Finite Group Databasebeta

← #25004462

Subgroups — #25004462

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582862C211yesmaximal, characteristic
2C2×#14582862C211yesmaximal, characteristic
3C2×#14582756C211yesmaximal, characteristic
4C2×#14582668C211yesmaximal, characteristic, complemented
5C2×#14582667C211yesmaximal, characteristic, complemented
6C2×#14582667C211yesmaximal, characteristic, complemented
7C2×C43×#343C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11C22×C4⋊Dic43C2211yescharacteristic
12C22×(C2×D43)⋊C4C412yes—
13#14582862—22no—
14#14582862—22no—
15#14582862—22no—
16#14582862—22no—
17C2×(C2×D43)⋊C8—21no—
18C2×(C2×D43)⋊C8—21no—
19C2×(C2×D43)⋊C8—21no—
20C2×(C2×D43)⋊C8—21no—
21#14582756—21no—
22#14582756—21no—
23#14582756—21no—
24#14582756—21no—
25C2×C43⋊#95C412yes—
26#14582668—22no—
27#14582667—22no—
28#14582667—22no—
29C22×M16×C43C2211yescharacteristic
30C22×M16×C43C2211yescharacteristic
31C22×C4⋊C4×C43C2211yescharacteristic
32C43×#343—22no—
33C24×D43C2×C411yescharacteristic
34C23×Dic43C2×C411yescharacteristic
35C23×Dic43C2×C412yes—
36C22×C4×D43—21no—
37C22×C4×D43—21no—
38C22×C4×D43—21no—
39C22×C4×D43—21no—
40C22×C4×D43—21no—
41C22×C4×D43—21no—
42C22×C4×D43—21no—
43C22×C4×D43—21no—
44C22×C4×D43—21no—
45C22×C4×D43—21no—
46C22×C4×D43—21no—
47C22×C4×D43—21no—
48C22×C4×D43D411yescharacteristic
49C22×C4×D43D411yescharacteristic
50C22×C4×D43D411yescharacteristic
51C22×C4×D43D411yescharacteristic
52C2×#10621877—21no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877—21no—
61C2×#10621877—21no—
62C2×#10621877D412yes—
63C2×#10621877D412yes—
64C22×C43⋊C8—21no—
65C22×C43⋊C8—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×(C2×D43)⋊C4—22no—
73C2×(C2×D43)⋊C4—22no—
74C2×(C2×D43)⋊C4—44no—
75(C2×D43)⋊C8—24no—
76(C2×D43)⋊C8—24no—
77(C2×D43)⋊C8—24no—
78(C2×D43)⋊C8—24no—
79C43⋊#95—22no—
80C43⋊#95—22no—
81C23×C4×C43C2×C412yes—
82C23×C4×C43C2311yescharacteristic
83C2×M16×C43—21no—
84C2×M16×C43—21no—
85C2×M16×C43—21no—
86C2×M16×C43—21no—
87C2×M16×C43—21no—
88C2×M16×C43—21no—
89C2×M16×C43—21no—
90C2×M16×C43—21no—
91C2×M16×C43—21no—
92C2×M16×C43—21no—
93C2×M16×C43D412yes—
94C2×M16×C43D412yes—
95C22×C8×C43—21no—
96C22×C8×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C24×C43C22×C411yescharacteristic
104C23×D43—21no—
105C23×D43—21no—
106C23×D43—22no—
107C23×D43—22no—
108C23×D43—21no—
109C23×D43—21no—
110C23×D43—21no—
111C23×D43—21no—
112C23×D43—41no—
113C23×D43—41no—
114C23×D43C22⋊C411yescharacteristic
115C23×D43C22⋊C411yescharacteristic
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—42no—
120C22×C4×C43—42no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43#4111yescharacteristic
128C22×C4×C43#4111yescharacteristic
129C22×C4×C43#4111yescharacteristic
130C22×C4×C43#4111yescharacteristic
131C22×C4×C43#4111yescharacteristic
132C22×C4×C43#4111yescharacteristic
133C22×C4×C43#4111yescharacteristic
134C22×C4×C43#4111yescharacteristic
135C22×Dic43—22no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—42no—
145C22×Dic43—42no—
146C22×Dic43C22⋊C411yescharacteristic
147C22×Dic43C22⋊C411yescharacteristic
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—41no—
173C2×C4×D43—41no—
