Finite Group Databasebeta

← #25001983

Subgroups — #25001983

Order 11008.

1522 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583372C211yesmaximal, characteristic
2C22×#13063239C211yesmaximal, characteristic
3#19137170C211yesmaximal, characteristic
4C2×#14582665C211yesmaximal, characteristic, complemented
5C2×#14582665C211yesmaximal, characteristic, complemented
6C2×#14582665C211yesmaximal, characteristic, complemented
7C2×C43×#342C211yesmaximal, characteristic, complemented
8C23×C22⋊D43C2211yescharacteristic
9#14583372—22no—
10#14583372—22no—
11#14583372—22no—
12#14583372C414yescomplemented
13C2×C4×C22⋊D43—22no—
14C2×(C22⋊D43)⋊C4—22no—
15C2×#13063281—21no—
16C22×C22⋊Dic43C2211yescharacteristic
17C22×C22⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2211yescharacteristic
19C2×C22⋊C4×D43—21no—
20C2×#13063239—22no—
21C2×#13063239—22no—
22C2×#13063239C414yescomplemented
23#14582778—22no—
24#14582776C414yescomplemented
25#14582760—21no—
26#14582754—21no—
27#14582665—22no—
28#14582665—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×Dic43C2×C412yescomplemented
52C23×Dic43D411yescharacteristic
53C22×C4×D43—22no—
54C4×C22⋊D43—28no—
55C4×C22⋊D43—28no—
56(C22⋊D43)⋊C4—28no—
57(C22⋊D43)⋊C4—28no—
58#13063281—24no—
59#13063281—24no—
60C2×Dic43⋊C4—22no—
61C2×C22⋊Dic43—21no—
62C2×C22⋊Dic43—21no—
63C2×C22⋊Dic43—21no—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—21no—
66C2×C22⋊Dic43—21no—
67C2×C22⋊Dic43—21no—
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⋊Dic43C2×C412yes—
76C2×C22⋊Dic43C2×C412yescomplemented
77C2×C22⋊Dic43D412yes—
78C2×C22⋊Dic43D412yes—
79C2×(C2×D43)⋊C4—22no—
80C2×(C2×D43)⋊C4—24no—
81C22⋊C4×D43—24no—
82C22⋊C4×D43—24no—
83C2×C4×Dic43—22no—
84#13063239—28no—
85C43⋊#95—24no—
86C25×C43C2311yescharacteristic
87C23×C4×C43—21no—
88C23×C4×C43—21no—
89C23×C4×C43—21no—
90C2×C22⋊C4×C43—21no—
91C2×C22⋊C4×C43—21no—
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×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43C2×C412yes—
104C2×C22⋊C4×C43C2×C412yescomplemented
105C2×C22⋊C4×C43C2×C412yescomplemented
106C2×C22⋊C4×C43D412yes—
107C2×C22⋊C4×C43D412yes—
108C24×C43—82no—
109C24×C43C22×C411yescharacteristic
110C24×C43C22×C411yescharacteristic
111C24×C43C22×C411yescharacteristic
112C24×C43C2×D411yescharacteristic
113C24×C43C2×D411yescharacteristic
114C24×C43C2×D411yescharacteristic
115C24×C43C2×D411yescharacteristic
116C24×C43C2×D411yescharacteristic
117C24×C43C2×D411yescharacteristic
118C24×C43C2×D411yescharacteristic
119C24×C43C2×Q811yescharacteristic
120C24×C43#4111yescharacteristic
121C24×C43#4111yescharacteristic
122C24×C43#4111yescharacteristic
123C24×C43#4111yescharacteristic
124C23×D43—21no—
125C23×D43—21no—
126C23×D43—21no—
127C23×D43—21no—
128C23×D43—82no—
129C23×D43C22⋊C412yes—
130C23×D43C22⋊C412yes—
131C23×D43C4⋊C412yes—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—41no—
138C22×C4×C43—41no—
139C22×C4×C43—41no—
140C22×C4×C43—41no—
141C22×C4×C43—82no—
142C22×C4×C43—82no—
143C22×C4×C43—82no—
144C2×C22⋊D43—22no—
145C2×C22⋊D43—22no—
146C2×C22⋊D43—22no—
147C2×C22⋊D43—22no—
148C2×C22⋊D43—22no—
