Finite Group Databasebeta

← #25004278

Subgroups — #25004278

Order 11008.

1110 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
1C22×#13063239C211yesmaximal, characteristic
2C22×#13063239C211yesmaximal, characteristic
3#19137170C211yesmaximal, characteristic
4C2×#14582666C211yesmaximal, characteristic, complemented
5C2×#14582665C211yesmaximal, characteristic, complemented
6C2×#14582665C211yesmaximal, characteristic, complemented
7C2×C43×#342C211yesmaximal, characteristic, complemented
8C23×C22⋊D43C2211yescharacteristic
9C22×C22⋊Dic43C2211yescharacteristic
10C22×C22⋊Dic43C2211yescharacteristic
11C22×C22⋊Dic43C2211yescharacteristic
12C2×#13063239—22no—
13C2×#13063239—22no—
14C2×#13063239—22no—
15C2×#13063239—22no—
16C2×#13063239—22no—
17C2×#13063239—22no—
18#14582778—22no—
19#14582776—22no—
20#14582760C412yescomplemented
21#14582754C412yescomplemented
22#14582666—22no—
23#14582665—22no—
24#14582665—22no—
25C22×C22⋊C4×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊C4×C43C2211yescharacteristic
28C43×#342—22no—
29C24×D43C2×C411yescharacteristic
30C22×C22⋊D43—21no—
31C22×C22⋊D43—21no—
32C22×C22⋊D43—21no—
33C22×C22⋊D43—21no—
34C22×C22⋊D43—21no—
35C22×C22⋊D43—21no—
36C22×C22⋊D43—21no—
37C22×C22⋊D43—21no—
38C22×C22⋊D43—21no—
39C22×C22⋊D43—21no—
40C22×C22⋊D43—21no—
41C22×C22⋊D43—21no—
42C22×C22⋊D43D412yes—
43C22×C22⋊D43D412yes—
44C23×Dic43—21no—
45C23×Dic43—21no—
46C23×Dic43—21no—
47C23×Dic43C2×C411yescharacteristic
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43—21no—
52C2×C22⋊Dic43—21no—
53C2×C22⋊Dic43—21no—
54C2×C22⋊Dic43—21no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—21no—
57C2×C22⋊Dic43—21no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—21no—
60C2×C22⋊Dic43—21no—
61C2×C22⋊Dic43—21no—
62C2×C22⋊Dic43—21no—
63C2×C22⋊Dic43C2×C412yes—
64C2×C22⋊Dic43D412yes—
65C2×C22⋊Dic43D412yes—
66C2×(C2×D43)⋊C4—24no—
67#13063239—28no—
68#13063239—28no—
69C43⋊#95—24no—
70C25×C43C2311yescharacteristic
71C23×C4×C43—21no—
72C23×C4×C43—21no—
73C23×C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—21no—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—21no—
80C2×C22⋊C4×C43—21no—
81C2×C22⋊C4×C43—21no—
82C2×C22⋊C4×C43—21no—
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×C43C2×C412yes—
90C2×C22⋊C4×C43D412yes—
91C2×C22⋊C4×C43D412yes—
92C24×C43—82no—
93C24×C43C22×C411yescharacteristic
94C24×C43C2×D411yescharacteristic
95C24×C43C2×D411yescharacteristic
96C24×C43C2×D411yescharacteristic
97C24×C43C2×D411yescharacteristic
98C24×C43C2×D411yescharacteristic
99C24×C43C2×D411yescharacteristic
100C24×C43#4111yescharacteristic
101C24×C43#4111yescharacteristic
102C24×C43#4111yescharacteristic
103C24×C43#4111yescharacteristic
104C24×C43#4111yescharacteristic
105C24×C43#4111yescharacteristic
106C24×C43#4111yescharacteristic
107C24×C43#4111yescharacteristic
108C23×D43—21no—
109C23×D43—21no—
110C23×D43—21no—
111C23×D43—21no—
112C23×D43—21no—
113C23×D43—21no—
114C23×D43—82no—
