Finite Group Databasebeta

← #25112115

Subgroups — #25112115

Order 11008.

1530 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583568C211yesmaximal, characteristic
2C2×#14582973C211yesmaximal, characteristic, complemented
3C2×#14582900C211yesmaximal, characteristic, complemented
4C2×#14582894C211yesmaximal, characteristic, complemented
5#19137526C211yesmaximal, characteristic, complemented
6#19135520C211yesmaximal, characteristic, complemented
7#19135417C211yesmaximal, characteristic, complemented
8#19135031C211yesmaximal, characteristic, complemented
9#19135020C211yesmaximal, characteristic, complemented
10#19134914C211yesmaximal, characteristic, complemented
11#19134910C211yesmaximal, characteristic, complemented
12#19134608C211yesmaximal, characteristic, complemented
13#19134534C211yesmaximal, characteristic, complemented
14#19134427C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583568—24no—
20#14583568C418yescomplemented
21C2×#13063321—21no—
22C2×#13063321C2211yescharacteristic
23C2×#13063299—21no—
24C2×#13063299C2211yescharacteristic
25C2×#13063296—21no—
26C2×#13063296C2211yescharacteristic
27C2×Q8×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43—21no—
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×#13063283C2211yescharacteristic
31C22×C4⋊Dic43C2211yescharacteristic
32#14582973—24no—
33C2×Dic43⋊C8C2211yescharacteristic
34#14582900—24no—
35#14582894—24no—
36C2×#13063249C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×#13063235C2211yescharacteristic
46#14582791—21no—
47#14582786—21no—
48#14582776—21no—
49#14582764C2211yescharacteristic
50#14582756C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic
52C22⋊C4×Dic43—21no—
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57C22×#41×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902—41no—
68C2×#10621902—41no—
69C2×#10621902C2×C414yescomplemented
70C22×D172—21no—
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C22×C22⋊D43—21no—
76C22×C22⋊D43D411yescharacteristic
77C23×Dic43—21no—
78C22×C4×D43—21no—
79C22×C4×D43C2311yescharacteristic
80C2×#10621877—22no—
81C2×#10621877—22no—
82C2×#10621877—41no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C2×C8×D43—22no—
86C2×C8×D43—22no—
87C2×C8×D43—41no—
88#13063321—28no—
89#13063321—22no—
90#13063321C2×C414yescomplemented
91#13063299—22no—
92#13063299—28no—
93#13063299C2×C414yes—
94#13063296—22no—
95#13063296—28no—
96#13063296C2×C414yescomplemented
97Q8×Dic43—22no—
98Q8×Dic43C2×C414yescomplemented
99C4×C22⋊D43—28no—
100C4×C22⋊D43C2×C414yes—
101C4×C22⋊D43D414yes—
102#13063283—22no—
103#13063283—41no—
104C2×C4⋊Dic43—21no—
105C2×C4⋊Dic43—22no—
106C2×C4⋊Dic43—21no—
107C2×C4⋊Dic43—41no—
108C2×C4⋊Dic43C2311yescharacteristic
109C2×C4⋊Dic43C2311yescharacteristic
110C2×C4⋊Dic43C2311yescharacteristic
111C2×Dic43⋊C4D411yescharacteristic
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43D411yescharacteristic
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4D411yescharacteristic
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43C2311yescharacteristic
122Dic43⋊C8—22no—
123#13063249—22no—
124#13063249D414yescomplemented
125#13063247—22no—
126#13063247—41no—
127#13063246—22no—
128#13063246—22no—
129#13063245—22no—
130#13063245—41no—
131(C2×D43)⋊C8—22no—
132#13063235—22no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C43⋊#95—21no—
137C2×#41×C43—22no—
138C2×#41×C43—22no—
139C2×#41×C43—22no—
140C2×#41×C43—41no—
141C2×#41×C43—41no—
142C2×#41×C43C2×C414yes—
143C22×Q8×C43C2311yescharacteristic
144C22×D4×C43—21no—
145C22×D4×C43C2311yescharacteristic
146C23×C4×C43—21no—
147C23×C4×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C22⋊C4×C43—21no—
153#103×C43—22no—
154#103×C43—22no—
155#102×C43—41no—
156#102×C43—41no—
157C22⋊C8×C43—22no—
158#95×C43—21no—
159C24×C43—21no—
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C23×D43C2×D411yescharacteristic
163#41×C43—28no—
164#41×C43—44no—
165#41×C43—44no—
166#41×C43—44no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43C22×C412yes—
171C2×Q8×C43C2×D412yes—
172C2×Q8×C43#4112yes—
173C2×D4×C43—21no—
