Finite Group Databasebeta

← #25002928

Subgroups — #25002928

Order 11008.

1234 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063240C211yesmaximal, characteristic
2#19137173C211yesmaximal, characteristic
3#19136948C211yesmaximal, characteristic, complemented
4C2×#14582666C211yesmaximal, characteristic, complemented
5C2×#14582665C211yesmaximal, characteristic, complemented
6C2×#14582665C211yesmaximal, characteristic, complemented
7C22×#99×C43C211yesmaximal, characteristic
8C22×C22⋊Dic43C2211yescharacteristic
9C22×C22⋊Dic43C2211yescharacteristic
10C22×C22⋊Dic43C2211yescharacteristic
11C22×C22⋊Dic43C2211yescharacteristic
12C2×#13063240—22no—
13C2×#13063240—22no—
14C2×#13063240C414yescomplemented
15#14582779—22no—
16#14582779—22no—
17#14582762C412yescomplemented
18#14582755C412yescomplemented
19C22⋊C4×Dic43—22no—
20C22⋊C4×Dic43—22no—
21C4×C22⋊Dic43—22no—
22#14582666—22no—
23#14582665—22no—
24#14582665—22no—
25C23×D4×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊C4×C43C2211yescharacteristic
28C2×#99×C43—22no—
29C2×#99×C43—22no—
30C2×#99×C43C414yescomplemented
31C23×Dic43—21no—
32C23×Dic43—21no—
33C23×Dic43—21no—
34C23×Dic43D412yes—
35C2×C22⋊Dic43—21no—
36C2×C22⋊Dic43—21no—
37C2×C22⋊Dic43—21no—
38C2×C22⋊Dic43—21no—
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×C22⋊Dic43—21no—
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43—21no—
52C2×C22⋊Dic43—24no—
53C2×C22⋊Dic43C2×C412yes—
54C2×C22⋊Dic43C2×C412yes—
55C2×C22⋊Dic43C2×C412yes—
56C2×C22⋊Dic43C2×C412yes—
57C2×C22⋊Dic43D412yes—
58C2×C22⋊Dic43D412yes—
59C2×C22⋊Dic43D412yes—
60C2×C4×Dic43—24no—
61#13063240—28no—
62C43⋊#95—24no—
63C43⋊#95—24no—
64C25×C43C2×C411yescharacteristic
65C25×C43C2311yescharacteristic
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43—21no—
75C22×D4×C43—21no—
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43C2×C412yes—
79C22×D4×C43C2×C412yes—
80C23×C4×C43—21no—
81C23×C4×C43—21no—
82C23×C4×C43C2×C411yescharacteristic
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C22⋊C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43C2×C412yes—
92C2×C22⋊C4×C43C2×C412yes—
93C2×C22⋊C4×C43D412yes—
94C2×C22⋊C4×C43D412yes—
95#99×C43—28no—
96C24×C43—21no—
97C24×C43—21no—
98C24×C43—21no—
99C24×C43—21no—
100C24×C43—21no—
101C24×C43—21no—
102C24×C43—82no—
103C24×C43—82no—
104C24×C43C4212yescomplemented
105C24×C43C22×C411yescharacteristic
106C24×C43C22×C411yescharacteristic
107C24×C43C22×C411yescharacteristic
108C24×C43C2×D411yescharacteristic
109C24×C43C2×D411yescharacteristic
110C24×C43C2×D411yescharacteristic
111C24×C43C2×D411yescharacteristic
112C24×C43C2×D411yescharacteristic
113C24×C43C2×D411yescharacteristic
114C24×C43#4111yescharacteristic
115C24×C43#4111yescharacteristic
116C24×C43#4111yescharacteristic
117C24×C43#4111yescharacteristic
118C24×C43#4111yescharacteristic
119C24×C43#4111yescharacteristic
120C2×D4×C43—22no—
121C2×D4×C43—22no—
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—22no—
125C2×D4×C43—22no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—22no—
130C2×D4×C43—22no—
131C2×D4×C43—22no—
