Finite Group Databasebeta

← #25003310

Subgroups — #25003310

Order 11008.

1558 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063314C211yesmaximal, characteristic
2C22×#13063249C211yesmaximal, characteristic, complemented
3C22×#13063247C211yesmaximal, characteristic
4C22×#13063245C211yesmaximal, characteristic
5C2×#14582653C211yesmaximal, characteristic, complemented
6#19132824C211yesmaximal, characteristic, complemented
7C22×#103×C43C211yesmaximal, characteristic, complemented
8C23×D172C2211yescharacteristic
9C23×C43⋊C8C2211yescharacteristic
10C2×#13063314—22no—
11C2×#13063314—22no—
12C2×#13063314—22no—
13C2×#13063314—22no—
14C2×#13063314—22no—
15C2×#13063314C414yescomplemented
16C22×C4⋊Dic43C2211yescharacteristic
17C22×(C2×D43)⋊C4—22no—
18C22×C4×Dic43C2211yescharacteristic
19C2×#13063249—22no—
20C2×#13063249—22no—
21C2×#13063249—22no—
22C2×#13063247—22no—
23C2×#13063247—22no—
24C2×#13063247—22no—
25C2×#13063245—22no—
26C2×#13063245—22no—
27C2×#13063245—22no—
28C2×C43⋊#95—22no—
29#14582653—22no—
30C23×Q8×C43C2211yescharacteristic
31C23×C8×C43C2211yescharacteristic
32C22×C4⋊C4×C43C2211yescharacteristic
33C2×#103×C43—22no—
34C2×#103×C43—22no—
35C2×#103×C43—22no—
36C24×D43—21no—
37C22×D172—21no—
38C22×D172—21no—
39C22×D172—21no—
40C22×D172—21no—
41C22×D172—21no—
42C22×D172—21no—
43C22×D172—21no—
44C22×D172—21no—
45C22×D172—21no—
46C22×D172—21no—
47C22×D172—21no—
48C22×D172C2×C412yes—
49C22×D172D412yes—
50C22×D172D412yes—
51C23×Dic43—21no—
52C23×Dic43D412yes—
53C22×C43⋊C8—21no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—21no—
56C22×C43⋊C8—21no—
57C22×C43⋊C8—21no—
58C22×C43⋊C8—21no—
59C22×C43⋊C8D412yes—
60#13063314—28no—
61#13063314—28no—
62#13063314—28no—
63#13063314—28no—
64C2×C4⋊Dic43—21no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43D412yes—
70C2×(C2×D43)⋊C4—28no—
71C2×(C2×D43)⋊C4—28no—
72C2×(C2×D43)⋊C4—28no—
73C2×C4×Dic43—21no—
74C2×C4×Dic43—21no—
75C2×C4×Dic43—21no—
76C2×C4×Dic43—21no—
77C2×C4×Dic43C2×C412yes—
78C2×C4×Dic43D412yes—
79#13063249—28no—
80#13063247—28no—
81#13063245—28no—
82C43⋊#95—44no—
83C22×Q8×C43—21no—
84C22×Q8×C43—21no—
85C22×Q8×C43—21no—
86C22×Q8×C43—21no—
87C22×Q8×C43—21no—
88C22×Q8×C43—21no—
89C22×Q8×C43—21no—
90C22×Q8×C43—21no—
91C22×Q8×C43—21no—
92C22×Q8×C43—21no—
93C22×Q8×C43—21no—
94C22×Q8×C43C2×C412yes—
95C22×Q8×C43D412yes—
96C22×Q8×C43D412yes—
97C23×C4×C43—21no—
98C23×C4×C43—21no—
99C23×C4×C43C2311yescharacteristic
100C22×C8×C43—21no—
101C22×C8×C43—21no—
102C22×C8×C43—21no—
103C22×C8×C43—21no—
104C22×C8×C43—21no—
105C22×C8×C43—21no—
106C22×C8×C43D412yes—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43D412yes—
113#103×C43—28no—
114C24×C43C2×D411yescharacteristic
115C23×D43—22no—
116C23×D43—22no—
117C23×D43—22no—
118C23×D43—41no—
119C23×D43—41no—
120C23×D43—41no—
121C23×D43—41no—
122C23×D43—42no—
123C23×D43—42no—
124C23×D43—42no—
125C23×D43—42no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43—22no—
129C2×Q8×C43—22no—
130C2×Q8×C43—22no—
