Finite Group Databasebeta

← C2×#21446340 #29681985

Subgroups — C2×#21446340 #29681985

Order 15616.

1686 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic
2C2×#16840338C211yesmaximal, characteristic
3C2×#16839772C211yesmaximal, characteristic, complemented
4C2×#16839770C211yesmaximal, characteristic, complemented
5C2×#16839735C211yesmaximal, characteristic
6#21446340C218yesmaximal, direct product factor
7C2×#16839518C211yesmaximal, characteristic, complemented
8C2×C61×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×Dic122C2211yescharacteristic
11#16840528—22no—
12#16840528—22no—
13#16840528—22no—
14#16840528C2214yes—
15C2×#14519785—22no—
16C2×#14519783—22no—
17C22×#11758194C2211yescharacteristic
18C2×M16×D61—22no—
19#16840338—22no—
20#16840338—22no—
21#16840338C414yescomplemented
22#16840338C2214yes—
23C2×#14519777C412yescomplemented
24C2×#14519765C412yescomplemented
25C2×#14519761—22no—
26C2×#14519757—22no—
27C2×#14519736C2211yescharacteristic
28#16839772—22no—
29#16839772C2214yescomplemented
30#16839770—22no—
31#16839770C2214yescomplemented
32C2×#14519702—22no—
33C2×#14519700—22no—
34#16839735—22no—
35#16839735C2214yes—
36C2×#14519691—22no—
37#16839518C2214yescomplemented
38C22×M16×C61C2211yescharacteristic
39C2×#117×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C61×H(3,ℤ/4)C2214yescomplemented
42C2×#11758222—21no—
43C2×#11758222—21no—
44C2×#11758222—21no—
45C2×#11758222—21no—
46C2×#11758222—21no—
47C2×#11758222—21no—
48C2×#11758222—21no—
49C2×#11758222—21no—
50C2×#11758222C2×C412yes—
51C2×#11758222D412yes—
52C2×#11758222D412yes—
53C2×#11758222C2312yes—
54C22×Dic122—21no—
55C22×Dic122—21no—
56C22×Dic122—21no—
57C22×Dic122—21no—
58C22×Dic122—21no—
59C22×Dic122—21no—
60C22×Dic122—21no—
61C22×Dic122—21no—
62C22×Dic122—21no—
63C22×Dic122—21no—
64C22×Dic122—21no—
65C22×Dic122C2×C412yes—
66C22×Dic122C2×C412yes—
67C22×Dic122C2×C411yescharacteristic
68C22×Dic122C2312yes—
69C22×D244C2×C411yescharacteristic
70C22×C22⋊D61D412yes—
71C23×Dic61—21no—
72C22×C4×D61D412yes—
73#14519785—28no—
74#14519785—28no—
75#14519783—28no—
76#14519783—28no—
77C2×#11758194—21no—
78C2×#11758194—21no—
79C2×#11758194—21no—
80C2×#11758194—21no—
81C2×#11758194D412yes—
82C2×#11758194C2312yes—
83C2×#11758189—24no—
84M16×D61—28no—
85M16×D61—28no—
86C22×#92418D412yes—
87C2×C8×D61—24no—
88#14519777—24no—
89#14519777C2×C418yescomplemented
90#14519765—24no—
91#14519765C2×C418yescomplemented
92#14519761—28no—
93#14519761—28no—
94#14519757—28no—
95#14519757—28no—
96#14519736—21no—
97#14519736—21no—
98#14519736—21no—
99#14519736C2312yes—
100C2×C4⋊Dic61—24no—
101C2×C4⋊Dic61—21no—
102C2×C22⋊Dic61—21no—
103C2×#11758198—24no—
104C2×C4×Dic61—21no—
105#14519702—28no—
106#14519700—28no—
107#14519691—28no—
108C23×C4×C61C2311yescharacteristic
109C2×M16×C61—21no—
110C2×M16×C61—21no—
111C2×M16×C61—21no—
112C2×M16×C61—21no—
113C2×M16×C61D412yes—
114C2×M16×C61C2312yes—
115C22×C8×C61D412yes—
