Finite Group Databasebeta

← #25018726

Subgroups — #25018726

Order 11008.

2546 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C211yesmaximal, characteristic
2C2×#14582775C212yesmaximal
3C2×#95×D43C211yesmaximal, characteristic, complemented
4#19132861C212yesmaximal, complemented
5#19132842C212yesmaximal, complemented
6#19132821C211yesmaximal, characteristic, complemented
7#19132820C211yesmaximal, characteristic, complemented
8#19132818C211yesmaximal, characteristic, complemented
9(C2×D43)⋊#95C211yesmaximal, characteristic, complemented
10(C2×D43)⋊#95C212yesmaximal, complemented
11C2×C43×#381C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C23×C4×D43C2212yes—
14C23×C4×D43C2211yescharacteristic
15C2×C4×C22⋊D43—28no—
16C2×C4×C22⋊D43C418yescomplemented
17C22×Dic43⋊C4C2211yescharacteristic
18C22×C22⋊Dic43C2212yes—
19C22×C22⋊Dic43C2211yescharacteristic
20C22×(C2×D43)⋊C4C2212yes—
21C22×(C2×D43)⋊C4C2211yescharacteristic
22C22×C4×Dic43C2211yescharacteristic
23#14582775—28no—
24C2×C43⋊#95C2211yescharacteristic
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33#95×D43—24no—
34C24×C4×C43C2211yescharacteristic
35C22×C22⋊C4×C43C2212yes—
36C43×#381—24no—
37C2×#95×C43C2211yescharacteristic
38C2×#95×C43C2212yes—
39C2×#95×C43C2211yescharacteristic
40C24×D43C2311yescharacteristic
41C22×C22⋊D43—22no—
42C22×C22⋊D43—24no—
43C22×C22⋊D43—22no—
44C22×C22⋊D43C2×C414yes—
45C22×C22⋊D43D418yes—
46C23×Dic43C2312yes—
47C23×Dic43C2311yescharacteristic
48C23×Dic43C2311yescharacteristic
49C23×Dic43C2312yes—
50C23×Dic43C2311yescharacteristic
51C22×C4×D43—24no—
52C22×C4×D43—24no—
53C22×C4×D43—24no—
54C22×C4×D43—22no—
55C22×C4×D43—22no—
56C22×C4×D43—24no—
57C22×C4×D43—24no—
58C22×C4×D43—24no—
59C22×C4×D43—42no—
60C22×C4×D43—42no—
61C22×C4×D43—42no—
62C22×C4×D43C2×C414yes—
63C4×C22⋊D43—232no—
64C2×Dic43⋊C4—24no—
65C2×Dic43⋊C4C2×C414yescomplemented
66C2×C22⋊Dic43—24no—
67C2×C22⋊Dic43—24no—
68C2×C22⋊Dic43—24no—
69C2×C22⋊Dic43—42no—
70C2×C22⋊Dic43C2×C414yescomplemented
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—24no—
73C2×(C2×D43)⋊C4—24no—
74C2×(C2×D43)⋊C4—24no—
75C2×(C2×D43)⋊C4C2×C414yes—
76C2×C4×Dic43—24no—
77C2×C4×Dic43C2×C414yescomplemented
78C43⋊#95—24no—
79C43⋊#95—22no—
80C43⋊#95—22no—
81C43⋊#95—24no—
82C43⋊#95—24no—
83C43⋊#95—24no—
84C43⋊#95—42no—
85C43⋊#95—42no—
86C43⋊#95—42no—
87C25×C43C2311yescharacteristic
88C23×C4×C43—24no—
89C23×C4×C43—22no—
90C23×C4×C43—22no—
91C23×C4×C43—42no—
92C23×C4×C43C2×C414yescomplemented
93C23×C4×C43C2312yes—
94C23×C4×C43C2311yescharacteristic
95C23×C4×C43C2312yes—
96C23×C4×C43C2311yescharacteristic
97C2×C22⋊C4×C43—24no—
98C2×C22⋊C4×C43—24no—
99C2×C22⋊C4×C43—42no—
100#95×C43—24no—
101#95×C43—22no—
102#95×C43D414yescomplemented
103C24×C43—21no—
104C24×C43—21no—
105C24×C43—22no—
106C24×C43—22no—
107C24×C43—21no—
108C24×C43—21no—
109C24×C43—22no—
110C24×C43—21no—
111C24×C43—21no—
112C24×C43C22×C412yes—
113C24×C43C2×D414yes—
114C24×C43C2411yescharacteristic
115C23×D43—21no—
116C23×D43—21no—
117C23×D43—22no—
118C23×D43—22no—
119C23×D43—21no—
120C23×D43—21no—
121C23×D43C22×C412yes—
122C23×D43C2×D414yes—
123C23×D43#4112yes—
124C23×D43#4114yes—
