Finite Group Databasebeta

← #25112156

Subgroups — #25112156

Order 11008.

1598 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583537C211yesmaximal, characteristic
2C2×#14582967C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic, complemented
4C2×#14582895C211yesmaximal, characteristic, complemented
5#19137539C211yesmaximal, characteristic, complemented
6#19135524C211yesmaximal, characteristic, complemented
7#19135408C211yesmaximal, characteristic, complemented
8#19135025C211yesmaximal, characteristic, complemented
9#19135021C211yesmaximal, characteristic, complemented
10#19134915C211yesmaximal, characteristic, complemented
11#19134904C211yesmaximal, characteristic, complemented
12#19134593C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134422C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C23×C43⋊C8C2211yescharacteristic, complemented
19#14583537—24no—
20#14583537C418yescomplemented
21C2×#13063314C2211yescharacteristic
22C2×#13063308—21no—
23C2×#13063301C2211yescharacteristic
24C2×#13063299C2211yescharacteristic
25C2×#13063297—21no—
26C2×#13063293—21no—
27C2×D4×Dic43C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063284C2211yescharacteristic, complemented
30C2×#13063283C2211yescharacteristic
31C22×(C2×D43)⋊C4—21no—
32#14582967—24no—
33C2×Dic43⋊C8C2211yescharacteristic, complemented
34#14582902—24no—
35#14582895—24no—
36C2×#13063249C2211yescharacteristic, complemented
37C2×#13063249C2211yescharacteristic, complemented
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063246C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063245C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×#13063235C2211yescharacteristic, complemented
46#14582799—21no—
47#14582793—21no—
48#14582788—21no—
49#14582768C2211yescharacteristic, complemented
50#14582756C2211yescharacteristic
51C4⋊C4×Dic43C2211yescharacteristic, complemented
52#14582750—21no—
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C22×#41×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic, complemented
59C2×#103×C43C2211yescharacteristic, complemented
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic, complemented
63C43×#380C2211yescharacteristic, complemented
64C24×D43—21no—
65C22×D172C2311yescharacteristic
66C22×C22⋊D43—21no—
67C22×C22⋊D43—21no—
68C22×C22⋊D43D411yescharacteristic
69C2×D4×D43—22no—
70C2×D4×D43—22no—
71C2×D4×D43—22no—
72C2×D4×D43—41no—
73C2×D4×D43—41no—
74C2×D4×D43C2×C414yes—
75C23×Dic43—21no—
76C22×C4×D43C2311yescharacteristic
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—41no—
80C22×C43⋊C8—22no—
81C22×C43⋊C8—22no—
82C22×C43⋊C8—41no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85#13063314—22no—
86#13063314C2×C414yes—
87#13063308—28no—
88#13063301—22no—
89#13063301C2×C414yes—
90#13063299—22no—
91#13063299C2×C414yes—
92#13063297—28no—
93#13063293—28no—
94D4×Dic43—22no—
95D4×Dic43C2×C414yes—
96C4×C22⋊D43C2×C414yes—
97C4×C22⋊D43D414yes—
98#13063284—22no—
99#13063284—41no—
100#13063283—22no—
101#13063283—41no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×Dic43⋊C4—21no—
108C2×Dic43⋊C4D411yescharacteristic
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43D411yescharacteristic
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—28no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4D411yescharacteristic
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43—21no—
123C2×C4×Dic43C2311yescharacteristic
124Dic43⋊C8—22no—
125#13063249—22no—
126#13063249—22no—
127#13063247—22no—
128#13063247—41no—
129#13063246—22no—
130#13063246D414yescomplemented
131#13063245—22no—
132#13063245—41no—
133(C2×D43)⋊C8—22no—
134#13063235—22no—
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—41no—
154#103×C43—41no—
155#102×C43—22no—
156#102×C43—22no—
157C22⋊C8×C43—22no—
158#95×C43—21no—
159C24×C43—21no—
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C23×D43—24no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—81no—
168C23×D43—81no—
169C23×D43C2×D411yescharacteristic
170#41×C43—28no—
171#41×C43—44no—
172#41×C43—44no—
173#41×C43—44no—
174C2×Q8×C43—21no—
175C2×Q8×C43—21no—
176C2×Q8×C43—21no—
177C2×Q8×C43—21no—
