Finite Group Databasebeta

← #25124457

Subgroups — #25124457

Order 11008.

1336 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583697C211yesmaximal, characteristic
2#19143159C211yesmaximal, characteristic, complemented
3C2×#14582917C211yesmaximal, characteristic, complemented
4C2×#14582883C211yesmaximal, characteristic, complemented
5C2×#14582881C211yesmaximal, characteristic, complemented
6#19135881C218yesmaximal, complemented
7C2×C43⋊#338C211yesmaximal, characteristic, complemented
8C2×C43×#421C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583697—22no—
11#14583697—22no—
12#14583697—22no—
13#14583697C2214yes—
14C2×#13063356—21no—
15C2×#13063355—21no—
16C2×#13063351—21no—
17C2×#13063350—21no—
18C2×#13063345—22no—
19C22×#10621877C2211yescharacteristic
20C22×#10621877C2211yescharacteristic
21C22×#10621877C2211yescharacteristic
22#14582926—22no—
23#14582926—22no—
24#14582923C2214yescomplemented
25#14582917—22no—
26#14582917—22no—
27C2×#13063253C2214yescomplemented
28#14582883—22no—
29#14582883C2214yescomplemented
30#14582881—22no—
31#14582881C2214yescomplemented
32C2×#13063244—21no—
33C2×#13063243—21no—
34C2×#13063242—21no—
35C2×#13063241—21no—
36C43⋊#338C2214yescomplemented
37C22×#41×C43C2211yescharacteristic
38C22×M16×C43C2211yescharacteristic
39C2×#117×C43C2211yescharacteristic
40C43×#421—22no—
41C43×#421—22no—
42C2×#104×C43C2214yescomplemented
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C2×#10621898—21no—
52C2×#10621898—21no—
53C2×#10621898D412yes—
54C2×#10621898C2312yes—
55C22×Dic86D411yescharacteristic
56C22×D172D411yescharacteristic
57C22×C22⋊D43—21no—
58C22×C4×D43—21no—
59#13063356—24no—
60#13063356—24no—
61#13063355—24no—
62#13063355—24no—
63#13063351—24no—
64#13063351—24no—
65#13063350—24no—
66#13063350—24no—
67#13063345—28no—
68#13063345—28no—
69C2×#10621885—22no—
70C2×#10621883—22no—
71C2×#10621884—22no—
72C2×#10621882—22no—
73C2×#10621877—21no—
74C2×#10621877—21no—
75C2×#10621877—21no—
76C2×#10621877—21no—
77C2×#10621877—21no—
78C2×#10621877—21no—
79C2×#10621877—21no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877—21no—
84C2×#10621877—21no—
85C2×#10621877—21no—
86C2×#10621877—21no—
87C2×#10621877D412yes—
88C2×#10621877C2312yes—
89C2×#10621877C2312yes—
90C2×#10621877C2312yes—
91C22×C43⋊C8—21no—
92C22×C43⋊C8—21no—
93C22×C43⋊C8D412yes—
94C4⋊(C43⋊C8)—28no—
95#13063253—28no—
96#13063244—24no—
97#13063243—24no—
98#13063242—24no—
99#13063241—24no—
100C2×#41×C43—21no—
101C2×#41×C43—21no—
102C2×#41×C43—21no—
103C2×#41×C43—21no—
104C2×#41×C43—21no—
105C2×#41×C43—21no—
106C2×#41×C43—21no—
107C2×#41×C43—21no—
108C2×#41×C43—21no—
109C2×#41×C43—21no—
110C2×#41×C43D412yes—
111C2×#41×C43C2312yes—
112C22×Q8×C43D411yescharacteristic
113C22×D4×C43—21no—
114C22×D4×C43D411yescharacteristic
115C23×C4×C43—21no—
116C23×C4×C43C2311yescharacteristic
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43—21no—
120C2×M16×C43—21no—
121C2×M16×C43—21no—
122C2×M16×C43C2312yes—
123C22×C8×C43—21no—
124#117×C43—21no—
125#117×C43—21no—
126#117×C43D412yes—
127#117×C43D412yes—
128C2×C4⋊C4×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C42×C43C2312yes—
131#104×C43—28no—
132C24×C43—21no—
133C24×C43#4111yescharacteristic
134C23×D43—21no—
135#41×C43—22no—
136#41×C43—22no—
137#41×C43—22no—
