Finite Group Databasebeta

← C2×#19144222 #25963752

Subgroups — C2×#19144222 #25963752

Order 11008.

2898 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063357C211yesmaximal, characteristic, complemented
2C23×#10621872C211yesmaximal, characteristic, complemented
3C2×#14583412C211yesmaximal, characteristic
4C2×C22⋊Q8×D43C211yesmaximal, characteristic, complemented
5#19144222C2116yesmaximal, direct product factor
6C2×#14583156C211yesmaximal, characteristic, complemented
7C2×#14583154C211yesmaximal, characteristic, complemented
8C2×#14583148C211yesmaximal, characteristic, complemented
9C2×#14583146C211yesmaximal, characteristic, complemented
10C2×#14583138C211yesmaximal, characteristic, complemented
11C2×#14583130C211yesmaximal, characteristic, complemented
12C2×#14583128C211yesmaximal, characteristic, complemented
13C2×#14582940C211yesmaximal, characteristic, complemented
14C2×#14582899C211yesmaximal, characteristic, complemented
15C2×#14582906C211yesmaximal, characteristic, complemented
16C2×C43×#467C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063357—28no—
21C2×#13063357C2218yescomplemented
22C22×#10621885C2211yescharacteristic, complemented
23C22×#10621873C2211yescharacteristic, complemented
24C22×#10621884C2211yescharacteristic, complemented
25C22×#10621872—28no—
26C22×#10621872C2211yescharacteristic
27C22×#10621872C2211yescharacteristic
28C22×#10621872C2211yescharacteristic
29C22×#10621872C2211yescharacteristic
30C22×#10621872C2218yescomplemented
31C23×C43⋊C8C2211yescharacteristic
32#14583412—24no—
33#14583412C2218yes—
34C2×#13063310—21no—
35C2×#13063305C2211yescharacteristic
36C2×#13063304C2211yescharacteristic
37C2×#13063303—21no—
38C2×#13063302—21no—
39C2×#13063301C2211yescharacteristic
40C2×#13063301C2211yescharacteristic
41C22⋊Q8×D43—24no—
42C22⋊Q8×D43C2218yescomplemented
43C2×#13063300C2211yescharacteristic
44C2×#13063299C2211yescharacteristic
45C2×#13063295—21no—
46C2×#13063287—21no—
47C2×(C22⋊D43)⋊C4—21no—
48C2×#13063283C2211yescharacteristic
49C2×C4⋊C4×D43—21no—
50C2×C4⋊C4×D43C2211yescharacteristic
51C2×C22⋊C4×D43—21no—
52#14583156C2218yescomplemented
53#14583154C2218yescomplemented
54#14583148C2218yescomplemented
55#14583146C2218yescomplemented
56#14583138C2218yescomplemented
57#14583130C2218yescomplemented
58#14583128C2218yescomplemented
59#14582940C2218yescomplemented
60C2×#13063258C2211yescharacteristic, complemented
61C2×#13063257C2211yescharacteristic, complemented
62C2×#13063256C2211yescharacteristic, complemented
63#14582906C2218yescomplemented
64#14582899C2218yescomplemented
65C2×#13063250C2211yescharacteristic, complemented
66C2×#13063249C2211yescharacteristic, complemented
67C2×#13063249C2211yescharacteristic, complemented
68C2×#13063248C2211yescharacteristic, complemented
69C2×#13063247C2211yescharacteristic, complemented
70C2×#13063245C2211yescharacteristic, complemented
71C22×Q16×C43C2211yescharacteristic, complemented
72C23×C8×C43C2211yescharacteristic
73C2×C22⋊Q8×C43C2211yescharacteristic
74C2×C22⋊Q8×C43C2211yescharacteristic
75C43×#467C2218yescomplemented
