Finite Group Databasebeta

← #25129385

Subgroups — #25129385

Order 11008.

1340 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583477C211yesmaximal, characteristic
2C2×#14583240C211yesmaximal, characteristic, complemented
3C2×#14583223C211yesmaximal, characteristic, complemented
4#19135798C211yesmaximal, characteristic, complemented
5#19135791C211yesmaximal, characteristic, complemented
6#19135784C211yesmaximal, characteristic, complemented
7#19135777C211yesmaximal, characteristic, complemented
8#19134912C211yesmaximal, characteristic, complemented
9#19134902C211yesmaximal, characteristic, complemented
10#19134787C211yesmaximal, characteristic, complemented
11#19134782C211yesmaximal, characteristic, complemented
12#19134533C211yesmaximal, characteristic, complemented
13#19134533C211yesmaximal, characteristic, complemented
14#19134507C211yesmaximal, characteristic, complemented
15C43×#2311C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17#14583477—24no—
18#14583477—24no—
19C2×#13063304C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063301—21no—
22C2×#13063299C2211yescharacteristic
23C2×#13063299C2211yescharacteristic
24C2×#13063297—21no—
25C2×#13063297—21no—
26C2×#13063296—21no—
27C22×C4⋊Dic43C2211yescharacteristic
28#14583240—24no—
29#14583223—24no—
30C2×#13063258C2211yescharacteristic
31C2×#13063258C2211yescharacteristic
32C2×#13063256C2211yescharacteristic
33C2×#13063256C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063248C2211yescharacteristic
36C2×#13063248C2211yescharacteristic
37C2×#13063248C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40C2×#13063245C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×C22⋊(C43⋊C8)C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44C2×C22⋊(C43⋊C8)C2211yescharacteristic
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47C2×C22⋊(C43⋊C8)C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52C22×#41×C43C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C22×C4⋊C4×C43C2211yescharacteristic
55C43×#391—21no—
56C43×#390—21no—
57C43×#386—21no—
58C43×#386—21no—
59C43×#380C2211yescharacteristic
60C43×#380C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#380C2211yescharacteristic
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C22×Dic86C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C22×C22⋊D43—21no—
74C23×Dic43—21no—
75C22×C4×D43—21no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80#13063304—22no—
81#13063304—22no—
82#13063304—22no—
83#13063304D414yes—
84#13063301—28no—
85#13063299—22no—
86#13063299—22no—
87#13063299—22no—
88#13063299D414yes—
89#13063297—28no—
90#13063297—28no—
91#13063296—28no—
92C2×C4⋊Dic43—21no—
93C2×C4⋊Dic43—22no—
94C2×C4⋊Dic43—22no—
95C2×C4⋊Dic43C2311yescharacteristic
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103#13063258—22no—
104#13063258—22no—
105#13063256—22no—
106#13063256—22no—
107#13063248—22no—
108#13063248—22no—
109#13063248—41no—
110#13063248—41no—
111#13063245—22no—
112#13063245—22no—
113#13063245—41no—
114#13063245—41no—
115C22⋊(C43⋊C8)—22no—
116C22⋊(C43⋊C8)—22no—
117C22⋊(C43⋊C8)—22no—
118C22⋊(C43⋊C8)—22no—
119C22⋊(C43⋊C8)—41no—
120C22⋊(C43⋊C8)—41no—
121C2×#41×C43—22no—
122C2×#41×C43—22no—
123C2×#41×C43—22no—
124C2×#41×C43—22no—
125C2×#41×C43—41no—
126C2×#41×C43—41no—
127C22×Q8×C43D411yescharacteristic
128C22×D4×C43D411yescharacteristic
129C22×D4×C43D411yescharacteristic
130C22×D4×C43D411yescharacteristic
131C23×C4×C43—21no—
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135#117×C43—22no—
136#117×C43—22no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43—41no—
139C2×C4⋊C4×C43—41no—
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C42×C43—21no—
150#95×C43—21no—
