Finite Group Databasebeta

← #25064438

Subgroups — #25064438

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148438C211yesmaximal, characteristic
2#19143621C211yesmaximal, characteristic, complemented
3#19137538C211yesmaximal, characteristic, complemented
4#19133152C211yesmaximal, characteristic, complemented
5#19133151C211yesmaximal, characteristic, complemented
6#19133144C211yesmaximal, characteristic, complemented
7#19133140C211yesmaximal, characteristic, complemented
8#19133137C211yesmaximal, characteristic, complemented
9#19133135C211yesmaximal, characteristic, complemented
10#19133105C211yesmaximal, characteristic, complemented
11#19133101C211yesmaximal, characteristic, complemented
12#19133098C211yesmaximal, characteristic, complemented
13#19133096C211yesmaximal, characteristic, complemented
14#19133084C211yesmaximal, characteristic, complemented
15C43×#1501C211yesmaximal, characteristic, complemented
16#14583633—21no—
17#14583632—21no—
18#14583620C411yescharacteristic, complemented
19#14583617C411yescharacteristic, complemented
20#14583613C411yescharacteristic, complemented
21#14583612C411yescharacteristic, complemented
22#14583598—21no—
23#14583594—21no—
24#14583568C411yescharacteristic, complemented
25#14583567C411yescharacteristic, complemented
26#14583551C411yescharacteristic, complemented
27#14583548C411yescharacteristic, complemented
28#14583484—21no—
29#14583482—21no—
30#14583464—21no—
31#14583451C2211yescharacteristic
32#14583444C2211yescharacteristic
33#14583412C2211yescharacteristic
34#14583410C2211yescharacteristic
35#14583409C2211yescharacteristic
36#14583378—21no—
37C2×C4×C22⋊D43C2211yescharacteristic
38#14582970—21no—
39#14582970—21no—
40#14582967—21no—
41#14582967—21no—
42#14582953C2211yescharacteristic
43#14582953C2211yescharacteristic
44#14582861C2211yescharacteristic
45#14582861C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47#14582787—21no—
48#14582783—21no—
49#14582775—21no—
50#14582766C2211yescharacteristic
51#14582762C2211yescharacteristic
52#14582758C2211yescharacteristic
53C4×(C2×D43)⋊C4—21no—
54#14582744C2211yescharacteristic
55#95×D43C2211yescharacteristic
56#14582637C2211yescharacteristic
57#14582637C2211yescharacteristic
58#14582636C2211yescharacteristic
59#14582636C2211yescharacteristic
60#14582635C2211yescharacteristic
61#14582635C2211yescharacteristic
62#14582634C2211yescharacteristic
63#14582634C2211yescharacteristic
64#14582633C2211yescharacteristic
65#14582633C2211yescharacteristic
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C43×#525C2211yescharacteristic
69C2×C22⋊C8×C43C2211yescharacteristic
70C4×C22⋊C4×C43C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic
76C2×#10621898C2×C411yescharacteristic, complemented
77C2×#10621900—21no—
78C2×#10621900C2×C411yescharacteristic
79C22×C22⋊D43D411yescharacteristic
80C22×C4×D43—21no—
81C22×C4×D43C2311yescharacteristic
82C2×#10621872—21no—
83C2×#10621872—21no—
84C22×C43⋊C8—21no—
85#13063324C2×C411yescharacteristic, complemented
86#13063324C2×C411yescharacteristic, complemented
