Finite Group Databasebeta

← #25003794

Subgroups — #25003794

Order 11008.

1154 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063239C211yesmaximal, characteristic
2C22×#13063239C211yesmaximal, characteristic
3C22×#13063239C211yesmaximal, characteristic
4C2×#14582665C211yesmaximal, characteristic, complemented
5C2×#14582665C211yesmaximal, characteristic, complemented
6C2×#14582665C211yesmaximal, characteristic, complemented
7C43×#2315C211yesmaximal, 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—
18C2×#13063239—22no—
19C2×#13063239—22no—
20C2×#13063239C414yescomplemented
21#14582665—22no—
22#14582665—22no—
23#14582665—22no—
24C22×C22⋊C4×C43C2211yescharacteristic
25C22×C22⋊C4×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2211yescharacteristic
27C43×#385—22no—
28C43×#385—22no—
29C43×#380—22no—
30C24×D43Q811yescharacteristic
31C22×C22⋊D43—21no—
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⋊D43C2×C412yes—
44C22×C22⋊D43D412yes—
45C23×Dic43—21no—
46C23×Dic43—21no—
47C23×Dic43—21no—
48C23×Dic43Q811yescharacteristic
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—21no—
60C2×C22⋊Dic43—21no—
61C2×C22⋊Dic43—21no—
62C2×C22⋊Dic43—21no—
63C2×C22⋊Dic43—21no—
64C2×C22⋊Dic43C2×C412yes—
65C2×C22⋊Dic43D412yes—
66C2×C22⋊Dic43D412yes—
67#13063239—28no—
68#13063239—28no—
69#13063239—28no—
70C25×C43C2311yescharacteristic
71C23×C4×C43—21no—
72C23×C4×C43—21no—
73C23×C4×C43—21no—
74C2×C4⋊C4×C43—24no—
75C2×C22⋊C4×C43—21no—
76C2×C22⋊C4×C43—21no—
77C2×C22⋊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×C43C2×C412yes—
89C2×C22⋊C4×C43D412yes—
90C2×C22⋊C4×C43D412yes—
91C2×C22⋊C4×C43D412yes—
92C2×C22⋊C4×C43D412yes—
93#95×C43—24no—
94C24×C43—82no—
95C24×C43C22×C411yescharacteristic
96C24×C43C2×D411yescharacteristic
97C24×C43C2×D411yescharacteristic
98C24×C43C2×D411yescharacteristic
99C24×C43C2×D411yescharacteristic
100C24×C43C2×D411yescharacteristic
101C24×C43C2×D411yescharacteristic
102C24×C43C2×D411yescharacteristic
103C24×C43C2×Q811yescharacteristic
104C24×C43#4111yescharacteristic
105C24×C43#4111yescharacteristic
106C24×C43#4111yescharacteristic
107C24×C43#4111yescharacteristic
108C24×C43#4111yescharacteristic
109C24×C43#4111yescharacteristic
110C23×D43—21no—
111C23×D43—21no—
112C23×D43—21no—
113C23×D43—21no—
114C23×D43—21no—
115C23×D43—21no—
116C23×D43—82no—
117C23×D43C4⋊C412yescomplemented
118C22×C4×C43—22no—
119C22×C4×C43—22no—
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—82no—
128C22×C4×C43—82no—
129C22×C4×C43—82no—
130C2×C22⋊D43—22no—
131C2×C22⋊D43—22no—
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—41no—
143C2×C22⋊D43—41no—
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—
158C22×Dic43—22no—
159C22×Dic43—22no—
160C22×Dic43—21no—
161C22×Dic43—21no—
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43—21no—
166C22×Dic43—22no—
167C22×Dic43—41no—
168C22×Dic43—41no—
169C22×Dic43—41no—
170C22×Dic43—41no—
171C22×Dic43—41no—
172C22×Dic43—41no—
173C22×Dic43—82no—
174C22×Dic43—82no—
175C22×Dic43—82no—
176C22×Dic43C4⋊C412yescomplemented
177C4⋊C4×C43—84no—
178C22⋊C4×C43—22no—
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×C43C22⋊C414yes—
190C22⋊Dic43—22no—
191C22⋊Dic43—22no—
192C22⋊Dic43—22no—
193C22⋊Dic43—22no—
194C22⋊Dic43—22no—
195C22⋊Dic43—22no—
196C22⋊Dic43—41no—
197C22⋊Dic43—41no—
198C22⋊Dic43—41no—
199C22⋊Dic43—41no—
200C22⋊Dic43—41no—
201C22⋊Dic43—41no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—81no—
210C23×C43—81no—
211C23×C43—81no—
212C23×C43—81no—
213C23×C43—81no—
214C23×C43—81no—
215C23×C43—81no—
