Finite Group Databasebeta

← #25111974

Subgroups — #25111974

Order 11008.

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×#14583555C211yesmaximal, characteristic
2M16×C22⋊D43C211yesmaximal, characteristic, complemented
3#19143327C211yesmaximal, characteristic, complemented
4C2×#14582880C211yesmaximal, characteristic, complemented
5C22×#13063243C211yesmaximal, characteristic, complemented
6#19135441C211yesmaximal, characteristic, complemented
7#19135441C211yesmaximal, characteristic, complemented
8#19135062C211yesmaximal, characteristic, complemented
9#19135062C211yesmaximal, characteristic, complemented
10#19135059C211yesmaximal, characteristic, complemented
11#19134590C211yesmaximal, characteristic, complemented
12#19134520C211yesmaximal, characteristic, complemented
13#19134518C211yesmaximal, characteristic, complemented
14#19134390C211yesmaximal, characteristic, complemented
15C43×#1900C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C23×Dic86C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20C2×M16×D43C2211yescharacteristic
21#14583555—21no—
22#14583555—21no—
23#14583555—21no—
24#14583555—21no—
25#14583555—21no—
26#14583555—21no—
27#14583555—21no—
28#14583555—21no—
29C2×#13063312C2211yescharacteristic
30C2×#13063311C412yes—
31C2×#13063305C2211yescharacteristic
32C2×#13063302C412yes—
33C2×#13063297C412yes—
34C2×#13063290C2211yescharacteristic
35C2×D4×Dic43C412yes—
36C2×C4×C22⋊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
47#14582880—24no—
48C2×#13063243—24no—
49C2×#13063243C2211yescharacteristic
50C2×#13063243C2211yescharacteristic
51C2×#13063243C2211yescharacteristic
52C2×#13063243C2211yescharacteristic
53C2×#13063243C2211yescharacteristic
54C2×#13063243C2211yescharacteristic
55C2×#13063243C2211yescharacteristic
56C2×#13063243C2211yescharacteristic
57C2×#13063242C2211yescharacteristic
58C2×#13063242C2211yescharacteristic
59#14582863C2211yescharacteristic
60#14582862C2211yescharacteristic
61#14582862C2211yescharacteristic
62M16×Dic43C2211yescharacteristic
63M16×Dic43C2211yescharacteristic
64#14582668C2211yescharacteristic
65#14582668C2211yescharacteristic
66C22×M16×C43C2211yescharacteristic
67C2×#121×C43C2211yescharacteristic
68C2×#100×C43C2211yescharacteristic
69C2×#100×C43C2211yescharacteristic
70C43×#407C2211yescharacteristic
71C43×#343C2211yescharacteristic
72C43×#343C2211yescharacteristic
73C2×#10621900—21no—
74C2×#10621900—21no—
75C2×#10621900—21no—
76C2×#10621900—21no—
77C2×#10621900—22no—
78C2×#10621900—22no—
79C2×#10621900—41no—
80C2×#10621900—41no—
81C22×Dic86—21no—
82C22×Dic86—21no—
83C22×Dic86—21no—
84C22×Dic86—21no—
85C22×Dic86—22no—
86C22×Dic86—22no—
87C22×Dic86—41no—
88C22×Dic86—41no—
89C22×Dic86C2×C412yes—
90C22×Dic86C2311yescharacteristic
91C22×Dic86C2311yescharacteristic
92C22×C22⋊D43C2×C412yes—
93C22×C22⋊D43C2×C411yescharacteristic
94C23×Dic43C2×C412yes—
95C23×Dic43C2×C412yes—
96C22×C4×D43C2311yescharacteristic
97C2×#10621877—21no—
98C2×#10621877—22no—
99C2×#10621877—41no—
100C2×#10621877C2311yescharacteristic
