Finite Group Databasebeta

← #25001827

Subgroups — #25001827

Order 11008.

1414 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D43C211yesmaximal, characteristic
2C2×#14582862C211yesmaximal, characteristic
3#19136974C211yesmaximal, characteristic
4C2×#14582656C211yesmaximal, characteristic, complemented
5C2×#14582655C211yesmaximal, characteristic, complemented
6C2×#14582655C211yesmaximal, characteristic, complemented
7C2×C43×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
8C23×C4×D43C2211yescharacteristic
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C2×#13063284C2211yescharacteristic
12C2×#13063283—21no—
13C2×#13063282C412yescomplemented
14C2×#13063281—21no—
15#117×D43—22no—
16#117×D43—22no—
17#117×D43—22no—
18#117×D43—22no—
19C2×C4⋊C4×D43—21no—
20C2×C22⋊C4×D43—21no—
21C2×C42×D43C412yescomplemented
22#14582862—21no—
23#14582862—21no—
24#14582862—22no—
25C2×(C2×D43)⋊C8C414yescomplemented
26#14582760—21no—
27#14582756—22no—
28#14582754—21no—
29C4×(C2×D43)⋊C4C414yescomplemented
30#14582656—22no—
31#14582655—22no—
32#14582655—22no—
33C22×M16×C43C2211yescharacteristic
34C2×#117×C43C2211yescharacteristic
35C2×#117×C43C2211yescharacteristic
36C43×H(3,ℤ/4)—22no—
37C24×D43D411yescharacteristic
38C23×Dic43D411yescharacteristic
39C22×C4×D43—21no—
40C22×C4×D43—21no—
41C22×C4×D43—21no—
42C22×C4×D43—21no—
43C22×C4×D43—21no—
44C22×C4×D43—21no—
45C22×C4×D43—21no—
46C22×C4×D43—21no—
47C22×C4×D43—22no—
48C22×C4×D43C2×C412yes—
49C22×C4×D43C2×C411yescharacteristic
50C22×C4×D43C2×C411yescharacteristic
51C22×C4×D43C2×C412yes—
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D412yes—
55C22×C4×D43Q812yes—
56C2×#10621877—21no—
57C2×#10621877—21no—
58C2×#10621877—21no—
59C2×#10621877—21no—
60C2×#10621877—21no—
61C2×#10621877—21no—
62C22×C43⋊C8C2×C412yescomplemented
63#13063284—21no—
64#13063284—21no—
65#13063284—21no—
66#13063284—21no—
67#13063284—21no—
68#13063284—21no—
69#13063284D412yes—
70#13063284D412yes—
71#13063283—24no—
72#13063283—24no—
73#13063282—24no—
74#13063282—24no—
75#13063281—24no—
76#13063281—24no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×Dic43⋊C4—22no—
80C4⋊C4×D43—24no—
81C4⋊C4×D43—24no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×(C2×D43)⋊C4—22no—
85C2×(C2×D43)⋊C4—24no—
86C22⋊C4×D43—24no—
87C22⋊C4×D43—24no—
88C2×C4×Dic43—22no—
89C2×C4×Dic43C2×C412yes—
90C2×C4×Dic43C2×C412yescomplemented
91C42×D43—24no—
92C42×D43—24no—
93(C2×D43)⋊C8—24no—
94(C2×D43)⋊C8—24no—
95C43⋊#95—24no—
96C23×C4×C43C2311yescharacteristic
97C2×M16×C43—21no—
98C2×M16×C43—21no—
99C2×M16×C43—21no—
100C2×M16×C43—21no—
101C2×M16×C43—21no—
102C2×M16×C43—21no—
103C22×C8×C43C2×C412yescomplemented
104#117×C43—21no—
105#117×C43—21no—
106#117×C43—21no—
107#117×C43—21no—
108#117×C43—21no—
109#117×C43—21no—
110#117×C43D412yes—
111#117×C43D412yes—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C42×C43C2×C412yes—
