Finite Group Databasebeta

← #25111951

Subgroups — #25111951

Order 11008.

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×#14583545C211yesmaximal, characteristic
2D4×#10621877C211yesmaximal, characteristic, complemented
3C2×#14582881C211yesmaximal, characteristic, complemented
4C22×#13063241C211yesmaximal, characteristic, complemented
5#19135444C211yesmaximal, characteristic, complemented
6#19135442C211yesmaximal, characteristic, complemented
7#19135063C211yesmaximal, characteristic, complemented
8#19135061C211yesmaximal, characteristic, complemented
9#19135058C211yesmaximal, characteristic, complemented
10#19135056C211yesmaximal, characteristic, complemented
11#19134584C211yesmaximal, characteristic, complemented
12#19134521C211yesmaximal, characteristic, complemented
13#19134515C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15D4×M16×C43C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×D172C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C22×#10621877C2211yescharacteristic, complemented
20#14583545—21no—
21#14583545—21no—
22#14583545—21no—
23#14583545—21no—
24#14583545—21no—
25#14583545—21no—
26#14583545—21no—
27#14583545—21no—
28C2×#13063313C2211yescharacteristic
29C2×#13063310C412yes—
30C2×#13063304C2211yescharacteristic
31C2×#13063299C2211yescharacteristic
32C2×#13063298C412yes—
33C2×#13063293C412yes—
34C2×C4×D172C2211yescharacteristic
35C2×C22⋊C4×D43C412yes—
36#14582977—21no—
37#14582971—21no—
38#14582971—21no—
39D4×C43⋊C8—21no—
40#14582923C2211yescharacteristic, complemented
41#14582881—24no—
42C2×#13063243C2211yescharacteristic, complemented
43C2×#13063243C2211yescharacteristic, complemented
44C2×#13063243C2211yescharacteristic, complemented
45C2×#13063243C2211yescharacteristic, complemented
46C2×#13063241—24no—
47C2×#13063241C2211yescharacteristic
48C2×#13063241C2211yescharacteristic
49C2×#13063241C2211yescharacteristic
50C2×#13063241C2211yescharacteristic
51C2×#13063241C2211yescharacteristic
52C2×#13063241C2211yescharacteristic
53C2×#13063241C2211yescharacteristic
54C2×#13063241C2211yescharacteristic
55#14582863C2211yescharacteristic
56#14582863C2211yescharacteristic, complemented
57C4×#10621877C2211yescharacteristic, complemented
58#14582667C2211yescharacteristic, complemented
59#14582667C2211yescharacteristic, complemented
60#14582667C2211yescharacteristic, complemented
61#14582667C2211yescharacteristic, complemented
62C22×M16×C43C2211yescharacteristic
63C22×M16×C43C2211yescharacteristic, complemented
64C2×C4×D4×C43C2211yescharacteristic
65C43×#436—21no—
66C43×#435—21no—
67C43×#435—21no—
68C8×D4×C43—21no—
69C43×#423C2211yescharacteristic, complemented
70C43×#407C2211yescharacteristic
71C43×#407C2211yescharacteristic, complemented
72C4×M16×C43C2211yescharacteristic, complemented
73C24×D43C2×C412yes—
74C2×#10621898—21no—
75C2×#10621898—21no—
76C2×#10621898—21no—
77C2×#10621898—21no—
78C2×#10621898—22no—
79C2×#10621898—22no—
80C2×#10621898—41no—
81C2×#10621898—41no—