76C2×#107×C43C2211yescharacteristic, complemented
77C2×#103×C43C2211yescharacteristic, complemented
78C2×#103×C43C2211yescharacteristic, complemented
79C24×D43D411yescharacteristic
80C2×#10621902—22no—
81C2×#10621902—24no—
82C2×#10621902—24no—
83C2×#10621902C2314yes—
84C22×Dic86—21no—
85C22×Dic86C2311yescharacteristic
86C2×Q8×D43—22no—
87C2×Q8×D43—24no—
88C2×Q8×D43—24no—
89C2×Q8×D43C2314yes—
90C22×D172—21no—
91C22×D172—21no—
92C22×D172C2311yescharacteristic
93C22×C22⋊D43—21no—
94C23×Dic43D411yescharacteristic
95C22×C4×D43—24no—
96C22×C4×D43—24no—
97C22×C4×D43—21no—
98C22×C4×D43—21no—
99C22×C4×D43—21no—
100C22×C4×D43D411yescharacteristic
101C22×C4×D43D411yescharacteristic
102C22×C4×D43D414yes—
103C22×C4×D43C2311yescharacteristic
104C22×C4×D43C2314yes—
105C22×C4×D43C2311yescharacteristic
106#13063357—232no—
107C2×#10621885—24no—
108C2×#10621885C2314yescomplemented
109C2×#10621873—24no—
110C2×#10621873C2314yescomplemented
111C2×#10621884—24no—
112C2×#10621884C2314yescomplemented
113C2×#10621872—24no—
114C2×#10621872—24no—
115C2×#10621872—24no—
116C2×#10621872—232no—
117C2×#10621872D418yescomplemented
118C2×#10621872C2314yes—
119C2×#10621872C2314yes—
120C2×#10621872C2314yes—
121C2×#10621872C2314yes—
122C22×C43⋊C8—24no—
123C22×C43⋊C8C2314yes—
124C22×C43⋊C8C2311yescharacteristic
125C22×C43⋊C8C2311yescharacteristic
126#13063310—28no—
127#13063305—22no—
128#13063305C2314yes—
129#13063304—22no—
130#13063304C2314yes—
131#13063303—28no—
132#13063302—28no—
133#13063301—22no—
134#13063301—22no—
135#13063301C2314yes—
136#13063301C2314yes—
137#13063300—22no—
138#13063300C2314yes—
139#13063299—22no—
140#13063299C2314yes—
141#13063295—28no—
142#13063287—28no—
143(C22⋊D43)⋊C4—28no—
144#13063283—22no—
145#13063283C2314yes—
146C2×C4⋊Dic43—21no—
147C2×C4⋊Dic43C2311yescharacteristic
148C2×C4⋊Dic43C2311yescharacteristic
149C2×Dic43⋊C4—21no—
150C2×Dic43⋊C4—21no—
151C2×Dic43⋊C4—21no—
152C2×Dic43⋊C4—21no—
153C4⋊C4×D43—28no—
154C4⋊C4×D43—22no—
155C4⋊C4×D43C2314yes—
156C2×C22⋊Dic43—21no—
157C2×(C2×D43)⋊C4—21no—
158C2×(C2×D43)⋊C4—21no—
159C2×(C2×D43)⋊C4—21no—
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C22⋊C4×D43—28no—
164C2×C4×Dic43—21no—
165#13063258C2314yescomplemented
166#13063257C2314yescomplemented
167#13063256C2314yescomplemented
168#13063250C2314yescomplemented
169#13063249C2314yescomplemented
170#13063249C2314yescomplemented
171#13063248C2314yescomplemented
172#13063247C2314yescomplemented
173#13063245C2314yescomplemented
174C22×Q8×C43C2311yescharacteristic
175C22×Q8×C43C2311yescharacteristic
176C23×C4×C43C2311yescharacteristic
177C2×Q16×C43—24no—
178C2×Q16×C43C2314yescomplemented
179C22×C8×C43—24no—
180C22×C8×C43C2314yes—
181C22×C8×C43C2311yescharacteristic
182C22×C8×C43C2311yescharacteristic
183C22⋊Q8×C43—22no—
184C22⋊Q8×C43—22no—
185C22⋊Q8×C43C2314yes—
186C22⋊Q8×C43C2314yes—
187C2×C4⋊C4×C43—21no—
188C2×C4⋊C4×C43—21no—
189C2×C4⋊C4×C43C2311yescharacteristic
190C2×C4⋊C4×C43C2311yescharacteristic
191C2×C22⋊C4×C43—21no—
192C2×C22⋊C4×C43—21no—
193#107×C43C2314yescomplemented
194#103×C43C2314yescomplemented
