Finite Group Databasebeta

← #29711351

Subgroups — #29711351

Order 15616.

2012 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519802C211yesmaximal, characteristic, complemented
2C2×#16839930C212yesmaximal, complemented
3#21455045C211yesmaximal, characteristic, complemented
4#21449457C211yesmaximal, characteristic, complemented
5#21446861C212yesmaximal, complemented
6#21446832C212yesmaximal, complemented
7#21446283C211yesmaximal, characteristic, complemented
8#21446195C212yesmaximal, complemented
9#21446122C211yesmaximal, characteristic, complemented
10#21445763C211yesmaximal, characteristic, complemented
11C61×#3488C211yesmaximal, characteristic, complemented
12C23×D244C2211yescharacteristic, complemented
13C2×#14519802—28no—
14C2×#14519802—21no—
15C2×#14519802—21no—
16C2×#14519802C2212yes—
17C2×#14519802C2212yescomplemented
18C2×#14519802C2212yescomplemented
19C22×#11758201—21no—
20C22×#11758199—21no—
21C22×#11758194C2211yescharacteristic, complemented
22C2×#14519773C2212yescomplemented
23C2×#14519745—22no—
24#16839930—28no—
25#16839912—21no—
26#16839912—21no—
27#16839895—21no—
28#16839895—21no—
29C2×#14519704C2212yescomplemented
30C2×#14519704C2212yescomplemented
31C2×#14519704C2212yescomplemented
32#16839766C2212yescomplemented
33C2×#14519694C2212yescomplemented
34#16839726C2211yescharacteristic, complemented
35#16839671—22no—
36#16839663C2212yescomplemented
37C4×C22⋊Dic61C2211yescharacteristic, complemented
38#16839531C2212yescomplemented
39#16839521C2212yescomplemented
40C2×H(5,𝔽2)×C61C2211yescharacteristic, complemented
41C22×#41×C61C2211yescharacteristic
42C61×#550—21no—
43C61×#548—21no—
44C61×#546—21no—
45C61×#546—22no—
46D42×C61—22no—
47D42×C61—21no—
48C61×#537—21no—
49C61×#537C2211yescharacteristic, complemented
50C61×#535—21no—
51C61×#535C2211yescharacteristic, complemented
52C61×#525—21no—
53C61×#525C2211yescharacteristic
54C2×#121×C61—21no—
55C2×#121×C61C2211yescharacteristic
56C61×#520C2211yescharacteristic, complemented
57C24×D61—21no—
58C22×D244—21no—
59C22×D244—21no—
60C22×D244—24no—
61C22×D244—21no—
62C22×D244—21no—
63C22×D244—21no—
64C22×D244—42no—
65C22×D244C2312yes—
66C22×C22⋊D61—24no—
67#14519802—28no—
68#14519802—28no—
69#14519802—24no—
70#14519802—24no—
71#14519802—24no—
72#14519802—24no—
73#14519802—42no—
74#14519802D418yescomplemented
75C2×#11758201—28no—
76C2×#11758201—22no—
77C2×#11758201—22no—
78C2×#11758201—22no—
79C2×#11758199—28no—
80C2×#11758199—22no—
81C2×#11758199—22no—
82C2×#11758199—22no—
83C2×#11758194—21no—
84C2×#11758194—24no—
85C2×#11758194C2312yes—
86C2×#11758194C2312yes—
87C22×#92418—21no—
88#14519773—24no—
89#14519773—42no—
90#14519745—48no—
91C2×C22⋊Dic61—21no—
92C2×#11758198—24no—
93C2×C4×Dic61C2312yes—
94#14519704—24no—
95#14519704—24no—
96#14519704—42no—
97#14519697—22no—
98#14519697—22no—
99#14519694—24no—
100C22⋊#92418—21no—
101C22⋊#92418—21no—
102#14519684—21no—