82C22×Dic86C2311yescharacteristic
83C22×D172—21no—
84C22×D172—21no—
85C22×D172—21no—
86C22×D172—21no—
87C22×D172—22no—
88C22×D172—22no—
89C22×D172—41no—
90C22×D172—41no—
91C22×D172C2×C412yes—
92C22×D172C2311yescharacteristic
93C22×D172C2311yescharacteristic
94C22×C22⋊D43C2×C412yes—
95C22×C22⋊D43C2×C412yes—
96C22×C4×D43C2×C412yes—
97C22×C4×D43C2×C412yes—
98C2×#10621877—21no—
99C2×#10621877—21no—
100C2×#10621877—22no—
101C2×#10621877—22no—
102C2×#10621877—41no—
103C2×#10621877—41no—
104C2×#10621877C2311yescharacteristic
105C2×#10621877C2311yescharacteristic
106C2×#10621877C2311yescharacteristic
107C2×#10621877C2311yescharacteristic
108C22×C43⋊C8—21no—
109C22×C43⋊C8—21no—
110#13063313—21no—
111#13063313—21no—
112#13063313—21no—
113#13063313—21no—
114#13063310—22no—
115#13063310—22no—
116#13063310—22no—
117#13063310—22no—
118#13063304—21no—
119#13063304—21no—
120#13063304—21no—
121#13063304—21no—
122#13063299—21no—
123#13063299—21no—
124#13063299—21no—
125#13063299—21no—
126#13063298—22no—
127#13063298—22no—
128#13063298—22no—
129#13063298—22no—
130#13063293—22no—
131#13063293—22no—
132#13063293—22no—
133#13063293—22no—
134C4×D172—21no—
135C4×D172—21no—
136C4×D172—21no—
137C4×D172—21no—
138C2×C4⋊Dic43C2311yescharacteristic
139C2×Dic43⋊C4C2×C412yes—
140C2×C22⋊Dic43C2×C412yes—
141C2×(C2×D43)⋊C4C2×C412yes—
142C2×(C2×D43)⋊C4C2×C412yes—
143C2×(C2×D43)⋊C4C2×C412yes—
144C2×(C2×D43)⋊C4C2×C412yes—
145C22⋊C4×D43—22no—
146C22⋊C4×D43—22no—
147C22⋊C4×D43—22no—
148C22⋊C4×D43—22no—
149C4⋊(C43⋊C8)—21no—
150C4⋊(C43⋊C8)—21no—
151#13063243—22no—
152#13063243—22no—
153#13063243—41no—
154#13063243—41no—
155#13063241—22no—
156#13063241—22no—
157#13063241—22no—
158#13063241—22no—
159#13063241—22no—
160#13063241—41no—
161#13063241—41no—
162#13063241D414yescomplemented
163C22⋊(C43⋊C8)—21no—
164C22⋊(C43⋊C8)—21no—
165C22⋊(C43⋊C8)—21no—
166C22⋊(C43⋊C8)—21no—
167#13063236—21no—
168C4×C43⋊C8—21no—
169C22×D4×C43C2×C411yescharacteristic
170C23×C4×C43C2311yescharacteristic
171C23×C4×C43C2311yescharacteristic
172C2×M16×C43—21no—
173C2×M16×C43—21no—
174C2×M16×C43—22no—
175C2×M16×C43—22no—
176C2×M16×C43—41no—
177C2×M16×C43—41no—
178C2×M16×C43C2311yescharacteristic
179C2×M16×C43C2311yescharacteristic
180C2×M16×C43C2311yescharacteristic
181C2×M16×C43C2311yescharacteristic
182C22×C8×C43—21no—
183C22×C8×C43—21no—
184C4×D4×C43D411yescharacteristic
185C4×D4×C43D411yescharacteristic
186C4×D4×C43D411yescharacteristic
187C4×D4×C43D411yescharacteristic
188C4×D4×C43D411yescharacteristic
189C4×D4×C43D411yescharacteristic
190C4×D4×C43D411yescharacteristic
191C4×D4×C43D411yescharacteristic
192C2×C4⋊C4×C43C2×C411yescharacteristic
193C2×C22⋊C4×C43C2×C411yescharacteristic
194C2×C22⋊C4×C43C2×C411yescharacteristic
195C2×C42×C43C2311yescharacteristic
196C4⋊C8×C43—21no—
197C4⋊C8×C43—21no—
198C22⋊C8×C43—21no—
199C22⋊C8×C43—21no—
200C22⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202#97×C43—21no—
203C4×C8×C43—21no—
204C24×C43C22×C411yescharacteristic
205C24×C43C22×C411yescharacteristic