195#103×C43C2314yescomplemented
196C24×C43C2×D411yescharacteristic
197C23×D43—24no—
198C23×D43—24no—
199C23×D43—21no—
200C23×D43—42no—
201C23×D43C2×D411yescharacteristic
202C23×D43C2×D414yes—
203C23×D43C2×D411yescharacteristic
204C2×Q8×C43—21no—
205C2×Q8×C43—21no—
206C2×Q8×C43—22no—
207C2×Q8×C43—22no—
208C2×Q8×C43—22no—
209C2×Q8×C43—22no—
210C2×Q8×C43C2412yes—
211C2×Q8×C43C2412yes—
212C22×C4×C43—22no—
213C22×C4×C43—22no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43C2×D411yescharacteristic
219C22×C4×C43C2×D412yes—
220C22×C4×C43C2412yes—
221C22×C4×C43C2411yescharacteristic
222C2×C22⋊D43—24no—
223C2×C22⋊D43—44no—
224C22×Dic43—24no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43C2×D411yescharacteristic
229C22×Dic43C2×D414yes—
230C22×Dic43C2×D411yescharacteristic
231#10621902—28no—
232#10621902—28no—
233#10621902—48no—
234Q8×D43—28no—
235Q8×D43—28no—
236Q8×D43—48no—
237C2×D172—21no—
238C2×D172—24no—
239C2×D172—24no—
240C2×D172—22no—
241C2×D172—22no—
242C2×D172—44no—
243C2×D172—44no—
244C2×D172C2412yes—
245C2×C4×D43—22no—
246C2×C4×D43—22no—
247C2×C4×D43—24no—
248C2×C4×D43—216no—
249C2×C4×D43—28no—
250C2×C4×D43—28no—
251C2×C4×D43—24no—
252C2×C4×D43—24no—
253C2×C4×D43—24no—
254C2×C4×D43—24no—
255C2×C4×D43—44no—
256C2×C4×D43—44no—
257C2×C4×D43—44no—
258C2×C4×D43C2×D414yes—
259C2×C4×D43C2×D414yes—
260C2×C4×D43C2×D414yes—
261C2×C4×D43C2×D412yes—
262C2×C4×D43C2×D412yes—
263C2×C4×D43#4114yes—
264C2×C4×D43C2412yes—
265C2×C4×D43C2412yes—
266C2×Dic86—22no—
267C2×Dic86—22no—
268C2×Dic86—21no—
269C2×Dic86—24no—
270C2×Dic86—44no—
271C2×Dic86C2412yes—
272Q16×C43—28no—
273C2×C8×C43—22no—
274C2×C8×C43—28no—
275C2×C8×C43C2×D414yes—
276C2×C8×C43C2412yes—
277C2×C8×C43C2412yes—
278C4⋊C4×C43—24no—
279C4⋊C4×C43—24no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43C2412yes—
283C4⋊C4×C43C2412yes—
284C22⋊C4×C43—24no—
285C22⋊C4×C43—24no—
286C22⋊Dic43—24no—
287#10621885—28no—
288#10621884—28no—
289(C2×D43)⋊C4—24no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4—24no—
292(C2×D43)⋊C4—24no—
293(C2×D43)⋊C4—24no—
294(C2×D43)⋊C4—24no—
295C4⋊Dic43—21no—
296C4⋊Dic43—21no—
297C4⋊Dic43—24no—
298C4⋊Dic43C2412yes—
299C4⋊Dic43C2412yes—
300Dic43⋊C4—24no—
301Dic43⋊C4—24no—
302Dic43⋊C4—24no—
303Dic43⋊C4—24no—
304C4×Dic43—24no—
305C2×C43⋊C8—22no—
306C2×C43⋊C8—28no—
307C2×C43⋊C8C2×D414yes—
308C2×C43⋊C8C2412yes—
309C2×C43⋊C8C2412yes—
310#10621873—28no—
311#10621872—28no—
312#10621872—28no—
313#10621872—28no—
314#10621872C2×D4116yescomplemented
315C23×C43—22no—
316C23×C43—22no—
317C23×C43#13714yescomplemented
318C23×C43C22×D412yes—
319C23×C43C22×D411yescharacteristic
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—22no—
324C22×D43—28no—
325C22×D43—22no—
326C22×D43—28no—
327C22×D43—22no—
328C22×D43—44no—
329C22×D43—416no—
330C22×D43—42no—
331C22×D43—42no—
332C22×D43—42no—
333C22×D43#12114yes—
334C22×D43C22×D412yes—
335C22×D43C22×D412yes—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—22no—
339Q8×C43—22no—
340Q8×C43—42no—
341Q8×C43—42no—
342C2×C4×C43—22no—
