Finite Group Databasebeta

← #25098229

Subgroups — #25098229

Order 11008.

2126 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583461C211yesmaximal, characteristic
2C2×#14583372C211yesmaximal, characteristic, complemented
3C22×#13063239C211yesmaximal, characteristic, complemented
4#19137170C211yesmaximal, characteristic, complemented
5#19137170C211yesmaximal, characteristic, complemented
6#19135007C214yesmaximal, complemented
7#19135002C214yesmaximal, complemented
8C2×#14582665C211yesmaximal, characteristic, complemented
9C2×C43×#342C211yesmaximal, characteristic, complemented
10C23×C22⋊D43C2211yescharacteristic
11C23×C22⋊D43C2211yescharacteristic
12#14583461—24no—
13#14583461C418yescomplemented
14C2×#13063309—21no—
15C2×#13063309C2212yes—
16C2×#13063299—22no—
17C2×#13063295—21no—
18C2×#13063295C2212yes—
19#14583372—22no—
20#14583372—22no—
21#14583372—22no—
22#14583372C2214yes—
23C2×C4×C22⋊D43—22no—
24C2×(C22⋊D43)⋊C4—22no—
25C2×#13063281—21no—
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C2×C22⋊C4×D43—21no—
29C2×#13063239—24no—
30C2×#13063239C2214yes—
31#14582778—22no—
32#14582778—22no—
33#14582776—22no—
34#14582776—22no—
35#14582760C2212yescomplemented
36#14582760C2212yescomplemented
37#14582754C2212yescomplemented
38#14582754C2212yescomplemented
39#14582665C2214yescomplemented
40C22×C22⋊C4×C43C2211yescharacteristic
41C22×C22⋊C4×C43C2211yescharacteristic
42C22×C22⋊C4×C43C2211yescharacteristic
43C43×#342C2214yescomplemented
44C24×D43D411yescharacteristic
45C24×D43C2311yescharacteristic
46C22×D172—22no—
47C22×C22⋊D43—21no—
48C22×C22⋊D43—21no—
49C22×C22⋊D43—21no—
50C22×C22⋊D43—21no—
51C22×C22⋊D43—22no—
52C22×C22⋊D43—22no—
53C22×C22⋊D43—21no—
54C22×C22⋊D43—21no—
55C22×C22⋊D43—22no—
56C22×C22⋊D43—21no—
57C22×C22⋊D43—21no—
58C22×C22⋊D43—21no—
59C22×C22⋊D43—21no—
60C22×C22⋊D43—22no—
61C22×C22⋊D43—22no—
62C22×C22⋊D43C2×C414yes—
63C22×C22⋊D43C2×C414yescomplemented
64C22×C22⋊D43D414yes—
65C22×C22⋊D43D412yes—
66C22×C22⋊D43C2312yes—
67C23×Dic43—21no—
68C23×Dic43D411yescharacteristic
69C23×Dic43D412yescomplemented
70C23×Dic43C2311yescharacteristic
71C22×C4×D43—22no—
72#13063309—24no—
73#13063309—28no—
74#13063309C2×C418yescomplemented
75#13063299—216no—
76#13063295—28no—
77#13063295—24no—
78#13063295C2×C418yescomplemented
79C4×C22⋊D43—28no—
80C4×C22⋊D43—28no—
81(C22⋊D43)⋊C4—28no—
82(C22⋊D43)⋊C4—28no—
83#13063281—24no—
84#13063281—24no—
85C2×C4⋊Dic43—22no—
86C2×Dic43⋊C4—22no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—22no—
92C2×C22⋊Dic43—22no—
93C2×C22⋊Dic43—21no—
94C2×C22⋊Dic43D412yescomplemented
95C2×C22⋊Dic43C2312yes—
96C2×C22⋊Dic43C2312yes—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—22no—
99C2×(C2×D43)⋊C4—22no—
100C2×(C2×D43)⋊C4—24no—
101C2×(C2×D43)⋊C4—24no—
102C22⋊C4×D43—24no—
103C22⋊C4×D43—24no—
104C2×C4×Dic43—22no—