206C23×D43—22no—
207C23×D43—22no—
208C23×D43—24no—
209C23×D43—42no—
210C23×D43—44no—
211C23×D43—82no—
212C23×D43C22×C412yes—
213C23×D43C22×C412yes—
214C2×D4×C43—42no—
215C2×D4×C43C22⋊C411yescharacteristic
216C2×D4×C43C22⋊C411yescharacteristic
217C2×D4×C43C22⋊C411yescharacteristic
218C2×D4×C43C22⋊C411yescharacteristic
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43—21no—
227C22×C4×C43C22×C411yescharacteristic
228C22×C4×C43C22×C411yescharacteristic
229C22×C4×C43C22×C411yescharacteristic
230C22×C4×C43C22×C411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2×D411yescharacteristic
235C22×C4×C43C2×D411yescharacteristic
236C22×C4×C43C2×D411yescharacteristic
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2411yescharacteristic
240C2×C22⋊D43—22no—
241C2×C22⋊D43—22no—
242C2×C22⋊D43—22no—
243C2×C22⋊D43—22no—
244C2×C22⋊D43—24no—
245C2×C22⋊D43—42no—
246C2×C22⋊D43—82no—
247C22×Dic43C22×C412yes—
248C22×Dic43C22×C412yes—
249#10621898—42no—
250#10621898—42no—
251#10621898—42no—
252#10621898—42no—
253#10621898—42no—
254#10621898—42no—
255#10621898—42no—
256#10621898—42no—
257C2×D172—21no—
258C2×D172—21no—
259C2×D172—21no—
260C2×D172—21no—
261C2×D172—22no—
262C2×D172—22no—
263C2×D172—21no—
264C2×D172—21no—
265C2×D172—21no—
266C2×D172—21no—
267C2×D172—21no—
268C2×D172—21no—
269C2×D172—24no—
270C2×D172—42no—
271C2×D172—42no—
272C2×D172—42no—
273C2×D172—42no—
274C2×D172—42no—
275C2×D172—42no—
276C2×D172—42no—
277C2×D172—42no—
278C2×D172—42no—
279C2×D172C2×D412yes—
280C2×D172#4112yes—
281C2×C4×D43—22no—
282C2×C4×D43—22no—
283C2×C4×D43—22no—
284C2×C4×D43—22no—
285C2×C4×D43—24no—
286C2×C4×D43—42no—
287C2×C4×D43—82no—
288C2×Dic86—21no—
289C2×Dic86—21no—
290C2×Dic86—21no—
291C2×Dic86—21no—
292C2×Dic86—21no—
293C2×Dic86—21no—
294M16×C43—21no—
295M16×C43—21no—
296M16×C43—21no—
297M16×C43—21no—
298M16×C43—21no—
299M16×C43—21no—
300M16×C43—21no—
301M16×C43—42no—
302M16×C43—42no—
303M16×C43C2×D412yes—
304C2×C8×C43—21no—
305C2×C8×C43—21no—
306C2×C8×C43—21no—
307C2×C8×C43—21no—
308C2×C8×C43—42no—
309C2×C8×C43—42no—
310C4⋊C4×C43C22⋊C411yescharacteristic
311C4⋊C4×C43C22⋊C411yescharacteristic
312C4⋊C4×C43C22⋊C411yescharacteristic
313C4⋊C4×C43C22⋊C411yescharacteristic
314C22⋊C4×C43C22⋊C411yescharacteristic
315C22⋊C4×C43C22⋊C411yescharacteristic
316C22⋊C4×C43C22⋊C411yescharacteristic
317C22⋊C4×C43C22⋊C411yescharacteristic
318C22⋊C4×C43C22⋊C411yescharacteristic
319C22⋊C4×C43C22⋊C411yescharacteristic
320C22⋊C4×C43C22⋊C411yescharacteristic
321C22⋊C4×C43C22⋊C411yescharacteristic
322C42×C43C2×D411yescharacteristic
323C42×C43C2×D411yescharacteristic
324C42×C43C2×D411yescharacteristic
325C42×C43C2×D411yescharacteristic
326C22⋊Dic43—22no—
327C22⋊Dic43—22no—
328(C2×D43)⋊C4—22no—
329(C2×D43)⋊C4—22no—
330(C2×D43)⋊C4—22no—
331(C2×D43)⋊C4—22no—
332(C2×D43)⋊C4—22no—
333(C2×D43)⋊C4—22no—
334(C2×D43)⋊C4—22no—
335(C2×D43)⋊C4—22no—
336C4⋊Dic43—21no—
337C4⋊Dic43—21no—
338Dic43⋊C4—22no—
339Dic43⋊C4—22no—
340#10621877—21no—
341#10621877—21no—
