Finite Group Databasebeta

← #25003180

Subgroups — #25003180

Order 11008.

1334 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×#14583477C211yesmaximal, characteristic
2C2×#14582916C211yesmaximal, characteristic, complemented
3C2×#14582881C211yesmaximal, characteristic, complemented
4C2×#14582872C211yesmaximal, characteristic, complemented
5#19134316C211yesmaximal, characteristic, complemented
6#19134315C211yesmaximal, characteristic, complemented
7C2×C43×#421C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10#14583477—22no—
11#14583477—22no—
12#14583477—22no—
13#14583477—22no—
14C2×#13063304—21no—
15C2×#13063301C412yescomplemented
16C2×#13063299—21no—
17C2×#13063297—22no—
18C2×#13063296C412yescomplemented
19C2×#13063284C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21#14582916—22no—
22#14582916—22no—
23C2×#13063252—22no—
24#14582881—22no—
25#14582881—22no—
26C2×#13063243—21no—
27C2×#13063241—21no—
28#14582872—22no—
29#14582872—22no—
30C2×#13063239—22no—
31#14582662—22no—
32#14582661—22no—
33C22×#41×C43C2211yescharacteristic
34C22×M16×C43C2211yescharacteristic
35C2×#117×C43C2211yescharacteristic
36C43×#421—22no—
37C43×#421—22no—
38C2×#104×C43—22no—
39C2×#10621898—21no—
40C2×#10621898—21no—
41C2×#10621898—21no—
42C2×#10621898—21no—
43C2×#10621898—21no—
44C2×#10621898—21no—
45C2×#10621898—21no—
46C2×#10621898—21no—
47C2×#10621898—21no—
48C2×#10621898—21no—
49C2×#10621898—21no—
50C2×#10621898—21no—
51C22×Dic86D411yescharacteristic
52C22×D172D411yescharacteristic
53C22×C22⋊D43—22no—
54C22×C22⋊D43D412yes—
55C23×Dic43—21no—
56C22×C4×D43C2×C412yes—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877—21no—
61C2×#10621877—21no—
62C2×#10621877D412yescomplemented
63C22×C43⋊C8—21no—
64#13063304—24no—
65#13063304—24no—
66#13063301—24no—
67#13063301—24no—
68#13063299—24no—
69#13063299—24no—
70#13063297—28no—
71#13063297—28no—
72#13063296—24no—
73#13063296—24no—
74#13063284—21no—
75#13063284—21no—
76#13063284—21no—
77#13063284D412yescomplemented
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43C2×C412yes—
83C2×C4⋊Dic43D412yes—
84C2×C4⋊Dic43D412yes—
85C2×Dic43⋊C4—22no—
86C2×C22⋊Dic43—22no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—22no—
89C2×C4×Dic43—21no—
90#13063252—28no—
91#13063243—24no—
92#13063241—24no—
93#13063239—28no—
94C2×#41×C43—21no—
95C2×#41×C43—21no—
96C2×#41×C43—21no—
97C2×#41×C43—21no—
98C2×#41×C43—21no—
99C2×#41×C43—21no—
100C2×#41×C43—21no—
101C2×#41×C43—21no—
102C2×#41×C43—21no—
103C2×#41×C43—21no—
104C2×#41×C43D412yes—
105C2×#41×C43D412yes—
106C22×Q8×C43C2×C411yescharacteristic
107C22×D4×C43—21no—
108C22×D4×C43C2×C411yescharacteristic
109C23×C4×C43—21no—
110C23×C4×C43C2311yescharacteristic
111C2×M16×C43—21no—
112C2×M16×C43—21no—
113C2×M16×C43—21no—
114C2×M16×C43—21no—
115C2×M16×C43—21no—
116C2×M16×C43D412yescomplemented
117C22×C8×C43—21no—
118#117×C43—21no—
119#117×C43—21no—
120#117×C43—21no—
121#117×C43D412yescomplemented
122C2×C4⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43—21no—
125#104×C43—28no—
126C24×C43—21no—
127C24×C43C2×D411yescharacteristic
128C23×D43C22⋊C412yes—
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—22no—
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—
