Finite Group Databasebeta

← #25003062

Subgroups — #25003062

Order 11008.

1526 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063240C211yesmaximal, characteristic
2C2×#14582779C211yesmaximal, characteristic
3C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
4C2×#14582665C211yesmaximal, characteristic, complemented
5C2×#14582665C211yesmaximal, characteristic, complemented
6#19132817C211yesmaximal, characteristic, complemented
7C22×#99×C43C211yesmaximal, characteristic
8C24×Dic43C2211yescharacteristic
9C22×C22⋊Dic43C412yescomplemented
10C22×C22⋊Dic43C2211yescharacteristic
11C22×C22⋊Dic43C2211yescharacteristic
12C22×C22⋊Dic43C2211yescharacteristic
13C22×C4×Dic43—21no—
14C2×#13063240—22no—
15C2×#13063240—22no—
16C2×#13063240C414yescomplemented
17#14582779—21no—
18#14582779—22no—
19#14582779—21no—
20C22⋊C4×Dic43—22no—
21C22⋊C4×Dic43—22no—
22C2×C43⋊#95—21no—
23C2×C43⋊#95—22no—
24C2×C43⋊#95C412yescomplemented
25#14582665—22no—
26#14582665—22no—
27C23×D4×C43C2211yescharacteristic
28C22×C22⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2211yescharacteristic
30C2×#99×C43—22no—
31C2×#99×C43—22no—
32C2×#99×C43C414yescomplemented
33C23×Dic43—21no—
34C23×Dic43—21no—
35C23×Dic43—21no—
36C23×Dic43—21no—
37C23×Dic43—21no—
38C23×Dic43—21no—
39C23×Dic43—44no—
40C23×Dic43C2×C412yes—
41C23×Dic43C2×C412yes—
42C23×Dic43D411yescharacteristic
43C23×Dic43D412yes—
44C23×Dic43D411yescharacteristic
45C2×C22⋊Dic43—21no—
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C22⋊Dic43—21no—
52C2×C22⋊Dic43—21no—
53C2×C22⋊Dic43—21no—
54C2×C22⋊Dic43—21no—
55C2×C22⋊Dic43—21no—
56C2×C22⋊Dic43—21no—
57C2×C22⋊Dic43—21no—
58C2×C22⋊Dic43—21no—
59C2×C22⋊Dic43—22no—
60C2×C22⋊Dic43—22no—
61C2×C22⋊Dic43—44no—
62C2×C22⋊Dic43C2×C412yes—
63C2×C22⋊Dic43C2×C412yes—
64C2×C22⋊Dic43D412yes—
65C2×C22⋊Dic43D412yes—
66C2×C4×Dic43—24no—
67C2×C4×Dic43—44no—
68#13063240—28no—
69C43⋊#95—24no—
70C43⋊#95—22no—
71C43⋊#95—22no—
72C43⋊#95—44no—
73C25×C43C2×C411yescharacteristic
74C25×C43C2311yescharacteristic
75C22×D4×C43—21no—
76C22×D4×C43—21no—
77C22×D4×C43—21no—
78C22×D4×C43—21no—
79C22×D4×C43—21no—
80C22×D4×C43—21no—
81C22×D4×C43—21no—
82C22×D4×C43—21no—
83C22×D4×C43—21no—
84C22×D4×C43—21no—
85C22×D4×C43—21no—
86C22×D4×C43—21no—
87C22×D4×C43C2×C412yes—
88C22×D4×C43C2×C412yes—
89C23×C4×C43—21no—
90C23×C4×C43—21no—
91C23×C4×C43C2×C411yescharacteristic
92C2×C22⋊C4×C43—21no—
93C2×C22⋊C4×C43—21no—
94C2×C22⋊C4×C43—21no—
95C2×C22⋊C4×C43—21no—
96C2×C22⋊C4×C43—21no—
97C2×C22⋊C4×C43—21no—
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43C2×C412yes—
101C2×C22⋊C4×C43C2×C412yes—
102C2×C22⋊C4×C43D412yes—
103C2×C22⋊C4×C43D412yes—
104#99×C43—28no—
105C24×C43—21no—
106C24×C43—21no—
107C24×C43—21no—
108C24×C43—21no—
109C24×C43—21no—
110C24×C43—21no—
111C24×C43—42no—
112C24×C43—42no—
113C24×C43—42no—
114C24×C43—42no—
115C24×C43C4212yescomplemented
116C24×C43C22×C411yescharacteristic
117C24×C43C22×C411yescharacteristic
