Finite Group Databasebeta

← #25003285

Subgroups — #25003285

Order 11008.

1462 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582916C211yesmaximal, characteristic, complemented
2#19143114C211yesmaximal, characteristic, complemented
3C2×#14582904C211yesmaximal, characteristic, complemented
4C2×#14582904C211yesmaximal, characteristic, complemented
5C2×#14582669C211yesmaximal, characteristic, complemented
6#19134327C211yesmaximal, characteristic, complemented
7C2×C43×#535C211yesmaximal, characteristic
8C22×#10621877C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12#14582916—22no—
13#14582916—22no—
14C2×#13063252—22no—
15#14582908—21no—
16#14582904—22no—
17#14582904—22no—
18#14582904—22no—
19#14582904—22no—
20#14582904—21no—
21#14582900—22no—
22#14582895—22no—
23C2×#13063246—22no—
24C2×#13063246—22no—
25#14582669—22no—
26#14582665—22no—
27C22×#41×C43C2211yescharacteristic
28C23×D4×C43C2211yescharacteristic
29C43×#535—22no—
30C43×#535—22no—
31C43×#535—22no—
32C43×#535C414yescomplemented
33C2×#127×C43—21no—
34C2×#124×C43—21no—
35C2×#121×C43—22no—
36C2×#120×C43—22no—
37C2×#117×C43C2211yescharacteristic
38C2×#10621877—21no—
39C2×#10621877—21no—
40C2×#10621877—21no—
41C2×#10621877—21no—
42C2×#10621877—21no—
43C2×#10621877—21no—
44C2×#10621877—21no—
45C2×#10621877—21no—
46C2×#10621877—21no—
47C2×#10621877—21no—
48C2×#10621877—21no—
49C2×#10621877D412yescomplemented
50C22×C43⋊C8—21no—
51C22×C43⋊C8D412yescomplemented
52#13063284—21no—
53#13063284—21no—
54#13063284—21no—
55#13063284—21no—
56#13063284—21no—
57#13063284—21no—
58#13063284—21no—
59#13063284D412yescomplemented
60C2×C4⋊Dic43—21no—
61C2×C4⋊Dic43D412yescomplemented
62C2×C22⋊Dic43—21no—
63C2×C22⋊Dic43—21no—
64C2×C4×Dic43—21no—
65C2×C4×Dic43—21no—
66#13063252—28no—
67#13063249—24no—
68#13063246—28no—
69#13063246—28no—
70#13063246—24no—
71C25×C43—21no—
72C2×#41×C43—21no—
73C2×#41×C43—21no—
74C2×#41×C43—21no—
75C2×#41×C43—21no—
76C2×#41×C43—21no—
77C2×#41×C43—21no—
78C2×#41×C43—21no—
79C2×#41×C43—21no—
80C2×#41×C43—21no—
81C2×#41×C43—21no—
82C2×#41×C43C2×C412yes—
83C2×#41×C43D412yes—
84C22×Q8×C43D411yescharacteristic
85C22×D4×C43—21no—
86C22×D4×C43—24no—
87C22×D4×C43—21no—
88C22×D4×C43—21no—
89C22×D4×C43—21no—
90C22×D4×C43—21no—
91C22×D4×C43—21no—
92C22×D4×C43—21no—
93C22×D4×C43—21no—
94C22×D4×C43—21no—
95C22×D4×C43—21no—
96C22×D4×C43—21no—
97C22×D4×C43—21no—
98C22×D4×C43C2×C412yes—
99C22×D4×C43D412yes—
100C22×D4×C43D411yescharacteristic
101C22×D4×C43D412yes—
102C23×C4×C43—21no—
103C23×C4×C43C2311yescharacteristic
104#127×C43—24no—
105#127×C43—24no—
106#124×C43—24no—
107#124×C43—24no—
108#121×C43—28no—
109#121×C43—28no—
110#120×C43—28no—
111#120×C43—28no—
112#117×C43—21no—
113#117×C43—21no—
114#117×C43C2×C412yes—
115#117×C43D412yes—
116C2×C4⋊C4×C43—21no—
117C2×C22⋊C4×C43—24no—
118C2×C22⋊C4×C43D412yes—
119C2×C42×C43—21no—
120C24×C43—22no—
121C24×C43—21no—
122C24×C43—22no—
123C24×C43—22no—
124C24×C43—41no—
125C24×C43—41no—
126C24×C43—41no—
127C24×C43—41no—
128C24×C43—84no—
129C24×C43C2×D411yescharacteristic
130#41×C43—22no—
131#41×C43—22no—
132#41×C43—22no—
133#41×C43—22no—
134#41×C43—22no—
135#41×C43—22no—
136#41×C43—22no—