103H(5,𝔽2)×C61—24no—
104H(5,𝔽2)×C61—42no—
105C2×#41×C61—21no—
106C2×#41×C61—21no—
107C2×#41×C61—21no—
108C2×#41×C61—21no—
109C2×#41×C61—24no—
110C2×#41×C61—42no—
111C2×#41×C61D411yescharacteristic, complemented
112C2×#41×C61D411yescharacteristic, complemented
113C2×#41×C61C2311yescharacteristic
114C2×#41×C61C2311yescharacteristic
115C2×#41×C61C2311yescharacteristic
116C22×Q8×C61D411yescharacteristic, complemented
117C22×D4×C61—21no—
118C22×D4×C61—22no—
119C22×D4×C61—22no—
120C22×D4×C61—21no—
121C22×D4×C61—21no—
122C22×D4×C61D412yes—
123C22×D4×C61D411yescharacteristic, complemented
124C22×D4×C61C2311yescharacteristic
125C23×C4×C61—21no—
126C23×C4×C61C2311yescharacteristic
127#127×C61—22no—
128#127×C61—21no—
129#124×C61—22no—
130#124×C61—21no—
131#123×C61—22no—
132#123×C61—21no—
133C22⋊Q8×C61—22no—
134C22⋊Q8×C61—21no—
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61D411yescharacteristic, complemented
137C22⋊Q8×C61D411yescharacteristic, complemented
138#121×C61—22no—
139#121×C61—22no—
140#121×C61—22no—
141#121×C61—22no—
142#121×C61—22no—
143#121×C61—21no—
144#121×C61—21no—
145#121×C61—21no—
146#121×C61—22no—
147#121×C61—21no—
148#121×C61—21no—
149#121×C61—21no—
150#121×C61—21no—
151#121×C61—21no—
152#121×C61D411yescharacteristic, complemented
153#121×C61D411yescharacteristic, complemented
154#120×C61—22no—
155#120×C61—22no—
156#120×C61—22no—
157#120×C61—22no—
158#120×C61—21no—
159C4×Q8×C61—21no—
160C4×D4×C61—22no—
161C4×D4×C61—22no—
162C4×D4×C61—21no—
163C4×D4×C61—22no—
164C4×D4×C61—21no—
165C4×D4×C61—21no—
166#117×C61—21no—
167#117×C61C2311yescharacteristic
168C2×C4⋊C4×C61—21no—
169C2×C4⋊C4×C61C2311yescharacteristic
170C2×C22⋊C4×C61—22no—
171C2×C22⋊C4×C61D412yes—
172C24×C61—22no—
173C24×C61—21no—
174C24×C61C2×D411yescharacteristic
175C24×C61C2×D412yes—
176C23×D61—22no—
177C23×D61—44no—
178C23×D61—41no—
179C23×D61—41no—
180C23×D61—44no—
181C23×D61—82no—
182#41×C61—22no—
183#41×C61—22no—
184#41×C61—22no—
185#41×C61—22no—
186#41×C61—22no—
187#41×C61—22no—
188#41×C61—22no—
189#41×C61—44no—
190#41×C61—41no—
191#41×C61—41no—
192#41×C61—44no—
193#41×C61—44no—
194#41×C61—42no—
195#41×C61—42no—
196#41×C61C2×D414yes—
197C2×Q8×C61—21no—
198C2×Q8×C61—22no—
199C2×Q8×C61—41no—
200C2×Q8×C61C2×D411yescharacteristic
201C2×Q8×C61C2×D411yescharacteristic
202C2×Q8×C61C2×D411yescharacteristic
203C2×D4×C61—21no—
204C2×D4×C61—22no—
205C2×D4×C61—22no—
206C2×D4×C61—22no—
207C2×D4×C61—22no—
208C2×D4×C61—21no—
209C2×D4×C61—21no—
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—22no—
214C2×D4×C61—22no—
215C2×D4×C61—22no—
216C2×D4×C61—21no—
217C2×D4×C61—22no—
218C2×D4×C61—21no—
219C2×D4×C61—21no—
220C2×D4×C61—21no—
221C2×D4×C61—22no—
222C2×D4×C61—22no—
223C2×D4×C61—41no—
224C2×D4×C61—44no—
225C2×D4×C61—44no—
226C2×D4×C61—48no—
227C2×D4×C61—42no—
228C2×D4×C61—42no—
229C2×D4×C61—44no—
230C2×D4×C61—84no—
231C2×D4×C61C2×D411yescharacteristic
