Finite Group Databasebeta

← #29695371

Subgroups — #29695371

Order 15616.

1544 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840403C211yesmaximal, characteristic
2M16×C22⋊D61C211yesmaximal, characteristic, complemented
3#21454551C211yesmaximal, characteristic, complemented
4C2×#16839745C211yesmaximal, characteristic, complemented
5C22×#14519693C211yesmaximal, characteristic, complemented
6#21446667C211yesmaximal, characteristic, complemented
7#21446667C211yesmaximal, characteristic, complemented
8#21446288C211yesmaximal, characteristic, complemented
9#21446281C211yesmaximal, characteristic, complemented
10#21446281C211yesmaximal, characteristic, complemented
11#21445810C211yesmaximal, characteristic, complemented
12#21445746C211yesmaximal, characteristic, complemented
13#21445739C211yesmaximal, characteristic, complemented
14#21445610C211yesmaximal, characteristic, complemented
15C61×#1901C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic, complemented
20C2×M16×D61C2211yescharacteristic, complemented
21#16840403—21no—
22#16840403—21no—
23#16840403—21no—
24#16840403—21no—
25#16840403—21no—
26#16840403—21no—
27#16840403—21no—
28#16840403—21no—
29C2×#14519766C2211yescharacteristic
30C2×#14519762C412yes—
31C2×#14519752C412yes—
32C2×#14519752C2211yescharacteristic
33C2×#14519747C412yes—
34C2×#14519739C2211yescharacteristic
35C2×C4×C22⋊D61C2211yescharacteristic
36C2×C22⋊C4×D61C412yes—
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
47#16839745—24no—
48C2×#14519696C2211yescharacteristic, complemented
49C2×#14519696C2211yescharacteristic, complemented
50C2×#14519693—24no—
51C2×#14519693C2211yescharacteristic
52C2×#14519693C2211yescharacteristic
53C2×#14519693C2211yescharacteristic
54C2×#14519693C2211yescharacteristic
55C2×#14519693C2211yescharacteristic
56C2×#14519693C2211yescharacteristic
57C2×#14519693C2211yescharacteristic
58C2×#14519693C2211yescharacteristic
59#16839726C2211yescharacteristic
60#16839725C2211yescharacteristic, complemented
61#16839725C2211yescharacteristic, complemented
62M16×Dic61C2211yescharacteristic, complemented
63M16×Dic61C2211yescharacteristic, complemented
64#16839531C2211yescharacteristic, complemented
65#16839531C2211yescharacteristic, complemented
66C22×M16×C61C2211yescharacteristic
67C2×C22⋊Q8×C61C2211yescharacteristic
68C2×#101×C61C2211yescharacteristic, complemented
69C2×#101×C61C2211yescharacteristic, complemented
70C61×#407C2211yescharacteristic
71C61×#343C2211yescharacteristic, complemented
72C61×#343C2211yescharacteristic, complemented
73C24×D61C2×C412yes—
74C2×#11758226—22no—
75C2×#11758226—22no—
76C2×#11758226—21no—
77C2×#11758226—21no—
78C2×#11758226—21no—
79C2×#11758226—21no—
80C2×#11758226—41no—
81C2×#11758226—41no—
82C22×D244—21no—
83C22×D244—21no—
84C22×D244—21no—
85C22×D244—21no—
86C22×D244—22no—
87C22×D244—22no—
88C22×D244—41no—
89C22×D244—41no—
