Finite Group Databasebeta

← #25116898

Subgroups — #25116898

Order 11008.

1146 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583041C211yesmaximal, characteristic
2C2×#14582996C211yesmaximal, characteristic, complemented
3C2×#14582892C211yesmaximal, characteristic, complemented
4#19137638C211yesmaximal, characteristic, complemented
5#19137434C211yesmaximal, characteristic, complemented
6#19135289C211yesmaximal, characteristic, complemented
7#19135212C211yesmaximal, characteristic, complemented
8#19135020C211yesmaximal, characteristic, complemented
9#19134953C211yesmaximal, characteristic, complemented
10#19134945C211yesmaximal, characteristic, complemented
11#19134860C211yesmaximal, characteristic, complemented
12#19134793C211yesmaximal, characteristic, complemented
13#19134426C211yesmaximal, characteristic, complemented
14#19134372C211yesmaximal, characteristic, complemented
15C43×#1972C211yesmaximal, characteristic, complemented
16C22×#10621900C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23C2×#13063283C2211yescharacteristic
24#14583041C418yescomplemented
25#14582996—24no—
26C2×#13063258C2211yescharacteristic
27#14582892—24no—
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×(C2×D43)⋊C8C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36#14582802C2211yescharacteristic
37#14582799—21no—
38#14582799—21no—
39#14582799—21no—
40#14582795C2211yescharacteristic
41#14582793—21no—
42#14582776—21no—
43#14582757—21no—
44#14582756C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46C22⋊C4×Dic43—21no—
47C22⋊C4×Dic43—21no—
48C4×(C2×D43)⋊C4C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×D8×C43C2211yescharacteristic
56C2×#106×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#97×C43C2211yescharacteristic
60C43×#390C2211yescharacteristic
61C43×#390C2211yescharacteristic
62C2×#10621900—22no—
63C2×#10621900—22no—
64C2×#10621900—22no—
65C2×#10621900—41no—
66C2×#10621900—41no—
67C2×#10621900C2×C414yescomplemented
68C22×Dic86C2311yescharacteristic
69C22×C22⋊D43—21no—
70C22×C22⋊D43—21no—
71C23×Dic43—21no—
72C23×Dic43—21no—
73C22×C4×D43C2311yescharacteristic
74C2×#10621883—22no—
75C2×#10621883—22no—
76C2×#10621883C2×C414yes—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C2×C8×D43—22no—
80C2×C8×D43—22no—
81C2×C8×D43—41no—
82#13063296—22no—
83#13063296C2×C414yes—
84C4×Dic86—22no—
85C4×Dic86—41no—
86#13063290—22no—
87#13063290—41no—
88D4×Dic43—22no—
89D4×Dic43—41no—
90#13063283—22no—
91#13063283—41no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4D411yescharacteristic
105C2×(C2×D43)⋊C4D411yescharacteristic
106C2×C4×Dic43—21no—
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43C2311yescharacteristic
111#13063258—22no—
112#13063250C2×C414yescomplemented
113#13063250D414yescomplemented
114#13063248—22no—
115#13063246—22no—
116#13063246—41no—
117#13063246C2×C414yescomplemented
118(C2×D43)⋊C8C2×C414yescomplemented
119#13063235—22no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95D411yescharacteristic
124C43⋊#95D411yescharacteristic
125C22×D4×C43C2311yescharacteristic
126C22×D4×C43C2311yescharacteristic
127C2×D8×C43—41no—
128C2×D8×C43—41no—
129C2×D8×C43C2×C414yes—
130C22×C8×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C42×C43C2311yescharacteristic
139#106×C43—41no—
140#102×C43—22no—
141#102×C43—22no—
142#97×C43—41no—
143C24×C43—21no—
144C24×C43—21no—
145C23×D43C2×D411yescharacteristic
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43C22×C412yes—
157C2×D4×C43C22×C412yes—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2×D411yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—24no—
164C2×C22⋊D43—24no—
165C2×C22⋊D43—42no—
