Finite Group Databasebeta

← #29681464

Subgroups — #29681464

Order 15616.

1850 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD16×D61C211yesmaximal, characteristic
2C2×#16840238C211yesmaximal, characteristic, complemented
3C2×#16839769C211yesmaximal, characteristic, complemented
4C2×#16839765C211yesmaximal, characteristic
5#21448398C211yesmaximal, characteristic
6#21446177C211yesmaximal, characteristic, complemented
7#21446176C211yesmaximal, characteristic, complemented
8#21446175C211yesmaximal, characteristic, complemented
9#21446174C211yesmaximal, characteristic, complemented
10#21446173C211yesmaximal, characteristic, complemented
11#21446172C211yesmaximal, characteristic, complemented
12#21446171C211yesmaximal, characteristic, complemented
13#21445534C211yesmaximal, characteristic, complemented
14#21445514C211yesmaximal, characteristic, complemented
15C61×#1880C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758190C2211yescharacteristic
19C22×#11758200C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C2×SD16×D61—24no—
22C2×SD16×D61—24no—
23C2×SD16×D61C418yescomplemented
24C22×#11758189C2211yescharacteristic
25C22×C8×D61C2211yescharacteristic
26#16840238—24no—
27#16840238—24no—
28C2×Q8×Dic61C2211yescharacteristic, complemented
29C2×C4×Dic122—21no—
30C2×C4×Dic122C2211yescharacteristic, complemented
31C2×#14519742—21no—
32C2×#14519742C2211yescharacteristic, complemented
33C2×#14519735—21no—
34C2×#14519735C2211yescharacteristic
35C2×#14519735C2211yescharacteristic
36C2×#14519734—21no—
37C2×#14519734C2211yescharacteristic
38#16839769—24no—
39#16839765—24no—
40C2×#14519702C2211yescharacteristic, complemented
41C2×#14519701C2211yescharacteristic, complemented
42C2×#14519700C2211yescharacteristic, complemented
43C2×#14519699C2211yescharacteristic
44C2×#14519698C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46#16839665C2211yescharacteristic
47#16839664C2211yescharacteristic
48#16839663C2211yescharacteristic
49#16839662—21no—
50#16839662—21no—
51#16839617—21no—
52#16839617—21no—
53#16839525C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839517C2211yescharacteristic, complemented
57#16839516C2211yescharacteristic, complemented
58#16839516C2211yescharacteristic, complemented
59C22×SD16×C61C2211yescharacteristic
60C2×C4×Q8×C61C2211yescharacteristic, complemented
61C2×#103×C61C2211yescharacteristic, complemented
62C2×#102×C61C2211yescharacteristic
63C61×#390C2211yescharacteristic
64C61×#340C2211yescharacteristic, complemented
65C61×#336C2211yescharacteristic, complemented
66C24×D61—21no—
67C22×Dic122—21no—
68C22×Dic122C2311yescharacteristic
69C2×Q8×D61—22no—
70C2×Q8×D61—22no—
71C2×Q8×D61—22no—
72C2×Q8×D61C2×C414yes—
73C2×Q8×D61D414yes—
74C2×Q8×D61D414yes—
75C22×D244C2311yescharacteristic
76C22×C22⋊D61—21no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—22no—
80C2×D4×D61—22no—
81C2×D4×D61—22no—
82C2×D4×D61C2×C414yes—
83C22×C4×D61—21no—
84C22×C4×D61C2311yescharacteristic
85C2×#11758190—22no—
86C2×#11758190—22no—
87C2×#11758190C2×C414yes—
88C2×#11758200—22no—
89C2×#11758200—22no—
90C2×#11758200C2×C414yes—
91C2×#11758201—22no—
92C2×#11758201—22no—
93C2×#11758201C2×C414yes—
94SD16×D61—232no—
95C2×#11758189—22no—
96C2×#11758189—22no—
97C2×#11758189—22no—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C2×C8×D61—22no—
101C2×C8×D61—22no—
102C2×C8×D61C2×C414yes—
103Q8×Dic61—22no—
104Q8×Dic61—22no—
105C4×Dic122—28no—
106C4×Dic122—22no—
107C4×Dic122—22no—
108#14519742—28no—
109#14519742—22no—
110#14519742—22no—
111#14519735—28no—
112#14519735—22no—
113#14519735—22no—
114#14519735—22no—
115#14519735D414yes—
116#14519734—28no—
117#14519734—22no—
118#14519734—22no—
119C2×C4⋊Dic61—21no—
120C2×C4⋊Dic61C2311yescharacteristic