149C2×C22⋊D43—22no—
150C2×C22⋊D43—22no—
151C2×C22⋊D43—22no—
152C2×C22⋊D43—22no—
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⋊D43C4214yes—
169C2×C22⋊D43C22⋊C414yes—
170C2×C22⋊D43C4⋊C414yes—
171C2×C22⋊D43C4⋊C414yes—
172C22×Dic43—22no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—21no—
178C22×Dic43—21no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—21no—
182C22×Dic43—21no—
183C22×Dic43—41no—
184C22×Dic43—41no—
185C22×Dic43—82no—
186C22×Dic43—82no—
187C22×Dic43—82no—
188C22×Dic43C22⋊C412yes—
189C22×Dic43C22⋊C412yes—
190C22×Dic43C4⋊C412yes—
191C2×C4×D43—28no—
192C2×C4×D43—84no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—22no—
195C22⋊C4×C43—22no—
196C22⋊C4×C43—22no—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—22no—
199C22⋊C4×C43—22no—
200C22⋊C4×C43—41no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43—41no—
203C22⋊C4×C43—41no—
204C22⋊C4×C43C22⋊C414yescomplemented
205C22⋊Dic43—22no—
206C22⋊Dic43—22no—
207C22⋊Dic43—22no—
208C22⋊Dic43—22no—
209C22⋊Dic43—22no—
210C22⋊Dic43—41no—
211C22⋊Dic43—41no—
212C22⋊Dic43—41no—
213C22⋊Dic43—41no—
214C22⋊Dic43—41no—
215C22⋊Dic43—41no—
216C22⋊Dic43C22⋊C414yescomplemented
217(C2×D43)⋊C4—28no—
218(C2×D43)⋊C4—84no—
219Dic43⋊C4—28no—
220C4×Dic43—28no—
221C23×C43—42no—
222C23×C43—42no—
223C23×C43—42no—
224C23×C43—42no—
225C23×C43—42no—
226C23×C43—42no—
227C23×C43—42no—
228C23×C43—81no—
229C23×C43—81no—
230C23×C43—81no—
231C23×C43—81no—
232C23×C43—81no—
233C23×C43—81no—
234C23×C43—81no—
235C23×C43—81no—
236C23×C43C2×C4211yescharacteristic
237C23×C43C2×C22⋊C411yescharacteristic
238C23×C43C2×C22⋊C411yescharacteristic
239C23×C43C2×C22⋊C411yescharacteristic
240C23×C43C2×C22⋊C411yescharacteristic
241C23×C43C2×C22⋊C411yescharacteristic
242C23×C43C2×C4⋊C411yescharacteristic
243C23×C43C2×C4⋊C411yescharacteristic
244C23×C43C2×C4⋊C411yescharacteristic
245C23×C43#11711yescharacteristic
246C23×C43#11711yescharacteristic
247C23×C43C4×D411yescharacteristic
248C23×C43C4×D411yescharacteristic
249C23×C43C4×D411yescharacteristic
250C23×C43C4×D411yescharacteristic
251C23×C43C4×D411yescharacteristic
252C23×C43C4×D411yescharacteristic
253C23×C43C4×D411yescharacteristic
254C23×C43C4×D411yescharacteristic
255C23×C43#12011yescharacteristic
256C23×C43#12011yescharacteristic
257C23×C43#12011yescharacteristic
258C23×C43#12011yescharacteristic
259C23×C43#12111yescharacteristic
260C23×C43#12111yescharacteristic
261C23×C43#12111yescharacteristic
262C23×C43#12111yescharacteristic
263C23×C43C22⋊Q811yescharacteristic
264C23×C43C22⋊Q811yescharacteristic
265C23×C43C22⋊Q811yescharacteristic
266C23×C43C22⋊Q811yescharacteristic
267C23×C43#12311yescharacteristic
268C23×C43#12311yescharacteristic
269C23×C43#12311yescharacteristic
270C23×C43#12311yescharacteristic
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—44no—
278C22×D43—44no—
279C22×D43—82no—
280C22×D43—82no—
281C22×D43—82no—
282C22×D43—82no—
283C22×D43—82no—
284C22×D43#9514yes—
285C2×C4×C43—24no—
286C2×C4×C43—44no—
287C2×C4×C43—44no—
288C2×C4×C43—42no—
289C2×C4×C43—42no—
290C2×C4×C43—82no—
291C2×C4×C43—82no—
292C2×C4×C43—82no—
293C2×C4×C43—82no—
