Finite Group Databasebeta

← #25005317

Subgroups — #25005317

Order 11008.

1262 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137207C211yesmaximal, characteristic
2C2×#14582774C211yesmaximal, characteristic
3C2×#14582771C211yesmaximal, characteristic
4C2×#14582665C211yesmaximal, characteristic
5C2×#14582665C211yesmaximal, characteristic
6#19132817C211yesmaximal, characteristic
7C2×C43×#342C211yesmaximal, characteristic
8C24×Dic43C2211yescharacteristic
9C22×C4⋊Dic43—21no—
10C22×Dic43⋊C4—21no—
11C22×C22⋊Dic43C2211yescharacteristic
12C22×C22⋊Dic43C2211yescharacteristic
13C22×C22⋊Dic43C2211yescharacteristic
14#14582774—22no—
15#14582774—22no—
16#14582772—21no—
17#14582772—21no—
18#14582771—21no—
19#14582771—21no—
20#14582771—22no—
21#14582771—22no—
22#14582757—22no—
23C2×C43⋊#95—21no—
24C2×C43⋊#95—22no—
25C2×C43⋊#95—21no—
26#14582665—22no—
27#14582665C414yescomplemented
28C22×C22⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2211yescharacteristic
30C22×C22⋊C4×C43C2211yescharacteristic
31C43×#342—22no—
32C23×Dic43—21no—
33C23×Dic43—21no—
34C23×Dic43—21no—
35C23×Dic43—21no—
36C23×Dic43—21no—
37C23×Dic43—21no—
38C23×Dic43—21no—
39C23×Dic43—44no—
40C23×Dic43D411yescharacteristic
41C23×Dic43D411yescharacteristic
42C23×Dic43D412yes—
43C23×Dic43D412yes—
44C2×C4⋊Dic43—24no—
45C2×C4⋊Dic43—44no—
46C2×Dic43⋊C4—24no—
47C2×Dic43⋊C4—22no—
48C2×Dic43⋊C4—22no—
49C2×Dic43⋊C4—44no—
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⋊Dic43C2×C412yes—
65C2×C22⋊Dic43D412yes—
66C2×C22⋊Dic43Q812yes—
67C2×C22⋊Dic43Q812yes—
68C43⋊#95—24no—
69C43⋊#95—24no—
70C43⋊#95—22no—
71C43⋊#95—22no—
72C43⋊#95—44no—
73C25×C43C2311yescharacteristic
74C23×C4×C43—21no—
75C23×C4×C43—21no—
76C23×C4×C43D411yescharacteristic
77C23×C4×C43D411yescharacteristic
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×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
92C2×C22⋊C4×C43C2×C412yes—
93C2×C22⋊C4×C43D412yes—
94C2×C22⋊C4×C43Q812yes—
95C2×C22⋊C4×C43Q812yes—
96C24×C43—42no—
97C24×C43—42no—
98C24×C43C22×C411yescharacteristic
99C24×C43C2×D411yescharacteristic
100C24×C43C2×D411yescharacteristic
101C24×C43C2×D411yescharacteristic
102C24×C43C2×D411yescharacteristic
103C24×C43C2×D411yescharacteristic
104C24×C43C2×D411yescharacteristic
105C24×C43C2×Q811yescharacteristic
106C24×C43C2×Q811yescharacteristic
107C24×C43C2×Q811yescharacteristic
108C24×C43C2×Q811yescharacteristic
109C24×C43#4111yescharacteristic
110C24×C43#4111yescharacteristic
111C24×C43#4111yescharacteristic
112C24×C43#4111yescharacteristic
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—42no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43—42no—
129C22×C4×C43—41no—
130C22×C4×C43—41no—
131C22×Dic43—24no—
132C22×Dic43—24no—
133C22×Dic43—24no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—22no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—42no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—42no—
153C22×Dic43—42no—
154C22×Dic43—42no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43—44no—
158C22×Dic43—44no—
159C22×Dic43—44no—
160C22×Dic43—44no—
161C22×Dic43—41no—
162C22×Dic43—41no—
163C22×Dic43—41no—
164C22×Dic43—41no—
165C22×Dic43C4⋊C414yescomplemented
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—41no—
172C22⋊C4×C43—41no—
173C22⋊C4×C43—41no—
174C22⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C22⋊C4×C43C4⋊C414yescomplemented
178C22⋊Dic43—22no—
179C22⋊Dic43—22no—
180C22⋊Dic43—22no—
181C22⋊Dic43—22no—
182C22⋊Dic43—22no—
183C22⋊Dic43—22no—
184C22⋊Dic43—22no—
185C22⋊Dic43—41no—
186C22⋊Dic43—41no—
