Finite Group Databasebeta

← #25112154

Subgroups — #25112154

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×#14583545C211yesmaximal, characteristic
2C2×#14582905C211yesmaximal, characteristic, complemented
3C2×#14582896C211yesmaximal, characteristic, complemented
4#19137544C211yesmaximal, characteristic, complemented
5#19135525C211yesmaximal, characteristic, complemented
6#19135411C211yesmaximal, characteristic, complemented
7#19135028C211yesmaximal, characteristic, complemented
8#19135023C211yesmaximal, characteristic, complemented
9#19134915C211yesmaximal, characteristic, complemented
10#19134905C211yesmaximal, characteristic, complemented
11#19134596C211yesmaximal, characteristic, complemented
12#19134536C211yesmaximal, characteristic, complemented
13#19134527C211yesmaximal, characteristic, complemented
14#19134421C211yesmaximal, characteristic, complemented
15C2×C43×#435C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C23×D172C2211yescharacteristic
18#14583545—24no—
19#14583545C418yescomplemented
20C2×#13063313C2211yescharacteristic
21C2×#13063310—21no—
22C2×#13063304C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063298—21no—
25C2×#13063293—21no—
26C2×C4×D172C2211yescharacteristic
27C2×#13063284C2211yescharacteristic
28C2×#13063284C2211yescharacteristic, complemented
29C2×C22⋊C4×D43—21no—
30#14582905—24no—
31#14582896—24no—
32C2×#13063250C2211yescharacteristic, complemented
33C2×#13063250C2211yescharacteristic, complemented
34C2×#13063250C2211yescharacteristic, complemented
35C2×#13063250C2211yescharacteristic, complemented
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063247C2211yescharacteristic
39C2×#13063247C2211yescharacteristic
40C2×#13063247C2211yescharacteristic
41C2×#13063247C2211yescharacteristic
42C2×#13063247C2211yescharacteristic
43C2×#13063247C2211yescharacteristic
44#14582802—21no—
45#14582792—21no—
46#14582792—21no—
47#14582769C2211yescharacteristic, complemented
48#14582759C2211yescharacteristic
49#14582759C2211yescharacteristic, complemented
50C4⋊C4×Dic43—21no—
51C4×C4⋊Dic43C2211yescharacteristic, complemented
52#14582662C2211yescharacteristic, complemented
53#14582662C2211yescharacteristic, complemented
54#14582662C2211yescharacteristic, complemented
55#14582662C2211yescharacteristic, complemented
56C22×M16×C43C2211yescharacteristic
57C23×C8×C43C2211yescharacteristic, complemented
58C2×C4×D4×C43C2211yescharacteristic
59C43×#435—24no—
60C2×C4⋊C8×C43C2211yescharacteristic, complemented
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic, complemented
63C2×#97×C43C2211yescharacteristic, 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×D172—22no—
73C22×D172—22no—
74C22×D172—21no—
75C22×D172—22no—
76C22×D172—41no—
77C22×D172—41no—
78C22×D172C2×C414yes—
79C22×D172C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—21no—
82C22×C22⋊D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43—21no—
85#13063313—22no—
86#13063313C2×C414yes—
87#13063310—28no—
88#13063304—22no—
89#13063304C2×C414yes—
90#13063299—22no—
91#13063299C2×C414yes—
92#13063298—28no—
93#13063293—28no—
94C4×D172—22no—
95C4×D172C2×C414yes—
96#13063284—22no—
97#13063284—22no—
98#13063284—41no—
99#13063284—41no—
100C2×C4⋊Dic43—21no—
101C2×C4⋊Dic43—21no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C22⋊C4×D43—28no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121#13063250—22no—
122#13063250—22no—
123#13063250—41no—
124#13063250—41no—
125#13063247—22no—
126#13063247—22no—
127#13063247—22no—
128#13063247—22no—
129#13063247—22no—
130#13063247—41no—
131#13063247—41no—
132#13063247D414yescomplemented
133C43⋊#95—21no—
134C43⋊#95—21no—
135C43⋊#95—21no—
136C22×D4×C43D411yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C2×M16×C43—22no—
140C2×M16×C43—22no—
141C2×M16×C43—41no—
142C22×C8×C43—22no—
143C22×C8×C43—22no—
144C22×C8×C43—41no—
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C22×C8×C43C2311yescharacteristic
