Finite Group Databasebeta

← #25117311

Subgroups — #25117311

Order 11008.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583051C211yesmaximal, characteristic
2C2×C4×#10621873C211yesmaximal, characteristic, complemented
3C2×#14582902C211yesmaximal, characteristic
4#19137621C211yesmaximal, characteristic, complemented
5#19137416C211yesmaximal, characteristic
6#19135477C211yesmaximal, characteristic, complemented
7#19135224C211yesmaximal, characteristic, complemented
8#19135027C211yesmaximal, characteristic, complemented
9#19134953C211yesmaximal, characteristic, complemented
10#19134930C211yesmaximal, characteristic, complemented
11#19134841C211yesmaximal, characteristic, complemented
12#19134795C211yesmaximal, characteristic, complemented
13#19134419C211yesmaximal, characteristic, complemented
14#19134378C211yesmaximal, characteristic, complemented
15C43×#1934C211yesmaximal, characteristic, complemented
16C22×D4×D43C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C22×#10621872C2211yescharacteristic
20C2×#13063305C2211yescharacteristic
21C2×C4×Dic86C2211yescharacteristic, complemented
22C2×C4×D172C2211yescharacteristic
23C2×#13063287C2211yescharacteristic
24C2×#13063283C2211yescharacteristic
25C2×C22⋊C4×D43—21no—
26#14583051C418yescomplemented
27C4×#10621873—24no—
28C2×#13063258C2211yescharacteristic, complemented
29C2×#13063257C2211yescharacteristic, complemented
30#14582902—24no—
31C2×#13063250C2211yescharacteristic, complemented
32C2×#13063248C2211yescharacteristic, complemented
33C2×#13063247C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063245C2211yescharacteristic
37C2×(C2×D43)⋊C8C2211yescharacteristic
38C2×#13063235C2211yescharacteristic, complemented
39#14582804C2211yescharacteristic, complemented
40#14582802C2211yescharacteristic
41#14582789—21no—
42#14582788—21no—
43#14582782—21no—
44#14582775—21no—
45#14582775—21no—
46#14582756C2211yescharacteristic
47#14582754—21no—
48C4⋊C4×Dic43—21no—
49C4⋊C4×Dic43C2211yescharacteristic, complemented
50C4×(C2×D43)⋊C4C2211yescharacteristic
51#14582661C2211yescharacteristic, complemented
52#14582661C2211yescharacteristic, complemented
53#14582654C2211yescharacteristic, complemented
54#14582653C2211yescharacteristic, complemented
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic, complemented
58C43×#390C2211yescharacteristic
59C43×#389C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C24×D43—21no—
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C22⋊D43—21no—
66C2×D4×D43—22no—
67C2×D4×D43—22no—
68C2×D4×D43—22no—
69C2×D4×D43—41no—
70C2×D4×D43—41no—
71C2×D4×D43C2×C414yes—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43C2311yescharacteristic
75C2×#10621873—22no—
76C2×#10621873—22no—
77C2×#10621873C2×C414yes—
78C2×#10621883—41no—
79C2×#10621883—41no—
80C2×#10621883C2×C414yescomplemented
81C2×#10621872—22no—
82C2×#10621872—22no—
83C2×#10621872—41no—
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86#13063305—22no—
87#13063305C2×C414yescomplemented
88C4×Dic86—22no—
89C4×Dic86—41no—
90C4×D172—22no—
91C4×D172—41no—
92#13063287—22no—
93#13063287—41no—
94#13063283—22no—
95#13063283—41no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×C22⋊Dic43—21no—
101C2×C22⋊Dic43—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4D411yescharacteristic
108C2×(C2×D43)⋊C4D411yescharacteristic
109C22⋊C4×D43—44no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43C2311yescharacteristic
114#13063258—41no—
115#13063257—22no—
116#13063250—22no—
117#13063248—41no—
118#13063247D414yes—
119#13063246—22no—
120#13063245—22no—
121#13063245C2×C414yes—
122(C2×D43)⋊C8C2×C414yescomplemented
123#13063235—41no—
124C43⋊#95—21no—
125C43⋊#95—21no—
126C43⋊#95—21no—
127C43⋊#95—21no—
128C43⋊#95D411yescharacteristic
129C43⋊#95D411yescharacteristic
130C22×D4×C43C2311yescharacteristic
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C22⋊C4×C43—21no—
138C2×C22⋊C4×C43—21no—
139C2×C42×C43C2311yescharacteristic
140#102×C43—22no—