342#10621877—21no—
343#10621877—21no—
344#10621877—21no—
345#10621877—21no—
346#10621877—21no—
347#10621877—42no—
348#10621877—42no—
349#10621877C2×D412yes—
350C2×C43⋊C8—21no—
351C2×C43⋊C8—21no—
352C2×C43⋊C8—21no—
353C2×C43⋊C8—21no—
354C2×C43⋊C8—42no—
355C2×C43⋊C8—42no—
356C23×C43—21no—
357C23×C43—21no—
358C23×C43—22no—
359C23×C43—21no—
360C23×C43—21no—
361C23×C43—41no—
362C23×C43—41no—
363C23×C43—41no—
364C23×C43C2×C22⋊C411yescharacteristic
365C23×C43C2×C22⋊C411yescharacteristic
366C23×C43C2×C22⋊C411yescharacteristic
367C23×C43C2×C22⋊C411yescharacteristic
368C23×C43C23×C411yescharacteristic
369C22×D43—22no—
370C22×D43—22no—
371C22×D43—22no—
372C22×D43—22no—
373C22×D43—22no—
374C22×D43—44no—
375C22×D43—44no—
376C22×D43—42no—
377C22×D43—42no—
378C22×D43—44no—
379C22×D43—44no—
380C22×D43—42no—
381C22×D43—42no—
382C22×D43—82no—
383C22×D43—82no—
384C22×D43—88no—
385C22×D43—88no—
386C22×D43C4×D414yes—
387D4×C43—22no—
388D4×C43—22no—
389D4×C43—41no—
390D4×C43—41no—
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—21no—
394C2×C4×C43—21no—
395C2×C4×C43—21no—
396C2×C4×C43—21no—
397C2×C4×C43—21no—
398C2×C4×C43—21no—
399C2×C4×C43—21no—
400C2×C4×C43—21no—
401C2×C4×C43—21no—
402C2×C4×C43—21no—
403C2×C4×C43—21no—
404C2×C4×C43—21no—
405C2×C4×C43—21no—
406C2×C4×C43—21no—
407C2×C4×C43—21no—
408C2×C4×C43—21no—
409C2×C4×C43—21no—
410C2×C4×C43—21no—
411C2×C4×C43—41no—
412C2×C4×C43—41no—
413C2×C4×C43C2×C22⋊C411yescharacteristic
414C2×C4×C43C2×C22⋊C411yescharacteristic
415C2×C4×C43C2×C22⋊C411yescharacteristic
416C2×C4×C43C2×C22⋊C411yescharacteristic
417C2×C4×C43C2×C22⋊C411yescharacteristic
418C2×C4×C43C2×C22⋊C411yescharacteristic
419C2×C4×C43C2×C22⋊C411yescharacteristic
420C2×C4×C43C2×C22⋊C411yescharacteristic
421C2×C4×C43C22×D411yescharacteristic
422C2×C4×C43C22×D411yescharacteristic
423C2×C4×C43C22×D411yescharacteristic
424C2×C4×C43C2×#4111yescharacteristic
425C2×C4×C43H(5,𝔽2)11yescharacteristic
426C2×C4×C43H(5,𝔽2)11yescharacteristic
427C22⋊D43—44no—
428C22⋊D43—44no—
429C22⋊D43—82no—
430C22⋊D43—82no—
431C2×Dic43—22no—
432C2×Dic43—22no—
433C2×Dic43—22no—
434C2×Dic43—22no—
435C2×Dic43—42no—
436D172—22no—
437D172—22no—
438D172—22no—
439D172—22no—
440D172—44no—
441D172—44no—
442D172—41no—
443D172—41no—
444D172—41no—
445D172—41no—
446C4×D43—44no—
447C4×D43—44no—
448C4×D43—82no—
449C4×D43—82no—
450Dic86—41no—
451Dic86—41no—
452Dic86—41no—
453Dic86—41no—
454C8×C43—22no—
455C8×C43—41no—
456C8×C43—41no—
457C8×C43—41no—
458C43⋊C8—22no—
459C43⋊C8—41no—
460C43⋊C8—41no—
461C43⋊C8—41no—
462#22408—431nomaximal, Sylow
463C22×C43—21no—
464C22×C43—21no—
465C22×C43—21no—
466C22×C43—21no—
467C22×C43—21no—
468C22×C43—21no—
469C22×C43—21no—
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—21no—
473C22×C43—21no—
474C22×C43—21no—
475C22×C43—21no—
476C22×C43—42no—
477C22×C43—42no—
478C22×C43—81no—
479C22×C43—81no—
480C22×C43#41312yescomplemented
481C22×C43C22×C22⋊C411yescharacteristic
482C22×C43C2×C4×D411yescharacteristic
483C22×C43#51811yescharacteristic
