Finite Group Databasebeta

← C2×#19134877 #25097679

Subgroups — C2×#19134877 #25097679

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×#14582776C211yesmaximal, characteristic
4C2×#14582774C211yesmaximal, characteristic, complemented
5C2×#14582771C211yesmaximal, characteristic, complemented
6#19134877C218yesmaximal, direct product factor
7C2×#14582665C211yesmaximal, characteristic, complemented
8C2×C43×#342C211yesmaximal, characteristic, complemented
9C23×C22⋊D43C2211yescharacteristic
10C24×Dic43C2211yescharacteristic
11#14583372—22no—
12#14583372—22no—
13#14583372—22no—
14#14583372C2214yes—
15C2×C4×C22⋊D43—21no—
16C2×C4×C22⋊D43—21no—
17C2×(C22⋊D43)⋊C4—21no—
18C2×(C22⋊D43)⋊C4—21no—
19C2×#13063281—21no—
20C22×C4⋊Dic43—21no—
21C22×Dic43⋊C4—21no—
22C22×C22⋊Dic43C2211yescharacteristic
23C22×C22⋊Dic43C2211yescharacteristic
24C22×(C2×D43)⋊C4—21no—
25C2×C22⋊C4×D43—21no—
26C2×#13063239C418yescomplemented
27C2×#13063239C2214yes—
28#14582776—22no—
29#14582776C2214yes—
30#14582774—22no—
31#14582774C2214yescomplemented
32#14582771—22no—
33#14582771C2214yescomplemented
34C2×C43⋊#95—21no—
35C2×C43⋊#95—21no—
36C2×C43⋊#95—21no—
37#14582665C2214yescomplemented
38C22×C22⋊C4×C43C2211yescharacteristic
39C22×C22⋊C4×C43C2211yescharacteristic
40C22×C22⋊C4×C43C2211yescharacteristic
41C43×#342C2214yescomplemented
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×Dic43—21no—
56C23×Dic43—21no—
57C23×Dic43—21no—
58C23×Dic43—21no—
59C23×Dic43—21no—
60C23×Dic43—44no—
61C23×Dic43D411yescharacteristic
62C23×Dic43D411yescharacteristic
63C23×Dic43D411yescharacteristic
64C23×Dic43C2312yes—
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C4×C22⋊D43—24no—
68C4×C22⋊D43—24no—
69C4×C22⋊D43—24no—
70C4×C22⋊D43—24no—
71(C22⋊D43)⋊C4—24no—
72(C22⋊D43)⋊C4—24no—
73(C22⋊D43)⋊C4—24no—
74(C22⋊D43)⋊C4—24no—
75#13063281—24no—
76#13063281—24no—
77C2×C4⋊Dic43—24no—
78C2×C4⋊Dic43—44no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4—24no—
82C2×Dic43⋊C4—44no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—22no—
89C2×C22⋊Dic43C2×C414yescomplemented
90C2×C22⋊Dic43D412yes—
91C2×C22⋊Dic43C2312yes—
92C2×C22⋊Dic43C2312yes—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95C2×(C2×D43)⋊C4—24no—
96C2×(C2×D43)⋊C4—44no—
97C22⋊C4×D43—24no—
98C22⋊C4×D43—24no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101#13063239C2×C4116yescomplemented
102C43⋊#95—24no—
103C43⋊#95—24no—
104C43⋊#95—24no—
105C25×C43C2311yescharacteristic
106C23×C4×C43—21no—
107C23×C4×C43—21no—
108C23×C4×C43D411yescharacteristic
109C23×C4×C43D411yescharacteristic
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—22no—
116C2×C22⋊C4×C43—22no—
117C2×C22⋊C4×C43—22no—
118C2×C22⋊C4×C43—21no—
119C2×C22⋊C4×C43C2×C414yescomplemented
120C2×C22⋊C4×C43D412yes—
121C2×C22⋊C4×C43C2312yes—
122C2×C22⋊C4×C43C2312yes—
123C2×C22⋊C4×C43C2312yes—
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—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—22no—
150C22×C4×C43—22no—
151C22×C4×C43—42no—
152C22×C4×C43—42no—
153C22×C4×C43—42no—
154C22×C4×C43—42no—
155C22×C4×C43—42no—
