Finite Group Databasebeta

← #25003195

Subgroups — #25003195

Order 11008.

1502 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583463C211yesmaximal, characteristic
2C2×#14582916C211yesmaximal, characteristic, complemented
3C22×#13063241C211yesmaximal, characteristic, complemented
4#19137175C211yesmaximal, characteristic, complemented
5C2×#14582656C211yesmaximal, characteristic, complemented
6C2×#14582655C211yesmaximal, characteristic, complemented
7C2×C43×#421C211yesmaximal, characteristic, complemented
8C23×D172C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10#14583463—22no—
11#14583463—22no—
12#14583463—22no—
13#14583463—22no—
14C2×#13063321C412yescomplemented
15C2×#13063314C412yescomplemented
16C2×#13063299—22no—
17C2×#13063293—22no—
18C2×#13063284C2211yescharacteristic
19C2×#13063284C2211yescharacteristic
20#14582916—22no—
21#14582916—22no—
22C2×#13063252—22no—
23C2×#13063241—22no—
24C2×#13063241—22no—
25C2×#13063241—22no—
26#14582801—22no—
27#14582800—22no—
28#14582754—22no—
29#14582656—22no—
30#14582655—22no—
31C22×#41×C43C2211yescharacteristic
32C22×M16×C43C2211yescharacteristic
33C2×#117×C43C2211yescharacteristic
34C43×#421—22no—
35C43×#421—22no—
36C2×#104×C43—22no—
37C24×D43D412yes—
38C22×D172—21no—
39C22×D172—21no—
40C22×D172—21no—
41C22×D172—21no—
42C22×D172—21no—
43C22×D172—21no—
44C22×D172—21no—
45C22×D172—21no—
46C22×D172—21no—
47C22×D172—21no—
48C22×D172—21no—
49C22×D172—21no—
50C22×D172C2×C412yes—
51C22×D172D412yes—
52C22×C22⋊D43—24no—
53C2×#10621877—21no—
54C2×#10621877—21no—
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877D412yescomplemented
59C22×C43⋊C8—21no—
60#13063321—24no—
61#13063321—24no—
62#13063314—24no—
63#13063314—24no—
64#13063299—28no—
65#13063299—28no—
66#13063293—28no—
67#13063293—28no—
68#13063284—21no—
69#13063284—21no—
70#13063284—21no—
71#13063284—21no—
72#13063284—21no—
73#13063284—21no—
74#13063284D412yes—
75#13063284D412yes—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×(C2×D43)⋊C4—24no—
81C2×(C2×D43)⋊C4—28no—
82C2×C4×Dic43C2×C412yes—
83C2×C4×Dic43D412yescomplemented
84#13063252—28no—
85#13063241—28no—
86C2×#41×C43—21no—
87C2×#41×C43—21no—
88C2×#41×C43—21no—
89C2×#41×C43—21no—
90C2×#41×C43—21no—
91C2×#41×C43—21no—
92C2×#41×C43—21no—
93C2×#41×C43—21no—
94C2×#41×C43—21no—
95C2×#41×C43—21no—
96C2×#41×C43D412yes—
97C2×#41×C43D412yes—
98C22×Q8×C43C2×C411yescharacteristic
99C22×D4×C43—21no—
100C22×D4×C43C2×C411yescharacteristic
101C23×C4×C43—21no—
102C23×C4×C43C2311yescharacteristic
103C2×M16×C43—21no—
104C2×M16×C43—21no—
105C2×M16×C43—21no—
106C2×M16×C43—21no—
107C2×M16×C43—21no—
108C2×M16×C43D412yescomplemented
109C22×C8×C43—21no—
110#117×C43—21no—
111#117×C43—21no—
112#117×C43—21no—
113#117×C43—21no—
114C2×C4⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C42×C43D412yescomplemented
117#104×C43—28no—
118C24×C43—21no—
119C24×C43C2×D411yescharacteristic
120C23×D43—22no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—22no—
124C23×D43—22no—
125C23×D43—22no—
126C23×D43—84no—
127C23×D43C22⋊C414yes—
128#41×C43—22no—
129#41×C43—22no—
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—41no—
137#41×C43—41no—
138#41×C43—41no—
139#41×C43—41no—
140#41×C43—41no—
141#41×C43—41no—
142#41×C43—41no—
