Finite Group Databasebeta

← C2×#21446350 #29682004

Subgroups — C2×#21446350 #29682004

Order 15616.

1974 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840331C211yesmaximal, characteristic
2C2×#16840236C211yesmaximal, characteristic, complemented
3C2×#16839780C211yesmaximal, characteristic, complemented
4C2×#16839778C211yesmaximal, characteristic, complemented
5C22×#14519693C211yesmaximal, characteristic, complemented
6#21446350C218yesmaximal, direct product factor
7C2×#16839518C211yesmaximal, characteristic, complemented
8C2×C61×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10C23×D244C2211yescharacteristic
11C22×#11758194C2211yescharacteristic
12#16840331—22no—
13#16840331—22no—
14#16840331C414yescomplemented
15#16840331C2214yes—
16C2×#14519774C412yescomplemented
17C2×#14519765C412yescomplemented
18C2×#14519752—22no—
19C2×#14519747—22no—
20#16840236—22no—
21#16840236—22no—
22#16840236—22no—
23#16840236C2214yescomplemented
24C2×C4×D244—22no—
25C2×#14519739—22no—
26C2×#14519736C2211yescharacteristic
27C2×C22⋊C4×D61—22no—
28#16839780—22no—
29#16839780C2214yescomplemented
30#16839778—22no—
31#16839778C2214yescomplemented
32C2×#14519705—22no—
33C2×#14519703—22no—
34C2×#14519693—22no—
35C2×#14519693—22no—
36C2×#14519693C2214yescomplemented
37#16839518C2214yescomplemented
38C22×M16×C61C2211yescharacteristic
39C2×#117×C61C2211yescharacteristic
40C2×#117×C61C2211yescharacteristic
41C61×H(3,ℤ/4)C2214yescomplemented
42C24×D61D412yes—
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×#11758222—21no—
53C2×#11758222C2×C412yescomplemented
54C2×#11758222C2312yes—
55C22×Dic122C2×C411yescharacteristic, complemented
56C22×D244—21no—
57C22×D244—21no—
58C22×D244—21no—
59C22×D244—21no—
60C22×D244—21no—
61C22×D244—21no—
62C22×D244—21no—
63C22×D244—21no—
64C22×D244—24no—
65C22×D244C2×C412yes—
66C22×D244C2×C412yes—
67C22×D244C2×C411yescharacteristic, complemented
68C22×D244D412yes—
69C22×D244D412yes—
70C22×D244D412yes—
71C22×D244C2312yes—
72C22×C22⋊D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61—24no—
75C2×#11758194—21no—
76C2×#11758194—21no—
77C2×#11758194—21no—
78C2×#11758194—21no—
79C2×#11758194—21no—
80C2×#11758194C2312yes—
81C22×#92418—21no—
82#14519774—24no—
83#14519774C2×C418yescomplemented
84#14519765—24no—
85#14519765C2×C418yescomplemented
86#14519752—28no—
87#14519752—28no—
88#14519747—28no—
89#14519747—28no—
90C4×D244—28no—
91C4×D244—28no—
92#14519739—28no—
93#14519739—28no—
94#14519736—21no—
95#14519736—21no—
96#14519736D412yescomplemented
97#14519736C2312yes—
98C2×C4⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×#11758198—24no—
101C2×#11758198—24no—
102C22⋊C4×D61—28no—
103C22⋊C4×D61—28no—
104C2×C4×Dic61D412yescomplemented
105#14519705—28no—
106#14519703—28no—
107#14519693—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×C412yescomplemented
121#117×C61D412yescomplemented
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×C412yescomplemented
129C2×C42×C61D412yescomplemented
130C24×C61C2×D411yescharacteristic
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—21no—
