Finite Group Databasebeta

← #25096416

Subgroups — #25096416

Order 11008.

1374 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583380C211yesmaximal, characteristic
2C2×#14582864C211yesmaximal, characteristic
3#19137184C211yesmaximal, characteristic
4#19134691C211yesmaximal, characteristic, complemented
5#19134689C211yesmaximal, characteristic, complemented
6#19134688C211yesmaximal, characteristic, complemented
7#19134687C211yesmaximal, characteristic, complemented
8#19134684C211yesmaximal, characteristic, complemented
9#19134681C211yesmaximal, characteristic, complemented
10#19134680C211yesmaximal, characteristic, complemented
11#19134313C211yesmaximal, characteristic, complemented
12#19134313C211yesmaximal, characteristic, complemented
13#19134310C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C43×#1824C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583380—24no—
20#14583380C418yescomplemented
21C2×#13063290—21no—
22C2×#13063287—21no—
23C2×C4×C22⋊D43—21no—
24C2×C4×C22⋊D43—21no—
25C2×#13063284C2211yescharacteristic
26C2×#13063283C2211yescharacteristic
27C2×#13063283C2211yescharacteristic
28C2×#13063283C2211yescharacteristic
29C2×C4⋊C4×D43C2211yescharacteristic
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582864—24no—
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36#14582803—21no—
37#14582799—21no—
38#14582777—21no—
39#14582775—21no—
40#14582759C2211yescharacteristic
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C22×C4⋊C4×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898C2×C414yes—
67C2×#10621898D414yes—
68C22×Dic86D411yescharacteristic
69C22×D172D411yescharacteristic
70C22×C22⋊D43D411yescharacteristic
71C22×C22⋊D43D411yescharacteristic
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43C2311yescharacteristic
76C22×C4×D43C2311yescharacteristic
77C2×#10621872—22no—
78C2×#10621872—22no—
79C2×#10621872—22no—
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C2×C8×D43—22no—
83C2×C8×D43—22no—
84C2×C8×D43—22no—
85#13063290—28no—
86#13063287—28no—
87C4×C22⋊D43—28no—
88C4×C22⋊D43—28no—
89#13063284—22no—
90#13063284C2×C414yescomplemented
91#13063283—22no—
92#13063283—22no—
93#13063283—22no—
94#13063283—22no—
95#13063283C2×C414yes—
96#13063283C2×C414yescomplemented
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×C4⋊Dic43C2311yescharacteristic
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C4⋊C4×D43—22no—
105C4⋊C4×D43—22no—
106C4⋊C4×D43—22no—
107C4⋊C4×D43—22no—
108C4⋊C4×D43C2×C414yes—
109C4⋊C4×D43C2×C414yescomplemented
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C22⋊(C43⋊C8)—22no—
122(C2×D43)⋊C8—22no—
123(C2×D43)⋊C8—22no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C23×C4×C43—21no—
128C23×C4×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—22no—
133C2×C4⋊C4×C43C2×C414yescomplemented
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C22⋊C8×C43—22no—
140#95×C43—21no—
141C24×C43C2×D411yescharacteristic
142C23×D43C2×D411yescharacteristic
143C23×D43C2×D411yescharacteristic
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—24no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—81no—
154C22×C4×C43—81no—
155C22×C4×C43C22×C412yes—
156C22×C4×C43C2×D412yes—
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43C22⋊C414yes—
164C2×C22⋊D43C22⋊C414yes—
165C22×Dic43—21no—
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171#10621898—28no—
