Finite Group Databasebeta

← C2×#21446877 #29707012

Subgroups — C2×#21446877 #29707012

Order 15616.

1926 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840560C211yesmaximal, characteristic
2C2×#16840336C211yesmaximal, characteristic, complemented
3C2×#16839778C211yesmaximal, characteristic, complemented
4C2×#16839771C211yesmaximal, characteristic, complemented
5C2×#16839736C211yesmaximal, characteristic, complemented
6#21446877C218yesmaximal, direct product factor
7C2×#16839534C211yesmaximal, characteristic, complemented
8C22×#137×C61C211yesmaximal, characteristic, complemented
9C22×#11758222C2211yescharacteristic
10#16840560—22no—
11#16840560—22no—
12#16840560—22no—
13#16840560C2214yes—
14C2×#14519808—21no—
15C2×#14519807—21no—
16C2×#14519803—21no—
17C2×#14519802—21no—
18C2×#14519797—22no—
19C22×#11758194C2211yescharacteristic
20#16840336—22no—
21#16840336—22no—
22#16840336—22no—
23#16840336C2214yescomplemented
24C2×#14519775—21no—
25C2×#14519766—21no—
26C2×#14519760—22no—
27C2×#14519753—22no—
28C2×#14519736C2211yescharacteristic
29C2×#14519736C2211yescharacteristic
30#16839778—22no—
31#16839778C2214yescomplemented
32C2×#14519703—22no—
33#16839771—22no—
34#16839771C2214yescomplemented
35C2×#14519701—22no—
36#16839736—22no—
37#16839736C2214yescomplemented
38C2×#14519692—22no—
39#16839534C2214yescomplemented
40C22×#41×C61C2211yescharacteristic
41C23×Q8×C61C2211yescharacteristic
42C2×#137×C61—22no—
43C2×#137×C61—22no—
44C2×#137×C61—22no—
45C2×#137×C61—22no—
46C2×#137×C61—22no—
47C2×#137×C61C2214yescomplemented
48C22×Q16×C61—21no—
49C22×SD16×C61—21no—
50C22×M16×C61C2211yescharacteristic
51C2×#11758222—21no—
52C2×#11758222—21no—
53C2×#11758222—21no—
54C2×#11758222—21no—
55C2×#11758222—21no—
56C2×#11758222—21no—
57C2×#11758222—21no—
58C2×#11758222—21no—
59C2×#11758222—21no—
60C2×#11758222—21no—
61C2×#11758222D412yes—
62C2×#11758222C2312yes—
63C22×Dic122D411yescharacteristic
64C22×D244D411yescharacteristic
65C22×C22⋊D61—21no—
66C22×C4×D61—21no—
67#14519808—24no—
68#14519808—24no—
69#14519807—24no—
70#14519807—24no—
71#14519803—24no—
72#14519803—24no—
73#14519802—24no—
74#14519802—24no—
75#14519797—28no—
76#14519797—28no—
77C2×#11758202—22no—
78C2×#11758200—22no—
79C2×#11758201—22no—
80C2×#11758199—22no—
81C2×#11758194—21no—
82C2×#11758194—21no—
83C2×#11758194—21no—
84C2×#11758194—21no—
85C2×#11758194D412yes—
86C2×#11758194C2312yes—
87C22×#92418D412yes—
88#14519775—24no—
89#14519775—24no—
90#14519766—24no—
91#14519766—24no—
92#14519760—28no—
93#14519760—28no—
94#14519753—28no—
95#14519753—28no—
96#14519736—21no—
97#14519736—21no—
98#14519736—21no—
99#14519736—21no—
100#14519736—21no—
101#14519736D412yes—
102#14519736C2312yes—
103#14519736C2312yes—
104C2×C4⋊Dic61—21no—
105C2×C4⋊Dic61—21no—
106C2×#11758196—24no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61D412yes—
109C2×#11758198—24no—
110C2×C4×Dic61—21no—
111C2×C4×Dic61—21no—
112#14519703—28no—
113#14519701—28no—