178C2×Q8×C43—21no—
179C2×Q8×C43C22×C412yes—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—24no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43C22×C412yes—
187C2×D4×C43C2×D412yes—
188C2×D4×C43#4112yes—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—24no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43—42no—
198C22×C4×C43—42no—
199C22×C4×C43C22×C412yes—
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—41no—
206C2×C22⋊D43—41no—
207C2×C22⋊D43—42no—
208C2×C22⋊D43—42no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43—81no—
211C2×C22⋊D43C22⋊C414yes—
212C22×Dic43—24no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—81no—
217C22×Dic43—81no—
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221D4×D43—28no—
222D4×D43—44no—
223D4×D43—44no—
224D4×D43—44no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—21no—
230C2×D172C22×C412yes—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43C22×C412yes—
236C2×C4×D43C2×D412yes—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C22⋊C4×C43—81no—
248C22⋊Dic43—24no—
249C22⋊Dic43—42no—
250C22⋊Dic43C22⋊C414yes—
251(C2×D43)⋊C4—24no—
252(C2×D43)⋊C4—24no—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—42no—
256(C2×D43)⋊C4—81no—
257(C2×D43)⋊C4C22⋊C414yes—
258C4⋊Dic43—21no—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43C22×C412yes—
263C4⋊Dic43C2×D412yes—
264Dic43⋊C4—24no—
265Dic43⋊C4—42no—
266Dic43⋊C4—81no—
267Dic43⋊C4C22⋊C414yes—
268C4×Dic43—42no—
269C4×Dic43—42no—
270C4×Dic43—42no—
271C4×Dic43C22×C412yes—
272C4×Dic43C2×D412yes—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8—21no—
276C2×C43⋊C8—21no—
277C2×C43⋊C8—21no—
278C2×C43⋊C8—44no—
279C2×C43⋊C8C2×D412yes—
280#10621872—44no—
281C23×C43—22no—
282C23×C43—21no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
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—48no—
304C22×D43—48no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43—84no—
316C22×D43C2×C22⋊C412yes—
317Q8×C43—22no—
318Q8×C43—22no—
319Q8×C43—41no—
320Q8×C43—41no—
321D4×C43—22no—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—48no—
325D4×C43C4×D414yes—
326C2×C4×C43—21no—
327C2×C4×C43—21no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—48no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—41no—
342C2×C4×C43C2×C22⋊C412yes—
343C2×C4×C43C23×C411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C2×#4111yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C2×C4×C43H(5,𝔽2)11yescharacteristic
349C22⋊D43—44no—
350C22⋊D43—48no—
351C22⋊D43—84no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—21no—
357C2×Dic43—21no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—84no—
368C2×Dic43C2×C22⋊C412yes—
369C2×Dic43C2×C22⋊C412yes—
370C2×Dic43C2×C22⋊C412yes—
371D172—22no—
372D172—22no—
373D172—41no—
374D172—41no—
375C4×D43—22no—
376C4×D43—22no—
377C4×D43—22no—
378C4×D43—22no—
379C8×C43—41no—
380C8×C43—41no—
381C43⋊C8—22no—
382C43⋊C8—41no—
383#22424—431nomaximal, Sylow
384C22×C43—24no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—41no—
394C22×C43—42no—
395C22×C43—41no—
396C22×C43—42no—
397C22×C43—41no—
398C22×C43C22×C22⋊C411yescharacteristic
399C22×C43D4211yescharacteristic
400C22×C43#54611yescharacteristic
401C22×C43#57511yescharacteristic
402C22×C43#57511yescharacteristic
403C22×C43#57611yescharacteristic
404C22×C43#57711yescharacteristic
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—41no—
409C2×D43—41no—
410C2×D43—41no—
411C2×D43—41no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—816no—
416C2×D43—81no—
417C2×D43—81no—
418C2×D43—81no—
419C2×D43—81no—
420C4×C43—22no—
421C4×C43—42no—
422C4×C43—81no—
423C4×C43—81no—
424C4×C43C2×C4×D411yescharacteristic
425C4×C43#51811yescharacteristic
426C4×C43D4211yescharacteristic
427C4×C43#54611yescharacteristic
428Dic43—22no—
429Dic43—22no—
430Dic43—22no—
431Dic43—42no—
432Dic43—42no—
433Dic43—81no—
434C2×#546—431no—
435C2×#435—431no—
436C2×#418—431no—
437C2×#416—431no—
438#2354—431no—
439#1983—431no—
440#1959—431no—
441#1894—431no—
442#1893—431no—
443#1875—431no—
444#1873—431no—
445#1802—431no—
446#1788D4311yescharacteristic, complemented
447#1786—431no—
