Finite Group Databasebeta

← #25112752

Subgroups — #25112752

Order 11008.

1322 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583549C211yesmaximal, characteristic
2M16×C22⋊D43C211yesmaximal, characteristic, complemented
3#19143327C211yesmaximal, characteristic, complemented
4#19135582C211yesmaximal, characteristic, complemented
5#19135582C211yesmaximal, characteristic, complemented
6#19135059C211yesmaximal, characteristic, complemented
7#19135055C211yesmaximal, characteristic, complemented
8#19135055C211yesmaximal, characteristic, complemented
9#19134674C211yesmaximal, characteristic, complemented
10#19134673C211yesmaximal, characteristic, complemented
11#19134585C211yesmaximal, characteristic, complemented
12#100×Dic43C211yesmaximal, characteristic, complemented
13C2×#14582667C211yesmaximal, characteristic, complemented
14#343×D43C211yesmaximal, characteristic, complemented
15C43×#1900C211yesmaximal, characteristic, complemented
16C22×#10621900C412yes—
17C22×#10621877C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20#14583549—21no—
21#14583549—21no—
22#14583549—21no—
23#14583549—21no—
24#14583549—21no—
25#14583549—21no—
26#14583549—21no—
27#14583549—21no—
28C2×#13063324C2211yescharacteristic
29C2×#13063307C412yes—
30C2×#13063306C412yes—
31C2×#13063302C412yes—
32C2×#13063296C2211yescharacteristic
33C2×D4×Dic43C2211yescharacteristic
34C2×C4×C22⋊D43C2211yescharacteristic
35C22×C4⋊Dic43C2211yescharacteristic
36C2×C4⋊C4×D43C2211yescharacteristic
37#14582975—21no—
38#14582974—21no—
39#14582973—21no—
40#14582970—21no—
41#14582968—21no—
42#14582967—21no—
43C8×C22⋊D43—21no—
44(C22⋊D43)⋊C8—21no—
45#14582922C2211yescharacteristic
46#14582922C2211yescharacteristic
47C2×#13063242C2211yescharacteristic
48C2×#13063242C2211yescharacteristic
49#14582863C2211yescharacteristic
50#14582862C2211yescharacteristic
51#14582862C2211yescharacteristic
52M16×Dic43C2211yescharacteristic
53M16×Dic43C2211yescharacteristic
54#14582668C2211yescharacteristic
55#14582668C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60#14582667C2211yescharacteristic
61#14582667C2211yescharacteristic
62#14582667C2211yescharacteristic
63#14582667C2211yescharacteristic
64C22×M16×C43C2211yescharacteristic
65C2×#121×C43C2211yescharacteristic
66C2×#100×C43C2211yescharacteristic
67C2×#100×C43C2211yescharacteristic
68C43×#407C2211yescharacteristic
69C43×#343C2211yescharacteristic
70C43×#343C2211yescharacteristic
71C2×#10621900—22no—
72C2×#10621900—22no—
73C2×#10621900—22no—
74C2×#10621900—22no—
75C2×#10621900—48no—
76C22×Dic86C2×C412yes—
77C22×C22⋊D43C2×C411yescharacteristic
78C22×C22⋊D43C2×C412yes—
79C23×Dic43C2×C412yes—
80C23×Dic43C2×C412yes—
81C22×C4×D43C2×C412yes—
82C22×C4×D43C2311yescharacteristic
83C2×#10621877—21no—
84C2×#10621877—22no—
85C2×#10621877—41no—