117C2×C42×C43C2×C412yescomplemented
118C24×C43C2×D411yescharacteristic
119C23×D43—21no—
120C23×D43—21no—
121C23×D43—21no—
122C23×D43—21no—
123C23×D43—44no—
124C23×D43C22⋊C411yescharacteristic
125C23×D43C22⋊C412yes—
126C23×D43C22⋊C411yescharacteristic
127C23×D43C4⋊C412yes—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43C22×C411yescharacteristic
131C22×C4×C43C22×C411yescharacteristic
132C22×C4×C43C22×C411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×Q811yescharacteristic
140C22×C4×C43#4111yescharacteristic
141C22×C4×C43#4111yescharacteristic
142C22×C4×C43#4111yescharacteristic
143C22×C4×C43#4111yescharacteristic
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C22⋊C412yes—
151C22×Dic43C22⋊C411yescharacteristic
152C22×Dic43C22⋊C411yescharacteristic
153C22×Dic43C4⋊C412yes—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—22no—
163C2×C4×D43—22no—
164C2×C4×D43—22no—
165C2×C4×D43—22no—
166C2×C4×D43—22no—
167C2×C4×D43—22no—
168C2×C4×D43—22no—
169C2×C4×D43—22no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—22no—
175C2×C4×D43—22no—
176C2×C4×D43—22no—
177C2×C4×D43—22no—
178C2×C4×D43—22no—
179C2×C4×D43—22no—
180C2×C4×D43—22no—
181C2×C4×D43—22no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—28no—
187C2×C4×D43—48no—
188C2×C4×D43C4212yes—
189C2×C4×D43C4212yes—
190C2×C4×D43C22⋊C412yes—
191C2×C4×D43C22⋊C412yes—
192C2×C4×D43C4⋊C412yes—
193C2×C4×D43C4⋊C412yes—
194C2×C4×D43C4⋊C412yes—
195C2×C4×D43C4⋊C412yes—
196M16×C43—41no—
197M16×C43—41no—
198M16×C43—41no—
199M16×C43—41no—
200C2×C8×C43—22no—
201C2×C8×C43—22no—
202C2×C8×C43—22no—
203C4⋊C4×C43—22no—
204C4⋊C4×C43—22no—
205C4⋊C4×C43—41no—
206C4⋊C4×C43—41no—
207C22⋊C4×C43—22no—
208C22⋊C4×C43—22no—
209C22⋊C4×C43—41no—
210C22⋊C4×C43—41no—
211C42×C43—22no—
212C42×C43—22no—
213C42×C43—22no—
214C42×C43C22⋊C414yescomplemented
215C22⋊Dic43—22no—
216C22⋊Dic43—22no—
217C22⋊Dic43—41no—
218C22⋊Dic43—41no—
219(C2×D43)⋊C4—28no—
220(C2×D43)⋊C4—48no—
221C4⋊Dic43—22no—
222C4⋊Dic43—22no—
223C4⋊Dic43—41no—
224C4⋊Dic43—41no—
225Dic43⋊C4—28no—
226C4×Dic43—28no—
227C4×Dic43—22no—
228C4×Dic43—22no—
229C4×Dic43—22no—
230C4×Dic43C22⋊C414yescomplemented
231#10621877—41no—
232#10621877—41no—
233#10621877—41no—
234#10621877—41no—
235C2×C43⋊C8—22no—
236C2×C43⋊C8—22no—
237C2×C43⋊C8—22no—
238C23×C43—42no—
239C23×C43C2×C22⋊C411yescharacteristic
240C23×C43C2×C22⋊C411yescharacteristic
241C23×C43C2×C4⋊C411yescharacteristic
242C23×C43#12011yescharacteristic
243C23×C43#12011yescharacteristic
244C23×C43#12311yescharacteristic
245C23×C43#12311yescharacteristic
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—24no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—22no—
252C22×D43—22no—
253C22×D43—22no—
254C22×D43—22no—
255C22×D43—24no—
256C22×D43—24no—
257C22×D43—42no—
258C22×D43—42no—
259C22×D43—42no—
260C22×D43—44no—