141#102×C43C2×C414yescomplemented
142C4×C8×C43—22no—
143#95×C43—21no—
144C24×C43—21no—
145C23×D43—21no—
146C23×D43—24no—
147C23×D43—42no—
148C23×D43—42no—
149C23×D43—42no—
150C23×D43—42no—
151C23×D43—81no—
152C23×D43—81no—
153C23×D43C2×D411yescharacteristic
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43C22×C412yes—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C2×C22⋊D43—24no—
167C2×C22⋊D43—42no—
168C2×C22⋊D43—42no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175D4×D43—28no—
176D4×D43—44no—
177D4×D43—44no—
178D4×D43—44no—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172C22×C412yes—
183C2×D172C2×D412yes—
184C2×D172#4112yes—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—42no—
190C2×C4×D43—42no—
191C2×C4×D43—42no—
192C2×C4×D43—42no—
193C2×C4×D43—81no—
194C2×C4×D43—81no—
195C2×C4×D43C22×C412yes—
196C2×C4×D43#4112yes—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86C22×C412yes—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43C22×C412yes—
208C2×C8×C43C2×D412yes—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—42no—
215C4⋊C4×C43C22×C412yes—
216C22⋊C4×C43—42no—
217C22⋊C4×C43—81no—
218C42×C43—21no—
219C42×C43—21no—
220C22⋊Dic43—42no—
221C22⋊Dic43—81no—
222#10621883—44no—
223(C2×D43)⋊C4—22no—
224(C2×D43)⋊C4—24no—
225(C2×D43)⋊C4—41no—
226(C2×D43)⋊C4—42no—
227(C2×D43)⋊C4—42no—
228(C2×D43)⋊C4—42no—
229(C2×D43)⋊C4—42no—
230C4⋊Dic43—21no—
231C4⋊Dic43—24no—
232C4⋊Dic43—21no—
233C4⋊Dic43—21no—
234C4⋊Dic43C2×D412yes—
235Dic43⋊C4—42no—
236C4×Dic43—21no—
237C4×Dic43—21no—
238C4×Dic43—42no—
239C4×Dic43—42no—
240C4×Dic43—42no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C22×C412yes—
247#10621873—28no—
248#10621872—44no—
249C23×C43—22no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43C22×D411yescharacteristic
257C22×D43—22no—
258C22×D43—21no—
259C22×D43—22no—
260C22×D43—22no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—48no—
267C22×D43—48no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271C22×D43—41no—
272C22×D43—84no—
273C22×D43—84no—
274C22×D43—84no—
275C22×D43—84no—
276C22×D43—84no—
277C22×D43C4×D412yes—
278D4×C43—22no—
279D4×C43—22no—
280D4×C43—41no—
281D4×C43—41no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—22no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43AGL(1,ℤ/8)12yes—
297C2×C4×C43C23×C411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43H(5,𝔽2)11yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C22⋊D43—48no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43C4×D412yes—
322D172—22no—
323D172—22no—
324D172—22no—
325D172C4×D414yes—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—84no—
331C4×D43—84no—
332Dic86—22no—
333Dic86—22no—
334Dic86—41no—
335Dic86—41no—
336C8×C43—22no—
337C8×C43—22no—
338C43⋊C8—22no—
339C43⋊C8—41no—
340#22884—431nomaximal, Sylow
341C22×C43—42no—
342C22×C43—42no—
343C22×C43—42no—
344C22×C43—81no—
345C22×C43—81no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43C2×C4×D411yescharacteristic
349C22×C43D4211yescharacteristic
350C22×C43#54611yescharacteristic
351C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
352C22×C43#57511yescharacteristic
353C22×C43#57711yescharacteristic
354C22×C43#57711yescharacteristic
355C2×D43—24no—
356C2×D43—22no—
357C2×D43—22no—
358C2×D43—22no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—41no—
362C2×D43—42no—
363C2×D43—41no—
364C2×D43—42no—
365C2×D43—41no—
366C2×D43—42no—
367C2×D43—41no—
368C2×D43—42no—
369C2×D43—816no—
370C4×C43—22no—
371C4×C43—42no—
372C4×C43—41no—
373C4×C43—81no—
374C4×C43—81no—
375C4×C43C2×C4×D411yescharacteristic
376C4×C43#51811yescharacteristic
377C4×C43#54611yescharacteristic
378C4×C43#55111yescharacteristic
379Dic43—22no—
380Dic43—42no—
381Dic43—42no—
382Dic43—41no—
383Dic43—41no—
384Dic43—81no—
385C2×#450—431no—
386C2×C4×SD16—431no—
387C2×#418—431no—
388#2362—431no—
389D4×C22⋊C4—431no—
390#1973—431no—
391#1934D4311yescharacteristic, complemented
392#1926—431no—
393#1894—431no—