86C2×#10621877C2311yescharacteristic
87C2×#10621877C2311yescharacteristic
88C2×#10621877C2311yescharacteristic
89C2×#10621877C2311yescharacteristic
90C2×#10621872—21no—
91C2×#10621872—21no—
92M16×D43—22no—
93M16×D43—22no—
94M16×D43—41no—
95M16×D43—41no—
96C22×C43⋊C8—21no—
97C2×C8×D43—21no—
98C2×C8×D43—21no—
99#13063324—21no—
100#13063324—21no—
101#13063324—21no—
102#13063324—21no—
103#13063307—22no—
104#13063307—22no—
105#13063307—22no—
106#13063307—22no—
107#13063306—22no—
108#13063306—22no—
109#13063306—22no—
110#13063306—22no—
111#13063302—22no—
112#13063302—22no—
113#13063302—22no—
114#13063302—22no—
115#13063296—21no—
116#13063296—21no—
117#13063296—21no—
118#13063296—21no—
119D4×Dic43—21no—
120D4×Dic43—21no—
121D4×Dic43—21no—
122D4×Dic43—21no—
123C4×C22⋊D43D411yescharacteristic
124C4×C22⋊D43D411yescharacteristic
125C4×C22⋊D43D411yescharacteristic
126C4×C22⋊D43D411yescharacteristic
127C4×C22⋊D43D411yescharacteristic
128C4×C22⋊D43D411yescharacteristic
129C4×C22⋊D43D411yescharacteristic
130C4×C22⋊D43D411yescharacteristic
131C2×C4⋊Dic43—21no—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43—21no—
135C2×C4⋊Dic43C2×C412yes—
136C2×C4⋊Dic43C2311yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4C2×C412yes—
139C2×Dic43⋊C4C2×C412yes—
140C2×Dic43⋊C4C2×C411yescharacteristic
141C4⋊C4×D43—21no—
142C4⋊C4×D43—21no—
143C4⋊C4×D43—21no—
144C4⋊C4×D43—21no—
145C2×C22⋊Dic43C2×C412yes—
146C2×C22⋊Dic43C2×C412yes—
147C2×C22⋊Dic43C2×C411yescharacteristic
148C2×(C2×D43)⋊C4C2×C411yescharacteristic
149C2×C4×Dic43C2311yescharacteristic
150Dic43⋊C8—21no—
151Dic43⋊C8—21no—
152Dic43⋊C8—21no—
153Dic43⋊C8—21no—
154#13063242—22no—
155#13063242—41no—
156C22⋊(C43⋊C8)—21no—
157C22⋊(C43⋊C8)—21no—
158(C2×D43)⋊C8—21no—
159(C2×D43)⋊C8—21no—
160(C2×D43)⋊C8—21no—
161(C2×D43)⋊C8—21no—
162#13063235—21no—
163#13063235—21no—
164C8×Dic43—21no—
165C8×Dic43—21no—
166C22×D4×C43C2×C412yes—
167C22×D4×C43C2311yescharacteristic
168C23×C4×C43C2311yescharacteristic
169C2×M16×C43—21no—
170C2×M16×C43—22no—
171C2×M16×C43—41no—
172C2×M16×C43C2311yescharacteristic
173C2×M16×C43C2311yescharacteristic
174C2×M16×C43C2311yescharacteristic
175C2×M16×C43C2311yescharacteristic
176C22×C8×C43—21no—
177#121×C43—21no—
178#121×C43—21no—
179#121×C43—21no—
180#121×C43—21no—
181C2×C4⋊C4×C43C2311yescharacteristic
182C2×C22⋊C4×C43C2×C412yes—
183#100×C43—22no—
184#100×C43—41no—
185C22⋊C8×C43—21no—
186C22⋊C8×C43—21no—
187C24×C43C22×C411yescharacteristic
188C24×C43C22×C412yes—
189C23×D43C22×C411yescharacteristic
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—21no—
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—44no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43C22×C411yescharacteristic
204C22×C4×C43C22×C412yes—
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2411yescharacteristic
210C2×C22⋊D43—24no—
