Finite Group Databasebeta

← C2×#19135010 #25098245

Subgroups — C2×#19135010 #25098245

Order 11008.

1870 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic, complemented
2C2×#14583410C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic, complemented
4C2×#14582863C211yesmaximal, characteristic, complemented
5#19135010C218yesmaximal, direct product factor
6C2×#14582671C211yesmaximal, characteristic, complemented
7C2×#14582670C211yesmaximal, characteristic, complemented
8C2×C43×#407C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10#14583665—22no—
11#14583665—22no—
12#14583665—22no—
13#14583665C2214yescomplemented
14C2×#13063333—22no—
15C2×#13063331—22no—
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C2×M16×D43—22no—
19#14583410—22no—
20#14583410—22no—
21#14583410C414yes—
22#14583410C2214yes—
23C2×#13063308C412yes—
24C2×#13063304—21no—
25C2×#13063299—21no—
26C2×#13063294C412yes—
27C2×C4×C22⋊D43—22no—
28C2×#13063284C2211yescharacteristic
29#14582881—22no—
30#14582881C2214yescomplemented
31C2×#13063243—21no—
32C2×#13063241—21no—
33#14582863—22no—
34#14582863C2214yescomplemented
35C2×C22⋊(C43⋊C8)—22no—
36#14582671C2214yescomplemented
37#14582670C2214yescomplemented
38C24×C4×C43C2211yescharacteristic
39C22×M16×C43C2211yescharacteristic
40C22×M16×C43C2211yescharacteristic
41C43×#407—22no—
42C43×#407C2214yescomplemented
43C2×C22⋊C8×C43—22no—
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×#10621898C2×C412yes—
53C2×#10621898D412yes—
54C2×#10621898D412yes—
55C2×#10621898C2312yes—
56C22×Dic86D411yescharacteristic
57C22×D172D411yescharacteristic
58C22×C22⋊D43—22no—
59C22×C22⋊D43C2×C412yes—
60C22×C4×D43D412yes—
61#13063333—28no—
62#13063333—28no—
63#13063331—28no—
64#13063331—28no—
65C2×#10621877—21no—
66C2×#10621877—21no—
67C2×#10621877—21no—
68C2×#10621877—21no—
69C2×#10621877—21no—
70C2×#10621877—21no—
71C2×#10621877—21no—
72C2×#10621877—21no—
73C2×#10621877—21no—
74C2×#10621877D412yescomplemented
75C2×#10621877C2312yes—
76C2×#10621877C2312yes—
77C2×#10621872—24no—
78M16×D43—28no—
79M16×D43—28no—
80C22×C43⋊C8—21no—
81C22×C43⋊C8D412yescomplemented
82C2×C8×D43—24no—
83#13063308—24no—
84#13063308C2×C418yes—
85#13063304—24no—
86#13063304—24no—
87#13063299—24no—
88#13063299—24no—
89#13063294—24no—
90#13063294C2×C418yes—
91C4×C22⋊D43—28no—
92C4×C22⋊D43—28no—
93#13063284—21no—
94#13063284—21no—
95#13063284C2×C412yes—
96#13063284C2312yes—
97C2×C4⋊Dic43—21no—
98C2×Dic43⋊C4—22no—
99C2×C22⋊Dic43—22no—
100C2×C22⋊Dic43C2×C412yes—
101C2×(C2×D43)⋊C4—22no—
102C2×C4×Dic43—21no—
103#13063243—24no—
104#13063241—24no—
105C22⋊(C43⋊C8)—28no—
106C25×C43C2×C411yescharacteristic
107C23×C4×C43—21no—
108C23×C4×C43—21no—
109C23×C4×C43—21no—
110C23×C4×C43—21no—
111C23×C4×C43—21no—
112C23×C4×C43—21no—
113C23×C4×C43—21no—
114C23×C4×C43—21no—
115C23×C4×C43—21no—
116C23×C4×C43—21no—
117C23×C4×C43—21no—
118C23×C4×C43—21no—
119C23×C4×C43C2×C411yescharacteristic
120C23×C4×C43C2×C412yes—
121C23×C4×C43C2312yes—
122C23×C4×C43C2311yescharacteristic
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×C43—21no—
132C2×M16×C43D412yescomplemented
133C2×M16×C43C2312yes—
134C2×M16×C43C2312yes—
135C22×C8×C43—21no—
136C22×C8×C43D412yescomplemented
137C22⋊C8×C43—28no—
138C24×C43—21no—
139C24×C43—21no—
140C24×C43—21no—
141C24×C43—21no—
142C24×C43—21no—
143C24×C43—21no—
144C24×C43—44no—
145C24×C43C22×C412yes—
146C24×C43C22×C411yescharacteristic
