Finite Group Databasebeta

← #25112200

Subgroups — #25112200

Order 11008.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583546C211yesmaximal, characteristic
2C2×#14582974C211yesmaximal, characteristic, complemented
3C2×#14582898C211yesmaximal, characteristic, complemented
4C2×#14582902C211yesmaximal, characteristic, complemented
5#19137520C211yesmaximal, characteristic, complemented
6#19135526C211yesmaximal, characteristic, complemented
7#19135405C211yesmaximal, characteristic, complemented
8#19135034C211yesmaximal, characteristic, complemented
9#19135027C211yesmaximal, characteristic, complemented
10#19134906C211yesmaximal, characteristic, complemented
11#19134604C211yesmaximal, characteristic, complemented
12#19134536C211yesmaximal, characteristic, complemented
13#19134524C211yesmaximal, characteristic, complemented
14#19134409C211yesmaximal, characteristic, complemented
15C43×#1874C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×D4×D43C2211yescharacteristic
18C22×#10621877C2211yescharacteristic, complemented
19C22×#10621872C2211yescharacteristic
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#14582974—24no—
32C2×Dic43⋊C8C2211yescharacteristic, complemented
33#14582902—24no—
34#14582898—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×C8×Dic43C2211yescharacteristic, complemented
47#14582789—21no—
48#14582780—21no—
49#14582778—21no—
50#14582764C2211yescharacteristic, complemented
51#14582759C2211yescharacteristic, complemented
52#14582756C2211yescharacteristic
53C4⋊C4×Dic43C2211yescharacteristic, complemented
54C4×C22⋊Dic43—21no—
55#14582661C2211yescharacteristic, complemented
56#14582661C2211yescharacteristic, complemented
57C2×#121×C43C2211yescharacteristic
58C22×C4⋊C4×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×C414yescomplemented
82C22×C4×D43—21no—
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C2×#10621877—22no—
86C2×#10621877—22no—
87C2×#10621877—41no—
88C2×#10621872—22no—
89C2×#10621872—22no—
90C2×#10621872—41no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93#13063312—22no—
94#13063312C2×C414yescomplemented
95#13063307—28no—
96#13063305—22no—
97#13063305C2×C414yescomplemented
98#13063296—28no—
99#13063293—28no—
100#13063287—22no—
101#13063287C2×C414yescomplemented
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⋊C4D411yescharacteristic
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
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)⋊C4—21no—
118C2×(C2×D43)⋊C4D411yescharacteristic
119C22⋊C4×D43—28no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123Dic43⋊C8—22no—
124#13063250—41no—
125#13063250—41no—
126#13063248—22no—
127#13063248—22no—
128#13063247—22no—
129#13063247—22no—
130#13063246—22no—
131#13063246—41no—
132#13063245—22no—
133#13063245D414yescomplemented
134(C2×D43)⋊C8—22no—
135C8×Dic43—22no—
136C43⋊#95—21no—
137C43⋊#95—21no—
138C43⋊#95—21no—
139C43⋊#95—21no—
140C43⋊#95—21no—
141C22×D4×C43—21no—
142C22×D4×C43C2311yescharacteristic
143C23×C4×C43—21no—
144C23×C4×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147#121×C43—22no—
148#121×C43C2×C414yes—
149C2×C4⋊C4×C43—22no—
150C2×C4⋊C4×C43—21no—
151C2×C4⋊C4×C43—41no—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C4⋊C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43C2311yescharacteristic
155C2×C22⋊C4×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×C43—42no—
187C22×C4×C43—42no—
188C22×C4×C43—81no—
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—41no—
196C2×C22⋊D43—41no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43—42no—
199C2×C22⋊D43—42no—
200C2×C22⋊D43—42no—
201C2×C22⋊D43C22⋊C414yes—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208D4×D43—28no—
209D4×D43—44no—
210D4×D43—44no—
211D4×D43—44no—
212#10621898—28no—
213#10621898—44no—
214#10621898—44no—
215#10621898—44no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172C22×C412yes—