87#13063323C2×C411yescharacteristic, complemented
88#13063321—21no—
89#13063321—21no—
90#13063321C2×C411yescharacteristic, complemented
91#13063320—21no—
92#13063319—21no—
93#13063318—21no—
94#13063318—21no—
95#13063315—21no—
96#13063313—21no—
97#13063312—21no—
98#13063311—21no—
99#13063311—21no—
100#13063311—21no—
101#13063311—21no—
102#13063311—21no—
103#13063310—21no—
104#13063310—21no—
105#13063308—21no—
106#13063308—21no—
107#13063307—21no—
108#13063307—21no—
109#13063306—21no—
110#13063305C2×C411yescharacteristic
111#13063304C2×C411yescharacteristic, complemented
112#13063304C2311yescharacteristic
113#13063302—21no—
114#13063301C2×C411yescharacteristic
115#13063300C2×C411yescharacteristic
116#13063299—21no—
117#13063299C2×C411yescharacteristic, complemented
118#13063299C2311yescharacteristic
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063297—21no—
123#13063297—21no—
124#13063297—21no—
125#13063297—21no—
126#13063296—21no—
127#13063296C2×C411yescharacteristic
128#13063295—21no—
129#13063294—21no—
130#13063293—21no—
131Q8×Dic43C2×C411yescharacteristic, complemented
132C4×Dic86—21no—
133#13063290—21no—
134#13063290—21no—
135#13063290C2×C411yescharacteristic, complemented
136D4×Dic43—21no—
137D4×Dic43C2×C411yescharacteristic, complemented
138#13063287—21no—
139#13063287C2×C411yescharacteristic, complemented
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43C2×C411yescharacteristic
146C4×C22⋊D43C2×C411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150C4×C22⋊D43D411yescharacteristic
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155#13063284C2×C411yescharacteristic, complemented
156#13063283C2×C411yescharacteristic
157#13063283C2×C411yescharacteristic
158#13063282—21no—
159#13063281—21no—
160#13063281—21no—
161C2×Dic43⋊C4—21no—
162C2×Dic43⋊C4—21no—
163C2×Dic43⋊C4D411yescharacteristic
164C4⋊C4×D43—21no—
165C2×C22⋊Dic43—21no—
166C2×C22⋊Dic43D411yescharacteristic
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4D411yescharacteristic
169C2×C4×Dic43—21no—
170C2×C4×Dic43C2311yescharacteristic
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)C2311yescharacteristic
175C22⋊(C43⋊C8)C2311yescharacteristic
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178#13063235—21no—
179#13063235—21no—
180C43⋊#95—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187C2×#41×C43C2×C411yescharacteristic, complemented
188C23×C4×C43C2311yescharacteristic
189C22×C8×C43—21no—
190#123×C43—21no—
191C22⋊Q8×C43C2×C411yescharacteristic, complemented
192C22⋊Q8×C43C2311yescharacteristic
193#121×C43C2×C411yescharacteristic, complemented
194#121×C43C2311yescharacteristic
195#120×C43—21no—
196C4×D4×C43—21no—
197C4×D4×C43—21no—
198#117×C43C2×C411yescharacteristic, complemented
199C2×C22⋊C4×C43—21no—
200C2×C42×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43C2×D411yescharacteristic
207C23×D43C2×D411yescharacteristic
208#41×C43—81no—
209C2×Q8×C43C22×C411yescharacteristic
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43C22×C411yescharacteristic
