Finite Group Databasebeta

← #29695386

Subgroups — #29695386

Order 15616.

1404 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840421C211yesmaximal, characteristic
2D4×#11758194C211yesmaximal, characteristic, complemented
3C2×#16839744C211yesmaximal, characteristic, complemented
4C22×#14519695C211yesmaximal, 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#21445812C211yesmaximal, characteristic, complemented
12#21445745C211yesmaximal, characteristic, complemented
13#21445742C211yesmaximal, characteristic, complemented
14C4×#14519695C211yesmaximal, characteristic, complemented
15D4×M16×C61C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×Dic122C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C22×#11758194C2211yescharacteristic
20#16840421—21no—
21#16840421—21no—
22#16840421—21no—
23#16840421—21no—
24#16840421—21no—
25#16840421—21no—
26#16840421—21no—
27#16840421—21no—
28C2×#14519765C2211yescharacteristic
29C2×#14519763C412yes—
30C2×#14519756C2211yescharacteristic
31C2×#14519755C412yes—
32C2×#14519751C2211yescharacteristic
33C2×#14519749C412yes—
34C2×C4×Dic122C2211yescharacteristic
35C2×#14519737C412yes—
36#16839840—21no—
37#16839834—21no—
38#16839834—21no—
39D4×#92418—21no—
40#16839786C2211yescharacteristic
41#16839744—24no—
42C2×#14519695—24no—
43C2×#14519695C2211yescharacteristic
44C2×#14519695C2211yescharacteristic
45C2×#14519695C2211yescharacteristic
46C2×#14519695C2211yescharacteristic
47C2×#14519695C2211yescharacteristic
48C2×#14519695C2211yescharacteristic
49C2×#14519695C2211yescharacteristic
50C2×#14519695C2211yescharacteristic
51C2×#14519693C2211yescharacteristic
52C2×#14519693C2211yescharacteristic
53C2×#14519693C2211yescharacteristic
54C2×#14519693C2211yescharacteristic
55#16839726C2211yescharacteristic
56#16839726C2211yescharacteristic
57C4×#11758194C2211yescharacteristic
58#16839530C2211yescharacteristic
59#16839530C2211yescharacteristic
60#16839530C2211yescharacteristic
61#16839530C2211yescharacteristic
62C22×M16×C61C2211yescharacteristic
63C22×M16×C61C2211yescharacteristic
64C2×C4×D4×C61C2211yescharacteristic
65C61×#436—21no—
66C61×#435—21no—
67C61×#435—21no—
68C8×D4×C61—21no—
69C61×#423C2211yescharacteristic
70C61×#407C2211yescharacteristic
71C61×#407C2211yescharacteristic
72C4×M16×C61C2211yescharacteristic
73C2×#11758222—21no—
74C2×#11758222—21no—
75C2×#11758222—21no—
76C2×#11758222—21no—
77C2×#11758222—22no—
78C2×#11758222—22no—
79C2×#11758222—41no—
80C2×#11758222—41no—
81C22×Dic122—21no—
82C22×Dic122—21no—
83C22×Dic122—21no—
84C22×Dic122—21no—
85C22×Dic122—22no—
86C22×Dic122—22no—
87C22×Dic122—41no—
88C22×Dic122—41no—
89C22×Dic122C2×C412yes—
90C22×Dic122C2311yescharacteristic
91C22×Dic122C2311yescharacteristic
92C22×D244C2311yescharacteristic
93C22×C22⋊D61C2×C412yes—
94C22×C22⋊D61C2×C412yes—
95C23×Dic61C2×C412yes—
96C22×C4×D61C2×C412yes—
97C2×#11758194—21no—
98C2×#11758194—21no—
99C2×#11758194—22no—
100C2×#11758194—22no—
101C2×#11758194—41no—
102C2×#11758194—41no—
