Finite Group Databasebeta

← #29695367

Subgroups — #29695367

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×#16840408C211yesmaximal, characteristic
2D4×#11758194C211yesmaximal, characteristic, complemented
3C2×#16839744C211yesmaximal, characteristic, complemented
4C22×#14519693C211yesmaximal, characteristic, complemented
5#21446668C211yesmaximal, characteristic, complemented
6#21446666C211yesmaximal, characteristic, complemented
7#21446287C211yesmaximal, characteristic, complemented
8#21446285C211yesmaximal, characteristic, complemented
9#21446282C211yesmaximal, characteristic, complemented
10#21446280C211yesmaximal, characteristic, complemented
11#21445808C211yesmaximal, characteristic, complemented
12#21445745C211yesmaximal, characteristic, complemented
13#21445739C211yesmaximal, characteristic, complemented
14C4×#14519693C211yesmaximal, characteristic, complemented
15D4×M16×C61C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C22×#11758194C2211yescharacteristic, complemented
20#16840408—21no—
21#16840408—21no—
22#16840408—21no—
23#16840408—21no—
24#16840408—21no—
25#16840408—21no—
26#16840408—21no—
27#16840408—21no—
28C2×#14519765C2211yescharacteristic
29C2×#14519762C412yes—
30C2×#14519756C2211yescharacteristic
31C2×#14519751C2211yescharacteristic
32C2×#14519750C412yes—
33C2×#14519745C412yes—
34C2×C4×D244C2211yescharacteristic
35C2×C22⋊C4×D61C412yes—
36#16839840—21no—
37#16839834—21no—
38#16839834—21no—
39D4×#92418—21no—
40#16839786C2211yescharacteristic, complemented
41#16839744—24no—
42C2×#14519695C2211yescharacteristic, complemented
43C2×#14519695C2211yescharacteristic, complemented
44C2×#14519695C2211yescharacteristic, complemented
45C2×#14519695C2211yescharacteristic, complemented
46C2×#14519693—24no—
47C2×#14519693C2211yescharacteristic
48C2×#14519693C2211yescharacteristic
49C2×#14519693C2211yescharacteristic
50C2×#14519693C2211yescharacteristic
51C2×#14519693C2211yescharacteristic
52C2×#14519693C2211yescharacteristic
53C2×#14519693C2211yescharacteristic
54C2×#14519693C2211yescharacteristic
55#16839726C2211yescharacteristic
56#16839726C2211yescharacteristic, complemented
57C4×#11758194C2211yescharacteristic, complemented
58#16839530C2211yescharacteristic, complemented
59#16839530C2211yescharacteristic, complemented
60#16839530C2211yescharacteristic, complemented
61#16839530C2211yescharacteristic, complemented
62C22×M16×C61C2211yescharacteristic
63C22×M16×C61C2211yescharacteristic, complemented
64C2×C4×D4×C61C2211yescharacteristic
65C61×#436—21no—
66C61×#435—21no—
67C61×#435—21no—
68C8×D4×C61—21no—
69C61×#423C2211yescharacteristic, complemented
70C61×#407C2211yescharacteristic
71C61×#407C2211yescharacteristic, complemented
72C4×M16×C61C2211yescharacteristic, complemented
73C24×D61C2×C412yes—
74C2×#11758222—21no—