116#117×C61—21no—
117#117×C61—21no—
118#117×C61—21no—
119#117×C61—21no—
120#117×C61—21no—
121#117×C61C2×C412yes—
122#117×C61C2312yes—
123#117×C61C2312yes—
124C2×C4⋊C4×C61—21no—
125C2×C4⋊C4×C61—21no—
126C2×C22⋊C4×C61—21no—
127C2×C22⋊C4×C61—21no—
128C2×C42×C61—21no—
129C2×C42×C61C2×C412yes—
130C24×C61C2×D411yescharacteristic
131C23×D61C22⋊C412yes—
132C22×C4×C61—22no—
133C22×C4×C61—41no—
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×D411yescharacteristic
138C22×C4×C61C2×D411yescharacteristic
139C22×C4×C61C2×D411yescharacteristic
140C22×C4×C61C2×D411yescharacteristic
141C22×C4×C61C2×D411yescharacteristic
142C22×C4×C61C2×D411yescharacteristic
143C22×C4×C61#4111yescharacteristic
144C22×C4×C61#4111yescharacteristic
145C22×C4×C61#4111yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C22×C4×C61C2411yescharacteristic
148C2×C22⋊D61—22no—
149C2×C22⋊D61—22no—
150C2×C22⋊D61—22no—
151C2×C22⋊D61—22no—
152C2×C22⋊D61C22⋊C414yes—
153C2×C22⋊D61C2×D414yes—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—41no—
158C22×Dic61—41no—
159C22×Dic61—41no—
160C22×Dic61—41no—
161C22×Dic61—41no—
162C22×Dic61C22⋊C412yes—
163#11758222—22no—
164#11758222—22no—
165#11758222—22no—
166#11758222—22no—
167#11758222—22no—
168#11758222—22no—
169#11758222—22no—
170#11758222—22no—
171#11758222—22no—
172#11758222—22no—
173#11758222—22no—
174#11758222—22no—
175#11758222—22no—
176#11758222—22no—
177#11758222—22no—
178#11758222—22no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244C22⋊C412yes—
184C2×D244C22×C412yes—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61C22⋊C414yes—
190C2×C4×D61C2×D414yes—
191C2×Dic122—21no—
192C2×Dic122—21no—
193C2×Dic122—21no—
194C2×Dic122—21no—
195C2×Dic122—22no—
196C2×Dic122—22no—
197C2×Dic122—22no—
198C2×Dic122—22no—
199C2×Dic122—22no—
200C2×Dic122—22no—
201C2×Dic122—22no—
202C2×Dic122—22no—
203C2×Dic122—22no—
204C2×Dic122—22no—
205C2×Dic122—22no—
206C2×Dic122—22no—
207C2×Dic122—22no—
208C2×Dic122—22no—
209C2×Dic122—22no—
210C2×Dic122—41no—
211C2×Dic122—41no—
212C2×Dic122—41no—
213C2×Dic122—41no—
214C2×Dic122—41no—
215C2×Dic122—41no—
216C2×Dic122—41no—
217C2×Dic122—41no—
218C2×Dic122—41no—
219C2×Dic122—41no—
220C2×Dic122—41no—
221C2×Dic122—41no—
222C2×Dic122C22⋊C412yes—
223C2×Dic122C22×C414yes—
224C2×Dic122C22×C412yes—
225M16×C61—22no—
226M16×C61—22no—
227M16×C61—22no—
228M16×C61—22no—
229C2×C8×C61—22no—
230C2×C8×C61—22no—
231C2×C8×C61C2×D414yes—
232C4⋊C4×C61—22no—
233C4⋊C4×C61—22no—
234C4⋊C4×C61—22no—
235C4⋊C4×C61—41no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—41no—
240C42×C61—22no—
241C42×C61—22no—
242C42×C61—41no—
243C42×C61C22×C414yes—
244C22⋊Dic61—22no—
245C22⋊Dic61—41no—
246#11758198—216no—
247C4⋊Dic61—216no—
248C4⋊Dic61—22no—
249C4⋊Dic61—41no—
250C4×Dic61—22no—
251C4×Dic61—41no—
252#11758194—22no—
253#11758194—22no—
254#11758194—22no—
255#11758194—22no—
256C2×#92418—22no—
257C2×#92418—22no—
258C2×#92418C2×D414yes—
