Finite Group Databasebeta

← #25098394

Subgroups — #25098394

Order 11008.

2102 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583458C211yesmaximal, characteristic
2C2×#14583372C211yesmaximal, characteristic, complemented
3C22×#13063240C211yesmaximal, characteristic, complemented
4#19137170C211yesmaximal, characteristic, complemented
5#19135050C214yesmaximal, complemented
6#19135045C214yesmaximal, complemented
7C2×#14582665C211yesmaximal, characteristic, complemented
8C2×#14582665C211yesmaximal, characteristic, complemented
9C22×#99×C43C211yesmaximal, characteristic, complemented
10C23×C22⋊D43C2211yescharacteristic
11#14583458—22no—
12#14583458—22no—
13#14583458—22no—
14#14583458—22no—
15C2×#13063308C412yescomplemented
16C2×#13063306C2212yes—
17C2×#13063297C414yescomplemented
18C2×#13063294C412yescomplemented
19C2×#13063293C2212yes—
20#14583372—24no—
21#14583372—24no—
22C2×C4×C22⋊D43—22no—
23C2×(C22⋊D43)⋊C4—22no—
24C2×#13063281C2212yescomplemented
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C2×C22⋊C4×D43C2212yescomplemented
29C2×#13063240—24no—
30C2×#13063240C2214yes—
31#14582778—22no—
32#14582776—22no—
33#14582760C2212yescomplemented
34#14582754C2212yescomplemented
35#14582665C2214yescomplemented
36#14582665C2214yescomplemented
37C23×D4×C43C2211yescharacteristic
38C22×C22⋊C4×C43C2211yescharacteristic
39C22×C22⋊C4×C43C2211yescharacteristic
40C2×#99×C43—24no—
41C2×#99×C43C2214yes—
42C24×D43C2311yescharacteristic
43C22×C22⋊D43—22no—
44C22×C22⋊D43—22no—
45C22×C22⋊D43—22no—
46C22×C22⋊D43—22no—
47C22×C22⋊D43C2×C412yes—
48C22×C22⋊D43C2×C412yes—
49C22×C22⋊D43C2×C414yescomplemented
50C22×C22⋊D43D412yes—
51C22×C22⋊D43D412yes—
52C22×C22⋊D43D412yes—
53C22×C22⋊D43D412yes—
54C23×Dic43—21no—
55C23×Dic43—21no—
56C23×Dic43C2×C412yescomplemented
57C23×Dic43C2311yescharacteristic
58C22×C4×D43—22no—
59#13063308—24no—
60#13063308—24no—
61#13063306—24no—
62#13063306—24no—
63#13063297—28no—
64#13063297—28no—
65#13063294—24no—
66#13063294—24no—
67#13063293—24no—
68#13063293—24no—
69C4×C22⋊D43—216no—
70(C22⋊D43)⋊C4—216no—
71#13063281—24no—
72#13063281—24no—
73C2×Dic43⋊C4—22no—
74C2×Dic43⋊C4C2×C414yescomplemented
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—22no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—22no—
82C2×C22⋊Dic43—22no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43C2×C412yescomplemented
85C2×C22⋊Dic43C2×C414yescomplemented
86C2×C22⋊Dic43D414yescomplemented
87C2×C22⋊Dic43C2312yes—
88C2×C22⋊Dic43C2312yes—
89C2×C22⋊Dic43C2312yes—
90C2×(C2×D43)⋊C4—22no—
91C2×(C2×D43)⋊C4—24no—
92C2×(C2×D43)⋊C4C2×C414yescomplemented
93C22⋊C4×D43—24no—
94C22⋊C4×D43—24no—
95C2×C4×Dic43—22no—
96#13063240—28no—
97C43⋊#95—24no—
98C25×C43C2×C411yescharacteristic, complemented
99C25×C43C2311yescharacteristic
100C22×D4×C43—22no—
101C22×D4×C43—21no—
102C22×D4×C43—21no—
103C22×D4×C43—21no—
104C22×D4×C43—21no—
105C22×D4×C43—22no—
106C22×D4×C43—22no—
107C22×D4×C43—22no—
108C22×D4×C43C2×C412yescomplemented
109C22×D4×C43C2312yes—
110C23×C4×C43—21no—
111C23×C4×C43—21no—
112C23×C4×C43C2×C411yescharacteristic, complemented
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—22no—
115C2×C22⋊C4×C43—22no—
116C2×C22⋊C4×C43—22no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43D414yescomplemented
