Finite Group Databasebeta

← #25245432

Subgroups — #25245432

Order 11008.

1468 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×Dic43C211yesmaximal, characteristic
2C2×#14583107C211yesmaximal, characteristic, complemented
3C2×#14583102C211yesmaximal, characteristic, complemented
4C2×#14583061C211yesmaximal, characteristic
5#19142943C211yesmaximal, characteristic, complemented
6#19134938C211yesmaximal, characteristic, complemented
7#19134934C211yesmaximal, characteristic, complemented
8#19134931C211yesmaximal, characteristic, complemented
9#19134927C211yesmaximal, characteristic, complemented
10#19134908C211yesmaximal, characteristic, complemented
11#19134905C211yesmaximal, characteristic, complemented
12#19134598C211yesmaximal, characteristic, complemented
13#19134593C211yesmaximal, characteristic, complemented
14#19134573C211yesmaximal, characteristic, complemented
15C2×C43×#452C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C2×#13063323C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20#41×Dic43—24no—
21#41×Dic43—24no—
22C2×Q8×Dic43C2211yescharacteristic
23C2×Q8×Dic43C2211yescharacteristic
24C2×D4×Dic43—21no—
25C2×D4×Dic43—21no—
26C2×D4×Dic43C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C2×#13063284—21no—
29C2×#13063284C2211yescharacteristic
30C22×C4×Dic43—21no—
31C22×C4×Dic43C2211yescharacteristic
32#14583107—24no—
33#14583102—24no—
34#14583061—24no—
35C2×Dic43⋊C8C2211yescharacteristic
36C2×Dic43⋊C8C2211yescharacteristic
37C2×#13063250C2211yescharacteristic
38C2×#13063250C2211yescharacteristic
39C2×#13063249C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063249C2211yescharacteristic
42C2×#13063246C2211yescharacteristic
43C2×C22⋊(C43⋊C8)C2211yescharacteristic
44#14582806C2211yescharacteristic
45#14582804C2211yescharacteristic
46#14582794—21no—
47#14582794—21no—
48#14582768C2211yescharacteristic
49#14582757—21no—
50#14582757—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582653C2211yescharacteristic
56#14582653C2211yescharacteristic
57C22×#41×C43C2211yescharacteristic
58C22×Q16×C43C2211yescharacteristic
59C22×SD16×C43C2211yescharacteristic
60C2×C22⋊Q8×C43C2211yescharacteristic
61C43×#452—24no—
62C2×#103×C43C2211yescharacteristic
63C2×#102×C43C2211yescharacteristic
64C2×C22⋊C8×C43C2211yescharacteristic
65C22×Dic86C2311yescharacteristic
66C23×Dic43—21no—
67C23×Dic43—21no—
68C23×Dic43D411yescharacteristic
69C23×Dic43D411yescharacteristic
70C2×#10621885—22no—
71C2×#10621885—22no—
72C2×#10621885—22no—
73C2×#10621883—22no—
74C2×#10621883—22no—
75C2×#10621883—22no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78#13063323—22no—
79#13063323—22no—
80#13063304—22no—
81#13063304—22no—
82Q8×Dic43—22no—
83Q8×Dic43—22no—
84Q8×Dic43—22no—
85Q8×Dic43D414yes—
86D4×Dic43—28no—
87D4×Dic43—28no—
88D4×Dic43—22no—
89D4×Dic43—22no—
90D4×Dic43—22no—
91D4×Dic43D414yes—
92#13063284—28no—
93#13063284—22no—
94#13063284—22no—
95C2×C4⋊Dic43—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×C4⋊Dic43C2311yescharacteristic
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×C22⋊Dic43—21no—
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C4×Dic43—28no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—22no—
