Finite Group Databasebeta

← C2×#19135880 #25124450

Subgroups — C2×#19135880 #25124450

Order 11008.

1382 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583697C211yesmaximal, characteristic
2C2×#14582922C211yesmaximal, characteristic, complemented
3C22×#13063252C211yesmaximal, characteristic, complemented
4C22×#13063251C211yesmaximal, characteristic, complemented
5C2×#14582881C211yesmaximal, characteristic, complemented
6#19135880C218yesmaximal, direct product factor
7C2×C43⋊#338C211yesmaximal, characteristic, complemented
8C2×C43×#413C211yesmaximal, 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×C4×Dic43C2211yescharacteristic
22#14582922—22no—
23#14582922C2214yescomplemented
24C2×Dic43⋊C8—22no—
25C2×#13063252—21no—
26C2×#13063252—21no—
27C2×#13063252—22no—
28C2×#13063252C2214yescomplemented
29C2×#13063251—21no—
30C2×#13063251—21no—
31C2×#13063251—22no—
32C2×#13063251C2214yescomplemented
33#14582881—22no—
34#14582881C2214yescomplemented
35C2×#13063243—21no—
36C2×#13063241—21no—
37C43⋊#338C2214yescomplemented
38C22×#41×C43C2211yescharacteristic
39C22×M16×C43C2211yescharacteristic
40C22×M16×C43C2211yescharacteristic
41C43×#413—22no—
42C43×#413C2214yescomplemented
43C2×#101×C43—21no—
44C2×#100×C43—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×#10621898—21no—
54C2×#10621898—21no—
55C2×#10621898D412yes—
56C2×#10621898C2312yes—
57C22×Dic86D411yescharacteristic
58C22×D172D411yescharacteristic
59C22×C22⋊D43—21no—
60C23×Dic43—21no—
61C22×C4×D43—21no—
62#13063356—24no—
63#13063356—24no—
64#13063355—24no—
65#13063355—24no—
66#13063351—24no—
67#13063351—24no—
68#13063350—24no—
69#13063350—24no—
70#13063345—28no—
71#13063345—28no—
72C2×#10621885—22no—
73C2×#10621883—22no—
74C2×#10621884—22no—
75C2×#10621882—22no—
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×#10621877D412yes—
86C2×#10621877C2312yes—
87C2×#10621877C2312yes—
88C22×C43⋊C8—21no—
89C22×C43⋊C8D412yes—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43D412yes—
95C2×C4×Dic43D411yescharacteristic
96C2×C4×Dic43C2312yes—
97Dic43⋊C8—28no—
98#13063252—24no—
99#13063252—24no—
100#13063251—24no—
101#13063251—24no—
102#13063243—24no—
103#13063241—24no—
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×C43—21no—
111C2×#41×C43—21no—
112C2×#41×C43—21no—
113C2×#41×C43—21no—
114C2×#41×C43D412yes—
115C2×#41×C43C2312yes—
116C22×Q8×C43D411yescharacteristic
117C22×D4×C43—21no—
118C22×D4×C43D411yescharacteristic
119C23×C4×C43—21no—
120C23×C4×C43C2311yescharacteristic
121C2×M16×C43—21no—
122C2×M16×C43—21no—
123C2×M16×C43—21no—
124C2×M16×C43—21no—
125C2×M16×C43—21no—
126C2×M16×C43—21no—
127C2×M16×C43—21no—
128C2×M16×C43—21no—
129C2×M16×C43—21no—
130C2×M16×C43—21no—
131C2×M16×C43C2312yes—
132C2×M16×C43C2312yes—
133C22×C8×C43—21no—
134C22×C8×C43—21no—
135#101×C43—24no—
136#100×C43—24no—
137C24×C43—21no—
138C24×C43#4111yescharacteristic
139C23×D43—21no—
140#41×C43—22no—
141#41×C43—22no—
142#41×C43—22no—
143#41×C43—22no—
144#41×C43—22no—
145#41×C43—22no—
146#41×C43—22no—
147#41×C43—22no—
148#41×C43—41no—
149#41×C43—41no—
150#41×C43—41no—
151#41×C43—41no—
152#41×C43—41no—
153#41×C43—41no—
154#41×C43—41no—
155#41×C43—41no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43C2×D412yes—
162C2×D4×C43—21no—
163C2×D4×C43—22no—
164C2×D4×C43—22no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