105#13063239—28no—
106C43⋊#95—24no—
107C43⋊#95—24no—
108C25×C43C2311yescharacteristic
109C23×C4×C43—21no—
110C23×C4×C43—21no—
111C23×C4×C43D412yescomplemented
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—22no—
118C2×C22⋊C4×C43—22no—
119C2×C22⋊C4×C43—22no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43C2×C414yescomplemented
122C2×C22⋊C4×C43D412yescomplemented
123C2×C22⋊C4×C43C2312yes—
124C2×C22⋊C4×C43C2312yes—
125C2×C22⋊C4×C43C2312yes—
126C24×C43—82no—
127C24×C43C22×C412yes—
128C24×C43C2×D411yescharacteristic
129C24×C43C2×D411yescharacteristic
130C24×C43C2×D411yescharacteristic
131C24×C43C2×D411yescharacteristic
132C24×C43C2×D411yescharacteristic
133C24×C43C2×D411yescharacteristic
134C24×C43C2×D412yes—
135C24×C43#4112yes—
136C24×C43#4112yes—
137C24×C43C2411yescharacteristic
138C23×D43—21no—
139C23×D43—21no—
140C23×D43—22no—
141C23×D43—21no—
142C23×D43—21no—
143C23×D43—21no—
144C23×D43—21no—
145C23×D43—21no—
146C23×D43—21no—
147C23×D43—82no—
148C23×D43—82no—
149C23×D43C22⋊C414yescomplemented
150C23×D43C22×C412yescomplemented
151C23×D43C2×D412yes—
152C22×C4×C43—24no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—42no—
158C22×C4×C43—82no—
159C22×C4×C43—82no—
160C22×C4×C43—82no—
161C22×C4×C43C2×D414yes—
162C2×C22⋊D43—24no—
163C2×C22⋊D43—24no—
164C2×C22⋊D43—24no—
165C2×C22⋊D43—24no—
166C2×C22⋊D43—24no—
167C2×C22⋊D43—24no—
168C2×C22⋊D43—24no—
169C2×C22⋊D43—24no—
170C2×C22⋊D43—24no—
171C2×C22⋊D43—24no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—22no—
174C2×C22⋊D43—24no—
175C2×C22⋊D43—24no—
176C2×C22⋊D43—24no—
177C2×C22⋊D43—24no—
178C2×C22⋊D43—24no—
179C2×C22⋊D43—22no—
180C2×C22⋊D43—22no—
181C2×C22⋊D43—22no—
182C2×C22⋊D43—22no—
183C2×C22⋊D43—41no—
184C2×C22⋊D43—41no—
185C2×C22⋊D43—41no—
186C2×C22⋊D43—41no—
187C2×C22⋊D43—42no—
188C2×C22⋊D43—42no—
189C2×C22⋊D43—42no—
190C2×C22⋊D43—42no—
191C2×C22⋊D43—42no—
192C2×C22⋊D43—42no—
193C2×C22⋊D43C22⋊C418yescomplemented
194C2×C22⋊D43C22×C414yes—
195C2×C22⋊D43C2×D414yes—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C22×Dic43—22no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208C22×Dic43—42no—
209C22×Dic43—82no—
210C22×Dic43—82no—
211C22×Dic43C22⋊C414yescomplemented
212C22×Dic43C22×C412yescomplemented
213C22×Dic43C2×D412yes—
214C22×Dic43C2×D414yes—
215C2×D172—28no—
216C2×D172—84no—
217C2×C4×D43—28no—
218C2×C4×D43—84no—
219C22⋊C4×C43—24no—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—22no—
224C22⋊C4×C43—22no—
225C22⋊C4×C43—22no—
226C22⋊C4×C43—22no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43C22×C414yescomplemented
229C22⋊Dic43—22no—
230C22⋊Dic43—22no—
231C22⋊Dic43—22no—
232C22⋊Dic43—22no—
233C22⋊Dic43—22no—
234C22⋊Dic43—22no—
235C22⋊Dic43—42no—
236(C2×D43)⋊C4—28no—
237(C2×D43)⋊C4—28no—
238(C2×D43)⋊C4—28no—
239(C2×D43)⋊C4—84no—
240(C2×D43)⋊C4—84no—
