Finite Group Databasebeta

← C2×#19135012 #25098247

Subgroups — C2×#19135012 #25098247

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×#14583411C211yesmaximal, characteristic
3C2×#14582881C211yesmaximal, characteristic, complemented
4C2×#14582862C211yesmaximal, characteristic, complemented
5C2×#14582862C211yesmaximal, characteristic, complemented
6#19135012C218yesmaximal, direct product factor
7C2×#14582669C211yesmaximal, characteristic, complemented
8C2×C43×#344C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C23×C4×D43C2211yescharacteristic
11#14583665—22no—
12#14583665—22no—
13#14583665—22no—
14#14583665C2214yescomplemented
15C2×#13063333—22no—
16C2×#13063331—22no—
17C22×#10621877C2211yescharacteristic
18C22×#10621877C2211yescharacteristic
19C2×M16×D43—22no—
20#14583411—22no—
21#14583411—22no—
22#14583411C414yes—
23#14583411C2214yes—
24C2×#13063309C412yes—
25C2×#13063305—21no—
26C2×#13063300—21no—
27C2×#13063295C412yes—
28C2×C4×D172—22no—
29#14582881—22no—
30#14582881C2214yescomplemented
31C2×#13063243—21no—
32C2×#13063241—21no—
33#14582862—22no—
34#14582862—22no—
35#14582862C2214yescomplemented
36#14582862C2214yescomplemented
37C2×(C2×D43)⋊C8—22no—
38C2×(C2×D43)⋊C8—22no—
39#14582669C2214yescomplemented
40C22×M16×C43C2211yescharacteristic
41C22×M16×C43C2211yescharacteristic
42C2×#117×C43C2211yescharacteristic
43C43×#344C2214yescomplemented
44C24×D43C2×C411yescharacteristic
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×#10621898C2×C412yes—
54C2×#10621898D412yes—
55C2×#10621898D412yes—
56C2×#10621898C2312yes—
57C22×Dic86D411yescharacteristic
58C22×D172—22no—
59C22×D172D411yescharacteristic
60C22×C22⋊D43C2×C412yes—
61C23×Dic43C2×C411yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43—21no—
64C22×C4×D43—21no—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C22×C4×D43—21no—
69C22×C4×D43—21no—
70C22×C4×D43—21no—
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43C2×C412yes—
75C22×C4×D43D412yes—
76C22×C4×D43C2312yes—
77#13063333—28no—
78#13063333—28no—
79#13063331—28no—
80#13063331—28no—
81C2×#10621877—21no—
82C2×#10621877—21no—
83C2×#10621877—21no—
84C2×#10621877—21no—
85C2×#10621877—21no—
86C2×#10621877—21no—
87C2×#10621877—21no—
88C2×#10621877—21no—
89C2×#10621877—21no—
90C2×#10621877D412yescomplemented
91C2×#10621877C2312yes—
92C2×#10621877C2312yes—
93C2×#10621872—24no—
94M16×D43—28no—
95M16×D43—28no—
96C22×C43⋊C8—21no—
97C22×C43⋊C8D412yescomplemented
98C2×C8×D43—24no—
99#13063309—24no—
100#13063309C2×C418yes—
101#13063305—24no—
102#13063305—24no—
103#13063300—24no—
104#13063300—24no—
105#13063295—24no—
106#13063295C2×C418yes—
107C4×D172—28no—
108C4×D172—28no—
109C2×C4⋊Dic43—22no—
110C2×(C2×D43)⋊C4—22no—
111C2×(C2×D43)⋊C4—22no—
112#13063243—24no—
113#13063241—24no—
114(C2×D43)⋊C8—28no—
115(C2×D43)⋊C8—28no—
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×C43—21no—
123C2×M16×C43—21no—
124C2×M16×C43—21no—
125C2×M16×C43—21no—
126C2×M16×C43D412yescomplemented
127C2×M16×C43C2312yes—
128C2×M16×C43C2312yes—
129C22×C8×C43—21no—
130C22×C8×C43D412yescomplemented
131#117×C43—21no—
132#117×C43—21no—
133#117×C43C2×C412yes—
134#117×C43C2312yes—
135C2×C4⋊C4×C43—21no—
136C2×C22⋊C4×C43C2×C412yes—
137C2×C42×C43—21no—
138C24×C43C22×C411yescharacteristic
139C23×D43—21no—
140C23×D43—21no—
141C23×D43—21no—
142C23×D43—21no—
143C23×D43—21no—
144C23×D43—21no—
145C23×D43—44no—
146C23×D43C22⋊C412yes—
147C23×D43C22×C412yes—
148C22×C4×C43—22no—
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4111yescharacteristic
159C22×C4×C43#4111yescharacteristic
160C22×C4×C43#4111yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43C22⋊C414yes—
168C2×C22⋊D43C22×C414yes—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43C22⋊C412yes—