169C2×D4×C43—41no—
170C2×D4×C43—41no—
171C2×D4×C43—41no—
172C2×D4×C43—41no—
173C2×D4×C43C2×D412yes—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—21no—
177C22×C4×C43—41no—
178C22×C4×C43—41no—
179C22×C4×C43—41no—
180C22×C4×C43—41no—
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43#4111yescharacteristic
190C22×C4×C43#4111yescharacteristic
191C22×C4×C43#4111yescharacteristic
192C22×C4×C43#4111yescharacteristic
193C22×C4×C43#4111yescharacteristic
194C22×C4×C43C2411yescharacteristic
195C2×C22⋊D43—22no—
196C2×C22⋊D43—22no—
197C2×C22⋊D43—41no—
198C2×C22⋊D43—41no—
199C2×C22⋊D43—41no—
200C2×C22⋊D43—41no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—22no—
204C22×Dic43—21no—
205C22×Dic43—22no—
206C22×Dic43—44no—
207#10621898—22no—
208#10621898—22no—
209#10621898—22no—
210#10621898—22no—
211#10621898—22no—
212#10621898—22no—
213#10621898—22no—
214#10621898—22no—
215#10621898—41no—
216#10621898—41no—
217#10621898—41no—
218#10621898—41no—
219#10621898—41no—
220#10621898—41no—
221#10621898—41no—
222#10621898—41no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172—21no—
228C2×D172C2×D412yes—
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43—41no—
232C2×C4×D43—41no—
233C2×C4×D43—41no—
234C2×C4×D43—41no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86C2×D412yes—
241M16×C43—22no—
242M16×C43—22no—
243M16×C43—22no—
244M16×C43—22no—
245M16×C43—41no—
246M16×C43—41no—
247M16×C43—41no—
248M16×C43—41no—
249C2×C8×C43—22no—
250C2×C8×C43—22no—
251C2×C8×C43—41no—
252C2×C8×C43—41no—
253C2×C8×C43—41no—
254C2×C8×C43—41no—
255#10621885—28no—
256#10621884—28no—
257#10621883—28no—
258#10621882—28no—
259C4×Dic43—21no—
260C4×Dic43—22no—
261C4×Dic43—21no—
262C4×Dic43—22no—
263C4×Dic43C2×D412yes—
264C4×Dic43C2×D412yes—
265#10621877—22no—
266#10621877—22no—
267#10621877—22no—
268#10621877—22no—
269#10621877—22no—
270#10621877—22no—
271#10621877—41no—
272#10621877—41no—
273C2×C43⋊C8—22no—
274C2×C43⋊C8—22no—
275C2×C43⋊C8—22no—
276C2×C43⋊C8—41no—
277C2×C43⋊C8—41no—
278C2×C43⋊C8C2×D414yes—
279C23×C43—22no—
280C23×C43—42no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—82no—
284C23×C43#12111yescharacteristic
285C23×C43#12111yescharacteristic
286C23×C43#12311yescharacteristic
287C23×C43#12311yescharacteristic
288C23×C43#12311yescharacteristic
289C23×C43#12311yescharacteristic
290C23×C43C2×#4111yescharacteristic
291C22×D43—22no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—82no—
295Q8×C43—22no—
296Q8×C43—22no—
297Q8×C43—41no—
298Q8×C43—41no—
299D4×C43—22no—
300D4×C43—22no—
301D4×C43—42no—
302D4×C43—42no—
303D4×C43—42no—
304D4×C43—42no—
305D4×C43—41no—
306D4×C43—41no—
307C2×C4×C43—22no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43#12011yescharacteristic
315C2×C4×C43#12011yescharacteristic
316C2×C4×C43#12011yescharacteristic
317C2×C4×C43#12011yescharacteristic
318C2×C4×C43#12111yescharacteristic
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#12311yescharacteristic
329C2×C4×C43#12311yescharacteristic
330C2×C4×C43#12311yescharacteristic
331C2×C4×C43#12311yescharacteristic
332C2×C4×C43#12411yescharacteristic
333C2×C4×C43#12411yescharacteristic
334C2×C4×C43#12411yescharacteristic
335C2×C4×C43#12411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43C2×#4111yescharacteristic
342C22⋊D43—42no—
343C22⋊D43—42no—
344C22⋊D43—42no—
345C22⋊D43—42no—