232C2×D4×C61C2×D411yescharacteristic
233C2×D4×C61C2×D411yescharacteristic
234C22×C4×C61—22no—
235C22×C4×C61—21no—
236C22×C4×C61—22no—
237C22×C4×C61—22no—
238C22×C4×C61—21no—
239C22×C4×C61—22no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—44no—
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2×D411yescharacteristic
248C22×C4×C61C2×D411yescharacteristic
249C22×C4×C61C2×D411yescharacteristic
250C22×C4×C61C2×D412yes—
251C22×C4×C61C2411yescharacteristic
252C2×C22⋊D61—48no—
253C2×C22⋊D61—48no—
254C2×C22⋊D61—84no—
255C22×Dic61—22no—
256C2×D244—24no—
257C2×D244—24no—
258C2×D244—22no—
259C2×D244—22no—
260C2×D244—22no—
261C2×D244—22no—
262C2×D244—22no—
263C2×D244—44no—
264C2×D244—44no—
265C2×D244—44no—
266C2×D244—42no—
267C2×D244—42no—
268C2×D244—41no—
269C2×D244—41no—
270C2×D244C2×D414yescomplemented
271C4⋊C4×C61—22no—
272C4⋊C4×C61—22no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61—21no—
276C4⋊C4×C61—21no—
277C4⋊C4×C61C2×D411yescharacteristic
278C4⋊C4×C61C2×D411yescharacteristic
279C22⋊C4×C61—22no—
280C22⋊C4×C61—22no—
281C22⋊C4×C61—22no—
282C22⋊C4×C61—22no—
283C22⋊C4×C61—22no—
284C22⋊C4×C61—21no—
285C22⋊C4×C61—21no—
286C22⋊C4×C61—21no—
287C22⋊C4×C61—21no—
288C22⋊C4×C61—22no—
289C22⋊C4×C61—22no—
290C22⋊C4×C61—21no—
291C42×C61—22no—
292C42×C61—21no—
293C22⋊Dic61—24no—
294#11758201—28no—
295#11758201—28no—
296#11758201—44no—
297#11758199—28no—
298#11758199—28no—
299#11758199—44no—
300#11758198—48no—
301C4×Dic61—22no—
302C4×Dic61—22no—
303#11758194—24no—
304#11758194—22no—
305#11758194—22no—
306#11758194—22no—
307#11758194C2×D414yescomplemented
308C2×#92418—24no—
309C2×#92418—22no—
310C2×#92418—22no—
311C23×C61—21no—
312C23×C61—22no—
313C23×C61—22no—
314C23×C61—22no—
315C23×C61—21no—
316C23×C61—21no—
317C23×C61—24no—
318C23×C61—41no—
319C23×C61—42no—
320C23×C61—44no—
321C23×C61—42no—
322C23×C61—42no—
323C23×C61—42no—
324C23×C61—81no—
325C23×C61—82no—
326C23×C61—82no—
327C23×C61#12011yescharacteristic
328C23×C61#12011yescharacteristic
329C23×C61C22×D411yescharacteristic
330C22×D61—24no—
331C22×D61—44no—
332C22×D61—44no—
333C22×D61—44no—
334C22×D61—44no—
335C22×D61—42no—
336C22×D61—42no—
337C22×D61—816no—
338C22×D61—82no—
339C22×D61—82no—
340C22×D61—82no—
341C22×D61—82no—
342Q8×C61—21no—
343Q8×C61—21no—
344Q8×C61—21no—
345Q8×C61—22no—
346Q8×C61—42no—
347Q8×C61#12012yescomplemented
348D4×C61—24no—
349D4×C61—21no—
350D4×C61—21no—
351D4×C61—21no—
352D4×C61—22no—
353D4×C61—42no—
354D4×C61—42no—
355D4×C61—44no—
356D4×C61—42no—
357D4×C61—44no—
358D4×C61—42no—
359D4×C61—42no—
360D4×C61—44no—
361D4×C61—42no—
362D4×C61—41no—
363D4×C61—41no—
364D4×C61—42no—
365D4×C61—81no—
366D4×C61—82no—
367D4×C61—82no—
368D4×C61—82no—
369D4×C61—82no—
370D4×C61#12012yescomplemented
371C2×C4×C61—21no—
372C2×C4×C61—22no—
373C2×C4×C61—21no—
374C2×C4×C61—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—22no—
378C2×C4×C61—22no—
379C2×C4×C61—24no—
380C2×C4×C61—21no—