151#95×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154C24×C43C2×D411yescharacteristic
155C24×C43C2×D411yescharacteristic
156C24×C43C2×D411yescharacteristic
157C23×D43—21no—
158#41×C43—44no—
159#41×C43—44no—
160#41×C43—44no—
161#41×C43—44no—
162C2×Q8×C43—22no—
163C2×Q8×C43—22no—
164C2×Q8×C43—41no—
165C2×D4×C43—22no—
166C2×D4×C43—22no—
167C2×D4×C43—22no—
168C2×D4×C43—22no—
169C2×D4×C43—22no—
170C2×D4×C43—22no—
171C2×D4×C43—41no—
172C2×D4×C43—41no—
173C2×D4×C43—41no—
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×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—42no—
193C22×C4×C43—81no—
194C22×C4×C43—81no—
195C22×C4×C43C2×D412yes—
196C22×C4×C43C2×D412yes—
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43#4112yes—
201C22×C4×C43#4112yes—
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—42no—
207C2×C22⋊D43—42no—
208C2×C22⋊D43—81no—
209C2×C22⋊D43—81no—
210C2×C22⋊D43—81no—
211C2×C22⋊D43—81no—
212C22×Dic43—24no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—21no—
216C22×Dic43—81no—
217C22×Dic43—81no—
218#10621898—44no—
219#10621898—44no—
220#10621898—44no—
221#10621898—44no—
222C2×D172—21no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172C2×D412yes—
228C2×C4×D43—24no—
229C2×C4×D43—42no—
230C2×C4×D43—42no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86C2×D412yes—
237C4⋊C4×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—42no—
246C22⋊C4×C43—42no—
247C22⋊C4×C43—81no—
248C22⋊C4×C43—81no—
249C22⋊C4×C43—81no—
250C22⋊C4×C43—81no—
251C42×C43—42no—
252C22⋊Dic43—24no—
253C22⋊Dic43—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
256C4⋊Dic43—24no—
257C4⋊Dic43—21no—
258C4⋊Dic43—21no—
259C4⋊Dic43C2×D412yes—
260C4⋊Dic43C2×D412yes—
261Dic43⋊C4—24no—
262Dic43⋊C4—24no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
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×C43—21no—
294C23×C43#12012yes—
295C23×C43#12312yes—
296C23×C43C22×D411yescharacteristic
297C22×D43—22no—
298C22×D43—41no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—41no—
304Q8×C43—44no—
305D4×C43—44no—
306D4×C43—44no—
307D4×C43—44no—
308C2×C4×C43—21no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
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×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—84no—
340C2×C4×C43#12012yes—
341C2×C4×C43#12312yes—
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C2×C4×C43C2×#4111yescharacteristic
346C2×C4×C43H(5,𝔽2)11yescharacteristic
347C2×C4×C43H(5,𝔽2)11yescharacteristic
348C22⋊D43—48no—
349C22⋊D43—84no—
350C22⋊D43—84no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—41no—
355C2×Dic43—41no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—84no—
361D172—22no—
362D172—22no—
363D172—41no—
364D172—41no—
365C4×D43—48no—
366Dic86—22no—
367Dic86—22no—
368Dic86—41no—
369Dic86—41no—
370C43⋊C8—41no—
371C43⋊C8—41no—
372C43⋊C8—41no—
373C43⋊C8—41no—
374#24017—431nomaximal, Sylow
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43C2×#12011yescharacteristic
397C22×C43C2×#12311yescharacteristic
398C22×C43#53411yescharacteristic
399C22×C43#57611yescharacteristic
400C22×C43#57711yescharacteristic
401C22×C43#57711yescharacteristic
402C22×C43#57811yescharacteristic
403C2×D43—42no—
404C2×D43—42no—
405C2×D43—42no—
406C2×D43—81no—
407C2×D43—81no—
408C2×D43—81no—
409C2×D43—81no—
410C4×C43—22no—
411C4×C43—22no—
412C4×C43—41no—
413C4×C43—81no—
414C4×C43—81no—
415C4×C43—81no—
416C4×C43—81no—
417C4×C43#54611yescharacteristic
418C4×C43#54611yescharacteristic
419C4×C43#54611yescharacteristic
420C4×C43#54611yescharacteristic
421Dic43—42no—
422Dic43—42no—
423Dic43—42no—
424C2×#537—431no—
425C2×#485—431no—
426C2×#482—431no—
427#2311D4311yescharacteristic, complemented
428#2036—431no—
429#2035—431no—
430#2034—431no—
431#2033—431no—