136C23×D61—84no—
137C23×D61C22⋊C414yes—
138C23×D61C22⋊C414yes—
139C23×D61C2×D414yes—
140C22×C4×C61—22no—
141C22×C4×C61—22no—
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C2×D411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61#4111yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C22×C4×C61#4111yescharacteristic
154C22×C4×C61#4111yescharacteristic
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—22no—
157C2×C22⋊D61—22no—
158C2×C22⋊D61—41no—
159C2×C22⋊D61—41no—
160C2×C22⋊D61—41no—
161C2×C22⋊D61—41no—
162C22×Dic61—21no—
163C22×Dic61—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—41no—
173#11758222—41no—
174#11758222—41no—
175#11758222—41no—
176#11758222—41no—
177#11758222—41no—
178#11758222—41no—
179#11758222—41no—
180C2×D244—22no—
181C2×D244—22no—
182C2×D244—22no—
183C2×D244—22no—
184C2×D244—22no—
185C2×D244—22no—
186C2×D244—22no—
187C2×D244—22no—
188C2×D244—22no—
189C2×D244—22no—
190C2×D244—22no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—22no—
194C2×D244—22no—
195C2×D244—22no—
196C2×D244—22no—
197C2×D244—22no—
198C2×D244—22no—
199C2×D244—22no—
200C2×D244—22no—
201C2×D244—22no—
202C2×D244—22no—
203C2×D244—22no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—216no—
210C2×D244—88no—
211C2×D244C22⋊C414yes—
212C2×D244C22⋊C414yes—
213C2×D244C22×C414yes—
214C2×D244C22×C412yescomplemented
215C2×D244C2×D414yes—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—216no—
219C2×C4×D61—41no—
220C2×C4×D61—41no—
221C2×C4×D61—41no—
222C2×C4×D61—41no—
223C2×C4×D61—88no—
224C2×Dic122—21no—
225C2×Dic122—21no—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122C22×C412yescomplemented
230M16×C61—22no—
231M16×C61—22no—
232M16×C61—41no—
233M16×C61—41no—
234C2×C8×C61—22no—
235C2×C8×C61—41no—
236C2×C8×C61—41no—
237C4⋊C4×C61—22no—
238C4⋊C4×C61—22no—
239C4⋊C4×C61—22no—
240C4⋊C4×C61—22no—
241C22⋊C4×C61—22no—
242C22⋊C4×C61—22no—
243C22⋊C4×C61—22no—
244C22⋊C4×C61—22no—
245C42×C61—22no—
246C42×C61—22no—
247C42×C61C22×C414yescomplemented
248C42×C61C2×D414yescomplemented
249C22⋊Dic61—22no—
250C22⋊Dic61—22no—
251#11758198—216no—
252#11758198—216no—
253C4⋊Dic61—22no—
254C4⋊Dic61—22no—
255C4×Dic61—22no—
256C4×Dic61C2×D414yescomplemented
257#11758194—22no—
258#11758194—22no—
259#11758194—41no—
260#11758194—41no—
261C2×#92418—22no—
262C2×#92418—41no—
263C2×#92418—41no—
264C23×C61—42no—
265C23×C61C2×C22⋊C411yescharacteristic
266C23×C61C2×C22⋊C411yescharacteristic
267C23×C61#12011yescharacteristic
268C23×C61#12011yescharacteristic
269C23×C61#12311yescharacteristic
270C23×C61#12311yescharacteristic
271C23×C61C22×D411yescharacteristic
272C22×D61—24no—
273C22×D61—24no—
274C22×D61—24no—
275C22×D61—24no—
276C22×D61—24no—
277C22×D61—24no—
278C22×D61—22no—
279C22×D61—48no—
280C22×D61—48no—
281C22×D61—44no—
282C22×D61—41no—
283C22×D61—41no—
284C22×D61—84no—
285C22×D61—84no—
286C22×D61—84no—
287C22×D61—84no—
288C22×D61—84no—
289C22×D61C2×C22⋊C418yes—
290C2×C4×C61—24no—
291C2×C4×C61—24no—
292C2×C4×C61—44no—
293C2×C4×C61—44no—
294C2×C4×C61C2×C22⋊C411yescharacteristic
