Finite Group Databasebeta

← #29695360

Subgroups — #29695360

Order 15616.

1862 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840396C211yesmaximal, characteristic
2M16×C22⋊D61C211yesmaximal, characteristic, complemented
3#21454551C211yesmaximal, characteristic, complemented
4C22×#14519693C211yesmaximal, characteristic, complemented
5C2×#100×D61C211yesmaximal, characteristic, complemented
6#21446657C211yesmaximal, characteristic, complemented
7#21446657C211yesmaximal, characteristic, complemented
8#21446283C211yesmaximal, characteristic, complemented
9#21446281C211yesmaximal, characteristic, complemented
10#21446281C211yesmaximal, characteristic, complemented
11#21445810C211yesmaximal, characteristic, complemented
12#21445739C211yesmaximal, characteristic, complemented
13#21445738C211yesmaximal, characteristic, complemented
14#21445610C211yesmaximal, characteristic, complemented
15C61×#1900C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×D4×D61C412yes—
18C22×D4×D61C2211yescharacteristic
19C22×#11758194C2211yescharacteristic, complemented
20C2×M16×D61C2211yescharacteristic, complemented
21C2×M16×D61C2211yescharacteristic, complemented
22#16840396—21no—
23#16840396—21no—
24#16840396—21no—
25#16840396—21no—
26#16840396—21no—
27#16840396—21no—
28#16840396—21no—
29#16840396—21no—
30C2×#14519773C2211yescharacteristic
31C2×#14519752C2211yescharacteristic
32C2×#14519750C412yes—
33C2×#14519747C412yes—
34C2×#14519745C412yes—
35C2×#14519739C2211yescharacteristic
36C2×C4×C22⋊D61C2211yescharacteristic
37#16839838—21no—
38#16839837—21no—
39#16839836—21no—
40#16839833—21no—
41#16839831—21no—
42#16839830—21no—
43C8×C22⋊D61—21no—
44#16839825—21no—
45#16839785C2211yescharacteristic, complemented
46#16839785C2211yescharacteristic, complemented
47C2×#14519694C2211yescharacteristic, complemented
48C2×#14519694C2211yescharacteristic, complemented
49C2×#14519693—24no—
50C2×#14519693C2211yescharacteristic
51C2×#14519693C2211yescharacteristic
52C2×#14519693C2211yescharacteristic
53C2×#14519693C2211yescharacteristic
54C2×#14519693C2211yescharacteristic, complemented
55C2×#14519693C2211yescharacteristic, complemented
56C2×#14519693C2211yescharacteristic, complemented
57C2×#14519693C2211yescharacteristic, complemented
58#100×D61—24no—
59#16839726C2211yescharacteristic, complemented
60#16839725C2211yescharacteristic, complemented
61#16839725C2211yescharacteristic, complemented
62M16×Dic61C2211yescharacteristic, complemented
63M16×Dic61C2211yescharacteristic, complemented
64#16839531C2211yescharacteristic, complemented
65#16839531C2211yescharacteristic, complemented
66C22×M16×C61C2211yescharacteristic, complemented
67C2×#121×C61C2211yescharacteristic
68C2×#100×C61C2211yescharacteristic, complemented
69C2×#100×C61C2211yescharacteristic, complemented
70C61×#407C2211yescharacteristic, complemented
71C61×#343C2211yescharacteristic, complemented
72C61×#343C2211yescharacteristic, complemented
73C24×D61C2×C412yes—
74C24×D61C2×C412yes—
75C22×D244—21no—
76C22×D244—21no—
77C22×D244—21no—
78C22×D244—21no—
79C22×D244—22no—
80C22×D244—22no—
81C22×D244—41no—