259#11758189—216no—
260C8×D61—216no—
261C23×C61—42no—
262C23×C61C2×C22⋊C411yescharacteristic
263C23×C61C2×C22⋊C411yescharacteristic
264C23×C61#12111yescharacteristic
265C23×C61#12111yescharacteristic
266C23×C61#12111yescharacteristic
267C23×C61#12111yescharacteristic
268C23×C61C22×D411yescharacteristic
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—44no—
272C22×D61C2×C22⋊C414yes—
273C2×C4×C61—24no—
274C2×C4×C61—44no—
275C2×C4×C61—42no—
276C2×C4×C61—82no—
277C2×C4×C61C2×C22⋊C411yescharacteristic
278C2×C4×C61C2×C22⋊C411yescharacteristic
279C2×C4×C61C4×D411yescharacteristic
280C2×C4×C61C4×D411yescharacteristic
281C2×C4×C61C4×D411yescharacteristic
282C2×C4×C61C4×D411yescharacteristic
283C2×C4×C61C4×D411yescharacteristic
284C2×C4×C61C4×D411yescharacteristic
285C2×C4×C61C4×D411yescharacteristic
286C2×C4×C61C4×D411yescharacteristic
287C2×C4×C61#12011yescharacteristic
288C2×C4×C61#12011yescharacteristic
289C2×C4×C61#12011yescharacteristic
290C2×C4×C61#12011yescharacteristic
291C2×C4×C61#12111yescharacteristic
292C2×C4×C61#12111yescharacteristic
293C2×C4×C61#12111yescharacteristic
294C2×C4×C61#12111yescharacteristic
295C2×C4×C61#12311yescharacteristic
296C2×C4×C61#12311yescharacteristic
297C2×C4×C61#12311yescharacteristic
298C2×C4×C61#12311yescharacteristic
299C2×C4×C61C23×C411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C22×D411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C2×#4111yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C22⋊D61—24no—
306C22⋊D61—24no—
307C22⋊D61—24no—
308C22⋊D61—24no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—24no—
312C2×Dic61—42no—
313C2×Dic61—42no—
314C2×Dic61—42no—
315C2×Dic61—42no—
316C2×Dic61—42no—
317C2×Dic61—42no—
318C2×Dic61—42no—
319C2×Dic61—82no—
320C2×Dic61C2×C22⋊C414yes—
321D244—22no—
322D244—22no—
323D244—22no—
324D244—22no—
325C4×D61—24no—
326C4×D61—24no—
327C4×D61—24no—
328C4×D61—24no—
329Dic122—22no—
330Dic122—22no—
331Dic122—22no—
332Dic122—22no—
333Dic122—24no—
334Dic122—24no—
335Dic122—42no—
336Dic122—42no—
337Dic122—42no—
338Dic122—42no—
339Dic122—42no—
340Dic122—42no—
341C8×C61—24no—
342#92418—24no—
343C2×#1909—611nomaximal, Sylow
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—22no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—41no—
351C22×C61#38611yescharacteristic
352C22×C61#38611yescharacteristic
353C22×C61#38611yescharacteristic
354C22×C61#38611yescharacteristic
355C22×C61C22×C22⋊C411yescharacteristic
356C22×C61C2×#12111yescharacteristic
357C22×C61C2×#12111yescharacteristic
358C2×D61—24no—
359C2×D61—44no—
360C2×D61—44no—
361C2×D61—82no—
362C4×C61—44no—
363C4×C61—82no—
364C4×C61#38611yescharacteristic
365C4×C61#38611yescharacteristic
366C4×C61#38611yescharacteristic
367C4×C61#38611yescharacteristic
368C4×C61C2×C4×D411yescharacteristic
369C4×C61C2×C4×D411yescharacteristic
370C4×C61C2×#12011yescharacteristic
371C4×C61C2×#12311yescharacteristic
372Dic61—24no—