381C2×C4×C61—22no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—42no—
386C2×C4×C61—42no—
387C2×C4×C61—42no—
388C2×C4×C61—44no—
389C2×C4×C61—41no—
390C2×C4×C61—41no—
391C2×C4×C61—42no—
392C2×C4×C61—42no—
393C2×C4×C61—82no—
394C2×C4×C61#12011yescharacteristic
395C2×C4×C61#12011yescharacteristic
396C2×C4×C61C22×D411yescharacteristic
397C2×C4×C61C22×D412yes—
398C2×C4×C61C22×D411yescharacteristic
399C2×C4×C61H(5,𝔽2)12yes—
400C22⋊D61—816no—
401C2×Dic61—24no—
402C2×Dic61—42no—
403C2×Dic61—42no—
404D244—24no—
405D244—24no—
406D244—44no—
407D244—44no—
408D244—42no—
409D244—42no—
410#92418—24no—
411#92418—42no—
412#23876—611nomaximal, Sylow
413C22×C61—21no—
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—21no—
417C22×C61—21no—
418C22×C61—22no—
419C22×C61—21no—
420C22×C61—21no—
421C22×C61—44no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—41no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—42no—
432C22×C61—41no—
433C22×C61—84no—
434C22×C61—84no—
435C22×C61—164no—
436C22×C61#45312yescomplemented
437C22×C61C2×#12011yescharacteristic
438C22×C61D4212yes—
439C2×D61—48no—
440C2×D61—44no—
441C2×D61—84no—
442C2×D61—88no—
443C2×D61—88no—
444C2×D61—82no—
445C2×D61—82no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—22no—
449C4×C61—41no—
450C4×C61—41no—
451C4×C61—42no—
452C4×C61—41no—
453C4×C61—41no—
454C4×C61C2×#12011yescharacteristic
455C4×C61#53411yescharacteristic
456C4×C61D4212yes—
457Dic61—44no—
458C22×AGL(1,ℤ/8)—611no—
459#3488D6111yescharacteristic, complemented
460C2×#453—612no—
461#3003—611no—
462#2433—611no—
463#2006—612no—
464#2002—612no—
465#1900—611no—
466#1883—612no—
467#1871—611no—
468#1789—611no—
469C2×C61—22no—
470C2×C61—22no—
471C2×C61—41no—
472C2×C61—42no—
473C2×C61—81no—
474C2×C61—82no—
475C2×C61—81no—
476C2×C61#240311yescharacteristic
477C2×C61C2×#45311yescharacteristic
478C2×C61#302111yescharacteristic
479D61—84no—
480C2×H(5,𝔽2)C2×D6111yescharacteristic, complemented
481C22×#41C2×D6111yescharacteristic
482C23×D4—611no—
483C2×AGL(1,ℤ/8)—612no—
484C2×AGL(1,ℤ/8)—612no—
485C2×AGL(1,ℤ/8)—612no—
486C2×AGL(1,ℤ/8)—1228no—
487C2×AGL(1,ℤ/8)—1221no—
488C2×AGL(1,ℤ/8)—1221no—
489C22×SD16—1221no—
490C22×D8—1221no—
491C22×M16—611no—
492#550—21no—
493#548—21no—
494#546—21no—
495#546—22no—
496D42—22no—
497D42—21no—
498#537—21no—
499#537C2×D6111yescharacteristic, complemented
500#535—21no—
501#535C2×D6111yescharacteristic, complemented
502C2×#127—612no—
503#525—21no—
504#525C2×D6111yescharacteristic
505C2×#121—21no—
506C2×#121C2×D6111yescharacteristic
507C2×#120—1222no—
508#520C2×D6111yescharacteristic, complemented
509#453—1228no—
510#450—1221no—
511#450—1221no—
512#447—1221no—
513#447—1221no—
514C2×#104—612no—
515C2×#104—612no—
516C2×#104—612no—
517#418—612no—
518C2×#100—612no—
519#407—611no—
520#392—1222no—
521#390—612no—
522C4×C22⋊C4—611no—
523#343—612no—
524#339—612no—
525C61#2387611yescharacteristic, complemented, Sylow
