Finite Group Databasebeta

← #25117300

Subgroups — #25117300

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×#14583050C211yesmaximal, characteristic
2C2×C4×#10621883C211yesmaximal, characteristic, complemented
3C2×#14582904C211yesmaximal, characteristic
4#19137620C211yesmaximal, characteristic, complemented
5#19135475C211yesmaximal, characteristic, complemented
6#19135281C211yesmaximal, characteristic, complemented
7#19135219C211yesmaximal, characteristic, complemented
8#19135026C211yesmaximal, characteristic, complemented
9#19134953C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic, complemented
11#19134842C211yesmaximal, characteristic, complemented
12#19134792C211yesmaximal, characteristic, complemented
13#19134420C211yesmaximal, characteristic, complemented
14#19134379C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C43C211yesmaximal, characteristic
16C22×#10621883C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic, complemented
21C2×#13063284C2211yescharacteristic
22#14583050C418yescomplemented
23C4×#10621883—24no—
24C2×#13063258C2211yescharacteristic, complemented
25C2×#13063256C2211yescharacteristic, complemented
26#14582904—24no—
27C2×#13063248C2211yescharacteristic, complemented
28C2×#13063248C2211yescharacteristic, complemented
29C2×#13063246C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063246C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063236C2211yescharacteristic, complemented
37C2×C4×C43⋊C8C2211yescharacteristic, complemented
38#14582805C2211yescharacteristic, complemented
39#14582797C2211yescharacteristic, complemented
40#14582793—21no—
41#14582787—21no—
42#14582781—21no—
43C4×C4⋊Dic43C2211yescharacteristic, complemented
44#14582750—21no—
45#14582661C2211yescharacteristic, complemented
46#14582661C2211yescharacteristic, complemented
47#14582661C2211yescharacteristic, complemented
48#14582661C2211yescharacteristic, complemented
49#14582654C2211yescharacteristic, complemented
50#14582654C2211yescharacteristic, complemented
51C23×D4×C43C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C22×C22⋊C4×C43—21no—
55C43×#390C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#386—21no—
58C43×#386—21no—
59C43×#380C2211yescharacteristic
60C43×#379—21no—
61C4×C22⋊C4×C43C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C2×#10621883—22no—
64C2×#10621883—22no—
65C2×#10621883—41no—
66C2×#10621883—41no—
67C2×#10621883C2×C414yes—
68C2×#10621883C2×C414yescomplemented
69C2×#10621877—22no—
70C2×#10621877—22no—
71C2×#10621877—41no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76#13063304—22no—
77#13063304C2×C414yescomplemented
78C4×Dic86—22no—
79C4×Dic86—41no—
80#13063284—22no—
81#13063284—41no—
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93#13063258—41no—
94#13063256—22no—
95#13063248—22no—
96#13063248—41no—
97#13063246—22no—
98#13063246—22no—
99#13063246—22no—
100#13063246C2×C414yes—
101#13063246C2×C414yescomplemented
102#13063246D414yes—
103C22⋊(C43⋊C8)C2×C414yescomplemented
104#13063236—41no—
105C4×C43⋊C8—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C25×C43—21no—
111C22×D4×C43—22no—
112C22×D4×C43—22no—
113C22×D4×C43—21no—
114C22×D4×C43—22no—
115C22×D4×C43—41no—
116C22×D4×C43—41no—
117C22×D4×C43C2×C414yes—
118C22×D4×C43C2311yescharacteristic
119C22×D4×C43C2311yescharacteristic
120C23×C4×C43—21no—
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125C4×D4×C43—41no—
126C4×D4×C43—41no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C22⋊C4×C43—21no—
134C2×C22⋊C4×C43—21no—
135C2×C22⋊C4×C43—21no—
136C2×C22⋊C4×C43—44no—
137C2×C22⋊C4×C43D411yescharacteristic
138C2×C22⋊C4×C43D411yescharacteristic