118C24×C43C22×C411yescharacteristic
119C24×C43C2×D411yescharacteristic
120C24×C43C2×D411yescharacteristic
121C24×C43C2×D411yescharacteristic
122C24×C43C2×D411yescharacteristic
123C24×C43C2×D411yescharacteristic
124C24×C43C2×D411yescharacteristic
125C24×C43#4111yescharacteristic
126C24×C43#4111yescharacteristic
127C24×C43#4111yescharacteristic
128C24×C43#4111yescharacteristic
129C24×C43#4111yescharacteristic
130C24×C43#4111yescharacteristic
131C2×D4×C43—22no—
132C2×D4×C43—22no—
133C2×D4×C43—22no—
134C2×D4×C43—22no—
135C2×D4×C43—22no—
136C2×D4×C43—22no—
137C2×D4×C43—22no—
138C2×D4×C43—22no—
139C2×D4×C43—22no—
140C2×D4×C43—22no—
141C2×D4×C43—22no—
142C2×D4×C43—22no—
143C2×D4×C43—41no—
144C2×D4×C43—41no—
145C2×D4×C43—41no—
146C2×D4×C43—41no—
147C2×D4×C43—41no—
148C2×D4×C43—41no—
149C2×D4×C43—41no—
150C2×D4×C43—41no—
151C2×D4×C43—41no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—41no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—22no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—42no—
170C22×C4×C43—42no—
171C22×C4×C43—42no—
172C22×C4×C43—42no—
173C22×C4×C43—41no—
174C22×C4×C43—41no—
175C22×C4×C43C4212yescomplemented
176C22×Dic43—24no—
177C22×Dic43—24no—
178C22×Dic43—24no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198C22×Dic43—42no—
199C22×Dic43—42no—
200C22×Dic43—42no—
201C22×Dic43—42no—
202C22×Dic43—42no—
203C22×Dic43—44no—
204C22×Dic43—44no—
205C22×Dic43—44no—
206C22×Dic43—44no—
207C22×Dic43—41no—
208C22×Dic43—41no—
209C22×Dic43C22⋊C412yes—
210C22×Dic43C22⋊C412yes—
211C22⋊C4×C43—22no—
212C22⋊C4×C43—22no—
213C22⋊C4×C43—22no—
214C22⋊C4×C43—22no—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—41no—
217C22⋊C4×C43—41no—
218C22⋊C4×C43C22⋊C414yescomplemented
219C22⋊Dic43—22no—
220C22⋊Dic43—22no—
221C22⋊Dic43—22no—
222C22⋊Dic43—22no—
223C22⋊Dic43—22no—
224C22⋊Dic43—44no—
225C22⋊Dic43—44no—
226C22⋊Dic43—41no—
227C22⋊Dic43—41no—
228C22⋊Dic43—41no—
229C22⋊Dic43—41no—
230C22⋊Dic43—41no—
231C22⋊Dic43—41no—
232C22⋊Dic43C22⋊C414yescomplemented
233C4×Dic43—48no—
234C23×C43—22no—
235C23×C43—22no—
236C23×C43—22no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—22no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—41no—
246C23×C43—41no—
247C23×C43—42no—
248C23×C43—42no—
249C23×C43—41no—
250C23×C43—42no—
251C23×C43—41no—
252C23×C43—42no—
253C23×C43—41no—
254C23×C43—42no—
255C23×C43—41no—
256C23×C43—42no—
257C23×C43—42no—
258C23×C43—42no—
259C23×C43—44no—
260C23×C43—44no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—42no—
266C23×C43—42no—
267C23×C43—81no—
268C23×C43—81no—
269C23×C43—81no—
270C23×C43—81no—
271C23×C43—82no—
272C23×C43—82no—
273C23×C43C2×C4211yescharacteristic
274C23×C43C2×C22⋊C411yescharacteristic
275C23×C43C2×C22⋊C411yescharacteristic
276C23×C43C2×C22⋊C411yescharacteristic
277C23×C43#11711yescharacteristic
278C23×C43#11711yescharacteristic
279C23×C43#11711yescharacteristic
280C23×C43C4×D411yescharacteristic
