Finite Group Databasebeta

← #25105969

Subgroups — #25105969

Order 11008.

1442 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583463C211yesmaximal, characteristic
2C2×#14582957C211yesmaximal, characteristic, complemented
3#19137202C211yesmaximal, characteristic, complemented
4#19135524C211yesmaximal, characteristic, complemented
5#19135524C211yesmaximal, characteristic, complemented
6#19135520C211yesmaximal, characteristic, complemented
7#19135520C211yesmaximal, characteristic, complemented
8#19135417C211yesmaximal, characteristic, complemented
9#19135408C211yesmaximal, characteristic, complemented
10#19135403C211yesmaximal, characteristic, complemented
11#19135399C211yesmaximal, characteristic, complemented
12#19134535C211yesmaximal, characteristic, complemented
13#19134527C211yesmaximal, characteristic, complemented
14#19134525C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17#14583463—24no—
18#14583463C418yescomplemented
19C2×#13063321C2211yescharacteristic
20C2×#13063321C2211yescharacteristic
21C2×#13063314C2211yescharacteristic
22C2×#13063314C2211yescharacteristic
23C2×#13063299—21no—
24C2×#13063299—21no—
25C2×#13063293—21no—
26C2×#13063293—21no—
27C2×#13063284C2211yescharacteristic
28#14582957—24no—
29C2×Dic43⋊C8C2211yescharacteristic, complemented
30C2×Dic43⋊C8C2211yescharacteristic, complemented
31C2×#13063249C2211yescharacteristic, complemented
32C2×#13063249C2211yescharacteristic, complemented
33C2×#13063247C2211yescharacteristic
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063246C2211yescharacteristic, complemented
38C2×#13063246C2211yescharacteristic, complemented
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×#13063235C2211yescharacteristic, complemented
45C2×C8×Dic43C2211yescharacteristic, complemented
46#14582793—21no—
47#14582787—21no—
48#14582784—21no—
49#14582782—21no—
50#14582768C2211yescharacteristic, complemented
51#14582764C2211yescharacteristic, complemented
52#14582759C2211yescharacteristic
53C4⋊C4×Dic43C2211yescharacteristic, complemented
54C4⋊C4×Dic43C2211yescharacteristic, complemented
55C22×#41×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic, complemented
57C2×#103×C43C2211yescharacteristic, complemented
58C2×#102×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic, complemented
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C24×D43—21no—
63C22×D172—21no—
64C22×D172—22no—
65C22×D172—41no—
66C22×D172—41no—
67C22×D172—41no—
68C22×D172—41no—
69C22×D172C2×C414yes—
70C22×D172C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C22×C22⋊D43—21no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063321—22no—
79#13063321—22no—
80#13063321C2×C414yes—
81#13063321C2×C414yes—
82#13063314—22no—
83#13063314—22no—
84#13063314C2×C414yes—
85#13063314C2×C414yes—
86#13063299—28no—
87#13063299—28no—
88#13063293—28no—
89#13063293—28no—
90#13063284C2×C414yes—
91#13063284D414yes—
92C2×C4⋊Dic43D411yescharacteristic
93C2×C4⋊Dic43D411yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43D411yescharacteristic
100C2×C22⋊Dic43D411yescharacteristic
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109Dic43⋊C8—22no—
110Dic43⋊C8—22no—
111#13063249—41no—
112#13063249—41no—
113#13063247—41no—
114#13063247—41no—
115#13063247—41no—
