Finite Group Databasebeta

← #26005322

Subgroups — #26005322

Order 11008.

6530 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149202C214yesmaximal, complemented
2#19149200C214yesmaximal, complemented
3#19149125C214yesmaximal, complemented
4#19149119C214yesmaximal, complemented
5#19149043C218yesmaximal, complemented
6#19148575C214yesmaximal, complemented
7#19148570C214yesmaximal, complemented
8#19148566C214yesmaximal, complemented
9#19148561C214yesmaximal, complemented
10#19148516C212yesmaximal, complemented
11#19148515C211yesmaximal, characteristic, complemented
12#19148421C211yesmaximal, characteristic, complemented
13#19148419C211yesmaximal, characteristic, complemented
14#19148417C212yesmaximal, complemented
15#19148302C212yesmaximal, complemented
16#19148299C218yesmaximal, complemented
17#19148298C212yesmaximal, complemented
18#19147890C211yesmaximal, characteristic, complemented
19#19147888C211yesmaximal, characteristic, complemented
20C2×#125×D43C211yesmaximal, characteristic, complemented
21C43×#3512C211yesmaximal, characteristic, complemented
22C43⋊#564C2218yescomplemented
23#14583652C2218yescomplemented
24#14583651C2218yescomplemented
25#14583644C2218yescomplemented
26#14583628C2214yescomplemented
27#14583626C2214yescomplemented
28#14583625C2214yescomplemented
29#14583625C2214yescomplemented
30#14583609C2214yes—
31#14583608C2218yes—
32#14583608C2218yes—
33#14583608C2214yescomplemented
34#14583608C2214yescomplemented
35#14583607C2214yes—
36#14583607C2214yes—
37#14583606C2218yes—
38#14583606C2214yescomplemented
39#14583605C2214yescomplemented
40#14583604C2214yes—
41#14583604C2218yes—
42#14583601C2218yes—
43#14583601C2214yescomplemented
44#14583599C2214yes—
45#14583596C2214yes—
46#14583596C2214yes—
47#14583596C2214yescomplemented
48#14583595C2214yescomplemented
49#14583593C2214yes—
50#14583592C2218yes—
51#14583592C2218yes—
52#14583591C2214yescomplemented
53#14583590C2214yes—
54#14583589C2218yescomplemented
55#14583589C2214yescomplemented
56#14583588C2214yes—
57#14583588C2218yes—
58#14583587C2218yes—
59#14583586C2218yescomplemented
60#14583585C2218yes—
61#14583585C2218yes—
62#14583585C2218yescomplemented
63#14583583C2214yes—
64#14583583C2214yes—
65#14583583C2214yescomplemented
66#14583582C2218yescomplemented
67#14583554C2214yes—
68#14583554C2218yes—
69#14583550C2214yes—
70#14583549C2218yes—
71#14583549C2214yes—
72#14583549C2214yes—
73#14583547C2218yes—
74#14583547C2218yes—
75#14583530C2212yes—
76#14583530C2214yescomplemented
77#14583529C2218yes—
78#14583529C2214yescomplemented
79#14583527C2212yes—
80#14583527C2214yescomplemented
81#14583527C2214yescomplemented
82#14583511C2218yescomplemented
83#14583510C2212yescomplemented
84#14583509C2214yescomplemented
85#14583508C2218yescomplemented
86#14583506C2218yescomplemented
87#14583506C2218yescomplemented
88#14583503C2212yescomplemented
89#14583502C2214yescomplemented
90#14583494C2218yes—
91#14583494C2218yescomplemented
92#14583493C2218yescomplemented
93#14583492C2218yes—
94#14583492C2218yes—
95#14583492C2218yescomplemented
96#14583491C2218yes—
97#14583491C2218yescomplemented
98#14583490C2218yes—
99#14583490C2218yes—
100#14583478C2218yes—
101#14583477C2212yes—
102#14583456C2211yescharacteristic
103#14583456C2212yescomplemented
104#14583455C2212yescomplemented
105#14583454C2212yes—
106#14583453C2212yes—
107#14583452C2211yescharacteristic
108#14583452C2214yescomplemented
109#14583447C2212yes—
110#14583446C2212yes—
111#14583445C2211yescharacteristic
112#14583436C2212yes—
113#14583435C2214yescomplemented
114#14583431C2212yes—
115#14583431C2214yes—
116#14583430C2214yes—
117#14583430C2214yescomplemented
118#14583429C2214yes—
119#14583428C2212yes—
120#14583428C2212yes—
121#14583428C2214yescomplemented
122#14583427C2214yes—
123C2×#13063317C2211yescharacteristic
124C2×#13063317C2212yescomplemented
125C2×#13063316C2212yes—
126C2×#13063316C2214yescomplemented
127C2×#13063315C2214yes—