139C2×C42×C43C2311yescharacteristic
140C2×C42×C43C2311yescharacteristic
141#95×C43—21no—
142#95×C43D411yescharacteristic
143#95×C43D411yescharacteristic
144C24×C43—21no—
145C24×C43—21no—
146C24×C43—24no—
147C24×C43—42no—
148C24×C43—42no—
149C24×C43—42no—
150C24×C43—42no—
151C24×C43—81no—
152C24×C43—81no—
153C24×C43C2×D411yescharacteristic
154C2×D4×C43—24no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—28no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C2×D4×C43—44no—
167C2×D4×C43—44no—
168C2×D4×C43—44no—
169C2×D4×C43C22×C412yes—
170C2×D4×C43C22×C412yes—
171C2×D4×C43C2×D412yes—
172C2×D4×C43#4112yes—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—42no—
180C22×C4×C43—42no—
181C22×C4×C43—42no—
182C22×C4×C43—42no—
183C22×C4×C43—81no—
184C22×C4×C43—81no—
185C22×C4×C43C22×C412yes—
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43#4112yes—
192C22×C4×C43C2411yescharacteristic
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—21no—
202C2×Dic86C22×C412yes—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C22⋊C4×C43—22no—
208C22⋊C4×C43—41no—
209C22⋊C4×C43—42no—
210C22⋊C4×C43—42no—
211C22⋊C4×C43—42no—
212C22⋊C4×C43—42no—
213C22⋊C4×C43—42no—
214C22⋊C4×C43—81no—
215C22⋊C4×C43—81no—
216C42×C43—21no—
217C42×C43—21no—
218C42×C43—21no—
219C42×C43—21no—
220C22⋊Dic43—24no—
221C22⋊Dic43—42no—
222#10621883—28no—
223#10621883—44no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—21no—
227C4⋊Dic43—21no—
228C4⋊Dic43C22×C412yes—
229C4⋊Dic43C2×D412yes—
230Dic43⋊C4—24no—
231Dic43⋊C4—42no—
232Dic43⋊C4—42no—
233C4×Dic43—42no—
234C4×Dic43—42no—
235C4×Dic43—42no—
236#10621877—44no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C22×C412yes—
247C2×C43⋊C8C22×C412yes—
248C2×C43⋊C8C2×D412yes—
249C23×C43—22no—
250C23×C43—21no—
251C23×C43—22no—
252C23×C43—22no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—22no—
259C23×C43—48no—
260C23×C43—48no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—84no—
272C23×C43—84no—
273C23×C43—84no—
274C23×C43—84no—
275C23×C43—84no—
276C23×C43C4×D412yes—
277C23×C43C22×D411yescharacteristic
278D4×C43—22no—
279D4×C43—22no—
280D4×C43—22no—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—48no—
284D4×C43—41no—
285D4×C43—41no—
286D4×C43C4×D414yes—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—84no—
311C2×C4×C43—84no—
312C2×C4×C43C4×D412yes—
313C2×C4×C43AGL(1,ℤ/8)12yes—
314C2×C4×C43C23×C411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332Dic86—22no—
333Dic86—22no—
334Dic86—41no—
335Dic86—41no—
336C43⋊C8—22no—
337C43⋊C8—22no—
338C43⋊C8—22no—
339C43⋊C8—41no—
340#22884—431nomaximal, Sylow
341C22×C43—24no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—42no—
346C22×C43—42no—
347C22×C43—41no—
348C22×C43—42no—
349C22×C43—41no—
350C22×C43—42no—
351C22×C43—41no—
352C22×C43—42no—
353C22×C43—41no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—816no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43C2×C4×D411yescharacteristic
364C22×C43D4211yescharacteristic
365C22×C43#54611yescharacteristic
366C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C43#57511yescharacteristic
368C22×C43#57711yescharacteristic
369C22×C43#57711yescharacteristic
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—41no—
373C4×C43—41no—
374C4×C43—41no—
375C4×C43—81no—
376C4×C43—81no—
377C4×C43C2×C4×D411yescharacteristic
378C4×C43#51811yescharacteristic
379C4×C43#54611yescharacteristic
380C4×C43#55111yescharacteristic
381Dic43—42no—
382Dic43—42no—
383Dic43—42no—
384Dic43—81no—
385C2×#450—431no—
386C2×C4×SD16—431no—
387C2×#418—431no—
388#2362—431no—
389D4×C22⋊C4D4311yescharacteristic
390#1973—431no—
391#1934—431no—