132C2×D4×C43—41no—
133C2×D4×C43—41no—
134C2×D4×C43—41no—
135C2×D4×C43—41no—
136C2×D4×C43—41no—
137C2×D4×C43—41no—
138C2×D4×C43—41no—
139C2×D4×C43—41no—
140C2×D4×C43—41no—
141C2×D4×C43—41no—
142C2×D4×C43—41no—
143C2×D4×C43—41no—
144C2×D4×C43—41no—
145C2×D4×C43—41no—
146C2×D4×C43—41no—
147C2×D4×C43—41no—
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×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C22×C4×C43—82no—
161C22×C4×C43—82no—
162C22×C4×C43C4212yescomplemented
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—41no—
171C22×Dic43—41no—
172C22×Dic43—41no—
173C22×Dic43—41no—
174C22×Dic43—82no—
175C22×Dic43—82no—
176C22×Dic43—82no—
177C22×Dic43—82no—
178C22×Dic43C22⋊C414yes—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—22no—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43C22⋊C414yescomplemented
187C22⋊Dic43—22no—
188C22⋊Dic43—22no—
189C22⋊Dic43—22no—
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198C22⋊Dic43—41no—
199C22⋊Dic43—41no—
200C22⋊Dic43—41no—
201C22⋊Dic43—41no—
202C22⋊Dic43—84no—
203C22⋊Dic43C22⋊C414yescomplemented
204C4×Dic43—84no—
205C23×C43—22no—
206C23×C43—22no—
207C23×C43—22no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43—42no—
214C23×C43—42no—
215C23×C43—44no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43—41no—
219C23×C43—41no—
220C23×C43—82no—
221C23×C43—82no—
222C23×C43—81no—
223C23×C43—81no—
224C23×C43—81no—
225C23×C43—81no—
226C23×C43—81no—
227C23×C43—81no—
228C23×C43—81no—
229C23×C43—81no—
230C23×C43—82no—
231C23×C43—82no—
232C23×C43—82no—
233C23×C43—82no—
234C23×C43C2×C4211yescharacteristic
235C23×C43C2×C22⋊C411yescharacteristic
236C23×C43C2×C22⋊C411yescharacteristic
237C23×C43C2×C22⋊C411yescharacteristic
238C23×C43#11711yescharacteristic
239C23×C43#11711yescharacteristic
240C23×C43#11711yescharacteristic
241C23×C43C4×D411yescharacteristic
242C23×C43C4×D411yescharacteristic
243C23×C43C4×D411yescharacteristic
244C23×C43C4×D411yescharacteristic
245C23×C43C4×D411yescharacteristic
246C23×C43C4×D411yescharacteristic
247C23×C43C4×D411yescharacteristic
248C23×C43C4×D411yescharacteristic
249C23×C43C4×D411yescharacteristic
250C23×C43C4×D411yescharacteristic
251C23×C43C4×D411yescharacteristic
252C23×C43C4×D411yescharacteristic
253C23×C43#12011yescharacteristic
254C23×C43#12111yescharacteristic
255C23×C43#12111yescharacteristic
256C23×C43#12111yescharacteristic
257C23×C43#12111yescharacteristic
258C23×C43#12111yescharacteristic
259C23×C43#12111yescharacteristic
260C23×C43#12311yescharacteristic
261C23×C43#12311yescharacteristic
262C23×C43#12311yescharacteristic
263C23×C43#12411yescharacteristic
264C23×C43#12411yescharacteristic
265C23×C43#12411yescharacteristic
266C23×C43#12611yescharacteristic
267C23×C43#12611yescharacteristic
268C23×C43#12711yescharacteristic
269D4×C43—42no—
270D4×C43—42no—
271D4×C43—42no—
272D4×C43—42no—
273D4×C43—42no—
274D4×C43—42no—
275D4×C43—42no—
276D4×C43—42no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—24no—
281C2×C4×C43—44no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—42no—