211C2×C22⋊D43—22no—
212C2×C22⋊D43—22no—
213C2×C22⋊D43—44no—
214C2×C22⋊D43C22⋊C411yescharacteristic
215C2×C22⋊D43C22⋊C411yescharacteristic
216C2×C22⋊D43C22⋊C411yescharacteristic
217C2×C22⋊D43C22⋊C411yescharacteristic
218C22×Dic43—22no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43—22no—
222C22×Dic43—44no—
223C22×Dic43—44no—
224C22×Dic43C22×C411yescharacteristic
225C22×Dic43C22×C411yescharacteristic
226C22×Dic43C22×C412yes—
227C22×Dic43C22×C412yes—
228C22×Dic43C22×C411yescharacteristic
229#10621900—48no—
230#10621900—48no—
231#10621900—48no—
232#10621900—48no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—22no—
238C2×C4×D43—22no—
239C2×C4×D43—44no—
240C2×C4×D43C2×D411yescharacteristic
241C2×C4×D43C2×D411yescharacteristic
242C2×C4×D43C2×D411yescharacteristic
243C2×C4×D43C2×D411yescharacteristic
244C2×Dic86—22no—
245C2×Dic86—22no—
246C2×Dic86—44no—
247M16×C43—21no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43—21no—
251M16×C43—21no—
252M16×C43—21no—
253M16×C43—21no—
254M16×C43—42no—
255M16×C43#4112yescomplemented
256C2×C8×C43—21no—
257C2×C8×C43—21no—
258C2×C8×C43—21no—
259C2×C8×C43—21no—
260C2×C8×C43—42no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C22⋊C4×C43—22no—
264C22⋊C4×C43—22no—
265C22⋊Dic43—22no—
266C22⋊Dic43—22no—
267C22⋊Dic43—22no—
268C22⋊Dic43—22no—
269C22⋊Dic43C22⋊C411yescharacteristic
270C22⋊Dic43C22⋊C411yescharacteristic
271C22⋊Dic43C22⋊C411yescharacteristic
272C22⋊Dic43C22⋊C411yescharacteristic
273(C2×D43)⋊C4C22⋊C411yescharacteristic
274(C2×D43)⋊C4C22⋊C411yescharacteristic
275(C2×D43)⋊C4C22⋊C411yescharacteristic
276(C2×D43)⋊C4C22⋊C411yescharacteristic
277C4⋊Dic43—22no—
278C4⋊Dic43—22no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283Dic43⋊C4—22no—
284Dic43⋊C4—22no—
285Dic43⋊C4—22no—
286Dic43⋊C4—22no—
287Dic43⋊C4C22⋊C411yescharacteristic
288Dic43⋊C4C22⋊C411yescharacteristic
289Dic43⋊C4C22⋊C411yescharacteristic
290Dic43⋊C4C22⋊C411yescharacteristic
291C4×Dic43C2×D411yescharacteristic
292C4×Dic43C2×D411yescharacteristic
293C4×Dic43C2×D411yescharacteristic
294C4×Dic43C2×D411yescharacteristic
295#10621877—21no—
296#10621877—21no—
297#10621877—21no—
298#10621877—21no—
299#10621877—21no—
300#10621877—21no—
301#10621877—21no—
302#10621877—42no—
303#10621877#4112yescomplemented
304C2×C43⋊C8—21no—
305C2×C43⋊C8—21no—
306C2×C43⋊C8—21no—
307C2×C43⋊C8—21no—
308C2×C43⋊C8—42no—
309#10621872—42no—
310#10621872—42no—
311C8×D43—42no—
312C8×D43—42no—
313C23×C43—21no—
314C23×C43—21no—
315C23×C43—22no—
316C23×C43—22no—
317C23×C43—22no—
318C23×C43—22no—
319C23×C43—41no—
320C23×C43—42no—
321C23×C43—42no—
322C23×C43C2×C22⋊C411yescharacteristic
323C23×C43C2×C22⋊C411yescharacteristic
324C23×C43C23×C411yescharacteristic
325C22×D43—21no—
326C22×D43—21no—
327C22×D43—22no—
328C22×D43—41no—
329C22×D43C2×C22⋊C411yescharacteristic