166C2×C22⋊D43—42no—
167C2×C22⋊D43—81no—
168C2×C22⋊D43—81no—
169C22×Dic43—24no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—42no—
175C22×Dic43—42no—
176C22×Dic43—42no—
177C22×Dic43—42no—
178C22×Dic43—81no—
179C22×Dic43C2×D411yescharacteristic
180C22×Dic43C2×D411yescharacteristic
181C22×Dic43C2×D411yescharacteristic
182#10621900—28no—
183#10621900—44no—
184#10621900—44no—
185#10621900—44no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—21no—
190C2×C4×D43C22×C412yes—
191C2×C4×D43#4112yes—
192C2×Dic86—21no—
193C2×Dic86—21no—
194C2×Dic86—21no—
195C2×Dic86C22×C412yes—
196C2×Dic86C2×D412yes—
197C2×Dic86#4112yes—
198D8×C43—44no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43C22×C412yes—
204C2×C8×C43C2×D412yes—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C22⋊C4×C43—42no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—81no—
212C22⋊C4×C43—81no—
213C42×C43—21no—
214C42×C43—21no—
215C22⋊Dic43—24no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218C22⋊Dic43—81no—
219#10621883—28no—
220(C2×D43)⋊C4—41no—
221(C2×D43)⋊C4—41no—
222(C2×D43)⋊C4—42no—
223(C2×D43)⋊C4—81no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43C22×C412yes—
229C4⋊Dic43C2×D412yes—
230Dic43⋊C4—42no—
231Dic43⋊C4—42no—
232Dic43⋊C4—81no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43—42no—
236C4×Dic43—42no—
237C4×Dic43—42no—
238C4×Dic43—81no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8C22×C412yes—
245C8×D43—44no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43C22×D411yescharacteristic
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43C4×D412yes—
268D4×C43—22no—
269D4×C43—22no—
270D4×C43—22no—
271D4×C43—22no—
272D4×C43—41no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—41no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—21no—
281C2×C4×C43—21no—
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×C43C23×C411yescharacteristic
289C2×C4×C43C22×D411yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C2×C4×C43H(5,𝔽2)11yescharacteristic
294C22⋊D43—48no—
295C22⋊D43—84no—
296C2×Dic43—22no—
297C2×Dic43—21no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—21no—
301C2×Dic43—22no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—22no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—48no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—84no—
318C2×Dic43C4×D412yes—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323Dic86—22no—
324Dic86—22no—
325Dic86—22no—
326Dic86C4×D414yes—
327C8×C43—22no—
328C8×C43—22no—
329C43⋊C8—22no—
330C43⋊C8—41no—
331#22857—431nomaximal, Sylow
332C22×C43—42no—
333C22×C43—42no—
334C22×C43—42no—
335C22×C43—42no—
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—81no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43—81no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43C2×C4×D411yescharacteristic
347C22×C43D4211yescharacteristic
348C22×C43#54611yescharacteristic
349C22×C43#57511yescharacteristic
350C22×C43#57511yescharacteristic
351C22×C43#57611yescharacteristic
352C22×C43#57711yescharacteristic
353C2×D43—22no—
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—41no—
357C2×D43—41no—
358C2×D43—41no—
359C2×D43—41no—
360C4×C43—41no—
361C4×C43—41no—
362C4×C43—81no—
363C4×C43—81no—
364C4×C43C2×C4×D411yescharacteristic
365C4×C43#51811yescharacteristic
366C4×C43#54611yescharacteristic
367C4×C43#55111yescharacteristic
368Dic43—24no—
369Dic43—22no—
370Dic43—42no—
371Dic43—41no—
372Dic43—42no—
373Dic43—41no—
374Dic43—81no—
375C2×#449—431no—
376C2×#440—431no—
377C2×#416—431no—
378#2363—431no—
379#2341—431no—
380#1972D4311yescharacteristic, complemented
381#1936—431no—
382#1925—431no—
383#1893—431no—
384#1880—431no—