75C2×#11758222—21no—
76C2×#11758222—21no—
77C2×#11758222—21no—
78C2×#11758222—22no—
79C2×#11758222—22no—
80C2×#11758222—41no—
81C2×#11758222—41no—
82C22×Dic122C2311yescharacteristic
83C22×D244—21no—
84C22×D244—21no—
85C22×D244—21no—
86C22×D244—21no—
87C22×D244—22no—
88C22×D244—22no—
89C22×D244—41no—
90C22×D244—41no—
91C22×D244C2×C412yes—
92C22×D244C2311yescharacteristic
93C22×D244C2311yescharacteristic
94C22×C22⋊D61C2×C412yes—
95C22×C22⋊D61C2×C412yes—
96C22×C4×D61C2×C412yes—
97C22×C4×D61C2×C412yes—
98C2×#11758194—21no—
99C2×#11758194—21no—
100C2×#11758194—22no—
101C2×#11758194—22no—
102C2×#11758194—41no—
103C2×#11758194—41no—
104C2×#11758194C2311yescharacteristic
105C2×#11758194C2311yescharacteristic
106C2×#11758194C2311yescharacteristic
107C2×#11758194C2311yescharacteristic
108C22×#92418—21no—
109C22×#92418—21no—
110#14519765—21no—
111#14519765—21no—
112#14519765—21no—
113#14519765—21no—
114#14519762—22no—
115#14519762—22no—
116#14519762—22no—
117#14519762—22no—
118#14519756—21no—
119#14519756—21no—
120#14519756—21no—
121#14519756—21no—
122#14519751—21no—
123#14519751—21no—
124#14519751—21no—
125#14519751—21no—
126#14519750—22no—
127#14519750—22no—
128#14519750—22no—
129#14519750—22no—
130#14519745—22no—
131#14519745—22no—
132#14519745—22no—
133#14519745—22no—
134C4×D244—21no—
135C4×D244—21no—
136C4×D244—21no—
137C4×D244—21no—
138C2×C4⋊Dic61C2311yescharacteristic
139C2×#11758196C2×C412yes—
140C2×C22⋊Dic61C2×C412yes—
141C2×#11758198C2×C412yes—
142C2×#11758198C2×C412yes—
143C2×#11758198C2×C412yes—
144C2×#11758198C2×C412yes—
145C22⋊C4×D61—22no—
146C22⋊C4×D61—22no—
147C22⋊C4×D61—22no—
148C22⋊C4×D61—22no—
149C4⋊#92418—21no—
150C4⋊#92418—21no—
151#14519695—22no—
152#14519695—22no—
153#14519695—41no—
154#14519695—41no—
155#14519693—22no—
156#14519693—22no—
157#14519693—22no—
158#14519693—22no—
159#14519693—22no—
160#14519693—41no—
161#14519693—41no—
162#14519693D414yescomplemented
163C22⋊#92418—21no—
164C22⋊#92418—21no—
165C22⋊#92418—21no—
166C22⋊#92418—21no—
167#14519688—21no—
168C4×#92418—21no—
169C22×D4×C61C2×C411yescharacteristic
170C23×C4×C61C2311yescharacteristic
171C23×C4×C61C2311yescharacteristic
172C2×M16×C61—21no—
173C2×M16×C61—21no—
174C2×M16×C61—22no—
175C2×M16×C61—22no—
176C2×M16×C61—41no—
177C2×M16×C61—41no—
178C2×M16×C61C2311yescharacteristic
179C2×M16×C61C2311yescharacteristic
180C2×M16×C61C2311yescharacteristic
181C2×M16×C61C2311yescharacteristic
182C22×C8×C61—21no—
183C22×C8×C61—21no—
184C4×D4×C61D411yescharacteristic
185C4×D4×C61D411yescharacteristic
186C4×D4×C61D411yescharacteristic
187C4×D4×C61D411yescharacteristic
188C4×D4×C61D411yescharacteristic
189C4×D4×C61D411yescharacteristic
190C4×D4×C61D411yescharacteristic
191C4×D4×C61D411yescharacteristic
192C2×C4⋊C4×C61C2×C411yescharacteristic
193C2×C22⋊C4×C61C2×C411yescharacteristic