101C2×#10621877C2311yescharacteristic
102C2×#10621877C2311yescharacteristic
103C2×#10621877C2311yescharacteristic
104C2×#10621872—21no—
105C2×#10621872—21no—
106M16×D43—22no—
107M16×D43—22no—
108M16×D43—41no—
109M16×D43—41no—
110C22×C43⋊C8—21no—
111C2×C8×D43—21no—
112C2×C8×D43—21no—
113#13063312—21no—
114#13063312—21no—
115#13063312—21no—
116#13063312—21no—
117#13063311—22no—
118#13063311—22no—
119#13063311—22no—
120#13063311—22no—
121#13063305—21no—
122#13063305—21no—
123#13063305—21no—
124#13063305—21no—
125#13063302—22no—
126#13063302—22no—
127#13063302—22no—
128#13063302—22no—
129#13063297—22no—
130#13063297—22no—
131#13063297—22no—
132#13063297—22no—
133#13063290—21no—
134#13063290—21no—
135#13063290—21no—
136#13063290—21no—
137D4×Dic43—22no—
138D4×Dic43—22no—
139D4×Dic43—22no—
140D4×Dic43—22no—
141C4×C22⋊D43D411yescharacteristic
142C4×C22⋊D43D411yescharacteristic
143C4×C22⋊D43D411yescharacteristic
144C4×C22⋊D43D411yescharacteristic
145C4×C22⋊D43D411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149C2×C4⋊Dic43C2×C412yes—
150C2×Dic43⋊C4C2×C412yes—
151C2×Dic43⋊C4C2×C411yescharacteristic
152C2×C22⋊Dic43C2×C412yes—
153C2×C22⋊Dic43C2×C412yes—
154C2×C22⋊Dic43C2×C411yescharacteristic
155C2×(C2×D43)⋊C4C2×C412yes—
156C2×(C2×D43)⋊C4C2×C411yescharacteristic
157C2×C4×Dic43C2×C412yes—
158C2×C4×Dic43C2311yescharacteristic
159Dic43⋊C8—21no—
160Dic43⋊C8—21no—
161Dic43⋊C8—21no—
162Dic43⋊C8—21no—
163#13063243—22no—
164#13063243—22no—
165#13063243—22no—
166#13063243—22no—
167#13063243—22no—
168#13063243—41no—
169#13063243—41no—
170#13063243D414yescomplemented
171#13063242—22no—
172#13063242—41no—
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)—21no—
175(C2×D43)⋊C8—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179#13063235—21no—
180#13063235—21no—
181C8×Dic43—21no—
182C8×Dic43—21no—
183C22×D4×C43C2×C412yes—
184C22×D4×C43C2311yescharacteristic
185C23×C4×C43C2311yescharacteristic
186C2×M16×C43—21no—
187C2×M16×C43—22no—
188C2×M16×C43—41no—
189C2×M16×C43C2311yescharacteristic
190C2×M16×C43C2311yescharacteristic
191C2×M16×C43C2311yescharacteristic
192C2×M16×C43C2311yescharacteristic
193C22×C8×C43—21no—
194#121×C43—21no—
195#121×C43—21no—
196#121×C43—21no—
197#121×C43—21no—
198C2×C4⋊C4×C43C2311yescharacteristic
199C2×C22⋊C4×C43C2×C412yes—
200#100×C43—22no—
201#100×C43—41no—
202C22⋊C8×C43—21no—
203C22⋊C8×C43—21no—
204C24×C43C22×C411yescharacteristic
205C24×C43C22×C412yes—
206C23×D43C22×C411yescharacteristic
207C2×D4×C43—21no—
208C2×D4×C43—21no—
209C2×D4×C43—21no—
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—22no—
214C2×D4×C43—22no—
215C2×D4×C43—44no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C22×C412yes—
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2411yescharacteristic
227C2×C22⋊D43—24no—
228C2×C22⋊D43—22no—
229C2×C22⋊D43—22no—
230C2×C22⋊D43—42no—
231C2×C22⋊D43—42no—
232C2×C22⋊D43C22⋊C411yescharacteristic
233C2×C22⋊D43C22⋊C411yescharacteristic
234C2×C22⋊D43C22⋊C411yescharacteristic
235C2×C22⋊D43C22⋊C411yescharacteristic