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—81no—
218C22×C4×C43C22×C411yescharacteristic
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2411yescharacteristic
224C2×C22⋊D43—21no—
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—41no—
232C2×C22⋊D43—41no—
233C2×C22⋊D43C22⋊C411yescharacteristic
234C2×C22⋊D43C22⋊C411yescharacteristic
235C2×C22⋊D43C22⋊C411yescharacteristic
236C2×C22⋊D43C22⋊C411yescharacteristic
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43C2×D411yescharacteristic
242C22×Dic43C2×D411yescharacteristic
243C22×Dic43C2×D411yescharacteristic
244#10621902—81no—
245#10621900—42no—
246#10621900—42no—
247#10621900—81no—
248#10621898—81no—
249C2×D172—21no—
250C2×D172—21no—
251C2×D172C22×C411yescharacteristic
252C2×C4×D43—21no—
253C2×C4×D43—21no—
254C2×C4×D43—21no—
255C2×C4×D43—42no—
256C2×C4×D43—42no—
257C2×C4×D43—81no—
258C2×C4×D43—81no—
259C2×C4×D43C22×C411yescharacteristic
260C2×C4×D43C22×C411yescharacteristic
261C2×C4×D43C2×D411yescharacteristic
262C2×C4×D43C2×D411yescharacteristic
263C2×Dic86—21no—
264C2×Dic86—21no—
265C2×Dic86C22×C411yescharacteristic
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—81no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43C22×C411yescharacteristic
272C4⋊C4×C43C22×C411yescharacteristic
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C22⋊C4×C43—21no—
277C22⋊C4×C43—21no—
278C22⋊C4×C43—42no—
279C42×C43—21no—
280C42×C43—81no—
281C22⋊Dic43—21no—
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43—21no—
285C22⋊Dic43—21no—
286C22⋊Dic43—81no—
287C22⋊Dic43C22⋊C411yescharacteristic
288C22⋊Dic43C22⋊C411yescharacteristic
289C22⋊Dic43C22⋊C411yescharacteristic
290C22⋊Dic43C22⋊C411yescharacteristic
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—42no—
300(C2×D43)⋊C4C22⋊C411yescharacteristic
301(C2×D43)⋊C4C22⋊C411yescharacteristic
302(C2×D43)⋊C4C22⋊C411yescharacteristic
303(C2×D43)⋊C4C22⋊C411yescharacteristic
304C4⋊Dic43—21no—
305C4⋊Dic43—21no—
306C4⋊Dic43C22×C411yescharacteristic
307C4⋊Dic43C22×C411yescharacteristic
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—81no—
317Dic43⋊C4C22⋊C411yescharacteristic
318Dic43⋊C4C22⋊C411yescharacteristic
319Dic43⋊C4C22⋊C411yescharacteristic
320Dic43⋊C4C22⋊C411yescharacteristic
321C4×Dic43—21no—
322C4×Dic43—21no—
323C4×Dic43—21no—
324C4×Dic43—21no—
325C4×Dic43—21no—
326C4×Dic43—42no—
327C4×Dic43C22×C411yescharacteristic
328C4×Dic43C22×C411yescharacteristic
329C4×Dic43C2×D411yescharacteristic
330C4×Dic43C2×D411yescharacteristic
331C2×C43⋊C8—21no—
332C2×C43⋊C8—21no—
333C2×C43⋊C8—81no—
334#10621872—81no—
335#10621872—81no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—21no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43C2×C22⋊C411yescharacteristic
342C23×C43C2×C22⋊C411yescharacteristic
343C23×C43C22×D411yescharacteristic
344C22×D43—21no—
345C22×D43—21no—
346C22×D43—21no—
347C22×D43—41no—
348C22×D43—41no—
349C22×D43C2×C22⋊C411yescharacteristic
350C22×D43C2×C22⋊C411yescharacteristic
351Q8×C43—41no—
352D4×C43—41no—
353D4×C43—41no—
