Finite Group Databasebeta

← #25001938

Subgroups — #25001938

Order 11008.

1794 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583372C211yesmaximal, characteristic
2C22×#13063239C211yesmaximal, characteristic
3C2×#14582776C211yesmaximal, characteristic
4C2×#14582665C211yesmaximal, characteristic, complemented
5#19132817C211yesmaximal, characteristic, complemented
6#19132817C211yesmaximal, characteristic, complemented
7C2×C43×#342C211yesmaximal, characteristic, complemented
8C23×C22⋊D43C2211yescharacteristic
9C24×Dic43C2211yescharacteristic
10#14583372—22no—
11#14583372—22no—
12#14583372—22no—
13#14583372C414yescomplemented
14C2×C4×C22⋊D43—22no—
15C2×(C22⋊D43)⋊C4—22no—
16C2×#13063281—21no—
17C22×C22⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2211yescharacteristic
19C22×(C2×D43)⋊C4—21no—
20C2×C22⋊C4×D43—21no—
21C2×#13063239—22no—
22C2×#13063239—22no—
23C2×#13063239C414yescomplemented
24#14582776—22no—
25#14582776C414yescomplemented
26C2×C43⋊#95—21no—
27C2×C43⋊#95—22no—
28C2×C43⋊#95—22no—
29#14582665—22no—
30C22×C22⋊C4×C43C2211yescharacteristic
31C22×C22⋊C4×C43C2211yescharacteristic
32C22×C22⋊C4×C43C2211yescharacteristic
33C43×#342—22no—
34C24×D43D411yescharacteristic
35C22×C22⋊D43—21no—
36C22×C22⋊D43—21no—
37C22×C22⋊D43—21no—
38C22×C22⋊D43—21no—
39C22×C22⋊D43—21no—
40C22×C22⋊D43—21no—
41C22×C22⋊D43—21no—
42C22×C22⋊D43—21no—
43C22×C22⋊D43C2×C412yes—
44C22×C22⋊D43C2×C412yes—
45C22×C22⋊D43C2×C412yes—
46C22×C22⋊D43D412yes—
47C22×C22⋊D43D412yes—
48C22×C22⋊D43Q812yes—
49C23×Dic43—21no—
50C23×Dic43—21no—
51C23×Dic43—21no—
52C23×Dic43—21no—
53C23×Dic43—21no—
54C23×Dic43—21no—
55C23×Dic43—21no—
56C23×Dic43—44no—
57C23×Dic43C2×C412yescomplemented
58C23×Dic43D411yescharacteristic
59C23×Dic43D412yes—
60C22×C4×D43—22no—
61C4×C22⋊D43—28no—
62C4×C22⋊D43—28no—
63(C22⋊D43)⋊C4—28no—
64(C22⋊D43)⋊C4—28no—
65#13063281—24no—
66#13063281—24no—
67C2×Dic43⋊C4—22no—
68C2×C22⋊Dic43—21no—
69C2×C22⋊Dic43—21no—
70C2×C22⋊Dic43—21no—
71C2×C22⋊Dic43—21no—
72C2×C22⋊Dic43—21no—
73C2×C22⋊Dic43—21no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43C2×C412yes—
78C2×C22⋊Dic43C2×C412yescomplemented
79C2×C22⋊Dic43D412yes—
80C2×(C2×D43)⋊C4—22no—
81C2×(C2×D43)⋊C4—24no—
82C2×(C2×D43)⋊C4—44no—
83C22⋊C4×D43—24no—
84C22⋊C4×D43—24no—
85C2×C4×Dic43—22no—
86#13063239—28no—
87C43⋊#95—24no—
88C43⋊#95—44no—
89C43⋊#95—44no—
90C25×C43C2311yescharacteristic
91C23×C4×C43—21no—
92C23×C4×C43—21no—
93C23×C4×C43D412yes—
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×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43C2×C412yes—
109C2×C22⋊C4×C43C2×C412yescomplemented
110C2×C22⋊C4×C43C2×C412yescomplemented
111C2×C22⋊C4×C43D412yes—
112C24×C43—42no—
113C24×C43—42no—
114C24×C43C22×C411yescharacteristic
115C24×C43C22×C411yescharacteristic
116C24×C43C22×C411yescharacteristic
117C24×C43C2×D411yescharacteristic
118C24×C43C2×D411yescharacteristic
119C24×C43C2×D411yescharacteristic
120C24×C43C2×D411yescharacteristic
121C24×C43C2×D411yescharacteristic
122C24×C43C2×D411yescharacteristic
