Finite Group Databasebeta

← #26005181

Subgroups — #26005181

Order 11008.

7210 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148512C214yesmaximal, complemented
2#19148498C214yesmaximal, complemented
3#19148492C212yesmaximal, complemented
4#19148486C212yesmaximal, complemented
5#19148476C212yesmaximal, complemented
6#19148466C212yesmaximal, complemented
7#19148453C214yesmaximal, complemented
8#19148440C214yesmaximal, complemented
9#19148425C218yesmaximal, complemented
10#19148188C218yesmaximal, complemented
11#19148149C218yesmaximal, complemented
12#19147980C214yesmaximal, complemented
13#19147928C211yesmaximal, characteristic, complemented
14#19147924C211yesmaximal, characteristic, complemented
15#19147888C214yesmaximal, complemented
16C2×#14583452C211yesmaximal, characteristic, complemented
17C2×#14583445C211yesmaximal, characteristic, complemented
18#19147796C211yesmaximal, characteristic, complemented
19C2×#14583367C211yesmaximal, characteristic, complemented
20C43×#3428C211yesmaximal, characteristic, complemented
21C22×#10621898C2211yescharacteristic
22C22×#10621898C2211yescharacteristic
23#14583634C2218yescomplemented
24#14583632C2218yescomplemented
25#14583632C2218yescomplemented
26#14583627C2218yescomplemented
27#14583621C2218yescomplemented
28#14583621C2218yescomplemented
29#14583619C2218yescomplemented
30#14583617C2218yescomplemented
31#14583612C2218yescomplemented
32#14583604C2218yescomplemented
33#14583598C22116yescomplemented
34#14583598C22116yescomplemented
35#14583597C2218yescomplemented
36#14583595C22116yescomplemented
37#14583593C2218yescomplemented
38#14583588C2218yescomplemented
39#14583584C2218yescomplemented
40#14583582C22116yescomplemented
41#14583575C22116yescomplemented
42#14583573C22116yescomplemented
43#14583570C2218yescomplemented
44#14583558C22116yescomplemented
45#14583550C2218yescomplemented
46#14583539C22116yescomplemented
47#14583521C2218yescomplemented
48#14583514C2218yescomplemented
49#14583507C2218yescomplemented
50#14583500C2218yescomplemented
51#14583491C22116yescomplemented
52#14583482C22116yescomplemented
53#14583480C2214yescomplemented
54#14583477C2214yescomplemented
55#14583475C2212yes—
56#14583475C2212yescomplemented
57#14583473C2212yes—
58#14583470C2212yescomplemented
59#14583468C2212yes—
60#14583468C2212yescomplemented
61#14583466C2212yes—
62#14583463C2212yescomplemented
63#14583461C2214yes—
64#14583458C2214yes—
65#14583453C2218yescomplemented
66#14583452C2212yescomplemented
67#14583452C2214yescomplemented
68#14583452C2214yescomplemented
69#14583452C2212yescomplemented
70#14583452C2212yescomplemented
71#14583452C2212yescomplemented
72#14583449C2214yescomplemented
73#14583446C2218yescomplemented
74#14583445C2212yes—
75#14583445C2214yes—
76#14583445C2212yes—
77#14583445C2214yescomplemented
78#14583445C2212yescomplemented
79#14583445C2212yescomplemented
80#14583445C2214yescomplemented
81C2×#13063324C2212yescomplemented
82C2×#13063323C2211yescharacteristic, complemented
83C2×#13063321C2211yescharacteristic, complemented
84#14583436C2218yescomplemented
85#14583433C22116yescomplemented
86#14583431C2218yescomplemented
87#14583429C22116yescomplemented
88#14583427C22116yescomplemented
89#14583427C22116yescomplemented
90C2×#13063316C2212yescomplemented
91C2×#13063314C2211yescharacteristic, complemented
92C2×#13063312C2211yescharacteristic, complemented
93#14583411C2214yes—
94#14583411C2214yescomplemented
95#14583410C2214yes—
96#14583408C22116yescomplemented
97#14583406C2214yescomplemented
98C2×#13063302C2214yes—
99C2×#13063297C2214yes—
100#14583380C2214yescomplemented
101#14583379C2214yescomplemented
102#14583376C2212yescomplemented
103#14583373C2212yescomplemented
104#14583372C2214yes—
105C4×#10621898C2214yescomplemented
