Finite Group Databasebeta

← #25111970

Subgroups — #25111970

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×#14583558C211yesmaximal, characteristic
2D4×#10621877C211yesmaximal, characteristic, complemented
3C2×#14582881C211yesmaximal, characteristic, complemented
4C22×#13063243C211yesmaximal, 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#19134588C211yesmaximal, characteristic, complemented
12#19134521C211yesmaximal, characteristic, complemented
13#19134518C211yesmaximal, characteristic, complemented
14C4×#13063243C211yesmaximal, characteristic, complemented
15D4×M16×C43C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×Dic86C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20#14583558—21no—
21#14583558—21no—
22#14583558—21no—
23#14583558—21no—
24#14583558—21no—
25#14583558—21no—
26#14583558—21no—
27#14583558—21no—
28C2×#13063313C2211yescharacteristic
29C2×#13063311C412yes—
30C2×#13063304C2211yescharacteristic
31C2×#13063303C412yes—
32C2×#13063299C2211yescharacteristic
33C2×#13063297C412yes—
34C2×C4×Dic86C2211yescharacteristic
35C2×(C22⋊D43)⋊C4C412yes—
36#14582977—21no—
37#14582971—21no—
38#14582971—21no—
39D4×C43⋊C8—21no—
40#14582923C2211yescharacteristic
41#14582881—24no—
42C2×#13063243—24no—
43C2×#13063243C2211yescharacteristic
44C2×#13063243C2211yescharacteristic
45C2×#13063243C2211yescharacteristic
46C2×#13063243C2211yescharacteristic
47C2×#13063243C2211yescharacteristic
48C2×#13063243C2211yescharacteristic
49C2×#13063243C2211yescharacteristic
50C2×#13063243C2211yescharacteristic
51C2×#13063241C2211yescharacteristic
52C2×#13063241C2211yescharacteristic
53C2×#13063241C2211yescharacteristic
54C2×#13063241C2211yescharacteristic
55#14582863C2211yescharacteristic
56#14582863C2211yescharacteristic
57C4×#10621877C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582667C2211yescharacteristic
60#14582667C2211yescharacteristic
61#14582667C2211yescharacteristic
62C22×M16×C43C2211yescharacteristic
63C22×M16×C43C2211yescharacteristic
64C2×C4×D4×C43C2211yescharacteristic
65C43×#436—21no—
66C43×#435—21no—
67C43×#435—21no—
68C8×D4×C43—21no—
69C43×#423C2211yescharacteristic
70C43×#407C2211yescharacteristic
71C43×#407C2211yescharacteristic
72C4×M16×C43C2211yescharacteristic
73C2×#10621898—21no—
74C2×#10621898—21no—
75C2×#10621898—21no—
76C2×#10621898—21no—
77C2×#10621898—22no—
78C2×#10621898—22no—
79C2×#10621898—41no—
80C2×#10621898—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×D172C2311yescharacteristic
93C22×C22⋊D43C2×C412yes—
94C22×C22⋊D43C2×C412yes—
95C23×Dic43C2×C412yes—
96C22×C4×D43C2×C412yes—
97C2×#10621877—21no—
98C2×#10621877—21no—
99C2×#10621877—22no—
100C2×#10621877—22no—
101C2×#10621877—41no—
102C2×#10621877—41no—
103C2×#10621877C2311yescharacteristic
104C2×#10621877C2311yescharacteristic
105C2×#10621877C2311yescharacteristic
106C2×#10621877C2311yescharacteristic
107C22×C43⋊C8—21no—
108C22×C43⋊C8—21no—
109#13063313—21no—
110#13063313—21no—
111#13063313—21no—
112#13063313—21no—
113#13063311—22no—
114#13063311—22no—