143#41×C43—41no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43C22⋊C412yescomplemented
150C2×D4×C43—21no—
151C2×D4×C43—22no—
152C2×D4×C43—22no—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43C22⋊C412yescomplemented
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—21no—
165C22×C4×C43—22no—
166C22×C4×C43—41no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170C22×C4×C43C22×C411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43C2×D411yescharacteristic
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43#4111yescharacteristic
181C22×C4×C43#4111yescharacteristic
182C22×C4×C43#4111yescharacteristic
183C22×C4×C43#4111yescharacteristic
184C2×C22⋊D43—216no—
185C2×C22⋊D43—88no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C2×D172—22no—
189C2×D172—22no—
190C2×D172—22no—
191C2×D172—22no—
192C2×D172—22no—
193C2×D172—22no—
194C2×D172—22no—
195C2×D172—22no—
196C2×D172—22no—
197C2×D172—22no—
198C2×D172—22no—
199C2×D172—22no—
200C2×D172—41no—
201C2×D172—41no—
202C2×D172—41no—
203C2×D172—41no—
204C2×D172—41no—
205C2×D172—41no—
206C2×D172—41no—
207C2×D172—41no—
208C2×D172—41no—
209C2×D172—41no—
210C2×D172—41no—
211C2×D172—41no—
212C2×D172—41no—
213C2×D172—41no—
214C2×D172—41no—
215C2×D172—41no—
216M16×C43—22no—
217M16×C43—22no—
218M16×C43—41no—
219M16×C43—41no—
220C2×C8×C43—22no—
221C2×C8×C43—41no—
222C2×C8×C43—41no—
223C4⋊C4×C43—41no—
224C4⋊C4×C43—41no—
225C22⋊C4×C43—41no—
226C22⋊C4×C43—41no—
227C42×C43—22no—
228C42×C43—22no—
229C22⋊Dic43—22no—
230C22⋊Dic43—22no—
231C22⋊Dic43—41no—
232C22⋊Dic43—41no—
233(C2×D43)⋊C4—216no—
234(C2×D43)⋊C4—88no—
235C4⋊Dic43—22no—
236C4⋊Dic43—22no—
237C4⋊Dic43—41no—
238C4⋊Dic43—41no—
239C4×Dic43—22no—
240C4×Dic43—22no—
241C4×Dic43—22no—
242C4×Dic43C22⋊C414yescomplemented
243#10621877—22no—
244#10621877—22no—
245#10621877—41no—
246#10621877—41no—
247C2×C43⋊C8—22no—
248C2×C43⋊C8—41no—
249C2×C43⋊C8—41no—
250C23×C43—22no—
251C23×C43—42no—
252C23×C43—44no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43C2×C22⋊C411yescharacteristic
256C23×C43#12011yescharacteristic
257C23×C43#12011yescharacteristic
258C23×C43#12011yescharacteristic
259C23×C43#12111yescharacteristic
260C23×C43#12111yescharacteristic
261C23×C43#12311yescharacteristic
262C22×D43—24no—
263C22×D43—24no—
264C22×D43—24no—
265C22×D43—48no—
266C22×D43—48no—
267C22×D43—42no—
268C22×D43—42no—
269C22×D43—42no—
270C22×D43—42no—
271C22×D43—84no—
272C22×D43—84no—
273C22×D43—84no—
274C22×D43—84no—
275C22×D43—84no—
276Q8×C43—22no—
277Q8×C43—22no—
278Q8×C43—41no—
279Q8×C43—41no—
280D4×C43—22no—
281D4×C43—22no—
282D4×C43—42no—
283D4×C43—42no—
284D4×C43—42no—
285D4×C43—42no—
286D4×C43—41no—
287D4×C43—41no—
288C2×C4×C43—22no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43—44no—
296C2×C4×C43—42no—
297C2×C4×C43C2×C22⋊C411yescharacteristic
298C2×C4×C43C2×C22⋊C411yescharacteristic
299C2×C4×C43C4×D411yescharacteristic
300C2×C4×C43C4×D411yescharacteristic
301C2×C4×C43C4×D411yescharacteristic
302C2×C4×C43C4×D411yescharacteristic
303C2×C4×C43#12011yescharacteristic
304C2×C4×C43#12011yescharacteristic
305C2×C4×C43#12011yescharacteristic
306C2×C4×C43#12011yescharacteristic
307C2×C4×C43#12011yescharacteristic
308C2×C4×C43#12111yescharacteristic
309C2×C4×C43#12111yescharacteristic
310C2×C4×C43#12111yescharacteristic
311C2×C4×C43#12111yescharacteristic