114#14519692—28no—
115C2×#41×C61—21no—
116C2×#41×C61—21no—
117C2×#41×C61—21no—
118C2×#41×C61—21no—
119C2×#41×C61—21no—
120C2×#41×C61—21no—
121C2×#41×C61—21no—
122C2×#41×C61—21no—
123C2×#41×C61—21no—
124C2×#41×C61—21no—
125C2×#41×C61D412yes—
126C2×#41×C61C2312yes—
127C22×Q8×C61—21no—
128C22×Q8×C61—21no—
129C22×Q8×C61—21no—
130C22×Q8×C61—21no—
131C22×Q8×C61—21no—
132C22×Q8×C61—21no—
133C22×Q8×C61—21no—
134C22×Q8×C61—21no—
135C22×Q8×C61—21no—
136C22×Q8×C61—21no—
137C22×Q8×C61—21no—
138C22×Q8×C61D411yescharacteristic
139C22×Q8×C61D412yes—
140C22×Q8×C61D412yes—
141C22×Q8×C61C2312yes—
142C22×D4×C61—21no—
143C22×D4×C61D411yescharacteristic
144C23×C4×C61—21no—
145C23×C4×C61—21no—
146C23×C4×C61C2311yescharacteristic
147#137×C61—28no—
148#137×C61—28no—
149#137×C61—28no—
150#137×C61—28no—
151C2×Q16×C61—24no—
152C2×Q16×C61—24no—
153C2×Q16×C61—24no—
154C2×SD16×C61—24no—
155C2×SD16×C61—24no—
156C2×SD16×C61—24no—
157C2×M16×C61—21no—
158C2×M16×C61—21no—
159C2×M16×C61—21no—
160C2×M16×C61D412yes—
161C2×M16×C61D412yes—
162C2×M16×C61C2312yes—
163C22×C8×C61—21no—
164C24×C61—21no—
165C24×C61C2×D411yescharacteristic
166C23×D61—21no—
167#41×C61—22no—
168#41×C61—22no—
169#41×C61—22no—
170#41×C61—22no—
171#41×C61—22no—
172#41×C61—22no—
173#41×C61—22no—
174#41×C61—22no—
175#41×C61—41no—
176#41×C61—41no—
177#41×C61—41no—
178#41×C61—41no—
179#41×C61—41no—
180#41×C61—41no—
181#41×C61—41no—
182#41×C61—41no—
183C2×Q8×C61—22no—
184C2×Q8×C61—22no—
185C2×Q8×C61—21no—
186C2×Q8×C61—22no—
187C2×Q8×C61—21no—
188C2×Q8×C61—22no—
189C2×Q8×C61—22no—
190C2×Q8×C61—21no—
191C2×Q8×C61—21no—
192C2×Q8×C61—22no—
193C2×Q8×C61—22no—
194C2×Q8×C61—21no—
195C2×Q8×C61—22no—
196C2×Q8×C61—22no—
197C2×Q8×C61—22no—
198C2×Q8×C61—22no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61—22no—
202C2×Q8×C61—22no—
203C2×Q8×C61—41no—
204C2×Q8×C61—41no—
205C2×Q8×C61—41no—
206C2×Q8×C61—41no—
207C2×Q8×C61—41no—
208C2×Q8×C61—41no—
209C2×Q8×C61—41no—
210C2×Q8×C61—41no—
211C2×Q8×C61—41no—
212C2×Q8×C61—41no—
213C2×Q8×C61—41no—
214C2×Q8×C61—41no—
215C2×Q8×C61C2×D412yes—
216C2×Q8×C61C2×D414yes—
217C2×D4×C61—22no—
218C2×D4×C61—22no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—21no—
222C2×D4×C61—21no—
223C2×D4×C61—21no—
224C2×D4×C61—41no—
225C2×D4×C61—41no—
226C2×D4×C61—41no—
227C2×D4×C61—41no—
228C2×D4×C61C2×D412yes—
229C22×C4×C61—22no—
230C22×C4×C61—22no—
231C22×C4×C61—21no—
232C22×C4×C61—22no—
233C22×C4×C61—22no—
234C22×C4×C61—22no—
235C22×C4×C61—41no—
236C22×C4×C61—41no—
237C22×C4×C61—41no—
238C22×C4×C61—41no—
239C22×C4×C61—41no—
240C22×C4×C61—41no—
241C22×C4×C61—41no—
242C22×C4×C61—41no—
243C22×C4×C61C2×D411yescharacteristic
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61#4111yescharacteristic
255C22×C4×C61#4111yescharacteristic
256C22×C4×C61C2411yescharacteristic
257C2×C22⋊D61—22no—
258C2×C22⋊D61—22no—
259C2×C22⋊D61—41no—
260C2×C22⋊D61—41no—
261C2×C22⋊D61—41no—
262C2×C22⋊D61—41no—
263C22×Dic61—21no—
264C22×Dic61—22no—