176C22×Dic43C22×C412yes—
177#10621898—22no—
178#10621898—22no—
179#10621898—22no—
180#10621898—22no—
181#10621898—22no—
182#10621898—22no—
183#10621898—22no—
184#10621898—22no—
185#10621898—22no—
186#10621898—22no—
187#10621898—22no—
188#10621898—22no—
189#10621898—22no—
190#10621898—22no—
191#10621898—22no—
192#10621898—22no—
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—28no—
198C2×D172—48no—
199C2×D172C22⋊C412yes—
200C2×D172C2×D412yes—
201C2×C4×D43—22no—
202C2×C4×D43—22no—
203C2×C4×D43—22no—
204C2×C4×D43—22no—
205C2×C4×D43—22no—
206C2×C4×D43—22no—
207C2×C4×D43—22no—
208C2×C4×D43—22no—
209C2×C4×D43—22no—
210C2×C4×D43—22no—
211C2×C4×D43—22no—
212C2×C4×D43—22no—
213C2×C4×D43—22no—
214C2×C4×D43—22no—
215C2×C4×D43—22no—
216C2×C4×D43—22no—
217C2×C4×D43—41no—
218C2×C4×D43—41no—
219C2×C4×D43—41no—
220C2×C4×D43—41no—
221C2×C4×D43—41no—
222C2×C4×D43—41no—
223C2×C4×D43—41no—
224C2×C4×D43—41no—
225C2×C4×D43—41no—
226C2×C4×D43—41no—
227C2×C4×D43—41no—
228C2×C4×D43—41no—
229C2×C4×D43—41no—
230C2×C4×D43—41no—
231C2×C4×D43—41no—
232C2×C4×D43—41no—
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
255C4⋊C4×C43—22no—
256C4⋊C4×C43—22no—
257C22⋊C4×C43—22no—
258C22⋊C4×C43C22×C414yes—
259C42×C43—22no—
260C42×C43—22no—
261(C2×D43)⋊C4—28no—
262(C2×D43)⋊C4—28no—
263C4⋊Dic43—28no—
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—42no—
281C23×C43C2×C22⋊C411yescharacteristic
282C23×C43C2×C22⋊C411yescharacteristic
283C23×C43C4×D411yescharacteristic
284C23×C43C4×D411yescharacteristic
285C23×C43C4×D411yescharacteristic
286C23×C43C4×D411yescharacteristic
287C23×C43C23×C411yescharacteristic
288C22×D43—24no—
289C22×D43—24no—
290C22×D43—24no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—44no—
297C22×D43—44no—
298C22×D43—44no—
299C22×D43—44no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43—42no—
303C22×D43—41no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—44no—
308C22×D43C2×C22⋊C414yes—
309C2×C4×C43—24no—
310C2×C4×C43—44no—
311C2×C4×C43C2×C22⋊C411yescharacteristic
312C2×C4×C43C2×C22⋊C411yescharacteristic
313C2×C4×C43C4×D411yescharacteristic
314C2×C4×C43C4×D411yescharacteristic
315C2×C4×C43C4×D411yescharacteristic
316C2×C4×C43C4×D411yescharacteristic
317C2×C4×C43#12011yescharacteristic
318C2×C4×C43#12011yescharacteristic
319C2×C4×C43#12011yescharacteristic
320C2×C4×C43#12011yescharacteristic
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#12111yescharacteristic
329C2×C4×C43#12311yescharacteristic
330C2×C4×C43#12311yescharacteristic
331C2×C4×C43#12311yescharacteristic
332C2×C4×C43#12311yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C2×#4111yescharacteristic
338C2×C4×C43C2×#4111yescharacteristic
339C22⋊D43—24no—
340C22⋊D43—24no—
341C22⋊D43—24no—
342C22⋊D43—24no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43C2×C22⋊C414yes—
353D172—22no—
354D172—22no—
355D172—22no—
356D172—22no—
357D172—416no—
358C4×D43—24no—
359C4×D43—24no—
360C4×D43—24no—
361C4×D43—24no—
362C4×D43—42no—
363C4×D43—42no—
364C4×D43—42no—
365C4×D43—42no—
366C4×D43—42no—
367C4×D43—42no—
368C4×D43—42no—
369C4×D43—42no—
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—41no—
383C22×C43—41no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43#38611yescharacteristic
387C22×C43#38611yescharacteristic
388C22×C43#38611yescharacteristic
389C22×C43#38611yescharacteristic
390C22×C43C22×C22⋊C411yescharacteristic
391C22×C43C2×C4×D411yescharacteristic
392C22×C43C2×C4×D411yescharacteristic
393C2×D43—24no—
394C2×D43—24no—
395C2×D43—24no—
396C2×D43—24no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—44no—
401C2×D43—44no—
402C2×D43—44no—
403C2×D43—44no—
404C2×D43—44no—
405C2×D43—42no—
406C2×D43—44no—
407C2×D43—82no—