114C2×C4×Dic43—22no—
115C2×C4×Dic43D411yescharacteristic
116C2×C4×Dic43D411yescharacteristic
117C2×C4×Dic43C2311yescharacteristic
118C2×C4×Dic43C2311yescharacteristic
119Dic43⋊C8—22no—
120Dic43⋊C8—22no—
121#13063250—22no—
122#13063250—22no—
123#13063249—22no—
124#13063249—22no—
125#13063249—22no—
126#13063246—22no—
127C22⋊(C43⋊C8)—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C2×#41×C43—22no—
133C2×#41×C43—22no—
134C2×#41×C43—22no—
135C2×#41×C43—22no—
136C2×#41×C43—22no—
137C2×#41×C43D414yes—
138C22×Q8×C43C2311yescharacteristic
139C22×Q8×C43C2311yescharacteristic
140C22×D4×C43—21no—
141C22×D4×C43C2311yescharacteristic
142C23×C4×C43—21no—
143C23×C4×C43C2311yescharacteristic
144C2×Q16×C43—22no—
145C2×Q16×C43—22no—
146C2×Q16×C43—22no—
147C2×SD16×C43—22no—
148C2×SD16×C43—22no—
149C2×SD16×C43—22no—
150C22×C8×C43C2311yescharacteristic
151C22×C8×C43C2311yescharacteristic
152C22⋊Q8×C43—22no—
153C22⋊Q8×C43—22no—
154C2×C4⋊C4×C43—21no—
155C2×C4⋊C4×C43C2311yescharacteristic
156C2×C22⋊C4×C43—21no—
157#103×C43—22no—
158#102×C43—22no—
159C22⋊C8×C43—22no—
160C24×C43—21no—
161C24×C43C2×D411yescharacteristic
162#41×C43—28no—
163#41×C43—28no—
164#41×C43—28no—
165#41×C43—28no—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43—21no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43C2×D412yes—
176C2×Q8×C43C2×D412yes—
177C2×Q8×C43#4112yes—
178C2×D4×C43—24no—
179C2×D4×C43—24no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—24no—
184C2×D4×C43C2×D412yes—
185C2×D4×C43C2×D412yes—
186C2×D4×C43#4112yes—
187C22×C4×C43—24no—
188C22×C4×C43—24no—
189C22×C4×C43—24no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43—21no—
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43#4112yes—
200C22×C4×C43C2411yescharacteristic
201C22×Dic43—24no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—24no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43—41no—
213C22×Dic43—42no—
214C22×Dic43—42no—
215C22×Dic43—42no—
216C22×Dic43—42no—
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219C22×Dic43C2×D411yescharacteristic
220C22×Dic43C2×D411yescharacteristic
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86—21no—
227Q16×C43—44no—
228SD16×C43—44no—
229C2×C8×C43—21no—
230C2×C8×C43—21no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C4⋊C4×C43—21no—
236C4⋊C4×C43—21no—
237C4⋊C4×C43—42no—
238C22⋊C4×C43—42no—
239C22⋊Dic43—24no—
240C22⋊Dic43—24no—
241C22⋊Dic43—24no—
242C22⋊Dic43—42no—
243#10621885—44no—
244#10621883—44no—
245C4⋊Dic43—24no—
246C4⋊Dic43—21no—
247C4⋊Dic43—21no—
248C4⋊Dic43—24no—
249C4⋊Dic43—21no—
250C4⋊Dic43—21no—
251C4⋊Dic43C2×D412yes—
252C4⋊Dic43C2×D412yes—
253Dic43⋊C4—42no—
254Dic43⋊C4—42no—
255Dic43⋊C4—42no—
256Dic43⋊C4—42no—
257Dic43⋊C4—42no—
258C4×Dic43—24no—
259C4×Dic43—24no—
260C4×Dic43—21no—
261C4×Dic43—21no—
262C4×Dic43—22no—
263C4×Dic43—24no—
264C4×Dic43—22no—
265C4×Dic43C2×D412yes—
266C4×Dic43C2×D412yes—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—21no—
271C2×C43⋊C8—21no—
272C2×C43⋊C8—21no—
273C23×C43—21no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—21no—
277C23×C43—22no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—41no—
283C23×C43—41no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43#12112yes—
