Finite Group Databasebeta

← #25018275

Subgroups — #25018275

Order 11008.

2702 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C211yesmaximal, characteristic
2C22×#13063282C211yesmaximal, characteristic, complemented
3C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
5#19132846C212yesmaximal, complemented
6#19132843C212yesmaximal, complemented
7#19132838C212yesmaximal, complemented
8#19132834C212yesmaximal
9C4×C43⋊#95C211yesmaximal, characteristic, complemented
10C4×C43⋊#95C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
12C23×C22⋊D43C2211yescharacteristic
13C23×C4×D43C2211yescharacteristic
14C2×C4×C22⋊D43—24no—
15C2×C4×C22⋊D43—24no—
16C2×C4×C22⋊D43C418yescomplemented
17C2×#13063282—24no—
18C2×#13063282—24no—
19C2×#13063282—24no—
20C22×Dic43⋊C4C2212yes—
21C22×Dic43⋊C4C2211yescharacteristic
22C22×C22⋊Dic43C2212yes—
23C22×C22⋊Dic43C2211yescharacteristic
24C22×(C2×D43)⋊C4C2212yes—
25C22×(C2×D43)⋊C4C2212yes—
26C22×(C2×D43)⋊C4C2211yescharacteristic
27C22×C4×Dic43C2211yescharacteristic
28C22×C4×Dic43C2211yescharacteristic
29C22×C4×Dic43C2211yescharacteristic
30C4×(C2×D43)⋊C4—24no—
31C4×C22⋊Dic43—24no—
32C2×C43⋊#95C2212yes—
33C2×C43⋊#95C2212yes—
34C2×C43⋊#95C2212yes—
35C2×C43⋊#95C2212yes—
36C2×C43⋊#95C2212yes—
37C2×C43⋊#95C2212yes—
38C24×C4×C43C2211yescharacteristic
39C22×C22⋊C4×C43C2212yes—
40C22×C42×C43C2211yescharacteristic
41C22×C42×C43C2211yescharacteristic
42C4×C22⋊C4×C43—24no—
43C2×#95×C43C2212yes—
44C24×D43C2311yescharacteristic
45C22×C22⋊D43—24no—
46C22×C22⋊D43—22no—
47C22×C22⋊D43—22no—
48C22×C22⋊D43—24no—
49C22×C22⋊D43C2×C414yes—
50C23×Dic43C2311yescharacteristic
51C23×Dic43C2312yes—
52C23×Dic43C2312yes—
53C23×Dic43C2311yescharacteristic
54C23×Dic43C2311yescharacteristic
55C22×C4×D43—22no—
56C22×C4×D43—22no—
57C22×C4×D43—22no—
58C22×C4×D43—22no—
59C22×C4×D43C2×C414yes—
60C22×C4×D43D414yes—
61C22×C4×D43D414yes—
62C4×C22⋊D43—232no—
63#13063282—232no—
64C2×Dic43⋊C4—24no—
65C2×Dic43⋊C4—24no—
66C2×Dic43⋊C4—24no—
67C2×Dic43⋊C4—22no—
68C2×Dic43⋊C4—22no—
69C2×Dic43⋊C4C2×C414yes—
70C2×C22⋊Dic43—24no—
71C2×C22⋊Dic43—22no—
72C2×C22⋊Dic43—22no—
73C2×C22⋊Dic43—24no—
74C2×C22⋊Dic43—24no—
75C2×C22⋊Dic43C2×C414yes—
76C2×(C2×D43)⋊C4—24no—
77C2×(C2×D43)⋊C4—22no—
78C2×(C2×D43)⋊C4—22no—
79C2×(C2×D43)⋊C4—24no—
80C2×(C2×D43)⋊C4—24no—
81C2×(C2×D43)⋊C4—24no—
82C2×(C2×D43)⋊C4—24no—
83C2×(C2×D43)⋊C4—24no—
84C2×(C2×D43)⋊C4C2×C414yes—
85C2×C4×Dic43—22no—
86C2×C4×Dic43—22no—
87C2×C4×Dic43—22no—
88C2×C4×Dic43—22no—
89C2×C4×Dic43—22no—
90C2×C4×Dic43—22no—
91C2×C4×Dic43—22no—
92C2×C4×Dic43C2×C414yes—
93C2×C4×Dic43D414yescomplemented
94C43⋊#95—24no—
95C43⋊#95—24no—
96C43⋊#95—24no—
97C43⋊#95—24no—
98C43⋊#95—24no—
99C43⋊#95—24no—
100C25×C43C2311yescharacteristic