125C23×D43#4112yes—
126C22×C4×C43—28no—
127C22×C4×C43—28no—
128C22×C4×C43—22no—
129C22×C4×C43—21no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—22no—
136C22×C4×C43—22no—
137C22×C4×C43—22no—
138C22×C4×C43—22no—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—22no—
142C22×C4×C43—22no—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—22no—
146C22×C4×C43—22no—
147C22×C4×C43—44no—
148C22×C4×C43—48no—
149C22×C4×C43—48no—
150C22×C4×C43C22×C412yes—
151C22×C4×C43C22×C412yes—
152C22×C4×C43C2×D414yes—
153C22×C4×C43C2×D412yes—
154C22×C4×C43#4112yes—
155C2×C22⋊D43—28no—
156C2×C22⋊D43—28no—
157C2×C22⋊D43—216no—
158C2×C22⋊D43—216no—
159C2×C22⋊D43C22⋊C4116yes—
160C22×Dic43—21no—
161C22×Dic43—22no—
162C22×Dic43—22no—
163C22×Dic43—22no—
164C22×Dic43—22no—
165C22×Dic43—22no—
166C22×Dic43—22no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—22no—
170C22×Dic43—22no—
171C22×Dic43—22no—
172C22×Dic43—21no—
173C22×Dic43—22no—
174C22×Dic43—22no—
175C22×Dic43—22no—
176C22×Dic43—22no—
177C22×Dic43—21no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—21no—
184C22×Dic43C22×C412yes—
185C22×Dic43C22×C412yes—
186C22×Dic43C22×C412yes—
187C22×Dic43C2×D414yes—
188C22×Dic43#4114yes—
189C2×C4×D43—216no—
190C2×C4×D43—28no—
191C2×C4×D43—28no—
192C2×C4×D43—44no—
193C2×C4×D43—48no—
194C2×C4×D43—48no—
195C2×C4×D43—48no—
196C2×C4×D43—48no—
197C2×C4×D43—48no—
198C2×C4×D43—48no—
199C2×C4×D43—48no—
200C2×C4×D43—48no—
201C22⋊C4×C43—48no—
202C22⋊Dic43—28no—
203C22⋊Dic43—48no—
204(C2×D43)⋊C4—28no—
205(C2×D43)⋊C4—48no—
206Dic43⋊C4—28no—
207C4×Dic43—28no—
208C23×C43—22no—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—22no—
213C23×C43—22no—
214C23×C43—24no—
215C23×C43—24no—
216C23×C43—24no—
217C23×C43—24no—
218C23×C43—24no—
219C23×C43—24no—
220C23×C43—42no—
221C23×C43—42no—
222C23×C43—42no—
223C23×C43—42no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—42no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—42no—
230C23×C43C2×C22⋊C414yes—
231C23×C43C23×C411yescharacteristic
232C23×C43C22×D412yes—
233C23×C43C22×D411yescharacteristic
234C23×C43C2×#4112yes—
235C23×C43C2×#4111yescharacteristic
236C23×C43C2×#4111yescharacteristic
237C23×C43C2×#4112yes—
238C23×C43C2×#4111yescharacteristic
239C23×C43H(5,𝔽2)12yes—
240C23×C43H(5,𝔽2)11yescharacteristic
241C23×C432−1+411yescharacteristic
242C22×D43—22no—
243C22×D43—22no—
244C22×D43—22no—
245C22×D43—22no—
246C22×D43—24no—
247C22×D43—24no—
248C22×D43—24no—
249C22×D43—24no—
250C22×D43—24no—
251C22×D43—22no—
252C22×D43—24no—
253C22×D43—24no—
254C22×D43—24no—
255C22×D43—22no—
256C22×D43—24no—
257C22×D43—22no—
258C22×D43—22no—
259C22×D43—24no—
260C22×D43C2×C22⋊C414yes—
261C22×D43#11714yes—
262C22×D43#11714yes—
263C22×D43#12318yes—
264C22×D43#12318yes—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—24no—
268C2×C4×C43—24no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—24no—
273C2×C4×C43—24no—
274C2×C4×C43—24no—
275C2×C4×C43—416no—
276C2×C4×C43—42no—
277C2×C4×C43—42no—
278C2×C4×C43—42no—
279C2×C4×C43—42no—
280C2×C4×C43—42no—
281C2×C4×C43—42no—
282C2×C4×C43—42no—
283C2×C4×C43—42no—
284C2×C4×C43—42no—
285C2×C4×C43—42no—
286C2×C4×C43—42no—
287C2×C4×C43—42no—