115C23×D43C22⋊C412yes—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—41no—
120C22×C4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43—82no—
126C22×C4×C43—82no—
127C22×C4×C43—82no—
128C2×C22⋊D43—22no—
129C2×C22⋊D43—22no—
130C2×C22⋊D43—22no—
131C2×C22⋊D43—22no—
132C2×C22⋊D43—22no—
133C2×C22⋊D43—22no—
134C2×C22⋊D43—22no—
135C2×C22⋊D43—22no—
136C2×C22⋊D43—22no—
137C2×C22⋊D43—22no—
138C2×C22⋊D43—22no—
139C2×C22⋊D43—22no—
140C2×C22⋊D43—41no—
141C2×C22⋊D43—41no—
142C2×C22⋊D43—41no—
143C2×C22⋊D43—41no—
144C2×C22⋊D43—41no—
145C2×C22⋊D43—41no—
146C2×C22⋊D43—41no—
147C2×C22⋊D43—41no—
148C2×C22⋊D43—41no—
149C2×C22⋊D43—41no—
150C2×C22⋊D43—41no—
151C2×C22⋊D43—41no—
152C2×C22⋊D43—41no—
153C2×C22⋊D43—41no—
154C2×C22⋊D43—41no—
155C2×C22⋊D43—41no—
156C22×Dic43—22no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—41no—
166C22×Dic43—41no—
167C22×Dic43—41no—
168C22×Dic43—41no—
169C22×Dic43—41no—
170C22×Dic43—41no—
171C22×Dic43—82no—
172C22×Dic43—82no—
173C22×Dic43—82no—
174C22×Dic43C22⋊C412yes—
175C22⋊C4×C43—22no—
176C22⋊C4×C43—22no—
177C22⋊C4×C43—22no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C22⋊C4×C43—41no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43—41no—
187C22⋊Dic43—22no—
188C22⋊Dic43—22no—
189C22⋊Dic43—22no—
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—41no—
194C22⋊Dic43—41no—
195C22⋊Dic43—41no—
196C22⋊Dic43—41no—
197C22⋊Dic43—41no—
198C22⋊Dic43—41no—
199(C2×D43)⋊C4—84no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—81no—
208C23×C43—81no—
209C23×C43—81no—
210C23×C43—81no—
211C23×C43—81no—
212C23×C43—81no—
213C23×C43—81no—
214C23×C43—81no—
215C23×C43C2×C22⋊C411yescharacteristic
216C23×C43#11711yescharacteristic
217C23×C43#11711yescharacteristic
218C23×C43C4×D411yescharacteristic
219C23×C43C4×D411yescharacteristic
220C23×C43C4×D411yescharacteristic
221C23×C43C4×D411yescharacteristic
222C23×C43#12011yescharacteristic
223C23×C43#12011yescharacteristic
224C23×C43#12111yescharacteristic
225C23×C43#12111yescharacteristic
226C23×C43#12111yescharacteristic
227C23×C43#12111yescharacteristic
228C23×C43#12111yescharacteristic
229C23×C43#12111yescharacteristic
230C23×C43#12111yescharacteristic
231C23×C43#12111yescharacteristic
232C23×C43#12311yescharacteristic
233C23×C43#12311yescharacteristic
234C23×C43#12311yescharacteristic
235C23×C43#12311yescharacteristic
236C23×C43#12311yescharacteristic
237C23×C43#12311yescharacteristic
238C23×C43#12311yescharacteristic
239C23×C43#12311yescharacteristic
240C23×C43#12311yescharacteristic
241C23×C43#12311yescharacteristic
242C23×C43#12411yescharacteristic
243C23×C43#12411yescharacteristic
244C23×C43#12411yescharacteristic
245C23×C43#12411yescharacteristic
246C23×C43#12611yescharacteristic
247C23×C43#12611yescharacteristic
248C23×C43#12611yescharacteristic
249C23×C43#12611yescharacteristic
250C22×D43—22no—
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—41no—
254C22×D43—41no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—44no—
258C22×D43—82no—
259C22×D43—82no—