343C2×C4×C43—24no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—42no—
351C2×C4×C43—42no—
352C2×C4×C43—42no—
353C2×C4×C43—42no—
354C2×C4×C43C22×D412yes—
355C2×C4×C43C22×D411yescharacteristic
356C2×C4×C43C22×D412yes—
357C2×C4×C43C2×#4112yes—
358C2×C4×C43C2511yescharacteristic
359C22⋊D43—48no—
360C2×Dic43—22no—
361C2×Dic43—28no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—42no—
366C2×Dic43—42no—
367C2×Dic43—42no—
368C2×Dic43#12114yes—
369C2×Dic43C22×D412yes—
370C2×Dic43C22×D412yes—
371D172—22no—
372D172—22no—
373D172—48no—
374D172—48no—
375D172—42no—
376C4×D43—28no—
377C4×D43—24no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—28no—
381C4×D43—48no—
382C4×D43—48no—
383C4×D43—48no—
384C4×D43#12118yes—
385C4×D43C22×D414yes—
386C4×D43C2×#4114yes—
387Dic86—22no—
388Dic86—22no—
389Dic86—42no—
390Dic86—48no—
391C8×C43—22no—
392C8×C43C22×D414yes—
393C43⋊C8—22no—
394C43⋊C8C22×D414yes—
395C2×#3056—431nomaximal, Sylow
396C22×C43—22no—
397C22×C43—28no—
398C22×C43—22no—
399C22×C43C2×#12112yes—
400C22×C43C2×#13712yes—
401C22×C43C2×#13714yescomplemented
402C22×C43#57512yes—
403C22×C43C23×D411yescharacteristic
404C2×D43—28no—
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—416no—
411C2×D43—44no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—84no—
416C2×D43C2×#12114yes—
417C4×C43—22no—
418C4×C43—42no—
419C4×C43—42no—
420C4×C43—42no—
421C4×C43—42no—
422C4×C43C2×#12112yes—
423C4×C43C23×D411yescharacteristic
424C4×C43C22×#4111yescharacteristic
425Dic43—22no—
426Dic43—42no—
427Dic43—42no—
428Dic43—42no—
429Dic43C2×#12114yes—
430C22×#137—431no—
431C23×M16—431no—
432C2×#525—431no—
433C22×C22⋊Q8—431no—
434#3056—4316no—
435C2×#470—431no—
436C2×#470—431no—
437C2×#468—431no—
438C2×#468—431no—
439C2×#467—431no—
440C2×#467D4311yescharacteristic, complemented
441C2×#465—431no—
442C2×#465—431no—
443C2×#428—431no—
444C2×#417—431no—
445C2×#419—431no—
446C2×C43—24no—
447C2×C43#305614yescomplemented
448C2×C43C22×#12111yescharacteristic
449C2×C43C22×#13711yescharacteristic
450C2×C43C2×#57511yescharacteristic
451D43—24no—
452D43—42no—
453D43—82no—
454C22×#41—431no—
455C23×Q8—431no—
456C24×C4—431no—
457C2×#137—438no—
458C2×#137—868no—
459C22×Q16—431no—
460C22×Q16C2×D4311yescharacteristic, complemented
461C22×SD16—431no—
462C22×SD16—431no—
463C22×M16—431no—
464C22×M16—431no—
465C22×M16—431no—
466C22×M16—431no—
467C22×M16—438no—
468C22×M16—868no—
469C23×C8—431no—
470C23×C8C2×D4311yescharacteristic
471#525—438no—
472#525—864no—
473C2×#123—861no—
474C2×C22⋊Q8—431no—
475C2×C22⋊Q8—431no—
476C2×C22⋊Q8—431no—
477C2×C22⋊Q8—438no—
478C2×C22⋊Q8—431no—
479C2×C22⋊Q8—861no—
480C2×C22⋊Q8—861no—
481C2×C22⋊Q8—864no—
482C2×C22⋊Q8C2×D4311yescharacteristic
483C2×C22⋊Q8C2×D4311yescharacteristic
484C2×#121—431no—
485C2×#121—431no—
486C2×#120—861no—
487C2×C4×D4—861no—
488C2×C4×D4—861no—
489C2×#117—431no—
490C22×C4⋊C4—431no—
491C22×C4⋊C4—861no—
492C22×C22⋊C4—861no—
493#470—438no—
494#470—438no—
495#468—438no—
496#468—438no—
497#467—438no—
498#467C2×D4318yescomplemented
499#465—438no—
500#465—438no—
501#428—438no—
502C2×#107—431no—
503C2×#107C2×D4311yescharacteristic, complemented