123C24×C43C2×D411yescharacteristic
124C24×C43C2×Q811yescharacteristic
125C24×C43#4111yescharacteristic
126C24×C43#4111yescharacteristic
127C24×C43#4111yescharacteristic
128C24×C43#4111yescharacteristic
129C23×D43—21no—
130C23×D43—21no—
131C23×D43—21no—
132C23×D43—21no—
133C23×D43—42no—
134C23×D43—42no—
135C23×D43C22⋊C412yes—
136C23×D43C22⋊C412yes—
137C23×D43C4⋊C412yes—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—42no—
143C22×C4×C43—42no—
144C22×C4×C43—42no—
145C22×C4×C43—42no—
146C22×C4×C43—42no—
147C22×C4×C43—42no—
148C22×C4×C43—41no—
149C22×C4×C43—41no—
150C22×C4×C43—41no—
151C22×C4×C43—41no—
152C22×C4×C43C22⋊C414yescomplemented
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—22no—
158C2×C22⋊D43—22no—
159C2×C22⋊D43—22no—
160C2×C22⋊D43—22no—
161C2×C22⋊D43—22no—
162C2×C22⋊D43—22no—
163C2×C22⋊D43—22no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43—22no—
167C2×C22⋊D43—22no—
168C2×C22⋊D43—22no—
169C2×C22⋊D43—22no—
170C2×C22⋊D43—22no—
171C2×C22⋊D43—22no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—22no—
174C2×C22⋊D43—22no—
175C2×C22⋊D43—22no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43C4214yes—
178C2×C22⋊D43C22⋊C414yes—
179C2×C22⋊D43C4⋊C414yes—
180C2×C22⋊D43C4⋊C414yes—
181C22×Dic43—24no—
182C22×Dic43—24no—
183C22×Dic43—24no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—21no—
189C22×Dic43—21no—
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—44no—
202C22×Dic43—44no—
203C22×Dic43—44no—
204C22×Dic43—44no—
205C22×Dic43—41no—
206C22×Dic43—41no—
207C22×Dic43—41no—
208C22×Dic43—41no—
209C22×Dic43—41no—
210C22×Dic43—41no—
211C22×Dic43C22⋊C412yes—
212C22×Dic43C22⋊C412yes—
213C22×Dic43C22⋊C414yescomplemented
214C22×Dic43C4⋊C412yes—
215C2×C4×D43—28no—
216C2×C4×D43—82no—
217C2×C4×D43—82no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
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—41no—
227C22⋊C4×C43—41no—
228C22⋊C4×C43—41no—
229C22⋊C4×C43—41no—
230C22⋊Dic43—22no—
231C22⋊Dic43—22no—
232C22⋊Dic43—22no—
233C22⋊Dic43—22no—
234C22⋊Dic43—22no—
235C22⋊Dic43—22no—
236C22⋊Dic43—41no—
237C22⋊Dic43—41no—
238(C2×D43)⋊C4—28no—
239(C2×D43)⋊C4—48no—
240Dic43⋊C4—28no—
241C4×Dic43—28no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
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—42no—
260C23×C43—42no—
261C23×C43—41no—
262C23×C43—42no—
263C23×C43—41no—
264C23×C43C2×C4211yescharacteristic
265C23×C43C2×C22⋊C411yescharacteristic
266C23×C43C2×C22⋊C411yescharacteristic
267C23×C43C2×C22⋊C411yescharacteristic
268C23×C43C2×C22⋊C411yescharacteristic
269C23×C43C2×C22⋊C411yescharacteristic
270C23×C43C2×C4⋊C411yescharacteristic
271C23×C43C2×C4⋊C411yescharacteristic
272C23×C43C2×C4⋊C411yescharacteristic
273C23×C43#11711yescharacteristic
274C23×C43#11711yescharacteristic
275C23×C43C4×D411yescharacteristic
276C23×C43C4×D411yescharacteristic
277C23×C43C4×D411yescharacteristic
278C23×C43C4×D411yescharacteristic
279C23×C43C4×D411yescharacteristic
280C23×C43C4×D411yescharacteristic
281C23×C43C4×D411yescharacteristic