115#13063311—22no—
116#13063311—22no—
117#13063304—21no—
118#13063304—21no—
119#13063304—21no—
120#13063304—21no—
121#13063303—22no—
122#13063303—22no—
123#13063303—22no—
124#13063303—22no—
125#13063299—21no—
126#13063299—21no—
127#13063299—21no—
128#13063299—21no—
129#13063297—22no—
130#13063297—22no—
131#13063297—22no—
132#13063297—22no—
133C4×Dic86—21no—
134C4×Dic86—21no—
135C4×Dic86—21no—
136C4×Dic86—21no—
137(C22⋊D43)⋊C4—22no—
138(C22⋊D43)⋊C4—22no—
139(C22⋊D43)⋊C4—22no—
140(C22⋊D43)⋊C4—22no—
141C2×C4⋊Dic43C2311yescharacteristic
142C2×Dic43⋊C4C2×C412yes—
143C2×Dic43⋊C4C2×C412yes—
144C2×C22⋊Dic43C2×C412yes—
145C2×(C2×D43)⋊C4C2×C412yes—
146C2×(C2×D43)⋊C4C2×C412yes—
147C2×(C2×D43)⋊C4C2×C412yes—
148C2×C4×Dic43C2×C412yes—
149C4⋊(C43⋊C8)—21no—
150C4⋊(C43⋊C8)—21no—
151#13063243—22no—
152#13063243—22no—
153#13063243—22no—
154#13063243—22no—
155#13063243—22no—
156#13063243—41no—
157#13063243—41no—
158#13063243D414yescomplemented
159#13063241—22no—
160#13063241—22no—
161#13063241—41no—
162#13063241—41no—
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×D43C22×C412yes—
207C2×D4×C43—42no—
208C2×D4×C43C22⋊C411yescharacteristic
209C2×D4×C43C22⋊C411yescharacteristic
210C2×D4×C43C22⋊C411yescharacteristic
211C2×D4×C43C22⋊C411yescharacteristic
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C22×C411yescharacteristic
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2411yescharacteristic
233C2×C22⋊D43—24no—
234C2×C22⋊D43—22no—
235C2×C22⋊D43—22no—
236C2×C22⋊D43—22no—
237C2×C22⋊D43—22no—
238C2×C22⋊D43—42no—
239C2×C22⋊D43—44no—
240C22×Dic43—24no—
241C22×Dic43—22no—
242C22×Dic43—22no—
243C22×Dic43—42no—
244C22×Dic43C22×C412yes—
245C22×Dic43C22×C412yes—
246C22×Dic43C22×C412yes—
247#10621898—42no—
248#10621898—42no—
249#10621898—42no—
250#10621898—42no—
251#10621898—42no—
252#10621898—42no—
253#10621898—42no—
254#10621898—42no—
255C2×D172—21no—
256C2×D172—21no—
257C2×D172—21no—
258C2×D172—21no—
259C2×D172—21no—
260C2×D172—21no—
261C2×C4×D43—22no—
262C2×C4×D43—22no—
263C2×C4×D43—24no—
264C2×C4×D43—42no—
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×C43—42no—
298M16×C43C2×D412yes—
299C2×C8×C43—21no—
300C2×C8×C43—21no—
301C2×C8×C43—21no—
302C2×C8×C43—21no—
303C2×C8×C43—42no—
304C2×C8×C43—42no—
305C4⋊C4×C43C22⋊C411yescharacteristic
306C4⋊C4×C43C22⋊C411yescharacteristic
307C4⋊C4×C43C22⋊C411yescharacteristic
308C4⋊C4×C43C22⋊C411yescharacteristic
309C22⋊C4×C43C22⋊C411yescharacteristic
310C22⋊C4×C43C22⋊C411yescharacteristic
311C22⋊C4×C43C22⋊C411yescharacteristic
312C22⋊C4×C43C22⋊C411yescharacteristic
313C22⋊C4×C43C22⋊C411yescharacteristic
314C22⋊C4×C43C22⋊C411yescharacteristic
315C22⋊C4×C43C22⋊C411yescharacteristic
316C22⋊C4×C43C22⋊C411yescharacteristic
317C42×C43C2×D411yescharacteristic
318C42×C43C2×D411yescharacteristic
319C42×C43C2×D411yescharacteristic
320C42×C43C2×D411yescharacteristic
321C22⋊Dic43—22no—
322C22⋊Dic43—22no—
323(C2×D43)⋊C4—22no—
324(C2×D43)⋊C4—22no—
325(C2×D43)⋊C4—22no—
326(C2×D43)⋊C4—22no—
327(C2×D43)⋊C4—22no—
328(C2×D43)⋊C4—22no—
329C4⋊Dic43—21no—