504C2×#106—431no—
505C2×#106—431no—
506#419—438no—
507#417—438no—
508C2×#103—431no—
509C2×#103—431no—
510C2×#103—431no—
511C2×#103—431no—
512C2×#103C2×D4311yescharacteristic, complemented
513C2×#103C2×D4311yescharacteristic, complemented
514C2×#102—431no—
515C2×#102—431no—
516C43C2×#305611yescharacteristic, complemented, Sylow
517C25—431no—
518C2×#41—434no—
519C2×#41—862no—
520C2×#41—864no—
521C2×#41—864no—
522C22×Q8—434no—
523C22×Q8—431no—
524C22×Q8—861no—
525C22×Q8—862no—
526C22×Q8—864no—
527C22×Q8—864no—
528C22×Q8C22×D4311yescharacteristic
529C22×Q8C22×D4311yescharacteristic
530C22×D4—431no—
531C22×D4—861no—
532C22×D4—861no—
533C22×D4—861no—
534C23×C4—431no—
535C23×C4—431no—
536C23×C4—431no—
537C23×C4—431no—
538C23×C4—434no—
539C23×C4—431no—
540C23×C4—434no—
541C23×C4—864no—
542C23×C4—864no—
543C23×C4—861no—
544C23×C4—861no—
545C23×C4—861no—
546C23×C4C22×D4311yescharacteristic
547#137—8632no—
548C2×Q16—24no—
549C2×Q16—434no—
550C2×Q16—864no—
551C2×Q16C22×D4314yescomplemented
552C2×SD16—434no—
553C2×SD16—434no—
554C2×SD16—864no—
555C2×SD16—864no—
556C2×M16—438no—
557C2×M16—434no—
558C2×M16—434no—
559C2×M16—434no—
560C2×M16—434no—
561C2×M16—864no—
562C2×M16—8632no—
563C2×M16—864no—
564C2×M16—864no—
565C22×C8—24no—
566C22×C8—431no—
567C22×C8—431no—
568C22×C8—434no—
569C22×C8—864no—
570C22×C8C22×D4311yescharacteristic
571C22×C8C22×D4314yes—
572C22×C8C22×D4311yescharacteristic
573#123—868no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—434no—
577C22⋊Q8—434no—
578C22⋊Q8—434no—
579C22⋊Q8—434no—
580C22⋊Q8—868no—
581C22⋊Q8—868no—
582C22⋊Q8—862no—
583C22⋊Q8—862no—
584C22⋊Q8—862no—
585C22⋊Q8—862no—
586C22⋊Q8C22×D4314yes—
587C22⋊Q8C22×D4314yes—
588#121—434no—
589#121—434no—
590#121—862no—
591#121—862no—
592#120—868no—
593C4×D4—868no—
594C4×D4—868no—
595#117—434no—
596#117—862no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—434no—
602C2×C4⋊C4—862no—
603C2×C4⋊C4—868no—
604C2×C4⋊C4—861no—
605C2×C4⋊C4—861no—
606C2×C4⋊C4—861no—
607C2×C4⋊C4—861no—
608C2×C4⋊C4—861no—
609C2×C4⋊C4C22×D4311yescharacteristic
610C2×C4⋊C4C22×D4311yescharacteristic
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—868no—
614C2×C22⋊C4—861no—
615C2×C22⋊C4—861no—
616C2×C22⋊C4—861no—
617C2×C22⋊C4—861no—
618C2×C22⋊C4—861no—
619C2×C22⋊C4—861no—
620C2×C22⋊C4—861no—
621C2×C42—861no—
622#107—434no—
623#107C22×D4314yescomplemented
624#106—434no—
625#106—434no—
626#103—434no—
627#103—434no—
628#103—434no—
629#103—434no—
630#103C22×D4314yescomplemented
631#103C22×D4314yescomplemented
632#102—434no—
633#102—434no—
634C24—431no—
635C24—431no—
636C24—434no—
637C24—864no—
638C24—864no—
639C24—861no—
640C24—1722no—
641C24D4×D4311yescharacteristic
642#41—868no—
643#41—868no—
644#41—1728no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—22no—
650C2×Q8—22no—
651C2×Q8—432no—
652C2×Q8—864no—
653C2×Q8—868no—
654C2×Q8—868no—
655C2×Q8—861no—
656C2×Q8—862no—
657C2×Q8—862no—
658C2×Q8—1724no—
659C2×Q8—1728no—
660C2×Q8C23×D4312yes—
661C2×Q8C23×D4312yes—
662C2×D4—432no—
663C2×D4—864no—
664C2×D4—864no—
665C2×D4—864no—