106C4×#10621898C22116yescomplemented
107#14583367C2214yes—
108#14583367C2212yes—
109#14583367C2212yes—
110#14583367C2214yescomplemented
111#14583367C2214yescomplemented
112#14583367C2212yescomplemented
113#14583367C2212yescomplemented
114C2×C4×Dic86C2214yescomplemented
115C2×#13063290C2212yescomplemented
116C2×#13063287C2212yescomplemented
117C2×C4×C22⋊D43C2214yescomplemented
118C2×(C22⋊D43)⋊C4C2214yes—
119C2×#13063284C2211yescharacteristic
120C2×#13063282C2212yescomplemented
121#117×D43C2214yescomplemented
122C22×C4×Dic43C2211yescharacteristic
123C2×C42×D43C2212yescomplemented
124C22×#41×C43C2211yescharacteristic
125C43×#520C2214yescomplemented
126C43×#520C2214yescomplemented
127C43×#519C2212yescomplemented
128C43×#518C2214yes—
129C43×#518C2212yescomplemented
130C4×#41×C43C2214yescomplemented
131C4×#41×C43C2214yescomplemented
132C2×#117×C43C2211yescharacteristic
133C2×#117×C43C2211yescharacteristic
134C2×#117×C43C2214yescomplemented
135C2×#10621898—28no—
136C2×#10621898—28no—
137C2×#10621898C2312yes—
138C2×#10621898C2312yes—
139C2×#10621898C2312yes—
140C2×#10621898C2312yes—
141C2×#10621898C2312yes—
142C2×#10621898C2312yes—
143C2×#10621898C2312yes—
144C2×#10621898C2312yes—
145C2×#10621898C23116yes—
146C22×Dic86C2311yescharacteristic
147C22×Dic86C2311yescharacteristic
148C22×Dic86C2314yes—
149C22×D172C2311yescharacteristic
150C22×D172C2311yescharacteristic
151C22×C22⋊D43C2312yes—
152C22×C22⋊D43C2312yes—
153C22×C22⋊D43C2314yes—
154C23×Dic43C2312yes—
155C22×C4×D43C2312yes—
156C22×C4×D43C2312yes—
157C22×C4×D43C2314yes—
158#13063325C2314yes—
159#13063324C2314yes—
160#13063324C2314yes—
161#13063324C2314yes—
162#13063324C2314yes—
163#13063323C2314yes—
164#13063323C2314yes—
165#13063323C2312yes—
166#13063323C2312yes—
167#13063322C2314yes—
168#13063321C2314yes—
169#13063321C2314yes—
170#13063321C2312yes—
171#13063321C2312yes—
172#13063320C23116yes—
173#13063320C23116yes—
174#13063319C23116yes—
175#13063319C23116yes—
176#13063318C23116yes—
177#13063318C23116yes—
178#13063317C23116yes—
179#13063316C2314yes—
180#13063316C2314yes—
181#13063316C2314yes—
182#13063316C2314yes—
183#13063315C23116yes—
184#13063315C23116yes—
185#13063314C2314yes—
186#13063314C2314yes—
187#13063314C2312yes—
188#13063314C2312yes—
189#13063313C23116yes—
190#13063313C2314yes—
191#13063313C2314yes—
192#13063312C2314yes—
193#13063312C2314yes—
194#13063312C2312yes—
195#13063312C2312yes—
196#13063311C23116yes—
197#13063311C23116yes—
198#13063310C23116yes—
199#13063310C23116yes—
200#13063309C2318yes—
201#13063309C2318yes—
202#13063308C2318yes—
203#13063308C23116yes—
204#13063308C23116yes—
205#13063307C23116yes—
206#13063307C23116yes—
207#13063306C2318yes—
208#13063305C2318yes—
209#13063305C2318yes—
210#13063304C23116yes—
211#13063304C2318yes—
212#13063303C23116yes—
213#13063303C23116yes—
214#13063302C2318yes—
215#13063302C2318yes—
216#13063302C2318yes—
217#13063302C2318yes—
218#13063301C2318yes—
219#13063300C2318yes—
220#13063300C2318yes—
221#13063299C23116yes—
222#13063299C23116yes—
223#13063299C2318yes—
224#13063298C23116yes—
225#13063298C23116yes—
226#13063297C2318yes—
227#13063297C23116yes—
228#13063297C2318yes—
229#13063297C2318yes—
230#13063297C2318yes—
231#13063296C2318yes—
232#13063295C2318yes—
233#13063295C2318yes—
234#13063294C2318yes—
235#13063293C2318yes—
236C4×Dic86C23116yes—
237C4×Dic86C2318yes—
238C4×Dic86C2318yes—
239C4×Dic86C2318yes—
240C4×Dic86C2318yes—
241C4×Dic86C2318yes—
242#13063290C2314yes—
243#13063290C2314yes—
244#13063290C2314yes—
245#13063290C2314yes—
246#13063290C2318yes—
247C4×D172C23116yes—
248C4×D172C2318yes—
249C4×D172C23116yes—
250#13063287C2314yes—
251#13063287C2318yes—
252#13063287C2314yes—
253#13063287C2314yes—
254#13063287C2314yes—
255C4×C22⋊D43C23116yes—
256C4×C22⋊D43C2318yes—