174C2×D4×C43—24no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—42no—
180C2×D4×C43—42no—
181C2×D4×C43C22×C412yes—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—24no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
192C22×C4×C43C22×C412yes—
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2411yescharacteristic
196C2×C22⋊D43—24no—
197C2×C22⋊D43—24no—
198C2×C22⋊D43—24no—
199C2×C22⋊D43—24no—
200C2×C22⋊D43—41no—
201C2×C22⋊D43—41no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—81no—
205C2×C22⋊D43—81no—
206C2×C22⋊D43—81no—
207C2×C22⋊D43—81no—
208C2×C22⋊D43—81no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43C22⋊C414yes—
211C22×Dic43—21no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—42no—
215C22×Dic43—42no—
216C22×Dic43—81no—
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220#10621902—28no—
221#10621902—44no—
222#10621902—44no—
223#10621902—44no—
224C2×D172—21no—
225C2×D172—24no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—21no—
230C2×D172—42no—
231C2×D172—42no—
232C2×D172C22×C412yes—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—24no—
238C2×C4×D43—42no—
239C2×C4×D43—42no—
240C2×C4×D43C22×C412yes—
241C2×C4×D43C2×D412yes—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C22⋊C4×C43—42no—
253C22⋊Dic43—24no—
254C22⋊Dic43C22⋊C414yes—
255(C2×D43)⋊C4—24no—
256(C2×D43)⋊C4—42no—
257(C2×D43)⋊C4—81no—
258(C2×D43)⋊C4C22⋊C414yes—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—24no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—42no—
265C4⋊Dic43C22×C412yes—
266C4⋊Dic43C2×D412yes—
267Dic43⋊C4C22⋊C414yes—
268C4×Dic43—24no—
269C4×Dic43—42no—
270C4×Dic43—81no—
271C4×Dic43C22×C412yes—
272C4×Dic43C2×D412yes—
273#10621877—44no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—21no—
279C2×C43⋊C8C2×D412yes—
280C8×D43—44no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—22no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43C2×C22⋊C412yes—
295C23×C43C22×D411yescharacteristic
296C22×D43—21no—
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—21no—
300C22×D43—21no—
301C22×D43—21no—
302C22×D43—22no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43C2×C22⋊C412yes—
310Q8×C43—22no—
311Q8×C43—22no—
312Q8×C43—22no—
313Q8×C43C4×D414yes—
314D4×C43—22no—
315D4×C43—22no—
316D4×C43—48no—
317D4×C43—41no—
318D4×C43—41no—
319C2×C4×C43—22no—
320C2×C4×C43—21no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—48no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43C2×C22⋊C412yes—
336C2×C4×C43C23×C411yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C2×#4111yescharacteristic
340C2×C4×C43H(5,𝔽2)11yescharacteristic
341C2×C4×C43H(5,𝔽2)11yescharacteristic
342C22⋊D43—44no—
343C22⋊D43—48no—
344C22⋊D43—84no—
345C22⋊D43—84no—
346C22⋊D43—84no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—84no—
363C2×Dic43C2×C22⋊C412yes—
364C2×Dic43C2×C22⋊C412yes—
365C2×Dic43C2×C22⋊C412yes—
366D172—22no—
367D172—22no—
368D172—48no—
369D172—41no—
370D172—41no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—22no—
374C4×D43—22no—
375C4×D43—48no—
376C8×C43—41no—
377C8×C43—41no—
378C43⋊C8—22no—
379C43⋊C8—41no—
380#22422—431nomaximal, Sylow
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43C22×C22⋊C411yescharacteristic
396C22×C43D4211yescharacteristic
397C22×C43#54611yescharacteristic
398C22×C43#57511yescharacteristic
399C22×C43#57511yescharacteristic
400C22×C43#57611yescharacteristic
401C22×C43#57711yescharacteristic
402C2×D43—22no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—41no—
406C2×D43—41no—
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—81no—
413C2×D43—81no—
414C2×D43—81no—
415C2×D43—81no—
416C4×C43—24no—
417C4×C43—22no—
418C4×C43—81no—
419C4×C43—81no—
420C4×C43C2×C4×D411yescharacteristic
421C4×C43#51811yescharacteristic
422C4×C43D4211yescharacteristic
423C4×C43#54611yescharacteristic
424Dic43—22no—
425Dic43—22no—
426Dic43—22no—
427Dic43—42no—
428Dic43—42no—
429Dic43—81no—
430C2×#550—431no—
431C2×#435—431no—
432C2×#417—431no—
433C2×#416—431no—
434#2352—431no—
435#1982—431no—
436#1961—431no—
437#1895—431no—
438#1893—431no—