194C2×C22⋊C4×C61C2×C411yescharacteristic
195C2×C42×C61C2311yescharacteristic
196C4⋊C8×C61—21no—
197C4⋊C8×C61—21no—
198C22⋊C8×C61—21no—
199C22⋊C8×C61—21no—
200C22⋊C8×C61—21no—
201C22⋊C8×C61—21no—
202#97×C61—21no—
203C4×C8×C61—21no—
204C24×C61C22×C411yescharacteristic
205C24×C61C22×C411yescharacteristic
206C23×D61—22no—
207C23×D61—22no—
208C23×D61—24no—
209C23×D61—42no—
210C23×D61—44no—
211C23×D61—82no—
212C23×D61C22×C412yes—
213C23×D61C22×C412yes—
214C2×D4×C61—42no—
215C2×D4×C61C22⋊C411yescharacteristic
216C2×D4×C61C22⋊C411yescharacteristic
217C2×D4×C61C22⋊C411yescharacteristic
218C2×D4×C61C22⋊C411yescharacteristic
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—21no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61C22×C411yescharacteristic
228C22×C4×C61C22×C411yescharacteristic
229C22×C4×C61C22×C411yescharacteristic
230C22×C4×C61C22×C411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2×D411yescharacteristic
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D411yescharacteristic
239C22×C4×C61C2411yescharacteristic
240C2×C22⋊D61—22no—
241C2×C22⋊D61—22no—
242C2×C22⋊D61—24no—
243C2×C22⋊D61—22no—
244C2×C22⋊D61—22no—
245C2×C22⋊D61—42no—
246C2×C22⋊D61—82no—
247C22×Dic61C22×C412yes—
248C22×Dic61C22×C412yes—
249#11758222—42no—
250#11758222—42no—
251#11758222—42no—
252#11758222—42no—
253#11758222—42no—
254#11758222—42no—
255#11758222—42no—
256#11758222—42no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—21no—
261C2×D244—24no—
262C2×D244—22no—
263C2×D244—22no—
264C2×D244—21no—
265C2×D244—21no—
266C2×D244—21no—
267C2×D244—21no—
268C2×D244—21no—
269C2×D244—21no—
270C2×D244—42no—
271C2×D244—42no—
272C2×D244—42no—
273C2×D244—42no—
274C2×D244—42no—
275C2×D244—42no—
276C2×D244—42no—
277C2×D244—42no—
278C2×D244—42no—
279C2×D244C2×D412yes—
280C2×D244#4112yes—
281C2×C4×D61—24no—
282C2×C4×D61—22no—
283C2×C4×D61—22no—
284C2×C4×D61—22no—
285C2×C4×D61—22no—
286C2×C4×D61—42no—
287C2×C4×D61—82no—
288C2×Dic122—21no—
289C2×Dic122—21no—
290C2×Dic122—21no—
291C2×Dic122—21no—
292C2×Dic122—21no—
293C2×Dic122—21no—
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×C61—42no—
303M16×C61C2×D412yes—
304C2×C8×C61—21no—
305C2×C8×C61—21no—
306C2×C8×C61—21no—
307C2×C8×C61—21no—
308C2×C8×C61—42no—
309C2×C8×C61—42no—
310C4⋊C4×C61C22⋊C411yescharacteristic
311C4⋊C4×C61C22⋊C411yescharacteristic
312C4⋊C4×C61C22⋊C411yescharacteristic
313C4⋊C4×C61C22⋊C411yescharacteristic
314C22⋊C4×C61C22⋊C411yescharacteristic
315C22⋊C4×C61C22⋊C411yescharacteristic
316C22⋊C4×C61C22⋊C411yescharacteristic
317C22⋊C4×C61C22⋊C411yescharacteristic
318C22⋊C4×C61C22⋊C411yescharacteristic
319C22⋊C4×C61C22⋊C411yescharacteristic
320C22⋊C4×C61C22⋊C411yescharacteristic
321C22⋊C4×C61C22⋊C411yescharacteristic
322C42×C61C2×D411yescharacteristic
323C42×C61C2×D411yescharacteristic