288C2×C4×C43—42no—
289C2×C4×C43C4×D414yes—
290C22⋊D43—232no—
291C2×Dic43—22no—
292C2×Dic43—22no—
293C2×Dic43—24no—
294C2×Dic43—24no—
295C2×Dic43—22no—
296C2×Dic43—22no—
297C2×Dic43—22no—
298C2×Dic43—22no—
299C2×Dic43—22no—
300C2×Dic43—22no—
301C2×Dic43—24no—
302C2×Dic43—24no—
303C2×Dic43—24no—
304C2×Dic43—42no—
305C2×Dic43—42no—
306C2×Dic43—42no—
307C2×Dic43—42no—
308C2×Dic43—42no—
309C2×Dic43—42no—
310C2×Dic43—42no—
311C2×Dic43—42no—
312C2×Dic43—42no—
313C2×Dic43—42no—
314C2×Dic43—42no—
315C2×Dic43—42no—
316C2×Dic43—42no—
317C2×Dic43—42no—
318C2×Dic43—42no—
319C2×Dic43C2×C22⋊C414yes—
320C4×D43—416no—
321C4×D43—432no—
322#13894—431nomaximal, Sylow
323C22×C43—24no—
324C22×C43—24no—
325C22×C43—24no—
326C22×C43—42no—
327C22×C43—42no—
328C22×C43—42no—
329C22×C43—44no—
330C22×C43—44no—
331C22×C43—44no—
332C22×C43—44no—
333C22×C43—42no—
334C22×C43C22×C22⋊C411yescharacteristic
335C22×C43C2×#11711yescharacteristic
336C22×C43C2×#11711yescharacteristic
337C22×C43C2×C4×D411yescharacteristic
338C22×C43C4×#4111yescharacteristic
339C22×C43#51811yescharacteristic
340C22×C43#52011yescharacteristic
341C22×C43C2×#12312yes—
342C22×C43C2×#12312yes—
343C22×C43#52512yes—
344C22×C43#52912yes—
345C22×C43#53812yes—
346C22×C43#53912yes—
347C22×C43D4212yes—
348C22×C43#54611yescharacteristic
349C22×C43#54612yes—
350C22×C43#54612yes—
351C22×C43#54712yes—
352C22×C43#54811yescharacteristic
353C22×C43#55112yes—
354C22×C43#55211yescharacteristic
355C22×C43#55311yescharacteristic
356C22×C43#55312yes—
357C2×D43—24no—
358C2×D43—24no—
359C2×D43—24no—
360C2×D43—24no—
361C2×D43—24no—
362C2×D43—28no—
363C2×D43—28no—
364C2×D43—28no—
365C2×D43—28no—
366C2×D43—24no—
367C2×D43#38118yescomplemented
368C4×C43—24no—
369C4×C43—42no—
370C4×C43—44no—
371C4×C43—82no—
372Dic43—24no—
373Dic43—42no—
374Dic43—42no—
375Dic43—44no—
376Dic43—82no—
377C22×C4×D4—431no—
378C2×#386—432no—
379C2×#381D4311yescharacteristic, complemented
380C22×#95—431no—
381#1445—432no—
382#1440—432no—
383#1434—431no—
384#1434—431no—
385C22⋊#95—432no—
386C22⋊#95—431no—
387C22⋊#95—431no—
388C2×C43—44no—
389C2×C43C2×#38111yescharacteristic
390C2×C43#229011yescharacteristic
391C2×C43#231811yescharacteristic
392C2×C43D4×C22⋊C411yescharacteristic
393C2×C43#233911yescharacteristic
394C2×C43#235211yescharacteristic
395C2×C43#235311yescharacteristic
396C2×C43#241812yes—
397C2×C43#241912yes—
398C2×C43#244312yes—
399C2×C43#244412yes—
400D43—28no—
401C23×D4—431no—
402C24×C4—431no—
403C24×C4—432no—
404C24×C4C2×D4311yescharacteristic
405C2×C4×D4—438no—
406C2×C4×D4—868no—
407C22×C4⋊C4—431no—
408C22×C22⋊C4—431no—
409C22×C22⋊C4—431no—
410C22×C22⋊C4—432no—
411C22×C22⋊C4—432no—
412C22×C22⋊C4C2×D4312yes—
413C22×C42—431no—
414#386—868no—
415#381—24no—
416C2×#95—431no—
417C2×#95—432no—
418C2×#95—431no—
419C2×#95—432no—
420C2×#95—432no—
421C2×#95—432no—
422C2×#95—432no—
423C2×#95—432no—
424C2×#95—432no—
425C2×#95—864no—
426C2×#95C2×D4311yescharacteristic
427C2×#95C2×D4312yes—
428C2×#95C2×D4311yescharacteristic
429C43#1389411yescharacteristic, complemented, Sylow
430C25—431no—
431C25C22×D4311yescharacteristic
432C22×D4—434no—
433C22×D4—438no—
434C22×D4—862no—
435C22×D4—864no—