439#1875—431no—
440#1874—431no—
441#1805—431no—
442#1788—431no—
443#1788D4311yescharacteristic, complemented
444#1763—431no—
445C2×C43—42no—
446C2×C43—82no—
447C2×C43D4×C22⋊C411yescharacteristic
448C2×C43#289611yescharacteristic
449C2×C43#289711yescharacteristic
450C2×C43#326811yescharacteristic
451C2×C43#327111yescharacteristic
452C2×C43#330911yescharacteristic
453C2×C43#331711yescharacteristic
454D43—42no—
455D43—82no—
456C22×#41—431no—
457C22×#41C2×D4311yescharacteristic
458C22×M16—431no—
459C23×C8—431no—
460#550—438no—
461#550—864no—
462C2×#127—431no—
463C2×#127—861no—
464C2×#121—431no—
465C2×#121—431no—
466C2×#121—861no—
467C2×#121—861no—
468C2×C4×Q8—431no—
469C2×C4×D4—431no—
470C2×C4×D4—861no—
471C2×#117—431no—
472C22×C4⋊C4—431no—
473#435—864no—
474C2×C4⋊C8—431no—
475#417—864no—
476#416—864no—
477C2×#103—431no—
478C2×#103—431no—
479C2×#103C2×D4311yescharacteristic
480C2×#103C2×D4311yescharacteristic
481C2×#102—431no—
482C2×#102—431no—
483C2×#102—431no—
484C2×#102—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102C2×D4311yescharacteristic
488C2×#102C2×D4311yescharacteristic
489C2×C22⋊C8—431no—
490C2×C22⋊C8C2×D4311yescharacteristic
491C2×#97—431no—
492#388—861no—
493#387—861no—
494#386—861no—
495#382—431no—
496#380—431no—
497#380C2×D4311yescharacteristic
498C4×C4⋊C4—431no—
499C4×C22⋊C4—861no—
500#340—431no—
501#340—431no—
502#340—431no—
503#340—431no—
504C43#2242211yescharacteristic, complemented, Sylow
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—22no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—434no—
511C2×#41—862no—
512C2×#41—862no—
513C2×#41—862no—
514C2×#41—1721no—
515C2×#41—1721no—
516C2×#41C4×D4314yes—
517C22×Q8C22×D4311yescharacteristic
518C22×D4—21no—
519C22×D4—431no—
520C22×D4—431no—
521C22×D4—861no—
522C22×D4—861no—
523C22×D4—861no—
524C22×D4—861no—
525C22×D4—861no—
526C22×D4C22×D4311yescharacteristic
527C23×C4—21no—
528C23×C4—431no—
529C23×C4—861no—
530C23×C4—861no—
531C23×C4C22×D4311yescharacteristic
532C2×M16—862no—
533C2×M16—862no—
534C2×M16—1721no—
535C22×C8—431no—
536C22×C8—431no—
537C22×C8—862no—
538C22×C8—862no—
539C22×C8—1721no—
540C22×C8C22×D4311yescharacteristic
541C22×C8C22×D4311yescharacteristic
542#127—434no—
543#127—862no—
544#127—868no—
545#121—434no—
546#121—434no—
547#121—868no—
548#121—868no—
549#121—862no—
550#121—862no—
551C4×Q8—434no—
552C4×Q8—862no—
553C4×D4—434no—
554C4×D4—434no—
555C4×D4—868no—
556#117—862no—
557#117—1721no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—431no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—862no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—1721no—
566C2×C4⋊C4C22×D4311yescharacteristic
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C22⋊C4—21no—
569C2×C22⋊C4—431no—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C42—431no—
576C2×C42—861no—
577C2×C42—861no—
578C2×C42—861no—
579C4⋊C8—862no—
580#103—22no—
581#103—22no—
582#103—434no—
583#103—862no—
584#102—41no—
585#102—41no—
586#102—862no—
587#102—862no—
588#102—862no—
589#102—862no—
590#102—1721no—
591#102—1721no—
592C22⋊C8—22no—
593C22⋊C8—862no—
594#97—862no—
595#95—21no—
596#95—861no—
597#95—861no—
598#95—861no—
599#95—861no—
600C24—21no—
601C24—431no—
602C24—861no—
603C24D4×D4311yescharacteristic
604#41—28no—
605#41—44no—
606#41—44no—
607#41—44no—
608#41—868no—
609#41—1724no—
610#41—1724no—
611#41—1724no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8C2×C4×D4312yes—
616C2×Q8D4×D4312yes—
617C2×Q8#1062190012yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—434no—
627C2×D4—432no—
628C2×D4—864no—
629C2×D4—864no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—861no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—3441no—
639C2×D4—3441no—
640C2×D4—3441no—
641C2×D4—3441no—
642C2×D4—3441no—
643C2×D4—3441no—
644C2×D4—1722no—
645C2×D4—1722no—
646C2×D4—1721no—
647C2×D4—1721no—
648C2×D4—1722no—
649C2×D4—1722no—
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—432no—
665C22×C4—432no—
666C22×C4—864no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—3441no—
675C22×C4—1722no—
676C22×C4—1722no—
677C22×C4—1722no—