257C4×C22⋊D43C23116yes—
258C4×C22⋊D43C2318yes—
259C4×C22⋊D43C2318yes—
260C4×C22⋊D43C2318yes—
261C4×C22⋊D43C23116yes—
262C4×C22⋊D43C23116yes—
263(C22⋊D43)⋊C4C2318yes—
264(C22⋊D43)⋊C4C23116yes—
265(C22⋊D43)⋊C4C2318yes—
266(C22⋊D43)⋊C4C2318yes—
267(C22⋊D43)⋊C4C2318yes—
268#13063284C23116yes—
269#13063284C2312yes—
270#13063284C2312yes—
271#13063284C2312yes—
272#13063284C2312yes—
273#13063283C2318yes—
274#13063282C23116yes—
275#13063282C23116yes—
276#13063282C2318yes—
277#13063282C2318yes—
278#13063282C2314yes—
279#13063282C2314yes—
280#13063281C2318yes—
281C2×C4⋊Dic43C2314yes—
282C2×C4⋊Dic43C2312yes—
283C2×Dic43⋊C4C2314yes—
284C2×Dic43⋊C4C2314yes—
285C2×Dic43⋊C4C2314yes—
286C2×Dic43⋊C4C2314yes—
287C4⋊C4×D43C2318yes—
288C2×C22⋊Dic43C2314yes—
289C2×C22⋊Dic43C2312yes—
290C2×(C2×D43)⋊C4C2314yes—
291C2×(C2×D43)⋊C4C2314yes—
292C22⋊C4×D43C2318yes—
293C2×C4×Dic43C2311yescharacteristic
294C2×C4×Dic43C2314yes—
295C2×C4×Dic43C2311yescharacteristic
296C2×C4×Dic43C2312yes—
297C2×C4×Dic43C2312yes—
298C2×C4×Dic43C2312yes—
299C2×C4×Dic43C2311yescharacteristic
300C2×C4×Dic43C2311yescharacteristic
301C2×C4×Dic43C2311yescharacteristic
302C2×C4×Dic43C2311yescharacteristic
303C2×C4×Dic43C2312yes—
304C42×D43C2318yes—
305C42×D43C2314yes—
306C42×D43C2314yes—
307C42×D43C2318yes—
308C2×#41×C43—28no—
309C2×#41×C43C2312yes—
310C2×#41×C43C2312yes—
311C2×#41×C43C2312yes—
312C2×#41×C43C2312yes—
313C22×Q8×C43C2311yescharacteristic
314C22×D4×C43C2312yes—
315C22×D4×C43C2311yescharacteristic
316C23×C4×C43C2312yes—
317C23×C4×C43C2311yescharacteristic
318C4×Q8×C43C2318yes—
319C4×Q8×C43C2318yes—
320C4×D4×C43C23116yes—
321C4×D4×C43C2318yes—
322C4×D4×C43C23116yes—
323C4×D4×C43C2318yes—
324#117×C43C2312yes—
325#117×C43C2312yes—
326#117×C43C2312yes—
327#117×C43C2312yes—
328#117×C43C2312yes—
329#117×C43C2312yes—
330#117×C43C2312yes—
331#117×C43C2312yes—
332#117×C43C2318yes—
333#117×C43C2318yes—
334#117×C43C2318yes—
335C2×C4⋊C4×C43C2312yes—
336C2×C4⋊C4×C43C2312yes—
337C2×C4⋊C4×C43C2318yes—
338C2×C22⋊C4×C43C2312yes—
339C2×C22⋊C4×C43C2312yes—
340C2×C22⋊C4×C43C2318yes—
341C2×C42×C43C2312yes—
342C2×C42×C43C2312yes—
343C2×C42×C43C2318yes—
344C24×C43C2412yes—
345C24×C43C2411yescharacteristic
346C23×D43C2412yes—
347C23×D43C2412yes—
348#41×C43—28no—
349#41×C43—28no—
350#41×C43—28no—
351#41×C43—28no—
352C2×Q8×C43—24no—
353C2×Q8×C43C2412yes—
354C2×Q8×C43C2412yes—
355C2×D4×C43—24no—
356C2×D4×C43—28no—
357C2×D4×C43C2414yes—
358C2×D4×C43C2412yes—
359C2×D4×C43C2414yes—
360C2×D4×C43C2412yes—
361C22×C4×C43—28no—
362C22×C4×C43#4118yescomplemented
363C22×C4×C43C2414yes—
364C22×C4×C43C2414yes—
365C22×C4×C43C2412yes—
366C22×C4×C43C2414yes—
367C22×C4×C43C2414yes—
368C22×C4×C43C24116yes—
369C22×C4×C43C2411yescharacteristic
370C22×C4×C43C2411yescharacteristic
371C22×C4×C43C2411yescharacteristic
372C22×C4×C43C2411yescharacteristic
373C22×C4×C43C2411yescharacteristic
374C22×C4×C43C2411yescharacteristic
375C2×C22⋊D43—28no—
376C2×C22⋊D43—28no—
377C2×C22⋊D43—48no—
378C2×C22⋊D43C2414yes—
379C2×C22⋊D43C2414yes—
380C2×C22⋊D43C2414yes—
381C2×C22⋊D43C2414yes—
382C2×C22⋊D43C2418yes—
383C2×C22⋊D43C24116yes—
384C2×C22⋊D43C2418yes—
385C22×Dic43—44no—
386C22×Dic43C2412yes—
387C22×Dic43C2412yes—
388C22×Dic43C2412yes—
389C22×Dic43C2412yes—
390C22×Dic43C2412yes—
391C22×Dic43C2412yes—
392C22×Dic43C2412yes—
393C22×Dic43C2412yes—
394C22×Dic43C2414yes—
395#10621898—28no—
396#10621898—28no—
397#10621898—28no—
398#10621898—28no—
399#10621898—28no—
400#10621898—28no—
401#10621898—28no—
402#10621898—28no—
403#10621898—432no—
404C2×D172—24no—
405C2×D172—24no—
406C2×D172C2412yes—
407C2×D172C2412yes—
408C2×D172C2412yes—
409C2×D172C2412yes—
410C2×D172C24116yes—
411C2×C4×D43—28no—
412C2×C4×D43—28no—
413C2×C4×D43—48no—
414C2×C4×D43C2418yes—
415C2×C4×D43C2414yes—