354D4×C43—41no—
355D4×C43—81no—
356D4×C43—81no—
357C2×C4×C43—22no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—41no—
369C2×C4×C43—41no—
370C2×C4×C43—41no—
371C2×C4×C43—41no—
372C2×C4×C43—81no—
373C2×C4×C43C2×C22⋊C411yescharacteristic
374C2×C4×C43C2×C22⋊C411yescharacteristic
375C2×C4×C43C23×C411yescharacteristic
376C2×C4×C43C22×D411yescharacteristic
377C22⋊D43—41no—
378C22⋊D43—41no—
379C22⋊D43—41no—
380C22⋊D43—41no—
381C22⋊D43—42no—
382C22⋊D43—41no—
383C22⋊D43—41no—
384C22⋊D43—81no—
385C22⋊D43—81no—
386C22⋊D43—81no—
387C22⋊D43—81no—
388C22⋊D43—81no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—21no—
392C2×Dic43—21no—
393C2×Dic43—21no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—42no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403C2×Dic43—81no—
404C2×Dic43C2×C22⋊C411yescharacteristic
405C2×Dic43C2×C22⋊C411yescharacteristic
406C2×Dic43C2×C22⋊C411yescharacteristic
407C2×Dic43C2×C22⋊C411yescharacteristic
408C2×Dic43C2×C22⋊C411yescharacteristic
409C2×Dic43C2×C22⋊C411yescharacteristic
410D172—41no—
411D172—81no—
412D172—81no—
413C4×D43—41no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—41no—
417C4×D43—42no—
418C4×D43—81no—
419C4×D43—81no—
420C4×D43—84no—
421Dic86—42no—
422Dic86—41no—
423Dic86—81no—
424C8×C43—41no—
425C8×C43—41no—
426C43⋊C8—41no—
427C43⋊C8—41no—
428#17629—431nomaximal, Sylow
429C22×C43—21no—
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—21no—
433C22×C43—21no—
434C22×C43—21no—
435C22×C43—21no—
436C22×C43—21no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—81no—
441C22×C43—81no—
442C22×C43C22×C22⋊C411yescharacteristic
443C22×C43#57511yescharacteristic
444C22×C43#57511yescharacteristic
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—21no—
450C2×D43—21no—
451C2×D43—42no—
452C2×D43—42no—
453C2×D43—41no—
454C2×D43—41no—
455C2×D43—41no—
456C4×C43—21no—
457C4×C43—21no—
458C4×C43—21no—
459C4×C43—21no—
460C4×C43—42no—
461C4×C43—41no—
462C4×C43—41no—
463C4×C43—41no—
464C4×C43—81no—
465Dic43—21no—
466Dic43—21no—
467Dic43—21no—
468Dic43—21no—
469Dic43—21no—
470Dic43—21no—
471Dic43—41no—
472Dic43—41no—
473Dic43—41no—
474Dic43—81no—
475Dic43—81no—
476#3506—431no—
477#2973—431no—
478#2353—431no—
479#1516—431no—
480#1516—431no—
481#1515—431no—
482#1514—431no—
483#1513—431no—
484#1513—431no—
485#1506—431no—
486#1505—431no—
487#1504—431no—
488#1504—431no—
489#1501—431no—
490#1501D4311yescharacteristic, complemented
491C2×C43—21no—
492C2×C43—21no—
493C2×C43—41no—
494C2×C43—41no—
495C2×C43—81no—
496C2×C43#288311yescharacteristic
497C2×C43#289611yescharacteristic
498C2×C43#290111yescharacteristic
499D43—41no—
500D43—41no—
501D43—81no—
502#559—861no—
503#559—861no—
504#556—431no—
505#556—431no—
506#555—431no—
507#555—431no—
508#553—861no—
509#553—861no—
510#550—431no—
511#550—431no—
512#547—431no—
513#547—431no—
514#538—861no—
515#538—861no—
516#535—861no—
517#533—431no—
518#532—431no—
519#525—431no—
520#525—431no—
521#525—431no—
522#525C2×D4311yescharacteristic
523#520—861no—
524C2×C4×D4—431no—
525#435—861no—
526#435—861no—
