Finite Group Databasebeta

← #29681667

Subgroups — #29681667

Order 15616.

1700 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic, complemented
2#21459148C211yesmaximal, characteristic
3C2×#16839744C211yesmaximal, characteristic, complemented
4#21454264C211yesmaximal, characteristic, complemented
5#21446234C218yesmaximal, complemented
6C2×#16839534C211yesmaximal, characteristic, complemented
7C2×#16839533C211yesmaximal, characteristic, complemented
8C61×#2879C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840528—22no—
11#16840528—22no—
12#16840528—22no—
13#16840528C2214yes—
14C2×#14519785—22no—
15C2×#14519783—22no—
16C22×#11758194C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C2×M16×D61—22no—
19#16840340—22no—
20#16840336C412yes—
21#16840333—21no—
22#16840329C412yes—
23#16840326—21no—
24#16840321C414yes—
25#16840308—22no—
26#16840273C2214yes—
27#16840269—22no—
28C2×#14519736C2211yescharacteristic
29#16839744—22no—
30#16839744C2214yes—
31C2×#14519695—21no—
32C2×#14519693—21no—
33#16839729—22no—
34#16839729—22no—
35#16839726C2214yescomplemented
36#16839534C2214yescomplemented
37#16839533C2214yescomplemented
38C22×#41×C61C2211yescharacteristic
39C22×M16×C61C2211yescharacteristic
40C22×M16×C61C2211yescharacteristic
41C61×#408—22no—
42C61×#408—22no—
43C61×#407C2214yescomplemented
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×#11758222D412yes—
54C2×#11758222D412yes—
55C2×#11758222C2312yes—
56C22×Dic122D411yescharacteristic
57C22×D244D411yescharacteristic
58C22×C22⋊D61C2×C412yes—
59C22×C4×D61D412yes—
60#14519785—28no—
61#14519785—28no—
62#14519783—28no—
63#14519783—28no—
64C2×#11758194—21no—
65C2×#11758194—21no—
66C2×#11758194—21no—
67C2×#11758194—21no—
68C2×#11758194—21no—
69C2×#11758194—21no—
70C2×#11758194—21no—
71C2×#11758194—21no—
72C2×#11758194—21no—
73C2×#11758194D412yescomplemented
74C2×#11758194C2312yes—
75C2×#11758194C2312yes—
76C2×#11758189—24no—
77M16×D61—28no—
78M16×D61—28no—
79C22×#92418—21no—
80C22×#92418D412yescomplemented
81C2×C8×D61—24no—
82#14519775—22no—
83#14519773—22no—
84#14519766—22no—
85#14519764—22no—
86#14519760C2×C418yes—
87#14519758—24no—
88#14519756—24no—
89#14519753—24no—
90#14519751—24no—
91#14519749—28no—
92#14519748—24no—
93#14519746C2×C418yes—
94#14519745—24no—
95C4×C22⋊D61—28no—
96#14519736—21no—
97#14519736—21no—
98#14519736C2×C412yes—
99#14519736C2312yes—
100C2×C4⋊Dic61—21no—
101C2×C22⋊Dic61C2×C412yes—
102C2×C4×Dic61—21no—
103#14519695—24no—
104#14519693—24no—
105C22⋊#92418—28no—
106C2×#41×C61—21no—
107C2×#41×C61—21no—
108C2×#41×C61—21no—
109C2×#41×C61—21no—
110C2×#41×C61—21no—
111C2×#41×C61—21no—
112C2×#41×C61—21no—
113C2×#41×C61—21no—
114C2×#41×C61—21no—
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118C22×Q8×C61C2×C411yescharacteristic
119C22×D4×C61C2×C412yes—
120C22×D4×C61C2×C411yescharacteristic
121C23×C4×C61C2312yes—
122C23×C4×C61C2311yescharacteristic
123C2×M16×C61—21no—
124C2×M16×C61—21no—
125C2×M16×C61—21no—
126C2×M16×C61—21no—
127C2×M16×C61—21no—
128C2×M16×C61—21no—
129C2×M16×C61—21no—
130C2×M16×C61—21no—
131C2×M16×C61—21no—
132C2×M16×C61D412yescomplemented
133C2×M16×C61C2312yes—
134C2×M16×C61C2312yes—
135C22×C8×C61—21no—
136C22×C8×C61D412yescomplemented
137C22⋊C8×C61—28no—
138C24×C61C22×C412yes—
139C24×C61C22×C411yescharacteristic
140C23×D61C22⋊C412yes—
141#41×C61—41no—
142#41×C61—41no—
143#41×C61—41no—
144#41×C61—41no—
145#41×C61—41no—
146#41×C61—41no—
147#41×C61—41no—
148#41×C61—41no—