416C2×C4×D43C2414yes—
417C2×C4×D43C2414yes—
418C2×C4×D43C2414yes—
419C2×C4×D43C2418yes—
420C2×C4×D43C24116yes—
421C2×Dic86—24no—
422C2×Dic86—24no—
423C2×Dic86—48no—
424C2×Dic86C2412yes—
425C2×Dic86C2412yes—
426C2×Dic86C2412yes—
427C2×Dic86C2418yes—
428C2×Dic86C2412yes—
429C2×Dic86C2418yes—
430C4⋊C4×C43C2414yes—
431C4⋊C4×C43C2414yes—
432C4⋊C4×C43C2414yes—
433C4⋊C4×C43C2414yes—
434C4⋊C4×C43C24116yes—
435C22⋊C4×C43C2414yes—
436C22⋊C4×C43C2414yes—
437C22⋊C4×C43C2414yes—
438C22⋊C4×C43C2414yes—
439C22⋊C4×C43C24116yes—
440C42×C43C2414yes—
441C42×C43C2414yes—
442C42×C43C2414yes—
443C42×C43C24116yes—
444C42×C43C2414yes—
445C22⋊Dic43C2414yes—
446C22⋊Dic43C2414yes—
447C22⋊Dic43C2418yes—
448C22⋊Dic43C2418yes—
449C22⋊Dic43C24116yes—
450(C2×D43)⋊C4C24116yes—
451(C2×D43)⋊C4C2418yes—
452(C2×D43)⋊C4C2418yes—
453(C2×D43)⋊C4C2418yes—
454(C2×D43)⋊C4C2418yes—
455(C2×D43)⋊C4C24116yes—
456(C2×D43)⋊C4C24116yes—
457(C2×D43)⋊C4C24116yes—
458C4⋊Dic43C2414yes—
459C4⋊Dic43C2414yes—
460C4⋊Dic43C2418yes—
461C4⋊Dic43C2418yes—
462C4⋊Dic43C24116yes—
463Dic43⋊C4C24116yes—
464Dic43⋊C4C2418yes—
465Dic43⋊C4C2418yes—
466Dic43⋊C4C2418yes—
467Dic43⋊C4C2418yes—
468Dic43⋊C4C2418yes—
469Dic43⋊C4C2418yes—
470Dic43⋊C4C2418yes—
471Dic43⋊C4C2418yes—
472Dic43⋊C4C24116yes—
473C4×Dic43C2412yes—
474C4×Dic43C2411yescharacteristic
475C4×Dic43C2411yescharacteristic
476C4×Dic43C2418yes—
477C4×Dic43C2414yes—
478C4×Dic43C2418yes—
479C4×Dic43C24116yes—
480C4×Dic43C2412yes—
481C4×Dic43C2411yescharacteristic
482C4×Dic43C2411yescharacteristic
483C4×Dic43C2412yes—
484C4×Dic43C2412yes—
485C4×Dic43C2412yes—
486C4×Dic43C2412yes—
487C4×Dic43C2414yes—
488C23×C43—24no—
489C23×C43—42no—
490C23×C43—44no—
491C23×C43C2×#4114yes—
492C23×C43C2514yes—
493C23×C43C2511yescharacteristic
494C23×C43C2511yescharacteristic
495C23×C43C2511yescharacteristic
496C22×D43—24no—
497C22×D43—24no—
498C22×D43—44no—
499C22×D43—44no—
500C22×D43C2514yes—
501C22×D43C2514yes—
502Q8×C43—24no—
503Q8×C43—24no—
504D4×C43—28no—
505D4×C43—28no—
506D4×C43—24no—
507D4×C43—24no—
508C2×C4×C43—24no—
509C2×C4×C43—28no—
510C2×C4×C43—28no—
511C2×C4×C43—44no—
512C2×C4×C43—44no—
513C2×C4×C43—416no—
514C2×C4×C43C2×#4114yes—
515C2×C4×C43C2×#4114yes—
516C2×C4×C43C2×#4114yes—
517C2×C4×C43C2×#4114yes—
518C2×C4×C43C2×#4114yes—
519C2×C4×C43C2×#4114yes—
520C2×C4×C43C2518yes—
521C2×C4×C43C2514yes—
522C2×C4×C43C2518yes—
523C2×C4×C43C2511yescharacteristic
524C2×C4×C43C2511yescharacteristic
525C2×C4×C43C2511yescharacteristic
526C2×C4×C43C2511yescharacteristic
527C22⋊D43—28no—
528C22⋊D43—28no—
529C22⋊D43—28no—
530C22⋊D43—28no—
531C22⋊D43—216no—
532C22⋊D43—416no—
533C22⋊D43—48no—
534C2×Dic43—24no—
535C2×Dic43—24no—
536C2×Dic43—24no—
537C2×Dic43—24no—
538C2×Dic43—24no—
539C2×Dic43—44no—
540C2×Dic43—42no—
541C2×Dic43—42no—
542C2×Dic43—42no—
543C2×Dic43C2512yes—
544C2×Dic43C2512yes—
545C2×Dic43C2514yes—
546C2×Dic43C2514yes—
547C2×Dic43C2518yes—
548C2×Dic43C2512yes—
549C2×Dic43C2512yes—
550D172—24no—
551D172—24no—
552D172—24no—
553D172—24no—
554D172—416no—
555C4×D43—28no—
556C4×D43—28no—
557C4×D43—28no—
558C4×D43—28no—
559C4×D43—216no—
560C4×D43—48no—
561C4×D43—416no—
562Dic86—24no—
563Dic86—24no—
564Dic86—24no—
565Dic86—24no—
566Dic86—216no—
567Dic86—48no—
568#62815—431nomaximal, Sylow
569C22×C43—22no—
570C22×C43—22no—
571C22×C43—22no—
572C22×C43—24no—
573C22×C43—28no—
574C22×C43—44no—
575C22×C43—84no—
576C22×C43C22×#4112yes—
577C22×C43C22×#4112yes—
578C22×C43C22×#4112yes—
579C22×C43C2611yescharacteristic
580C2×D43—24no—
581C2×D43—24no—
582C2×D43—28no—
583C2×D43—28no—
584C2×D43—48no—
585C2×D43—84no—
586C4×C43—24no—
587C4×C43—28no—
588C4×C43—28no—
589C4×C43C22×#4112yes—
590C4×C43C22×#4112yes—
591C4×C43C22×#4112yes—
592C4×C43C22×#4112yes—
593Dic43—24no—
594Dic43—24no—
595Dic43—28no—
596Dic43—22no—
597Dic43—22no—