137#41×C43—22no—
138#41×C43—41no—
139#41×C43—41no—
140#41×C43—41no—
141#41×C43—41no—
142#41×C43—41no—
143#41×C43—41no—
144#41×C43—41no—
145#41×C43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43C22⋊C412yes—
152C2×D4×C43—216no—
153C2×D4×C43—22no—
154C2×D4×C43—22no—
155C2×D4×C43—22no—
156C2×D4×C43—21no—
157C2×D4×C43—22no—
158C2×D4×C43—22no—
159C2×D4×C43—22no—
160C2×D4×C43—22no—
161C2×D4×C43—22no—
162C2×D4×C43—22no—
163C2×D4×C43—22no—
164C2×D4×C43—22no—
165C2×D4×C43—21no—
166C2×D4×C43—22no—
167C2×D4×C43—22no—
168C2×D4×C43—22no—
169C2×D4×C43—22no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—22no—
173C2×D4×C43—22no—
174C2×D4×C43—21no—
175C2×D4×C43—41no—
176C2×D4×C43—41no—
177C2×D4×C43—41no—
178C2×D4×C43—41no—
179C2×D4×C43—41no—
180C2×D4×C43—41no—
181C2×D4×C43—41no—
182C2×D4×C43—41no—
183C2×D4×C43—41no—
184C2×D4×C43—41no—
185C2×D4×C43—41no—
186C2×D4×C43—41no—
187C2×D4×C43—41no—
188C2×D4×C43—41no—
189C2×D4×C43—41no—
190C2×D4×C43—41no—
191C2×D4×C43—88no—
192C2×D4×C43C22⋊C414yes—
193C2×D4×C43C22⋊C412yes—
194C22×C4×C43—22no—
195C22×C4×C43—22no—
196C22×C4×C43—22no—
197C22×C4×C43—21no—
198C22×C4×C43—41no—
199C22×C4×C43—41no—
200C22×C4×C43—41no—
201C22×C4×C43—41no—
202C22×C4×C43C22×C411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D411yescharacteristic
212C22×C4×C43#4111yescharacteristic
213C22×C4×C43#4111yescharacteristic
214C22×C4×C43#4111yescharacteristic
215C22×C4×C43#4111yescharacteristic
216C22×Dic43—22no—
217C22×Dic43—41no—
218C4⋊C4×C43—22no—
219C4⋊C4×C43—22no—
220C22⋊C4×C43—216no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43C22⋊C414yes—
223C42×C43—22no—
224C42×C43—22no—
225C22⋊Dic43—22no—
226C22⋊Dic43—41no—
227C22⋊Dic43—41no—
228C22⋊Dic43—41no—
229C4⋊Dic43—22no—
230C4⋊Dic43—22no—
231C4⋊Dic43—22no—
232C4⋊Dic43—41no—
233C4×Dic43—22no—
234C4×Dic43—41no—
235C4×Dic43—41no—
236C4×Dic43—41no—
237#10621877—22no—
238#10621877—22no—
239#10621877—41no—
240#10621877—41no—
241#10621877—41no—
242#10621877—41no—
243#10621877—41no—
244#10621877—41no—
245C2×C43⋊C8—22no—
246C2×C43⋊C8—22no—
247C2×C43⋊C8—22no—
248C2×C43⋊C8—22no—
249C2×C43⋊C8—41no—
250C2×C43⋊C8—41no—
251C23×C43—24no—
252C23×C43—22no—
253C23×C43—42no—
254C23×C43—44no—
255C23×C43—48no—
256C23×C43—42no—
257C23×C43—42no—
258C23×C43—41no—
259C23×C43—42no—
260C23×C43—42no—
261C23×C43—41no—
262C23×C43—42no—
263C23×C43—42no—
264C23×C43—84no—
265C23×C43—84no—
266C23×C43—84no—
267C23×C43—84no—
268C23×C43—84no—
269C23×C43—84no—
270C23×C43C2×C22⋊C411yescharacteristic
271C23×C43#12011yescharacteristic
272C23×C43#12011yescharacteristic
273C23×C43#12111yescharacteristic
274C23×C43#12111yescharacteristic
275C23×C43#12411yescharacteristic
276C23×C43#12711yescharacteristic
277Q8×C43—22no—
278Q8×C43—22no—
279Q8×C43—41no—
280Q8×C43—41no—
281D4×C43—24no—
282D4×C43—24no—
283D4×C43—22no—
284D4×C43—22no—
285D4×C43—42no—
286D4×C43—42no—
287D4×C43—42no—
288D4×C43—42no—
289D4×C43—42no—
290D4×C43—42no—
291D4×C43—42no—
292D4×C43—42no—
293D4×C43—41no—
294D4×C43—42no—
295D4×C43—42no—
296D4×C43—41no—
297D4×C43—816no—
298C2×C4×C43—24no—
299C2×C4×C43—22no—
300C2×C4×C43—44no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43C2×C22⋊C411yescharacteristic