90C22×D244C2×C412yes—
91C22×D244C2×C412yes—
92C22×D244C2×C412yes—
93C22×D244C2311yescharacteristic
94C22×D244C2311yescharacteristic
95C22×C22⋊D61C2×C411yescharacteristic
96C22×C4×D61C2×C412yes—
97C22×C4×D61C2×C412yes—
98C22×C4×D61C2311yescharacteristic
99C2×#11758194—21no—
100C2×#11758194—22no—
101C2×#11758194—41no—
102C2×#11758194C2311yescharacteristic
103C2×#11758194C2311yescharacteristic
104C2×#11758194C2311yescharacteristic
105C2×#11758194C2311yescharacteristic
106C2×#11758189—21no—
107C2×#11758189—21no—
108M16×D61—22no—
109M16×D61—22no—
110M16×D61—41no—
111M16×D61—41no—
112C22×#92418—21no—
113C2×C8×D61—21no—
114C2×C8×D61—21no—
115#14519766—21no—
116#14519766—21no—
117#14519766—21no—
118#14519766—21no—
119#14519762—22no—
120#14519762—22no—
121#14519762—22no—
122#14519762—22no—
123#14519752—21no—
124#14519752—21no—
125#14519752—21no—
126#14519752—21no—
127#14519752—22no—
128#14519752—22no—
129#14519752—22no—
130#14519752—22no—
131#14519747—22no—
132#14519747—22no—
133#14519747—22no—
134#14519747—22no—
135#14519739—21no—
136#14519739—21no—
137#14519739—21no—
138#14519739—21no—
139C4×C22⋊D61D411yescharacteristic
140C4×C22⋊D61D411yescharacteristic
141C4×C22⋊D61D411yescharacteristic
142C4×C22⋊D61D411yescharacteristic
143C4×C22⋊D61D411yescharacteristic
144C4×C22⋊D61D411yescharacteristic
145C4×C22⋊D61D411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C2×#11758196C2×C411yescharacteristic
148C2×C22⋊Dic61C2×C411yescharacteristic
149C2×#11758198C2×C412yes—
150C2×#11758198C2×C412yes—
151C2×#11758198C2×C412yes—
152C2×#11758198C2×C412yes—
153C2×#11758198C2×C411yescharacteristic
154C22⋊C4×D61—22no—
155C22⋊C4×D61—22no—
156C22⋊C4×D61—22no—
157C22⋊C4×D61—22no—
158C2×C4×Dic61C2311yescharacteristic
159#14519706—21no—
160#14519706—21no—
161#14519706—21no—
162#14519706—21no—
163#14519696—22no—
164#14519696—41no—
165#14519693—22no—
166#14519693—22no—
167#14519693—22no—
168#14519693—22no—
169#14519693—22no—
170#14519693—41no—
171#14519693—41no—
172#14519693D414yescomplemented
173C22⋊#92418—21no—
174C22⋊#92418—21no—
175#14519689—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519687—21no—
180#14519687—21no—
181C8×Dic61—21no—
182C8×Dic61—21no—
183C22×Q8×C61C2311yescharacteristic
184C23×C4×C61C2311yescharacteristic
185C2×M16×C61—21no—
186C2×M16×C61—22no—
187C2×M16×C61—41no—
188C2×M16×C61C2311yescharacteristic
189C2×M16×C61C2311yescharacteristic
190C2×M16×C61C2311yescharacteristic
191C2×M16×C61C2311yescharacteristic
192C22×C8×C61—21no—
193C22⋊Q8×C61—21no—
194C22⋊Q8×C61—21no—
195C22⋊Q8×C61—21no—
196C22⋊Q8×C61—21no—
197C2×C4⋊C4×C61C2×C412yes—
198C2×C4⋊C4×C61C2311yescharacteristic
199C2×C22⋊C4×C61C2×C412yes—
200#101×C61—22no—
201#101×C61—41no—
202C22⋊C8×C61—21no—
203C22⋊C8×C61—21no—
204C24×C61C22×C411yescharacteristic
205C23×D61—22no—
206C23×D61—22no—
207C23×D61—24no—
208C23×D61—42no—
209C23×D61—44no—