121C2×C4⋊Dic61C2311yescharacteristic
122C2×#11758196—21no—
123C2×#11758196—21no—
124C2×#11758196D411yescharacteristic
125C2×#11758196D411yescharacteristic
126C2×C22⋊Dic61—21no—
127C2×C22⋊Dic61—21no—
128C2×#11758198—21no—
129C2×#11758198—21no—
130C2×#11758198—21no—
131C2×#11758198—21no—
132C2×#11758198—21no—
133C2×#11758198—21no—
134C2×#11758198D411yescharacteristic
135C2×#11758198D411yescharacteristic
136C2×C4×Dic61—21no—
137C2×C4×Dic61—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61C2311yescharacteristic
142#14519702—22no—
143#14519701—22no—
144#14519700—22no—
145#14519699—22no—
146#14519698—22no—
147#14519697—22no—
148C22×Q8×C61C2311yescharacteristic
149C22×D4×C61C2311yescharacteristic
150C2×SD16×C61—22no—
151C2×SD16×C61—22no—
152C2×SD16×C61C2×C414yes—
153C22×C8×C61C2311yescharacteristic
154C22×C8×C61C2311yescharacteristic
155C4×Q8×C61—22no—
156C4×Q8×C61—22no—
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61C2311yescharacteristic
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C42×C61—21no—
163C2×C42×C61C2311yescharacteristic
164#103×C61—22no—
165#102×C61—22no—
166C24×C61—21no—
167C23×D61—21no—
168C23×D61—24no—
169C23×D61—42no—
170C23×D61—42no—
171C23×D61—81no—
172C23×D61—81no—
173C23×D61—81no—
174C23×D61—81no—
175C23×D61C2×D411yescharacteristic
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61C22×C412yes—
180C2×Q8×C61C2×D412yes—
181C2×Q8×C61C2×D412yes—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61C22×C412yes—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—24no—
195C2×C22⋊D61—42no—
196C2×C22⋊D61—42no—
197C22×Dic61—21no—
198C22×Dic61—21no—
199C22×Dic61—21no—
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202C22×Dic61C2×D411yescharacteristic
203Q8×D61—28no—
204Q8×D61—28no—
205Q8×D61—28no—
206Q8×D61C22⋊C4116yescomplemented
207D4×D61—28no—
208D4×D61—28no—
209D4×D61—44no—
210D4×D61—44no—
211C2×D244—21no—
212C2×D244—21no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244C22×C412yes—
217C2×C4×D61—24no—
218C2×C4×D61—24no—
219C2×C4×D61—24no—
220C2×C4×D61C22×C412yes—
221C2×C4×D61C2×D412yes—
222C2×C4×D61C2×D412yes—
223C2×C4×D61C2×D412yes—
224C2×C4×D61#4112yes—
225C2×C4×D61#4112yes—
226C2×Dic122—21no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—24no—
230C2×Dic122—24no—
231C2×Dic122—24no—
232C2×Dic122C22×C412yes—
233C2×Dic122C2×D412yes—
234C2×Dic122C2×D412yes—
235SD16×C61—28no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61C22×C412yes—
242C4⋊C4×C61—24no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61C2×D412yes—
247C22⋊C4×C61—81no—
248C22⋊C4×C61—81no—
249C42×C61—24no—
250C42×C61—21no—
251C42×C61—21no—
252C22⋊Dic61—81no—
253C22⋊Dic61—81no—
254#11758201—28no—
255#11758200—28no—
256#11758198—24no—
257#11758198—22no—
258#11758198—22no—
259#11758198—42no—
260#11758198—81no—
261#11758198—81no—
262#11758198—81no—
263#11758198—81no—
264C4⋊Dic61—24no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61C2×D412yes—
269#11758196—24no—
270#11758196—24no—
271#11758196—22no—
272#11758196—22no—
273C4×Dic61—24no—
274C4×Dic61—24no—
275C4×Dic61—24no—
276C4×Dic61—21no—
277C4×Dic61—21no—
278C4×Dic61—24no—
279C4×Dic61—42no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418C22×C412yes—
286#11758190—28no—
287#11758189—44no—
288C8×D61—28no—
289C23×C61—22no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61C22×D411yescharacteristic
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—22no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—48no—
309C22×D61—84no—
310C22×D61—84no—
311C22×D61—84no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61C4×D412yes—
316C22×D61#12012yes—
317C22×D61#12112yes—
318Q8×C61—22no—
319Q8×C61—22no—
320Q8×C61—22no—