131C2×Q8×C43—22no—
132C2×Q8×C43—22no—
133C2×Q8×C43—22no—
134C2×Q8×C43—22no—
135C2×Q8×C43—22no—
136C2×Q8×C43—22no—
137C2×Q8×C43—22no—
138C2×Q8×C43—22no—
139C2×Q8×C43—22no—
140C2×Q8×C43—22no—
141C2×Q8×C43—41no—
142C2×Q8×C43—41no—
143C2×Q8×C43—41no—
144C2×Q8×C43—41no—
145C2×Q8×C43—41no—
146C2×Q8×C43—41no—
147C2×Q8×C43—41no—
148C2×Q8×C43—41no—
149C2×Q8×C43—41no—
150C2×Q8×C43—41no—
151C2×Q8×C43—41no—
152C2×Q8×C43—41no—
153C2×Q8×C43C22⋊C414yes—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—41no—
159C22×C4×C43—41no—
160C22×C4×C43—41no—
161C22×C4×C43—41no—
162C22×C4×C43—41no—
163C22×C4×C43—41no—
164C22×C4×C43—42no—
165C22×C4×C43—42no—
166C22×C4×C43C22×C411yescharacteristic
167C22×C4×C43C2×D411yescharacteristic
168C22×C4×C43C2×D411yescharacteristic
169C22×C4×C43C2×D411yescharacteristic
170C22×C4×C43C2×D411yescharacteristic
171C22×C4×C43C2×D411yescharacteristic
172C22×C4×C43C2×D411yescharacteristic
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2×D411yescharacteristic
176C22×C4×C43#4111yescharacteristic
177C22×C4×C43#4111yescharacteristic
178C22×C4×C43#4111yescharacteristic
179C22×C4×C43#4111yescharacteristic
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—41no—
188C22×Dic43—41no—
189C22×Dic43—42no—
190C22×Dic43—42no—
191C22×Dic43C22⋊C414yes—
192C2×D172—22no—
193C2×D172—22no—
194C2×D172—22no—
195C2×D172—22no—
196C2×D172—22no—
197C2×D172—22no—
198C2×D172—22no—
199C2×D172—22no—
200C2×D172—22no—
201C2×D172—22no—
202C2×D172—22no—
203C2×D172—22no—
204C2×D172—22no—
205C2×D172—22no—
206C2×D172—22no—
207C2×D172—41no—
208C2×D172—41no—
209C2×D172—41no—
210C2×D172—41no—
211C2×D172—41no—
212C2×D172—41no—
213C2×D172—41no—
214C2×D172—41no—
215C2×D172—41no—
216C2×D172—41no—
217C2×D172—41no—
218C2×D172—41no—
219C2×D172C22⋊C414yes—
220C2×C8×C43—22no—
221C2×C8×C43—22no—
222C2×C8×C43—22no—
223C2×C8×C43—41no—
224C2×C8×C43—41no—
225C2×C8×C43—41no—
226C2×C8×C43—41no—
227C4⋊C4×C43—22no—
228C4⋊C4×C43—22no—
229C4⋊C4×C43—41no—
230C4⋊C4×C43—41no—
231(C2×D43)⋊C4—232no—
232C4⋊Dic43—22no—
233C4⋊Dic43—22no—
234C4⋊Dic43—41no—
235C4⋊Dic43—41no—
236C4×Dic43—22no—
237C4×Dic43—22no—
238C4×Dic43—22no—
239C4×Dic43—22no—
240C2×C43⋊C8—22no—
241C2×C43⋊C8—22no—
242C2×C43⋊C8—22no—
243C2×C43⋊C8—41no—
244C2×C43⋊C8—41no—
245C2×C43⋊C8—41no—
246C2×C43⋊C8—41no—
247C23×C43C2×C22⋊C411yescharacteristic
248C23×C43#12011yescharacteristic
249C23×C43#12011yescharacteristic
250C23×C43#12111yescharacteristic
251C23×C43#12111yescharacteristic
252C23×C43#12411yescharacteristic
253C23×C43#12711yescharacteristic
254C23×C43#13512yes—
255C23×C43#13512yes—
256C23×C43AGL(1,ℤ/8)12yes—
257C23×C43#13712yes—
258C22×D43—24no—
259C22×D43—42no—
260C22×D43—42no—
261C22×D43—42no—
262C22×D43—42no—
263C22×D43—42no—
264C22×D43—42no—
265C22×D43—44no—
266C22×D43—44no—
267C22×D43—44no—
268C22×D43—44no—
269C22×D43—44no—
270C22×D43—44no—
271C22×D43—82no—
272C22×D43—82no—
273C22×D43—82no—
274C22×D43—82no—
275C22×D43—82no—
276C22×D43—82no—
277C22×D43—81no—
278C22×D43—81no—