236C22×Dic43—22no—
237C22×Dic43—22no—
238C22×Dic43—24no—
239C22×Dic43—24no—
240C22×Dic43—22no—
241C22×Dic43—22no—
242C22×Dic43—42no—
243C22×Dic43—42no—
244C22×Dic43C22×C412yes—
245C22×Dic43C22×C411yescharacteristic
246C22×Dic43C22×C412yes—
247C22×Dic43C22×C411yescharacteristic
248C22×Dic43C22×C411yescharacteristic
249#10621900—42no—
250#10621900—42no—
251#10621900—42no—
252#10621900—42no—
253#10621900—42no—
254#10621900—42no—
255#10621900—42no—
256#10621900—42no—
257C2×C4×D43—21no—
258C2×C4×D43—21no—
259C2×C4×D43—21no—
260C2×C4×D43—21no—
261C2×C4×D43C2×D411yescharacteristic
262C2×C4×D43C2×D411yescharacteristic
263C2×C4×D43C2×D411yescharacteristic
264C2×C4×D43C2×D411yescharacteristic
265C2×Dic86—21no—
266C2×Dic86—21no—
267C2×Dic86—21no—
268C2×Dic86—21no—
269C2×Dic86—22no—
270C2×Dic86—22no—
271C2×Dic86—21no—
272C2×Dic86—21no—
273C2×Dic86—21no—
274C2×Dic86—21no—
275C2×Dic86—21no—
276C2×Dic86—21no—
277C2×Dic86—24no—
278C2×Dic86—42no—
279C2×Dic86—42no—
280C2×Dic86—42no—
281C2×Dic86—42no—
282C2×Dic86—42no—
283C2×Dic86—42no—
284C2×Dic86—42no—
285C2×Dic86—42no—
286C2×Dic86—42no—
287C2×Dic86C2×D412yes—
288C2×Dic86#4112yes—
289M16×C43—21no—
290M16×C43—21no—
291M16×C43—21no—
292M16×C43—21no—
293M16×C43—21no—
294M16×C43—21no—
295M16×C43—21no—
296M16×C43—42no—
297M16×C43C2×D412yes—
298C2×C8×C43—21no—
299C2×C8×C43—21no—
300C2×C8×C43—21no—
301C2×C8×C43—21no—
302C2×C8×C43—42no—
303C4⋊C4×C43—21no—
304C4⋊C4×C43—21no—
305C22⋊C4×C43—22no—
306C22⋊C4×C43—22no—
307C22⋊Dic43—22no—
308C22⋊Dic43—22no—
309C22⋊Dic43—22no—
310C22⋊Dic43—22no—
311C22⋊Dic43C22⋊C411yescharacteristic
312C22⋊Dic43C22⋊C411yescharacteristic
313C22⋊Dic43C22⋊C411yescharacteristic
314C22⋊Dic43C22⋊C411yescharacteristic
315(C2×D43)⋊C4—22no—
316(C2×D43)⋊C4—22no—
317(C2×D43)⋊C4C22⋊C411yescharacteristic
318(C2×D43)⋊C4C22⋊C411yescharacteristic
319(C2×D43)⋊C4C22⋊C411yescharacteristic
320(C2×D43)⋊C4C22⋊C411yescharacteristic
321C4⋊Dic43—22no—
322C4⋊Dic43—22no—
323Dic43⋊C4—22no—
324Dic43⋊C4—22no—
325Dic43⋊C4C22⋊C411yescharacteristic
326Dic43⋊C4C22⋊C411yescharacteristic
327Dic43⋊C4C22⋊C411yescharacteristic
328Dic43⋊C4C22⋊C411yescharacteristic
329C4×Dic43—22no—
330C4×Dic43—22no—
331C4×Dic43C2×D411yescharacteristic
332C4×Dic43C2×D411yescharacteristic
333C4×Dic43C2×D411yescharacteristic
334C4×Dic43C2×D411yescharacteristic
335#10621877—21no—
336#10621877—21no—
337#10621877—21no—
338#10621877—21no—
339#10621877—21no—
340#10621877—21no—
341#10621877—21no—
342#10621877—42no—
343#10621877C2×D412yes—
344C2×C43⋊C8—21no—
345C2×C43⋊C8—21no—
346C2×C43⋊C8—21no—
347C2×C43⋊C8—21no—
348C2×C43⋊C8—42no—
349#10621872—42no—
350#10621872—42no—
351C8×D43—42no—
352C8×D43—42no—
353C23×C43—21no—
354C23×C43—21no—
355C23×C43—22no—
356C23×C43—22no—
357C23×C43—22no—
358C23×C43—22no—
359C23×C43—41no—
360C23×C43—42no—
361C23×C43—42no—
362C23×C43C2×C22⋊C411yescharacteristic
363C23×C43C2×C22⋊C411yescharacteristic
364C23×C43C23×C411yescharacteristic
365C22×D43—21no—
366C22×D43—21no—
367C22×D43—41no—
368C22×D43—41no—
369C22×D43C2×C22⋊C411yescharacteristic