260C22×D43—82no—
261C22×D43—82no—
262C22×D43—82no—
263C22×D43—82no—
264C2×C4×C43—44no—
265C2×C4×C43—42no—
266C2×C4×C43—42no—
267C2×C4×C43—42no—
268C2×C4×C43—82no—
269C2×C4×C43—82no—
270C2×C4×C43—82no—
271C2×C4×C43—82no—
272C2×C4×C43—82no—
273C2×C4×C43—82no—
274C2×C4×C43—82no—
275C2×C4×C43—82no—
276C22⋊D43—42no—
277C22⋊D43—42no—
278C22⋊D43—42no—
279C22⋊D43—42no—
280C22⋊D43—42no—
281C22⋊D43—42no—
282C22⋊D43—42no—
283C22⋊D43—42no—
284C2×Dic43—22no—
285C2×Dic43—22no—
286C2×Dic43—22no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—44no—
292C2×Dic43—42no—
293C2×Dic43—42no—
294C2×Dic43—42no—
295C2×Dic43—82no—
296C2×Dic43—82no—
297C2×Dic43—82no—
298C2×Dic43—82no—
299C2×Dic43—82no—
300C2×Dic43—82no—
301C2×Dic43—82no—
302C2×Dic43—82no—
303#11166—431nomaximal, Sylow
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—22no—
307C22×C43—22no—
308C22×C43—22no—
309C22×C43—22no—
310C22×C43—22no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43—41no—
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#38111yescharacteristic
340C22×C43#38611yescharacteristic
341C22×C43#38611yescharacteristic
342C22×C43#38811yescharacteristic
343C22×C43#38811yescharacteristic
344C22×C43#38811yescharacteristic
345C22×C43#38811yescharacteristic
346C22×C43#39411yescharacteristic
347C22×C43#39411yescharacteristic
348C22×C43#39411yescharacteristic
349C22×C43#39411yescharacteristic
350C22×C43#39711yescharacteristic
351C22×C43#39711yescharacteristic
352C22×C43#39711yescharacteristic
353C22×C43#39711yescharacteristic
354C2×D43—44no—
355C2×D43—42no—
356C2×D43—82no—
357C2×D43—82no—
358C2×D43—82no—
359C2×D43—82no—
360C2×D43—82no—
361C2×D43—82no—
362C4×C43—82no—
363C4×C43—82no—
364C4×C43—82no—
365Dic43—42no—
366Dic43—82no—
367Dic43—82no—
368Dic43—82no—
369C22×#99—431no—
370C22×#99—431no—
371#2308—431no—
372C2×#342—431no—
373C2×#342—431no—
374C2×#342—431no—
375C2×#342D4311yescharacteristic, complemented
376C2×C43—21no—
377C2×C43—21no—
378C2×C43—21no—
379C2×C43—21no—
380C2×C43—21no—
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#144011yescharacteristic
391C2×C43#182812yes—
392D43—82no—
393C23×D4—431no—
394C22×C22⋊C4—431no—
395C22×C22⋊C4—431no—
396C22×C22⋊C4—431no—
397C22×C22⋊C4C2×D4311yescharacteristic
398C22×C22⋊C4C2×D4311yescharacteristic
399C22×C22⋊C4C2×D4311yescharacteristic
400C2×#99—862no—
401C2×#99—862no—
402C2×#99—862no—
403C2×#99—862no—
404C2×#99—862no—
405C2×#99—862no—
406#386—862no—
407#386—862no—
408#381—432no—
409#379—432no—
410#342—22no—
411#342—862no—
412#342—862no—
413#342—862no—
414C43#1116611yescharacteristic, complemented, Sylow
415C25—431no—
416C25C22×D4311yescharacteristic
417C22×D4—432no—
418C22×D4—432no—
419C22×D4—861no—
420C22×D4—861no—
421C22×D4—861no—
422C22×D4—861no—
423C22×D4—861no—
424C22×D4—861no—
425C22×D4—861no—
426C22×D4—861no—
427C22×D4—861no—
428C22×D4—861no—
429C22×D4—861no—
430C22×D4—861no—
431C23×C4—21no—
432C23×C4—21no—
433C23×C4—21no—
434C23×C4—431no—
435C23×C4—861no—
436C23×C4—861no—