119C2×C22⋊C4×C43C2312yes—
120C2×C22⋊C4×C43C2312yes—
121#99×C43—28no—
122C24×C43—21no—
123C24×C43—21no—
124C24×C43—22no—
125C24×C43—22no—
126C24×C43—82no—
127C24×C43—82no—
128C24×C43C22×C412yes—
129C24×C43C22×C411yescharacteristic
130C24×C43C22×C411yescharacteristic
131C24×C43C2×D411yescharacteristic
132C24×C43C2×D411yescharacteristic
133C24×C43C2×D411yescharacteristic
134C24×C43C2×D411yescharacteristic
135C24×C43C2×D412yes—
136C24×C43C2×D412yes—
137C24×C43#4112yes—
138C24×C43#4112yes—
139C24×C43C2411yescharacteristic
140C23×D43—21no—
141C23×D43—21no—
142C23×D43—21no—
143C23×D43—21no—
144C23×D43—82no—
145C23×D43C22×C412yes—
146C23×D43C2×D412yes—
147C23×D43C2×D412yes—
148C2×D4×C43—22no—
149C2×D4×C43—22no—
150C2×D4×C43—24no—
151C2×D4×C43—24no—
152C2×D4×C43—22no—
153C2×D4×C43—22no—
154C2×D4×C43—22no—
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—42no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—42no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—24no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—42no—
174C22×C4×C43—82no—
175C22×C4×C43—82no—
176C22×C4×C43C22×C412yes—
177C2×C22⋊D43—24no—
178C2×C22⋊D43—24no—
179C2×C22⋊D43—24no—
180C2×C22⋊D43—24no—
181C2×C22⋊D43—24no—
182C2×C22⋊D43—24no—
183C2×C22⋊D43—24no—
184C2×C22⋊D43—24no—
185C2×C22⋊D43—24no—
186C2×C22⋊D43—24no—
187C2×C22⋊D43—24no—
188C2×C22⋊D43—24no—
189C2×C22⋊D43—28no—
190C2×C22⋊D43—84no—
191C2×C22⋊D43C22⋊C414yes—
192C2×C22⋊D43C22⋊C414yes—
193C2×C22⋊D43C22⋊C414yes—
194C2×C22⋊D43C22⋊C414yes—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—24no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—42no—
205C22×Dic43—82no—
206C22×Dic43—82no—
207C22×Dic43—82no—
208C22×Dic43C22×C412yes—
209C22×Dic43C22×C414yes—
210C22×Dic43C2×D412yes—
211C22×Dic43C2×D412yes—
212C2×C4×D43—28no—
213C2×C4×D43—84no—
214C22⋊C4×C43—24no—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—22no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—42no—
219C22⋊C4×C43C2×D414yes—
220C22⋊Dic43—28no—
221C22⋊Dic43—22no—
222C22⋊Dic43—22no—
223C22⋊Dic43—24no—
224C22⋊Dic43—22no—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227C22⋊Dic43—22no—
228C22⋊Dic43—22no—
229C22⋊Dic43—42no—
230C22⋊Dic43C2×D414yes—
231(C2×D43)⋊C4—28no—
232(C2×D43)⋊C4—28no—
233(C2×D43)⋊C4—84no—
234Dic43⋊C4—28no—
235Dic43⋊C4—28no—
236C4×Dic43—28no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—42no—
241C23×C43—42no—
242C23×C43—42no—
243C23×C43—42no—
244C23×C43—42no—
245C23×C43—42no—
246C23×C43—42no—
247C23×C43—44no—
248C23×C43—42no—
249C23×C43—42no—
250C23×C43—82no—
251C23×C43—82no—
252C23×C43—82no—
253C23×C43—82no—
254C23×C43—82no—
255C23×C43—82no—
256C23×C43—84no—
257C23×C43—84no—
258C23×C43C2×C22⋊C411yescharacteristic
259C23×C43C2×C22⋊C411yescharacteristic
260C23×C43C2×C22⋊C411yescharacteristic
261C23×C43C2×C22⋊C411yescharacteristic
262C23×C43C4×D412yes—
263C23×C43C4×D412yes—
264C23×C43C4×D412yes—
265C23×C43C4×D412yes—
266C23×C43#12012yes—
267C23×C43#12012yes—
268C23×C43#12112yes—
269C23×C43#12112yes—
270C23×C43#12112yes—
271C23×C43#12112yes—
272C23×C43#12312yes—
273C23×C43#12312yes—
274C23×C43C23×C411yescharacteristic
275C23×C43C22×D411yescharacteristic
276C23×C43C22×D411yescharacteristic
277C23×C43C22×D411yescharacteristic
278C23×C43C22×D411yescharacteristic