394#1880—431no—
395#1877—431no—
396#1862—431no—
397#1854—431no—
398#1762—431no—
399#1753—431no—
400C2×C43—82no—
401C2×C43#235811yescharacteristic
402C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
403C2×C43#294911yescharacteristic
404C2×C43#326511yescharacteristic
405C2×C43#326711yescharacteristic
406C2×C43#332311yescharacteristic
407C2×C43#332411yescharacteristic
408D43—42no—
409D43—44no—
410C23×D4—431no—
411C22×SD16—431no—
412C22×SD16—431no—
413C22×M16—431no—
414C2×C22⋊Q8—431no—
415C2×C4×Q8—431no—
416C2×C4×D4—431no—
417C2×C4×D4—431no—
418C2×#117—431no—
419C22×C22⋊C4—861no—
420#450—438no—
421C4×SD16—864no—
422C2×#107—431no—
423C2×#106—431no—
424#418—864no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#102—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×#102C2×D4311yescharacteristic
432C2×#102C2×D4311yescharacteristic
433C2×C22⋊C8—431no—
434C2×#97—431no—
435C2×C4×C8C2×D4311yescharacteristic, complemented
436#391—431no—
437#390—431no—
438#390C2×D4311yescharacteristic
439#389C2×D4311yescharacteristic, complemented
440#388—861no—
441#388—861no—
442#387—861no—
443#386—861no—
444#386—861no—
445#380—431no—
446#379—861no—
447C4×C4⋊C4—431no—
448C4×C4⋊C4—861no—
449C4×C22⋊C4—431no—
450#340—431no—
451#340—431no—
452#340C2×D4311yescharacteristic, complemented
453#340C2×D4311yescharacteristic, complemented
454#336—431no—
455#336—431no—
456C43#2288411yescharacteristic, complemented, Sylow
457C25—861no—
458C22×Q8—431no—
459C22×D4—434no—
460C22×D4—431no—
461C22×D4—862no—
462C22×D4—861no—
463C22×D4—862no—
464C22×D4—862no—
465C22×D4—1721no—
466C22×D4—1721no—
467C22×D4C22×D4311yescharacteristic
468C23×C4—431no—
469C23×C4—861no—
470C23×C4—861no—
471C2×SD16—434no—
472C2×SD16—434no—
473C2×SD16—862no—
474C2×SD16—862no—
475C2×SD16—1721no—
476C2×SD16—1721no—
477C2×M16—862no—
478C2×M16—862no—
479C2×M16—1721no—
480C22×C8—431no—
481C22×C8—431no—
482C22×C8C22×D4311yescharacteristic
483C22×C8C22×D4311yescharacteristic
484C22⋊Q8—434no—
485C22⋊Q8—862no—
486C4×Q8—862no—
487C4×Q8—1721no—
488C4×D4—862no—
489C4×D4—862no—
490C4×D4—1721no—
491C4×D4—1721no—
492#117—862no—
493#117—1721no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—431no—
505C2×C22⋊C4—431no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—1724no—
514C2×C42—431no—
515C2×C42—861no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42C22×D4311yescharacteristic
519#107—1721no—
520#106—862no—
521#103—862no—
522#103—1721no—
523#102—22no—
524#102—434no—
525#102—434no—
526#102—862no—
527#102—862no—
528#102C4×D4314yescomplemented
529C22⋊C8—434no—
530#97—1721no—
531C4×C8—22no—
532#95—21no—
533#95—431no—
534#95—431no—
535#95—861no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24—431no—
541C24—864no—
542C24—861no—
543C24—3441no—
544C24—3441no—
545C24—1722no—
546C24—1722no—
547C24—1722no—
548C24—1722no—
549C2×Q8—432no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—432no—
561C2×D4—432no—
562C2×D4—432no—
563C2×D4—864no—
564C2×D4—868no—
565C2×D4—861no—
566C2×D4—861no—
567C2×D4—861no—
568C2×D4—1724no—
569C2×D4—1724no—
570C2×D4—1724no—
571C2×D4—1722no—
572C2×D4—1722no—
573C2×D4C2×C4×D4312yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—431no—
578C22×C4—432no—
579C22×C4—432no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—3441no—
590C22×C4—3441no—
591C22×C4—1722no—
592C22×C4—1722no—
593C22×C4—1722no—
594C22×C4—1722no—
595C22×C4D4×D4311yescharacteristic
596C22×C4D4×D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598SD16—868no—
599SD16—1724no—
600M16—1724no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—432no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8C2×C4×D4312yes—
612C2×C8D4×D4312yes—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—42no—
619C4⋊C4—432no—
620C4⋊C4—864no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—1722no—
625C4⋊C4C2×C4×D4312yes—
626C22⋊C4—42no—
627C22⋊C4—81no—
628C22⋊C4—864no—
629C22⋊C4—862no—
630C22⋊C4—3441no—
631C22⋊C4—1721no—
632C22⋊C4—1722no—