103C2×#11758194C2311yescharacteristic
104C2×#11758194C2311yescharacteristic
105C2×#11758194C2311yescharacteristic
106C2×#11758194C2311yescharacteristic
107C22×#92418—21no—
108C22×#92418—21no—
109#14519765—21no—
110#14519765—21no—
111#14519765—21no—
112#14519765—21no—
113#14519763—22no—
114#14519763—22no—
115#14519763—22no—
116#14519763—22no—
117#14519756—21no—
118#14519756—21no—
119#14519756—21no—
120#14519756—21no—
121#14519755—22no—
122#14519755—22no—
123#14519755—22no—
124#14519755—22no—
125#14519751—21no—
126#14519751—21no—
127#14519751—21no—
128#14519751—21no—
129#14519749—22no—
130#14519749—22no—
131#14519749—22no—
132#14519749—22no—
133C4×Dic122—21no—
134C4×Dic122—21no—
135C4×Dic122—21no—
136C4×Dic122—21no—
137#14519737—22no—
138#14519737—22no—
139#14519737—22no—
140#14519737—22no—
141C2×C4⋊Dic61C2311yescharacteristic
142C2×#11758196C2×C412yes—
143C2×#11758196C2×C412yes—
144C2×C22⋊Dic61C2×C412yes—
145C2×#11758198C2×C412yes—
146C2×#11758198C2×C412yes—
147C2×#11758198C2×C412yes—
148C2×C4×Dic61C2×C412yes—
149C4⋊#92418—21no—
150C4⋊#92418—21no—
151#14519695—22no—
152#14519695—22no—
153#14519695—22no—
154#14519695—22no—
155#14519695—22no—
156#14519695—41no—
157#14519695—41no—
158#14519695D414yescomplemented
159#14519693—22no—
160#14519693—22no—
161#14519693—41no—
162#14519693—41no—
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×D61C22×C412yes—
207C2×D4×C61—42no—
208C2×D4×C61C22⋊C411yescharacteristic
209C2×D4×C61C22⋊C411yescharacteristic
210C2×D4×C61C22⋊C411yescharacteristic
211C2×D4×C61C22⋊C411yescharacteristic
212C22×C4×C61—21no—
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2×D411yescharacteristic
231C22×C4×C61C2×D411yescharacteristic
232C22×C4×C61C2411yescharacteristic
233C2×C22⋊D61—22no—
234C2×C22⋊D61—22no—
235C2×C22⋊D61—22no—
236C2×C22⋊D61—22no—
237C2×C22⋊D61—24no—
238C2×C22⋊D61—42no—
239C2×C22⋊D61—44no—
240C22×Dic61—22no—
241C22×Dic61—22no—
242C22×Dic61—24no—
243C22×Dic61—42no—
244C22×Dic61C22×C412yes—
245C22×Dic61C22×C412yes—
246C22×Dic61C22×C412yes—
247#11758222—42no—
248#11758222—42no—
249#11758222—42no—
250#11758222—42no—
251#11758222—42no—
252#11758222—42no—
253#11758222—42no—
254#11758222—42no—
255C2×D244—21no—
256C2×D244—21no—
257C2×D244—21no—
258C2×D244—21no—
259C2×D244—21no—
260C2×D244—21no—
261C2×C4×D61—22no—
262C2×C4×D61—22no—
263C2×C4×D61—24no—
264C2×C4×D61—42no—
265C2×Dic122—21no—
266C2×Dic122—21no—
267C2×Dic122—21no—
268C2×Dic122—21no—
269C2×Dic122—22no—
270C2×Dic122—22no—
271C2×Dic122—21no—
272C2×Dic122—21no—
273C2×Dic122—21no—
274C2×Dic122—21no—
275C2×Dic122—21no—
276C2×Dic122—21no—
277C2×Dic122—24no—
278C2×Dic122—42no—
279C2×Dic122—42no—
280C2×Dic122—42no—
281C2×Dic122—42no—
282C2×Dic122—42no—
283C2×Dic122—42no—
284C2×Dic122—42no—
285C2×Dic122—42no—
286C2×Dic122—42no—
287C2×Dic122C2×D412yes—
288C2×Dic122#4112yes—
289M16×C61—21no—
290M16×C61—21no—
291M16×C61—21no—
292M16×C61—21no—
293M16×C61—21no—
294M16×C61—21no—
295M16×C61—21no—
296M16×C61—42no—