346C2×Dic43—24no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—44no—
351C2×Dic43—44no—
352C2×Dic43—42no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355D172—22no—
356D172—22no—
357D172—41no—
358D172—41no—
359C4×D43—42no—
360C4×D43—42no—
361C4×D43—42no—
362C4×D43—42no—
363Dic86—22no—
364Dic86—22no—
365Dic86—41no—
366Dic86—41no—
367C8×C43—42no—
368C8×C43—42no—
369C43⋊C8—24no—
370C43⋊C8—42no—
371C2×#2050—431nomaximal, Sylow
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—42no—
380C22×C43—82no—
381C22×C43—82no—
382C22×C43—82no—
383C22×C43#39411yescharacteristic
384C22×C43#39411yescharacteristic
385C22×C43#39411yescharacteristic
386C22×C43#39411yescharacteristic
387C22×C43C2×#12111yescharacteristic
388C22×C43C2×#12311yescharacteristic
389C22×C43C2×#12311yescharacteristic
390C2×D43—42no—
391C2×D43—82no—
392C2×D43—82no—
393C2×D43—82no—
394C4×C43—42no—
395C4×C43#39411yescharacteristic
396C4×C43#39411yescharacteristic
397C4×C43#39411yescharacteristic
398C4×C43#39411yescharacteristic
399C4×C43C2×#12011yescharacteristic
400C4×C43C2×#12111yescharacteristic
401C4×C43C2×#12111yescharacteristic
402C4×C43C2×#12411yescharacteristic
403Dic43—24no—
404Dic43—42no—
405Dic43—42no—
406C2×#575—431no—
407C2×#423—431no—
408C22×#104—431no—
409C22×#104—431no—
410C2×#413—431no—
411C2×#413D4311yescharacteristic, complemented
412#2050—438no—
413C2×#338—431no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43—21no—
417C2×C43—21no—
418C2×C43—21no—
419C2×C43—21no—
420C2×C43—82no—
421C2×C43#205012yescomplemented
422C2×C43C2×#39411yescharacteristic
423D43—82no—
424C22×#41—431no—
425C22×#41C2×D4311yescharacteristic
426#575—434no—
427#575—862no—
428#575—862no—
429#575—862no—
430C2×#137—861no—
431C2×#137—861no—
432C2×AGL(1,ℤ/8)—861no—
433C2×AGL(1,ℤ/8)—861no—
434C2×#135—862no—
435C22×M16—431no—
436C22×M16—431no—
437C22×M16C2×D4311yescharacteristic
438C22×M16C2×D4311yescharacteristic
439C22×C42—431no—
440#423—434no—
441#423—862no—
442C2×C4⋊C8—862no—
443C2×#104—434no—
444C2×#104—434no—
445C2×#104—861no—
446C2×#104—862no—
447C2×#104—861no—
448C2×#104—861no—
449C2×#104—862no—
450C2×#104—861no—
451#413—22no—
452#413—434no—
453#413—862no—
454#413C2×D4314yescomplemented
455C2×#101—21no—
456C2×#101—861no—
457C2×#100—21no—
458C2×#100—861no—
459#338—434no—
460C43C2×#205011yescharacteristic, complemented, Sylow
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—432no—
472C2×#41—432no—
473C2×#41—861no—
474C2×#41—861no—
475C2×#41—861no—
476C2×#41—861no—
477C2×#41—861no—
478C2×#41—861no—
479C2×#41—861no—
480C2×#41—861no—
481C2×#41—861no—
482C2×#41—861no—
483C2×#41C22⋊D4312yes—
484C2×#41C22×D4312yes—
485C22×Q8—431no—
486C22×Q8C22⋊D4311yescharacteristic
487C22×D4—21no—
488C22×D4—431no—
489C22×D4—861no—
490C22×D4C22⋊D4311yescharacteristic
491C23×C4—21no—
492C23×C4—861no—
493C23×C4—861no—
494C23×C4C22×D4311yescharacteristic
495#137—864no—
496#137—864no—
497#137—864no—
498#137—864no—
499AGL(1,ℤ/8)—864no—
500AGL(1,ℤ/8)—864no—
501AGL(1,ℤ/8)—864no—
502AGL(1,ℤ/8)—864no—
503#135—868no—
504#135—868no—
505C2×Q16—862no—
506C2×SD16—862no—
507C2×SD16—862no—
508C2×D8—862no—
509C2×M16—21no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—21no—
514C2×M16—21no—
515C2×M16—21no—
516C2×M16—21no—
517C2×M16—21no—
518C2×M16—21no—
519C2×M16—432no—
520C2×M16—432no—
521C2×M16—432no—
522C2×M16—861no—