128#125×D43C2214yes—
129#125×D43C2214yes—
130#125×D43C2214yes—
131#125×D43C2214yes—
132#125×D43C2212yescomplemented
133#14583411C2211yescharacteristic
134#14583409C2218yes—
135#14583409C2214yes—
136#14583408C2218yes—
137#14583408C2214yes—
138#14583406C2212yes—
139#14583406C2211yescharacteristic
140#14583382C2212yes—
141#14583382C2212yes—
142#14583380C2212yes—
143#14583379C2218yes—
144#14583378C2218yes—
145#41×Dic43C2212yes—
146C4×#10621898C2214yes—
147C4×#10621898C2211yescharacteristic
148C4×#10621900C2214yes—
149C2×C4⋊C4×D43C2212yes—
150C2×C4⋊C4×D43C2214yes—
151C2×C42×D43C2211yescharacteristic
152C43×#553C2218yes—
153C43×#553C2214yescomplemented
154C43×#552C2214yescomplemented
155C43×#541C2212yescomplemented
156C43×#540C2212yescomplemented
157C43×#537C2212yes—
158C43×#532C2211yescharacteristic
159C43×#529C2214yescomplemented
160C2×#125×C43C2211yescharacteristic
161C43×#520C2212yes—
162C4×#41×C43C2211yescharacteristic
163C2×#10621898C2311yescharacteristic
164C2×#10621898C2314yes—
165C2×#10621898C2318yes—
166C2×#10621900C2314yes—
167C2×#10621900C2318yes—
168C22×C4×D43C2311yescharacteristic
169C22×C4×D43C2312yes—
170C22×C4×D43C2314yes—
171#13063325C2318yes—
172#13063325C2314yes—
173#13063325C2312yes—
174#13063324C2314yes—
175#13063324C2318yes—
176#13063324C2314yes—
177#13063324C2314yes—
178#13063324C2318yes—
179#13063324C2318yes—
180#13063324C2312yes—
181#13063323C2311yescharacteristic
182#13063321C2311yescharacteristic
183#13063320C2318yes—
184#13063320C2318yes—
185#13063320C2314yes—
186#13063319C2318yes—
187#13063318C2318yes—
188#13063318C2318yes—
189#13063318C2318yes—
190#13063318C2318yes—
191#13063318C2318yes—
192#13063318C2318yes—
193#13063318C2318yes—
194#13063318C2314yes—
195#13063318C2314yes—
196#13063318C2314yes—
197#13063317C2318yes—
198#13063317C2318yes—
199#13063317C2318yes—
200#13063317C2314yes—
201#13063317C2314yes—
202#13063317C2312yes—
203#13063317C2312yes—
204#13063317C2311yescharacteristic
205#13063317C2311yescharacteristic
206#13063316C2314yes—
207#13063316C2314yes—
208#13063316C2314yes—
209#13063316C2318yes—
210#13063316C2318yes—
211#13063316C2318yes—
212#13063316C2318yes—
213#13063316C2318yes—
214#13063316C2314yes—
215#13063316C2314yes—
216#13063316C2314yes—
217#13063316C2314yes—
218#13063316C2314yes—
219#13063316C2312yes—
220#13063315C2318yes—
221#13063315C2318yes—
222#13063315C2318yes—
223#13063315C2318yes—
224#13063315C2318yes—
225#13063315C2318yes—
226#13063315C2318yes—
227#13063315C2318yes—
228#13063315C2318yes—
229#13063315C2314yes—
230#13063315C2318yes—
231#13063315C2318yes—
232#13063314C2311yescharacteristic
233#13063312C2314yes—
234#13063312C2311yescharacteristic
235#13063311C2314yes—
236#13063310C2314yes—
237#13063310C2318yes—
238#13063309C2318yes—
239#13063309C2318yes—
240#13063309C2312yes—
241#13063308C2318yes—
242#13063307C2314yes—
243#13063307C2318yes—
244#13063307C2318yes—
245#13063307C2318yes—
246#13063307C2318yes—
247#13063307C2318yes—
248#13063307C2318yes—
249#13063307C2314yes—
250#13063307C2314yes—
251#13063306C2318yes—
252#13063306C2318yes—
253#13063306C2318yes—
254#13063306C2318yes—
255#13063306C2312yes—
256#13063306C2314yes—
257#13063305C2318yes—
258#13063305C2318yes—
259#13063305C2312yes—
260#13063305C2314yes—
261#13063304C2318yes—
262#13063304C2318yes—
263#13063304C2318yes—
264#13063304C2314yes—
265#13063304C2318yes—
266#13063304C2318yes—
267#13063304C2314yes—
268#13063303C2318yes—
269#13063303C2318yes—
270#13063303C2318yes—
271#13063303C2318yes—
272#13063303C2314yes—
273#13063302C2318yes—
274#13063302C2318yes—
275#13063302C2318yes—
276#13063302C2318yes—
277#13063302C2318yes—
278#13063302C2318yes—
279#13063302C2314yes—
280#13063302C2318yes—
281#13063302C2318yes—
282#13063302C2318yes—
283#13063301C2312yes—
284#13063301C2312yes—
285#13063301C2314yes—
286#13063301C2312yes—
287#13063300C2312yes—
288#13063299C2314yes—
289#13063298C2318yes—
290#13063298C2314yes—
291#13063297C2318yes—