370C22×D43C2×C22⋊C411yescharacteristic
371D4×C43—44no—
372D4×C43—44no—
373D4×C43—41no—
374D4×C43—41no—
375D4×C43—41no—
376D4×C43—41no—
377C2×C4×C43—21no—
378C2×C4×C43—21no—
379C2×C4×C43—21no—
380C2×C4×C43—21no—
381C2×C4×C43—21no—
382C2×C4×C43—21no—
383C2×C4×C43—21no—
384C2×C4×C43—21no—
385C2×C4×C43—21no—
386C2×C4×C43—21no—
387C2×C4×C43—22no—
388C2×C4×C43—42no—
389C2×C4×C43C2×C22⋊C411yescharacteristic
390C2×C4×C43C2×C22⋊C411yescharacteristic
391C2×C4×C43C22×D411yescharacteristic
392C2×C4×C43C22×D411yescharacteristic
393C2×C4×C43C22×D411yescharacteristic
394C2×C4×C43C2×#4111yescharacteristic
395C2×C4×C43H(5,𝔽2)11yescharacteristic
396C2×C4×C43H(5,𝔽2)11yescharacteristic
397C22⋊D43—22no—
398C22⋊D43—22no—
399C22⋊D43—41no—
400C22⋊D43—41no—
401C22⋊D43—44no—
402C22⋊D43—44no—
403C2×Dic43—22no—
404C2×Dic43—21no—
405C2×Dic43—22no—
406C2×Dic43—21no—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—44no—
413C2×Dic43—44no—
414C2×Dic43—44no—
415C2×Dic43—44no—
416C2×Dic43C2×C22⋊C411yescharacteristic
417C2×Dic43C2×C22⋊C411yescharacteristic
418C2×Dic43C2×C22⋊C411yescharacteristic
419C2×Dic43C2×C22⋊C411yescharacteristic
420C2×Dic43C2×C22⋊C411yescharacteristic
421C2×Dic43C2×C22⋊C411yescharacteristic
422C2×Dic43C4×D414yes—
423C4×D43—21no—
424C4×D43—21no—
425C4×D43—21no—
426C4×D43—21no—
427C4×D43—21no—
428C4×D43—21no—
429C4×D43—21no—
430C4×D43—21no—
431Dic86—22no—
432Dic86—22no—
433Dic86—22no—
434Dic86—22no—
435Dic86—44no—
436Dic86—44no—
437Dic86—41no—
438Dic86—41no—
439Dic86—41no—
440Dic86—41no—
441C8×C43—22no—
442C8×C43—41no—
443C8×C43—41no—
444C8×C43—41no—
445C43⋊C8—22no—
446C43⋊C8—41no—
447C43⋊C8—41no—
448C43⋊C8—41no—
449#22410—431nomaximal, Sylow
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—21no—
456C22×C43—21no—
457C22×C43—42no—
458C22×C43—42no—
459C22×C43—42no—
460C22×C43—42no—
461C22×C43—42no—
462C22×C43—82no—
463C22×C43—82no—
464C22×C43#41312yescomplemented
465C22×C43C22×C22⋊C411yescharacteristic
466C22×C43C2×C4×D411yescharacteristic
467C22×C43#51811yescharacteristic
468C2×D43—21no—
469C2×D43—21no—
470C2×D43—21no—
471C2×D43—21no—
472C2×D43—21no—
473C2×D43—21no—
474C2×D43—81no—
475C2×D43—81no—
476C4×C43—21no—
477C4×C43—21no—
478C4×C43—42no—
479C4×C43D4211yescharacteristic
480C4×C43D4211yescharacteristic
481C4×C43#54611yescharacteristic
482C4×C43#54611yescharacteristic
483Dic43—24no—
484Dic43—21no—
485Dic43—21no—
486Dic43—21no—
487Dic43—21no—
488Dic43—21no—
489Dic43—21no—
490Dic43—42no—
491C2×#548—431no—
492D4×M16—431no—
493D4×M16—431no—
494C2×#413—431no—
495C22×#101—431no—
496#1967—431no—
497#1967—431no—
498#1901—431no—
499#1901—431no—
500#1900—431no—
501#1900D4311yescharacteristic, complemented
502#1801—431no—
503#1785—431no—
504#1784—431no—
505C4×#101—431no—
506C2×C43—21no—
507C2×C43—21no—
508C2×C43—22no—
509C2×C43—41no—
510C2×C43—82no—
511C2×C43D4×C22⋊C411yescharacteristic
512C2×C43C2×#41311yescharacteristic
513C2×C43#288911yescharacteristic
514D43—41no—
515D43—41no—
516C22×#41—431no—
517C23×Q8—431no—
518C22×M16—431no—
519C22×M16—431no—
520C22×M16—431no—