287C2×C4×C43—82no—
288C2×C4×C43—82no—
289C2×C4×C43—82no—
290C2×C4×C43—82no—
291C2×C4×C43—82no—
292C2×Dic43—24no—
293C2×Dic43—24no—
294C2×Dic43—44no—
295C2×Dic43—44no—
296C2×Dic43—44no—
297C2×Dic43—44no—
298C2×Dic43—42no—
299C2×Dic43—42no—
300C2×Dic43—82no—
301C2×Dic43—82no—
302C2×Dic43—82no—
303C2×Dic43—82no—
304C2×Dic43—82no—
305C2×Dic43—82no—
306C2×Dic43—82no—
307C2×Dic43—82no—
308#10938—431nomaximal, Sylow
309C22×C43—22no—
310C22×C43—22no—
311C22×C43—22no—
312C22×C43—22no—
313C22×C43—22no—
314C22×C43—22no—
315C22×C43—22no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43—41no—
320C22×C43—41no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—44no—
345C22×C43—42no—
346C22×C43—82no—
347C22×C43—82no—
348C22×C43—82no—
349C22×C43—82no—
350C22×C43—82no—
351C22×C43—82no—
352C22×C43C4×C22⋊C411yescharacteristic
353C22×C43C4×C22⋊C411yescharacteristic
354C22×C43C4×C22⋊C411yescharacteristic
355C22×C43#38611yescharacteristic
356C22×C43#38611yescharacteristic
357C22×C43#38611yescharacteristic
358C22×C43#38811yescharacteristic
359C22×C43#38811yescharacteristic
360C22×C43#38811yescharacteristic
361C22×C43#38811yescharacteristic
362C22×C43#38811yescharacteristic
363C22×C43#38811yescharacteristic
364C22×C43#39011yescharacteristic
365C22×C43#39011yescharacteristic
366C22×C43#39011yescharacteristic
367C4×C43—44no—
368C4×C43—42no—
369C4×C43—82no—
370Dic43—44no—
371Dic43—44no—
372Dic43—82no—
373Dic43—82no—
374C22×#99—431no—
375C22×#99D4311yescharacteristic
376#2308—431no—
377#2273—431no—
378C2×#342—431no—
379C2×#342—431no—
380C2×#342—431no—
381C2×C43—21no—
382C2×C43—21no—
383C2×C43—21no—
384C2×C43—21no—
385C2×C43—21no—
386C2×C43—21no—
387C2×C43—21no—
388C2×C43—21no—
389C2×C43—21no—
390C2×C43—21no—
391C2×C43—21no—
392C2×C43—21no—
393C2×C43—21no—
394C2×C43—21no—
395C2×C43—82no—
396C2×C43#143711yescharacteristic
397C2×C43#191312yes—
398C23×D4C2×D4311yescharacteristic
399C22×C22⋊C4—431no—
400C22×C22⋊C4—431no—
401C22×C22⋊C4—431no—
402C22×C22⋊C4—431no—
403C22×C22⋊C4C2×D4311yescharacteristic
404C22×C22⋊C4C2×D4311yescharacteristic
405C2×#99—22no—
406C2×#99—22no—
407C2×#99—434no—
408C2×#99—862no—
409C2×#99—862no—
410C2×#99Dic4314yescomplemented
411#386—862no—
412#386—862no—
413#381—432no—
414#379—432no—
415C4×C22⋊C4—862no—
416C4×C22⋊C4—862no—
417C4×C22⋊C4—862no—
418#342—862no—
419#342—862no—
420#342—862no—
421C43#1093811yescharacteristic, complemented, Sylow
422C25C4×D4311yescharacteristic
423C25C22×D4311yescharacteristic
424C22×D4—21no—
425C22×D4—21no—
426C22×D4—21no—
427C22×D4—21no—
428C22×D4—21no—
429C22×D4—21no—
430C22×D4—21no—
431C22×D4—21no—
432C22×D4—21no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4C4×D4312yes—
437C22×D4C2×Dic4312yes—
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—432no—
441C23×C4—861no—
442C23×C4—861no—
443C23×C4—861no—
444C23×C4C4×D4311yescharacteristic
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—432no—
454C2×C22⋊C4—432no—
455C2×C22⋊C4—432no—
456C2×C22⋊C4—432no—
457C2×C22⋊C4—432no—
458C2×C22⋊C4—432no—
459C2×C22⋊C4—432no—
460C2×C22⋊C4—861no—
461C2×C22⋊C4—861no—
462C2×C22⋊C4—861no—