210C23×D61—82no—
211C23×D61C22×C412yes—
212C23×D61C22×C411yescharacteristic
213C23×D61C22×C412yes—
214C2×Q8×C61—21no—
215C2×Q8×C61—21no—
216C2×Q8×C61—21no—
217C2×Q8×C61—21no—
218C2×Q8×C61—21no—
219C2×Q8×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61C22×C412yes—
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C22×C412yes—
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2411yescharacteristic
232C2×C22⋊D61—42no—
233C2×C22⋊D61C22⋊C411yescharacteristic
234C2×C22⋊D61C22⋊C411yescharacteristic
235C2×C22⋊D61C22⋊C411yescharacteristic
236C2×C22⋊D61C22⋊C411yescharacteristic
237C22×Dic61C22×C411yescharacteristic
238C22×Dic61C22×C411yescharacteristic
239C22×Dic61C22×C411yescharacteristic
240#11758226—42no—
241#11758226—42no—
242#11758226—42no—
243#11758226—42no—
244#11758226—42no—
245#11758226—42no—
246#11758226—42no—
247#11758226—42no—
248C2×D244—21no—
249C2×D244—21no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244—22no—
253C2×D244—22no—
254C2×D244—24no—
255C2×D244—24no—
256C2×D244—22no—
257C2×D244—22no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—21no—
261C2×D244—21no—
262C2×D244—21no—
263C2×D244—21no—
264C2×D244—22no—
265C2×D244—22no—
266C2×D244—42no—
267C2×D244—42no—
268C2×D244—42no—
269C2×D244—42no—
270C2×D244—42no—
271C2×D244—42no—
272C2×D244—42no—
273C2×D244—42no—
274C2×D244—42no—
275C2×D244—42no—
276C2×D244—82no—
277C2×D244C2×D412yes—
278C2×D244#4112yes—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—24no—
284C2×C4×D61—22no—
285C2×C4×D61—22no—
286C2×C4×D61—22no—
287C2×C4×D61—22no—
288C2×C4×D61—42no—
289C2×C4×D61—82no—
290C2×C4×D61C2×D411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2×D411yescharacteristic
293C2×C4×D61C2×D411yescharacteristic
294M16×C61—21no—
295M16×C61—21no—
296M16×C61—21no—
297M16×C61—21no—
298M16×C61—21no—
299M16×C61—21no—
300M16×C61—21no—
301M16×C61—42no—
302M16×C61C2×D412yes—
303C2×C8×C61—21no—
304C2×C8×C61—21no—
305C2×C8×C61—21no—
306C2×C8×C61—21no—
307C2×C8×C61—42no—
308C4⋊C4×C61—22no—
309C4⋊C4×C61—22no—
310C4⋊C4×C61—21no—
311C4⋊C4×C61—21no—
312C22⋊C4×C61—22no—
313C22⋊C4×C61—22no—
314C22⋊Dic61C22⋊C411yescharacteristic
315C22⋊Dic61C22⋊C411yescharacteristic
316C22⋊Dic61C22⋊C411yescharacteristic
317C22⋊Dic61C22⋊C411yescharacteristic
318#11758198—22no—
319#11758198—22no—
320#11758198—22no—
321#11758198—22no—
322#11758198—22no—
323#11758198—22no—
324#11758198—22no—
325#11758198—22no—
326#11758198C22⋊C411yescharacteristic
327#11758198C22⋊C411yescharacteristic
328#11758198C22⋊C411yescharacteristic
329#11758198C22⋊C411yescharacteristic
330#11758196C22⋊C411yescharacteristic
331#11758196C22⋊C411yescharacteristic
332#11758196C22⋊C411yescharacteristic
333#11758196C22⋊C411yescharacteristic
334C4×Dic61C2×D411yescharacteristic
335C4×Dic61C2×D411yescharacteristic
336C4×Dic61C2×D411yescharacteristic
337C4×Dic61C2×D411yescharacteristic
338#11758194—21no—