308C2×C4×C43C2×C22⋊C411yescharacteristic
309C2×C4×C43C4×D411yescharacteristic
310C2×C4×C43C4×D411yescharacteristic
311C2×C4×C43C4×D411yescharacteristic
312C2×C4×C43C4×D411yescharacteristic
313C2×C4×C43#12011yescharacteristic
314C2×C4×C43#12011yescharacteristic
315C2×C4×C43#12011yescharacteristic
316C2×C4×C43#12011yescharacteristic
317C2×C4×C43#12011yescharacteristic
318C2×C4×C43#12011yescharacteristic
319C2×C4×C43#12111yescharacteristic
320C2×C4×C43#12111yescharacteristic
321C2×C4×C43#12111yescharacteristic
322C2×C4×C43#12111yescharacteristic
323C2×C4×C43#12111yescharacteristic
324C2×C4×C43#12111yescharacteristic
325C2×C4×C43#12111yescharacteristic
326C2×C4×C43#12111yescharacteristic
327C2×C4×C43#12111yescharacteristic
328C2×C4×C43#12111yescharacteristic
329C2×C4×C43#12311yescharacteristic
330C2×C4×C43#12311yescharacteristic
331C2×C4×C43#12311yescharacteristic
332C2×C4×C43#12311yescharacteristic
333C2×C4×C43#12411yescharacteristic
334C2×C4×C43#12711yescharacteristic
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—82no—
338C2×Dic43—82no—
339C43⋊C8—42no—
340C43⋊C8—42no—
341#11004—431nomaximal, Sylow
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—48no—
350C22×C43—44no—
351C22×C43—44no—
352C22×C43—42no—
353C22×C43—82no—
354C22×C43—84no—
355C22×C43—84no—
356C22×C43—84no—
357C22×C43—84no—
358C22×C43—84no—
359C22×C43—82no—
360C22×C43—84no—
361C22×C43#37911yescharacteristic
362C22×C43#39011yescharacteristic
363C22×C43#39011yescharacteristic
364C22×C43#39211yescharacteristic
365C22×C43#39211yescharacteristic
366C22×C43#39411yescharacteristic
367C22×C43#39411yescharacteristic
368C4×C43—44no—
369C4×C43—42no—
370C4×C43#38611yescharacteristic
371C4×C43#38611yescharacteristic
372C4×C43#38611yescharacteristic
373C4×C43#38611yescharacteristic
374C4×C43#39211yescharacteristic
375C4×C43#39211yescharacteristic
376C4×C43#39411yescharacteristic
377C4×C43#39411yescharacteristic
378Dic43—82no—
379Dic43—82no—
380C2×#535D4311yescharacteristic
381C2×#421—431no—
382#2896—431no—
383C2×#418—431no—
384C2×#418—431no—
385C2×#344—431no—
386#1740—431no—
387C2×C43—21no—
388C2×C43—21no—
389C2×C43—21no—
390C2×C43—21no—
391C2×C43—21no—
392C2×C43—21no—
393C2×C43—82no—
394C2×C43—84no—
395C2×C43#143811yescharacteristic
396C2×C43#200812yes—
397C22×#41C2×D4311yescharacteristic
398C23×D4C2×D4311yescharacteristic
399C22×M16—431no—
400C22×M16—431no—
401#535—22no—
402#535—22no—
403#535—22no—
404#535Dic4314yescomplemented
405C2×#127—21no—
406C2×#124—21no—
407C2×#121—22no—
408C2×#120—22no—
409C2×#117—431no—
410C2×#117—431no—
411C2×#117C2×D4311yescharacteristic
412#421—862no—
413#421—862no—
414C2×#104—862no—
415#419—861no—
416#418—862no—
417#418—862no—
418#418—862no—
419#418—862no—
420#418—861no—
421#417—862no—
422#416—862no—
423C2×#102—862no—
424C2×#102—862no—
425#344—862no—
426#342—862no—
427C43#1100411yescharacteristic, complemented, Sylow
428C25—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41C2×Dic4312yes—
440C2×#41C22⋊D4312yes—
441C22×Q8C22⋊D4311yescharacteristic
442C22×D4—21no—
443C22×D4—24no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—21no—
455C22×D4C2×Dic4312yes—
456C22×D4C22⋊D4312yes—