294C2×C4×C43—82no—
295C2×C4×C43—82no—
296C2×C4×C43—82no—
297C22⋊D43—24no—
298C22⋊D43—24no—
299C22⋊D43—24no—
300C22⋊D43—24no—
301C22⋊D43—24no—
302C22⋊D43—24no—
303C22⋊D43—24no—
304C22⋊D43—24no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—24no—
312C2×Dic43—44no—
313C2×Dic43—44no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—82no—
317C2×Dic43—82no—
318C2×Dic43—82no—
319C2×Dic43—82no—
320C2×Dic43—82no—
321C2×Dic43—82no—
322C2×Dic43—82no—
323C2×Dic43#9514yes—
324C4×D43—88no—
325#10754—431nomaximal, Sylow
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43C2×#9511yescharacteristic
362C22×C43C4×C22⋊C411yescharacteristic
363C22×C43C4×C22⋊C411yescharacteristic
364C22×C43#37911yescharacteristic
365C22×C43#38011yescharacteristic
366C22×C43#38011yescharacteristic
367C22×C43#38111yescharacteristic
368C22×C43#38511yescharacteristic
369C22×C43#38511yescharacteristic
370C22×C43#38511yescharacteristic
371C22×C43#38511yescharacteristic
372C22×C43#38611yescharacteristic
373C22×C43#38611yescharacteristic
374C22×C43#38611yescharacteristic
375C22×C43#38611yescharacteristic
376C2×D43—24no—
377C2×D43—44no—
378C2×D43—44no—
379C2×D43—44no—
380C2×D43—44no—
381C2×D43—82no—
382C2×D43—82no—
383C2×D43—82no—
384C4×C43—44no—
385C4×C43—82no—
386C4×C43—82no—
387Dic43—24no—
388Dic43—44no—
389Dic43—82no—
390Dic43—82no—
391C2×#518—431no—
392C22×#99—431no—
393#2308—431no—
394C2×#342—431no—
395C2×#342—431no—
396C2×#342—431no—
397C2×#342D4311yescharacteristic, complemented
398C2×C43—21no—
399C2×C43—21no—
400C2×C43—21no—
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—21no—
404C2×C43—21no—
405C2×C43—21no—
406C2×C43—21no—
407C2×C43—21no—
408C2×C43—21no—
409C2×C43—21no—
410C2×C43—21no—
411C2×C43—21no—
412C2×C43C22⋊#9511yescharacteristic
413C2×C43#191312yes—
414D43—44no—
415C23×D4—431no—
416#518—434no—
417#518—862no—
418#518—862no—
419#518—862no—
420C2×C4×D4—862no—
421C2×C4×D4—862no—
422C2×#117—861no—
423C22×C22⋊C4—431no—
424C22×C22⋊C4—431no—
425C22×C22⋊C4—431no—
426C22×C22⋊C4—861no—
427C22×C22⋊C4C2×D4311yescharacteristic
428C22×C22⋊C4C2×D4311yescharacteristic
429C22×C22⋊C4C2×D4311yescharacteristic
430C2×#99—434no—
431C2×#99—862no—
432C2×#99—862no—
433#386—434no—
434#386—862no—
435#381—861no—
436#379—861no—
437#342—22no—
438#342—862no—
439#342—862no—
440#342—862no—
441C43#1075411yescharacteristic, complemented, Sylow
442C25—431no—
443C25C22×D4311yescharacteristic
444C22×D4—432no—
445C22×D4—432no—
446C22×D4—432no—
447C22×D4—432no—
448C22×D4—432no—
449C22×D4—432no—
450C22×D4—861no—
451C22×D4—861no—
452C22×D4—861no—
453C22×D4—861no—
454C22×D4—861no—
455C22×D4—861no—
456C22×D4—861no—
457C22×D4—861no—
458C23×C4—21no—
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—431no—
462C23×C4—432no—
463C23×C4—862no—
464C23×C4—861no—
465C23×C4—861no—
466C4×D4—868no—
467C4×D4—868no—
468C4×D4—868no—
469C4×D4—868no—
470#117—864no—
471#117—864no—
472C2×C4⋊C4—862no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—432no—
487C2×C22⋊C4—432no—
488C2×C22⋊C4—432no—
489C2×C22⋊C4—432no—
490C2×C22⋊C4—864no—
491C2×C22⋊C4—864no—
492C2×C22⋊C4—862no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4—861no—