521C22×M16C2×D4311yescharacteristic
522#548—861no—
523#548—861no—
524#548—861no—
525#548—861no—
526#548—861no—
527#548—861no—
528#548—861no—
529#548—861no—
530C2×#124—431no—
531C2×#124—432no—
532C2×C22⋊Q8—431no—
533C2×C22⋊Q8—432no—
534C2×#121—432no—
535C2×#121C2×D4311yescharacteristic
536C2×C4×Q8—431no—
537C2×C4×D4—431no—
538C2×C4×D4—432no—
539#436—861no—
540#436—861no—
541#435—861no—
542#435—861no—
543#435—861no—
544#435—861no—
545C8×D4—861no—
546C8×D4—861no—
547#423—431no—
548#423—431no—
549#413—864no—
550C2×#101—431no—
551C2×#101—431no—
552C2×#101—431no—
553C2×#101—431no—
554C2×#101—431no—
555C2×#101—431no—
556C2×#101—431no—
557C2×#101—431no—
558C2×#101—864no—
559C2×#100—431no—
560C2×#100—431no—
561C2×#100C2×D4311yescharacteristic
562C2×#100C2×D4311yescharacteristic
563#407—431no—
564#407—431no—
565#407—431no—
566#407C2×D4311yescharacteristic
567C4×M16—431no—
568C4×M16—431no—
569#343—431no—
570#343—431no—
571#343C2×D4311yescharacteristic
572#343C2×D4311yescharacteristic
573C43#2241011yescharacteristic, complemented, Sylow
574C2×#41—861no—
575C2×#41—861no—
576C2×#41—861no—
577C2×#41—861no—
578C2×#41—862no—
579C2×#41—862no—
580C2×#41—1721no—
581C2×#41—1721no—
582C22×Q8—432no—
583C22×Q8—431no—
584C22×Q8—431no—
585C22×Q8—862no—
586C22×Q8—862no—
587C22×Q8—861no—
588C22×Q8—861no—
589C22×Q8—861no—
590C22×Q8—861no—
591C22×Q8—1721no—
592C22×Q8—1721no—
593C22×D4—431no—
594C22×D4—432no—
595C22×D4C4×D4312yes—
596C22×D4C22×D4311yescharacteristic
597C23×C4—431no—
598C23×C4—432no—
599C23×C4—432no—
600C23×C4C22×D4311yescharacteristic
601C2×M16—21no—
602C2×M16—22no—
603C2×M16—41no—
604C2×M16—431no—
605C2×M16—431no—
606C2×M16—431no—
607C2×M16—431no—
608C2×M16—861no—
609C2×M16—861no—
610C2×M16—861no—
611C2×M16—862no—
612C2×M16—862no—
613C2×M16—862no—
614C2×M16—1721no—
615C2×M16—1721no—
616C2×M16—1721no—
617C2×M16C22×D4311yescharacteristic
618C2×M16C22×D4311yescharacteristic
619C2×M16C22×D4311yescharacteristic
620C2×M16C22×D4311yescharacteristic
621C22×C8—21no—
622C22×C8—861no—
623C22×C8—861no—
624C22×C8—861no—
625#124—861no—
626#124—861no—
627#124—861no—
628#124—861no—
629#124—862no—
630#124—862no—
631#124—862no—
632#124—862no—
633C22⋊Q8—862no—
634C22⋊Q8—862no—
635C22⋊Q8—862no—
636C22⋊Q8—862no—
637C22⋊Q8—861no—
638C22⋊Q8—861no—
639C22⋊Q8—861no—
640C22⋊Q8—861no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—862no—
646#121—862no—
647#121—862no—
648#121—862no—
649C4×Q8—861no—
650C4×Q8—861no—
651C4×Q8—861no—
652C4×Q8—861no—
653C4×D4—431no—
654C4×D4—431no—
655C4×D4—431no—
656C4×D4—431no—
657C4×D4—431no—
658C4×D4—431no—
659C4×D4—431no—
660C4×D4—431no—
661C4×D4—862no—
662C4×D4—862no—
663C4×D4—862no—
664C4×D4—862no—
665C2×C4⋊C4—431no—
666C2×C4⋊C4—432no—
667C2×C4⋊C4—432no—
668C2×C4⋊C4C22×D4311yescharacteristic
669C2×C22⋊C4—431no—
670C2×C22⋊C4—431no—
671C2×C22⋊C4—432no—
672C2×C22⋊C4—432no—
673C2×C22⋊C4—432no—
674C2×C22⋊C4C4×D4312yes—
675C2×C42—431no—
676C2×C42—432no—
677C4⋊C8—861no—
678C4⋊C8—861no—
679C4⋊C8—861no—
680C4⋊C8—861no—
681#101—434no—
682#101—862no—
683#101—862no—
684#101—862no—