330C4⋊Dic43—21no—
331Dic43⋊C4—22no—
332Dic43⋊C4—22no—
333Dic43⋊C4—22no—
334Dic43⋊C4—22no—
335C4×Dic43—22no—
336C4×Dic43—22no—
337#10621877—21no—
338#10621877—21no—
339#10621877—21no—
340#10621877—21no—
341#10621877—21no—
342#10621877—21no—
343#10621877—21no—
344#10621877—42no—
345#10621877—42no—
346#10621877C2×D412yes—
347C2×C43⋊C8—21no—
348C2×C43⋊C8—21no—
349C2×C43⋊C8—21no—
350C2×C43⋊C8—21no—
351C2×C43⋊C8—42no—
352C2×C43⋊C8—42no—
353C23×C43—21no—
354C23×C43—21no—
355C23×C43—22no—
356C23×C43—21no—
357C23×C43—21no—
358C23×C43—41no—
359C23×C43—41no—
360C23×C43—41no—
361C23×C43C2×C22⋊C411yescharacteristic
362C23×C43C2×C22⋊C411yescharacteristic
363C23×C43C2×C22⋊C411yescharacteristic
364C23×C43C2×C22⋊C411yescharacteristic
365C23×C43C23×C411yescharacteristic
366C22×D43—22no—
367C22×D43—22no—
368C22×D43—22no—
369C22×D43—42no—
370C22×D43—42no—
371D4×C43—22no—
372D4×C43—22no—
373D4×C43—41no—
374D4×C43—41no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
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—21no—
388C2×C4×C43—21no—
389C2×C4×C43—21no—
390C2×C4×C43—21no—
391C2×C4×C43—21no—
392C2×C4×C43—21no—
393C2×C4×C43—21no—
394C2×C4×C43—21no—
395C2×C4×C43—41no—
396C2×C4×C43—41no—
397C2×C4×C43C2×C22⋊C411yescharacteristic
398C2×C4×C43C2×C22⋊C411yescharacteristic
399C2×C4×C43C2×C22⋊C411yescharacteristic
400C2×C4×C43C2×C22⋊C411yescharacteristic
401C2×C4×C43C2×C22⋊C411yescharacteristic
402C2×C4×C43C2×C22⋊C411yescharacteristic
403C2×C4×C43C2×C22⋊C411yescharacteristic
404C2×C4×C43C2×C22⋊C411yescharacteristic
405C2×C4×C43C22×D411yescharacteristic
406C2×C4×C43C22×D411yescharacteristic
407C2×C4×C43C22×D411yescharacteristic
408C2×C4×C43C2×#4111yescharacteristic
409C2×C4×C43H(5,𝔽2)11yescharacteristic
410C2×C4×C43H(5,𝔽2)11yescharacteristic
411C22⋊D43—44no—
412C22⋊D43—44no—
413C22⋊D43—44no—
414C22⋊D43—44no—
415C2×Dic43—22no—
416C2×Dic43—22no—
417C2×Dic43—22no—
418C2×Dic43—22no—
419C2×Dic43—22no—
420C2×Dic43—22no—
421C2×Dic43—44no—
422C2×Dic43—44no—
423C2×Dic43—42no—
424C2×Dic43C4×D414yes—
425D172—41no—
426D172—41no—
427D172—41no—
428D172—41no—
429C4×D43—44no—
430C4×D43—44no—
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—21no—
458C22×C43—21no—
459C22×C43—21no—
460C22×C43—21no—
461C22×C43—21no—
462C22×C43—21no—
463C22×C43—42no—
464C22×C43—42no—
465C22×C43—81no—
466C22×C43—81no—
467C22×C43#41312yescomplemented
468C22×C43C22×C22⋊C411yescharacteristic
469C22×C43C2×C4×D411yescharacteristic
470C22×C43#51811yescharacteristic
471C2×D43—42no—
472C2×D43—42no—
473C2×D43—42no—
474C2×D43—82no—
475C2×D43—82no—
476C4×C43—21no—
477C4×C43—21no—
478C4×C43—21no—
479C4×C43—21no—
480C4×C43—21no—
481C4×C43—21no—
482C4×C43—21no—
483C4×C43—21no—
484C4×C43D4211yescharacteristic
485C4×C43D4211yescharacteristic
486C4×C43#54611yescharacteristic
487C4×C43#54611yescharacteristic
488Dic43—24no—
489Dic43—42no—
490Dic43—42no—
491C2×#548—431no—
492D4×M16—431no—
493D4×M16D4311yescharacteristic, complemented
494C2×#413—431no—
495C22×#101—431no—
496#1967—431no—
497#1967—431no—
498#1901—431no—