287C23×C43C22×D411yescharacteristic
288Q8×C43—22no—
289Q8×C43—22no—
290Q8×C43—22no—
291Q8×C43—41no—
292Q8×C43—41no—
293Q8×C43—41no—
294Q8×C43—41no—
295Q8×C43#12114yes—
296D4×C43—216no—
297D4×C43—22no—
298D4×C43—22no—
299D4×C43—22no—
300D4×C43#12114yes—
301C2×C4×C43—216no—
302C2×C4×C43—21no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—21no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43#12112yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C22×D411yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C2×#4111yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—44no—
334C2×Dic43—48no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—44no—
340C2×Dic43—48no—
341C2×Dic43—41no—
342C2×Dic43—41no—
343C2×Dic43—41no—
344C2×Dic43—41no—
345C2×Dic43—41no—
346C2×Dic43—41no—
347C2×Dic43#12012yes—
348C2×Dic43#12012yes—
349C2×Dic43#13512yes—
350C2×Dic43#13712yes—
351C2×Dic43#13712yes—
352Dic86—41no—
353Dic86—41no—
354Dic86—41no—
355Dic86—41no—
356C8×C43—41no—
357C8×C43—41no—
358C43⋊C8—41no—
359C43⋊C8—41no—
360#32907—431nomaximal, Sylow
361C22×C43—24no—
362C22×C43—22no—
363C22×C43—22no—
364C22×C43—22no—
365C22×C43—41no—
366C22×C43—42no—
367C22×C43—41no—
368C22×C43—42no—
369C22×C43—41no—
370C22×C43—42no—
371C22×C43—41no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43C2×#12011yescharacteristic
376C22×C43C2×#12111yescharacteristic
377C22×C43#52511yescharacteristic
378C22×C43C2×#13511yescharacteristic
379C22×C43C2×#13711yescharacteristic
380C22×C43C2×#13711yescharacteristic
381C22×C43#57511yescharacteristic
382C4×C43—22no—
383C4×C43—24no—
384C4×C43—81no—
385C4×C43—81no—
386C4×C43C2×#12111yescharacteristic
387C4×C43C2×#12111yescharacteristic
388C4×C43#52511yescharacteristic
389C4×C43#52511yescharacteristic
390Dic43—22no—
391Dic43—22no—
392Dic43—41no—
393Dic43—42no—
394Dic43—42no—
395Dic43—81no—
396Dic43—81no—
397Dic43#45214yescomplemented
398C2×C4×#41—431no—
399C2×#462—431no—
400C2×#461—431no—
401C2×#452—431no—
402C2×#452D4311yescharacteristic
403#2857—431no—
404#1878—431no—
405#1878—431no—
406#1877—431no—
407#1877—431no—
408#1873—431no—
409#1873—431no—
410#1803—431no—
411#1802—431no—
412#1797—431no—
413C2×C43—42no—
414C2×C43—44no—
415C2×C43#284711yescharacteristic
416C2×C43C2×#45211yescharacteristic
417C2×C43#300711yescharacteristic
418C2×C43#303511yescharacteristic
419C2×C43#303911yescharacteristic
420C2×C43#310711yescharacteristic
421C2×C43#311611yescharacteristic
422C22×#41C2×D4311yescharacteristic
423C22×Q16—431no—
424C22×Q16C2×D4311yescharacteristic
425C22×SD16—431no—
426C22×SD16C2×D4311yescharacteristic
427C2×C4⋊Q8—431no—
428C2×C22⋊Q8—431no—
429C2×C22⋊Q8C2×D4311yescharacteristic
430C4×#41—864no—
431C4×#41—864no—
432C2×C4×Q8—431no—
433C2×C4×Q8—431no—
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×C4×D4—861no—
438C2×#117—431no—
439C2×#117—861no—
440C22×C42—431no—
441C22×C42—861no—
442#462—864no—
443#461—864no—
444#452—24no—
445#452—864no—
446C2×C4⋊C8—431no—
447C2×C4⋊C8—431no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#103—431no—
453C2×#103C2×D4311yescharacteristic
454C2×#102—431no—
455C2×#102C2×D4311yescharacteristic
456C2×C22⋊C8—431no—
457C2×C22⋊C8C2×D4311yescharacteristic
458#391—431no—