526C25—1221no—
527H(5,𝔽2)—24no—
528H(5,𝔽2)—42no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—21no—
532C2×#41—21no—
533C2×#41—24no—
534C2×#41—42no—
535C2×#41C22⋊D6111yescharacteristic, complemented
536C2×#41C22⋊D6111yescharacteristic, complemented
537C2×#41C22×D6111yescharacteristic
538C2×#41C22×D6111yescharacteristic
539C2×#41C22×D6111yescharacteristic
540C22×Q8C22⋊D6111yescharacteristic, complemented
541C22×D4—21no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—612no—
547C22×D4—1224no—
548C22×D4—1224no—
549C22×D4—1221no—
550C22×D4—1221no—
551C22×D4—1221no—
552C22×D4—1221no—
553C22×D4—1221no—
554C22×D4—2442no—
555C22×D4C22⋊D6112yes—
556C22×D4C22⋊D6111yescharacteristic, complemented
557C22×D4C22×D6111yescharacteristic
558C23×C4—21no—
559C23×C4C22×D6111yescharacteristic
560AGL(1,ℤ/8)—618no—
561AGL(1,ℤ/8)—1224no—
562AGL(1,ℤ/8)—1224no—
563AGL(1,ℤ/8)—1228no—
564AGL(1,ℤ/8)—1228no—
565AGL(1,ℤ/8)—1224no—
566AGL(1,ℤ/8)—1224no—
567AGL(1,ℤ/8)—2442no—
568C2×SD16—1228no—
569C2×SD16—1222no—
570C2×SD16—1222no—
571C2×SD16—1222no—
572C2×D8—1228no—
573C2×D8—1222no—
574C2×D8—1222no—
575C2×D8—1222no—
576C2×M16—612no—
577C2×M16—612no—
578C2×M16—1224no—
579C2×M16—1221no—
580C22×C8—1221no—
581#127—22no—
582#127—21no—
583#127—1224no—
584#127—2442no—
585#124—22no—
586#124—21no—
587#123—22no—
588#123—21no—
589C22⋊Q8—22no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8C22⋊D6111yescharacteristic, complemented
593C22⋊Q8C22⋊D6111yescharacteristic, complemented
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—22no—
606#121—21no—
607#121—21no—
608#121C22⋊D6111yescharacteristic, complemented
609#121C22⋊D6111yescharacteristic, complemented
610#120—22no—
611#120—22no—
612#120—22no—
613#120—21no—
614#120—22no—
615#120—2448no—
616C4×Q8—21no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—21no—
620C4×D4—22no—
621C4×D4—21no—
622C4×D4—21no—
623#117—21no—
624#117C22×D6111yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4C22×D6111yescharacteristic
627C2×C22⋊C4—22no—
628C2×C22⋊C4—1221no—
629C2×C22⋊C4—1224no—
630C2×C22⋊C4C22⋊D6112yes—
631C2×C42—612no—
632#104—1224no—
633#104—1224no—
634#104—2442no—
635#102—1222no—
636#102—1222no—
637#100—1224no—
638C22⋊C8—1221no—
639C22⋊C8—1221no—
640#95—1221no—
641C24—22no—
642C24—21no—
643C24—1222no—
644C24—4882no—
645C24—2444no—
646C24—2444no—
647C24—2441no—
648C24—2441no—
649C24C2×C22⋊D6111yescharacteristic
650C24C2×C22⋊D6112yes—
651#41—22no—
652#41—22no—
653#41—22no—
654#41—22no—
655#41—22no—
656#41—22no—
657#41—22no—
658#41—44no—
659#41—41no—
660#41—41no—
661#41—44no—
662#41—44no—
663#41—42no—
664#41—42no—
665#41D4×D6114yes—
666C2×Q8—21no—
667C2×Q8—22no—
668C2×Q8—41no—
669C2×Q8C2×C22⋊D6111yescharacteristic
670C2×Q8C2×C22⋊D6111yescharacteristic
671C2×Q8C2×C22⋊D6111yescharacteristic
672C2×D4—21no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—21no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—21no—
