Finite Group Databasebeta

← #25017998

Subgroups — #25017998

Order 11008.

4254 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D43C212yesmaximal
2C2×#14582754C211yesmaximal, characteristic
3C2×C4×(C2×D43)⋊C4C212yesmaximal, complemented
4C2×#14582746C212yesmaximal, complemented
5#19132832C212yesmaximal, complemented
6#19132832C211yesmaximal, characteristic, complemented
7(C2×D43)⋊#95C212yesmaximal, complemented
8(C2×D43)⋊#95C212yesmaximal, complemented
9C43×#1437C211yesmaximal, characteristic, complemented
10C25×D43C2211yescharacteristic
11C23×C4×D43C2212yes—
12C23×C4×D43C2212yes—
13C22×C22⋊Dic43C2212yes—
14C22×C22⋊Dic43C2211yescharacteristic
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C2×C22⋊C4×D43—28no—
20C2×C22⋊C4×D43—28no—
21C2×C22⋊C4×D43C4116yescomplemented
22C22×C4×Dic43C2211yescharacteristic, complemented
23C22×C4×Dic43C2212yescomplemented
24#14582754C418yescomplemented
25C4×(C2×D43)⋊C4—28no—
26#14582746—28no—
27C2×C43⋊#95C2212yescomplemented
28C2×C43⋊#95C2212yescomplemented
29C2×C43⋊#95C2212yescomplemented
30C2×C43⋊#95C2211yescharacteristic, complemented
31C2×C43⋊#95C2212yescomplemented
32C22×C22⋊C4×C43C2212yes—
33C22×C22⋊C4×C43C2211yescharacteristic
34C22×C42×C43C2211yescharacteristic, complemented
35C2×#95×C43C2212yescomplemented
36C2×#95×C43C2211yescharacteristic, complemented
37C24×D43—24no—
38C24×D43—24no—
39C24×D43—24no—
40C24×D43—24no—
41C24×D43—41no—
42C24×D43—41no—
43C24×D43—42no—
44C24×D43C2×C418yes—
45C24×D43C2×C414yes—
46C24×D43C2312yes—
47C23×Dic43C2312yes—
48C23×Dic43C2312yes—
49C23×Dic43C2312yes—
50C22×C4×D43—24no—
51C22×C4×D43—24no—
52C22×C4×D43—24no—
53C22×C4×D43—24no—
54C22×C4×D43—24no—
55C22×C4×D43—24no—
56C22×C4×D43—24no—
57C22×C4×D43—24no—
58C22×C4×D43—42no—
59C22×C4×D43—42no—
60C22×C4×D43—42no—
61C22×C4×D43—42no—
62C22×C4×D43C2×C418yescomplemented
63C22×C4×D43C2×C418yescomplemented
64C2×C22⋊Dic43—24no—
65C2×C22⋊Dic43—24no—
66C2×C22⋊Dic43—42no—
67C2×C22⋊Dic43C2×C418yescomplemented
68C2×C22⋊Dic43C2×C414yescomplemented
69C2×(C2×D43)⋊C4—24no—
70C2×(C2×D43)⋊C4—24no—
71C2×(C2×D43)⋊C4—24no—
72C2×(C2×D43)⋊C4—24no—
73C2×(C2×D43)⋊C4—24no—
74C2×(C2×D43)⋊C4—24no—
75C2×(C2×D43)⋊C4C2×C418yes—
76C2×(C2×D43)⋊C4C2×C418yes—
77C2×(C2×D43)⋊C4C2×C418yescomplemented
78C2×(C2×D43)⋊C4C2×C418yescomplemented
79C2×(C2×D43)⋊C4D418yes—
80C2×(C2×D43)⋊C4D418yes—
81C22⋊C4×D43—264no—
82C2×C4×Dic43—24no—
83C2×C4×Dic43—24no—
84C2×C4×Dic43—24no—
85C2×C4×Dic43—41no—
86C2×C4×Dic43—42no—
87C43⋊#95—24no—
88C43⋊#95—24no—
89C43⋊#95—24no—
90C43⋊#95—42no—
91C43⋊#95—41no—
92C25×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2311yescharacteristic
95C23×C4×C43C2312yes—
96C23×C4×C43C2312yes—
97C2×C22⋊C4×C43—24no—
98C2×C22⋊C4×C43—24no—
99C2×C22⋊C4×C43—41no—
100C2×C22⋊C4×C43—41no—
101C2×C22⋊C4×C43C2×C418yescomplemented