116#13063247—41no—
117#13063246—41no—
118#13063246—41no—
119#13063245—41no—
120#13063245—41no—
121#13063245—41no—
122#13063245—41no—
123C22⋊(C43⋊C8)—22no—
124#13063235—22no—
125C8×Dic43—22no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C2×#41×C43—22no—
132C2×#41×C43—41no—
133C2×#41×C43—41no—
134C2×#41×C43—41no—
135C2×#41×C43—41no—
136C2×#41×C43C2×C414yes—
137C22×Q8×C43C2311yescharacteristic
138C22×D4×C43—21no—
139C22×D4×C43C2311yescharacteristic
140C23×C4×C43—21no—
141C23×C4×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147#103×C43—41no—
148#103×C43—41no—
149#102×C43—41no—
150#102×C43—41no—
151C22⋊C8×C43—22no—
152#95×C43—21no—
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155C23×D43—21no—
156C23×D43—21no—
157C23×D43—24no—
158C23×D43—42no—
159C23×D43—42no—
160C23×D43—81no—
161C23×D43—81no—
162C23×D43—81no—
163C23×D43—81no—
164#41×C43—44no—
165#41×C43—44no—
166#41×C43—44no—
167#41×C43—44no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43C22×C412yes—
174C2×D4×C43—21no—
175C2×D4×C43—24no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—42no—
181C2×D4×C43—42no—
182C2×D4×C43C22×C412yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—24no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—42no—
192C22×C4×C43—42no—
193C22×C4×C43C22×C412yes—
194C22×C4×C43C2×D412yes—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—24no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—81no—
202C2×C22⋊D43—81no—
203C2×C22⋊D43—81no—
204C2×C22⋊D43—81no—
205C2×C22⋊D43—81no—
206C2×C22⋊D43—81no—
207C2×C22⋊D43—81no—
208C2×C22⋊D43—81no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215C2×D172—24no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172—44no—
227C2×D172—44no—
228C2×D172—44no—
229C2×D172—44no—
230C2×D172—42no—
231C2×D172—42no—
232C2×D172C22×C412yes—
233C2×D172C22×C412yes—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C22⋊C4×C43—81no—
245C22⋊Dic43—81no—
246C22⋊Dic43C22⋊C414yes—
247C22⋊Dic43C22⋊C414yes—
248(C2×D43)⋊C4—24no—
249(C2×D43)⋊C4—24no—
250(C2×D43)⋊C4—24no—
251(C2×D43)⋊C4—24no—
252C4⋊Dic43—21no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43C22⋊C414yes—
257C4⋊Dic43C22⋊C414yes—
258Dic43⋊C4—81no—
259Dic43⋊C4—81no—
260C4×Dic43—81no—
261C4×Dic43—81no—
262C4×Dic43C22×C412yes—
263C4×Dic43C22×C412yes—
264C4×Dic43C2×D412yes—
265C4×Dic43C2×D412yes—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—22no—
279C23×C43—41no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43C2×C22⋊C412yes—
286C23×C43C22×D411yescharacteristic
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—48no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—84no—
303C22×D43—84no—
304C22×D43—84no—
305C22×D43—84no—
306C22×D43—84no—
307C22×D43—84no—
308Q8×C43—22no—
309Q8×C43—22no—
310Q8×C43—41no—
311Q8×C43—41no—
312D4×C43—22no—
313D4×C43—22no—
314D4×C43—48no—
315D4×C43—41no—
316D4×C43—41no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—48no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43C2×C22⋊C412yes—
334C2×C4×C43C23×C411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43H(5,𝔽2)11yescharacteristic
337C2×C4×C43H(5,𝔽2)11yescharacteristic
338C2×C4×C43H(5,𝔽2)11yescharacteristic
339C2×C4×C43H(5,𝔽2)11yescharacteristic
340C22⋊D43—84no—
341C22⋊D43—84no—
