Finite Group Databasebeta

← #26005289

Subgroups — #26005289

Order 11008.

7274 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149151C218yesmaximal, complemented
2#19149133C214yesmaximal, complemented
3#19149118C214yesmaximal, complemented
4#19148952C214yesmaximal, complemented
5#19148939C212yesmaximal, complemented
6#19148928C212yesmaximal, complemented
7#19148672C214yesmaximal, complemented
8#19148622C214yesmaximal, complemented
9#19148535C218yesmaximal, complemented
10#19148429C214yesmaximal, complemented
11#19148352C214yesmaximal, complemented
12#19148325C218yesmaximal, complemented
13#19148239C214yesmaximal, complemented
14C2×#14583433C212yesmaximal, complemented
15C2×C43×#532C211yesmaximal, characteristic, complemented
16C2×#13063370C2214yescomplemented
17#14583649C2214yescomplemented
18#14583648C2218yescomplemented
19#14583643C2218yescomplemented
20#14583641C2214yescomplemented
21#14583636C2218yescomplemented
22#14583635C2212yescomplemented
23#14583632C2218yescomplemented
24#14583629C2212yescomplemented
25#14583615C2212yescomplemented
26#14583611C2218yescomplemented
27#14583610C2214yescomplemented
28#14583608C2218yescomplemented
29#14583601C2218yescomplemented
30#14583599C2218yescomplemented
31#14583598C22116yescomplemented
32#14583592C22116yescomplemented
33#14583584C2218yescomplemented
34#14583579C2218yescomplemented
35#14583578C22116yescomplemented
36#14583575C22116yescomplemented
37#14583569C2214yescomplemented
38#14583555C2218yescomplemented
39#14583550C2218yescomplemented
40#14583549C2218yescomplemented
41#14583548C22116yescomplemented
42#14583548C22116yescomplemented
43#14583544C2218yescomplemented
44#14583543C2218yescomplemented
45#14583539C22116yescomplemented
46#14583538C22116yescomplemented
47#14583537C22116yescomplemented
48#14583537C22116yescomplemented
49#14583534C2212yescomplemented
50#14583533C2218yescomplemented
51D4×C22⋊D43C2218yescomplemented
52#14583526C2218yescomplemented
53#14583523C2218yescomplemented
54#14583514C2218yescomplemented
55#14583513C22116yescomplemented
56#14583503C2218yescomplemented
57#14583500C2218yescomplemented
58#14583494C2218yescomplemented
59#14583491C22116yescomplemented
60#14583486C2218yescomplemented
61#14583483C22116yescomplemented
62#14583482C22116yescomplemented
63#14583476C2218yescomplemented
64#14583473C2218yescomplemented
65#14583462C2218yescomplemented
66#14583458C2218yescomplemented
67#14583458C2218yescomplemented
68#14583457C2218yescomplemented
69#14583444C2218yescomplemented
70#14583433C2214yescomplemented
71#14583433C2214yescomplemented
72#14583433C2214yescomplemented
73#14583433C2214yescomplemented
74#14583433C2214yescomplemented
75#14583433C2214yescomplemented
76#14583433C2214yescomplemented
77#14583433C2214yescomplemented
78#14583430C2218yescomplemented
79C2×#13063319C2214yescomplemented
80C2×#13063317C2212yescomplemented
81C2×#13063313C2212yescomplemented
82#14583410C2218yescomplemented
83#14583409C2218yescomplemented
84C2×#13063308C2214yescomplemented
85C2×#13063308C2218yescomplemented