339#11758194—21no—
340#11758194—21no—
341#11758194—21no—
342#11758194—21no—
343#11758194—21no—
344#11758194—21no—
345#11758194—42no—
346#11758194C2×D412yes—
347C2×#92418—21no—
348C2×#92418—21no—
349C2×#92418—21no—
350C2×#92418—21no—
351C2×#92418—42no—
352#11758189—42no—
353#11758189—42no—
354C8×D61—42no—
355C8×D61—42no—
356C23×C61—21no—
357C23×C61—21no—
358C23×C61—22no—
359C23×C61—41no—
360C23×C61C2×C22⋊C411yescharacteristic
361C23×C61C2×C22⋊C411yescharacteristic
362C23×C61C23×C411yescharacteristic
363C22×D61—22no—
364C22×D61—22no—
365C22×D61—21no—
366C22×D61—21no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—41no—
371C22×D61—41no—
372C22×D61—44no—
373C22×D61—44no—
374C22×D61—42no—
375C22×D61—42no—
376C22×D61—44no—
377C22×D61—44no—
378C22×D61—42no—
379C22×D61—42no—
380C22×D61—82no—
381C22×D61—82no—
382C22×D61—88no—
383C22×D61—88no—
384C22×D61C2×C22⋊C411yescharacteristic
385C22×D61C2×C22⋊C411yescharacteristic
386C22×D61C4×D414yes—
387Q8×C61—41no—
388Q8×C61—41no—
389Q8×C61—41no—
390Q8×C61—41no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—21no—
396C2×C4×C61—21no—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—22no—
402C2×C4×C61—22no—
403C2×C4×C61—22no—
404C2×C4×C61—22no—
405C2×C4×C61—42no—
406C2×C4×C61C2×C22⋊C411yescharacteristic
407C2×C4×C61C2×C22⋊C411yescharacteristic
408C2×C4×C61C22×D411yescharacteristic
409C2×C4×C61C22×D411yescharacteristic
410C2×C4×C61C22×D411yescharacteristic
411C2×C4×C61C2×#4111yescharacteristic
412C2×C4×C61H(5,𝔽2)11yescharacteristic
413C2×C4×C61H(5,𝔽2)11yescharacteristic
414C22⋊D61—22no—
415C22⋊D61—22no—
416C22⋊D61—41no—
417C22⋊D61—41no—
418C2×Dic61—21no—
419C2×Dic61—21no—
420C2×Dic61—41no—
421C2×Dic61—41no—
422C2×Dic61C2×C22⋊C411yescharacteristic
423C2×Dic61C2×C22⋊C411yescharacteristic
424C2×Dic61C2×C22⋊C411yescharacteristic
425C2×Dic61C2×C22⋊C411yescharacteristic
426C2×Dic61C2×C22⋊C411yescharacteristic
427C2×Dic61C2×C22⋊C411yescharacteristic
428D244—22no—
429D244—22no—
430D244—22no—
431D244—22no—
432D244—44no—
433D244—44no—
434D244—44no—
435D244—44no—
436D244—41no—
437D244—41no—
438D244—41no—
439D244—41no—
440D244—82no—
441D244—82no—
442C4×D61—21no—
443C4×D61—21no—
444C4×D61—21no—
445C4×D61—21no—
446C4×D61—21no—
447C4×D61—21no—
448C4×D61—21no—
449C4×D61—21no—
450C4×D61—44no—
451C4×D61—44no—
452C4×D61—82no—
453C4×D61—82no—
454C8×C61—22no—
455C8×C61—41no—
456C8×C61—41no—
457C8×C61—41no—
458#92418—22no—
459#92418—41no—
460#92418—41no—
461#92418—41no—
462#22408—611nomaximal, Sylow
463C22×C61—21no—
464C22×C61—21no—
465C22×C61—21no—
466C22×C61—21no—
467C22×C61—21no—
468C22×C61—21no—
469C22×C61—21no—
470C22×C61—42no—
471C22×C61—42no—
472C22×C61#41312yescomplemented
473C22×C61C22×C22⋊C411yescharacteristic
474C22×C61C2×C4×D411yescharacteristic
475C22×C61#51811yescharacteristic
476C2×D61—21no—
477C2×D61—21no—
478C2×D61—24no—
479C2×D61—21no—
480C2×D61—21no—
481C2×D61—21no—