82C22×D244—41no—
83C22×D244C2×C412yes—
84C22×D244C2×C412yes—
85C22×D244C2311yescharacteristic
86C22×D244C2311yescharacteristic
87C22×C22⋊D61C2×C412yes—
88C22×C22⋊D61C2×C411yescharacteristic
89C22×C22⋊D61C2×C412yes—
90C22×C22⋊D61C2×C412yes—
91C2×D4×D61—22no—
92C2×D4×D61—22no—
93C2×D4×D61—22no—
94C2×D4×D61—22no—
95C2×D4×D61—22no—
96C2×D4×D61—22no—
97C2×D4×D61—21no—
98C2×D4×D61—21no—
99C2×D4×D61—21no—
100C2×D4×D61—21no—
101C2×D4×D61—41no—
102C2×D4×D61—41no—
103C2×D4×D61—48no—
104C22×C4×D61C2×C412yes—
105C22×C4×D61C2311yescharacteristic
106C2×#11758194—21no—
107C2×#11758194—22no—
108C2×#11758194—41no—
109C2×#11758194C2311yescharacteristic
110C2×#11758194C2311yescharacteristic
111C2×#11758194C2311yescharacteristic
112C2×#11758194C2311yescharacteristic
113C2×#11758189—21no—
114C2×#11758189—21no—
115M16×D61—22no—
116M16×D61—22no—
117M16×D61—41no—
118M16×D61—41no—
119C22×#92418—21no—
120C2×C8×D61—21no—
121C2×C8×D61—21no—
122#14519773—21no—
123#14519773—21no—
124#14519773—21no—
125#14519773—21no—
126#14519752—21no—
127#14519752—21no—
128#14519752—21no—
129#14519752—21no—
130#14519750—22no—
131#14519750—22no—
132#14519750—22no—
133#14519750—22no—
134#14519747—22no—
135#14519747—22no—
136#14519747—22no—
137#14519747—22no—
138#14519745—22no—
139#14519745—22no—
140#14519745—22no—
141#14519745—22no—
142#14519739—21no—
143#14519739—21no—
144#14519739—21no—
145#14519739—21no—
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150C4×C22⋊D61D411yescharacteristic
151C4×C22⋊D61D411yescharacteristic
152C4×C22⋊D61D411yescharacteristic
153C4×C22⋊D61D411yescharacteristic
154C2×#11758196C2×C411yescharacteristic
155C2×C22⋊Dic61C2×C411yescharacteristic
156C2×#11758198C2×C412yes—
157C2×#11758198C2×C412yes—
158C2×#11758198C2×C411yescharacteristic
159C2×C4×Dic61C2311yescharacteristic
160#14519706—21no—
161#14519706—21no—
162#14519706—21no—
163#14519706—21no—
164#14519694—22no—
165#14519694—41no—
166#14519693—22no—
167#14519693—22no—
168#14519693—22no—
169#14519693—22no—
170#14519693—22no—
171#14519693—41no—
172#14519693—41no—
173#14519693D414yescomplemented
174C22⋊#92418—21no—
175C22⋊#92418—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519689—21no—
180#14519687—21no—
181#14519687—21no—
182C8×Dic61—21no—
183C8×Dic61—21no—
184C22×D4×C61C2×C412yes—
185C22×D4×C61C2311yescharacteristic
186C23×C4×C61C2311yescharacteristic
187C2×M16×C61—21no—
188C2×M16×C61—22no—
189C2×M16×C61—41no—
190C2×M16×C61C2311yescharacteristic
191C2×M16×C61C2311yescharacteristic
192C2×M16×C61C2311yescharacteristic
193C2×M16×C61C2311yescharacteristic
194C22×C8×C61—21no—
195#121×C61—21no—
196#121×C61—21no—
197#121×C61—21no—
198#121×C61—21no—
199C2×C4⋊C4×C61C2311yescharacteristic
200C2×C22⋊C4×C61C2×C412yes—
201#100×C61—22no—
202#100×C61—41no—
203C22⋊C8×C61—21no—
204C22⋊C8×C61—21no—
205C24×C61C22×C411yescharacteristic
206C24×C61C22×C412yes—
207C23×D61—22no—
208C23×D61—22no—
209C23×D61—22no—
210C23×D61—22no—
211C23×D61—24no—
212C23×D61—24no—
213C23×D61—42no—
214C23×D61—42no—
215C23×D61—44no—
216C23×D61—44no—
217C23×D61—82no—
218C23×D61—82no—
219C23×D61C22×C411yescharacteristic