598Dic43—22no—
599Dic43#58514yes—
600#3512—434no—
601#3511—434no—
602#3510—432no—
603#3510—432no—
604#3509—432no—
605#3508—432no—
606#3507—434no—
607#3506—434no—
608#3505—438no—
609#3480—438no—
610#3475—438no—
611#3455—434no—
612#3449—431no—
613#3449—431no—
614#3444—434no—
615C2×#533—431no—
616C2×#532—431no—
617#3428—431no—
618#3428D4311yescharacteristic, complemented
619C2×C4×#41—431no—
620C2×C43—22no—
621C2×C43—22no—
622C2×C43—22no—
623C2×C43—44no—
624C2×C43C23×#4111yescharacteristic
625C2×C43C2×#58512yes—
626D43—44no—
627D43—44no—
628C22×#41—431no—
629C22×#41—431no—
630C22×#41C2×D4311yescharacteristic
631#559—438no—
632#559—438no—
633#559—438no—
634#557—438no—
635#556—438no—
636#556—438no—
637#556—438no—
638#556—438no—
639#555—438no—
640#554—438no—
641#553—4316no—
642#553—4316no—
643#553—4316no—
644#553—438no—
645#553—438no—
646#552—4316no—
647#552—438no—
648#552—438no—
649#551—4316no—
650#551—4316no—
651#550—438no—
652#548—4316no—
653#547—438no—
654#546—4316no—
655#542—438no—
656#542—438no—
657#541—438no—
658#540—438no—
659#539—4316no—
660#538—4316no—
661#537—434no—
662#537—434no—
663#536—432no—
664#536—432no—
665#536—432no—
666#536—432no—
667#535—432no—
668#535—432no—
669#535—432no—
670#535—432no—
671#534—434no—
672#534—434no—
673#533—438no—
674#533—432no—
675#533—432no—
676#533—434no—
677#533—434no—
678#533—432no—
679#533—432no—
680#532—432no—
681#532—432no—
682#532—434no—
683#532—434no—
684#532—432no—
685#532—432no—
686#532—434no—
687#532—438no—
688#532—434no—
689C2×C4⋊Q8—431no—
690C2×C4⋊Q8—432no—
691C2×#127—431no—
692#529—438no—
693#529—4316no—
694#529—438no—
695#529—4316no—
696#529—4316no—
697#529—4316no—
698C2×#125—432no—
699C2×#124—431no—
700C2×#124—431no—
701#525—434no—
702#525—434no—
703#525—4316no—
704#525—434no—
705#525—434no—
706C2×C22⋊Q8—434no—
707C2×#121—434no—
708#520—434no—
709#520—434no—
710#520C2×D4314yescomplemented
711#520C2×D4314yescomplemented
712#519—432no—
713#519C2×D4312yescomplemented
714#518—432no—
715#518—434no—
716#518C2×D4314yes—
717#518C2×D4312yescomplemented
718C4×#41—434no—
719C4×#41—432no—
720C4×#41—432no—
721C4×#41—434no—
722C4×#41—432no—
723C4×#41—432no—
724C4×#41—434no—
725C4×#41—434no—
726C4×#41—4316no—
727C4×#41C2×D4314yescomplemented
728C4×#41C2×D4314yescomplemented
729C2×C4×Q8—432no—
730C2×C4×Q8—434no—
731C2×C4×D4—434no—
732C2×C4×D4—432no—
733C2×C4×D4—434no—
734C2×#117—431no—
735C2×#117—434no—
736C2×#117—432no—
737C2×#117C2×D4311yescharacteristic
738C2×#117C2×D4311yescharacteristic
739C2×#117C2×D4314yescomplemented
740C22×C42—431no—
741C22×C42—432no—
742C43#6281511yescharacteristic, complemented, Sylow
743C2×#41—28no—
744C2×#41—432no—
745C2×#41—432no—
746C2×#41—432no—
747C2×#41—432no—
748C2×#41—432no—
749C2×#41—432no—
750C2×#41—432no—
751C2×#41—432no—
752C2×#41—4316no—
753C2×#41—868no—
754C2×#41—868no—
755C2×#41C22×D4312yes—
756C2×#41C22×D4312yes—
757C2×#41C22×D4312yes—
758C2×#41C22×D4312yes—
759C22×Q8—431no—
760C22×Q8—431no—
761C22×Q8—434no—
762C22×Q8C22×D4311yescharacteristic
763C22×D4—432no—
764C22×D4—432no—
765C22×D4—434no—
766C22×D4—431no—
767C22×D4—431no—
768C22×D4C22×D4312yes—
769C22×D4C22×D4311yescharacteristic
770C23×C4—432no—
771C23×C4—432no—
772C23×C4—432no—
773C23×C4—434no—
774C23×C4C22×D4312yes—
775C23×C4C22×D4311yescharacteristic
776C4⋊Q8—432no—
777C4⋊Q8—432no—
778C4⋊Q8—434no—
779C4⋊Q8—434no—
780C4⋊Q8—434no—
781C4⋊Q8—434no—
782C4⋊Q8—434no—
783C4⋊Q8—434no—
784C4⋊Q8—434no—
785#127—432no—
786#127—432no—
787#127—434no—
788#127—434no—
789#127—434no—
790#126—4316no—
791#126—4316no—
792#126—4316no—
793#126—4316no—
794#126—4316no—
795#126—4316no—
796#125—434no—
797#125—434no—
798#125—434no—
799#125—434no—
800#125—4316no—
801#125—4316no—
802#125—4316no—
803#124—432no—
804#124—432no—
805#124—434no—
806#124—434no—
