Finite Group Databasebeta

← #25002044

Subgroups — #25002044

Order 11008.

1498 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×#14583372C211yesmaximal, characteristic
2C22×#13063239C211yesmaximal, characteristic
3C22×#13063239C211yesmaximal, characteristic
4C2×#14582666C211yesmaximal, 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#14583372—22no—
13C2×C4×C22⋊D43—22no—
14C2×(C22⋊D43)⋊C4—22no—
15C2×#13063281C412yescomplemented
16C22×C22⋊Dic43C2211yescharacteristic
17C22×C22⋊Dic43C2211yescharacteristic
18C22×C22⋊Dic43C2211yescharacteristic
19C2×C22⋊C4×D43C412yescomplemented
20C2×#13063239—22no—
21C2×#13063239—22no—
22C2×#13063239—22no—
23C2×#13063239—22no—
24C2×#13063239C414yescomplemented
25C2×#13063239C414yescomplemented
26#14582666—22no—
27#14582665—22no—
28#14582665—22no—
29C22×C22⋊C4×C43C2211yescharacteristic
30C22×C22⋊C4×C43C2211yescharacteristic
31C22×C22⋊C4×C43C2211yescharacteristic
32C43×#342—22no—
33C24×D43C2×C411yescharacteristic
34C22×C22⋊D43—21no—
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⋊D43C2×C412yes—
43C22×C22⋊D43C2×C412yes—
44C22×C22⋊D43D412yes—
45C22×C22⋊D43D412yes—
46C22×C22⋊D43D412yes—
47C22×C22⋊D43Q812yes—
48C23×Dic43—21no—
49C23×Dic43—21no—
50C23×Dic43—21no—
51C23×Dic43C2×C411yescharacteristic
52C22×C4×D43—22no—
53C4×C22⋊D43—28no—
54C4×C22⋊D43—28no—
55(C22⋊D43)⋊C4—28no—
56(C22⋊D43)⋊C4—28no—
57#13063281—24no—
58#13063281—24no—
59C2×Dic43⋊C4—22no—
60C2×C22⋊Dic43—21no—
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⋊Dic43C2×C412yes—
74C2×C22⋊Dic43C2×C412yescomplemented
75C2×C22⋊Dic43C2×C412yescomplemented
76C2×C22⋊Dic43D412yes—
77C2×C22⋊Dic43D412yes—
78C2×(C2×D43)⋊C4—22no—
79C22⋊C4×D43—24no—
80C22⋊C4×D43—24no—
81C2×C4×Dic43—22no—
82#13063239—28no—
83#13063239—28no—
84C25×C43C2311yescharacteristic
85C23×C4×C43—21no—
86C23×C4×C43—21no—
87C23×C4×C43—21no—
88C2×C22⋊C4×C43—21no—
89C2×C22⋊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×C43C2×C412yes—
102C2×C22⋊C4×C43C2×C412yescomplemented
103C2×C22⋊C4×C43C2×C412yescomplemented
104C2×C22⋊C4×C43D412yes—
105C2×C22⋊C4×C43D412yes—
106C24×C43—82no—
107C24×C43C22×C411yescharacteristic
108C24×C43C22×C411yescharacteristic
109C24×C43C22×C411yescharacteristic
110C24×C43C2×D411yescharacteristic
111C24×C43C2×D411yescharacteristic
112C24×C43C2×D411yescharacteristic
113C24×C43C2×D411yescharacteristic
114C24×C43C2×D411yescharacteristic
115C24×C43C2×D411yescharacteristic
116C24×C43C2×D411yescharacteristic
117C24×C43C2×Q811yescharacteristic
118C24×C43#4111yescharacteristic
119C24×C43#4111yescharacteristic
120C24×C43#4111yescharacteristic
121C24×C43#4111yescharacteristic
122C23×D43—21no—
123C23×D43—21no—
124C23×D43—21no—
125C23×D43—21no—
126C23×D43—82no—
127C23×D43C4212yes—
128C23×D43C22⋊C412yes—
129C23×D43C4⋊C412yes—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—41no—
136C22×C4×C43—41no—
137C22×C4×C43—41no—
138C22×C4×C43—41no—
139C22×C4×C43—82no—
140C22×C4×C43—82no—
141C22×C4×C43—82no—
142C2×C22⋊D43—22no—
143C2×C22⋊D43—22no—