220C23×D61C22×C412yes—
221C23×D61C22×C412yes—
222C2×D4×C61—22no—
223C2×D4×C61—22no—
224C2×D4×C61—21no—
225C2×D4×C61—21no—
226C2×D4×C61—21no—
227C2×D4×C61—21no—
228C2×D4×C61—21no—
229C2×D4×C61—21no—
230C2×D4×C61—44no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61C22×C411yescharacteristic
236C22×C4×C61C22×C412yes—
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2411yescharacteristic
242C2×C22⋊D61—24no—
243C2×C22⋊D61—24no—
244C2×C22⋊D61—22no—
245C2×C22⋊D61—22no—
246C2×C22⋊D61—22no—
247C2×C22⋊D61—22no—
248C2×C22⋊D61—22no—
249C2×C22⋊D61—22no—
250C2×C22⋊D61—42no—
251C2×C22⋊D61—44no—
252C2×C22⋊D61—82no—
253C2×C22⋊D61C22⋊C411yescharacteristic
254C2×C22⋊D61C22⋊C411yescharacteristic
255C2×C22⋊D61C22⋊C411yescharacteristic
256C2×C22⋊D61C22⋊C411yescharacteristic
257C22×Dic61C22×C411yescharacteristic
258C22×Dic61C22×C411yescharacteristic
259C22×Dic61C22×C411yescharacteristic
260D4×D61—42no—
261D4×D61—42no—
262D4×D61—42no—
263D4×D61—42no—
264D4×D61—42no—
265D4×D61—42no—
266D4×D61—42no—
267D4×D61—42no—
268D4×D61—48no—
269D4×D61—48no—
270D4×D61—48no—
271D4×D61—48no—
272C2×D244—21no—
273C2×D244—21no—
274C2×D244—21no—
275C2×D244—21no—
276C2×D244—22no—
277C2×D244—22no—
278C2×D244—24no—
279C2×D244—22no—
280C2×D244—22no—
281C2×D244—21no—
282C2×D244—21no—
283C2×D244—21no—
284C2×D244—21no—
285C2×D244—21no—
286C2×D244—21no—
287C2×D244—42no—
288C2×D244—42no—
289C2×D244—42no—
290C2×D244—42no—
291C2×D244—42no—
292C2×D244—42no—
293C2×D244—42no—
294C2×D244—42no—
295C2×D244—42no—
296C2×D244—44no—
297C2×D244C2×D412yes—
298C2×D244#4112yes—
299C2×C4×D61—21no—
300C2×C4×D61—21no—
301C2×C4×D61—21no—
302C2×C4×D61—21no—
303C2×C4×D61—22no—
304C2×C4×D61—22no—
305C2×C4×D61—44no—
306C2×C4×D61C2×D411yescharacteristic
307C2×C4×D61C2×D411yescharacteristic
308C2×C4×D61C2×D411yescharacteristic
309C2×C4×D61C2×D411yescharacteristic
310M16×C61—21no—
311M16×C61—21no—
312M16×C61—21no—
313M16×C61—21no—
314M16×C61—21no—
315M16×C61—21no—
316M16×C61—21no—
317M16×C61—42no—
318M16×C61C2×D412yescomplemented
319C2×C8×C61—21no—
320C2×C8×C61—21no—
321C2×C8×C61—21no—
322C2×C8×C61—21no—
323C2×C8×C61—42no—
324C4⋊C4×C61—21no—
325C4⋊C4×C61—21no—
326C22⋊C4×C61—22no—
327C22⋊C4×C61—22no—
328C22⋊Dic61C22⋊C411yescharacteristic
329C22⋊Dic61C22⋊C411yescharacteristic
330C22⋊Dic61C22⋊C411yescharacteristic
331C22⋊Dic61C22⋊C411yescharacteristic
332#11758198—22no—
333#11758198—22no—
334#11758198—22no—
335#11758198—22no—
336#11758198C22⋊C411yescharacteristic
337#11758198C22⋊C411yescharacteristic
338#11758198C22⋊C411yescharacteristic
339#11758198C22⋊C411yescharacteristic
340#11758196C22⋊C411yescharacteristic
341#11758196C22⋊C411yescharacteristic
342#11758196C22⋊C411yescharacteristic
343#11758196C22⋊C411yescharacteristic
344C4×Dic61C2×D411yescharacteristic
345C4×Dic61C2×D411yescharacteristic
346C4×Dic61C2×D411yescharacteristic
347C4×Dic61C2×D411yescharacteristic
348#11758194—21no—
349#11758194—21no—
350#11758194—21no—
351#11758194—21no—
352#11758194—21no—
353#11758194—21no—
354#11758194—21no—
355#11758194—42no—
356#11758194C2×D412yescomplemented
357C2×#92418—21no—
358C2×#92418—21no—
359C2×#92418—21no—