86C2×#13063304C2212yescomplemented
87C2×#13063299C2212yes—
88#121×D43C2218yescomplemented
89#14583378C2218yescomplemented
90#14583374C2214yescomplemented
91#14583371C2218yescomplemented
92C2×C4×Dic86C2212yescomplemented
93C2×C4×D172C2212yescomplemented
94C2×C4×C22⋊D43C2214yescomplemented
95C2×#13063282C2214yescomplemented
96C22×#41×C43C2212yescomplemented
97C43×#532C2214yescomplemented
98C43×#532C2214yescomplemented
99C43×#532C2214yescomplemented
100C43×#532C2214yescomplemented
101C2×C4⋊Q8×C43C2211yescharacteristic, complemented
102C2×#127×C43C2211yescharacteristic, complemented
103C2×#124×C43C2212yescomplemented
104C2×#121×C43C2214yescomplemented
105C2×C4×D4×C43C2214yescomplemented
106C22×C42×C43C2211yescharacteristic, complemented
107#13063370—416no—
108C2×#10621898C2318yes—
109C2×#10621900C2318yes—
110C2×#10621900C23116yes—
111C22×Dic86C2312yes—
112C22×D172C2312yes—
113C22×C22⋊D43C2314yes—
114C22×C22⋊D43C2318yes—
115C2×D4×D43C2318yes—
116C2×D4×D43C23116yes—
117C22×C4×D43C2314yes—
118#13063324C2318yes—
119#13063323C2318yes—
120#13063323C2318yes—
121#13063321C2318yes—
122#13063320C23116yes—
123#13063319C2318yes—
124#13063319C2318yes—
125#13063319C2318yes—
126#13063319C2318yes—
127#13063318C23116yes—
128#13063318C23116yes—
129#13063317C2314yes—
130#13063317C2314yes—
131#13063317C2314yes—
132#13063317C2314yes—
133#13063316C2318yes—
134#13063315C23116yes—
135#13063314C2318yes—
136#13063314C2318yes—
137#13063313C2314yes—
138#13063313C2314yes—
139#13063313C2314yes—
140#13063313C2314yes—
141#13063312C2318yes—
142#13063311C23116yes—
143#13063311C23116yes—
144#13063310C23116yes—
145#13063309C23116yes—
146#13063308C23116yes—
147#13063308C23116yes—
148#13063308C23116yes—
149#13063308C2318yes—
150#13063308C2318yes—
151#13063308C2318yes—
152#13063308C2318yes—
153#13063307C23116yes—
154#13063307C23116yes—
155#13063306C23116yes—
156#13063306C2318yes—
157#13063306C2318yes—
158#13063306C23116yes—
159#13063305C2318yes—
160#13063304C2314yes—
161#13063304C23116yes—
162#13063304C2314yes—
163#13063304C2314yes—
164#13063304C2314yes—
165#13063303C23116yes—
166#13063302C23116yes—
167#13063302C23116yes—
168#13063301C23116yes—
169#13063301C23116yes—
170#13063300C2318yes—
171#13063299C23116yes—
172#13063299C2314yes—
173#13063299C2314yes—
174#13063299C2314yes—
175#13063299C2314yes—
176#13063298C23116yes—
177#13063298C23116yes—
178#13063297C23116yes—
179#13063297C23116yes—
180#13063297C23116yes—
181#13063297C23116yes—
182#13063297C23116yes—
183#13063297C23116yes—
184#13063296C2318yes—
185#13063296C2318yes—
186#13063295C23116yes—
187#13063294C23116yes—
188#13063293C23116yes—
189#13063293C2318yes—
190#13063293C2318yes—
191#13063293C23116yes—
192C4×Dic86C2314yes—
193C4×Dic86C2314yes—
194C4×Dic86C2314yes—
195C4×Dic86C2314yes—
196#13063290C2318yes—
197C4×D172C2314yes—
198C4×D172C2314yes—
199C4×D172C2314yes—
200C4×D172C2314yes—
201D4×Dic43C23116yes—
202D4×Dic43C2318yes—
203D4×Dic43C23116yes—
204D4×Dic43C2318yes—
205#13063287C2318yes—
206C4×C22⋊D43C2318yes—
207C4×C22⋊D43C2318yes—