101C23×C4×C43—22no—
102C23×C4×C43—22no—
103C23×C4×C43—22no—
104C23×C4×C43—22no—
105C23×C4×C43—22no—
106C23×C4×C43—22no—
107C23×C4×C43C2×C414yes—
108C23×C4×C43C2311yescharacteristic
109C23×C4×C43C2312yes—
110C23×C4×C43C2312yes—
111C23×C4×C43C2311yescharacteristic
112C2×C22⋊C4×C43—24no—
113C2×C22⋊C4×C43—24no—
114C2×C22⋊C4×C43—24no—
115C2×C42×C43—22no—
116C2×C42×C43—22no—
117C2×C42×C43—22no—
118C2×C42×C43—22no—
119C2×C42×C43—22no—
120C2×C42×C43D414yescomplemented
121#95×C43—24no—
122C24×C43—21no—
123C24×C43—21no—
124C24×C43—21no—
125C24×C43—21no—
126C24×C43—22no—
127C24×C43—21no—
128C24×C43—21no—
129C24×C43—22no—
130C24×C43—22no—
131C24×C43C22×C412yes—
132C24×C43#4114yes—
133C24×C43C2411yescharacteristic
134C23×D43—21no—
135C23×D43—21no—
136C23×D43—22no—
137C23×D43—22no—
138C23×D43—21no—
139C23×D43—21no—
140C23×D43—22no—
141C23×D43—22no—
142C23×D43C22×C412yes—
143C23×D43C2×D412yes—
144C23×D43C2×D412yes—
145C22×C4×C43—28no—
146C22×C4×C43—28no—
147C22×C4×C43—28no—
148C22×C4×C43—21no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—22no—
152C22×C4×C43—22no—
153C22×C4×C43—21no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—22no—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—44no—
167C22×C4×C43—44no—
168C22×C4×C43—44no—
169C22×C4×C43—44no—
170C22×C4×C43C22×C412yes—
171C22×C4×C43C22×C412yes—
172C22×C4×C43C2×D412yes—
173C22×C4×C43C2×D412yes—
174C22×C4×C43C2×D412yes—
175C22×C4×C43C2×D414yes—
176C22×C4×C43C2×D412yes—
177C22×C4×C43#4114yes—
178C22×C4×C43#4112yes—
179C22×C4×C43#4112yes—
180C2×C22⋊D43—216no—
181C2×C22⋊D43—216no—
182C2×C22⋊D43—28no—
183C2×C22⋊D43—28no—
184C2×C22⋊D43—28no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—21no—
192C22×Dic43—21no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43C22×C412yes—
209C22×Dic43C22×C412yes—
210C22×Dic43C22×C412yes—
211C22×Dic43C2×D414yes—
212C22×Dic43C2×D412yes—
213C22×Dic43C2×D412yes—
214C22×Dic43#4114yes—
215C22×Dic43#4114yes—
216C2×C4×D43—28no—
217C2×C4×D43—28no—
218C2×C4×D43—28no—
219C2×C4×D43—28no—
220C2×C4×D43—28no—
221C2×C4×D43—28no—
222C2×C4×D43C22⋊C4116yescomplemented
223C22⋊C4×C43—216no—
224C42×C43—28no—
225C42×C43—44no—
226C22⋊Dic43—216no—
227C22⋊Dic43—28no—
228(C2×D43)⋊C4—216no—
229(C2×D43)⋊C4—216no—
230(C2×D43)⋊C4—28no—
231Dic43⋊C4—216no—
232Dic43⋊C4—28no—
233C4×Dic43—28no—
234C4×Dic43—28no—
235C4×Dic43—44no—
236C23×C43—22no—
237C23×C43—22no—
238C23×C43—22no—
239C23×C43—22no—
240C23×C43—22no—
241C23×C43—22no—
242C23×C43—24no—
243C23×C43—24no—
244C23×C43—24no—
245C23×C43—24no—
246C23×C43—24no—
247C23×C43—24no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—42no—
253C23×C43—42no—
254C23×C43—42no—
255C23×C43—42no—
256C23×C43—42no—
257C23×C43—42no—