678C22×C4—1722no—
679C22×C4C2×C4×D4312yes—
680C22×C4D4×D4311yescharacteristic
681C22×C4D4×D4312yes—
682C22×C4C23×D4311yescharacteristic
683M16—1724no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—432no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—861no—
696C2×C8—1724no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—434no—
702C4⋊C4—432no—
703C4⋊C4—432no—
704C4⋊C4—864no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—1722no—
710C22⋊C4—42no—
711C22⋊C4—434no—
712C22⋊C4—434no—
713C22⋊C4—864no—
714C22⋊C4—864no—
715C22⋊C4—3441no—
716C22⋊C4—1722no—
717C42—432no—
718C42—432no—
719C42—864no—
720C42—3441no—
721C42—1722no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—432no—
736C23—861no—
737C23—861no—
738C23—861no—
739C23—861no—
740C23—861no—
741C23—861no—
742C23—862no—
743C23—1721no—
744C23—1721no—
745C23—1721no—
746C23—1721no—
747C23—1721no—
748C23—1721no—
749C23C22⋊C4×D4312yes—
750C23C2×D4×D4311yescharacteristic
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8(C22⋊D43)⋊C414yes—
755D4—22no—
756D4—22no—
757D4—48no—
758D4—41no—
759D4—41no—
760D4—862no—
761D4—862no—
762D4—3444no—
763D4—3444no—
764D4—3444no—
765D4—1728no—
766D4—1724no—
767D4—1728no—
768D4—1721no—
769D4—1721no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—48no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—432no—
787C2×C4—432no—
788C2×C4—432no—
789C2×C4—861no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—861no—
793C2×C4—861no—
794C2×C4—861no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—862no—
798C2×C4—862no—
799C2×C4—862no—
800C2×C4—862no—
801C2×C4—3444no—
802C2×C4—1728no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4C22⋊C4×D4312yes—
811C2×C4C22×C4×D4311yescharacteristic
812C2×C4C2×D4×D4311yescharacteristic
813C2×C4C2×D4×D4311yescharacteristic
814C2×C4C2×#1062190011yescharacteristic
815C2×C4#1306337011yescharacteristic
816C2×C4#1306337011yescharacteristic
817C8—41no—
818C8—41no—
819C8—862no—
820C8—1721no—
821C22—22no—
822C22—22no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—862no—
836C22—862no—
837C22—862no—
838C22—3441no—
839C22—3441no—
840C22—3441no—
841C22—3441no—
842C22—1722no—
843C22—1722no—
844C22—1722no—
845C22—1721no—
846C22—1721no—
847C22—1721no—
848C22—1721no—
849C22C2×C22⋊C4×D4311yescharacteristic
850C22#1458353111yescharacteristic
851C22#1458353611yescharacteristic
852C22#1458369511yescharacteristic
853C22#1458369811yescharacteristic
854C22#1458370111yescharacteristic
855C22#1458370611yescharacteristic
856C4—22no—
857C4—24no—
858C4—81no—
859C4—81no—
860C4—862no—
861C4—862no—
862C4—862no—
863C4—3441no—
864C4—1722no—
865C4—1722no—
866C4C2×(C22⋊D43)⋊C411yescharacteristic
867C4#1458337211yescharacteristic
868C4#1458353111yescharacteristic
869C4#1458353611yescharacteristic
870C2—42no—
871C2—82no—
872C2—3442no—
873C2—1722no—
874C2#1913741111yescharacteristic
875C2#1914311111yescharacteristic
876C2#1914311711yescharacteristic
877C2#1914613811yescharacteristic
878C2#1914617811yescharacteristic
879C2#1914659411yescharacteristic
880C2#1914671411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583568C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#22422
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×#14582973C2semidirect
3. C2×#14582900C2semidirect
4. C2×#14582894C2semidirect
5. #19137526C2semidirect
6. #19135520C2semidirect
7. #19135417C2semidirect
8. #19135031C2semidirect
9. #19135020C2semidirect
10. #19134914C2semidirect
11. #19134910C2semidirect
12. #19134608C2semidirect
13. #19134534C2semidirect
14. #19134427C2semidirect
15. C43×#1788C2semidirect
20. #14583568C4semidirect
69. C2×#10621902C2×C4semidirect
90. #13063321C2×C4semidirect
96. #13063296C2×C4semidirect
98. Q8×Dic43C2×C4semidirect
124. #13063249D4semidirect
443. #1788D43semidirect
504. C43#22422semidirect

Maximal subgroups

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

subgroupindex
C2×#145835682
C2×#145829732
C2×#145829002
C2×#145828942
#191375262
#191355202
#191354172
#191350312
#191350202
#191349142
#191349102
#191346082
#191345342
#191344272
C43×#17882
#2242243