324C42×C61C2×D411yescharacteristic
325C42×C61C2×D411yescharacteristic
326C22⋊Dic61—22no—
327C22⋊Dic61—22no—
328#11758198—22no—
329#11758198—22no—
330#11758198—22no—
331#11758198—22no—
332#11758198—22no—
333#11758198—22no—
334#11758198—22no—
335#11758198—22no—
336C4⋊Dic61—21no—
337C4⋊Dic61—21no—
338#11758196—22no—
339#11758196—22no—
340#11758194—21no—
341#11758194—21no—
342#11758194—21no—
343#11758194—21no—
344#11758194—21no—
345#11758194—21no—
346#11758194—21no—
347#11758194—42no—
348#11758194—42no—
349#11758194C2×D412yes—
350C2×#92418—21no—
351C2×#92418—21no—
352C2×#92418—21no—
353C2×#92418—21no—
354C2×#92418—42no—
355C2×#92418—42no—
356C23×C61—21no—
357C23×C61—21no—
358C23×C61—22no—
359C23×C61—21no—
360C23×C61—21no—
361C23×C61—41no—
362C23×C61—41no—
363C23×C61—41no—
364C23×C61C2×C22⋊C411yescharacteristic
365C23×C61C2×C22⋊C411yescharacteristic
366C23×C61C2×C22⋊C411yescharacteristic
367C23×C61C2×C22⋊C411yescharacteristic
368C23×C61C23×C411yescharacteristic
369C22×D61—22no—
370C22×D61—22no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—44no—
375C22×D61—44no—
376C22×D61—42no—
377C22×D61—42no—
378C22×D61—44no—
379C22×D61—44no—
380C22×D61—42no—
381C22×D61—42no—
382C22×D61—82no—
383C22×D61—82no—
384C22×D61—88no—
385C22×D61—88no—
386C22×D61C4×D414yes—
387D4×C61—22no—
388D4×C61—22no—
389D4×C61—41no—
390D4×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—21no—
402C2×C4×C61—21no—
403C2×C4×C61—21no—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—41no—
412C2×C4×C61—41no—
413C2×C4×C61C2×C22⋊C411yescharacteristic
414C2×C4×C61C2×C22⋊C411yescharacteristic
415C2×C4×C61C2×C22⋊C411yescharacteristic
416C2×C4×C61C2×C22⋊C411yescharacteristic
417C2×C4×C61C2×C22⋊C411yescharacteristic
418C2×C4×C61C2×C22⋊C411yescharacteristic
419C2×C4×C61C2×C22⋊C411yescharacteristic
420C2×C4×C61C2×C22⋊C411yescharacteristic
421C2×C4×C61C22×D411yescharacteristic
422C2×C4×C61C22×D411yescharacteristic
423C2×C4×C61C22×D411yescharacteristic
424C2×C4×C61C2×#4111yescharacteristic
425C2×C4×C61H(5,𝔽2)11yescharacteristic
426C2×C4×C61H(5,𝔽2)11yescharacteristic
427C22⋊D61—44no—
428C22⋊D61—44no—
429C22⋊D61—82no—
430C22⋊D61—82no—
431C2×Dic61—22no—
432C2×Dic61—22no—
433C2×Dic61—22no—
434C2×Dic61—22no—
435C2×Dic61—42no—
436D244—22no—
437D244—22no—
438D244—22no—
439D244—22no—
440D244—44no—
441D244—44no—
442D244—41no—
443D244—41no—
444D244—41no—
445D244—41no—
446C4×D61—44no—
447C4×D61—44no—
448C4×D61—82no—
449C4×D61—82no—
450Dic122—41no—
451Dic122—41no—
452Dic122—41no—
453Dic122—41no—
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—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—42no—
477C22×C61—42no—
478C22×C61—81no—
479C22×C61—81no—
480C22×C61#41312yescomplemented
481C22×C61C22×C22⋊C411yescharacteristic
482C22×C61C2×C4×D411yescharacteristic