282C23×C43C4×D411yescharacteristic
283C23×C43#12011yescharacteristic
284C23×C43#12011yescharacteristic
285C23×C43#12011yescharacteristic
286C23×C43#12011yescharacteristic
287C23×C43#12111yescharacteristic
288C23×C43#12111yescharacteristic
289C23×C43#12111yescharacteristic
290C23×C43#12111yescharacteristic
291C23×C43C22⋊Q811yescharacteristic
292C23×C43C22⋊Q811yescharacteristic
293C23×C43C22⋊Q811yescharacteristic
294C23×C43C22⋊Q811yescharacteristic
295C23×C43#12311yescharacteristic
296C23×C43#12311yescharacteristic
297C23×C43#12311yescharacteristic
298C23×C43#12311yescharacteristic
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—42no—
306C22×D43—42no—
307C22×D43—42no—
308C22×D43—42no—
309C22×D43—44no—
310C22×D43—44no—
311C22×D43—82no—
312C22×D43—81no—
313C22×D43—81no—
314C22×D43—82no—
315C22×D43#9514yescomplemented
316C2×C4×C43—24no—
317C2×C4×C43—42no—
318C2×C4×C43—42no—
319C2×C4×C43—44no—
320C2×C4×C43—42no—
321C2×C4×C43—44no—
322C2×C4×C43—42no—
323C2×C4×C43—42no—
324C2×C4×C43—42no—
325C2×C4×C43—82no—
326C2×C4×C43—82no—
327C2×C4×C43—81no—
328C2×C4×C43—81no—
329C2×C4×C43—82no—
330C2×C4×C43—82no—
331C22⋊D43—24no—
332C22⋊D43—24no—
333C22⋊D43—24no—
334C22⋊D43—24no—
335C22⋊D43—24no—
336C22⋊D43—24no—
337C22⋊D43—24no—
338C22⋊D43—24no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—24no—
346C2×Dic43—24no—
347C2×Dic43—24no—
348C2×Dic43—24no—
349C2×Dic43—42no—
350C2×Dic43—44no—
351C2×Dic43—42no—
352C2×Dic43—42no—
353C2×Dic43—44no—
354C2×Dic43—44no—
355C2×Dic43—42no—
356C2×Dic43—42no—
357C2×Dic43—44no—
358C2×Dic43—42no—
359C2×Dic43—44no—
360C2×Dic43—44no—
361C2×Dic43—42no—
362C2×Dic43—82no—
363C2×Dic43—81no—
364C2×Dic43—81no—
365C2×Dic43—82no—
366C2×Dic43#9514yescomplemented
367C4×D43—88no—
368#10745—431nomaximal, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—21no—
376C22×C43—21no—
377C22×C43—21no—
378C22×C43—21no—
379C22×C43—21no—
380C22×C43—21no—
381C22×C43—21no—
382C22×C43—21no—
383C22×C43—21no—
384C22×C43—21no—
385C22×C43—21no—
386C22×C43—21no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—22no—
392C22×C43—22no—
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—41no—
404C22×C43—41no—
405C22×C43—41no—
406C22×C43—41no—
407C22×C43—41no—
408C22×C43—41no—
409C22×C43C2×#9511yescharacteristic
410C22×C43C4×C22⋊C411yescharacteristic
411C22×C43C4×C22⋊C411yescharacteristic
412C22×C43#37911yescharacteristic
413C22×C43#38011yescharacteristic
414C22×C43#38011yescharacteristic
415C22×C43#38111yescharacteristic
416C22×C43#38511yescharacteristic
417C22×C43#38511yescharacteristic
418C22×C43#38511yescharacteristic
419C22×C43#38511yescharacteristic
420C22×C43#38611yescharacteristic
421C22×C43#38611yescharacteristic
422C22×C43#38611yescharacteristic
423C22×C43#38611yescharacteristic
424C22×C43B(4,𝔽2)12yes—
425C22×C43#45812yes—
426C2×D43—24no—
427C2×D43—44no—
428C2×D43—42no—
429C2×D43—42no—
430C2×D43—44no—
431C2×D43—44no—
432C2×D43—82no—
433C2×D43—82no—
434C2×D43—82no—
435C4×C43—44no—
436C4×C43—82no—
437C4×C43—82no—
438Dic43—24no—
439Dic43—44no—