482C2×D61—21no—
483C2×D61—44no—
484C2×D61—42no—
485C2×D61—42no—
486C2×D61—44no—
487C2×D61—42no—
488C2×D61—42no—
489C2×D61—42no—
490C2×D61—81no—
491C2×D61—81no—
492C2×D61—88no—
493C2×D61—88no—
494C2×D61—82no—
495C2×D61—82no—
496C4×C61—21no—
497C4×C61—21no—
498C4×C61—42no—
499C4×C61—42no—
500C4×C61D4211yescharacteristic
501C4×C61D4211yescharacteristic
502C4×C61#54611yescharacteristic
503C4×C61#54611yescharacteristic
504Dic61—21no—
505Dic61—21no—
506Dic61—21no—
507Dic61—21no—
508Dic61—21no—
509Dic61—21no—
510C2×#546—611no—
511D4×M16—611no—
512D4×M16—611no—
513C2×#413—611no—
514C22×#100—611no—
515#1967—611no—
516#1967—611no—
517#1901—611no—
518#1901D6111yescharacteristic, complemented
519#1900—611no—
520#1900—611no—
521#1800—611no—
522#1785—611no—
523#1783—611no—
524C4×#100—611no—
525C2×C61—21no—
526C2×C61—21no—
527C2×C61—22no—
528C2×C61—41no—
529C2×C61D4×C22⋊C411yescharacteristic
530C2×C61C2×#41311yescharacteristic
531C2×C61#288811yescharacteristic
532D61—41no—
533D61—41no—
534D61—44no—
535D61—82no—
536C22×#41—611no—
537C23×D4—611no—
538C22×M16—611no—
539C22×M16—611no—
540C22×M16—611no—
541C22×M16C2×D6111yescharacteristic
542#546—1221no—
543#546—1221no—
544#546—1221no—
545#546—1221no—
546#546—1221no—
547#546—1221no—
548#546—1221no—
549#546—1221no—
550C2×#124—611no—
551C2×#123—612no—
552C2×C22⋊Q8C2×D6111yescharacteristic
553C2×#121—612no—
554C2×#121—611no—
555C2×#120—612no—
556C2×C4×D4—611no—
557C2×C4×D4—611no—
558C22×C22⋊C4—612no—
559#436—1221no—
560#436—1221no—
561#435—1221no—
562#435—1221no—
563#435—1221no—
564#435—1221no—
565C8×D4—1221no—
566C8×D4—1221no—
567#423—611no—
568#423—611no—
569#413—1224no—
570C2×#101—611no—
571C2×#101—611no—
572C2×#101C2×D6111yescharacteristic, complemented
573C2×#101C2×D6111yescharacteristic, complemented
574C2×#100—611no—
575C2×#100—611no—
576C2×#100—611no—
577C2×#100—611no—
578C2×#100—611no—
579C2×#100—611no—
580C2×#100—611no—
581C2×#100—611no—
582C2×#100—1224no—
583#407—611no—
584#407—611no—
585#407—611no—
586#407C2×D6111yescharacteristic
587C4×M16—611no—
588C4×M16—611no—
589#343—611no—
590#343—611no—
591#343C2×D6111yescharacteristic, complemented
592#343C2×D6111yescharacteristic, complemented
593C61#2240811yescharacteristic, complemented, Sylow
594C25—612no—
595C2×#41—1221no—
596C2×#41—1221no—
597C2×#41—1221no—
598C2×#41—1221no—
599C2×#41—1222no—
600C2×#41—1222no—
601C2×#41—2441no—
602C2×#41—2441no—
603C22×Q8C22×D6111yescharacteristic
604C22×D4—611no—
605C22×D4—612no—
606C22×D4—612no—
607C22×D4—612no—
608C22×D4—611no—
609C22×D4—611no—
610C22×D4—1222no—
611C22×D4—1222no—
612C22×D4—1221no—
613C22×D4—1221no—
614C22×D4—1221no—
615C22×D4—1221no—
616C22×D4—2441no—
617C22×D4—2441no—
618C23×C4—611no—
619C23×C4—612no—
620C23×C4—612no—
621C23×C4C22×D6111yescharacteristic
622C2×M16—21no—
623C2×M16—22no—
624C2×M16—41no—
625C2×M16—611no—
626C2×M16—611no—
627C2×M16—611no—