483C22×C61#51811yescharacteristic
484C2×D61—24no—
485C2×D61—44no—
486C2×D61—42no—
487C2×D61—42no—
488C2×D61—44no—
489C2×D61—42no—
490C2×D61—42no—
491C2×D61—42no—
492C2×D61—88no—
493C2×D61—88no—
494C2×D61—82no—
495C2×D61—82no—
496C4×C61—21no—
497C4×C61—21no—
498C4×C61—21no—
499C4×C61—21no—
500C4×C61—21no—
501C4×C61—21no—
502C4×C61—21no—
503C4×C61—21no—
504C4×C61D4211yescharacteristic
505C4×C61D4211yescharacteristic
506C4×C61#54611yescharacteristic
507C4×C61#54611yescharacteristic
508Dic61—42no—
509Dic61—42no—
510C2×#546—611no—
511D4×M16—611no—
512D4×M16D6111yescharacteristic, complemented
513C2×#413—611no—
514C22×#100—611no—
515#1967—611no—
516#1967—611no—
517#1901—611no—
518#1901—611no—
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×C61—41no—
530C2×C61—41no—
531C2×C61D4×C22⋊C411yescharacteristic
532C2×C61C2×#41311yescharacteristic
533C2×C61#288811yescharacteristic
534D61—44no—
535D61—82no—
536C22×#41—611no—
537C23×D4—611no—
538C22×M16—611no—
539C22×M16—611no—
540C22×M16C2×D6111yescharacteristic
541C22×M16C2×D6111yescharacteristic, complemented
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⋊Q8—611no—
553C2×#121—611no—
554C2×#121—612no—
555C2×#120—612no—
556C2×C4×D4—611no—
557C2×C4×D4C2×D6111yescharacteristic
558C22×C22⋊C4—612no—
559#436—21no—
560#436—1221no—
561#435—21no—
562#435—21no—
563#435—1221no—
564#435—1221no—
565C8×D4—21no—
566C8×D4—1221no—
567#423—611no—
568#423C2×D6111yescharacteristic, complemented
569#413—1224no—
570C2×#101—611no—
571C2×#101—611no—
572C2×#101—611no—
573C2×#101—611no—
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#407C2×D6111yescharacteristic
586#407C2×D6111yescharacteristic, complemented
587C4×M16—611no—
588C4×M16C2×D6111yescharacteristic, complemented
589#343—611no—
590#343—611no—
591#343—611no—
592#343—611no—
593C61#2240811yescharacteristic, complemented, Sylow
594C25—612no—
595C2×#41—1222no—
596C2×#41—1222no—
597C2×#41—1221no—
598C2×#41—1221no—
599C2×#41—1221no—
600C2×#41—1221no—
601C2×#41—2441no—
602C2×#41—2441no—
603C22×Q8—611no—
604C22×D4—612no—
605C22×D4—612no—
606C22×D4—612no—
607C22×D4—611no—
608C22×D4—611no—
609C22×D4—1222no—
610C22×D4—1222no—
611C22×D4—1221no—
612C22×D4—1221no—
613C22×D4—1221no—
614C22×D4—1221no—
615C22×D4—2441no—
616C22×D4—2441no—
617C22×D4C4×D6111yescharacteristic
618C23×C4—612no—
619C23×C4—612no—
620C23×C4C22×D6111yescharacteristic
621C23×C4C22×D6111yescharacteristic
622C2×M16—21no—
623C2×M16—21no—
624C2×M16—22no—
625C2×M16—22no—
626C2×M16—41no—
627C2×M16—41no—
628C2×M16—611no—
629C2×M16—611no—
630C2×M16—611no—
631C2×M16—611no—
632C2×M16—1221no—
633C2×M16—1221no—
634C2×M16—1222no—
635C2×M16—1222no—
636C2×M16—2441no—
637C2×M16—2441no—
638C2×M16C22×D6111yescharacteristic
639C2×M16C22×D6111yescharacteristic
640C2×M16C22×D6111yescharacteristic
641C2×M16C22×D6111yescharacteristic