208C4×C22⋊D43C23116yes—
209C4×C22⋊D43C2318yes—
210C4×C22⋊D43C2318yes—
211C4×C22⋊D43C23116yes—
212(C22⋊D43)⋊C4C23116yes—
213(C22⋊D43)⋊C4C23116yes—
214#13063284C2318yes—
215#13063283C2318yes—
216#13063282C2318yes—
217#13063282C2318yes—
218#13063282C2318yes—
219#13063282C2318yes—
220#13063281C23116yes—
221C2×C4⋊Dic43C2312yes—
222C2×C4⋊Dic43C2312yes—
223C2×Dic43⋊C4C2314yes—
224C2×Dic43⋊C4C23116yes—
225C2×Dic43⋊C4C2314yes—
226C2×Dic43⋊C4C2314yes—
227C2×Dic43⋊C4C2314yes—
228C4⋊C4×D43C2318yes—
229C2×C22⋊Dic43C2318yes—
230C2×C22⋊Dic43C2314yes—
231C2×(C2×D43)⋊C4C23116yes—
232C2×(C2×D43)⋊C4C2314yes—
233C2×(C2×D43)⋊C4C2314yes—
234C2×(C2×D43)⋊C4C2314yes—
235C2×(C2×D43)⋊C4C2314yes—
236C22⋊C4×D43C23116yes—
237C2×C4×Dic43C2314yes—
238C2×#41×C43—48no—
239C2×#41×C43C2318yes—
240C2×#41×C43C2318yes—
241C22×Q8×C43C2312yes—
242C22×D4×C43C2314yes—
243C22×D4×C43C2314yes—
244C22×D4×C43C2312yes—
245C23×C4×C43C2311yescharacteristic
246C23×C4×C43C2312yes—
247C23×C4×C43C2314yes—
248C4⋊Q8×C43C2312yes—
249C4⋊Q8×C43C2312yes—
250C4⋊Q8×C43C2314yes—
251#127×C43C2312yes—
252#127×C43C2312yes—
253#127×C43C2314yes—
254#124×C43C2314yes—
255#124×C43C2314yes—
256#124×C43C2318yes—
257#121×C43C2318yes—
258#121×C43C2318yes—
259#121×C43C2318yes—
260#121×C43C2318yes—
261C4×D4×C43C2318yes—
262C4×D4×C43C2318yes—
263C4×D4×C43C2318yes—
264C4×D4×C43C2318yes—
265C2×C4⋊C4×C43C2314yes—
266C2×C22⋊C4×C43C2318yes—
267C2×C42×C43C2312yes—
268C2×C42×C43C2311yescharacteristic
269C2×C42×C43C2311yescharacteristic
270C2×C42×C43C2312yes—
271C2×C42×C43C2312yes—
272C2×C42×C43C2312yes—
273C2×C42×C43C2312yes—
274C24×C43C2414yes—
275C24×C43C2411yescharacteristic
276C23×D43C2414yes—
277C23×D43C2418yes—
278#41×C43—416no—
279#41×C43—416no—
280C2×Q8×C43—44no—
281C2×Q8×C43C2414yes—
282C2×Q8×C43C2414yes—
283C2×D4×C43—216no—
284C2×D4×C43—44no—
285C2×D4×C43—48no—
286C2×D4×C43C2418yes—
287C2×D4×C43C24116yes—
288C2×D4×C43C2418yes—
289C2×D4×C43C2414yes—
290C2×D4×C43C2414yes—
291C22×C4×C43—24no—
292C22×C4×C43—48no—
293C22×C4×C43—44no—
294C22×C4×C43C2412yes—
295C22×C4×C43C2412yes—
296C22×C4×C43C2412yes—
297C22×C4×C43C2411yescharacteristic
298C22×C4×C43C2411yescharacteristic
299C22×C4×C43C2412yes—
300C22×C4×C43C2412yes—
301C22×C4×C43C2414yes—
302C22×C4×C43C2412yes—
303C22×C4×C43C2412yes—
304C22×C4×C43C2412yes—
305C22×C4×C43C24116yes—
306C2×C22⋊D43—216no—
307C2×C22⋊D43—416no—
308C2×C22⋊D43C2418yes—
309C2×C22⋊D43C2418yes—
310C2×C22⋊D43C24116yes—
311C2×C22⋊D43C24116yes—
312C2×C22⋊D43C24116yes—
313C22×Dic43C2414yes—
314C22×Dic43C2414yes—
315C22×Dic43C2414yes—
316C22×Dic43C24116yes—
317C22×Dic43C2418yes—
318#10621900—416no—
319#10621900—432no—
320D4×D43—432no—
321D4×D43—416no—
322#10621898—416no—
323C2×D172—44no—
324C2×D172C2414yes—
325C2×D172C2414yes—
326C2×D172C2418yes—
327C2×C4×D43—48no—
328C2×C4×D43C2418yes—
329C2×C4×D43C2418yes—
330C2×C4×D43C24116yes—
331C2×Dic86—44no—
332C2×Dic86C2414yes—
333C2×Dic86C2414yes—
334C2×Dic86C2418yes—
335C4⋊C4×C43C2418yes—
336C4⋊C4×C43C2418yes—
337C22⋊C4×C43C24116yes—
338C22⋊C4×C43C24116yes—
339C42×C43C2412yes—