258C23×C43#11714yescomplemented
259C23×C43C23×C411yescharacteristic
260C23×C43C22×D411yescharacteristic
261C23×C43C22×D411yescharacteristic
262C23×C43C22×D411yescharacteristic
263C23×C43C22×D411yescharacteristic
264C23×C43C2×#4112yes—
265C23×C43C2×#4112yes—
266C23×C43C2×#4111yescharacteristic
267C23×C43C2×#4112yes—
268C23×C43C2×#4111yescharacteristic
269C23×C43C2×#4112yes—
270C22×D43—22no—
271C22×D43—22no—
272C22×D43—22no—
273C22×D43—22no—
274C22×D43—22no—
275C22×D43—22no—
276C22×D43—22no—
277C22×D43—22no—
278C22×D43—22no—
279C22×D43—22no—
280C22×D43—24no—
281C22×D43—24no—
282C22×D43—24no—
283C22×D43—24no—
284C22×D43—42no—
285C22×D43—42no—
286C22×D43—42no—
287C22×D43—42no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43—42no—
291C22×D43—42no—
292C22×D43C2×C22⋊C414yes—
293C2×C4×C43—22no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—24no—
297C2×C4×C43—24no—
298C2×C4×C43—24no—
299C2×C4×C43—24no—
300C2×C4×C43—24no—
301C2×C4×C43—24no—
302C2×C4×C43—41no—
303C2×C4×C43—42no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
306C2×C4×C43—41no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—416no—
315C2×C4×C43C2×C22⋊C414yes—
316C2×C4×C43C4×D414yes—
317C2×C4×C43C4×D414yes—
318C2×C4×C43#12014yes—
319C2×C4×C43#12114yes—
320C2×C4×C43#12114yes—
321C2×C4×C43#12314yes—
322C22⋊D43—232no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—24no—
332C2×Dic43—24no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—24no—
337C2×Dic43—24no—
338C2×Dic43—24no—
339C2×Dic43—24no—
340C2×Dic43—24no—
341C2×Dic43—24no—
342C2×Dic43—42no—
343C2×Dic43—42no—
344C2×Dic43—42no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43—42no—
348C2×Dic43—42no—
349C2×Dic43—42no—
350C2×Dic43—42no—
351C2×Dic43—42no—
352C2×Dic43C2×C22⋊C414yes—
353C2×Dic43#11714yescomplemented
354C4×D43—232no—
355#13839—431nomaximal, Sylow
356C22×C43—24no—
357C22×C43—24no—
358C22×C43—24no—
359C22×C43—44no—
360C22×C43—44no—
361C22×C43—44no—
362C22×C43—44no—
363C22×C43—42no—
364C22×C43—42no—
365C22×C43—42no—
366C22×C43—42no—
367C22×C43C22×C22⋊C411yescharacteristic
368C22×C43C2×#11711yescharacteristic
369C22×C43C2×#11711yescharacteristic
370C22×C43C2×C4×D411yescharacteristic
371C22×C43C2×C4×D411yescharacteristic
372C22×C43C4×#4111yescharacteristic
373C22×C43C4×#4111yescharacteristic
374C22×C43C2×#12011yescharacteristic
375C22×C43C2×#12111yescharacteristic
376C22×C43C2×#12111yescharacteristic
377C22×C43C2×#12311yescharacteristic
378C22×C43#52512yes—
379C22×C43#52512yes—
380C22×C43#52512yes—
381C22×C43#52512yes—
382C22×C43#52512yes—
383C22×C43#52912yes—
384C22×C43#52912yes—
385C22×C43#52912yes—
386C22×C43#52912yes—
387C22×C43#53212yes—
388C22×C43#53212yes—
389C22×C43#53212yes—
390C2×D43—24no—
