Finite Group Databasebeta

← #25102421

Subgroups — #25102421

Order 11008.

1420 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583061C211yesmaximal, characteristic
2C2×#14582999C211yesmaximal, characteristic, complemented
3C2×C4×#10621885C211yesmaximal, characteristic, complemented
4#19137277C211yesmaximal, characteristic, complemented
5#19134936C211yesmaximal, characteristic, complemented
6#19134929C211yesmaximal, characteristic, complemented
7#19134902C211yesmaximal, characteristic, complemented
8#19134849C211yesmaximal, characteristic, complemented
9#19134842C211yesmaximal, characteristic, complemented
10#19134783C211yesmaximal, characteristic, complemented
11#19134535C211yesmaximal, characteristic
12#19134425C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic, complemented
14#19134361C211yesmaximal, characteristic, complemented
15C2×C43×#520C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583061C418yescomplemented
21#14582999—24no—
22C4×#10621885—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×#13063236C2211yescharacteristic
36C2×C4×C43⋊C8C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582794—21no—
40#14582793—21no—
41#14582787—21no—
42#14582780—21no—
43#14582759C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51C22×#41×C43C2211yescharacteristic
52C43×#520—24no—
53C43×#520—24no—
54C2×C4×Q8×C43C2211yescharacteristic
55C2×C4×Q8×C43C2211yescharacteristic
56C2×C4×D4×C43—21no—
57C2×C4×D4×C43—21no—
58C2×C4×D4×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C2×#117×C43—21no—
61C2×#117×C43C2211yescharacteristic
62C22×C4⋊C4×C43—21no—
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×Dic86C2311yescharacteristic
65C2×#10621885—22no—
66C2×#10621885—22no—
67C2×#10621885C2×C414yescomplemented
68C2×#10621883—22no—
69C2×#10621883—22no—
70C2×#10621883C2×C414yescomplemented
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063304—22no—
76#13063304C2×C414yescomplemented
77C4×Dic86—22no—
78C4×Dic86—22no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89#13063258—22no—
90#13063258—22no—
91#13063249—22no—
92#13063249—22no—
93#13063249C2×C414yescomplemented
94#13063248—22no—
95#13063248—22no—
96#13063246—22no—
97#13063246—22no—
98#13063246C2×C414yescomplemented
99C22⋊(C43⋊C8)—22no—
100C22⋊(C43⋊C8)C2×C414yescomplemented
101#13063236—22no—
102C4×C43⋊C8—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C2×#41×C43—22no—
109C2×#41×C43—22no—
110C2×#41×C43—22no—
111C2×#41×C43—22no—
112C2×#41×C43—22no—
113C2×#41×C43C2×C414yes—
114C22×Q8×C43C2311yescharacteristic
115C22×D4×C43—21no—
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C23×C4×C43—21no—
119C23×C4×C43—21no—
120C23×C4×C43—21no—
121C23×C4×C43C2311yescharacteristic
122C4×Q8×C43—22no—
123C4×Q8×C43—22no—
124C4×Q8×C43—22no—
125C4×Q8×C43D414yes—
126C4×D4×C43—28no—
127C4×D4×C43—28no—
128C4×D4×C43—22no—
129C4×D4×C43—22no—
130C4×D4×C43—22no—
131C4×D4×C43D414yes—
132#117×C43—28no—
133#117×C43—22no—
134#117×C43—22no—
135C2×C4⋊C4×C43—28no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43—22no—
140C2×C4⋊C4×C43—22no—
141C2×C4⋊C4×C43D411yescharacteristic
142C2×C4⋊C4×C43D411yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C22⋊C4×C43—21no—
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43D411yescharacteristic
148C2×C22⋊C4×C43D411yescharacteristic
149C2×C42×C43—21no—
150C2×C42×C43—21no—
151C2×C42×C43C2311yescharacteristic
152C2×C42×C43C2311yescharacteristic
153C24×C43—21no—
154C24×C43C2×D411yescharacteristic
155#41×C43—28no—
156#41×C43—28no—
157#41×C43—28no—
158#41×C43—28no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43C22×C412yes—
163C2×Q8×C43C2×D412yes—
164C2×Q8×C43#4112yes—
165C2×D4×C43—24no—