297M16×C61—42no—
298M16×C61C2×D412yes—
299C2×C8×C61—21no—
300C2×C8×C61—21no—
301C2×C8×C61—21no—
302C2×C8×C61—21no—
303C2×C8×C61—42no—
304C2×C8×C61—42no—
305C4⋊C4×C61C22⋊C411yescharacteristic
306C4⋊C4×C61C22⋊C411yescharacteristic
307C4⋊C4×C61C22⋊C411yescharacteristic
308C4⋊C4×C61C22⋊C411yescharacteristic
309C22⋊C4×C61C22⋊C411yescharacteristic
310C22⋊C4×C61C22⋊C411yescharacteristic
311C22⋊C4×C61C22⋊C411yescharacteristic
312C22⋊C4×C61C22⋊C411yescharacteristic
313C22⋊C4×C61C22⋊C411yescharacteristic
314C22⋊C4×C61C22⋊C411yescharacteristic
315C22⋊C4×C61C22⋊C411yescharacteristic
316C22⋊C4×C61C22⋊C411yescharacteristic
317C42×C61C2×D411yescharacteristic
318C42×C61C2×D411yescharacteristic
319C42×C61C2×D411yescharacteristic
320C42×C61C2×D411yescharacteristic
321C22⋊Dic61—22no—
322C22⋊Dic61—22no—
323#11758198—22no—
324#11758198—22no—
325#11758198—22no—
326#11758198—22no—
327#11758198—22no—
328#11758198—22no—
329C4⋊Dic61—21no—
330C4⋊Dic61—21no—
331#11758196—22no—
332#11758196—22no—
333#11758196—22no—
334#11758196—22no—
335C4×Dic61—22no—
336C4×Dic61—22no—
337#11758194—21no—
338#11758194—21no—
339#11758194—21no—
340#11758194—21no—
341#11758194—21no—
342#11758194—21no—
343#11758194—21no—
344#11758194—42no—
345#11758194—42no—
346#11758194C2×D412yes—
347C2×#92418—21no—
348C2×#92418—21no—
349C2×#92418—21no—
350C2×#92418—21no—
351C2×#92418—42no—
352C2×#92418—42no—
353C23×C61—21no—
354C23×C61—21no—
355C23×C61—22no—
356C23×C61—21no—
357C23×C61—21no—
358C23×C61—41no—
359C23×C61—41no—
360C23×C61—41no—
361C23×C61C2×C22⋊C411yescharacteristic
362C23×C61C2×C22⋊C411yescharacteristic
363C23×C61C2×C22⋊C411yescharacteristic
364C23×C61C2×C22⋊C411yescharacteristic
365C23×C61C23×C411yescharacteristic
366C22×D61—22no—
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—42no—
370C22×D61—42no—
371D4×C61—22no—
372D4×C61—22no—
373D4×C61—41no—
374D4×C61—41no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—21no—
378C2×C4×C61—21no—
379C2×C4×C61—21no—
380C2×C4×C61—21no—
381C2×C4×C61—21no—
382C2×C4×C61—21no—
383C2×C4×C61—21no—
384C2×C4×C61—21no—
385C2×C4×C61—21no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—21no—
391C2×C4×C61—21no—
392C2×C4×C61—21no—
393C2×C4×C61—21no—
394C2×C4×C61—21no—
395C2×C4×C61—41no—
396C2×C4×C61—41no—
397C2×C4×C61C2×C22⋊C411yescharacteristic
398C2×C4×C61C2×C22⋊C411yescharacteristic
399C2×C4×C61C2×C22⋊C411yescharacteristic
400C2×C4×C61C2×C22⋊C411yescharacteristic
401C2×C4×C61C2×C22⋊C411yescharacteristic
402C2×C4×C61C2×C22⋊C411yescharacteristic
403C2×C4×C61C2×C22⋊C411yescharacteristic
404C2×C4×C61C2×C22⋊C411yescharacteristic
405C2×C4×C61C22×D411yescharacteristic
406C2×C4×C61C22×D411yescharacteristic
407C2×C4×C61C22×D411yescharacteristic
408C2×C4×C61C2×#4111yescharacteristic
409C2×C4×C61H(5,𝔽2)11yescharacteristic
410C2×C4×C61H(5,𝔽2)11yescharacteristic
411C22⋊D61—44no—
412C22⋊D61—44no—
413C22⋊D61—44no—
414C22⋊D61—44no—
415C2×Dic61—22no—
416C2×Dic61—22no—
417C2×Dic61—22no—
418C2×Dic61—22no—
419C2×Dic61—22no—
420C2×Dic61—22no—