340C42×C43C2412yes—
341C42×C43C2412yes—
342C42×C43C2412yes—
343C42×C43C2411yescharacteristic
344C42×C43C2412yes—
345C42×C43C2411yescharacteristic
346C42×C43C2412yes—
347C42×C43C2411yescharacteristic
348C42×C43C2411yescharacteristic
349C22⋊Dic43C24116yes—
350C22⋊Dic43C2418yes—
351C22⋊Dic43C2418yes—
352C22⋊Dic43C2418yes—
353C22⋊Dic43C2418yes—
354C22⋊Dic43C24116yes—
355(C2×D43)⋊C4C2418yes—
356(C2×D43)⋊C4C24116yes—
357(C2×D43)⋊C4C2418yes—
358(C2×D43)⋊C4C2418yes—
359(C2×D43)⋊C4C2418yes—
360(C2×D43)⋊C4C2418yes—
361(C2×D43)⋊C4C24116yes—
362(C2×D43)⋊C4C2418yes—
363(C2×D43)⋊C4C2418yes—
364(C2×D43)⋊C4C2418yes—
365C4⋊Dic43C2414yes—
366C4⋊Dic43C2414yes—
367C4⋊Dic43C2414yes—
368C4⋊Dic43C2414yes—
369C4⋊Dic43C24116yes—
370Dic43⋊C4C24116yes—
371Dic43⋊C4C2418yes—
372Dic43⋊C4C2418yes—
373Dic43⋊C4C2418yes—
374Dic43⋊C4C2418yes—
375Dic43⋊C4C2418yes—
376Dic43⋊C4C24116yes—
377Dic43⋊C4C2418yes—
378Dic43⋊C4C2418yes—
379Dic43⋊C4C2418yes—
380C4×Dic43C2418yes—
381C4×Dic43C2418yes—
382C4×Dic43C2418yes—
383C4×Dic43C2418yes—
384C23×C43—28no—
385C23×C43—42no—
386C23×C43—48no—
387C23×C43H(5,𝔽2)14yes—
388C23×C43C2518yes—
389C23×C43C2511yescharacteristic
390C23×C43C2512yes—
391C22×D43—28no—
392C22×D43—44no—
393C22×D43—44no—
394C22×D43—48no—
395C22×D43—416no—
396C22×D43C2518yes—
397Q8×C43—44no—
398Q8×C43—44no—
399D4×C43—232no—
400D4×C43—216no—
401D4×C43—48no—
402D4×C43—44no—
403D4×C43—44no—
404C2×C4×C43—28no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—24no—
408C2×C4×C43—24no—
409C2×C4×C43—24no—
410C2×C4×C43—24no—
411C2×C4×C43—24no—
412C2×C4×C43—42no—
413C2×C4×C43—42no—
414C2×C4×C43—42no—
415C2×C4×C43—416no—
416C2×C4×C43C2512yes—
417C2×C4×C43C2518yes—
418C2×C4×C43C2512yes—
419C2×C4×C43C2512yes—
420C2×C4×C43C2511yescharacteristic
421C2×C4×C43C2511yescharacteristic
422C2×C4×C43C2512yes—
423C2×C4×C43C2512yes—
424C22⋊D43—216no—
425C22⋊D43—216no—
426C22⋊D43—416no—
427C22⋊D43—416no—
428C22⋊D43—416no—
429C2×Dic43—28no—
430C2×Dic43—44no—
431C2×Dic43—44no—
432C2×Dic43—48no—
433C2×Dic43—416no—
434C2×Dic43C2518yes—
435C2×Dic43C2518yes—
436C2×Dic43C2518yes—
437D172—28no—
438D172—44no—
439D172—48no—
440C4×D43—216no—
441C4×D43—48no—
442C4×D43—416no—
443Dic86—28no—
444Dic86—44no—
445Dic86—48no—
446#62822—431nomaximal, Sylow
447C22×C43—22no—
448C22×C43—22no—
449C22×C43—22no—
450C22×C43—28no—
451C22×C43—216no—
452C22×C43—44no—
453C22×C43—88no—
454C22×C43C2×H(5,𝔽2)14yes—
455C22×C43C2×H(5,𝔽2)12yes—
456C22×C43C2611yescharacteristic
457C2×D43—28no—
458C2×D43—28no—
459C2×D43—28no—
460C2×D43—88no—
461C2×D43—168no—
462C4×C43—28no—
463C4×C43—22no—
464C4×C43—21no—
465C4×C43—21no—
466C4×C43—22no—
467C4×C43—22no—
468C4×C43—22no—
469C4×C43#58514yes—
470Dic43—28no—
471Dic43—28no—
472Dic43—28no—
473#3560—438no—
474#3559—434no—
475#3558—434no—
476#3545—434no—
477#3544—432no—
478#3543—432no—
479#3522—434no—
480#3519—434no—
481#3513—438no—
482#3505—434no—
483#3496—434no—
484#3494—438no—
485#3485—434no—
486C2×#532D4311yescharacteristic, complemented
487C2×#529—432no—
488C2×C43—24no—
489C2×C43—22no—
490C2×C43—48no—