156C22×C4×C43—42no—
157C22×C4×C43—42no—
158C22×C4×C43C2×D412yes—
159C22×C4×C43C2×D412yes—
160C2×C22⋊D43—24no—
161C2×C22⋊D43—24no—
162C2×C22⋊D43—24no—
163C2×C22⋊D43—24no—
164C2×C22⋊D43—22no—
165C2×C22⋊D43—22no—
166C2×C22⋊D43—24no—
167C2×C22⋊D43—24no—
168C2×C22⋊D43—24no—
169C2×C22⋊D43—24no—
170C2×C22⋊D43—24no—
171C2×C22⋊D43—22no—
172C2×C22⋊D43—22no—
173C2×C22⋊D43—22no—
174C2×C22⋊D43—22no—
175C2×C22⋊D43C4⋊C418yescomplemented
176C2×C22⋊D43C22×C414yes—
177C2×C22⋊D43C2×Q814yes—
178C22×Dic43—24no—
179C22×Dic43—24no—
180C22×Dic43—24no—
181C22×Dic43—24no—
182C22×Dic43—21no—
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—42no—
194C22×Dic43—42no—
195C22×Dic43—42no—
196C22×Dic43—42no—
197C22×Dic43—42no—
198C22×Dic43—42no—
199C22×Dic43—42no—
200C22×Dic43—44no—
201C22×Dic43—44no—
202C22×Dic43—44no—
203C22×Dic43—44no—
204C22×Dic43—41no—
205C22×Dic43—41no—
206C22×Dic43—41no—
207C22×Dic43—41no—
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—
216C22⋊C4×C43—24no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—22no—
219C22⋊C4×C43—22no—
220C22⋊C4×C43—22no—
221C22⋊C4×C43—22no—
222C22⋊C4×C43—22no—
223C22⋊C4×C43—22no—
224C22⋊C4×C43—42no—
225C22⋊C4×C43C22×C414yescomplemented
226C22⋊Dic43—24no—
227C22⋊Dic43—22no—
228C22⋊Dic43—22no—
229C22⋊Dic43—22no—
230C22⋊Dic43—22no—
231C22⋊Dic43—22no—
232C22⋊Dic43C22×C414yescomplemented
233(C2×D43)⋊C4—24no—
234(C2×D43)⋊C4—24no—
235(C2×D43)⋊C4—48no—
236C4⋊Dic43—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—22no—
298C2×C4×C43—22no—
299C2×C4×C43—42no—
300C2×C4×C43—48no—
301C2×C4×C43—42no—
302C2×C4×C43—42no—
303C2×C4×C43—42no—
304C2×C4×C43—42no—
305C2×C4×C43—42no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43—81no—
310C2×C4×C43—81no—
311C2×C4×C43—84no—
312C22⋊D43—24no—
313C22⋊D43—24no—
314C22⋊D43—24no—
315C22⋊D43—24no—
316C22⋊D43—28no—
317C22⋊D43—28no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—24no—
321C2×Dic43—24no—
322C2×Dic43—24no—
323C2×Dic43—24no—
324C2×Dic43—24no—
325C2×Dic43—24no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—42no—
329C2×Dic43—48no—
330C2×Dic43—42no—
331C2×Dic43—42no—
332C2×Dic43—44no—
333C2×Dic43—44no—
334C2×Dic43—44no—
335C2×Dic43—42no—
336C2×Dic43—42no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43—44no—
340C2×Dic43—42no—
341C2×Dic43—42no—
342C2×Dic43—42no—
343C2×Dic43—81no—
344C2×Dic43—81no—
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—42no—
400C4×C43—82no—
401Dic43—24no—
402Dic43—44no—
403Dic43—42no—
404Dic43—44no—
405Dic43—42no—
406C2×#518—431no—
407C22×#99—431no—
408C2×#386—431no—
409C2×#385—431no—
410C2×#385—431no—
411#1867—438no—
412C2×#342—431no—
413C2×#342D4311yescharacteristic, complemented
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×C4—431no—
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—861no—
440C22×C4⋊C4—861no—
441C22×C22⋊C4—431no—
442C22×C22⋊C4—431no—
443C22×C22⋊C4—861no—
444C22×C22⋊C4—861no—
445C22×C22⋊C4C2×D4311yescharacteristic
446C22×C22⋊C4C2×D4311yescharacteristic
447C22×C22⋊C4C2×D4311yescharacteristic
448C2×#99—434no—
449C2×#99—438no—
450#386—434no—
451#386—862no—