421C2×Dic61—44no—
422C2×Dic61—44no—
423C2×Dic61—42no—
424C2×Dic61C4×D414yes—
425D244—41no—
426D244—41no—
427D244—41no—
428D244—41no—
429C4×D61—44no—
430C4×D61—44no—
431Dic122—22no—
432Dic122—22no—
433Dic122—22no—
434Dic122—22no—
435Dic122—44no—
436Dic122—44no—
437Dic122—41no—
438Dic122—41no—
439Dic122—41no—
440Dic122—41no—
441C8×C61—22no—
442C8×C61—41no—
443C8×C61—41no—
444C8×C61—41no—
445#92418—22no—
446#92418—41no—
447#92418—41no—
448#92418—41no—
449#22410—611nomaximal, Sylow
450C22×C61—21no—
451C22×C61—21no—
452C22×C61—21no—
453C22×C61—21no—
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—21no—
457C22×C61—21no—
458C22×C61—21no—
459C22×C61—21no—
460C22×C61—21no—
461C22×C61—21no—
462C22×C61—21no—
463C22×C61—42no—
464C22×C61—42no—
465C22×C61—81no—
466C22×C61—81no—
467C22×C61#41312yescomplemented
468C22×C61C22×C22⋊C411yescharacteristic
469C22×C61C2×C4×D411yescharacteristic
470C22×C61#51811yescharacteristic
471C2×D61—42no—
472C2×D61—42no—
473C2×D61—42no—
474C2×D61—82no—
475C2×D61—82no—
476C4×C61—21no—
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—21no—
480C4×C61—21no—
481C4×C61—21no—
482C4×C61—21no—
483C4×C61—21no—
484C4×C61D4211yescharacteristic
485C4×C61D4211yescharacteristic
486C4×C61#54611yescharacteristic
487C4×C61#54611yescharacteristic
488Dic61—24no—
489Dic61—42no—
490Dic61—42no—
491C2×#548—611no—
492D4×M16—611no—
493D4×M16D6111yescharacteristic, complemented
494C2×#413—611no—
495C22×#101—611no—
496#1967—611no—
497#1967—611no—
498#1901—611no—
499#1901—611no—
500#1900—611no—
501#1900—611no—
502#1801—611no—
503#1785—611no—
504#1784—611no—
505C4×#101—611no—
506C2×C61—21no—
507C2×C61—21no—
508C2×C61—22no—
509C2×C61—41no—
510C2×C61—41no—
511C2×C61—41no—
512C2×C61D4×C22⋊C411yescharacteristic
513C2×C61C2×#41311yescharacteristic
514C2×C61#288911yescharacteristic
515D61—82no—
516C22×#41—611no—
517C23×Q8—611no—
518C22×M16—611no—
519C22×M16—611no—
520C22×M16C2×D6111yescharacteristic
521C22×M16C2×D6111yescharacteristic
522#548—1221no—
523#548—1221no—
524#548—1221no—
525#548—1221no—
526#548—1221no—
527#548—1221no—
528#548—1221no—
529#548—1221no—
530C2×#124—612no—
531C2×#124—611no—
532C2×C22⋊Q8—611no—
533C2×C22⋊Q8—612no—
534C2×#121—612no—
535C2×#121—611no—
536C2×C4×Q8—611no—
537C2×C4×D4—612no—
538C2×C4×D4C2×D6111yescharacteristic
539#436—21no—
540#436—1221no—
541#435—21no—
542#435—21no—
543#435—1221no—
544#435—1221no—
545C8×D4—21no—
546C8×D4—1221no—
547#423—611no—
548#423C2×D6111yescharacteristic
549#413—1224no—
550C2×#101—611no—
551C2×#101—611no—
552C2×#101—611no—
553C2×#101—611no—
554C2×#101—611no—
555C2×#101—611no—
556C2×#101—611no—
557C2×#101—611no—
558C2×#101—1224no—
559C2×#100—611no—
560C2×#100—611no—
561C2×#100—611no—
562C2×#100—611no—
563#407—611no—
564#407—611no—
565#407C2×D6111yescharacteristic
566#407C2×D6111yescharacteristic
567C4×M16—611no—
568C4×M16C2×D6111yescharacteristic
569#343—611no—
570#343—611no—
571#343—611no—
572#343—611no—
573C61#2241011yescharacteristic, complemented, Sylow