321Q8×C61C2×C22⋊C414yes—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—41no—
325D4×C61—41no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—21no—
330C2×C4×C61—22no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61C23×C411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C2×C4×C61C2×#4111yescharacteristic
346C2×C4×C61C2×#4111yescharacteristic
347C22⋊D61—48no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—22no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—21no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61C4×D412yes—
364C2×Dic61#12012yes—
365C2×Dic61#12112yes—
366D244—22no—
367D244—22no—
368D244—41no—
369D244—41no—
370C4×D61—216no—
371C4×D61C2×C22⋊C414yes—
372C4×D61C4×D414yes—
373C4×D61#12114yes—
374C4×D61#12314yes—
375Dic122—22no—
376Dic122—22no—
377Dic122—22no—
378Dic122—216no—
379Dic122C2×C22⋊C414yes—
380C8×C61—22no—
381C8×C61—41no—
382#92418—22no—
383#92418—41no—
384#20936—611nomaximal, Sylow
385C22×C61—42no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61—81no—
389C22×C61—81no—
390C22×C61—81no—
391C22×C61—81no—
392C22×C61C2×C4×D411yescharacteristic
393C22×C61C2×#12011yescharacteristic
394C22×C61C2×#12111yescharacteristic
395C22×C61#57711yescharacteristic
396C22×C61#57711yescharacteristic
397C22×C61#57711yescharacteristic
398C22×C61#57711yescharacteristic
399C2×D61—22no—
400C2×D61—22no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—22no—
404C2×D61—22no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—42no—
408C2×D61—816no—
409C2×D61—81no—
410C2×D61—81no—
411C2×D61—81no—
412C2×D61—81no—
413C2×D61#38614yes—
414C4×C61—24no—
415C4×C61—41no—
416C4×C61—41no—
417C4×C61—42no—
418C4×C61—81no—
419C4×C61C22×C22⋊C411yescharacteristic
420C4×C61C2×C4×D411yescharacteristic
421C4×C61C2×#12111yescharacteristic
422C4×C61C2×#12311yescharacteristic
423Dic61—24no—
424Dic61—41no—
425Dic61—41no—
426Dic61—42no—
427Dic61—81no—
428Dic61#38614yes—
429C23×SD16—611no—
430C2×#519—611no—
431C2×#419—611no—
432C2×#418—611no—
433#2309—611no—
434#1880—611no—
435#1880—611no—
436#1880—611no—
437#1880—611no—
438#1880—611no—
439#1880—611no—
440#1880—611no—
441#1880D6111yescharacteristic, complemented
442#1735—611no—
443#1729—611no—
444C2×C61—82no—
445C2×C61C2×#38611yescharacteristic
446C2×C61#294911yescharacteristic
447C2×C61#294911yescharacteristic
448C2×C61#301011yescharacteristic
449C2×C61#301011yescharacteristic
450C2×C61#304311yescharacteristic
451C2×C61#304311yescharacteristic
452D61—24no—
453D61—82no—
454C23×Q8—611no—
455C23×D4—611no—
456C22×SD16—611no—
457C22×SD16—611no—
458C22×SD16—618no—
459C22×SD16—611no—
460C22×SD16—1224no—
461C22×SD16—1224no—
462C22×SD16C2×D6111yescharacteristic
463C22×M16—611no—
464C23×C8—611no—
465#519—1224no—
466#519—1224no—
467C2×C4×Q8—611no—
468C2×C4×Q8—611no—
469C2×C4×Q8—611no—
470C2×C4×Q8—1221no—
471C2×C4×Q8—1221no—
472C2×C4×Q8C2×D6111yescharacteristic, complemented
473C2×#117—611no—
474C2×#117—611no—
475C2×#117—611no—
476C2×#117—1221no—
477C2×#117—1221no—
478#419—1224no—
479#418—1224no—
480C2×#103—611no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103C2×D6111yescharacteristic, complemented
484C2×#102—611no—
485C2×#102—611no—
486C2×#102—611no—
487C2×#102C2×D6111yescharacteristic
488#390—611no—
489#390—611no—
490#390—611no—
491#390—1221no—
492#390—1221no—
493#390C2×D6111yescharacteristic
494#379—1221no—
495#379—1221no—
496#340—611no—
497#340—611no—
498#340—611no—
499#340C2×D6111yescharacteristic, complemented
500#336—611no—
501#336—611no—
502#336—611no—
503#336C2×D6111yescharacteristic, complemented
504C61#2093611yescharacteristic, complemented, Sylow
505C25—1221no—
506C22×Q8—614no—
507C22×Q8—614no—
508C22×Q8—614no—
509C22×Q8—611no—
510C22×Q8—1221no—
511C22×Q8—1222no—
512C22×Q8—1222no—