527#435—861no—
528#435—861no—
529#432—431no—
530#432—431no—
531#407—431no—
532#407—431no—
533C2×C22⋊C8—431no—
534C2×C22⋊C8C2×D4311yescharacteristic
535#388—861no—
536#387—861no—
537#386—861no—
538#383—431no—
539#381—431no—
540#380—431no—
541C4×C22⋊C4—861no—
542C4×C22⋊C4C2×D4311yescharacteristic
543#376—431no—
544C2×#95—431no—
545#328—431no—
546#328—431no—
547#328—431no—
548#328—431no—
549#328—431no—
550#328—431no—
551#328C2×D4311yescharacteristic
552#328C2×D4311yescharacteristic
553#327—431no—
554#327—431no—
555#327—431no—
556#327—431no—
557#327—431no—
558#327—431no—
559#327C2×D4311yescharacteristic
560#327C2×D4311yescharacteristic
561C43#1762911yescharacteristic, complemented, Sylow
562C2×#41—431no—
563C2×#41—431no—
564C2×#41—431no—
565C2×#41—861no—
566C2×#41C4×D4311yescharacteristic, complemented
567C22×D4—431no—
568C23×C4—431no—
569C23×C4—861no—
570C23×C4C22×D4311yescharacteristic
571C2×M16—861no—
572C2×M16—861no—
573C22×C8—21no—
574C22×C8—861no—
575C4⋊Q8—431no—
576C4⋊Q8—431no—
577C4⋊Q8—431no—
578#127—431no—
579#127—861no—
580#127—861no—
581#126—861no—
582#126—861no—
583#126—861no—
584#126—861no—
585#125—861no—
586#124—861no—
587#124—861no—
588#124—861no—
589#124—861no—
590#124—861no—
591#124—861no—
592#124—861no—
593#123—21no—
594#123—861no—
595#123—861no—
596#123—861no—
597#123—861no—
598#123—861no—
599#123—861no—
600#123—861no—
601C22⋊Q8—431no—
602C22⋊Q8—431no—
603C22⋊Q8—431no—
604C22⋊Q8—431no—
605C22⋊Q8—861no—
606C22⋊Q8C4×D4311yescharacteristic, complemented
607C22⋊Q8C22×D4311yescharacteristic
608#121—431no—
609#121—431no—
610#121—431no—
611#121—431no—
612#121—861no—
613#121—861no—
614#121—861no—
615#121—861no—
616#121—861no—
617#121—861no—
618#121—861no—
619#121—861no—
620#121—861no—
621#121C4×D4311yescharacteristic, complemented
622#121C22×D4311yescharacteristic
623#120—21no—
624#120—861no—
625#120—861no—
626#120—861no—
627C4×Q8—431no—
628C4×Q8—431no—
629C4×Q8—861no—
630C4×Q8—861no—
631C4×Q8—861no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—431no—
635C4×D4—431no—
636C4×D4—431no—
637C4×D4—431no—
638C4×D4—431no—
639C4×D4—431no—
640C4×D4—431no—
641C4×D4—431no—
642C4×D4—431no—
643C4×D4—431no—
644C4×D4—861no—
645C4×D4—861no—
646C4×D4—861no—
647C4×D4—861no—
648C4×D4—861no—
649C4×D4—861no—
650C4×D4—861no—
651C4×D4—861no—
652C4×D4—861no—
653#117—431no—
654#117—431no—
655#117—431no—
656#117—861no—
657#117—861no—
658#117—861no—
659#117C4×D4311yescharacteristic, complemented
660C2×C4⋊C4—431no—
661C2×C4⋊C4—861no—
662C2×C4⋊C4—861no—
663C2×C4⋊C4—861no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—431no—
666C2×C22⋊C4—431no—
667C2×C22⋊C4—861no—
668C2×C22⋊C4—861no—
669C2×C42—21no—
670C2×C42—431no—
671C2×C42—861no—
672C4⋊C8—861no—
673C4⋊C8—861no—
674C22⋊C8—21no—
675C22⋊C8—431no—
676C22⋊C8—431no—
677C22⋊C8—861no—
678C22⋊C8—861no—
679C22⋊C8—861no—
680C22⋊C8C22×D4311yescharacteristic
681C22⋊C8C22×D4311yescharacteristic
682#97—861no—
683#97—861no—
684#95—431no—
685#95—431no—
686#95—861no—
687#95—861no—
688#95—861no—
689#95—861no—
690#95—861no—