628C2×M16—611no—
629C2×M16—1221no—
630C2×M16—1221no—
631C2×M16—1221no—
632C2×M16—1222no—
633C2×M16—1222no—
634C2×M16—1222no—
635C2×M16—2441no—
636C2×M16—2441no—
637C2×M16—2441no—
638C2×M16C22×D6111yescharacteristic
639C2×M16C22×D6111yescharacteristic
640C2×M16C22×D6111yescharacteristic
641C2×M16C22×D6111yescharacteristic
642C22×C8—21no—
643C22×C8—1221no—
644C22×C8—1221no—
645C22×C8—1221no—
646#124—1221no—
647#124—1221no—
648#124—1221no—
649#124—1221no—
650#123—1222no—
651#123—1222no—
652#123—1222no—
653#123—1222no—
654C22⋊Q8—21no—
655C22⋊Q8—21no—
656C22⋊Q8—21no—
657C22⋊Q8—21no—
658#121—1222no—
659#121—1222no—
660#121—1222no—
661#121—1222no—
662#121—1221no—
663#121—1221no—
664#121—1221no—
665#121—1221no—
666#120—1222no—
667#120—1222no—
668#120—1222no—
669#120—1222no—
670C4×D4—611no—
671C4×D4—611no—
672C4×D4—611no—
673C4×D4—611no—
674C4×D4—611no—
675C4×D4—611no—
676C4×D4—611no—
677C4×D4—611no—
678C4×D4—1221no—
679C4×D4—1221no—
680C4×D4—1221no—
681C4×D4—1221no—
682C2×C4⋊C4—611no—
683C2×C4⋊C4C4×D6112yes—
684C2×C4⋊C4C22×D6111yescharacteristic
685C2×C22⋊C4—611no—
686C2×C22⋊C4—611no—
687C2×C22⋊C4—612no—
688C2×C22⋊C4—612no—
689C2×C22⋊C4—612no—
690C2×C22⋊C4—612no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1222no—
694C2×C22⋊C4—1222no—
695C2×C22⋊C4C4×D6112yes—
696C2×C42—611no—
697C4⋊C8—1221no—
698C4⋊C8—1221no—
699C4⋊C8—1221no—
700C4⋊C8—1221no—
701#101—22no—
702#101—41no—
703#101—1222no—
704#101—2441no—
705#100—614no—
706#100—1222no—
707#100—1222no—
708#100—1222no—
709#100—1222no—
710#100—1222no—
711#100—2441no—
712#100—2441no—
713C22⋊C8—21no—
714C22⋊C8—21no—
715C22⋊C8—1221no—
716C22⋊C8—1221no—
717C22⋊C8—1221no—
718C22⋊C8—1221no—
719C22⋊C8—1221no—
720C22⋊C8—1221no—
721#97—1221no—
722#97—1221no—
723C4×C8—1221no—
724C4×C8—1221no—
725C24—612no—
726C24—611no—
727C24—612no—
728C24—1224no—
729C24—1222no—
730C24—1222no—
731C24—4882no—
732C24—2442no—
733C24—2444no—
734C24C2×C4×D6111yescharacteristic
735#41—2442no—
736#41—2442no—
737#41—2442no—
738#41—2442no—
739#41—2442no—
740#41—2442no—
741#41—2442no—
742#41—2442no—
743C2×Q8—21no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—21no—
747C2×Q8—21no—
748C2×Q8—21no—
749C2×D4—611no—
750C2×D4—611no—
751C2×D4—611no—
752C2×D4—611no—
753C2×D4—612no—
754C2×D4—612no—
755C2×D4—1222no—
756C2×D4—1222no—
757C2×D4—1222no—
758C2×D4—1222no—
759C2×D4—1224no—
760C2×D4—1224no—
761C2×D4—1221no—
762C2×D4—1221no—
763C2×D4—1221no—
764C2×D4—1221no—
765C2×D4—1221no—
766C2×D4—1221no—
767C2×D4—1221no—
768C2×D4—1221no—
769C2×D4—1221no—
770C2×D4—1221no—
771C2×D4—1222no—
772C2×D4—1222no—
773C2×D4—4882no—
774C2×D4—2442no—
775C2×D4—2442no—
776C2×D4—2442no—
777C2×D4—2442no—
778C2×D4—2442no—
779C2×D4—2442no—
780C2×D4—2442no—
781C2×D4—2442no—
782C2×D4—2442no—
783C2×D4—2442no—
784C2×D4—2442no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—611no—
790C22×C4—611no—
791C22×C4—611no—
792C22×C4—611no—