144#41×C43—41no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43C22⋊C412yes—
151C2×D4×C43—21no—
152C2×D4×C43—22no—
153C2×D4×C43—22no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—41no—
159C2×D4×C43—41no—
160C2×D4×C43—41no—
161C2×D4×C43—41no—
162C2×D4×C43C22⋊C412yes—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—21no—
166C22×C4×C43—41no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170C22×C4×C43—41no—
171C22×C4×C43C22×C411yescharacteristic
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×C43C2×D411yescharacteristic
181C22×C4×C43#4111yescharacteristic
182C22×C4×C43#4111yescharacteristic
183C22×C4×C43#4111yescharacteristic
184C22×C4×C43#4111yescharacteristic
185C2×C22⋊D43—28no—
186C2×C22⋊D43—22no—
187C2×C22⋊D43—22no—
188C2×C22⋊D43—22no—
189C2×C22⋊D43—22no—
190C2×C22⋊D43—22no—
191C2×C22⋊D43—22no—
192C2×C22⋊D43—84no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—41no—
197C22×Dic43—82no—
198C22×Dic43C22⋊C412yes—
199#10621898—41no—
200#10621898—41no—
201#10621898—41no—
202#10621898—41no—
203#10621898—41no—
204#10621898—41no—
205#10621898—41no—
206#10621898—41no—
207#10621898—41no—
208#10621898—41no—
209#10621898—41no—
210#10621898—41no—
211#10621898—41no—
212#10621898—41no—
213#10621898—41no—
214#10621898—41no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172—21no—
221C2×C4×D43—22no—
222C2×C4×D43—22no—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—22no—
226C2×C4×D43—22no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233M16×C43—22no—
234M16×C43—22no—
235M16×C43—41no—
236M16×C43—41no—
237C2×C8×C43—22no—
238C2×C8×C43—41no—
239C2×C8×C43—41no—
240C4⋊C4×C43—22no—
241C4⋊C4×C43—41no—
242C22⋊C4×C43—22no—
243C22⋊C4×C43—41no—
244C42×C43—22no—
245C42×C43—41no—
246C22⋊Dic43—28no—
247C22⋊Dic43—22no—
248C22⋊Dic43—41no—
249(C2×D43)⋊C4—28no—
250C4⋊Dic43—22no—
251C4⋊Dic43—22no—
252C4⋊Dic43—22no—
253C4⋊Dic43—22no—
254C4⋊Dic43—41no—
255C4⋊Dic43C22⋊C414yes—
256Dic43⋊C4—28no—
257C4×Dic43—22no—
258C4×Dic43—41no—
259#10621877—22no—
260#10621877—22no—
261#10621877—41no—
262#10621877—41no—
263C2×C43⋊C8—22no—
264C2×C43⋊C8—41no—
265C2×C43⋊C8—41no—
266C23×C43—22no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—42no—
270C23×C43—42no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43C2×C22⋊C411yescharacteristic
274C23×C43#12011yescharacteristic
275C23×C43#12011yescharacteristic
276C23×C43#12011yescharacteristic
277C23×C43#12111yescharacteristic
278C23×C43#12111yescharacteristic
279C23×C43#12311yescharacteristic
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—42no—
284C22×D43—42no—
285Q8×C43—22no—
286Q8×C43—22no—
287Q8×C43—41no—
288Q8×C43—41no—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—42no—
292D4×C43—42no—
293D4×C43—42no—
294D4×C43—42no—
295D4×C43—41no—
296D4×C43—41no—
297C2×C4×C43—22no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
300C2×C4×C43—42no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—81no—
306C2×C4×C43—81no—
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#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#12411yescharacteristic
332C2×C4×C43#12411yescharacteristic
333C2×C4×C43#12711yescharacteristic