147C23×D43C22⋊C412yes—
148C22×C4×C43—22no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
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×C43—41no—
172C22×C4×C43—41no—
173C22×C4×C43—41no—
174C22×C4×C43—41no—
175C22×C4×C43—41no—
176C22×C4×C43—41no—
177C22×C4×C43—41no—
178C22×C4×C43—41no—
179C22×C4×C43—41no—
180C22×C4×C43—41no—
181C22×C4×C43—41no—
182C22×C4×C43C22×C412yes—
183C22×C4×C43C22×C411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43C2×D411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43#4111yescharacteristic
193C22×C4×C43#4111yescharacteristic
194C22×C4×C43#4111yescharacteristic
195C22×C4×C43#4111yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—22no—
198C2×C22⋊D43—22no—
199C2×C22⋊D43—22no—
200C2×C22⋊D43—22no—
201C2×C22⋊D43—28no—
202C2×C22⋊D43—48no—
203C2×C22⋊D43C22⋊C414yes—
204C2×C22⋊D43C22×C414yes—
205C22×Dic43—22no—
206C22×Dic43C22⋊C412yes—
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—22no—
216#10621898—22no—
217#10621898—22no—
218#10621898—22no—
219#10621898—22no—
220#10621898—22no—
221#10621898—22no—
222#10621898—22no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—21no—
226C2×D172—21no—
227C2×D172C22⋊C412yes—
228C2×D172C2×D412yes—
229C2×C4×D43—22no—
230C2×C4×D43—22no—
231C2×C4×D43—22no—
232C2×C4×D43—22no—
233C2×C4×D43C22⋊C414yes—
234C2×C4×D43C2×D414yes—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86C22⋊C412yes—
240C2×Dic86C2×D412yes—
241M16×C43—22no—
242M16×C43—22no—
243M16×C43—22no—
244M16×C43—22no—
245M16×C43—22no—
246M16×C43—22no—
247M16×C43—41no—
248M16×C43—41no—
249C2×C8×C43—22no—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43—41no—
253C2×C8×C43—41no—
254C2×C8×C43C2×D414yescomplemented
255C22⋊Dic43—28no—
256C22⋊Dic43—22no—
257C22⋊Dic43C22×C414yes—
258(C2×D43)⋊C4—28no—
259C4⋊Dic43—22no—
260C4⋊Dic43—22no—
261Dic43⋊C4—28no—
262C4×Dic43—22no—
263C4×Dic43—22no—
264#10621877—22no—
265#10621877—22no—
266#10621877—22no—
267#10621877—22no—
268#10621877—22no—
269#10621877—22no—
270#10621877—41no—
271#10621877—41no—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—22no—
274C2×C43⋊C8—22no—
275C2×C43⋊C8—41no—
276C2×C43⋊C8—41no—
277C2×C43⋊C8C2×D414yescomplemented
278#10621872—216no—
279C8×D43—216no—
280C23×C43—24no—
281C23×C43—24no—
282C23×C43—24no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—42no—
287C23×C43—44no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43—44no—
292C23×C43—44no—
293C23×C43—44no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43C2×C22⋊C411yescharacteristic
299C23×C43C2×C22⋊C411yescharacteristic
300C23×C43C4×D411yescharacteristic
301C23×C43C4×D411yescharacteristic
302C23×C43C4×D411yescharacteristic
303C23×C43C4×D411yescharacteristic
304C23×C43C23×C411yescharacteristic
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—44no—
308C22×D43C2×C22⋊C414yes—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43C2×C22⋊C411yescharacteristic
325C2×C4×C43C2×C22⋊C411yescharacteristic
326C2×C4×C43C4×D411yescharacteristic
327C2×C4×C43C4×D411yescharacteristic
328C2×C4×C43C4×D411yescharacteristic
329C2×C4×C43C4×D411yescharacteristic
330C2×C4×C43#12011yescharacteristic
331C2×C4×C43#12011yescharacteristic
332C2×C4×C43#12011yescharacteristic
333C2×C4×C43#12011yescharacteristic
334C2×C4×C43#12111yescharacteristic
335C2×C4×C43#12111yescharacteristic
336C2×C4×C43#12111yescharacteristic
337C2×C4×C43#12111yescharacteristic