685#101—862no—
686#101—862no—
687#101—1721no—
688#101—1721no—
689#100—22no—
690#100—41no—
691#100—862no—
692#100—1721no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—861no—
696C22⋊C8—861no—
697C22⋊C8—861no—
698C22⋊C8—861no—
699C22⋊C8—861no—
700C22⋊C8—861no—
701#97—861no—
702#97—861no—
703C4×C8—861no—
704C4×C8—861no—
705C24—431no—
706C24C2×C4×D4311yescharacteristic
707C24C2×C4×D4312yes—
708#41—1722no—
709#41—1722no—
710#41—1722no—
711#41—1722no—
712#41—1722no—
713#41—1722no—
714#41—1722no—
715#41—1722no—
716C2×Q8—432no—
717C2×Q8—432no—
718C2×Q8—864no—
719C2×Q8—862no—
720C2×Q8—862no—
721C2×Q8—861no—
722C2×Q8—861no—
723C2×Q8—861no—
724C2×Q8—861no—
725C2×Q8—861no—
726C2×Q8—861no—
727C2×Q8—861no—
728C2×Q8—861no—
729C2×Q8—861no—
730C2×Q8—861no—
731C2×Q8—1722no—
732C2×Q8—1722no—
733C2×Q8—1722no—
734C2×Q8—1722no—
735C2×Q8—1722no—
736C2×Q8—1722no—
737C2×Q8—1722no—
738C2×Q8—1722no—
739C2×Q8—1722no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—21no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—44no—
749C2×D4—431no—
750C2×D4—431no—
751C2×D4—431no—
752C2×D4—431no—
753C2×D4—864no—
754C2×D4—862no—
755C2×D4—862no—
756C2×D4—1722no—
757C2×D4—1722no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—432no—
763C22×C4—431no—
764C22×C4—431no—
765C22×C4—431no—
766C22×C4—431no—
767C22×C4—431no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—432no—
771C22×C4—862no—
772C22×C4—862no—
773C22×C4—864no—
774C22×C4—864no—
775C22×C4—861no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—862no—
780C22×C4—862no—
781C22×C4—1722no—
782C22×C4—1722no—
783C22×C4C2×C4×D4311yescharacteristic
784C22×C4C2×C4×D4312yes—
785C22×C4D4×D4311yescharacteristic
786C22×C4D4×D4311yescharacteristic
787C22×C4D4×D4311yescharacteristic
788C22×C4D4×D4311yescharacteristic
789C22×C4C23×D4311yescharacteristic
790M16—21no—
791M16—21no—
792M16—21no—
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—42no—
798M16—432no—
799M16—861no—
800M16—861no—
801M16—861no—
802M16—861no—
803M16—861no—
804M16—861no—
805M16—861no—
806M16—1722no—
807M16—1722no—
808M16—1722no—
809M16D4×D4312yes—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—42no—
815C2×C8—861no—
816C2×C8—861no—
817C2×C8—861no—
818C2×C8—861no—
819C2×C8—1722no—
820C2×C8—1722no—
821C2×C8—1722no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—431no—
825C4⋊C4—431no—
826C4⋊C4—431no—
827C4⋊C4—431no—
828C4⋊C4—862no—
829C4⋊C4—862no—
830C4⋊C4—862no—
831C4⋊C4—862no—
832C22⋊C4—22no—
833C22⋊C4—22no—
834C22⋊C4—431no—
835C22⋊C4—431no—
836C22⋊C4—431no—
837C22⋊C4—431no—
838C22⋊C4—431no—
839C22⋊C4—431no—
840C22⋊C4—431no—
841C22⋊C4—431no—
842C22⋊C4—862no—
843C22⋊C4—862no—
844C22⋊C4—862no—
845C22⋊C4—862no—
846C22⋊C4—862no—
847C22⋊C4—862no—
848C42—431no—
849C42—431no—
850C42—431no—
851C42—431no—
852C42—862no—
853C42—862no—
854C23—21no—
855C23—21no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—41no—
861C23—42no—
862C23—42no—
863C23—431no—
864C23—431no—
865C23—861no—
866C23—861no—
867C23—1721no—
868C23—1721no—
869C23C22⋊C4×D4311yescharacteristic