281C23×C43C4×D411yescharacteristic
282C23×C43C4×D411yescharacteristic
283C23×C43C4×D411yescharacteristic
284C23×C43C4×D411yescharacteristic
285C23×C43C4×D411yescharacteristic
286C23×C43C4×D411yescharacteristic
287C23×C43C4×D411yescharacteristic
288C23×C43C4×D411yescharacteristic
289C23×C43C4×D411yescharacteristic
290C23×C43C4×D411yescharacteristic
291C23×C43C4×D411yescharacteristic
292C23×C43#12011yescharacteristic
293C23×C43#12111yescharacteristic
294C23×C43#12111yescharacteristic
295C23×C43#12111yescharacteristic
296C23×C43#12111yescharacteristic
297C23×C43#12111yescharacteristic
298C23×C43#12111yescharacteristic
299C23×C43#12311yescharacteristic
300C23×C43#12311yescharacteristic
301C23×C43#12311yescharacteristic
302C23×C43#12411yescharacteristic
303C23×C43#12411yescharacteristic
304C23×C43#12411yescharacteristic
305C23×C43#12611yescharacteristic
306C23×C43#12611yescharacteristic
307C23×C43#12711yescharacteristic
308D4×C43—42no—
309D4×C43—42no—
310D4×C43—42no—
311D4×C43—42no—
312D4×C43—42no—
313D4×C43—42no—
314D4×C43—42no—
315D4×C43—42no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—24no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—44no—
323C2×C4×C43—44no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—44no—
329C2×C4×C43—42no—
330C2×C4×C43—81no—
331C2×C4×C43—81no—
332C2×C4×C43—82no—
333C2×Dic43—24no—
334C2×Dic43—24no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—24no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—44no—
342C2×Dic43—44no—
343C2×Dic43—44no—
344C2×Dic43—44no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—44no—
348C2×Dic43—44no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43—44no—
352C2×Dic43—42no—
353C2×Dic43—42no—
354C2×Dic43—42no—
355C2×Dic43—42no—
356C2×Dic43—81no—
357C2×Dic43—81no—
358C2×Dic43—82no—
359C2×Dic43—82no—
360C2×Dic43—82no—
361C2×Dic43#9914yescomplemented
362#10960—431nomaximal, Sylow
363C22×C43—21no—
364C22×C43—21no—
365C22×C43—21no—
366C22×C43—21no—
367C22×C43—21no—
368C22×C43—21no—
369C22×C43—21no—
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—21no—
374C22×C43—21no—
375C22×C43—22no—
376C22×C43—22no—
377C22×C43—22no—
378C22×C43—22no—
379C22×C43—22no—
380C22×C43—22no—
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—41no—
388C22×C43—41no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—41no—
396C22×C43—41no—
397C22×C43—41no—
398C22×C43—41no—
399C22×C43—41no—
400C22×C43—41no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—42no—
404C22×C43—44no—
405C22×C43—82no—
406C22×C43—82no—
407C22×C43—82no—
408C22×C43—82no—
409C22×C43—81no—
410C22×C43—81no—
411C22×C43—82no—
412C22×C43C4×C22⋊C411yescharacteristic
413C22×C43C4×C22⋊C411yescharacteristic
414C22×C43C4×C22⋊C411yescharacteristic
415C22×C43#38611yescharacteristic
416C22×C43#38611yescharacteristic
417C22×C43#38611yescharacteristic
418C22×C43#38811yescharacteristic
419C22×C43#38811yescharacteristic