373Dic61—44no—
374Dic61—82no—
375C2×#568—611no—
376C2×#536—611no—
377C2×#419—611no—
378C2×#419—611no—
379C2×#410—611no—
380#1909—618no—
381C2×H(3,ℤ/4)—611no—
382C2×H(3,ℤ/4)D6111yescharacteristic, complemented
383C2×C61—21no—
384C2×C61—21no—
385C2×C61—21no—
386C2×C61—21no—
387C2×C61—21no—
388C2×C61—21no—
389C2×C61#190912yescomplemented
390C2×C61C2×#38611yescharacteristic
391D61—44no—
392C22×#41—611no—
393C23×Q8—611no—
394#568—614no—
395#568—1222no—
396#568—1222no—
397#568—1222no—
398C2×#131—1222no—
399C2×#131—1222no—
400C22×M16—611no—
401C22×M16—1222no—
402C22×M16C2×D6111yescharacteristic
403#536—614no—
404#536—614no—
405#536—1222no—
406#536—1222no—
407C2×C4⋊Q8—612no—
408C2×#124—612no—
409C2×#123—1222no—
410C2×C22⋊Q8—1222no—
411C2×#117—611no—
412C2×#117C2×D6111yescharacteristic
413C2×#117C2×D6111yescharacteristic
414#419—614no—
415#419—614no—
416#419—1222no—
417#419—1222no—
418C2×#103—1222no—
419C2×#103—1222no—
420#410—614no—
421#410—1222no—
422C2×#99—1222no—
423H(3,ℤ/4)—614no—
424H(3,ℤ/4)C2×D6114yescomplemented
425C61C2×#190911yescharacteristic, complemented, Sylow
426C2×#41—612no—
427C2×#41—612no—
428C2×#41—612no—
429C2×#41—612no—
430C2×#41—1221no—
431C2×#41—1221no—
432C2×#41—1221no—
433C2×#41—1221no—
434C2×#41—1221no—
435C2×#41—1221no—
436C2×#41—1221no—
437C2×#41—1221no—
438C22×Q8—611no—
439C22×Q8—612no—
440C22×Q8—612no—
441C22×Q8—612no—
442C22×Q8—1221no—
443C22×Q8—1221no—
444C22×Q8—1221no—
445C22×Q8—1221no—
446C22×Q8—1221no—
447C22×Q8—1221no—
448C22×Q8—1221no—
449C22×Q8—1221no—
450C22×Q8—1221no—
451C22×Q8—1221no—
452C22×Q8—1221no—
453C22×D4—612no—
454C22×D4—611no—
455C23×C4—612no—
456C23×C4—1221no—
457C23×C4C22×D6111yescharacteristic
458#131—1228no—
459#131—1228no—
460#131—1228no—
461#131—1228no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—612no—
467C2×M16—612no—
468C2×M16—1224no—
469C2×M16—1228no—
470C2×M16—1228no—
471C2×M16—1221no—
472C2×M16—1221no—
473C2×M16—1221no—
474C2×M16—1221no—
475C2×M16D24412yes—
476C2×M16C22×D6112yes—
477C22×C8—612no—
478C22×C8—1224no—
479C22×C8D24412yes—
480C4⋊Q8—618no—
481C4⋊Q8—1224no—
482#124—618no—
483#124—1224no—
484#123—1228no—
485#123—1228no—
486C22⋊Q8—1228no—
487C22⋊Q8—1228no—
488#117—21no—
489#117—21no—
490#117—21no—
491#117—21no—
492#117—21no—
493#117—612no—
494#117—1221no—
495#117—1221no—
496#117—1221no—
497#117C4×D6112yes—
498#117C22×D6112yes—
499#117C22×D6112yes—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—1224no—
503C2×C4⋊C4—1221no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—1224no—
507C2×C22⋊C4—1221no—
508C2×C42—21no—
509C2×C42—1221no—
510C2×C42C4×D6112yes—
511#103—1228no—
512#103—1228no—
513#99—1228no—
514C24—612no—
515C24D4×D6111yescharacteristic
516#41—1222no—
517#41—1222no—
518#41—1222no—
519#41—1222no—
520#41—1222no—
521#41—1222no—
522#41—1222no—
523#41—1222no—
524#41—1222no—
525#41—1222no—
526#41—1222no—
527#41—1222no—
528#41—1222no—
529#41—1222no—
530#41—1222no—