102C2×C22⋊C4×C43C2×C414yescomplemented
103C2×C42×C43—24no—
104C2×C42×C43—41no—
105#95×C43—24no—
106#95×C43—41no—
107C24×C43—22no—
108C24×C43—22no—
109C24×C43—22no—
110C24×C43—22no—
111C24×C43—21no—
112C24×C43—21no—
113C24×C43—22no—
114C24×C43C22×C414yes—
115C24×C43C22×C412yes—
116C24×C43C2411yescharacteristic
117C23×D43—22no—
118C23×D43—22no—
119C23×D43—22no—
120C23×D43—22no—
121C23×D43—22no—
122C23×D43—22no—
123C23×D43—22no—
124C23×D43—22no—
125C23×D43—216no—
126C23×D43—216no—
127C23×D43—216no—
128C23×D43—216no—
129C23×D43—216no—
130C23×D43—216no—
131C23×D43—48no—
132C23×D43—48no—
133C23×D43—44no—
134C23×D43—44no—
135C23×D43—44no—
136C23×D43—48no—
137C23×D43—44no—
138C23×D43—48no—
139C23×D43—48no—
140C23×D43—48no—
141C23×D43—48no—
142C23×D43—48no—
143C23×D43—44no—
144C23×D43—44no—
145C23×D43C42116yescomplemented
146C23×D43C22×C414yes—
147C23×D43C22×C414yes—
148C23×D43C22×C414yes—
149C23×D43C2×D414yes—
150C23×D43C2×D414yes—
151C23×D43#4114yes—
152C23×D43#4114yes—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—21no—
166C22×C4×C43—22no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—22no—
171C22×C4×C43C22×C414yes—
172C22×C4×C43C22×C412yes—
173C22×C4×C43C22×C412yes—
174C22×C4×C43C22×C414yes—
175C22×C4×C43C2×D414yes—
176C22×C4×C43C2×D414yes—
177C22×Dic43—22no—
178C22×Dic43—22no—
179C22×Dic43—22no—
180C22×Dic43—22no—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—22no—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43C22×C414yes—
194C22×Dic43C22×C414yes—
195C22×Dic43C22×C414yes—
196C22×Dic43C2×D414yes—
197C22×Dic43C2×D414yes—
198C2×C4×D43—216no—
199C2×C4×D43—216no—
200C2×C4×D43—216no—
201C2×C4×D43—216no—
202C2×C4×D43—48no—
203C2×C4×D43—48no—
204C2×C4×D43—48no—
205C2×C4×D43—48no—
206C2×C4×D43—48no—
207C2×C4×D43—48no—
208C2×C4×D43—48no—
209C2×C4×D43—48no—
210C2×C4×D43—48no—
211C2×C4×D43—48no—
212C22⋊C4×C43—216no—
213C22⋊C4×C43—44no—
214C42×C43—44no—
215C22⋊Dic43—216no—
216C22⋊Dic43—44no—
217(C2×D43)⋊C4—216no—
218(C2×D43)⋊C4—216no—
219(C2×D43)⋊C4—216no—
220(C2×D43)⋊C4C22⋊C4132yescomplemented
221C4×Dic43—44no—
222C4×Dic43—48no—
223C23×C43—24no—
224C23×C43—24no—
225C23×C43—24no—
226C23×C43—24no—
227C23×C43—24no—
228C23×C43—24no—
229C23×C43—22no—
230C23×C43—22no—
231C23×C43—24no—
232C23×C43—24no—
233C23×C43—41no—
234C23×C43—42no—
235C23×C43—41no—
236C23×C43—42no—
237C23×C43—42no—
238C23×C43—42no—
239C23×C43—42no—
240C23×C43—42no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43C2×C4214yes—
244C23×C43C23×C412yes—
245C23×C43C23×C411yescharacteristic
246C23×C43C22×D412yes—
247C23×C43C22×D412yes—
248C23×C43C2×#4112yes—
249C23×C43C2×#4112yes—
250C23×C43H(5,𝔽2)11yescharacteristic
251C23×C43H(5,𝔽2)11yescharacteristic
252C23×C43H(5,𝔽2)12yes—
253C22×D43—24no—
254C22×D43—24no—
255C22×D43—24no—
