Finite Group Databasebeta

← #25002925

Subgroups — #25002925

Order 11008.

1234 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#19137170C211yesmaximal, characteristic
4#19136948C211yesmaximal, characteristic, complemented
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×#13063239C414yescomplemented
17C2×#13063239C414yescomplemented
18#14582778—22no—
19#14582776—22no—
20#14582760C412yescomplemented
21#14582754C412yescomplemented
22C22⋊C4×Dic43—22no—
23C22⋊C4×Dic43—22no—
24C4×C22⋊Dic43—22no—
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⋊D43C2×C412yes—
45C22×C22⋊D43C2×C412yes—
46C23×Dic43—21no—
47C23×Dic43—21no—
48C23×Dic43C2×C411yescharacteristic
49C23×Dic43D412yes—
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⋊Dic43C2×C412yes—
63C2×C22⋊Dic43C2×C412yes—
64C2×C22⋊Dic43C2×C412yes—
65C2×C22⋊Dic43D412yes—
66C2×C22⋊Dic43D412yes—
67C2×C22⋊Dic43D412yes—
68C2×(C2×D43)⋊C4—24no—
69C2×C4×Dic43—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×C43C2×C412yes—
92C2×C22⋊C4×C43C2×C412yes—
93C2×C22⋊C4×C43C2×C412yes—
94C2×C22⋊C4×C43D412yes—
95C2×C22⋊C4×C43D412yes—
96C24×C43—82no—
97C24×C43C22×C411yescharacteristic
98C24×C43C22×C411yescharacteristic
99C24×C43C22×C411yescharacteristic
100C24×C43C2×D411yescharacteristic
101C24×C43C2×D411yescharacteristic
102C24×C43C2×D411yescharacteristic
103C24×C43C2×D411yescharacteristic
104C24×C43C2×D411yescharacteristic
105C24×C43C2×D411yescharacteristic
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×D43C4212yescomplemented
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
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—22no—
171C22×Dic43—22no—
172C22×Dic43—41no—
173C22×Dic43—41no—
174C22×Dic43—82no—
175C22×Dic43—82no—
176C22×Dic43—82no—
177C22×Dic43C4212yescomplemented
178C22×Dic43C22⋊C414yes—
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—22no—
186C22⋊C4×C43—41no—
187C22⋊C4×C43—41no—
188C22⋊C4×C43—41no—
189C22⋊C4×C43—41no—
190C22⋊C4×C43C22⋊C414yescomplemented
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—22no—
200C22⋊Dic43—41no—
201C22⋊Dic43—41no—
202C22⋊Dic43C22⋊C414yescomplemented
203(C2×D43)⋊C4—84no—
204C4×Dic43—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×C4211yescharacteristic
221C23×C43C2×C22⋊C411yescharacteristic
222C23×C43C2×C22⋊C411yescharacteristic
223C23×C43C2×C22⋊C411yescharacteristic
224C23×C43#11711yescharacteristic
225C23×C43#11711yescharacteristic
226C23×C43#11711yescharacteristic
227C23×C43C4×D411yescharacteristic
228C23×C43C4×D411yescharacteristic
229C23×C43C4×D411yescharacteristic
230C23×C43C4×D411yescharacteristic
231C23×C43C4×D411yescharacteristic
232C23×C43C4×D411yescharacteristic
233C23×C43C4×D411yescharacteristic
234C23×C43C4×D411yescharacteristic
235C23×C43C4×D411yescharacteristic
236C23×C43C4×D411yescharacteristic
237C23×C43C4×D411yescharacteristic
238C23×C43C4×D411yescharacteristic
239C23×C43#12011yescharacteristic
240C23×C43#12111yescharacteristic
241C23×C43#12111yescharacteristic
242C23×C43#12111yescharacteristic
243C23×C43#12111yescharacteristic
244C23×C43#12111yescharacteristic
245C23×C43#12111yescharacteristic
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—24no—
270C2×C4×C43—44no—
271C2×C4×C43—44no—
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—24no—
294C2×Dic43—44no—
295C2×Dic43—44no—
296C2×Dic43—41no—
297C2×Dic43—41no—
298C2×Dic43—41no—
299C2×Dic43—41no—
300C2×Dic43—44no—
301C2×Dic43—42no—
302C2×Dic43—82no—
303C2×Dic43—82no—
304C2×Dic43—82no—
305C2×Dic43—82no—
306C2×Dic43—82no—
307C2×Dic43—82no—
308#10938—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×C43C4×C22⋊C411yescharacteristic
345C22×C43C4×C22⋊C411yescharacteristic
346C22×C43C4×C22⋊C411yescharacteristic
347C22×C43#38611yescharacteristic
348C22×C43#38611yescharacteristic
349C22×C43#38611yescharacteristic
350C22×C43#38811yescharacteristic
351C22×C43#38811yescharacteristic
352C22×C43#38811yescharacteristic
353C22×C43#38811yescharacteristic
354C22×C43#38811yescharacteristic
355C22×C43#38811yescharacteristic
356C22×C43#39011yescharacteristic
357C22×C43#39011yescharacteristic
358C22×C43#39011yescharacteristic
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—44no—
368C4×C43—82no—
369C4×C43—82no—
370Dic43—44no—
371Dic43—44no—
372Dic43—42no—
373Dic43—82no—
374C22×#99—431no—
375C22×#99—431no—
376#2308—431no—
377#2273—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#143711yescharacteristic
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—434no—
406C2×#99—434no—
407C2×#99—862no—
408C2×#99—862no—
409C2×#99—862no—
410C2×#99—862no—
411#386—862no—
412#386—862no—
413#381—432no—
414#379—432no—
415C4×C22⋊C4—862no—
416C4×C22⋊C4—862no—
417C4×C22⋊C4—862no—
