Finite Group Databasebeta

← C2×#19146098 #25971571

Subgroups — C2×#19146098 #25971571

Order 11008.

2882 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063357C211yesmaximal, characteristic, complemented
2C23×#10621884C211yesmaximal, characteristic, complemented
3C2×Q8×C22⋊D43C211yesmaximal, characteristic, complemented
4C2×#14583540C211yesmaximal, characteristic
5#19146098C2116yesmaximal, direct product factor
6C2×#14583292C211yesmaximal, characteristic, complemented
7C2×#14583148C211yesmaximal, characteristic, complemented
8C2×#14583138C211yesmaximal, characteristic, complemented
9C2×#14583123C211yesmaximal, characteristic, complemented
10C2×#14583103C211yesmaximal, characteristic, complemented
11C2×#14583060C211yesmaximal, characteristic, complemented
12C2×#14583039C211yesmaximal, characteristic, complemented
13C2×#14583052C211yesmaximal, characteristic, complemented
14C2×#14583002C211yesmaximal, characteristic, complemented
15C2×#14582967C211yesmaximal, characteristic, complemented
16C2×C43×#451C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic, complemented
19C23×D172C2211yescharacteristic
20C2×#13063357—28no—
21C2×#13063357C2218yescomplemented
22C22×#10621885C2211yescharacteristic, complemented
23C22×#10621873C2211yescharacteristic
24C22×#10621873C2211yescharacteristic
25C22×#10621884—28no—
26C22×#10621884C2211yescharacteristic
27C22×#10621884C2211yescharacteristic
28C22×#10621884C2211yescharacteristic
29C22×#10621884C2211yescharacteristic
30C22×#10621884C2218yescomplemented
31C22×#10621872C2211yescharacteristic, complemented
32C23×C43⋊C8C2211yescharacteristic
33Q8×C22⋊D43—24no—
34Q8×C22⋊D43C2218yescomplemented
35#14583540—24no—
36#14583540C2218yes—
37C2×#13063323—21no—
38C2×#13063323C2211yescharacteristic, complemented
39C2×#13063314C2211yescharacteristic
40C2×#13063310—21no—
41C2×#13063304—21no—
42C2×#13063304C2211yescharacteristic
43C2×#13063301—21no—
44C2×#13063301C2211yescharacteristic, complemented
45C2×#13063300—21no—
46C2×#13063300C2211yescharacteristic
47C2×#13063295—21no—
48C2×Q8×Dic43C2211yescharacteristic, complemented
49C2×#13063287C2211yescharacteristic
50C2×C4×C22⋊D43—21no—
51C2×C4×C22⋊D43C2211yescharacteristic
52C2×C22⋊C4×D43—21no—
53#14583292C2218yescomplemented
54#14583148C2218yescomplemented
55#14583138C2218yescomplemented
56#14583123C2218yescomplemented
57#14583103C2218yescomplemented
58#14583060C2218yescomplemented
59#14583052C2218yescomplemented
60#14583039C2218yescomplemented
61#14583002C2218yescomplemented
62#14582967C2218yescomplemented
63C2×#13063258C2211yescharacteristic, complemented
64C2×Dic43⋊C8C2211yescharacteristic, complemented
65C2×#13063249C2211yescharacteristic, complemented
66C2×#13063248C2211yescharacteristic, complemented