360C2×#92418—21no—
361C2×#92418—42no—
362#11758189—42no—
363#11758189—42no—
364C8×D61—42no—
365C8×D61—42no—
366C23×C61—21no—
367C23×C61—21no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—41no—
373C23×C61—42no—
374C23×C61—42no—
375C23×C61C2×C22⋊C411yescharacteristic
376C23×C61C2×C22⋊C411yescharacteristic
377C23×C61C23×C411yescharacteristic
378C22×D61—22no—
379C22×D61—21no—
380C22×D61—21no—
381C22×D61—22no—
382C22×D61—22no—
383C22×D61—22no—
384C22×D61—22no—
385C22×D61—22no—
386C22×D61—41no—
387C22×D61—44no—
388C22×D61—44no—
389C22×D61—44no—
390C22×D61—44no—
391C22×D61—44no—
392C22×D61—42no—
393C22×D61—42no—
394C22×D61—44no—
395C22×D61—44no—
396C22×D61—44no—
397C22×D61—42no—
398C22×D61—42no—
399C22×D61—82no—
400C22×D61—82no—
401C22×D61—82no—
402C22×D61—82no—
403C22×D61—88no—
404C22×D61—88no—
405C22×D61—88no—
406C22×D61—88no—
407C22×D61C2×C22⋊C411yescharacteristic
408C22×D61C2×C22⋊C411yescharacteristic
409C22×D61C4×D414yes—
410D4×C61—44no—
411D4×C61—44no—
412D4×C61—41no—
413D4×C61—41no—
414D4×C61—41no—
415D4×C61—41no—
416C2×C4×C61—21no—
417C2×C4×C61—21no—
418C2×C4×C61—21no—
419C2×C4×C61—21no—
420C2×C4×C61—21no—
421C2×C4×C61—21no—
422C2×C4×C61—21no—
423C2×C4×C61—21no—
424C2×C4×C61—21no—
425C2×C4×C61—21no—
426C2×C4×C61—22no—
427C2×C4×C61—42no—
428C2×C4×C61C2×C22⋊C411yescharacteristic
429C2×C4×C61C2×C22⋊C411yescharacteristic
430C2×C4×C61C22×D411yescharacteristic
431C2×C4×C61C22×D411yescharacteristic
432C2×C4×C61C22×D411yescharacteristic
433C2×C4×C61C2×#4111yescharacteristic
434C2×C4×C61H(5,𝔽2)11yescharacteristic
435C2×C4×C61H(5,𝔽2)11yescharacteristic
436C22⋊D61—22no—
437C22⋊D61—22no—
438C22⋊D61—22no—
439C22⋊D61—44no—
440C22⋊D61—44no—
441C22⋊D61—44no—
442C22⋊D61—44no—
443C22⋊D61—82no—
444C22⋊D61—82no—
445C22⋊D61#10014yescomplemented
446C2×Dic61—21no—
447C2×Dic61—21no—
448C2×Dic61—22no—
449C2×Dic61—41no—
450C2×Dic61C2×C22⋊C411yescharacteristic
451C2×Dic61C2×C22⋊C411yescharacteristic
452C2×Dic61C2×C22⋊C411yescharacteristic
453C2×Dic61C2×C22⋊C411yescharacteristic
454C2×Dic61C2×C22⋊C411yescharacteristic
455C2×Dic61C2×C22⋊C411yescharacteristic
456D244—22no—
457D244—22no—
458D244—22no—
459D244—22no—
460D244—44no—
461D244—44no—
462D244—44no—
463D244—44no—
464D244—41no—
465D244—41no—
466D244—41no—
467D244—41no—
468C4×D61—21no—
469C4×D61—21no—
470C4×D61—21no—
471C4×D61—21no—
472C4×D61—21no—
473C4×D61—21no—
474C4×D61—21no—
475C4×D61—21no—
476C4×D61—44no—
477C4×D61—44no—
478C8×C61—22no—
479C8×C61—41no—
480C8×C61—41no—
481C8×C61—41no—
482#92418—22no—
483#92418—41no—
484#92418—41no—
485#92418—41no—
486D4×#100—611nomaximal, Sylow
487C22×C61—21no—
488C22×C61—21no—
489C22×C61—21no—
490C22×C61—21no—
491C22×C61—21no—
492C22×C61—21no—
493C22×C61—21no—
494C22×C61—42no—
495C22×C61—42no—
496C22×C61—42no—
497C22×C61—42no—
498C22×C61—42no—
499C22×C61—82no—
500C22×C61—82no—
501C22×C61C2×#10012yescomplemented
502C22×C61C22×C22⋊C411yescharacteristic
503C22×C61C2×C4×D411yescharacteristic
504C22×C61#51811yescharacteristic
505C2×D61—21no—
506C2×D61—21no—
507C2×D61—21no—
508C2×D61—24no—
509C2×D61—21no—
510C2×D61—21no—
511C2×D61—42no—
512C2×D61—42no—
513C2×D61—44no—