342C22⋊D43—84no—
343C22⋊D43—84no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43C2×C22⋊C412yes—
359C2×Dic43C2×C22⋊C412yes—
360C2×Dic43C2×C22⋊C412yes—
361C2×Dic43C2×C22⋊C412yes—
362D172—22no—
363D172—22no—
364D172—22no—
365D172—22no—
366D172—48no—
367D172—41no—
368D172—41no—
369D172—41no—
370D172—41no—
371C8×C43—41no—
372C8×C43—41no—
373C43⋊C8—41no—
374C43⋊C8—41no—
375#21813—431nomaximal, Sylow
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43C22×C22⋊C411yescharacteristic
391C22×C43#53511yescharacteristic
392C22×C43#53511yescharacteristic
393C22×C43#57611yescharacteristic
394C22×C43#57611yescharacteristic
395C22×C43#57711yescharacteristic
396C22×C43#57711yescharacteristic
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—42no—
402C2×D43—42no—
403C2×D43—816no—
404C2×D43—81no—
405C2×D43—81no—
406C2×D43—81no—
407C2×D43—81no—
408C2×D43—81no—
409C2×D43—81no—
410C2×D43—81no—
411C2×D43—81no—
412C4×C43—22no—
413C4×C43—42no—
414C4×C43—81no—
415C4×C43—81no—
416C4×C43#51811yescharacteristic
417C4×C43#51811yescharacteristic
418C4×C43#53511yescharacteristic
419C4×C43#53511yescharacteristic
420Dic43—22no—
421Dic43—22no—
422Dic43—22no—
423Dic43—22no—
424Dic43—81no—
425Dic43—81no—
426C2×#535—431no—
427C2×#433—431no—
428#2314—431no—
429#1983—431no—
430#1983—431no—
431#1982—431no—
432#1982—431no—
433#1961—431no—
434#1959—431no—
435#1958—431no—
436#1957—431no—
437#1788—431no—
438#1788D4311yescharacteristic, complemented
439#1786—431no—
440#1786—431no—
441C2×C43—42no—
442C2×C43—82no—
443C2×C43#230911yescharacteristic
444C2×C43#289711yescharacteristic
445C2×C43#289711yescharacteristic
446C2×C43#322011yescharacteristic
447C2×C43#322211yescharacteristic
448C2×C43#322411yescharacteristic
449C2×C43#322411yescharacteristic
450D43—82no—
451D43—82no—
452C22×#41C2×D4311yescharacteristic
453C23×D4—431no—
454#535—438no—
455#535—864no—
456C2×#127—431no—
457C2×#127—431no—
458C2×#124—431no—
459C2×#124—431no—
460C2×#121—861no—
461C2×#121—861no—
462C2×#120—861no—
463C2×#120—861no—
464C2×#117—431no—
465#433—864no—
466C2×C4⋊C8—431no—
467C2×C4⋊C8—431no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103C2×D4311yescharacteristic, complemented
471C2×#103C2×D4311yescharacteristic, complemented
472C2×#102—431no—
473C2×#102—431no—
474C2×#102—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102C2×D4311yescharacteristic, complemented
483C2×#102C2×D4311yescharacteristic, complemented
484C2×C22⋊C8—431no—
485C2×C22⋊C8C2×D4311yescharacteristic
486C2×#97—431no—
487C2×C4×C8—431no—
488#388—861no—
489#388—861no—
490#387—861no—
491#387—861no—
492#384—431no—
493#382—431no—
494#380—431no—
495#380C2×D4311yescharacteristic
496C4×C4⋊C4—431no—
497C4×C4⋊C4—431no—
498C43#2181311yescharacteristic, complemented, Sylow
499C25—861no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41C4×D4314yes—
506C22×Q8C22×D4311yescharacteristic
507C22×D4—21no—
508C22×D4—434no—
509C22×D4—431no—
510C22×D4—431no—
511C22×D4—861no—
512C22×D4—861no—
513C22×D4—861no—
514C22×D4—861no—
515C22×D4—861no—
516C22×D4—862no—
517C22×D4—1721no—
518C22×D4—1721no—
519C22×D4—1721no—
520C22×D4—1721no—
521C22×D4C22×D4311yescharacteristic
522C23×C4—21no—
523C23×C4C22×D4311yescharacteristic
524C22×C8—431no—
525C22×C8—431no—
526C22×C8C22×D4311yescharacteristic
