Finite Group Databasebeta

← #25003535

Subgroups — #25003535

Order 11008.

1178 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063239C211yesmaximal, characteristic
2C22×#13063239C211yesmaximal, characteristic
3#19137207C211yesmaximal, characteristic, complemented
4#19137170C211yesmaximal, characteristic
5C2×#14582665C211yesmaximal, characteristic, complemented
6C2×#14582665C211yesmaximal, characteristic, complemented
7C2×C43×#342C211yesmaximal, characteristic, complemented
8C23×C22⋊D43C2211yescharacteristic
9C22×C22⋊Dic43C2211yescharacteristic
10C22×C22⋊Dic43C2211yescharacteristic
11C22×C22⋊Dic43C2211yescharacteristic
12C2×#13063239—22no—
13C2×#13063239—22no—
14C2×#13063239—22no—
15C2×#13063239—22no—
16C2×#13063239—22no—
17C2×#13063239—22no—
18#14582778—22no—
19#14582776—22no—
20#14582772—22no—
21#14582771—22no—
22#14582760C412yescomplemented
23#14582757—22no—
24#14582754C412yescomplemented
25#14582665—22no—
26#14582665—22no—
27C22×C22⋊C4×C43C2211yescharacteristic
28C22×C22⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2211yescharacteristic
30C43×#342—22no—
31C24×D43C2×C411yescharacteristic
32C22×C22⋊D43—21no—
33C22×C22⋊D43—21no—
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⋊D43—21no—
43C22×C22⋊D43—21no—
44C22×C22⋊D43D412yes—
45C22×C22⋊D43Q812yes—
46C23×Dic43—21no—
47C23×Dic43—21no—
48C23×Dic43C2×C411yescharacteristic
49C23×Dic43D412yes—
50C2×Dic43⋊C4—24no—
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—21no—
60C2×C22⋊Dic43—21no—
61C2×C22⋊Dic43—21no—
62C2×C22⋊Dic43—21no—
63C2×C22⋊Dic43—21no—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43C2×C412yes—
66C2×C22⋊Dic43D412yes—
67C2×C22⋊Dic43D412yes—
68C2×C22⋊Dic43D412yes—
69C2×(C2×D43)⋊C4—24no—
70#13063239—28no—
71#13063239—28no—
72C43⋊#95—24no—
73C43⋊#95—24no—
74C25×C43C2311yescharacteristic
75C23×C4×C43—21no—
76C23×C4×C43—21no—
77C23×C4×C43—21no—
78C2×C22⋊C4×C43—21no—
79C2×C22⋊C4×C43—21no—
80C2×C22⋊C4×C43—21no—
81C2×C22⋊C4×C43—21no—
82C2×C22⋊C4×C43—21no—
83C2×C22⋊C4×C43—21no—
84C2×C22⋊C4×C43—21no—
85C2×C22⋊C4×C43—21no—
86C2×C22⋊C4×C43—21no—
87C2×C22⋊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×C43C2×C412yes—
94C2×C22⋊C4×C43D412yes—
95C2×C22⋊C4×C43D412yes—
96C24×C43—82no—
97C24×C43C22×C411yescharacteristic
98C24×C43C2×D411yescharacteristic
99C24×C43C2×D411yescharacteristic
100C24×C43C2×D411yescharacteristic
101C24×C43C2×D411yescharacteristic
102C24×C43C2×D411yescharacteristic
103C24×C43C2×D411yescharacteristic
104C24×C43C2×D411yescharacteristic
105C24×C43C2×Q811yescharacteristic
106C24×C43#4111yescharacteristic
107C24×C43#4111yescharacteristic
108C24×C43#4111yescharacteristic
109C24×C43#4111yescharacteristic
110C24×C43#4111yescharacteristic
111C24×C43#4111yescharacteristic
112C23×D43—21no—
113C23×D43—21no—
114C23×D43—21no—
115C23×D43—21no—
116C23×D43—21no—
117C23×D43—21no—
118C23×D43—82no—
119C23×D43C4⋊C412yescomplemented
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—41no—
124C22×C4×C43—41no—
125C22×C4×C43—41no—
126C22×C4×C43—41no—
127C22×C4×C43—41no—
128C22×C4×C43—41no—
129C22×C4×C43—82no—
130C22×C4×C43—82no—
131C22×C4×C43—82no—
132C2×C22⋊D43—22no—