448#1762—431no—
449C2×C43—44no—
450C2×C43—42no—
451C2×C43D4×C22⋊C411yescharacteristic
452C2×C43#289611yescharacteristic
453C2×C43#289711yescharacteristic
454C2×C43#326711yescharacteristic
455C2×C43#326811yescharacteristic
456C2×C43#331111yescharacteristic
457C2×C43#331911yescharacteristic
458D43—42no—
459D43—82no—
460C22×#41C2×D4311yescharacteristic
461C23×D4—431no—
462C22×M16—431no—
463C23×C8—431no—
464#546—438no—
465#546—864no—
466C2×#124—431no—
467C2×#123—861no—
468C2×C22⋊Q8—431no—
469C2×#121—431no—
470C2×#121—861no—
471C2×#120—861no—
472C2×C4×D4—431no—
473C2×C4×D4—431no—
474C2×#117—431no—
475C2×#117—431no—
476C22×C22⋊C4—861no—
477#435—864no—
478C2×C4⋊C8—431no—
479#418—864no—
480#416—864no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103C2×D4311yescharacteristic, complemented
484C2×#103C2×D4311yescharacteristic, complemented
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102C2×D4311yescharacteristic
492C2×#102C2×D4311yescharacteristic
493C2×C22⋊C8—431no—
494C2×C22⋊C8C2×D4311yescharacteristic, complemented
495C2×#97—431no—
496#390—861no—
497#388—861no—
498#388—861no—
499#384—431no—
500#380—431no—
501#380C2×D4311yescharacteristic, complemented
502C4×C4⋊C4—431no—
503C4×C4⋊C4—861no—
504#340—431no—
505#340—431no—
506#340—431no—
507#340—431no—
508C43#2242411yescharacteristic, complemented, Sylow
509C25—861no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C4×D4314yes—
516C22×Q8C22×D4311yescharacteristic
517C22×D4—21no—
518C22×D4—431no—
519C22×D4—434no—
520C22×D4—431no—
521C22×D4—862no—
522C22×D4—861no—
523C22×D4—862no—
524C22×D4—862no—
525C22×D4—861no—
526C22×D4—1721no—
527C22×D4—1721no—
528C22×D4C22×D4311yescharacteristic
529C23×C4—21no—
530C23×C4—431no—
531C23×C4—861no—
532C23×C4C22×D4311yescharacteristic
533C2×M16—862no—
534C2×M16—862no—
535C2×M16—1721no—
536C22×C8—431no—
537C22×C8—431no—
538C22×C8—862no—
539C22×C8—862no—
540C22×C8—1721no—
541C22×C8C22×D4311yescharacteristic
542C22×C8C22×D4311yescharacteristic
543#124—434no—
544#124—862no—
545#123—868no—
546C22⋊Q8—434no—
547C22⋊Q8—862no—
548#121—434no—
549#121—868no—
550#121—862no—
551#120—868no—
552C4×D4—434no—
553C4×D4—434no—
554C4×D4—434no—
555C4×D4—862no—
556#117—862no—
557#117—862no—
558#117—1721no—
559#117—1721no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—431no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—868no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C42—431no—
582C2×C42—861no—
583C2×C42—861no—
584C2×C42—861no—
585C4⋊C8—862no—
586#103—41no—
587#103—41no—
588#103—862no—
589#103—862no—
590#102—22no—
591#102—22no—
592#102—434no—
593#102—862no—
594#102—862no—
595#102—862no—
596#102—1721no—
597#102—1721no—
598C22⋊C8—22no—
599C22⋊C8—862no—
600#97—862no—
601#95—21no—
602#95—861no—
603#95—861no—
604C24—21no—
605C24—431no—
606C24—864no—
607C24—861no—
608C24—3441no—
609C24—3441no—
610C24—1722no—
611C24—1722no—
612C24—1722no—
613C24—1722no—
614C24D4×D4311yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C2×C4×D4312yes—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—434no—
632C2×D4—432no—
633C2×D4—864no—
634C2×D4—868no—
635C2×D4—864no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—3441no—
642C2×D4—3441no—
643C2×D4—1724no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4—1721no—
647C2×D4—1721no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4C2×C4×D4312yes—
651C2×D4D4×D4312yes—
652C2×D4#1062190012yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—24no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—431no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—432no—
667C22×C4—432no—
668C22×C4—864no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—3441no—
677C22×C4—3441no—
678C22×C4C2×C4×D4312yes—
679C22×C4D4×D4311yescharacteristic
680C22×C4D4×D4312yes—
681C22×C4C23×D4311yescharacteristic
682M16—1724no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—432no—
690C2×C8—861no—
691C2×C8—861no—
692C2×C8—861no—
693C2×C8—861no—
694C2×C8—861no—
695C2×C8—1724no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—434no—
701C4⋊C4—432no—
702C4⋊C4—432no—
703C4⋊C4—864no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—3441no—