265C22×Dic61—41no—
266#11758222—22no—
267#11758222—22no—
268#11758222—22no—
269#11758222—22no—
270#11758222—22no—
271#11758222—22no—
272#11758222—22no—
273#11758222—22no—
274#11758222—41no—
275#11758222—41no—
276#11758222—41no—
277#11758222—41no—
278#11758222—41no—
279#11758222—41no—
280#11758222—41no—
281#11758222—41no—
282C2×D244—21no—
283C2×D244—21no—
284C2×D244—21no—
285C2×D244—21no—
286C2×D244—21no—
287C2×D244C2×D412yes—
288C2×C4×D61—22no—
289C2×C4×D61—22no—
290C2×C4×D61—41no—
291C2×C4×D61—41no—
292C2×C4×D61—41no—
293C2×C4×D61—41no—
294C2×Dic122—21no—
295C2×Dic122—21no—
296C2×Dic122—21no—
297C2×Dic122—21no—
298C2×Dic122—21no—
299C2×Dic122C2×D412yes—
300Q16×C61—216no—
301SD16×C61—216no—
302M16×C61—22no—
303M16×C61—22no—
304M16×C61—22no—
305M16×C61C2×D414yes—
306C2×C8×C61—22no—
307C2×C8×C61—22no—
308C2×C8×C61—22no—
309C22⋊Dic61—22no—
310C22⋊Dic61—22no—
311C22⋊Dic61—41no—
312C22⋊Dic61C2×D414yes—
313#11758202—28no—
314#11758201—28no—
315#11758200—28no—
316#11758199—28no—
317#11758198—216no—
318C4⋊Dic61—22no—
319C4⋊Dic61—22no—
320C4⋊Dic61—22no—
321C4⋊Dic61—41no—
322#11758196—216no—
323C4×Dic61—22no—
324C4×Dic61—22no—
325C4×Dic61—22no—
326C4×Dic61—41no—
327#11758194—22no—
328#11758194—22no—
329#11758194—22no—
330#11758194—22no—
331C2×#92418—22no—
332C2×#92418—22no—
333C2×#92418C2×D414yes—
334C23×C61—22no—
335C23×C61—42no—
336C23×C61—41no—
337C23×C61—41no—
338C23×C61—82no—
339C23×C61#12011yescharacteristic
340C23×C61#12011yescharacteristic
341C23×C61#12111yescharacteristic
342C23×C61#12111yescharacteristic
343C23×C61#12711yescharacteristic
344C23×C61#12711yescharacteristic
345C23×C61C22×D411yescharacteristic
346C22×D61—22no—
347C22×D61—44no—
348C22×D61—41no—
349C22×D61—41no—
350Q8×C61—22no—
351Q8×C61—24no—
352Q8×C61—22no—
353Q8×C61—24no—
354Q8×C61—42no—
355Q8×C61—42no—
356Q8×C61—42no—
357Q8×C61—42no—
358Q8×C61—42no—
359Q8×C61—42no—
360Q8×C61—41no—
361Q8×C61—41no—
362D4×C61—22no—
363D4×C61—22no—
364D4×C61—42no—
365D4×C61—42no—
366D4×C61—42no—
367D4×C61—42no—
368D4×C61—41no—
369D4×C61—41no—
370C2×C4×C61—24no—
371C2×C4×C61—22no—
372C2×C4×C61—42no—
373C2×C4×C61—42no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—42no—
377C2×C4×C61—42no—
378C2×C4×C61—42no—
379C2×C4×C61—42no—
380C2×C4×C61—42no—
381C2×C4×C61—42no—
382C2×C4×C61—42no—
383C2×C4×C61—42no—
384C2×C4×C61#12011yescharacteristic
385C2×C4×C61#12011yescharacteristic
386C2×C4×C61#12011yescharacteristic
387C2×C4×C61#12011yescharacteristic
388C2×C4×C61#12011yescharacteristic
389C2×C4×C61#12011yescharacteristic
390C2×C4×C61#12011yescharacteristic
391C2×C4×C61#12011yescharacteristic
392C2×C4×C61#12011yescharacteristic
393C2×C4×C61#12011yescharacteristic
394C2×C4×C61#12111yescharacteristic
395C2×C4×C61#12111yescharacteristic
396C2×C4×C61#12111yescharacteristic
397C2×C4×C61#12111yescharacteristic
398C2×C4×C61#12111yescharacteristic
399C2×C4×C61#12111yescharacteristic
400C2×C4×C61#12111yescharacteristic
401C2×C4×C61#12111yescharacteristic