491C2×C43C22×H(5,𝔽2)11yescharacteristic
492C2×C43C2×#58512yes—
493D43—48no—
494C2×H(5,𝔽2)—434no—
495C22×#41C2×D4312yescomplemented
496#563—438no—
497#563—434no—
498#562—438no—
499H(3,𝔽4)—434no—
500#560—438no—
501#559—432no—
502#559—438no—
503Q82—432no—
504#555—432no—
505#555—438no—
506#554—434no—
507#554—438no—
508#553—4316no—
509#553—438no—
510#553—4316no—
511#553—438no—
512#552—438no—
513#551—438no—
514#551—4316no—
515#551—4316no—
516#550—434no—
517#548—438no—
518#547—4316no—
519#547—4316no—
520#547—438no—
521#547—438no—
522#546—4316no—
523#546—4316no—
524#546—438no—
525#546—4316no—
526#546—438no—
527#546—4316no—
528D42—438no—
529D42—432no—
530D42—438no—
531#544—438no—
532#542—438no—
533#542—4316no—
534#542—438no—
535#540—438no—
536#540—438no—
537#539—438no—
538#539—4316no—
539#538—4316no—
540#538—438no—
541#538—4316no—
542#537—438no—
543#536—438no—
544#535—438no—
545#534—438no—
546#534—438no—
547#534—438no—
548#532—438no—
549#532C2×D4314yescomplemented
550#532C2×D4314yescomplemented
551#532C2×D4314yescomplemented
552#532C2×D4314yescomplemented
553C2×C4⋊Q8C2×D4311yescharacteristic, complemented
554C2×#127C2×D4311yescharacteristic, complemented
555#529—438no—
556#529—434no—
557#529—434no—
558#529—434no—
559#529—434no—
560#529—434no—
561#529—434no—
562#529—434no—
563#529—434no—
564C2×#126—434no—
565C2×#125—432no—
566C2×#124—432no—
567C2×#124C2×D4312yescomplemented
568#525—438no—
569#525—438no—
570C2×#123—434no—
571C2×#123—438no—
572C2×C22⋊Q8—432no—
573C2×#121—432no—
574C2×#121—438no—
575C2×#121C2×D4314yescomplemented
576#520—438no—
577#518—434no—
578#518—438no—
579C2×C4×Q8—432no—
580C2×C4×D4—434no—
581C2×C4×D4—432no—
582C2×C4×D4C2×D4314yescomplemented
583C2×#117—434no—
584C22×C42C2×D4311yescharacteristic, complemented
585C43#6282211yescharacteristic, complemented, Sylow
586H(5,𝔽2)—17216no—
587C2×#41—48no—
588C2×#41—438no—
589C2×#41—4316no—
590C2×#41—438no—
591C2×#41C22×D4318yes—
592C2×#41C22×D4318yes—
593C22×Q8—432no—
594C22×Q8C22×D4312yes—
595C22×D4—434no—
596C22×D4—438no—
597C22×D4—438no—
598C22×D4—4316no—
599C22×D4—432no—
600C22×D4C22×D4314yes—
601C22×D4C22×D4314yes—
602C22×D4C22×D4312yes—
603C23×C4—434no—
604C23×C4C22×D4311yescharacteristic
605C23×C4C22×D4312yes—
606C23×C4C22×D4314yes—
607C4⋊Q8—438no—
608C4⋊Q8—438no—
609C4⋊Q8—438no—
610C4⋊Q8C22×D4314yes—
611C4⋊Q8C22×D4312yes—
612C4⋊Q8C22×D4312yes—
613#127—438no—
614#127C22×D4314yes—
615#127C22×D4312yes—
616#127C22×D4312yes—
617#126—4316no—
618#126—4316no—
619#126—4316no—
620#126—438no—
621#126—438no—
622#126—438no—
623#126—438no—
624#125—438no—
625#125—4316no—
626#125—434no—
627#125—434no—
628#125—434no—
629#125—434no—
630#124—438no—
631#124—438no—
632#124—438no—
633#124—4316no—
634#124—4316no—
635#124—434no—
636#124—434no—
637#124—434no—
638#124—434no—
639#124C22×D4318yes—
640#124C22×D4314yes—
641#124C22×D4314yes—
642#123—4316no—
643#123—438no—
644#123—438no—
645#123—4316no—
646#123—438no—
647#123—438no—
648#123—438no—
649#123—438no—
650#123—4316no—
651#123—4316no—
652#123—4316no—
653#123—4316no—
654#123—4316no—