149C4×D4×C43C2×C414yes—
150C4×D4×C43D414yes—
151C2×C4⋊C4×C43D411yescharacteristic
152C2×C22⋊C4×C43D411yescharacteristic
153C2×C22⋊C4×C43D411yescharacteristic
154C2×C42×C43C2311yescharacteristic
155C4⋊C8×C43—22no—
156C22⋊C8×C43—22no—
157C22⋊C8×C43—22no—
158#97×C43—22no—
159C24×C43C2×D411yescharacteristic
160C24×C43C2×D411yescharacteristic
161C23×D43—21no—
162C23×D43—21no—
163C23×D43—24no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—42no—
167C23×D43—42no—
168C23×D43—81no—
169C23×D43—81no—
170C2×D4×C43—41no—
171C2×D4×C43—41no—
172C2×D4×C43C22⋊C414yes—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43C22×C412yes—
182C22×C4×C43C22×C412yes—
183C22×C4×C43C2×D412yes—
184C22×C4×C43C2×D412yes—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2411yescharacteristic
190C2×C22⋊D43—24no—
191C2×C22⋊D43—24no—
192C2×C22⋊D43—42no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—81no—
195C2×C22⋊D43—81no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202#10621898—28no—
203#10621898—44no—
204#10621898—44no—
205#10621898—44no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—24no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—28no—
216C2×D172—42no—
217C2×D172—42no—
218C2×D172—44no—
219C2×D172—44no—
220C2×D172—44no—
221C2×D172C22×C412yes—
222C2×D172C22×C412yes—
223C2×D172C2×D412yes—
224C2×D172#4112yes—
225C2×C4×D43—24no—
226C2×C4×D43—24no—
227C2×C4×D43—42no—
228C2×C4×D43—42no—
229C2×C4×D43—81no—
230C2×C4×D43—81no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86C22×C412yes—
237M16×C43—44no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C2×C8×C43—21no—
247C2×C8×C43—21no—
248C2×C8×C43—21no—
249C2×C8×C43—44no—
250C2×C8×C43C2×D412yes—
251C4⋊C4×C43C22⋊C414yes—
252C22⋊C4×C43C22⋊C414yes—
253C22⋊C4×C43C22⋊C414yes—
254C42×C43C22×C412yes—
255C42×C43C2×D412yes—
256C22⋊Dic43—24no—
257C22⋊Dic43—42no—
258C22⋊Dic43—42no—
259C22⋊Dic43—81no—
260C22⋊Dic43—81no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43—21no—
269C4⋊Dic43—21no—
270C4⋊Dic43—21no—
271C4⋊Dic43—21no—
272C4⋊Dic43—21no—
273C4⋊Dic43—42no—
274C4⋊Dic43—81no—
275C4⋊Dic43C22×C412yes—
276C4⋊Dic43C2×D412yes—
277Dic43⋊C4—24no—
278C4×Dic43—42no—
279C4×Dic43—42no—
280C4×Dic43—42no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—21no—
289C23×C43—21no—
290C23×C43—21no—
291C23×C43—21no—
292C23×C43—21no—
293C23×C43C2×C22⋊C412yes—
294C23×C43C2×C22⋊C412yes—
295C23×C43C22×D411yescharacteristic
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—48no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—48no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—41no—
311C22×D43—41no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315C22×D43—84no—
316C22×D43—84no—
317D4×C43—44no—
318C2×C4×C43—21no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43C2×C22⋊C412yes—
335C2×C4×C43C2×C22⋊C412yes—
336C2×C4×C43C2×C22⋊C412yes—
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—48no—
345C22⋊D43—84no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—41no—
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×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364D172—22no—
365D172—22no—
366D172—22no—
367D172—22no—
368D172—22no—
369D172—48no—
370D172—41no—
371D172—41no—
372D172C4×D414yes—
373C4×D43—48no—
374C4×D43—84no—
375Dic86—22no—
376Dic86—22no—
377Dic86—41no—
378Dic86—41no—
379C8×C43—22no—
380C8×C43—41no—
381C8×C43—41no—
382C8×C43—41no—
383#22424—431nomaximal, Sylow
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
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—24no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
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—22no—
422C4×C43—22no—
423C4×C43—22no—
424C4×C43C2×C4×D411yescharacteristic
425C4×C43#51811yescharacteristic
426C4×C43D4211yescharacteristic
427C4×C43#54611yescharacteristic
428Dic43—42no—
429Dic43—42no—
430Dic43—42no—
431Dic43—81no—
432Dic43—81no—