172#10621898—28no—
173#10621898—28no—
174#10621898—28no—
175C2×D172—22no—
176C2×D172—22no—
177C2×D172C22⋊C414yes—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—24no—
183C2×C4×D43—24no—
184C2×C4×D43—42no—
185C2×C4×D43—81no—
186C2×C4×D43—81no—
187C2×C4×D43—81no—
188C2×C4×D43—81no—
189C2×C4×D43—81no—
190C2×C4×D43—81no—
191C2×C4×D43C22×C412yes—
192C2×C4×D43C22×C412yes—
193C2×C4×D43C2×D412yes—
194C2×C4×D43C2×D412yes—
195C2×C4×D43#4112yes—
196C2×C4×D43#4112yes—
197C2×C4×D43#4112yes—
198C2×C4×D43#4112yes—
199C2×Dic86—22no—
200C2×Dic86—22no—
201C2×Dic86C22⋊C414yes—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C4⋊C4×C43—24no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43C22×C412yes—
216C4⋊C4×C43C22×C412yes—
217C22⋊C4×C43—81no—
218C22⋊Dic43—24no—
219C22⋊Dic43—81no—
220(C2×D43)⋊C4—24no—
221(C2×D43)⋊C4—24no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—81no—
224(C2×D43)⋊C4—81no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43C22×C412yes—
232C4⋊Dic43C22×C412yes—
233Dic43⋊C4—24no—
234Dic43⋊C4—24no—
235Dic43⋊C4—42no—
236C4×Dic43—24no—
237C4×Dic43—24no—
238C4×Dic43—24no—
239C4×Dic43—42no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246#10621872—44no—
247C8×D43—44no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43C2×C22⋊C412yes—
255C23×C43C22×D411yescharacteristic
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43C2×C22⋊C412yes—
267C22×D43C2×C22⋊C412yes—
268C22×D43#12312yes—
269C22×D43#12312yes—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—84no—
289C2×C4×C43C2×C22⋊C412yes—
290C2×C4×C43C23×C411yescharacteristic
291C2×C4×C43C22×D411yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×C4×C43C2×#4111yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C22⋊D43—28no—
297C22⋊D43—28no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—41no—
303C2×Dic43—41no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43C2×C22⋊C412yes—
313C2×Dic43C2×C22⋊C412yes—
314C2×Dic43#12312yes—
315C2×Dic43#12312yes—
316D172—28no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—84no—
322C4×D43—84no—
323C4×D43—84no—
324C4×D43#11714yes—
325C4×D43#11714yes—
326C4×D43#12314yes—
327C4×D43#12314yes—
328Dic86—28no—
329C8×C43—41no—
330C8×C43—41no—
331C43⋊C8—41no—
332C43⋊C8—41no—
333#20703—431nomaximal, Sylow
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43C22×C22⋊C411yescharacteristic
342C22×C43C2×#12311yescharacteristic
343C22×C43C2×#12311yescharacteristic
344C22×C43#57611yescharacteristic
345C22×C43#57711yescharacteristic
346C22×C43#57711yescharacteristic
347C22×C43#57811yescharacteristic
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—41no—
360C2×D43—41no—
361C2×D43#38114yes—
362C4×C43—22no—
363C4×C43—42no—
364C4×C43—42no—
365C4×C43—81no—
366C4×C43—81no—
367C4×C43C2×#11711yescharacteristic
368C4×C43C2×#11711yescharacteristic
369C4×C43C2×#12311yescharacteristic
370C4×C43C2×#12311yescharacteristic
371Dic43—22no—
372Dic43—42no—
373Dic43—42no—
374Dic43—81no—
375Dic43—81no—
376Dic43#38114yes—
377C2×#520—431no—
378C2×#408—431no—
379#2311—431no—
380#1825—431no—
381#1825—431no—
382#1825—431no—
383#1825—431no—
384#1824—431no—
385#1824D4311yescharacteristic, complemented
386#1823—431no—
387#1823—431no—
388#1736—431no—
389#1736—431no—
390#1735—431no—
391C2×#340—431no—
392C2×C43—42no—
393C2×C43C2×#38111yescharacteristic
394C2×C43#289711yescharacteristic
395C2×C43#289811yescharacteristic
396C2×C43#309611yescharacteristic