655#123—4316no—
656#123—4316no—
657C22⋊Q8—4316no—
658C22⋊Q8—4316no—
659C22⋊Q8—434no—
660C22⋊Q8—434no—
661C22⋊Q8—434no—
662C22⋊Q8—434no—
663C22⋊Q8—4316no—
664C22⋊Q8—438no—
665C22⋊Q8—4316no—
666C22⋊Q8—4316no—
667C22⋊Q8—4316no—
668#121—4316no—
669#121—438no—
670#121—438no—
671#121—4316no—
672#121—4316no—
673#121—4316no—
674#121—4316no—
675#121—4316no—
676#121—434no—
677#121—434no—
678#121—434no—
679#121—434no—
680#121—4316no—
681#121—438no—
682#121—4316no—
683#121—4316no—
684#121C22×D4318yes—
685#121C22×D4318yes—
686#121C22×D4318yes—
687#121C22×D4318yes—
688#120—4316no—
689#120—4316no—
690#120—438no—
691#120—4316no—
692#120—438no—
693#120—4316no—
694C4×Q8—438no—
695C4×Q8—434no—
696C4×Q8—434no—
697C4×Q8—434no—
698C4×Q8—434no—
699C4×D4—4316no—
700C4×D4—4316no—
701C4×D4—438no—
702C4×D4—438no—
703C4×D4—438no—
704C4×D4—438no—
705C4×D4—438no—
706C4×D4—438no—
707C4×D4—4316no—
708C4×D4—4316no—
709C4×D4—438no—
710C4×D4—4316no—
711C4×D4—4316no—
712C4×D4—434no—
713C4×D4—434no—
714C4×D4—434no—
715C4×D4—434no—
716C4×D4C22×D4318yes—
717C4×D4C22×D4318yes—
718C4×D4C22×D4318yes—
719C4×D4C22×D4318yes—
720#117—438no—
721#117—438no—
722#117—4316no—
723#117—438no—
724#117—438no—
725#117—438no—
726#117—438no—
727C2×C4⋊C4—434no—
728C2×C4⋊C4—434no—
729C2×C4⋊C4—432no—
730C2×C4⋊C4—434no—
731C2×C4⋊C4—432no—
732C2×C4⋊C4—434no—
733C2×C4⋊C4—4316no—
734C2×C4⋊C4—438no—
735C2×C4⋊C4C22×D4314yes—
736C2×C22⋊C4—434no—
737C2×C22⋊C4—438no—
738C2×C22⋊C4—434no—
739C2×C22⋊C4—434no—
740C2×C22⋊C4—434no—
741C2×C22⋊C4—434no—
742C2×C22⋊C4—4316no—
743C2×C22⋊C4—4316no—
744C2×C22⋊C4C22×D4318yes—
745C2×C42—434no—
746C2×C42C22×D4312yes—
747C2×C42C22×D4312yes—
748C2×C42C22×D4312yes—
749C2×C42C22×D4312yes—
750C2×C42C22×D4311yescharacteristic
751C2×C42C22×D4312yes—
752C2×C42C22×D4311yescharacteristic
753C24—434no—
754C24—438no—
755C24C23×D4314yes—
756C24C23×D4311yescharacteristic
757#41—416no—
758#41—416no—
759#41—17216no—
760#41—17232no—
761#41—17216no—
762C2×Q8—44no—
763C2×Q8—434no—
764C2×Q8—434no—
765C2×Q8—438no—
766C2×Q8—1724no—
767C2×Q8C23×D4314yes—
768C2×Q8C23×D4314yes—
769C2×D4—216no—
770C2×D4—48no—
771C2×D4—44no—
772C2×D4—438no—
773C2×D4—438no—
774C2×D4—4316no—
775C2×D4—4316no—
776C2×D4—4316no—
777C2×D4—434no—
778C2×D4—434no—
779C2×D4—438no—
780C2×D4—8616no—
781C2×D4—1724no—
782C2×D4—17216no—
783C2×D4—17232no—
784C2×D4—17216no—
785C2×D4C23×D4318yes—
786C2×D4C23×D43116yes—
787C2×D4C23×D4318yes—
788C2×D4C23×D4314yes—
789C2×D4C23×D4314yes—
790C22×C4—24no—
791C22×C4—44no—
792C22×C4—48no—
793C22×C4—434no—
794C22×C4—434no—
795C22×C4—434no—
796C22×C4—4316no—
797C22×C4—438no—
798C22×C4—438no—
799C22×C4—438no—
800C22×C4—4316no—
801C22×C4—1728no—
802C22×C4C23×D4312yes—
803C22×C4C23×D4312yes—
804C22×C4C23×D4312yes—
805C22×C4C23×D4312yes—
806C22×C4C23×D4312yes—
807C22×C4C23×D4311yescharacteristic
808C22×C4C23×D4311yescharacteristic
809C22×C4C23×D4314yes—
810C22×C4C23×D4312yes—
811C22×C4C23×D4312yes—
812C22×C4C23×D4312yes—
813C22×C4C23×D43116yes—
814C4⋊C4—438no—
815C4⋊C4—434no—
816C4⋊C4—438no—
817C4⋊C4—4316no—
818C4⋊C4—438no—