295C2×C4×C61C2×C22⋊C411yescharacteristic
296C2×C4×C61C4×D411yescharacteristic
297C2×C4×C61C4×D411yescharacteristic
298C2×C4×C61C4×D411yescharacteristic
299C2×C4×C61C4×D411yescharacteristic
300C2×C4×C61C4×D411yescharacteristic
301C2×C4×C61C4×D411yescharacteristic
302C2×C4×C61C4×D411yescharacteristic
303C2×C4×C61C4×D411yescharacteristic
304C2×C4×C61#12011yescharacteristic
305C2×C4×C61#12011yescharacteristic
306C2×C4×C61#12111yescharacteristic
307C2×C4×C61#12111yescharacteristic
308C2×C4×C61#12111yescharacteristic
309C2×C4×C61#12111yescharacteristic
310C2×C4×C61#12111yescharacteristic
311C2×C4×C61#12111yescharacteristic
312C2×C4×C61#12111yescharacteristic
313C2×C4×C61#12111yescharacteristic
314C2×C4×C61#12311yescharacteristic
315C2×C4×C61#12311yescharacteristic
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C22×D411yescharacteristic
318C2×C4×C61C22×D411yescharacteristic
319C2×C4×C61C22×D411yescharacteristic
320C2×C4×C61C2×#4111yescharacteristic
321C2×C4×C61C2×#4111yescharacteristic
322C22⋊D61—42no—
323C22⋊D61—42no—
324C22⋊D61—42no—
325C22⋊D61—42no—
326C2×Dic61—22no—
327C2×Dic61—24no—
328C2×Dic61—44no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331D244—24no—
332D244—24no—
333D244—22no—
334D244—22no—
335D244—24no—
336D244—24no—
337D244—24no—
338D244—24no—
339D244—24no—
340D244—24no—
341D244—41no—
342D244—41no—
343D244—816no—
344C4×D61—42no—
345C4×D61—42no—
346C4×D61—42no—
347C4×D61—42no—
348C4×D61—816no—
349Dic122—22no—
350Dic122—22no—
351Dic122—41no—
352Dic122—41no—
353C8×C61—42no—
354#92418—42no—
355C2×#1911—611nomaximal, Sylow
356C22×C61—22no—
357C22×C61—22no—
358C22×C61—22no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61#38611yescharacteristic
364C22×C61#38611yescharacteristic
365C22×C61#38611yescharacteristic
366C22×C61#38611yescharacteristic
367C22×C61C22×C22⋊C411yescharacteristic
368C22×C61C2×#12011yescharacteristic
369C22×C61C2×#12311yescharacteristic
370C2×D61—28no—
371C2×D61—48no—
372C2×D61—48no—
373C2×D61—48no—
374C2×D61—48no—
375C2×D61—44no—
376C2×D61—42no—
377C2×D61—84no—
378C2×D61—84no—
379C2×D61—84no—
380C2×D61—82no—
381C2×D61—82no—
382C4×C61—44no—
383C4×C61—44no—
384C4×C61#38611yescharacteristic
385C4×C61#38611yescharacteristic
386C4×C61#38611yescharacteristic
387C4×C61#38611yescharacteristic
388C4×C61C2×C4×D411yescharacteristic
389C4×C61C2×C4×D411yescharacteristic
390C4×C61C2×#12111yescharacteristic
391C4×C61C2×#12111yescharacteristic
392Dic61—44no—
393Dic61—42no—
394C2×#535—611no—
395C2×#518—611no—
396C2×#421—611no—
397C2×#421—611no—
398C22×#100—611no—
399#1911—618no—
400C2×H(3,ℤ/4)—611no—
401C2×H(3,ℤ/4)D6111yescharacteristic, complemented
402C2×C61—21no—
403C2×C61—21no—
404C2×C61—21no—
405C2×C61—21no—
406C2×C61—21no—
407C2×C61—21no—
408C2×C61#191112yescomplemented
409C2×C61C2×#38611yescharacteristic
410D61—48no—
411D61—82no—
412C22×#41—611no—
413C23×D4—611no—
414C22×M16—611no—
415C22×M16C2×D6111yescharacteristic
416#535—614no—
417#535—614no—
418#535—1222no—
419#535—1222no—
420C2×#127—612no—
421C2×#124—612no—
422C2×#121—1222no—
423C2×#120—1222no—
424#518—614no—
425#518—1222no—