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
70C2×#13063235C2211yescharacteristic, complemented
71C23×Q8×C43C2211yescharacteristic
72C22×Q16×C43C2211yescharacteristic, complemented
73C22×Q16×C43C2211yescharacteristic, complemented
74C2×C22⋊Q8×C43C2211yescharacteristic
75C43×#451C2218yescomplemented
76C2×#103×C43C2211yescharacteristic, complemented
77C2×#103×C43C2211yescharacteristic, complemented
78C2×C22⋊C8×C43C2211yescharacteristic
79C24×D43—21no—
80C2×#10621902—22no—
81C2×#10621902—24no—
82C2×#10621902—42no—
83C2×#10621902C2314yes—
84C22×Dic86—21no—
85C22×Dic86C2311yescharacteristic
86C2×Q8×D43—22no—
87C2×Q8×D43—24no—
88C2×Q8×D43—42no—
89C2×Q8×D43C2314yescomplemented
90C22×D172—24no—
91C22×D172—21no—
92C22×D172—21no—
93C22×D172—22no—
94C22×D172—21no—
95C22×D172—42no—
96C22×D172C2311yescharacteristic
97C22×D172C2314yes—
98C22×D172C2311yescharacteristic
99C22×C22⋊D43D411yescharacteristic
100C22×C4×D43—21no—
101C22×C4×D43—21no—
102C22×C4×D43—21no—
103C22×C4×D43C2311yescharacteristic
104#13063357—232no—
105C2×#10621885—24no—
106C2×#10621885C2314yescomplemented
107C2×#10621873—24no—
108C2×#10621873—42no—
109C2×#10621873C2314yes—
110C2×#10621873C2314yes—
111C2×#10621884—24no—
112C2×#10621884—24no—
113C2×#10621884—232no—
114C2×#10621884—24no—
115C2×#10621884D418yescomplemented
116C2×#10621884C2314yes—
117C2×#10621884C2314yes—
118C2×#10621884C2314yes—
119C2×#10621884C2314yes—
120C2×#10621872—24no—
121C2×#10621872C2314yescomplemented
122C22×C43⋊C8—24no—
123C22×C43⋊C8C2311yescharacteristic
124C22×C43⋊C8C2314yes—
125C22×C43⋊C8C2311yescharacteristic
126#13063323—28no—
127#13063323—22no—
128#13063323C2314yescomplemented
129#13063314—22no—
130#13063314C2314yes—
131#13063310—28no—
132#13063304—22no—
133#13063304—28no—
134#13063304C2314yes—
135#13063301—22no—
136#13063301—28no—
137#13063301C2314yescomplemented
138#13063300—22no—
139#13063300—28no—
140#13063300C2314yes—
141#13063295—28no—
142Q8×Dic43—22no—
143Q8×Dic43C2314yescomplemented
144#13063287—22no—
145#13063287C2314yes—
146C4×C22⋊D43—28no—
147C4×C22⋊D43D414yes—
148C4×C22⋊D43C2314yes—
149C2×C4⋊Dic43—21no—
150C2×C4⋊Dic43C2311yescharacteristic
151C2×Dic43⋊C4—21no—
152C2×Dic43⋊C4—21no—
153C2×Dic43⋊C4—21no—
154C2×Dic43⋊C4—21no—
155C2×Dic43⋊C4D411yescharacteristic
156C2×C22⋊Dic43—21no—
157C2×C22⋊Dic43D411yescharacteristic
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—
163C2×(C2×D43)⋊C4D411yescharacteristic
164C22⋊C4×D43—28no—
165C2×C4×Dic43—21no—
166C2×C4×Dic43C2311yescharacteristic
167#13063258C2314yescomplemented
168Dic43⋊C8C2314yescomplemented
169#13063249C2314yescomplemented
170#13063248C2314yescomplemented
171#13063247C2314yes—
172#13063247C2314yes—
173(C2×D43)⋊C8C2314yescomplemented
174#13063235C2314yescomplemented
175C22×Q8×C43—22no—
