4⋊C411yescharacteristic
755C22C2×#89211yescharacteristic
756C22C2×#89511yescharacteristic
757C22C2×#89711yescharacteristic
758C22C22×(C2×D3)⋊C411yescharacteristic
759C22C2×#93811yescharacteristic
760C22C2×#94611yescharacteristic
761C4—22no—
762C4—22no—
763C4—22no—
764C4—64no—
765C4—84no—
766C4—122no—
767C4—122no—
768C4—244no—
769C4C2×#80614yescomplemented
770C3C2×#179911yescharacteristic, complemented, Sylow
771C2—21no—
772C2—21no—
773C2—22no—
774C2—21no—
775C2—21no—
776C2—22no—
777C2—22no—
778C2—21no—
779C2—21no—
780C2—124no—
781C2#6953014yesdirect product factor
782C2C22×#80611yescharacteristic
783C2C2×#498711yescharacteristic
784C2C2×#500611yescharacteristic
subgroupG/H
centerC23C2×(C2×D3)⋊C4
commutatorC23×C3C23×C4
FrattiniC24C23×D3
FittingC2×C3×#380C2
socleC23×C3C2×C22⋊C4
prime radicalC23×#67C22
cosocleC24×C3C24
hypercenterC2×#380D3
hypocenterC3C2×#1799
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×C3×#380C2semidirect
3. C2×#5212C2semidirect
5. C2×#4527C2semidirect
6. #69530C2direct (N × H)
10. C23×C4×D3C4semidirect
21. C2×C4×#67C4semidirect
23. C22×(C2×D3)⋊C4C4semidirect
25. C22×Dic3⋊C4C4semidirect
26. C22×C4×Dic3C4semidirect
28. C3×#380C22semidirect
31. #5212C22semidirect
35. #4527C22semidirect
39. C2×#380D3semidirect
74. C22×C4×D3C2×C4semidirect
102. C2×(C2×D3)⋊C4C2×C4semidirect
108. C2×Dic3⋊C4C2×C4semidirect
112. C2×C4×Dic3C2×C4semidirect
140. #380C2×D3semidirect
162. C23×D3C4⋊C4semidirect
209. C2×#67C4⋊C4semidirect
225. C22×Dic3C4⋊C4semidirect
380. C22×D3C2×C4⋊C4semidirect
400. C2×C3×C4#99semidirect
427. C2×Dic3C2×C4⋊C4semidirect
591. C3×C4C2×#99semidirect
694. C2×C4#806semidirect
708. C2×C3#1799semidirect
769. C4C2×#806semidirect
770. C3C2×#1799semidirect
781. C2#69530direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×#672
C2×C3×#3802
C2×#52122
C22×#8062
C2×#45272
#695302
C2×#17993