440Dic43—44no—
441Dic43—82no—
442C2×#518—431no—
443C22×#99—431no—
444C2×#386—431no—
445C2×#342—431no—
446C2×#342D4311yescharacteristic, complemented
447C22⋊#95—431no—
448C22⋊#95—431no—
449C2×C43—21no—
450C2×C43—21no—
451C2×C43—21no—
452C2×C43—21no—
453C2×C43—21no—
454C2×C43—21no—
455C2×C43—21no—
456C2×C43—21no—
457C2×C43—21no—
458C2×C43—21no—
459C2×C43—21no—
460C2×C43—21no—
461C2×C43C22⋊#9511yescharacteristic
462C2×C43#179012yes—
463C2×C43#186712yes—
464C2×C43#188911yescharacteristic
465C2×C43#189011yescharacteristic
466D43—44no—
467C23×D4—431no—
468C24×C4—431no—
469#518—434no—
470#518—862no—
471#518—862no—
472#518—862no—
473C2×C4×D4—862no—
474C2×C4×D4—862no—
475C2×#117—861no—
476C22×C22⋊C4—431no—
477C22×C22⋊C4—431no—
478C22×C22⋊C4—861no—
479C22×C22⋊C4—861no—
480C22×C22⋊C4C2×D4311yescharacteristic
481C22×C22⋊C4C2×D4311yescharacteristic
482C22×C22⋊C4C2×D4311yescharacteristic
483C2×#99—434no—
484C2×#99—862no—
485C2×#99—862no—
486#386—434no—
487#386—862no—
488C2×#95—861no—
489C2×#95—862no—
490C2×#95—862no—
491#342—22no—
492#342—862no—
493C43#1074511yescharacteristic, complemented, Sylow
494C25—431no—
495C25C22×D4311yescharacteristic
496C22×D4—432no—
497C22×D4—432no—
498C22×D4—432no—
499C22×D4—432no—
500C22×D4—432no—
501C22×D4—432no—
502C22×D4—861no—
503C22×D4—861no—
504C22×D4—861no—
505C22×D4—861no—
506C22×D4—861no—
507C22×D4—861no—
508C22×D4—861no—
509C22×D4—861no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—431no—
513C23×C4—432no—
514C23×C4—432no—
515C23×C4—862no—
516C23×C4—861no—
517C23×C4—861no—
518C23×C4—861no—
519C23×C4—861no—
520C23×C4—861no—
521C23×C4—861no—
522C23×C4—861no—
523C23×C4—1724no—
524C23×C4D17212yes—
525C4×D4—868no—
526C4×D4—868no—
527C4×D4—868no—
528C4×D4—868no—
529#117—864no—
530#117—864no—
531C2×C4⋊C4—862no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—432no—
547C2×C22⋊C4—432no—
548C2×C22⋊C4—432no—
549C2×C22⋊C4—864no—
550C2×C22⋊C4—864no—
551C2×C22⋊C4—862no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C22⋊C4—861no—
557C2×C22⋊C4—861no—
558C2×C22⋊C4—861no—
559C2×C22⋊C4—861no—
560C2×C22⋊C4—864no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—1724no—
563C2×C22⋊C4C4×D4312yes—
564C2×C22⋊C4C4×D4312yescomplemented
565C2×C22⋊C4C4×D4312yescomplemented
566C2×C22⋊C4C22⋊D4312yes—
567C2×C42—862no—
568#99—868no—
569#95—864no—
570#95—1724no—
571#95—1724no—
572C24—42no—
573C24—42no—
574C24—432no—
575C24—432no—
576C24—432no—
577C24—861no—
578C24—861no—
579C24—861no—
580C24—861no—
581C24—1722no—
582C24—1722no—
583C24C2×C4×D4311yescharacteristic
584C24C2×C4×D4311yescharacteristic
585C24C2×C4×D4311yescharacteristic
586C24C2×D17211yescharacteristic
587C24#1062189811yescharacteristic
588C24#1062189811yescharacteristic
589C24D4×D4311yescharacteristic
590C24D4×D4311yescharacteristic
591C24D4×D4311yescharacteristic
592C24D4×D4311yescharacteristic
593C24D4×D4311yescharacteristic
594C24#1062190011yescharacteristic
595C24Q8×D4311yescharacteristic
596C24#1062190211yescharacteristic
597C24C2×C22⋊D4311yescharacteristic
598C2×D4—434no—