642C22×C8—21no—
643C22×C8—21no—
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—1221no—
655C22⋊Q8—1221no—
656C22⋊Q8—1221no—
657C22⋊Q8—1221no—
658#121—1221no—
659#121—1221no—
660#121—1221no—
661#121—1221no—
662#121—1222no—
663#121—1222no—
664#121—1222no—
665#121—1222no—
666#120—1222no—
667#120—1222no—
668#120—1222no—
669#120—1222no—
670C4×D4—1221no—
671C4×D4—1221no—
672C4×D4—1221no—
673C4×D4—1221no—
674C4×D4D24411yescharacteristic
675C4×D4D24411yescharacteristic
676C4×D4D24411yescharacteristic
677C4×D4D24411yescharacteristic
678C4×D4C22⋊D6111yescharacteristic
679C4×D4C22⋊D6111yescharacteristic
680C4×D4C22⋊D6111yescharacteristic
681C4×D4C22⋊D6111yescharacteristic
682C2×C4⋊C4—612no—
683C2×C4⋊C4—611no—
684C2×C4⋊C4C4×D6111yescharacteristic
685C2×C22⋊C4—612no—
686C2×C22⋊C4—612no—
687C2×C22⋊C4—612no—
688C2×C22⋊C4—612no—
689C2×C22⋊C4—612no—
690C2×C22⋊C4—1222no—
691C2×C22⋊C4—1222no—
692C2×C22⋊C4—1222no—
693C2×C22⋊C4—1222no—
694C2×C22⋊C4C4×D6111yescharacteristic
695C2×C22⋊C4C4×D6111yescharacteristic
696C2×C42C22×D6111yescharacteristic
697C4⋊C8—21no—
698C4⋊C8—21no—
699C4⋊C8—1221no—
700C4⋊C8—1221no—
701#101—1222no—
702#101—1222no—
703#101—2441no—
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—21no—
716C22⋊C8—21no—
717C22⋊C8—1221no—
718C22⋊C8—1221no—
719C22⋊C8—1221no—
720C22⋊C8—1221no—
721#97—21no—
722#97—1221no—
723C4×C8—21no—
724C4×C8—1221no—
725C24—612no—
726C24—612no—
727C24—1224no—
728C24—1222no—
729C24—1222no—
730C24—4882no—
731C24—2442no—
732C24—2444no—
733C24C2×C4×D6111yescharacteristic
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—1221no—
744C2×Q8—1221no—
745C2×Q8—1221no—
746C2×Q8—1221no—
747C2×Q8—1221no—
748C2×Q8—1221no—
749C2×D4—42no—
750C2×D4—612no—
751C2×D4—612no—
752C2×D4—1224no—
753C2×D4—1222no—
754C2×D4—1222no—
755C2×D4—1224no—
756C2×D4—1222no—
757C2×D4—1222no—
758C2×D4—1221no—
759C2×D4—1221no—
760C2×D4—1221no—
761C2×D4—1221no—
762C2×D4—1221no—
763C2×D4—1221no—
764C2×D4—1221no—
765C2×D4—1221no—
766C2×D4—1221no—
767C2×D4—1221no—
768C2×D4—1222no—
769C2×D4—1222no—
770C2×D4—4882no—
771C2×D4—2442no—
772C2×D4—2442no—
773C2×D4—2442no—
774C2×D4—2442no—
775C2×D4—2442no—
776C2×D4—2442no—
777C2×D4—2442no—
778C2×D4—2442no—
779C2×D4—2442no—
780C2×D4—2442no—
781C2×D4#1175819811yescharacteristic
782C2×D4#1175819811yescharacteristic
783C2×D4#1175819811yescharacteristic
784C2×D4#1175819811yescharacteristic
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—612no—
794C22×C4—612no—
795C22×C4—1224no—
796C22×C4—1222no—
797C22×C4—1222no—
798C22×C4—1222no—
799C22×C4—1222no—
800C22×C4—4882no—
801C22×C4—2442no—
802C22×C4C2×C4×D6111yescharacteristic
803C22×C4C2×C4×D6111yescharacteristic
804C22×C4C2×C4×D6111yescharacteristic
805C22×C4C2×C4×D6111yescharacteristic
806C22×C4C2×D24411yescharacteristic
807C22×C4C2×D24411yescharacteristic