484C2×D43—24no—
485C2×D43—44no—
486C2×D43—42no—
487C2×D43—42no—
488C2×D43—44no—
489C2×D43—42no—
490C2×D43—42no—
491C2×D43—42no—
492C2×D43—88no—
493C2×D43—88no—
494C2×D43—82no—
495C2×D43—82no—
496C4×C43—21no—
497C4×C43—21no—
498C4×C43—21no—
499C4×C43—21no—
500C4×C43—21no—
501C4×C43—21no—
502C4×C43—21no—
503C4×C43—21no—
504C4×C43D4211yescharacteristic
505C4×C43D4211yescharacteristic
506C4×C43#54611yescharacteristic
507C4×C43#54611yescharacteristic
508Dic43—42no—
509Dic43—42no—
510C2×#546—431no—
511D4×M16—431no—
512D4×M16D4311yescharacteristic, complemented
513C2×#413—431no—
514C22×#100—431no—
515#1967—431no—
516#1967—431no—
517#1901—431no—
518#1901—431no—
519#1900—431no—
520#1900—431no—
521#1800—431no—
522#1785—431no—
523#1783—431no—
524C4×#100—431no—
525C2×C43—21no—
526C2×C43—21no—
527C2×C43—22no—
528C2×C43—41no—
529C2×C43—41no—
530C2×C43—41no—
531C2×C43D4×C22⋊C411yescharacteristic
532C2×C43C2×#41311yescharacteristic
533C2×C43#288811yescharacteristic
534D43—44no—
535D43—82no—
536C22×#41—431no—
537C23×D4—431no—
538C22×M16—431no—
539C22×M16—431no—
540C22×M16C2×D4311yescharacteristic
541C22×M16C2×D4311yescharacteristic, complemented
542#546—861no—
543#546—861no—
544#546—861no—
545#546—861no—
546#546—861no—
547#546—861no—
548#546—861no—
549#546—861no—
550C2×#124—431no—
551C2×#123—432no—
552C2×C22⋊Q8—431no—
553C2×#121—431no—
554C2×#121—432no—
555C2×#120—432no—
556C2×C4×D4—431no—
557C2×C4×D4C2×D4311yescharacteristic
558C22×C22⋊C4—432no—
559#436—21no—
560#436—861no—
561#435—21no—
562#435—21no—
563#435—861no—
564#435—861no—
565C8×D4—21no—
566C8×D4—861no—
567#423—431no—
568#423C2×D4311yescharacteristic, complemented
569#413—864no—
570C2×#101—431no—
571C2×#101—431no—
572C2×#101—431no—
573C2×#101—431no—
574C2×#100—431no—
575C2×#100—431no—
576C2×#100—431no—
577C2×#100—431no—
578C2×#100—431no—
579C2×#100—431no—
580C2×#100—431no—
581C2×#100—431no—
582C2×#100—864no—
583#407—431no—
584#407—431no—
585#407C2×D4311yescharacteristic
586#407C2×D4311yescharacteristic, complemented
587C4×M16—431no—
588C4×M16C2×D4311yescharacteristic, complemented
589#343—431no—
590#343—431no—
591#343—431no—
592#343—431no—
593C43#2240811yescharacteristic, complemented, Sylow
594C25—432no—
595C2×#41—862no—
596C2×#41—862no—
597C2×#41—861no—
598C2×#41—861no—
599C2×#41—861no—
600C2×#41—861no—
601C2×#41—1721no—
602C2×#41—1721no—
603C22×Q8—431no—
604C22×D4—432no—
605C22×D4—432no—
606C22×D4—432no—
607C22×D4—431no—
608C22×D4—431no—
609C22×D4—862no—
610C22×D4—862no—
611C22×D4—861no—
612C22×D4—861no—
613C22×D4—861no—
614C22×D4—861no—
615C22×D4—1721no—
616C22×D4—1721no—
617C22×D4C4×D4311yescharacteristic
618C23×C4—432no—
619C23×C4—432no—
620C23×C4C22×D4311yescharacteristic
621C23×C4C22×D4311yescharacteristic
622C2×M16—21no—
623C2×M16—21no—
624C2×M16—22no—
625C2×M16—22no—
626C2×M16—41no—
627C2×M16—41no—
628C2×M16—431no—
629C2×M16—431no—
630C2×M16—431no—
631C2×M16—431no—
632C2×M16—861no—
633C2×M16—861no—
634C2×M16—862no—
635C2×M16—862no—
636C2×M16—1721no—