691#95C22×D4311yescharacteristic
692#95C22×D4311yescharacteristic
693C24—431no—
694C24D4×D4311yescharacteristic
695#41—81no—
696#41—3441no—
697#41—3441no—
698#41—3441no—
699#41—1722no—
700#41—1722no—
701C2×Q8—431no—
702C2×Q8—861no—
703C2×Q8—861no—
704C2×Q8C2×C4×D4311yescharacteristic
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—431no—
709C2×D4—431no—
710C2×D4—431no—
711C2×D4—431no—
712C2×D4—431no—
713C2×D4—861no—
714C2×D4—861no—
715C2×D4—861no—
716C2×D4—861no—
717C2×D4—861no—
718C2×D4—861no—
719C2×D4—861no—
720C2×D4—861no—
721C2×D4—861no—
722C2×D4—1721no—
723C2×D4—1721no—
724C2×D4C2×C4×D4311yescharacteristic
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—81no—
729C22×C4—431no—
730C22×C4—431no—
731C22×C4—431no—
732C22×C4—431no—
733C22×C4—431no—
734C22×C4—431no—
735C22×C4—431no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—3441no—
744C22×C4—3441no—
745C22×C4—1722no—
746C22×C4—1722no—
747C22×C4C2×C4×D4311yescharacteristic
748C22×C4C2×C4×D4311yescharacteristic
749C22×C4D4×D4311yescharacteristic
750C22×C4D4×D4311yescharacteristic
751C22×C4D4×D4311yescharacteristic
752C22×C4C23×D4311yescharacteristic
753M16—3441no—
754M16—3441no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—81no—
758C2×C8—861no—
759C2×C8—861no—
760C2×C8—3441no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—431no—
764C4⋊C4—431no—
765C4⋊C4—431no—
766C4⋊C4—431no—
767C4⋊C4—431no—
768C4⋊C4—431no—
769C4⋊C4—861no—
770C4⋊C4—861no—
771C4⋊C4—861no—
772C4⋊C4—861no—
773C4⋊C4—861no—
774C4⋊C4—861no—
775C4⋊C4—861no—
776C4⋊C4—861no—
777C4⋊C4—861no—
778C4⋊C4—861no—
779C4⋊C4—3441no—
780C4⋊C4C2×C4×D4311yescharacteristic
781C4⋊C4C2×C4×D4311yescharacteristic
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—42no—
788C22⋊C4—431no—
789C22⋊C4—431no—
790C22⋊C4—431no—
791C22⋊C4—431no—
792C22⋊C4—431no—
793C22⋊C4—431no—
794C22⋊C4—431no—
795C22⋊C4—431no—
796C22⋊C4—861no—
797C22⋊C4—861no—
798C22⋊C4—861no—
799C22⋊C4—861no—
800C22⋊C4—861no—
801C22⋊C4—861no—
802C22⋊C4—861no—
803C22⋊C4—861no—
804C22⋊C4—861no—
805C22⋊C4—861no—
806C22⋊C4—861no—
807C22⋊C4—861no—
808C22⋊C4—861no—
809C22⋊C4—3441no—
810C22⋊C4—1722no—
811C42—21no—
812C42—81no—
813C42—431no—
814C42—431no—
815C42—431no—
816C42—431no—
817C42—861no—
818C42—861no—
819C42—861no—
820C42—861no—
821C42—861no—
822C42—1722no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—431no—
829C23—431no—
830C23—861no—
831C23—861no—
832C23—861no—
833C23—1721no—
834C23—1721no—
835C23C22⋊C4×D4311yescharacteristic
836C23C22⋊C4×D4311yescharacteristic
837C23C2×D4×D4311yescharacteristic
838Q8—41no—
839Q8—3441no—
840Q8—1721no—
841Q8—1722no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—81no—
846D4—81no—
847D4—3441no—
848D4—3441no—
849D4—3441no—
850D4—3441no—
851D4—3441no—
852D4—3441no—
853D4—3441no—
854D4—1721no—
855D4—1721no—
856D4—1721no—
857D4—1721no—
858D4—1721no—
859D4—1722no—
860D4—1721no—
861D4—1721no—
862C2×C4—22no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—81no—
878C2×C4—431no—
879C2×C4—431no—
880C2×C4—431no—
881C2×C4—431no—
882C2×C4—431no—
883C2×C4—431no—