174C2×C4×D43—41no—
175C2×C4×D43—41no—
176C2×C4×D43—41no—
177C2×C4×D43—41no—
178C2×C4×D43—41no—
179C2×C4×D43—41no—
180C2×C4×D43—41no—
181C2×C4×D43—41no—
182C2×C4×D43—41no—
183C2×C4×D43—41no—
184C2×C4×D43—41no—
185C2×C4×D43—41no—
186C2×C4×D43—41no—
187C2×C4×D43—41no—
188M16×C43—22no—
189M16×C43—22no—
190M16×C43—22no—
191M16×C43—22no—
192M16×C43—41no—
193M16×C43—41no—
194M16×C43—41no—
195M16×C43—41no—
196C2×C8×C43—22no—
197C2×C8×C43—22no—
198C2×C8×C43—41no—
199C2×C8×C43—41no—
200C2×C8×C43—41no—
201C2×C8×C43—41no—
202C4⋊C4×C43—41no—
203C4⋊C4×C43—41no—
204C4⋊C4×C43—41no—
205C4⋊C4×C43—41no—
206(C2×D43)⋊C4—44no—
207(C2×D43)⋊C4—44no—
208C4⋊Dic43—41no—
209C4⋊Dic43—41no—
210C4⋊Dic43—41no—
211C4⋊Dic43—41no—
212#10621877—22no—
213#10621877—22no—
214#10621877—22no—
215#10621877—22no—
216#10621877—41no—
217#10621877—41no—
218#10621877—41no—
219#10621877—41no—
220C2×C43⋊C8—22no—
221C2×C43⋊C8—22no—
222C2×C43⋊C8—41no—
223C2×C43⋊C8—41no—
224C2×C43⋊C8—41no—
225C2×C43⋊C8—41no—
226C23×C43—21no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43C2×C22⋊C411yescharacteristic
231C23×C43#11711yescharacteristic
232C23×C43#11711yescharacteristic
233C23×C43C4×D411yescharacteristic
234C23×C43C4×D411yescharacteristic
235C23×C43C4×D411yescharacteristic
236C23×C43C4×D411yescharacteristic
237C22×D43—24no—
238C22×D43—24no—
239C22×D43—21no—
240C22×D43—21no—
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—42no—
252C22×D43—42no—
253C22×D43—42no—
254C22×D43—42no—
255C22×D43—42no—
256C22×D43—42no—
257C22×D43—42no—
258C22×D43—42no—
259C22×D43—42no—
260C22×D43—42no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43#10012yes—
266C22×D43#10112yes—
267C2×C4×C43—42no—
268C2×C4×C43—42no—
269C2×C4×C43—42no—
270C2×C4×C43—82no—
271C2×C4×C43—82no—
272C2×C4×C43#12011yescharacteristic
273C2×C4×C43#12011yescharacteristic
274C2×C4×C43#12111yescharacteristic
275C2×C4×C43#12111yescharacteristic
276C2×C4×C43#12111yescharacteristic
277C2×C4×C43#12111yescharacteristic
278C2×C4×C43#12111yescharacteristic
279C2×C4×C43#12111yescharacteristic
280C2×C4×C43#12111yescharacteristic
281C2×C4×C43#12111yescharacteristic
282C2×C4×C43#12311yescharacteristic
283C2×C4×C43#12311yescharacteristic
284C2×C4×C43#12311yescharacteristic
285C2×C4×C43#12311yescharacteristic
286C2×C4×C43#12311yescharacteristic
287C2×C4×C43#12311yescharacteristic
288C2×C4×C43#12311yescharacteristic
289C2×C4×C43#12311yescharacteristic
290C2×C4×C43#12311yescharacteristic
291C2×C4×C43#12311yescharacteristic
292C2×C4×C43#12411yescharacteristic
293C2×C4×C43#12411yescharacteristic
294C2×C4×C43#12411yescharacteristic
295C2×C4×C43#12411yescharacteristic
296C2×C4×C43#12611yescharacteristic
297C2×C4×C43#12611yescharacteristic
298C2×C4×C43#12611yescharacteristic
299C2×C4×C43#12611yescharacteristic
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—21no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—82no—
314C2×Dic43—82no—
315C4×D43—41no—
316C4×D43—41no—
317C4×D43—41no—
318C4×D43—41no—
319C4×D43—41no—
320C4×D43—41no—
321C4×D43—41no—
322C4×D43—41no—
323C4×D43—41no—
324C4×D43—41no—
325C4×D43—41no—
326C4×D43—41no—
327C4×D43—41no—
328C4×D43—41no—
329C4×D43—41no—
330C4×D43—41no—