514C2×D61—42no—
515C2×D61—42no—
516C2×D61—44no—
517C2×D61—42no—
518C2×D61—42no—
519C2×D61—42no—
520C2×D61—88no—
521C2×D61—88no—
522C2×D61—88no—
523C2×D61—88no—
524C2×D61—82no—
525C2×D61—82no—
526C2×D61C2×#10012yescomplemented
527C4×C61—21no—
528C4×C61—21no—
529C4×C61—42no—
530C4×C61D4211yescharacteristic
531C4×C61D4211yescharacteristic
532C4×C61#54611yescharacteristic
533C4×C61#54611yescharacteristic
534Dic61—21no—
535Dic61—21no—
536Dic61—21no—
537Dic61—21no—
538Dic61—21no—
539Dic61C2×#10012yescomplemented
540C2×D42—611no—
541D4×M16—611no—
542D4×M16—611no—
543C22×#100—611no—
544C22×#100—611no—
545#1965—611no—
546#1965—611no—
547#1900—611no—
548#1900—611no—
549#1900—611no—
550#1900D6111yescharacteristic, complemented
551#1800—611no—
552#1783—611no—
553#1783—611no—
554C4×#100—611no—
555C2×C61—21no—
556C2×C61—21no—
557C2×C61—22no—
558C2×C61—41no—
559C2×C61—82no—
560C2×C61D4×C22⋊C411yescharacteristic
561C2×C61C22×#10011yescharacteristic
562C2×C61#288811yescharacteristic
563D61—22no—
564D61—41no—
565D61—44no—
566D61—82no—
567C23×D4—611no—
568C23×D4—612no—
569C23×D4—611no—
570C22×M16—611no—
571C22×M16—611no—
572C22×M16—611no—
573C22×M16C2×D6111yescharacteristic, complemented
574D42—1221no—
575D42—1221no—
576D42—1221no—
577D42—1221no—
578D42—1221no—
579D42—1221no—
580D42—1221no—
581D42—1221no—
582C2×#127—611no—
583C2×#121—611no—
584C2×#121—612no—
585C2×#121C2×D6111yescharacteristic
586C2×#120—612no—
587C2×#120—612no—
588C2×C4×D4—611no—
589C2×C4×D4—611no—
590#436—1221no—
591#436—1221no—
592#435—1221no—
593#435—1221no—
594#435—1221no—
595#435—1221no—
596C8×D4—1221no—
597C8×D4—1221no—
598#423—611no—
599#423—611no—
600C2×#100—611no—
601C2×#100—611no—
602C2×#100—611no—
603C2×#100—611no—
604C2×#100—611no—
605C2×#100—611no—
606C2×#100—611no—
607C2×#100—611no—
608C2×#100—611no—
609C2×#100—611no—
610C2×#100—1224no—
611C2×#100—1224no—
612C2×#100C2×D6111yescharacteristic, complemented
613C2×#100C2×D6111yescharacteristic, complemented
614#407—611no—
615#407—611no—
616#407—611no—
617#407C2×D6111yescharacteristic, complemented
618C4×M16—611no—
619C4×M16—611no—
620#343—611no—
621#343—611no—
622#343C2×D6111yescharacteristic, complemented
623#343C2×D6111yescharacteristic, complemented
624C61D4×#10011yescharacteristic, complemented, Sylow
625C25—612no—
626C25—612no—
627C22×D4—611no—
628C22×D4—612no—
629C22×D4—612no—
630C22×D4—612no—
631C22×D4—612no—
632C22×D4—612no—
633C22×D4—611no—
634C22×D4—611no—
635C22×D4—1222no—
636C22×D4—1222no—
637C22×D4—1221no—
638C22×D4—1221no—
639C22×D4—1221no—
640C22×D4—1221no—
641C22×D4—1222no—
642C22×D4—1222no—
643C22×D4—1222no—
644C22×D4—1222no—
645C22×D4—1222no—
646C22×D4—1222no—
647C22×D4—1221no—
648C22×D4—1221no—
649C22×D4—1221no—
650C22×D4—1221no—
651C22×D4—2441no—
652C22×D4—2441no—
653C22×D4—2441no—
654C22×D4—2441no—
655C22×D4—2448no—
656C22×D4C4×D6112yes—
657C22×D4C22×D6111yescharacteristic
658C23×C4—611no—
659C23×C4—612no—
660C23×C4C22×D6111yescharacteristic
661C2×M16—21no—
662C2×M16—22no—
663C2×M16—41no—
664C2×M16—611no—
665C2×M16—611no—
666C2×M16—611no—
667C2×M16—611no—
668C2×M16—1221no—
669C2×M16—1221no—