312C2×C4×C43#12111yescharacteristic
313C2×C4×C43#12111yescharacteristic
314C2×C4×C43#12111yescharacteristic
315C2×C4×C43#12111yescharacteristic
316C2×C4×C43#12111yescharacteristic
317C2×C4×C43#12111yescharacteristic
318C2×C4×C43#12311yescharacteristic
319C2×C4×C43#12311yescharacteristic
320C2×C4×C43#12311yescharacteristic
321C2×C4×C43#12411yescharacteristic
322C2×C4×C43#12411yescharacteristic
323C2×C4×C43#12711yescharacteristic
324C2×C4×C43#12711yescharacteristic
325C22⋊D43—816no—
326C2×Dic43—24no—
327C2×Dic43—44no—
328C2×Dic43—44no—
329C2×Dic43—42no—
330D172—42no—
331D172—42no—
332D172—42no—
333D172—42no—
334D172—42no—
335D172—42no—
336D172—42no—
337D172—42no—
338C8×C43—42no—
339C43⋊C8—42no—
340#10989—431nomaximal, Sylow
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—44no—
349C22×C43—42no—
350C22×C43—82no—
351C22×C43—82no—
352C22×C43#37911yescharacteristic
353C22×C43#38611yescharacteristic
354C22×C43#38611yescharacteristic
355C22×C43#39211yescharacteristic
356C22×C43#39211yescharacteristic
357C22×C43#39411yescharacteristic
358C22×C43#39411yescharacteristic
359C2×D43—48no—
360C2×D43—48no—
361C2×D43—44no—
362C2×D43—84no—
363C2×D43—84no—
364C2×D43—84no—
365C2×D43—84no—
366C2×D43—84no—
367C4×C43—42no—
368C4×C43—82no—
369C4×C43#38611yescharacteristic
370C4×C43#38611yescharacteristic
371C4×C43#39011yescharacteristic
372C4×C43#39011yescharacteristic
373C4×C43#39211yescharacteristic
374C4×C43#39211yescharacteristic
375C4×C43#39411yescharacteristic
376C4×C43#39411yescharacteristic
377Dic43—44no—
378Dic43—82no—
379C2×#535—431no—
380C2×#421—431no—
381C2×#421D4311yescharacteristic, complemented
382C22×#100—431no—
383#2309—431no—
384C2×H(3,ℤ/4)—431no—
385C2×H(3,ℤ/4)—431no—
386C2×C43—21no—
387C2×C43—21no—
388C2×C43—21no—
389C2×C43—21no—
390C2×C43—21no—
391C2×C43—21no—
392C2×C43—82no—
393C2×C43#143811yescharacteristic
394C2×C43#191112yes—
395D43—84no—
396C22×#41C2×D4311yescharacteristic
397C23×D4—431no—
398C22×M16—431no—
399C22×M16C2×D4311yescharacteristic
400#535—862no—
401#535—862no—
402#535—862no—
403#535—862no—
404C2×#127—432no—
405C2×#124—432no—
406C2×#121—862no—
407C2×#120—862no—
408C2×#117—431no—
409C2×#117—431no—
410C2×#117C2×D4311yescharacteristic
411#421—22no—
412#421—22no—
413#421—862no—
414#421—862no—
415C2×#104—22no—
416C2×#104—862no—
417C2×#100—862no—
418C2×#100—862no—
419C2×#100—862no—
420#390—862no—
421#390—862no—
422#379—862no—
423H(3,ℤ/4)—862no—
424H(3,ℤ/4)—862no—
425C43#1098911yescharacteristic, complemented, Sylow
426C25—432no—
427C2×#41—21no—
428C2×#41—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×#41D17212yes—
438C2×#41C22⋊D4312yes—
439C22×Q8C4×D4311yescharacteristic
440C22×D4—21no—
441C22×D4—432no—
442C22×D4—432no—
443C22×D4—864no—
444C22×D4—861no—
445C22×D4—861no—
446C22×D4—861no—
447C22×D4—861no—
448C22×D4—861no—
449C22×D4—861no—
450C22×D4—861no—
451C22×D4—861no—
452C22×D4—861no—
453C22×D4—861no—
454C22×D4—861no—
455C22×D4—861no—
456C22×D4C4×D4311yescharacteristic
457C23×C4—21no—
458C23×C4C22×D4311yescharacteristic
459C2×M16—21no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—21no—
464C2×M16—432no—
465C2×M16—861no—
466C2×M16—861no—
467C2×M16—861no—
468C2×M16—861no—
469C2×M16—861no—
470C2×M16C22⋊D4312yescomplemented
471C22×C8—21no—
472C22×C8—861no—
