Finite Group Databasebeta

← C2×#19134874 #25097676

Subgroups — C2×#19134874 #25097676

Order 11008.

1994 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583372C211yesmaximal, characteristic
2C22×#13063239C211yesmaximal, characteristic
3C2×#14582778C211yesmaximal, characteristic
4C2×#14582772C211yesmaximal, characteristic, complemented
5#19134874C218yesmaximal, direct product factor
6C2×#14582666C211yesmaximal, characteristic, complemented
7C2×#14582665C211yesmaximal, characteristic, complemented
8C2×C43×#385C211yesmaximal, characteristic, complemented
9C23×C22⋊D43C2211yescharacteristic
10#14583372—22no—
11#14583372—22no—
12#14583372—22no—
13#14583372C2214yes—
14C2×C4×C22⋊D43—21no—
15C2×C4×C22⋊D43—21no—
16C2×(C22⋊D43)⋊C4—21no—
17C2×(C22⋊D43)⋊C4—21no—
18C2×#13063281—21no—
19C22×Dic43⋊C4—21no—
20C22×C22⋊Dic43C2211yescharacteristic
21C22×C22⋊Dic43C2211yescharacteristic
22C22×C22⋊Dic43C2211yescharacteristic
23C22×(C2×D43)⋊C4—21no—
24C2×C22⋊C4×D43—21no—
25C2×#13063239C418yescomplemented
26C2×#13063239C2214yes—
27#14582778—22no—
28#14582778C2214yes—
29#14582772—22no—
30#14582772C2214yescomplemented
31C2×C43⋊#95—21no—
32C2×C43⋊#95—21no—
33#14582666C2214yescomplemented
34#14582665C2214yescomplemented
35C24×C4×C43C2211yescharacteristic
36C22×C4⋊C4×C43—21no—
37C22×C22⋊C4×C43C2211yescharacteristic
38C22×C22⋊C4×C43C2211yescharacteristic
39C43×#385—22no—
40C43×#385C2214yescomplemented
41C2×#95×C43—21no—
42C24×D43D411yescharacteristic
43C22×C22⋊D43—21no—
44C22×C22⋊D43—21no—
45C22×C22⋊D43—21no—
46C22×C22⋊D43—21no—
47C22×C22⋊D43—22no—
48C22×C22⋊D43—22no—
49C22×C22⋊D43C2×C414yes—
50C22×C22⋊D43D412yes—
51C22×C22⋊D43Q814yes—
52C22×C22⋊D43C2312yes—
53C23×Dic43—21no—
54C23×Dic43—21no—
55C23×Dic43D411yescharacteristic
56C23×Dic43D411yescharacteristic
57C23×Dic43D411yescharacteristic
58C22×C4×D43—21no—
59C22×C4×D43—21no—
60C4×C22⋊D43—24no—
61C4×C22⋊D43—24no—
62C4×C22⋊D43—24no—
63C4×C22⋊D43—24no—
64(C22⋊D43)⋊C4—24no—
65(C22⋊D43)⋊C4—24no—
66(C22⋊D43)⋊C4—24no—
67(C22⋊D43)⋊C4—24no—
68#13063281—24no—
69#13063281—24no—
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—24no—
73C2×Dic43⋊C4—44no—
74C2×C22⋊Dic43—21no—
75C2×C22⋊Dic43—21no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—22no—
80C2×C22⋊Dic43—22no—
81C2×C22⋊Dic43—22no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43C2×C414yescomplemented
84C2×C22⋊Dic43D412yes—
85C2×C22⋊Dic43C2312yes—
86C2×C22⋊Dic43C2312yes—
87C2×C22⋊Dic43C2312yes—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—24no—
91C2×(C2×D43)⋊C4—44no—
92C22⋊C4×D43—24no—
93C22⋊C4×D43—24no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96#13063239C2×C4116yescomplemented
97C43⋊#95—24no—
98C43⋊#95—24no—
99C25×C43C2311yescharacteristic
100C23×C4×C43—21no—
101C23×C4×C43—21no—
102C23×C4×C43—21no—
103C23×C4×C43—21no—
104C23×C4×C43—21no—
105C23×C4×C43—21no—
106C23×C4×C43—21no—