599C2×D4—434no—
600C2×D4—434no—
601C2×D4—434no—
602C2×D4—862no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—862no—
606C2×D4—862no—
607C2×D4—862no—
608C2×D4—862no—
609C2×D4—862no—
610C2×D4—862no—
611C2×D4—862no—
612C2×D4—862no—
613C2×D4—862no—
614C2×D4—862no—
615C2×D4—862no—
616C2×D4—862no—
617C2×D4—862no—
618C2×D4—862no—
619C2×D4—862no—
620C2×D4—862no—
621C2×D4—862no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—862no—
625C2×D4—862no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—41no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—432no—
641C22×C4—432no—
642C22×C4—432no—
643C22×C4—434no—
644C22×C4—868no—
645C22×C4—861no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—861no—
649C22×C4—862no—
650C22×C4—864no—
651C22×C4—864no—
652C22×C4—864no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—862no—
657C22×C4—862no—
658C22×C4—3442no—
659C22×C4—3442no—
660C22×C4—1724no—
661C22×C4—1724no—
662C22×C4—1724no—
663C22×C4—1724no—
664C22×C4—1722no—
665C22×C4—1722no—
666C22×C4—1721no—
667C22×C4—1721no—
668C22×C4—1722no—
669C22×C4—1722no—
670C22×C4—1722no—
671C22×C4—1722no—
672C22×C4—1722no—
673C22×C4—1721no—
674C22×C4—1721no—
675C22×C4—1721no—
676C22×C4—1721no—
677C22×C4(C2×D43)⋊C414yescomplemented
678C4⋊C4—868no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—41no—
691C22⋊C4—868no—
692C22⋊C4—862no—
693C22⋊C4—862no—
694C22⋊C4—862no—
695C22⋊C4—862no—
696C22⋊C4—862no—
697C22⋊C4—862no—
698C22⋊C4—1728no—
699C22⋊C4—1721no—
700C22⋊C4—1721no—
701C42—868no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—42no—
715C23—41no—
716C23—42no—
717C23—41no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—41no—
723C23—42no—
724C23—434no—
725C23—862no—
726C23—862no—
727C23—862no—
728C23—862no—
729C23—862no—
730C23—862no—
731C23—3441no—
732C23—3441no—
733C23—3442no—
734C23—3442no—
735C23—1722no—
736C23—1722no—
737C23—1724no—
738C23—1724no—
739C23—1722no—
740C23—1722no—
741C23C42×D4311yescharacteristic
742C23C22⋊C4×D4311yescharacteristic
743C23C22⋊C4×D4311yescharacteristic
744C23C22⋊C4×D4311yescharacteristic
745C23C22⋊C4×D4311yescharacteristic
746C23C2×(C2×D43)⋊C411yescharacteristic
747C23C4⋊C4×D4311yescharacteristic
748C23C4⋊C4×D4311yescharacteristic
749C23C4⋊C4×D4311yescharacteristic
750C23#1306328211yescharacteristic
751C23#1306328311yescharacteristic
752C23(C22⋊D43)⋊C411yescharacteristic
753C23(C22⋊D43)⋊C411yescharacteristic
754C23C4×C22⋊D4311yescharacteristic
755C23C4×C22⋊D4311yescharacteristic
756C23#1306328711yescharacteristic
757C23#1306328711yescharacteristic
758C23C4×D17211yescharacteristic
759C23C4×D17211yescharacteristic
760C23#1306329311yescharacteristic
761C23#1306329311yescharacteristic
762C23#1306329511yescharacteristic
763C23#1306329511yescharacteristic
764C23#1306329611yescharacteristic
765C23#1306329811yescharacteristic
766C23#1306329811yescharacteristic
767C23#1306330011yescharacteristic
768C23#1306330111yescharacteristic
769C23#1306330311yescharacteristic
770C23#1306330311yescharacteristic