496C2×C22⋊C4—861no—
497C2×C22⋊C4—861no—
498C2×C22⋊C4—861no—
499C2×C22⋊C4—861no—
500C2×C22⋊C4—864no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4C4×D4312yes—
509C2×C22⋊C4C4×D4312yescomplemented
510C2×C22⋊C4C4×D4312yescomplemented
511C2×C22⋊C4D17212yes—
512C2×C22⋊C4C22⋊D4312yes—
513C2×C42—862no—
514#99—868no—
515#95—864no—
516C24—82no—
517C24—432no—
518C24—432no—
519C24—432no—
520C24—861no—
521C24—861no—
522C24—861no—
523C24—861no—
524C24—3442no—
525C24C2×C4×D4311yescharacteristic
526C24C2×C4×D4311yescharacteristic
527C24C2×C4×D4311yescharacteristic
528C24C2×D17211yescharacteristic
529C24#1062189811yescharacteristic
530C24#1062189811yescharacteristic
531C24D4×D4311yescharacteristic
532C24D4×D4311yescharacteristic
533C24D4×D4311yescharacteristic
534C24D4×D4311yescharacteristic
535C24D4×D4311yescharacteristic
536C24#1062190011yescharacteristic
537C24Q8×D4311yescharacteristic
538C24#1062190211yescharacteristic
539C24C2×C22⋊D4311yescharacteristic
540C2×D4—434no—
541C2×D4—434no—
542C2×D4—434no—
543C2×D4—434no—
544C2×D4—862no—
545C2×D4—862no—
546C2×D4—862no—
547C2×D4—862no—
548C2×D4—862no—
549C2×D4—862no—
550C2×D4—862no—
551C2×D4—862no—
552C2×D4—862no—
553C2×D4—862no—
554C2×D4—862no—
555C2×D4—862no—
556C2×D4—862no—
557C2×D4—862no—
558C2×D4—862no—
559C2×D4—862no—
560C2×D4—862no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—862no—
564C2×D4—862no—
565C2×D4—862no—
566C2×D4—862no—
567C2×D4—862no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—41no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—41no—
577C22×C4—82no—
578C22×C4—82no—
579C22×C4—82no—
580C22×C4—432no—
581C22×C4—432no—
582C22×C4—432no—
583C22×C4—868no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—861no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—3444no—
596C22×C4—3442no—
597C22×C4—3442no—
598C22×C4—3442no—
599C22×C4—1721no—
600C22×C4—1721no—
601C4⋊C4—868no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—434no—
614C22⋊C4—868no—
615C22⋊C4—862no—
616C22⋊C4—862no—
617C22⋊C4—862no—
618C22⋊C4—862no—
619C22⋊C4—862no—
620C22⋊C4—3444no—
621C22⋊C4—1721no—
622C22⋊C4—1721no—
623C22⋊C4—1721no—
624C22⋊C4—1721no—
625C22⋊C4—1721no—
626C22⋊C4—1721no—
627C22⋊C4(C2×D43)⋊C414yescomplemented
628C42—868no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—81no—
637C23—81no—
638C23—81no—
639C23—81no—
640C23—81no—
641C23—81no—
642C23—81no—
643C23—81no—
644C23—434no—
645C23—862no—
646C23—862no—
647C23—862no—
648C23—862no—
649C23—862no—
650C23—862no—
651C23—3442no—
652C23—3442no—
653C23—3442no—
654C23—3442no—
655C23—3442no—
656C23—1724no—
657C23—1724no—
658C23C42×D4311yescharacteristic
659C23C22⋊C4×D4311yescharacteristic
660C23C22⋊C4×D4311yescharacteristic
661C23C22⋊C4×D4311yescharacteristic
662C23C22⋊C4×D4311yescharacteristic
663C23C2×(C2×D43)⋊C411yescharacteristic
664C23C4⋊C4×D4311yescharacteristic
665C23C4⋊C4×D4311yescharacteristic
666C23C4⋊C4×D4311yescharacteristic
667C23#1306328211yescharacteristic
668C23#1306328311yescharacteristic
669C23(C22⋊D43)⋊C411yescharacteristic
670C23(C22⋊D43)⋊C411yescharacteristic
671C23C4×C22⋊D4311yescharacteristic