133C2×C22⋊D43—22no—
134C2×C22⋊D43—22no—
135C2×C22⋊D43—22no—
136C2×C22⋊D43—22no—
137C2×C22⋊D43—22no—
138C2×C22⋊D43—22no—
139C2×C22⋊D43—22no—
140C2×C22⋊D43—22no—
141C2×C22⋊D43—22no—
142C2×C22⋊D43—22no—
143C2×C22⋊D43—22no—
144C2×C22⋊D43—41no—
145C2×C22⋊D43—41no—
146C2×C22⋊D43—41no—
147C2×C22⋊D43—41no—
148C2×C22⋊D43—41no—
149C2×C22⋊D43—41no—
150C2×C22⋊D43—41no—
151C2×C22⋊D43—41no—
152C2×C22⋊D43—41no—
153C2×C22⋊D43—41no—
154C2×C22⋊D43—41no—
155C2×C22⋊D43—41no—
156C2×C22⋊D43—41no—
157C2×C22⋊D43—41no—
158C2×C22⋊D43—41no—
159C2×C22⋊D43—41no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—22no—
167C22×Dic43—22no—
168C22×Dic43—22no—
169C22×Dic43—22no—
170C22×Dic43—41no—
171C22×Dic43—41no—
172C22×Dic43—41no—
173C22×Dic43—41no—
174C22×Dic43—82no—
175C22×Dic43—82no—
176C22×Dic43—82no—
177C22×Dic43C22⋊C414yes—
178C22×Dic43C4⋊C412yescomplemented
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—22no—
182C22⋊C4×C43—22no—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—41no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43—41no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—22no—
197C22⋊Dic43—22no—
198C22⋊Dic43—22no—
199C22⋊Dic43—41no—
200C22⋊Dic43—41no—
201C22⋊Dic43—41no—
202C22⋊Dic43—41no—
203(C2×D43)⋊C4—84no—
204Dic43⋊C4—84no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—42no—
211C23×C43—42no—
212C23×C43—81no—
213C23×C43—81no—
214C23×C43—81no—
215C23×C43—81no—
216C23×C43—81no—
217C23×C43—81no—
218C23×C43—81no—
219C23×C43—81no—
220C23×C43C2×C22⋊C411yescharacteristic
221C23×C43C2×C4⋊C411yescharacteristic
222C23×C43#11711yescharacteristic
223C23×C43C4×D411yescharacteristic
224C23×C43C4×D411yescharacteristic
225C23×C43C4×D411yescharacteristic
226C23×C43C4×D411yescharacteristic
227C23×C43#12011yescharacteristic
228C23×C43#12011yescharacteristic
229C23×C43#12011yescharacteristic
230C23×C43#12111yescharacteristic
231C23×C43#12111yescharacteristic
232C23×C43#12111yescharacteristic
233C23×C43#12111yescharacteristic
234C23×C43#12111yescharacteristic
235C23×C43#12111yescharacteristic
236C23×C43#12111yescharacteristic
237C23×C43#12111yescharacteristic
238C23×C43C22⋊Q811yescharacteristic
239C23×C43C22⋊Q811yescharacteristic
240C23×C43C22⋊Q811yescharacteristic
241C23×C43C22⋊Q811yescharacteristic
242C23×C43C22⋊Q811yescharacteristic
243C23×C43C22⋊Q811yescharacteristic
244C23×C43#12311yescharacteristic
245C23×C43#12311yescharacteristic
246C23×C43#12311yescharacteristic
247C23×C43#12311yescharacteristic
248C23×C43#12311yescharacteristic
249C23×C43#12411yescharacteristic
250C23×C43#12411yescharacteristic
251C23×C43#12411yescharacteristic
252C23×C43#12611yescharacteristic
253C23×C43#12611yescharacteristic
254C23×C43#12711yescharacteristic
255C22×D43—22no—
256C22×D43—22no—
257C22×D43—22no—
258C22×D43—44no—
259C22×D43—41no—
260C22×D43—41no—
261C22×D43—41no—
262C22×D43—41no—
263C22×D43—82no—
264C22×D43—82no—
265C22×D43—82no—
266C22×D43—82no—
267C22×D43—82no—
268C22×D43—82no—
269C2×C4×C43—44no—
270C2×C4×C43—44no—
271C2×C4×C43—42no—
272C2×C4×C43—42no—
273C2×C4×C43—42no—
274C2×C4×C43—82no—
275C2×C4×C43—82no—
276C2×C4×C43—82no—
277C2×C4×C43—82no—