330C22×D43C2×C22⋊C411yescharacteristic
331D4×C43—44no—
332D4×C43—44no—
333D4×C43—41no—
334D4×C43—41no—
335D4×C43—41no—
336D4×C43—41no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—21no—
341C2×C4×C43—21no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—21no—
347C2×C4×C43—22no—
348C2×C4×C43—42no—
349C2×C4×C43C2×C22⋊C411yescharacteristic
350C2×C4×C43C2×C22⋊C411yescharacteristic
351C2×C4×C43C22×D411yescharacteristic
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43C2×#4111yescharacteristic
354C2×C4×C43C2×#4111yescharacteristic
355C2×C4×C43H(5,𝔽2)11yescharacteristic
356C2×C4×C432−1+411yescharacteristic
357C22⋊D43—22no—
358C22⋊D43—22no—
359C22⋊D43—22no—
360C22⋊D43—44no—
361C22⋊D43—44no—
362C22⋊D43#10014yescomplemented
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—22no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—41no—
369C2×Dic43—44no—
370C2×Dic43—44no—
371C2×Dic43—44no—
372C2×Dic43—44no—
373C2×Dic43—42no—
374C2×Dic43—42no—
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377C2×Dic43C2×C22⋊C411yescharacteristic
378C2×Dic43C2×C22⋊C411yescharacteristic
379C2×Dic43C2×C22⋊C411yescharacteristic
380C2×Dic43C2×C22⋊C411yescharacteristic
381C4×D43—21no—
382C4×D43—21no—
383C4×D43—21no—
384C4×D43—21no—
385C4×D43—21no—
386C4×D43—21no—
387C4×D43—21no—
388C4×D43—21no—
389C4×D43—44no—
390C4×D43—44no—
391Dic86—44no—
392Dic86—44no—
393C8×C43—22no—
394C8×C43—41no—
395C8×C43—41no—
396C8×C43—41no—
397C43⋊C8—22no—
398C43⋊C8—41no—
399C43⋊C8—41no—
400C43⋊C8—41no—
401#22479—431nomaximal, Sylow
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—21no—
409C22×C43—42no—
410C22×C43—42no—
411C22×C43—42no—
412C22×C43—42no—
413C22×C43—42no—
414C22×C43—82no—
415C22×C43—82no—
416C22×C43C2×#10012yes—
417C22×C43C22×C22⋊C411yescharacteristic
418C22×C43C4×#4111yescharacteristic
419C22×C43#52011yescharacteristic
420C2×D43—21no—
421C2×D43—21no—
422C2×D43—21no—
423C2×D43—21no—
424C2×D43—21no—
425C2×D43—42no—
426C2×D43—42no—
427C2×D43C2×#10012yes—
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—42no—
431C4×C43#54611yescharacteristic
432C4×C43#54611yescharacteristic
433C4×C43#54711yescharacteristic
434C4×C43#54711yescharacteristic
435Dic43—21no—
436Dic43—21no—
437Dic43—21no—
438Dic43—21no—
439Dic43—21no—
440Dic43—42no—
441Dic43—42no—
442Dic43C2×#10012yes—
443C2×#547—431no—
444D4×M16—431no—
445D4×M16—431no—
446#1997—431no—
447#1997—431no—
448#1900—431no—
449#1900—431no—
450#1900—431no—
451#1900D4311yescharacteristic, complemented
452#1821—431no—
453#1821—431no—
454#1800—431no—
455C4×#100—431no—
456C2×#343—431no—
457C2×#343—431no—
458C2×C43—21no—
459C2×C43—21no—
460C2×C43—22no—
461C2×C43—41no—
462C2×C43—82no—
463C2×C43#233911yescharacteristic
464C2×C43C22×#10011yescharacteristic
465C2×C43#288911yescharacteristic
466D43—22no—
467D43—41no—