402C2×C4×C61#12111yescharacteristic
403C2×C4×C61#12111yescharacteristic
404C2×C4×C61#12711yescharacteristic
405C2×C4×C61#12711yescharacteristic
406C2×C4×C61C22×D411yescharacteristic
407C2×C4×C61C22×D411yescharacteristic
408C2×C4×C61C22×D411yescharacteristic
409C2×C4×C61C22×D411yescharacteristic
410C2×C4×C61C22×D411yescharacteristic
411C2×C4×C61C2×#4111yescharacteristic
412C22⋊D61—42no—
413C22⋊D61—42no—
414C22⋊D61—42no—
415C22⋊D61—42no—
416C2×Dic61—24no—
417C2×Dic61—22no—
418C2×Dic61—44no—
419C2×Dic61—41no—
420C2×Dic61—41no—
421C2×Dic61—42no—
422C2×Dic61—82no—
423D244—22no—
424D244—22no—
425D244—41no—
426D244—41no—
427C4×D61—42no—
428C4×D61—42no—
429C4×D61—42no—
430C4×D61—42no—
431Dic122—22no—
432Dic122—22no—
433Dic122—41no—
434Dic122—41no—
435C8×C61—24no—
436#92418—24no—
437C2×#2009—611nomaximal, Sylow
438C22×C61—22no—
439C22×C61—22no—
440C22×C61—22no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—41no—
444C22×C61—41no—
445C22×C61—42no—
446C22×C61—82no—
447C22×C61—82no—
448C22×C61—82no—
449C22×C61#39211yescharacteristic
450C22×C61#39211yescharacteristic
451C22×C61#39211yescharacteristic
452C22×C61#39211yescharacteristic
453C22×C61C2×#12011yescharacteristic
454C22×C61C2×#12111yescharacteristic
455C22×C61C2×#12711yescharacteristic
456C2×D61—44no—
457C2×D61—42no—
458C2×D61—82no—
459C2×D61—82no—
460C4×C61—42no—
461C4×C61—44no—
462C4×C61#39211yescharacteristic
463C4×C61#39211yescharacteristic
464C4×C61#39211yescharacteristic
465C4×C61#39211yescharacteristic
466C4×C61C2×#12011yescharacteristic
467C4×C61C2×#12011yescharacteristic
468C4×C61C2×#12111yescharacteristic
469C4×C61C2×#12111yescharacteristic
470Dic61—44no—
471Dic61—42no—
472Dic61—82no—
473C2×#575—611no—
474C22×#137D6111yescharacteristic, complemented
475C2×#536—611no—
476C2×#421—611no—
477C2×#419—611no—
478C2×#410—611no—
479#2009—618no—
480C2×#344—611no—
481C2×C61—21no—
482C2×C61—21no—
483C2×C61—21no—
484C2×C61—21no—
485C2×C61—21no—
486C2×C61—21no—
487C2×C61—82no—
488C2×C61#200912yescomplemented
489C2×C61C2×#39211yescharacteristic
490D61—82no—
491C22×#41—611no—
492C22×#41C2×D6111yescharacteristic
493C23×Q8C2×D6111yescharacteristic
494#575—614no—
495#575—1222no—
496#575—1222no—
497#575—1222no—
498C2×#137—22no—
499C2×#137—22no—
500C2×#137—22no—
501C2×#137—22no—
502C2×#137—22no—
503C2×#137—1221no—
504C2×#137—1221no—
505C2×#137C2×D6114yescomplemented
506C2×AGL(1,ℤ/8)—1221no—
507C2×AGL(1,ℤ/8)—1221no—
508C2×#135—1222no—
509C22×Q16—21no—
510C22×SD16—21no—
511C22×M16—611no—
512C22×M16C2×D6111yescharacteristic
513#536—614no—
514#536—1222no—
515#536—1222no—
516#536—1222no—
517C2×C4⋊Q8—1221no—
518C2×#124—1221no—
519C2×#123—1222no—
520C2×C22⋊Q8—1222no—
521C2×#117—611no—
522C2×#117—611no—
523#421—614no—
524#421—1222no—
525C2×#104—1222no—
526#419—614no—
527#419—1222no—
528C2×#103—1222no—
529#410—614no—
530#410—1222no—
531C2×#99—1222no—
532#344—614no—
533C61C2×#200911yescharacteristic, complemented, Sylow
534C2×#41—21no—