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—42no—
401C2×C43—44no—
402C2×C43—82no—
403C2×C43#235811yescharacteristic
404C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
405C2×C43#294911yescharacteristic
406C2×C43#326511yescharacteristic
407C2×C43#326711yescharacteristic
408C2×C43#332311yescharacteristic
409C2×C43#332411yescharacteristic
410C23×D4C2×D4311yescharacteristic
411C22×SD16—431no—
412C22×SD16—431no—
413C22×M16—431no—
414C2×C22⋊Q8—431no—
415C2×C4×Q8—431no—
416C2×C4×D4C2×D4311yescharacteristic
417C2×C4×D4C2×D4311yescharacteristic
418C2×#117—431no—
419C22×C22⋊C4—21no—
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×#102—431no—
432C2×#102—431no—
433C2×C22⋊C8—431no—
434C2×#97—431no—
435C2×C4×C8—431no—
436#391—431no—
437#390C2×D4311yescharacteristic
438#390C2×D4311yescharacteristic
439#389—431no—
440#388—861no—
441#388—861no—
442#387—861no—
443#386—21no—
444#386—21no—
445#380C2×D4311yescharacteristic
446#379—21no—
447C4×C4⋊C4—431no—
448C4×C4⋊C4—861no—
449C4×C22⋊C4C2×D4311yescharacteristic
450#340—431no—
451#340—431no—
452#340—431no—
453#340—431no—
454#336—431no—
455#336—431no—
456C43#2288411yescharacteristic, complemented, Sylow
457C25—21no—
458C22×Q8—431no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—21no—
463C22×D4—41no—
464C22×D4—41no—
465C22×D4C4×D4314yes—
466C22×D4C22×D4311yescharacteristic
467C22×D4C22×D4311yescharacteristic
468C23×C4—21no—
469C23×C4—21no—
470C23×C4C22×D4311yescharacteristic
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×C8—431no—
483C22×C8—431no—
484C22⋊Q8—434no—
485C22⋊Q8—862no—
486C4×Q8—862no—
487C4×Q8—1721no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—41no—
491C4×D4—41no—
492#117—862no—
493#117—1721no—
494C2×C4⋊C4—431no—
495C2×C4⋊C4—431no—
496C2×C4⋊C4—431no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4—861no—
499C2×C4⋊C4—861no—
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C4⋊C4C22×D4311yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4C22⋊D4311yescharacteristic
513C2×C22⋊C4C22⋊D4311yescharacteristic
514C2×C42—861no—
515C2×C42—861no—
516C2×C42—861no—
517C2×C42C22×D4311yescharacteristic
518C2×C42C22×D4311yescharacteristic
519#107—1721no—
520#106—862no—
521#103—862no—
522#103—1721no—
523#102—434no—
524#102—434no—
525#102—434no—
526#102—862no—
527#102—862no—
528#102—862no—
529C22⋊C8—434no—
530#97—1721no—
531C4×C8—862no—
532#95—21no—
533#95—861no—
534#95—861no—
535#95—861no—
536#95—861no—
537#95C22⋊D4311yescharacteristic
538#95C22⋊D4311yescharacteristic
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—42no—
545C24—42no—
546C24—81no—
547C24—81no—
548C24C2×C22⋊D4311yescharacteristic
549C2×Q8—432no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8—861no—
555C2×D4—28no—
556C2×D4—24no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4C2×C4×D4312yes—
571C2×D4C2×C4×D4312yes—
572C2×D4D4×D4312yes—
573C2×D4#1062190012yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—42no—
583C22×C4—42no—
584C22×C4—81no—
585C22×C4—81no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4C2×C4×D4312yes—
591C22×C4#1062189812yes—
592C22×C4C2×C22⋊D4311yescharacteristic
593C22×C4C2×C22⋊D4311yescharacteristic
594C22×C4C2×C22⋊D4311yescharacteristic
595C22×C4C2×C22⋊D4311yescharacteristic
596C22×C4C2×C22⋊D4311yescharacteristic
597C22×C4C23×D4311yescharacteristic
598SD16—868no—
599SD16—1724no—
600M16—1724no—
601C2×C8—432no—
602C2×C8—432no—
603C2×C8—432no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C2×C8—861no—
612C2×C8—861no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—432no—
618C4⋊C4—432no—
619C4⋊C4—864no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—1722no—
625C4⋊C4—1722no—