292#13063297C2314yes—
293#13063297C2318yes—
294#13063297C2318yes—
295#13063296C2312yes—
296#13063296C2318yes—
297#13063296C2314yes—
298#13063296C2318yes—
299#13063296C2312yes—
300#13063296C2312yes—
301#13063296C2314yes—
302#13063295C2312yes—
303#13063293C2314yes—
304#13063293C2312yes—
305Q8×Dic43C2314yes—
306Q8×Dic43C2314yes—
307Q8×Dic43C2312yes—
308Q8×Dic43C2312yes—
309C4×Dic86C2318yes—
310C4×Dic86C2318yes—
311C4×Dic86C2318yes—
312C4×Dic86C2312yes—
313C4×Dic86C2314yes—
314C4×Dic86C2314yes—
315C4×Dic86C2314yes—
316#13063290C2318yes—
317#13063290C2314yes—
318#13063290C2314yes—
319C4×D172C2318yes—
320C4×D172C2314yes—
321C4×D172C2312yes—
322C4×D172C2314yes—
323D4×Dic43C2318yes—
324D4×Dic43C2314yes—
325D4×Dic43C2318yes—
326D4×Dic43C2318yes—
327D4×Dic43C2314yes—
328D4×Dic43C2314yes—
329D4×Dic43C2312yes—
330D4×Dic43C2314yes—
331D4×Dic43C2312yes—
332D4×Dic43C2314yes—
333#13063287C2314yes—
334C4×C22⋊D43C2314yes—
335C4×C22⋊D43C2314yes—
336C4×C22⋊D43C2314yes—
337C4×C22⋊D43C2314yes—
338C4×C22⋊D43C2318yes—
339C4×C22⋊D43C2314yes—
340C4×C22⋊D43C2318yes—
341C4×C22⋊D43C2314yes—
342C4×C22⋊D43C2314yes—
343(C22⋊D43)⋊C4C2318yes—
344(C22⋊D43)⋊C4C2318yes—
345(C22⋊D43)⋊C4C2318yes—
346(C22⋊D43)⋊C4C2318yes—
347(C22⋊D43)⋊C4C2314yes—
348(C22⋊D43)⋊C4C2314yes—
349#13063284C2314yes—
350#13063284C2314yes—
351#13063284C2314yes—
352#13063284C2311yescharacteristic
353#13063284C2312yes—
354#13063284C2314yes—
355#13063283C2318yes—
356#13063283C2318yes—
357#13063283C2314yes—
358#13063283C2314yes—
359#13063282C2314yes—
360#13063282C2314yes—
361#13063282C2318yes—
362#13063282C2312yes—
363#13063281C2314yes—
364#13063281C2318yes—
365#13063281C2318yes—
366#13063281C2314yes—
367C2×C4⋊Dic43C2314yes—
368C2×C4⋊Dic43C2318yes—
369C2×C4⋊Dic43C2314yes—
370C2×C4⋊Dic43C2314yes—
371C2×C4⋊Dic43C2312yes—
372C2×Dic43⋊C4C2318yes—
373C2×Dic43⋊C4C2318yes—
374C2×Dic43⋊C4C2314yes—
375C2×Dic43⋊C4C2314yes—
376C2×Dic43⋊C4C2314yes—
377C4⋊C4×D43C2314yes—
378C4⋊C4×D43C2314yes—
379C4⋊C4×D43C2318yes—
380C4⋊C4×D43C2318yes—
381C4⋊C4×D43C2314yes—
382C4⋊C4×D43C2318yes—
383C4⋊C4×D43C2314yes—
384C4⋊C4×D43C2314yes—
385C4⋊C4×D43C2318yes—
386C4⋊C4×D43C2318yes—
387C2×C4×Dic43C2311yescharacteristic
388C2×C4×Dic43C2312yes—
389C2×C4×Dic43C2314yes—
390C42×D43C2312yes—
391C42×D43C2312yes—
392C42×D43C2312yes—
393C42×D43C2312yes—
394C42×D43C2312yes—
395C2×#41×C43C2311yescharacteristic
396C2×#41×C43C2312yes—
397C4⋊Q8×C43C2311yescharacteristic
398#127×C43C2311yescharacteristic
399#126×C43C2318yes—
400#126×C43C2318yes—
401#125×C43C2312yes—
402#125×C43C2312yes—
403#125×C43C2314yes—
404#125×C43C2318yes—
405#124×C43C2312yes—
406#123×C43C2318yes—
407#123×C43C2318yes—
408C22⋊Q8×C43C2314yes—
409C22⋊Q8×C43C2314yes—
410#121×C43C2314yes—
411#121×C43C2314yes—
412#121×C43C2318yes—
413#121×C43C2314yes—
414#121×C43C2318yes—
415C4×Q8×C43C2312yes—
416C4×Q8×C43C2314yes—
417C4×D4×C43C2314yes—
418C4×D4×C43C2318yes—
419C4×D4×C43C2314yes—
420C4×D4×C43C2312yes—
421C4×D4×C43C2318yes—
422C4×D4×C43C2314yes—
423#117×C43C2311yescharacteristic
424#117×C43C2312yes—
425#117×C43C2314yes—
426#117×C43C2318yes—
427C2×C4⋊C4×C43C2312yes—
428C2×C4⋊C4×C43C2314yes—
429C2×C4⋊C4×C43C2314yes—
430C2×C42×C43C2311yescharacteristic
431C2×C42×C43C2312yes—
432C23×D43C2411yescharacteristic
433#41×C43—24no—
434#41×C43—28no—
435C2×Q8×C43C2411yescharacteristic
436C2×Q8×C43C2412yes—
437C2×D4×C43C2412yes—
438C2×D4×C43C2414yes—
439C2×D4×C43C2411yescharacteristic
440C2×D4×C43C2412yes—
441C2×D4×C43C2418yes—
442C2×D4×C43C2414yes—
443C22×C4×C43C2412yes—
444C22×C4×C43C2414yes—
445C22×C4×C43C2412yes—
446C22×C4×C43C2414yes—
447C22×C4×C43C2414yes—
448C22×C4×C43C2418yes—
449C22×C4×C43C2411yescharacteristic
450C2×C22⋊D43C2414yes—
451C2×C22⋊D43C2414yes—
452C2×C22⋊D43C2414yes—
453C2×C22⋊D43C2412yes—
454C2×C22⋊D43C2418yes—
455C2×C22⋊D43C2414yes—
456C22×Dic43C2411yescharacteristic
457C22×Dic43C2412yes—
458C22×Dic43C2414yes—
459C22×Dic43C2414yes—
460C22×Dic43C2414yes—