187C22⋊Dic43—41no—
188C22⋊Dic43—41no—
189C22⋊Dic43C4⋊C414yescomplemented
190C4⋊Dic43—48no—
191Dic43⋊C4—48no—
192Dic43⋊C4—82no—
193Dic43⋊C4—82no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43—22no—
197C23×C43—22no—
198C23×C43—22no—
199C23×C43—22no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—42no—
205C23×C43—41no—
206C23×C43—41no—
207C23×C43—41no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43—41no—
214C23×C43—42no—
215C23×C43—42no—
216C23×C43C2×C4⋊C411yescharacteristic
217C23×C43C2×C4⋊C411yescharacteristic
218C23×C43C2×C4⋊C411yescharacteristic
219C23×C43C4×D411yescharacteristic
220C23×C43C4×D411yescharacteristic
221C23×C43C4×D411yescharacteristic
222C23×C43C4×Q811yescharacteristic
223C23×C43#12011yescharacteristic
224C23×C43#12011yescharacteristic
225C23×C43#12011yescharacteristic
226C23×C43#12111yescharacteristic
227C23×C43#12111yescharacteristic
228C23×C43#12111yescharacteristic
229C23×C43C22⋊Q811yescharacteristic
230C23×C43C22⋊Q811yescharacteristic
231C23×C43C22⋊Q811yescharacteristic
232C23×C43C22⋊Q811yescharacteristic
233C23×C43C22⋊Q811yescharacteristic
234C23×C43C22⋊Q811yescharacteristic
235C23×C43C22⋊Q811yescharacteristic
236C23×C43C22⋊Q811yescharacteristic
237C23×C43C22⋊Q811yescharacteristic
238C23×C43#12311yescharacteristic
239C23×C43#12311yescharacteristic
240C23×C43#12311yescharacteristic
241C23×C43#12511yescharacteristic
242C23×C43#12511yescharacteristic
243C23×C43#12511yescharacteristic
244C23×C43#12711yescharacteristic
245C23×C43C4⋊Q811yescharacteristic
246C23×C43C4⋊Q811yescharacteristic
247C23×C43C4⋊Q811yescharacteristic
248C23×C43C4⋊Q811yescharacteristic
249C23×C43C4⋊Q811yescharacteristic
250C23×C43C4⋊Q811yescharacteristic
251C2×C4×C43—24no—
252C2×C4×C43—42no—
253C2×C4×C43—44no—
254C2×C4×C43—44no—
255C2×C4×C43—42no—
256C2×C4×C43—42no—
257C2×C4×C43—44no—
258C2×C4×C43—42no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—42no—
262C2×C4×C43—42no—
263C2×C4×C43—42no—
264C2×C4×C43—82no—
265C2×C4×C43—81no—
266C2×C4×C43—81no—
267C2×C4×C43—81no—
268C2×C4×C43—81no—
269C2×Dic43—24no—
270C2×Dic43—24no—
271C2×Dic43—24no—
272C2×Dic43—24no—
273C2×Dic43—24no—
274C2×Dic43—42no—
275C2×Dic43—44no—
276C2×Dic43—44no—
277C2×Dic43—42no—
278C2×Dic43—42no—
279C2×Dic43—42no—
280C2×Dic43—42no—
281C2×Dic43—44no—
282C2×Dic43—44no—
283C2×Dic43—44no—
284C2×Dic43—42no—
285C2×Dic43—42no—
286C2×Dic43—44no—
287C2×Dic43—42no—
288C2×Dic43—44no—
289C2×Dic43—42no—
290C2×Dic43—42no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—42no—
294C2×Dic43—42no—
295C2×Dic43—82no—
296C2×Dic43—81no—
297C2×Dic43—81no—
298#11344—431nomaximal, Sylow
299C22×C43—22no—
300C22×C43—22no—
301C22×C43—22no—
302C22×C43—22no—
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—22no—
307C22×C43—22no—
308C22×C43—22no—
309C22×C43—22no—
310C22×C43—22no—
311C22×C43—21no—
312C22×C43—21no—
313C22×C43—21no—
314C22×C43—21no—
315C22×C43—21no—
316C22×C43—21no—
317C22×C43—21no—
318C22×C43—21no—
319C22×C43—21no—
320C22×C43—21no—
321C22×C43—21no—
322C22×C43—21no—
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#38411yescharacteristic
340C22×C43#38511yescharacteristic
341C22×C43#38511yescharacteristic
342C22×C43#38511yescharacteristic
343C22×C43#38911yescharacteristic
344C22×C43#38911yescharacteristic
345C22×C43#38911yescharacteristic
346C22×C43#39211yescharacteristic
347C22×C43#39511yescharacteristic
348C22×C43#39511yescharacteristic
349C22×C43#39511yescharacteristic
350C22×C43#39811yescharacteristic
351C22×C43#39811yescharacteristic
352C22×C43#39811yescharacteristic