807#124—432no—
808#124—432no—
809#124—434no—
810#124—434no—
811#124—4316no—
812#124—4316no—
813#124—4316no—
814#124—434no—
815#124—434no—
816#123—438no—
817#123—438no—
818#123—4316no—
819#123—4316no—
820#123—4316no—
821#123—4316no—
822#123—438no—
823#123—4316no—
824#123—438no—
825#123—4316no—
826C22⋊Q8—438no—
827C22⋊Q8—438no—
828C22⋊Q8—4316no—
829C22⋊Q8—438no—
830C22⋊Q8—4316no—
831C22⋊Q8—438no—
832C22⋊Q8—4316no—
833C22⋊Q8—438no—
834C22⋊Q8—438no—
835C22⋊Q8—438no—
836C22⋊Q8—438no—
837#121—438no—
838#121—438no—
839#121—438no—
840#121—438no—
841#121—438no—
842#121—4316no—
843#121—438no—
844#121—4316no—
845#121—4316no—
846#121—438no—
847#121—438no—
848#121—4316no—
849#121—4316no—
850#120—438no—
851#120—438no—
852#120—438no—
853#120—438no—
854C4×Q8—434no—
855C4×Q8—434no—
856C4×Q8—434no—
857C4×Q8—434no—
858C4×Q8—438no—
859C4×Q8—438no—
860C4×Q8—438no—
861C4×Q8—438no—
862C4×Q8—438no—
863C4×Q8—438no—
864C4×Q8—4316no—
865C4×Q8C22×D4318yes—
866C4×Q8C22×D4318yes—
867C4×D4—438no—
868C4×D4—438no—
869C4×D4—438no—
870C4×D4—438no—
871C4×D4—4316no—
872C4×D4—4316no—
873C4×D4—4316no—
874C4×D4—4316no—
875C4×D4—434no—
876C4×D4—434no—
877C4×D4—434no—
878C4×D4—434no—
879C4×D4—438no—
880C4×D4—438no—
881C4×D4—438no—
882C4×D4—438no—
883C4×D4—438no—
884C4×D4—4316no—
885C4×D4—438no—
886C4×D4—4316no—
887C4×D4—4316no—
888C4×D4C22×D43116yes—
889C4×D4C22×D43116yes—
890C4×D4C22×D4318yes—
891C4×D4C22×D4318yes—
892#117—432no—
893#117—432no—
894#117—432no—
895#117—432no—
896#117—4316no—
897#117—438no—
898#117—438no—
899#117—438no—
900#117—438no—
901#117—434no—
902#117—434no—
903#117—4316no—
904#117—4316no—
905#117C22×D4312yes—
906#117C22×D4312yes—
907#117C22×D4312yes—
908#117C22×D4312yes—
909#117C22×D4312yes—
910#117C22×D4312yes—
911#117C22×D4312yes—
912#117C22×D4312yes—
913#117C22×D4318yes—
914#117C22×D4318yes—
915#117C22×D4318yes—
916C2×C4⋊C4—434no—
917C2×C4⋊C4—432no—
918C2×C4⋊C4—434no—
919C2×C4⋊C4—434no—
920C2×C4⋊C4—434no—
921C2×C4⋊C4—434no—
922C2×C4⋊C4—438no—
923C2×C4⋊C4C22×D4312yes—
924C2×C4⋊C4C22×D4312yes—
925C2×C4⋊C4C22×D4318yes—
926C2×C22⋊C4—432no—
927C2×C22⋊C4—434no—
928C2×C22⋊C4—434no—
929C2×C22⋊C4—434no—
930C2×C22⋊C4—438no—
931C2×C22⋊C4C22×D4312yes—
932C2×C22⋊C4C22×D4312yes—
933C2×C22⋊C4C22×D4318yes—
934C2×C42—431no—
935C2×C42—432no—
936C2×C42—432no—
937C2×C42—434no—
938C2×C42—432no—
939C2×C42—432no—
940C2×C42—431no—
941C2×C42—431no—
942C2×C42—431no—
943C2×C42—431no—
944C2×C42—431no—
945C2×C42—438no—
946C2×C42—438no—
947C2×C42—434no—
948C2×C42—434no—
949C2×C42C22×D4312yes—
950C2×C42C22×D4312yes—
951C2×C42C22×D4318yes—
952C24—432no—
953C24—432no—
954C24C23×D4312yes—
955C24C23×D4311yescharacteristic
956#41—28no—
957#41—28no—
958#41—28no—
959#41—28no—
960#41—868no—
961#41—868no—
962#41—868no—
963#41—868no—
964#41—868no—
965#41—868no—
966#41—868no—
967#41—868no—
968#41—17232no—
969C2×Q8—24no—
970C2×Q8—432no—
971C2×Q8—438no—
972C2×Q8—432no—
973C2×Q8—432no—
974C2×Q8—432no—
975C2×Q8—438no—
976C2×Q8—864no—
977C2×Q8—864no—
978C2×Q8—1728no—
979C2×Q8C23×D4312yes—
980C2×Q8C23×D4312yes—
981C2×D4—28no—
982C2×D4—24no—
983C2×D4—434no—
984C2×D4—434no—
985C2×D4—434no—
986C2×D4—434no—
987C2×D4—438no—
988C2×D4—4316no—
989C2×D4—438no—
990C2×D4—432no—
991C2×D4—432no—
992C2×D4—432no—
993C2×D4—432no—
994C2×D4—4316no—
995C2×D4—868no—
996C2×D4—868no—
997C2×D4—864no—
998C2×D4—864no—
999C2×D4—1728no—
1000C2×D4C23×D4314yes—
1001C2×D4C23×D4314yes—
1002C2×D4C23×D4312yes—
1003C2×D4C23×D4312yes—
1004C22×C4—28no—
1005C22×C4—432no—
1006C22×C4—432no—
1007C22×C4—432no—
1008C22×C4—432no—
1009C22×C4—432no—
1010C22×C4—432no—
1011C22×C4—432no—
1012C22×C4—432no—
1013C22×C4—434no—
1014C22×C4—438no—
1015C22×C4—434no—
1016C22×C4—434no—
1017C22×C4—434no—
1018C22×C4—434no—
1019C22×C4—438no—
1020C22×C4—4316no—
1021C22×C4—868no—
1022C22×C4—868no—