535C2×#41—21no—
536C2×#41—21no—
537C2×#41—21no—
538C2×#41—21no—
539C2×#41—21no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—21no—
543C2×#41—21no—
544C2×#41—612no—
545C2×#41—612no—
546C2×#41—1221no—
547C2×#41—1221no—
548C2×#41—1221no—
549C2×#41—1221no—
550C2×#41—1221no—
551C2×#41—1221no—
552C2×#41—1221no—
553C2×#41—1221no—
554C2×#41—1221no—
555C2×#41—1221no—
556C2×#41C22⋊D6112yes—
557C2×#41C22×D6112yes—
558C22×Q8—21no—
559C22×Q8—21no—
560C22×Q8—21no—
561C22×Q8—21no—
562C22×Q8—21no—
563C22×Q8—21no—
564C22×Q8—21no—
565C22×Q8—21no—
566C22×Q8—21no—
567C22×Q8—21no—
568C22×Q8—21no—
569C22×Q8—611no—
570C22×Q8C22⋊D6112yes—
571C22×Q8C22⋊D6112yes—
572C22×Q8C22⋊D6111yescharacteristic
573C22×Q8C22×D6112yes—
574C22×D4—21no—
575C22×D4—611no—
576C22×D4—1221no—
577C22×D4C22⋊D6111yescharacteristic
578C23×C4—21no—
579C23×C4—21no—
580C23×C4—1221no—
581C23×C4C22×D6111yescharacteristic
582#137—28no—
583#137—28no—
584#137—28no—
585#137—28no—
586#137—1224no—
587#137—1224no—
588#137—1224no—
589#137—1224no—
590AGL(1,ℤ/8)—1224no—
591AGL(1,ℤ/8)—1224no—
592AGL(1,ℤ/8)—1224no—
593AGL(1,ℤ/8)—1224no—
594#135—1228no—
595#135—1228no—
596C2×Q16—24no—
597C2×Q16—24no—
598C2×Q16—24no—
599C2×Q16—1222no—
600C2×SD16—24no—
601C2×SD16—24no—
602C2×SD16—24no—
603C2×SD16—1222no—
604C2×SD16—1222no—
605C2×D8—1222no—
606C2×M16—21no—
607C2×M16—21no—
608C2×M16—21no—
609C2×M16—612no—
610C2×M16—612no—
611C2×M16—1221no—
612C2×M16—1221no—
613C2×M16—1221no—
614C2×M16—1221no—
615C2×M16C22⋊D6112yes—
616C2×M16C22⋊D6112yes—
617C2×M16C22×D6112yes—
618C22×C8—21no—
619C22×C8—612no—
620C4⋊Q8—1224no—
621C4⋊Q8—1224no—
622#124—1224no—
623#124—1224no—
624#123—1228no—
625#123—1228no—
626C22⋊Q8—1228no—
627C22⋊Q8—1228no—
628#117—612no—
629#117—612no—
630#117—612no—
631#117—1221no—
632#117—1221no—
633#117—1221no—
634#117—1221no—
635#117—1221no—
636C2×C4⋊C4—1224no—
637C2×C4⋊C4—1221no—
638C2×C4⋊C4—1221no—
639C2×C22⋊C4—612no—
640C2×C22⋊C4—1224no—
641C2×C22⋊C4—1221no—
642C2×C42—1221no—
643C2×C42—1221no—
644#104—1228no—
645#103—1228no—
646#99—1228no—
647C24—21no—
648C24—1221no—
649C24D4×D6111yescharacteristic
650#41—22no—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—41no—
659#41—41no—
660#41—41no—
661#41—41no—
662#41—41no—
663#41—41no—
664#41—41no—
665#41—41no—
666#41—1222no—
667#41—1222no—
668#41—1222no—
669#41—1222no—
670#41—1222no—
671#41—1222no—
672#41—1222no—
673#41—1222no—
674#41—2441no—
675#41—2441no—
676#41—2441no—
677#41—2441no—
678#41—2441no—
679#41—2441no—
680#41—2441no—
681#41—2441no—
682C2×Q8—22no—
683C2×Q8—22no—
684C2×Q8—22no—
685C2×Q8—21no—
686C2×Q8—22no—
687C2×Q8—22no—
688C2×Q8—22no—
689C2×Q8—22no—
690C2×Q8—21no—
691C2×Q8—21no—
692C2×Q8—22no—
693C2×Q8—22no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—22no—
697C2×Q8—22no—
698C2×Q8—22no—
699C2×Q8—22no—
700C2×Q8—22no—
701C2×Q8—22no—
702C2×Q8—41no—
703C2×Q8—41no—
704C2×Q8—41no—
705C2×Q8—41no—
706C2×Q8—41no—
707C2×Q8—41no—
708C2×Q8—41no—
709C2×Q8—41no—
710C2×Q8—41no—
