Finite Group Databasebeta

← #29681556

Subgroups — #29681556

Order 15616.

1708 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840528C211yesmaximal, characteristic, complemented
2#21459148C211yesmaximal, characteristic
3C2×#16839779C211yesmaximal, characteristic, complemented
4C2×#16839735C211yesmaximal, characteristic, complemented
5#21446199C218yesmaximal, complemented
6#21445530C211yesmaximal, characteristic, complemented
7#21445528C211yesmaximal, characteristic, complemented
8C2×C61×#421C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840528—22no—
11#16840528—22no—
12#16840528—22no—
13#16840528C2214yescomplemented
14C2×#14519785—22no—
15C2×#14519783—22no—
16C22×#11758194C2211yescharacteristic
17C2×M16×D61—22no—
18#16840340—22no—
19#16840336C412yescomplemented
20#16840333C412yescomplemented
21#16840329C412yescomplemented
22#16840326C412yescomplemented
23#16840321—22no—
24#16840308C2214yes—
25#16840273—22no—
26#16840269—22no—
27C2×#14519736C2211yescharacteristic
28C2×#14519736C2211yescharacteristic
29#16839779—22no—
30#16839779C2214yescomplemented
31C2×#14519704—22no—
32#16839735—22no—
33#16839735C2214yescomplemented
34C2×#14519691—22no—
35#16839523C2214yescomplemented
36#16839521C2214yescomplemented
37C22×#41×C61C2211yescharacteristic
38C22×M16×C61C2211yescharacteristic
39C2×#117×C61C2211yescharacteristic
40C61×#421—22no—
41C61×#421C2214yescomplemented
42C2×#104×C61—22no—
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×#11758222C2×C412yes—
52C2×#11758222D412yes—
53C2×#11758222D412yes—
54C2×#11758222C2312yes—
55C22×Dic122C2×C411yescharacteristic
56C22×D244C2×C411yescharacteristic
57C22×C22⋊D61D412yes—
58C22×C4×D61D412yes—
59#14519785—28no—
60#14519785—28no—
61#14519783—28no—
62#14519783—28no—
63C2×#11758194—21no—
64C2×#11758194—21no—
65C2×#11758194—21no—
66C2×#11758194D412yescomplemented
67C2×#11758194D412yescomplemented
68C2×#11758194C2312yes—
69C2×#11758189—24no—
70M16×D61—28no—
71M16×D61—28no—
72C22×#92418—21no—
73C2×C8×D61—24no—
74#14519775C2×C414yescomplemented
75#14519773C2×C414yescomplemented
76#14519766C2×C414yescomplemented
77#14519764C2×C414yescomplemented
78#14519760—24no—
79#14519758—24no—
80#14519756—24no—
81#14519753—24no—
82#14519751—24no—
83#14519749—28no—
84#14519748—24no—
85#14519746—24no—
86#14519745—24no—
87C4×C22⋊D61—28no—
88#14519736—21no—
89#14519736—21no—
90#14519736—21no—
91#14519736—21no—
92#14519736—21no—
93#14519736C2×C412yes—
94#14519736C2×C412yes—
95#14519736C2312yes—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61—21no—
98C2×C22⋊Dic61—21no—
99C2×C22⋊Dic61—21no—
100C2×C4×Dic61—21no—
101C2×C4×Dic61C2312yes—
102#14519704—28no—
103#14519691—28no—
104C2×#41×C61—21no—
105C2×#41×C61—21no—
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×C61C2×C412yes—
115C2×#41×C61C2312yes—
116C22×Q8×C61C2×C411yescharacteristic
117C22×D4×C61—21no—
118C22×D4×C61C2×C411yescharacteristic
119C23×C4×C61—21no—
120C23×C4×C61C2311yescharacteristic
121C2×M16×C61—21no—
122C2×M16×C61—21no—
123C2×M16×C61—21no—
124C2×M16×C61D412yescomplemented
125C2×M16×C61D412yescomplemented
126C2×M16×C61C2312yes—
127C22×C8×C61—21no—
128#117×C61—21no—
129#117×C61—21no—
130#117×C61—21no—
131#117×C61C2312yes—
132C2×C4⋊C4×C61—21no—