637C2×M16—1721no—
638C2×M16C22×D4311yescharacteristic
639C2×M16C22×D4311yescharacteristic
640C2×M16C22×D4311yescharacteristic
641C2×M16C22×D4311yescharacteristic
642C22×C8—21no—
643C22×C8—21no—
644C22×C8—861no—
645C22×C8—861no—
646#124—861no—
647#124—861no—
648#124—861no—
649#124—861no—
650#123—862no—
651#123—862no—
652#123—862no—
653#123—862no—
654C22⋊Q8—861no—
655C22⋊Q8—861no—
656C22⋊Q8—861no—
657C22⋊Q8—861no—
658#121—861no—
659#121—861no—
660#121—861no—
661#121—861no—
662#121—862no—
663#121—862no—
664#121—862no—
665#121—862no—
666#120—862no—
667#120—862no—
668#120—862no—
669#120—862no—
670C4×D4—861no—
671C4×D4—861no—
672C4×D4—861no—
673C4×D4—861no—
674C4×D4D17211yescharacteristic
675C4×D4D17211yescharacteristic
676C4×D4D17211yescharacteristic
677C4×D4D17211yescharacteristic
678C4×D4C22⋊D4311yescharacteristic
679C4×D4C22⋊D4311yescharacteristic
680C4×D4C22⋊D4311yescharacteristic
681C4×D4C22⋊D4311yescharacteristic
682C2×C4⋊C4—432no—
683C2×C4⋊C4—431no—
684C2×C4⋊C4C4×D4311yescharacteristic
685C2×C22⋊C4—432no—
686C2×C22⋊C4—432no—
687C2×C22⋊C4—432no—
688C2×C22⋊C4—432no—
689C2×C22⋊C4—432no—
690C2×C22⋊C4—862no—
691C2×C22⋊C4—862no—
692C2×C22⋊C4—862no—
693C2×C22⋊C4—862no—
694C2×C22⋊C4C4×D4311yescharacteristic
695C2×C22⋊C4C4×D4311yescharacteristic
696C2×C42C22×D4311yescharacteristic
697C4⋊C8—21no—
698C4⋊C8—21no—
699C4⋊C8—861no—
700C4⋊C8—861no—
701#101—862no—
702#101—862no—
703#101—1721no—
704#101—1721no—
705#100—434no—
706#100—862no—
707#100—862no—
708#100—862no—
709#100—862no—
710#100—862no—
711#100—1721no—
712#100—1721no—
713C22⋊C8—21no—
714C22⋊C8—21no—
715C22⋊C8—21no—
716C22⋊C8—21no—
717C22⋊C8—861no—
718C22⋊C8—861no—
719C22⋊C8—861no—
720C22⋊C8—861no—
721#97—21no—
722#97—861no—
723C4×C8—21no—
724C4×C8—861no—
725C24—432no—
726C24—432no—
727C24—864no—
728C24—862no—
729C24—862no—
730C24—3442no—
731C24—1722no—
732C24—1724no—
733C24C2×C4×D4311yescharacteristic
734C24C2×C4×D4311yescharacteristic
735#41—1722no—
736#41—1722no—
737#41—1722no—
738#41—1722no—
739#41—1722no—
740#41—1722no—
741#41—1722no—
742#41—1722no—
743C2×Q8—861no—
744C2×Q8—861no—
745C2×Q8—861no—
746C2×Q8—861no—
747C2×Q8—861no—
748C2×Q8—861no—
749C2×D4—42no—
750C2×D4—432no—
751C2×D4—432no—
752C2×D4—864no—
753C2×D4—862no—
754C2×D4—862no—
755C2×D4—864no—
756C2×D4—862no—
757C2×D4—862no—
758C2×D4—862no—
759C2×D4—862no—
760C2×D4—861no—
761C2×D4—861no—
762C2×D4—861no—
763C2×D4—861no—
764C2×D4—861no—
765C2×D4—861no—
766C2×D4—861no—
767C2×D4—861no—
768C2×D4—861no—
769C2×D4—861no—
770C2×D4—3442no—
771C2×D4—1722no—
772C2×D4—1722no—
773C2×D4—1722no—
774C2×D4—1722no—
775C2×D4—1722no—
776C2×D4—1722no—
777C2×D4—1722no—
778C2×D4—1722no—
779C2×D4—1722no—
780C2×D4—1722no—
781C2×D4(C2×D43)⋊C411yescharacteristic
782C2×D4(C2×D43)⋊C411yescharacteristic
783C2×D4(C2×D43)⋊C411yescharacteristic
784C2×D4(C2×D43)⋊C411yescharacteristic
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—432no—
794C22×C4—432no—
795C22×C4—864no—
796C22×C4—862no—
797C22×C4—862no—
798C22×C4—862no—
799C22×C4—862no—