107C23×C4×C43—44no—
108C23×C4×C43D411yescharacteristic
109C23×C4×C43D411yescharacteristic
110C23×C4×C43C2312yes—
111C2×C4⋊C4×C43—24no—
112C2×C4⋊C4×C43—44no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—22no—
119C2×C22⋊C4×C43C2×C414yescomplemented
120C2×C22⋊C4×C43D412yes—
121C2×C22⋊C4×C43C2312yes—
122C2×C22⋊C4×C43C2312yes—
123#95×C43—24no—
124C24×C43—42no—
125C24×C43—42no—
126C24×C43C22×C412yes—
127C24×C43C2×D411yescharacteristic
128C24×C43C2×D411yescharacteristic
129C24×C43C2×D411yescharacteristic
130C24×C43C2×D411yescharacteristic
131C24×C43C2×D411yescharacteristic
132C24×C43C2×D411yescharacteristic
133C24×C43C2×Q812yes—
134C24×C43#4112yes—
135C24×C43#4112yes—
136C24×C43C2411yescharacteristic
137C23×D43—21no—
138C23×D43—21no—
139C23×D43—22no—
140C23×D43—42no—
141C23×D43—42no—
142C23×D43C4⋊C414yescomplemented
143C23×D43C2×D412yes—
144C22×C4×C43—24no—
145C22×C4×C43—24no—
146C22×C4×C43—24no—
147C22×C4×C43—24no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—22no—
155C22×C4×C43—22no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43—42no—
159C22×C4×C43—42no—
160C22×C4×C43—42no—
161C22×C4×C43—42no—
162C22×C4×C43—42no—
163C22×C4×C43—44no—
164C22×C4×C43—44no—
165C22×C4×C43—44no—
166C22×C4×C43—44no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169C22×C4×C43—41no—
170C22×C4×C43—41no—
171C22×C4×C43C2×D412yes—
172C22×C4×C43C2×D412yes—
173C2×C22⋊D43—24no—
174C2×C22⋊D43—24no—
175C2×C22⋊D43—24no—
176C2×C22⋊D43—24no—
177C2×C22⋊D43—22no—
178C2×C22⋊D43—22no—
179C2×C22⋊D43—24no—
180C2×C22⋊D43—24no—
181C2×C22⋊D43—24no—
182C2×C22⋊D43—24no—
183C2×C22⋊D43—24no—
184C2×C22⋊D43—22no—
185C2×C22⋊D43—22no—
186C2×C22⋊D43—22no—
187C2×C22⋊D43—22no—
188C2×C22⋊D43C4⋊C418yescomplemented
189C2×C22⋊D43C22×C414yes—
190C2×C22⋊D43C2×Q814yes—
191C22×Dic43—24no—
192C22×Dic43—21no—
193C22×Dic43—21no—
194C22×Dic43—21no—
195C22×Dic43—21no—
196C22×Dic43—21no—
197C22×Dic43—21no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—42no—
202C22×Dic43—42no—
203C22×Dic43—42no—
204C22×Dic43—42no—
205C22×Dic43—42no—
206C22×Dic43—42no—
207C22×Dic43—42no—
208C22×Dic43C4⋊C414yescomplemented
209C22×Dic43C2×D412yes—
210C22×Dic43C2×D412yes—
211C22×Dic43C2×D412yes—
212C2×C4×D43—24no—
213C2×C4×D43—24no—
214C2×C4×D43—82no—
215C2×C4×D43—82no—
216C4⋊C4×C43—48no—
217C22⋊C4×C43—24no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43C22×C414yescomplemented
224C22⋊Dic43—24no—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227C22⋊Dic43—22no—
228C22⋊Dic43—22no—
229C22⋊Dic43—22no—
230C22⋊Dic43—22no—
231C22⋊Dic43—22no—
232C22⋊Dic43—42no—
233C22⋊Dic43C22×C414yescomplemented
234(C2×D43)⋊C4—24no—
235(C2×D43)⋊C4—24no—
236(C2×D43)⋊C4—48no—
237Dic43⋊C4—24no—
238Dic43⋊C4—24no—
239Dic43⋊C4—48no—
240C4×Dic43—24no—
241C4×Dic43—24no—
242C23×C43—22no—
243C23×C43—22no—
244C23×C43—22no—
245C23×C43—22no—
246C23×C43—22no—
247C23×C43—22no—