808C22×C4C2×D24411yescharacteristic
809C22×C4C2×D24411yescharacteristic
810C22×C4C2×C22⋊D6111yescharacteristic
811C22×C4C2×C22⋊D6111yescharacteristic
812C22×C4C2×C22⋊D6111yescharacteristic
813C22×C4C2×C22⋊D6111yescharacteristic
814C22×C4C23×D6111yescharacteristic
815M16—21no—
816M16—21no—
817M16—21no—
818M16—21no—
819M16—21no—
820M16—21no—
821M16—21no—
822M16—42no—
823M16—42no—
824M16—612no—
825M16—1221no—
826M16—1221no—
827M16—1221no—
828M16—1221no—
829M16—1221no—
830M16—1221no—
831M16—1221no—
832M16—2442no—
833M16—2442no—
834M16D4×D6112yes—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—42no—
840C2×C8—42no—
841C2×C8—1221no—
842C2×C8—1221no—
843C2×C8—1221no—
844C2×C8—1221no—
845C2×C8—2442no—
846C2×C8—2442no—
847C4⋊C4—1221no—
848C4⋊C4—1221no—
849C4⋊C4—1222no—
850C4⋊C4—1222no—
851C4⋊C4#1175819811yescharacteristic
852C4⋊C4#1175819811yescharacteristic
853C4⋊C4#1175819811yescharacteristic
854C4⋊C4#1175819811yescharacteristic
855C22⋊C4—1222no—
856C22⋊C4—1222no—
857C22⋊C4—1222no—
858C22⋊C4—1222no—
859C22⋊C4—1222no—
860C22⋊C4—1222no—
861C22⋊C4—1222no—
862C22⋊C4—1222no—
863C22⋊C4—1222no—
864C22⋊C4—1222no—
865C22⋊C4#1175819811yescharacteristic
866C22⋊C4#1175819811yescharacteristic
867C22⋊C4#1175819811yescharacteristic
868C22⋊C4#1175819811yescharacteristic
869C22⋊C4#1175819811yescharacteristic
870C22⋊C4#1175819811yescharacteristic
871C22⋊C4#1175819811yescharacteristic
872C22⋊C4#1175819811yescharacteristic
873C42C2×D24411yescharacteristic
874C42C2×D24411yescharacteristic
875C42C2×C22⋊D6111yescharacteristic
876C42C2×C22⋊D6111yescharacteristic
877C23—21no—
878C23—21no—
879C23—22no—
880C23—21no—
881C23—21no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—614no—
886C23—1222no—
887C23—1222no—
888C23—1222no—
889C23—1222no—
890C23—1222no—
891C23—4882no—
892C23—4882no—
893C23—4888no—
894C23—4888no—
895C23—2444no—
896C23—2444no—
897C23—2442no—
898C23—2442no—
899C23—2444no—
900C23—2442no—
901C23—2442no—
902C23—2444no—
903C23C2×#1175819811yescharacteristic
904C23C2×#1175819811yescharacteristic
905C23C2×#1175819811yescharacteristic
906C23C2×#1175819811yescharacteristic
907C23C22×C4×D6111yescharacteristic
908Q8—2441no—
909Q8—2441no—
910Q8—2441no—
911Q8—2441no—
912D4—22no—
913D4—22no—
914D4—41no—
915D4—41no—
916D4—1222no—
917D4—1222no—
918D4—1222no—
919D4—1222no—
920D4—4882no—
921D4—4882no—
922D4—2444no—
923D4—2444no—
924D4—2444no—
925D4—2444no—
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—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—1222no—
953C2×C4—1222no—
954C2×C4—1222no—
955C2×C4—1222no—
956C2×C4—4882no—
957C2×C4—4882no—
958C2×C4—2444no—
959C2×C4—2444no—
960C2×C4—2442no—
961C2×C4C2×#1175819811yescharacteristic
962C2×C4C2×#1175819811yescharacteristic
963C2×C4C2×#1175819811yescharacteristic
964C2×C4C2×#1175819811yescharacteristic