666C2×D4—862no—
667C2×D4—861no—
668C2×D4—862no—
669C2×D4—1724no—
670C2×D4—1724no—
671C2×D4—1724no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—431no—
679C22×C4—432no—
680C22×C4—434no—
681C22×C4—434no—
682C22×C4—432no—
683C22×C4—434no—
684C22×C4—431no—
685C22×C4—434no—
686C22×C4—434no—
687C22×C4—432no—
688C22×C4—432no—
689C22×C4—868no—
690C22×C4—864no—
691C22×C4—8616no—
692C22×C4—868no—
693C22×C4—864no—
694C22×C4—864no—
695C22×C4—864no—
696C22×C4—864no—
697C22×C4—864no—
698C22×C4—862no—
699C22×C4—862no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—1724no—
704C22×C4—1724no—
705C22×C4—1724no—
706C22×C4D4×D4312yes—
707C22×C4D4×D4311yescharacteristic
708C22×C4C23×D4312yes—
709C22×C4C23×D4311yescharacteristic
710Q16—28no—
711Q16—868no—
712SD16—868no—
713SD16—868no—
714M16—4316no—
715M16—868no—
716M16—868no—
717M16—868no—
718C2×C8—22no—
719C2×C8—28no—
720C2×C8—434no—
721C2×C8—432no—
722C2×C8—432no—
723C2×C8—868no—
724C2×C8—862no—
725C2×C8D4×D4314yes—
726C2×C8C23×D4312yes—
727C2×C8C23×D4312yes—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—432no—
733C4⋊C4—432no—
734C4⋊C4—864no—
735C4⋊C4—864no—
736C4⋊C4—864no—
737C4⋊C4—864no—
738C4⋊C4—861no—
739C4⋊C4—861no—
740C4⋊C4—864no—
741C4⋊C4C23×D4312yes—
742C4⋊C4C23×D4312yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—864no—
746C22⋊C4—864no—
747C22⋊C4—864no—
748C22⋊C4—864no—
749C22⋊C4—864no—
750C22⋊C4—864no—
751C22⋊C4—864no—
752C42—864no—
753C23—22no—
754C23—22no—
755C23—434no—
756C23—432no—
757C23—432no—
758C23—868no—
759C23—862no—
760C23—862no—
761C23—862no—
762C23—862no—
763C23—868no—
764C23—862no—
765C23—862no—
766C23—1724no—
767C23—17216no—
768C23—1722no—
769C23—1722no—
770C23—1722no—
771C23#1306335714yescomplemented
772C23C2×D4×D4312yes—
773C23C2×D4×D4311yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—22no—
777Q8—22no—
778Q8—42no—
779Q8—42no—
780Q8—862no—
781Q8—862no—
782Q8—1728no—
783Q8—1722no—
784D4—862no—
785D4—862no—
786D4—1728no—
787D4—1728no—
788D4—1728no—
789D4—1722no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—434no—
803C2×C4—432no—
804C2×C4—438no—
805C2×C4—434no—
806C2×C4—434no—
807C2×C4—432no—
808C2×C4—868no—
809C2×C4—868no—
810C2×C4—868no—
811C2×C4—862no—
812C2×C4—864no—
813C2×C4—862no—
814C2×C4—862no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—1728no—
819C2×C4—1728no—
820C2×C4—1728no—
821C2×C4—1722no—
822C2×C4—1722no—
823C2×C4—1722no—
824C2×C4C2×D4×D4312yes—
825C2×C4C2×D4×D4311yescharacteristic
826C2×C4C2×D4×D4312yes—
827C2×C4#41×D4312yes—
828C2×C4C24×D4311yescharacteristic
829C8—22no—
830C8—434no—
831C8—862no—
832C8C2×D4×D4314yes—
833C22—22no—
834C22—28no—
835C22—22no—
836C22—434no—
837C22—862no—
838C22—862no—
839C22—868no—
840C22—862no—
841C22—862no—
842C22—862no—
843C22—3444no—
844C22—17216no—
845C22—1722no—
846C22—1722no—
847C22—1722no—
848C22—1724no—
849C22#121×D4312yes—
850C22C2×#1306335712yes—
851C22C2×#1306335714yescomplemented
852C22#1458369612yes—
853C22C22×D4×D4311yescharacteristic
854C4—22no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—434no—
860C4—862no—
861C4—1722no—