261C22×D43—44no—
262C22×D43—44no—
263C22×D43—44no—
264C22×D43#9512yes—
265C22×D43#9512yes—
266C2×C4×C43—24no—
267C2×C4×C43—44no—
268C2×C4×C43—44no—
269C2×C4×C43—42no—
270C2×C4×C43C2×C4211yescharacteristic
271C2×C4×C43C2×C22⋊C411yescharacteristic
272C2×C4×C43C2×C22⋊C411yescharacteristic
273C2×C4×C43C2×C22⋊C411yescharacteristic
274C2×C4×C43C2×C4⋊C411yescharacteristic
275C2×C4×C43C2×C4⋊C411yescharacteristic
276C2×C4×C43#11711yescharacteristic
277C2×C4×C43#11711yescharacteristic
278C2×C4×C43C4×D411yescharacteristic
279C2×C4×C43C4×D411yescharacteristic
280C2×C4×C43C4×D411yescharacteristic
281C2×C4×C43C4×D411yescharacteristic
282C2×C4×C43C4×D411yescharacteristic
283C2×C4×C43C4×D411yescharacteristic
284C2×C4×C43C4×D411yescharacteristic
285C2×C4×C43C4×D411yescharacteristic
286C2×C4×C43#12011yescharacteristic
287C2×C4×C43#12011yescharacteristic
288C2×C4×C43#12111yescharacteristic
289C2×C4×C43#12111yescharacteristic
290C2×C4×C43#12111yescharacteristic
291C2×C4×C43#12111yescharacteristic
292C2×C4×C43C22⋊Q811yescharacteristic
293C2×C4×C43C22⋊Q811yescharacteristic
294C2×C4×C43C22⋊Q811yescharacteristic
295C2×C4×C43C22⋊Q811yescharacteristic
296C2×C4×C43#12311yescharacteristic
297C2×C4×C43#12311yescharacteristic
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—24no—
307C2×Dic43—44no—
308C2×Dic43—44no—
309C2×Dic43—42no—
310C2×Dic43#9512yes—
311C2×Dic43#9512yes—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—22no—
318C4×D43—22no—
319C4×D43—22no—
320C4×D43—22no—
321C4×D43—22no—
322C4×D43—22no—
323C4×D43—22no—
324C4×D43—22no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—416no—
329C8×C43—42no—
330C43⋊C8—42no—
331#10716—431nomaximal, Sylow
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43—41no—
339C22×C43C2×#9511yescharacteristic
340C22×C43#37911yescharacteristic
341C22×C43#38111yescharacteristic
342C22×C43#38511yescharacteristic
343C22×C43#38511yescharacteristic
344C22×C43#38611yescharacteristic
345C22×C43#38611yescharacteristic
346C2×D43—24no—
347C2×D43—24no—
348C2×D43—22no—
349C2×D43—22no—
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—44no—
354C2×D43—44no—
355C2×D43—44no—
356C2×D43—44no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43H(3,ℤ/4)14yescomplemented
360C4×C43—44no—
361C4×C43—82no—
362C4×C43C4×C22⋊C411yescharacteristic
363C4×C43C4×C22⋊C411yescharacteristic
364C4×C43#38011yescharacteristic
365C4×C43#38011yescharacteristic
366C4×C43#38511yescharacteristic
367C4×C43#38511yescharacteristic
368C4×C43#38611yescharacteristic
369C4×C43#38611yescharacteristic
370Dic43—22no—
371Dic43—22no—
372Dic43—44no—
373Dic43—82no—
374C22×#117—431no—
375C2×#407—431no—
376#2280—431no—
377C2×H(3,ℤ/4)—431no—
378C2×H(3,ℤ/4)—431no—
379C2×H(3,ℤ/4)—431no—
380C2×H(3,ℤ/4)D4311yescharacteristic, complemented
381C2×C43—21no—
382C2×C43—21no—
383C2×C43—21no—
384C2×C43—21no—
385C2×C43—21no—