278C2×C4×C43—82no—
279C2×C4×C43—82no—
280C2×C4×C43—82no—
281C22⋊D43—42no—
282C22⋊D43—42no—
283C22⋊D43—42no—
284C22⋊D43—42no—
285C22⋊D43—42no—
286C22⋊D43—42no—
287C22⋊D43—42no—
288C22⋊D43—42no—
289C2×Dic43—22no—
290C2×Dic43—22no—
291C2×Dic43—22no—
292C2×Dic43—24no—
293C2×Dic43—44no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—44no—
299C2×Dic43—44no—
300C2×Dic43—42no—
301C2×Dic43—42no—
302C2×Dic43—82no—
303C2×Dic43—82no—
304C2×Dic43—82no—
305C2×Dic43—82no—
306C2×Dic43—82no—
307C2×Dic43—82no—
308#11046—431nomaximal, Sylow
309C22×C43—22no—
310C22×C43—22no—
311C22×C43—22no—
312C22×C43—22no—
313C22×C43—22no—
314C22×C43—22no—
315C22×C43—22no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43—41no—
320C22×C43—41no—
321C22×C43—41no—
322C22×C43—41no—
323C22×C43—41no—
324C22×C43—41no—
325C22×C43—41no—
326C22×C43—41no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
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#38011yescharacteristic
345C22×C43#38511yescharacteristic
346C22×C43#38511yescharacteristic
347C22×C43#38611yescharacteristic
348C22×C43#38811yescharacteristic
349C22×C43#38811yescharacteristic
350C22×C43#39011yescharacteristic
351C22×C43#39211yescharacteristic
352C22×C43#39311yescharacteristic
353C22×C43#39411yescharacteristic
354C22×C43#39411yescharacteristic
355C22×C43#39611yescharacteristic
356C22×C43#39611yescharacteristic
357C22×C43#39711yescharacteristic
358C22×C43#39911yescharacteristic
359C2×D43—44no—
360C2×D43—42no—
361C2×D43—82no—
362C2×D43—82no—
363C2×D43—82no—
364C2×D43—82no—
365C2×D43—82no—
366C2×D43—82no—
367C4×C43—82no—
368C4×C43—82no—
369C4×C43—82no—
370Dic43—44no—
371Dic43—42no—
372Dic43—82no—
373Dic43—82no—
374C22×#99—431no—
375C22×#99—431no—
376#2315—431no—
377#2308—431no—
378C2×#342—431no—
379C2×#342—431no—
380C2×#342D4311yescharacteristic, complemented
381C2×C43—21no—
382C2×C43—21no—
383C2×C43—21no—
384C2×C43—21no—
385C2×C43—21no—
386C2×C43—21no—
387C2×C43—21no—
388C2×C43—21no—
389C2×C43—21no—
390C2×C43—21no—
391C2×C43—21no—
392C2×C43—21no—
393C2×C43—21no—
394C2×C43—21no—
395C2×C43#143911yescharacteristic
396C2×C43#191312yes—
397D43—82no—
398C23×D4—431no—
399C22×C22⋊C4—431no—
400C22×C22⋊C4—431no—
401C22×C22⋊C4—431no—
402C22×C22⋊C4C2×D4311yescharacteristic
403C22×C22⋊C4C2×D4311yescharacteristic
404C22×C22⋊C4C2×D4311yescharacteristic
405C2×#99—862no—
406C2×#99—862no—
407C2×#99—862no—
408C2×#99—862no—
409C2×#99—862no—
410C2×#99—862no—
411#386—862no—
412#386—862no—
413#385—862no—
414#385—862no—
415#381—432no—
416#380—862no—
417#379—432no—
418#342—22no—
419#342—862no—
420#342—862no—
421C43#1104611yescharacteristic, complemented, Sylow
422C25—431no—
423C25C22×D4311yescharacteristic
424C22×D4—432no—
425C22×D4—432no—
426C22×D4—861no—
427C22×D4—861no—
428C22×D4—861no—
429C22×D4—861no—
430C22×D4—861no—
431C22×D4—861no—
432C22×D4—861no—
433C22×D4—861no—
434C22×D4—861no—
435C22×D4—861no—
436C22×D4—861no—
437C22×D4—861no—
438C23×C4—21no—
439C23×C4—21no—
440C23×C4—21no—
441C23×C4—431no—
442C23×C4—432no—
443C23×C4—861no—
444C23×C4—861no—
445C2×C4⋊C4—864no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—432no—
462C2×C22⋊C4—432no—