248C23×C43—41no—
249C23×C43—41no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—44no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—44no—
257C23×C43—44no—
258C23×C43—44no—
259C23×C43—41no—
260C23×C43C2×C4⋊C412yes—
261C23×C43C2×C4⋊C412yes—
262C23×C43C4×D412yes—
263C23×C43C4×D412yes—
264C23×C43C4×D412yes—
265C23×C43C4×D412yes—
266C23×C43#12011yescharacteristic
267C23×C43#12011yescharacteristic
268C23×C43#12011yescharacteristic
269C23×C43#12011yescharacteristic
270C23×C43C22⋊Q812yes—
271C23×C43C22⋊Q812yes—
272C23×C43C22⋊Q812yes—
273C23×C43C22⋊Q812yes—
274C23×C43#12312yes—
275C23×C43#12312yes—
276C23×C43C23×C411yescharacteristic
277C23×C43C22×D411yescharacteristic
278C23×C43C22×D411yescharacteristic
279C23×C43C22×D411yescharacteristic
280C23×C43C22×Q811yescharacteristic
281C23×C43C2×#4111yescharacteristic
282C23×C43C2×#4111yescharacteristic
283C22×D43—22no—
284C22×D43—24no—
285C22×D43—22no—
286C22×D43—24no—
287C22×D43—42no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43—48no—
291C22×D43—42no—
292C22×D43—84no—
293C22×D43—81no—
294C22×D43—81no—
295C22×D43C2×C4⋊C414yescomplemented
296C2×C4×C43—24no—
297C2×C4×C43—24no—
298C2×C4×C43—24no—
299C2×C4×C43—24no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—42no—
303C2×C4×C43—48no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—44no—
307C2×C4×C43—44no—
308C2×C4×C43—44no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—42no—
313C2×C4×C43—44no—
314C2×C4×C43—42no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43—81no—
318C2×C4×C43—81no—
319C22⋊D43—24no—
320C22⋊D43—24no—
321C22⋊D43—24no—
322C22⋊D43—24no—
323C22⋊D43—28no—
324C22⋊D43—28no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—24no—
328C2×Dic43—24no—
329C2×Dic43—24no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—42no—
333C2×Dic43—48no—
334C2×Dic43—42no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43—42no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—81no—
343C2×Dic43—81no—
344C2×Dic43—84no—
345C2×Dic43C2×C4⋊C414yescomplemented
346C4×D43—84no—
347C4×D43—84no—
348C2×#1867—431nomaximal, Sylow
349C22×C43—24no—
350C22×C43—24no—
351C22×C43—24no—
352C22×C43—24no—
353C22×C43—24no—
354C22×C43—24no—
355C22×C43—21no—
356C22×C43—21no—
357C22×C43—21no—
358C22×C43—21no—
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—21no—
362C22×C43—21no—
363C22×C43—21no—
364C22×C43—21no—
365C22×C43—21no—
366C22×C43—21no—
367C22×C43—42no—
368C22×C43—42no—
369C22×C43—42no—
370C22×C43—42no—
371C22×C43—42no—
372C22×C43—42no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43#38512yes—
378C22×C43#38512yes—
379C22×C43#38512yes—
380C22×C43#38512yes—
381C22×C43B(4,𝔽2)12yes—
382C22×C43#45812yes—
383C22×C43C22×C4⋊C411yescharacteristic
384C22×C43C2×C4×D411yescharacteristic
385C22×C43C2×C4×D411yescharacteristic
386C22×C43C2×#12011yescharacteristic
