Finite Group Databasebeta

← C2×#21446355 #29682010

Subgroups — C2×#21446355 #29682010

Order 15616.

1694 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×#16840338C211yesmaximal, characteristic
2C2×#16840239C211yesmaximal, characteristic, complemented
3C2×#16839780C211yesmaximal, characteristic
4C2×#16839778C211yesmaximal, characteristic
5C22×#14519695C211yesmaximal, characteristic, complemented
6#21446355C218yesmaximal, direct product factor
7C2×#16839518C211yesmaximal, characteristic, complemented
8C2×C61×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×Dic122C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12#16840338—22no—
13#16840338—22no—
14#16840338C414yescomplemented
15#16840338C2214yes—
16C2×#14519777C412yescomplemented
17C2×#14519765C412yescomplemented
18C2×#14519761—22no—
19C2×#14519757—22no—
20#16840239—22no—
21#16840239—22no—
22#16840239—22no—
23#16840239C2214yescomplemented
24C2×C4×Dic122—22no—
25C2×#14519742—22no—
26C2×#14519736C2211yescharacteristic
27C2×#14519733—22no—
28#16839780—22no—
29#16839780C2214yes—
30#16839778—22no—
31#16839778C2214yes—
32C2×#14519705—22no—
33C2×#14519703—22no—
34C2×#14519695—22no—
35C2×#14519695—22no—
36C2×#14519695C2214yescomplemented
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×#11758222—21no—
51C2×#11758222—21no—
52C2×#11758222C2×C412yes—
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×Dic122C2×C411yescharacteristic
63C22×Dic122C2×C412yes—
64C22×Dic122C2×C412yes—
65C22×Dic122D412yes—
66C22×Dic122D412yes—
67C22×Dic122D412yes—
68C22×Dic122C2312yes—
69C22×D244C2×C411yescharacteristic
70C22×C22⋊D61—21no—
71C23×Dic61D412yes—
72C22×C4×D61—21no—
73C2×#11758194—21no—
74C2×#11758194—21no—
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758194C2312yes—
79C22×#92418—21no—
80#14519777—24no—
81#14519777C2×C418yescomplemented
82#14519765—24no—
83#14519765C2×C418yescomplemented
84#14519761—28no—
85#14519761—28no—
86#14519757—28no—
87#14519757—28no—
88C4×Dic122—28no—
89C4×Dic122—28no—
90#14519742—28no—
91#14519742—28no—
92#14519736—21no—
93#14519736—21no—
94#14519736D412yes—
95#14519736C2312yes—
96#14519733—28no—
97#14519733—28no—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61—24no—
100C2×#11758196—24no—
101C2×C22⋊Dic61—21no—
102C2×#11758198—24no—
103C2×C4×Dic61—24no—
104C2×C4×Dic61D412yes—
105#14519705—28no—
106#14519703—28no—
107#14519695—28no—
108C23×C4×C61C2311yescharacteristic
109C2×M16×C61—21no—
110C2×M16×C61—21no—
111C2×M16×C61—21no—
112C2×M16×C61—21no—
113C2×M16×C61—21no—
114C2×M16×C61C2312yes—
115C22×C8×C61—21no—
116#117×C61—21no—
117#117×C61—21no—
118#117×C61—21no—
119#117×C61—21no—
120#117×C61C2×C412yes—
121#117×C61D412yes—
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×C61C2×C412yes—
129C2×C42×C61D412yes—
130C24×C61C2×D411yescharacteristic
131C23×D61—21no—
132C22×C4×C61—22no—
133C22×C4×C61—22no—
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—41no—
151C2×C22⋊D61—41no—
152C2×C22⋊D61—41no—
153C2×C22⋊D61—41no—
154C22×Dic61—22no—
155C22×Dic61—22no—
156C22×Dic61—22no—
157C22×Dic61—22no—
158C22×Dic61—21no—
159C22×Dic61—22no—
160C22×Dic61C22⋊C414yes—
161C22×Dic61C22⋊C414yes—
162C22×Dic61C2×D414yes—
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—41no—
172#11758222—41no—
173#11758222—41no—
174#11758222—41no—
175#11758222—41no—
176#11758222—41no—
177#11758222—41no—