138#41×C43—22no—
139#41×C43—22no—
140#41×C43—22no—
141#41×C43—22no—
142#41×C43—22no—
143#41×C43—41no—
144#41×C43—41no—
145#41×C43—41no—
146#41×C43—41no—
147#41×C43—41no—
148#41×C43—41no—
149#41×C43—41no—
150#41×C43—41no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43C2×D412yes—
157C2×D4×C43—21no—
158C2×D4×C43—22no—
159C2×D4×C43—22no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—41no—
165C2×D4×C43—41no—
166C2×D4×C43—41no—
167C2×D4×C43—41no—
168C2×D4×C43C2×D412yes—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—21no—
172C22×C4×C43—22no—
173C22×C4×C43—41no—
174C22×C4×C43—41no—
175C22×C4×C43—41no—
176C22×C4×C43—41no—
177C22×C4×C43C2×D411yescharacteristic
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43#4111yescharacteristic
186C22×C4×C43#4111yescharacteristic
187C22×C4×C43#4111yescharacteristic
188C22×C4×C43#4111yescharacteristic
189C22×C4×C43#4111yescharacteristic
190C22×C4×C43C2411yescharacteristic
191C2×C22⋊D43—22no—
192C2×C22⋊D43—22no—
193C2×C22⋊D43—41no—
194C2×C22⋊D43—41no—
195C2×C22⋊D43—41no—
196C2×C22⋊D43—41no—
197C22×Dic43—21no—
198#10621898—22no—
199#10621898—22no—
200#10621898—22no—
201#10621898—22no—
202#10621898—22no—
203#10621898—22no—
204#10621898—22no—
205#10621898—22no—
206#10621898—41no—
207#10621898—41no—
208#10621898—41no—
209#10621898—41no—
210#10621898—41no—
211#10621898—41no—
212#10621898—41no—
213#10621898—41no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172C2×D412yes—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—41no—
223C2×C4×D43—41no—
224C2×C4×D43—41no—
225C2×C4×D43—41no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86C2×D412yes—
232M16×C43—22no—
233M16×C43—22no—
234M16×C43—41no—
235M16×C43—41no—
236C2×C8×C43—22no—
237C2×C8×C43—41no—
238C2×C8×C43—41no—
239C4⋊C4×C43—22no—
240C4⋊C4×C43—22no—
241C22⋊C4×C43—22no—
242C22⋊C4×C43—22no—
243C42×C43—22no—
244C42×C43C2×D414yes—
245#10621885—28no—
246#10621884—28no—
247#10621883—28no—
248#10621882—28no—
249#10621877—22no—
250#10621877—22no—
251#10621877—22no—
252#10621877—22no—
253#10621877—22no—
254#10621877—22no—
255#10621877—22no—
256#10621877—22no—
257#10621877—41no—
258#10621877—41no—
259#10621877—41no—
260#10621877—41no—
261C2×C43⋊C8—22no—
262C2×C43⋊C8—22no—
263C2×C43⋊C8—22no—
264C2×C43⋊C8—22no—
265C2×C43⋊C8—41no—
266C2×C43⋊C8—41no—
267C2×C43⋊C8—41no—
268C2×C43⋊C8—41no—
269C2×C43⋊C8C2×D414yes—
270C23×C43—22no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—81no—
274C23×C43—82no—
275C23×C43#12111yescharacteristic
276C23×C43#12111yescharacteristic
277C23×C43#12311yescharacteristic
278C23×C43#12311yescharacteristic
279C23×C43#12311yescharacteristic
280C23×C43#12311yescharacteristic
281C23×C43C2×#4111yescharacteristic
282C22×D43—22no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—82no—
286Q8×C43—22no—
287Q8×C43—22no—
288Q8×C43—41no—
289Q8×C43—41no—
290D4×C43—22no—
291D4×C43—22no—
292D4×C43—42no—
293D4×C43—42no—
294D4×C43—42no—
295D4×C43—42no—
296D4×C43—41no—
297D4×C43—41no—
298C2×C4×C43—24no—
299C2×C4×C43—22no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—82no—
307C2×C4×C43#12011yescharacteristic
308C2×C4×C43#12011yescharacteristic
309C2×C4×C43#12011yescharacteristic
310C2×C4×C43#12011yescharacteristic
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#12111yescharacteristic