793C22×C4—611no—
794C22×C4—611no—
795C22×C4—611no—
796C22×C4—1222no—
797C22×C4—1222no—
798C22×C4—1222no—
799C22×C4—1222no—
800C22×C4—1224no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—4882no—
806C22×C4—2442no—
807C22×C4C2×C4×D6112yes—
808C22×C4C2×C4×D6111yescharacteristic
809C22×C4C2×C4×D6112yes—
810C22×C4D4×D6111yescharacteristic
811C22×C4D4×D6111yescharacteristic
812C22×C4D4×D6111yescharacteristic
813C22×C4D4×D6111yescharacteristic
814C22×C4C23×D6111yescharacteristic
815M16—21no—
816M16—21no—
817M16—21no—
818M16—21no—
819M16—21no—
820M16—21no—
821M16—21no—
822M16—42no—
823M16—612no—
824M16—1221no—
825M16—1221no—
826M16—1221no—
827M16—1221no—
828M16—1221no—
829M16—1221no—
830M16—1221no—
831M16—2442no—
832M16—2442no—
833M16—2442no—
834M16D4×D6112yes—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—42no—
840C2×C8—1221no—
841C2×C8—1221no—
842C2×C8—1221no—
843C2×C8—1221no—
844C2×C8—2442no—
845C2×C8—2442no—
846C2×C8—2442no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—611no—
852C4⋊C4—611no—
853C4⋊C4—611no—
854C4⋊C4—611no—
855C22⋊C4—22no—
856C22⋊C4—22no—
857C22⋊C4—611no—
858C22⋊C4—611no—
859C22⋊C4—611no—
860C22⋊C4—611no—
861C22⋊C4—611no—
862C22⋊C4—611no—
863C22⋊C4—611no—
864C22⋊C4—611no—
865C22⋊C4—1222no—
866C22⋊C4—1222no—
867C22⋊C4—1222no—
868C22⋊C4—1222no—
869C22⋊C4—1222no—
870C22⋊C4—1222no—
871C22⋊C4—1222no—
872C22⋊C4—1222no—
873C42—611no—
874C42—611no—
875C42—611no—
876C42—611no—
877C23—21no—
878C23—21no—
879C23—22no—
880C23—41no—
881C23—611no—
882C23—611no—
883C23—614no—
884C23—1221no—
885C23—1221no—
886C23—1222no—
887C23—1222no—
888C23—1222no—
889C23—1222no—
890C23—1222no—
891C23—4882no—
892C23—4882no—
893C23—4888no—
894C23—4888no—
895C23—2441no—
896C23—2441no—
897C23—2444no—
898C23—2444no—
899C23—2442no—
900C23—2442no—
901C23—2444no—
902C23—2442no—
903C23—2442no—
904C23—2444no—
905C23C22⋊C4×D6111yescharacteristic
906C23C22⋊C4×D6111yescharacteristic
907C23C22×C4×D6111yescharacteristic
908Q8—41no—
909Q8—41no—
910Q8—41no—
911Q8—41no—
912D4—1222no—
913D4—1222no—
914D4—1222no—
915D4—1222no—
916D4—1222no—
917D4—1222no—
918D4—4882no—
919D4—4882no—
920D4—2444no—
921D4—2444no—
922D4—2444no—
923D4—2444no—
924D4—2441no—
925D4—2441no—
926D4—2441no—
927D4—2441no—
928D4—2441no—
929D4—2441no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—42no—
945C2×C4—611no—
946C2×C4—611no—
947C2×C4—611no—
948C2×C4—611no—
949C2×C4—611no—
950C2×C4—611no—
951C2×C4—1221no—
952C2×C4—1221no—
953C2×C4—1221no—
954C2×C4—1221no—
955C2×C4—1221no—
956C2×C4—1221no—
957C2×C4—1221no—
958C2×C4—1221no—
959C2×C4—1221no—
960C2×C4—1221no—
961C2×C4—4882no—
962C2×C4—4882no—
963C2×C4—2444no—
964C2×C4—2444no—
965C2×C4—2441no—
966C2×C4—2441no—
967C2×C4C22⋊C4×D6111yescharacteristic
968C2×C4C22⋊C4×D6111yescharacteristic
969C2×C4C2×D4×D6111yescharacteristic
970C2×C4C2×D4×D6111yescharacteristic
971C2×C4C2×D4×D6111yescharacteristic