437C23×C4—861no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
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—861no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C22⋊C4—861no—
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—864no—
469C2×C22⋊C4—861no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4—861no—
472C2×C22⋊C4C4×D4312yes—
473C2×C22⋊C4D17212yes—
474C2×C22⋊C4C22⋊D4312yes—
475#99—868no—
476#99—868no—
477#95—864no—
478C24—82no—
479C24—432no—
480C24—861no—
481C24—861no—
482C24—861no—
483C24—861no—
484C24—861no—
485C24—861no—
486C24—3442no—
487C24C2×C4×D4311yescharacteristic
488C24C2×D17211yescharacteristic
489C24#1062189811yescharacteristic
490C24#1062189811yescharacteristic
491C24#1062189811yescharacteristic
492C24#1062189811yescharacteristic
493C24D4×D4311yescharacteristic
494C24D4×D4311yescharacteristic
495C24D4×D4311yescharacteristic
496C24D4×D4311yescharacteristic
497C24#1062190011yescharacteristic
498C24#1062190011yescharacteristic
499C24#1062190211yescharacteristic
500C24#1062190211yescharacteristic
501C24C2×C22⋊D4311yescharacteristic
502C2×D4—862no—
503C2×D4—862no—
504C2×D4—862no—
505C2×D4—862no—
506C2×D4—862no—
507C2×D4—862no—
508C2×D4—862no—
509C2×D4—862no—
510C2×D4—862no—
511C2×D4—862no—
512C2×D4—862no—
513C2×D4—862no—
514C2×D4—1721no—
515C2×D4—1721no—
516C2×D4—1721no—
517C2×D4—1721no—
518C2×D4—1721no—
519C2×D4—1721no—
520C2×D4—1721no—
521C2×D4—1721no—
522C2×D4—1721no—
523C2×D4—1721no—
524C2×D4—1721no—
525C2×D4—1721no—
526C2×D4—1721no—
527C2×D4—1721no—
528C2×D4—1721no—
529C2×D4—1721no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—82no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4—432no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—862no—
550C22×C4—862no—
551C22×C4—862no—
552C22×C4—3442no—
553C22×C4—3442no—
554C22×C4—3442no—
555C22×C4—1721no—
556C22×C4—1721no—
557C22×C4—1721no—
558C22×C4—1721no—
559C22×C4—1721no—
560C22×C4—1721no—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—862no—
574C22⋊C4—862no—
575C22⋊C4—862no—
576C22⋊C4—862no—
577C22⋊C4—862no—
578C22⋊C4—862no—
579C22⋊C4—3444no—
580C22⋊C4—1721no—
581C22⋊C4—1721no—
582C22⋊C4—1721no—
583C22⋊C4—1721no—
584C22⋊C4—1721no—
585C22⋊C4—1721no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—81no—
594C23—81no—
595C23—81no—
596C23—81no—
597C23—81no—
598C23—81no—
599C23—81no—
600C23—81no—
601C23—862no—
602C23—862no—
603C23—862no—
604C23—3442no—
605C23—3442no—
606C23—3442no—
607C23—3442no—
608C23—3442no—
609C23—3442no—
610C23—1724no—
611C23—1721no—
612C23—1721no—
613C23—1721no—
614C23—1721no—
615C23C22⋊C4×D4311yescharacteristic
616C23#1306328211yescharacteristic
617C23#1306328311yescharacteristic
618C23(C22⋊D43)⋊C411yescharacteristic
619C23C4×C22⋊D4311yescharacteristic
620C23#1306328711yescharacteristic
621C23C4×D17211yescharacteristic
622C23#1306329311yescharacteristic
623C23#1306329511yescharacteristic
624C23#1306329611yescharacteristic
625C23#1306329711yescharacteristic
626C23#1306329811yescharacteristic