386C2×C43—21no—
387C2×C43C22⋊#9511yescharacteristic
388C2×C43C2×H(3,ℤ/4)12yes—
389D43—24no—
390D43—42no—
391C24×C4—431no—
392C22×M16—431no—
393C22×M16C2×D4311yescharacteristic
394C2×#117—431no—
395C2×#117—431no—
396C2×#117—432no—
397C2×#117—861no—
398C2×#117—861no—
399C2×#117—862no—
400C2×#117—862no—
401C2×#117—862no—
402C2×#117—862no—
403C2×#117C2×D4311yescharacteristic
404C2×#117C2×D4311yescharacteristic
405C22×C4⋊C4—861no—
406C22×C22⋊C4—861no—
407C22×C42—432no—
408#407—861no—
409#407—861no—
410#407—862no—
411C2×C22⋊C8—434no—
412#381—861no—
413#380—862no—
414#379—861no—
415C4×C22⋊C4—434no—
416H(3,ℤ/4)—22no—
417H(3,ℤ/4)—862no—
418H(3,ℤ/4)—862no—
419H(3,ℤ/4)—862no—
420C43#1071611yescharacteristic, complemented, Sylow
421C25—431no—
422C23×C4—431no—
423C23×C4—431no—
424C23×C4—432no—
425C23×C4—432no—
426C23×C4—431no—
427C23×C4—431no—
428C23×C4—431no—
429C23×C4—432no—
430C23×C4—432no—
431C23×C4—862no—
432C23×C4—861no—
433C23×C4—861no—
434C23×C4—861no—
435C23×C4—861no—
436C23×C4—861no—
437C23×C4—861no—
438C23×C4—861no—
439C23×C4—861no—
440C23×C4C22×D4311yescharacteristic
441C2×M16—21no—
442C2×M16—21no—
443C2×M16—21no—
444C2×M16—21no—
445C2×M16—21no—
446C2×M16—21no—
447C2×M16—861no—
448C2×M16—861no—
449C2×M16—861no—
450C2×M16—861no—
451C2×M16—861no—
452C2×M16—861no—
453C22×C8—432no—
454C22×C8C4×D4312yescomplemented
455#117—21no—
456#117—21no—
457#117—21no—
458#117—21no—
459#117—21no—
460#117—21no—
461#117—432no—
462#117—432no—
463#117—864no—
464#117—864no—
465#117—864no—
466#117—864no—
467#117—864no—
468#117—861no—
469#117—861no—
470#117—861no—
471#117—861no—
472#117—861no—
473#117—861no—
474#117—864no—
475#117D17212yes—
476#117C22⋊D4312yes—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—864no—
480C2×C4⋊C4—864no—
481C2×C4⋊C4—862no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—864no—
487C2×C22⋊C4—864no—
488C2×C22⋊C4—862no—
489C2×C22⋊C4—861no—
490C2×C22⋊C4—864no—
491C2×C22⋊C4—861no—
492C2×C42—432no—
493C2×C42—432no—
494C2×C42—864no—
495C2×C42—862no—
496C2×C42—864no—
497C2×C42C4×D4312yes—
498C2×C42C4×D4312yescomplemented
499C22⋊C8—864no—
500C22⋊C8—864no—
501#95—864no—
502C24—431no—
503C24—432no—
504C24—432no—
505C24—431no—
506C24—861no—
507C24—861no—
508C24—861no—
509C24—861no—
510C24—1724no—
511C24D4×D4311yescharacteristic
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—432no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—432no—
518C22×C4—432no—
519C22×C4—432no—
520C22×C4—432no—
521C22×C4—432no—
522C22×C4—432no—
523C22×C4—432no—
524C22×C4—432no—
525C22×C4—432no—
526C22×C4—868no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4—861no—
530C22×C4—861no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—861no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—861no—
537C22×C4—861no—
538C22×C4—861no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—862no—
542C22×C4—862no—