385#1879—431no—
386#1865—431no—
387#1854—431no—
388#1763—431no—
389#1752—431no—
390C2×C43—82no—
391C2×C43—82no—
392C2×C43#235811yescharacteristic
393C2×C43#294311yescharacteristic
394C2×C43#294611yescharacteristic
395C2×C43#326811yescharacteristic
396C2×C43#327111yescharacteristic
397C2×C43#330911yescharacteristic
398C2×C43#332111yescharacteristic
399D43—42no—
400C22×#41—431no—
401C22×SD16—431no—
402C22×D8C2×D4311yescharacteristic
403C23×C8—431no—
404C2×#121—431no—
405C2×C4×Q8—431no—
406C2×C4×Q8—431no—
407C2×C4×D4—431no—
408C2×#117—431no—
409#449—438no—
410#440—864no—
411C2×#107—431no—
412C2×#106C2×D4311yescharacteristic
413#416—864no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103—431no—
417C2×#102—431no—
418C2×#102—431no—
419C2×#102—431no—
420C2×#102C2×D4311yescharacteristic
421C2×#102C2×D4311yescharacteristic
422C2×C22⋊C8—431no—
423C2×#97—431no—
424C2×#97C2×D4311yescharacteristic
425#390—431no—
426#390—861no—
427#390—861no—
428#390—861no—
429#390C2×D4311yescharacteristic
430#390C2×D4311yescharacteristic
431#389—431no—
432#388—861no—
433#386—861no—
434#380—431no—
435#380—861no—
436C4×C4⋊C4—431no—
437C4×C22⋊C4—431no—
438C4×C22⋊C4—861no—
439C4×C22⋊C4—861no—
440#340—431no—
441#340—431no—
442#340—431no—
443#340—431no—
444#336—431no—
445#336—431no—
446C43#2285711yescharacteristic, complemented, Sylow
447C2×#41—434no—
448C2×#41—862no—
449C2×#41—862no—
450C2×#41—862no—
451C2×#41—1721no—
452C2×#41—1721no—
453C22×Q8—431no—
454C22×D4—861no—
455C22×D4—861no—
456C22×D4C22×D4311yescharacteristic
457C22×D4C22×D4311yescharacteristic
458C23×C4—431no—
459C23×C4—861no—
460C23×C4—861no—
461C2×SD16—434no—
462C2×SD16—862no—
463C2×SD16—862no—
464C2×D8—41no—
465C2×D8—41no—
466C2×D8C4×D4314yes—
467C22×C8—431no—
468C22×C8—431no—
469C22×C8—862no—
470C22×C8—862no—
471C22×C8—1721no—
472C22×C8C22×D4311yescharacteristic
473C22×C8C22×D4311yescharacteristic
474#121—434no—
475#121—862no—
476C4×Q8—862no—
477C4×Q8—862no—
478C4×Q8—1721no—
479C4×Q8—1721no—
480C4×D4—862no—
481C4×D4—1721no—
482#117—862no—
483#117—1721no—
484C2×C4⋊C4—431no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—861no—
488C2×C4⋊C4—861no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—431no—
497C2×C22⋊C4—431no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C42—431no—
505C2×C42—861no—
506C2×C42—861no—
507C2×C42—861no—
508C2×C42—861no—
509C2×C42C22×D4311yescharacteristic
510#107—862no—
511#106—41no—
512#103—434no—
513#103—434no—
514#103—862no—
515#102—22no—
516#102—22no—
517#102—434no—
518#102—862no—
519#102—1721no—
520C22⋊C8—434no—
521#97—41no—
522#97—862no—
523#95—431no—
524#95—431no—
525#95—861no—
526#95—861no—
527#95—861no—
528C24—21no—
529C24—21no—
530C24—431no—
531#41—868no—
532#41—1724no—
533#41—1724no—
534#41—1724no—
535C2×Q8—432no—
536C2×Q8—432no—
537C2×Q8—432no—
538C2×Q8—861no—
539C2×Q8—861no—
540C2×Q8—861no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—864no—
552C2×D4—864no—
553C2×D4—3441no—
554C2×D4—3441no—
555C2×D4—1722no—
556C2×D4—1722no—
557C2×D4C2×C4×D4312yes—
558C2×D4C2×C4×D4312yes—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—431no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—431no—
565C22×C4—431no—
566C22×C4—864no—
567C22×C4—861no—
568C22×C4—861no—
569C22×C4—861no—
570C22×C4—861no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—3441no—
576C22×C4—1722no—
577C22×C4—1722no—
578C22×C4—1722no—
579C22×C4—1722no—
580C22×C4D4×D4311yescharacteristic
581C22×C4D4×D4311yescharacteristic
582C22×C4C23×D4311yescharacteristic
583SD16—868no—
584D8—44no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—432no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—1724no—