279C23×C43C2×#4111yescharacteristic
280C23×C43C2×#4111yescharacteristic
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—44no—
288C22×D43—44no—
289C22×D43—44no—
290C22×D43—82no—
291C22×D43—82no—
292C22×D43—82no—
293C22×D43—82no—
294C22×D43C2×C22⋊C414yes—
295D4×C43—42no—
296D4×C43—42no—
297D4×C43—42no—
298D4×C43—42no—
299D4×C43—44no—
300D4×C43—44no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—24no—
305C2×C4×C43—44no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43—44no—
309C2×C4×C43—42no—
310C2×C4×C43—84no—
311C2×C4×C43—84no—
312C22⋊D43—28no—
313C22⋊D43—28no—
314C22⋊D43—28no—
315C22⋊D43—28no—
316C22⋊D43—88no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—24no—
324C2×Dic43—24no—
325C2×Dic43—44no—
326C2×Dic43—44no—
327C2×Dic43—44no—
328C2×Dic43—42no—
329C2×Dic43—82no—
330C2×Dic43—82no—
331C2×Dic43—84no—
332C2×Dic43—84no—
333C2×Dic43C2×C22⋊C414yes—
334C4×D43—88no—
335#20984—431nomaximal, Sylow
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—22no—
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—44no—
360C22×C43—42no—
361C22×C43—82no—
362C22×C43—82no—
363C22×C43—84no—
364C22×C43—84no—
365C22×C43#38612yes—
366C22×C43#38612yes—
367C22×C43#38612yes—
368C22×C43#38612yes—
369C22×C43C22×C22⋊C411yescharacteristic
370C22×C43C2×C4×D411yescharacteristic
371C22×C43C2×C4×D411yescharacteristic
372C22×C43C2×#12011yescharacteristic
373C22×C43C2×#12111yescharacteristic
374C22×C43C2×#12111yescharacteristic
375C22×C43C2×#12311yescharacteristic
376C2×D43—28no—
377C2×D43—24no—
378C2×D43—44no—
379C2×D43—44no—
380C2×D43—82no—
381C2×D43—82no—
382C2×D43—82no—
383C2×D43—82no—
384C4×C43—44no—
385C4×C43—42no—
386C4×C43—82no—
387Dic43—24no—
388Dic43—44no—
389Dic43—44no—
390Dic43—82no—
391C2×#534—431no—
392C2×#518—431no—
393C22×#99—431no—
394C22×#99D4311yescharacteristic, complemented
395#2308—431no—
396#1899—434no—
397#1898—434no—
398C2×#342—431no—
399C2×#342—431no—
400C2×C43—21no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—21no—
404C2×C43—21no—
405C2×C43—21no—
406C2×C43—22no—
407C2×C43—22no—
408C2×C43—22no—
409C2×C43—22no—
410C2×C43—82no—
411C2×C43C2×#38611yescharacteristic
412C2×C43#288312yes—
413D43—44no—
414C23×D4—431no—
415C23×D4C2×D4311yescharacteristic
416#534—862no—
417#534—862no—
418#534—862no—
419#534—862no—
420C2×#123—432no—
421C2×#123—432no—
422C2×#121—434no—
423C2×#120—432no—
424C2×#120—432no—
425#518—864no—
426#518—864no—
427C2×C4×D4—862no—
428C2×C4×D4—862no—
429C2×#117—432no—
430C22×C22⋊C4—431no—
431C22×C22⋊C4—431no—
432C22×C22⋊C4—431no—
433C22×C22⋊C4—432no—
434C22×C22⋊C4C2×D4311yescharacteristic
435C22×C22⋊C4C2×D4311yescharacteristic
436C2×#99—24no—
437C2×#99—434no—
438C2×#99—864no—
439C2×#99C2×D4314yes—
440#386—862no—
441#386—862no—
442#381—432no—
443#379—432no—
444#342—434no—
445#342—434no—
446C43#2098411yescharacteristic, complemented, Sylow
447C25—431no—
448C25C4×D4311yescharacteristic, complemented
449C25C22×D4311yescharacteristic
450C22×D4—22no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—21no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—432no—
459C22×D4—432no—
460C22×D4—432no—
461C22×D4—432no—
462C22×D4—432no—
463C22×D4—432no—
464C22×D4—434no—
465C22×D4—862no—
466C22×D4—862no—
467C22×D4—862no—
468C22×D4—862no—
469C22×D4C4×D4312yescomplemented
