Finite Group Databasebeta

← #25105967

Subgroups — #25105967

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×#14583466C211yesmaximal, characteristic
2C2×#14582957C211yesmaximal, characteristic, complemented
3#19137202C211yesmaximal, characteristic, complemented
4#19135526C211yesmaximal, characteristic, complemented
5#19135526C211yesmaximal, characteristic, complemented
6#19135520C211yesmaximal, characteristic, complemented
7#19135520C211yesmaximal, characteristic, complemented
8#19135417C211yesmaximal, characteristic, complemented
9#19135410C211yesmaximal, characteristic, complemented
10#19135405C211yesmaximal, characteristic, complemented
11#19135399C211yesmaximal, characteristic, complemented
12#19134536C211yesmaximal, characteristic, complemented
13#19134533C211yesmaximal, characteristic, complemented
14#19134526C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17#14583466—24no—
18#14583466C418yescomplemented
19C2×#13063321C2211yescharacteristic
20C2×#13063321C2211yescharacteristic
21C2×#13063312C2211yescharacteristic
22C2×#13063312C2211yescharacteristic
23C2×#13063296—21no—
24C2×#13063296—21no—
25C2×#13063294—21no—
26C2×#13063294—21no—
27C2×#13063284C2211yescharacteristic
28#14582957—24no—
29C2×Dic43⋊C8C2211yescharacteristic, complemented
30C2×Dic43⋊C8C2211yescharacteristic, complemented
31C2×#13063250C2211yescharacteristic, complemented
32C2×#13063250C2211yescharacteristic, complemented
33C2×#13063248C2211yescharacteristic, complemented
34C2×#13063248C2211yescharacteristic, complemented
35C2×#13063247C2211yescharacteristic, complemented
36C2×#13063247C2211yescharacteristic, complemented
37C2×#13063246C2211yescharacteristic
38C2×#13063246C2211yescharacteristic
39C2×#13063246C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063245C2211yescharacteristic, complemented
42C2×#13063245C2211yescharacteristic, complemented
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
55C23×D4×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C2×#10621898—22no—
63C2×#10621898—41no—
64C2×#10621898—41no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C2×#10621898C2×C414yes—
68C22×Dic86C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C22⋊D43—21no—
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C22×C4×D43—21no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063321—22no—
79#13063321—22no—
80#13063321C2×C414yes—
81#13063321C2×C414yes—
82#13063312—22no—
83#13063312—22no—
84#13063312C2×C414yes—
85#13063312C2×C414yes—
86#13063296—28no—
87#13063296—28no—
88#13063294—28no—
89#13063294—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⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×C22⋊Dic43—21no—
103C2×C22⋊Dic43D411yescharacteristic
104C2×C22⋊Dic43D411yescharacteristic
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109Dic43⋊C8—22no—
110Dic43⋊C8—22no—
111#13063250—41no—
112#13063250—41no—
113#13063248—41no—
114#13063248—41no—
115#13063247—41no—
116#13063247—41no—
117#13063246—41no—
118#13063246—41no—
119#13063246—41no—
120#13063246—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—
131C25×C43—21no—
132C22×D4×C43—21no—
133C22×D4×C43—22no—
134C22×D4×C43—41no—
135C22×D4×C43—41no—
136C22×D4×C43—41no—
137C22×D4×C43—41no—
138C22×D4×C43C2×C414yes—
139C22×D4×C43C2311yescharacteristic
140C22×D4×C43C2311yescharacteristic
141C23×C4×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147#102×C43—41no—
148#102×C43—41no—
149#102×C43—41no—
150#102×C43—41no—
151C22⋊C8×C43—22no—
152#95×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—24no—
156C24×C43—42no—
157C24×C43—42no—
158C24×C43—81no—
159C24×C43—81no—
160C24×C43—81no—
161C24×C43—81no—
162C24×C43C2×D411yescharacteristic
163C23×D43—21no—
164C2×D4×C43—24no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—44no—
176C2×D4×C43—44no—
177C2×D4×C43—44no—
178C2×D4×C43—44no—
179C2×D4×C43—42no—
180C2×D4×C43—42no—
181C2×D4×C43C22×C412yes—
182C2×D4×C43C22×C412yes—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43C22×C412yes—
190C22×C4×C43C2×D412yes—
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2411yescharacteristic
193C2×C22⋊D43—24no—
194C2×C22⋊D43—24no—