499#1901—431no—
500#1900—431no—
501#1900—431no—
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—41no—
511C2×C43—41no—
512C2×C43D4×C22⋊C411yescharacteristic
513C2×C43C2×#41311yescharacteristic
514C2×C43#288911yescharacteristic
515D43—82no—
516C22×#41—431no—
517C23×Q8—431no—
518C22×M16—431no—
519C22×M16—431no—
520C22×M16C2×D4311yescharacteristic
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—432no—
531C2×#124—431no—
532C2×C22⋊Q8—431no—
533C2×C22⋊Q8—432no—
534C2×#121—432no—
535C2×#121—431no—
536C2×C4×Q8—431no—
537C2×C4×D4—432no—
538C2×C4×D4C2×D4311yescharacteristic
539#436—21no—
540#436—861no—
541#435—21no—
542#435—21no—
543#435—861no—
544#435—861no—
545C8×D4—21no—
546C8×D4—861no—
547#423—431no—
548#423C2×D4311yescharacteristic
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×#100—431no—
562C2×#100—431no—
563#407—431no—
564#407—431no—
565#407C2×D4311yescharacteristic
566#407C2×D4311yescharacteristic
567C4×M16—431no—
568C4×M16C2×D4311yescharacteristic
569#343—431no—
570#343—431no—
571#343—431no—
572#343—431no—
573C43#2241011yescharacteristic, complemented, Sylow
574C2×#41—862no—
575C2×#41—862no—
576C2×#41—861no—
577C2×#41—861no—
578C2×#41—861no—
579C2×#41—861no—
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—432no—
594C22×D4—432no—
595C22×D4—431no—
596C22×D4C4×D4311yescharacteristic
597C23×C4—432no—
598C23×C4—432no—
599C23×C4C22×D4311yescharacteristic
600C23×C4C22×D4311yescharacteristic
601C2×M16—21no—
602C2×M16—21no—
603C2×M16—22no—
604C2×M16—22no—
605C2×M16—41no—
606C2×M16—41no—
607C2×M16—431no—
608C2×M16—431no—
609C2×M16—431no—
610C2×M16—431no—
611C2×M16—861no—
612C2×M16—861no—
613C2×M16—862no—
614C2×M16—862no—
615C2×M16—1721no—
616C2×M16—1721no—
617C2×M16C22×D4311yescharacteristic
618C2×M16C22×D4311yescharacteristic
619C2×M16C22×D4311yescharacteristic
620C2×M16C22×D4311yescharacteristic
621C22×C8—21no—
622C22×C8—21no—
623C22×C8—861no—
624C22×C8—861no—
625#124—862no—
626#124—862no—
627#124—862no—
628#124—862no—
629#124—861no—
630#124—861no—
631#124—861no—
632#124—861no—
633C22⋊Q8—861no—
634C22⋊Q8—861no—
635C22⋊Q8—861no—
636C22⋊Q8—861no—
637C22⋊Q8—862no—
638C22⋊Q8—862no—
639C22⋊Q8—862no—
640C22⋊Q8—862no—
641#121—862no—
642#121—862no—
643#121—862no—
644#121—862no—
645#121—861no—
646#121—861no—
647#121—861no—
648#121—861no—
649C4×Q8—861no—
650C4×Q8—861no—
651C4×Q8—861no—
652C4×Q8—861no—
653C4×D4—862no—
654C4×D4—862no—
655C4×D4—862no—
656C4×D4—862no—
657C4×D4D17211yescharacteristic
658C4×D4D17211yescharacteristic
659C4×D4D17211yescharacteristic
660C4×D4D17211yescharacteristic
661C4×D4C22⋊D4311yescharacteristic
662C4×D4C22⋊D4311yescharacteristic
663C4×D4C22⋊D4311yescharacteristic
664C4×D4C22⋊D4311yescharacteristic
665C2×C4⋊C4—432no—
666C2×C4⋊C4—432no—
667C2×C4⋊C4—431no—
668C2×C4⋊C4C4×D4311yescharacteristic
669C2×C22⋊C4—432no—
670C2×C22⋊C4—432no—
671C2×C22⋊C4—432no—
672C2×C22⋊C4—432no—
673C2×C22⋊C4C4×D4311yescharacteristic
674C2×C22⋊C4C4×D4311yescharacteristic
675C2×C42—432no—
676C2×C42C22×D4311yescharacteristic
677C4⋊C8—21no—
