Finite Group Databasebeta

← #25112150

Subgroups — #25112150

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×#14583546C211yesmaximal, characteristic
2C2×#14582967C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic, complemented
4C2×#14582893C211yesmaximal, characteristic, complemented
5#19137545C211yesmaximal, characteristic, complemented
6#19135526C211yesmaximal, characteristic, complemented
7#19135410C211yesmaximal, characteristic, complemented
8#19135027C211yesmaximal, characteristic, complemented
9#19135024C211yesmaximal, characteristic, complemented
10#19134906C211yesmaximal, characteristic, complemented
11#19134594C211yesmaximal, characteristic, complemented
12#19134536C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134419C211yesmaximal, characteristic, complemented
15C43×#1875C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic, complemented
20#14583546—24no—
21#14583546C418yescomplemented
22C2×#13063312C2211yescharacteristic
23C2×#13063307—21no—
24C2×#13063305C2211yescharacteristic
25C2×#13063296—21no—
26C2×#13063293—21no—
27C2×#13063287C2211yescharacteristic
28C2×C4×C22⋊D43C2211yescharacteristic
29C2×#13063283C2211yescharacteristic
30C2×C22⋊C4×D43—21no—
31#14582967—24no—
32C2×Dic43⋊C8C2211yescharacteristic, complemented
33#14582902—24no—
34#14582893—24no—
35C2×#13063250C2211yescharacteristic, complemented
36C2×#13063250C2211yescharacteristic, complemented
37C2×#13063248C2211yescharacteristic, complemented
38C2×#13063248C2211yescharacteristic, complemented
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063246C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×#13063245C2211yescharacteristic
44C2×#13063245C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×#13063235C2211yescharacteristic, complemented
47#14582799—21no—
48#14582790—21no—
49#14582787—21no—
50#14582768C2211yescharacteristic, complemented
51#14582759C2211yescharacteristic, complemented
52#14582756C2211yescharacteristic
53C4⋊C4×Dic43C2211yescharacteristic, complemented
54C4×Dic43⋊C4—21no—
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C2×#121×C43C2211yescharacteristic
58C2×#117×C43C2211yescharacteristic, complemented
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C43×#340C2211yescharacteristic, complemented
64C24×D43—21no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—22no—
68C2×#10621898—41no—
69C2×#10621898—41no—
70C2×#10621898C2×C414yes—
71C22×Dic86C2311yescharacteristic
72C22×D172C2311yescharacteristic
73C22×C22⋊D43—21no—
74C22×C22⋊D43—21no—
75C22×C22⋊D43D411yescharacteristic
76C2×D4×D43—22no—
77C2×D4×D43—22no—
78C2×D4×D43—22no—
79C2×D4×D43—41no—
80C2×D4×D43—41no—
81C2×D4×D43C2×C414yes—
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C2×#10621872—22no—
86C2×#10621872—22no—
87C2×#10621872—41no—
88C22×C43⋊C8—22no—
89C22×C43⋊C8—22no—
90C22×C43⋊C8—41no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93#13063312—22no—
94#13063312C2×C414yes—
95#13063307—28no—
96#13063305—22no—
97#13063305C2×C414yes—
98#13063296—28no—
99#13063293—28no—
100#13063287—22no—
101#13063287C2×C414yes—
102C4×C22⋊D43C2×C414yes—
103C4×C22⋊D43D414yes—
104#13063283—22no—
105#13063283—41no—
106C2×C4⋊Dic43—21no—
107C2×C4⋊Dic43C2311yescharacteristic
108C2×C4⋊Dic43C2311yescharacteristic
109C2×Dic43⋊C4—21no—
110C2×Dic43⋊C4—21no—
111C2×Dic43⋊C4D411yescharacteristic
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—21no—
114C2×C22⋊Dic43—21no—
115C2×C22⋊Dic43D411yescharacteristic
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×(C2×D43)⋊C4D411yescharacteristic
121C22⋊C4×D43—28no—
122C2×C4×Dic43—21no—
123C2×C4×Dic43—21no—
124C2×C4×Dic43C2311yescharacteristic
125Dic43⋊C8—22no—
126#13063250—41no—
127#13063250—41no—
128#13063248—22no—