420C22×C43#38811yescharacteristic
421C22×C43#38811yescharacteristic
422C22×C43#38811yescharacteristic
423C22×C43#38811yescharacteristic
424C22×C43#39011yescharacteristic
425C22×C43#39011yescharacteristic
426C22×C43#39011yescharacteristic
427C22×C43C2×#9912yes—
428C22×C43#41012yes—
429C4×C43—44no—
430C4×C43—42no—
431C4×C43—82no—
432Dic43—24no—
433Dic43—44no—
434Dic43—42no—
435Dic43—82no—
436Dic43—82no—
437C22×#99—431no—
438C22×#99D4311yescharacteristic
439C2×#386—431no—
440C2×C4×C22⋊C4—431no—
441C2×#342—431no—
442C2×#342—431no—
443C22⋊#95—431no—
444C2×C43—21no—
445C2×C43—21no—
446C2×C43—21no—
447C2×C43—21no—
448C2×C43—21no—
449C2×C43—21no—
450C2×C43—21no—
451C2×C43—21no—
452C2×C43—21no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—21no—
456C2×C43—82no—
457C2×C43#143711yescharacteristic
458C2×C43C4×#9912yes—
459C2×C43#189811yescharacteristic
460C2×C43#189911yescharacteristic
461C2×C43#196412yes—
462C23×D4C2×D4311yescharacteristic
463C24×C4—431no—
464C22×C22⋊C4—431no—
465C22×C22⋊C4—431no—
466C22×C22⋊C4—431no—
467C22×C22⋊C4—432no—
468C22×C22⋊C4C2×D4311yescharacteristic
469C22×C22⋊C4C2×D4311yescharacteristic
470C22×C42—861no—
471C2×#99—22no—
472C2×#99—22no—
473C2×#99—434no—
474C2×#99—862no—
475C2×#99—862no—
476C2×#99Dic4314yescomplemented
477#386—861no—
478#386—862no—
479#386—861no—
480C4×C22⋊C4—862no—
481C4×C22⋊C4—862no—
482C2×#95—432no—
483C2×#95—861no—
484C2×#95—862no—
485#342—862no—
486#342—862no—
487C43#1096011yescharacteristic, complemented, Sylow
488C25C4×D4311yescharacteristic
489C25C22×D4311yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C4×D4312yes—
503C22×D4C2×Dic4312yes—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—431no—
507C23×C4—432no—
508C23×C4—432no—
509C23×C4—431no—
510C23×C4—432no—
511C23×C4—861no—
512C23×C4—861no—
513C23×C4—861no—
514C23×C4—861no—
515C23×C4—861no—
516C23×C4—861no—
517C23×C4—1724no—
518C23×C4C4×D4311yescharacteristic
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—432no—
528C2×C22⋊C4—432no—
529C2×C22⋊C4—432no—
530C2×C22⋊C4—432no—
531C2×C22⋊C4—861no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—861no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—862no—
539C2×C22⋊C4—862no—
540C2×C22⋊C4—861no—
541C2×C22⋊C4—861no—
542C2×C22⋊C4—861no—
543C2×C22⋊C4—861no—
544C2×C22⋊C4—861no—
545C2×C22⋊C4—861no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—1724no—
548C2×C22⋊C4C2×Dic4312yes—
549C2×C22⋊C4C2×Dic4312yes—
550C2×C22⋊C4C22⋊D4312yes—
551C2×C22⋊C4C22⋊D4312yes—
552C2×C42—864no—
553C2×C42—1724no—
554#99—28no—
555#99—868no—
556#95—862no—
557#95—862no—
558#95—864no—
559#95—1724no—
560C24—21no—
561C24—21no—
562C24—21no—
563C24—21no—
564C24—21no—
565C24—21no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24C4×Dic4312yescomplemented
571C24C2×C4×D4311yescharacteristic
572C24C2×C4×D4311yescharacteristic
573C24#1062189811yescharacteristic
574C24#1062189811yescharacteristic
575C24D4×D4311yescharacteristic