468C22×#41—432no—
469C22×M16—431no—
470C22×M16—431no—
471C22×M16—431no—
472C22×M16C2×D4311yescharacteristic
473#547—861no—
474#547—861no—
475#547—861no—
476#547—861no—
477#547—861no—
478#547—861no—
479#547—861no—
480#547—861no—
481C2×C4⋊Q8—431no—
482C2×#123—432no—
483C2×#123—432no—
484C2×C22⋊Q8—432no—
485C2×#121—431no—
486C2×#121C2×D4311yescharacteristic
487C2×C4×D4—431no—
488C2×C4×D4—431no—
489C22×C4⋊C4—431no—
490C22×C4⋊C4—431no—
491#436—861no—
492#436—861no—
493#435—861no—
494#435—861no—
495#435—861no—
496#435—861no—
497C8×D4—861no—
498C8×D4—861no—
499#423—431no—
500#423—431no—
501C2×#100—431no—
502C2×#100—431no—
503C2×#100C2×D4311yescharacteristic
504C2×#100C2×D4311yescharacteristic
505#407—431no—
506#407—431no—
507#407—431no—
508#407C2×D4311yescharacteristic
509C4×M16—431no—
510C4×M16—431no—
511#343—431no—
512#343—431no—
513#343—431no—
514#343—431no—
515#343—431no—
516#343—431no—
517#343—431no—
518#343—431no—
519#343—431no—
520#343—431no—
521#343C2×D4311yescharacteristic
522#343C2×D4311yescharacteristic
523C43#2247911yescharacteristic, complemented, Sylow
524C2×#41—862no—
525C2×#41—862no—
526C2×#41—862no—
527C2×#41—862no—
528C2×#41—1728no—
529C22×Q8—432no—
530C22×D4—431no—
531C22×D4—432no—
532C22×D4C4×D4312yes—
533C22×D4C22×D4311yescharacteristic
534C23×C4—431no—
535C23×C4—432no—
536C23×C4—432no—
537C23×C4—432no—
538C23×C4C22×D4311yescharacteristic
539C2×M16—21no—
540C2×M16—22no—
541C2×M16—41no—
542C2×M16—431no—
543C2×M16—431no—
544C2×M16—431no—
545C2×M16—431no—
546C2×M16—861no—
547C2×M16—861no—
548C2×M16—861no—
549C2×M16—862no—
550C2×M16—862no—
551C2×M16—862no—
552C2×M16—1721no—
553C2×M16—1721no—
554C2×M16—1721no—
555C2×M16C22×D4311yescharacteristic
556C2×M16C22×D4311yescharacteristic
557C2×M16C22×D4311yescharacteristic
558C2×M16C22×D4311yescharacteristic
559C22×C8—21no—
560C22×C8—861no—
561C22×C8—861no—
562C22×C8—861no—
563C4⋊Q8—861no—
564C4⋊Q8—861no—
565C4⋊Q8—861no—
566C4⋊Q8—861no—
567#123—862no—
568#123—862no—
569#123—862no—
570#123—862no—
571#123—862no—
572#123—862no—
573#123—862no—
574#123—862no—
575C22⋊Q8—862no—
576C22⋊Q8—862no—
577C22⋊Q8—862no—
578C22⋊Q8—862no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—861no—
584#121—861no—
585#121—861no—
586#121—861no—
587C4×D4—431no—
588C4×D4—431no—
589C4×D4—431no—
590C4×D4—431no—
591C4×D4—431no—
592C4×D4—431no—
593C4×D4—431no—
594C4×D4—431no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4—861no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—432no—
601C2×C4⋊C4—432no—
602C2×C4⋊C4—432no—
603C2×C4⋊C4—431no—
604C2×C4⋊C4—431no—
605C2×C4⋊C4—861no—
606C2×C4⋊C4—861no—
607C2×C4⋊C4—861no—
608C2×C4⋊C4—861no—
609C2×C4⋊C4—861no—
610C2×C4⋊C4—861no—
611C2×C4⋊C4—861no—
612C2×C4⋊C4—861no—
613C2×C4⋊C4C22×D4311yescharacteristic
614C2×C22⋊C4—431no—
615C2×C22⋊C4—431no—
616C2×C22⋊C4—432no—