133C2×C22⋊C4×C61—21no—
134C2×C42×C61—21no—
135#104×C61—28no—
136C24×C61—21no—
137C24×C61C2×D411yescharacteristic
138C23×D61C22⋊C412yes—
139#41×C61—22no—
140#41×C61—22no—
141#41×C61—22no—
142#41×C61—22no—
143#41×C61—22no—
144#41×C61—22no—
145#41×C61—22no—
146#41×C61—22no—
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—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61C22×C412yes—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—41no—
169C2×D4×C61—41no—
170C2×D4×C61—41no—
171C2×D4×C61—41no—
172C2×D4×C61C22×C412yes—
173C22×C4×C61—21no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—41no—
177C22×C4×C61—41no—
178C22×C4×C61—41no—
179C22×C4×C61—41no—
180C22×C4×C61—41no—
181C22×C4×C61C22×C411yescharacteristic
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×C61#4111yescharacteristic
191C22×C4×C61#4111yescharacteristic
192C22×C4×C61#4111yescharacteristic
193C22×C4×C61#4111yescharacteristic
194C22×C4×C61C2411yescharacteristic
195C2×C22⋊D61—22no—
196C2×C22⋊D61—22no—
197C2×C22⋊D61—22no—
198C2×C22⋊D61—22no—
199C2×C22⋊D61—28no—
200C2×C22⋊D61C22⋊C414yes—
201C2×C22⋊D61C2×D414yes—
202C22×Dic61—22no—
203C22×Dic61—41no—
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×D244C22×C412yes—
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×Dic122C22×C412yes—
239M16×C61—22no—
240M16×C61—22no—
241M16×C61—22no—
242M16×C61C2×D414yes—
243C2×C8×C61—22no—
244C2×C8×C61—22no—
245C2×C8×C61—22no—
246C4⋊C4×C61—22no—
247C4⋊C4×C61—41no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—41no—
250C42×C61—22no—
251C42×C61—41no—
252C22⋊Dic61—22no—
253C22⋊Dic61—22no—
254C22⋊Dic61—28no—
255C22⋊Dic61—22no—
256C22⋊Dic61—41no—
257#11758198—28no—
258C4⋊Dic61—22no—
259C4⋊Dic61—22no—
260C4⋊Dic61—22no—
261C4⋊Dic61—41no—
262#11758196—28no—
263C4×Dic61—22no—
264C4×Dic61—22no—
265C4×Dic61—41no—
266C4×Dic61C22×C414yes—
267#11758194—22no—
268#11758194—22no—
269#11758194—22no—
270#11758194C2×D414yes—
271C2×#92418—22no—
272C2×#92418—22no—
273C2×#92418—22no—
274#11758189—216no—
275C8×D61—216no—
276C23×C61—22no—
277C23×C61—41no—
278C23×C61—41no—
279C23×C61—81no—
280C23×C61—82no—
281C23×C61C2×C22⋊C411yescharacteristic
282C23×C61C2×C22⋊C411yescharacteristic
283C23×C61#12111yescharacteristic
284C23×C61#12111yescharacteristic
285C23×C61#12111yescharacteristic
286C23×C61#12111yescharacteristic
287C23×C61C22×D411yescharacteristic
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—82no—
291C22×D61C2×C22⋊C414yes—
292Q8×C61—22no—
293Q8×C61—22no—
294Q8×C61—41no—
295Q8×C61—41no—
296D4×C61—22no—
297D4×C61—22no—
298D4×C61—42no—
299D4×C61—42no—
300D4×C61—42no—
301D4×C61—42no—
302D4×C61—41no—
303D4×C61—41no—
304C2×C4×C61—22no—
305C2×C4×C61—41no—
306C2×C4×C61—41no—
307C2×C4×C61—42no—
308C2×C4×C61—42no—
309C2×C4×C61—42no—
310C2×C4×C61—42no—
311C2×C4×C61—42no—
312C2×C4×C61—82no—
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×C61C4×D411yescharacteristic
320C2×C4×C61C4×D411yescharacteristic
321C2×C4×C61C4×D411yescharacteristic
322C2×C4×C61C4×D411yescharacteristic
323C2×C4×C61#12011yescharacteristic
324C2×C4×C61#12011yescharacteristic
325C2×C4×C61#12011yescharacteristic
326C2×C4×C61#12011yescharacteristic
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×C61C23×C411yescharacteristic