433Dic43—81no—
434C2×#546—431no—
435C2×#435D4311yescharacteristic, complemented
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#1788—431no—
447#1786—431no—
448#1762—431no—
449C2×C43—42no—
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—44no—
459D43—82no—
460C22×#41—431no—
461C23×D4—431no—
462C22×M16C2×D4311yescharacteristic
463C23×C8C2×D4311yescharacteristic, complemented
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×D4C2×D4311yescharacteristic
474C2×#117—431no—
475C2×#117—431no—
476C22×C22⋊C4—861no—
477#435—24no—
478C2×C4⋊C8C2×D4311yescharacteristic, complemented
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×#102—431no—
492C2×#102—431no—
493C2×C22⋊C8C2×D4311yescharacteristic
494C2×C22⋊C8C2×D4311yescharacteristic, complemented
495C2×#97C2×D4311yescharacteristic, complemented
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#340—431no—
507#340—431no—
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—434no—
518C22×D4—431no—
519C22×D4—431no—
520C22×D4—862no—
521C22×D4—862no—
522C22×D4—861no—
523C22×D4—861no—
524C22×D4—861no—
525C22×D4—862no—
526C22×D4—1721no—
527C22×D4—1721no—
528C22×D4D17211yescharacteristic
529C23×C4—861no—
530C23×C4—861no—
531C23×C4C22×D4311yescharacteristic
532C23×C4C22×D4311yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C22×C8—22no—
537C22×C8—22no—
538C22×C8—41no—
539C22×C8C22×D4311yescharacteristic
540C22×C8C22×D4311yescharacteristic
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—862no—
550#121—868no—
551#120—868no—
552C4×D4—434no—
553C4×D4—862no—
554C4×D4C4×D4314yes—
555C4×D4C22⋊D4314yes—
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—431no—
565C2×C4⋊C4—861no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4—861no—
568C2×C4⋊C4D17211yescharacteristic
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—868no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4D17211yescharacteristic
580C2×C22⋊C4D17211yescharacteristic
581C2×C42—861no—
582C2×C42—861no—
583C2×C42—861no—
584C2×C42C22×D4311yescharacteristic
585C4⋊C8—22no—
586#103—862no—
587#103—862no—
588#103—1721no—
589#103—1721no—
590#102—434no—
591#102—862no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—862no—
596#102—1721no—
597#102—1721no—
598C22⋊C8—22no—
599C22⋊C8—22no—
600#97—22no—
601#95—861no—
602#95—861no—
603#95—861no—
604C24—861no—
605C24—864no—
606C24—861no—
607C24—3441no—
608C24—3441no—
609C24—1722no—
610C24—1722no—
611C24—1722no—
612C24—1722no—
613C24C2×D17211yescharacteristic
614C24C2×D17211yescharacteristic
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—41no—
626C2×D4—41no—
627C2×D4—432no—
628C2×D4—432no—
629C2×D4—432no—
630C2×D4—432no—
631C2×D4—868no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—864no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—3441no—
644C2×D4—3441no—
645C2×D4—1724no—
646C2×D4—1724no—
647C2×D4—1724no—
648C2×D4—1722no—
649C2×D4—1722no—
650C2×D4—1722no—
651C2×D4—1722no—
652C2×D4(C2×D43)⋊C414yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—861no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—864no—
665C22×C4—864no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—861no—
669C22×C4—3441no—
670C22×C4—3441no—
671C22×C4—1722no—
672C22×C4—1722no—
673C22×C4C2×C4×D4312yes—
674C22×C4C2×C4×D4312yes—
675C22×C4C2×D17211yescharacteristic
676C22×C4C2×D17211yescharacteristic
677C22×C4C2×D17211yescharacteristic
678C22×C4C2×D17211yescharacteristic
679C22×C4C2×C22⋊D4312yes—
680C22×C4C2×C22⋊D4312yes—
681C22×C4C23×D4311yescharacteristic
682M16—44no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—44no—
695C2×C8D4×D4312yes—
696C4⋊C4—432no—
697C4⋊C4—432no—
698C4⋊C4—864no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—3441no—
708C4⋊C4—1722no—
709C4⋊C4(C2×D43)⋊C414yes—
710C22⋊C4—864no—
711C22⋊C4—864no—
712C22⋊C4—864no—
713C22⋊C4—864no—
714C22⋊C4—864no—
715C22⋊C4—3441no—
716C22⋊C4—3441no—
717C22⋊C4—1722no—
718C22⋊C4—1722no—