617C2×C22⋊C4—432no—
618C2×C22⋊C4C4×D4312yes—
619C2×C42—431no—
620C4⋊C8—861no—
621C4⋊C8—861no—
622C4⋊C8—861no—
623C4⋊C8—861no—
624#100—22no—
625#100—41no—
626#100—862no—
627#100—1721no—
628C22⋊C8—21no—
629C22⋊C8—21no—
630C22⋊C8—861no—
631C22⋊C8—861no—
632C22⋊C8—861no—
633C22⋊C8—861no—
634C22⋊C8—861no—
635C22⋊C8—861no—
636#97—861no—
637#97—861no—
638C4×C8—861no—
639C4×C8—861no—
640C24—431no—
641C24C2×C4×D4311yescharacteristic
642C24C2×C4×D4312yes—
643#41—1728no—
644#41—1728no—
645#41—1728no—
646#41—1728no—
647C2×Q8—862no—
648C2×Q8—862no—
649C2×Q8—1724no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—44no—
659C2×D4—431no—
660C2×D4—431no—
661C2×D4—431no—
662C2×D4—431no—
663C2×D4—864no—
664C2×D4—862no—
665C2×D4—862no—
666C2×D4—1724no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—431no—
674C22×C4—431no—
675C22×C4—431no—
676C22×C4—431no—
677C22×C4—431no—
678C22×C4—432no—
679C22×C4—432no—
680C22×C4—862no—
681C22×C4—862no—
682C22×C4—862no—
683C22×C4—862no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—862no—
689C22×C4—862no—
690C22×C4—1724no—
691C22×C4—1724no—
692C22×C4—1724no—
693C22×C4C2×C4×D4311yescharacteristic
694C22×C4C2×C4×D4312yes—
695C22×C4D4×D4311yescharacteristic
696C22×C4D4×D4311yescharacteristic
697C22×C4D4×D4311yescharacteristic
698C22×C4D4×D4311yescharacteristic
699C22×C4C23×D4311yescharacteristic
700M16—21no—
701M16—21no—
702M16—21no—
703M16—21no—
704M16—21no—
705M16—21no—
706M16—21no—
707M16—42no—
708M16—432no—
709M16—861no—
710M16—861no—
711M16—861no—
712M16—861no—
713M16—861no—
714M16—861no—
715M16—861no—
716M16—1722no—
717M16—1722no—
718M16—1722no—
719M16#1062190012yescomplemented
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—42no—
725C2×C8—861no—
726C2×C8—861no—
727C2×C8—861no—
728C2×C8—861no—
729C2×C8—1722no—
730C2×C8—1722no—
731C2×C8—1722no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—431no—
735C4⋊C4—431no—
736C4⋊C4—431no—
737C4⋊C4—431no—
738C4⋊C4—862no—
739C4⋊C4—862no—
740C4⋊C4—862no—
741C4⋊C4—862no—
742C4⋊C4—862no—
743C4⋊C4—862no—
744C4⋊C4—861no—
745C4⋊C4—861no—
746C4⋊C4—861no—
747C4⋊C4—861no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—431no—
751C22⋊C4—431no—
752C22⋊C4—431no—
753C22⋊C4—431no—
754C22⋊C4—431no—
755C22⋊C4—431no—
756C22⋊C4—431no—
757C22⋊C4—431no—
758C22⋊C4—862no—
759C22⋊C4—862no—
760C22⋊C4—862no—
761C22⋊C4—862no—
762C42—431no—
763C42—431no—
764C42—431no—
765C42—431no—
766C23—21no—
767C23—21no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—41no—
773C23—42no—
774C23—42no—
775C23—431no—
776C23—431no—
777C23—862no—
778C23—861no—
779C23—861no—
780C23—1721no—
781C23C22⋊C4×D4311yescharacteristic
782C23C22⋊C4×D4311yescharacteristic
783C23C22×C4×D4311yescharacteristic
784Q8—1724no—
785Q8—1724no—
786D4—44no—
787D4—44no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—434no—