670C2×M16—1221no—
671C2×M16—1222no—
672C2×M16—1222no—
673C2×M16—1222no—
674C2×M16—2441no—
675C2×M16—2441no—
676C2×M16—2441no—
677C2×M16C22×D6111yescharacteristic
678C2×M16C22×D6111yescharacteristic
679C2×M16C22×D6111yescharacteristic
680C2×M16C22×D6111yescharacteristic
681C22×C8—21no—
682C22×C8—1221no—
683C22×C8—1221no—
684C22×C8—1221no—
685#127—1221no—
686#127—1221no—
687#127—1221no—
688#127—1221no—
689#121—21no—
690#121—21no—
691#121—21no—
692#121—21no—
693#121—1222no—
694#121—1222no—
695#121—1222no—
696#121—1222no—
697#121—1221no—
698#121—1221no—
699#121—1221no—
700#121—1221no—
701#120—1222no—
702#120—1222no—
703#120—1222no—
704#120—1222no—
705#120—1222no—
706#120—1222no—
707#120—1222no—
708#120—1222no—
709C4×D4—611no—
710C4×D4—611no—
711C4×D4—611no—
712C4×D4—611no—
713C4×D4—611no—
714C4×D4—611no—
715C4×D4—611no—
716C4×D4—611no—
717C4×D4—1221no—
718C4×D4—1221no—
719C4×D4—1221no—
720C4×D4—1221no—
721C2×C4⋊C4—611no—
722C2×C4⋊C4C22×D6111yescharacteristic
723C2×C22⋊C4—611no—
724C2×C22⋊C4—611no—
725C2×C22⋊C4—612no—
726C2×C22⋊C4—612no—
727C2×C22⋊C4C4×D6112yes—
728C2×C42—611no—
729C4⋊C8—1221no—
730C4⋊C8—1221no—
731C4⋊C8—1221no—
732C4⋊C8—1221no—
733#100—22no—
734#100—41no—
735#100—614no—
736#100—1222no—
737#100—1222no—
738#100—1222no—
739#100—1222no—
740#100—1222no—
741#100—1222no—
742#100—2441no—
743#100—2441no—
744#100—2441no—
745C22⋊C8—21no—
746C22⋊C8—21no—
747C22⋊C8—1221no—
748C22⋊C8—1221no—
749C22⋊C8—1221no—
750C22⋊C8—1221no—
751C22⋊C8—1221no—
752C22⋊C8—1221no—
753#97—1221no—
754#97—1221no—
755C4×C8—1221no—
756C4×C8—1221no—
757C24—611no—
758C24—612no—
759C24—612no—
760C24—1224no—
761C24—1224no—
762C24—1222no—
763C24—1222no—
764C24—1222no—
765C24—1222no—
766C24—4882no—
767C24—4882no—
768C24—2442no—
769C24—2442no—
770C24—2444no—
771C24—2444no—
772C24C2×C4×D6111yescharacteristic
773C24C2×C4×D6112yes—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—44no—
783C2×D4—611no—
784C2×D4—611no—
785C2×D4—611no—
786C2×D4—611no—
787C2×D4—612no—
788C2×D4—612no—
789C2×D4—1222no—
790C2×D4—1222no—
791C2×D4—1224no—
792C2×D4—1222no—
793C2×D4—1222no—
794C2×D4—1222no—
795C2×D4—1222no—
796C2×D4—1222no—
797C2×D4—1222no—
798C2×D4—1224no—
799C2×D4—1224no—
800C2×D4—1221no—
801C2×D4—1221no—
802C2×D4—1221no—
803C2×D4—1221no—
804C2×D4—1221no—
805C2×D4—1221no—
806C2×D4—1221no—
807C2×D4—1221no—
808C2×D4—1221no—
809C2×D4—1221no—
810C2×D4—1222no—
811C2×D4—1222no—
812C2×D4—4882no—
813C2×D4—2442no—
814C2×D4—2442no—
815C2×D4—2442no—
816C2×D4—2442no—
817C2×D4—2442no—
818C2×D4—2442no—
819C2×D4—2442no—
820C2×D4—2442no—
821C2×D4—2442no—
822C2×D4—2444no—
823C2×D4—2442no—
824C2×D4—2442no—
825C2×D4—2442no—
826C2×D4—2442no—
827C2×D4—2442no—
828C2×D4—2442no—
829C2×D4—2442no—
830C2×D4—2442no—
831C2×D4—2442no—
832C2×D4—2444no—
833C2×D4—2448no—
834C2×D4—2448no—
835C2×D4—2448no—
836C2×D4—2448no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—611no—
842C22×C4—611no—
843C22×C4—611no—
844C22×C4—611no—
845C22×C4—611no—
846C22×C4—611no—
847C22×C4—611no—
848C22×C4—1222no—
849C22×C4—1222no—
850C22×C4—1221no—
851C22×C4—1221no—
852C22×C4—1221no—
853C22×C4—1221no—
854C22×C4—2444no—