426#518—1222no—
427#518—1222no—
428C2×C4×D4—1222no—
429C2×C4×D4—1222no—
430C2×#117—611no—
431C2×#117C2×D6111yescharacteristic
432C2×#117C2×D6111yescharacteristic
433C22×C22⋊C4—1222no—
434#421—614no—
435#421—614no—
436#421—1222no—
437#421—1222no—
438C2×#104—1222no—
439C2×#104—1222no—
440C2×#100—614no—
441C2×#100—1222no—
442C2×#100—1222no—
443H(3,ℤ/4)—614no—
444H(3,ℤ/4)C2×D6114yescomplemented
445C61C2×#191111yescharacteristic, complemented, Sylow
446C25—612no—
447C2×#41—612no—
448C2×#41—612no—
449C2×#41—1221no—
450C2×#41—1221no—
451C2×#41—1221no—
452C2×#41—1221no—
453C2×#41—1221no—
454C2×#41—1221no—
455C2×#41—1221no—
456C2×#41—1221no—
457C2×#41—1221no—
458C2×#41—1221no—
459C22×Q8—611no—
460C22×D4—612no—
461C22×D4—612no—
462C22×D4—611no—
463C22×D4—612no—
464C22×D4—612no—
465C22×D4—612no—
466C22×D4—612no—
467C22×D4—1224no—
468C22×D4—1221no—
469C22×D4—1221no—
470C22×D4—1221no—
471C22×D4—1221no—
472C22×D4—1221no—
473C22×D4—1221no—
474C22×D4—1221no—
475C22×D4—1221no—
476C22×D4—1221no—
477C23×C4—1224no—
478C23×C4—1221no—
479C23×C4C22×D6111yescharacteristic
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—612no—
486C2×M16—1221no—
487C2×M16—1221no—
488C2×M16—1221no—
489C2×M16—1221no—
490C2×M16—1221no—
491C2×M16C22×D6112yes—
492C22×C8—21no—
493C22×C8—1221no—
494#127—618no—
495#127—1224no—
496#124—618no—
497#124—1224no—
498#121—1228no—
499#121—1228no—
500#120—1228no—
501#120—1228no—
502C4×D4—1228no—
503C4×D4—1228no—
504C4×D4—1228no—
505C4×D4—1228no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117—612no—
511#117—612no—
512#117—1221no—
513#117—1221no—
514#117C4×D6112yescomplemented
515#117D24412yescomplemented
516#117C22×D6112yes—
517#117C22×D6112yes—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—1221no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—1228no—
524C2×C22⋊C4—1228no—
525C2×C22⋊C4—1224no—
526C2×C22⋊C4—1224no—
527C2×C22⋊C4—1221no—
528C2×C42—612no—
529C2×C42C4×D6112yescomplemented
530C2×C42D24412yescomplemented
531#104—1228no—
532#104—1228no—
533#100—1228no—
534C24—614no—
535C24—614no—
536C24—614no—
537C24—1222no—
538C24—1222no—
539C24—1222no—
540C24—1222no—
541C24—1221no—
542C24—4884no—
543C24D4×D6111yescharacteristic
544#41—1222no—
545#41—1222no—
546#41—1222no—
547#41—1222no—
548#41—1222no—
549#41—1222no—
550#41—1222no—
551#41—1222no—
552#41—2441no—
553#41—2441no—
554#41—2441no—
555#41—2441no—
556#41—2441no—
557#41—2441no—
558#41—2441no—
559#41—2441no—
560C2×Q8—612no—
561C2×Q8—1221no—
562C2×Q8—1221no—
563C2×Q8—1221no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×D4—614no—
567C2×D4—612no—
568C2×D4—614no—
569C2×D4—614no—
570C2×D4—614no—
571C2×D4—12216no—
572C2×D4—1222no—
573C2×D4—1222no—
574C2×D4—1222no—
575C2×D4—1222no—
576C2×D4—1222no—
577C2×D4—1222no—
578C2×D4—1221no—
579C2×D4—1222no—
580C2×D4—1222no—
581C2×D4—1222no—
582C2×D4—1222no—
583C2×D4—1221no—
584C2×D4—1221no—
585C2×D4—1222no—
586C2×D4—1222no—
587C2×D4—1222no—
588C2×D4—1222no—
589C2×D4—1221no—
590C2×D4—1221no—
591C2×D4—1222no—
592C2×D4—1222no—
593C2×D4—1222no—
594C2×D4—1222no—
595C2×D4—1222no—