457C22×D4C22⋊D4311yescharacteristic
458C22×D4C22⋊D4312yes—
459C23×C4—21no—
460C23×C4C22×D4311yescharacteristic
461C2×M16—432no—
462C2×M16—861no—
463C2×M16—861no—
464C2×M16—861no—
465C2×M16—861no—
466C2×M16—861no—
467C2×M16—861no—
468C2×M16—861no—
469C2×M16—861no—
470C2×M16—861no—
471C2×M16—861no—
472C2×M16—861no—
473C22×C8—432no—
474C22×C8—861no—
475#127—24no—
476#127—24no—
477#124—24no—
478#124—24no—
479#121—28no—
480#121—28no—
481#120—28no—
482#120—28no—
483#117—21no—
484#117—21no—
485#117—432no—
486#117—861no—
487#117—861no—
488#117—861no—
489#117—861no—
490#117—861no—
491#117—861no—
492#117—861no—
493#117C2×Dic4312yes—
494#117C22⋊D4312yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—432no—
497C2×C4⋊C4—861no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—861no—
501C2×C22⋊C4C22⋊D4312yes—
502C2×C42—21no—
503C2×C42—861no—
504C2×C42—861no—
505#104—868no—
506#103—864no—
507#102—868no—
508#102—868no—
509#102—864no—
510C24—22no—
511C24—21no—
512C24—22no—
513C24—22no—
514C24—41no—
515C24—41no—
516C24—41no—
517C24—41no—
518C24—84no—
519C24C2×C22⋊D4311yescharacteristic
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—22no—
525#41—22no—
526#41—22no—
527#41—22no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—41no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—41no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8C22⋊Dic4312yes—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—216no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—88no—
582C2×D4C22⋊Dic4314yes—
583C2×D4C22⋊Dic4312yes—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—862no—
593C22×C4—1721no—
594C22×C4D4×D4311yescharacteristic
595C22×C4D4×D4311yescharacteristic
596C22×C4D4×D4311yescharacteristic
597C22×C4D4×D4311yescharacteristic
598C22×C4#1062190011yescharacteristic
599C22×C4#1062190011yescharacteristic
600C22×C4#1062190011yescharacteristic
601C22×C4#1062190011yescharacteristic
602C22×C4C22×Dic4311yescharacteristic
603C22×C4C2×C22⋊D4311yescharacteristic
604C22×C4C2×C22⋊D4311yescharacteristic
605C22×C4C2×C22⋊D4311yescharacteristic
606C22×C4C2×C22⋊D4311yescharacteristic
607C22×C4C2×C22⋊D4311yescharacteristic
608M16—862no—
609M16—862no—
610M16—1721no—
611M16—1721no—
612M16—1721no—
613M16—1721no—
614M16—1721no—
615M16—1721no—
616C2×C8—862no—
617C2×C8—862no—
618C2×C8—862no—
619C2×C8—862no—
620C2×C8—1721no—
621C2×C8—1721no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—862no—
625C4⋊C4—862no—
626C4⋊C4—862no—
627C4⋊C4—1721no—
628C22⋊C4—216no—
629C22⋊C4—22no—
630C22⋊C4—862no—
631C22⋊C4—1721no—
632C22⋊C4—1721no—
633C22⋊C4—1721no—
634C22⋊C4C22⋊Dic4314yes—
635C42—22no—
636C42—22no—
637C42—862no—
638C42—1721no—
639C42—1721no—
640C42—1721no—
641C23—24no—
642C23—22no—
643C23—42no—
644C23—44no—
645C23—48no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—41no—
650C23—42no—
651C23—41no—
652C23—42no—
653C23—42no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23C2×C22⋊Dic4311yescharacteristic
661C23#1306329411yescharacteristic
662C23#1306329411yescharacteristic
663C23#1306329611yescharacteristic
664C23#1306329611yescharacteristic
665C23#1306331211yescharacteristic
666C23#1306332111yescharacteristic