195C2×C22⋊D43—24no—
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—42no—
199C2×C22⋊D43—42no—
200C2×C22⋊D43—81no—
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—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215#10621898—44no—
216#10621898—44no—
217#10621898—44no—
218#10621898—44no—
219C2×D172—21no—
220C2×D172—21no—
221C2×D172—21no—
222C2×D172—21no—
223C2×D172—21no—
224C2×D172C22×C412yes—
225C2×C4×D43—24no—
226C2×C4×D43—42no—
227C2×C4×D43—42no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86C22×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—24no—
246C22⋊Dic43—24no—
247C22⋊Dic43—24no—
248C22⋊Dic43—24no—
249C22⋊Dic43—81no—
250C22⋊Dic43C22⋊C414yes—
251C22⋊Dic43C22⋊C414yes—
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—22no—
280C23×C43—48no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—84no—
294C23×C43—84no—
295C23×C43—84no—
296C23×C43—84no—
297C23×C43—84no—
298C23×C43—84no—
299C23×C43C2×C22⋊C412yes—
300C23×C43C22×D411yescharacteristic
301C22×D43—22no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308D4×C43—22no—
309D4×C43—22no—
310D4×C43—22no—
311D4×C43—22no—
312D4×C43—48no—
313D4×C43—41no—
314D4×C43—41no—
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—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43C2×C22⋊C412yes—
330C2×C4×C43C23×C411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C2×C4×C43H(5,𝔽2)11yescharacteristic
336C22⋊D43—48no—
337C22⋊D43—84no—
338C22⋊D43—84no—
339C22⋊D43—84no—
340C22⋊D43—84no—
341C2×Dic43—21no—
342C2×Dic43—21no—
343C2×Dic43—21no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—21no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—22no—
350C2×Dic43—41no—
351C2×Dic43—41no—
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—41no—
365D172—41no—
366C4×D43—48no—
367Dic86—22no—
368Dic86—22no—
369Dic86—41no—
370Dic86—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—42no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—816no—
390C22×C43—81no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43C22×C22⋊C411yescharacteristic
399C22×C43#53511yescharacteristic
400C22×C43#53511yescharacteristic
401C22×C43#57611yescharacteristic
402C22×C43#57611yescharacteristic
403C22×C43#57711yescharacteristic
404C22×C43#57711yescharacteristic
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—81no—
409C2×D43—81no—
410C2×D43—81no—
411C2×D43—81no—
412C4×C43—22no—
413C4×C43—81no—
414C4×C43—81no—
415C4×C43#51811yescharacteristic
416C4×C43#51811yescharacteristic
417C4×C43#53511yescharacteristic
418C4×C43#53511yescharacteristic
419Dic43—22no—
420Dic43—22no—
421Dic43—22no—
422Dic43—22no—
423Dic43—42no—
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#1788—431no—
439#1786—431no—
440#1786D4311yescharacteristic, complemented
441C2×C43—42no—
442C2×C43—82no—
443C2×C43—82no—
444C2×C43#230911yescharacteristic
445C2×C43#289711yescharacteristic
446C2×C43#289711yescharacteristic
447C2×C43#322011yescharacteristic
448C2×C43#322211yescharacteristic
449C2×C43#322411yescharacteristic
450C2×C43#322411yescharacteristic
451D43—82no—
452C22×#41—431no—
453C23×D4C2×D4311yescharacteristic
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×#103—431no—
471C2×#103—431no—
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×#102C2×D4311yescharacteristic
481C2×#102C2×D4311yescharacteristic
482C2×#102C2×D4311yescharacteristic
483C2×#102C2×D4311yescharacteristic
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—21no—
500C2×#41—434no—
501C2×#41—862no—
502C2×#41—1721no—
503C2×#41—1721no—
504C2×#41—1721no—
505C2×#41—1721no—
506C22×Q8—431no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—431no—
514C22×D4—861no—
515C22×D4—861no—
516C22×D4—861no—
517C22×D4—861no—
518C22×D4—861no—
519C22×D4C4×D4314yes—
520C22×D4C22×D4311yescharacteristic
521C22×D4C22×D4311yescharacteristic
522C23×C4—861no—
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—1721no—
565#103—1721no—
566#103—1721no—
567#103—1721no—
568#102—41no—
569#102—41no—
570#102—41no—
571#102—41no—
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—21no—
592C24—24no—
593C24—42no—
594C24—42no—
595C24—81no—