800C22×C4—3442no—
801C22×C4—1722no—
802C22×C4C2×C4×D4311yescharacteristic
803C22×C4C2×C4×D4311yescharacteristic
804C22×C4C2×C4×D4311yescharacteristic
805C22×C4C2×C4×D4311yescharacteristic
806C22×C4C2×D17211yescharacteristic
807C22×C4C2×D17211yescharacteristic
808C22×C4C2×D17211yescharacteristic
809C22×C4C2×D17211yescharacteristic
810C22×C4C2×C22⋊D4311yescharacteristic
811C22×C4C2×C22⋊D4311yescharacteristic
812C22×C4C2×C22⋊D4311yescharacteristic
813C22×C4C2×C22⋊D4311yescharacteristic
814C22×C4C23×D4311yescharacteristic
815M16—21no—
816M16—21no—
817M16—21no—
818M16—21no—
819M16—21no—
820M16—21no—
821M16—21no—
822M16—42no—
823M16—42no—
824M16—432no—
825M16—861no—
826M16—861no—
827M16—861no—
828M16—861no—
829M16—861no—
830M16—861no—
831M16—861no—
832M16—1722no—
833M16—1722no—
834M16D4×D4312yes—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—42no—
840C2×C8—42no—
841C2×C8—861no—
842C2×C8—861no—
843C2×C8—861no—
844C2×C8—861no—
845C2×C8—1722no—
846C2×C8—1722no—
847C4⋊C4—862no—
848C4⋊C4—862no—
849C4⋊C4—861no—
850C4⋊C4—861no—
851C4⋊C4(C2×D43)⋊C411yescharacteristic
852C4⋊C4(C2×D43)⋊C411yescharacteristic
853C4⋊C4(C2×D43)⋊C411yescharacteristic
854C4⋊C4(C2×D43)⋊C411yescharacteristic
855C22⋊C4—862no—
856C22⋊C4—862no—
857C22⋊C4—862no—
858C22⋊C4—862no—
859C22⋊C4—862no—
860C22⋊C4—862no—
861C22⋊C4—862no—
862C22⋊C4—862no—
863C22⋊C4—862no—
864C22⋊C4—862no—
865C22⋊C4(C2×D43)⋊C411yescharacteristic
866C22⋊C4(C2×D43)⋊C411yescharacteristic
867C22⋊C4(C2×D43)⋊C411yescharacteristic
868C22⋊C4(C2×D43)⋊C411yescharacteristic
869C22⋊C4(C2×D43)⋊C411yescharacteristic
870C22⋊C4(C2×D43)⋊C411yescharacteristic
871C22⋊C4(C2×D43)⋊C411yescharacteristic
872C22⋊C4(C2×D43)⋊C411yescharacteristic
873C42C2×D17211yescharacteristic
874C42C2×D17211yescharacteristic
875C42C2×C22⋊D4311yescharacteristic
876C42C2×C22⋊D4311yescharacteristic
877C23—21no—
878C23—21no—
879C23—22no—
880C23—21no—
881C23—21no—
882C23—41no—
883C23—41no—
884C23—41no—
885C23—434no—
886C23—862no—
887C23—862no—
888C23—862no—
889C23—862no—
890C23—862no—
891C23—3442no—
892C23—3442no—
893C23—3448no—
894C23—3448no—
895C23—1724no—
896C23—1724no—
897C23—1722no—
898C23—1722no—
899C23—1724no—
900C23—1722no—
901C23—1722no—
902C23—1724no—
903C23C2×(C2×D43)⋊C411yescharacteristic
904C23C2×(C2×D43)⋊C411yescharacteristic
905C23C2×(C2×D43)⋊C411yescharacteristic
906C23C2×(C2×D43)⋊C411yescharacteristic
907C23C22×C4×D4311yescharacteristic
908Q8—1721no—
909Q8—1721no—
910Q8—1721no—
911Q8—1721no—
912D4—22no—
913D4—22no—
914D4—41no—
915D4—41no—
916D4—862no—
917D4—862no—
918D4—862no—
919D4—862no—
920D4—3442no—
921D4—3442no—
922D4—1724no—
923D4—1724no—
924D4—1724no—
925D4—1724no—
926D4—1721no—
927D4—1721no—
928D4—1721no—
929D4—1721no—
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—862no—
953C2×C4—862no—
954C2×C4—862no—
955C2×C4—862no—
956C2×C4—3442no—
957C2×C4—3442no—
958C2×C4—1724no—
959C2×C4—1724no—
960C2×C4—1722no—
961C2×C4C2×(C2×D43)⋊C411yescharacteristic
962C2×C4C2×(C2×D43)⋊C411yescharacteristic