149#41×C61—41no—
150#41×C61—41no—
151#41×C61—41no—
152#41×C61—41no—
153#41×C61—41no—
154#41×C61—41no—
155#41×C61—41no—
156#41×C61—41no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61—21no—
163C2×D4×C61—22no—
164C2×D4×C61—22no—
165C2×D4×C61—22no—
166C2×D4×C61—22no—
167C2×D4×C61—22no—
168C2×D4×C61—22no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—21no—
172C2×D4×C61—21no—
173C2×D4×C61—21no—
174C2×D4×C61—21no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61C22×C412yes—
182C22×C4×C61C22×C411yescharacteristic
183C22×C4×C61C2×D411yescharacteristic
184C22×C4×C61C2×D411yescharacteristic
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61C2×D411yescharacteristic
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D411yescharacteristic
190C22×C4×C61C2×D411yescharacteristic
191C22×C4×C61#4111yescharacteristic
192C22×C4×C61#4111yescharacteristic
193C22×C4×C61#4111yescharacteristic
194C22×C4×C61#4111yescharacteristic
195C22×C4×C61C2411yescharacteristic
196C2×C22⋊D61—22no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—22no—
200C2×C22⋊D61—28no—
201C2×C22⋊D61C22⋊C414yes—
202C2×C22⋊D61C22×C414yes—
203C22×Dic61—22no—
204C22×Dic61C22⋊C412yes—
205#11758222—22no—
206#11758222—22no—
207#11758222—22no—
208#11758222—22no—
209#11758222—22no—
210#11758222—22no—
211#11758222—22no—
212#11758222—22no—
213#11758222—22no—
214#11758222—22no—
215#11758222—22no—
216#11758222—22no—
217#11758222—22no—
218#11758222—22no—
219#11758222—22no—
220#11758222—22no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244C22⋊C412yes—
226C2×D244C2×D412yes—
227C2×C4×D61—22no—
228C2×C4×D61—22no—
229C2×C4×D61—22no—
230C2×C4×D61—22no—
231C2×C4×D61C22⋊C414yes—
232C2×C4×D61C2×D414yes—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122C22⋊C412yes—
238C2×Dic122C2×D412yes—
239M16×C61—22no—
240M16×C61—22no—
241M16×C61—22no—
242M16×C61—22no—
243M16×C61—22no—
244M16×C61—22no—
245M16×C61—41no—
246M16×C61—41no—
247C2×C8×C61—22no—
248C2×C8×C61—22no—
249C2×C8×C61—22no—
250C2×C8×C61—41no—
251C2×C8×C61—41no—
252C2×C8×C61C2×D414yes—
253C22⋊Dic61—22no—
254C22⋊Dic61—28no—
255C22⋊Dic61C22×C414yes—
256#11758198—28no—
257C4⋊Dic61—22no—
258C4⋊Dic61—22no—
259#11758196—28no—
260C4×Dic61—22no—
261C4×Dic61—22no—
262#11758194—22no—
263#11758194—22no—
264#11758194—22no—
265#11758194—22no—
266#11758194—22no—
267#11758194—22no—
268#11758194—41no—
269#11758194—41no—
270C2×#92418—22no—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418—41no—
274C2×#92418—41no—
275C2×#92418C2×D414yes—
276#11758189—216no—
277C8×D61—216no—
278C23×C61—22no—
279C23×C61—22no—
280C23×C61—22no—
281C23×C61—81no—
282C23×C61—82no—
283C23×C61C2×C22⋊C411yescharacteristic
284C23×C61C2×C22⋊C411yescharacteristic
285C23×C61C4×D411yescharacteristic
286C23×C61C4×D411yescharacteristic
287C23×C61C4×D411yescharacteristic
288C23×C61C4×D411yescharacteristic
289C23×C61C23×C411yescharacteristic
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—82no—
293C22×D61C2×C22⋊C414yes—
294Q8×C61—41no—
295Q8×C61—41no—
296Q8×C61—41no—
297Q8×C61—41no—
298D4×C61—42no—
299D4×C61—42no—
300D4×C61—42no—
301D4×C61—42no—
302D4×C61—41no—
303D4×C61—41no—
304D4×C61—41no—
305D4×C61—41no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—42no—
313C2×C4×C61C2×C22⋊C411yescharacteristic
314C2×C4×C61C2×C22⋊C411yescharacteristic
315C2×C4×C61C4×D411yescharacteristic
316C2×C4×C61C4×D411yescharacteristic
317C2×C4×C61C4×D411yescharacteristic
318C2×C4×C61C4×D411yescharacteristic