678C4⋊C8—21no—
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—862no—
690#100—862no—
691#100—1721no—
692#100—1721no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695C22⋊C8—21no—
696C22⋊C8—21no—
697C22⋊C8—861no—
698C22⋊C8—861no—
699C22⋊C8—861no—
700C22⋊C8—861no—
701#97—21no—
702#97—861no—
703C4×C8—21no—
704C4×C8—861no—
705C24—432no—
706C24C2×C4×D4311yescharacteristic
707C24C2×C4×D4311yescharacteristic
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—42no—
741C2×D4—864no—
742C2×D4—862no—
743C2×D4—862no—
744C2×D4—862no—
745C2×D4—862no—
746C2×D4—861no—
747C2×D4—861no—
748C2×D4—861no—
749C2×D4—861no—
750C2×D4—861no—
751C2×D4—861no—
752C2×D4—1722no—
753C2×D4—1724no—
754C2×D4(C2×D43)⋊C411yescharacteristic
755C2×D4(C2×D43)⋊C411yescharacteristic
756C2×D4(C2×D43)⋊C411yescharacteristic
757C2×D4(C2×D43)⋊C411yescharacteristic
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—432no—
767C22×C4—432no—
768C22×C4—432no—
769C22×C4—864no—
770C22×C4—864no—
771C22×C4—862no—
772C22×C4—862no—
773C22×C4—862no—
774C22×C4—862no—
775C22×C4—1722no—
776C22×C4—1722no—
777C22×C4C2×C4×D4311yescharacteristic
778C22×C4C2×C4×D4311yescharacteristic
779C22×C4C2×C4×D4311yescharacteristic
780C22×C4C2×C4×D4311yescharacteristic
781C22×C4C2×D17211yescharacteristic
782C22×C4C2×D17211yescharacteristic
783C22×C4C2×D17211yescharacteristic
784C22×C4C2×D17211yescharacteristic
785C22×C4C2×C22⋊D4311yescharacteristic
786C22×C4C2×C22⋊D4311yescharacteristic
787C22×C4C2×C22⋊D4311yescharacteristic
788C22×C4C2×C22⋊D4311yescharacteristic
789C22×C4C23×D4311yescharacteristic
790M16—21no—
791M16—21no—
792M16—21no—
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—42no—
798M16—42no—
799M16—432no—
800M16—861no—
801M16—861no—
802M16—861no—
803M16—861no—
804M16—861no—
805M16—861no—
806M16—861no—
807M16—1722no—
808M16—1722no—
809M16D4×D4312yes—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—42no—
815C2×C8—42no—
816C2×C8—861no—
817C2×C8—861no—
818C2×C8—861no—
819C2×C8—861no—
820C2×C8—1722no—
821C2×C8—1722no—
822C4⋊C4—862no—
823C4⋊C4—862no—
824C4⋊C4—862no—
825C4⋊C4—862no—
826C4⋊C4—861no—
827C4⋊C4—861no—
828C4⋊C4(C2×D43)⋊C411yescharacteristic
829C4⋊C4(C2×D43)⋊C411yescharacteristic
830C4⋊C4(C2×D43)⋊C411yescharacteristic
831C4⋊C4(C2×D43)⋊C411yescharacteristic
832C22⋊C4—862no—
833C22⋊C4—862no—
834C22⋊C4—862no—
835C22⋊C4—862no—
836C22⋊C4—862no—
837C22⋊C4—862no—
838C22⋊C4—862no—
839C22⋊C4—862no—
840C22⋊C4(C2×D43)⋊C411yescharacteristic
841C22⋊C4(C2×D43)⋊C411yescharacteristic
842C22⋊C4(C2×D43)⋊C411yescharacteristic
843C22⋊C4(C2×D43)⋊C411yescharacteristic
844C22⋊C4(C2×D43)⋊C411yescharacteristic
845C22⋊C4(C2×D43)⋊C411yescharacteristic
846C22⋊C4(C2×D43)⋊C411yescharacteristic
847C22⋊C4(C2×D43)⋊C411yescharacteristic
848C42—862no—
849C42—862no—
850C42C2×D17211yescharacteristic
851C42C2×D17211yescharacteristic
852C42C2×C22⋊D4311yescharacteristic
853C42C2×C22⋊D4311yescharacteristic
854C23—21no—
855C23—21no—
856C23—22no—
857C23—21no—
858C23—21no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—862no—