692C2×D4—41no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—48no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—84no—
700C2×D4—614no—
701C2×D4—1224no—
702C2×D4—1224no—
703C2×D4—1222no—
704C2×D4—1222no—
705C2×D4—1222no—
706C2×D4—1222no—
707C2×D4—1222no—
708C2×D4—4884no—
709C2×D4—2444no—
710C2×D4—2444no—
711C2×D4—2444no—
712C2×D4—2442no—
713C2×D4—2442no—
714C2×D4—2448no—
715C2×D4—2448no—
716C2×D4—2441no—
717C2×D4—2441no—
718C2×D4C2×C22⋊D6111yescharacteristic
719C2×D4C2×C22⋊D6111yescharacteristic
720C2×D4C2×C22⋊D6111yescharacteristic
721C22×C4—22no—
722C22×C4—21no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—44no—
732C22×C4—1222no—
733C22×C4C2×C22⋊D6111yescharacteristic
734C22×C4C2×C22⋊D6111yescharacteristic
735C22×C4C2×C22⋊D6111yescharacteristic
736C22×C4C2×C22⋊D6111yescharacteristic
737C22×C4C2×C22⋊D6111yescharacteristic
738C22×C4C2×C22⋊D6112yes—
739C22×C4C23×D6111yescharacteristic
740SD16—1228no—
741SD16—1228no—
742SD16—2444no—
743D8—1228no—
744D8—1228no—
745D8—2444no—
746M16—614no—
747M16—1224no—
748M16—1222no—
749M16—1222no—
750M16—1222no—
751C2×C8—1224no—
752C2×C8—1222no—
753C2×C8—1222no—
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4C2×C22⋊D6111yescharacteristic
761C4⋊C4C2×C22⋊D6111yescharacteristic
762C22⋊C4—22no—
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—22no—
772C22⋊C4—22no—
773C22⋊C4—21no—
774C22⋊C4—1224no—
775C22⋊C4—2448no—
776C42—22no—
777C42—21no—
778C42—1222no—
779C42—1222no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—24no—
787C23—41no—
788C23—42no—
789C23—44no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—1224no—
797C23—4882no—
798C23—4882no—
799C23—4882no—
800C23—48816no—
801C23—4882no—
802C23—2444no—
803C23—2444no—
804C23—2444no—
805C23—2444no—
806C23—2442no—
807C23—2442no—
808C23#1451974611yescharacteristic
809C23#1451974611yescharacteristic
810C23C22×C22⋊D6111yescharacteristic
811Q8—21no—
812Q8—21no—
813Q8—21no—
814Q8—22no—
815Q8—42no—
816Q8#1451974512yescomplemented
817D4—24no—
818D4—21no—
819D4—21no—
820D4—21no—
821D4—22no—
822D4—42no—
823D4—42no—
824D4—44no—
825D4—42no—
826D4—44no—
827D4—42no—
828D4—42no—
829D4—44no—
830D4—42no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—81no—
835D4—82no—
836D4—82no—
837D4—82no—
838D4—82no—
839D4—1224no—
840D4—1224no—
841D4—48816no—
842D4—2444no—
843D4—2444no—
844D4—2442no—
845D4—2442no—
846D4#1451974512yescomplemented
847C2×C4—21no—
848C2×C4—22no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—44no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—82no—
870C2×C4—1224no—
871C2×C4—2442no—
872C2×C4—2442no—
873C2×C4#1451974611yescharacteristic
874C2×C4#1451974611yescharacteristic
875C2×C4C2×D4×D6112yes—
876C2×C4C22×C22⋊D6111yescharacteristic
877C2×C4C22×C22⋊D6111yescharacteristic
878C2×C4#1451982212yes—
879C8—1224no—
880C8—2442no—
881C22—21no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—44no—