461C22×Dic43C2418yes—
462C22×Dic43C2418yes—
463#10621900—416no—
464#10621900—48no—
465#10621898—24no—
466#10621898—48no—
467#10621898—416no—
468C2×D172C2411yescharacteristic
469C2×D172C2414yes—
470C2×C4×D43—24no—
471C2×C4×D43—44no—
472C2×C4×D43—48no—
473C2×C4×D43C2412yes—
474C2×C4×D43C2412yes—
475C2×C4×D43C2412yes—
476C2×C4×D43C2412yes—
477C2×C4×D43C2412yes—
478C2×C4×D43C2418yes—
479C2×C4×D43C2412yes—
480C2×C4×D43C2412yes—
481C2×C4×D43C2414yes—
482C2×C4×D43C2418yes—
483C2×C4×D43C2418yes—
484C2×Dic86C2411yescharacteristic
485C2×Dic86C2418yes—
486C2×Dic86C2414yes—
487C2×Dic86C2418yes—
488C2×Dic86C2414yes—
489C4⋊C4×C43C2412yes—
490C4⋊C4×C43C2414yes—
491C4⋊C4×C43C2418yes—
492C4⋊C4×C43C2414yes—
493C4⋊C4×C43C2418yes—
494C4⋊C4×C43C2418yes—
495C4⋊C4×C43C2414yes—
496C4⋊C4×C43C2418yes—
497C4⋊C4×C43C2414yes—
498C22⋊C4×C43C2414yes—
499C22⋊C4×C43C2412yes—
500C22⋊C4×C43C2414yes—
501C22⋊C4×C43C2418yes—
502C22⋊C4×C43C2418yes—
503C22⋊C4×C43C2414yes—
504C22⋊C4×C43C2418yes—
505C42×C43C2411yescharacteristic
506C42×C43C2412yes—
507C42×C43C2414yes—
508C42×C43C2411yescharacteristic
509C42×C43C2412yes—
510C42×C43C2418yes—
511C22⋊Dic43C2414yes—
512C22⋊Dic43C2418yes—
513C22⋊Dic43C2414yes—
514C22⋊Dic43C2414yes—
515C22⋊Dic43C2414yes—
516C22⋊Dic43C2412yes—
517C22⋊Dic43C2414yes—
518C22⋊Dic43C2414yes—
519C22⋊Dic43C2418yes—
520C22⋊Dic43C2414yes—
521C22⋊Dic43C2418yes—
522(C2×D43)⋊C4C2414yes—
523(C2×D43)⋊C4C2414yes—
524(C2×D43)⋊C4C2414yes—
525(C2×D43)⋊C4C2414yes—
526(C2×D43)⋊C4C2414yes—
527(C2×D43)⋊C4C2414yes—
528(C2×D43)⋊C4C2414yes—
529(C2×D43)⋊C4C2418yes—
530(C2×D43)⋊C4C2418yes—
531C4⋊Dic43C2418yes—
532C4⋊Dic43C2414yes—
533C4⋊Dic43C2414yes—
534C4⋊Dic43C2418yes—
535C4⋊Dic43C2412yes—
536C4⋊Dic43C2418yes—
537C4⋊Dic43C2412yes—
538C4⋊Dic43C2412yes—
539C4⋊Dic43C2414yes—
540C4⋊Dic43C2418yes—
541C4⋊Dic43C2418yes—
542C4⋊Dic43C2418yes—
543C4⋊Dic43C2414yes—
544C4⋊Dic43C2414yes—
545C4⋊Dic43C2414yes—
546C4⋊Dic43C2414yes—
547Dic43⋊C4C2418yes—
548Dic43⋊C4C2418yes—
549Dic43⋊C4C2418yes—
550Dic43⋊C4C2418yes—
551Dic43⋊C4C2418yes—
552Dic43⋊C4C2418yes—
553Dic43⋊C4C2414yes—
554Dic43⋊C4C2418yes—
555Dic43⋊C4C2418yes—
556Dic43⋊C4C2414yes—
557Dic43⋊C4C2414yes—
558Dic43⋊C4C2418yes—
559Dic43⋊C4C2418yes—
560Dic43⋊C4C2418yes—
561Dic43⋊C4C2418yes—
562Dic43⋊C4C2414yes—
563Dic43⋊C4C2414yes—
564Dic43⋊C4C2414yes—
565Dic43⋊C4C2414yes—
566Dic43⋊C4C2414yes—
567Dic43⋊C4C2414yes—
568C4×Dic43C2411yescharacteristic
569C4×Dic43C2412yes—
570C4×Dic43C2411yescharacteristic
571C4×Dic43C2412yes—
572C4×Dic43C2412yes—
573C4×Dic43C2412yes—
574C4×Dic43C2412yes—
575C4×Dic43C2414yes—
576C4×Dic43C2412yes—
577C4×Dic43C2414yes—
578C4×Dic43C2414yes—
579C4×Dic43C2414yes—
580C4×Dic43C2418yes—
581C4×Dic43C2418yes—
582C4×Dic43C2418yes—
583C23×C43C2514yes—
584C23×C43C2512yes—
585C23×C43C2511yescharacteristic
586C22×D43—22no—
587C22×D43—24no—
588C22×D43C2512yes—
589C22×D43C2512yes—
590Q8×C43—22no—
591Q8×C43—24no—
592D4×C43—24no—
593D4×C43—28no—
594D4×C43—22no—
595D4×C43—24no—
596D4×C43—44no—
597D4×C43—48no—
598C2×C4×C43—28no—
599C2×C4×C43—24no—
600C2×C4×C43—42no—
601C2×C4×C43—44no—
602C2×C4×C43—48no—
603C2×C4×C43—44no—
604C2×C4×C432−1+414yes—
605C2×C4×C43C2512yes—
606C2×C4×C43C2514yes—
607C2×C4×C43C2512yes—
608C2×C4×C43C2512yes—
609C2×C4×C43C2518yes—
610C2×C4×C43C2514yes—
611C2×C4×C43C2511yescharacteristic
612C2×C4×C43C2511yescharacteristic
613C22⋊D43—24no—
614C22⋊D43—28no—
615C22⋊D43—28no—
616C22⋊D43—28no—
617C22⋊D43—44no—
618C22⋊D43—48no—
619C2×Dic43—22no—
620C2×Dic43—42no—
621C2×Dic43—44no—
622C2×Dic43—44no—
623C2×Dic43—48no—
624C2×Dic43—48no—
625C2×Dic43—44no—
626C2×Dic43C2512yes—
627C2×Dic43C2512yes—
628C2×Dic43C2512yes—
629C2×Dic43C2514yes—
630C2×Dic43C2512yes—
631C2×Dic43C2514yes—
632C2×Dic43C2514yes—
633C2×Dic43C2518yes—
634D172—28no—
635D172—22no—
636C4×D43—24no—
637C4×D43—216no—
638C4×D43—24no—
639C4×D43—24no—
640C4×D43—24no—
641C4×D43—24no—
642C4×D43—42no—
643C4×D43—48no—
644C4×D43—42no—
645C4×D43—48no—
646C4×D43—44no—