331C8×C43—42no—
332C8×C43—42no—
333C43⋊C8—42no—
334C43⋊C8—42no—
335#11198—431nomaximal, Sylow
336C22×C43—21no—
337C22×C43—21no—
338C22×C43—21no—
339C22×C43—21no—
340C22×C43—21no—
341C22×C43—21no—
342C22×C43—21no—
343C22×C43—21no—
344C22×C43—21no—
345C22×C43—21no—
346C22×C43—21no—
347C22×C43—21no—
348C22×C43#38111yescharacteristic
349C22×C43#38611yescharacteristic
350C22×C43#38611yescharacteristic
351C22×C43#38811yescharacteristic
352C22×C43#38811yescharacteristic
353C22×C43#38811yescharacteristic
354C22×C43#38811yescharacteristic
355C22×C43C2×#10011yescharacteristic
356C22×C43C2×#10111yescharacteristic
357C22×C43#41311yescharacteristic
358C22×C43#41311yescharacteristic
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—44no—
366C2×D43—44no—
367C2×D43—44no—
368C2×D43—44no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—41no—
375C2×D43—41no—
376C2×D43—41no—
377C4×C43—82no—
378C4×C43#39411yescharacteristic
379C4×C43#39411yescharacteristic
380C4×C43#39411yescharacteristic
381C4×C43#39411yescharacteristic
382C4×C43#39711yescharacteristic
383C4×C43#39711yescharacteristic
384C4×C43#39711yescharacteristic
385C4×C43#39711yescharacteristic
386Dic43—41no—
387Dic43—41no—
388Dic43—82no—
389C2×#407—431no—
390C2×#407—431no—
391C2×#380—431no—
392C2×#343—431no—
393C2×#343—431no—
394C2×#343—431no—
395C2×#343D4311yescharacteristic, complemented
396C2×C43—21no—
397C2×C43—21no—
398C2×C43—21no—
399C2×C43—21no—
400C2×C43#144011yescharacteristic
401C2×C43#182111yescharacteristic
402C2×C43#182211yescharacteristic
403C2×C43#190011yescharacteristic
404C2×C43#190011yescharacteristic
405C2×C43#190111yescharacteristic
406C2×C43#190111yescharacteristic
407D43—42no—
408D43—42no—
409C24×C4—431no—
410C22×M16—431no—
411C22×M16—431no—
412C22×M16C2×D4311yescharacteristic
413C22×M16C2×D4311yescharacteristic
414C22×C4⋊C4—431no—
415C22×C4⋊C4C2×D4311yescharacteristic
416C22×C22⋊C4—432no—
417#407—862no—
418#407—862no—
419#407—862no—
420#407—862no—
421C2×C22⋊C8—861no—
422C2×C22⋊C8—861no—
423C2×C22⋊C8—861no—
424C2×C22⋊C8—861no—
425#380—861no—
426#380—861no—
427#380—861no—
428#380—861no—
429C2×#95—432no—
430#343—22no—
431#343—862no—
432#343—862no—
433#343—862no—
434C43#1119811yescharacteristic, complemented, Sylow
435C25—431no—
436C23×C4—431no—
437C23×C4—431no—
438C23×C4—431no—
439C23×C4—431no—
440C23×C4—431no—
441C23×C4—432no—
442C23×C4—861no—
443C23×C4—861no—
444C23×C4—861no—
445C23×C4—861no—
446C23×C4—861no—
447C23×C4—861no—
448C23×C4—861no—
449C23×C4—861no—
450C23×C4—861no—
451C23×C4—861no—
452C23×C4—861no—
453C23×C4—861no—
454C23×C4C4×D4312yes—
455C23×C4C22×D4311yescharacteristic
456C2×M16—21no—
457C2×M16—21no—
458C2×M16—21no—
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—21no—
465C2×M16—21no—
466C2×M16—432no—
467C2×M16—432no—
468C2×M16—861no—
469C2×M16—861no—
470C2×M16—861no—
471C2×M16—861no—
472C2×M16—861no—
473C2×M16—861no—
474C2×M16—861no—
475C2×M16—861no—
476C2×M16—861no—
477C2×M16—861no—
478C2×M16D17212yes—
479C2×M16C22⋊D4312yes—
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—861no—
483C22×C8—861no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—861no—
491C2×C4⋊C4—861no—