408C4×C43—44no—
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—42no—
419C2×#568—431no—
420C2×#525—431no—
421C2×#413—431no—
422C2×#407—431no—
423C2×#407—431no—
424#1891—438no—
425C2×#344—431no—
426C2×#344D4311yescharacteristic, complemented
427C2×C43—21no—
428C2×C43—21no—
429C2×C43—21no—
430C2×C43—21no—
431C2×C43—21no—
432C2×C43—21no—
433C2×C43#189112yescomplemented
434C2×C43C2×#38611yescharacteristic
435D43—44no—
436D43—44no—
437C22×#41—431no—
438C24×C4—431no—
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×#117C2×D4311yescharacteristic
460#413—434no—
461#413—862no—
462C2×#101—861no—
463C2×#100—861no—
464#407—434no—
465#407—434no—
466#407—862no—
467#407—862no—
468C2×C22⋊C8—862no—
469C2×C22⋊C8—862no—
470#344—434no—
471#344C2×D4314yescomplemented
472C43C2×#189111yescharacteristic, complemented, Sylow
473C25—431no—
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—432no—
491C23×C4—431no—
492C23×C4—432no—
493C23×C4—432no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4—861no—
497C23×C4—861no—
498C23×C4—861no—
499C23×C4—861no—
500C23×C4—861no—
501C23×C4—861no—
502C23×C4—861no—
503C23×C4—861no—
504C23×C4—861no—
505C23×C4—861no—
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×M16D17212yescomplemented
536C2×M16C22×D4312yes—
537C2×M16C22×D4312yes—
538C22×C8—21no—
539C22×C8—432no—
540C22×C8—864no—
541C22×C8—861no—
542C22×C8D17212yescomplemented
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—21no—
554#117—21no—
555#117C4×D4312yes—
556#117C22×D4312yes—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—862no—
559C2×C22⋊C4—862no—
560C2×C22⋊C4—862no—
561C2×C22⋊C4C4×D4312yes—
562C2×C42—21no—
563#101—864no—
564#100—864no—
565C22⋊C8—868no—
566C22⋊C8—868no—
567C24—432no—
568C24—432no—
569C24—861no—
570C24—861no—
571C24—861no—
572C24—861no—
573C24—861no—
574C24—861no—
575C24—1724no—
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—868no—
604C2×D4—862no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—862no—
608C2×D4—861no—
609C2×D4—861no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—1728no—
613C22×C4—22no—
614C22×C4—432no—
615C22×C4—434no—
616C22×C4—434no—
617C22×C4—432no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—861no—
627C22×C4—861no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—1721no—
641C22×C4—1721no—
642C22×C4—1721no—
643C22×C4—1721no—
644C22×C4—1721no—
645C22×C4—1721no—
646C22×C4—1721no—
647C22×C4—1721no—
648C22×C4—1721no—
649C22×C4—1721no—
650C22×C4—1721no—
651C22×C4—1721no—
652C22×C4—1721no—
653C22×C4—1721no—
654C22×C4—1721no—
655C22×C4—1721no—
656C22×C4C2×C4×D4311yescharacteristic
657C22×C4C2×D17211yescharacteristic
658C22×C4C2×D17211yescharacteristic
659C22×C4#1062189811yescharacteristic
660C22×C4#1062189811yescharacteristic
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663C22×C4D4×D4311yescharacteristic
664C22×C4D4×D4311yescharacteristic
665C22×C4D4×D4311yescharacteristic
666C22×C4D4×D4311yescharacteristic
667C22×C4#1062190211yescharacteristic
668C22×C4#1062190211yescharacteristic
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×D17214yescomplemented
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—868no—
703C22⋊C4—22no—
704C22⋊C4—868no—
705C22⋊C4—868no—
706C22⋊C4C2×C4×D4314yes—
707C42—22no—
708C42—22no—
709C23—42no—
710C23—434no—
711C23—864no—
712C23—864no—
713C23—864no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—862no—
718C23—862no—
719C23—1724no—
720C23—1722no—
721C23—1722no—
722C23—1722no—
723C23—1724no—
724C23—1724no—
725C23—1724no—
726C23—1724no—
727C23—1721no—
728C23—1721no—
729C23—1721no—
730C23—1721no—
731C23C22⋊C4×D4311yescharacteristic
732C23C22⋊C4×D4311yescharacteristic
733C23#1306328711yescharacteristic
734C23#1306328711yescharacteristic