647Dic86—22no—
648Dic86—48no—
649Dic86—44no—
650Dic86—44no—
651Dic86—48no—
652#62825—431nomaximal, Sylow
653C22×C43—22no—
654C22×C43—24no—
655C22×C43—22no—
656C22×C43—24no—
657C22×C43—24no—
658C22×C43—24no—
659C22×C43C2×2−1+412yes—
660C22×C43C2611yescharacteristic
661C2×D43—28no—
662C2×D43—22no—
663C2×D43—22no—
664C2×D43—22no—
665C2×D43—24no—
666C2×D43#58514yes—
667C4×C43—24no—
668C4×C43—22no—
669C4×C43—24no—
670C4×C43—22no—
671C4×C43—28no—
672C4×C43—22no—
673C4×C43C2×2−1+412yes—
674C4×C43C2×2−1+412yes—
675Dic43—22no—
676Dic43—22no—
677Dic43—24no—
678Dic43—24no—
679Dic43—24no—
680Dic43—22no—
681Dic43—28no—
682Dic43—22no—
683#3563—434no—
684#3563—434no—
685#3559—434no—
686#3559—434no—
687#3553—438no—
688#3515—434no—
689#3515—434no—
690#3515—434no—
691#3515—434no—
692#3512—432no—
693#3512—431no—
694#3512D4311yescharacteristic, complemented
695#3504—431no—
696#3504—432no—
697#3504—431no—
698#3492—438no—
699#3492—432no—
700#3492—432no—
701#3444—431no—
702#3444—431no—
703C22×#125—431no—
704C2×C43—22no—
705C2×C43—44no—
706C2×C43—42no—
707C2×C43C22×2−1+411yescharacteristic
708C2×C43C2×#58512yes—
709D43—24no—
710D43—42no—
711#564—438no—
712#563—438no—
713#563—438no—
714#562—438no—
715#557—434no—
716#557—434no—
717#557—434no—
718#557—434no—
719#554—434no—
720#554—434no—
721#554—434no—
722#554—434no—
723#554—438no—
724#554—434no—
725#554—438no—
726#554—438no—
727#554—434no—
728#554—434no—
729#554—438no—
730#554—434no—
731#553—438no—
732#553—438no—
733#553—434no—
734#553—434no—
735#553—434no—
736#553—438no—
737#553—434no—
738#553—434no—
739#553—434no—
740#553—434no—
741#553C2×D4318yes—
742#553C2×D4314yescomplemented
743#552—438no—
744#552—438no—
745#552—438no—
746#552—438no—
747#552—438no—
748#552—434no—
749#552—434no—
750#552—434no—
751#552—434no—
752#552—434no—
753#552—434no—
754#552—438no—
755#552—438no—
756#552—438no—
757#552—434no—
758#552C2×D4314yescomplemented
759#547—438no—
760#547—438no—
761#547—438no—
762#547—434no—
763#547—434no—
764#547—438no—
765#547—434no—
766#547—434no—
767#544—438no—
768#544—434no—
769#544—432no—
770#544—434no—
771#544—434no—
772#544—432no—
773#544—434no—
774#541—432no—
775#541—438no—
776#541—438no—
777#541—438no—
778#541—434no—
779#541—438no—
780#541C2×D4312yescomplemented
781#540—432no—
782#540—434no—
783#540C2×D4312yescomplemented
784#539—438no—
785#539—438no—
786#539—438no—
787#539—438no—
788#539—438no—
789#539—438no—
790#539—438no—
791#539—438no—
792#539—438no—
793#539—438no—
794#537—432no—
795#537—438no—
796#537C2×D4312yes—
797#533—432no—
798#533—432no—
799#533—432no—
800#533—431no—
801#533—434no—
802#533—431no—
803#533—432no—
804#532—431no—
805#532—432no—
806#532—432no—
807#532C2×D4311yescharacteristic
808#529—432no—
809#529—432no—
810#529—434no—
811#529—434no—
812#529—434no—
813#529—434no—
814#529—432no—
815#529—434no—
816#529—432no—
817#529—434no—
818#529—434no—
819#529C2×D4314yescomplemented
820C2×#125—434no—
821C2×#125—434no—
822C2×#125—434no—
823C2×#125—434no—
824C2×#125—432no—
825C2×#125—434no—
826C2×#125—432no—
827C2×#125—434no—
828C2×#125—431no—
829C2×#125—432no—
830C2×#125C2×D4311yescharacteristic
831#525—432no—
832#525—431no—
833#525—434no—
834#525—438no—
835#525—434no—
836#525—438no—
837#525—431no—
838#520—432no—
839#520—432no—
840#520—438no—
841#520—438no—
842#520—432no—
843#520C2×D4312yes—
844C4×#41—432no—
845C4×#41—434no—
846C4×#41—431no—
847C4×#41—434no—
848C4×#41C2×D4311yescharacteristic
849C22×C4⋊C4—432no—
850C22×C4⋊C4—434no—
851C22×C42—431no—
852C43#6282511yescharacteristic, complemented, Sylow
853C2×#41—434no—
854C2×#41—438no—
855C2×#41—431no—
856C2×#41—434no—
857C2×#41—438no—
858C2×#41C22×D4312yes—
859C2×#41C22×D4311yescharacteristic
860C23×C4—431no—
861C23×C4—434no—
862C23×C4—432no—
863C4⋊Q8—431no—
864C4⋊Q8—432no—
865C4⋊Q8—434no—
866C4⋊Q8—434no—
867C4⋊Q8—434no—
868C4⋊Q8—438no—
869C4⋊Q8—438no—
870C4⋊Q8—438no—
871C4⋊Q8—432no—
872C4⋊Q8—434no—
873C4⋊Q8—438no—
874C4⋊Q8C22×D4311yescharacteristic