711C2×Q8—41no—
712C2×Q8—41no—
713C2×Q8—41no—
714C2×Q8—612no—
715C2×Q8—1221no—
716C2×Q8—1221no—
717C2×Q8—1221no—
718C2×Q8—1221no—
719C2×Q8—1221no—
720C2×Q8C2×C22⋊D6114yes—
721C2×Q8C2×C22⋊D6112yes—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—41no—
730C2×D4—41no—
731C2×D4—41no—
732C2×D4—41no—
733C2×D4—612no—
734C2×D4—1222no—
735C2×D4—1222no—
736C2×D4—1221no—
737C2×D4—1221no—
738C2×D4—1221no—
739C2×D4—1221no—
740C2×D4—1221no—
741C2×D4—2441no—
742C2×D4—2441no—
743C2×D4—2441no—
744C2×D4—2441no—
745C2×D4C2×C22⋊D6112yes—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—41no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—41no—
759C22×C4—41no—
760C22×C4—1222no—
761C22×C4—1221no—
762C22×C4—1222no—
763C22×C4—1222no—
764C22×C4—2441no—
765C22×C4—2441no—
766C22×C4—2441no—
767C22×C4—2441no—
768C22×C4—2441no—
769C22×C4D4×D6111yescharacteristic
770C22×C4D4×D6111yescharacteristic
771C22×C4D4×D6111yescharacteristic
772C22×C4D4×D6111yescharacteristic
773C22×C4D4×D6111yescharacteristic
774C22×C4#1175822411yescharacteristic
775C22×C4#1175822411yescharacteristic
776C22×C4C2×C22⋊D6111yescharacteristic
777C22×C4C2×C22⋊D6111yescharacteristic
778C22×C4C2×C22⋊D6111yescharacteristic
779C22×C4C2×C22⋊D6111yescharacteristic
780C22×C4C2×C22⋊D6111yescharacteristic
781C22×C4C2×C22⋊D6111yescharacteristic
782C22×C4C23×D6111yescharacteristic
783Q16—216no—
784Q16—1228no—
785SD16—216no—
786SD16—1228no—
787SD16—1228no—
788D8—1228no—
789M16—22no—
790M16—22no—
791M16—22no—
792M16—1222no—
793M16—1222no—
794M16—1222no—
795M16—1222no—
796M16C2×C22⋊D6114yes—
797C2×C8—22no—
798C2×C8—22no—
799C2×C8—22no—
800C2×C8—614no—
801C2×C8—1222no—
802C2×C8—1222no—
803C4⋊C4—12216no—
804C4⋊C4—1222no—
805C4⋊C4—1222no—
806C4⋊C4—1222no—
807C4⋊C4—2441no—
808C22⋊C4—614no—
809C22⋊C4—12216no—
810C22⋊C4—1222no—
811C22⋊C4—1222no—
812C22⋊C4—2441no—
813C42—1222no—
814C42—1222no—
815C42—1222no—
816C42—2441no—
817C23—22no—
818C23—42no—
819C23—41no—
820C23—41no—
821C23—82no—
822C23—1222no—
823C23—2444no—
824C23—2441no—
825C23—2441no—
826C23#1451974511yescharacteristic
827C23#1451974511yescharacteristic
828C23#1451974911yescharacteristic
829C23#1451974911yescharacteristic
830C23#1451977311yescharacteristic
831C23#1451977311yescharacteristic
832C23C2×D4×D6111yescharacteristic
833Q8—22no—
834Q8—24no—
835Q8—22no—
836Q8—24no—
837Q8—42no—
838Q8—42no—
839Q8—42no—
840Q8—42no—
841Q8—42no—
842Q8—42no—
843Q8—41no—
844Q8—41no—
845Q8—1222no—
846Q8—1222no—
847Q8—2441no—
848Q8—2441no—
849D4—22no—
850D4—22no—
851D4—42no—
852D4—42no—
853D4—42no—
854D4—42no—
855D4—41no—
856D4—41no—
857D4—1222no—
858D4—1222no—
859D4—2442no—
860D4—2442no—
861D4—2442no—
862D4—2442no—
863D4—2441no—
864D4—2441no—
865C2×C4—24no—
866C2×C4—22no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—1224no—
880C2×C4—1222no—
881C2×C4—4882no—
882C2×C4—2442no—
883C2×C4—2444no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2442no—
887C2×C4—2442no—
888C2×C4—2442no—