855C22×C4C2×C4×D6111yescharacteristic
856C22×C4C2×C4×D6112yes—
857C22×C4D4×D6111yescharacteristic
858C22×C4D4×D6111yescharacteristic
859C22×C4D4×D6111yescharacteristic
860C22×C4D4×D6111yescharacteristic
861C22×C4C23×D6111yescharacteristic
862M16—21no—
863M16—21no—
864M16—21no—
865M16—21no—
866M16—21no—
867M16—21no—
868M16—21no—
869M16—42no—
870M16—612no—
871M16—1221no—
872M16—1221no—
873M16—1221no—
874M16—1221no—
875M16—1221no—
876M16—1221no—
877M16—1221no—
878M16—2442no—
879M16—2442no—
880M16—2442no—
881M16D4×D6112yescomplemented
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—42no—
887C2×C8—1221no—
888C2×C8—1221no—
889C2×C8—1221no—
890C2×C8—1221no—
891C2×C8—2442no—
892C2×C8—2442no—
893C2×C8—2442no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—611no—
897C4⋊C4—611no—
898C4⋊C4—611no—
899C4⋊C4—611no—
900C22⋊C4—22no—
901C22⋊C4—22no—
902C22⋊C4—611no—
903C22⋊C4—611no—
904C22⋊C4—611no—
905C22⋊C4—611no—
906C22⋊C4—611no—
907C22⋊C4—611no—
908C22⋊C4—611no—
909C22⋊C4—611no—
910C22⋊C4—1222no—
911C22⋊C4—1222no—
912C22⋊C4—1222no—
913C22⋊C4—1222no—
914C42—611no—
915C42—611no—
916C42—611no—
917C42—611no—
918C23—21no—
919C23—21no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—41no—
925C23—42no—
926C23—42no—
927C23—611no—
928C23—611no—
929C23—614no—
930C23—1222no—
931C23—1222no—
932C23—1221no—
933C23—1221no—
934C23—1222no—
935C23—1222no—
936C23—1222no—
937C23—1222no—
938C23—4882no—
939C23—4882no—
940C23—4882no—
941C23—4882no—
942C23—4888no—
943C23—4888no—
944C23—4888no—
945C23—4888no—
946C23—2441no—
947C23—2444no—
948C23—2444no—
949C23—2442no—
950C23—2442no—
951C23—2444no—
952C23—2442no—
953C23—2442no—
954C23—2444no—
955C23—2444no—
956C23—2444no—
957C23—2444no—
958C23—2444no—
959C23C22⋊C4×D6111yescharacteristic
960C23C22⋊C4×D6111yescharacteristic
961C23C22×C4×D6111yescharacteristic
962D4—44no—
963D4—44no—
964D4—41no—
965D4—41no—
966D4—41no—
967D4—41no—
968D4—614no—
969D4—1222no—
970D4—1222no—
971D4—1222no—
972D4—1222no—
973D4—1222no—
974D4—1222no—
975D4—1222no—
976D4—4882no—
977D4—4882no—
978D4—2444no—
979D4—2444no—
980D4—2444no—
981D4—2444no—
982D4—2444no—
983D4—2444no—
984D4—2444no—
985D4—2444no—
986D4—2441no—
987D4—2441no—
988D4—2441no—
989D4—2441no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—42no—
1002C2×C4—611no—
1003C2×C4—611no—
1004C2×C4—611no—
1005C2×C4—611no—
1006C2×C4—611no—
1007C2×C4—611no—
1008C2×C4—1222no—
1009C2×C4—1221no—
1010C2×C4—1221no—
1011C2×C4—1221no—
1012C2×C4—1221no—
1013C2×C4—1221no—
1014C2×C4—1221no—
1015C2×C4—1221no—
1016C2×C4—1221no—
1017C2×C4—1221no—
1018C2×C4—1221no—
1019C2×C4—2444no—
1020C2×C4—2444no—
1021C2×C4—2441no—
1022C2×C4C22⋊C4×D6111yescharacteristic
1023C2×C4C22⋊C4×D6111yescharacteristic
1024C2×C4C2×D4×D6111yescharacteristic
1025C2×C4C2×D4×D6111yescharacteristic
1026C2×C4C2×D4×D6111yescharacteristic
1027C2×C4#41×D6111yescharacteristic
1028C2×C4#1451982211yescharacteristic
1029C2×C4#1451982311yescharacteristic
1030C8—22no—
1031C8—41no—
1032C8—41no—
1033C8—41no—
1034C8—1222no—
1035C8—2441no—
1036C8—2441no—
1037C8—2441no—
1038C22—21no—
1039C22—21no—
1040C22—21no—
1041C22—21no—