596C2×D4—1222no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—1222no—
601C2×D4—1222no—
602C2×D4—1222no—
603C2×D4—4888no—
604C2×D4—2441no—
605C2×D4—2441no—
606C2×D4—2441no—
607C2×D4—2441no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—12216no—
611C22×C4—1221no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—4888no—
616C22×C4—2441no—
617C22×C4—2441no—
618C22×C4—2441no—
619C22×C4—2441no—
620C22×C4C2×C4×D6111yescharacteristic
621C22×C4C2×C4×D6111yescharacteristic
622C22×C4C2×D24411yescharacteristic
623C22×C4C2×D24411yescharacteristic
624C22×C4#1175822211yescharacteristic
625C22×C4#1175822211yescharacteristic
626C22×C4D4×D6111yescharacteristic
627C22×C4D4×D6111yescharacteristic
628C22×C4D4×D6111yescharacteristic
629C22×C4D4×D6111yescharacteristic
630C22×C4D4×D6111yescharacteristic
631C22×C4#1175822611yescharacteristic
632C22×C4#1175822611yescharacteristic
633C22×C4C23×D6111yescharacteristic
634M16—22no—
635M16—22no—
636M16—41no—
637M16—41no—
638M16—1222no—
639M16—1222no—
640M16—2441no—
641M16—2441no—
642C2×C8—22no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—1222no—
646C2×C8—2441no—
647C2×C8—2441no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—1222no—
653C4⋊C4—1222no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—12216no—
659C22⋊C4—12216no—
660C22⋊C4—1222no—
661C22⋊C4—1222no—
662C42—22no—
663C42—22no—
664C42—614no—
665C42—1222no—
666C42C2×C4×D6114yescomplemented
667C42C2×D24414yescomplemented
668C23—42no—
669C23—618no—
670C23—1224no—
671C23—1224no—
672C23—1224no—
673C23—1224no—
674C23—1224no—
675C23—1224no—
676C23—1222no—
677C23—4884no—
678C23—4884no—
679C23—4884no—
680C23—4884no—
681C23—4884no—
682C23—2444no—
683C23—2448no—
684C23—2448no—
685C23—2441no—
686C23—2441no—
687C23C22⋊C4×D6111yescharacteristic
688C23C22⋊C4×D6111yescharacteristic
689C23#1451974711yescharacteristic
690C23#1451974711yescharacteristic
691C23#1451976211yescharacteristic
692C23#1451976211yescharacteristic
693C23C2×D4×D6111yescharacteristic
694Q8—1222no—
695Q8—1222no—
696Q8—2441no—
697Q8—2441no—
698D4—1224no—
699D4—1222no—
700D4—1224no—
701D4—1222no—
702D4—1224no—
703D4—1224no—
704D4—1224no—
705D4—1224no—
706D4—1224no—
707D4—1224no—
708D4—48816no—
709D4—2442no—
710D4—2442no—
711D4—2442no—
712D4—2442no—
713D4—2441no—
714D4—2441no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—1222no—
720C2×C4—1224no—
721C2×C4—48816no—
722C2×C4—2444no—
723C2×C4—2441no—
724C2×C4—2441no—
725C2×C4—2442no—
726C2×C4—2442no—
727C2×C4—2442no—
728C2×C4—2442no—
729C2×C4C22⋊C4×D6111yescharacteristic
730C2×C4C22⋊C4×D6111yescharacteristic
731C2×C4#1451973911yescharacteristic
732C2×C4#1451973911yescharacteristic
733C2×C4#1451973911yescharacteristic
734C2×C4#1451973911yescharacteristic
735C2×C4C4×D24411yescharacteristic
736C2×C4C4×D24411yescharacteristic
737C2×C4C4×D24411yescharacteristic
738C2×C4C4×D24411yescharacteristic
739C2×C4#1451974711yescharacteristic
740C2×C4#1451974711yescharacteristic
741C2×C4#1451975011yescharacteristic
742C2×C4#1451975011yescharacteristic
743C2×C4#1451975011yescharacteristic
744C2×C4#1451975011yescharacteristic