432#1874—431no—
433#1872—431no—
434#1853—431no—
435#1852—431no—
436#1788—431no—
437#1788—431no—
438#1780—431no—
439C2×C43—42no—
440C2×C43—42no—
441C2×C43—81no—
442C2×C43#240511yescharacteristic
443C2×C43#301211yescharacteristic
444C2×C43#301311yescharacteristic
445C2×C43#309811yescharacteristic
446C2×C43#309911yescharacteristic
447C2×C43#319811yescharacteristic
448C2×C43#320111yescharacteristic
449D43—82no—
450C22×#41—431no—
451C22×#41C2×D4311yescharacteristic
452#537—864no—
453#537—864no—
454C2×C22⋊Q8—431no—
455C2×C22⋊Q8—431no—
456C2×C22⋊Q8—861no—
457C2×#121—431no—
458C2×#121—431no—
459C2×#121—861no—
460C2×#121—861no—
461C2×#121—861no—
462C2×#117C2×D4311yescharacteristic
463C22×C4⋊C4—431no—
464C22×C4⋊C4C2×D4311yescharacteristic
465#485—864no—
466#482—864no—
467C2×#107—431no—
468C2×#107—431no—
469C2×#106—431no—
470C2×#106—431no—
471C2×#103—431no—
472C2×#103—431no—
473C2×#103—431no—
474C2×#103—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102—431no—
478C2×#102—431no—
479C2×C22⋊C8—431no—
480C2×C22⋊C8—431no—
481C2×C22⋊C8—431no—
482C2×C22⋊C8—431no—
483C2×C22⋊C8—431no—
484C2×C22⋊C8—431no—
485#391—21no—
486#390—21no—
487#386—21no—
488#386—21no—
489#380C2×D4311yescharacteristic
490#380C2×D4311yescharacteristic
491#380C2×D4311yescharacteristic
492#380C2×D4311yescharacteristic
493#340—431no—
494#340—431no—
495#340—431no—
496#340—431no—
497C43#2401711yescharacteristic, complemented, Sylow
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—862no—
505C2×#41—862no—
506C2×#41—862no—
507C2×#41—862no—
508C2×#41—1721no—
509C2×#41—1721no—
510C22×Q8—431no—
511C22×Q8C22⋊D4311yescharacteristic
512C22×D4—431no—
513C22×D4—861no—
514C22×D4—861no—
515C22×D4—861no—
516C22×D4C22⋊D4311yescharacteristic
517C22×D4C22⋊D4311yescharacteristic
518C22×D4C22⋊D4311yescharacteristic
519C23×C4—21no—
520C23×C4—861no—
521C23×C4—861no—
522C23×C4C22×D4311yescharacteristic
523C23×C4C22×D4311yescharacteristic
524C23×C4C22×D4311yescharacteristic
525C22×C8—431no—
526C22×C8—431no—
527C22×C8—431no—
528C22×C8—431no—
529C22⋊Q8—434no—
530C22⋊Q8—862no—
531C22⋊Q8—862no—
532C22⋊Q8—868no—
533C22⋊Q8—862no—
534#121—434no—
535#121—862no—
536#121—862no—
537#121—868no—
538#121—868no—
539#121—868no—
540#121—862no—
541#117—22no—
542#117—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—41no—
545C2×C4⋊C4—41no—
546C2×C4⋊C4—431no—
547C2×C4⋊C4—431no—
548C2×C4⋊C4—862no—
549C2×C4⋊C4—862no—
550C2×C4⋊C4—861no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4C22×D4311yescharacteristic
554C2×C4⋊C4C22×D4311yescharacteristic
555C2×C4⋊C4C22×D4311yescharacteristic
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C42—21no—
567#107—862no—
568#107—862no—
569#106—862no—
570#106—862no—
571#103—862no—
572#103—862no—
573#103—1721no—
574#103—1721no—
575#102—862no—
576#102—862no—
577#102—1721no—
578#102—1721no—
579C22⋊C8—862no—
580C22⋊C8—862no—
581C22⋊C8—862no—
582C22⋊C8—862no—
583C22⋊C8—1721no—
584C22⋊C8—1721no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—861no—
590C24C2×C22⋊D4311yescharacteristic
591C24C2×C22⋊D4311yescharacteristic
592C24C2×C22⋊D4311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—1724no—
598#41—1724no—
599#41—1724no—
600#41—1724no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—41no—
604C2×Q8—432no—
605C2×Q8—861no—
606C2×Q8—861no—
607C2×Q8—861no—
608C2×Q8—861no—
609C2×Q8—861no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—41no—
619C2×D4—432no—
620C2×D4—864no—
621C2×D4—864no—
622C2×D4—864no—
623C2×D4—861no—
624C2×D4—861no—
625C2×D4—861no—
626C2×D4—861no—
627C2×D4—861no—
628C2×D4—3441no—
629C2×D4—3441no—
630C2×D4—3441no—
631C2×D4—3441no—
632C2×D4—1722no—
633C2×D4—1722no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—42no—
653C22×C4—81no—
654C22×C4—81no—
655C22×C4—864no—