166C2×D4×C43—24no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—21no—
170C2×D4×C43—24no—
171C2×D4×C43C22×C412yes—
172C2×D4×C43C2×D412yes—
173C2×D4×C43#4112yes—
174C22×C4×C43—24no—
175C22×C4×C43—24no—
176C22×C4×C43—24no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—24no—
182C22×C4×C43—24no—
183C22×C4×C43—24no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—81no—
188C22×C4×C43—81no—
189C22×C4×C43—81no—
190C22×C4×C43—81no—
191C22×C4×C43—81no—
192C22×C4×C43—81no—
193C22×C4×C43C22×C412yes—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43#4112yes—
200C22×C4×C43C2411yescharacteristic
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86C22×C412yes—
211C4⋊C4×C43—24no—
212C4⋊C4×C43—24no—
213C4⋊C4×C43—22no—
214C4⋊C4×C43—24no—
215C4⋊C4×C43—22no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43C2×D412yes—
219C4⋊C4×C43C2×D412yes—
220C22⋊C4×C43—24no—
221C22⋊C4×C43—24no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—22no—
224C42×C43—24no—
225C42×C43—24no—
226C42×C43—21no—
227C42×C43—21no—
228C42×C43C2×D412yes—
229C42×C43C2×D412yes—
230C22⋊Dic43—24no—
231C22⋊Dic43—81no—
232#10621885—28no—
233#10621883—28no—
234C4⋊Dic43—21no—
235C4⋊Dic43—21no—
236C4⋊Dic43—21no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43C22×C412yes—
240Dic43⋊C4—24no—
241Dic43⋊C4—42no—
242Dic43⋊C4—81no—
243C4×Dic43—42no—
244C4×Dic43—81no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8C22×C412yes—
256C2×C43⋊C8C22×C412yes—
257C23×C43—22no—
258C23×C43—21no—
259C23×C43—22no—
260C23×C43—21no—
261C23×C43—22no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43C4×D412yes—
271C23×C43C22×D411yescharacteristic
272Q8×C43—22no—
273Q8×C43—22no—
274Q8×C43—22no—
275Q8×C43C4×D414yes—
276D4×C43—216no—
277D4×C43—22no—
278D4×C43—22no—
279D4×C43—22no—
280D4×C43C4×D414yes—
281C2×C4×C43—216no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
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—22no—
298C2×C4×C43—22no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—84no—
308C2×C4×C43—84no—
309C2×C4×C43—84no—
310C2×C4×C43C4×D412yes—
311C2×C4×C43#12012yes—
312C2×C4×C43#12012yes—
313C2×C4×C43C23×C411yescharacteristic
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43C2×#4111yescharacteristic
318C2×C4×C43C2×#4111yescharacteristic
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43—41no—
326C2×Dic43—41no—
327C2×Dic43—41no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331Dic86—22no—
332Dic86—22no—
333Dic86—41no—
334Dic86—41no—
335C43⋊C8—22no—
336C43⋊C8—22no—
337C43⋊C8—41no—
338C43⋊C8—41no—
339#21465—431nomaximal, Sylow
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—24no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—42no—
346C22×C43—41no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—41no—
351C22×C43—42no—
352C22×C43—41no—
353C22×C43—42no—
354C22×C43C2×C4×D411yescharacteristic
355C22×C43C2×#12011yescharacteristic
356C22×C43#52511yescharacteristic
357C22×C43#57611yescharacteristic
358C22×C43#57711yescharacteristic
359C22×C43#57811yescharacteristic
360C22×C43#57811yescharacteristic
361C4×C43—22no—
362C4×C43—22no—
363C4×C43—22no—
364C4×C43—24no—
365C4×C43—41no—
366C4×C43—41no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43C2×C4×D411yescharacteristic
370C4×C43C2×C4×D411yescharacteristic
371C4×C43#52511yescharacteristic
372C4×C43#52511yescharacteristic
373Dic43—42no—
374Dic43—42no—
375Dic43—81no—
376Dic43—81no—
377C2×#520D4311yescharacteristic
378C2×#452—431no—
379C2×#440—431no—
380C2×C4×Q16—431no—
381#2323—431no—
382#1878—431no—
383#1877—431no—
384#1872—431no—
385#1863—431no—
386#1862—431no—
387#1852—431no—
388#1788—431no—
389#1763—431no—
390C4×#102—431no—