965C2×C4C2×#1175819811yescharacteristic
966C2×C4C2×#1175819811yescharacteristic
967C2×C4C2×#1175819811yescharacteristic
968C2×C4C2×#1175819811yescharacteristic
969C2×C4C2×D4×D6111yescharacteristic
970C2×C4C22×C22⋊D6111yescharacteristic
971C2×C4C22×D24411yescharacteristic
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—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—42no—
997C22—42no—
998C22—81no—
999C22—81no—
1000C22—1224no—
1001C22—4882no—
1002C22—4882no—
1003C22—4888no—
1004C22—4888no—
1005C22—2444no—
1006C22—2444no—
1007C22—2442no—
1008C22—2442no—
1009C22—2442no—
1010C22—2442no—
1011C22—2442no—
1012C22#1683974412yescomplemented
1013C22C22×#1175819811yescharacteristic
1014C22C4×D4×D6111yescharacteristic
1015C22#1684023411yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—21no—
1023C4—21no—
1024C4—2442no—
1025C4—2442no—
1026C4D4×C22⋊D6111yescharacteristic
1027C4D4×D24411yescharacteristic
1028C4#1684040011yescharacteristic
1029C4#1684040711yescharacteristic
1030C2—21no—
1031C2—21no—
1032C2—22no—
1033C2—41no—
1034C2—41no—
1035C2—41no—
1036C2—4882no—
1037C2—2444no—
1038C2D4×#1175819811yescharacteristic
1039C2C2×#1683974411yescharacteristic
1040C2#2145429711yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingD4×M16×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840408C2
cosocleC22×C4×C61C24
hypercenterD4×M16D61
hypocenterC61#22408
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. D4×#11758194C2semidirect
3. C2×#16839744C2semidirect
4. C22×#14519693C2semidirect
5. #21446668C2semidirect
6. #21446666C2semidirect
7. #21446287C2semidirect
8. #21446285C2semidirect
9. #21446282C2semidirect
10. #21446280C2semidirect
11. #21445808C2semidirect
12. #21445745C2semidirect
13. #21445739C2semidirect
14. C4×#14519693C2semidirect
15. D4×M16×C61C2semidirect
19. C22×#11758194C22semidirect
40. #16839786C22semidirect
42. C2×#14519695C22semidirect
43. C2×#14519695C22semidirect
44. C2×#14519695C22semidirect
45. C2×#14519695C22semidirect
56. #16839726C22semidirect
57. C4×#11758194C22semidirect
58. #16839530C22semidirect
59. #16839530C22semidirect
60. #16839530C22semidirect
61. #16839530C22semidirect
63. C22×M16×C61C22semidirect
69. C61×#423C22semidirect
71. C61×#407C22semidirect
72. C4×M16×C61C22semidirect
162. #14519693D4semidirect
480. C22×C61#413semidirect
512. D4×M16D61semidirect
541. C22×M16C2×D61semidirect
568. #423C2×D61semidirect
586. #407C2×D61semidirect
588. C4×M16C2×D61semidirect
593. C61#22408semidirect
1012. C22#16839744semidirect

Maximal subgroups

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

subgroupindex
C2×#168404082
D4×#117581942
C2×#168397442
C22×#145196932
#214466682
#214466662
#214462872
#214462852
#214462822
#214462802
#214458082
#214457452
#214457392
C4×#145196932
D4×M16×C612
#2240861