972C2×C4#41×D6111yescharacteristic
973C2×C4#1451982211yescharacteristic
974C2×C4#1451982311yescharacteristic
975C8—22no—
976C8—41no—
977C8—41no—
978C8—41no—
979C8—1222no—
980C8—2441no—
981C8—2441no—
982C8—2441no—
983C22—21no—
984C22—21no—
985C22—21no—
986C22—21no—
987C22—21no—
988C22—21no—
989C22—21no—
990C22—42no—
991C22—42no—
992C22—1221no—
993C22—1221no—
994C22—1224no—
995C22—1221no—
996C22—1221no—
997C22—1221no—
998C22—1221no—
999C22—4882no—
1000C22—4882no—
1001C22—4888no—
1002C22—4881no—
1003C22—4881no—
1004C22—4888no—
1005C22—2444no—
1006C22—2444no—
1007C22—2442no—
1008C22—2442no—
1009C22—2442no—
1010C22—2442no—
1011C22—2442no—
1012C22#1683974512yescomplemented
1013C22C2×C22⋊C4×D6111yescharacteristic
1014C22C4×D4×D6111yescharacteristic
1015C22#1684023411yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—42no—
1019C4—42no—
1020C4—1221no—
1021C4—1221no—
1022C4—1221no—
1023C4—1221no—
1024C4—1221no—
1025C4—1221no—
1026C4#1684039411yescharacteristic
1027C4#1684039611yescharacteristic
1028C4#1684040111yescharacteristic
1029C4#1684040411yescharacteristic
1030C2—22no—
1031C2—21no—
1032C2—21no—
1033C2—41no—
1034C2—4882no—
1035C2—2441no—
1036C2—2441no—
1037C2—2444no—
1038C2#2144863711yescharacteristic
1039C2C2×#1683974511yescharacteristic
1040C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1901C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840403C2
cosocleC22×C4×C61C24
hypercenter#1901D61
hypocenterC61#22408
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1901

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D61C2semidirect
3. #21454551C2semidirect
4. C2×#16839745C2semidirect
5. C22×#14519693C2semidirect
6. #21446667C2semidirect
7. #21446667C2semidirect
8. #21446288C2semidirect
9. #21446281C2semidirect
10. #21446281C2semidirect
11. #21445810C2semidirect
12. #21445746C2semidirect
13. #21445739C2semidirect
14. #21445610C2semidirect
15. C61×#1901C2semidirect
19. C2×M16×D61C22semidirect
20. C2×M16×D61C22semidirect
45. #16839785C22semidirect
46. #16839785C22semidirect
48. C2×#14519696C22semidirect
49. C2×#14519696C22semidirect
60. #16839725C22semidirect
61. #16839725C22semidirect
62. M16×Dic61C22semidirect
63. M16×Dic61C22semidirect
64. #16839531C22semidirect
65. #16839531C22semidirect
68. C2×#101×C61C22semidirect
69. C2×#101×C61C22semidirect
71. C61×#343C22semidirect
72. C61×#343C22semidirect
172. #14519693D4semidirect
472. C22×C61#413semidirect
518. #1901D61semidirect
572. C2×#101C2×D61semidirect
573. C2×#101C2×D61semidirect
591. #343C2×D61semidirect
592. #343C2×D61semidirect
593. C61#22408semidirect
1012. C22#16839745semidirect

Maximal subgroups

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

subgroupindex
C2×#168404032
M16×C22⋊D612
#214545512
C2×#168397452
C22×#145196932
#214466672
#214462882
#214462812
#214458102
#214457462
#214457392
#214456102
C61×#19012
#2240861