596C2×C8C2×C4×D4312yes—
597C2×C8D4×D4312yes—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—432no—
603C4⋊C4—432no—
604C4⋊C4—861no—
605C4⋊C4—861no—
606C4⋊C4—861no—
607C4⋊C4—861no—
608C4⋊C4—3441no—
609C4⋊C4—1722no—
610C4⋊C4—1722no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—81no—
614C22⋊C4—81no—
615C22⋊C4—864no—
616C22⋊C4—3441no—
617C22⋊C4—3441no—
618C22⋊C4—1721no—
619C22⋊C4—1721no—
620C22⋊C4—1722no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C42—21no—
624C42—21no—
625C42—861no—
626C42—861no—
627C42—3441no—
628C42—1722no—
629C42—1722no—
630C42—1722no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—432no—
646C23—861no—
647C23—861no—
648C23—861no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23C2×D4×D4311yescharacteristic
653Q8—434no—
654Q8—862no—
655Q8—862no—
656Q8—862no—
657D4—22no—
658D4—22no—
659D4—22no—
660D4—22no—
661D4—41no—
662D4—41no—
663D4—41no—
664D4—41no—
665D4—3444no—
666D4—1728no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—432no—
680C2×C4—862no—
681C2×C4—861no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—861no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—862no—
697C2×C4—3444no—
698C2×C4—1728no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4C22×C4×D4311yescharacteristic
707C2×C4C2×D4×D4311yescharacteristic
708C2×C4#41×D4311yescharacteristic
709C2×C4#41×D4311yescharacteristic
710C2×C4#1306337011yescharacteristic
711C2×C4#1306337011yescharacteristic
712C8—22no—
713C8—22no—
714C8—862no—
715C8—1721no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—81no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—862no—
731C22—862no—
732C22—862no—
733C22—1721no—
734C22—1721no—
735C22—1721no—
736C22—1721no—
737C22C4×D4×D4311yescharacteristic
738C22#1458353411yescharacteristic
739C22#1458353811yescharacteristic
740C22#1458369511yescharacteristic
741C22#1458369511yescharacteristic
742C22#1458370311yescharacteristic
743C22#1458370911yescharacteristic
744C4—41no—
745C4—41no—
746C4—81no—
747C4—81no—
748C4—862no—
749C4—864no—
750C4—3441no—
751C4—1722no—
752C4—1721no—
753C4—1722no—
754C4—1721no—
755C4C4×D4×D4311yescharacteristic
756C4#1458337211yescharacteristic
757C4#1458353811yescharacteristic
758C4#1458357911yescharacteristic
759C2—82no—
760C2—82no—
761C2—1722no—
762C2#1913757611yescharacteristic
763C2#1914339211yescharacteristic
764C2#1914342411yescharacteristic
765C2#1914613411yescharacteristic
766C2#1914617911yescharacteristic
767C2#1914659611yescharacteristic
768C2#1914677611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1972C2
socleC23×C43C22×D4
prime radicalC2×#14583041C2
cosocleC22×C4×C43C24
hypercenter#1972D43
hypocenterC43#22857
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1972

Complements

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

NH ≅ G/Ntype
2. C2×#14582996C2semidirect
3. C2×#14582892C2semidirect
4. #19137638C2semidirect
5. #19137434C2semidirect
6. #19135289C2semidirect
7. #19135212C2semidirect
8. #19135020C2semidirect
9. #19134953C2semidirect
10. #19134945C2semidirect
11. #19134860C2semidirect
12. #19134793C2semidirect
13. #19134426C2semidirect
14. #19134372C2semidirect
15. C43×#1972C2semidirect
24. #14583041C4semidirect
67. C2×#10621900C2×C4semidirect
112. #13063250C2×C4semidirect
113. #13063250D4semidirect
117. #13063246C2×C4semidirect
118. (C2×D43)⋊C8C2×C4semidirect
380. #1972D43semidirect
446. C43#22857semidirect

Maximal subgroups

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

subgroupindex
C2×#145830412
C2×#145829962
C2×#145828922
#191376382
#191374342
#191352892
#191352122
#191350202
#191349532
#191349452
#191348602
#191347932
#191344262
#191343722
C43×#19722
#2285743