319C2×C4×C43#12111yescharacteristic
320C2×C4×C43#12111yescharacteristic
321C2×C4×C43#12311yescharacteristic
322C2×C4×C43#12311yescharacteristic
323C2×C4×C43#12311yescharacteristic
324C2×C4×C43#12311yescharacteristic
325C2×C4×C43#12411yescharacteristic
326C2×C4×C43#12411yescharacteristic
327C2×C4×C43#12411yescharacteristic
328C2×C4×C43#12411yescharacteristic
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C2×#4111yescharacteristic
334C2×C4×C43C2×#4111yescharacteristic
335C22⋊D43—42no—
336C22⋊D43—42no—
337C22⋊D43—42no—
338C22⋊D43—42no—
339C2×Dic43—22no—
340C2×Dic43—41no—
341C2×Dic43—41no—
342D172—22no—
343D172—22no—
344D172—41no—
345D172—41no—
346C4×D43—42no—
347C4×D43—42no—
348C4×D43—42no—
349C4×D43—42no—
350Dic86—22no—
351Dic86—22no—
352Dic86—41no—
353Dic86—41no—
354C8×C43—42no—
355C43⋊C8—24no—
356C43⋊C8—42no—
357C43⋊C8—42no—
358#23527—431nomaximal, Sylow
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—42no—
367C22×C43—82no—
368C22×C43—82no—
369C22×C43—82no—
370C22×C43#39411yescharacteristic
371C22×C43#39411yescharacteristic
372C22×C43#39411yescharacteristic
373C22×C43#39411yescharacteristic
374C22×C43C2×#12111yescharacteristic
375C22×C43C2×#12311yescharacteristic
376C22×C43C2×#12311yescharacteristic
377C2×D43—42no—
378C2×D43—82no—
379C2×D43—82no—
380C2×D43—82no—
381C4×C43—44no—
382C4×C43—42no—
383C4×C43#39411yescharacteristic
384C4×C43#39411yescharacteristic
385C4×C43#39411yescharacteristic
386C4×C43#39411yescharacteristic
387C4×C43C2×#12011yescharacteristic
388C4×C43C2×#12111yescharacteristic
389C4×C43C2×#12111yescharacteristic
390C4×C43C2×#12411yescharacteristic
391Dic43—42no—
392C2×#575—431no—
393#2905—431no—
394C2×#421—431no—
395C2×#421D4311yescharacteristic, complemented
396C2×#413—431no—
397C2×#413—431no—
398#2050—438no—
399C2×#338—431no—
400C2×C43—21no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—21no—
404C2×C43—21no—
405C2×C43—21no—
406C2×C43—21no—
407C2×C43—82no—
408C2×C43C2×#39411yescharacteristic
409D43—82no—
410C22×#41—431no—
411C22×#41C2×D4311yescharacteristic
412#575—434no—
413#575—862no—
414#575—862no—
415#575—862no—
416C2×#137—861no—
417C2×#137—861no—
418C2×AGL(1,ℤ/8)—861no—
419C2×AGL(1,ℤ/8)—861no—
420C2×#135—862no—
421C22×M16—431no—
422C22×M16—431no—
423C22×M16—431no—
424C22×M16C2×D4311yescharacteristic
425C2×#117C2×D4311yescharacteristic
426#424—862no—
427#424—862no—
428#423—434no—
429#421—22no—
430#421—22no—
431#421—862no—
432#421—862no—
433C2×#104—434no—
434C2×#104C2×D4314yescomplemented
435#413—434no—
436#413—434no—
437#413—862no—
438#413—862no—
439C2×#101—861no—
440C2×#101—861no—
441C2×#100—861no—
442C2×#100—861no—
443#338—434no—
444C43#2352711yescharacteristic, complemented, Sylow
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—432no—
456C2×#41—432no—
457C2×#41—861no—
458C2×#41—861no—
459C2×#41—861no—
460C2×#41—861no—
461C2×#41—861no—
462C2×#41—861no—
463C2×#41—861no—
464C2×#41—861no—
465C2×#41—861no—
466C2×#41—861no—
467C2×#41D17212yes—
468C2×#41C22×D4312yes—
469C22×Q8—431no—
470C22×Q8D17211yescharacteristic
471C22×D4—21no—
472C22×D4—431no—
473C22×D4—861no—
474C22×D4D17211yescharacteristic
475C23×C4—21no—
476C23×C4—861no—
477C23×C4C22×D4311yescharacteristic
478#137—864no—
479#137—864no—
480#137—864no—
481#137—864no—
482AGL(1,ℤ/8)—864no—
483AGL(1,ℤ/8)—864no—