633C22⋊C4—1722no—
634C22⋊C4—1722no—
635C22⋊C4—1722no—
636C22⋊C4—1722no—
637C42—21no—
638C42—21no—
639C42—861no—
640C42—861no—
641C42—1722no—
642C42—1722no—
643C42—1722no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—432no—
652C23—862no—
653C23—861no—
654C23—861no—
655C23—861no—
656C23—861no—
657C23—861no—
658C23—862no—
659C23—862no—
660C23—861no—
661C23—3444no—
662C23—3444no—
663C23—3444no—
664C23—3444no—
665C23—3444no—
666C23—1728no—
667C23—1728no—
668C23—1721no—
669C23—1721no—
670C23—1721no—
671C23—1721no—
672C23C2×D4×D4311yescharacteristic
673Q8—862no—
674Q8—862no—
675Q8—1721no—
676Q8—1721no—
677D4—22no—
678D4—22no—
679D4—41no—
680D4—41no—
681D4—434no—
682D4—862no—
683D4—862no—
684D4—862no—
685D4—1728no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—432no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—862no—
704C2×C4—862no—
705C2×C4—862no—
706C2×C4—862no—
707C2×C4—862no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—862no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—3444no—
716C2×C4—3444no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4#1306334912yes—
725C2×C4C22×C4×D4311yescharacteristic
726C2×C4C2×D4×D4311yescharacteristic
727C2×C4#41×D4311yescharacteristic
728C2×C4#41×D4311yescharacteristic
729C2×C4#1306337111yescharacteristic
730C2×C4#1306337111yescharacteristic
731C8—22no—
732C8—22no—
733C8—862no—
734C8—1721no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—862no—
743C22—862no—
744C22—864no—
745C22—862no—
746C22—34416no—
747C22—1722no—
748C22—1721no—
749C22—1722no—
750C22—1722no—
751C22—1721no—
752C22—1722no—
753C22—1721no—
754C22—1721no—
755C22—1722no—
756C22—1722no—
757C22C4×D4×D4311yescharacteristic
758C22#1458353311yescharacteristic
759C22#1458354211yescharacteristic
760C22C2×#1306334911yescharacteristic
761C22#1458369611yescharacteristic
762C22#1458370511yescharacteristic
763C22#1458370611yescharacteristic
764C4—22no—
765C4—41no—
766C4—42no—
767C4—81no—
768C4—81no—
769C4—862no—
770C4—3441no—
771C4—1722no—
772C4—1721no—
773C4—1721no—
774C4—1722no—
775C4C4×D4×D4311yescharacteristic
776C4#1458337311yescharacteristic
777C4#1458354111yescharacteristic
778C4#1458357411yescharacteristic
779C2—82no—
780C2—1722no—
781C2—1724no—
782C2#1913757311yescharacteristic
783C2C4×#1306334911yescharacteristic
784C2#1914344911yescharacteristic
785C2#1914608711yescharacteristic
786C2#1914611711yescharacteristic
787C2#1914681011yescharacteristic
788C2#1914682511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1934C2
socleC23×C43C22×D4
prime radicalC22×D4×D43C22
cosocleC22×C4×C43C24
hypercenter#1934D43
hypocenterC43#22884
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621873C2semidirect
4. #19137621C2semidirect
6. #19135477C2semidirect
7. #19135224C2semidirect
8. #19135027C2semidirect
9. #19134953C2semidirect
10. #19134930C2semidirect
11. #19134841C2semidirect
12. #19134795C2semidirect
13. #19134419C2semidirect
14. #19134378C2semidirect
15. C43×#1934C2semidirect
21. C2×C4×Dic86C22semidirect
26. #14583051C4semidirect
28. C2×#13063258C22semidirect
29. C2×#13063257C22semidirect
31. C2×#13063250C22semidirect
32. C2×#13063248C22semidirect
38. C2×#13063235C22semidirect
39. #14582804C22semidirect
49. C4⋊C4×Dic43C22semidirect
51. #14582661C22semidirect
52. #14582661C22semidirect
53. #14582654C22semidirect
54. #14582653C22semidirect
57. C2×C4×C8×C43C22semidirect
59. C43×#389C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
80. C2×#10621883C2×C4semidirect
87. #13063305C2×C4semidirect
122. (C2×D43)⋊C8C2×C4semidirect
141. #102×C43C2×C4semidirect
391. #1934D43semidirect
435. C2×C4×C8C2×D43semidirect
439. #389C2×D43semidirect
452. #340C2×D43semidirect
453. #340C2×D43semidirect
456. C43#22884semidirect
528. #102C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830512
C2×C4×#106218732
C2×#145829022
#191376212
#191374162
#191354772
#191352242
#191350272
#191349532
#191349302
#191348412
#191347952
#191344192
#191343782
C43×#19342
#2288443