875#127—431no—
876#127C22×D4311yescharacteristic
877#126—434no—
878#126—438no—
879#126—438no—
880#126—434no—
881#126—434no—
882#126—434no—
883#126—438no—
884#126—438no—
885#126—438no—
886#126—438no—
887#126—438no—
888#126—438no—
889#126—438no—
890#126—438no—
891#126C22×D4318yes—
892#126C22×D4318yes—
893#125—434no—
894#125—438no—
895#125—438no—
896#125—434no—
897#125—438no—
898#125—434no—
899#125—434no—
900#125—438no—
901#125—432no—
902#125—438no—
903#125—438no—
904#125—438no—
905#125—434no—
906#125—434no—
907#125—434no—
908#125—434no—
909#125—434no—
910#125—438no—
911#125—438no—
912#125—438no—
913#125—438no—
914#125—438no—
915#125—438no—
916#125—438no—
917#125—438no—
918#125—438no—
919#125—432no—
920#125—432no—
921#125—434no—
922#125—431no—
923#125—431no—
924#125—438no—
925#125—434no—
926#125—438no—
927#125—438no—
928#125C22×D4312yes—
929#125C22×D4312yes—
930#125C22×D4314yes—
931#125C22×D4318yes—
932#124—431no—
933#124—431no—
934#124—434no—
935#124—434no—
936#124C22×D4312yes—
937#123—434no—
938#123—432no—
939#123—438no—
940#123—438no—
941#123—438no—
942#123—438no—
943#123—438no—
944#123—434no—
945#123—438no—
946#123—432no—
947#123—434no—
948#123—434no—
949#123—434no—
950#123—438no—
951#123—438no—
952#123—438no—
953#123—438no—
954#123—438no—
955#123—438no—
956#123—438no—
957#123—438no—
958#123C22×D4318yes—
959#123C22×D4318yes—
960C22⋊Q8—432no—
961C22⋊Q8—432no—
962C22⋊Q8—432no—
963C22⋊Q8—434no—
964C22⋊Q8—434no—
965C22⋊Q8—438no—
966C22⋊Q8—434no—
967C22⋊Q8—438no—
968C22⋊Q8—438no—
969C22⋊Q8—438no—
970C22⋊Q8—438no—
971C22⋊Q8—434no—
972C22⋊Q8—434no—
973C22⋊Q8—432no—
974C22⋊Q8—438no—
975C22⋊Q8—438no—
976C22⋊Q8—438no—
977C22⋊Q8—438no—
978C22⋊Q8—438no—
979C22⋊Q8—438no—
980C22⋊Q8—434no—
981C22⋊Q8—438no—
982C22⋊Q8—438no—
983C22⋊Q8—438no—
984C22⋊Q8—438no—
985C22⋊Q8—438no—
986C22⋊Q8—438no—
987C22⋊Q8—438no—
988C22⋊Q8—438no—
989C22⋊Q8—438no—
990C22⋊Q8C22×D4314yes—
991C22⋊Q8C22×D4314yes—
992#121—434no—
993#121—432no—
994#121—432no—
995#121—432no—
996#121—434no—
997#121—438no—
998#121—438no—
999#121—434no—
1000#121—438no—
1001#121—438no—
1002#121—438no—
1003#121—434no—
1004#121—432no—
1005#121—434no—
1006#121—438no—
1007#121C22×D4314yes—
1008#121C22×D4318yes—
1009#121C22×D4314yes—
1010#121C22×D4314yes—
1011#121C22×D4318yes—
1012#120—434no—
1013#120—432no—
1014#120—432no—
1015C4×Q8—432no—
1016C4×Q8—432no—
1017C4×Q8—434no—
1018C4×Q8—434no—
1019C4×Q8—434no—
1020C4×Q8—434no—
1021C4×Q8—438no—
1022C4×Q8—434no—
1023C4×Q8—432no—
1024C4×Q8—434no—
1025C4×Q8—434no—
1026C4×Q8—438no—
1027C4×Q8—438no—
1028C4×Q8—438no—
1029C4×Q8C22×D4312yes—
1030C4×Q8C22×D4314yes—
1031C4×D4—434no—
1032C4×D4—434no—
1033C4×D4—434no—
1034C4×D4—432no—
1035C4×D4—432no—
1036C4×D4—438no—
1037C4×D4—438no—
1038C4×D4—438no—
1039C4×D4—434no—
1040C4×D4—434no—
1041C4×D4—434no—
1042C4×D4—434no—
1043C4×D4—434no—
1044C4×D4—434no—
1045C4×D4—434no—
1046C4×D4—434no—
1047C4×D4—434no—
1048C4×D4—438no—
1049C4×D4—438no—
1050C4×D4—434no—
1051C4×D4—434no—
1052C4×D4—434no—
1053C4×D4—438no—
1054C4×D4—438no—
1055C4×D4—438no—
1056C4×D4—438no—
1057C4×D4—434no—
1058C4×D4—434no—
1059C4×D4—432no—
1060C4×D4—438no—
1061C4×D4C22×D4314yes—
1062C4×D4C22×D4314yes—
1063C4×D4C22×D4312yes—
1064C4×D4C22×D4318yes—
1065C4×D4C22×D4318yes—
1066C4×D4C22×D4314yes—
1067#117—432no—
1068#117—431no—
1069#117—434no—
1070#117—434no—
1071#117—434no—
1072#117—434no—
1073#117—434no—
1074#117—438no—
1075#117—438no—
1076#117—434no—
1077#117—434no—
1078#117—434no—
1079#117—438no—
1080#117—438no—
1081#117—434no—
1082#117—432no—
1083#117—434no—
1084#117—438no—
1085#117C22×D4311yescharacteristic
1086#117C22×D4312yes—
1087#117C22×D4318yes—
1088#117C22×D4314yes—
1089C2×C4⋊C4—432no—
1090C2×C4⋊C4—434no—
1091C2×C4⋊C4—434no—
1092C2×C4⋊C4—434no—
1093C2×C4⋊C4—434no—
1094C2×C4⋊C4—438no—
1095C2×C4⋊C4—438no—
1096C2×C4⋊C4—438no—
1097C2×C4⋊C4—434no—
1098C2×C4⋊C4—434no—
1099C2×C4⋊C4—438no—
1100C2×C4⋊C4—438no—
1101C2×C4⋊C4—434no—