1042C22—21no—
1043C22—21no—
1044C22—21no—
1045C22—42no—
1046C22—42no—
1047C22—42no—
1048C22—42no—
1049C22—42no—
1050C22—82no—
1051C22—82no—
1052C22—612no—
1053C22—1221no—
1054C22—1221no—
1055C22—1221no—
1056C22—1224no—
1057C22—1221no—
1058C22—1221no—
1059C22—4882no—
1060C22—4882no—
1061C22—4888no—
1062C22—4888no—
1063C22—4888no—
1064C22—4888no—
1065C22—2442no—
1066C22—2442no—
1067C22—2444no—
1068C22—2444no—
1069C22—2442no—
1070C22—2442no—
1071C22—2442no—
1072C22—2442no—
1073C22—2442no—
1074C22#100×D6112yescomplemented
1075C22C2×C22⋊C4×D6111yescharacteristic
1076C22C4×D4×D6111yescharacteristic
1077C22#1684023411yescharacteristic
1078C4—21no—
1079C4—21no—
1080C4—42no—
1081C4—612no—
1082C4—1221no—
1083C4—1221no—
1084C4—1221no—
1085C4—1221no—
1086C4—1221no—
1087C4#1684039411yescharacteristic
1088C4#1684039611yescharacteristic
1089C4#1684040111yescharacteristic
1090C4#1684040411yescharacteristic
1091C2—21no—
1092C2—21no—
1093C2—22no—
1094C2—41no—
1095C2—82no—
1096C2—1222no—
1097C2—4882no—
1098C2—2441no—
1099C2—2444no—
1100C2#2144863711yescharacteristic
1101C2C2×#100×D6111yescharacteristic
1102C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1900C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840396C2
cosocleC22×C4×C61C24
hypercenter#1900D61
hypocenterC61D4×#100
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1900

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D61C2semidirect
3. #21454551C2semidirect
4. C22×#14519693C2semidirect
5. C2×#100×D61C2semidirect
6. #21446657C2semidirect
7. #21446657C2semidirect
8. #21446283C2semidirect
9. #21446281C2semidirect
10. #21446281C2semidirect
11. #21445810C2semidirect
12. #21445739C2semidirect
13. #21445738C2semidirect
14. #21445610C2semidirect
15. C61×#1900C2semidirect
19. C22×#11758194C22semidirect
20. C2×M16×D61C22semidirect
21. C2×M16×D61C22semidirect
45. #16839785C22semidirect
46. #16839785C22semidirect
47. C2×#14519694C22semidirect
48. C2×#14519694C22semidirect
54. C2×#14519693C22semidirect
55. C2×#14519693C22semidirect
56. C2×#14519693C22semidirect
57. C2×#14519693C22semidirect
59. #16839726C22semidirect
60. #16839725C22semidirect
61. #16839725C22semidirect
62. M16×Dic61C22semidirect
63. M16×Dic61C22semidirect
64. #16839531C22semidirect
65. #16839531C22semidirect
66. C22×M16×C61C22semidirect
68. C2×#100×C61C22semidirect
69. C2×#100×C61C22semidirect
70. C61×#407C22semidirect
71. C61×#343C22semidirect
72. C61×#343C22semidirect
173. #14519693D4semidirect
318. M16×C61C2×D4semidirect
356. #11758194C2×D4semidirect
445. C22⋊D61#100semidirect
501. C22×C61C2×#100semidirect
526. C2×D61C2×#100semidirect
539. Dic61C2×#100semidirect
550. #1900D61semidirect
573. C22×M16C2×D61semidirect
612. C2×#100C2×D61semidirect
613. C2×#100C2×D61semidirect
617. #407C2×D61semidirect
622. #343C2×D61semidirect
623. #343C2×D61semidirect
624. C61D4×#100semidirect
881. M16D4×D61semidirect
1074. C22#100×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403962
M16×C22⋊D612
#214545512
C22×#145196932
C2×#100×D612
#214466572
#214462832
#214462812
#214458102
#214457392
#214457382
#214456102
C61×#19002
D4×#10061