473#127—864no—
474#127—864no—
475#124—864no—
476#124—864no—
477#121—868no—
478#121—868no—
479#120—868no—
480#120—868no—
481#117—21no—
482#117—21no—
483#117—21no—
484#117—21no—
485#117—432no—
486#117—432no—
487#117—861no—
488#117—861no—
489#117—861no—
490#117—861no—
491#117—861no—
492#117—861no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—864no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—868no—
500C2×C22⋊C4—861no—
501C2×C42—432no—
502C2×C42—432no—
503C2×C42C22⋊D4312yescomplemented
504#104—28no—
505#104—868no—
506#100—868no—
507C24—21no—
508C24—434no—
509C24—862no—
510C24—862no—
511C24—862no—
512C24—862no—
513C24—862no—
514C24—862no—
515C24—3444no—
516C24D4×D4311yescharacteristic
517#41—22no—
518#41—22no—
519#41—22no—
520#41—22no—
521#41—22no—
522#41—22no—
523#41—22no—
524#41—22no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—41no—
532#41—41no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8(C2×D43)⋊C412yescomplemented
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—8616no—
551C2×D4—862no—
552C2×D4—862no—
553C2×D4—862no—
554C2×D4—862no—
555C2×D4—862no—
556C2×D4—862no—
557C2×D4—862no—
558C2×D4—862no—
559C2×D4—862no—
560C2×D4—862no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—3448no—
564C2×D4—1721no—
565C2×D4—1721no—
566C2×D4—1721no—
567C2×D4—1721no—
568C2×D4—1721no—
569C2×D4—1721no—
570C2×D4—1721no—
571C2×D4—1721no—
572C2×D4—1721no—
573C2×D4—1721no—
574C2×D4—1721no—
575C2×D4—1721no—
576C2×D4—1721no—
577C2×D4—1721no—
578C2×D4—1721no—
579C2×D4—1721no—
580C2×D4(C2×D43)⋊C412yescomplemented
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4C2×C4×D4311yescharacteristic
592C22×C4C2×D17211yescharacteristic
593C22×C4#1062189811yescharacteristic
594C22×C4#1062189811yescharacteristic
595C22×C4D4×D4311yescharacteristic
596C22×C4D4×D4311yescharacteristic
597C22×C4D4×D4311yescharacteristic
598C22×C4D4×D4311yescharacteristic
599C22×C4D4×D4311yescharacteristic
600C22×C4#1062190011yescharacteristic
601C22×C4#1062190011yescharacteristic
602C22×C4C2×C22⋊D4311yescharacteristic
603C22×C4C2×C22⋊D4311yescharacteristic
604C22×C4C2×C22⋊D4311yescharacteristic
605M16—22no—
606M16—22no—
607M16—41no—
608M16—41no—
609M16—862no—
610M16—862no—
611M16—1721no—
612M16—1721no—
613C2×C8—22no—
614C2×C8—41no—
615C2×C8—41no—
616C2×C8—862no—
617C2×C8—1721no—
618C2×C8—1721no—
619C4⋊C4—41no—
620C4⋊C4—41no—
621C4⋊C4—862no—
622C4⋊C4—862no—
623C4⋊C4—1721no—
624C4⋊C4—1721no—
625C22⋊C4—41no—
626C22⋊C4—41no—
627C22⋊C4—8616no—
628C22⋊C4—862no—
629C22⋊C4—862no—
630C22⋊C4—3448no—
631C22⋊C4—1721no—
632C22⋊C4—1721no—
633C42—22no—
634C42—22no—
635C42—434no—
636C42—862no—
637C42—862no—
638C42—862no—
639C23—22no—
640C23—42no—
641C23—44no—
642C23—41no—
643C23—41no—
644C23—864no—
645C23—864no—
646C23—864no—
647C23—3444no—
648C23—3444no—
649C23—3444no—
650C23—3444no—
651C23—3444no—
652C23—1728no—
653C23—1728no—
654C23—1722no—
655C23—1722no—
656C23—1722no—
657C23—1722no—
658C23C22⋊C4×D4311yescharacteristic
659C23#1306329311yescharacteristic
660C23#1306329311yescharacteristic
661C23#1306329511yescharacteristic
662C23#1306329611yescharacteristic
663C23#1306329811yescharacteristic
664C23#1306330711yescharacteristic
665Q8—22no—
666Q8—22no—
667Q8—41no—
668Q8—41no—
669D4—22no—
670D4—22no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—41no—
