Finite Group Databasebeta

← #25003216

Subgroups — #25003216

Order 11008.

1458 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583410C211yesmaximal, characteristic
2C2×#14582881C211yesmaximal, characteristic, complemented
3#19143039C211yesmaximal, characteristic, complemented
4C2×#14582863C211yesmaximal, characteristic, complemented
5C2×#14582671C211yesmaximal, characteristic, complemented
6C2×#14582670C211yesmaximal, characteristic, complemented
7C2×C43×#407C211yesmaximal, characteristic, complemented
8C22×#10621898C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C22×#10621877C2211yescharacteristic
11#14583410—22no—
12#14583410—22no—
13#14583410—22no—
14#14583410—22no—
15C2×#13063308C412yes—
16C2×#13063304—21no—
17C2×#13063299—21no—
18C2×#13063294C412yes—
19C2×C4×C22⋊D43—22no—
20C2×#13063284C2211yescharacteristic
21#14582881—22no—
22#14582881—22no—
23C2×#13063243—21no—
24C2×#13063241—21no—
25#14582867—22no—
26#14582865—22no—
27#14582863—22no—
28#14582863—22no—
29#14582862—22no—
30C2×C22⋊(C43⋊C8)—22no—
31#14582671—22no—
32#14582670—22no—
33C24×C4×C43C2211yescharacteristic
34C22×M16×C43C2211yescharacteristic
35C22×M16×C43C2211yescharacteristic
36C43×#407—22no—
37C43×#407—22no—
38C2×C22⋊C8×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⋊D43C2×C412yes—
55C22×C4×D43D412yes—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877—21no—
61C2×#10621877—21no—
62C2×#10621877—21no—
63C2×#10621877—21no—
64C2×#10621877—21no—
65C2×#10621877—21no—
66C2×#10621877—21no—
67C2×#10621877D412yescomplemented
68C22×C43⋊C8—21no—
69C22×C43⋊C8D412yescomplemented
70#13063308—24no—
71#13063308—24no—
72#13063304—24no—
73#13063304—24no—
74#13063299—24no—
75#13063299—24no—
76#13063294—24no—
77#13063294—24no—
78C4×C22⋊D43—28no—
79C4×C22⋊D43—28no—
80#13063284—21no—
81#13063284—21no—
82#13063284D412yes—
83#13063284D412yes—
84C2×C4⋊Dic43—21no—
85C2×Dic43⋊C4—22no—
86C2×C22⋊Dic43—22no—
87C2×C22⋊Dic43C2×C412yes—
88C2×(C2×D43)⋊C4—22no—
89C2×C4×Dic43—21no—
90#13063243—24no—
91#13063241—24no—
92C22⋊(C43⋊C8)—28no—
93(C2×D43)⋊C8—28no—
94C25×C43C2×C411yescharacteristic
95C23×C4×C43—21no—
96C23×C4×C43—21no—
97C23×C4×C43—21no—
98C23×C4×C43—21no—
99C23×C4×C43—21no—
100C23×C4×C43—21no—
101C23×C4×C43—21no—
102C23×C4×C43—21no—
103C23×C4×C43—21no—
104C23×C4×C43—21no—
105C23×C4×C43—21no—
106C23×C4×C43—21no—
107C23×C4×C43C2×C411yescharacteristic
108C23×C4×C43D412yes—
109C23×C4×C43D412yes—
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×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43—21no—
119C2×M16×C43—21no—
120C2×M16×C43—21no—
121C2×M16×C43—21no—
122C2×M16×C43D412yescomplemented
123C22×C8×C43—21no—
124C22×C8×C43D412yescomplemented
125C22⋊C8×C43—28no—
126C24×C43—21no—
127C24×C43—21no—
128C24×C43—21no—
129C24×C43—21no—
130C24×C43—21no—
131C24×C43—21no—
132C24×C43—44no—
133C24×C43C22⋊C412yes—
134C24×C43C22×C411yescharacteristic
135C23×D43C22⋊C412yes—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—22no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C22×C4×C43—41no—
156C22×C4×C43—41no—
157C22×C4×C43—41no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C22×C4×C43—41no—
163C22×C4×C43—41no—
164C22×C4×C43—41no—
165C22×C4×C43—41no—
166C22×C4×C43—41no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170C22×C4×C43C22⋊C412yes—
171C22×C4×C43C2×D411yescharacteristic
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—48no—
193C22×Dic43—22no—
194C22×Dic43C22⋊C412yes—
195#10621898—41no—
196#10621898—41no—
197#10621898—41no—
198#10621898—41no—
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—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—22no—
220C2×C4×D43—22no—
221C2×C4×D43—22no—