574C2×#41—1222no—
575C2×#41—1222no—
576C2×#41—1221no—
577C2×#41—1221no—
578C2×#41—1221no—
579C2×#41—1221no—
580C2×#41—2441no—
581C2×#41—2441no—
582C22×Q8—612no—
583C22×Q8—611no—
584C22×Q8—611no—
585C22×Q8—1222no—
586C22×Q8—1222no—
587C22×Q8—1221no—
588C22×Q8—1221no—
589C22×Q8—1221no—
590C22×Q8—1221no—
591C22×Q8—2441no—
592C22×Q8—2441no—
593C22×D4—612no—
594C22×D4—612no—
595C22×D4—611no—
596C22×D4C4×D6111yescharacteristic
597C23×C4—612no—
598C23×C4—612no—
599C23×C4C22×D6111yescharacteristic
600C23×C4C22×D6111yescharacteristic
601C2×M16—21no—
602C2×M16—21no—
603C2×M16—22no—
604C2×M16—22no—
605C2×M16—41no—
606C2×M16—41no—
607C2×M16—611no—
608C2×M16—611no—
609C2×M16—611no—
610C2×M16—611no—
611C2×M16—1221no—
612C2×M16—1221no—
613C2×M16—1222no—
614C2×M16—1222no—
615C2×M16—2441no—
616C2×M16—2441no—
617C2×M16C22×D6111yescharacteristic
618C2×M16C22×D6111yescharacteristic
619C2×M16C22×D6111yescharacteristic
620C2×M16C22×D6111yescharacteristic
621C22×C8—21no—
622C22×C8—21no—
623C22×C8—1221no—
624C22×C8—1221no—
625#124—1222no—
626#124—1222no—
627#124—1222no—
628#124—1222no—
629#124—1221no—
630#124—1221no—
631#124—1221no—
632#124—1221no—
633C22⋊Q8—1221no—
634C22⋊Q8—1221no—
635C22⋊Q8—1221no—
636C22⋊Q8—1221no—
637C22⋊Q8—1222no—
638C22⋊Q8—1222no—
639C22⋊Q8—1222no—
640C22⋊Q8—1222no—
641#121—1222no—
642#121—1222no—
643#121—1222no—
644#121—1222no—
645#121—1221no—
646#121—1221no—
647#121—1221no—
648#121—1221no—
649C4×Q8—1221no—
650C4×Q8—1221no—
651C4×Q8—1221no—
652C4×Q8—1221no—
653C4×D4—1222no—
654C4×D4—1222no—
655C4×D4—1222no—
656C4×D4—1222no—
657C4×D4D24411yescharacteristic
658C4×D4D24411yescharacteristic
659C4×D4D24411yescharacteristic
660C4×D4D24411yescharacteristic
661C4×D4C22⋊D6111yescharacteristic
662C4×D4C22⋊D6111yescharacteristic
663C4×D4C22⋊D6111yescharacteristic
664C4×D4C22⋊D6111yescharacteristic
665C2×C4⋊C4—612no—
666C2×C4⋊C4—612no—
667C2×C4⋊C4—611no—
668C2×C4⋊C4C4×D6111yescharacteristic
669C2×C22⋊C4—612no—
670C2×C22⋊C4—612no—
671C2×C22⋊C4—612no—
672C2×C22⋊C4—612no—
673C2×C22⋊C4C4×D6111yescharacteristic
674C2×C22⋊C4C4×D6111yescharacteristic
675C2×C42—612no—
676C2×C42C22×D6111yescharacteristic
677C4⋊C8—21no—
678C4⋊C8—21no—
679C4⋊C8—1221no—
680C4⋊C8—1221no—
681#101—614no—
682#101—1222no—
683#101—1222no—
684#101—1222no—
685#101—1222no—
686#101—1222no—
687#101—2441no—
688#101—2441no—
689#100—1222no—
690#100—1222no—
691#100—2441no—
692#100—2441no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8—1221no—
698C22⋊C8—1221no—
699C22⋊C8—1221no—
700C22⋊C8—1221no—
701#97—21no—
702#97—1221no—
703C4×C8—21no—
704C4×C8—1221no—
705C24—612no—
706C24C2×C4×D6111yescharacteristic
707C24C2×C4×D6111yescharacteristic
708#41—2442no—
709#41—2442no—
710#41—2442no—
711#41—2442no—
712#41—2442no—
713#41—2442no—
714#41—2442no—
715#41—2442no—
716C2×Q8—612no—
717C2×Q8—612no—
718C2×Q8—1224no—
719C2×Q8—1221no—
720C2×Q8—1221no—
721C2×Q8—1221no—
722C2×Q8—1221no—
723C2×Q8—1221no—
724C2×Q8—1221no—
725C2×Q8—1221no—
726C2×Q8—1221no—