176C22×Q8×C43—21no—
177C22×Q8×C43—24no—
178C22×Q8×C43—42no—
179C22×Q8×C43C2311yescharacteristic
180C22×Q8×C43C2311yescharacteristic
181C22×Q8×C43C2314yes—
182C22×Q8×C43C2311yescharacteristic
183C23×C4×C43—21no—
184C23×C4×C43C2311yescharacteristic
185C2×Q16×C43—24no—
186C2×Q16×C43—42no—
187C2×Q16×C43C2314yescomplemented
188C2×Q16×C43C2314yescomplemented
189C22×C8×C43C2311yescharacteristic
190C22×C8×C43C2311yescharacteristic
191C22⋊Q8×C43—22no—
192C22⋊Q8×C43C2314yes—
193C2×C4⋊C4×C43—21no—
194C2×C4⋊C4×C43C2311yescharacteristic
195C2×C22⋊C4×C43—21no—
196#103×C43C2314yescomplemented
197#103×C43C2314yescomplemented
198C22⋊C8×C43C2314yes—
199C24×C43C2×D411yescharacteristic
200C23×D43—21no—
201C23×D43—21no—
202C23×D43—24no—
203C23×D43—44no—
204C23×D43—44no—
205C23×D43—82no—
206C23×D43C2×D411yescharacteristic
207C2×Q8×C43—21no—
208C2×Q8×C43—21no—
209C2×Q8×C43—24no—
210C2×Q8×C43—21no—
211C2×Q8×C43—22no—
212C2×Q8×C43—28no—
213C2×Q8×C43—22no—
214C2×Q8×C43—22no—
215C2×Q8×C43—22no—
216C2×Q8×C43—22no—
217C2×Q8×C43—44no—
218C2×Q8×C43—44no—
219C2×Q8×C43—48no—
220C2×Q8×C43C2×D414yes—
221C2×Q8×C43C2412yes—
222C2×Q8×C43C2412yes—
223C2×Q8×C43C2412yes—
224C22×C4×C43—22no—
225C22×C4×C43—22no—
226C22×C4×C43—21no—
227C22×C4×C43—21no—
228C22×C4×C43—21no—
229C22×C4×C43—21no—
230C22×C4×C43—24no—
231C22×C4×C43—44no—
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D412yes—
234C22×C4×C43C2412yes—
235C22×C4×C43C2411yescharacteristic
236C2×C22⋊D43—24no—
237C2×C22⋊D43C2×D414yes—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43C2×D411yescharacteristic
241C22×Dic43C2×D411yescharacteristic
242C22×Dic43C2×D411yescharacteristic
243#10621902—28no—
244#10621902—44no—
245#10621902—48no—
246Q8×D43—28no—
247Q8×D43—44no—
248Q8×D43—48no—
249C2×D172—21no—
250C2×D172—22no—
251C2×D172—24no—
252C2×D172—21no—
253C2×D172—24no—
254C2×D172—24no—
255C2×D172—22no—
256C2×D172—22no—
257C2×D172—28no—
258C2×D172—44no—
259C2×D172—44no—
260C2×D172—44no—
261C2×D172—48no—
262C2×D172—82no—
263C2×D172C2×D414yes—
264C2×D172C2412yes—
265C2×D172C2412yes—
266C2×C4×D43—22no—
267C2×C4×D43—22no—
268C2×C4×D43—24no—
269C2×C4×D43—24no—
270C2×C4×D43—24no—
271C2×C4×D43—44no—
272C2×C4×D43—44no—
273C2×C4×D43—82no—
274C2×C4×D43C2×D412yes—
275C2×C4×D43C2412yes—
276C2×Dic86—22no—
277C2×Dic86—22no—
278C2×Dic86—21no—
279C2×Dic86—24no—
280C2×Dic86—44no—
281C2×Dic86C2412yes—
282Q16×C43—28no—
283Q16×C43—44no—
284C2×C8×C43—22no—
285C2×C8×C43—22no—
286C2×C8×C43C2412yes—
287C2×C8×C43C2412yes—
288C4⋊C4×C43—24no—
289C4⋊C4×C43—21no—
290C4⋊C4×C43C2412yes—
291C22⋊C4×C43—24no—
292C22⋊Dic43—24no—
293C22⋊Dic43C2×D414yes—
294#10621885—28no—
295#10621884—28no—
296#10621884—28no—
297#10621884—28no—
298#10621884C2×D4116yescomplemented
299(C2×D43)⋊C4—24no—