484AGL(1,ℤ/8)—864no—
485AGL(1,ℤ/8)—864no—
486#135—868no—
487#135—868no—
488C2×Q16—862no—
489C2×SD16—862no—
490C2×SD16—862no—
491C2×D8—862no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—432no—
498C2×M16—432no—
499C2×M16—432no—
500C2×M16—432no—
501C2×M16—861no—
502C2×M16—861no—
503C2×M16—861no—
504C2×M16—861no—
505C2×M16—861no—
506C2×M16—861no—
507C2×M16—861no—
508C2×M16—861no—
509C2×M16—861no—
510C2×M16—861no—
511C2×M16—861no—
512C2×M16—861no—
513C2×M16—861no—
514C2×M16—861no—
515C2×M16C22×D4312yes—
516C22×C8—21no—
517C22×C8—432no—
518C22×C8—861no—
519C22×C8—861no—
520#117—21no—
521#117—21no—
522#117C22⋊D4312yes—
523#117C22⋊D4312yes—
524C2×C4⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C42C22×D4312yes—
527C4⋊C8—868no—
528#104—28no—
529#104—868no—
530#101—864no—
531#101—864no—
532#100—864no—
533#100—864no—
534C24—21no—
535C24—861no—
536C24#1062190011yescharacteristic
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—862no—
554#41—862no—
555#41—862no—
556#41—862no—
557#41—862no—
558#41—862no—
559#41—862no—
560#41—862no—
561#41—1721no—
562#41—1721no—
563#41—1721no—
564#41—1721no—
565#41—1721no—
566#41—1721no—
567#41—1721no—
568#41—1721no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8—432no—
575C2×Q8—861no—
576C2×Q8—861no—
577C2×Q8—861no—
578C2×Q8—861no—
579C2×Q8—861no—
580C2×Q8C2×D17212yes—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—432no—
593C2×D4—862no—
594C2×D4—862no—
595C2×D4—861no—
596C2×D4—861no—
597C2×D4—861no—
598C2×D4—861no—
599C2×D4—861no—
600C2×D4—1721no—
601C2×D4—1721no—
602C2×D4—1721no—
603C2×D4—1721no—
604C2×D4C2×D17212yes—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—861no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—1721no—
617C22×C4—1721no—
618C22×C4—1721no—
619C22×C4—1721no—
620C22×C4C2×D17211yescharacteristic
621C22×C4C2×D17211yescharacteristic
622C22×C4#1062189811yescharacteristic
623C22×C4#1062189811yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4D4×D4311yescharacteristic
626C22×C4D4×D4311yescharacteristic
627C22×C4D4×D4311yescharacteristic
628C22×C4#1062190011yescharacteristic
629C22×C4#1062190011yescharacteristic
630C22×C4#1062190011yescharacteristic
631C22×C4C2×C22⋊D4311yescharacteristic
632C22×C4C2×C22⋊D4311yescharacteristic
633C22×C4C23×D4311yescharacteristic
634Q16—868no—
635SD16—868no—
636SD16—868no—
637D8—868no—
638M16—22no—
639M16—22no—
640M16—41no—
641M16—41no—
642M16—862no—
643M16—862no—
644M16—862no—
645M16—862no—
646M16—862no—
647M16—862no—
648M16—862no—
649M16—862no—
650M16—1721no—
651M16—1721no—
652M16—1721no—
653M16—1721no—
654C2×C8—22no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8—434no—
658C2×C8—862no—
659C2×C8—862no—
660C2×C8—862no—
661C2×C8—862no—
662C2×C8—1721no—
663C2×C8—1721no—
664C2×C8—1721no—
665C2×C8—1721no—
666C4⋊C4—22no—
667C4⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C42—22no—
671C42C2×C22⋊D4314yes—
672C23—22no—
673C23—41no—
674C23—41no—
675C23—81no—
676C23—82no—
677C23—862no—
678C23—3442no—
679C23—1721no—
680C23—1721no—
681C23#1306329711yescharacteristic
682C23#1306329711yescharacteristic
683C23#1306330711yescharacteristic
684C23#1306330711yescharacteristic
685C23#1306330911yescharacteristic
686C23#1306330911yescharacteristic
687C23C2×#1062190011yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—41no—