452#385—434no—
453#385—434no—
454#385—862no—
455#385—862no—
456C2×#95—861no—
457C2×#95—861no—
458C2×#95—861no—
459#342—434no—
460#342C2×D4314yescomplemented
461C43C2×#186711yescharacteristic, complemented, Sylow
462C25—431no—
463C25C22×D4311yescharacteristic
464C22×D4—434no—
465C22×D4—432no—
466C22×D4—434no—
467C22×D4—432no—
468C22×D4—861no—
469C22×D4—861no—
470C22×D4—862no—
471C22×D4—861no—
472C22×D4—861no—
473C22×D4—862no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—432no—
480C23×C4—861no—
481C23×C4—861no—
482C23×C4—861no—
483C23×C4—861no—
484C23×C4—861no—
485C23×C4—861no—
486C23×C4—861no—
487C23×C4—861no—
488C23×C4—861no—
489C23×C4—1724no—
490C23×C4D17211yescharacteristic
491C23×C4D17211yescharacteristic
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—861no—
503C2×C4⋊C4—861no—
504C2×C4⋊C4—864no—
505C2×C4⋊C4—864no—
506C2×C4⋊C4—1724no—
507C2×C4⋊C4—1724no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—434no—
518C2×C22⋊C4—432no—
519C2×C22⋊C4—432no—
520C2×C22⋊C4—432no—
521C2×C22⋊C4—864no—
522C2×C22⋊C4—864no—
523C2×C22⋊C4—861no—
524C2×C22⋊C4—861no—
525C2×C22⋊C4—861no—
526C2×C22⋊C4—861no—
527C2×C22⋊C4—861no—
528C2×C22⋊C4—862no—
529C2×C22⋊C4—861no—
530C2×C22⋊C4—861no—
531C2×C22⋊C4—864no—
532C2×C22⋊C4—1724no—
533C2×C22⋊C4C4×D4314yescomplemented
534C2×C22⋊C4D17212yes—
535C2×C22⋊C4C22×D4312yes—
536C2×C22⋊C4C22×D4312yes—
537C2×C22⋊C4C22×D4312yes—
538C2×C42—861no—
539C2×C42—861no—
540#99—4316no—
541#95—864no—
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—
554C24C2×D17211yescharacteristic
555C24C2×D17211yescharacteristic
556C24#1062189812yes—
557C24D4×D4311yescharacteristic
558C24D4×D4311yescharacteristic
559C24D4×D4311yescharacteristic
560C24D4×D4311yescharacteristic
561C24#1062190012yes—
562C24Q8×D4312yes—
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—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—434no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—864no—
601C22×C4—864no—
602C22×C4—861no—
603C22×C4—861no—
604C22×C4—862no—
605C22×C4—861no—
606C22×C4—861no—
607C22×C4—864no—
608C22×C4—864no—
609C22×C4—864no—
610C22×C4—864no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—3442no—
618C22×C4—3442no—
619C22×C4—1724no—
620C22×C4—1724no—
621C22×C4—1724no—
622C22×C4—1724no—
623C22×C4—1722no—
624C22×C4—1722no—
625C22×C4—1722no—
626C22×C4—1722no—
627C22×C4—1722no—
628C22×C4—1722no—
629C22×C4—1722no—
630C22×C4—1721no—
631C22×C4—1721no—
632C22×C4—1721no—
633C22×C4—1721no—
634C22×C4C2×D17212yes—
635C22×C4C2×D17212yes—
636C4⋊C4—864no—
637C4⋊C4—864no—
638C4⋊C4—1728no—
639C4⋊C4—1728no—
640C22⋊C4—24no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—42no—
649C22⋊C4—434no—
650C22⋊C4—864no—
651C22⋊C4—864no—
652C22⋊C4—864no—
653C22⋊C4—862no—
654C22⋊C4—862no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—862no—
658C22⋊C4—1728no—
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—41no—
674C23—44no—
675C23—41no—
676C23—41no—
677C23—44no—
678C23—44no—
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—
695C23(C22⋊D43)⋊C412yes—
696C23(C22⋊D43)⋊C412yes—