459#391—431no—
460#389—861no—
461#389—861no—
462#384—431no—
463#380—861no—
464#380—861no—
465#340—431no—
466#340—431no—
467#340—431no—
468#340—431no—
469#336—431no—
470#336—431no—
471C43#3290711yescharacteristic, complemented, Sylow
472C2×#41—22no—
473C2×#41—22no—
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41C22⋊D4314yes—
478C22×Q8—431no—
479C22×Q8C22×D4311yescharacteristic
480C22×Q8C22×D4311yescharacteristic
481C22×D4—21no—
482C22×D4C22×D4311yescharacteristic
483C23×C4—21no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—861no—
487C23×C4—861no—
488C23×C4C22×D4311yescharacteristic
489C2×Q16—22no—
490C2×Q16—22no—
491C2×Q16—22no—
492C2×Q16—862no—
493C2×Q16—862no—
494C2×Q16—862no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—862no—
499C2×SD16—862no—
500C2×SD16—862no—
501C22×C8—431no—
502C22×C8—431no—
503C22×C8C22×D4311yescharacteristic
504C22×C8C22×D4311yescharacteristic
505C4⋊Q8—862no—
506C4⋊Q8—862no—
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—862no—
510C22⋊Q8—862no—
511C4×Q8—434no—
512C4×Q8—862no—
513C4×Q8—862no—
514C4×Q8—862no—
515C4×D4—434no—
516C4×D4—862no—
517C4×D4—862no—
518C4×D4—868no—
519C4×D4—868no—
520C4×D4—862no—
521#117—862no—
522#117—862no—
523#117—868no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—431no—
526C2×C4⋊C4—431no—
527C2×C4⋊C4—431no—
528C2×C4⋊C4—861no—
529C2×C4⋊C4—861no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4—861no—
535C2×C4⋊C4C22×D4311yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4—861no—
540C2×C22⋊C4—861no—
541C2×C42—431no—
542C2×C42—431no—
543C2×C42—431no—
544C2×C42—431no—
545C2×C42—862no—
546C2×C42—862no—
547C2×C42—861no—
548C2×C42—861no—
549C2×C42—868no—
550C2×C42—861no—
551C4⋊C8—862no—
552C4⋊C8—862no—
553#103—22no—
554#103—862no—
555#103—862no—
556#103—862no—
557#103—862no—
558#103—862no—
559#102—22no—
560#102—862no—
561C22⋊C8—22no—
562C22⋊C8—862no—
563#95—861no—
564#95—861no—
565#95—861no—
566#95—861no—
567C24—21no—
568C24D4×D4311yescharacteristic
569#41—28no—
570#41—28no—
571#41—28no—
572#41—28no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
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×Q8D4×D4312yes—
589C2×Q8#1062190012yes—
590C2×Q8C2×C22⋊D4312yes—
591C2×D4—24no—
592C2×D4—24no—
593C2×D4—24no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4D4×D4312yes—
598C2×D4#1062190012yes—
599C2×D4C2×C22⋊D4312yes—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—21no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—864no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—864no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4—1722no—
628C22×C4—1721no—
629C22×C4—1722no—
630C22×C4D4×D4311yescharacteristic
631C22×C4#1062190012yes—
632C22×C4C2×C22⋊D4312yes—
633C22×C4C23×D4311yescharacteristic
634Q16—44no—
635Q16—1724no—
636SD16—44no—
637SD16—1724no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—861no—
645C2×C8—861no—
646C2×C8—861no—
647C2×C8—861no—
648C2×C8—861no—
649C2×C8—861no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4—432no—
654C4⋊C4—432no—
655C4⋊C4—864no—
656C4⋊C4—864no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—1722no—
662C4⋊C4—1722no—
663C4⋊C4—1722no—
664C4⋊C4—1722no—
665C4⋊C4—1722no—
666C22⋊C4—42no—