397C2×C43#309711yescharacteristic
398C2×C43#309811yescharacteristic
399C2×C43#309911yescharacteristic
400D43—24no—
401D43—42no—
402C22×#41—431no—
403C22×M16—431no—
404C23×C8—431no—
405#520—438no—
406#520—864no—
407C2×C4×Q8—861no—
408C2×C4×D4—861no—
409C2×C4×D4—861no—
410C2×C4×D4—861no—
411C2×#117—431no—
412C2×#117—431no—
413C2×#117—431no—
414C2×#117—431no—
415C22×C4⋊C4—431no—
416C22×C4⋊C4—431no—
417C22×C4⋊C4—431no—
418C22×C4⋊C4C2×D4311yescharacteristic
419#408—864no—
420C2×C22⋊C8—431no—
421C2×C22⋊C8—431no—
422C2×C22⋊C8—431no—
423C2×C22⋊C8C2×D4311yescharacteristic
424#391—861no—
425#390—861no—
426#386—861no—
427#386—861no—
428#380—431no—
429#380—431no—
430#380—431no—
431#380C2×D4311yescharacteristic
432#340—431no—
433#340—431no—
434#340—431no—
435#340—431no—
436#340—431no—
437#340—431no—
438#340—431no—
439#340—431no—
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444#340C2×D4311yescharacteristic
445#340C2×D4311yescharacteristic
446#340C2×D4311yescharacteristic
447#340C2×D4311yescharacteristic
448C43#2070311yescharacteristic, complemented, Sylow
449C2×#41—434no—
450C2×#41—434no—
451C2×#41—862no—
452C2×#41—862no—
453C2×#41—862no—
454C2×#41—862no—
455C22×Q8—431no—
456C22×D4—431no—
457C22×D4—431no—
458C22×D4—431no—
459C23×C4—21no—
460C23×C4—431no—
461C23×C4—431no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4—861no—
465C23×C4C22×D4311yescharacteristic
466C2×M16—862no—
467C2×M16—862no—
468C2×M16—862no—
469C22×C8—431no—
470C22×C8—431no—
471C22×C8—862no—
472C22×C8—862no—
473C22×C8—862no—
474C22×C8C22×D4311yescharacteristic
475C22×C8C22×D4311yescharacteristic
476C4×Q8—868no—
477C4×D4—868no—
478C4×D4—868no—
479C4×D4—868no—
480#117—434no—
481#117—434no—
482#117—434no—
483#117—862no—
484#117—862no—
485#117—862no—
486#117—862no—
487#117—862no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—434no—
493C2×C4⋊C4—434no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—862no—
497C2×C4⋊C4—862no—
498C2×C4⋊C4—862no—
499C2×C4⋊C4—862no—
500C2×C4⋊C4—861no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4C4×D4314yescomplemented
504C2×C4⋊C4C22×D4311yescharacteristic
505C2×C4⋊C4C22×D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—861no—
515C2×C22⋊C4—861no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519C2×C42—861no—
520C22⋊C8—22no—
521C22⋊C8—862no—
522C22⋊C8—862no—
523C22⋊C8—862no—
524#95—21no—
525#95—861no—
526#95—861no—
527#95—861no—
528C24—431no—
529C24—431no—
530C24D4×D4311yescharacteristic
531#41—868no—
532#41—868no—
533#41—868no—
534#41—868no—
535C2×Q8—434no—
536C2×Q8—862no—
537C2×Q8—862no—
538C2×D4—434no—
539C2×D4—434no—
540C2×D4—434no—
541C2×D4—862no—
542C2×D4—862no—
543C2×D4—862no—
544C2×D4—862no—
545C2×D4—862no—
546C2×D4—862no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—431no—
559C22×C4—432no—
560C22×C4—432no—
561C22×C4—432no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—431no—
566C22×C4—432no—
567C22×C4—432no—
568C22×C4—864no—
569C22×C4—864no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—3441no—
579C22×C4—3441no—
580C22×C4—3441no—
581C22×C4—3441no—
582C22×C4—3441no—
583C22×C4—3441no—
584C22×C4—1722no—
585C22×C4C2×C4×D4312yes—
586C22×C4D4×D4311yescharacteristic
587C22×C4D4×D4312yes—
588C22×C4C23×D4311yescharacteristic
589M16—1724no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—1724no—
603C4⋊C4—24no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—432no—