793D4—862no—
794D4—862no—
795D4—862no—
796D4—1724no—
797D4—1724no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—42no—
810C2×C4—431no—
811C2×C4—431no—
812C2×C4—431no—
813C2×C4—431no—
814C2×C4—431no—
815C2×C4—431no—
816C2×C4—862no—
817C2×C4—861no—
818C2×C4—861no—
819C2×C4—861no—
820C2×C4—861no—
821C2×C4—861no—
822C2×C4—861no—
823C2×C4—861no—
824C2×C4—861no—
825C2×C4—861no—
826C2×C4—861no—
827C2×C4—862no—
828C2×C4—862no—
829C2×C4—1724no—
830C2×C4—1724no—
831C2×C4—1724no—
832C2×C4—1721no—
833C2×C4—1724no—
834C2×C4—1724no—
835C2×C4—1724no—
836C2×C4—1722no—
837C2×C4—1722no—
838C2×C4C22⋊C4×D4311yescharacteristic
839C2×C4C22⋊C4×D4311yescharacteristic
840C2×C4C2×D4×D4311yescharacteristic
841C2×C4C2×D4×D4311yescharacteristic
842C2×C4#41×D4311yescharacteristic
843C2×C4C2×#1062190011yescharacteristic
844C2×C4#1306337011yescharacteristic
845C2×C4#1306337211yescharacteristic
846C8—22no—
847C8—41no—
848C8—41no—
849C8—41no—
850C8—862no—
851C8—1721no—
852C8—1721no—
853C8—1721no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—82no—
867C22—82no—
868C22—432no—
869C22—861no—
870C22—861no—
871C22—861no—
872C22—861no—
873C22—861no—
874C22—1722no—
875C22—1722no—
876C22#100×D4312yes—
877C22C2×C22⋊C4×D4311yescharacteristic
878C22C4×#1062190011yescharacteristic
879C22#1458337811yescharacteristic
880C4—21no—
881C4—21no—
882C4—42no—
883C4—432no—
884C4—861no—
885C4—861no—
886C4—861no—
887C4—861no—
888C4—861no—
889C4—1722no—
890C4—1722no—
891C4#1458353611yescharacteristic
892C4#1458353811yescharacteristic
893C4#1458354711yescharacteristic
894C4#1458354911yescharacteristic
895C2—21no—
896C2—21no—
897C2—22no—
898C2—41no—
899C2—82no—
900C2—862no—
901C2—1721no—
902C2#1913742111yescharacteristic
903C2C2×#100×D4311yescharacteristic
904C2#1914307611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1900C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583549C2
cosocleC22×C4×C43C24
hypercenter#1900D43
hypocenterC43#22479
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1900

Complements

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

NH ≅ G/Ntype
2. M16×C22⋊D43C2semidirect
3. #19143327C2semidirect
4. #19135582C2semidirect
5. #19135582C2semidirect
6. #19135059C2semidirect
7. #19135055C2semidirect
8. #19135055C2semidirect
9. #19134674C2semidirect
10. #19134673C2semidirect
11. #19134585C2semidirect
12. #100×Dic43C2semidirect
13. C2×#14582667C2semidirect
14. #343×D43C2semidirect
15. C43×#1900C2semidirect
255. M16×C43#41semidirect
303. #10621877#41semidirect
362. C22⋊D43#100semidirect
451. #1900D43semidirect
523. C43#22479semidirect
719. M16#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#145835492
M16×C22⋊D432
#191433272
#191355822
#191350592
#191350552
#191346742
#191346732
#191345852
#100×Dic432
C2×#145826672
#343×D432
C43×#19002
#2247943