338C2×C4×C43#12111yescharacteristic
339C2×C4×C43#12111yescharacteristic
340C2×C4×C43#12111yescharacteristic
341C2×C4×C43#12111yescharacteristic
342C2×C4×C43#12311yescharacteristic
343C2×C4×C43#12311yescharacteristic
344C2×C4×C43#12311yescharacteristic
345C2×C4×C43#12311yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C22×D411yescharacteristic
350C2×C4×C43C2×#4111yescharacteristic
351C2×C4×C43C2×#4111yescharacteristic
352C22⋊D43—24no—
353C22⋊D43—24no—
354C22⋊D43—24no—
355C22⋊D43—24no—
356C22⋊D43—416no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—24no—
360C2×Dic43—44no—
361C2×Dic43C2×C22⋊C414yes—
362D172—22no—
363D172—22no—
364D172—22no—
365D172—22no—
366C4×D43—24no—
367C4×D43—24no—
368C4×D43—24no—
369C4×D43—24no—
370Dic86—22no—
371Dic86—22no—
372Dic86—22no—
373Dic86—22no—
374C8×C43—24no—
375C8×C43—42no—
376C43⋊C8—24no—
377C43⋊C8—42no—
378C2×#1891—431nomaximal, Sylow
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—24no—
383C22×C43—24no—
384C22×C43—24no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—42no—
390C22×C43—44no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43—44no—
394C22×C43—44no—
395C22×C43—44no—
396C22×C43—42no—
397C22×C43#38611yescharacteristic
398C22×C43#38611yescharacteristic
399C22×C43#38611yescharacteristic
400C22×C43#38611yescharacteristic
401C22×C43C22×C22⋊C411yescharacteristic
402C22×C43C2×C4×D411yescharacteristic
403C22×C43C2×C4×D411yescharacteristic
404C2×D43—24no—
405C2×D43—44no—
406C2×D43—44no—
407C2×D43—82no—
408C4×C43—42no—
409C4×C43#38611yescharacteristic
410C4×C43#38611yescharacteristic
411C4×C43#38611yescharacteristic
412C4×C43#38611yescharacteristic
413C4×C43C2×#12011yescharacteristic
414C4×C43C2×#12111yescharacteristic
415C4×C43C2×#12111yescharacteristic
416C4×C43C2×#12311yescharacteristic
417Dic43—24no—
418Dic43—44no—
419C2×#568—431no—
420C2×#525—431no—
421C2×#413—431no—
422C2×#407—431no—
423C2×#407D4311yescharacteristic, complemented
424#1891—438no—
425C2×#344—431no—
426C2×#344—431no—
427C2×C43—21no—
428C2×C43—21no—
429C2×C43—21no—
430C2×C43—21no—
431C2×C43—21no—
432C2×C43—21no—
433C2×C43—44no—
434C2×C43#189112yescomplemented
435C2×C43C2×#38611yescharacteristic
436D43—44no—
437C22×#41—431no—
438C24×C4C2×D4311yescharacteristic
439#568—434no—
440#568—862no—
441#568—862no—
442#568—862no—
443C2×#131—862no—
444C2×#131—862no—
445C22×M16—431no—
446C22×M16—431no—
447C22×M16—862no—
448C22×M16C2×D4311yescharacteristic
449C22×M16C2×D4311yescharacteristic
450#525—434no—
451#525—434no—
452#525—862no—
453#525—862no—
454C2×#123—432no—
455C2×C22⋊Q8—861no—
456C2×#121—861no—
457C2×#120—432no—
458C2×C4×D4—862no—
459C2×#117—431no—
460#413—434no—
461#413—862no—
462C2×#101—861no—
463C2×#100—861no—
464#407—22no—
465#407—434no—
466#407—862no—
467#407C2×D4314yescomplemented
468C2×C22⋊C8—22no—
469C2×C22⋊C8—862no—
470#344—434no—
471#344—434no—
472C43C2×#189111yescharacteristic, complemented, Sylow
473C25C4×D4311yescharacteristic
474C2×#41—432no—
475C2×#41—432no—
476C2×#41—432no—
477C2×#41—432no—
478C2×#41—861no—
479C2×#41—861no—
480C2×#41—861no—
481C2×#41—861no—
482C2×#41—861no—
483C2×#41—861no—
484C2×#41—861no—
485C2×#41—861no—
486C22×Q8—431no—
487C22×D4—432no—
488C22×D4—431no—
489C22×D4—862no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—432no—
503C23×C4C4×D4311yescharacteristic
504C23×C4C4×D4312yes—
505C23×C4C22×D4312yes—
506C23×C4C22×D4311yescharacteristic
507#131—868no—
508#131—868no—