819C4⋊C4—434no—
820C4⋊C4—438no—
821C4⋊C4—438no—
822C4⋊C4—438no—
823C4⋊C4—438no—
824C4⋊C4—434no—
825C4⋊C4—4316no—
826C4⋊C4—434no—
827C4⋊C4—438no—
828C4⋊C4—4316no—
829C4⋊C4C23×D4318yes—
830C4⋊C4C23×D4318yes—
831C22⋊C4—438no—
832C22⋊C4—438no—
833C22⋊C4—4316no—
834C22⋊C4—438no—
835C22⋊C4—438no—
836C22⋊C4—4316no—
837C22⋊C4—438no—
838C22⋊C4—438no—
839C22⋊C4—438no—
840C22⋊C4—4316no—
841C22⋊C4—438no—
842C22⋊C4—438no—
843C22⋊C4—438no—
844C22⋊C4—438no—
845C22⋊C4—4316no—
846C22⋊C4—438no—
847C22⋊C4C23×D43116yes—
848C22⋊C4C23×D43116yes—
849C42—438no—
850C42—438no—
851C42—438no—
852C42—438no—
853C42C23×D4311yescharacteristic
854C42C23×D4312yes—
855C42C23×D4312yes—
856C42C23×D4312yes—
857C42C23×D4311yescharacteristic
858C42C23×D4312yes—
859C42C23×D4312yes—
860C42C23×D4312yes—
861C42C23×D4311yescharacteristic
862C42C23×D4311yescharacteristic
863C23—28no—
864C23—42no—
865C23—48no—
866C23—438no—
867C23—868no—
868C23—1724no—
869C23—1724no—
870C23—1728no—
871C23—17216no—
872C23#1306337014yes—
873C23C24×D4318yes—
874C23C24×D4311yescharacteristic
875C23C24×D4312yes—
876Q8—44no—
877Q8—44no—
878Q8—868no—
879Q8—1724no—
880Q8—1728no—
881D4—232no—
882D4—216no—
883D4—44no—
884D4—44no—
885D4—48no—
886D4—8616no—
887D4—8616no—
888D4—868no—
889D4—1728no—
890D4—1724no—
891D4—17216no—
892D4—17216no—
893D4—17216no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—28no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—416no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
906C2×C4—438no—
907C2×C4—438no—
908C2×C4—438no—
909C2×C4—868no—
910C2×C4—8616no—
911C2×C4—1728no—
912C2×C4—17216no—
913C2×C4—1724no—
914C2×C4—1728no—
915C2×C4—1724no—
916C2×C4—17216no—
917C2×C4C24×D4312yes—
918C2×C4C24×D4318yes—
919C2×C4C24×D4312yes—
920C2×C4C24×D4312yes—
921C2×C4C24×D4311yescharacteristic
922C2×C4C24×D4311yescharacteristic
923C2×C4C24×D4312yes—
924C2×C4C24×D4312yes—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—28no—
929C22—216no—
930C22—44no—
931C22—88no—
932C22—868no—
933C22—868no—
934C22—868no—
935C22—3448no—
936C22—6888no—
937C22C2×#1306337012yes—
938C22C2×#1306337014yes—
939C22C25×D4311yescharacteristic
940C4—22no—
941C4—21no—
942C4—21no—
943C4—28no—
944C4—22no—
945C4—22no—
946C4—22no—
947C4—868no—
948C4—868no—
949C4—868no—
950C4#1458373514yes—
951C2—22no—
952C2—24no—
953C2—48no—
954C2—1728no—
955C2C22×#1306337011yescharacteristic
956C2C2×#1458373512yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC2×C43×#532C2
hypercenterC2×#532D43
hypocenterC43#62822
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #19149151C2semidirect
2. #19149133C2semidirect
3. #19149118C2semidirect
4. #19148952C2semidirect
5. #19148939C2semidirect
6. #19148928C2semidirect
7. #19148672C2semidirect
8. #19148622C2semidirect
9. #19148535C2semidirect
10. #19148429C2semidirect
11. #19148352C2semidirect
12. #19148325C2semidirect
13. #19148239C2semidirect
14. C2×#14583433C2semidirect
15. C2×C43×#532C2semidirect
16. C2×#13063370C22semidirect
17. #14583649C22semidirect
18. #14583648C22semidirect