676D4—41no—
677D4—34416no—
678D4—1722no—
679D4—1722no—
680D4—1722no—
681D4—1722no—
682D4—1722no—
683D4—1722no—
684D4—1722no—
685D4—1722no—
686C2×C4—22no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—42no—
695C2×C4—864no—
696C2×C4—1724no—
697C2×C4—1722no—
698C2×C4—1724no—
699C2×C4C22⋊C4×D4311yescharacteristic
700C2×C4C2×(C2×D43)⋊C411yescharacteristic
701C2×C4(C22⋊D43)⋊C411yescharacteristic
702C2×C4(C22⋊D43)⋊C411yescharacteristic
703C2×C4C4×C22⋊D4311yescharacteristic
704C2×C4C4×C22⋊D4311yescharacteristic
705C2×C4#1306329311yescharacteristic
706C2×C4#1306329311yescharacteristic
707C2×C4#1306329411yescharacteristic
708C2×C4#1306329511yescharacteristic
709C2×C4#1306329511yescharacteristic
710C2×C4#1306329611yescharacteristic
711C2×C4#1306329711yescharacteristic
712C2×C4#1306329711yescharacteristic
713C2×C4#1306329711yescharacteristic
714C2×C4#1306329711yescharacteristic
715C2×C4#1306329811yescharacteristic
716C2×C4#1306329811yescharacteristic
717C2×C4#1306329811yescharacteristic
718C2×C4#1306329911yescharacteristic
719C2×C4#1306329911yescharacteristic
720C2×C4#1306330711yescharacteristic
721C2×C4#1306330811yescharacteristic
722C2×C4#1306330911yescharacteristic
723C2×C4#1306331111yescharacteristic
724C2×C4#1306331111yescharacteristic
725C2×C4#1306332111yescharacteristic
726C2×C4#1306332111yescharacteristic
727C8—42no—
728C8—1722no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—44no—
737C22—42no—
738C22—82no—
739C22—82no—
740C22—3444no—
741C22—3444no—
742C22—3444no—
743C22—3444no—
744C22—3444no—
745C22—1728no—
746C22—1728no—
747C22—1724no—
748C22#1458275411yescharacteristic
749C22#1458277511yescharacteristic
750C22#1458277511yescharacteristic
751C22#1458280711yescharacteristic
752C22#1458280811yescharacteristic
753C22#1458281411yescharacteristic
754C22#1458281511yescharacteristic
755C4—42no—
756C4—82no—
757C4—3442no—
758C4—1724no—
759C4#1458277611yescharacteristic
760C4#1458277811yescharacteristic
761C4#1458279911yescharacteristic
762C4#1458279911yescharacteristic
763C4#1458280711yescharacteristic
764C4#1458280811yescharacteristic
765C4#1458281411yescharacteristic
766C4#1458281511yescharacteristic
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—82no—
774C2—3444no—
775C2#1913283411yescharacteristic
776C2#1913512412yes—
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#421C2
socleC22×C43#386
prime radicalC2×#14583463C2
cosocleC23×C4×C43C23
hypercenterC2×#421D43
hypocenterC43#10989
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#14582916C2semidirect
3. C22×#13063241C2semidirect
4. #19137175C2semidirect
5. C2×#14582656C2semidirect
6. C2×#14582655C2semidirect
7. C2×C43×#421C2semidirect
14. C2×#13063321C4semidirect
15. C2×#13063314C4semidirect
58. C2×#10621877D4semidirect
83. C2×C4×Dic43D4semidirect
108. C2×M16×C43D4semidirect
116. C2×C42×C43D4semidirect
149. C2×Q8×C43C22⋊C4semidirect
161. C2×D4×C43C22⋊C4semidirect
242. C4×Dic43C22⋊C4semidirect
381. C2×#421D43semidirect
425. C43#10989semidirect
470. C2×M16C22⋊D43semidirect
503. C2×C42C22⋊D43semidirect
538. C2×Q8(C2×D43)⋊C4semidirect
580. C2×D4(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145834632
C2×#145829162
C22×#130632412
#191371752
C2×#145826562
C2×#145826552
C2×C43×#4212
#1098943