334C2×C4×C43#12711yescharacteristic
335C22⋊D43—42no—
336C22⋊D43—42no—
337C22⋊D43—42no—
338C22⋊D43—42no—
339C22⋊D43—88no—
340C2×Dic43—22no—
341C2×Dic43—24no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—44no—
345C2×Dic43—42no—
346C2×Dic43—82no—
347C2×Dic43—82no—
348C2×Dic43—81no—
349C2×Dic43—81no—
350D172—41no—
351D172—41no—
352D172—41no—
353D172—41no—
354C4×D43—42no—
355C4×D43—42no—
356C4×D43—42no—
357C4×D43—42no—
358Dic86—41no—
359Dic86—41no—
360Dic86—41no—
361Dic86—41no—
362C8×C43—42no—
363C43⋊C8—42no—
364#10986—431nomaximal, Sylow
365C22×C43—21no—
366C22×C43—21no—
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—21no—
370C22×C43—21no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—82no—
379C22×C43—82no—
380C22×C43#37911yescharacteristic
381C22×C43#38611yescharacteristic
382C22×C43#38611yescharacteristic
383C22×C43#39211yescharacteristic
384C22×C43#39211yescharacteristic
385C22×C43#39411yescharacteristic
386C22×C43#39411yescharacteristic
387C2×D43—42no—
388C2×D43—42no—
389C2×D43—42no—
390C2×D43—82no—
391C2×D43—82no—
392C4×C43—42no—
393C4×C43—82no—
394C4×C43#38611yescharacteristic
395C4×C43#38611yescharacteristic
396C4×C43#39011yescharacteristic
397C4×C43#39011yescharacteristic
398C4×C43#39211yescharacteristic
399C4×C43#39211yescharacteristic
400C4×C43#39411yescharacteristic
401C4×C43#39411yescharacteristic
402Dic43—44no—
403Dic43—42no—
404Dic43—82no—
405C2×#537—431no—
406C2×#421—431no—
407C2×#421D4311yescharacteristic, complemented
408C2×#413—431no—
409C2×#410—431no—
410#1736—431no—
411#1736—431no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43—21no—
417C2×C43—21no—
418C2×C43—82no—
419C2×C43#143811yescharacteristic
420C2×C43#179511yescharacteristic
421C2×C43#179611yescharacteristic
422D43—82no—
423C22×#41—431no—
424C22×#41C2×D4311yescharacteristic
425C22×M16—431no—
426C22×M16C2×D4311yescharacteristic
427#537—862no—
428#537—862no—
429#537—862no—
430#537—862no—
431C2×C22⋊Q8—432no—
432C2×C22⋊Q8—861no—
433C2×#121—432no—
434C2×#121—861no—
435C2×#121—862no—
436C2×#117—431no—
437C2×#117C2×D4311yescharacteristic
438C22×C4⋊C4—431no—
439#421—22no—
440#421—22no—
441#421—862no—
442#421—862no—
443C2×#104—22no—
444C2×#104—862no—
445#413—862no—
446#413—862no—
447C2×#101—861no—
448C2×#100—861no—
449#410—862no—
450#410—862no—
451C2×#99—862no—
452#340—862no—
453#340—862no—
454C43#1098611yescharacteristic, complemented, Sylow
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—861no—
466C2×#41—861no—
467C2×#41—861no—
468C2×#41—861no—
469C2×#41—861no—
470C2×#41—861no—
471C2×#41—861no—
472C2×#41—861no—
473C2×#41—861no—
474C2×#41—861no—
475C2×#41—861no—
476C2×#41—861no—
477C2×#41D17212yes—
478C2×#41C22⋊D4312yes—
479C22×Q8—431no—
480C22×Q8C4×D4311yescharacteristic
481C22×D4—21no—
482C22×D4—432no—
483C22×D4—431no—
484C22×D4—862no—
485C22×D4C4×D4311yescharacteristic
486C23×C4—21no—
487C23×C4—432no—
488C23×C4—861no—
489C23×C4C22×D4311yescharacteristic
490C2×M16—21no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—432no—
496C2×M16—861no—
497C2×M16—861no—
498C2×M16—861no—
499C2×M16—861no—
500C2×M16—861no—
501C2×M16C22⋊D4312yescomplemented
502C22×C8—21no—
503C22×C8—861no—
504C22⋊Q8—864no—
505C22⋊Q8—864no—
506C22⋊Q8—864no—