436C22×D4—862no—
437C23×C4—24no—
438C23×C4—22no—
439C23×C4—22no—
440C23×C4—42no—
441C23×C4—431no—
442C23×C4—431no—
443C23×C4—431no—
444C23×C4—432no—
445C23×C4—434no—
446C23×C4—432no—
447C23×C4—864no—
448C23×C4—864no—
449C23×C4—864no—
450C23×C4—864no—
451C23×C4—864no—
452C23×C4—862no—
453C23×C4—864no—
454C23×C4—862no—
455C23×C4—1722no—
456C23×C4—1722no—
457C23×C4—1722no—
458C23×C4C4×D4314yescomplemented
459C23×C4C22×D4312yes—
460C23×C4C22×D4311yescharacteristic
461C23×C4C22×D4312yes—
462C23×C4C22×D4311yescharacteristic
463C4×D4—8632no—
464C2×C4⋊C4—434no—
465C2×C4⋊C4—864no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—434no—
470C2×C22⋊C4—434no—
471C2×C22⋊C4—864no—
472C2×C22⋊C4—864no—
473C2×C22⋊C4—864no—
474C2×C22⋊C4—864no—
475C2×C22⋊C4—864no—
476C2×C22⋊C4—864no—
477C2×C22⋊C4—864no—
478C2×C22⋊C4—1722no—
479C2×C42—434no—
480C2×C42—864no—
481#95—24no—
482#95—22no—
483#95—864no—
484#95—864no—
485#95—864no—
486#95—862no—
487#95—864no—
488#95—862no—
489#95—1722no—
490#95—1722no—
491#95—1722no—
492#95C22⋊D4314yescomplemented
493C24—21no—
494C24—22no—
495C24—21no—
496C24—21no—
497C24—22no—
498C24—21no—
499C24—22no—
500C24—21no—
501C24—21no—
502C24—432no—
503C24—434no—
504C24—432no—
505C24—434no—
506C24—432no—
507C24—861no—
508C24—862no—
509C24—861no—
510C24—862no—
511C24—861no—
512C24—861no—
513C24C2×C4×D4312yes—
514C24D4×D4314yes—
515C24C23×D4311yescharacteristic
516C2×D4—4316no—
517C2×D4—868no—
518C2×D4—868no—
519C2×D4—8616no—
520C2×D4—8616no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—28no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—28no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—44no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—432no—
546C22×C4—434no—
547C22×C4—432no—
548C22×C4—432no—
549C22×C4—434no—
550C22×C4—868no—
551C22×C4—8616no—
552C22×C4—861no—
553C22×C4—861no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—861no—
559C22×C4—862no—
560C22×C4—862no—
561C22×C4—862no—
562C22×C4—862no—
563C22×C4—861no—
564C22×C4—862no—
565C22×C4—862no—
566C22×C4—861no—
567C22×C4—862no—
568C22×C4—861no—
569C22×C4—868no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—1724no—
578C22×C4—1728no—
579C22×C4—1728no—
580C22×C4—1728no—
581C22×C4—1728no—
582C22×C4—1728no—
583C22×C4—1728no—
584C22×C4—1728no—
585C22×C4—1728no—
586C22×C4C2×C4×D4312yes—
587C22×C4C2×C4×D4312yes—
588C22×C4#1062189812yes—
589C22×C4C2×C22⋊D4314yes—
590C22×C4C2×C22⋊D4312yes—
591C4⋊C4—868no—
592C22⋊C4—48no—
593C22⋊C4—868no—
594C22⋊C4—868no—
595C22⋊C4—1728no—
596C22⋊C4—1728no—
597C42—868no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—41no—
611C23—42no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—41no—
620C23—434no—
621C23—434no—
622C23—434no—
623C23—438no—
624C23—438no—
625C23—862no—
626C23—864no—
627C23—862no—
628C23—862no—
629C23—864no—
630C23—862no—
631C23—862no—
632C23—862no—
633C23—862no—
634C23—864no—
635C23—864no—
636C23—864no—
637C23—864no—
638C23—864no—
639C23—862no—
640C23—864no—
641C23—864no—
642C23—864no—
643C23C22⋊C4×D4314yes—
644C23C22×C4×D4311yescharacteristic
645C23C2×D4×D4312yes—
646C23C22×C22⋊D4311yescharacteristic
647C23#41×D4311yescharacteristic