241C4⋊Dic43—28no—
242Dic43⋊C4—28no—
243C4×Dic43—28no—
244C23×C43—42no—
245C23×C43—42no—
246C23×C43—42no—
247C23×C43—42no—
248C23×C43—42no—
249C23×C43—42no—
250C23×C43—42no—
251C23×C43—82no—
252C23×C43—82no—
253C23×C43—82no—
254C23×C43—82no—
255C23×C43C2×C22⋊C412yes—
256C23×C43C2×C22⋊C412yes—
257C23×C43C4×D412yes—
258C23×C43C4×D412yes—
259C23×C43C4×D412yes—
260C23×C43C4×D412yes—
261C23×C43#12011yescharacteristic
262C23×C43#12011yescharacteristic
263C23×C43#12011yescharacteristic
264C23×C43#12011yescharacteristic
265C23×C43#12112yes—
266C23×C43#12112yes—
267C23×C43#12112yes—
268C23×C43#12112yes—
269C23×C43#12312yes—
270C23×C43#12312yes—
271C23×C43C23×C411yescharacteristic
272C23×C43C22×D411yescharacteristic
273C23×C43C22×D411yescharacteristic
274C23×C43C22×D411yescharacteristic
275C23×C43C22×D411yescharacteristic
276C23×C43C2×#4111yescharacteristic
277C23×C43C2×#4111yescharacteristic
278C22×D43—22no—
279C22×D43—24no—
280C22×D43—22no—
281C22×D43—24no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—44no—
286C22×D43—44no—
287C22×D43—44no—
288C22×D43—44no—
289C22×D43—44no—
290C22×D43—41no—
291C22×D43—41no—
292C22×D43—41no—
293C22×D43—41no—
294C22×D43—82no—
295C22×D43—84no—
296C22×D43—82no—
297C22×D43—84no—
298C22×D43—82no—
299C22×D43—82no—
300C22×D43—82no—
301C22×D43C2×C22⋊C414yes—
302C2×C4×C43—24no—
303C2×C4×C43—24no—
304C2×C4×C43—44no—
305C2×C4×C43—44no—
306C2×C4×C43—44no—
307C2×C4×C43—44no—
308C2×C4×C43—42no—
309C2×C4×C43—82no—
310C2×C4×C43—84no—
311C2×C4×C43—84no—
312C22⋊D43—24no—
313C22⋊D43—24no—
314C22⋊D43—24no—
315C22⋊D43—24no—
316C22⋊D43—28no—
317C22⋊D43—28no—
318C22⋊D43—44no—
319C22⋊D43—44no—
320C22⋊D43—44no—
321C22⋊D43—44no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—24no—
325C2×Dic43—24no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—24no—
330C2×Dic43—44no—
331C2×Dic43—41no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—44no—
336C2×Dic43—44no—
337C2×Dic43—42no—
338C2×Dic43—82no—
339C2×Dic43—84no—
340C2×Dic43C2×C22⋊C414yes—
341D172—88no—
342C4×D43—88no—
343#20960—431nomaximal, Sylow
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—42no—
362C22×C43—42no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43#38612yes—
368C22×C43#38612yes—
369C22×C43#38612yes—
370C22×C43#38612yes—
371C22×C43C22×C22⋊C411yescharacteristic
372C22×C43C2×C4×D411yescharacteristic
373C22×C43C2×C4×D411yescharacteristic
374C22×C43C2×#12011yescharacteristic
375C22×C43C2×#12111yescharacteristic
376C22×C43C2×#12111yescharacteristic
377C22×C43C2×#12311yescharacteristic
378C2×D43—24no—
379C2×D43—48no—
380C2×D43—44no—
381C2×D43—44no—
382C2×D43—44no—
383C2×D43—44no—
384C2×D43—44no—
385C2×D43—42no—
386C2×D43—82no—
387C2×D43—84no—
388C2×D43—82no—
389C2×D43—82no—
390C2×D43—82no—
391C2×D43—82no—
392C4×C43—44no—
393C4×C43—44no—
394C4×C43—82no—
395Dic43—24no—