531#41—1222no—
532C2×Q8—612no—
533C2×Q8—612no—
534C2×Q8—614no—
535C2×Q8—1222no—
536C2×Q8—1222no—
537C2×Q8—1222no—
538C2×Q8—1221no—
539C2×Q8—1221no—
540C2×Q8—1221no—
541C2×Q8—1221no—
542C2×Q8—1222no—
543C2×Q8—1222no—
544C2×Q8—1222no—
545C2×Q8—1222no—
546C2×Q8—1222no—
547C2×Q8—1222no—
548C2×Q8—1222no—
549C2×Q8—1222no—
550C2×Q8—1222no—
551C2×Q8—1222no—
552C2×Q8—1222no—
553C2×Q8—1222no—
554C2×Q8—2441no—
555C2×Q8—2441no—
556C2×Q8—2441no—
557C2×Q8—2441no—
558C2×Q8—2441no—
559C2×Q8—2441no—
560C2×Q8—2441no—
561C2×Q8—2441no—
562C2×Q8—2441no—
563C2×Q8—2441no—
564C2×Q8—2441no—
565C2×Q8—2441no—
566C2×D4—614no—
567C2×D4—614no—
568C2×D4—612no—
569C2×D4—612no—
570C2×D4—1222no—
571C2×D4—1222no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—1221no—
578C22×C4—22no—
579C22×C4—41no—
580C22×C4—612no—
581C22×C4—614no—
582C22×C4—614no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—2441no—
591C22×C4—2441no—
592C22×C4—2441no—
593C22×C4—2441no—
594C22×C4—2441no—
595C22×C4C2×C4×D6111yescharacteristic
596C22×C4C2×C4×D6111yescharacteristic
597C22×C4C2×D24411yescharacteristic
598C22×C4C2×D24411yescharacteristic
599C22×C4#1175822211yescharacteristic
600C22×C4#1175822211yescharacteristic
601C22×C4D4×D6111yescharacteristic
602C22×C4D4×D6111yescharacteristic
603C22×C4D4×D6111yescharacteristic
604C22×C4D4×D6111yescharacteristic
605C22×C4D4×D6111yescharacteristic
606C22×C4#1175822611yescharacteristic
607C22×C4#1175822611yescharacteristic
608C22×C4C23×D6111yescharacteristic
609M16—22no—
610M16—22no—
611M16—22no—
612M16—22no—
613M16—12216no—
614M16—1222no—
615M16—1222no—
616M16—1222no—
617M16—1222no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8—614no—
621C2×C8—12216no—
622C2×C8—1222no—
623C2×C8—1222no—
624C2×C8C2×D24414yes—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—41no—
629C4⋊C4—12216no—
630C4⋊C4—1222no—
631C4⋊C4—2441no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—41no—
636C22⋊C4—12216no—
637C22⋊C4—1222no—
638C22⋊C4—2441no—
639C42—22no—
640C42—22no—
641C42—41no—
642C42—1222no—
643C42—2441no—
644C42C2×C4×D6114yes—
645C23—42no—
646C23—614no—
647C23—1222no—
648C23—1222no—
649C23—2444no—
650C23C22⋊C4×D6111yescharacteristic
651C23C22⋊C4×D6111yescharacteristic
652C23#1451975011yescharacteristic
653C23#1451975011yescharacteristic
654C23#1451975211yescharacteristic
655C23#1451975211yescharacteristic
656C23C2×D4×D6111yescharacteristic
657Q8—1222no—
658Q8—1222no—
659Q8—1222no—
660Q8—1222no—
661Q8—1224no—
662Q8—1224no—
663Q8—2442no—
664Q8—2442no—
665Q8—2442no—
666Q8—2442no—
667Q8—2442no—
668Q8—2442no—
669D4—1224no—
670D4—1224no—
671D4—1224no—
672D4—1224no—
673D4—1222no—
674D4—1222no—
675D4—1222no—
676D4—1222no—
677C2×C4—24no—
678C2×C4—44no—
679C2×C4—42no—
680C2×C4—82no—
681C2×C4—614no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1224no—
685C2×C4—1224no—
686C2×C4—1224no—
687C2×C4—1224no—
688C2×C4—1224no—
689C2×C4—4882no—
690C2×C4—2442no—
691C2×C4—2442no—