129#13063248—22no—
130#13063247—22no—
131#13063247—22no—
132#13063246—22no—
133#13063246—41no—
134#13063245—22no—
135#13063245D414yescomplemented
136(C2×D43)⋊C8—22no—
137#13063235—22no—
138C43⋊#95—21no—
139C43⋊#95—21no—
140C43⋊#95—21no—
141C22×D4×C43—21no—
142C22×D4×C43C2311yescharacteristic
143C23×C4×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146#121×C43—22no—
147#121×C43C2×C414yes—
148#117×C43—22no—
149#117×C43—41no—
150C2×C4⋊C4×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154C2×C22⋊C4×C43—21no—
155C2×C42×C43—21no—
156#102×C43—22no—
157#102×C43—41no—
158C22⋊C8×C43—22no—
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
170C2×D4×C43—21no—
171C2×D4×C43—24no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—81no—
177C2×D4×C43—81no—
178C2×D4×C43C22×C412yes—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43C22×C412yes—
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—24no—
191C2×C22⋊D43—24no—
192C2×C22⋊D43—41no—
193C2×C22⋊D43—41no—
194C2×C22⋊D43—42no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43C22⋊C414yes—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43C2×D411yescharacteristic
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205D4×D43—28no—
206D4×D43—44no—
207D4×D43—44no—
208D4×D43—44no—
209#10621898—28no—
210#10621898—44no—
211#10621898—44no—
212#10621898—44no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172C22×C412yes—
217C2×D172C2×D412yes—
218C2×D172#4112yes—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—24no—
224C2×C4×D43—24no—
225C2×C4×D43—42no—
226C2×C4×D43—42no—
227C2×C4×D43—81no—
228C2×C4×D43—81no—
229C2×C4×D43C22×C412yes—
230C2×C4×D43C2×D412yes—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86C22×C412yes—
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—
247C4⋊C4×C43C22×C412yes—
248C4⋊C4×C43C2×D412yes—
249C22⋊C4×C43—24no—
250C22⋊C4×C43—42no—
251C42×C43—42no—
252C22⋊Dic43—24no—
253C22⋊Dic43—24no—
254C22⋊Dic43—81no—
255C22⋊Dic43C22⋊C414yes—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—42no—
259(C2×D43)⋊C4—81no—
260(C2×D43)⋊C4C22⋊C414yes—
261C4⋊Dic43—24no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266Dic43⋊C4—42no—
267Dic43⋊C4—81no—
268Dic43⋊C4C22⋊C414yes—
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—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—22no—
297C22×D43—21no—
298C22×D43—22no—
299C22×D43—21no—
300C22×D43—22no—
301C22×D43—21no—
302C22×D43—21no—
303C22×D43—21no—
304C22×D43—21no—
305C22×D43—48no—
306C22×D43—48no—
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—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—41no—
320D4×C43—41no—
321D4×C43—84no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43C2×C22⋊C412yes—
338C2×C4×C43C23×C411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C2×#4111yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C2×C4×C43H(5,𝔽2)11yescharacteristic
344C22⋊D43—44no—
345C22⋊D43—48no—
346C22⋊D43—48no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—22no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43C2×C22⋊C412yes—
363C2×Dic43C2×C22⋊C412yes—
364C2×Dic43C2×C22⋊C412yes—
365D172—22no—
366D172—22no—
367D172—22no—
368D172C4×D414yes—
369C4×D43—22no—
370C4×D43—22no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—48no—
374C4×D43—84no—
375Dic86—22no—
376Dic86—22no—
377Dic86—41no—
378Dic86—41no—
379C8×C43—41no—
380C8×C43—41no—
381C43⋊C8—22no—
382C43⋊C8—41no—
383#22424—431nomaximal, Sylow
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—81no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43C22×C22⋊C411yescharacteristic
399C22×C43D4211yescharacteristic
400C22×C43#54611yescharacteristic
401C22×C43#57511yescharacteristic
402C22×C43#57511yescharacteristic
403C22×C43#57611yescharacteristic