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⋊D43C22⋊C414yes—
167C2×C22⋊D43C22⋊C414yes—
168C2×C22⋊D43C4⋊C414yes—
169C2×C22⋊D43C4⋊C414yes—
170C22×Dic43—21no—
171C22×Dic43—21no—
172C22×Dic43—22no—
173C22×Dic43—21no—
174C22×Dic43—21no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—41no—
180C22×Dic43—41no—
181C22×Dic43—41no—
182C22×Dic43—41no—
183C22×Dic43—82no—
184C22×Dic43—82no—
185C22×Dic43—82no—
186C22×Dic43C4212yes—
187C22×Dic43C22⋊C412yes—
188C22×Dic43C4⋊C412yes—
189C2×C4×D43—28no—
190C2×C4×D43—84no—
191C22⋊C4×C43—22no—
192C22⋊C4×C43—22no—
193C22⋊C4×C43—22no—
194C22⋊C4×C43—22no—
195C22⋊C4×C43—22no—
196C22⋊C4×C43—22no—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—41no—
199C22⋊C4×C43—41no—
200C22⋊C4×C43—41no—
201C22⋊C4×C43—41no—
202C22⋊C4×C43C22⋊C414yes—
203C22⋊Dic43—22no—
204C22⋊Dic43—22no—
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⋊Dic43C22⋊C414yes—
215(C2×D43)⋊C4—28no—
216Dic43⋊C4—28no—
217C4×Dic43—28no—
218C23×C43—42no—
219C23×C43—42no—
220C23×C43—42no—
221C23×C43—42no—
222C23×C43—42no—
223C23×C43—42no—
224C23×C43—42no—
225C23×C43—81no—
226C23×C43—81no—
227C23×C43—81no—
228C23×C43—81no—
229C23×C43—81no—
230C23×C43—81no—
231C23×C43—81no—
232C23×C43—81no—
233C23×C43C2×C4211yescharacteristic
234C23×C43C2×C22⋊C411yescharacteristic
235C23×C43C2×C22⋊C411yescharacteristic
236C23×C43C2×C22⋊C411yescharacteristic
237C23×C43C2×C22⋊C411yescharacteristic
238C23×C43C2×C22⋊C411yescharacteristic
239C23×C43C2×C4⋊C411yescharacteristic
240C23×C43C2×C4⋊C411yescharacteristic
241C23×C43C2×C4⋊C411yescharacteristic
242C23×C43#11711yescharacteristic
243C23×C43#11711yescharacteristic
244C23×C43C4×D411yescharacteristic
245C23×C43C4×D411yescharacteristic
246C23×C43C4×D411yescharacteristic
247C23×C43C4×D411yescharacteristic
248C23×C43C4×D411yescharacteristic
249C23×C43C4×D411yescharacteristic
250C23×C43C4×D411yescharacteristic
251C23×C43C4×D411yescharacteristic
252C23×C43#12011yescharacteristic
253C23×C43#12011yescharacteristic
254C23×C43#12011yescharacteristic
255C23×C43#12011yescharacteristic
256C23×C43#12111yescharacteristic
257C23×C43#12111yescharacteristic
258C23×C43#12111yescharacteristic
259C23×C43#12111yescharacteristic
260C23×C43C22⋊Q811yescharacteristic
261C23×C43C22⋊Q811yescharacteristic
262C23×C43C22⋊Q811yescharacteristic
263C23×C43C22⋊Q811yescharacteristic
264C23×C43#12311yescharacteristic
265C23×C43#12311yescharacteristic
266C23×C43#12311yescharacteristic
267C23×C43#12311yescharacteristic
268C22×D43—22no—
269C22×D43—22no—
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—44no—
275C22×D43—82no—
276C22×D43—82no—
277C22×D43—82no—
278C22×D43—82no—
279C22×D43—82no—
280C22×D43—82no—
281C22×D43#9514yes—
282C2×C4×C43—24no—
283C2×C4×C43—44no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—82no—
287C2×C4×C43—82no—
288C2×C4×C43—82no—
289C2×C4×C43—82no—
290C2×C4×C43—82no—
291C2×C4×C43—82no—
292C2×C4×C43—82no—
293C2×C4×C43—82no—
294C22⋊D43—24no—
295C22⋊D43—24no—
296C22⋊D43—24no—
297C22⋊D43—24no—
298C22⋊D43—24no—
299C22⋊D43—24no—