513C22×Q8—1222no—
514C22×Q8C22×D6111yescharacteristic
515C22×D4—614no—
516C22×D4—611no—
517C22×D4—1222no—
518C22×D4—1222no—
519C22×D4—1222no—
520C22×D4—1222no—
521C22×D4—1222no—
522C22×D4—1221no—
523C22×D4C22×D6111yescharacteristic
524C23×C4—611no—
525C23×C4—1221no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—614no—
529C2×SD16—614no—
530C2×SD16—614no—
531C2×SD16—1222no—
532C2×SD16—1222no—
533C2×SD16—12232no—
534C2×SD16—1222no—
535C2×SD16—1222no—
536C2×SD16—1222no—
537C2×SD16—1222no—
538C2×SD16C4×D6114yes—
539C2×M16—1222no—
540C2×M16—1222no—
541C2×M16—1222no—
542C22×C8—611no—
543C22×C8—614no—
544C22×C8—611no—
545C22×C8—1222no—
546C22×C8—1222no—
547C22×C8C22×D6111yescharacteristic
548C22×C8C22×D6111yescharacteristic
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—1222no—
552C4×Q8—1222no—
553C4×Q8—1228no—
554C4×Q8—1222no—
555C4×Q8—1228no—
556C4×Q8—1222no—
557C4×Q8—1222no—
558C4×Q8—1222no—
559#117—614no—
560#117—1222no—
561#117—1222no—
562#117—1228no—
563#117—1222no—
564#117—1228no—
565#117—1222no—
566#117—1222no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—611no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4—1221no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4C22×D6111yescharacteristic
576C2×C4⋊C4C22×D6111yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—611no—
580C2×C22⋊C4—611no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C42—21no—
590C2×C42—611no—
591C2×C42—1221no—
592C2×C42—1221no—
593C2×C42—1221no—
594C2×C42—1221no—
595C2×C42—1221no—
596C2×C42C22×D6111yescharacteristic
597#103—22no—
598#103—1222no—
599#103—1222no—
600#103—1222no—
601#102—22no—
602#102—1222no—
603#102—1222no—
604#102—1222no—
605C24—21no—
606C24—611no—
607C24—1224no—
608C24—1221no—
609C24—4881no—
610C24—4881no—
611C24—4881no—
612C24—4881no—
613C24—2442no—
614C24—2442no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—6116no—
619C2×Q8—612no—
620C2×Q8—612no—
621C2×Q8—612no—
622C2×Q8—1224no—
623C2×Q8—1224no—
624C2×Q8—1224no—
625C2×Q8—1228no—
626C2×Q8—1228no—
627C2×Q8—1228no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—1221no—
631C2×Q8C2×C4×D6112yes—
632C2×Q8D4×D6112yes—
633C2×Q8D4×D6112yes—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—612no—
640C2×D4—1228no—
641C2×D4—1228no—
642C2×D4—1224no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—2444no—
649C2×D4—2444no—
650C2×D4—2442no—
651C2×D4—2442no—
652C2×D4C2×C4×D6112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—611no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—612no—
660C22×C4—612no—
661C22×C4—612no—
662C22×C4—612no—
663C22×C4—611no—
664C22×C4—611no—
665C22×C4—1224no—
666C22×C4—1224no—
667C22×C4—1224no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1221no—
671C22×C4D4×D6111yescharacteristic
672C22×C4D4×D6111yescharacteristic
673C22×C4C23×D6111yescharacteristic
674SD16—28no—
675SD16—1228no—
676SD16—1228no—
677SD16—1228no—
678M16—2444no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—612no—
685C2×C8—1228no—
686C2×C8—1221no—
687C2×C8—1221no—
688C2×C8—1221no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8C2×C4×D6112yes—
692C4⋊C4—24no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—612no—
697C4⋊C4—1222no—
698C4⋊C4—1222no—
699C4⋊C4—1224no—
700C4⋊C4—1224no—
701C4⋊C4—1224no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4D4×D6112yes—
706C22⋊C4—81no—
707C22⋊C4—81no—
708C22⋊C4—1222no—
709C22⋊C4—1222no—
710C22⋊C4—1224no—
711C22⋊C4—4881no—
712C22⋊C4—4881no—
713C22⋊C4—4881no—
714C22⋊C4—4881no—
715C22⋊C4—4881no—
716C22⋊C4—4881no—
717C22⋊C4—2442no—
718C42—24no—
719C42—21no—
720C42—21no—
721C42—1224no—
722C42—1224no—
723C42—1224no—
724C42—1224no—
725C42—1221no—
726C42—1221no—
727C42—2442no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—612no—