1023C22×C4—1728no—
1024C22×C4—1724no—
1025C22×C4#1062189818yescomplemented
1026C22×C4C23×D4312yes—
1027C22×C4C23×D4314yes—
1028C22×C4C23×D4314yes—
1029C22×C4C23×D4314yes—
1030C22×C4C23×D4314yes—
1031C22×C4C23×D43116yes—
1032C22×C4C23×D4311yescharacteristic
1033C22×C4C23×D4311yescharacteristic
1034C22×C4C23×D4311yescharacteristic
1035C22×C4C23×D4311yescharacteristic
1036C22×C4C23×D4311yescharacteristic
1037C22×C4C23×D4311yescharacteristic
1038C4⋊C4—434no—
1039C4⋊C4—438no—
1040C4⋊C4—438no—
1041C4⋊C4—434no—
1042C4⋊C4—438no—
1043C4⋊C4—438no—
1044C4⋊C4—4316no—
1045C4⋊C4—438no—
1046C4⋊C4—438no—
1047C4⋊C4—438no—
1048C4⋊C4—438no—
1049C4⋊C4—438no—
1050C4⋊C4—438no—
1051C4⋊C4—4316no—
1052C4⋊C4—4316no—
1053C4⋊C4C23×D4314yes—
1054C4⋊C4C23×D4314yes—
1055C4⋊C4C23×D4314yes—
1056C4⋊C4C23×D4314yes—
1057C4⋊C4C23×D43116yes—
1058C22⋊C4—434no—
1059C22⋊C4—434no—
1060C22⋊C4—438no—
1061C22⋊C4—438no—
1062C22⋊C4—4316no—
1063C22⋊C4—438no—
1064C22⋊C4—438no—
1065C22⋊C4—4316no—
1066C22⋊C4—438no—
1067C22⋊C4—438no—
1068C22⋊C4—4316no—
1069C22⋊C4—4316no—
1070C22⋊C4—4316no—
1071C22⋊C4C23×D4314yes—
1072C22⋊C4C23×D4314yes—
1073C22⋊C4C23×D4314yes—
1074C22⋊C4C23×D4314yes—
1075C22⋊C4C23×D43116yes—
1076C42—431no—
1077C42—431no—
1078C42—438no—
1079C42—431no—
1080C42—431no—
1081C42—432no—
1082C42—432no—
1083C42—438no—
1084C42—432no—
1085C42—432no—
1086C42—4316no—
1087C42—434no—
1088C42—432no—
1089C42—432no—
1090C42—434no—
1091C42C23×D4314yes—
1092C42C23×D43116yes—
1093C42C23×D4314yes—
1094C42C23×D4314yes—
1095C42C23×D4314yes—
1096C23—24no—
1097C23—42no—
1098C23—44no—
1099C23—434no—
1100C23—434no—
1101C23—864no—
1102C23—864no—
1103C23—1724no—
1104C23—1724no—
1105C23C2×#1062189814yes—
1106C23C24×D4314yes—
1107C23C24×D4311yescharacteristic
1108C23C24×D4311yescharacteristic
1109C23C24×D4311yescharacteristic
1110Q8—24no—
1111Q8—24no—
1112Q8—8616no—
1113Q8—864no—
1114Q8—864no—
1115Q8—864no—
1116Q8—864no—
1117Q8—1728no—
1118D4—28no—
1119D4—28no—
1120D4—24no—
1121D4—24no—
1122D4—8616no—
1123D4—868no—
1124D4—868no—
1125D4—868no—
1126D4—868no—
1127D4—864no—
1128D4—864no—
1129D4—864no—
1130D4—864no—
1131D4—17216no—
1132D4—1728no—
1133D4—17216no—
1134C2×C4—24no—
1135C2×C4—28no—
1136C2×C4—28no—
1137C2×C4—44no—
1138C2×C4—44no—
1139C2×C4—416no—
1140C2×C4—432no—
1141C2×C4—432no—
1142C2×C4—432no—
1143C2×C4—434no—
1144C2×C4—434no—
1145C2×C4—438no—
1146C2×C4—432no—
1147C2×C4—8616no—
1148C2×C4—864no—
1149C2×C4—864no—
1150C2×C4—864no—
1151C2×C4—864no—
1152C2×C4—864no—
1153C2×C4—868no—
1154C2×C4—868no—
1155C2×C4—868no—
1156C2×C4—868no—
1157C2×C4—1728no—
1158C2×C4—17216no—
1159C2×C4—1722no—
1160C2×C4—1722no—
1161C2×C4—1722no—
1162C2×C4—1724no—
1163C2×C4C2×#1062189814yes—
1164C2×C4C2×#1062189814yes—
1165C2×C4C2×#1062189814yes—
1166C2×C4C2×#1062189814yes—
1167C2×C4C2×#1062189814yes—
1168C2×C4C2×#1062189814yes—
1169C2×C4C24×D4318yes—
1170C2×C4C24×D4314yes—
1171C2×C4C24×D4318yes—
1172C2×C4C24×D4311yescharacteristic
1173C2×C4C24×D4311yescharacteristic
1174C2×C4C24×D4311yescharacteristic
1175C2×C4C24×D4311yescharacteristic
1176C22—22no—
1177C22—22no—
1178C22—22no—
1179C22—24no—
1180C22—28no—
1181C22—44no—
1182C22—84no—
1183C22—864no—
1184C22—864no—
1185C22—868no—
1186C22—868no—
1187C22—3444no—
1188C22—1728no—
1189C22C22×#1062189812yes—
1190C22C22×#1062189812yes—
1191C22C22×#1062189812yes—
1192C22C25×D4311yescharacteristic
1193C4—24no—
1194C4—28no—
1195C4—28no—
1196C4—434no—
1197C4—864no—
1198C4—864no—
1199C4—862no—
1200C4—862no—
1201C4—862no—
1202C4—868no—
1203C4C22×#1062189812yes—
1204C4C22×#1062189812yes—
1205C4C22×#1062189812yes—
1206C4C22×#1062189812yes—
1207C2—22no—
1208C2—22no—
1209C2—22no—
1210C2—44no—
1211C2—1724no—
1212C2—1724no—
1213C2C23×#1062189811yescharacteristic
1214C2#585×D4312yes—
subgroupG/H
centerC2×C4C24×D43