300(C2×D43)⋊C4—24no—
301(C2×D43)⋊C4—24no—
302(C2×D43)⋊C4—24no—
303(C2×D43)⋊C4—24no—
304(C2×D43)⋊C4C2×D414yes—
305C4⋊Dic43—21no—
306C4⋊Dic43—24no—
307C4⋊Dic43C2412yes—
308Dic43⋊C4—24no—
309Dic43⋊C4—24no—
310Dic43⋊C4—24no—
311Dic43⋊C4—24no—
312Dic43⋊C4C2×D414yes—
313C4×Dic43—24no—
314C4×Dic43C2×D412yes—
315C4×Dic43C2412yes—
316C2×C43⋊C8—22no—
317C2×C43⋊C8—28no—
318C2×C43⋊C8C2×D414yes—
319C2×C43⋊C8C2412yes—
320C2×C43⋊C8C2412yes—
321#10621873—28no—
322#10621873—44no—
323#10621872—28no—
324C23×C43—22no—
325C23×C43—22no—
326C23×C43#13714yescomplemented
327C23×C43C22×D412yes—
328C23×C43C22×D411yescharacteristic
329C22×D43—22no—
330C22×D43—24no—
331C22×D43—22no—
332C22×D43—22no—
333C22×D43—22no—
334C22×D43—22no—
335C22×D43—48no—
336C22×D43—42no—
337C22×D43—42no—
338C22×D43—42no—
339C22×D43—42no—
340C22×D43—48no—
341C22×D43—42no—
342C22×D43—84no—
343C22×D43—816no—
344C22×D43C22×D412yes—
345Q8×C43—24no—
346Q8×C43—22no—
347Q8×C43—22no—
348Q8×C43—22no—
349Q8×C43—22no—
350Q8×C43—22no—
351Q8×C43—48no—
352Q8×C43—42no—
353Q8×C43—42no—
354Q8×C43C22×D414yes—
355C2×C4×C43—24no—
356C2×C4×C43—22no—
357C2×C4×C43—22no—
358C2×C4×C43—24no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—22no—
363C2×C4×C43—22no—
364C2×C4×C43—48no—
365C2×C4×C43—42no—
366C2×C4×C43—42no—
367C2×C4×C43—42no—
368C2×C4×C43C22×D412yes—
369C2×C4×C43C22×D411yescharacteristic
370C2×C4×C43C22×D412yes—
371C2×C4×C43H(5,𝔽2)12yes—
372C2×C4×C43C2511yescharacteristic
373C22⋊D43—28no—
374C2×Dic43—22no—
375C2×Dic43—22no—
376C2×Dic43—22no—
377C2×Dic43—22no—
378C2×Dic43—22no—
379C2×Dic43—42no—
380C2×Dic43—42no—
381C2×Dic43C22×D412yes—
382C2×Dic43C22×D412yes—
383C2×Dic43C22×D412yes—
384D172—24no—
385D172—22no—
386D172—22no—
387D172—22no—
388D172—48no—
389D172—48no—
390D172—42no—
391D172—84no—
392D172C22×D414yes—
393C4×D43—24no—
394C4×D43—22no—
395C4×D43—22no—
396C4×D43—48no—
397C4×D43—48no—
398C4×D43—84no—
399Dic86—22no—
400Dic86—22no—
401Dic86—48no—
402Dic86—42no—
403C8×C43—22no—
404C8×C43—22no—
405C43⋊C8—22no—
406C43⋊C8C22×D414yes—
407C2×#3266—431nomaximal, Sylow
408C22×C43—22no—
409C22×C43—28no—
410C22×C43—22no—
411C22×C43D4212yes—
412C22×C43C2×#13712yes—
413C22×C43C2×#13714yescomplemented
414C22×C43#57712yes—
415C22×C43C23×D411yescharacteristic
416C2×D43—24no—
417C2×D43—22no—
418C2×D43—22no—
419C2×D43—22no—
420C2×D43—44no—
421C2×D43—48no—
422C2×D43—42no—
423C2×D43—42no—
424C2×D43—42no—
425C2×D43—42no—
426C2×D43—42no—
427C2×D43—816no—
428C2×D43—84no—
429C4×C43—24no—
430C4×C43—22no—
431C4×C43—42no—
432C4×C43—42no—
433C4×C43—42no—
434C4×C43D4212yes—
435C4×C43C23×D411yescharacteristic
436C4×C43C2×H(5,𝔽2)11yescharacteristic
437Dic43—22no—
438Dic43—22no—
439Dic43—22no—
440Dic43—42no—
441Dic43—42no—
442C22×#137—431no—
443C23×SD16—431no—
444C2×D4×Q8—431no—