178#11758222—41no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244C22×C412yes—
185C2×C4×D61—22no—
186C2×C4×D61—22no—
187C2×C4×D61—41no—
188C2×C4×D61—41no—
189C2×C4×D61—41no—
190C2×C4×D61—41no—
191C2×Dic122—22no—
192C2×Dic122—22no—
193C2×Dic122—22no—
194C2×Dic122—22no—
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—22no—
211C2×Dic122—22no—
212C2×Dic122—22no—
213C2×Dic122—22no—
214C2×Dic122—22no—
215C2×Dic122—21no—
216C2×Dic122—21no—
217C2×Dic122—21no—
218C2×Dic122—21no—
219C2×Dic122—21no—
220C2×Dic122C22⋊C414yes—
221C2×Dic122C22⋊C414yes—
222C2×Dic122C22×C412yes—
223C2×Dic122C22×C414yes—
224C2×Dic122C2×D414yes—
225M16×C61—22no—
226M16×C61—22no—
227M16×C61—41no—
228M16×C61—41no—
229C2×C8×C61—22no—
230C2×C8×C61—41no—
231C2×C8×C61—41no—
232C4⋊C4×C61—22no—
233C4⋊C4×C61—22no—
234C4⋊C4×C61—22no—
235C4⋊C4×C61—22no—
236C22⋊C4×C61—22no—
237C22⋊C4×C61—22no—
238C22⋊C4×C61—22no—
239C22⋊C4×C61—22no—
240C42×C61—22no—
241C42×C61—22no—
242C42×C61C22×C414yes—
243C42×C61C2×D414yes—
244C22⋊Dic61—22no—
245C22⋊Dic61—22no—
246#11758198—216no—
247C4⋊Dic61—22no—
248C4⋊Dic61—22no—
249C4⋊Dic61—216no—
250#11758196—216no—
251C4×Dic61—216no—
252C4×Dic61—22no—
253C4×Dic61C2×D414yes—
254#11758194—22no—
255#11758194—22no—
256#11758194—41no—
257#11758194—41no—
258C2×#92418—22no—
259C2×#92418—41no—
260C2×#92418—41no—
261C23×C61—42no—
262C23×C61C2×C22⋊C411yescharacteristic
263C23×C61C2×C22⋊C411yescharacteristic
264C23×C61#12011yescharacteristic
265C23×C61#12011yescharacteristic
266C23×C61#12311yescharacteristic
267C23×C61#12311yescharacteristic
268C23×C61C22×D411yescharacteristic
269C22×D61—22no—
270C22×D61—44no—
271C22×D61—41no—
272C22×D61—41no—
273C2×C4×C61—24no—
274C2×C4×C61—24no—
275C2×C4×C61—44no—
276C2×C4×C61—44no—
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#12111yescharacteristic
290C2×C4×C61#12111yescharacteristic
291C2×C4×C61#12111yescharacteristic
292C2×C4×C61#12111yescharacteristic
293C2×C4×C61#12111yescharacteristic
294C2×C4×C61#12111yescharacteristic
295C2×C4×C61#12111yescharacteristic
296C2×C4×C61#12111yescharacteristic
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—42no—
306C22⋊D61—42no—
307C22⋊D61—42no—
308C22⋊D61—42no—
309C2×Dic61—24no—
310C2×Dic61—24no—
311C2×Dic61—24no—
312C2×Dic61—24no—
313C2×Dic61—24no—
314C2×Dic61—24no—
315C2×Dic61—22no—
316C2×Dic61—24no—
317C2×Dic61—44no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61C2×C22⋊C418yes—
321D244—22no—
322D244—22no—
323D244—41no—
324D244—41no—
325C4×D61—42no—
326C4×D61—42no—
327C4×D61—42no—
328C4×D61—42no—
329Dic122—24no—
330Dic122—24no—
331Dic122—24no—
332Dic122—24no—
333Dic122—24no—
334Dic122—24no—
335Dic122—24no—
336Dic122—24no—
337Dic122—22no—
338Dic122—22no—
339Dic122—41no—
340Dic122—41no—
341C8×C61—42no—
342#92418—42no—
343C2×#1912—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×#12011yescharacteristic
357C22×C61C2×#12311yescharacteristic
358C2×D61—44no—
359C2×D61—42no—
360C2×D61—82no—
361C2×D61—82no—
362C4×C61—44no—
363C4×C61—44no—
364C4×C61#38611yescharacteristic
365C4×C61#38611yescharacteristic
366C4×C61#38611yescharacteristic
367C4×C61#38611yescharacteristic
368C4×C61C2×C4×D411yescharacteristic
369C4×C61C2×C4×D411yescharacteristic
370C4×C61C2×#12111yescharacteristic
371C4×C61C2×#12111yescharacteristic
372Dic61—28no—
373Dic61—44no—
374Dic61—42no—
375C2×#536—611no—
376C2×#519—611no—