596C24—81no—
597C24—81no—
598C24—81no—
599C24—861no—
600C24D4×D4311yescharacteristic
601#41—1724no—
602#41—1724no—
603#41—1724no—
604#41—1724no—
605C2×Q8—432no—
606C2×Q8—861no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8—861no—
610C2×Q8—861no—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—44no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—432no—
629C2×D4—864no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—3441no—
640C2×D4—3441no—
641C2×D4—3441no—
642C2×D4—3441no—
643C2×D4—3441no—
644C2×D4—3441no—
645C2×D4—3441no—
646C2×D4—3441no—
647C2×D4—1722no—
648C2×D4—1722no—
649C2×D4C2×C4×D4312yes—
650C2×D4C2×C4×D4312yes—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—861no—
662C22×C4—864no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—1722no—
666C22×C4—1722no—
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—22no—
717C23—48no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—84no—
731C23—84no—
732C23—84no—
733C23—84no—
734C23—84no—
735C23—84no—
736C23—862no—
737C23—1721no—
738C23—1721no—
739C23—1721no—
740C23—1721no—
741C23—1721no—
742C23—1721no—
743C23C22⋊C4×D4312yes—
744C23C2×D4×D4311yescharacteristic
745Q8—862no—
746Q8—862no—
747Q8—1721no—
748Q8—1721no—
749D4—22no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—48no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—41no—
758D4—862no—
759D4—862no—
760D4—3444no—
761D4—3444no—
762D4—3444no—
763D4—3444no—
764D4—1728no—
765D4—1721no—
766D4—1721no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—432no—
780C2×C4—432no—
781C2×C4—432no—
782C2×C4—432no—
783C2×C4—861no—
784C2×C4—861no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—861no—
791C2×C4—862no—
792C2×C4—1728no—
793C2×C4—1721no—
794C2×C4—1721no—
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—42no—
823C22—42no—
824C22—42no—
825C22—816no—
826C22—81no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—3441no—
835C22—3441no—
836C22—3441no—
837C22—3441no—
838C22—1722no—
839C22—1722no—
840C22—1722no—
841C22C2×C22⋊C4×D4311yescharacteristic
842C22#1458346411yescharacteristic
843C22#1458346411yescharacteristic
844C22#1458370011yescharacteristic
845C22#1458370311yescharacteristic
846C22#1458370511yescharacteristic
847C22#1458370911yescharacteristic
848C4—22no—
849C4—81no—
850C4—81no—
851C4—862no—
852C4—862no—
853C4—862no—
854C4—862no—
855C4—3441no—
856C4—3441no—
857C4—1722no—
858C4#1458337211yescharacteristic
859C4#1458337211yescharacteristic
860C4#1458346411yescharacteristic
861C4#1458346411yescharacteristic
862C2—42no—
863C2—82no—
864C2—82no—
865C2—3442no—
866C2#1913717611yescharacteristic
867C2#1914311611yescharacteristic
868C2#1914312011yescharacteristic
869C2#1914564111yescharacteristic
870C2#1914566311yescharacteristic
871C2#1914568511yescharacteristic
872C2#1914569311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radicalC2×#14583466C2
cosocleC22×C4×C43C24
hypercenter#1786D43
hypocenterC43#21813
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#14582957C2semidirect
3. #19137202C2semidirect
4. #19135526C2semidirect
5. #19135526C2semidirect
6. #19135520C2semidirect
7. #19135520C2semidirect
8. #19135417C2semidirect
9. #19135410C2semidirect
10. #19135405C2semidirect
11. #19135399C2semidirect
12. #19134536C2semidirect
13. #19134533C2semidirect
14. #19134526C2semidirect
15. C43×#1786C2semidirect
18. #14583466C4semidirect
29. C2×Dic43⋊C8C22semidirect
30. C2×Dic43⋊C8C22semidirect
31. C2×#13063250C22semidirect
32. C2×#13063250C22semidirect
33. C2×#13063248C22semidirect
34. C2×#13063248C22semidirect
35. C2×#13063247C22semidirect
36. C2×#13063247C22semidirect
41. C2×#13063245C22semidirect
42. C2×#13063245C22semidirect
44. C2×#13063235C22semidirect
45. C2×C8×Dic43C22semidirect
50. #14582768C22semidirect
51. #14582764C22semidirect
53. C4⋊C4×Dic43C22semidirect
54. C4⋊C4×Dic43C22semidirect
440. #1786D43semidirect
498. C43#21813semidirect

Maximal subgroups

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

subgroupindex
C2×#145834662
C2×#145829572
#191372022
#191355262
#191355202
#191354172
#191354102
#191354052
#191353992
#191345362
#191345332
#191345262
C43×#17862
#2181343