222C2×C4×D43—22no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229M16×C43—22no—
230M16×C43—22no—
231M16×C43—41no—
232M16×C43—41no—
233M16×C43—41no—
234M16×C43—41no—
235M16×C43—41no—
236M16×C43—41no—
237C2×C8×C43—22no—
238C2×C8×C43—22no—
239C2×C8×C43—22no—
240C2×C8×C43—22no—
241C2×C8×C43—41no—
242C2×C8×C43—41no—
243C22⋊Dic43—28no—
244C22⋊Dic43—22no—
245C22⋊Dic43C22⋊C414yes—
246(C2×D43)⋊C4—28no—
247C4⋊Dic43—22no—
248C4⋊Dic43—22no—
249Dic43⋊C4—28no—
250C4×Dic43—22no—
251C4×Dic43—22no—
252#10621877—22no—
253#10621877—22no—
254#10621877—41no—
255#10621877—41no—
256#10621877—41no—
257#10621877—41no—
258#10621877—41no—
259#10621877—41no—
260C2×C43⋊C8—22no—
261C2×C43⋊C8—22no—
262C2×C43⋊C8—22no—
263C2×C43⋊C8—22no—
264C2×C43⋊C8—41no—
265C2×C43⋊C8—41no—
266C23×C43—24no—
267C23×C43—24no—
268C23×C43—24no—
269C23×C43—22no—
270C23×C43—22no—
271C23×C43—22no—
272C23×C43—44no—
273C23×C43—42no—
274C23×C43—42no—
275C23×C43—42no—
276C23×C43—42no—
277C23×C43—44no—
278C23×C43—44no—
279C23×C43—44no—
280C23×C43—41no—
281C23×C43—41no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43C2×C22⋊C411yescharacteristic
285C23×C43C2×C22⋊C411yescharacteristic
286C23×C43C2×C22⋊C411yescharacteristic
287C23×C43C4×D411yescharacteristic
288C23×C43C4×D411yescharacteristic
289C23×C43C4×D411yescharacteristic
290C23×C43C4×D411yescharacteristic
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—44no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—41no—
299C2×C4×C43—41no—
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—42no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43#12011yescharacteristic
311C2×C4×C43#12011yescharacteristic
312C2×C4×C43#12011yescharacteristic
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#12111yescharacteristic
329C2×C4×C43#12111yescharacteristic
330C2×C4×C43#12311yescharacteristic
331C2×C4×C43#12311yescharacteristic
332C2×C4×C43#12311yescharacteristic
333C2×C4×C43#12311yescharacteristic
334C2×C4×C43#12411yescharacteristic
335C2×C4×C43#12411yescharacteristic
336C2×C4×C43#12711yescharacteristic
337C2×C4×C43#12711yescharacteristic
338C22⋊D43—416no—
339C22⋊D43—42no—
340C22⋊D43—42no—
341C22⋊D43—42no—
342C22⋊D43—42no—
343C2×Dic43—24no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—44no—
348D172—41no—
349D172—41no—
350D172—41no—
351D172—41no—
352C4×D43—42no—
353C4×D43—42no—
354C4×D43—42no—
355C4×D43—42no—
356Dic86—41no—
357Dic86—41no—
358Dic86—41no—
359Dic86—41no—
360C8×C43—42no—
361C8×C43—42no—
362C43⋊C8—42no—
363C43⋊C8—42no—
364#10993—431nomaximal, Sylow
365C22×C43—22no—
366C22×C43—22no—
367C22×C43—22no—
368C22×C43—24no—
369C22×C43—24no—
370C22×C43—24no—
371C22×C43—41no—
372C22×C43—41no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—42no—
376C22×C43—44no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—44no—
380C22×C43—44no—
381C22×C43—44no—
382C22×C43—42no—
383C22×C43#37911yescharacteristic
384C22×C43#38611yescharacteristic
385C22×C43#38611yescharacteristic
386C22×C43#38611yescharacteristic
387C22×C43#38611yescharacteristic
388C22×C43#39011yescharacteristic
389C22×C43#39011yescharacteristic
390C2×D43—44no—
391C2×D43—44no—
392C2×D43—42no—
393C2×D43—82no—
394C4×C43—42no—
395C4×C43#39211yescharacteristic
396C4×C43#39211yescharacteristic
397C4×C43#39211yescharacteristic
398C4×C43#39211yescharacteristic
399C4×C43#39411yescharacteristic
400C4×C43#39411yescharacteristic
401C4×C43#39411yescharacteristic
402C4×C43#39411yescharacteristic
403Dic43—44no—
404Dic43—42no—
405C2×#525—431no—
406C2×#413—431no—
407#2879—431no—
408C2×#407—431no—
409C2×#407D4311yescharacteristic, complemented
410C2×#344—431no—
411C2×#344—431no—
412C2×C43—21no—