19. #14583643C22semidirect
20. #14583641C22semidirect
21. #14583636C22semidirect
22. #14583635C22semidirect
23. #14583632C22semidirect
24. #14583629C22semidirect
25. #14583615C22semidirect
26. #14583611C22semidirect
27. #14583610C22semidirect
28. #14583608C22semidirect
29. #14583601C22semidirect
30. #14583599C22semidirect
31. #14583598C22semidirect
32. #14583592C22semidirect
33. #14583584C22semidirect
34. #14583579C22semidirect
35. #14583578C22semidirect
36. #14583575C22semidirect
37. #14583569C22semidirect
38. #14583555C22semidirect
39. #14583550C22semidirect
40. #14583549C22semidirect
41. #14583548C22semidirect
42. #14583548C22semidirect
43. #14583544C22semidirect
44. #14583543C22semidirect
45. #14583539C22semidirect
46. #14583538C22semidirect
47. #14583537C22semidirect
48. #14583537C22semidirect
49. #14583534C22semidirect
50. #14583533C22semidirect
51. D4×C22⋊D43C22semidirect
52. #14583526C22semidirect
53. #14583523C22semidirect
54. #14583514C22semidirect
55. #14583513C22semidirect
56. #14583503C22semidirect
57. #14583500C22semidirect
58. #14583494C22semidirect
59. #14583491C22semidirect
60. #14583486C22semidirect
61. #14583483C22semidirect
62. #14583482C22semidirect
63. #14583476C22semidirect
64. #14583473C22semidirect
65. #14583462C22semidirect
66. #14583458C22semidirect
67. #14583458C22semidirect
68. #14583457C22semidirect
69. #14583444C22semidirect
70. #14583433C22semidirect
71. #14583433C22semidirect
72. #14583433C22semidirect
73. #14583433C22semidirect
74. #14583433C22semidirect
75. #14583433C22semidirect
76. #14583433C22semidirect
77. #14583433C22semidirect
78. #14583430C22semidirect
79. C2×#13063319C22semidirect
80. C2×#13063317C22semidirect
81. C2×#13063313C22semidirect
82. #14583410C22semidirect
83. #14583409C22semidirect
84. C2×#13063308C22semidirect
85. C2×#13063308C22semidirect
86. C2×#13063304C22semidirect
88. #121×D43C22semidirect
89. #14583378C22semidirect
90. #14583374C22semidirect
91. #14583371C22semidirect
92. C2×C4×Dic86C22semidirect
93. C2×C4×D172C22semidirect
94. C2×C4×C22⋊D43C22semidirect
95. C2×#13063282C22semidirect
96. C22×#41×C43C22semidirect
97. C43×#532C22semidirect
98. C43×#532C22semidirect
99. C43×#532C22semidirect
100. C43×#532C22semidirect
101. C2×C4⋊Q8×C43C22semidirect
102. C2×#127×C43C22semidirect
103. C2×#124×C43C22semidirect
104. C2×#121×C43C22semidirect
105. C2×C4×D4×C43C22semidirect
106. C22×C42×C43C22semidirect
486. C2×#532D43semidirect
495. C22×#41C2×D43semidirect
549. #532C2×D43semidirect
550. #532C2×D43semidirect
551. #532C2×D43semidirect
552. #532C2×D43semidirect
553. C2×C4⋊Q8C2×D43semidirect
554. C2×#127C2×D43semidirect
567. C2×#124C2×D43semidirect
575. C2×#121C2×D43semidirect
582. C2×C4×D4C2×D43semidirect
584. C22×C42C2×D43semidirect
585. C43#62822semidirect

Maximal subgroups

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

subgroupindex
#191491512
#191491332
#191491182
#191489522
#191489392
#191489282
#191486722
#191486222
#191485352
#191484292
#191483522
#191483252
#191482392
C2×#145834332
C2×C43×#5322
#6282243