445C2×#546—431no—
446#3266—4316no—
447C2×#497—431no—
448C2×#468—431no—
449C2×#467—431no—
450C2×#464—431no—
451C2×#461—431no—
452C2×#452—431no—
453C2×#451D4311yescharacteristic, complemented
454C2×#448—431no—
455C2×#450—431no—
456C2×#440—431no—
457C2×#435—431no—
458C2×C43—24no—
459C2×C43#326614yescomplemented
460C2×C43C2×D4211yescharacteristic
461C2×C43C22×#13711yescharacteristic
462C2×C43C2×#57711yescharacteristic
463D43—42no—
464D43—44no—
465D43—82no—
466C22×#41—431no—
467C23×Q8—431no—
468C23×Q8C2×D4311yescharacteristic
469C23×D4—431no—
470C2×#137—438no—
471C2×#137—868no—
472C22×Q16—431no—
473C22×Q16C2×D4311yescharacteristic, complemented
474C22×Q16C2×D4311yescharacteristic, complemented
475C22×SD16—431no—
476C22×SD16—431no—
477C22×SD16—431no—
478C22×SD16—431no—
479C22×SD16—438no—
480C22×SD16—431no—
481C22×SD16—431no—
482C22×SD16—868no—
483C22×M16—431no—
484C23×C8—431no—
485D4×Q8—438no—
486D4×Q8—864no—
487#546—438no—
488#546—864no—
489C2×C4⋊Q8—431no—
490C2×C4⋊Q8—861no—
491C2×#124—431no—
492C2×#123—861no—
493C2×C22⋊Q8—431no—
494C2×C22⋊Q8—431no—
495C2×C22⋊Q8—861no—
496C2×C22⋊Q8—861no—
497C2×C22⋊Q8C2×D4311yescharacteristic
498C2×#121—431no—
499C2×#121—861no—
500C2×#120—861no—
501C2×C4×Q8—431no—
502C2×C4×D4—431no—
503C2×C4×D4—431no—
504C2×C4×D4—861no—
505C22×C22⋊C4—861no—
506#497—438no—
507#468—438no—
508#467—438no—
509#464—438no—
510#461—438no—
511#452—438no—
512#451C2×D4318yescomplemented
513#450—438no—
514#448—438no—
515#440—438no—
516#435—438no—
517C2×#107—431no—
518C2×C4⋊C8—431no—
519C2×#103—431no—
520C2×#103—431no—
521C2×#103C2×D4311yescharacteristic, complemented
522C2×#103C2×D4311yescharacteristic, complemented
523C2×#102—431no—
524C2×#102—431no—
525C2×C22⋊C8—431no—
526C2×C22⋊C8C2×D4311yescharacteristic
527C2×#97—431no—
528C43C2×#326611yescharacteristic, complemented, Sylow
529C25—861no—
530C2×#41—434no—
531C2×#41—862no—
532C2×#41—864no—
533C2×#41—1722no—
534C22×Q8—21no—
535C22×Q8—22no—
536C22×Q8—24no—
537C22×Q8—42no—
538C22×Q8—434no—
539C22×Q8—431no—
540C22×Q8—861no—
541C22×Q8—862no—
542C22×Q8—864no—
543C22×Q8—1722no—
544C22×Q8C22×D4311yescharacteristic
545C22×Q8C22×D4311yescharacteristic
546C22×Q8C22×D4314yes—
547C22×Q8C22×D4311yescharacteristic
548C22×D4—431no—
549C22×D4—431no—
550C22×D4—431no—
551C22×D4—434no—
552C22×D4—864no—
553C22×D4—861no—
554C22×D4—861no—
555C22×D4—861no—
556C22×D4—862no—
557C22×D4—1722no—
558C23×C4—21no—
559C23×C4—431no—
560C23×C4—861no—
561C23×C4—861no—
562C23×C4—861no—
563C23×C4C22×D4311yescharacteristic
564#137—8632no—
565C2×Q16—24no—
566C2×Q16—42no—
567C2×Q16—434no—
568C2×Q16—864no—
569C2×Q16C22×D4314yescomplemented
570C2×Q16C22×D4314yescomplemented
571C2×SD16—438no—
572C2×SD16—434no—
573C2×SD16—434no—
574C2×SD16—434no—
575C2×SD16—434no—
576C2×SD16—434no—