523C2×M16—861no—
524C2×M16—861no—
525C2×M16—861no—
526C2×M16—861no—
527C2×M16—861no—
528C2×M16—861no—
529C2×M16—861no—
530C2×M16—861no—
531C2×M16C22×D4312yes—
532C2×M16C22×D4312yes—
533C22×C8—21no—
534C22×C8—21no—
535C22×C8—432no—
536C22×C8—861no—
537C2×C42—431no—
538C2×C42—432no—
539C2×C42—431no—
540C2×C42—432no—
541C2×C42—861no—
542C2×C42—861no—
543C2×C42—861no—
544C4⋊C8—868no—
545#104—864no—
546#104—864no—
547#104—864no—
548#104—864no—
549#101—24no—
550#101—864no—
551#100—24no—
552#100—864no—
553C24—21no—
554C24—861no—
555C24#1062189811yescharacteristic
556#41—22no—
557#41—22no—
558#41—22no—
559#41—22no—
560#41—22no—
561#41—22no—
562#41—22no—
563#41—22no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—862no—
573#41—862no—
574#41—862no—
575#41—862no—
576#41—862no—
577#41—862no—
578#41—862no—
579#41—862no—
580#41—1721no—
581#41—1721no—
582#41—1721no—
583#41—1721no—
584#41—1721no—
585#41—1721no—
586#41—1721no—
587#41—1721no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—432no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×Q8C2×C22⋊D4312yes—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—432no—
612C2×D4—862no—
613C2×D4—862no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—861no—
618C2×D4—861no—
619C2×D4—1721no—
620C2×D4—1721no—
621C2×D4—1721no—
622C2×D4—1721no—
623C2×D4C2×C22⋊D4312yes—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—41no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—861no—
632C22×C4—862no—
633C22×C4—861no—
634C22×C4—861no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—1724no—
639C22×C4—1721no—
640C22×C4—1721no—
641C22×C4—1721no—
642C22×C4—1721no—
643C22×C4#1062189811yescharacteristic
644C22×C4#1062189811yescharacteristic
645C22×C4#1062189811yescharacteristic
646C22×C4D4×D4311yescharacteristic
647C22×C4D4×D4311yescharacteristic
648C22×C4D4×D4311yescharacteristic
649C22×C4D4×D4311yescharacteristic
650C22×C4D4×D4311yescharacteristic
651C22×C4D4×D4311yescharacteristic
652C22×C4#1062190011yescharacteristic
653C22×C4#1062190011yescharacteristic
654C22×C4C2×C22⋊D4311yescharacteristic
655C22×C4C2×C22⋊D4311yescharacteristic
656C22×C4C23×D4311yescharacteristic
657Q16—868no—
658SD16—868no—
659SD16—868no—
660D8—868no—
661M16—22no—
662M16—22no—
663M16—22no—
664M16—22no—
665M16—41no—
666M16—41no—
667M16—41no—
668M16—41no—
669M16—862no—
670M16—862no—
671M16—862no—
672M16—862no—
673M16—862no—
674M16—862no—
675M16—1721no—
676M16—1721no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—41no—
680C2×C8—41no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—434no—
684C2×C8—862no—
685C2×C8—862no—
686C2×C8—862no—
687C2×C8—1721no—
688C2×C8—1721no—
689C42—432no—
690C42—432no—
691C42—861no—
692C42—862no—
693C42—861no—
694C42—862no—
695C23—22no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—82no—
700C23—862no—
701C23—3442no—
702C23—1721no—
703C23—1721no—
704C23#1306329811yescharacteristic
705C23#1306329811yescharacteristic
706C23#1306330711yescharacteristic
707C23#1306330711yescharacteristic
708C23#1306330811yescharacteristic
709C23#1306330811yescharacteristic
710C23C2×#1062189811yescharacteristic
711Q8—22no—
712Q8—22no—
713Q8—41no—
714Q8—41no—
715Q8—862no—
716Q8—862no—
717Q8—1721no—
718Q8—1721no—
719D4—22no—
720D4—22no—
721D4—42no—
722D4—42no—
723D4—42no—
724D4—42no—
725D4—41no—
726D4—41no—
727D4—862no—
728D4—862no—