279C22×D43—81no—
280C22×D43—81no—
281Q8×C43—24no—
282Q8×C43—24no—
283Q8×C43—42no—
284Q8×C43—42no—
285Q8×C43—42no—
286Q8×C43—42no—
287Q8×C43—42no—
288Q8×C43—42no—
289C2×C4×C43—24no—
290C2×C4×C43—42no—
291C2×C4×C43—42no—
292C2×C4×C43—42no—
293C2×C4×C43—42no—
294C2×C4×C43—42no—
295C2×C4×C43—42no—
296C2×C4×C43—42no—
297C2×C4×C43—44no—
298C2×C4×C43—82no—
299C2×C4×C43—81no—
300C2×C4×C43—81no—
301C2×C4×C43C2×C22⋊C411yescharacteristic
302C2×C4×C43C2×C22⋊C411yescharacteristic
303C2×C4×C43C4×D411yescharacteristic
304C2×C4×C43C4×D411yescharacteristic
305C2×C4×C43C4×D411yescharacteristic
306C2×C4×C43C4×D411yescharacteristic
307C2×C4×C43#12011yescharacteristic
308C2×C4×C43#12011yescharacteristic
309C2×C4×C43#12011yescharacteristic
310C2×C4×C43#12011yescharacteristic
311C2×C4×C43#12011yescharacteristic
312C2×C4×C43#12011yescharacteristic
313C2×C4×C43#12111yescharacteristic
314C2×C4×C43#12111yescharacteristic
315C2×C4×C43#12111yescharacteristic
316C2×C4×C43#12111yescharacteristic
317C2×C4×C43#12111yescharacteristic
318C2×C4×C43#12111yescharacteristic
319C2×C4×C43#12111yescharacteristic
320C2×C4×C43#12111yescharacteristic
321C2×C4×C43#12111yescharacteristic
322C2×C4×C43#12111yescharacteristic
323C2×C4×C43#12311yescharacteristic
324C2×C4×C43#12311yescharacteristic
325C2×C4×C43#12311yescharacteristic
326C2×C4×C43#12311yescharacteristic
327C2×C4×C43#12411yescharacteristic
328C2×C4×C43#12711yescharacteristic
329C2×Dic43—24no—
330C2×Dic43—24no—
331C2×Dic43—24no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—44no—
338C2×Dic43—82no—
339C2×Dic43—81no—
340C2×Dic43—81no—
341D172—24no—
342D172—24no—
343D172—42no—
344D172—42no—
345D172—42no—
346D172—42no—
347D172—42no—
348D172—42no—
349C8×C43—42no—
350C43⋊C8—42no—
351#11009—431nomaximal, Sylow
352C22×C43#37911yescharacteristic
353C22×C43#39011yescharacteristic
354C22×C43#39011yescharacteristic
355C22×C43#39211yescharacteristic
356C22×C43#39211yescharacteristic
357C22×C43#39411yescharacteristic
358C22×C43#39411yescharacteristic
359C22×C43#41612yes—
360C22×C43#41712yes—
361C22×C43#44912yes—
362C22×C43#44912yes—
363C22×C43#45212yes—
364C22×C43#45212yes—
365C22×C43#46312yes—
366C22×C43#46312yes—
367C22×C43#46412yes—
368C22×C43#46412yes—
369C22×C43#48812yes—
370C22×C43#48912yes—
371C22×C43#49511yescharacteristic
372C22×C43#49511yescharacteristic
373C22×C43#49611yescharacteristic
374C22×C43#49711yescharacteristic
375C2×D43—44no—
376C2×D43—48no—
377C2×D43—82no—
378C2×D43—82no—
379C2×D43—84no—
380C2×D43—82no—
381C2×D43—82no—
382C2×D43—82no—
383C2×D43—82no—
384C2×D43—84no—
385C2×D43—84no—
386C4×C43—44no—
387C4×C43—82no—
388C4×C43#38611yescharacteristic
389C4×C43#38611yescharacteristic
390C4×C43#38611yescharacteristic
391C4×C43#38611yescharacteristic
392C4×C43#39211yescharacteristic
393C4×C43#39211yescharacteristic
394C4×C43#39411yescharacteristic
395C4×C43#39411yescharacteristic
396Dic43—44no—
397Dic43—82no—
398C22×#124—431no—
399C22×#103—431no—
400C22×#103D4311yescharacteristic, complemented