870C23C22⋊C4×D4311yescharacteristic
871C23C22×C4×D4311yescharacteristic
872Q8—862no—
873Q8—862no—
874Q8—862no—
875Q8—862no—
876Q8—1724no—
877Q8—1724no—
878Q8—1721no—
879Q8—1721no—
880Q8—1721no—
881Q8—1721no—
882D4—44no—
883D4—44no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—862no—
889D4—862no—
890D4—1721no—
891D4—1721no—
892D4—1724no—
893D4—1724no—
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—22no—
905C2×C4—42no—
906C2×C4—431no—
907C2×C4—431no—
908C2×C4—431no—
909C2×C4—431no—
910C2×C4—431no—
911C2×C4—431no—
912C2×C4—434no—
913C2×C4—862no—
914C2×C4—861no—
915C2×C4—861no—
916C2×C4—862no—
917C2×C4—861no—
918C2×C4—861no—
919C2×C4—861no—
920C2×C4—861no—
921C2×C4—861no—
922C2×C4—861no—
923C2×C4—861no—
924C2×C4—861no—
925C2×C4—862no—
926C2×C4—862no—
927C2×C4—862no—
928C2×C4—1721no—
929C2×C4—1721no—
930C2×C4—1724no—
931C2×C4—1724no—
932C2×C4—1724no—
933C2×C4—1724no—
934C2×C4C22⋊C4×D4311yescharacteristic
935C2×C4C22⋊C4×D4311yescharacteristic
936C2×C4C2×D4×D4311yescharacteristic
937C2×C4C2×D4×D4311yescharacteristic
938C2×C4C2×D4×D4311yescharacteristic
939C2×C4#41×D4311yescharacteristic
940C2×C4#1306337011yescharacteristic
941C2×C4#1306337111yescharacteristic
942C8—22no—
943C8—41no—
944C8—41no—
945C8—41no—
946C8—862no—
947C8—1721no—
948C8—1721no—
949C8—1721no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—82no—
963C22—82no—
964C22—861no—
965C22—861no—
966C22—861no—
967C22—861no—
968C22—861no—
969C22—861no—
970C22—3441no—
971C22—3441no—
972C22#1458288012yescomplemented
973C22C2×C22⋊C4×D4311yescharacteristic
974C22C4×D4×D4311yescharacteristic
975C22#1458337111yescharacteristic
976C4—21no—
977C4—21no—
978C4—42no—
979C4—861no—
980C4—861no—
981C4—864no—
982C4—861no—
983C4—861no—
984C4—861no—
985C4—861no—
986C4—1722no—
987C4#1458353111yescharacteristic
988C4#1458353311yescharacteristic
989C4#1458353811yescharacteristic
990C4#1458354111yescharacteristic
991C2—21no—
992C2—21no—
993C2—22no—
994C2—41no—
995C2—82no—
996C2—1721no—
997C2—1721no—
998C2#1913741311yescharacteristic
999C2C2×#1458288011yescharacteristic
1000C2#1914307611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1900C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583555C2
cosocleC22×C4×C43C24
hypercenter#1900D43
hypocenterC43#22410
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. C2×#14582880C2semidirect
5. C22×#13063243C2semidirect
6. #19135441C2semidirect
7. #19135441C2semidirect
8. #19135062C2semidirect
9. #19135062C2semidirect
10. #19135059C2semidirect
11. #19134590C2semidirect
12. #19134520C2semidirect
13. #19134518C2semidirect
14. #19134390C2semidirect
15. C43×#1900C2semidirect
170. #13063243D4semidirect
464. C22×C43#413semidirect
501. #1900D43semidirect
573. C43#22410semidirect
972. C22#14582880semidirect

Maximal subgroups

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

subgroupindex
C2×#145835552
M16×C22⋊D432
#191433272
C2×#145828802
C22×#130632432
#191354412
#191350622
#191350592
#191345902
#191345202
#191345182
#191343902
C43×#19002
#2241043