220C2×D172C2×D412yes—
221C2×D172#4112yes—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—21no—
225C2×C4×D43—21no—
226C2×C4×D43—24no—
227C2×C4×D43—24no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×C4×D43—81no—
231C2×C4×D43—81no—
232C2×C4×D43C22×C412yes—
233C2×C4×D43C2×D412yes—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86C22×C412yes—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C2×C8×C43—21no—
245C2×C8×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—42no—
251C4⋊C4×C43C22×C412yes—
252C4⋊C4×C43C2×D412yes—
253C22⋊C4×C43—24no—
254C22⋊Dic43—24no—
255C22⋊Dic43—24no—
256C22⋊Dic43—42no—
257C22⋊Dic43C22⋊C414yes—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—42no—
261(C2×D43)⋊C4—81no—
262(C2×D43)⋊C4C22⋊C414yes—
263C4⋊Dic43—24no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268Dic43⋊C4C22⋊C414yes—
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—
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×C43—84no—
338C2×C4×C43C2×C22⋊C412yes—
339C2×C4×C43C23×C411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C2×#4111yescharacteristic
343C2×C4×C43H(5,𝔽2)11yescharacteristic
344C2×C4×C43H(5,𝔽2)11yescharacteristic
345C22⋊D43—44no—
346C22⋊D43—48no—
347C22⋊D43—48no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—21no—
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—41no—
363C2×Dic43C2×C22⋊C412yes—
364C2×Dic43C2×C22⋊C412yes—
365C2×Dic43C2×C22⋊C412yes—
366D172—22no—
367D172—22no—
368D172—22no—
369D172C4×D414yes—
370C4×D43—22no—
371C4×D43—22no—
372C4×D43—22no—
373C4×D43—22no—
374C4×D43—48no—
375C4×D43—84no—
376Dic86—22no—
377Dic86—22no—
378Dic86—41no—
379Dic86—41no—
380C8×C43—41no—
381C8×C43—41no—
382C43⋊C8—22no—
383C43⋊C8—41no—
384#22427—431nomaximal, Sylow
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—81no—
396C22×C43—81no—
397C22×C43—81no—
398C22×C43—81no—
399C22×C43C22×C22⋊C411yescharacteristic
400C22×C43D4211yescharacteristic
401C22×C43#54611yescharacteristic
402C22×C43#57511yescharacteristic
403C22×C43#57511yescharacteristic
404C22×C43#57611yescharacteristic
405C22×C43#57711yescharacteristic
406C2×D43—24no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—41no—
413C2×D43—42no—
414C2×D43—41no—
415C2×D43—42no—
416C2×D43—41no—
417C2×D43—42no—
418C2×D43—41no—
419C2×D43—42no—
420C2×D43—816no—
421C4×C43—22no—
422C4×C43—42no—
423C4×C43—42no—
424C4×C43—81no—
425C4×C43C2×C4×D411yescharacteristic
426C4×C43#51811yescharacteristic
427C4×C43D4211yescharacteristic
428C4×C43#54611yescharacteristic
429Dic43—22no—
430Dic43—22no—
431Dic43—22no—
432Dic43—42no—
433Dic43—81no—
434Dic43—81no—
435C2×#546—431no—
436C2×#436—431no—
437C2×#417—431no—
438C2×#418—431no—
439#2352—431no—
440#1983—431no—
441#1958—431no—
442#1895—431no—
443#1894—431no—
444#1874D4311yescharacteristic, complemented
445#1873—431no—
446#1804—431no—
447#1788—431no—
448#1786—431no—
449C4×#102—431no—
450C2×C43—42no—
451C2×C43—82no—
452C2×C43D4×C22⋊C411yescharacteristic
453C2×C43#289611yescharacteristic
454C2×C43#289711yescharacteristic
455C2×C43#327311yescharacteristic
456C2×C43#327511yescharacteristic
457C2×C43#332211yescharacteristic
458C2×C43#332311yescharacteristic
459D43—42no—
460D43—44no—
461C22×#41—431no—
462C23×D4—431no—
463C22×M16—431no—
464C22×M16—431no—
465#546—438no—
466#546—864no—
467C2×#124—431no—
468C2×#123—861no—
469C2×C22⋊Q8—431no—
470C2×#121—861no—
471C2×#121C2×D4311yescharacteristic
472C2×#120—861no—
473C2×C4×D4—431no—
474C2×C4×D4—431no—
475C2×#117—431no—
476C22×C4⋊C4C2×D4311yescharacteristic, complemented
477C22×C22⋊C4—861no—
478#436—864no—
479C2×C4⋊C8—431no—
480#418—864no—
481#417—864no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#103—431no—
485C2×#103—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—431no—
491C2×#102—431no—
492C2×#102C2×D4311yescharacteristic
493C2×#102C2×D4311yescharacteristic
494C2×C22⋊C8—431no—