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—42no—
350C2×Dic61—82no—
351C2×Dic61—82no—
352C2×Dic61C2×C22⋊C414yes—
353D244—22no—
354D244—22no—
355D244—22no—
356D244—22no—
357C4×D61—24no—
358C4×D61—24no—
359C4×D61—24no—
360C4×D61—24no—
361Dic122—22no—
362Dic122—22no—
363Dic122—22no—
364Dic122—22no—
365C8×C61—24no—
366#92418—24no—
367#20947—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—42no—
377C22×C61—82no—
378C22×C61—82no—
379C22×C61#38611yescharacteristic
380C22×C61#38611yescharacteristic
381C22×C61#38611yescharacteristic
382C22×C61#38611yescharacteristic
383C22×C61C22×C22⋊C411yescharacteristic
384C22×C61C2×#12111yescharacteristic
385C22×C61C2×#12111yescharacteristic
386C2×D61—24no—
387C2×D61—44no—
388C2×D61—44no—
389C2×D61—82no—
390C4×C61—42no—
391C4×C61—82no—
392C4×C61#38611yescharacteristic
393C4×C61#38611yescharacteristic
394C4×C61#38611yescharacteristic
395C4×C61#38611yescharacteristic
396C4×C61C2×C4×D411yescharacteristic
397C4×C61C2×C4×D411yescharacteristic
398C4×C61C2×#12011yescharacteristic
399C4×C61C2×#12311yescharacteristic
400Dic61—24no—
401Dic61—44no—
402Dic61—82no—
403C2×#568—611no—
404#3449—611no—
405C2×#421—611no—
406C2×#421D6111yescharacteristic, complemented
407C2×#410—611no—
408#1884—618no—
409#1733—611no—
410#1733—611no—
411C2×C61—21no—
412C2×C61—21no—
413C2×C61—21no—
414C2×C61—21no—
415C2×C61—21no—
416C2×C61—21no—
417C2×C61—21no—
418C2×C61—82no—
419C2×C61C2×#38611yescharacteristic
420D61—44no—
421C22×#41—611no—
422C22×#41C2×D6111yescharacteristic
423#568—614no—
424#568—1222no—
425#568—1222no—
426#568—1222no—
427C2×#131—1222no—
428C2×#131—1222no—
429C22×M16—611no—
430C22×M16—1222no—
431C22×M16C2×D6111yescharacteristic
432#537—1222no—
433#536—612no—
434#536—612no—
435#535—612no—
436#535—612no—
437#534—1222no—
438#532—614no—
439#525—1222no—
440#525—1222no—
441C2×#117—611no—
442C2×#117—611no—
443C2×#117C2×D6111yescharacteristic
444#421—22no—
445#421—614no—
446#421—1222no—
447#421C2×D6114yescomplemented
448C2×#104—22no—
449C2×#104—1222no—
450#410—614no—
451#410—1222no—
452C2×#99—1222no—
453#339—614no—
454#339—614no—
455C61#2094711yescharacteristic, complemented, Sylow
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—612no—
467C2×#41—612no—
468C2×#41—612no—
469C2×#41—612no—
470C2×#41—1221no—
471C2×#41—1221no—
472C2×#41—1221no—
473C2×#41—1221no—
474C2×#41—1221no—
475C2×#41—1221no—
476C2×#41—1221no—
477C2×#41—1221no—
478C2×#41C4×D6112yes—
479C2×#41C22×D6112yes—
480C22×Q8—611no—
481C22×Q8C4×D6111yescharacteristic
482C22×D4—21no—
483C22×D4—612no—
484C22×D4—611no—
485C22×D4C4×D6111yescharacteristic
486C23×C4—21no—
487C23×C4—612no—
488C23×C4C22×D6111yescharacteristic
489#131—1228no—
490#131—1228no—
491#131—1228no—
492#131—1228no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—612no—
497C2×M16—612no—
498C2×M16—612no—
499C2×M16—1224no—
500C2×M16—1228no—
501C2×M16—1228no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C2×M16C22⋊D6112yescomplemented
506C2×M16C22⋊D6112yescomplemented
507C2×M16C22×D6112yes—
508C22×C8—21no—
509C22×C8—1224no—
510C22×C8—1221no—
511C4⋊Q8—614no—
512#127—614no—
513#124—614no—
514#124—614no—
515#123—1224no—
516#123—1224no—
517C22⋊Q8—1224no—
518C22⋊Q8—1224no—
519#121—1224no—