656C22×C4—864no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—3441no—
661C22×C4—3441no—
662C22×C4—1722no—
663C22×C4—1722no—
664C22×C4#1062189812yes—
665C22×C4#1062189812yes—
666C22×C4D4×D4312yes—
667C22×C4D4×D4312yes—
668C22×C4C2×C22⋊D4311yescharacteristic
669C22×C4C2×C22⋊D4311yescharacteristic
670C22×C4C2×C22⋊D4311yescharacteristic
671C22×C4C23×D4311yescharacteristic
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—861no—
676C2×C8—861no—
677C2×C8—861no—
678C2×C8—861no—
679C2×C8—861no—
680C2×C8—861no—
681C2×C8—861no—
682C2×C8—861no—
683C2×C8—861no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—42no—
693C4⋊C4—432no—
694C4⋊C4—432no—
695C4⋊C4—864no—
696C4⋊C4—864no—
697C4⋊C4—864no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C22⋊C4—42no—
701C22⋊C4—81no—
702C22⋊C4—81no—
703C22⋊C4—81no—
704C22⋊C4—81no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C42—42no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—862no—
730C23—1721no—
731C23—1721no—
732C23—1721no—
733C23—1721no—
734C23—1721no—
735C23—1721no—
736C23#1306329312yes—
737C23#1306330812yes—
738C23C22×C22⋊D4311yescharacteristic
739Q8—44no—
740Q8—862no—
741Q8—862no—
742Q8—1721no—
743Q8—1721no—
744D4—44no—
745D4—44no—
746D4—44no—
747D4—862no—
748D4—862no—
749D4—3444no—
750D4—3444no—
751D4—1728no—
752D4—1721no—
753D4—1721no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—84no—
786C2×C4—862no—
787C2×C4—862no—
788C2×C4—862no—
789C2×C4—3444no—
790C2×C4—1728no—
791C2×C4—1721no—
792C2×C4—1721no—
793C2×C4—1721no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1721no—
797C2×C4#1306329312yes—
798C2×C4#1306330812yes—
799C2×C4C2×D4×D4311yescharacteristic
800C2×C4C2×D4×D4311yescharacteristic
801C2×C4C2×#1062189811yescharacteristic
802C2×C4C2×#1062189811yescharacteristic
803C2×C4#1306337011yescharacteristic
804C2×C4#1306337011yescharacteristic
805C8—1721no—
806C8—1721no—
807C8—1721no—
808C8—1721no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—3441no—
831C22—3441no—
832C22—3441no—
833C22—3441no—
834C22—1722no—
835C22—1722no—
836C22—1722no—
837C22C2×#1306329311yescharacteristic
838C22C2×#1306330811yescharacteristic
839C22#1458345811yescharacteristic
840C22#1458370211yescharacteristic
841C22#1458370711yescharacteristic
842C22#1458371011yescharacteristic
843C22#1458371411yescharacteristic
844C4—22no—
845C4—22no—
846C4—41no—
847C4—81no—
848C4—81no—
849C4—81no—
850C4—81no—
851C4—1722no—
852C4—1722no—
853C4—1722no—
854C4#1458353911yescharacteristic
855C4#1458353911yescharacteristic
856C4#1458353911yescharacteristic
857C4#1458353911yescharacteristic
858C2—42no—
859C2—42no—
860C2—81no—
861C2—3442no—
862C2#1913792211yescharacteristic
863C2#1914389611yescharacteristic
864C2#1914390711yescharacteristic
865C2#1914457311yescharacteristic
866C2#1914458411yescharacteristic
867C2#1914544711yescharacteristic
868C2#1914547711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2311C2
socleC23×C43C22×D4
prime radicalC2×#14583477C2
hypercenter#2311D43
hypocenterC43#24017
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. C2×#14583240C2semidirect
3. C2×#14583223C2semidirect
4. #19135798C2semidirect
5. #19135791C2semidirect
6. #19135784C2semidirect
7. #19135777C2semidirect
8. #19134912C2semidirect
9. #19134902C2semidirect
10. #19134787C2semidirect
11. #19134782C2semidirect
12. #19134533C2semidirect
13. #19134533C2semidirect
14. #19134507C2semidirect
15. C43×#2311C2semidirect
427. #2311D43semidirect
497. C43#24017semidirect

Maximal subgroups

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

subgroupindex
C2×#145834772
C2×#145832402
C2×#145832232
#191357982
#191357912
#191357842
#191357772
#191349122
#191349022
#191347872
#191347822
#191345332
#191345072
C43×#23112
#2401743