771C23#1306330511yescharacteristic
772C23#1306330711yescharacteristic
773C23#1306330711yescharacteristic
774C23#1306331011yescharacteristic
775C23#1306331011yescharacteristic
776D4—864no—
777D4—864no—
778D4—864no—
779D4—864no—
780D4—864no—
781D4—864no—
782D4—864no—
783D4—864no—
784C2×C4—24no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—82no—
794C2×C4—81no—
795C2×C4—81no—
796C2×C4—82no—
797C2×C4—82no—
798C2×C4—82no—
799C2×C4—434no—
800C2×C4—862no—
801C2×C4—862no—
802C2×C4—862no—
803C2×C4—862no—
804C2×C4—862no—
805C2×C4—862no—
806C2×C4—864no—
807C2×C4—864no—
808C2×C4—864no—
809C2×C4—864no—
810C2×C4—3448no—
811C2×C4—3441no—
812C2×C4—3441no—
813C2×C4—3442no—
814C2×C4—3442no—
815C2×C4—1724no—
816C2×C4—1722no—
817C2×C4—1722no—
818C2×C4—1724no—
819C2×C4—1722no—
820C2×C4—1722no—
821C2×C4—1724no—
822C2×C4—1724no—
823C2×C4—1724no—
824C2×C4—1722no—
825C2×C4—1722no—
826C2×C4—1722no—
827C2×C4—1724no—
828C22—21no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—864no—
869C22—3442no—
870C22—3442no—
871C22—3442no—
872C22—1724no—
873C22—1722no—
874C22—1722no—
875C22—1724no—
876C22—1724no—
877C22#95×D4311yescharacteristic
878C22#1458274611yescharacteristic
879C22C4×(C2×D43)⋊C411yescharacteristic
880C22#1458275411yescharacteristic
881C22#1458275611yescharacteristic
882C22#1458275811yescharacteristic
883C22#1458276111yescharacteristic
884C22#1458277011yescharacteristic
885C22#1458277011yescharacteristic
886C22#1458277311yescharacteristic
887C22#1458277311yescharacteristic
888C22#1458277511yescharacteristic
889C22#1458277511yescharacteristic
890C22#1458277711yescharacteristic
891C22#1458277711yescharacteristic
892C22#1458308712yes—
893C22#1458309012yes—
894C4—44no—
895C4—82no—
896C4—82no—
897C4—864no—
898C4—3442no—
899C4—1724no—
900C4—1724no—
901C2—21no—
902C2—21no—
903C2—21no—
904C2—21no—
905C2—21no—
906C2—21no—
907C2—21no—
908C2—21no—
909C2—21no—
910C2—21no—
911C2—21no—
912C2—21no—
913C2—1724no—
914C2(C2×D43)⋊#9511yescharacteristic
915C2#1913454112yes—
916C2#1913487712yes—
917C2#1913500211yescharacteristic
918C2#1913500711yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC23×C43C2×C42
FrattiniC25C22×D43
FittingC2×C43×#342C2
socleC23×C43#120
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenterC2×#342D43
hypocenterC43#10745
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. C2×#14582665C2semidirect
5. #19132817C2semidirect
6. #19132817C2semidirect
7. C2×C43×#342C2semidirect
13. #14583372C4semidirect
23. C2×#13063239C4semidirect
25. #14582776C4semidirect
57. C23×Dic43C2×C4semidirect
78. C2×C22⋊Dic43C2×C4semidirect
109. C2×C22⋊C4×C43C2×C4semidirect
110. C2×C22⋊C4×C43C2×C4semidirect
152. C22×C4×C43C22⋊C4semidirect
213. C22×Dic43C22⋊C4semidirect
315. C22×D43#95semidirect
366. C2×Dic43#95semidirect
446. C2×#342D43semidirect
493. C43#10745semidirect
564. C2×C22⋊C4C4×D43semidirect
565. C2×C22⋊C4C4×D43semidirect
677. C22×C4(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145833722
C22×#130632392
C2×#145827762
C2×#145826652
#191328172
C2×C43×#3422
#1074543