1102C2×C4⋊C4—434no—
1103C2×C4⋊C4—438no—
1104C2×C4⋊C4—438no—
1105C2×C4⋊C4—434no—
1106C2×C4⋊C4—434no—
1107C2×C4⋊C4—438no—
1108C2×C4⋊C4—434no—
1109C2×C4⋊C4C22×D4312yes—
1110C2×C4⋊C4C22×D4314yes—
1111C2×C4⋊C4C22×D4314yes—
1112C2×C42—434no—
1113C2×C42—431no—
1114C2×C42—432no—
1115C2×C42—432no—
1116C2×C42—432no—
1117C2×C42—432no—
1118C2×C42—432no—
1119C2×C42—432no—
1120C2×C42C22×D4312yes—
1121C2×C42C22×D4311yescharacteristic
1122C24—431no—
1123#41—28no—
1124#41—24no—
1125#41—864no—
1126#41—1728no—
1127#41—17216no—
1128#41—1728no—
1129#41—17216no—
1130C2×Q8—431no—
1131C2×Q8—438no—
1132C2×Q8—438no—
1133C2×Q8—434no—
1134C2×Q8—434no—
1135C2×Q8C23×D4312yes—
1136C2×Q8C23×D4311yescharacteristic
1137C2×D4—432no—
1138C2×D4—434no—
1139C2×D4—434no—
1140C2×D4—434no—
1141C2×D4—438no—
1142C2×D4—434no—
1143C2×D4—431no—
1144C2×D4—434no—
1145C2×D4C23×D4314yes—
1146C2×D4C23×D4312yes—
1147C2×D4C23×D4312yes—
1148C2×D4C23×D4311yescharacteristic
1149C2×D4C23×D4318yes—
1150C2×D4C23×D4314yes—
1151C22×C4—431no—
1152C22×C4—432no—
1153C22×C4—434no—
1154C22×C4—434no—
1155C22×C4—434no—
1156C22×C4—438no—
1157C22×C4—438no—
1158C22×C4—432no—
1159C22×C4—432no—
1160C22×C4—432no—
1161C22×C4—432no—
1162C22×C4—432no—
1163C22×C4—438no—
1164C22×C4—432no—
1165C22×C4—432no—
1166C22×C4—434no—
1167C22×C4—438no—
1168C22×C4—438no—
1169C22×C4—864no—
1170C22×C4—1728no—
1171C22×C4—1724no—
1172C22×C4C23×D4314yes—
1173C22×C4C23×D4312yes—
1174C22×C4C23×D4312yes—
1175C22×C4C23×D4314yes—
1176C22×C4C23×D4314yes—
1177C22×C4C23×D4318yes—
1178C22×C4C23×D4311yescharacteristic
1179C4⋊C4—434no—
1180C4⋊C4—434no—
1181C4⋊C4—438no—
1182C4⋊C4—438no—
1183C4⋊C4—438no—
1184C4⋊C4—438no—
1185C4⋊C4—438no—
1186C4⋊C4—438no—
1187C4⋊C4—438no—
1188C4⋊C4—438no—
1189C4⋊C4—432no—
1190C4⋊C4—432no—
1191C4⋊C4—432no—
1192C4⋊C4—434no—
1193C4⋊C4—434no—
1194C4⋊C4—434no—
1195C4⋊C4—434no—
1196C4⋊C4—438no—
1197C4⋊C4—438no—
1198C4⋊C4—438no—
1199C4⋊C4—438no—
1200C4⋊C4—438no—
1201C4⋊C4—438no—
1202C4⋊C4—438no—
1203C4⋊C4—438no—
1204C4⋊C4—438no—
1205C4⋊C4—438no—
1206C4⋊C4—434no—
1207C4⋊C4—434no—
1208C4⋊C4—434no—
1209C4⋊C4—434no—
1210C4⋊C4—434no—
1211C4⋊C4—434no—
1212C4⋊C4—434no—
1213C4⋊C4—434no—
1214C4⋊C4—434no—
1215C4⋊C4—434no—
1216C4⋊C4C23×D4314yes—
1217C4⋊C4C23×D4318yes—
1218C4⋊C4C23×D4314yes—
1219C4⋊C4C23×D4318yes—
1220C4⋊C4C23×D4312yes—
1221C4⋊C4C23×D4318yes—
1222C4⋊C4C23×D4318yes—
1223C4⋊C4C23×D4314yes—
1224C4⋊C4C23×D4314yes—
1225C22⋊C4—434no—
1226C22⋊C4—434no—
1227C22⋊C4—432no—
1228C22⋊C4—434no—
1229C22⋊C4—434no—
1230C22⋊C4—438no—
1231C22⋊C4—438no—
1232C22⋊C4—438no—
1233C22⋊C4—434no—
1234C22⋊C4—434no—
1235C22⋊C4—434no—
1236C22⋊C4—434no—
1237C22⋊C4—434no—
1238C22⋊C4—434no—
1239C22⋊C4—434no—
1240C22⋊C4—434no—
1241C22⋊C4—434no—
1242C22⋊C4—438no—
1243C22⋊C4—438no—
1244C22⋊C4—434no—
1245C22⋊C4C23×D4314yes—
1246C22⋊C4C23×D4314yes—
1247C22⋊C4C23×D4318yes—
1248C22⋊C4C23×D4318yes—
1249C22⋊C4C23×D4312yes—
1250C22⋊C4C23×D4314yes—
1251C22⋊C4C23×D4318yes—
1252C42—431no—
1253C42—432no—
1254C42—431no—
1255C42—432no—
1256C42—432no—
1257C42—432no—
1258C42—432no—
1259C42—434no—
1260C42—434no—
1261C42—434no—
1262C42—434no—
1263C42—432no—
1264C42—438no—
1265C42—438no—
1266C42—438no—
1267C42C23×D4311yescharacteristic
1268C42C23×D4311yescharacteristic
1269C42C23×D4312yes—
1270C42C23×D4314yes—
1271C42C23×D4312yes—
1272C42C23×D4318yes—
1273C23—432no—
1274C23—432no—
1275C23—864no—
1276C23—862no—
1277C23C24×D4314yes—
1278C23C24×D4312yes—
1279C23C24×D4311yescharacteristic
1280Q8—22no—
1281Q8—24no—
1282Q8—862no—
1283Q8—1728no—
1284Q8—1724no—
1285Q8—1728no—
1286Q8—1724no—
1287D4—28no—
1288D4—24no—
1289D4—22no—
1290D4—24no—
1291D4—48no—
1292D4—44no—
1293D4—868no—
1294D4—868no—
1295D4—868no—
1296D4—868no—
1297D4—864no—
1298D4—862no—
1299D4—1728no—
1300D4—1724no—
1301C2×C4—28no—
1302C2×C4—24no—
1303C2×C4—42no—
1304C2×C4—44no—
1305C2×C4—44no—
1306C2×C4—48no—
1307C2×C4—432no—
1308C2×C4—432no—
1309C2×C4—432no—
1310C2×C4—434no—
1311C2×C4—434no—
1312C2×C4—434no—