216C23×C43—81no—
217C23×C43C2×C22⋊C411yescharacteristic
218C23×C43C2×C4⋊C411yescharacteristic
219C23×C43#11711yescharacteristic
220C23×C43C4×D411yescharacteristic
221C23×C43C4×D411yescharacteristic
222C23×C43C4×D411yescharacteristic
223C23×C43C4×D411yescharacteristic
224C23×C43#12011yescharacteristic
225C23×C43#12011yescharacteristic
226C23×C43#12011yescharacteristic
227C23×C43#12111yescharacteristic
228C23×C43#12111yescharacteristic
229C23×C43#12111yescharacteristic
230C23×C43#12111yescharacteristic
231C23×C43#12111yescharacteristic
232C23×C43#12111yescharacteristic
233C23×C43#12111yescharacteristic
234C23×C43#12111yescharacteristic
235C23×C43C22⋊Q811yescharacteristic
236C23×C43C22⋊Q811yescharacteristic
237C23×C43C22⋊Q811yescharacteristic
238C23×C43C22⋊Q811yescharacteristic
239C23×C43C22⋊Q811yescharacteristic
240C23×C43C22⋊Q811yescharacteristic
241C23×C43#12311yescharacteristic
242C23×C43#12311yescharacteristic
243C23×C43#12311yescharacteristic
244C23×C43#12311yescharacteristic
245C23×C43#12311yescharacteristic
246C23×C43#12411yescharacteristic
247C23×C43#12411yescharacteristic
248C23×C43#12411yescharacteristic
249C23×C43#12611yescharacteristic
250C23×C43#12611yescharacteristic
251C23×C43#12711yescharacteristic
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—22no—
255C22×D43—41no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—41no—
259C22×D43—82no—
260C22×D43—82no—
261C22×D43—82no—
262C22×D43—82no—
263C22×D43—82no—
264C22×D43—82no—
265C22×D43—82no—
266C2×C4×C43—24no—
267C2×C4×C43—44no—
268C2×C4×C43—44no—
269C2×C4×C43—44no—
270C2×C4×C43—42no—
271C2×C4×C43—42no—
272C2×C4×C43—82no—
273C2×C4×C43—82no—
274C2×C4×C43—82no—
275C2×C4×C43—82no—
276C2×C4×C43—82no—
277C2×C4×C43—82no—
278C22⋊D43—42no—
279C22⋊D43—42no—
280C22⋊D43—42no—
281C22⋊D43—42no—
282C22⋊D43—42no—
283C22⋊D43—42no—
284C22⋊D43—42no—
285C22⋊D43—42no—
286C2×Dic43—22no—
287C2×Dic43—22no—
288C2×Dic43—22no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—42no—
294C2×Dic43—42no—
295C2×Dic43—42no—
296C2×Dic43—82no—
297C2×Dic43—82no—
298C2×Dic43—82no—
299C2×Dic43—82no—
300C2×Dic43—82no—
301C2×Dic43—82no—
302C2×Dic43—82no—
303C2×Dic43—82no—
304C2×Dic43—82no—
305#11089—431nomaximal, Sylow
306C22×C43—22no—
307C22×C43—22no—
308C22×C43—22no—
309C22×C43—22no—
310C22×C43—22no—
311C22×C43—22no—
312C22×C43—22no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43—41no—
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#38011yescharacteristic
342C22×C43#38511yescharacteristic
343C22×C43#38511yescharacteristic
344C22×C43#38611yescharacteristic
345C22×C43#38811yescharacteristic
346C22×C43#38811yescharacteristic
347C22×C43#39011yescharacteristic
348C22×C43#39211yescharacteristic
349C22×C43#39311yescharacteristic
350C22×C43#39411yescharacteristic
351C22×C43#39411yescharacteristic
352C22×C43#39611yescharacteristic
353C22×C43#39611yescharacteristic
354C22×C43#39711yescharacteristic
355C22×C43#39911yescharacteristic
356C2×D43—42no—
357C2×D43—82no—
358C2×D43—82no—
359C2×D43—82no—
360C2×D43—82no—
361C2×D43—82no—
362C2×D43—82no—
363C2×D43—82no—
364C4×C43—44no—
365C4×C43—82no—
366C4×C43—82no—
367Dic43—42no—
368Dic43—82no—
369Dic43—82no—
370Dic43—82no—
371C22×#99—431no—
372C22×#99—431no—
373C22×#99—431no—
374#2315D4311yescharacteristic, complemented
375C2×#342—431no—
376C2×#342—431no—
377C2×#342—431no—
378C2×C43—21no—
379C2×C43—21no—
380C2×C43—21no—
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#143911yescharacteristic
393C2×C43#203212yes—
394D43—82no—
395C23×D4—431no—
396C22×C22⋊C4—431no—
397C22×C22⋊C4—431no—