300C22⋊D43—24no—
301C22⋊D43—24no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—24no—
309C2×Dic43—44no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—82no—
313C2×Dic43—82no—
314C2×Dic43—82no—
315C2×Dic43—82no—
316C2×Dic43—82no—
317C2×Dic43—82no—
318C2×Dic43—82no—
319C2×Dic43—82no—
320C2×Dic43#9514yes—
321C4×D43—88no—
322#10768—431nomaximal, Sylow
323C22×C43—22no—
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—22no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
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×C43C2×#9511yescharacteristic
359C22×C43C4×C22⋊C411yescharacteristic
360C22×C43C4×C22⋊C411yescharacteristic
361C22×C43#37911yescharacteristic
362C22×C43#38011yescharacteristic
363C22×C43#38011yescharacteristic
364C22×C43#38111yescharacteristic
365C22×C43#38511yescharacteristic
366C22×C43#38511yescharacteristic
367C22×C43#38511yescharacteristic
368C22×C43#38511yescharacteristic
369C22×C43#38611yescharacteristic
370C22×C43#38611yescharacteristic
371C22×C43#38611yescharacteristic
372C22×C43#38611yescharacteristic
373C2×D43—24no—
374C2×D43—44no—
375C2×D43—44no—
376C2×D43—44no—
377C2×D43—82no—
378C2×D43—82no—
379C2×D43—82no—
380C2×D43—82no—
381C4×C43—44no—
382C4×C43—82no—
383C4×C43—82no—
384Dic43—24no—
385Dic43—44no—
386Dic43—82no—
387Dic43—82no—
388C2×#518—431no—
389C22×#99—431no—
390C22×#99—431no—
391C2×#342—431no—
392C2×#342—431no—
393C2×#342—431no—
394C2×#342D4311yescharacteristic, complemented
395C2×C43—21no—
396C2×C43—21no—
397C2×C43—21no—
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×C43C22⋊#9511yescharacteristic
410C2×C43#182812yes—
411D43—44no—
412C23×D4—431no—
413#518—862no—
414#518—862no—
415#518—862no—
416#518—862no—
417C2×C4×D4—862no—
418C2×C4×D4—862no—
419C2×#117—432no—
420C22×C22⋊C4—431no—
421C22×C22⋊C4—431no—
422C22×C22⋊C4—431no—
423C22×C22⋊C4—432no—
424C22×C22⋊C4C2×D4311yescharacteristic
425C22×C22⋊C4C2×D4311yescharacteristic
426C22×C22⋊C4C2×D4311yescharacteristic
427C2×#99—434no—
428C2×#99—434no—
429C2×#99—862no—
430C2×#99—862no—
431C2×#99—862no—
432C2×#99—862no—
433#342—22no—
434#342—862no—
435#342—862no—
436#342—862no—
437C43#1076811yescharacteristic, complemented, Sylow
438C25—431no—
439C25C22×D4311yescharacteristic
440C22×D4—432no—
441C22×D4—432no—
442C22×D4—432no—
443C22×D4—432no—
444C22×D4—432no—
445C22×D4—432no—
446C22×D4—861no—
447C22×D4—861no—
448C22×D4—861no—
449C22×D4—861no—
450C22×D4—861no—
451C22×D4—861no—
452C22×D4—861no—
453C22×D4—861no—
454C23×C4—21no—
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—431no—
458C23×C4—862no—
459C23×C4—861no—
460C23×C4—861no—
461C23×C4—861no—
462C4×D4—868no—
463C4×D4—868no—
464C4×D4—868no—
465C4×D4—868no—
466#117—864no—
467#117—864no—
468C2×C4⋊C4—862no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
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—432no—
483C2×C22⋊C4—432no—
484C2×C22⋊C4—432no—
485C2×C22⋊C4—432no—
486C2×C22⋊C4—432no—
487C2×C22⋊C4—864no—
488C2×C22⋊C4—862no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—861no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—864no—