492C2×C4⋊C4—861no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C22⋊C4—862no—
497C2×C22⋊C4—862no—
498C2×C22⋊C4—1724no—
499C22⋊C8—864no—
500C22⋊C8—864no—
501C22⋊C8—864no—
502C22⋊C8—864no—
503#95—862no—
504#95—862no—
505C24—431no—
506C24—431no—
507C24—862no—
508C24—862no—
509C24—861no—
510C24—861no—
511C24—861no—
512C24—861no—
513C24—861no—
514C24—861no—
515C24—1721no—
516C24—1721no—
517C24C2×C4×D4311yescharacteristic
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—431no—
524C22×C4—431no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—861no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—861no—
537C22×C4—861no—
538C22×C4—861no—
539C22×C4—861no—
540C22×C4—861no—
541C22×C4—861no—
542C22×C4—861no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—861no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—1722no—
559C22×C4—1722no—
560C22×C4—1721no—
561C22×C4—1721no—
562C22×C4—1721no—
563C22×C4—1721no—
564C22×C4—1721no—
565C22×C4—1721no—
566C22×C4—1721no—
567C22×C4—1721no—
568C22×C4—1721no—
569C22×C4—1721no—
570C22×C4—1721no—
571C22×C4—1721no—
572C22×C4—1721no—
573C22×C4—1721no—
574C22×C4—1721no—
575C22×C4—1721no—
576C22×C4C2×D17211yescharacteristic
577C22×C4#1062189811yescharacteristic
578C22×C4#1062189811yescharacteristic
579C22×C4#1062189811yescharacteristic
580C22×C4#1062189811yescharacteristic
581C22×C4D4×D4311yescharacteristic
582C22×C4D4×D4311yescharacteristic
583C22×C4D4×D4311yescharacteristic
584C22×C4D4×D4311yescharacteristic
585C22×C4#1062190011yescharacteristic
586C22×C4#1062190011yescharacteristic
587C22×C4#1062190211yescharacteristic
588C22×C4#1062190211yescharacteristic
589C22×C4C2×C22⋊D4311yescharacteristic
590M16—22no—
591M16—22no—
592M16—22no—
593M16—22no—
594M16—41no—
595M16—41no—
596M16—41no—
597M16—41no—
598M16—862no—
599M16—862no—
600M16—862no—
601M16—862no—
602M16—1721no—
603M16—1721no—
604M16—1721no—
605M16—1721no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—41no—
609C2×C8—41no—
610C2×C8—41no—
611C2×C8—41no—
612C2×C8—862no—
613C2×C8—862no—
614C2×C8—1721no—
615C2×C8—1721no—
616C2×C8—1721no—
617C2×C8—1721no—
618C4⋊C4—41no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—41no—
622C4⋊C4—1721no—
623C4⋊C4—1721no—
624C4⋊C4—1721no—
625C4⋊C4—1721no—
626C22⋊C4—1724no—
627C22⋊C4—1724no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—432no—
633C23—432no—
634C23—864no—
635C23—864no—
636C23—861no—
637C23—861no—
638C23—861no—
639C23—861no—
640C23—861no—
641C23—861no—
642C23—861no—
643C23—861no—
644C23—861no—
645C23—861no—
646C23—861no—
647C23—861no—
648C23—1722no—
649C23—1722no—
650C23—1722no—
651C23—1722no—
652C23—1722no—
653C23—1722no—
654C23—1722no—
655C23—1722no—
656C23—1722no—
657C23—1722no—
658C23—1721no—
659C23—1721no—
660C23—1721no—
661C23—1721no—
662C23C22⋊C4×D4311yescharacteristic
663C23#1306328211yescharacteristic
664C23#1306328311yescharacteristic
665C23(C22⋊D43)⋊C411yescharacteristic
666C23C4×C22⋊D4311yescharacteristic
667C23#1306328711yescharacteristic
668C23C4×D17211yescharacteristic
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—82no—
673C2×C4—82no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—3442no—
681C2×C4—3442no—
682C2×C4—1722no—
683C2×C4—1722no—