398C22×C22⋊C4—431no—
399C22×C22⋊C4C2×D4311yescharacteristic
400C22×C22⋊C4C2×D4311yescharacteristic
401C22×C22⋊C4C2×D4311yescharacteristic
402C2×#99—434no—
403C2×#99—862no—
404C2×#99—862no—
405C2×#99—862no—
406C2×#99—862no—
407C2×#99—862no—
408C2×#99—862no—
409C2×#99—862no—
410C2×#99—862no—
411#385—22no—
412#385—22no—
413#380—22no—
414#342—862no—
415#342—862no—
416#342—862no—
417C43#1108911yescharacteristic, complemented, Sylow
418C25—431no—
419C25C22×D4311yescharacteristic
420C22×D4—432no—
421C22×D4—432no—
422C22×D4—861no—
423C22×D4—861no—
424C22×D4—861no—
425C22×D4—861no—
426C22×D4—861no—
427C22×D4—861no—
428C22×D4—861no—
429C22×D4—861no—
430C22×D4—861no—
431C22×D4—861no—
432C22×D4—861no—
433C22×D4—861no—
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—21no—
437C23×C4—431no—
438C23×C4—861no—
439C23×C4—861no—
440C23×C4—861no—
441C2×C4⋊C4—24no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
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—432no—
456C2×C22⋊C4—432no—
457C2×C22⋊C4—432no—
458C2×C22⋊C4—861no—
459C2×C22⋊C4—861no—
460C2×C22⋊C4—861no—
461C2×C22⋊C4—861no—
462C2×C22⋊C4—861no—
463C2×C22⋊C4—861no—
464C2×C22⋊C4—861no—
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⋊C4C4×D4312yes—
474C2×C22⋊C4D17212yes—
475C2×C22⋊C4C22⋊D4312yes—
476C2×C22⋊C4C22⋊D4312yes—
477C2×C22⋊C4C22⋊D4312yes—
478#99—868no—
479#99—868no—
480#99—868no—
481#95—24no—
482C24—82no—
483C24—432no—
484C24—861no—
485C24—861no—
486C24—861no—
487C24—861no—
488C24—861no—
489C24—861no—
490C24—3442no—
491C24C2×C4×D4311yescharacteristic
492C24C2×D17211yescharacteristic
493C24#1062189811yescharacteristic
494C24#1062189811yescharacteristic
495C24D4×D4311yescharacteristic
496C24D4×D4311yescharacteristic
497C24D4×D4311yescharacteristic
498C24#1062190011yescharacteristic
499C24Q8×D4311yescharacteristic
500C24#1062190211yescharacteristic
501C24#1062190211yescharacteristic
502C24#1062190211yescharacteristic
503C24C2×C22⋊D4311yescharacteristic
504C24C2×C22⋊D4311yescharacteristic
505C24C2×C22⋊D4311yescharacteristic
506C2×D4—862no—
507C2×D4—862no—
508C2×D4—862no—
509C2×D4—862no—
510C2×D4—862no—
511C2×D4—862no—
512C2×D4—862no—
513C2×D4—862no—
514C2×D4—862no—
515C2×D4—862no—
516C2×D4—862no—
517C2×D4—862no—
518C2×D4—1721no—
519C2×D4—1721no—
520C2×D4—1721no—
521C2×D4—1721no—
522C2×D4—1721no—
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—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—41no—
540C22×C4—41no—
541C22×C4—41no—
542C22×C4—41no—
543C22×C4—82no—
544C22×C4—82no—
545C22×C4—82no—
546C22×C4—432no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—861no—
552C22×C4—861no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—3442no—
557C22×C4—3442no—
558C22×C4—3442no—
559C22×C4—1721no—
560C22×C4—1721no—
561C22×C4—1721no—
562C22×C4—1721no—
563C22×C4—1721no—
564C22×C4—1721no—
565C4⋊C4—84no—
566C22⋊C4—22no—
567C22⋊C4—22no—
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—862no—
578C22⋊C4—862no—
579C22⋊C4—862no—
580C22⋊C4—862no—
581C22⋊C4—862no—
582C22⋊C4—862no—
583C22⋊C4—1721no—
584C22⋊C4—1721no—
585C22⋊C4—1721no—
586C22⋊C4—1721no—
587C22⋊C4—1721no—
588C22⋊C4—1721no—
589C22⋊C4(C2×D43)⋊C414yes—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—81no—
598C23—81no—
599C23—81no—
600C23—81no—
601C23—81no—
602C23—81no—
603C23—81no—
604C23—81no—
605C23—862no—
606C23—862no—
607C23—862no—
608C23—3442no—
609C23—3442no—
610C23—3442no—
611C23—3442no—
612C23—3442no—
613C23—3442no—
614C23—3442no—
615C23—1721no—
616C23—1721no—
617C23—1721no—
618C23—1721no—
619C23C2×(C2×D43)⋊C411yescharacteristic