256C22×D43—24no—
257C22×D43—24no—
258C22×D43—24no—
259C22×D43—24no—
260C22×D43—24no—
261C22×D43—24no—
262C22×D43—24no—
263C22×D43—24no—
264C22×D43—24no—
265C22×D43—24no—
266C22×D43—24no—
267C22×D43—24no—
268C22×D43—24no—
269C22×D43—24no—
270C22×D43—24no—
271C22×D43—24no—
272C22×D43—24no—
273C22×D43—24no—
274C22×D43—24no—
275C22×D43—24no—
276C22×D43—24no—
277C22×D43—24no—
278C22×D43—24no—
279C22×D43—24no—
280C22×D43—24no—
281C22×D43—264no—
282C22×D43—416no—
283C22×D43—432no—
284C22×D43—432no—
285C22×D43—432no—
286C22×D43—432no—
287C22×D43—432no—
288C22×D43—416no—
289C22×D43—416no—
290C22×D43C2×C4218yes—
291C22×D43C2×C22⋊C418yes—
292C22×D43#11718yes—
293C22×D43C4×D418yes—
294C22×D43C4×D418yes—
295C22×D43C4×D418yes—
296C22×D43C4×D418yes—
297C2×C4×C43—24no—
298C2×C4×C43—24no—
299C2×C4×C43—24no—
300C2×C4×C43—24no—
301C2×C4×C43—24no—
302C2×C4×C43—24no—
303C2×C4×C43—24no—
304C2×C4×C43—24no—
305C2×C4×C43—24no—
306C2×C4×C43—24no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—24no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—42no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43C2×C22⋊C418yescomplemented
321C2×Dic43—24no—
322C2×Dic43—24no—
323C2×Dic43—24no—
324C2×Dic43—24no—
325C2×Dic43—24no—
326C2×Dic43—24no—
327C2×Dic43—24no—
328C2×Dic43—24no—
329C2×Dic43—24no—
330C2×Dic43—24no—
331C2×Dic43—24no—
332C2×Dic43—24no—
333C2×Dic43—42no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43C2×C22⋊C418yescomplemented
342C4×D43—432no—
343C4×D43—432no—
344C22⋊C42—431nomaximal, Sylow
345C22×C43—28no—
346C22×C43—24no—
347C22×C43—44no—
348C22×C43—44no—
349C22×C43—44no—
350C22×C43—44no—
351C22×C43—44no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43C22×C4211yescharacteristic
355C22×C43C22×C22⋊C412yes—
356C22×C43C2×#11712yes—
357C22×C43C2×C4×D412yes—
358C22×C43C2×C4×D412yes—
359C22×C43C2×C4×D412yes—
360C22×C43C2×C4×D412yes—
361C22×C43#51812yes—
362C22×C43#51812yes—
363C22×C43#51811yescharacteristic
364C22×C43#51811yescharacteristic
365C22×C43D4211yescharacteristic
366C22×C43D4212yes—
367C22×C43D4211yescharacteristic
368C22×C43#54612yes—
369C22×C43#54612yes—
370C22×C43#54612yes—
371C22×C43#54612yes—
372C22×C43#55112yes—
373C22×C43#55111yescharacteristic
374C22×C43#55111yescharacteristic
375C2×D43—28no—
376C2×D43—28no—
377C2×D43—28no—
378C2×D43—28no—
379C2×D43—28no—
380C2×D43—28no—
381C2×D43—28no—
382C2×D43—28no—
383C2×D43—28no—
384C2×D43—28no—
385C2×D43—28no—
386C2×D43—28no—
387C2×D43—28no—
388C2×D43—28no—
389C2×D43—464no—
390C2×D43C4×C22⋊C4116yescomplemented
391C4×C43—28no—
392C4×C43—44no—
393C4×C43—42no—
394C4×C43—42no—
395Dic43—28no—
396Dic43—44no—
397Dic43—44no—
398C23×C22⋊C4—432no—
399C2×#379—431no—
400C2×C4×C22⋊C4—432no—
401C2×C4×C22⋊C4—432no—
402#1437—431no—
403#1437—432no—
404#1437D4311yescharacteristic, complemented