963C2×C4C2×(C2×D43)⋊C411yescharacteristic
964C2×C4C2×(C2×D43)⋊C411yescharacteristic
965C2×C4C2×(C2×D43)⋊C411yescharacteristic
966C2×C4C2×(C2×D43)⋊C411yescharacteristic
967C2×C4C2×(C2×D43)⋊C411yescharacteristic
968C2×C4C2×(C2×D43)⋊C411yescharacteristic
969C2×C4C2×D4×D4311yescharacteristic
970C2×C4C22×C22⋊D4311yescharacteristic
971C2×C4C22×D17211yescharacteristic
972C2×C4#41×D4311yescharacteristic
973C2×C4#1306337011yescharacteristic
974C2×C4#1306337111yescharacteristic
975C8—22no—
976C8—41no—
977C8—41no—
978C8—41no—
979C8—862no—
980C8—1721no—
981C8—1721no—
982C8—1721no—
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—864no—
1001C22—3442no—
1002C22—3442no—
1003C22—3448no—
1004C22—3448no—
1005C22—1724no—
1006C22—1724no—
1007C22—1722no—
1008C22—1722no—
1009C22—1722no—
1010C22—1722no—
1011C22—1722no—
1012C22#1458288112yescomplemented
1013C22C22×(C2×D43)⋊C411yescharacteristic
1014C22C4×D4×D4311yescharacteristic
1015C22#1458337111yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—21no—
1023C4—21no—
1024C4—1722no—
1025C4—1722no—
1026C4D4×C22⋊D4311yescharacteristic
1027C4D4×D17211yescharacteristic
1028C4#1458353711yescharacteristic
1029C4#1458354411yescharacteristic
1030C2—21no—
1031C2—21no—
1032C2—22no—
1033C2—41no—
1034C2—41no—
1035C2—41no—
1036C2—3442no—
1037C2—1724no—
1038C2D4×(C2×D43)⋊C411yescharacteristic
1039C2C2×#1458288111yescharacteristic
1040C2#1914307311yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×M16×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583545C2
cosocleC22×C4×C43C24
hypercenterD4×M16D43
hypocenterC43#22408
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. D4×#10621877C2semidirect
3. C2×#14582881C2semidirect
4. C22×#13063241C2semidirect
5. #19135444C2semidirect
6. #19135442C2semidirect
7. #19135063C2semidirect
8. #19135061C2semidirect
9. #19135058C2semidirect
10. #19135056C2semidirect
11. #19134584C2semidirect
12. #19134521C2semidirect
13. #19134515C2semidirect
14. C4×#13063241C2semidirect
15. D4×M16×C43C2semidirect
19. C22×#10621877C22semidirect
40. #14582923C22semidirect
42. C2×#13063243C22semidirect
43. C2×#13063243C22semidirect
44. C2×#13063243C22semidirect
45. C2×#13063243C22semidirect
56. #14582863C22semidirect
57. C4×#10621877C22semidirect
58. #14582667C22semidirect
59. #14582667C22semidirect
60. #14582667C22semidirect
61. #14582667C22semidirect
63. C22×M16×C43C22semidirect
69. C43×#423C22semidirect
71. C43×#407C22semidirect
72. C4×M16×C43C22semidirect
162. #13063241D4semidirect
480. C22×C43#413semidirect
512. D4×M16D43semidirect
541. C22×M16C2×D43semidirect
568. #423C2×D43semidirect
586. #407C2×D43semidirect
588. C4×M16C2×D43semidirect
593. C43#22408semidirect
1012. C22#14582881semidirect

Maximal subgroups

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

subgroupindex
C2×#145835452
D4×#106218772
C2×#145828812
C22×#130632412
#191354442
#191354422
#191350632
#191350612
#191350582
#191350562
#191345842
#191345212
#191345152
C4×#130632412
D4×M16×C432
#2240843