1313C2×C4—432no—
1314C2×C4—438no—
1315C2×C4—864no—
1316C2×C4—8616no—
1317C2×C4—864no—
1318C2×C4—862no—
1319C2×C4—864no—
1320C2×C4—864no—
1321C2×C4—864no—
1322C2×C4—1722no—
1323C2×C4—1728no—
1324C2×C4—1722no—
1325C2×C4—1724no—
1326C2×C4—1728no—
1327C2×C4—1722no—
1328C2×C4—1724no—
1329C2×C4—1724no—
1330C2×C4—1724no—
1331C2×C4—1728no—
1332C2×C4—1728no—
1333C2×C4#1306337214yes—
1334C2×C4C24×D4312yes—
1335C2×C4C24×D4314yes—
1336C2×C4C24×D4312yes—
1337C2×C4C24×D4312yes—
1338C2×C4C24×D4318yes—
1339C2×C4C24×D4314yes—
1340C2×C4C24×D4311yescharacteristic
1341C2×C4C24×D4311yescharacteristic
1342C22—22no—
1343C22—24no—
1344C22—22no—
1345C22—24no—
1346C22—24no—
1347C22—24no—
1348C22—434no—
1349C22—868no—
1350C22—862no—
1351C22—862no—
1352C22—862no—
1353C22—864no—
1354C22C2×#1306337212yes—
1355C22C25×D4311yescharacteristic
1356C4—24no—
1357C4—22no—
1358C4—22no—
1359C4—24no—
1360C4—28no—
1361C4—22no—
1362C4—862no—
1363C4—862no—
1364C4—862no—
1365C4—868no—
1366C4—862no—
1367C4—864no—
1368C4—864no—
1369C4—864no—
1370C4C2×#1306337212yes—
1371C4C2×#1306337212yes—
1372C2—22no—
1373C2—44no—
1374C2—42no—
1375C2—864no—
1376C2—1722no—
1377C2C22×#1306337211yescharacteristic
1378C2#585×D4312yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3512C2
hypercenter#3512D43
hypocenterC43#62825
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3512

Complements

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

NH ≅ G/Ntype
1. #19149202C2semidirect
2. #19149200C2semidirect
3. #19149125C2semidirect
4. #19149119C2semidirect
5. #19149043C2semidirect
6. #19148575C2semidirect
7. #19148570C2semidirect
8. #19148566C2semidirect
9. #19148561C2semidirect
10. #19148516C2semidirect
11. #19148515C2semidirect
12. #19148421C2semidirect
13. #19148419C2semidirect
14. #19148417C2semidirect
15. #19148302C2semidirect
16. #19148299C2semidirect
17. #19148298C2semidirect
18. #19147890C2semidirect
19. #19147888C2semidirect
20. C2×#125×D43C2semidirect
21. C43×#3512C2semidirect
22. C43⋊#564C22semidirect
23. #14583652C22semidirect
24. #14583651C22semidirect
25. #14583644C22semidirect
26. #14583628C22semidirect
27. #14583626C22semidirect
28. #14583625C22semidirect
29. #14583625C22semidirect
33. #14583608C22semidirect
34. #14583608C22semidirect
38. #14583606C22semidirect
39. #14583605C22semidirect
43. #14583601C22semidirect
47. #14583596C22semidirect
48. #14583595C22semidirect
52. #14583591C22semidirect
54. #14583589C22semidirect
55. #14583589C22semidirect
59. #14583586C22semidirect
62. #14583585C22semidirect
65. #14583583C22semidirect
66. #14583582C22semidirect
76. #14583530C22semidirect
78. #14583529C22semidirect
80. #14583527C22semidirect
81. #14583527C22semidirect
82. #14583511C22semidirect
83. #14583510C22semidirect
84. #14583509C22semidirect
85. #14583508C22semidirect
86. #14583506C22semidirect
87. #14583506C22semidirect
88. #14583503C22semidirect
89. #14583502C22semidirect
91. #14583494C22semidirect
92. #14583493C22semidirect
95. #14583492C22semidirect
97. #14583491C22semidirect
103. #14583456C22semidirect
104. #14583455C22semidirect
108. #14583452C22semidirect
113. #14583435C22semidirect
117. #14583430C22semidirect
121. #14583428C22semidirect
124. C2×#13063317C22semidirect
126. C2×#13063316C22semidirect
132. #125×D43C22semidirect
153. C43×#553C22semidirect
154. C43×#552C22semidirect
155. C43×#541C22semidirect
156. C43×#540C22semidirect
159. C43×#529C22semidirect
694. #3512D43semidirect
742. #553C2×D43semidirect
758. #552C2×D43semidirect
780. #541C2×D43semidirect
783. #540C2×D43semidirect
819. #529C2×D43semidirect
852. C43#62825semidirect

Maximal subgroups

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

subgroupindex
#191492022
#191492002
#191491252
#191491192
#191490432
#191485752
#191485702
#191485662
#191485612
#191485162
#191485152
#191484212
#191484192
#191484172
#191483022
#191482992
#191482982
#191478902
#191478882
C2×#125×D432
C43×#35122
#6282543