405C22⋊#95—432no—
406C22⋊#95—432no—
407C2×C43—44no—
408C2×C43C2×C4×C22⋊C412yes—
409C2×C43#227311yescharacteristic
410C2×C43D4×C22⋊C412yes—
411C2×C43D4×C22⋊C412yes—
412C2×C43#234212yes—
413C2×C43#234212yes—
414C2×C43#235812yes—
415C2×C43#235811yescharacteristic
416C2×C43#235811yescharacteristic
417D43—216no—
418C26—431no—
419C24×C4—432no—
420C24×C4—432no—
421C22×C22⋊C4—432no—
422C22×C22⋊C4—432no—
423C22×C22⋊C4—432no—
424C22×C22⋊C4—432no—
425C22×C22⋊C4—432no—
426C22×C22⋊C4—431no—
427C22×C22⋊C4—4316no—
428C22×C22⋊C4—868no—
429C22×C22⋊C4—868no—
430C22×C22⋊C4C2×D4312yes—
431C22×C22⋊C4C2×D4311yescharacteristic
432C22×C42—431no—
433C22×C42—432no—
434C22×C42C2×D4311yescharacteristic, complemented
435#379—438no—
436C4×C22⋊C4—868no—
437C4×C22⋊C4—868no—
438C2×#95—432no—
439C2×#95—432no—
440C2×#95—432no—
441C2×#95—432no—
442C2×#95—431no—
443C2×#95C2×D4312yescomplemented
444C2×#95C2×D4311yescharacteristic, complemented
445C43C22⋊C4211yescharacteristic, complemented, Sylow
446C25—432no—
447C25—438no—
448C25—434no—
449C25—864no—
450C25—864no—
451C25—864no—
452C25—864no—
453C25—1721no—
454C25—1721no—
455C25—1722no—
456C25C22×D4311yescharacteristic
457C23×C4—432no—
458C23×C4—432no—
459C23×C4—432no—
460C23×C4—438no—
461C23×C4—438no—
462C23×C4—864no—
463C23×C4—864no—
464C23×C4—864no—
465C23×C4—864no—
466C23×C4—864no—
467C23×C4—864no—
468C23×C4—864no—
469C23×C4—864no—
470C23×C4—1722no—
471C23×C4—1722no—
472C23×C4—1722no—
473C23×C4—1722no—
474C23×C4C22×D4311yescharacteristic
475C23×C4C22×D4311yescharacteristic
476C23×C4C22×D4312yes—
477C23×C4C22×D4312yes—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—41no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—438no—
483C2×C22⋊C4—438no—
484C2×C22⋊C4—438no—
485C2×C22⋊C4—438no—
486C2×C22⋊C4—438no—
487C2×C22⋊C4—438no—
488C2×C22⋊C4—438no—
489C2×C22⋊C4—434no—
490C2×C22⋊C4—8664no—
491C2×C22⋊C4—864no—
492C2×C22⋊C4—864no—
493C2×C22⋊C4—864no—
494C2×C22⋊C4—864no—
495C2×C22⋊C4—864no—
496C2×C22⋊C4—864no—
497C2×C22⋊C4—864no—
498C2×C22⋊C4—864no—
499C2×C22⋊C4—1722no—
500C2×C22⋊C4C4×D4318yescomplemented
501C2×C22⋊C4C4×D4314yescomplemented
502C2×C42—24no—
503C2×C42—41no—
504C2×C42—864no—
505C2×C42—864no—
506C2×C42—864no—
507C2×C42—1722no—
508C2×C42—1721no—
509#95—24no—
510#95—41no—
511#95—864no—
512#95—864no—
513#95—864no—
514#95—1721no—
515#95—1722no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—21no—
521C24—21no—
522C24—22no—
523C24—434no—
524C24—434no—
525C24—434no—
526C24—434no—
527C24—434no—
528C24—434no—
529C24—434no—
530C24—4316no—
531C24—8616no—
532C24—8616no—
533C24—8616no—
534C24—8616no—
535C24—8616no—
536C24—8616no—
537C24—862no—
538C24—862no—
539C24—862no—
540C24—862no—
541C24—862no—
542C24—862no—
543C24—862no—
544C24—862no—
545C24—1728no—
546C24—1728no—