396Dic43—44no—
397Dic43—42no—
398Dic43—82no—
399C2×#534—431no—
400C2×#518—431no—
401C22×#99—431no—
402#2308—431no—
403#2308—431no—
404#1890—434no—
405#1889—434no—
406C2×#342—431no—
407C2×#342D4311yescharacteristic, complemented
408C2×C43—21no—
409C2×C43—21no—
410C2×C43—21no—
411C2×C43—21no—
412C2×C43—21no—
413C2×C43—22no—
414C2×C43—21no—
415C2×C43—22no—
416C2×C43—22no—
417C2×C43—22no—
418C2×C43C2×#38611yescharacteristic
419C2×C43#302612yes—
420D43—44no—
421D43—82no—
422C23×D4—431no—
423C23×D4—431no—
424#534—438no—
425#534—864no—
426C2×#123—432no—
427C2×#123—861no—
428C2×#121—862no—
429C2×#120—432no—
430C2×#120—861no—
431#518—434no—
432#518—862no—
433#518—862no—
434#518—862no—
435C2×C4×D4—862no—
436C2×C4×D4—862no—
437C2×#117—861no—
438C22×C22⋊C4—431no—
439C22×C22⋊C4—431no—
440C22×C22⋊C4—861no—
441C22×C22⋊C4C2×D4311yescharacteristic
442C22×C22⋊C4C2×D4311yescharacteristic
443C22×C22⋊C4C2×D4311yescharacteristic
444C2×#99—434no—
445C2×#99—864no—
446#386—862no—
447#386—862no—
448#386—862no—
449#386—862no—
450#381—432no—
451#381—432no—
452#379—432no—
453#379—432no—
454#342—434no—
455#342C2×D4314yescomplemented
456C43#2096011yescharacteristic, complemented, Sylow
457C25—431no—
458C25—431no—
459C25C22×D4311yescharacteristic
460C22×D4—434no—
461C22×D4—432no—
462C22×D4—434no—
463C22×D4—432no—
464C22×D4—434no—
465C22×D4—862no—
466C22×D4—861no—
467C22×D4—861no—
468C22×D4—862no—
469C22×D4—861no—
470C22×D4—861no—
471C22×D4—862no—
472C22×D4—861no—
473C22×D4—861no—
474C22×D4—862no—
475C22×D4—861no—
476C22×D4—861no—
477C22×D4—862no—
478C22×D4—861no—
479C22×D4—861no—
480C22×D4—862no—
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—432no—
486C23×C4—862no—
487C23×C4—861no—
488C23×C4D17212yescomplemented
489#123—438no—
490#123—868no—
491#123—864no—
492#121—8616no—
493#120—438no—
494#120—864no—
495#120—868no—
496C4×D4—868no—
497C4×D4—868no—
498C4×D4—868no—
499C4×D4—868no—
500#117—864no—
501#117—864no—
502C2×C4⋊C4—862no—
503C2×C4⋊C4—862no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—432no—
514C2×C22⋊C4—432no—
515C2×C22⋊C4—432no—
516C2×C22⋊C4—864no—
517C2×C22⋊C4—864no—
518C2×C22⋊C4—862no—
519C2×C22⋊C4—862no—
520C2×C22⋊C4—862no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—862no—
526C2×C22⋊C4—862no—
527C2×C22⋊C4—864no—
528C2×C22⋊C4—864no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4C4×D4314yescomplemented
531C2×C22⋊C4D17212yescomplemented
532C2×C22⋊C4C22×D4312yes—
533C2×C22⋊C4C22×D4312yes—
534C2×C22⋊C4C22×D4312yes—
535C2×C42—862no—
536#99—868no—
537#95—864no—
538#95—864no—
539C24—82no—
540C24—434no—
541C24—432no—
542C24—432no—
543C24—861no—
544C24—862no—
545C24—861no—
546C24—861no—
547C24—861no—
548C24—861no—
549C24—861no—
550C24—861no—
551C24—861no—
552C24—3442no—
553C24—3442no—
554C24C2×C4×D4312yes—
555C24C2×D17211yescharacteristic