413C2×C43—21no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43—21no—
417C2×C43—21no—
418C2×C43—44no—
419C2×C43#143811yescharacteristic
420C2×C43#189112yes—
421D43—82no—
422C22×#41—431no—
423C24×C4C2×D4311yescharacteristic
424C22×M16—431no—
425C22×M16—431no—
426C22×M16C2×D4311yescharacteristic
427C22×M16C2×D4311yescharacteristic
428#525—862no—
429#525—862no—
430#525—862no—
431#525—862no—
432C2×#123—432no—
433C2×C22⋊Q8—861no—
434C2×#121—861no—
435C2×#120—432no—
436C2×C4×D4—862no—
437C2×#117—431no—
438#413—862no—
439#413—862no—
440C2×#101—861no—
441C2×#100—861no—
442#408—862no—
443#408—862no—
444#407—22no—
445#407—22no—
446#407—862no—
447#407—862no—
448#407—862no—
449C2×C22⋊C8—22no—
450C2×C22⋊C8—862no—
451#344—862no—
452#344—862no—
453C43#1099311yescharacteristic, complemented, Sylow
454C25C4×D4311yescharacteristic
455C2×#41—861no—
456C2×#41—861no—
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—
467C22×Q8—431no—
468C22×D4—432no—
469C22×D4—431no—
470C22×D4—862no—
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—21no—
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—432no—
484C23×C4C4×D4311yescharacteristic
485C23×C4D17212yes—
486C23×C4C22⋊D4312yes—
487C23×C4C22×D4311yescharacteristic
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—432no—
500C2×M16—861no—
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×M16C22⋊D4312yescomplemented
512C22×C8—21no—
513C22×C8—432no—
514C22×C8—861no—
515C22×C8C22⋊D4312yescomplemented
516#123—864no—
517#123—864no—
518C22⋊Q8—864no—
519C22⋊Q8—864no—
520#121—864no—
521#121—864no—
522#120—864no—
523#120—864no—
524C4×D4—868no—
525C4×D4—868no—
526#117—432no—
527#117—432no—
528#117—861no—
529#117—861no—
530C2×C4⋊C4—862no—
531C2×C4⋊C4—861no—
532C2×C22⋊C4—432no—
533C2×C22⋊C4—862no—
534C2×C22⋊C4—862no—
535C2×C42—861no—
536#101—864no—
537#100—864no—
538C22⋊C8—28no—
539C22⋊C8—868no—
540C22⋊C8—868no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—44no—
548C24—432no—
549C24(C2×D43)⋊C412yes—
550C24C2×C4×D4311yescharacteristic
551#41—1721no—
552#41—1721no—
553#41—1721no—
554#41—1721no—
555#41—1721no—
556#41—1721no—
557#41—1721no—
558#41—1721no—
559#41—1721no—
560#41—1721no—
561#41—1721no—
562#41—1721no—
563#41—1721no—
564#41—1721no—
565#41—1721no—
566#41—1721no—
567C2×Q8—861no—
568C2×Q8—861no—
569C2×Q8—861no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—861no—
573C2×D4—868no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—862no—
578C2×D4—862no—
579C2×D4—862no—
580C2×D4—861no—
581C2×D4—861no—
582C2×D4—861no—
583C2×D4—861no—
584C2×D4—861no—
585C2×D4—861no—
586C2×D4—1728no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—432no—
622C22×C4—862no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4(C2×D43)⋊C412yes—
630C22×C4C2×D17211yescharacteristic
631C22×C4#1062189811yescharacteristic
632C22×C4#1062189811yescharacteristic
633C22×C4D4×D4311yescharacteristic
634C22×C4D4×D4311yescharacteristic
635C22×C4D4×D4311yescharacteristic
636C22×C4D4×D4311yescharacteristic
637C22×C4D4×D4311yescharacteristic
638C22×C4D4×D4311yescharacteristic
639C22×C4#1062190011yescharacteristic
640C22×C4#1062190011yescharacteristic
641C22×C4C2×C22⋊D4311yescharacteristic
642C22×C4C2×C22⋊D4311yescharacteristic
643C22×C4C2×C22⋊D4311yescharacteristic
644M16—22no—
645M16—22no—
646M16—41no—
647M16—41no—
648M16—41no—
649M16—41no—
650M16—41no—
651M16—41no—
652M16—862no—
653M16—862no—
654M16—1721no—
655M16—1721no—
656M16—1721no—
657M16—1721no—
658M16—1721no—
659M16—1721no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—22no—
664C2×C8—41no—
665C2×C8—41no—
666C2×C8—862no—
667C2×C8—862no—
668C2×C8—862no—
669C2×C8—862no—
670C2×C8—1721no—
671C2×C8—1721no—