620C23C4⋊C4×D4311yescharacteristic
621C23#1306328311yescharacteristic
622C23C4×C22⋊D4311yescharacteristic
623C23C4×C22⋊D4311yescharacteristic
624C23#1306328711yescharacteristic
625C23#1306328711yescharacteristic
626C23#1306329311yescharacteristic
627C23#1306329311yescharacteristic
628C23#1306329411yescharacteristic
629C23#1306329611yescharacteristic
630C23#1306329711yescharacteristic
631C23#1306329711yescharacteristic
632C23#1306329911yescharacteristic
633C23#1306329911yescharacteristic
634C23#1306330011yescharacteristic
635C23#1306330011yescharacteristic
636C23#1306330011yescharacteristic
637C23#1306330111yescharacteristic
638C23#1306330111yescharacteristic
639C23#1306330111yescharacteristic
640C23#1306330311yescharacteristic
641C23#1306330311yescharacteristic
642C23#1306330511yescharacteristic
643C23#1306330811yescharacteristic
644C23#1306331011yescharacteristic
645C23#1306331011yescharacteristic
646C23#1306331011yescharacteristic
647C23#1306331011yescharacteristic
648C23#1306331411yescharacteristic
649C23#1306331411yescharacteristic
650C23#1306331411yescharacteristic
651C23#1306332011yescharacteristic
652C23#1306332011yescharacteristic
653C23#1306332111yescharacteristic
654D4—1722no—
655D4—1722no—
656D4—1722no—
657D4—1722no—
658D4—1722no—
659D4—1722no—
660D4—1722no—
661D4—1722no—
662C2×C4—24no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—82no—
669C2×C4—82no—
670C2×C4—82no—
671C2×C4—82no—
672C2×C4—82no—
673C2×C4—82no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—3442no—
678C2×C4—3442no—
679C2×C4—3442no—
680C2×C4—3442no—
681C2×C4—3442no—
682C2×C4—3442no—
683C2×C4—3442no—
684C2×C4—3442no—
685C2×C4—3442no—
686C2×C4—1722no—
687C2×C4—1722no—
688C2×C4—1722no—
689C2×C4—1721no—
690C2×C4—1721no—
691C2×C4—1721no—
692C2×C4—1721no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
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—3442no—
729C22—3442no—
730C22—3442no—
731C22—3442no—
732C22—3442no—
733C22—3442no—
734C22—3442no—
735C22—1722no—
736C22#1458275611yescharacteristic
737C22#1458277011yescharacteristic
738C22#1458277011yescharacteristic
739C22#1458277811yescharacteristic
740C22#1458278911yescharacteristic
741C22#1458278911yescharacteristic
742C22#1458280011yescharacteristic
743C22#1458280711yescharacteristic
744C22#1458281011yescharacteristic
745C22#1458281611yescharacteristic
746C22#1458281611yescharacteristic
747C22#1458282111yescharacteristic
748C22#1458282111yescharacteristic
749C22#1458282511yescharacteristic
750C22#1458283411yescharacteristic
751C4—44no—
752C4—82no—
753C4—82no—
754C4—3442no—
755C4—3442no—
756C4—3442no—
757C4—1722no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—21no—
764C2—21no—
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—21no—
772C2—3442no—
773C2#1913283711yescharacteristic
774C2#1913577112yes—
subgroupG/H
centerC22#14582810
commutatorC24×C43C22×C4
FrattiniC25C22×D43
FittingC43×#2315C2
socleC22×C43#393
prime radicalC23×C22⋊D43C22
cosocleC25×C43C23
hypercenter#2315D43
hypocenterC43#11089
LCSG ▷ C24×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #2315

Complements

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

NH ≅ G/Ntype
4. C2×#14582665C2semidirect
5. C2×#14582665C2semidirect
6. C2×#14582665C2semidirect
7. C43×#2315C2semidirect
20. C2×#13063239C4semidirect
117. C23×D43C4⋊C4semidirect
176. C22×Dic43C4⋊C4semidirect
374. #2315D43semidirect
417. C43#11089semidirect

Maximal subgroups

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

subgroupindex
C22×#130632392
C2×#145826652
C43×#23152
#1108943