commutator, socle, cosocleC22×C43C26
FrattiniC22C25×D43
FittingC43×#3428C2
hypercenter#3428D43
hypocenterC43#62815
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. #19148512C2semidirect
2. #19148498C2semidirect
3. #19148492C2semidirect
4. #19148486C2semidirect
5. #19148476C2semidirect
6. #19148466C2semidirect
7. #19148453C2semidirect
8. #19148440C2semidirect
9. #19148425C2semidirect
10. #19148188C2semidirect
11. #19148149C2semidirect
12. #19147980C2semidirect
13. #19147928C2semidirect
14. #19147924C2semidirect
15. #19147888C2semidirect
16. C2×#14583452C2semidirect
17. C2×#14583445C2semidirect
18. #19147796C2semidirect
19. C2×#14583367C2semidirect
20. C43×#3428C2semidirect
23. #14583634C22semidirect
24. #14583632C22semidirect
25. #14583632C22semidirect
26. #14583627C22semidirect
27. #14583621C22semidirect
28. #14583621C22semidirect
29. #14583619C22semidirect
30. #14583617C22semidirect
31. #14583612C22semidirect
32. #14583604C22semidirect
33. #14583598C22semidirect
34. #14583598C22semidirect
35. #14583597C22semidirect
36. #14583595C22semidirect
37. #14583593C22semidirect
38. #14583588C22semidirect
39. #14583584C22semidirect
40. #14583582C22semidirect
41. #14583575C22semidirect
42. #14583573C22semidirect
43. #14583570C22semidirect
44. #14583558C22semidirect
45. #14583550C22semidirect
46. #14583539C22semidirect
47. #14583521C22semidirect
48. #14583514C22semidirect
49. #14583507C22semidirect
50. #14583500C22semidirect
51. #14583491C22semidirect
52. #14583482C22semidirect
53. #14583480C22semidirect
54. #14583477C22semidirect
56. #14583475C22semidirect
58. #14583470C22semidirect
60. #14583468C22semidirect
62. #14583463C22semidirect
65. #14583453C22semidirect
66. #14583452C22semidirect
67. #14583452C22semidirect
68. #14583452C22semidirect
69. #14583452C22semidirect
70. #14583452C22semidirect
71. #14583452C22semidirect
72. #14583449C22semidirect
73. #14583446C22semidirect
77. #14583445C22semidirect
78. #14583445C22semidirect
79. #14583445C22semidirect
80. #14583445C22semidirect
81. C2×#13063324C22semidirect
82. C2×#13063323C22semidirect
83. C2×#13063321C22semidirect
84. #14583436C22semidirect
85. #14583433C22semidirect
86. #14583431C22semidirect
87. #14583429C22semidirect
88. #14583427C22semidirect
89. #14583427C22semidirect
90. C2×#13063316C22semidirect
91. C2×#13063314C22semidirect
92. C2×#13063312C22semidirect
94. #14583411C22semidirect
96. #14583408C22semidirect
97. #14583406C22semidirect
100. #14583380C22semidirect
101. #14583379C22semidirect
102. #14583376C22semidirect
103. #14583373C22semidirect
105. C4×#10621898C22semidirect
106. C4×#10621898C22semidirect
110. #14583367C22semidirect
111. #14583367C22semidirect
112. #14583367C22semidirect
113. #14583367C22semidirect
114. C2×C4×Dic86C22semidirect
115. C2×#13063290C22semidirect
116. C2×#13063287C22semidirect
117. C2×C4×C22⋊D43C22semidirect
120. C2×#13063282C22semidirect
121. #117×D43C22semidirect
123. C2×C42×D43C22semidirect
125. C43×#520C22semidirect
126. C43×#520C22semidirect
127. C43×#519C22semidirect
129. C43×#518C22semidirect
130. C4×#41×C43C22semidirect
131. C4×#41×C43C22semidirect
134. C2×#117×C43C22semidirect
362. C22×C4×C43#41semidirect
618. #3428D43semidirect
710. #520C2×D43semidirect
711. #520C2×D43semidirect
713. #519C2×D43semidirect
717. #518C2×D43semidirect
727. C4×#41C2×D43semidirect
728. C4×#41C2×D43semidirect
739. C2×#117C2×D43semidirect
742. C43#62815semidirect
1025. C22×C4#10621898semidirect

Maximal subgroups

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

subgroupindex
#191485122
#191484982
#191484922
#191484862
#191484762
#191484662
#191484532
#191484402
#191484252
#191481882
#191481492
#191479802
#191479282
#191479242
#191478882
C2×#145834522
C2×#145834452
#191477962
C2×#145833672
C43×#34282
#6281543