736C23—612no—
737C23—612no—
738C23—1221no—
739C23—1221no—
740C23—1221no—
741C23—1221no—
742C23—1222no—
743C23—4884no—
744C23—4884no—
745C23—4884no—
746C23—4884no—
747C23—4884no—
748C23—4884no—
749C23—2448no—
750C23—2441no—
751C23—2441no—
752C23—2441no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23C2×D4×D6111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8—614no—
761Q8—12216no—
762Q8—1222no—
763Q8—1222no—
764Q8—1222no—
765Q8C22⋊C4×D6114yes—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—41no—
770D4—1222no—
771D4—1222no—
772D4—2448no—
773D4—2441no—
774D4—2441no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—612no—
791C2×C4—612no—
792C2×C4—612no—
793C2×C4—614no—
794C2×C4—614no—
795C2×C4—614no—
796C2×C4—614no—
797C2×C4—12216no—
798C2×C4—1222no—
799C2×C4—1222no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—2441no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4C22×C4×D6111yescharacteristic
814C2×C4C2×D4×D6111yescharacteristic
815C2×C4C2×D4×D6111yescharacteristic
816C2×C4C2×D4×D6111yescharacteristic
817C2×C4#41×D6111yescharacteristic
818C2×C4#41×D6111yescharacteristic
819C8—22no—
820C8—41no—
821C8—1222no—
822C8—2441no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—614no—
831C22—1222no—
832C22—1222no—
833C22—1222no—
834C22—1222no—
835C22—1222no—
836C22—1222no—
837C22—48816no—
838C22—4881no—
839C22—4881no—
840C22—4881no—
841C22—4881no—
842C22—2442no—
843C22—2442no—
844C22—2442no—
845C22C4×D4×D6111yescharacteristic
846C22#120×D6111yescharacteristic
847C22#121×D6111yescharacteristic
848C22#1684056811yescharacteristic
849C22#1684056911yescharacteristic
850C22#1684057111yescharacteristic
851C22#1684057211yescharacteristic
852C4—24no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—81no—
857C4—614no—
858C4—1224no—
859C4—4881no—
860C4—2441no—
861C4—2442no—
862C4—2441no—
863C4C2×C22⋊C4×D6111yescharacteristic
864C4C4×D4×D6111yescharacteristic
865C4#121×D6111yescharacteristic
866C4#123×D6111yescharacteristic
867C2—82no—
868C2—1224no—
869C2—4882no—
870C2#386×D6111yescharacteristic
871C2#2145467311yescharacteristic
872C2#2145467511yescharacteristic
873C2#2145510011yescharacteristic
874C2#2145510211yescharacteristic
875C2#2145533511yescharacteristic
876C2#2145533811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1880C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1880D61
hypocenterC61#20936
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×#16840238C2semidirect
3. C2×#16839769C2semidirect
6. #21446177C2semidirect
7. #21446176C2semidirect
8. #21446175C2semidirect
9. #21446174C2semidirect
10. #21446173C2semidirect
11. #21446172C2semidirect
12. #21446171C2semidirect
13. #21445534C2semidirect
14. #21445514C2semidirect
15. C61×#1880C2semidirect
23. C2×SD16×D61C4semidirect
28. C2×Q8×Dic61C22semidirect
30. C2×C4×Dic122C22semidirect
32. C2×#14519742C22semidirect
40. C2×#14519702C22semidirect
41. C2×#14519701C22semidirect
42. C2×#14519700C22semidirect
53. #16839525C22semidirect
54. #16839524C22semidirect
55. #16839524C22semidirect
56. #16839517C22semidirect
57. #16839516C22semidirect
58. #16839516C22semidirect
60. C2×C4×Q8×C61C22semidirect
61. C2×#103×C61C22semidirect
64. C61×#340C22semidirect
65. C61×#336C22semidirect
206. Q8×D61C22⋊C4semidirect
441. #1880D61semidirect
472. C2×C4×Q8C2×D61semidirect
483. C2×#103C2×D61semidirect
499. #340C2×D61semidirect
503. #336C2×D61semidirect
504. C61#20936semidirect

Maximal subgroups

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

subgroupindex
C22×SD16×D612
C2×#168402382
C2×#168397692
C2×#168397652
#214483982
#214461772
#214461762
#214461752
#214461742
#214461732
#214461722
#214461712
#214455342
#214455142
C61×#18802
#2093661