890C22—41no—
891C22—41no—
892C22—42no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—42no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—84no—
902C22—84no—
903C22—164no—
904C22—4888no—
905C22—4884no—
906C22—4888no—
907C22—4882no—
908C22—4882no—
909C22—2448no—
910C22—2444no—
911C22#1683993012yescomplemented
912C22C2×#1451974611yescharacteristic
913C22D4×C22⋊D6112yes—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—42no—
918C4—41no—
919C4—41no—
920C4—41no—
921C4—41no—
922C4—2444no—
923C4C2×#1451974511yescharacteristic
924C4#1684032111yescharacteristic
925C4D4×C22⋊D6112yes—
926C2—22no—
927C2—22no—
928C2—41no—
929C2—42no—
930C2—81no—
931C2—82no—
932C2—81no—
933C2—4884no—
934C2#2144912911yescharacteristic
935C2C2×#1683993011yescharacteristic
936C2#2145519111yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3488C2
socleC22×C61C2×#120
hypercenter#3488D61
hypocenterC61#23876
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. C22×#14519802C2semidirect
2. C2×#16839930C2semidirect
3. #21455045C2semidirect
4. #21449457C2semidirect
5. #21446861C2semidirect
6. #21446832C2semidirect
7. #21446283C2semidirect
8. #21446195C2semidirect
9. #21446122C2semidirect
10. #21445763C2semidirect
11. C61×#3488C2semidirect
12. C23×D244C22semidirect
17. C2×#14519802C22semidirect
18. C2×#14519802C22semidirect
21. C22×#11758194C22semidirect
22. C2×#14519773C22semidirect
29. C2×#14519704C22semidirect
30. C2×#14519704C22semidirect
31. C2×#14519704C22semidirect
32. #16839766C22semidirect
33. C2×#14519694C22semidirect
34. #16839726C22semidirect
36. #16839663C22semidirect
37. C4×C22⋊Dic61C22semidirect
38. #16839531C22semidirect
39. #16839521C22semidirect
40. C2×H(5,𝔽2)×C61C22semidirect
49. C61×#537C22semidirect
51. C61×#535C22semidirect
56. C61×#520C22semidirect
74. #14519802D4semidirect
111. C2×#41×C61D4semidirect
112. C2×#41×C61D4semidirect
116. C22×Q8×C61D4semidirect
123. C22×D4×C61D4semidirect
136. C22⋊Q8×C61D4semidirect
137. C22⋊Q8×C61D4semidirect
152. #121×C61D4semidirect
153. #121×C61D4semidirect
270. C2×D244C2×D4semidirect
307. #11758194C2×D4semidirect
347. Q8×C61#120semidirect
370. D4×C61#120semidirect
436. C22×C61#453semidirect
459. #3488D61semidirect
480. C2×H(5,𝔽2)C2×D61semidirect
499. #537C2×D61semidirect
501. #535C2×D61semidirect
508. #520C2×D61semidirect
525. C61#23876semidirect
535. C2×#41C22⋊D61semidirect
536. C2×#41C22⋊D61semidirect
540. C22×Q8C22⋊D61semidirect
556. C22×D4C22⋊D61semidirect
592. C22⋊Q8C22⋊D61semidirect
593. C22⋊Q8C22⋊D61semidirect
608. #121C22⋊D61semidirect
609. #121C22⋊D61semidirect
816. Q8#14519745semidirect
846. D4#14519745semidirect
911. C22#16839930semidirect

Maximal subgroups

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

subgroupindex
C22×#145198022
C2×#168399302
#214550452
#214494572
#214468612
#214468322
#214462832
#214461952
#214461222
#214457632
C61×#34882
#2387661