391C2×D43—24no—
392C2×D43—24no—
393C2×D43—44no—
394C2×D43—44no—
395C2×D43—44no—
396C2×D43—44no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C4×C43—44no—
402C4×C43—44no—
403C4×C43—42no—
404C4×C43#38618yes—
405Dic43—24no—
406Dic43—24no—
407Dic43—44no—
408Dic43—44no—
409Dic43—42no—
410C22×C4×D4—431no—
411C22×#117—431no—
412C2×C4×C22⋊C4—431no—
413C2×C4×C22⋊C4—431no—
414C2×C4×C22⋊C4D4311yescharacteristic, complemented
415#1441—432no—
416#1440—432no—
417#1439—432no—
418#1438—432no—
419C4×#95—431no—
420C4×#95—431no—
421C2×C43—44no—
422C2×C43#228011yescharacteristic
423C2×C43C2×#38611yescharacteristic
424C2×C43#229011yescharacteristic
425C2×C43#229011yescharacteristic
426C2×C43#229311yescharacteristic
427C2×C43#229311yescharacteristic
428C2×C43#229711yescharacteristic
429C2×C43#238812yes—
430C2×C43#239212yes—
431C2×C43#239212yes—
432C2×C43#239512yes—
433D43—44no—
434C23×D4—431no—
435C24×C4—431no—
436C24×C4C2×D4311yescharacteristic
437C2×C4×D4—438no—
438C2×C4×D4—864no—
439C2×C4×D4—864no—
440C2×#117—864no—
441C2×#117—864no—
442C2×#117—864no—
443C22×C4⋊C4—431no—
444C22×C4⋊C4—432no—
445C22×C22⋊C4—431no—
446C22×C22⋊C4—431no—
447C22×C22⋊C4—432no—
448C22×C22⋊C4—432no—
449C22×C22⋊C4—432no—
450C22×C22⋊C4C2×D4312yes—
451C22×C42—431no—
452C22×C42—431no—
453C22×C42—431no—
454C22×C42C2×D4311yescharacteristic
455C22×C42C2×D4311yescharacteristic
456C4×C22⋊C4—24no—
457C4×C22⋊C4—864no—
458C4×C22⋊C4—864no—
459C2×#95—432no—
460C2×#95—432no—
461C2×#95—432no—
462C2×#95—432no—
463C2×#95—432no—
464C2×#95—432no—
465C2×#95C2×D4312yes—
466C43#1383911yescharacteristic, complemented, Sylow
467C25—431no—
468C25C22×D4311yescharacteristic
469C22×D4—434no—
470C22×D4—864no—
471C22×D4—862no—
472C22×D4—862no—
473C22×D4—864no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—434no—
483C23×C4—434no—
484C23×C4—434no—
485C23×C4—432no—
486C23×C4—431no—
487C23×C4—432no—
488C23×C4—862no—
489C23×C4—862no—
490C23×C4—862no—
491C23×C4—862no—
492C23×C4C4×D4314yes—
493C23×C4C22×D4311yescharacteristic
494C23×C4C22×D4312yes—
495C23×C4C22×D4312yes—
496C23×C4C22×D4311yescharacteristic
497C4×D4—8632no—
498#117—8632no—
499C2×C4⋊C4—434no—
500C2×C4⋊C4—864no—
501C2×C4⋊C4—864no—
502C2×C4⋊C4—862no—
503C2×C4⋊C4—862no—
504C2×C4⋊C4—864no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—434no—
509C2×C22⋊C4—434no—
510C2×C22⋊C4—864no—
511C2×C22⋊C4—864no—
512C2×C22⋊C4—864no—
513C2×C22⋊C4—862no—
514C2×C22⋊C4—862no—
515C2×C22⋊C4—864no—
516C2×C22⋊C4—862no—
517C2×C22⋊C4—862no—
518C2×C22⋊C4—864no—
519C2×C22⋊C4—864no—
520C2×C22⋊C4—864no—
521C2×C22⋊C4—864no—
522C2×C22⋊C4—864no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—434no—
529C2×C42—434no—
530C2×C42—862no—
531C2×C42—862no—
532C2×C42—862no—
533C2×C42—862no—