495C2×C22⋊C8C2×D4311yescharacteristic, complemented
496C2×C4×C8—431no—
497#388—861no—
498#387—861no—
499#386—861no—
500#382—431no—
501#380—431no—
502#380—431no—
503C4×C4⋊C4—431no—
504C4×C22⋊C4—861no—
505#340—431no—
506#340—431no—
507#340C2×D4311yescharacteristic, complemented
508#340C2×D4311yescharacteristic, complemented
509C43#2242711yescharacteristic, complemented, Sylow
510C25—861no—
511C2×#41—434no—
512C2×#41—862no—
513C2×#41—862no—
514C2×#41—862no—
515C2×#41—1721no—
516C2×#41—1721no—
517C22×Q8—431no—
518C22×D4—21no—
519C22×D4—431no—
520C22×D4—434no—
521C22×D4—431no—
522C22×D4—862no—
523C22×D4—861no—
524C22×D4—862no—
525C22×D4—862no—
526C22×D4—861no—
527C22×D4—1721no—
528C22×D4—1721no—
529C22×D4C22×D4311yescharacteristic
530C23×C4—21no—
531C23×C4—431no—
532C23×C4—861no—
533C23×C4—861no—
534C23×C4C22×D4311yescharacteristic
535C2×M16—862no—
536C2×M16—862no—
537C2×M16—862no—
538C2×M16—862no—
539C2×M16—1721no—
540C2×M16—1721no—
541C22×C8—431no—
542C22×C8—431no—
543C22×C8C22×D4311yescharacteristic
544C22×C8C22×D4311yescharacteristic
545#124—434no—
546#124—862no—
547#123—868no—
548C22⋊Q8—434no—
549C22⋊Q8—862no—
550#121—22no—
551#121—868no—
552#121C4×D4314yes—
553#120—868no—
554C4×D4—434no—
555C4×D4—434no—
556C4×D4—434no—
557C4×D4—862no—
558#117—862no—
559#117—1721no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4—431no—
564C2×C4⋊C4—431no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—861no—
567C2×C4⋊C4C22×D4311yescharacteristic
568C2×C4⋊C4C22×D4311yescharacteristic
569C2×C4⋊C4C22×D4311yescharacteristic
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—431no—
582C2×C42—861no—
583C2×C42—861no—
584C4⋊C8—862no—
585#103—862no—
586#103—862no—
587#103—1721no—
588#103—1721no—
589#102—22no—
590#102—41no—
591#102—434no—
592#102—862no—
593#102—862no—
594#102—862no—
595#102—862no—
596#102—1721no—
597C22⋊C8—22no—
598C22⋊C8—862no—
599C4×C8—862no—
600#95—861no—
601#95—861no—
602#95—861no—
603#95—861no—
604#95—861no—
605C24—21no—
606C24—431no—
607C24—864no—
608C24—861no—
609C24—3441no—
610C24—3441no—
611C24—1722no—
612C24—1722no—
613C24—1722no—
614C24—1722no—
615C24D4×D4311yescharacteristic
616#41—868no—
617#41—1724no—
618#41—1724no—
619#41—1724no—
620C2×Q8—432no—
621C2×Q8—861no—
622C2×Q8—861no—
623C2×Q8—861no—
624C2×Q8—861no—
625C2×Q8—861no—
626C2×D4—24no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—81no—
633C2×D4—81no—
634C2×D4—434no—
635C2×D4—432no—
636C2×D4—432no—
637C2×D4—432no—
638C2×D4—864no—
639C2×D4—868no—
640C2×D4—864no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4—1724no—
647C2×D4—1721no—
648C2×D4—1721no—
649C2×D4—1722no—
650C2×D4—1722no—
651C2×D4—1722no—
652C2×D4—1722no—
653C2×D4C2×C4×D4312yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—81no—
664C22×C4—431no—
665C22×C4—431no—
666C22×C4—431no—
667C22×C4—432no—
668C22×C4—432no—
669C22×C4—864no—
670C22×C4—861no—
671C22×C4—861no—
672C22×C4—861no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—864no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—3441no—
679C22×C4—3441no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4C2×C4×D4312yes—
683C22×C4D4×D4311yescharacteristic
684C22×C4D4×D4312yes—
685C22×C4C23×D4311yescharacteristic
686M16—1724no—
687M16—1724no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—432no—
695C2×C8—861no—
696C2×C8—861no—
697C2×C8—861no—
698C2×C8—861no—
699C2×C8—861no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—42no—
705C4⋊C4—434no—
706C4⋊C4—864no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4C2×C4×D4312yes—
712C4⋊C4D4×D4312yes—
713C22⋊C4—24no—
714C22⋊C4—434no—
715C22⋊C4—434no—
716C22⋊C4—864no—
717C22⋊C4—864no—
718C22⋊C4—864no—
719C22⋊C4—864no—
720C22⋊C4—3441no—
721C22⋊C4—1722no—
722C22⋊C4—1722no—
723C42—432no—
724C42—432no—
725C42—3441no—
726C42—1722no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—432no—
741C23—862no—
742C23—861no—