387C22×C43C2×C22⋊Q811yescharacteristic
388C22×C43C2×C22⋊Q811yescharacteristic
389C22×C43C2×#12311yescharacteristic
390C2×D43—24no—
391C2×D43—48no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—44no—
395C2×D43—82no—
396C2×D43—84no—
397C4×C43—44no—
398C4×C43—42no—
399C4×C43—44no—
400C4×C43—42no—
401Dic43—24no—
402Dic43—44no—
403Dic43—42no—
404Dic43—42no—
405Dic43—82no—
406C2×#518—431no—
407C22×#99—431no—
408C2×#386—431no—
409C2×#385—431no—
410C2×#385D4311yescharacteristic, complemented
411#1867—438no—
412C2×#342—431no—
413C2×#342—431no—
414C2×C43—21no—
415C2×C43—21no—
416C2×C43—21no—
417C2×C43—21no—
418C2×C43—22no—
419C2×C43—21no—
420C2×C43—21no—
421C2×C43—22no—
422C2×C43—22no—
423C2×C43#186714yescomplemented
424C2×C43C2×#38511yescharacteristic
425C2×C43C2×B(4,𝔽2)11yescharacteristic
426C2×C43C2×#45811yescharacteristic
427D43—44no—
428C23×D4—431no—
429C24×C4C2×D4311yescharacteristic
430#518—434no—
431#518—862no—
432#518—862no—
433#518—862no—
434C2×C4×D4—861no—
435C2×C4×D4—861no—
436C2×C4×D4—861no—
437C2×C4×D4—861no—
438C2×#117—861no—
439C22×C4⋊C4—21no—
440C22×C4⋊C4—861no—
441C22×C22⋊C4—431no—
442C22×C22⋊C4—431no—
443C22×C22⋊C4—431no—
444C22×C22⋊C4—861no—
445C22×C22⋊C4—861no—
446C22×C22⋊C4C2×D4311yescharacteristic
447C22×C22⋊C4C2×D4311yescharacteristic
448C2×#99—434no—
449C2×#99—438no—
450#386—434no—
451#386—862no—
452#385—22no—
453#385—434no—
454#385—862no—
455#385C2×D4314yescomplemented
456C2×#95—21no—
457C2×#95—861no—
458C2×#95—861no—
459#342—434no—
460#342—434no—
461C43C2×#186711yescharacteristic, complemented, Sylow
462C25—431no—
463C25C22×D4311yescharacteristic
464C22×D4—434no—
465C22×D4—432no—
466C22×D4—434no—
467C22×D4—432no—
468C22×D4—862no—
469C22×D4—861no—
470C22×D4—861no—
471C22×D4—862no—
472C22×D4—861no—
473C22×D4—861no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—21no—
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4—44no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—861no—
486C23×C4—861no—
487C23×C4—861no—
488C23×C4—861no—
489C23×C4C22⋊D4311yescharacteristic
490C23×C4C22⋊D4311yescharacteristic
491C23×C4C22×D4312yes—
492C4×D4—864no—
493C4×D4—864no—
494C4×D4—864no—
495C4×D4—864no—
496C4×D4—864no—
497C4×D4—864no—
498C4×D4—864no—
499C4×D4—864no—
500#117—864no—
501#117—864no—
502C2×C4⋊C4—24no—
503C2×C4⋊C4—44no—
504C2×C4⋊C4—861no—
505C2×C4⋊C4—861no—
506C2×C4⋊C4—864no—
507C2×C4⋊C4—1724no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—434no—
515C2×C22⋊C4—432no—
516C2×C22⋊C4—432no—
517C2×C22⋊C4—432no—
518C2×C22⋊C4—432no—
519C2×C22⋊C4—864no—
520C2×C22⋊C4—864no—
521C2×C22⋊C4—861no—
522C2×C22⋊C4—861no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—862no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—861no—
529C2×C22⋊C4—862no—
530C2×C22⋊C4—862no—
531C2×C22⋊C4—864no—
532C2×C22⋊C4—861no—
533C2×C22⋊C4—1724no—
534C2×C22⋊C4C4×D4314yescomplemented