509#131—868no—
510#131—868no—
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—21no—
520C2×M16—432no—
521C2×M16—432no—
522C2×M16—432no—
523C2×M16—864no—
524C2×M16—868no—
525C2×M16—868no—
526C2×M16—861no—
527C2×M16—861no—
528C2×M16—861no—
529C2×M16—861no—
530C2×M16—861no—
531C2×M16—861no—
532C2×M16—861no—
533C2×M16—861no—
534C2×M16—861no—
535C2×M16C22⋊D4312yescomplemented
536C2×M16C22×D4312yes—
537C2×M16C22×D4312yes—
538C22×C8—21no—
539C22×C8—432no—
540C22×C8—864no—
541C22×C8—861no—
542C22×C8C22⋊D4312yescomplemented
543#123—438no—
544#123—864no—
545C22⋊Q8—864no—
546C22⋊Q8—864no—
547#121—864no—
548#121—864no—
549#120—438no—
550#120—864no—
551C4×D4—868no—
552C4×D4—868no—
553#117—432no—
554#117—432no—
555#117—861no—
556#117—861no—
557C2×C4⋊C4—862no—
558C2×C4⋊C4—861no—
559C2×C22⋊C4—432no—
560C2×C22⋊C4—862no—
561C2×C22⋊C4—862no—
562C2×C42—861no—
563#101—864no—
564#100—864no—
565C22⋊C8—28no—
566C22⋊C8—868no—
567C24—21no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—21no—
572C24—21no—
573C24—44no—
574C24—432no—
575C24C2×C4×D4312yes—
576C24C2×C4×D4311yescharacteristic
577#41—862no—
578#41—862no—
579#41—862no—
580#41—862no—
581#41—862no—
582#41—862no—
583#41—862no—
584#41—862no—
585#41—862no—
586#41—862no—
587#41—862no—
588#41—862no—
589#41—862no—
590#41—862no—
591#41—862no—
592#41—862no—
593C2×Q8—432no—
594C2×Q8—432no—
595C2×Q8—861no—
596C2×Q8—861no—
597C2×Q8—861no—
598C2×Q8—861no—
599C2×D4—434no—
600C2×D4—434no—
601C2×D4—432no—
602C2×D4—432no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—868no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—1728no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—41no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—432no—
648C22×C4—434no—
649C22×C4—434no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4C2×C4×D4312yes—
656C22×C4C2×C4×D4311yescharacteristic
657C22×C4#1062189811yescharacteristic
658C22×C4#1062189811yescharacteristic
659C22×C4D4×D4311yescharacteristic
660C22×C4D4×D4311yescharacteristic
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663C22×C4D4×D4311yescharacteristic
664C22×C4D4×D4311yescharacteristic
665C22×C4#1062190011yescharacteristic
666C22×C4#1062190011yescharacteristic
667C22×C4C2×C22⋊D4311yescharacteristic
668C22×C4C2×C22⋊D4311yescharacteristic
669C22×C4C23×D4311yescharacteristic
670M16—22no—
671M16—22no—
672M16—22no—
673M16—22no—
674M16—22no—
675M16—22no—
676M16—41no—
677M16—41no—
678M16—8616no—
679M16—862no—
680M16—862no—
681M16—862no—
682M16—862no—
683M16—862no—
684M16—862no—
685M16—1721no—
686M16—1721no—
687C2×C8—22no—
688C2×C8—22no—
689C2×C8—22no—
690C2×C8—41no—
691C2×C8—41no—
692C2×C8—434no—
693C2×C8—8616no—
694C2×C8—862no—
695C2×C8—862no—
696C2×C8—862no—
697C2×C8—1721no—
698C2×C8—1721no—
699C2×C8C2×C22⋊D4314yescomplemented
700C4⋊C4—868no—
701C4⋊C4—862no—
702C4⋊C4—862no—
703C22⋊C4—434no—
704C22⋊C4—868no—
705C22⋊C4—868no—
706C22⋊C4—862no—
707C42—862no—
708C42—862no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—42no—
716C23—44no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—434no—
728C23—862no—
729C23—862no—
730C23—1724no—
731C23C22⋊C4×D4311yescharacteristic
732C23C22⋊C4×D4311yescharacteristic
733C23(C22⋊D43)⋊C411yescharacteristic
734C23(C22⋊D43)⋊C411yescharacteristic
735C23C4×C22⋊D4311yescharacteristic
736C23C4×C22⋊D4311yescharacteristic
737C23C22×C4×D4311yescharacteristic
738Q8—862no—
739Q8—862no—
740Q8—862no—