353C22×C43#39911yescharacteristic
354C22×C43B(4,𝔽2)12yes—
355C22×C43#45812yes—
356C4×C43—44no—
357C4×C43—82no—
358C4×C43—81no—
359C4×C43—81no—
360Dic43—44no—
361Dic43—44no—
362Dic43—44no—
363Dic43—81no—
364Dic43—81no—
365#2315—431no—
366C2×#385—431no—
367C2×#385—431no—
368C2×#342—431no—
369C2×#342—431no—
370C2×#342D4311yescharacteristic
371C22⋊#95—431no—
372C2×C43—21no—
373C2×C43—21no—
374C2×C43—21no—
375C2×C43—21no—
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#144411yescharacteristic
385C2×C43#186712yes—
386C2×C43#202111yescharacteristic
387C2×C43#202211yescharacteristic
388C2×C43#206212yes—
389C24×C4—431no—
390C22×C4⋊C4—861no—
391C22×C4⋊C4—861no—
392C22×C22⋊C4—431no—
393C22×C22⋊C4—431no—
394C22×C22⋊C4—431no—
395C22×C22⋊C4C2×D4311yescharacteristic
396C22×C22⋊C4C2×D4311yescharacteristic
397C22×C22⋊C4C2×D4311yescharacteristic
398#385—862no—
399#385—861no—
400#385—861no—
401#385—862no—
402#385—862no—
403#385—861no—
404#385—861no—
405#385—862no—
406#380—862no—
407C2×#95—861no—
408C2×#95—861no—
409C2×#95—862no—
410#342—22no—
411#342—434no—
412#342—862no—
413C43#1134411yescharacteristic, complemented, Sylow
414C25C22×D4311yescharacteristic
415C23×C4—21no—
416C23×C4—21no—
417C23×C4—432no—
418C23×C4—431no—
419C23×C4—431no—
420C23×C4—432no—
421C23×C4—861no—
422C23×C4—861no—
423C23×C4—861no—
424C23×C4—861no—
425C23×C4—861no—
426C23×C4—861no—
427C23×C4—861no—
428C23×C4—1724no—
429C23×C4D17211yescharacteristic
430C23×C4D17211yescharacteristic
431C2×C4⋊C4—862no—
432C2×C4⋊C4—862no—
433C2×C4⋊C4—864no—
434C2×C4⋊C4—864no—
435C2×C4⋊C4—1724no—
436C2×C4⋊C4—1724no—
437C2×C22⋊C4—21no—
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—432no—
452C2×C22⋊C4—432no—
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—861no—
469C2×C22⋊C4Dic8612yes—
470C2×C22⋊C4Dic8612yes—
471C2×C22⋊C4C4×D4312yes—
472C2×C22⋊C4C22⋊D4312yes—
473#95—864no—
474#95—864no—
475#95—862no—
476#95—862no—
477#95—1724no—
478C24—42no—
479C24—42no—
480C24C2×Dic8611yescharacteristic
481C24C2×Dic8611yescharacteristic
482C24C2×C4×D4311yescharacteristic
483C24C2×D17211yescharacteristic
484C24#1062189811yescharacteristic
485C24#1062189811yescharacteristic
486C24D4×D4311yescharacteristic
487C24D4×D4311yescharacteristic
488C24D4×D4311yescharacteristic
489C24D4×D4311yescharacteristic
490C24#1062190011yescharacteristic
491C24#1062190011yescharacteristic
492C24Q8×D4311yescharacteristic
493C24Q8×D4311yescharacteristic
494C24C2×C22⋊D4311yescharacteristic
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—434no—
514C22×C4—862no—
515C22×C4—864no—
516C22×C4—864no—
517C22×C4—864no—
518C22×C4—862no—
519C22×C4—862no—
520C22×C4—862no—
521C22×C4—862no—
522C22×C4—862no—
523C22×C4—862no—
524C22×C4—862no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—1724no—
532C22×C4—1724no—
533C22×C4—1724no—
534C22×C4—1724no—
535C22×C4—1722no—
536C22×C4—1722no—
537C22×C4—1722no—
538C22×C4—1722no—
539C22×C4—1722no—
540C22×C4—1722no—
541C22×C4—1722no—
542C22×C4—1722no—
543C22×C4—1722no—
544C22×C4—1721no—
545C22×C4—1721no—
546C22×C4—1721no—
547C22×C4—1721no—
548C4⋊C4—3442no—
549C4⋊C4—3442no—
550C4⋊C4—1728no—
551C4⋊C4—1728no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—41no—
562C22⋊C4—41no—
563C22⋊C4—434no—
564C22⋊C4—862no—
565C22⋊C4—862no—
566C22⋊C4—862no—
567C22⋊C4—862no—
568C22⋊C4—862no—
569C22⋊C4—862no—
570C22⋊C4—862no—
571C22⋊C4—1721no—
572C22⋊C4—1721no—
573C22⋊C4—1721no—
574C22⋊C4—1721no—
575C22⋊C4Dic43⋊C414yescomplemented
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—41no—
598C23C4⋊C4×D4311yescharacteristic