507C22⋊Q8—864no—
508#121—864no—
509#121—864no—
510#121—864no—
511#121—868no—
512#121—868no—
513#121—864no—
514#117—21no—
515#117—21no—
516#117—21no—
517#117—432no—
518#117—861no—
519#117—861no—
520#117—861no—
521#117C22⋊D4312yescomplemented
522C2×C4⋊C4—21no—
523C2×C4⋊C4—432no—
524C2×C4⋊C4—432no—
525C2×C4⋊C4—432no—
526C2×C4⋊C4—862no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—862no—
533C2×C22⋊C4—862no—
534C2×C22⋊C4—861no—
535C2×C42—21no—
536C2×C42—861no—
537#104—28no—
538#104—868no—
539#101—864no—
540#100—864no—
541#99—868no—
542C24—21no—
543C24—432no—
544C24D4×D4311yescharacteristic
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561#41—1721no—
562#41—1721no—
563#41—1721no—
564#41—1721no—
565#41—1721no—
566#41—1721no—
567#41—1721no—
568#41—1721no—
569#41—1721no—
570#41—1721no—
571#41—1721no—
572#41—1721no—
573#41—1721no—
574#41—1721no—
575#41—1721no—
576#41—1721no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—861no—
583C2×Q8—861no—
584C2×Q8—861no—
585C2×Q8—861no—
586C2×Q8—861no—
587C2×Q8—861no—
588C2×Q8(C2×D43)⋊C412yes—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—41no—
597C2×D4—41no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—868no—
601C2×D4—862no—
602C2×D4—862no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—861no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—3444no—
614C2×D4(C2×D43)⋊C412yes—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—41no—
622C22×C4—41no—
623C22×C4—432no—
624C22×C4—862no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—3442no—
634C22×C4—1721no—
635C22×C4C2×C4×D4311yescharacteristic
636C22×C4C2×D17211yescharacteristic
637C22×C4#1062189811yescharacteristic
638C22×C4#1062189811yescharacteristic
639C22×C4D4×D4311yescharacteristic
640C22×C4D4×D4311yescharacteristic
641C22×C4D4×D4311yescharacteristic
642C22×C4D4×D4311yescharacteristic
643C22×C4D4×D4311yescharacteristic
644C22×C4#1062190011yescharacteristic
645C22×C4#1062190011yescharacteristic
646C22×C4C2×C22⋊D4311yescharacteristic
647C22×C4C2×C22⋊D4311yescharacteristic
648C22×C4C2×C22⋊D4311yescharacteristic
649M16—22no—
650M16—22no—
651M16—41no—
652M16—41no—
653M16—862no—
654M16—862no—
655M16—1721no—
656M16—1721no—
657C2×C8—22no—
658C2×C8—41no—
659C2×C8—41no—
660C2×C8—862no—
661C2×C8—1721no—
662C2×C8—1721no—
663C4⋊C4—22no—
664C4⋊C4—41no—
665C4⋊C4—434no—
666C4⋊C4—868no—
667C4⋊C4—862no—
668C4⋊C4—862no—
669C4⋊C4—862no—
670C4⋊C4—862no—
671C4⋊C4—1721no—
672C22⋊C4—22no—
673C22⋊C4—41no—
674C22⋊C4—868no—
675C22⋊C4—868no—
676C22⋊C4—862no—
677C22⋊C4—1721no—
678C42—22no—
679C42—41no—
680C42—862no—
681C42—1721no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—42no—
686C23—42no—
687C23—41no—
688C23—41no—
689C23—862no—
690C23—862no—
691C23—862no—
692C23—1722no—
693C23—1722no—
694C23C22⋊C4×D4311yescharacteristic
695C23#1306329311yescharacteristic
696C23#1306329311yescharacteristic
697C23#1306329511yescharacteristic
698C23#1306329611yescharacteristic
699C23#1306329811yescharacteristic
700C23#1306330711yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—41no—
704Q8—41no—
705Q8—1721no—
706Q8—1721no—
707Q8—1721no—
708Q8—1721no—
709D4—22no—
710D4—22no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—42no—