470C22×D4C22×D4312yes—
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—431no—
474C23×C4—432no—
475C23×C4—862no—
476C23×C4—861no—
477C23×C4—861no—
478C23×C4C4×D4311yescharacteristic, complemented
479#123—864no—
480#123—864no—
481#123—864no—
482#123—864no—
483#121—868no—
484#121—868no—
485#120—864no—
486#120—864no—
487#120—864no—
488#120—864no—
489C4×D4—8616no—
490C4×D4—8616no—
491#117—864no—
492#117—864no—
493C2×C4⋊C4—434no—
494C2×C4⋊C4—862no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—434no—
501C2×C22⋊C4—432no—
502C2×C22⋊C4—432no—
503C2×C22⋊C4—434no—
504C2×C22⋊C4—432no—
505C2×C22⋊C4—434no—
506C2×C22⋊C4—432no—
507C2×C22⋊C4—864no—
508C2×C22⋊C4—862no—
509C2×C22⋊C4—861no—
510C2×C22⋊C4—861no—
511C2×C22⋊C4—861no—
512C2×C22⋊C4—861no—
513C2×C22⋊C4—861no—
514C2×C22⋊C4—862no—
515C2×C22⋊C4—864no—
516C2×C22⋊C4—862no—
517C2×C22⋊C4—862no—
518C2×C22⋊C4—864no—
519C2×C22⋊C4—861no—
520C2×C22⋊C4C22⋊D4314yescomplemented
521C2×C22⋊C4C22×D4312yes—
522C2×C22⋊C4C22×D4312yes—
523C2×C42—862no—
524#99—28no—
525#99—868no—
526#95—864no—
527C24—21no—
528C24—21no—
529C24—22no—
530C24—22no—
531C24—82no—
532C24—82no—
533C24—432no—
534C24—432no—
535C24—432no—
536C24—861no—
537C24—861no—
538C24—861no—
539C24—861no—
540C24—3442no—
541C24C2×C4×D4312yes—
542C24C2×C4×D4311yescharacteristic
543C24C2×C4×D4311yescharacteristic
544C24#1062189812yes—
545C24D4×D4311yescharacteristic
546C24D4×D4311yescharacteristic
547C24D4×D4311yescharacteristic
548C24D4×D4311yescharacteristic
549C24D4×D4312yes—
550C24#1062190012yes—
551C24C2×C22⋊D4312yes—
552C24C23×D4311yescharacteristic
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—434no—
572C2×D4—434no—
573C2×D4—434no—
574C2×D4—434no—
575C2×D4—864no—
576C2×D4—864no—
577C2×D4—864no—
578C2×D4—864no—
579C2×D4—864no—
580C2×D4—864no—
581C2×D4—864no—
582C2×D4—864no—
583C2×D4—864no—
584C2×D4—864no—
585C2×D4—864no—
586C2×D4—864no—
587C2×D4—868no—
588C2×D4—3444no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—42no—
597C22×C4—82no—
598C22×C4—82no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—432no—
602C22×C4—434no—
603C22×C4—868no—
604C22×C4—861no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—861no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—864no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—3444no—
614C22×C4—3442no—
615C22×C4—3442no—
616C22×C4—3442no—
617C22×C4—1722no—
618C22×C4C2×C4×D4312yes—
619C4⋊C4—868no—
620C4⋊C4—868no—
621C22⋊C4—24no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—42no—
626C22⋊C4—434no—
627C22⋊C4—868no—
628C22⋊C4—868no—
629C22⋊C4—868no—
630C22⋊C4—862no—
631C22⋊C4—862no—
632C22⋊C4—864no—
633C22⋊C4—862no—
634C22⋊C4—862no—
635C22⋊C4—862no—
636C22⋊C4—862no—
637C22⋊C4—862no—
638C22⋊C4—3444no—
639C22⋊C4—1722no—
640C22⋊C4C2×C22⋊D4314yes—
641C42—868no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—44no—
653C23—42no—
654C23—42no—
655C23—82no—
656C23—82no—
657C23—82no—
658C23—82no—
659C23—82no—
660C23—82no—
661C23—84no—
662C23—84no—
663C23—434no—
664C23—862no—
665C23—862no—
666C23—862no—
667C23—862no—
668C23—862no—
669C23—862no—
670C23—3442no—
671C23—3442no—
672C23—3442no—
673C23—3442no—
674C23—1724no—
675C23—1724no—
676C23—1724no—
677C23C22⋊C4×D4311yescharacteristic
678C23C22⋊C4×D4311yescharacteristic
679C23C22⋊C4×D4311yescharacteristic