741Q8—862no—
742D4—864no—
743D4—864no—
744D4—864no—
745D4—864no—
746D4—862no—
747D4—862no—
748D4—862no—
749D4—862no—
750D4—17216no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—434no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—864no—
770C2×C4—864no—
771C2×C4—864no—
772C2×C4—864no—
773C2×C4—864no—
774C2×C4—1724no—
775C2×C4C22⋊C4×D4311yescharacteristic
776C2×C4C22⋊C4×D4311yescharacteristic
777C2×C4(C22⋊D43)⋊C411yescharacteristic
778C2×C4(C22⋊D43)⋊C411yescharacteristic
779C2×C4C4×C22⋊D4311yescharacteristic
780C2×C4C4×C22⋊D4311yescharacteristic
781C2×C4#1306329311yescharacteristic
782C2×C4#1306329311yescharacteristic
783C2×C4#1306329311yescharacteristic
784C2×C4#1306329311yescharacteristic
785C2×C4#1306329611yescharacteristic
786C2×C4#1306329611yescharacteristic
787C2×C4#1306329611yescharacteristic
788C2×C4#1306329611yescharacteristic
789C2×C4#1306329811yescharacteristic
790C2×C4#1306329811yescharacteristic
791C2×C4#1306329811yescharacteristic
792C2×C4#1306329811yescharacteristic
793C2×C4#1306330711yescharacteristic
794C2×C4#1306330711yescharacteristic
795C2×C4#1306330711yescharacteristic
796C2×C4#1306330711yescharacteristic
797C2×C4C2×D4×D4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C2×C4C2×D4×D4311yescharacteristic
800C2×C4C22×C22⋊D4311yescharacteristic
801C2×C4C2×#1062190011yescharacteristic
802C2×C4C2×#1062189811yescharacteristic
803C8—24no—
804C8—42no—
805C8—864no—
806C8—1722no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—42no—
825C22—864no—
826C22—3442no—
827C22—1724no—
828C22—1724no—
829C22#1458277511yescharacteristic
830C22#1458277511yescharacteristic
831C22#1458277511yescharacteristic
832C22#1458277511yescharacteristic
833C22C2×C22⋊C4×D4311yescharacteristic
834C22C2×(C22⋊D43)⋊C411yescharacteristic
835C22C2×C4×C22⋊D4311yescharacteristic
836C4—42no—
837C4—864no—
838C4—1724no—
839C4#1458277511yescharacteristic
840C4#1458277511yescharacteristic
841C4#1458277511yescharacteristic
842C4#1458277511yescharacteristic
843C4C2×#1306329311yescharacteristic
844C4C2×#1306329611yescharacteristic
845C4C2×#1306329811yescharacteristic
846C4C2×#1306330711yescharacteristic
847C2—21no—
848C2—21no—
849C2—21no—
850C2—21no—
851C2—21no—
852C2—21no—
853C2—44no—
854C2—1724no—
855C2#1913501012yesdirect product factor
856C2C2×#1458277511yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#407C2
socleC22×C43#386
prime radicalC2×#14583410C2
cosocleC22×C4×C43C24
hypercenterC2×#407D43
hypocenterC43C2×#1891
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14582881C2semidirect
4. C2×#14582863C2semidirect
5. #19135010C2direct (N × H)
6. C2×#14582671C2semidirect
7. C2×#14582670C2semidirect
8. C2×C43×#407C2semidirect
13. #14583665C22semidirect
30. #14582881C22semidirect
34. #14582863C22semidirect
36. #14582671C22semidirect
37. #14582670C22semidirect
42. C43×#407C22semidirect
74. C2×#10621877D4semidirect
81. C22×C43⋊C8D4semidirect
132. C2×M16×C43D4semidirect
136. C22×C8×C43D4semidirect
254. C2×C8×C43C2×D4semidirect
277. C2×C43⋊C8C2×D4semidirect
423. C2×#407D43semidirect
434. C2×C43#1891semidirect
467. #407C2×D43semidirect
472. C43C2×#1891semidirect
535. C2×M16C22⋊D43semidirect
542. C22×C8C22⋊D43semidirect
699. C2×C8C2×C22⋊D43semidirect
855. C2#19135010direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836652
C2×#145834102
C2×#145828812
C2×#145828632
#191350102
C2×#145826712
C2×#145826702
C2×C43×#4072
C2×#189143