Finite Group Databasebeta

← #25116937

Subgroups — #25116937

Order 11008.

1174 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×#14583046C211yesmaximal, characteristic
2C2×#14583010C211yesmaximal, characteristic, complemented
3C2×#14582893C211yesmaximal, characteristic, complemented
4#19137633C211yesmaximal, characteristic, complemented
5#19137423C211yesmaximal, characteristic, complemented
6#19135474C211yesmaximal, characteristic, complemented
7#19135283C211yesmaximal, characteristic, complemented
8#19135228C211yesmaximal, characteristic, complemented
9#19135021C211yesmaximal, characteristic, complemented
10#19134944C211yesmaximal, characteristic, complemented
11#19134930C211yesmaximal, characteristic, complemented
12#19134839C211yesmaximal, characteristic, complemented
13#19134419C211yesmaximal, characteristic, complemented
14#19134374C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063299C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×#13063287C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24#14583046C418yescomplemented
25#14583010—24no—
26#14582893—24no—
27C2×#13063250C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063247C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×#13063245C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582800C2211yescharacteristic
40#14582799—21no—
41#14582795C2211yescharacteristic
42#14582790—21no—
43#14582775—21no—
44#14582775—21no—
45#14582775—21no—
46#14582761—21no—
47C4⋊C4×Dic43C2211yescharacteristic
48C4×(C2×D43)⋊C4—21no—
49C4×C22⋊Dic43C2211yescharacteristic
50#95×D43—21no—
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C2×#107×C43C2211yescharacteristic
57C2×#106×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C2×#10621898C2×C414yescomplemented
68C22×Dic86C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C2×#10621873—41no—
78C2×#10621873—41no—
79C2×#10621873C2×C414yescomplemented
80C2×D344—22no—
81C2×D344—22no—
82C2×D344C2×C414yes—
83C22×C43⋊C8—22no—
84C22×C43⋊C8—22no—
85C22×C43⋊C8—41no—
86C22×C43⋊C8C2311yescharacteristic
87C22×C43⋊C8C2311yescharacteristic
88#13063299—22no—
89#13063299C2×C414yescomplemented
90#13063287—22no—
91#13063287—22no—
92#13063287—22no—
93#13063287—41no—
94#13063287—41no—
95#13063287—41no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43D411yescharacteristic
99C2×C22⋊Dic43D411yescharacteristic
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109#13063250C2×C414yescomplemented
110#13063248—22no—
111#13063248—22no—
112#13063247C2×C414yescomplemented
113#13063245—22no—
114#13063245—22no—
115#13063245—41no—
116#13063245D414yescomplemented
117#13063235—22no—
118#13063235—41no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95D411yescharacteristic
126C43⋊#95D411yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130#117×C43—22no—
131#117×C43—41no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C42×C43—21no—
139#107×C43—41no—
140#106×C43—22no—
141C22⋊C8×C43C2×C414yescomplemented
142#95×C43—21no—
143C24×C43C2×D411yescharacteristic
144C23×D43—21no—
145C23×D43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C22×C412yes—
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4112yes—
157C22×C4×C43C2411yescharacteristic
158C2×C22⋊D43—24no—
159C2×C22⋊D43—24no—
160C2×C22⋊D43—42no—
161C2×C22⋊D43—42no—
162C2×C22⋊D43—81no—
163C2×C22⋊D43—81no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D411yescharacteristic
170#10621898—28no—
171#10621898—44no—