577C2×SD16—434no—
578C2×SD16—864no—
579C2×SD16—864no—
580C2×SD16—8632no—
581C2×SD16—864no—
582C2×SD16—864no—
583C2×SD16—1722no—
584C2×M16—434no—
585C2×M16—864no—
586C22×C8—431no—
587C22×C8—431no—
588C22×C8—434no—
589C22×C8—864no—
590C22×C8C22×D4311yescharacteristic
591C22×C8C22×D4311yescharacteristic
592C4⋊Q8—434no—
593C4⋊Q8—862no—
594C4⋊Q8—868no—
595#124—434no—
596#124—862no—
597#123—868no—
598C22⋊Q8—22no—
599C22⋊Q8—434no—
600C22⋊Q8—434no—
601C22⋊Q8—868no—
602C22⋊Q8—868no—
603C22⋊Q8—862no—
604C22⋊Q8—862no—
605C22⋊Q8C22×D4314yes—
606#121—434no—
607#121—868no—
608#121—862no—
609#120—868no—
610C4×Q8—434no—
611C4×Q8—862no—
612C4×D4—434no—
613C4×D4—434no—
614C4×D4—434no—
615C4×D4—862no—
616C4×D4—868no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—431no—
619C2×C4⋊C4—431no—
620C2×C4⋊C4—861no—
621C2×C4⋊C4—861no—
622C2×C4⋊C4—861no—
623C2×C4⋊C4—861no—
624C2×C4⋊C4—861no—
625C2×C4⋊C4C22×D4311yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—431no—
628C2×C22⋊C4—431no—
629C2×C22⋊C4—868no—
630C2×C22⋊C4—861no—
631C2×C22⋊C4—861no—
632C2×C22⋊C4—861no—
633C2×C22⋊C4—861no—
634C2×C22⋊C4—861no—
635C2×C22⋊C4—861no—
636C2×C42—431no—
637C2×C42—861no—
638#107—434no—
639C4⋊C8—434no—
640#103—434no—
641#103—434no—
642#103C22×D4314yescomplemented
643#103C22×D4314yescomplemented
644#102—434no—
645#102—434no—
646C22⋊C8—434no—
647C22⋊C8C22×D4314yes—
648#97—434no—
649C24—431no—
650C24—861no—
651C24—864no—
652C24—861no—
653C24—3442no—
654C24—1724no—
655C24—1724no—
656C24D4×D4311yescharacteristic
657#41—868no—
658#41—1724no—
659#41—1728no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—24no—
663C2×Q8—21no—
664C2×Q8—22no—
665C2×Q8—28no—
666C2×Q8—22no—
667C2×Q8—22no—
668C2×Q8—22no—
669C2×Q8—22no—
670C2×Q8—44no—
671C2×Q8—44no—
672C2×Q8—48no—
673C2×Q8—432no—
674C2×Q8—864no—
675C2×Q8—861no—
676C2×Q8—868no—
677C2×Q8—862no—
678C2×Q8—862no—
679C2×Q8—1724no—
680C2×Q8—1724no—
681C2×Q8—1728no—
682C2×Q8D4×D4314yes—
683C2×Q8C23×D4312yes—
684C2×Q8C23×D4312yes—
685C2×Q8C23×D4312yes—
686C2×D4—434no—
687C2×D4—434no—
688C2×D4—432no—
689C2×D4—432no—
690C2×D4—868no—
691C2×D4—864no—
692C2×D4—864no—
693C2×D4—864no—
694C2×D4—861no—
695C2×D4—862no—
696C2×D4—864no—
697C2×D4—861no—
698C2×D4—862no—
699C2×D4—862no—
700C2×D4—3442no—
701C2×D4—1724no—
702C2×D4—1728no—
703C2×D4—1724no—
704C2×D4—1724no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—24no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—44no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—432no—
717C22×C4—432no—
718C22×C4—864no—
719C22×C4—864no—
720C22×C4—864no—
721C22×C4—862no—
722C22×C4—862no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—3442no—
726C22×C4—1724no—
727C22×C4—1724no—
728C22×C4D4×D4312yes—
729C22×C4D4×D4311yescharacteristic