576C24D4×D4311yescharacteristic
577C24D4×D4311yescharacteristic
578C24D4×D4311yescharacteristic
579C24#1062190011yescharacteristic
580C24#1062190011yescharacteristic
581C24#1062190011yescharacteristic
582C24#1062190011yescharacteristic
583C24C22×Dic4311yescharacteristic
584C24C2×C22⋊D4311yescharacteristic
585C24C2×C22⋊D4311yescharacteristic
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—432no—
631C22×C4—432no—
632C22×C4—864no—
633C22×C4—864no—
634C22×C4—864no—
635C22×C4—861no—
636C22×C4—861no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—861no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—861no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—862no—
650C22×C4—1722no—
651C22×C4—1722no—
652C22×C4—1722no—
653C22×C4—1724no—
654C22×C4—1724no—
655C22×C4—1724no—
656C22×C4—1724no—
657C22×C4—1722no—
658C22×C4—1722no—
659C22×C4—1721no—
660C22×C4—1721no—
661C22×C4—1722no—
662C22×C4—1722no—
663C22×C4—1722no—
664C22×C4—1722no—
665C22×C4C4×Dic4312yescomplemented
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—41no—
672C22⋊C4—41no—
673C22⋊C4—434no—
674C22⋊C4—862no—
675C22⋊C4—862no—
676C22⋊C4—862no—
677C22⋊C4—862no—
678C22⋊C4—862no—
679C22⋊C4—1724no—
680C22⋊C4—1724no—
681C22⋊C4—1721no—
682C22⋊C4—1721no—
683C22⋊C4—1721no—
684C22⋊C4—1721no—
685C22⋊C4—1721no—
686C22⋊C4—1721no—
687C22⋊C4C22⋊Dic4314yescomplemented
688C42—1728no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—41no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—42no—
703C23—41no—
704C23—42no—
705C23—41no—
706C23—42no—
707C23—41no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—44no—
715C23—44no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—42no—
720C23—42no—
721C23—41no—
722C23—81no—
723C23—81no—
724C23—81no—
725C23—81no—
726C23—82no—
727C23—82no—
728C23C2×C4×Dic4311yescharacteristic
729C23C22⋊C4×D4311yescharacteristic
730C23C22⋊C4×D4311yescharacteristic
731C23C2×C22⋊Dic4311yescharacteristic
732C23#1306328111yescharacteristic
733C23#1306328111yescharacteristic
734C23#1306328411yescharacteristic
735C23(C22⋊D43)⋊C411yescharacteristic
736C23(C22⋊D43)⋊C411yescharacteristic
737C23(C22⋊D43)⋊C411yescharacteristic
738C23(C22⋊D43)⋊C411yescharacteristic
739C23C4×C22⋊D4311yescharacteristic
740C23C4×C22⋊D4311yescharacteristic
741C23C4×C22⋊D4311yescharacteristic
742C23C4×C22⋊D4311yescharacteristic
743C23D4×Dic4311yescharacteristic
744C23D4×Dic4311yescharacteristic
745C23D4×Dic4311yescharacteristic
746C23D4×Dic4311yescharacteristic
747C23#1306329311yescharacteristic
748C23#1306329611yescharacteristic
749C23#1306329611yescharacteristic
750C23#1306329711yescharacteristic
751C23#1306329711yescharacteristic
752C23#1306329811yescharacteristic
753C23#1306329811yescharacteristic
754C23#1306330611yescharacteristic
755C23#1306330711yescharacteristic
756C23#1306330711yescharacteristic
757C23#1306331111yescharacteristic
758C23#1306331111yescharacteristic