463C2×C22⋊C4—861no—
464C2×C22⋊C4—861no—
465C2×C22⋊C4—861no—
466C2×C22⋊C4—861no—
467C2×C22⋊C4—861no—
468C2×C22⋊C4—861no—
469C2×C22⋊C4—861no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4—861no—
472C2×C22⋊C4—861no—
473C2×C22⋊C4—861no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—864no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4—861no—
478C2×C22⋊C4C2×Dic4312yes—
479C2×C22⋊C4C2×Dic4312yes—
480C2×C22⋊C4C22⋊D4312yes—
481C2×C22⋊C4C22⋊D4312yes—
482C2×C42—864no—
483#99—28no—
484#99—868no—
485#95—864no—
486#95—864no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—82no—
494C24—82no—
495C24C4×Dic4312yescomplemented
496C24C2×C4×D4311yescharacteristic
497C24C2×C4×D4311yescharacteristic
498C24#1062189811yescharacteristic
499C24#1062189811yescharacteristic
500C24D4×D4311yescharacteristic
501C24D4×D4311yescharacteristic
502C24D4×D4311yescharacteristic
503C24D4×D4311yescharacteristic
504C24#1062190011yescharacteristic
505C24#1062190011yescharacteristic
506C24#1062190011yescharacteristic
507C24#1062190011yescharacteristic
508C24C22×Dic4311yescharacteristic
509C24C2×C22⋊D4311yescharacteristic
510C24C2×C22⋊D4311yescharacteristic
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—22no—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—22no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—41no—
529C2×D4—41no—
530C2×D4—41no—
531C2×D4—41no—
532C2×D4—41no—
533C2×D4—41no—
534C2×D4—41no—
535C2×D4—41no—
536C2×D4—41no—
537C2×D4—41no—
538C2×D4—41no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—41no—
550C22×C4—41no—
551C22×C4—82no—
552C22×C4—82no—
553C22×C4—434no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—862no—
559C22×C4—862no—
560C22×C4—862no—
561C22×C4—3442no—
562C22×C4—3442no—
563C22×C4—3442no—
564C22×C4—3442no—
565C22×C4—1721no—
566C22×C4—1721no—
567C22×C4—1721no—
568C22×C4—1721no—
569C22×C4C4×Dic4312yescomplemented
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—41no—
576C22⋊C4—41no—
577C22⋊C4—434no—
578C22⋊C4—862no—
579C22⋊C4—862no—
580C22⋊C4—862no—
581C22⋊C4—862no—
582C22⋊C4—862no—
583C22⋊C4—862no—
584C22⋊C4—862no—
585C22⋊C4—862no—
586C22⋊C4—862no—
587C22⋊C4—862no—
588C22⋊C4—862no—
589C22⋊C4—3444no—
590C22⋊C4—1721no—
591C22⋊C4—1721no—
592C22⋊C4—1721no—
593C22⋊C4—1721no—
594C22⋊C4C22⋊Dic4314yescomplemented
595C42—3444no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—44no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—82no—
612C23—82no—
613C23—81no—
614C23—81no—
615C23—81no—
616C23—81no—
617C23—81no—
618C23—81no—
619C23—81no—
620C23—81no—
621C23—82no—
622C23—82no—
623C23—82no—
624C23—82no—
625C23C2×C4×Dic4311yescharacteristic
626C23C22⋊C4×D4311yescharacteristic
627C23C22⋊C4×D4311yescharacteristic
628C23C2×C22⋊Dic4311yescharacteristic
629C23#1306328111yescharacteristic
630C23#1306328111yescharacteristic
631C23#1306328411yescharacteristic
632C23(C22⋊D43)⋊C411yescharacteristic
633C23(C22⋊D43)⋊C411yescharacteristic
634C23(C22⋊D43)⋊C411yescharacteristic
635C23(C22⋊D43)⋊C411yescharacteristic
636C23C4×C22⋊D4311yescharacteristic
637C23C4×C22⋊D4311yescharacteristic