863C23—862no—
864C23—862no—
865C23—1722no—
866C23—1722no—
867C23C2×(C2×D43)⋊C411yescharacteristic
868C23C2×(C2×D43)⋊C411yescharacteristic
869C23C2×(C2×D43)⋊C411yescharacteristic
870C23C2×(C2×D43)⋊C411yescharacteristic
871C23C22×C4×D4311yescharacteristic
872Q8—862no—
873Q8—862no—
874Q8—862no—
875Q8—862no—
876Q8—1724no—
877Q8—1724no—
878Q8—1721no—
879Q8—1721no—
880Q8—1721no—
881Q8—1721no—
882D4—22no—
883D4—22no—
884D4—41no—
885D4—41no—
886D4—1724no—
887D4—1724no—
888D4—1724no—
889D4—1724no—
890D4—1721no—
891D4—1721no—
892D4—1721no—
893D4—1721no—
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—434no—
917C2×C4—862no—
918C2×C4—862no—
919C2×C4—862no—
920C2×C4—862no—
921C2×C4—862no—
922C2×C4—862no—
923C2×C4—1724no—
924C2×C4—1724no—
925C2×C4—1724no—
926C2×C4—1724no—
927C2×C4—1722no—
928C2×C4C2×(C2×D43)⋊C411yescharacteristic
929C2×C4C2×(C2×D43)⋊C411yescharacteristic
930C2×C4C2×(C2×D43)⋊C411yescharacteristic
931C2×C4C2×(C2×D43)⋊C411yescharacteristic
932C2×C4C2×(C2×D43)⋊C411yescharacteristic
933C2×C4C2×(C2×D43)⋊C411yescharacteristic
934C2×C4C2×(C2×D43)⋊C411yescharacteristic
935C2×C4C2×(C2×D43)⋊C411yescharacteristic
936C2×C4C2×D4×D4311yescharacteristic
937C2×C4C22×C22⋊D4311yescharacteristic
938C2×C4C22×D17211yescharacteristic
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—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—42no—
964C22—42no—
965C22—81no—
966C22—81no—
967C22—3442no—
968C22—3442no—
969C22—1722no—
970C22—1722no—
971C22—1722no—
972C22#1458288112yescomplemented
973C22C22×(C2×D43)⋊C411yescharacteristic
974C22C4×D4×D4311yescharacteristic
975C22#1458337111yescharacteristic
976C4—21no—
977C4—21no—
978C4—21no—
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—864no—
985C4—1722no—
986C4—1722no—
987C4D4×C22⋊D4311yescharacteristic
988C4D4×D17211yescharacteristic
989C4#1458353711yescharacteristic
990C4#1458354411yescharacteristic
991C2—21no—
992C2—21no—
993C2—22no—
994C2—41no—
995C2—41no—
996C2—41no—
997C2—3442no—
998C2D4×(C2×D43)⋊C411yescharacteristic
999C2C2×#1458288111yescharacteristic
1000C2#1914307711yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×M16×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583558C2
cosocleC22×C4×C43C24
hypercenterD4×M16D43
hypocenterC43#22410
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×#13063243C2semidirect
5. #19135444C2semidirect
6. #19135442C2semidirect
7. #19135063C2semidirect
8. #19135061C2semidirect
9. #19135058C2semidirect
10. #19135056C2semidirect
11. #19134588C2semidirect
12. #19134521C2semidirect
13. #19134518C2semidirect
14. C4×#13063243C2semidirect
15. D4×M16×C43C2semidirect
158. #13063243D4semidirect
467. C22×C43#413semidirect
493. D4×M16D43semidirect
573. C43#22410semidirect
972. C22#14582881semidirect

Maximal subgroups

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

subgroupindex
C2×#145835582
D4×#106218772
C2×#145828812
C22×#130632432
#191354442
#191354422
#191350632
#191350612
#191350582
#191350562
#191345882
#191345212
#191345182
C4×#130632432
D4×M16×C432
#2241043