401C22×#102—431no—
402C22×#102—431no—
403C2×#336—431no—
404C4⋊#95—431no—
405C2×C43#143811yescharacteristic
406C2×C43#178812yes—
407C2×C43#195811yescharacteristic
408C2×C43#195911yescharacteristic
409C2×C43#198312yes—
410C2×C43#201211yescharacteristic
411C2×C43#201211yescharacteristic
412C2×C43#201511yescharacteristic
413C2×C43#201511yescharacteristic
414C2×C43#204212yes—
415C2×C43#204212yes—
416D43—84no—
417C23×Q8C2×D4311yescharacteristic
418C23×D4—431no—
419C23×C8—431no—
420C23×C8C2×D4311yescharacteristic
421C2×#124—434no—
422C2×#124—862no—
423C2×#124—862no—
424C2×#124—862no—
425C2×#124—862no—
426C2×#124—862no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4C2×D4311yescharacteristic
429C22×C22⋊C4—862no—
430C22×C42—431no—
431C2×#103—22no—
432C2×#103—22no—
433C2×#103—22no—
434C2×#103—862no—
435C2×#103—862no—
436C2×#103—862no—
437C2×#102—862no—
438C2×#102—862no—
439C2×#102—862no—
440C2×#102—862no—
441C2×#102—862no—
442C2×#102—862no—
443C2×#95—862no—
444#336—862no—
445C43#1100911yescharacteristic, complemented, Sylow
446C25—861no—
447C22×Q8—21no—
448C22×Q8—21no—
449C22×Q8—21no—
450C22×Q8—21no—
451C22×Q8—21no—
452C22×Q8—21no—
453C22×Q8—21no—
454C22×Q8—21no—
455C22×Q8—21no—
456C22×Q8—21no—
457C22×Q8—21no—
458C22×Q8C4×D4312yes—
459C22×Q8D17212yes—
460C22×Q8C22⋊D4312yes—
461C22×D4—432no—
462C22×D4—432no—
463C22×D4—432no—
464C22×D4—861no—
465C22×D4—861no—
466C22×D4—861no—
467C22×D4—861no—
468C22×D4—861no—
469C22×D4—861no—
470C22×D4—861no—
471C22×D4—861no—
472C22×D4—861no—
473C22×D4—861no—
474C22×D4—861no—
475C23×C4—21no—
476C23×C4—21no—
477C23×C4—432no—
478C23×C4—861no—
479C23×C4C22×D4311yescharacteristic
480C22×C8—21no—
481C22×C8—21no—
482C22×C8—21no—
483C22×C8—21no—
484C22×C8—21no—
485C22×C8—21no—
486C22×C8—432no—
487C22×C8—861no—
488C22×C8—861no—
489C22×C8—861no—
490C22×C8—861no—
491C22×C8—861no—
492C22×C8—861no—
493C22×C8C22⋊D4312yes—
494#124—868no—
495#124—868no—
496#124—868no—
497#124—868no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—432no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—861no—
507C2×C4⋊C4—861no—
508C2×C4⋊C4—861no—
509C2×C4⋊C4C22⋊D4312yes—
510C2×C22⋊C4—868no—
511C2×C22⋊C4—868no—
512C2×C22⋊C4—868no—
513C2×C42—432no—
514C2×C42—432no—
515C2×C42—861no—
516C2×C42—861no—
517C2×C42—861no—
518C2×C42—861no—
519#103—28no—
520#103—868no—
521#102—868no—
522#102—868no—
523#95—1724no—
524C24—862no—
525C24—862no—
526C24—862no—
527C24—1721no—
528C24—1721no—
529C24—1721no—
530C24—1721no—
531C24—1722no—
532C24—1722no—
533C24—1722no—
534C24—1722no—
535C24D4×D4311yescharacteristic
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—41no—
552C2×Q8—41no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8—41no—
556C2×Q8—41no—
557C2×Q8—41no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×Q8—41no—
561C2×Q8—41no—
562C2×Q8—41no—
563C2×Q8(C2×D43)⋊C414yes—
564C2×D4—434no—
565C2×D4—862no—
566C2×D4—862no—
567C2×D4—862no—
568C2×D4—862no—
569C2×D4—862no—