527C22×C8C22×D4311yescharacteristic
528#127—434no—
529#127—434no—
530#127—862no—
531#127—862no—
532#124—434no—
533#124—434no—
534#124—862no—
535#124—862no—
536#121—868no—
537#121—868no—
538#120—868no—
539#120—868no—
540#117—434no—
541#117—434no—
542C2×C4⋊C4—431no—
543C2×C4⋊C4—431no—
544C2×C4⋊C4—431no—
545C2×C4⋊C4—431no—
546C2×C4⋊C4—861no—
547C2×C4⋊C4—861no—
548C2×C4⋊C4C22×D4311yescharacteristic
549C2×C4⋊C4C22×D4311yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—431no—
552C2×C22⋊C4—431no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C42—431no—
559C2×C42—431no—
560C2×C42—861no—
561C2×C42—861no—
562C4⋊C8—862no—
563C4⋊C8—862no—
564#103—41no—
565#103—41no—
566#103—1721no—
567#103—1721no—
568#102—41no—
569#102—41no—
570#102—1721no—
571#102—1721no—
572#102—1721no—
573#102—1721no—
574#102—1721no—
575#102—1721no—
576#102—1721no—
577#102—1721no—
578#102—1721no—
579#102—1721no—
580C22⋊C8—22no—
581C22⋊C8—862no—
582#97—862no—
583C4×C8—862no—
584#95—21no—
585#95—861no—
586#95—861no—
587#95—861no—
588#95—861no—
589#95—861no—
590C24—21no—
591C24—864no—
592C24—861no—
593C24—861no—
594C24—3441no—
595C24—3441no—
596C24—3441no—
597C24—3441no—
598C24—1722no—
599C24—1722no—
600C24D4×D4311yescharacteristic
601#41—44no—
602#41—44no—
603#41—44no—
604#41—44no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8C2×C4×D4312yes—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—432no—
620C2×D4—432no—
621C2×D4—864no—
622C2×D4—864no—
623C2×D4—864no—
624C2×D4—864no—
625C2×D4—864no—
626C2×D4—861no—
627C2×D4—861no—
628C2×D4—861no—
629C2×D4—861no—
630C2×D4—861no—
631C2×D4—861no—
632C2×D4—861no—
633C2×D4—861no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—3441no—
637C2×D4—3441no—
638C2×D4—3441no—
639C2×D4—3441no—
640C2×D4—3441no—
641C2×D4—3441no—
642C2×D4—3441no—
643C2×D4—3441no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4—1722no—
647C2×D4—1722no—
648C2×D4—1724no—
649C2×D4—1724no—
650C2×D4C2×C4×D4312yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—861no—
666C22×C4—861no—
667C22×C4C2×C4×D4312yes—
668C22×C4D4×D4311yescharacteristic
669C22×C4D4×D4312yes—
670C22×C4C23×D4311yescharacteristic
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8—861no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—861no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—434no—
688C4⋊C4—434no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—3441no—
694C4⋊C4—3441no—
695C22⋊C4—81no—
696C22⋊C4—434no—
697C22⋊C4—434no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4—3441no—
703C42—432no—
704C42—432no—
705C42—432no—
706C42—432no—
707C42—3441no—
708C42—3441no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—862no—
723C23—862no—
724C23—3444no—
725C23—3444no—
726C23—3444no—
727C23—3444no—
728C23—3444no—
729C23—3444no—
730C23—1728no—
731C23—1721no—
732C23—1721no—
733C23—1721no—
734C23—1721no—
735C23—1721no—
736C23—1721no—
737C23—1721no—
738C23—1721no—
739C23—1721no—
740C23—1721no—
741C23—1721no—
742C23—1721no—
743C23C22⋊C4×D4312yes—
744C23C2×D4×D4311yescharacteristic
745Q8—22no—
746Q8—22no—
747Q8—41no—
748Q8—41no—
749D4—22no—
750D4—22no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—862no—
755D4—862no—
756D4—862no—
757D4—862no—
758D4—3444no—
759D4—3444no—
760D4—3444no—
761D4—3444no—