626C22⋊C4—22no—
627C22⋊C4—41no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—81no—
634C22⋊C4—81no—
635C22⋊C4—864no—
636C22⋊C4—1722no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—1722no—
642C42—1722no—
643C42—1722no—
644C23—22no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—22no—
650C23—21no—
651C23—22no—
652C23—21no—
653C23—22no—
654C23—48no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23C4×C22⋊D4312yes—
672C23C22×C22⋊D4311yescharacteristic
673Q8—862no—
674Q8—862no—
675Q8—1721no—
676Q8—1721no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685D4(C22⋊D43)⋊C414yes—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—1721no—
715C2×C4—1721no—
716C2×C4—1721no—
717C2×C4—1721no—
718C2×C4—1721no—
719C2×C4—1721no—
720C2×C4—1721no—
721C2×C4—1721no—
722C2×C4—1721no—
723C2×C4C4×C22⋊D4312yes—
724C2×C4#1306335112yes—
725C2×C4C22×C4×D4311yescharacteristic
726C2×C4C2×D4×D4311yescharacteristic
727C2×C4C2×#1062190011yescharacteristic
728C2×C4C2×#1062189811yescharacteristic
729C2×C4#1306337011yescharacteristic
730C2×C4#1306337011yescharacteristic
731C8—862no—
732C8—862no—
733C8—862no—
734C8—1721no—
735C22—22no—
736C22—22no—
737C22—24no—
738C22—22no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—42no—
743C22—41no—
744C22—42no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—816no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C2×C4×C22⋊D4311yescharacteristic
758C22D4×C22⋊D4311yescharacteristic
759C22#1458354311yescharacteristic
760C22C2×#1306335111yescharacteristic
761C22#1458369711yescharacteristic
762C22#1458371011yescharacteristic
763C22#1458371011yescharacteristic
764C4—22no—
765C4—22no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—81no—
770C4—81no—
771C4—3441no—
772C4—1722no—
773C4—1722no—
774C4—1722no—
775C4C2×(C22⋊D43)⋊C411yescharacteristic
776C4#1458337211yescharacteristic
777C4#1458353911yescharacteristic
778C4#1458357511yescharacteristic
779C2—42no—
780C2—44no—
781C2—82no—
782C2#1913757411yescharacteristic
783C2C4×#1306335111yescharacteristic
784C2#1914345211yescharacteristic
785C2#1914608611yescharacteristic
786C2#1914611611yescharacteristic
787C2#1914681111yescharacteristic
788C2#1914682611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingD4×C22⋊C4×C43C2
socleC23×C43C22×D4
prime radicalC23×D4×C43C22
cosocleC22×C4×C43C24
hypercenterD4×C22⋊C4D43
hypocenterC43#22884
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#10621883C2semidirect
4. #19137620C2semidirect
5. #19135475C2semidirect
6. #19135281C2semidirect
7. #19135219C2semidirect
8. #19135026C2semidirect
9. #19134953C2semidirect
10. #19134929C2semidirect
11. #19134842C2semidirect
12. #19134792C2semidirect
13. #19134420C2semidirect
14. #19134379C2semidirect
20. C2×C4×Dic86C22semidirect
22. #14583050C4semidirect
24. C2×#13063258C22semidirect
25. C2×#13063256C22semidirect
27. C2×#13063248C22semidirect
28. C2×#13063248C22semidirect
36. C2×#13063236C22semidirect
37. C2×C4×C43⋊C8C22semidirect
38. #14582805C22semidirect
39. #14582797C22semidirect
43. C4×C4⋊Dic43C22semidirect
45. #14582661C22semidirect
46. #14582661C22semidirect
47. #14582661C22semidirect
48. #14582661C22semidirect
49. #14582654C22semidirect
50. #14582654C22semidirect
68. C2×#10621883C2×C4semidirect
77. #13063304C2×C4semidirect
101. #13063246C2×C4semidirect
103. C22⋊(C43⋊C8)C2×C4semidirect
456. C43#22884semidirect

Maximal subgroups

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

subgroupindex
C2×#145830502
C2×C4×#106218832
C2×#145829042
#191376202
#191354752
#191352812
#191352192
#191350262
#191349532
#191349292
#191348422
#191347922
#191344202
#191343792
D4×C22⋊C4×C432
#2288443