709C4⋊C4—1722no—
710C22⋊C4—81no—
711C22⋊C4—434no—
712C22⋊C4—434no—
713C22⋊C4—864no—
714C22⋊C4—864no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—3441no—
719C22⋊C4—1722no—
720C22⋊C4—1722no—
721C42—432no—
722C42—432no—
723C42—1722no—
724C42—1722no—
725C42—1722no—
726C23—22no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—22no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—432no—
740C23—861no—
741C23—861no—
742C23—861no—
743C23—861no—
744C23—861no—
745C23—861no—
746C23—862no—
747C23—3444no—
748C23—3444no—
749C23—3444no—
750C23—3444no—
751C23—3444no—
752C23—1728no—
753C23—1728no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23C22⋊C4×D4312yes—
761C23C2×D4×D4311yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—41no—
765Q8—41no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—48no—
770D4—862no—
771D4—862no—
772D4—3444no—
773D4—1724no—
774D4—1728no—
775D4—1721no—
776D4—1721no—
777D4(C22⋊D43)⋊C414yes—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—48no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—432no—
795C2×C4—432no—
796C2×C4—432no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—3444no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4C22⋊C4×D4312yes—
818C2×C4C22×C4×D4311yescharacteristic
819C2×C4C2×D4×D4311yescharacteristic
820C2×C4C2×D4×D4311yescharacteristic
821C2×C4C2×#1062190011yescharacteristic
822C2×C4#1306337011yescharacteristic
823C2×C4#1306337011yescharacteristic
824C8—41no—
825C8—41no—
826C8—862no—
827C8—1721no—
828C22—22no—
829C22—24no—
830C22—22no—
831C22—22no—
832C22—41no—
833C22—42no—
834C22—41no—
835C22—42no—
836C22—41no—
837C22—42no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—862no—
843C22—862no—
844C22—862no—
845C22—34416no—
846C22—3441no—
847C22—3441no—
848C22—3441no—
849C22—3441no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1721no—
854C22—1721no—
855C22—1721no—
856C22—1721no—
857C22C2×C22⋊C4×D4311yescharacteristic
858C22#1458353111yescharacteristic
859C22#1458353611yescharacteristic
860C22#1458369611yescharacteristic
861C22#1458369611yescharacteristic
862C22#1458370311yescharacteristic
863C22#1458370811yescharacteristic
864C4—22no—
865C4—42no—
866C4—81no—
867C4—81no—
868C4—862no—
869C4—862no—
870C4—862no—
871C4—3441no—
872C4—1722no—
873C4—1722no—
874C4C2×(C22⋊D43)⋊C411yescharacteristic
875C4#1458337211yescharacteristic
876C4#1458353111yescharacteristic
877C4#1458353611yescharacteristic
878C2—42no—
879C2—44no—
880C2—3442no—
881C2—1722no—
882C2#1913741111yescharacteristic
883C2#1914311011yescharacteristic
884C2#1914311911yescharacteristic
885C2#1914612411yescharacteristic
886C2#1914613911yescharacteristic
887C2#1914663511yescharacteristic
888C2#1914675511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC2×#14583537C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#22424
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×#14582967C2semidirect
3. C2×#14582902C2semidirect
4. C2×#14582895C2semidirect
5. #19137539C2semidirect
6. #19135524C2semidirect
7. #19135408C2semidirect
8. #19135025C2semidirect
9. #19135021C2semidirect
10. #19134915C2semidirect
11. #19134904C2semidirect
12. #19134593C2semidirect
13. #19134524C2semidirect
14. #19134422C2semidirect
15. C43×#1788C2semidirect
18. C23×C43⋊C8C22semidirect
20. #14583537C4semidirect
29. C2×#13063284C22semidirect
33. C2×Dic43⋊C8C22semidirect
36. C2×#13063249C22semidirect
37. C2×#13063249C22semidirect
45. C2×#13063235C22semidirect
49. #14582768C22semidirect
51. C4⋊C4×Dic43C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
58. C2×#103×C43C22semidirect
59. C2×#103×C43C22semidirect
62. C2×C22⋊C8×C43C22semidirect
63. C43×#380C22semidirect
130. #13063246D4semidirect
446. #1788D43semidirect
483. C2×#103C2×D43semidirect
484. C2×#103C2×D43semidirect
494. C2×C22⋊C8C2×D43semidirect
501. #380C2×D43semidirect
508. C43#22424semidirect

Maximal subgroups

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

subgroupindex
C2×#145835372
C2×#145829672
C2×#145829022
C2×#145828952
#191375392
#191355242
#191354082
#191350252
#191350212
#191349152
#191349042
#191345932
#191345242
#191344222
C43×#17882
#2242443