884C2×C4—861no—
885C2×C4—861no—
886C2×C4—861no—
887C2×C4—861no—
888C2×C4—861no—
889C2×C4—3441no—
890C2×C4—3441no—
891C2×C4—3444no—
892C2×C4—3441no—
893C2×C4—1721no—
894C2×C4—1721no—
895C2×C4—1721no—
896C2×C4—1721no—
897C2×C4—1722no—
898C2×C4—1721no—
899C2×C4—1721no—
900C2×C4—1722no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1721no—
907C2×C4C22⋊C4×D4311yescharacteristic
908C2×C4C22⋊C4×D4311yescharacteristic
909C2×C4C22×C4×D4311yescharacteristic
910C2×C4C2×D4×D4311yescharacteristic
911C8—41no—
912C8—41no—
913C8—1721no—
914C8—1721no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—81no—
927C22—81no—
928C22—861no—
929C22—861no—
930C22—861no—
931C22—861no—
932C22—861no—
933C22—861no—
934C22—1722no—
935C22—1722no—
936C22—1721no—
937C22—1721no—
938C22—1721no—
939C22C2×C22⋊C4×D4311yescharacteristic
940C22#1458369611yescharacteristic
941C22#1458369611yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—42no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—81no—
951C4—861no—
952C4—861no—
953C4—861no—
954C4—861no—
955C4—861no—
956C4—861no—
957C4—3441no—
958C4—3441no—
959C4—1721no—
960C4—1721no—
961C4—1721no—
962C2—21no—
963C2—21no—
964C2—41no—
965C2—41no—
966C2—81no—
967C2—3441no—
968C2—1721no—
969C2—1721no—
970C2#1914305311yescharacteristic
971C2#1914311011yescharacteristic
972C2#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1501C2
socleC22×C43C22×C22⋊C4
prime radical#19148438C2
cosocleC22×C4×C43C24
hypercenter#1501D43
hypocenterC43#17629
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1501

Complements

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

NH ≅ G/Ntype
2. #19143621C2semidirect
3. #19137538C2semidirect
4. #19133152C2semidirect
5. #19133151C2semidirect
6. #19133144C2semidirect
7. #19133140C2semidirect
8. #19133137C2semidirect
9. #19133135C2semidirect
10. #19133105C2semidirect
11. #19133101C2semidirect
12. #19133098C2semidirect
13. #19133096C2semidirect
14. #19133084C2semidirect
15. C43×#1501C2semidirect
18. #14583620C4semidirect
19. #14583617C4semidirect
20. #14583613C4semidirect
21. #14583612C4semidirect
24. #14583568C4semidirect
25. #14583567C4semidirect
26. #14583551C4semidirect
27. #14583548C4semidirect
76. C2×#10621898C2×C4semidirect
85. #13063324C2×C4semidirect
86. #13063324C2×C4semidirect
87. #13063323C2×C4semidirect
90. #13063321C2×C4semidirect
111. #13063304C2×C4semidirect
117. #13063299C2×C4semidirect
131. Q8×Dic43C2×C4semidirect
135. #13063290C2×C4semidirect
137. D4×Dic43C2×C4semidirect
139. #13063287C2×C4semidirect
155. #13063284C2×C4semidirect
187. C2×#41×C43C2×C4semidirect
191. C22⋊Q8×C43C2×C4semidirect
193. #121×C43C2×C4semidirect
198. #117×C43C2×C4semidirect
490. #1501D43semidirect
561. C43#17629semidirect
566. C2×#41C4×D43semidirect
606. C22⋊Q8C4×D43semidirect
621. #121C4×D43semidirect
659. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191484382
#191436212
#191375382
#191331522
#191331512
#191331442
#191331402
#191331372
#191331352
#191331052
#191331012
#191330982
#191330962
#191330842
C43×#15012
#1762943