735C23C4×D17211yescharacteristic
736C23C4×D17211yescharacteristic
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—24no—
752C2×C4—44no—
753C2×C4—434no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—864no—
757C2×C4—864no—
758C2×C4—864no—
759C2×C4—864no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—1721no—
764C2×C4—1721no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—1722no—
772C2×C4—1722no—
773C2×C4—1722no—
774C2×C4—1722no—
775C2×C4C22⋊C4×D4311yescharacteristic
776C2×C4C22⋊C4×D4311yescharacteristic
777C2×C4#1306328711yescharacteristic
778C2×C4#1306328711yescharacteristic
779C2×C4C4×D17211yescharacteristic
780C2×C4C4×D17211yescharacteristic
781C2×C4#1306329511yescharacteristic
782C2×C4#1306329511yescharacteristic
783C2×C4#1306329511yescharacteristic
784C2×C4#1306329511yescharacteristic
785C2×C4#1306329811yescharacteristic
786C2×C4#1306329811yescharacteristic
787C2×C4#1306329811yescharacteristic
788C2×C4#1306329811yescharacteristic
789C2×C4#1306330011yescharacteristic
790C2×C4#1306330011yescharacteristic
791C2×C4#1306330011yescharacteristic
792C2×C4#1306330011yescharacteristic
793C2×C4#1306331011yescharacteristic
794C2×C4#1306331011yescharacteristic
795C2×C4#1306331011yescharacteristic
796C2×C4#1306331011yescharacteristic
797C2×C4C2×D4×D4311yescharacteristic
798C2×C4C2×D4×D4311yescharacteristic
799C2×C4C2×D4×D4311yescharacteristic
800C2×C4C22×D17211yescharacteristic
801C2×C4C2×#1062189811yescharacteristic
802C2×C4C2×#1062190211yescharacteristic
803C8—24no—
804C8—42no—
805C8—864no—
806C8—1722no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—864no—
815C22—864no—
816C22—864no—
817C22—864no—
818C22—3442no—
819C22—1724no—
820C22—1722no—
821C22—1722no—
822C22—1722no—
823C22—1724no—
824C22—1724no—
825C22—1724no—
826C22—1724no—
827C22—1724no—
828C22—1722no—
829C22#1458277711yescharacteristic
830C22#1458277711yescharacteristic
831C22#1458277711yescharacteristic
832C22#1458277711yescharacteristic
833C22C2×C22⋊C4×D4311yescharacteristic
834C22C2×#1306328711yescharacteristic
835C22C2×C4×D17211yescharacteristic
836C4—44no—
837C4—864no—
838C4—1722no—
839C4#1458277711yescharacteristic
840C4#1458277711yescharacteristic
841C4#1458277711yescharacteristic
842C4#1458277711yescharacteristic
843C4C2×#1306329511yescharacteristic
844C4C2×#1306329811yescharacteristic
845C4C2×#1306330011yescharacteristic
846C4C2×#1306331011yescharacteristic
847C2—21no—
848C2—21no—
849C2—21no—
850C2—21no—
851C2—21no—
852C2—21no—
853C2—1724no—
854C2—1724no—
855C2#1913501212yesdirect product factor
856C2C2×#1458277711yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#344C2
socleC22×C43#386
prime radicalC2×#14583411C2
cosocleC22×C4×C43C24
hypercenterC2×#344D43
hypocenterC43C2×#1891
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#344

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14582881C2semidirect
4. C2×#14582862C2semidirect
5. C2×#14582862C2semidirect
6. #19135012C2direct (N × H)
7. C2×#14582669C2semidirect
8. C2×C43×#344C2semidirect
14. #14583665C22semidirect
30. #14582881C22semidirect
35. #14582862C22semidirect
36. #14582862C22semidirect
39. #14582669C22semidirect
43. C43×#344C22semidirect
90. C2×#10621877D4semidirect
97. C22×C43⋊C8D4semidirect
126. C2×M16×C43D4semidirect
130. C22×C8×C43D4semidirect
254. C2×C8×C43C2×D4semidirect
277. C2×C43⋊C8C2×D4semidirect
426. C2×#344D43semidirect
433. C2×C43#1891semidirect
471. #344C2×D43semidirect
472. C43C2×#1891semidirect
535. C2×M16D172semidirect
542. C22×C8D172semidirect
699. C2×C8C2×D172semidirect
855. C2#19135012direct (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×#145834112
C2×#145828812
C2×#145828622
#191350122
C2×#145826692
C2×C43×#3442
C2×#189143