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—861no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4C4×D4312yes—
504C2×C22⋊C4C4×D4312yescomplemented
505C2×C22⋊C4C4×D4312yescomplemented
506C2×C22⋊C4D17212yes—
507C2×C22⋊C4C22⋊D4312yes—
508C2×C42—862no—
509#99—868no—
510#99—868no—
511C24—82no—
512C24—432no—
513C24—432no—
514C24—432no—
515C24—861no—
516C24—861no—
517C24—861no—
518C24—861no—
519C24—3442no—
520C24C2×C4×D4311yescharacteristic
521C24C2×C4×D4311yescharacteristic
522C24C2×C4×D4311yescharacteristic
523C24C2×D17211yescharacteristic
524C24#1062189811yescharacteristic
525C24#1062189811yescharacteristic
526C24D4×D4311yescharacteristic
527C24D4×D4311yescharacteristic
528C24D4×D4311yescharacteristic
529C24D4×D4311yescharacteristic
530C24D4×D4311yescharacteristic
531C24#1062190011yescharacteristic
532C24Q8×D4311yescharacteristic
533C24#1062190211yescharacteristic
534C24C2×C22⋊D4311yescharacteristic
535C2×D4—434no—
536C2×D4—434no—
537C2×D4—434no—
538C2×D4—434no—
539C2×D4—862no—
540C2×D4—862no—
541C2×D4—862no—
542C2×D4—862no—
543C2×D4—862no—
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—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—41no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4—41no—
572C22×C4—82no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4—432no—
576C22×C4—432no—
577C22×C4—432no—
578C22×C4—868no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—862no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—862no—
588C22×C4—3444no—
589C22×C4—3442no—
590C22×C4—3442no—
591C22×C4—3442no—
592C22×C4—1721no—
593C22×C4—1721no—
594C22×C4—1721no—
595C22×C4—1721no—
596C4⋊C4—868no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—22no—
604C22⋊C4—41no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—41no—
608C22⋊C4—434no—
609C22⋊C4—868no—
610C22⋊C4—862no—
611C22⋊C4—862no—
612C22⋊C4—862no—
613C22⋊C4—862no—
614C22⋊C4—862no—
615C22⋊C4—862no—
616C22⋊C4—862no—
617C22⋊C4—1721no—
618C22⋊C4—1721no—
619C22⋊C4—1721no—
620C22⋊C4—1721no—
621C22⋊C4(C2×D43)⋊C414yes—
622C42—868no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23—81no—
638C23—434no—
639C23—862no—
640C23—862no—
641C23—862no—
642C23—862no—
643C23—862no—
644C23—862no—
645C23—3442no—
646C23—3442no—
647C23—3442no—
648C23—3442no—
649C23—3442no—
650C23—3442no—
651C23—1724no—
652C23C42×D4311yescharacteristic
653C23C22⋊C4×D4311yescharacteristic
654C23C22⋊C4×D4311yescharacteristic
655C23C22⋊C4×D4311yescharacteristic
656C23C22⋊C4×D4311yescharacteristic
657C23C2×(C2×D43)⋊C411yescharacteristic
658C23C4⋊C4×D4311yescharacteristic
659C23C4⋊C4×D4311yescharacteristic
660C23C4⋊C4×D4311yescharacteristic
661C23#1306328211yescharacteristic
662C23#1306328311yescharacteristic
663C23(C22⋊D43)⋊C411yescharacteristic
664C23(C22⋊D43)⋊C411yescharacteristic
665C23C4×C22⋊D4311yescharacteristic
666C23C4×C22⋊D4311yescharacteristic
667C23#1306328711yescharacteristic
668C23#1306328711yescharacteristic