729D4—1722no—
730D4—1722no—
731D4—1722no—
732D4—1722no—
733D4—1721no—
734D4—1721no—
735C2×C4—22no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—864no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—1724no—
747C2×C4—1724no—
748C2×C4—1722no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1722no—
752C2×C4—1722no—
753C2×C4—1722no—
754C2×C4—1722no—
755C2×C4#1306329311yescharacteristic
756C2×C4#1306329311yescharacteristic
757C2×C4#1306329311yescharacteristic
758C2×C4#1306329311yescharacteristic
759C2×C4#1306329711yescharacteristic
760C2×C4#1306329711yescharacteristic
761C2×C4#1306329711yescharacteristic
762C2×C4#1306329711yescharacteristic
763C2×C4#1306329811yescharacteristic
764C2×C4#1306329811yescharacteristic
765C2×C4#1306329811yescharacteristic
766C2×C4#1306329811yescharacteristic
767C2×C4#1306329811yescharacteristic
768C2×C4#1306329811yescharacteristic
769C2×C4#1306330711yescharacteristic
770C2×C4#1306330711yescharacteristic
771C2×C4#1306330811yescharacteristic
772C2×C4#1306330811yescharacteristic
773C2×C4#1306331111yescharacteristic
774C2×C4#1306331111yescharacteristic
775C2×C4#1306331111yescharacteristic
776C2×C4#1306331111yescharacteristic
777C2×C4C2×D4×D4311yescharacteristic
778C2×C4C2×D4×D4311yescharacteristic
779C2×C4C2×D4×D4311yescharacteristic
780C2×C4C22×C22⋊D4311yescharacteristic
781C2×C4C2×#1062190011yescharacteristic
782C2×C4C2×#1062189811yescharacteristic
783C8—42no—
784C8—42no—
785C8—864no—
786C8—1722no—
787C22—22no—
788C22—22no—
789C22—22no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—42no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—3442no—
799C22—3442no—
800C22—3442no—
801C22—1722no—
802C22#1458281411yescharacteristic
803C22#1458281411yescharacteristic
804C22#1458281411yescharacteristic
805C22#1458281411yescharacteristic
806C22C2×#1306329811yescharacteristic
807C22C2×#1306330711yescharacteristic
808C22C2×#1306330811yescharacteristic
809C4—42no—
810C4—864no—
811C4—1722no—
812C4—1722no—
813C4#1458281411yescharacteristic
814C4#1458281411yescharacteristic
815C4#1458281411yescharacteristic
816C4#1458281411yescharacteristic
817C4C2×#1306329311yescharacteristic
818C4C2×#1306329711yescharacteristic
819C4C2×#1306329811yescharacteristic
820C4C2×#1306331111yescharacteristic
821C2—21no—
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—21no—
827C2—82no—
828C2—3442no—
829C2#1913588012yesdirect product factor
830C2C2×#1458281411yescharacteristic
subgroupG/H
centerC2×C4#13063311
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#413C2
socleC22×C43#394
prime radicalC2×#14583697C2
hypercenterC2×#413D43
hypocenterC43C2×#2050
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#14582922C2semidirect
3. C22×#13063252C2semidirect
4. C22×#13063251C2semidirect
5. C2×#14582881C2semidirect
6. #19135880C2direct (N × H)
7. C2×C43⋊#338C2semidirect
8. C2×C43×#413C2semidirect
23. #14582922C22semidirect
28. C2×#13063252C22semidirect
32. C2×#13063251C22semidirect
34. #14582881C22semidirect
37. C43⋊#338C22semidirect
42. C43×#413C22semidirect
411. C2×#413D43semidirect
421. C2×C43#2050semidirect
454. #413C2×D43semidirect
460. C43C2×#2050semidirect
829. C2#19135880direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836972
C2×#145829222
C22×#130632522
C22×#130632512
C2×#145828812
#191358802
C2×C43⋊#3382
C2×C43×#4132
C2×#205043