319C2×C4×C61#12011yescharacteristic
320C2×C4×C61#12011yescharacteristic
321C2×C4×C61#12011yescharacteristic
322C2×C4×C61#12011yescharacteristic
323C2×C4×C61#12111yescharacteristic
324C2×C4×C61#12111yescharacteristic
325C2×C4×C61#12111yescharacteristic
326C2×C4×C61#12111yescharacteristic
327C2×C4×C61#12111yescharacteristic
328C2×C4×C61#12111yescharacteristic
329C2×C4×C61#12111yescharacteristic
330C2×C4×C61#12111yescharacteristic
331C2×C4×C61#12311yescharacteristic
332C2×C4×C61#12311yescharacteristic
333C2×C4×C61#12311yescharacteristic
334C2×C4×C61#12311yescharacteristic
335C2×C4×C61C22×D411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61C2×#4111yescharacteristic
341C22⋊D61—24no—
342C22⋊D61—24no—
343C22⋊D61—24no—
344C22⋊D61—24no—
345C22⋊D61—88no—
346C2×Dic61—22no—
347C2×Dic61—22no—
348C2×Dic61—24no—
349C2×Dic61—82no—
350C2×Dic61C2×C22⋊C414yes—
351D244—22no—
352D244—22no—
353D244—22no—
354D244—22no—
355C4×D61—24no—
356C4×D61—24no—
357C4×D61—24no—
358C4×D61—24no—
359Dic122—22no—
360Dic122—22no—
361Dic122—22no—
362Dic122—22no—
363C8×C61—24no—
364C8×C61—42no—
365#92418—24no—
366#92418—42no—
367#20964—611nomaximal, Sylow
368C22×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—44no—
376C22×C61—44no—
377C22×C61—44no—
378C22×C61—42no—
379C22×C61#38611yescharacteristic
380C22×C61#38611yescharacteristic
381C22×C61#38611yescharacteristic
382C22×C61#38611yescharacteristic
383C22×C61C22×C22⋊C411yescharacteristic
384C22×C61C2×C4×D411yescharacteristic
385C22×C61C2×C4×D411yescharacteristic
386C2×D61—24no—
387C2×D61—44no—
388C2×D61—44no—
389C2×D61—82no—
390C4×C61—42no—
391C4×C61#38611yescharacteristic
392C4×C61#38611yescharacteristic
393C4×C61#38611yescharacteristic
394C4×C61#38611yescharacteristic
395C4×C61C2×#12011yescharacteristic
396C4×C61C2×#12111yescharacteristic
397C4×C61C2×#12111yescharacteristic
398C4×C61C2×#12311yescharacteristic
399Dic61—24no—
400Dic61—44no—
401C2×#568—611no—
402#3449—611no—
403C2×#413—611no—
404#2879—611no—
405#2879D6111yescharacteristic, complemented
406#1891—618no—
407C2×#344—611no—
408C2×#344—611no—
409C2×C61—21no—
410C2×C61—21no—
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—21no—
414C2×C61—21no—
415C2×C61—21no—
416C2×C61—82no—
417C2×C61C2×#38611yescharacteristic
418D61—44no—
419C22×#41—611no—
420C22×#41C2×D6111yescharacteristic
421#568—614no—
422#568—1222no—
423#568—1222no—
424#568—1222no—
425C2×#131—1222no—
426C2×#131—1222no—
427C22×M16—611no—
428C22×M16—611no—
429C22×M16—1222no—
430C22×M16C2×D6111yescharacteristic
431C22×M16C2×D6111yescharacteristic
432#537—1222no—
433#536—612no—
434#536—1221no—
435#535—612no—
436#535—1221no—
437#534—614no—
438#532—1222no—
439#525—614no—
440#525—1222no—
441C2×#117—611no—
442#413—614no—
443#413—1222no—
444C2×#101—1221no—
445C2×#100—1221no—
446#408—22no—
447#408—22no—
448#408—1222no—
449#408—1222no—
450#407—614no—
451#407C2×D6114yescomplemented
452#344—614no—
453#344—614no—
454C61#2096411yescharacteristic, complemented, Sylow
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—612no—
468C2×#41—612no—
469C2×#41—612no—
470C2×#41—612no—
471C2×#41—1221no—
472C2×#41—1221no—
473C2×#41—1221no—
474C2×#41—1221no—
475C2×#41—1221no—
476C2×#41—1221no—
477C2×#41—1221no—
478C2×#41—1221no—
479C22×Q8—611no—
480C22×Q8C4×D6111yescharacteristic
481C22×D4—612no—
482C22×D4—611no—
483C22×D4C4×D6112yes—
484C22×D4C4×D6111yescharacteristic
485C23×C4—612no—
486C23×C4C22×D6112yes—