743C23—861no—
744C23—861no—
745C23—861no—
746C23—861no—
747C23—862no—
748C23—861no—
749C23—862no—
750C23—3444no—
751C23—3444no—
752C23—3444no—
753C23—3444no—
754C23—3444no—
755C23—1728no—
756C23—1728no—
757C23—1721no—
758C23—1721no—
759C23—1721no—
760C23—1721no—
761C23C22⋊C4×D4312yes—
762C23C2×D4×D4311yescharacteristic
763Q8—862no—
764Q8—862no—
765Q8—1721no—
766Q8—1721no—
767D4—22no—
768D4—22no—
769D4—41no—
770D4—41no—
771D4—84no—
772D4—434no—
773D4—862no—
774D4—862no—
775D4—862no—
776D4—1724no—
777D4—1728no—
778D4—1728no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—84no—
795C2×C4—432no—
796C2×C4—432no—
797C2×C4—432no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—861no—
803C2×C4—861no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—3444no—
810C2×C4—1728no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4—1721no—
816C2×C4—1721no—
817C2×C4—1721no—
818C2×C4—1721no—
819C2×C4C22⋊C4×D4312yes—
820C2×C4C22×C4×D4311yescharacteristic
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C2×D4×D4311yescharacteristic
823C2×C4#41×D4311yescharacteristic
824C2×C4#1306337011yescharacteristic
825C2×C4#1306337111yescharacteristic
826C8—41no—
827C8—41no—
828C8—862no—
829C8—1721no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—862no—
845C22—864no—
846C22—862no—
847C22—862no—
848C22—34416no—
849C22—1721no—
850C22—1722no—
851C22—1721no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1721no—
856C22—1722no—
857C22—1721no—
858C22—1722no—
859C22C2×C22⋊C4×D4311yescharacteristic
860C22#1458353111yescharacteristic
861C22#1458354111yescharacteristic
862C22#1458369511yescharacteristic
863C22#1458369811yescharacteristic
864C22#1458370011yescharacteristic
865C22#1458370511yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—81no—
870C4—862no—
871C4—862no—
872C4—862no—
873C4—3441no—
874C4—3441no—
875C4—1722no—
876C4C4×D4×D4311yescharacteristic
877C4#1458337111yescharacteristic
878C4#1458353311yescharacteristic
879C4#1458353811yescharacteristic
880C2—42no—
881C2—82no—
882C2—1722no—
883C2—1724no—
884C2#1913741311yescharacteristic
885C2#1914311111yescharacteristic
886C2#1914311611yescharacteristic
887C2#1914620611yescharacteristic
888C2#1914622911yescharacteristic
889C2#1914679911yescharacteristic
890C2#1914681411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1874C2
socleC23×C43C22×D4
prime radicalC2×#14583546C2
cosocleC22×C4×C43C24
hypercenter#1874D43
hypocenterC43#22427
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#14582974C2semidirect
3. C2×#14582898C2semidirect
4. C2×#14582902C2semidirect
5. #19137520C2semidirect
6. #19135526C2semidirect
7. #19135405C2semidirect
8. #19135034C2semidirect
9. #19135027C2semidirect
10. #19134906C2semidirect
11. #19134604C2semidirect
12. #19134536C2semidirect
13. #19134524C2semidirect
14. #19134409C2semidirect
15. C43×#1874C2semidirect
18. C22×#10621877C22semidirect
21. #14583546C4semidirect
32. C2×Dic43⋊C8C22semidirect
35. C2×#13063250C22semidirect
36. C2×#13063250C22semidirect
37. C2×#13063248C22semidirect
38. C2×#13063248C22semidirect
46. C2×C8×Dic43C22semidirect
50. #14582764C22semidirect
51. #14582759C22semidirect
53. C4⋊C4×Dic43C22semidirect
55. #14582661C22semidirect
56. #14582661C22semidirect
58. C22×C4⋊C4×C43C22semidirect
61. C2×C22⋊C8×C43C22semidirect
62. C43×#340C22semidirect
63. C43×#340C22semidirect
81. C2×D4×D43C2×C4semidirect
94. #13063312C2×C4semidirect
97. #13063305C2×C4semidirect
101. #13063287C2×C4semidirect
133. #13063245D4semidirect
444. #1874D43semidirect
476. C22×C4⋊C4C2×D43semidirect
495. C2×C22⋊C8C2×D43semidirect
507. #340C2×D43semidirect
508. #340C2×D43semidirect
509. C43#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#145835462
C2×#145829742
C2×#145828982
C2×#145829022
#191375202
#191355262
#191354052
#191350342
#191350272
#191349062
#191346042
#191345362
#191345242
#191344092
C43×#18742
#2242743