889C2×C4—2442no—
890C2×C4#1451974511yescharacteristic
891C2×C4#1451974511yescharacteristic
892C2×C4#1451974511yescharacteristic
893C2×C4#1451974511yescharacteristic
894C2×C4#1451974511yescharacteristic
895C2×C4#1451974511yescharacteristic
896C2×C4#1451974611yescharacteristic
897C2×C4#1451974611yescharacteristic
898C2×C4#1451974611yescharacteristic
899C2×C4#1451974611yescharacteristic
900C2×C4#1451974811yescharacteristic
901C2×C4#1451974811yescharacteristic
902C2×C4#1451974811yescharacteristic
903C2×C4#1451974811yescharacteristic
904C2×C4#1451974911yescharacteristic
905C2×C4#1451974911yescharacteristic
906C2×C4#1451974911yescharacteristic
907C2×C4#1451974911yescharacteristic
908C2×C4#1451974911yescharacteristic
909C2×C4#1451974911yescharacteristic
910C2×C4#1451977311yescharacteristic
911C2×C4#1451977311yescharacteristic
912C2×C4C2×D4×D6111yescharacteristic
913C2×C4C2×D4×D6111yescharacteristic
914C2×C4C22×C22⋊D6111yescharacteristic
915C2×C4C22×C22⋊D6111yescharacteristic
916C2×C4C22×C22⋊D6111yescharacteristic
917C2×C4C2×#1175822411yescharacteristic
918C8—24no—
919C8—1224no—
920C22—22no—
921C22—22no—
922C22—22no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—42no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22—4882no—
932C22—4882no—
933C22—2444no—
934C22—2442no—
935C22#1683967011yescharacteristic
936C22#1683967011yescharacteristic
937C22#1683967011yescharacteristic
938C22#1683967011yescharacteristic
939C22C2×#1451974511yescharacteristic
940C22C2×#1451974911yescharacteristic
941C22C2×#1451977311yescharacteristic
942C4—42no—
943C4—44no—
944C4—4882no—
945C4—2444no—
946C4—2442no—
947C4#1683967011yescharacteristic
948C4#1683967011yescharacteristic
949C4#1683967011yescharacteristic
950C4#1683967011yescharacteristic
951C4C2×#1451974511yescharacteristic
952C4C2×#1451974611yescharacteristic
953C4C2×#1451974811yescharacteristic
954C4C2×#1451974911yescharacteristic
955C2—21no—
956C2—21no—
957C2—21no—
958C2—21no—
959C2—21no—
960C2—21no—
961C2—82no—
962C2—4882no—
963C2#2144687712yesdirect product factor
964C2C2×#1683967011yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC22×#137×C61C2
socleC22×C61#392
prime radicalC2×#16840560C2
hypercenterC22×#137D61
hypocenterC61C2×#2009
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
2. C2×#16840336C2semidirect
3. C2×#16839778C2semidirect
4. C2×#16839771C2semidirect
5. C2×#16839736C2semidirect
6. #21446877C2direct (N × H)
7. C2×#16839534C2semidirect
8. C22×#137×C61C2semidirect
23. #16840336C22semidirect
31. #16839778C22semidirect
34. #16839771C22semidirect
37. #16839736C22semidirect
39. #16839534C22semidirect
47. C2×#137×C61C22semidirect
474. C22×#137D61semidirect
488. C2×C61#2009semidirect
505. C2×#137C2×D61semidirect
533. C61C2×#2009semidirect
963. C2#21446877direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168405602
C2×#168403362
C2×#168397782
C2×#168397712
C2×#168397362
#214468772
C2×#168395342
C22×#137×C612
C2×#200961