759C23#1306331211yescharacteristic
760C23#1306331811yescharacteristic
761C23#1306331811yescharacteristic
762C23#1306332111yescharacteristic
763D4—42no—
764D4—42no—
765D4—42no—
766D4—42no—
767D4—42no—
768D4—42no—
769D4—42no—
770D4—42no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—82no—
788C2×C4—434no—
789C2×C4—864no—
790C2×C4—864no—
791C2×C4—862no—
792C2×C4—862no—
793C2×C4—862no—
794C2×C4—862no—
795C2×C4—864no—
796C2×C4—862no—
797C2×C4—3441no—
798C2×C4—3441no—
799C2×C4—3442no—
800C2×C4—3442no—
801C2×C4—3442no—
802C2×C4—1724no—
803C2×C4—1724no—
804C2×C4—1724no—
805C2×C4—1724no—
806C2×C4—1724no—
807C2×C4—1722no—
808C2×C4—1722no—
809C2×C4—1722no—
810C2×C4—1722no—
811C2×C4—1722no—
812C2×C4—1722no—
813C2×C4—1722no—
814C2×C4—1722no—
815C2×C4—1724no—
816C2×C4—1724no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—21no—
829C22—22no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—42no—
858C22—44no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—81no—
864C22—81no—
865C22—82no—
866C22C4×C22⋊Dic4311yescharacteristic
867C22C22⋊C4×Dic4311yescharacteristic
868C22C22⋊C4×Dic4311yescharacteristic
869C22#1458277511yescharacteristic
870C22#1458277511yescharacteristic
871C22#1458277911yescharacteristic
872C22#1458278711yescharacteristic
873C22#1458278711yescharacteristic
874C22#1458279211yescharacteristic
875C22#1458279211yescharacteristic
876C22#1458279311yescharacteristic
877C22#1458279311yescharacteristic
878C22#1458279911yescharacteristic
879C22#1458279911yescharacteristic
880C22#1458280211yescharacteristic
881C22#99×D4312yes—
882C22#1458287112yes—
883C4—44no—
884C4—42no—
885C4—82no—
886C4—864no—
887C4—3442no—
888C4—3442no—
889C4—1724no—
890C4—1722no—
891C2—21no—
892C2—21no—
893C2—21no—
894C2—21no—
895C2—21no—
896C2—21no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—21no—
903C2—82no—
904C2#1913283211yescharacteristic
905C2#99×Dic4312yes—
906C2#1913504511yescharacteristic
907C2#1913505011yescharacteristic
908C2#1913542912yes—
subgroupG/H
centerC23C22⋊C4×D43
commutatorC23×C43C2×C42
FrattiniC25C22×D43
FittingC22×#99×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D4×C43C22
cosocleC25×C43C23
hypercenterC22×#99D43
hypocenterC43#10960
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic43C2semidirect
4. C2×#14582665C2semidirect
5. C2×#14582665C2semidirect
6. #19132817C2semidirect
9. C22×C22⋊Dic43C4semidirect
16. C2×#13063240C4semidirect
24. C2×C43⋊#95C4semidirect
32. C2×#99×C43C4semidirect
115. C24×C43C42semidirect
175. C22×C4×C43C42semidirect
218. C22⋊C4×C43C22⋊C4semidirect
232. C22⋊Dic43C22⋊C4semidirect
361. C2×Dic43#99semidirect
476. C2×#99Dic43semidirect
487. C43#10960semidirect
570. C24C4×Dic43semidirect
665. C22×C4C4×Dic43semidirect
687. C22⋊C4C22⋊Dic43semidirect

Maximal subgroups

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

subgroupindex
C22×#130632402
C2×#145827792
C2×C22⋊C4×Dic432
C2×#145826652
#191328172
C22×#99×C432
#1096043