691Q8—41no—
692Q8—862no—
693Q8—862no—
694Q8—1721no—
695Q8—1721no—
696D4—22no—
697D4—22no—
698D4—42no—
699D4—42no—
700D4—42no—
701D4—42no—
702D4—41no—
703D4—41no—
704D4—862no—
705D4—862no—
706D4—1722no—
707D4—1722no—
708D4—1722no—
709D4—1722no—
710D4—1721no—
711D4—1721no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—82no—
721C2×C4—862no—
722C2×C4—1721no—
723C2×C4—1721no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4—1722no—
728C2×C4#1306329511yescharacteristic
729C2×C4#1306329511yescharacteristic
730C2×C4#1306329511yescharacteristic
731C2×C4#1306329511yescharacteristic
732C2×C4#1306329611yescharacteristic
733C2×C4#1306329611yescharacteristic
734C2×C4#1306329611yescharacteristic
735C2×C4#1306329611yescharacteristic
736C2×C4#1306329711yescharacteristic
737C2×C4#1306329711yescharacteristic
738C2×C4#1306329911yescharacteristic
739C2×C4#1306329911yescharacteristic
740C2×C4#1306329911yescharacteristic
741C2×C4#1306329911yescharacteristic
742C2×C4#1306330711yescharacteristic
743C2×C4#1306330711yescharacteristic
744C2×C4#1306330911yescharacteristic
745C2×C4#1306330911yescharacteristic
746C2×C4#1306331111yescharacteristic
747C2×C4#1306331111yescharacteristic
748C2×C4#1306331111yescharacteristic
749C2×C4#1306331111yescharacteristic
750C2×C4C2×D4×D4311yescharacteristic
751C2×C4C2×D4×D4311yescharacteristic
752C2×C4C22×C22⋊D4311yescharacteristic
753C2×C4C22×D17211yescharacteristic
754C2×C4C2×#1062190011yescharacteristic
755C2×C4C2×#1062189811yescharacteristic
756C8—42no—
757C8—864no—
758C8—1722no—
759C8—1722no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—42no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—3442no—
772C22—3442no—
773C22—3442no—
774C22—1722no—
775C22#1458281511yescharacteristic
776C22#1458281511yescharacteristic
777C22#1458281511yescharacteristic
778C22#1458281511yescharacteristic
779C22C2×#1306329711yescharacteristic
780C22C2×#1306330711yescharacteristic
781C22C2×#1306330911yescharacteristic
782C4—44no—
783C4—42no—
784C4—1722no—
785C4#1458281511yescharacteristic
786C4#1458281511yescharacteristic
787C4#1458281511yescharacteristic
788C4#1458281511yescharacteristic
789C4C2×#1306329511yescharacteristic
790C4C2×#1306329611yescharacteristic
791C4C2×#1306329911yescharacteristic
792C4C2×#1306331111yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—82no—
801C2—3442no—
802C2C2×#1458281511yescharacteristic
subgroupG/H
centerC4C2×#13063311
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#421C2
socleC2×C43C2×#394
prime radicalC2×#14583697C2
hypercenterC2×#421D43
hypocenterC43#23527
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. #19143159C2semidirect
3. C2×#14582917C2semidirect
4. C2×#14582883C2semidirect
5. C2×#14582881C2semidirect
6. #19135881C2semidirect
7. C2×C43⋊#338C2semidirect
8. C2×C43×#421C2semidirect
24. #14582923C22semidirect
27. C2×#13063253C22semidirect
29. #14582883C22semidirect
31. #14582881C22semidirect
36. C43⋊#338C22semidirect
42. C2×#104×C43C22semidirect
395. C2×#421D43semidirect
434. C2×#104C2×D43semidirect
444. C43#23527semidirect

Maximal subgroups

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

subgroupindex
C2×#145836972
#191431592
C2×#145829172
C2×#145828832
C2×#145828812
#191358812
C2×C43⋊#3382
C2×C43×#4212
#2352743