715D4—41no—
716D4—41no—
717D4—3448no—
718D4—1722no—
719D4—1722no—
720D4—1722no—
721D4—1722no—
722D4—1721no—
723D4—1721no—
724D4—1721no—
725D4—1721no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—864no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—3441no—
741C2×C4—3441no—
742C2×C4—3442no—
743C2×C4—3442no—
744C2×C4—1722no—
745C2×C4—1724no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4—1722no—
750C2×C4C22⋊C4×D4311yescharacteristic
751C2×C4C2×(C2×D43)⋊C411yescharacteristic
752C2×C4(C22⋊D43)⋊C411yescharacteristic
753C2×C4(C22⋊D43)⋊C411yescharacteristic
754C2×C4C4×C22⋊D4311yescharacteristic
755C2×C4C4×C22⋊D4311yescharacteristic
756C2×C4#1306329311yescharacteristic
757C2×C4#1306329311yescharacteristic
758C2×C4#1306329411yescharacteristic
759C2×C4#1306329511yescharacteristic
760C2×C4#1306329511yescharacteristic
761C2×C4#1306329611yescharacteristic
762C2×C4#1306329711yescharacteristic
763C2×C4#1306329711yescharacteristic
764C2×C4#1306329711yescharacteristic
765C2×C4#1306329711yescharacteristic
766C2×C4#1306329811yescharacteristic
767C2×C4#1306329811yescharacteristic
768C2×C4#1306329811yescharacteristic
769C2×C4#1306329911yescharacteristic
770C2×C4#1306329911yescharacteristic
771C2×C4#1306330711yescharacteristic
772C2×C4#1306330811yescharacteristic
773C2×C4#1306330911yescharacteristic
774C2×C4#1306331111yescharacteristic
775C2×C4#1306331111yescharacteristic
776C2×C4#1306332111yescharacteristic
777C2×C4#1306332111yescharacteristic
778C8—42no—
779C8—1722no—
780C22—21no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—82no—
794C22—82no—
795C22—3442no—
796C22—3442no—
797C22—1722no—
798C22—1722no—
799C22—1722no—
800C22#1458275411yescharacteristic
801C22#1458277511yescharacteristic
802C22#1458277511yescharacteristic
803C22#1458280711yescharacteristic
804C22#1458280811yescharacteristic
805C22#1458281411yescharacteristic
806C22#1458281511yescharacteristic
807C4—42no—
808C4—82no—
809C4—3442no—
810C4—1724no—
811C4—1722no—
812C4#1458277611yescharacteristic
813C4#1458277811yescharacteristic
814C4#1458279911yescharacteristic
815C4#1458279911yescharacteristic
816C4#1458280711yescharacteristic
817C4#1458280811yescharacteristic
818C4#1458281411yescharacteristic
819C4#1458281511yescharacteristic
820C2—21no—
821C2—21no—
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—82no—
827C2—3442no—
828C2#1913283411yescharacteristic
829C2#1913456411yescharacteristic
830C2#1913456911yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#421C2
socleC22×C43#379
prime radicalC2×#14583477C2
cosocleC23×C4×C43C23
hypercenterC2×#421D43
hypocenterC43#10986
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. C2×#14582881C2semidirect
4. C2×#14582872C2semidirect
5. #19134316C2semidirect
6. #19134315C2semidirect
7. C2×C43×#421C2semidirect
15. C2×#13063301C4semidirect
18. C2×#13063296C4semidirect
62. C2×#10621877D4semidirect
77. #13063284D4semidirect
116. C2×M16×C43D4semidirect
121. #117×C43D4semidirect
407. C2×#421D43semidirect
454. C43#10986semidirect
501. C2×M16C22⋊D43semidirect
521. #117C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834772
C2×#145829162
C2×#145828812
C2×#145828722
#191343162
#191343152
C2×C43×#4212
#1098643