463C2×C22⋊C4—432no—
464C2×C22⋊C4—432no—
465C2×C22⋊C4—861no—
466C2×C22⋊C4—861no—
467C2×C22⋊C4—861no—
468C2×C22⋊C4—861no—
469C2×C22⋊C4—861no—
470C2×C22⋊C4—861no—
471C2×C22⋊C4—861no—
472C2×C22⋊C4—861no—
473C2×C22⋊C4—861no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—861no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4—864no—
478C2×C22⋊C4—861no—
479C2×C22⋊C4—861no—
480C2×C22⋊C4C4×D4312yes—
481C2×C22⋊C4D17212yes—
482C2×C22⋊C4C22⋊D4312yes—
483#99—868no—
484#99—868no—
485#95—864no—
486#95—864no—
487C24—82no—
488C24—432no—
489C24—861no—
490C24—861no—
491C24—861no—
492C24—861no—
493C24—861no—
494C24—861no—
495C24—3442no—
496C24C2×C4×D4311yescharacteristic
497C24C2×D17211yescharacteristic
498C24#1062189811yescharacteristic
499C24#1062189811yescharacteristic
500C24#1062189811yescharacteristic
501C24#1062189811yescharacteristic
502C24D4×D4311yescharacteristic
503C24D4×D4311yescharacteristic
504C24D4×D4311yescharacteristic
505C24D4×D4311yescharacteristic
506C24D4×D4311yescharacteristic
507C24#1062190011yescharacteristic
508C24Q8×D4311yescharacteristic
509C24#1062190211yescharacteristic
510C24C2×C22⋊D4311yescharacteristic
511C2×D4—862no—
512C2×D4—862no—
513C2×D4—862no—
514C2×D4—862no—
515C2×D4—862no—
516C2×D4—862no—
517C2×D4—862no—
518C2×D4—862no—
519C2×D4—862no—
520C2×D4—862no—
521C2×D4—862no—
522C2×D4—862no—
523C2×D4—1721no—
524C2×D4—1721no—
525C2×D4—1721no—
526C2×D4—1721no—
527C2×D4—1721no—
528C2×D4—1721no—
529C2×D4—1721no—
530C2×D4—1721no—
531C2×D4—1721no—
532C2×D4—1721no—
533C2×D4—1721no—
534C2×D4—1721no—
535C2×D4—1721no—
536C2×D4—1721no—
537C2×D4—1721no—
538C2×D4—1721no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—41no—
543C22×C4—41no—
544C22×C4—41no—
545C22×C4—41no—
546C22×C4—41no—
547C22×C4—41no—
548C22×C4—82no—
549C22×C4—82no—
550C22×C4—82no—
551C22×C4—432no—
552C22×C4—434no—
553C22×C4—862no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4—862no—
563C22×C4—3442no—
564C22×C4—3442no—
565C22×C4—3442no—
566C22×C4—1721no—
567C22×C4—1721no—
568C22×C4—1721no—
569C22×C4—1721no—
570C4⋊C4—3444no—
571C22⋊C4—22no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—41no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—41no—
581C22⋊C4—41no—
582C22⋊C4—41no—
583C22⋊C4—862no—
584C22⋊C4—862no—
585C22⋊C4—862no—
586C22⋊C4—862no—
587C22⋊C4—862no—
588C22⋊C4—862no—
589C22⋊C4—862no—
590C22⋊C4—862no—
591C22⋊C4—3444no—
592C22⋊C4—1721no—
593C22⋊C4—1721no—
594C22⋊C4—1721no—
595C22⋊C4—1721no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—81no—
604C23—81no—
605C23—81no—
606C23—81no—
607C23—81no—
608C23—81no—
609C23—81no—
610C23—81no—
611C23—862no—
612C23—862no—
613C23—862no—
614C23—3442no—
615C23—3442no—
616C23—3442no—
617C23—3442no—
618C23—3442no—
619C23—3442no—
620C23—1724no—
621C23—1721no—
622C23—1721no—
623C23—1721no—
624C23—1721no—
625C23C22⋊C4×D4311yescharacteristic
626C23C4⋊C4×D4311yescharacteristic
627C23#1306328211yescharacteristic
628C23(C22⋊D43)⋊C411yescharacteristic
629C23C4×C22⋊D4311yescharacteristic
630C23#1306328711yescharacteristic
631C23C4×D17211yescharacteristic
632C23#1306329311yescharacteristic
633C23#1306329511yescharacteristic