487C23×C4C22×D6111yescharacteristic
488#131—1228no—
489#131—1228no—
490#131—1228no—
491#131—1228no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—612no—
502C2×M16—612no—
503C2×M16—612no—
504C2×M16—1224no—
505C2×M16—1228no—
506C2×M16—1228no—
507C2×M16—1221no—
508C2×M16—1221no—
509C2×M16—1221no—
510C2×M16—1221no—
511C2×M16—1221no—
512C2×M16—1221no—
513C2×M16—1221no—
514C2×M16—1221no—
515C2×M16—1221no—
516C2×M16C22⋊D6112yescomplemented
517C2×M16C22×D6112yes—
518C2×M16C22×D6112yes—
519C22×C8—21no—
520C22×C8—612no—
521C22×C8—1224no—
522C22×C8—1221no—
523C22×C8C22⋊D6112yescomplemented
524C4⋊Q8—1222no—
525#127—1222no—
526#124—1222no—
527#124—1222no—
528#123—618no—
529#123—1224no—
530C22⋊Q8—1224no—
531C22⋊Q8—1224no—
532#121—1224no—
533#121—1224no—
534#121—1228no—
535#120—618no—
536#120—1224no—
537C4×D4—1228no—
538#117—612no—
539#117—612no—
540#117—1221no—
541#117—1221no—
542C2×C4⋊C4—1221no—
543C2×C22⋊C4—612no—
544C2×C42—1221no—
545#101—1224no—
546#100—1224no—
547C22⋊C8—28no—
548C22⋊C8—1228no—
549C24—612no—
550C24C2×C4×D6112yes—
551C24C2×C4×D6111yescharacteristic
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—1222no—
569#41—1222no—
570#41—1222no—
571#41—1222no—
572#41—1222no—
573#41—1222no—
574#41—1222no—
575#41—1222no—
576#41—1222no—
577#41—1222no—
578#41—1222no—
579#41—1222no—
580#41—1222no—
581#41—1222no—
582#41—1222no—
583#41—1222no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—612no—
591C2×Q8—612no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8—1221no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—614no—
609C2×D4—614no—
610C2×D4—612no—
611C2×D4—612no—
612C2×D4—1222no—
613C2×D4—1222no—
614C2×D4—1222no—
615C2×D4—1222no—
616C2×D4—1228no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4—1221no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—612no—
628C22×C4—614no—
629C22×C4—614no—
630C22×C4—1222no—
631C22×C4—1222no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4C2×C4×D6112yes—
636C22×C4C2×C4×D6111yescharacteristic
637C22×C4#1175822211yescharacteristic
638C22×C4#1175822211yescharacteristic
639C22×C4D4×D6111yescharacteristic
640C22×C4D4×D6111yescharacteristic
641C22×C4D4×D6111yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4D4×D6111yescharacteristic
645C22×C4#1175822411yescharacteristic
646C22×C4#1175822411yescharacteristic
647C22×C4C2×C22⋊D6111yescharacteristic
648C22×C4C2×C22⋊D6111yescharacteristic
649C22×C4C23×D6111yescharacteristic
650M16—22no—
651M16—22no—
652M16—22no—
653M16—22no—
654M16—22no—
655M16—22no—
656M16—41no—
657M16—41no—
658M16—12216no—
659M16—1222no—
660M16—1222no—
661M16—1222no—
662M16—1222no—
663M16—1222no—
664M16—1222no—
665M16—2441no—
666M16—2441no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—41no—
671C2×C8—41no—
672C2×C8—614no—
673C2×C8—12216no—
674C2×C8—1222no—
675C2×C8—1222no—
676C2×C8—1222no—
677C2×C8—2441no—
678C2×C8—2441no—
679C2×C8C2×C22⋊D6114yes—
680C4⋊C4—1228no—
681C4⋊C4—1222no—
682C4⋊C4—1222no—
683C22⋊C4—614no—
684C22⋊C4—1228no—
685C22⋊C4—1228no—
686C22⋊C4—1222no—
687C42—1222no—
688C42—1222no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—81no—
693C23—82no—
694C23—614no—
695C23—1222no—
696C23—1222no—
697C23—4882no—
698C23C22⋊C4×D6111yescharacteristic
699C23C22⋊C4×D6111yescharacteristic
700C23#1451973711yescharacteristic
701C23#1451973711yescharacteristic
702C23C4×C22⋊D6111yescharacteristic
703C23C4×C22⋊D6111yescharacteristic
704C23C22×C4×D6111yescharacteristic