727C2×Q8—1221no—
728C2×Q8—1221no—
729C2×Q8—1222no—
730C2×Q8—1222no—
731C2×Q8—2442no—
732C2×Q8—2442no—
733C2×Q8—2442no—
734C2×Q8—2442no—
735C2×Q8—2442no—
736C2×Q8—2442no—
737C2×Q8—2442no—
738C2×Q8—2442no—
739C2×Q8—2442no—
740C2×D4—42no—
741C2×D4—1224no—
742C2×D4—1222no—
743C2×D4—1222no—
744C2×D4—1222no—
745C2×D4—1222no—
746C2×D4—1221no—
747C2×D4—1221no—
748C2×D4—1221no—
749C2×D4—1221no—
750C2×D4—1221no—
751C2×D4—1221no—
752C2×D4—2442no—
753C2×D4—2444no—
754C2×D4#1175819811yescharacteristic
755C2×D4#1175819811yescharacteristic
756C2×D4#1175819811yescharacteristic
757C2×D4#1175819811yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—612no—
767C22×C4—612no—
768C22×C4—612no—
769C22×C4—1224no—
770C22×C4—1224no—
771C22×C4—1222no—
772C22×C4—1222no—
773C22×C4—1222no—
774C22×C4—1222no—
775C22×C4—2442no—
776C22×C4—2442no—
777C22×C4C2×C4×D6111yescharacteristic
778C22×C4C2×C4×D6111yescharacteristic
779C22×C4C2×C4×D6111yescharacteristic
780C22×C4C2×C4×D6111yescharacteristic
781C22×C4C2×D24411yescharacteristic
782C22×C4C2×D24411yescharacteristic
783C22×C4C2×D24411yescharacteristic
784C22×C4C2×D24411yescharacteristic
785C22×C4C2×C22⋊D6111yescharacteristic
786C22×C4C2×C22⋊D6111yescharacteristic
787C22×C4C2×C22⋊D6111yescharacteristic
788C22×C4C2×C22⋊D6111yescharacteristic
789C22×C4C23×D6111yescharacteristic
790M16—21no—
791M16—21no—
792M16—21no—
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—42no—
798M16—42no—
799M16—612no—
800M16—1221no—
801M16—1221no—
802M16—1221no—
803M16—1221no—
804M16—1221no—
805M16—1221no—
806M16—1221no—
807M16—2442no—
808M16—2442no—
809M16D4×D6112yes—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—42no—
815C2×C8—42no—
816C2×C8—1221no—
817C2×C8—1221no—
818C2×C8—1221no—
819C2×C8—1221no—
820C2×C8—2442no—
821C2×C8—2442no—
822C4⋊C4—1221no—
823C4⋊C4—1221no—
824C4⋊C4—1222no—
825C4⋊C4—1222no—
826C4⋊C4—1222no—
827C4⋊C4—1222no—
828C4⋊C4#1175819811yescharacteristic
829C4⋊C4#1175819811yescharacteristic
830C4⋊C4#1175819811yescharacteristic
831C4⋊C4#1175819811yescharacteristic
832C22⋊C4—1222no—
833C22⋊C4—1222no—
834C22⋊C4—1222no—
835C22⋊C4—1222no—
836C22⋊C4—1222no—
837C22⋊C4—1222no—
838C22⋊C4—1222no—
839C22⋊C4—1222no—
840C22⋊C4#1175819811yescharacteristic
841C22⋊C4#1175819811yescharacteristic
842C22⋊C4#1175819811yescharacteristic
843C22⋊C4#1175819811yescharacteristic
844C22⋊C4#1175819811yescharacteristic
845C22⋊C4#1175819811yescharacteristic
846C22⋊C4#1175819811yescharacteristic
847C22⋊C4#1175819811yescharacteristic
848C42—1222no—
849C42—1222no—
850C42C2×D24411yescharacteristic
851C42C2×D24411yescharacteristic
852C42C2×C22⋊D6111yescharacteristic
853C42C2×C22⋊D6111yescharacteristic
854C23—21no—
855C23—21no—
856C23—22no—
857C23—21no—
858C23—21no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—1222no—
863C23—1222no—
864C23—1222no—
865C23—2442no—
866C23—2442no—
867C23C2×#1175819811yescharacteristic
868C23C2×#1175819811yescharacteristic
869C23C2×#1175819811yescharacteristic