534C2×C42—862no—
535C2×C42—862no—
536C2×C42—862no—
537C2×C42C22⋊D4314yescomplemented
538#95—24no—
539#95—864no—
540#95—864no—
541#95—864no—
542#95—864no—
543#95—864no—
544#95—864no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—22no—
550C24—22no—
551C24—21no—
552C24—22no—
553C24—21no—
554C24—432no—
555C24—432no—
556C24—432no—
557C24—861no—
558C24—861no—
559C24—862no—
560C24—862no—
561C24—861no—
562C24—862no—
563C24—861no—
564C24—862no—
565C24C2×C4×D4312yes—
566C24#1062189814yes—
567C24C23×D4311yescharacteristic
568C2×D4—868no—
569C2×D4—868no—
570C2×D4—8616no—
571C2×D4—8616no—
572C2×D4—868no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—432no—
602C22×C4—434no—
603C22×C4—4316no—
604C22×C4—432no—
605C22×C4—434no—
606C22×C4—434no—
607C22×C4—861no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—862no—
614C22×C4—868no—
615C22×C4—868no—
616C22×C4—868no—
617C22×C4—868no—
618C22×C4—868no—
619C22×C4—868no—
620C22×C4—862no—
621C22×C4—862no—
622C22×C4—861no—
623C22×C4—861no—
624C22×C4—862no—
625C22×C4—862no—
626C22×C4—862no—
627C22×C4—862no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—862no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4C2×C4×D4312yes—
637C22×C4C2×C4×D4312yes—
638C22×C4#1062189814yes—
639C22×C4#1062189812yes—
640C22×C4D4×D4312yes—
641C22×C4D4×D4312yes—
642C22×C4D4×D4312yes—
643C22×C4#1062190012yes—
644C22×C4C2×C22⋊D4314yes—
645C22×C4C2×C22⋊D4312yes—
646C4⋊C4—868no—
647C4⋊C4—8616no—
648C22⋊C4—216no—
649C22⋊C4—868no—
650C22⋊C4—8616no—
651C22⋊C4—8616no—
652C22⋊C4—868no—
653C22⋊C4—8616no—
654C42—28no—
655C42—44no—
656C42—868no—
657C42—868no—
658C42—1724no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—434no—
682C23—862no—
683C23—862no—
684C23—862no—
685C23—862no—
686C23—862no—
687C23—862no—
688C23—862no—
689C23—862no—
690C23—862no—
691C23—862no—
692C23—864no—
693C23—864no—
694C23—864no—
695C23—864no—
696C23—1722no—
697C23—1722no—
698C23—1722no—
699C23—1722no—
700C23—1722no—
701C23—1722no—
702C23—1722no—
703C23—1722no—
704C23#1306328214yescomplemented
705C23C22×C4×D4311yescharacteristic
706C23C2×D4×D4311yescharacteristic
707C23C2×D4×D4311yescharacteristic
708C23C2×D4×D4311yescharacteristic
709C23C22×C22⋊D4311yescharacteristic
710C23#41×D4312yes—
711C23#41×D4312yes—
712C23C2×#1062190011yescharacteristic
713C23C2×#1062189812yes—
714C23C2×#1062189811yescharacteristic
715C23C2×#1062189812yes—
716D4—8632no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—416no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—864no—
750C2×C4—864no—
751C2×C4—8632no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—864no—
756C2×C4—864no—
757C2×C4—864no—
758C2×C4—864no—
759C2×C4—864no—