418#342—22no—
419#342—862no—
420#342—862no—
421C43#1093811yescharacteristic, 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×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—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—432no—
459C2×C22⋊C4—432no—
460C2×C22⋊C4—432no—
461C2×C22⋊C4—432no—
462C2×C22⋊C4—432no—
463C2×C22⋊C4—432no—
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⋊C4—861no—
474C2×C22⋊C4—861no—
475C2×C22⋊C4—864no—
476C2×C22⋊C4—861no—
477C2×C22⋊C4C4×D4312yes—
478C2×C22⋊C4C4×D4312yes—
479C2×C22⋊C4C4×D4312yes—
480C2×C22⋊C4D17212yes—
481C2×C22⋊C4C22⋊D4312yes—
482C2×C42—864no—
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×C4×D4311yescharacteristic
498C24C2×C4×D4311yescharacteristic
499C24C2×D17211yescharacteristic
500C24#1062189811yescharacteristic
501C24#1062189811yescharacteristic
502C24D4×D4311yescharacteristic
503C24D4×D4311yescharacteristic
504C24D4×D4311yescharacteristic
505C24D4×D4311yescharacteristic
506C24#1062190011yescharacteristic
507C24#1062190011yescharacteristic
508C24#1062190211yescharacteristic
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—22no—
543C22×C4—22no—
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—862no—
555C22×C4—862no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—862no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—3442no—
566C22×C4—3442no—
567C22×C4—3442no—
568C22×C4—1721no—
569C22×C4—1721no—
570C22⋊C4—22no—
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—434no—
582C22⋊C4—862no—
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(C2×D43)⋊C414yescomplemented
595C42—3444no—
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—
625C23C42×D4311yescharacteristic
626C23C22⋊C4×D4311yescharacteristic
627C23C22⋊C4×D4311yescharacteristic
628C23C2×(C2×D43)⋊C411yescharacteristic
629C23#1306328211yescharacteristic
630C23#1306328311yescharacteristic
631C23#1306328311yescharacteristic
632C23(C22⋊D43)⋊C411yescharacteristic
633C23(C22⋊D43)⋊C411yescharacteristic
634C23(C22⋊D43)⋊C411yescharacteristic
635C23(C22⋊D43)⋊C411yescharacteristic
636C23C4×C22⋊D4311yescharacteristic
637C23C4×C22⋊D4311yescharacteristic
638C23#1306328711yescharacteristic
639C23#1306328711yescharacteristic
640C23#1306328711yescharacteristic
641C23#1306328711yescharacteristic
642C23C4×D17211yescharacteristic
643C23C4×D17211yescharacteristic
644C23#1306329511yescharacteristic
645C23#1306329711yescharacteristic
646C23#1306329711yescharacteristic
647C23#1306329811yescharacteristic
648C23#1306329811yescharacteristic
649C23#1306330011yescharacteristic
650C23#1306330011yescharacteristic
651C23#1306330911yescharacteristic
652C23#1306331011yescharacteristic
653C23#1306331011yescharacteristic
654C23#1306331111yescharacteristic
655C23#1306331111yescharacteristic
656C23#1306331411yescharacteristic
657C23#1306332011yescharacteristic
658C23#1306332011yescharacteristic
659C23#1306332111yescharacteristic
660D4—1722no—
661D4—1722no—
662D4—1722no—
663D4—1722no—
664D4—1722no—
665D4—1722no—
666D4—1722no—
667D4—1722no—
668C2×C4—24no—
669C2×C4—44no—
670C2×C4—44no—
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—864no—
685C2×C4—3442no—
686C2×C4—3442no—
687C2×C4—3442no—
688C2×C4—3442no—
689C2×C4—3442no—
690C2×C4—3442no—
691C2×C4—1722no—
692C2×C4—1724no—
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#1458274611yescharacteristic
743C22#1458274611yescharacteristic
744C22C4×(C2×D43)⋊C411yescharacteristic
745C22#1458277611yescharacteristic
746C22#1458277711yescharacteristic
747C22#1458277711yescharacteristic
748C22#1458278811yescharacteristic
749C22#1458278811yescharacteristic
750C22#1458278911yescharacteristic
751C22#1458278911yescharacteristic
752C22#1458279111yescharacteristic
753C22#1458279111yescharacteristic
754C22#1458279911yescharacteristic
755C22#1458279911yescharacteristic
756C22#1458280011yescharacteristic
757C4—44no—
758C4—82no—
759C4—82no—
760C4—3442no—
761C4—1724no—
762C4—1722no—
763C4—1724no—
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#1913283111yescharacteristic
780C2#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#10938
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. #19136948C2semidirect
5. C2×#14582665C2semidirect
6. C2×#14582665C2semidirect
7. C2×C43×#342C2semidirect
16. C2×#13063239C4semidirect
17. C2×#13063239C4semidirect
20. #14582760C4semidirect
21. #14582754C4semidirect
119. C23×D43C42semidirect
177. C22×Dic43C42semidirect
190. C22⋊C4×C43C22⋊C4semidirect
202. C22⋊Dic43C22⋊C4semidirect
380. C2×#342D43semidirect
421. C43#10938semidirect
594. 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
C22×#130632392
#191371702
#191369482
C2×#145826652
C2×C43×#3422
#1093843