684C2×C4—1722no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C2×C4—1721no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4—1721no—
702C2×C4—1721no—
703C2×C4—1721no—
704C2×C4—1721no—
705C2×C4#1306329311yescharacteristic
706C2×C4#1306329511yescharacteristic
707C2×C4#1306329611yescharacteristic
708C2×C4#1306329711yescharacteristic
709C2×C4#1306329811yescharacteristic
710C2×C4#1306329811yescharacteristic
711C2×C4#1306329811yescharacteristic
712C2×C4#1306329911yescharacteristic
713C2×C4#1306330011yescharacteristic
714C2×C4#1306330011yescharacteristic
715C2×C4#1306330711yescharacteristic
716C2×C4#1306330711yescharacteristic
717C2×C4#1306330711yescharacteristic
718C2×C4#1306330811yescharacteristic
719C2×C4#1306330911yescharacteristic
720C2×C4#1306331011yescharacteristic
721C2×C4#1306331011yescharacteristic
722C2×C4#1306331011yescharacteristic
723C2×C4#1306331011yescharacteristic
724C2×C4#1306331011yescharacteristic
725C2×C4#1306331111yescharacteristic
726C2×C4#1306331111yescharacteristic
727C2×C4#1306331311yescharacteristic
728C2×C4#1306331411yescharacteristic
729C2×C4#1306331911yescharacteristic
730C2×C4#1306332011yescharacteristic
731C2×C4#1306332011yescharacteristic
732C2×C4#1306332011yescharacteristic
733C8—42no—
734C8—42no—
735C8—1722no—
736C8—1722no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—862no—
750C22—862no—
751C22—862no—
752C22—862no—
753C22—862no—
754C22—862no—
755C22—1724no—
756C22—1724no—
757C22—1724no—
758C22—1724no—
759C22—1721no—
760C22—1721no—
761C22—1721no—
762C22—1721no—
763C22—1721no—
764C22—1721no—
765C22—1721no—
766C22—1721no—
767C22#1458276111yescharacteristic
768C22#1458277511yescharacteristic
769C22#1458277711yescharacteristic
770C22#1458278811yescharacteristic
771C22#1458278911yescharacteristic
772C22#1458279011yescharacteristic
773C22#1458279111yescharacteristic
774C22#100×D4311yescharacteristic
775C22#101×D4311yescharacteristic
776C22#1458288011yescharacteristic
777C22#1458288211yescharacteristic
778C4—82no—
779C4—3442no—
780C4—1721no—
781C4—1721no—
782C4#1458281411yescharacteristic
783C4#1458281511yescharacteristic
784C4#1458281611yescharacteristic
785C4#1458281711yescharacteristic
786C4#1458282511yescharacteristic
787C4#1458282611yescharacteristic
788C4#1458282811yescharacteristic
789C4#1458282811yescharacteristic
790C2—21no—
791C2—21no—
792C2—21no—
793C2—21no—
794C2—1722no—
795C2—1722no—
796C2#1913284311yescharacteristic
797C2#1913467411yescharacteristic
798C2#1913467711yescharacteristic
799C2#1913505511yescharacteristic
800C2#1913505711yescharacteristic
801C2#1913506011yescharacteristic
802C2#1913506211yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#343C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43C2×C4
cosocleC23×C4×C43C23
hypercenterC2×#343D43
hypocenterC43#11198
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
4. C2×#14582668C2semidirect
5. C2×#14582667C2semidirect
6. C2×#14582667C2semidirect
7. C2×C43×#343C2semidirect
395. C2×#343D43semidirect
434. C43#11198semidirect

Maximal subgroups

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

subgroupindex
C2×#145828622
C2×#145827562
C2×#145826682
C2×#145826672
C2×C43×#3432
#1119843