692C2×C4—2442no—
693C2×C4—2442no—
694C2×C4—2442no—
695C2×C4—2442no—
696C2×C4—2442no—
697C2×C4C22⋊C4×D6111yescharacteristic
698C2×C4C22⋊C4×D6111yescharacteristic
699C2×C4#1451973911yescharacteristic
700C2×C4#1451973911yescharacteristic
701C2×C4#1451973911yescharacteristic
702C2×C4#1451973911yescharacteristic
703C2×C4C4×D24411yescharacteristic
704C2×C4C4×D24411yescharacteristic
705C2×C4C4×D24411yescharacteristic
706C2×C4C4×D24411yescharacteristic
707C2×C4#1451974711yescharacteristic
708C2×C4#1451974711yescharacteristic
709C2×C4#1451974711yescharacteristic
710C2×C4#1451974711yescharacteristic
711C2×C4#1451975011yescharacteristic
712C2×C4#1451975011yescharacteristic
713C2×C4#1451975211yescharacteristic
714C2×C4#1451975211yescharacteristic
715C2×C4#1451976211yescharacteristic
716C2×C4#1451976211yescharacteristic
717C2×C4#1451976211yescharacteristic
718C2×C4#1451976211yescharacteristic
719C2×C4C22×C4×D6111yescharacteristic
720C2×C4C2×D4×D6111yescharacteristic
721C2×C4C2×D4×D6111yescharacteristic
722C2×C4C22×D24411yescharacteristic
723C2×C4C2×#1175822211yescharacteristic
724C2×C4C2×#1175822611yescharacteristic
725C8—24no—
726C8—1224no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—1224no—
735C22—4882no—
736C22—2444no—
737C22—2444no—
738C22#1683964011yescharacteristic
739C22#1683964011yescharacteristic
740C22#1683964011yescharacteristic
741C22#1683964011yescharacteristic
742C22C2×C22⋊C4×D6111yescharacteristic
743C22C2×#1451975011yescharacteristic
744C22C2×#1451975211yescharacteristic
745C4—44no—
746C4—82no—
747C4—1224no—
748C4—4882no—
749C4—2444no—
750C4#1683964011yescharacteristic
751C4#1683964011yescharacteristic
752C4#1683964011yescharacteristic
753C4#1683964011yescharacteristic
754C4C2×#1451973911yescharacteristic
755C4C2×C4×D24411yescharacteristic
756C4C2×#1451974711yescharacteristic
757C4C2×#1451976211yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—2444no—
765C2#2144634012yesdirect product factor
766C2C2×#1683964011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×H(3,ℤ/4)C2
socleC22×C61#386
prime radicalC22×#11758222C22
cosocleC22×C4×C61C24
hypercenterC2×H(3,ℤ/4)D61
hypocenterC61C2×#1909
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
3. C2×#16839772C2semidirect
4. C2×#16839770C2semidirect
6. #21446340C2direct (N × H)
7. C2×#16839518C2semidirect
8. C2×C61×H(3,ℤ/4)C2semidirect
21. #16840338C4semidirect
23. C2×#14519777C4semidirect
24. C2×#14519765C4semidirect
29. #16839772C22semidirect
31. #16839770C22semidirect
37. #16839518C22semidirect
41. C61×H(3,ℤ/4)C22semidirect
89. #14519777C2×C4semidirect
91. #14519765C2×C4semidirect
382. C2×H(3,ℤ/4)D61semidirect
389. C2×C61#1909semidirect
424. H(3,ℤ/4)C2×D61semidirect
425. C61C2×#1909semidirect
765. C2#21446340direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405282
C2×#168403382
C2×#168397722
C2×#168397702
C2×#168397352
#214463402
C2×#168395182
C2×C61×H(3,ℤ/4)2
C2×#190961