667Q8—22no—
668Q8—22no—
669Q8—41no—
670Q8—41no—
671D4—24no—
672D4—24no—
673D4—22no—
674D4—22no—
675D4—42no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—41no—
682D4—42no—
683D4—42no—
684D4—41no—
685D4—42no—
686D4—42no—
687D4—816no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—44no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—3442no—
698C2×C4—3442no—
699C2×C4—1722no—
700C2×C4—1722no—
701C2×C4C2×C22⋊Dic4311yescharacteristic
702C2×C4C2×C22⋊Dic4311yescharacteristic
703C2×C4D4×Dic4311yescharacteristic
704C2×C4D4×Dic4311yescharacteristic
705C2×C4D4×Dic4311yescharacteristic
706C2×C4D4×Dic4311yescharacteristic
707C2×C4#1306329311yescharacteristic
708C2×C4#1306329311yescharacteristic
709C2×C4#1306329311yescharacteristic
710C2×C4#1306329311yescharacteristic
711C2×C4#1306329411yescharacteristic
712C2×C4#1306329411yescharacteristic
713C2×C4#1306329611yescharacteristic
714C2×C4#1306329611yescharacteristic
715C2×C4#1306329711yescharacteristic
716C2×C4#1306329711yescharacteristic
717C2×C4#1306329711yescharacteristic
718C2×C4#1306329711yescharacteristic
719C2×C4#1306329711yescharacteristic
720C2×C4#1306329711yescharacteristic
721C2×C4#1306329711yescharacteristic
722C2×C4#1306329711yescharacteristic
723C2×C4#1306330611yescharacteristic
724C2×C4#1306330611yescharacteristic
725C2×C4#1306330611yescharacteristic
726C2×C4#1306330611yescharacteristic
727C2×C4#1306331211yescharacteristic
728C2×C4#1306332111yescharacteristic
729C8—1722no—
730C8—1722no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—44no—
739C22—48no—
740C22—42no—
741C22—44no—
742C22—84no—
743C22—82no—
744C22—84no—
745C22—84no—
746C22—84no—
747C22—84no—
748C22—84no—
749C22—82no—
750C22#1458275511yescharacteristic
751C22#1458280211yescharacteristic
752C22#1458280211yescharacteristic
753C22#1458280711yescharacteristic
754C22#1458280711yescharacteristic
755C22#1458281311yescharacteristic
756C22#1458281311yescharacteristic
757C4—44no—
758C4—42no—
759C4—3442no—
760C4—3442no—
761C4#1458277911yescharacteristic
762C4#1458277911yescharacteristic
763C4#1458277911yescharacteristic
764C4#1458277911yescharacteristic
765C4#1458280711yescharacteristic
766C4#1458280711yescharacteristic
767C4#1458281311yescharacteristic
768C4#1458281311yescharacteristic
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—84no—
776C2—82no—
777C2#1913283611yescharacteristic
778C2#1913564812yes—
subgroupG/H
centerC22#14582807
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
Fitting, prime radicalC2×C43×#535C2
socleC22×C43#392
cosocleC23×C4×C43C23
hypercenterC2×#535D43
hypocenterC43#11004
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#14582916C2semidirect
2. #19143114C2semidirect
3. C2×#14582904C2semidirect
4. C2×#14582904C2semidirect
5. C2×#14582669C2semidirect
6. #19134327C2semidirect
32. C43×#535C4semidirect
49. C2×#10621877D4semidirect
51. C22×C43⋊C8D4semidirect
59. #13063284D4semidirect
61. C2×C4⋊Dic43D4semidirect
404. #535Dic43semidirect
427. C43#11004semidirect

Maximal subgroups

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

subgroupindex
C2×#145829162
#191431142
C2×#145829042
C2×#145826692
#191343272
C2×C43×#5352
#1100443