377C2×#421—611no—
378C2×#421—611no—
379C22×#101—611no—
380#1912—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#191212yescomplemented
390C2×C61C2×#38611yescharacteristic
391D61—82no—
392C22×#41—611no—
393C23×Q8—611no—
394C22×M16—611no—
395C22×M16C2×D6111yescharacteristic
396#536—614no—
397#536—614no—
398#536—1222no—
399#536—1222no—
400C2×C4⋊Q8—612no—
401C2×#124—612no—
402C2×#123—1222no—
403C2×C22⋊Q8—1222no—
404#519—614no—
405#519—1222no—
406#519—1222no—
407#519—1222no—
408C2×C4×Q8—1222no—
409C2×C4×Q8—1222no—
410C2×#117—611no—
411C2×#117—1222no—
412C2×#117C2×D6111yescharacteristic
413C2×#117C2×D6111yescharacteristic
414#421—614no—
415#421—614no—
416#421—1222no—
417#421—1222no—
418C2×#104—1222no—
419C2×#104—1222no—
420C2×#101—614no—
421C2×#101—1222no—
422C2×#101—1222no—
423H(3,ℤ/4)—614no—
424H(3,ℤ/4)C2×D6114yescomplemented
425C61C2×#191211yescharacteristic, complemented, Sylow
426C2×#41—612no—
427C2×#41—612no—
428C2×#41—1221no—
429C2×#41—1221no—
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—612no—
439C22×Q8—612no—
440C22×Q8—612no—
441C22×Q8—612no—
442C22×Q8—612no—
443C22×Q8—612no—
444C22×Q8—611no—
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—611no—
454C22×D4—1221no—
455C23×C4—612no—
456C23×C4—1221no—
457C23×C4C22×D6111yescharacteristic
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—612no—
464C2×M16—1221no—
465C2×M16—1221no—
466C2×M16—1221no—
467C2×M16—1221no—
468C2×M16—1221no—
469C2×M16C22×D6112yes—
470C22×C8—21no—
471C22×C8—1221no—
472C4⋊Q8—618no—
473C4⋊Q8—1224no—
474#124—618no—
475#124—1224no—
476#123—1228no—
477#123—1228no—
478C22⋊Q8—1228no—
479C22⋊Q8—1228no—
480C4×Q8—1228no—
481C4×Q8—1228no—
482C4×Q8—1228no—
483C4×Q8—1228no—
484#117—21no—
485#117—21no—
486#117—21no—
487#117—21no—
488#117—612no—
489#117—612no—
490#117—1228no—
491#117—1228no—
492#117—1221no—
493#117—1221no—
494#117C4×D6112yes—
495#117D24412yes—
496#117C22×D6112yes—
497#117C22×D6112yes—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—1224no—
501C2×C4⋊C4—1224no—
502C2×C4⋊C4—1221no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—1224no—
506C2×C22⋊C4—1221no—
507C2×C42—612no—
508C2×C42—1224no—
509C2×C42C4×D6112yes—
510C2×C42D24412yes—
511#104—1228no—
512#104—1228no—
513#101—1228no—
514C24—1221no—
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—2441no—
525#41—2441no—
526#41—2441no—
527#41—2441no—
528#41—2441no—
529#41—2441no—
530#41—2441no—
531#41—2441no—
532C2×Q8—614no—
533C2×Q8—614no—
534C2×Q8—614no—
535C2×Q8—614no—
536C2×Q8—612no—
537C2×Q8—1222no—
538C2×Q8—1222no—
539C2×Q8—1222no—
540C2×Q8—1222no—
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—1222no—
555C2×Q8—1222no—
556C2×Q8—1222no—
557C2×Q8—1222no—
558C2×Q8—1222no—
559C2×Q8—1222no—
560C2×Q8—1222no—
561C2×Q8—1222no—
562C2×Q8—1221no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×D4—612no—
567C2×D4—1222no—
568C2×D4—1222no—
569C2×D4—1221no—
570C2×D4—1221no—
571C2×D4—1221no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—2441no—
575C2×D4—2441no—
576C2×D4—2441no—
577C2×D4—2441no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—614no—
581C22×C4—614no—
582C22×C4—614no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1221no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
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—41no—
612M16—41no—
613M16—1222no—
614M16—1222no—