520#121—1224no—
521#121—1228no—
522#120—1224no—
523#120—1224no—
524C4×D4—1228no—
525#117—21no—
526#117—21no—
527#117—21no—
528#117—612no—
529#117—612no—
530#117—612no—
531#117—1221no—
532#117—1221no—
533#117—1221no—
534#117—1221no—
535#117—1221no—
536#117C22×D6112yes—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—1221no—
539C2×C4⋊C4—1221no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—1221no—
542C2×C22⋊C4—1221no—
543C2×C42—21no—
544C2×C42—612no—
545C2×C42—1221no—
546#104—28no—
547#104—1228no—
548#99—1228no—
549C24—21no—
550C24—612no—
551C24D4×D6111yescharacteristic
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
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—612no—
590C2×Q8—612no—
591C2×Q8—1221no—
592C2×Q8—1221no—
593C2×Q8—1221no—
594C2×Q8—1221no—
595C2×Q8C2×C4×D6112yes—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—614no—
608C2×D4—614no—
609C2×D4—612no—
610C2×D4—612no—
611C2×D4—1222no—
612C2×D4—1222no—
613C2×D4—1222no—
614C2×D4—1222no—
615C2×D4—1228no—
616C2×D4—1221no—
617C2×D4—1221no—
618C2×D4—1221no—
619C2×D4—1221no—
620C2×D4C2×C4×D6112yes—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—612no—
630C22×C4—614no—
631C22×C4—614no—
632C22×C4—1222no—
633C22×C4—1222no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—2441no—
638C22×C4C2×C4×D6111yescharacteristic
639C22×C4C2×C4×D6111yescharacteristic
640C22×C4#1175822211yescharacteristic
641C22×C4#1175822211yescharacteristic
642C22×C4D4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4D4×D6111yescharacteristic
645C22×C4D4×D6111yescharacteristic
646C22×C4D4×D6111yescharacteristic
647C22×C4#1175822411yescharacteristic
648C22×C4#1175822411yescharacteristic
649C22×C4C2×C22⋊D6111yescharacteristic
650C22×C4C2×C22⋊D6111yescharacteristic
651C22×C4C23×D6111yescharacteristic
652M16—22no—
653M16—22no—
654M16—22no—
655M16—614no—
656M16—12216no—
657M16—1222no—
658M16—1222no—
659M16—1222no—
660M16C2×C22⋊D6114yes—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—12216no—
665C2×C8—1222no—
666C2×C8—1222no—
667C2×C8—1222no—
668C4⋊C4—22no—
669C4⋊C4—41no—
670C4⋊C4—1228no—
671C4⋊C4—1222no—
672C4⋊C4—1222no—
673C4⋊C4—1222no—
674C4⋊C4—2441no—
675C22⋊C4—22no—
676C22⋊C4—41no—
677C22⋊C4—1228no—
678C22⋊C4—1228no—
679C22⋊C4—1222no—
680C22⋊C4—1222no—
681C22⋊C4—1222no—
682C22⋊C4—2441no—
683C42—22no—
684C42—41no—
685C42—614no—
686C42—1222no—
687C42—1222no—
688C42—2441no—
689C23—22no—
690C23—41no—
691C23—41no—
692C23—81no—
693C23—82no—
694C23—614no—
695C23—1222no—
696C23—1222no—
697C23—4882no—
698C23C22⋊C4×D6111yescharacteristic
699C23C22⋊C4×D6111yescharacteristic
700C23#1451974811yescharacteristic
701C23#1451974811yescharacteristic
702C23#1451975011yescharacteristic
703C23#1451975011yescharacteristic
704C23C2×D4×D6111yescharacteristic
705Q8—22no—
706Q8—22no—
707Q8—41no—
708Q8—41no—
709Q8—1222no—
710Q8—1222no—
711Q8—1222no—
712Q8—1222no—
713D4—22no—
714D4—22no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—42no—
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—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—82no—
739C2×C4—614no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1224no—
743C2×C4—1224no—
744C2×C4—1224no—
745C2×C4—1224no—
746C2×C4—1224no—
747C2×C4—4882no—