391#1750—431no—
392C2×C43—42no—
393C2×C43—44no—
394C2×C43C4×#12011yescharacteristic
395C2×C43#294711yescharacteristic
396C2×C43#295111yescharacteristic
397C2×C43#301111yescharacteristic
398C2×C43#301211yescharacteristic
399C2×C43#312011yescharacteristic
400C2×C43#312411yescharacteristic
401C22×#41C2×D4311yescharacteristic
402C22×Q16—431no—
403C22×SD16—431no—
404C2×C22⋊Q8—431no—
405#520—24no—
406#520—24no—
407C2×C4×Q8—431no—
408C2×C4×Q8C2×D4311yescharacteristic
409C2×C4×Q8C2×D4311yescharacteristic
410C2×C4×D4—21no—
411C2×C4×D4—21no—
412C2×C4×D4C2×D4311yescharacteristic
413C2×C4×D4C2×D4311yescharacteristic
414C2×#117—21no—
415C2×#117C2×D4311yescharacteristic
416C22×C4⋊C4—21no—
417C22×C4⋊C4C2×D4311yescharacteristic
418#452—438no—
419#440—864no—
420C4×Q16—864no—
421C2×#107—431no—
422C2×#107—431no—
423C2×#103—431no—
424C2×#103—431no—
425C2×#103—431no—
426C2×#103—431no—
427C2×#103—431no—
428C2×#102—431no—
429C2×#102—431no—
430C2×#102—431no—
431C2×C22⋊C8—431no—
432C2×C22⋊C8—431no—
433C2×#97—431no—
434C2×C4×C8—431no—
435#391—431no—
436#389—431no—
437#389—861no—
438#388—861no—
439#388—861no—
440#387—861no—
441#380—431no—
442C4×C4⋊C4—431no—
443#340—431no—
444#340—431no—
445#340—431no—
446#340—431no—
447#336—431no—
448#336—431no—
449C43#2146511yescharacteristic, complemented, Sylow
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—22no—
455C2×#41C4×D4314yes—
456C22×Q8—431no—
457C22×Q8C22×D4311yescharacteristic
458C22×D4—21no—
459C22×D4C22×D4311yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—21no—
463C23×C4—21no—
464C23×C4C22×D4311yescharacteristic
465C2×Q16—434no—
466C2×Q16—862no—
467C2×Q16—862no—
468C2×SD16—434no—
469C2×SD16—862no—
470C2×SD16—862no—
471C22×C8—431no—
472C22×C8—431no—
473C22×C8—431no—
474C22×C8—431no—
475C22⋊Q8—434no—
476C22⋊Q8—862no—
477C4×Q8—22no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—862no—
481C4×Q8—862no—
482C4×Q8C22⋊D4314yes—
483C4×D4—28no—
484C4×D4—28no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4C22⋊D4314yes—
489#117—28no—
490#117—22no—
491#117—22no—
492C2×C4⋊C4—28no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—431no—
499C2×C4⋊C4—431no—
500C2×C4⋊C4—431no—
501C2×C4⋊C4—861no—
502C2×C4⋊C4—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4C22⋊D4311yescharacteristic
505C2×C4⋊C4C22⋊D4311yescharacteristic
506C2×C4⋊C4C22×D4311yescharacteristic
507C2×C4⋊C4C22×D4311yescharacteristic
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4C22⋊D4311yescharacteristic
513C2×C22⋊C4C22⋊D4311yescharacteristic
514C2×C42—21no—
515C2×C42—21no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42C22×D4311yescharacteristic
519C2×C42C22×D4311yescharacteristic
520#107—862no—
521#107—862no—
522#103—434no—
523#103—862no—
524#103—862no—
525#103—862no—
526#103—862no—
527#102—434no—
528#102—862no—
529#102—862no—
530C22⋊C8—434no—
531C22⋊C8—862no—
532#97—862no—
533C4×C8—862no—
534#95—861no—
535#95—861no—
536#95—861no—
537#95—861no—
538#95—861no—
539C24—21no—
540C24C2×C22⋊D4311yescharacteristic
541#41—28no—
542#41—28no—
543#41—28no—
544#41—28no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—432no—
549C2×Q8—861no—
550C2×Q8—861no—
551C2×Q8—861no—
552C2×Q8—861no—
553C2×Q8—861no—
554C2×Q8C2×C4×D4312yes—
555C2×Q8#1062189812yes—
556C2×Q8C2×C22⋊D4312yes—
557C2×D4—24no—
558C2×D4—24no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4C2×C4×D4312yes—
564C2×D4#1062189812yes—
565C2×D4C2×C22⋊D4312yes—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4C2×C4×D4312yes—
590C22×C4#1062189812yes—
591C22×C4C2×C22⋊D4311yescharacteristic
592C22×C4C2×C22⋊D4311yescharacteristic
593C22×C4C2×C22⋊D4311yescharacteristic
594C22×C4C2×C22⋊D4311yescharacteristic
595C22×C4C2×C22⋊D4311yescharacteristic