172#10621898—44no—
173#10621898—44no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172C22×C412yes—
183C2×D172C22×C412yes—
184C2×D172C2×D412yes—
185C2×D172#4112yes—
186C2×C4×D43—24no—
187C2×C4×D43—42no—
188C2×C4×D43—42no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—42no—
194C2×C4×D43—42no—
195C2×C4×D43—81no—
196C2×C4×D43—81no—
197C2×C4×D43—81no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86—21no—
203C2×Dic86C22×C412yes—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43C22×C412yes—
209C2×C8×C43C22×C412yes—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43C2×D412yes—
218C22⋊C4×C43—42no—
219C22⋊C4×C43—81no—
220C42×C43—42no—
221C22⋊Dic43—41no—
222C22⋊Dic43—41no—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—81no—
229C4⋊Dic43—21no—
230C4⋊Dic43C22×C412yes—
231Dic43⋊C4—81no—
232C4×Dic43—21no—
233C4×Dic43—21no—
234C4×Dic43—21no—
235C4×Dic43—21no—
236C4×Dic43—81no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—44no—
243C2×C43⋊C8C2×D412yes—
244D344—28no—
245#10621873—44no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43C4×D412yes—
253C23×C43C22×D411yescharacteristic
254C22×D43—22no—
255C22×D43—22no—
256C22×D43—22no—
257C22×D43—22no—
258C22×D43—41no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
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×C43C4×D412yes—
287C2×C4×C43C23×C411yescharacteristic
288C2×C4×C43C22×D411yescharacteristic
289C2×C4×C43C2×#4111yescharacteristic
290C2×C4×C43C2×#4111yescharacteristic
291C2×C4×C43H(5,𝔽2)11yescharacteristic
292C2×C4×C43H(5,𝔽2)11yescharacteristic
293C22⋊D43—48no—
294C22⋊D43—84no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—21no—
308C2×Dic43—21no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313D172—22no—
314D172—22no—
315D172—22no—
316D172—22no—
317D172—22no—
318D172—41no—
319D172—41no—
320D172C4×D414yes—
321C4×D43—48no—
322C4×D43—84no—
323C4×D43—84no—
324C4×D43—84no—
325Dic86—22no—
326Dic86—22no—
327Dic86—41no—
328Dic86—41no—
329C8×C43—22no—
330C8×C43—22no—
331C43⋊C8—22no—
332C43⋊C8—41no—
333#22860—431nomaximal, Sylow
334C22×C43—22no—
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43C2×C4×D411yescharacteristic
342C22×C43D4211yescharacteristic
343C22×C43#54611yescharacteristic
344C22×C43#57511yescharacteristic
345C22×C43#57511yescharacteristic
346C22×C43#57611yescharacteristic
347C22×C43#57711yescharacteristic
348C2×D43—24no—
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43—42no—
355C2×D43—42no—
356C2×D43—42no—
357C2×D43—42no—
358C2×D43—81no—
359C2×D43—81no—
360C2×D43—81no—
361C2×D43—81no—
362C4×C43—22no—
363C4×C43—42no—
364C4×C43—81no—
365C4×C43—81no—
366C4×C43—81no—
367C4×C43C2×C4×D411yescharacteristic
368C4×C43#51811yescharacteristic
369C4×C43#54611yescharacteristic
370C4×C43#55111yescharacteristic
371Dic43—42no—
372Dic43—42no—
373Dic43—41no—
374Dic43—41no—
375Dic43—41no—
376Dic43—41no—
377C2×#449—431no—
378C2×#442—431no—
379C2×#416—431no—
380#2363—431no—
381#2339—431no—
382#1973—431no—
383#1935—431no—
384#1927—431no—
385#1893—431no—
386#1879—431no—
387#1877—431no—
388#1862—431no—
389#1854D4311yescharacteristic, complemented
390#1762—431no—
391#1752—431no—
392C2×C43—42no—
393C2×C43#235811yescharacteristic
394C2×C43#294311yescharacteristic
395C2×C43#294611yescharacteristic
396C2×C43#326711yescharacteristic
397C2×C43#326811yescharacteristic
398C2×C43#330711yescharacteristic
399C2×C43#331911yescharacteristic
400D43—44no—
401D43—82no—
402C22×#41—431no—
403C22×SD16—431no—