599C23C4⋊C4×D4311yescharacteristic
600C23C2×Dic43⋊C411yescharacteristic
601C23(C22⋊D43)⋊C411yescharacteristic
602C23(C22⋊D43)⋊C411yescharacteristic
603C23C4×D17211yescharacteristic
604C23C4×Dic8611yescharacteristic
605C23#1306329311yescharacteristic
606C23#1306329511yescharacteristic
607C23#1306329511yescharacteristic
608C23#1306329811yescharacteristic
609C23#1306329811yescharacteristic
610C23#1306329911yescharacteristic
611C23#1306330211yescharacteristic
612C23#1306330211yescharacteristic
613C23#1306330211yescharacteristic
614C23#1306330211yescharacteristic
615C23#1306330311yescharacteristic
616C23#1306330311yescharacteristic
617C23#1306330411yescharacteristic
618C23#1306330511yescharacteristic
619C23#1306330511yescharacteristic
620C23#1306330611yescharacteristic
621C23#1306330711yescharacteristic
622C23#1306330711yescharacteristic
623C23#1306331511yescharacteristic
624C23#1306331511yescharacteristic
625C23#1306331711yescharacteristic
626C23#1306332111yescharacteristic
627C23#1306332311yescharacteristic
628C23#1306332411yescharacteristic
629C23#1306332411yescharacteristic
630C23#1306332411yescharacteristic
631C23#1306332411yescharacteristic
632C23#1306332511yescharacteristic
633C2×C4—24no—
634C2×C4—42no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—44no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—82no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—864no—
652C2×C4—864no—
653C2×C4—864no—
654C2×C4—864no—
655C2×C4—864no—
656C2×C4—3441no—
657C2×C4—3441no—
658C2×C4—3442no—
659C2×C4—1722no—
660C2×C4—1722no—
661C2×C4—1721no—
662C2×C4—1721no—
663C2×C4—1722no—
664C2×C4—1722no—
665C2×C4—1722no—
666C2×C4—1722no—
667C2×C4—1722no—
668C2×C4—1724no—
669C2×C4—1724no—
670C2×C4—1722no—
671C2×C4—1724no—
672C2×C4—1724no—
673C2×C4—1724no—
674C2×C4—1722no—
675C2×C4—1722no—
676C2×C4—1722no—
677C2×C4—1724no—
678C2×C4—1722no—
679C2×C4—1724no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22—21no—
700C22—21no—
701C22—21no—
702C22—21no—
703C22—21no—
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#1458276811yescharacteristic
721C22#1458277111yescharacteristic
722C22#1458277311yescharacteristic
723C22#1458277311yescharacteristic
724C22#1458279611yescharacteristic
725C22#1458279611yescharacteristic
726C22#1458279711yescharacteristic
727C22#1458280811yescharacteristic
728C22#1458281911yescharacteristic
729C22#1458282011yescharacteristic
730C22#1458282011yescharacteristic
731C22#1458282911yescharacteristic
732C22#1458283311yescharacteristic
733C22#1458283311yescharacteristic
734C22#1458283511yescharacteristic
735C22#1458308712yes—
736C22#1458309012yes—
737C4—44no—
738C4—82no—
739C4—81no—
740C4—81no—
741C4—3441no—
742C4—3441no—
743C4—1724no—
744C4—1724no—
745C4—1724no—
746C2—21no—
747C2—21no—
748C2—21no—
749C2—21no—
750C2—21no—
751C2—21no—
752C2—21no—
753C2—21no—
754C2—21no—
755C2—21no—
756C2—21no—
757C2—21no—
758C2#1913285911yescharacteristic
759C2#1913487712yes—
760C2#1913572011yescharacteristic
761C2#1913572511yescharacteristic
762C2#1913594912yes—
subgroupG/H
centerC23#13063295
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC2×C43×#342C2
socleC23×C43#120
prime radical, cosocleC25×C43C23
hypercenterC2×#342D43
hypocenterC43#11344
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
27. #14582665C4semidirect
165. C22×Dic43C4⋊C4semidirect
177. C22⋊C4×C43C4⋊C4semidirect
189. C22⋊Dic43C4⋊C4semidirect
413. C43#11344semidirect
575. C22⋊C4Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
#191372072
C2×#145827742
C2×#145827712
C2×#145826652
#191328172
C2×C43×#3422
#1134443