730C22×C4C23×D4312yes—
731C22×C4C23×D4311yescharacteristic
732Q16—28no—
733Q16—44no—
734Q16—868no—
735SD16—4316no—
736SD16—868no—
737SD16—868no—
738SD16—868no—
739SD16—868no—
740SD16—1724no—
741M16—868no—
742C2×C8—22no—
743C2×C8—22no—
744C2×C8—434no—
745C2×C8—432no—
746C2×C8—432no—
747C2×C8—868no—
748C2×C8—862no—
749C2×C8C23×D4312yes—
750C2×C8C23×D4312yes—
751C4⋊C4—24no—
752C4⋊C4—21no—
753C4⋊C4—434no—
754C4⋊C4—432no—
755C4⋊C4—864no—
756C4⋊C4—864no—
757C4⋊C4—864no—
758C4⋊C4—864no—
759C4⋊C4—861no—
760C4⋊C4—864no—
761C4⋊C4C23×D4312yes—
762C22⋊C4—24no—
763C22⋊C4—434no—
764C22⋊C4—434no—
765C22⋊C4—864no—
766C22⋊C4—864no—
767C22⋊C4—864no—
768C22⋊C4—864no—
769C22⋊C4—864no—
770C22⋊C4—864no—
771C42—432no—
772C42—432no—
773C42—864no—
774C23—22no—
775C23—22no—
776C23—432no—
777C23—862no—
778C23—862no—
779C23—862no—
780C23—862no—
781C23—864no—
782C23—862no—
783C23—34416no—
784C23—3444no—
785C23—1728no—
786C23—1722no—
787C23—1728no—
788C23—1722no—
789C23—1722no—
790C23—1722no—
791C23—1722no—
792C23#1306335714yescomplemented
793C23C2×D4×D4312yes—
794C23C2×D4×D4311yescharacteristic
795Q8—22no—
796Q8—24no—
797Q8—22no—
798Q8—22no—
799Q8—22no—
800Q8—22no—
801Q8—48no—
802Q8—42no—
803Q8—42no—
804Q8—862no—
805Q8—862no—
806Q8—1728no—
807Q8—1722no—
808Q8C2×D4×D4314yes—
809D4—434no—
810D4—868no—
811D4—862no—
812D4—862no—
813D4—862no—
814D4—864no—
815D4—3444no—
816D4—1728no—
817D4—1728no—
818D4—1722no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—48no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—432no—
833C2×C4—432no—
834C2×C4—432no—
835C2×C4—862no—
836C2×C4—862no—
837C2×C4—862no—
838C2×C4—862no—
839C2×C4—862no—
840C2×C4—864no—
841C2×C4—862no—
842C2×C4—862no—
843C2×C4—3444no—
844C2×C4—1728no—
845C2×C4—1728no—
846C2×C4—1722no—
847C2×C4—1722no—
848C2×C4C2×D4×D4312yes—
849C2×C4C2×D4×D4312yes—
850C2×C4C2×D4×D4311yescharacteristic
851C2×C4#1306337012yes—
852C2×C4C24×D4311yescharacteristic
853C8—22no—
854C8—22no—
855C8—434no—
856C8—862no—
857C22—22no—
858C22—28no—
859C22—22no—
860C22—862no—
861C22—862no—
862C22—862no—
863C22—864no—
864C22—34416no—
865C22—3444no—
866C22—1722no—
867C22—1722no—
868C22—1722no—
869C22—1722no—
870C22—1722no—
871C22—1724no—
872C22—1728no—
873C22#1458353112yes—
874C22C2×#1306335712yes—
875C22C2×#1306335714yescomplemented
876C22#1458370812yes—
877C22C22×D4×D4311yescharacteristic
878C4—22no—
879C4—24no—
880C4—42no—
881C4—42no—
882C4—42no—
883C4—862no—
884C4—862no—
885C4—862no—
886C4—1722no—
887C4—1722no—
888C4#1458353112yes—
889C4C22×D4×D4311yescharacteristic
890C4C2×#1306337011yescharacteristic
891C2—24no—
892C2—3442no—
893C2—1722no—
894C2—1724no—
895C2#1914609814yesdirect product factor
896C2C2×#1458353111yescharacteristic
897C2C22×#1306335711yescharacteristic