404C22×C43#57711yescharacteristic
405C2×D43—24no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—41no—
412C2×D43—42no—
413C2×D43—41no—
414C2×D43—42no—
415C2×D43—41no—
416C2×D43—42no—
417C2×D43—41no—
418C2×D43—42no—
419C2×D43—816no—
420C4×C43—22no—
421C4×C43—42no—
422C4×C43—42no—
423C4×C43—81no—
424C4×C43C2×C4×D411yescharacteristic
425C4×C43#51811yescharacteristic
426C4×C43D4211yescharacteristic
427C4×C43#54611yescharacteristic
428Dic43—22no—
429Dic43—22no—
430Dic43—22no—
431Dic43—42no—
432Dic43—81no—
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#1875D4311yescharacteristic, complemented
444#1873—431no—
445#1802—431no—
446#1788—431no—
447#1786—431no—
448#1762—431no—
449C2×C43—42no—
450C2×C43—82no—
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—44no—
460C22×#41—431no—
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—861no—
470C2×#121C2×D4311yescharacteristic
471C2×#120—861no—
472C2×C4×D4—431no—
473C2×C4×D4—431no—
474C2×#117—431no—
475C2×#117C2×D4311yescharacteristic, complemented
476C22×C22⋊C4—861no—
477#435—864no—
478C2×C4⋊C8—431no—
479#418—864no—
480#416—864no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
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#380—431no—
502C4×C4⋊C4—431no—
503C4×C4⋊C4—861no—
504#340—431no—
505#340—431no—
506#340C2×D4311yescharacteristic, complemented
507#340C2×D4311yescharacteristic, complemented
508C43#2242411yescharacteristic, complemented, Sylow
509C25—861no—
510C2×#41—434no—
511C2×#41—862no—
512C2×#41—862no—
513C2×#41—862no—
514C2×#41—1721no—
515C2×#41—1721no—
516C22×Q8—431no—
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—431no—
530C23×C4—861no—
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—22no—
549#121—868no—
550#121C4×D4314yes—
551#120—868no—
552C4×D4—434no—
553C4×D4—434no—
554C4×D4—434no—
555C4×D4—862no—
556#117—22no—
557#117—41no—
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—431no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4—861no—
564C2×C4⋊C4—861no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4C22×D4311yescharacteristic
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—431no—
572C2×C22⋊C4—431no—
573C2×C22⋊C4—868no—
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—21no—
582C2×C42—431no—
583C2×C42—861no—
584C2×C42—861no—
585C4⋊C8—862no—
586#103—862no—
587#103—862no—
588#103—1721no—
589#103—1721no—
590#102—22no—
591#102—41no—
592#102—434no—
593#102—862no—
594#102—862no—
595#102—862no—
596#102—862no—
597#102—1721no—
598C22⋊C8—22no—
599C22⋊C8—862no—
600#97—862no—
601#95—861no—
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—868no—
616#41—1724no—
617#41—1724no—
618#41—1724no—
619C2×Q8—432no—
620C2×Q8—861no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—81no—
632C2×D4—81no—
633C2×D4—434no—
634C2×D4—432no—
635C2×D4—432no—
636C2×D4—432no—
637C2×D4—864no—
638C2×D4—868no—
639C2×D4—864no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—1724no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4—1721no—
647C2×D4—1721no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4—1722no—
651C2×D4—1722no—
652C2×D4C2×C4×D4312yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—864no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—861no—
670C22×C4—861no—
671C22×C4—864no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—3441no—
675C22×C4—3441no—
676C22×C4—1722no—
677C22×C4—1722no—
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—864no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—3441no—
707C4⋊C4—1722no—
708C4⋊C4C2×C4×D4312yes—
709C4⋊C4D4×D4312yes—
710C22⋊C4—24no—
711C22⋊C4—42no—
712C22⋊C4—434no—
713C22⋊C4—434no—
714C22⋊C4—864no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—3441no—