634C23#1306329511yescharacteristic
635C23#1306329711yescharacteristic
636C23#1306329811yescharacteristic
637C23#1306329811yescharacteristic
638C23#1306329811yescharacteristic
639C23#1306329811yescharacteristic
640C23#1306329811yescharacteristic
641C23#1306329911yescharacteristic
642C23#1306330011yescharacteristic
643C23#1306330111yescharacteristic
644C23#1306330311yescharacteristic
645C23#1306330311yescharacteristic
646C23#1306330311yescharacteristic
647C23#1306330311yescharacteristic
648C23#1306330511yescharacteristic
649C23#1306330711yescharacteristic
650C23#1306330811yescharacteristic
651C23#1306331011yescharacteristic
652C23#1306331011yescharacteristic
653C23#1306331011yescharacteristic
654C23#1306331111yescharacteristic
655C23#1306331111yescharacteristic
656C23#1306331311yescharacteristic
657C23#1306331911yescharacteristic
658C23#1306332011yescharacteristic
659C23#1306332111yescharacteristic
660D4—1722no—
661D4—1722no—
662D4—1722no—
663D4—1722no—
664D4—1722no—
665D4—1722no—
666D4—1722no—
667D4—1722no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—82no—
674C2×C4—82no—
675C2×C4—82no—
676C2×C4—82no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—864no—
684C2×C4—3442no—
685C2×C4—3442no—
686C2×C4—3442no—
687C2×C4—3442no—
688C2×C4—3442no—
689C2×C4—3442no—
690C2×C4—1724no—
691C2×C4—1722no—
692C2×C4—1722no—
693C2×C4—1724no—
694C2×C4—1721no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1724no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—3442no—
735C22—3442no—
736C22—3442no—
737C22—3442no—
738C22—3442no—
739C22—3442no—
740C22—1724no—
741C22—1722no—
742C22#1458275811yescharacteristic
743C22#1458277011yescharacteristic
744C22#1458277311yescharacteristic
745C22#1458277711yescharacteristic
746C22#1458278811yescharacteristic
747C22#1458279011yescharacteristic
748C22#1458279911yescharacteristic
749C22#1458280811yescharacteristic
750C22#1458281211yescharacteristic
751C22#1458281411yescharacteristic
752C22#1458281711yescharacteristic
753C22#1458282111yescharacteristic
754C22#1458282311yescharacteristic
755C22#1458282811yescharacteristic
756C22#1458283411yescharacteristic
757C4—82no—
758C4—82no—
759C4—82no—
760C4—3442no—
761C4—3442no—
762C4—1724no—
763C4—1722no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—21no—
773C2—21no—
774C2—21no—
775C2—21no—
776C2—21no—
777C2—21no—
778C2—3442no—
779C2#1913283911yescharacteristic
780C2#1913513612yes—
subgroupG/H
centerC22#14582777
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC2×C43×#342C2
socleC22×C43#386
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenterC2×#342D43
hypocenterC43#11046
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
3. #19137207C2semidirect
5. C2×#14582665C2semidirect
6. C2×#14582665C2semidirect
7. C2×C43×#342C2semidirect
22. #14582760C4semidirect
24. #14582754C4semidirect
119. C23×D43C4⋊C4semidirect
178. C22×Dic43C4⋊C4semidirect
380. C2×#342D43semidirect
421. C43#11046semidirect

Maximal subgroups

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

subgroupindex
C22×#130632392
#191372072
#191371702
C2×#145826652
C2×C43×#3422
#1104643