638C23C4×C22⋊D4311yescharacteristic
639C23C4×C22⋊D4311yescharacteristic
640C23D4×Dic4311yescharacteristic
641C23D4×Dic4311yescharacteristic
642C23D4×Dic4311yescharacteristic
643C23D4×Dic4311yescharacteristic
644C23#1306329311yescharacteristic
645C23#1306329611yescharacteristic
646C23#1306329611yescharacteristic
647C23#1306329711yescharacteristic
648C23#1306329711yescharacteristic
649C23#1306329811yescharacteristic
650C23#1306329811yescharacteristic
651C23#1306330611yescharacteristic
652C23#1306330711yescharacteristic
653C23#1306330711yescharacteristic
654C23#1306331111yescharacteristic
655C23#1306331111yescharacteristic
656C23#1306331211yescharacteristic
657C23#1306331811yescharacteristic
658C23#1306331811yescharacteristic
659C23#1306332111yescharacteristic
660D4—42no—
661D4—42no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—42no—
667D4—42no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—44no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4—82no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4—864no—
684C2×C4—864no—
685C2×C4—3442no—
686C2×C4—3442no—
687C2×C4—3442no—
688C2×C4—3442no—
689C2×C4—3442no—
690C2×C4—3442no—
691C2×C4—3442no—
692C2×C4—3442no—
693C2×C4—1724no—
694C2×C4—1722no—
695C2×C4—1722no—
696C2×C4—1724no—
697C2×C4—1724no—
698C2×C4—1724no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—44no—
735C22—42no—
736C22—82no—
737C22—82no—
738C22—82no—
739C22—82no—
740C22—82no—
741C22—82no—
742C22C4×C22⋊Dic4311yescharacteristic
743C22C22⋊C4×Dic4311yescharacteristic
744C22C22⋊C4×Dic4311yescharacteristic
745C22#1458277511yescharacteristic
746C22#1458277511yescharacteristic
747C22#1458277911yescharacteristic
748C22#1458278711yescharacteristic
749C22#1458278711yescharacteristic
750C22#1458279211yescharacteristic
751C22#1458279211yescharacteristic
752C22#1458279311yescharacteristic
753C22#1458279311yescharacteristic
754C22#1458279911yescharacteristic
755C22#1458279911yescharacteristic
756C22#1458280211yescharacteristic
757C4—44no—
758C4—42no—
759C4—82no—
760C4—3442no—
761C4—3442no—
762C4—1724no—
763C4—1724no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2—21no—
777C2—21no—
778C2—82no—
779C2#1913283211yescharacteristic
780C2#1913513412yes—
subgroupG/H
centerC22#14582775
commutatorC23×C43C2×C42
FrattiniC25C22×D43
FittingC22×#99×C43C2
socleC22×C43#386
prime radicalC23×D4×C43C22
cosocleC25×C43C23
hypercenterC22×#99D43
hypocenterC43#10938
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
3. #19136948C2semidirect
4. C2×#14582666C2semidirect
5. C2×#14582665C2semidirect
6. C2×#14582665C2semidirect
14. C2×#13063240C4semidirect
17. #14582762C4semidirect
18. #14582755C4semidirect
30. C2×#99×C43C4semidirect
104. C24×C43C42semidirect
162. C22×C4×C43C42semidirect
186. C22⋊C4×C43C22⋊C4semidirect
203. C22⋊Dic43C22⋊C4semidirect
410. C2×#99Dic43semidirect
421. C43#10938semidirect
495. C24C4×Dic43semidirect
569. C22×C4C4×Dic43semidirect
594. C22⋊C4C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632402
#191371732
#191369482
C2×#145826662
C2×#145826652
C22×#99×C432
#1093843