669C23C4×D17211yescharacteristic
670C23C4×D17211yescharacteristic
671C23#1306329311yescharacteristic
672C23#1306329311yescharacteristic
673C23#1306329511yescharacteristic
674C23#1306329511yescharacteristic
675C23#1306329611yescharacteristic
676C23#1306329811yescharacteristic
677C23#1306329811yescharacteristic
678C23#1306330011yescharacteristic
679C23#1306330111yescharacteristic
680C23#1306330311yescharacteristic
681C23#1306330311yescharacteristic
682C23#1306330511yescharacteristic
683C23#1306330711yescharacteristic
684C23#1306330711yescharacteristic
685C23#1306331011yescharacteristic
686C23#1306331011yescharacteristic
687D4—864no—
688D4—864no—
689D4—864no—
690D4—864no—
691D4—864no—
692D4—864no—
693D4—864no—
694D4—864no—
695C2×C4—24no—
696C2×C4—44no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4—82no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4—82no—
707C2×C4—434no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—864no—
715C2×C4—3448no—
716C2×C4—3442no—
717C2×C4—3442no—
718C2×C4—3442no—
719C2×C4—3442no—
720C2×C4—3442no—
721C2×C4—3442no—
722C2×C4—3442no—
723C2×C4—3442no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1724no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
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—864no—
763C22—3442no—
764C22—3442no—
765C22—3442no—
766C22—3442no—
767C22—1724no—
768C22—1724no—
769C22—1724no—
770C22#95×D4311yescharacteristic
771C22#1458274611yescharacteristic
772C22C4×(C2×D43)⋊C411yescharacteristic
773C22#1458275411yescharacteristic
774C22#1458275611yescharacteristic
775C22#1458275811yescharacteristic
776C22#1458276111yescharacteristic
777C22#1458277011yescharacteristic
778C22#1458277011yescharacteristic
779C22#1458277311yescharacteristic
780C22#1458277311yescharacteristic
781C22#1458277511yescharacteristic
782C22#1458277511yescharacteristic
783C22#1458277711yescharacteristic
784C22#1458277711yescharacteristic
785C4—44no—
786C4—82no—
787C4—82no—
788C4—864no—
789C4—3442no—
790C4—3442no—
791C4—1724no—
792C2—21no—
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—21no—
804C2—21no—
805C2—21no—
806C2—1724no—
807C2(C2×D43)⋊#9511yescharacteristic
808C2#1913470212yes—
subgroupG/H
centerC22#14582761
commutatorC23×C43C2×C42
FrattiniC25C22×D43
FittingC2×C43×#342C2
socleC22×C43#381
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenterC2×#342D43
hypocenterC43#10768
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×#14582666C2semidirect
5. C2×#14582665C2semidirect
6. C2×#14582665C2semidirect
7. C2×C43×#342C2semidirect
15. C2×#13063281C4semidirect
19. C2×C22⋊C4×D43C4semidirect
24. C2×#13063239C4semidirect
25. C2×#13063239C4semidirect
74. C2×C22⋊Dic43C2×C4semidirect
75. C2×C22⋊Dic43C2×C4semidirect
102. C2×C22⋊C4×C43C2×C4semidirect
103. C2×C22⋊C4×C43C2×C4semidirect
394. C2×#342D43semidirect
437. C43#10768semidirect
504. C2×C22⋊C4C4×D43semidirect
505. C2×C22⋊C4C4×D43semidirect

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×#145826662
C2×#145826652
C2×C43×#3422
#1076843