719C22⋊C4(C2×D43)⋊C414yes—
720C22⋊C4(C2×D43)⋊C414yes—
721C42—1722no—
722C42—1722no—
723C42—1722no—
724C42C2×C4×D4312yes—
725C42C2×C22⋊D4312yes—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—862no—
739C23—862no—
740C23—862no—
741C23—862no—
742C23—3444no—
743C23—3444no—
744C23—3444no—
745C23—3444no—
746C23—3444no—
747C23—1728no—
748C23—1728no—
749C23—1721no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23—1721no—
758C23—1721no—
759C23C2×(C2×D43)⋊C412yes—
760C23C2×(C2×D43)⋊C412yes—
761C23C22×D17211yescharacteristic
762Q8—862no—
763Q8—862no—
764Q8—1721no—
765Q8—1721no—
766D4—44no—
767D4—434no—
768D4—862no—
769D4—862no—
770D4—862no—
771D4—862no—
772D4—862no—
773D4—3444no—
774D4—1728no—
775D4—1728no—
776D4—1721no—
777D4—1721no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—862no—
795C2×C4—862no—
796C2×C4—862no—
797C2×C4—3444no—
798C2×C4—1728no—
799C2×C4—1721no—
800C2×C4—1721no—
801C2×C4—1721no—
802C2×C4—1721no—
803C2×C4—1721no—
804C2×C4—1721no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4C2×(C2×D43)⋊C412yes—
815C2×C4C2×(C2×D43)⋊C412yes—
816C2×C4C2×(C2×D43)⋊C412yes—
817C2×C4C2×(C2×D43)⋊C412yes—
818C2×C4C22×C4×D4311yescharacteristic
819C2×C4C2×D4×D4311yescharacteristic
820C2×C4C22×C22⋊D4311yescharacteristic
821C2×C4#41×D4311yescharacteristic
822C2×C4#1306337011yescharacteristic
823C2×C4#1306337111yescharacteristic
824C8—22no—
825C8—41no—
826C8—41no—
827C8—41no—
828C22—22no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—864no—
843C22—34416no—
844C22—3441no—
845C22—3441no—
846C22—3441no—
847C22—3441no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1722no—
856C22—1722no—
857C22C22×(C2×D43)⋊C411yescharacteristic
858C22D4×D17211yescharacteristic
859C22#1458354411yescharacteristic
860C22#1458369911yescharacteristic
861C22#1458369911yescharacteristic
862C22#1458370411yescharacteristic
863C22#1458371111yescharacteristic
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—3441no—
869C4—3441no—
870C4—3441no—
871C4—1722no—
872C4—1722no—
873C4—1722no—
874C4C4×D4×D4311yescharacteristic
875C4#1458337111yescharacteristic
876C4D4×C22⋊D4311yescharacteristic
877C4#1458353711yescharacteristic
878C2—42no—
879C2—42no—
880C2—3442no—
881C2—1724no—
882C2D4×(C2×D43)⋊C411yescharacteristic
883C2#1914311511yescharacteristic
884C2#1914312211yescharacteristic
885C2#1914612511yescharacteristic
886C2#1914614011yescharacteristic
887C2#1914663311yescharacteristic
888C2#1914675311yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#435C2
socleC23×C43C22×D4
prime radicalC2×#14583545C2
cosocleC22×C4×C43C24
hypercenterC2×#435D43
hypocenterC43#22424
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#14582905C2semidirect
3. C2×#14582896C2semidirect
4. #19137544C2semidirect
5. #19135525C2semidirect
6. #19135411C2semidirect
7. #19135028C2semidirect
8. #19135023C2semidirect
9. #19134915C2semidirect
10. #19134905C2semidirect
11. #19134596C2semidirect
12. #19134536C2semidirect
13. #19134527C2semidirect
14. #19134421C2semidirect
15. C2×C43×#435C2semidirect
19. #14583545C4semidirect
28. C2×#13063284C22semidirect
32. C2×#13063250C22semidirect
33. C2×#13063250C22semidirect
34. C2×#13063250C22semidirect
35. C2×#13063250C22semidirect
47. #14582769C22semidirect
49. #14582759C22semidirect
51. C4×C4⋊Dic43C22semidirect
52. #14582662C22semidirect
53. #14582662C22semidirect
54. #14582662C22semidirect
55. #14582662C22semidirect
57. C23×C8×C43C22semidirect
60. C2×C4⋊C8×C43C22semidirect
62. C2×C22⋊C8×C43C22semidirect
63. C2×#97×C43C22semidirect
132. #13063247D4semidirect
435. C2×#435D43semidirect
463. C23×C8C2×D43semidirect
478. C2×C4⋊C8C2×D43semidirect
494. C2×C22⋊C8C2×D43semidirect
495. C2×#97C2×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×#145835452
C2×#145829052
C2×#145828962
#191375442
#191355252
#191354112
#191350282
#191350232
#191349152
#191349052
#191345962
#191345362
#191345272
#191344212
C2×C43×#4352
#2242443