556C24C2×D17211yescharacteristic
557C24#1062189812yes—
558C24D4×D4311yescharacteristic
559C24D4×D4311yescharacteristic
560C24D4×D4311yescharacteristic
561C24D4×D4311yescharacteristic
562C24D4×D4312yes—
563C24#1062190212yes—
564C24C23×D4311yescharacteristic
565C2×D4—438no—
566C2×D4—434no—
567C2×D4—434no—
568C2×D4—868no—
569C2×D4—864no—
570C2×D4—864no—
571C2×D4—864no—
572C2×D4—864no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—864no—
576C2×D4—864no—
577C2×D4—864no—
578C2×D4—864no—
579C2×D4—864no—
580C2×D4—862no—
581C2×D4—862no—
582C2×D4—862no—
583C2×D4—862no—
584C2×D4—864no—
585C2×D4—864no—
586C2×D4—864no—
587C2×D4—864no—
588C2×D4—864no—
589C2×D4—864no—
590C2×D4—3444no—
591C2×D4—1721no—
592C2×D4—1721no—
593C2×D4—1721no—
594C2×D4—1721no—
595C2×D4—1722no—
596C2×D4—1722no—
597C2×D4—1722no—
598C2×D4—1722no—
599C2×D4—1722no—
600C2×D4—1722no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—42no—
607C22×C4—82no—
608C22×C4—82no—
609C22×C4—82no—
610C22×C4—434no—
611C22×C4—432no—
612C22×C4—432no—
613C22×C4—434no—
614C22×C4—868no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—861no—
625C22×C4—861no—
626C22×C4—862no—
627C22×C4—3444no—
628C22×C4—3442no—
629C22×C4—3442no—
630C22×C4—1722no—
631C22×C4C2×D17214yes—
632C4⋊C4—868no—
633C4⋊C4—868no—
634C22⋊C4—24no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—42no—
643C22⋊C4—868no—
644C22⋊C4—868no—
645C22⋊C4—868no—
646C22⋊C4—862no—
647C22⋊C4—862no—
648C22⋊C4—862no—
649C22⋊C4—862no—
650C22⋊C4—862no—
651C22⋊C4—862no—
652C22⋊C4—3444no—
653C22⋊C4—3444no—
654C22⋊C4—1722no—
655C22⋊C4C2×C4×D4314yescomplemented
656C42—868no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—82no—
665C23—82no—
666C23—82no—
667C23—82no—
668C23—434no—
669C23—862no—
670C23—864no—
671C23—862no—
672C23—864no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—3442no—
677C23—3444no—
678C23—3442no—
679C23—3442no—
680C23—3442no—
681C23—3444no—
682C23—3442no—
683C23—1724no—
684C23—1724no—
685C23—1724no—
686C23—1724no—
687C23—1724no—
688C23—1721no—
689C23—1721no—
690C23—1721no—
691C23—1721no—
692C23C22⋊C4×D4312yes—
693C23C22⋊C4×D4312yes—
694C23#1306328712yes—
695C23#1306328712yes—
696C23C4×D17212yes—
697C23C4×D17212yes—
698C23#1306329511yescharacteristic
699C23#1306329511yescharacteristic
700C23#1306329511yescharacteristic
701C23#1306329511yescharacteristic
702C23#1306329812yes—
703C23#1306329812yes—
704C23#1306330012yes—
705C23#1306330012yes—
706C23#1306331012yes—
707C23#1306331012yes—
708C23C22×C4×D4311yescharacteristic
709C23C2×D4×D4311yescharacteristic
710C23C2×D4×D4311yescharacteristic
711C23C2×D4×D4311yescharacteristic
712C23C22×D17211yescharacteristic
713C23C2×#1062189811yescharacteristic
714C23C2×#1062190211yescharacteristic
715D4—864no—
716D4—864no—
717D4—864no—
718D4—864no—
719D4—868no—
720D4—868no—
721D4—3448no—