898C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#451C2
socleC23×C43C22×D4
prime radicalC2×#14583540C2
hypercenterC2×#451D43
hypocenterC43C2×#3266
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C22×#13063357C2semidirect
2. C23×#10621884C2semidirect
3. C2×Q8×C22⋊D43C2semidirect
5. #19146098C2direct (N × H)
6. C2×#14583292C2semidirect
7. C2×#14583148C2semidirect
8. C2×#14583138C2semidirect
9. C2×#14583123C2semidirect
10. C2×#14583103C2semidirect
11. C2×#14583060C2semidirect
12. C2×#14583039C2semidirect
13. C2×#14583052C2semidirect
14. C2×#14583002C2semidirect
15. C2×#14582967C2semidirect
16. C2×C43×#451C2semidirect
18. C22×Q8×D43C22semidirect
21. C2×#13063357C22semidirect
22. C22×#10621885C22semidirect
30. C22×#10621884C22semidirect
31. C22×#10621872C22semidirect
34. Q8×C22⋊D43C22semidirect
38. C2×#13063323C22semidirect
44. C2×#13063301C22semidirect
48. C2×Q8×Dic43C22semidirect
53. #14583292C22semidirect
54. #14583148C22semidirect
55. #14583138C22semidirect
56. #14583123C22semidirect
57. #14583103C22semidirect
58. #14583060C22semidirect
59. #14583052C22semidirect
60. #14583039C22semidirect
61. #14583002C22semidirect
62. #14582967C22semidirect
63. C2×#13063258C22semidirect
64. C2×Dic43⋊C8C22semidirect
65. C2×#13063249C22semidirect
66. C2×#13063248C22semidirect
69. C2×(C2×D43)⋊C8C22semidirect
70. C2×#13063235C22semidirect
72. C22×Q16×C43C22semidirect
73. C22×Q16×C43C22semidirect
75. C43×#451C22semidirect
76. C2×#103×C43C22semidirect
77. C2×#103×C43C22semidirect
89. C2×Q8×D43C23semidirect
106. C2×#10621885C23semidirect
115. C2×#10621884D4semidirect
121. C2×#10621872C23semidirect
128. #13063323C23semidirect
137. #13063301C23semidirect
143. Q8×Dic43C23semidirect
167. #13063258C23semidirect
168. Dic43⋊C8C23semidirect
169. #13063249C23semidirect
170. #13063248C23semidirect
173. (C2×D43)⋊C8C23semidirect
174. #13063235C23semidirect
187. C2×Q16×C43C23semidirect
188. C2×Q16×C43C23semidirect
196. #103×C43C23semidirect
197. #103×C43C23semidirect
298. #10621884C2×D4semidirect
326. C23×C43#137semidirect
413. C22×C43C2×#137semidirect
453. C2×#451D43semidirect
459. C2×C43#3266semidirect
473. C22×Q16C2×D43semidirect
474. C22×Q16C2×D43semidirect
512. #451C2×D43semidirect
521. C2×#103C2×D43semidirect
522. C2×#103C2×D43semidirect
528. C43C2×#3266semidirect
569. C2×Q16C22×D43semidirect
570. C2×Q16C22×D43semidirect
642. #103C22×D43semidirect
643. #103C22×D43semidirect
792. C23#13063357semidirect
875. C22C2×#13063357semidirect
895. C2#19146098direct (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×#106218842
C2×Q8×C22⋊D432
C2×#145835402
#191460982
C2×#145832922
C2×#145831482
C2×#145831382
C2×#145831232
C2×#145831032
C2×#145830602
C2×#145830392
C2×#145830522
C2×#145830022
C2×#145829672
C2×C43×#4512
C2×#326643