404C22×D8—431no—
405C23×C8—431no—
406C2×#121—431no—
407C2×C4×D4—431no—
408C2×C4×D4—431no—
409C2×C4×D4—431no—
410C2×#117C2×D4311yescharacteristic
411#449—438no—
412#442—864no—
413C2×#107C2×D4311yescharacteristic
414C2×#106C2×D4311yescharacteristic
415#416—864no—
416C2×#103—431no—
417C2×#103—431no—
418C2×#103—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422C2×#102—431no—
423C2×#102—431no—
424C2×C22⋊C8C2×D4311yescharacteristic
425C2×#97—431no—
426C2×#97—431no—
427#391—431no—
428#391—431no—
429#390—431no—
430#390—861no—
431#389—431no—
432#388—861no—
433#386—861no—
434#386—861no—
435#386—861no—
436#381—861no—
437#380C2×D4311yescharacteristic
438C4×C4⋊C4—431no—
439C4×C22⋊C4—431no—
440C4×C22⋊C4—861no—
441C2×#95—861no—
442#340—431no—
443#340—431no—
444#340C2×D4311yescharacteristic
445#340C2×D4311yescharacteristic
446#336—431no—
447#336—431no—
448C43#2286011yescharacteristic, complemented, Sylow
449C2×#41—434no—
450C2×#41—862no—
451C2×#41—862no—
452C2×#41—862no—
453C2×#41—1721no—
454C2×#41—1721no—
455C22×Q8—431no—
456C22×D4—431no—
457C22×D4—431no—
458C22×D4—861no—
459C22×D4—861no—
460C23×C4—861no—
461C23×C4—861no—
462C23×C4—861no—
463C23×C4—861no—
464C23×C4C22×D4311yescharacteristic
465C2×SD16—434no—
466C2×SD16—1721no—
467C2×SD16—1721no—
468C2×D8—434no—
469C2×D8—862no—
470C2×D8—862no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—862no—
474C22×C8—862no—
475C22×C8—1721no—
476C22×C8C22×D4311yescharacteristic
477C22×C8C22×D4311yescharacteristic
478#121—434no—
479#121—862no—
480C4×D4—862no—
481C4×D4—862no—
482C4×D4—862no—
483C4×D4—1721no—
484C4×D4—1721no—
485C4×D4—1721no—
486#117—22no—
487#117—41no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—861no—
490C2×C4⋊C4C22×D4311yescharacteristic
491C2×C4⋊C4C22×D4311yescharacteristic
492C2×C4⋊C4C22×D4311yescharacteristic
493C2×C4⋊C4C22×D4311yescharacteristic
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—21no—
505C2×C42—431no—
506C2×C42—431no—
507C2×C42—861no—
508#107—41no—
509#106—22no—
510#103—434no—
511#103—862no—
512#103—862no—
513#102—434no—
514#102—434no—
515#102—862no—
516#102—862no—
517#102—1721no—
518C22⋊C8C4×D4314yescomplemented
519#97—862no—
520#97—1721no—
521#95—21no—
522#95—431no—
523#95—431no—
524#95—861no—
525#95—861no—
526#95—861no—
527#95—861no—
528#95—861no—
529#95—861no—
530C24—861no—
531C24—861no—
532C24D4×D4311yescharacteristic
533#41—868no—
534#41—1724no—
535#41—1724no—
536#41—1724no—
537C2×Q8—432no—
538C2×Q8—861no—
539C2×Q8—861no—
540C2×Q8—861no—
541C2×Q8—861no—
542C2×Q8—861no—
543C2×D4—432no—
544C2×D4—432no—
545C2×D4—432no—
546C2×D4—432no—
547C2×D4—864no—
548C2×D4—864no—
549C2×D4—861no—
550C2×D4—861no—
551C2×D4—861no—
552C2×D4—861no—
553C2×D4—861no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—3441no—
558C2×D4—3441no—
559C2×D4—1722no—
560C2×D4—1722no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—431no—
570C22×C4—431no—
571C22×C4—431no—
572C22×C4—431no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—864no—
576C22×C4—3441no—
577C22×C4—3441no—
578C22×C4—3441no—
579C22×C4—1722no—
580C22×C4—1722no—
581C22×C4—1722no—
582C22×C4—1722no—
583C22×C4—1722no—
584C22×C4—1722no—
585C22×C4—1722no—
586C22×C4—1722no—
587C22×C4C2×C4×D4312yes—
588C22×C4D4×D4311yescharacteristic
589C22×C4#1062190212yes—
590C22×C4C23×D4311yescharacteristic
591SD16—1724no—
592D8—868no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—432no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—1724no—
604C2×C8C2×C4×D4312yes—