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—1222no—
710Q8—1222no—
711Q8—1222no—
712Q8—1222no—
713D4—42no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—1224no—
722D4—1224no—
723D4—1224no—
724D4—1224no—
725D4—1222no—
726D4—1222no—
727D4—1222no—
728D4—1222no—
729D4—4888no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—614no—
738C2×C4—1222no—
739C2×C4—1222no—
740C2×C4—1224no—
741C2×C4—1224no—
742C2×C4—1224no—
743C2×C4—1224no—
744C2×C4—1224no—
745C2×C4—4882no—
746C2×C4C22⋊C4×D6111yescharacteristic
747C2×C4C22⋊C4×D6111yescharacteristic
748C2×C4#1451973711yescharacteristic
749C2×C4#1451973711yescharacteristic
750C2×C4C4×C22⋊D6111yescharacteristic
751C2×C4C4×C22⋊D6111yescharacteristic
752C2×C4#1451974511yescharacteristic
753C2×C4#1451974511yescharacteristic
754C2×C4#1451974511yescharacteristic
755C2×C4#1451974511yescharacteristic
756C2×C4#1451974811yescharacteristic
757C2×C4#1451974811yescharacteristic
758C2×C4#1451974811yescharacteristic
759C2×C4#1451974811yescharacteristic
760C2×C4#1451975011yescharacteristic
761C2×C4#1451975011yescharacteristic
762C2×C4#1451975011yescharacteristic
763C2×C4#1451975011yescharacteristic
764C2×C4#1451975911yescharacteristic
765C2×C4#1451975911yescharacteristic
766C2×C4#1451975911yescharacteristic
767C2×C4#1451975911yescharacteristic
768C2×C4C2×D4×D6111yescharacteristic
769C2×C4C2×D4×D6111yescharacteristic
770C2×C4C2×D4×D6111yescharacteristic
771C2×C4C22×C22⋊D6111yescharacteristic
772C2×C4C2×#1175822411yescharacteristic
773C2×C4C2×#1175822211yescharacteristic
774C8—24no—
775C8—42no—
776C8—1224no—
777C8—2442no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—42no—
789C22—1224no—
790C22—4882no—
791C22—2444no—
792C22—2444no—
793C22#1683963811yescharacteristic
794C22#1683963811yescharacteristic
795C22#1683963811yescharacteristic
796C22#1683963811yescharacteristic
797C22C2×C22⋊C4×D6111yescharacteristic
798C22C2×#1451973711yescharacteristic
799C22C2×C4×C22⋊D6111yescharacteristic
800C4—42no—
801C4—1224no—
802C4—2444no—
803C4#1683963811yescharacteristic
804C4#1683963811yescharacteristic
805C4#1683963811yescharacteristic
806C4#1683963811yescharacteristic
807C4C2×#1451974511yescharacteristic
808C4C2×#1451974811yescharacteristic
809C4C2×#1451975011yescharacteristic
810C4C2×#1451975911yescharacteristic
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—21no—
817C2—21no—
818C2—82no—
819C2—2444no—
820C2C2×#1683963811yescharacteristic
subgroupG/H
centerC4C2×#14519745
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#2879C2
socleC2×C61C2×#386
prime radical#21459148C2
cosocleC22×C4×C61C24
hypercenter#2879D61
hypocenterC61#20964
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ #2879

Complements

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

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. C2×#16839744C2semidirect
4. #21454264C2semidirect
5. #21446234C2semidirect
6. C2×#16839534C2semidirect
7. C2×#16839533C2semidirect
8. C61×#2879C2semidirect
35. #16839726C22semidirect
36. #16839534C22semidirect
37. #16839533C22semidirect
43. C61×#407C22semidirect
73. C2×#11758194D4semidirect
80. C22×#92418D4semidirect
132. C2×M16×C61D4semidirect
136. C22×C8×C61D4semidirect
405. #2879D61semidirect
451. #407C2×D61semidirect
454. C61#20964semidirect
516. C2×M16C22⋊D61semidirect
523. C22×C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168405282
#214591482
C2×#168397442
#214542642
#214462342
C2×#168395342
C2×#168395332
C61×#28792
#2096461