672C4⋊C4—868no—
673C4⋊C4—862no—
674C4⋊C4—862no—
675C22⋊C4—434no—
676C22⋊C4—868no—
677C22⋊C4—868no—
678C22⋊C4—862no—
679C42—862no—
680C42—862no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—44no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—862no—
700C23—862no—
701C23—862no—
702C23—1724no—
703C23C22⋊C4×D4311yescharacteristic
704C23C22⋊C4×D4311yescharacteristic
705C23C2×(C2×D43)⋊C411yescharacteristic
706C23(C22⋊D43)⋊C411yescharacteristic
707C23(C22⋊D43)⋊C411yescharacteristic
708C23C4×C22⋊D4311yescharacteristic
709C23C4×C22⋊D4311yescharacteristic
710Q8—1721no—
711Q8—1721no—
712Q8—1721no—
713Q8—1721no—
714D4—17216no—
715D4—1722no—
716D4—1722no—
717D4—1722no—
718D4—1722no—
719D4—1721no—
720D4—1721no—
721D4—1721no—
722D4—1721no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—864no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—1724no—
743C2×C4—1722no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4#1306329311yescharacteristic
748C2×C4#1306329311yescharacteristic
749C2×C4#1306329311yescharacteristic
750C2×C4#1306329311yescharacteristic
751C2×C4#1306329411yescharacteristic
752C2×C4#1306329511yescharacteristic
753C2×C4#1306329511yescharacteristic
754C2×C4#1306329511yescharacteristic
755C2×C4#1306329611yescharacteristic
756C2×C4#1306329611yescharacteristic
757C2×C4#1306329711yescharacteristic
758C2×C4#1306329711yescharacteristic
759C2×C4#1306329711yescharacteristic
760C2×C4#1306329711yescharacteristic
761C2×C4#1306329811yescharacteristic
762C2×C4#1306329811yescharacteristic
763C2×C4#1306329811yescharacteristic
764C2×C4#1306329811yescharacteristic
765C2×C4#1306329911yescharacteristic
766C2×C4#1306329911yescharacteristic
767C2×C4#1306330711yescharacteristic
768C2×C4#1306330711yescharacteristic
769C2×C4#1306330811yescharacteristic
770C2×C4#1306330911yescharacteristic
771C2×C4#1306331111yescharacteristic
772C2×C4#1306331111yescharacteristic
773C2×C4#1306332111yescharacteristic
774C2×C4#1306332111yescharacteristic
775C8—42no—
776C8—42no—
777C8—1722no—
778C8—1722no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—42no—
797C22—3442no—
798C22—1724no—
799C22—1724no—
800C22—1722no—
801C22#1458275411yescharacteristic
802C22#1458277511yescharacteristic
803C22#1458277511yescharacteristic
804C22#1458277611yescharacteristic
805C22#1458277811yescharacteristic
806C22#1458279911yescharacteristic
807C22#1458279911yescharacteristic
808C4—42no—
809C4—1724no—
810C4—1722no—
811C4#1458280711yescharacteristic
812C4#1458280711yescharacteristic
813C4#1458280811yescharacteristic
814C4#1458280811yescharacteristic
815C4#1458281411yescharacteristic
816C4#1458281411yescharacteristic
817C4#1458281511yescharacteristic
818C4#1458281511yescharacteristic
819C2—21no—
820C2—21no—
821C2—21no—
822C2—21no—
823C2—21no—
824C2—21no—
825C2—44no—
826C2—3442no—
827C2#1913283411yescharacteristic
828C2#1913501012yes—
subgroupG/H
centerC2×C4#13063293
commutatorC24×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#407C2
socleC22×C43#386
prime radicalC2×#14583410C2
cosocleC23×C4×C43C23
hypercenterC2×#407D43
hypocenterC43#10993
LCSG ▷ C24×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
2. C2×#14582881C2semidirect
3. #19143039C2semidirect
4. C2×#14582863C2semidirect
5. C2×#14582671C2semidirect
6. C2×#14582670C2semidirect
7. C2×C43×#407C2semidirect
67. C2×#10621877D4semidirect
69. C22×C43⋊C8D4semidirect
122. C2×M16×C43D4semidirect
124. C22×C8×C43D4semidirect
409. C2×#407D43semidirect
453. C43#10993semidirect
511. C2×M16C22⋊D43semidirect
515. C22×C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834102
C2×#145828812
#191430392
C2×#145828632
C2×#145826712
C2×#145826702
C2×C43×#4072
#1099343