697C23C4×D17212yes—
698C23C4×D17212yes—
699C23#1306329511yescharacteristic
700C23#1306329511yescharacteristic
701C23#1306329511yescharacteristic
702C23#1306329511yescharacteristic
703C23#1306330312yes—
704C23#1306330312yes—
705C23#1306330512yes—
706C23#1306330512yes—
707C23#1306330712yes—
708C23#1306330712yes—
709C23C22×C4×D4311yescharacteristic
710C23C2×D4×D4311yescharacteristic
711C23C2×D4×D4311yescharacteristic
712C23C22×D17211yescharacteristic
713C23C2×Q8×D4311yescharacteristic
714C23C2×#1062190011yescharacteristic
715C23C2×#1062189811yescharacteristic
716D4—864no—
717D4—864no—
718D4—864no—
719D4—864no—
720D4—868no—
721D4—868no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—84no—
738C2×C4—434no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—864no—
742C2×C4—864no—
743C2×C4—864no—
744C2×C4—864no—
745C2×C4—864no—
746C2×C4—864no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—3444no—
750C2×C4—3444no—
751C2×C4—3441no—
752C2×C4—3441no—
753C2×C4—1722no—
754C2×C4—1722no—
755C2×C4—1722no—
756C2×C4—1722no—
757C2×C4—1724no—
758C2×C4—1724no—
759C2×C4—1724no—
760C2×C4—1722no—
761C2×C4—1728no—
762C2×C4—1724no—
763C2×C4—1722no—
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#1458277312yes—
804C22#1458277312yes—
805C22#1458277312yes—
806C22#1458277312yes—
807C22#1458308712yes—
808C22#1458309012yes—
809C22C2×C4⋊C4×D4311yescharacteristic
810C22C2×(C22⋊D43)⋊C411yescharacteristic
811C22C2×C4×D17211yescharacteristic
812C22C2×#1306329511yescharacteristic
813C22C2×#1306330311yescharacteristic
814C22C2×#1306330511yescharacteristic
815C22C2×#1306330711yescharacteristic
816C4—44no—
817C4—42no—
818C4—42no—
819C4—82no—
820C4—864no—
821C4—1724no—
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#1913487714yesdirect product factor
836C2C2×#1458277311yescharacteristic
837C2C2×#1458308711yescharacteristic
838C2C2×#1458309011yescharacteristic
subgroupG/H
centerC23#13063295
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC2×C43×#342C2
socleC23×C43#120
prime radicalC23×C22⋊D43C22
cosocleC24×C43C24
hypercenterC2×#342D43
hypocenterC43C2×#1867
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. C2×#14582774C2semidirect
5. C2×#14582771C2semidirect
6. #19134877C2direct (N × H)
7. C2×#14582665C2semidirect
8. C2×C43×#342C2semidirect
26. C2×#13063239C4semidirect
31. #14582774C22semidirect
33. #14582771C22semidirect
37. #14582665C22semidirect
41. C43×#342C22semidirect
89. C2×C22⋊Dic43C2×C4semidirect
101. #13063239C2×C4semidirect
119. C2×C22⋊C4×C43C2×C4semidirect
142. C23×D43C4⋊C4semidirect
175. C2×C22⋊D43C4⋊C4semidirect
208. C22×Dic43C4⋊C4semidirect
225. C22⋊C4×C43C22×C4semidirect
232. C22⋊Dic43C22×C4semidirect
295. C22×D43C2×C4⋊C4semidirect
345. C2×Dic43C2×C4⋊C4semidirect
413. C2×#342D43semidirect
423. C2×C43#1867semidirect
460. #342C2×D43semidirect
461. C43C2×#1867semidirect
533. C2×C22⋊C4C4×D43semidirect
659. C22⋊C4C2×C4×D43semidirect
835. C2#19134877direct (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×#145827762
C2×#145827742
C2×#145827712
#191348772
C2×#145826652
C2×C43×#3422
C2×#186743