547C24—1724no—
548C24—1724no—
549C24—1728no—
550C24—1724no—
551C24—1724no—
552C24—1724no—
553C24—1728no—
554C24—1724no—
555C24—1728no—
556C24—1728no—
557C24—1728no—
558C24—1728no—
559C24C2×C4×D4314yes—
560C24C2×C4×D4312yes—
561C24C23×D4311yescharacteristic
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—434no—
581C22×C4—434no—
582C22×C4—434no—
583C22×C4—434no—
584C22×C4—434no—
585C22×C4—8616no—
586C22×C4—8616no—
587C22×C4—8616no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—862no—
591C22×C4—862no—
592C22×C4—862no—
593C22×C4—862no—
594C22×C4—862no—
595C22×C4—862no—
596C22×C4—862no—
597C22×C4—862no—
598C22×C4—862no—
599C22×C4—862no—
600C22×C4—862no—
601C22×C4—862no—
602C22×C4—862no—
603C22×C4—862no—
604C22×C4—8616no—
605C22×C4—1728no—
606C22×C4—1728no—
607C22×C4—1728no—
608C22×C4—1728no—
609C22×C4—1728no—
610C22×C4—1728no—
611C22×C4—1728no—
612C22×C4—1728no—
613C22×C4—1728no—
614C22×C4—1728no—
615C22×C4C2×C4×D4312yes—
616C22×C4C2×C4×D4312yes—
617C22×C4C2×C4×D4314yes—
618C22×C4C2×C4×D4314yes—
619C22×C4D4×D4314yes—
620C22×C4D4×D4314yes—
621C22⋊C4—216no—
622C22⋊C4—44no—
623C22⋊C4—4332no—
624C22⋊C4—8616no—
625C22⋊C4—8616no—
626C22⋊C4—8616no—
627C22⋊C4—8616no—
628C22⋊C4—1724no—
629C42—44no—
630C42—1728no—
631C42—1724no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—22no—
641C23—22no—
642C23—42no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—42no—
647C23—41no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—438no—
653C23—438no—
654C23—438no—
655C23—438no—
656C23—438no—
657C23—438no—
658C23—438no—
659C23—8664no—
660C23—864no—
661C23—864no—
662C23—864no—
663C23—864no—
664C23—864no—
665C23—864no—
666C23—864no—
667C23—864no—
668C23—864no—
669C23—864no—
670C23—864no—
671C23—864no—
672C23—864no—
673C23—864no—
674C23—864no—
675C23—864no—
676C23—864no—
677C23—864no—
678C23—864no—
679C23—864no—
680C23—864no—
681C23—864no—
682C23—864no—
683C23—864no—
684C23—864no—
685C23—864no—
686C23—864no—
687C23—864no—
688C23—17216no—
689C23—17232no—
690C23—17216no—
691C23—17216no—
692C23—17232no—
693C23—17232no—
694C23—17232no—
695C23—17232no—
696C23C42×D4314yes—
697C23C22×C4×D4312yes—
698C23C22×C4×D4311yescharacteristic
699C23C2×D4×D4312yes—
700C23C2×D4×D4312yes—
701C23#41×D4312yes—
702C23#41×D4312yes—
703C23#1306337011yescharacteristic
704C23#1306337011yescharacteristic
705C23#1306337112yes—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—438no—
730C2×C4—864no—
731C2×C4—864no—
732C2×C4—864no—
733C2×C4—864no—
734C2×C4—864no—
735C2×C4—864no—
736C2×C4—864no—
737C2×C4—864no—
738C2×C4—864no—
739C2×C4—864no—
740C2×C4—864no—
741C2×C4—864no—
742C2×C4—17232no—
743C2×C4—17232no—
744C2×C4—1722no—
745C2×C4—1722no—
746C2×C4—1722no—
747C2×C4—1722no—
748C2×C4—1722no—
749C2×C4—1722no—
750C2×C4—1722no—
751C2×C4—1722no—