672C23C4×C22⋊D4311yescharacteristic
673C23#1306328711yescharacteristic
674C23#1306328711yescharacteristic
675C23C4×D17211yescharacteristic
676C23C4×D17211yescharacteristic
677C23#1306329311yescharacteristic
678C23#1306329311yescharacteristic
679C23#1306329511yescharacteristic
680C23#1306329511yescharacteristic
681C23#1306329611yescharacteristic
682C23#1306329811yescharacteristic
683C23#1306329811yescharacteristic
684C23#1306330011yescharacteristic
685C23#1306330111yescharacteristic
686C23#1306330311yescharacteristic
687C23#1306330311yescharacteristic
688C23#1306330511yescharacteristic
689C23#1306330711yescharacteristic
690C23#1306330711yescharacteristic
691C23#1306331011yescharacteristic
692C23#1306331011yescharacteristic
693D4—864no—
694D4—864no—
695D4—864no—
696D4—864no—
697D4—864no—
698D4—864no—
699D4—864no—
700D4—864no—
701C2×C4—24no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—82no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4—82no—
713C2×C4—434no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—864no—
721C2×C4—3448no—
722C2×C4—3442no—
723C2×C4—3442no—
724C2×C4—3442no—
725C2×C4—3442no—
726C2×C4—3442no—
727C2×C4—3442no—
728C2×C4—3442no—
729C2×C4—1724no—
730C2×C4—1722no—
731C2×C4—1722no—
732C2×C4—1724no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—864no—
769C22—3442no—
770C22—3442no—
771C22—3442no—
772C22—1724no—
773C22—1724no—
774C22—1724no—
775C22—1724no—
776C22#95×D4311yescharacteristic
777C22#1458274611yescharacteristic
778C22C4×(C2×D43)⋊C411yescharacteristic
779C22#1458275411yescharacteristic
780C22#1458275611yescharacteristic
781C22#1458275811yescharacteristic
782C22#1458276111yescharacteristic
783C22#1458277011yescharacteristic
784C22#1458277011yescharacteristic
785C22#1458277311yescharacteristic
786C22#1458277311yescharacteristic
787C22#1458277511yescharacteristic
788C22#1458277511yescharacteristic
789C22#1458277711yescharacteristic
790C22#1458277711yescharacteristic
791C4—44no—
792C4—82no—
793C4—82no—
794C4—864no—
795C4—3442no—
796C4—3442no—
797C4—1724no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—21no—
807C2—21no—
808C2—21no—
809C2—21no—
810C2—21no—
811C2—21no—
812C2—1724no—
813C2(C2×D43)⋊#9511yescharacteristic
814C2#1913513612yes—
subgroupG/H
centerC22#14582777
commutatorC23×C43C2×C42
FrattiniC25C22×D43
FittingC2×C43×#342C2
socleC22×C43#386
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenterC2×#342D43
hypocenterC43#10754
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
4. C2×#14582665C2semidirect
5. C2×#14582665C2semidirect
6. C2×#14582665C2semidirect
7. C2×C43×#342C2semidirect
12. #14583372C4semidirect
22. C2×#13063239C4semidirect
24. #14582776C4semidirect
51. C23×Dic43C2×C4semidirect
76. C2×C22⋊Dic43C2×C4semidirect
104. C2×C22⋊C4×C43C2×C4semidirect
105. C2×C22⋊C4×C43C2×C4semidirect
204. C22⋊C4×C43C22⋊C4semidirect
216. C22⋊Dic43C22⋊C4semidirect
397. C2×#342D43semidirect
441. C43#10754semidirect
509. C2×C22⋊C4C4×D43semidirect
510. C2×C22⋊C4C4×D43semidirect
627. 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
#191371702
C2×#145826652
C2×C43×#3422
#1075443