745C2×C4#1451975211yescharacteristic
746C2×C4#1451975211yescharacteristic
747C2×C4#1451975211yescharacteristic
748C2×C4#1451975211yescharacteristic
749C2×C4#1451976211yescharacteristic
750C2×C4#1451976211yescharacteristic
751C2×C4C22×C4×D6111yescharacteristic
752C2×C4C2×D4×D6111yescharacteristic
753C2×C4C2×D4×D6111yescharacteristic
754C2×C4C22×D24411yescharacteristic
755C2×C4C2×#1175822211yescharacteristic
756C2×C4C2×#1175822611yescharacteristic
757C8—42no—
758C8—2442no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—1228no—
767C22—4882no—
768C22—4884no—
769C22—4884no—
770C22—4884no—
771C22—4882no—
772C22—2444no—
773C22—2448no—
774C22—2448no—
775C22—2448no—
776C22—2442no—
777C22—2448no—
778C22#1683964011yescharacteristic
779C22#1683964011yescharacteristic
780C22#1683964011yescharacteristic
781C22#1683964011yescharacteristic
782C22C2×C22⋊C4×D6111yescharacteristic
783C22C2×#1451974711yescharacteristic
784C22C2×#1451976211yescharacteristic
785C4—44no—
786C4—44no—
787C4—2444no—
788C4—2442no—
789C4#1683964011yescharacteristic
790C4#1683964011yescharacteristic
791C4#1683964011yescharacteristic
792C4#1683964011yescharacteristic
793C4C2×#1451973911yescharacteristic
794C4C2×C4×D24411yescharacteristic
795C4C2×#1451975011yescharacteristic
796C4C2×#1451975211yescharacteristic
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—4882no—
804C2—2448no—
805C2#2144635012yesdirect product factor
806C2C2×#1683964011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×H(3,ℤ/4)C2
socleC22×C61#386
prime radicalC2×#16840331C2
cosocleC22×C4×C61C24
hypercenterC2×H(3,ℤ/4)D61
hypocenterC61C2×#1911
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×#16840236C2semidirect
3. C2×#16839780C2semidirect
4. C2×#16839778C2semidirect
5. C22×#14519693C2semidirect
6. #21446350C2direct (N × H)
7. C2×#16839518C2semidirect
8. C2×C61×H(3,ℤ/4)C2semidirect
14. #16840331C4semidirect
16. C2×#14519774C4semidirect
17. C2×#14519765C4semidirect
23. #16840236C22semidirect
29. #16839780C22semidirect
31. #16839778C22semidirect
36. C2×#14519693C22semidirect
37. #16839518C22semidirect
41. C61×H(3,ℤ/4)C22semidirect
53. C2×#11758222C2×C4semidirect
55. C22×Dic122C2×C4semidirect
67. C22×D244C2×C4semidirect
83. #14519774C2×C4semidirect
85. #14519765C2×C4semidirect
96. #14519736D4semidirect
104. C2×C4×Dic61D4semidirect
120. #117×C61C2×C4semidirect
121. #117×C61D4semidirect
128. C2×C42×C61C2×C4semidirect
129. C2×C42×C61D4semidirect
214. C2×D244C22×C4semidirect
229. C2×Dic122C22×C4semidirect
247. C42×C61C22×C4semidirect
248. C42×C61C2×D4semidirect
256. C4×Dic61C2×D4semidirect
401. C2×H(3,ℤ/4)D61semidirect
408. C2×C61#1911semidirect
444. H(3,ℤ/4)C2×D61semidirect
445. C61C2×#1911semidirect
514. #117C4×D61semidirect
515. #117D244semidirect
529. C2×C42C4×D61semidirect
530. C2×C42D244semidirect
666. C42C2×C4×D61semidirect
667. C42C2×D244semidirect
805. C2#21446350direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168403312
C2×#168402362
C2×#168397802
C2×#168397782
C22×#145196932
#214463502
C2×#168395182
C2×C61×H(3,ℤ/4)2
C2×#191161