722D4—1724no—
723D4—1724no—
724D4—1724no—
725D4—1724no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—82no—
734C2×C4—84no—
735C2×C4—84no—
736C2×C4—434no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—864no—
740C2×C4—864no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—864no—
745C2×C4—3448no—
746C2×C4—3444no—
747C2×C4—3442no—
748C2×C4—1724no—
749C2×C4—1722no—
750C2×C4—1724no—
751C2×C4—1721no—
752C2×C4—1721no—
753C2×C4—1721no—
754C2×C4—1721no—
755C2×C4—1724no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—864no—
780C22—3442no—
781C22—3442no—
782C22—3442no—
783C22—3444no—
784C22—3442no—
785C22—3442no—
786C22—1724no—
787C22—1724no—
788C22—1724no—
789C22—1724no—
790C22—1728no—
791C22—1722no—
792C22—1724no—
793C22#1458277712yes—
794C22#1458277712yes—
795C22#1458277712yes—
796C22#1458277712yes—
797C22C2×C22⋊C4×D4311yescharacteristic
798C22C2×#1306328711yescharacteristic
799C22C2×C4×D17211yescharacteristic
800C22C2×#1306329511yescharacteristic
801C22C2×#1306329811yescharacteristic
802C22C2×#1306330011yescharacteristic
803C22C2×#1306331011yescharacteristic
804C4—44no—
805C4—44no—
806C4—82no—
807C4—864no—
808C4—3442no—
809C4—1724no—
810C4—1722no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—22no—
816C2—21no—
817C2—21no—
818C2—22no—
819C2—22no—
820C2—22no—
821C2—3442no—
822C2—1724no—
823C2C2×#1458277711yescharacteristic
824C2#1914399412yes—
subgroupG/H
centerC22C2×#13063295
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC2×C43×#342C2
socleC22×C43C2×#120
prime radicalC2×#14583461C2
cosocleC24×C43C24
hypercenterC2×#342D43
hypocenterC43#20960
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
2. C2×#14583372C2semidirect
3. C22×#13063239C2semidirect
4. #19137170C2semidirect
5. #19137170C2semidirect
6. #19135007C2semidirect
7. #19135002C2semidirect
8. C2×#14582665C2semidirect
9. C2×C43×#342C2semidirect
13. #14583461C4semidirect
35. #14582760C22semidirect
36. #14582760C22semidirect
37. #14582754C22semidirect
38. #14582754C22semidirect
39. #14582665C22semidirect
43. C43×#342C22semidirect
63. C22×C22⋊D43C2×C4semidirect
69. C23×Dic43D4semidirect
74. #13063309C2×C4semidirect
78. #13063295C2×C4semidirect
94. C2×C22⋊Dic43D4semidirect
111. C23×C4×C43D4semidirect
121. C2×C22⋊C4×C43C2×C4semidirect
122. C2×C22⋊C4×C43D4semidirect
149. C23×D43C22⋊C4semidirect
150. C23×D43C22×C4semidirect
193. C2×C22⋊D43C22⋊C4semidirect
211. C22×Dic43C22⋊C4semidirect
212. C22×Dic43C22×C4semidirect
228. C22⋊C4×C43C22×C4semidirect
407. C2×#342D43semidirect
455. #342C2×D43semidirect
456. C43#20960semidirect
488. C23×C4D172semidirect
530. C2×C22⋊C4C4×D43semidirect
531. C2×C22⋊C4D172semidirect
655. C22⋊C4C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834612
C2×#145833722
C22×#130632392
#191371702
#191350072
#191350022
C2×#145826652
C2×C43×#3422
#2096043