627C23#1306329811yescharacteristic
628C23#1306329811yescharacteristic
629C23#1306329911yescharacteristic
630C23#1306330011yescharacteristic
631C23#1306330011yescharacteristic
632C23#1306330711yescharacteristic
633C23#1306330711yescharacteristic
634C23#1306330711yescharacteristic
635C23#1306330811yescharacteristic
636C23#1306330911yescharacteristic
637C23#1306331011yescharacteristic
638C23#1306331011yescharacteristic
639C23#1306331011yescharacteristic
640C23#1306331011yescharacteristic
641C23#1306331011yescharacteristic
642C23#1306331111yescharacteristic
643C23#1306331111yescharacteristic
644C23#1306331311yescharacteristic
645C23#1306331411yescharacteristic
646C23#1306331911yescharacteristic
647C23#1306332011yescharacteristic
648C23#1306332011yescharacteristic
649C23#1306332011yescharacteristic
650D4—1722no—
651D4—1722no—
652D4—1722no—
653D4—1722no—
654D4—1722no—
655D4—1722no—
656D4—1722no—
657D4—1722no—
658C2×C4—44no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—82no—
663C2×C4—82no—
664C2×C4—82no—
665C2×C4—82no—
666C2×C4—82no—
667C2×C4—82no—
668C2×C4—82no—
669C2×C4—82no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—3442no—
674C2×C4—3442no—
675C2×C4—3442no—
676C2×C4—3442no—
677C2×C4—3442no—
678C2×C4—3442no—
679C2×C4—3442no—
680C2×C4—3442no—
681C2×C4—1724no—
682C2×C4—1722no—
683C2×C4—1722no—
684C2×C4—1722no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
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—3442no—
725C22—3442no—
726C22—3442no—
727C22—3442no—
728C22—3442no—
729C22—3442no—
730C22—1722no—
731C22—1724no—
732C22#1458276111yescharacteristic
733C22#1458277511yescharacteristic
734C22#1458277711yescharacteristic
735C22#1458278811yescharacteristic
736C22#1458278911yescharacteristic
737C22#1458279011yescharacteristic
738C22#1458279111yescharacteristic
739C22#1458281411yescharacteristic
740C22#1458281511yescharacteristic
741C22#1458281611yescharacteristic
742C22#1458281711yescharacteristic
743C22#1458282511yescharacteristic
744C22#1458282611yescharacteristic
745C22#1458282811yescharacteristic
746C22#1458282811yescharacteristic
747C4—82no—
748C4—82no—
749C4—82no—
750C4—3442no—
751C4—3442no—
752C4—3442no—
753C4—1722no—
754C2—21no—
755C2—21no—
756C2—21no—
757C2—21no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—3442no—
769C2#1913284311yescharacteristic
770C2#1913470212yes—
subgroupG/H
centerC22#14582761
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC2×C43×#342C2
socleC22×C43#381
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenterC2×#342D43
hypocenterC43#11166
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. C2×#14582666C2semidirect
5. C2×#14582665C2semidirect
6. C2×#14582665C2semidirect
7. C2×C43×#342C2semidirect
20. #14582760C4semidirect
21. #14582754C4semidirect
375. C2×#342D43semidirect
414. C43#11166semidirect

Maximal subgroups

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

subgroupindex
C22×#130632392
#191371702
C2×#145826662
C2×#145826652
C2×C43×#3422
#1116643