648C23#41×D4311yescharacteristic
649C23#41×D4312yes—
650C23#41×D4312yes—
651C23C2×#1062189811yescharacteristic
652C23#1306337012yes—
653C23#1306337111yescharacteristic
654C23#1306337211yescharacteristic
655D4—8632no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—416no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—434no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—864no—
684C2×C4—864no—
685C2×C4—864no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—864no—
693C2×C4—864no—
694C2×C4—17216no—
695C2×C4—17232no—
696C2×C4—1722no—
697C2×C4—1722no—
698C2×C4—1722no—
699C2×C4—1722no—
700C2×C4—1722no—
701C2×C4—1722no—
702C2×C4—1722no—
703C2×C4—1722no—
704C2×C4—1722no—
705C2×C4—1722no—
706C2×C4—1722no—
707C2×C4—1722no—
708C2×C4—1722no—
709C2×C4—1722no—
710C2×C4—1722no—
711C2×C4C4×C22⋊D4314yes—
712C22—24no—
713C22—24no—
714C22—24no—
715C22—44no—
716C22—42no—
717C22—44no—
718C22—44no—
719C22—44no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—438no—
724C22—868no—
725C22—864no—
726C22—868no—
727C22—868no—
728C22—868no—
729C22—864no—
730C22—864no—
731C22—864no—
732C22—864no—
733C22—864no—
734C22C2×C22⋊C4×D4311yescharacteristic
735C22#117×D4311yescharacteristic
736C22#117×D4311yescharacteristic
737C22C2×C4×C22⋊D4311yescharacteristic
738C22#1458336711yescharacteristic
739C22#1458337211yescharacteristic
740C22#1458337911yescharacteristic
741C22#123×D4312yes—
742C22#123×D4312yes—
743C22#1458340612yes—
744C22#1458342712yes—
745C22#1458348512yes—
746C22#1458349212yes—
747C22D4×C22⋊D4312yes—
748C22#1458353711yescharacteristic
749C22#1458353912yes—
750C22#1458354112yes—
751C22#1458354712yes—
752C22#1458355611yescharacteristic
753C22#1458357712yes—
754C22#1458358811yescharacteristic
755C22#1458359311yescharacteristic
756C22#1458359412yes—
757C4—24no—
758C4—44no—
759C4—42no—
760C4—82no—
761C4—864no—
762C4—3442no—
763C4—1724no—
764C4—1722no—
765C4—1722no—
766C2—44no—
767C2—868no—
768C2#381×D4311yescharacteristic
769C2#1913703211yescharacteristic
770C2#1913722411yescharacteristic
771C2C22⋊C4×C22⋊D4311yescharacteristic
772C2#1913741911yescharacteristic
773C2#1913752511yescharacteristic
774C2#1913753211yescharacteristic
775C2#1913805412yes—
776C2#1913806912yes—
777C2#1913832712yes—
778C2#1913834412yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#381C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×#381D43
hypocenterC43#13894
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. C2×#95×D43C2semidirect
4. #19132861C2semidirect
5. #19132842C2semidirect
6. #19132821C2semidirect
7. #19132820C2semidirect
8. #19132818C2semidirect
9. (C2×D43)⋊#95C2semidirect
10. (C2×D43)⋊#95C2semidirect
11. C2×C43×#381C2semidirect
16. C2×C4×C22⋊D43C4semidirect
65. C2×Dic43⋊C4C2×C4semidirect
70. C2×C22⋊Dic43C2×C4semidirect
77. C2×C4×Dic43C2×C4semidirect
92. C23×C4×C43C2×C4semidirect
102. #95×C43D4semidirect
367. C2×D43#381semidirect
379. C2×#381D43semidirect
429. C43#13894semidirect
458. C23×C4C4×D43semidirect
492. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C2×#145827752
C2×#95×D432
#191328612
#191328422
#191328212
#191328202
#191328182
(C2×D43)⋊#952
C2×C43×#3812
#1389443