752C2×C4C22⋊C4×D4318yescomplemented
753C22—28no—
754C22—24no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—4316no—
763C22—868no—
764C22—868no—
765C22—868no—
766C22—868no—
767C22—868no—
768C22—868no—
769C22—868no—
770C22—868no—
771C22—868no—
772C22—868no—
773C22—868no—
774C22—868no—
775C22—868no—
776C22—868no—
777C22—17264no—
778C22C2×C42×D4311yescharacteristic
779C22C2×C22⋊C4×D4312yes—
780C22#117×D4312yes—
781C22C4×D4×D4312yes—
782C22C4×D4×D4312yes—
783C22C4×D4×D4312yes—
784C22C4×D4×D4312yes—
785C22#1458337112yes—
786C22#1458337112yes—
787C22#1458337211yescharacteristic
788C22#1458337311yescharacteristic
789C22#1458353111yescharacteristic
790C22#1458353312yes—
791C22#1458353411yescharacteristic
792C22#1458353812yes—
793C22#1458354112yes—
794C22#1458354212yes—
795C22#1458354612yes—
796C22#1458357412yes—
797C22#1458357711yescharacteristic
798C22#1458357911yescharacteristic
799C4—28no—
800C4—42no—
801C4—42no—
802C4—44no—
803C4—868no—
804C4—1724no—
805C4—1724no—
806C2—44no—
807C2—8616no—
808C2C4×C22⋊C4×D4312yes—
809C2#1913694711yescharacteristic
810C2#1913741312yes—
811C2#1913741612yes—
812C2#1913743912yes—
813C2#1913744312yes—
814C2#1913757312yes—
815C2#1913757611yescharacteristic
816C2#1913757811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC22×C43C22×C42
FittingC43×#1437C2
socle, cosocleC24×C43C24
prime radicalC25×D43C22
hypercenter#1437D43
hypocenterC43C22⋊C42
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×C4×(C2×D43)⋊C4C2semidirect
4. C2×#14582746C2semidirect
5. #19132832C2semidirect
6. #19132832C2semidirect
7. (C2×D43)⋊#95C2semidirect
8. (C2×D43)⋊#95C2semidirect
9. C43×#1437C2semidirect
21. C2×C22⋊C4×D43C4semidirect
22. C22×C4×Dic43C22semidirect
23. C22×C4×Dic43C22semidirect
24. #14582754C4semidirect
27. C2×C43⋊#95C22semidirect
28. C2×C43⋊#95C22semidirect
29. C2×C43⋊#95C22semidirect
30. C2×C43⋊#95C22semidirect
31. C2×C43⋊#95C22semidirect
34. C22×C42×C43C22semidirect
35. C2×#95×C43C22semidirect
36. C2×#95×C43C22semidirect
62. C22×C4×D43C2×C4semidirect
63. C22×C4×D43C2×C4semidirect
67. C2×C22⋊Dic43C2×C4semidirect
68. C2×C22⋊Dic43C2×C4semidirect
77. C2×(C2×D43)⋊C4C2×C4semidirect
78. C2×(C2×D43)⋊C4C2×C4semidirect
101. C2×C22⋊C4×C43C2×C4semidirect
102. C2×C22⋊C4×C43C2×C4semidirect
145. C23×D43C42semidirect
220. (C2×D43)⋊C4C22⋊C4semidirect
320. C2×C4×C43C2×C22⋊C4semidirect
341. C2×Dic43C2×C22⋊C4semidirect
390. C2×D43C4×C22⋊C4semidirect
404. #1437D43semidirect
434. C22×C42C2×D43semidirect
443. C2×#95C2×D43semidirect
444. C2×#95C2×D43semidirect
445. C43C22⋊C42semidirect
500. C2×C22⋊C4C4×D43semidirect
501. C2×C22⋊C4C4×D43semidirect
752. C2×C4C22⋊C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D432
C2×#145827542
C2×C4×(C2×D43)⋊C42
C2×#145827462
#191328322
(C2×D43)⋊#952
C43×#14372
C22⋊C4243