596C22×C4C23×D4311yescharacteristic
597Q16—868no—
598SD16—868no—
599C2×C8—432no—
600C2×C8—432no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C2×C8—861no—
607C2×C8—861no—
608C2×C8—861no—
609C2×C8—861no—
610C2×C8—861no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—24no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—432no—
619C4⋊C4—864no—
620C4⋊C4—861no—
621C4⋊C4—861no—
622C4⋊C4—861no—
623C4⋊C4—861no—
624C4⋊C4—861no—
625C4⋊C4—3441no—
626C4⋊C4—1722no—
627C4⋊C4C2×C22⋊D4312yes—
628C4⋊C4C2×C22⋊D4312yes—
629C22⋊C4—24no—
630C22⋊C4—24no—
631C22⋊C4—22no—
632C22⋊C4—22no—
633C22⋊C4—864no—
634C22⋊C4—3441no—
635C42—24no—
636C42—24no—
637C42—21no—
638C42—21no—
639C42—3441no—
640C42—1722no—
641C42C2×C22⋊D4312yes—
642C42C2×C22⋊D4312yes—
643C23—22no—
644C23—21no—
645C23—22no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23C4×C22⋊D4312yes—
657C23C22×C22⋊D4311yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—862no—
662Q8—862no—
663Q8—1721no—
664Q8—1721no—
665Q8C4×C22⋊D4314yes—
666D4—216no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4C4×C22⋊D4314yes—
671C2×C4—216no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—84no—
700C2×C4—862no—
701C2×C4—862no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4C4×C22⋊D4312yes—
713C2×C4#1306329412yes—
714C2×C4#1306329412yes—
715C2×C4C22×C4×D4311yescharacteristic
716C2×C4C22×C22⋊D4311yescharacteristic
717C2×C4C22×C22⋊D4311yescharacteristic
718C2×C4C2×#1062189811yescharacteristic
719C2×C4C2×#1062189811yescharacteristic
720C2×C4C2×#1062189811yescharacteristic
721C8—862no—
722C8—862no—
723C8—1721no—
724C8—1721no—
725C22—22no—
726C22—22no—
727C22—22no—
728C22—24no—
729C22—42no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—41no—
734C22—42no—
735C22—41no—
736C22—42no—
737C22—41no—
738C22—42no—
739C22C2×C4×C22⋊D4311yescharacteristic
740C22C2×#1306329411yescharacteristic
741C22#1458341011yescharacteristic
742C22#1458370211yescharacteristic
743C22#1458371011yescharacteristic
744C22#1458371411yescharacteristic
745C22#1458371411yescharacteristic
746C4—22no—
747C4—24no—
748C4—22no—
749C4—22no—
750C4—41no—
751C4—41no—
752C4—42no—
753C4—42no—
754C4—3441no—
755C4—3441no—
756C4—1722no—
757C4—1722no—
758C4C2×C4×C22⋊D4311yescharacteristic
759C4C2×C4×C22⋊D4311yescharacteristic
760C4#1458341011yescharacteristic
761C4#1458341011yescharacteristic
762C2—42no—
763C2—44no—
764C2C4×#1306329411yescharacteristic
765C2#1914343411yescharacteristic
766C2#1914346811yescharacteristic
767C2#1914389011yescharacteristic
768C2#1914389911yescharacteristic
769C2#1914480911yescharacteristic
770C2#1914485711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#520C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
cosocleC22×C4×C43C24
hypercenterC2×#520D43
hypocenterC43#21465
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. C2×#14582999C2semidirect
3. C2×C4×#10621885C2semidirect
4. #19137277C2semidirect
5. #19134936C2semidirect
6. #19134929C2semidirect
7. #19134902C2semidirect
8. #19134849C2semidirect
9. #19134842C2semidirect
10. #19134783C2semidirect
12. #19134425C2semidirect
13. C4×#13063246C2semidirect
14. #19134361C2semidirect
20. #14583061C4semidirect
67. C2×#10621885C2×C4semidirect
70. C2×#10621883C2×C4semidirect
76. #13063304C2×C4semidirect
93. #13063249C2×C4semidirect
98. #13063246C2×C4semidirect
100. C22⋊(C43⋊C8)C2×C4semidirect
449. C43#21465semidirect

Maximal subgroups

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

subgroupindex
C2×#145830612
C2×#145829992
C2×C4×#106218852
#191372772
#191349362
#191349292
#191349022
#191348492
#191348422
#191347832
#191345352
#191344252
C4×#130632462
#191343612
C2×C43×#5202
#2146543