748C2×C4—4882no—
749C2×C4—2442no—
750C2×C4C22⋊C4×D6111yescharacteristic
751C2×C4C22⋊C4×D6111yescharacteristic
752C2×C4#1451973711yescharacteristic
753C2×C4#1451973711yescharacteristic
754C2×C4#1451973711yescharacteristic
755C2×C4#1451973711yescharacteristic
756C2×C4C4×C22⋊D6111yescharacteristic
757C2×C4C4×C22⋊D6111yescharacteristic
758C2×C4C4×C22⋊D6111yescharacteristic
759C2×C4C4×C22⋊D6111yescharacteristic
760C2×C4#1451974511yescharacteristic
761C2×C4#1451974511yescharacteristic
762C2×C4#1451974511yescharacteristic
763C2×C4#1451974511yescharacteristic
764C2×C4#1451974811yescharacteristic
765C2×C4#1451974811yescharacteristic
766C2×C4#1451975011yescharacteristic
767C2×C4#1451975011yescharacteristic
768C2×C4#1451975911yescharacteristic
769C2×C4#1451975911yescharacteristic
770C2×C4#1451975911yescharacteristic
771C2×C4#1451975911yescharacteristic
772C2×C4C22×C4×D6111yescharacteristic
773C2×C4C2×D4×D6111yescharacteristic
774C2×C4C2×D4×D6111yescharacteristic
775C2×C4C22×C22⋊D6111yescharacteristic
776C2×C4C2×#1175822411yescharacteristic
777C2×C4C2×#1175822211yescharacteristic
778C8—24no—
779C8—1224no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—44no—
788C22—42no—
789C22—82no—
790C22—82no—
791C22—1224no—
792C22—4882no—
793C22—2444no—
794C22—2444no—
795C22#1683963811yescharacteristic
796C22#1683963811yescharacteristic
797C22#1683963811yescharacteristic
798C22#1683963811yescharacteristic
799C22C2×C22⋊C4×D6111yescharacteristic
800C22C2×#1451974811yescharacteristic
801C22C2×#1451975011yescharacteristic
802C4—42no—
803C4—82no—
804C4—1224no—
805C4—4882no—
806C4—2444no—
807C4#1683963811yescharacteristic
808C4#1683963811yescharacteristic
809C4#1683963811yescharacteristic
810C4#1683963811yescharacteristic
811C4C2×#1451973711yescharacteristic
812C4C2×C4×C22⋊D6111yescharacteristic
813C4C2×#1451974511yescharacteristic
814C4C2×#1451975911yescharacteristic
815C2—21no—
816C2—21no—
817C2—21no—
818C2—21no—
819C2—21no—
820C2—21no—
821C2—21no—
822C2—82no—
823C2—2444no—
824C2C2×#1683963811yescharacteristic
subgroupG/H
centerC4C2×#14519745
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#421C2
socleC2×C61C2×#386
prime radical#21459148C2
cosocleC22×C4×C61C24
hypercenterC2×#421D61
hypocenterC61#20947
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#16840528C2semidirect
3. C2×#16839779C2semidirect
4. C2×#16839735C2semidirect
5. #21446199C2semidirect
6. #21445530C2semidirect
7. #21445528C2semidirect
8. C2×C61×#421C2semidirect
13. #16840528C22semidirect
19. #16840336C4semidirect
20. #16840333C4semidirect
21. #16840329C4semidirect
22. #16840326C4semidirect
30. #16839779C22semidirect
33. #16839735C22semidirect
35. #16839523C22semidirect
36. #16839521C22semidirect
41. C61×#421C22semidirect
66. C2×#11758194D4semidirect
67. C2×#11758194D4semidirect
74. #14519775C2×C4semidirect
75. #14519773C2×C4semidirect
76. #14519766C2×C4semidirect
77. #14519764C2×C4semidirect
124. C2×M16×C61D4semidirect
125. C2×M16×C61D4semidirect
406. C2×#421D61semidirect
447. #421C2×D61semidirect
455. C61#20947semidirect
505. C2×M16C22⋊D61semidirect
506. C2×M16C22⋊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×#168397792
C2×#168397352
#214461992
#214455302
#214455282
C2×C61×#4212
#2094761