760C2×C4—864no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1722no—
764C2×C4—1722no—
765C2×C4—1722no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4C22⋊C4×D4314yes—
772C2×C4(C22⋊D43)⋊C414yes—
773C2×C4C4×C22⋊D4314yes—
774C2×C4#1306329314yes—
775C2×C4#1306329614yes—
776C2×C4#1306329814yes—
777C2×C4#1306330714yes—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—44no—
785C22—44no—
786C22—42no—
787C22—44no—
788C22—42no—
789C22—864no—
790C22—864no—
791C22—864no—
792C22—1722no—
793C22—1722no—
794C22—1724no—
795C22—1722no—
796C22—1722no—
797C22—1724no—
798C22—1724no—
799C22—1724no—
800C22C2×C22⋊C4×D4311yescharacteristic
801C22#117×D4311yescharacteristic
802C22C2×#1306328211yescharacteristic
803C22C2×(C22⋊D43)⋊C411yescharacteristic
804C22C2×C4×C22⋊D4311yescharacteristic
805C22#1458336711yescharacteristic
806C22C4×#1062189811yescharacteristic
807C22C2×#1306329311yescharacteristic
808C22C2×#1306329611yescharacteristic
809C22C2×#1306329811yescharacteristic
810C22C2×#1306330711yescharacteristic
811C22#1458340812yes—
812C22#1458340812yes—
813C22#1458340812yes—
814C22#1458340812yes—
815C22#1458341012yes—
816C22#1458342712yes—
817C22#1458342912yes—
818C22#1458342912yes—
819C22#1458343312yes—
820C22#1458344512yes—
821C22#1458344612yes—
822C22#1458344612yes—
823C4—44no—
824C4—44no—
825C4—42no—
826C4—864no—
827C4—864no—
828C4—1724no—
829C4—1724no—
830C4—1722no—
831C4#1458277518yes—
832C2—44no—
833C2—1724no—
834C2#1913697611yescharacteristic
835C2C2×#1458277511yescharacteristic
836C2#1913703411yescharacteristic
837C2#1913703811yescharacteristic
838C2#1913705411yescharacteristic
839C2#1913705811yescharacteristic
840C2#1913708111yescharacteristic
841C2#1913781012yes—
842C2#1913783312yes—
843C2#1913783912yes—
844C2#1913785612yes—
subgroupG/H
centerC23×C4C22×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC2×C4×C22⋊C4×C43C2
socle, cosocleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC2×C4×C22⋊C4D43
hypocenterC43#13839
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#13063282C2semidirect
3. C2×C4×(C2×D43)⋊C4C2semidirect
4. C2×C4×C22⋊Dic43C2semidirect
5. #19132846C2semidirect
6. #19132843C2semidirect
7. #19132838C2semidirect
9. C4×C43⋊#95C2semidirect
10. C4×C43⋊#95C2semidirect
11. C2×C4×C22⋊C4×C43C2semidirect
16. C2×C4×C22⋊D43C4semidirect
93. C2×C4×Dic43D4semidirect
120. C2×C42×C43D4semidirect
222. C2×C4×D43C22⋊C4semidirect
258. C23×C43#117semidirect
353. C2×Dic43#117semidirect
414. C2×C4×C22⋊C4D43semidirect
466. C43#13839semidirect
537. C2×C42C22⋊D43semidirect
704. C23#13063282semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C22×#130632822
C2×C4×(C2×D43)⋊C42
C2×C4×C22⋊Dic432
#191328462
#191328432
#191328382
#191328342
C4×C43⋊#952
C2×C4×C22⋊C4×C432
#1383943