611C4⋊C4—432no—
612C4⋊C4—864no—
613C4⋊C4—864no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—861no—
618C4⋊C4—861no—
619C4⋊C4—861no—
620C4⋊C4—1722no—
621C4⋊C4C2×C4×D4312yes—
622C4⋊C4C2×C4×D4312yes—
623C22⋊C4—81no—
624C22⋊C4—864no—
625C22⋊C4—864no—
626C22⋊C4—864no—
627C22⋊C4—3441no—
628C22⋊C4—3441no—
629C22⋊C4—3441no—
630C22⋊C4—1722no—
631C42—864no—
632C42—864no—
633C42—864no—
634C42—1722no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—432no—
642C23—432no—
643C23—432no—
644C23—432no—
645C23—861no—
646C23—861no—
647C23—861no—
648C23—861no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23—861no—
653C23—861no—
654C23—861no—
655C23C22⋊C4×D4312yes—
656C23C2×D4×D4311yescharacteristic
657Q8—868no—
658D4—868no—
659D4—868no—
660D4—868no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—84no—
680C2×C4—432no—
681C2×C4—432no—
682C2×C4—432no—
683C2×C4—434no—
684C2×C4—434no—
685C2×C4—434no—
686C2×C4—434no—
687C2×C4—432no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—862no—
693C2×C4—862no—
694C2×C4—862no—
695C2×C4—862no—
696C2×C4—3444no—
697C2×C4—3444no—
698C2×C4—3444no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4C22⋊C4×D4312yes—
710C2×C4C22×C4×D4311yescharacteristic
711C2×C4C2×D4×D4311yescharacteristic
712C2×C4#41×D4311yescharacteristic
713C2×C4#41×D4311yescharacteristic
714C2×C4#41×D4311yescharacteristic
715C2×C4#41×D4311yescharacteristic
716C8—41no—
717C8—41no—
718C8—1721no—
719C8—1721no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—434no—
728C22—862no—
729C22—862no—
730C22—862no—
731C22—862no—
732C22—862no—
733C22—862no—
734C22—862no—
735C22—862no—
736C22—862no—
737C22—1721no—
738C22—1721no—
739C22—1721no—
740C22—1721no—
741C22C2×C22⋊C4×D4311yescharacteristic
742C22#123×D4311yescharacteristic
743C22#123×D4311yescharacteristic
744C22#1458370311yescharacteristic
745C22#1458370511yescharacteristic
746C22#1458370911yescharacteristic
747C22#1458371211yescharacteristic
748C4—22no—
749C4—42no—
750C4—42no—
751C4—81no—
752C4—81no—
753C4—434no—
754C4—862no—
755C4—3441no—
756C4—3441no—
757C4—1722no—
758C4—1722no—
759C4#117×D4311yescharacteristic
760C4#117×D4311yescharacteristic
761C4#123×D4311yescharacteristic
762C4#123×D4311yescharacteristic
763C2—42no—
764C2—864no—
765C2—1722no—
766C2#381×D4311yescharacteristic
767C2#1914312011yescharacteristic
768C2#1914312311yescharacteristic
769C2#1914455211yescharacteristic
770C2#1914456311yescharacteristic
771C2#1914457411yescharacteristic
772C2#1914458511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1824C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1824D43
hypocenterC43#20703
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
4. #19134691C2semidirect
5. #19134689C2semidirect
6. #19134688C2semidirect
7. #19134687C2semidirect
8. #19134684C2semidirect
9. #19134681C2semidirect
10. #19134680C2semidirect
11. #19134313C2semidirect
12. #19134313C2semidirect
13. #19134310C2semidirect
14. #340×D43C2semidirect
15. C43×#1824C2semidirect
20. #14583380C4semidirect
90. #13063284C2×C4semidirect
96. #13063283C2×C4semidirect
109. C4⋊C4×D43C2×C4semidirect
133. C2×C4⋊C4×C43C2×C4semidirect
385. #1824D43semidirect
448. C43#20703semidirect
503. C2×C4⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833802
C2×#145828642
#191371842
#191346912
#191346892
#191346882
#191346872
#191346842
#191346812
#191346802
#191343132
#191343102
#340×D432
C43×#18242
#2070343