543C22×C4—862no—
544C22×C4—862no—
545C22×C4—862no—
546C22×C4—862no—
547C22×C4—861no—
548C22×C4—861no—
549C22×C4—861no—
550C22×C4—861no—
551C22×C4—862no—
552C22×C4—862no—
553C22×C4—862no—
554C22×C4—862no—
555C22×C4—862no—
556C22×C4—862no—
557C22×C4—862no—
558C22×C4—862no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—862no—
564C22×C4—862no—
565C22×C4—1728no—
566C22×C4C2×C4×D4311yescharacteristic
567C22×C4C2×C4×D4311yescharacteristic
568C22×C4C2×C4×D4311yescharacteristic
569C22×C4C2×D17211yescharacteristic
570C22×C4#1062189811yescharacteristic
571C22×C4#1062189811yescharacteristic
572C22×C4D4×D4311yescharacteristic
573C22×C4D4×D4311yescharacteristic
574C22×C4D4×D4311yescharacteristic
575C22×C4D4×D4311yescharacteristic
576C22×C4#1062190011yescharacteristic
577C22×C4Q8×D4311yescharacteristic
578C22×C4#1062190211yescharacteristic
579C22×C4C2×C22⋊D4311yescharacteristic
580M16—41no—
581M16—41no—
582M16—41no—
583M16—41no—
584M16—1721no—
585M16—1721no—
586M16—1721no—
587M16—1721no—
588C2×C8—22no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—862no—
592C2×C8—862no—
593C2×C8—862no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—868no—
599C4⋊C4—862no—
600C4⋊C4—862no—
601C4⋊C4—1721no—
602C4⋊C4—1721no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—41no—
606C22⋊C4—41no—
607C22⋊C4—868no—
608C22⋊C4—862no—
609C22⋊C4—862no—
610C22⋊C4—1728no—
611C22⋊C4—1721no—
612C22⋊C4—1721no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—434no—
617C42—868no—
618C42—862no—
619C42—862no—
620C42—862no—
621C42(C2×D43)⋊C414yescomplemented
622C23—42no—
623C23—432no—
624C23—432no—
625C23—864no—
626C23—864no—
627C23—864no—
628C23—861no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—862no—
633C23—862no—
634C23—862no—
635C23—862no—
636C23—1722no—
637C23—1722no—
638C23—1722no—
639C23—1724no—
640C23—1724no—
641C23—1724no—
642C23—1724no—
643C23C22⋊C4×D4311yescharacteristic
644C23C22⋊C4×D4311yescharacteristic
645C23C4⋊C4×D4311yescharacteristic
646C23#1306329311yescharacteristic
647C23#1306329511yescharacteristic
648C23#1306330711yescharacteristic
649C23#1306331011yescharacteristic
650C2×C4—24no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—42no—
654C2×C4—432no—
655C2×C4—432no—
656C2×C4—861no—
657C2×C4—861no—
658C2×C4—861no—
659C2×C4—861no—
660C2×C4—862no—
661C2×C4—862no—
662C2×C4—862no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—862no—
668C2×C4—862no—
669C2×C4—862no—
670C2×C4—862no—
671C2×C4—862no—
672C2×C4—862no—
673C2×C4—862no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—864no—
681C2×C4—17216no—
682C2×C4—1724no—
683C2×C4—1722no—
684C2×C4—1724no—
685C2×C4C42×D4311yescharacteristic
686C2×C4C22⋊C4×D4311yescharacteristic
687C2×C4C22⋊C4×D4311yescharacteristic
688C2×C4C2×(C2×D43)⋊C411yescharacteristic
689C2×C4C4⋊C4×D4311yescharacteristic
690C2×C4C4⋊C4×D4311yescharacteristic