570C2×D4—862no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—862no—
574C2×D4—862no—
575C2×D4—862no—
576C2×D4—862no—
577C2×D4—862no—
578C2×D4—862no—
579C2×D4—862no—
580C2×D4—1721no—
581C2×D4—1721no—
582C2×D4—1721no—
583C2×D4—1721no—
584C2×D4—1721no—
585C2×D4—1721no—
586C2×D4—1721no—
587C2×D4—1721no—
588C2×D4—1721no—
589C2×D4—1721no—
590C2×D4—1721no—
591C2×D4—1721no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—41no—
601C22×C4—41no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—434no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—1721no—
613C22×C4—1721no—
614C22×C4—1722no—
615C22×C4—1722no—
616C22×C4C2×C4×D4311yescharacteristic
617C22×C4C2×D17211yescharacteristic
618C22×C4#1062189811yescharacteristic
619C22×C4#1062189811yescharacteristic
620C22×C4D4×D4311yescharacteristic
621C22×C4D4×D4311yescharacteristic
622C22×C4D4×D4311yescharacteristic
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4#1062190011yescharacteristic
626C22×C4#1062190011yescharacteristic
627C22×C4C2×C22⋊D4311yescharacteristic
628C22×C4C2×C22⋊D4311yescharacteristic
629C22×C4C2×C22⋊D4311yescharacteristic
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—41no—
634C2×C8—41no—
635C2×C8—41no—
636C2×C8—41no—
637C2×C8—862no—
638C2×C8—862no—
639C2×C8—862no—
640C2×C8—1721no—
641C2×C8—1721no—
642C2×C8—1721no—
643C2×C8—1721no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—41no—
647C4⋊C4—41no—
648C4⋊C4—862no—
649C4⋊C4—862no—
650C4⋊C4—1721no—
651C4⋊C4—1721no—
652C22⋊C4—8632no—
653C42—862no—
654C42—862no—
655C42—862no—
656C42—862no—
657C23—864no—
658C23—3442no—
659C23—3442no—
660C23—3442no—
661C23—3442no—
662C23—3442no—
663C23—3442no—
664C23—3441no—
665C23—3441no—
666C23—3441no—
667C23—3441no—
668C23—1724no—
669C23—1724no—
670C23—1722no—
671C23—1722no—
672C23—1724no—
673C23—1722no—
674C23—1722no—
675C23—1724no—
676C23—1722no—
677C23—1722no—
678C23—1724no—
679C23—1724no—
680C23C22⋊C4×D4311yescharacteristic
681C23#1306329311yescharacteristic
682C23#1306329511yescharacteristic
683C23#1306329711yescharacteristic
684C23#1306329811yescharacteristic
685C23#1306331111yescharacteristic
686C23#1306332111yescharacteristic
687C23#1306334612yes—
688C23#1306334812yes—
689C23#1306335212yes—
690C23#1306335712yes—
691Q8—24no—
692Q8—24no—
693Q8—42no—
694Q8—42no—
695Q8—42no—
696Q8—42no—
697Q8—42no—
698Q8—42no—
699D4—864no—
700D4—864no—
701D4—1722no—
702D4—1722no—
703D4—1722no—
704D4—1722no—
705D4—1722no—
706D4—1722no—
707C2×C4—24no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—82no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—864no—
720C2×C4—864no—
721C2×C4—864no—
722C2×C4—3442no—
723C2×C4—3441no—
724C2×C4—3441no—
725C2×C4—1722no—
726C2×C4—1724no—
727C2×C4—1722no—
728C2×C4—1722no—
729C2×C4—1722no—
730C2×C4—1722no—
731C2×C4C22⋊C4×D4311yescharacteristic
732C2×C4C2×(C2×D43)⋊C411yescharacteristic
733C2×C4(C22⋊D43)⋊C411yescharacteristic
734C2×C4(C22⋊D43)⋊C411yescharacteristic
735C2×C4C4×C22⋊D4311yescharacteristic
736C2×C4C4×C22⋊D4311yescharacteristic