667C22⋊C4—864no—
668C22⋊C4—864no—
669C22⋊C4—864no—
670C22⋊C4—1722no—
671C42—432no—
672C42—432no—
673C42—862no—
674C42—862no—
675C42—864no—
676C42—864no—
677C42—864no—
678C42—861no—
679C42—861no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—21no—
684C23—22no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23#1306329712yes—
694C23C2×D4×D4311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—41no—
699Q8—41no—
700Q8—41no—
701Q8—41no—
702Q8—1721no—
703Q8—1721no—
704Q8—1721no—
705Q8—1721no—
706Q8#1306329714yes—
707D4—216no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4#1306329714yes—
712C2×C4—216no—
713C2×C4—21no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—432no—
729C2×C4—432no—
730C2×C4—432no—
731C2×C4—432no—
732C2×C4—432no—
733C2×C4—861no—
734C2×C4—861no—
735C2×C4—861no—
736C2×C4—861no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—861no—
740C2×C4—861no—
741C2×C4—861no—
742C2×C4—1724no—
743C2×C4—1728no—
744C2×C4—1724no—
745C2×C4—1728no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4—1721no—
750C2×C4—1721no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1721no—
756C2×C4#1306329712yes—
757C2×C4C2×D4×D4311yescharacteristic
758C2×C4C2×D4×D4311yescharacteristic
759C2×C4C22×C22⋊D4311yescharacteristic
760C2×C4C2×#1062190011yescharacteristic
761C2×C4C2×#1062190011yescharacteristic
762C2×C4C2×#1062190011yescharacteristic
763C8—41no—
764C8—41no—
765C8—1721no—
766C8—1721no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—24no—
771C22—41no—
772C22—42no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22#120×D4311yescharacteristic
782C22C2×#1306329711yescharacteristic
783C22#1458340511yescharacteristic
784C22#135×D4311yescharacteristic
785C22#137×D4311yescharacteristic
786C22#137×D4311yescharacteristic
787C22#1458369611yescharacteristic
788C4—22no—
789C4—24no—
790C4—81no—
791C4—81no—
792C4—434no—
793C4—862no—
794C4—862no—
795C4—3441no—
796C4—3441no—
797C4—1721no—
798C4—1722no—
799C4—1722no—
800C4C2×#1306329711yescharacteristic
801C4C2×#1306329711yescharacteristic
802C4#1458340511yescharacteristic
803C4#1458340511yescharacteristic
804C2—42no—
805C2—44no—
806C2#1914287511yescharacteristic
807C2#452×D4311yescharacteristic
808C2#1914385211yescharacteristic
809C2#1914404611yescharacteristic
810C2#1914408011yescharacteristic
811C2#1914465911yescharacteristic
812C2#1914475011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#452C2
socleC23×C43C22×D4
prime radicalC22×#41×C43C22
hypercenterC2×#452D43
hypocenterC43#32907
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
2. C2×#14583107C2semidirect
3. C2×#14583102C2semidirect
5. #19142943C2semidirect
6. #19134938C2semidirect
7. #19134934C2semidirect
8. #19134931C2semidirect
9. #19134927C2semidirect
10. #19134908C2semidirect
11. #19134905C2semidirect
12. #19134598C2semidirect
13. #19134593C2semidirect
14. #19134573C2semidirect
397. Dic43#452semidirect
471. C43#32907semidirect

Maximal subgroups

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

subgroupindex
C2×#41×Dic432
C2×#145831072
C2×#145831022
C2×#145830612
#191429432
#191349382
#191349342
#191349312
#191349272
#191349082
#191349052
#191345982
#191345932
#191345732
C2×C43×#4522
#3290743