615M16—2441no—
616M16—2441no—
617C2×C8—22no—
618C2×C8—41no—
619C2×C8—41no—
620C2×C8—1222no—
621C2×C8—2441no—
622C2×C8—2441no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—12216no—
628C4⋊C4—12216no—
629C4⋊C4—1222no—
630C4⋊C4—1222no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—12216no—
636C22⋊C4—1222no—
637C22⋊C4—1222no—
638C42—22no—
639C42—22no—
640C42—614no—
641C42—12216no—
642C42—1222no—
643C42C2×C4×D6114yes—
644C42C2×D24414yes—
645C23—42no—
646C23—1222no—
647C23—2444no—
648C23—2441no—
649C23—2441no—
650C23C22⋊C4×D6111yescharacteristic
651C23C22⋊C4×D6111yescharacteristic
652C23#1451974711yescharacteristic
653C23#1451974711yescharacteristic
654C23#1451976211yescharacteristic
655C23#1451976211yescharacteristic
656C23C2×D4×D6111yescharacteristic
657Q8—1224no—
658Q8—1224no—
659Q8—1224no—
660Q8—1224no—
661Q8—1224no—
662Q8—1224no—
663Q8—1224no—
664Q8—1224no—
665Q8—1222no—
666Q8—1222no—
667Q8—2441no—
668Q8—2441no—
669D4—1222no—
670D4—1222no—
671D4—2442no—
672D4—2442no—
673D4—2442no—
674D4—2442no—
675D4—2441no—
676D4—2441no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—618no—
682C2×C4—1224no—
683C2×C4—1224no—
684C2×C4—1224no—
685C2×C4—1224no—
686C2×C4—1224no—
687C2×C4—1224no—
688C2×C4—1222no—
689C2×C4—1224no—
690C2×C4—2444no—
691C2×C4—2441no—
692C2×C4—2441no—
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#1451975011yescharacteristic
710C2×C4#1451975011yescharacteristic
711C2×C4#1451975011yescharacteristic
712C2×C4#1451975011yescharacteristic
713C2×C4#1451975211yescharacteristic
714C2×C4#1451975211yescharacteristic
715C2×C4#1451975211yescharacteristic
716C2×C4#1451975211yescharacteristic
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—42no—
726C8—2442no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—4882no—
735C22—4882no—
736C22—2444no—
737C22—2442no—
738C22#1683964011yescharacteristic
739C22#1683964011yescharacteristic
740C22#1683964011yescharacteristic
741C22#1683964011yescharacteristic
742C22C2×C22⋊C4×D6111yescharacteristic
743C22C2×#1451974711yescharacteristic
744C22C2×#1451976211yescharacteristic
745C4—44no—
746C4—44no—
747C4—1228no—
748C4—2444no—
749C4—2442no—
750C4#1683964011yescharacteristic
751C4#1683964011yescharacteristic
752C4#1683964011yescharacteristic
753C4#1683964011yescharacteristic
754C4C2×#1451973911yescharacteristic
755C4C2×C4×D24411yescharacteristic
756C4C2×#1451975011yescharacteristic
757C4C2×#1451975211yescharacteristic
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—4882no—
765C2#2144635512yesdirect 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×#1912
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
2. C2×#16840239C2semidirect
5. C22×#14519695C2semidirect
6. #21446355C2direct (N × H)
7. C2×#16839518C2semidirect
8. C2×C61×H(3,ℤ/4)C2semidirect
14. #16840338C4semidirect
16. C2×#14519777C4semidirect
17. C2×#14519765C4semidirect
23. #16840239C22semidirect
36. C2×#14519695C22semidirect
37. #16839518C22semidirect
41. C61×H(3,ℤ/4)C22semidirect
81. #14519777C2×C4semidirect
83. #14519765C2×C4semidirect
382. C2×H(3,ℤ/4)D61semidirect
389. C2×C61#1912semidirect
424. H(3,ℤ/4)C2×D61semidirect
425. C61C2×#1912semidirect
765. C2#21446355direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403382
C2×#168402392
C2×#168397802
C2×#168397782
C22×#145196952
#214463552
C2×#168395182
C2×C61×H(3,ℤ/4)2
C2×#191261