762D4—1728no—
763D4—1721no—
764D4—1721no—
765D4—1721no—
766D4—1721no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—48no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—432no—
784C2×C4—432no—
785C2×C4—432no—
786C2×C4—432no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—861no—
793C2×C4—861no—
794C2×C4—861no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4—1721no—
798C2×C4—1721no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4C22⋊C4×D4312yes—
802C2×C4C22×C4×D4311yescharacteristic
803C2×C4C2×D4×D4311yescharacteristic
804C2×C4#1306337011yescharacteristic
805C2×C4#1306337011yescharacteristic
806C2×C4#1306337011yescharacteristic
807C2×C4#1306337011yescharacteristic
808C8—41no—
809C8—41no—
810C8—1721no—
811C8—1721no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22—81no—
826C22—34416no—
827C22—3441no—
828C22—3441no—
829C22—3441no—
830C22—3441no—
831C22—3441no—
832C22—3441no—
833C22—3441no—
834C22—3441no—
835C22—1722no—
836C22—1722no—
837C22—1722no—
838C22—1722no—
839C22—1722no—
840C22—1722no—
841C22C2×C22⋊C4×D4311yescharacteristic
842C22#1458346411yescharacteristic
843C22#1458346411yescharacteristic
844C22#1458370111yescharacteristic
845C22#1458370311yescharacteristic
846C22#1458370611yescharacteristic
847C22#1458370811yescharacteristic
848C4—22no—
849C4—42no—
850C4—81no—
851C4—81no—
852C4—862no—
853C4—862no—
854C4—862no—
855C4—862no—
856C4—3441no—
857C4—3441no—
858C4#1458337211yescharacteristic
859C4#1458337211yescharacteristic
860C4#1458346411yescharacteristic
861C4#1458346411yescharacteristic
862C2—42no—
863C2—82no—
864C2—3442no—
865C2—3442no—
866C2#1913717611yescharacteristic
867C2#1914311711yescharacteristic
868C2#1914311911yescharacteristic
869C2#1914564311yescharacteristic
870C2#1914566511yescharacteristic
871C2#1914568711yescharacteristic
872C2#1914569511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583463C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#21813
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#14582957C2semidirect
3. #19137202C2semidirect
4. #19135524C2semidirect
5. #19135524C2semidirect
6. #19135520C2semidirect
7. #19135520C2semidirect
8. #19135417C2semidirect
9. #19135408C2semidirect
10. #19135403C2semidirect
11. #19135399C2semidirect
12. #19134535C2semidirect
13. #19134527C2semidirect
14. #19134525C2semidirect
15. C43×#1788C2semidirect
18. #14583463C4semidirect
29. C2×Dic43⋊C8C22semidirect
30. C2×Dic43⋊C8C22semidirect
31. C2×#13063249C22semidirect
32. C2×#13063249C22semidirect
37. C2×#13063246C22semidirect
38. C2×#13063246C22semidirect
44. C2×#13063235C22semidirect
45. C2×C8×Dic43C22semidirect
50. #14582768C22semidirect
51. #14582764C22semidirect
53. C4⋊C4×Dic43C22semidirect
54. C4⋊C4×Dic43C22semidirect
56. C2×#103×C43C22semidirect
57. C2×#103×C43C22semidirect
58. C2×#102×C43C22semidirect
59. C2×#102×C43C22semidirect
438. #1788D43semidirect
470. C2×#103C2×D43semidirect
471. C2×#103C2×D43semidirect
482. C2×#102C2×D43semidirect
483. C2×#102C2×D43semidirect
498. C43#21813semidirect

Maximal subgroups

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

subgroupindex
C2×#145834632
C2×#145829572
#191372022
#191355242
#191355202
#191354172
#191354082
#191354032
#191353992
#191345352
#191345272
#191345252
C43×#17882
#2181343