605C2×C8C2×C4×D4312yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—432no—
614C4⋊C4—861no—
615C4⋊C4—3441no—
616C4⋊C4D4×D4312yes—
617C22⋊C4—42no—
618C22⋊C4—81no—
619C22⋊C4—864no—
620C22⋊C4—3441no—
621C22⋊C4—1722no—
622C22⋊C4—1722no—
623C22⋊C4—1722no—
624C22⋊C4—1722no—
625C22⋊C4—1721no—
626C22⋊C4—1721no—
627C42—42no—
628C42—861no—
629C42—861no—
630C42—861no—
631C42—861no—
632C42—3441no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—862no—
640C23—862no—
641C23—862no—
642C23—862no—
643C23—1721no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23—1721no—
649C23—1721no—
650C23—1721no—
651C23—1721no—
652C23—1721no—
653C23#1306328712yes—
654C23C2×D4×D4311yescharacteristic
655Q8—862no—
656Q8—862no—
657Q8—1721no—
658Q8—1721no—
659D4—434no—
660D4—862no—
661D4—862no—
662D4—862no—
663D4—862no—
664D4—862no—
665D4—3444no—
666D4—1728no—
667D4—1721no—
668D4—1721no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—3444no—
702C2×C4—3444no—
703C2×C4—3444no—
704C2×C4—1728no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4#1306328712yes—
710C2×C4C22×C4×D4311yescharacteristic
711C2×C4C2×D4×D4311yescharacteristic
712C2×C4#41×D4311yescharacteristic
713C2×C4C2×#1062190211yescharacteristic
714C2×C4#1306337011yescharacteristic
715C2×C4#1306337111yescharacteristic
716C8—22no—
717C8—22no—
718C8—862no—
719C8—1721no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—864no—
728C22—3441no—
729C22—3441no—
730C22—3441no—
731C22—3441no—
732C22—1722no—
733C22—1722no—
734C22—1722no—
735C22—1722no—
736C22—1722no—
737C22—1722no—
738C22—1722no—
739C22—1722no—
740C22—1722no—
741C22C2×#1306328711yescharacteristic
742C22#1458353111yescharacteristic
743C22#1458354111yescharacteristic
744C22#1458369611yescharacteristic
745C22#1458369611yescharacteristic
746C22#1458370311yescharacteristic
747C22#1458370811yescharacteristic
748C4—22no—
749C4—42no—
750C4—81no—
751C4—81no—
752C4—81no—
753C4—1722no—
754C4—1722no—
755C4—1721no—
756C4—1721no—
757C4—1721no—
758C4—1721no—
759C4C4×D4×D4311yescharacteristic
760C4#1458337111yescharacteristic
761C4#1458354011yescharacteristic
762C4#1458357611yescharacteristic
763C2—42no—
764C2—3442no—
765C2—1724no—
766C2#1913757111yescharacteristic
767C2#1914339511yescharacteristic
768C2#1914342511yescharacteristic
769C2#1914612411yescharacteristic
770C2#1914612811yescharacteristic
771C2#1914656911yescharacteristic
772C2#1914674911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC2×#14583046C2
cosocleC22×C4×C43C24
hypercenter#1854D43
hypocenterC43#22860
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#14583010C2semidirect
3. C2×#14582893C2semidirect
4. #19137633C2semidirect
5. #19137423C2semidirect
6. #19135474C2semidirect
7. #19135283C2semidirect
8. #19135228C2semidirect
9. #19135021C2semidirect
10. #19134944C2semidirect
11. #19134930C2semidirect
12. #19134839C2semidirect
13. #19134419C2semidirect
14. #19134374C2semidirect
15. C43×#1854C2semidirect
24. #14583046C4semidirect
67. C2×#10621898C2×C4semidirect
79. C2×#10621873C2×C4semidirect
89. #13063299C2×C4semidirect
109. #13063250C2×C4semidirect
112. #13063247C2×C4semidirect
116. #13063245D4semidirect
141. C22⋊C8×C43C2×C4semidirect
389. #1854D43semidirect
448. C43#22860semidirect
518. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830462
C2×#145830102
C2×#145828932
#191376332
#191374232
#191354742
#191352832
#191352282
#191350212
#191349442
#191349302
#191348392
#191344192
#191343742
C43×#18542
#2286043