535C2×C22⋊C4C22⋊D4312yes—
536C2×C22⋊C4C22×D4312yes—
537C2×C22⋊C4C22×D4312yes—
538C2×C42—861no—
539C2×C42—861no—
540#99—4316no—
541#95—24no—
542#95—864no—
543#95—864no—
544C24—42no—
545C24—42no—
546C24—434no—
547C24—432no—
548C24—861no—
549C24—862no—
550C24—861no—
551C24—1722no—
552C24—1722no—
553C24C2×C4×D4312yes—
554C24#1062189812yes—
555C24D4×D4311yescharacteristic
556C24D4×D4311yescharacteristic
557C24D4×D4311yescharacteristic
558C24D4×D4311yescharacteristic
559C24Q8×D4312yes—
560C24#1062190212yes—
561C24C2×C22⋊D4311yescharacteristic
562C24C2×C22⋊D4311yescharacteristic
563C24C23×D4311yescharacteristic
564C2×D4—438no—
565C2×D4—434no—
566C2×D4—434no—
567C2×D4—864no—
568C2×D4—864no—
569C2×D4—864no—
570C2×D4—864no—
571C2×D4—862no—
572C2×D4—862no—
573C2×D4—864no—
574C2×D4—864no—
575C2×D4—864no—
576C2×D4—864no—
577C2×D4—864no—
578C2×D4—862no—
579C2×D4—862no—
580C2×D4—862no—
581C2×D4—862no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—434no—
610C22×C4—432no—
611C22×C4—432no—
612C22×C4—432no—
613C22×C4—864no—
614C22×C4—864no—
615C22×C4—861no—
616C22×C4—861no—
617C22×C4—862no—
618C22×C4—861no—
619C22×C4—861no—
620C22×C4—864no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—862no—
624C22×C4—862no—
625C22×C4—3442no—
626C22×C4—3442no—
627C22×C4—1722no—
628C22×C4—1722no—
629C22×C4—1722no—
630C22×C4—1722no—
631C22×C4—1722no—
632C22×C4—1722no—
633C22×C4—1722no—
634C22×C4C2×C22⋊D4312yes—
635C22×C4C2×C22⋊D4312yes—
636C4⋊C4—48no—
637C4⋊C4—864no—
638C4⋊C4—864no—
639C4⋊C4—1728no—
640C22⋊C4—24no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—434no—
647C22⋊C4—864no—
648C22⋊C4—864no—
649C22⋊C4—864no—
650C22⋊C4—862no—
651C22⋊C4—862no—
652C22⋊C4—862no—
653C22⋊C4—862no—
654C22⋊C4—862no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—1728no—
658C22⋊C4—1722no—
659C22⋊C4C2×C4×D4314yescomplemented
660C42—864no—
661C42—864no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—44no—
673C23—44no—
674C23—41no—
675C23—41no—
676C23—44no—
677C23—44no—
678C23—41no—
679C23—41no—
680C23—434no—
681C23—862no—
682C23—864no—
683C23—862no—
684C23—864no—
685C23—3441no—
686C23—3441no—
687C23—3444no—
688C23—1722no—
689C23—1722no—
690C23—1728no—
691C23—1722no—
692C23—1722no—
693C23C4⋊C4×D4312yes—
694C23C4⋊C4×D4312yes—
695C23C4×C22⋊D4312yes—
696C23C4×C22⋊D4312yes—
697C23#1306328712yes—
698C23#1306328712yes—
699C23#1306329311yescharacteristic
700C23#1306329311yescharacteristic
701C23#1306329311yescharacteristic
702C23#1306329311yescharacteristic
703C23#1306330112yes—
704C23#1306330112yes—
705C23#1306330312yes—
706C23#1306330312yes—
707C23#1306331012yes—
708C23#1306331012yes—
709C23C22×C4×D4311yescharacteristic
710C23C2×D4×D4311yescharacteristic
711C23C2×D4×D4311yescharacteristic
712C23C22×C22⋊D4311yescharacteristic
713C23C2×Q8×D4311yescharacteristic
714C23C2×#1062189811yescharacteristic
715C23C2×#1062190211yescharacteristic