870C23C2×#1175819811yescharacteristic
871C23C22×C4×D6111yescharacteristic
872Q8—1222no—
873Q8—1222no—
874Q8—1222no—
875Q8—1222no—
876Q8—2444no—
877Q8—2444no—
878Q8—2441no—
879Q8—2441no—
880Q8—2441no—
881Q8—2441no—
882D4—22no—
883D4—22no—
884D4—41no—
885D4—41no—
886D4—2444no—
887D4—2444no—
888D4—2444no—
889D4—2444no—
890D4—2441no—
891D4—2441no—
892D4—2441no—
893D4—2441no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—614no—
917C2×C4—1222no—
918C2×C4—1222no—
919C2×C4—1222no—
920C2×C4—1222no—
921C2×C4—1222no—
922C2×C4—1222no—
923C2×C4—2444no—
924C2×C4—2444no—
925C2×C4—2444no—
926C2×C4—2444no—
927C2×C4—2442no—
928C2×C4C2×#1175819811yescharacteristic
929C2×C4C2×#1175819811yescharacteristic
930C2×C4C2×#1175819811yescharacteristic
931C2×C4C2×#1175819811yescharacteristic
932C2×C4C2×#1175819811yescharacteristic
933C2×C4C2×#1175819811yescharacteristic
934C2×C4C2×#1175819811yescharacteristic
935C2×C4C2×#1175819811yescharacteristic
936C2×C4C2×D4×D6111yescharacteristic
937C2×C4C22×C22⋊D6111yescharacteristic
938C2×C4C22×D24411yescharacteristic
939C2×C4#41×D6111yescharacteristic
940C2×C4#1451982211yescharacteristic
941C2×C4#1451982311yescharacteristic
942C8—22no—
943C8—41no—
944C8—41no—
945C8—41no—
946C8—1222no—
947C8—2441no—
948C8—2441no—
949C8—2441no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—42no—
964C22—42no—
965C22—81no—
966C22—81no—
967C22—4882no—
968C22—4882no—
969C22—2442no—
970C22—2442no—
971C22—2442no—
972C22#1683974412yescomplemented
973C22C22×#1175819811yescharacteristic
974C22C4×D4×D6111yescharacteristic
975C22#1684023411yescharacteristic
976C4—21no—
977C4—21no—
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—1224no—
985C4—2442no—
986C4—2442no—
987C4D4×C22⋊D6111yescharacteristic
988C4D4×D24411yescharacteristic
989C4#1684040011yescharacteristic
990C4#1684040711yescharacteristic
991C2—21no—
992C2—21no—
993C2—22no—
994C2—41no—
995C2—41no—
996C2—41no—
997C2—4882no—
998C2D4×#1175819811yescharacteristic
999C2C2×#1683974411yescharacteristic
1000C2#2145430111yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingD4×M16×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840421C2
cosocleC22×C4×C61C24
hypercenterD4×M16D61
hypocenterC61#22410
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×#14519695C2semidirect
5. #21446668C2semidirect
6. #21446666C2semidirect
7. #21446287C2semidirect
8. #21446285C2semidirect
9. #21446282C2semidirect
10. #21446280C2semidirect
11. #21445812C2semidirect
12. #21445745C2semidirect
13. #21445742C2semidirect
14. C4×#14519695C2semidirect
15. D4×M16×C61C2semidirect
158. #14519695D4semidirect
467. C22×C61#413semidirect
493. D4×M16D61semidirect
573. C61#22410semidirect
972. C22#16839744semidirect

Maximal subgroups

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

subgroupindex
C2×#168404212
D4×#117581942
C2×#168397442
C22×#145196952
#214466682
#214466662
#214462872
#214462852
#214462822
#214462802
#214458122
#214457452
#214457422
C4×#145196952
D4×M16×C612
#2241061