737C2×C4#1306329311yescharacteristic
738C2×C4#1306329311yescharacteristic
739C2×C4#1306329311yescharacteristic
740C2×C4#1306329411yescharacteristic
741C2×C4#1306329511yescharacteristic
742C2×C4#1306329511yescharacteristic
743C2×C4#1306329611yescharacteristic
744C2×C4#1306329611yescharacteristic
745C2×C4#1306329711yescharacteristic
746C2×C4#1306329711yescharacteristic
747C2×C4#1306329711yescharacteristic
748C2×C4#1306329811yescharacteristic
749C2×C4#1306329811yescharacteristic
750C2×C4#1306329811yescharacteristic
751C2×C4#1306329911yescharacteristic
752C2×C4#1306329911yescharacteristic
753C2×C4#1306330711yescharacteristic
754C2×C4#1306330711yescharacteristic
755C2×C4#1306330811yescharacteristic
756C2×C4#1306330911yescharacteristic
757C2×C4#1306331111yescharacteristic
758C2×C4#1306332111yescharacteristic
759C8—42no—
760C8—1722no—
761C22—3444no—
762C22—3444no—
763C22—3444no—
764C22—3442no—
765C22—3442no—
766C22—3442no—
767C22—3442no—
768C22—3442no—
769C22—3442no—
770C22—1728no—
771C22—1724no—
772C22#1458275411yescharacteristic
773C22#1458279911yescharacteristic
774C22#1458279911yescharacteristic
775C22#1458280711yescharacteristic
776C22#1458280811yescharacteristic
777C22#1458281411yescharacteristic
778C22#1458281511yescharacteristic
779C22#1458289412yes—
780C22#1458289912yes—
781C22#1458304312yes—
782C22#1458304712yes—
783C22#1458306012yes—
784C22#1458306412yes—
785C22#1458311612yes—
786C22#1458311712yes—
787C22#1458312312yes—
788C22#1458312412yes—
789C22#1458325512yes—
790C22#1458326012yes—
791C22#1458328011yescharacteristic
792C22#1458328411yescharacteristic
793C22#1458328511yescharacteristic
794C22#1458329211yescharacteristic
795C4—44no—
796C4—82no—
797C4—3442no—
798C4—1724no—
799C4#1458277511yescharacteristic
800C4#1458277511yescharacteristic
801C4#1458277611yescharacteristic
802C4#1458277811yescharacteristic
803C4#1458280711yescharacteristic
804C4#1458280811yescharacteristic
805C4#1458281411yescharacteristic
806C4#1458281511yescharacteristic
807C2—3444no—
808C2#1913283411yescharacteristic
809C2#1913453412yes—
810C2#1913540311yescharacteristic
811C2#1913540811yescharacteristic
812C2#1913552412yes—
813C2#1913566911yescharacteristic
814C2#1913567311yescharacteristic
815C2#1913568611yescharacteristic
816C2#1913569011yescharacteristic
817C2#1913583212yes—
818C2#1913583312yes—
subgroupG/H
centerC24D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC22×#103×C43C2
socleC24×C43C2×D4
prime radicalC23×D172C22
cosocleC23×C4×C43C23
hypercenterC22×#103D43
hypocenterC43#11009
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C22×#13063249C2semidirect
5. C2×#14582653C2semidirect
6. #19132824C2semidirect
7. C22×#103×C43C2semidirect
15. C2×#13063314C4semidirect
400. C22×#103D43semidirect
445. C43#11009semidirect

Maximal subgroups

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

subgroupindex
C22×#130633142
C22×#130632492
C22×#130632472
C22×#130632452
C2×#145826532
#191328242
C22×#103×C432
#1100943