680C23C22⋊C4×D4311yescharacteristic
681C23(C22⋊D43)⋊C412yes—
682C23(C22⋊D43)⋊C412yes—
683C23C4×C22⋊D4312yes—
684C23C4×C22⋊D4312yes—
685C23#1306329312yes—
686C23#1306329312yes—
687C23#1306329612yes—
688C23#1306329612yes—
689C23#1306329812yes—
690C23#1306329812yes—
691C23#1306330712yes—
692C23#1306330712yes—
693C23C22×C4×D4311yescharacteristic
694C23C2×D4×D4311yescharacteristic
695C23C2×D4×D4311yescharacteristic
696C23C2×D4×D4311yescharacteristic
697C23C22×C22⋊D4311yescharacteristic
698C23C2×#1062190011yescharacteristic
699C23C2×#1062189811yescharacteristic
700D4—42no—
701D4—42no—
702D4—42no—
703D4—42no—
704D4—44no—
705D4—44no—
706D4—868no—
707D4—868no—
708D4—868no—
709D4—868no—
710D4—3448no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—84no—
721C2×C4—84no—
722C2×C4—434no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—864no—
730C2×C4—864no—
731C2×C4—3448no—
732C2×C4—3444no—
733C2×C4—3442no—
734C2×C4—3442no—
735C2×C4—3444no—
736C2×C4—1724no—
737C2×C4—1722no—
738C2×C4—1724no—
739C2×C4—1724no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—44no—
764C22—42no—
765C22—82no—
766C22—82no—
767C22—84no—
768C22—84no—
769C22—868no—
770C22—864no—
771C22—3442no—
772C22—3442no—
773C22—3442no—
774C22—3442no—
775C22—1724no—
776C22—1724no—
777C22#1458277512yes—
778C22#1458277512yes—
779C22#1458277512yes—
780C22#1458277512yes—
781C22C2×C22⋊C4×D4311yescharacteristic
782C22C2×(C22⋊D43)⋊C411yescharacteristic
783C22C2×C4×C22⋊D4311yescharacteristic
784C22C2×#1306329311yescharacteristic
785C22C2×#1306329611yescharacteristic
786C22C2×#1306329811yescharacteristic
787C22C2×#1306330711yescharacteristic
788C4—44no—
789C4—42no—
790C4—82no—
791C4—864no—
792C4—3442no—
793C4—1724no—
794C4—1724no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—22no—
801C2—22no—
802C2—21no—
803C2—22no—
804C2—22no—
805C2—82no—
806C2—1724no—
807C2C2×#1458277511yescharacteristic
808C2#1914305312yes—
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC22×#99×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583458C2
cosocleC24×C43C24
hypercenterC22×#99D43
hypocenterC43#20984
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
2. C2×#14583372C2semidirect
3. C22×#13063240C2semidirect
4. #19137170C2semidirect
5. #19135050C2semidirect
6. #19135045C2semidirect
7. C2×#14582665C2semidirect
8. C2×#14582665C2semidirect
9. C22×#99×C43C2semidirect
15. C2×#13063308C4semidirect
17. C2×#13063297C4semidirect
18. C2×#13063294C4semidirect
24. C2×#13063281C22semidirect
28. C2×C22⋊C4×D43C22semidirect
33. #14582760C22semidirect
34. #14582754C22semidirect
35. #14582665C22semidirect
36. #14582665C22semidirect
49. C22×C22⋊D43C2×C4semidirect
56. C23×Dic43C2×C4semidirect
74. C2×Dic43⋊C4C2×C4semidirect
84. C2×C22⋊Dic43C2×C4semidirect
85. C2×C22⋊Dic43C2×C4semidirect
86. C2×C22⋊Dic43D4semidirect
92. C2×(C2×D43)⋊C4C2×C4semidirect
98. C25×C43C2×C4semidirect
108. C22×D4×C43C2×C4semidirect
112. C23×C4×C43C2×C4semidirect
118. C2×C22⋊C4×C43D4semidirect
394. C22×#99D43semidirect
446. C43#20984semidirect
448. C25C4×D43semidirect
469. C22×D4C4×D43semidirect
478. C23×C4C4×D43semidirect
520. C2×C22⋊C4C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834582
C2×#145833722
C22×#130632402
#191371702
#191350502
#191350452
C2×#145826652
C22×#99×C432
#2098443