719C22⋊C4—3441no—
720C22⋊C4—1722no—
721C42—42no—
722C42—432no—
723C42—432no—
724C42—1722no—
725C42—1722no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—432no—
740C23—862no—
741C23—861no—
742C23—861no—
743C23—861no—
744C23—861no—
745C23—861no—
746C23—862no—
747C23—861no—
748C23—862no—
749C23—3444no—
750C23—3444no—
751C23—3444no—
752C23—3444no—
753C23—3444no—
754C23—1728no—
755C23—1728no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23C22⋊C4×D4312yes—
761C23C2×D4×D4311yescharacteristic
762Q8—862no—
763Q8—862no—
764Q8—1721no—
765Q8—1721no—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—41no—
770D4—84no—
771D4—434no—
772D4—862no—
773D4—862no—
774D4—862no—
775D4—1724no—
776D4—1728no—
777D4—1728no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—432no—
794C2×C4—432no—
795C2×C4—432no—
796C2×C4—861no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—3444no—
808C2×C4—1728no—
809C2×C4—1721no—
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×C4#41×D4311yescharacteristic
822C2×C4#1306337011yescharacteristic
823C2×C4#1306337111yescharacteristic
824C8—41no—
825C8—41no—
826C8—862no—
827C8—1721no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22—81no—
842C22—862no—
843C22—864no—
844C22—862no—
845C22—862no—
846C22—34416no—
847C22—1721no—
848C22—1722no—
849C22—1721no—
850C22—1722no—
851C22—1721no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1721no—
856C22—1722no—
857C22C2×C22⋊C4×D4311yescharacteristic
858C22#1458353111yescharacteristic
859C22#1458354111yescharacteristic
860C22#1458369611yescharacteristic
861C22#1458369611yescharacteristic
862C22#1458370311yescharacteristic
863C22#1458370911yescharacteristic
864C4—22no—
865C4—42no—
866C4—42no—
867C4—81no—
868C4—862no—
869C4—862no—
870C4—862no—
871C4—3441no—
872C4—3441no—
873C4—1722no—
874C4C4×D4×D4311yescharacteristic
875C4#1458337111yescharacteristic
876C4#1458353311yescharacteristic
877C4#1458353811yescharacteristic
878C2—42no—
879C2—82no—
880C2—1722no—
881C2—1724no—
882C2#1913741311yescharacteristic
883C2#1914311011yescharacteristic
884C2#1914312011yescharacteristic
885C2#1914611311yescharacteristic
886C2#1914612811yescharacteristic
887C2#1914662911yescharacteristic
888C2#1914674911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1875C2
socleC23×C43C22×D4
prime radicalC2×#14583546C2
cosocleC22×C4×C43C24
hypercenter#1875D43
hypocenterC43#22424
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1875

Complements

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

NH ≅ G/Ntype
2. C2×#14582967C2semidirect
3. C2×#14582902C2semidirect
4. C2×#14582893C2semidirect
5. #19137545C2semidirect
6. #19135526C2semidirect
7. #19135410C2semidirect
8. #19135027C2semidirect
9. #19135024C2semidirect
10. #19134906C2semidirect
11. #19134594C2semidirect
12. #19134536C2semidirect
13. #19134524C2semidirect
14. #19134419C2semidirect
15. C43×#1875C2semidirect
19. C23×C43⋊C8C22semidirect
21. #14583546C4semidirect
32. C2×Dic43⋊C8C22semidirect
35. C2×#13063250C22semidirect
36. C2×#13063250C22semidirect
37. C2×#13063248C22semidirect
38. C2×#13063248C22semidirect
46. C2×#13063235C22semidirect
50. #14582768C22semidirect
51. #14582759C22semidirect
53. C4⋊C4×Dic43C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
58. C2×#117×C43C22semidirect
61. C2×C22⋊C8×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
135. #13063245D4semidirect
443. #1875D43semidirect
475. C2×#117C2×D43semidirect
494. C2×C22⋊C8C2×D43semidirect
506. #340C2×D43semidirect
507. #340C2×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×#145835462
C2×#145829672
C2×#145829022
C2×#145828932
#191375452
#191355262
#191354102
#191350272
#191350242
#191349062
#191345942
#191345362
#191345242
#191344192
C43×#18752
#2242443