862C4—1722no—
863C4—1722no—
864C4#121×D4312yes—
865C4C22×D4×D4311yescharacteristic
866C4C2×#41×D4311yescharacteristic
867C2—24no—
868C2—864no—
869C2—3442no—
870C2—1722no—
871C2#1914422214yesdirect product factor
872C2C2×#121×D4311yescharacteristic
873C2C22×#1306335711yescharacteristic
874C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#467C2
socleC23×C43C22×D4
prime radicalC2×#14583412C2
hypercenterC2×#467D43
hypocenterC43C2×#3056
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#13063357C2semidirect
2. C23×#10621872C2semidirect
4. C2×C22⋊Q8×D43C2semidirect
5. #19144222C2direct (N × H)
6. C2×#14583156C2semidirect
7. C2×#14583154C2semidirect
8. C2×#14583148C2semidirect
9. C2×#14583146C2semidirect
10. C2×#14583138C2semidirect
11. C2×#14583130C2semidirect
12. C2×#14583128C2semidirect
13. C2×#14582940C2semidirect
14. C2×#14582899C2semidirect
15. C2×#14582906C2semidirect
16. C2×C43×#467C2semidirect
21. C2×#13063357C22semidirect
22. C22×#10621885C22semidirect
23. C22×#10621873C22semidirect
24. C22×#10621884C22semidirect
30. C22×#10621872C22semidirect
42. C22⋊Q8×D43C22semidirect
52. #14583156C22semidirect
53. #14583154C22semidirect
54. #14583148C22semidirect
55. #14583146C22semidirect
56. #14583138C22semidirect
57. #14583130C22semidirect
58. #14583128C22semidirect
59. #14582940C22semidirect
60. C2×#13063258C22semidirect
61. C2×#13063257C22semidirect
62. C2×#13063256C22semidirect
63. #14582906C22semidirect
64. #14582899C22semidirect
65. C2×#13063250C22semidirect
66. C2×#13063249C22semidirect
67. C2×#13063249C22semidirect
68. C2×#13063248C22semidirect
69. C2×#13063247C22semidirect
70. C2×#13063245C22semidirect
71. C22×Q16×C43C22semidirect
75. C43×#467C22semidirect
76. C2×#107×C43C22semidirect
77. C2×#103×C43C22semidirect
78. C2×#103×C43C22semidirect
108. C2×#10621885C23semidirect
110. C2×#10621873C23semidirect
112. C2×#10621884C23semidirect
117. C2×#10621872D4semidirect
165. #13063258C23semidirect
166. #13063257C23semidirect
167. #13063256C23semidirect
168. #13063250C23semidirect
169. #13063249C23semidirect
170. #13063249C23semidirect
171. #13063248C23semidirect
172. #13063247C23semidirect
173. #13063245C23semidirect
178. C2×Q16×C43C23semidirect
193. #107×C43C23semidirect
194. #103×C43C23semidirect
195. #103×C43C23semidirect
314. #10621872C2×D4semidirect
317. C23×C43#137semidirect
401. C22×C43C2×#137semidirect
440. C2×#467D43semidirect
447. C2×C43#3056semidirect
460. C22×Q16C2×D43semidirect
498. #467C2×D43semidirect
503. C2×#107C2×D43semidirect
512. C2×#103C2×D43semidirect
513. C2×#103C2×D43semidirect
516. C43C2×#3056semidirect
551. C2×Q16C22×D43semidirect
623. #107C22×D43semidirect
630. #103C22×D43semidirect
631. #103C22×D43semidirect
771. C23#13063357semidirect
851. C22C2×#13063357semidirect
871. C2#19144222direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633572
C23×#106218722
C2×#145834122
C2×C22⋊Q8×D432
#191442222
C2×#145831562
C2×#145831542
C2×#145831482
C2×#145831462
C2×#145831382
C2×#145831302
C2×#145831282
C2×#145829402
C2×#145828992
C2×#145829062
C2×C43×#4672
C2×#305643