691C2×C4#1306328211yescharacteristic
692C2×C4#1306328311yescharacteristic
693C2×C4(C22⋊D43)⋊C411yescharacteristic
694C2×C4(C22⋊D43)⋊C411yescharacteristic
695C2×C4C4×C22⋊D4311yescharacteristic
696C2×C4C4×C22⋊D4311yescharacteristic
697C2×C4#1306328711yescharacteristic
698C2×C4#1306328711yescharacteristic
699C2×C4C4×D17211yescharacteristic
700C2×C4C4×D17211yescharacteristic
701C2×C4#1306329311yescharacteristic
702C2×C4#1306329511yescharacteristic
703C2×C4#1306329611yescharacteristic
704C2×C4#1306329811yescharacteristic
705C2×C4#1306329811yescharacteristic
706C2×C4#1306330011yescharacteristic
707C2×C4#1306330111yescharacteristic
708C2×C4#1306330311yescharacteristic
709C2×C4#1306330311yescharacteristic
710C2×C4#1306330511yescharacteristic
711C2×C4#1306330711yescharacteristic
712C2×C4#1306331011yescharacteristic
713C8—42no—
714C8—1722no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—434no—
723C22—864no—
724C22—864no—
725C22—862no—
726C22—862no—
727C22—862no—
728C22—862no—
729C22—862no—
730C22—1724no—
731C22—1724no—
732C22—1724no—
733C22—1724no—
734C22—1722no—
735C22—1722no—
736C22#95×D4311yescharacteristic
737C22#1458275411yescharacteristic
738C22#1458276111yescharacteristic
739C22#1458277011yescharacteristic
740C22#1458277311yescharacteristic
741C22#1458277511yescharacteristic
742C22#1458277711yescharacteristic
743C4—44no—
744C4—82no—
745C4—862no—
746C4—862no—
747C4—3442no—
748C4—1724no—
749C4#1458274611yescharacteristic
750C4C4×(C2×D43)⋊C411yescharacteristic
751C4#1458275611yescharacteristic
752C4#1458275811yescharacteristic
753C4#1458277011yescharacteristic
754C4#1458277311yescharacteristic
755C4#1458277511yescharacteristic
756C4#1458277711yescharacteristic
757C2—21no—
758C2—21no—
759C2—21no—
760C2—21no—
761C2—21no—
762C2—21no—
763C2—864no—
764C2—1722no—
765C2(C2×D43)⋊#9511yescharacteristic
766C2H(3,ℤ/4)×D4312yes—
subgroupG/H
centerC2×C4C42×D43
commutatorC2×C4×C43C2×C42
FrattiniC23×C4C22×D43
FittingC2×C43×H(3,ℤ/4)C2
socleC22×C43C2×#95
prime radicalC24×D43D4
cosocleC23×C4×C43C23
hypercenterC2×H(3,ℤ/4)D43
hypocenterC43#10716
LCSG ▷ C2×C4×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
4. C2×#14582656C2semidirect
5. C2×#14582655C2semidirect
6. C2×#14582655C2semidirect
7. C2×C43×H(3,ℤ/4)C2semidirect
13. C2×#13063282C4semidirect
21. C2×C42×D43C4semidirect
25. C2×(C2×D43)⋊C8C4semidirect
29. C4×(C2×D43)⋊C4C4semidirect
62. C22×C43⋊C8C2×C4semidirect
90. C2×C4×Dic43C2×C4semidirect
103. C22×C8×C43C2×C4semidirect
117. C2×C42×C43C2×C4semidirect
214. C42×C43C22⋊C4semidirect
230. C4×Dic43C22⋊C4semidirect
359. C2×D43H(3,ℤ/4)semidirect
380. C2×H(3,ℤ/4)D43semidirect
420. C43#10716semidirect
454. C22×C8C4×D43semidirect
498. C2×C42C4×D43semidirect
621. C42(C2×D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D432
C2×#145828622
#191369742
C2×#145826562
C2×#145826552
C2×C43×H(3,ℤ/4)2
#1071643