716D4—864no—
717D4—864no—
718D4—864no—
719D4—864no—
720D4—868no—
721D4—868no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—48no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—434no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—864no—
749C2×C4—864no—
750C2×C4—864no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—3444no—
754C2×C4—3444no—
755C2×C4—3444no—
756C2×C4—3441no—
757C2×C4—3441no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4—1722no—
761C2×C4—1722no—
762C2×C4—1722no—
763C2×C4—1728no—
764C2×C4—1722no—
765C2×C4—1722no—
766C2×C4—1722no—
767C2×C4—1722no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—21no—
778C22—21no—
779C22—21no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—864no—
797C22—3442no—
798C22—3444no—
799C22—1724no—
800C22—1722no—
801C22—1722no—
802C22—1728no—
803C22#1458277012yes—
804C22#1458277012yes—
805C22#1458277012yes—
806C22#1458277012yes—
807C22#1458308512yes—
808C22#1458308812yes—
809C22C2×C4⋊C4×D4311yescharacteristic
810C22C2×C4×C22⋊D4311yescharacteristic
811C22C2×#1306328711yescharacteristic
812C22C2×#1306329311yescharacteristic
813C22C2×#1306330111yescharacteristic
814C22C2×#1306330311yescharacteristic
815C22C2×#1306331011yescharacteristic
816C4—44no—
817C4—44no—
818C4—42no—
819C4—42no—
820C4—864no—
821C4—3442no—
822C4—1724no—
823C4—1722no—
824C4—1722no—
825C2—21no—
826C2—21no—
827C2—21no—
828C2—22no—
829C2—21no—
830C2—21no—
831C2—21no—
832C2—22no—
833C2—22no—
834C2—1724no—
835C2#1913487414yesdirect product factor
836C2C2×#1458277011yescharacteristic
837C2C2×#1458308511yescharacteristic
838C2C2×#1458308811yescharacteristic
subgroupG/H
centerC23#13063293
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC2×C43×#385C2
socleC23×C43#120
prime radicalC23×C22⋊D43C22
cosocleC24×C43C24
hypercenterC2×#385D43
hypocenterC43C2×#1867
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C2×#14582772C2semidirect
5. #19134874C2direct (N × H)
6. C2×#14582666C2semidirect
7. C2×#14582665C2semidirect
8. C2×C43×#385C2semidirect
25. C2×#13063239C4semidirect
30. #14582772C22semidirect
33. #14582666C22semidirect
34. #14582665C22semidirect
40. C43×#385C22semidirect
83. C2×C22⋊Dic43C2×C4semidirect
96. #13063239C2×C4semidirect
119. C2×C22⋊C4×C43C2×C4semidirect
142. C23×D43C4⋊C4semidirect
188. C2×C22⋊D43C4⋊C4semidirect
208. C22×Dic43C4⋊C4semidirect
223. C22⋊C4×C43C22×C4semidirect
233. C22⋊Dic43C22×C4semidirect
295. C22×D43C2×C4⋊C4semidirect
345. C2×Dic43C2×C4⋊C4semidirect
410. C2×#385D43semidirect
423. C2×C43#1867semidirect
455. #385C2×D43semidirect
461. C43C2×#1867semidirect
534. C2×C22⋊C4C4×D43semidirect
659. C22⋊C4C2×C4×D43semidirect
835. C2#19134874direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145833722
C22×#130632392
C2×#145827782
C2×#145827722
#191348742
C2×#145826662
C2×#145826652
C2×C43×#3852
C2×#186743