Finite Group Databasebeta

← #25064383

Subgroups — #25064383

Order 11008.

1014 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148423C211yesmaximal, characteristic
2#19143634C211yesmaximal, characteristic, complemented
3#19137531C211yesmaximal, characteristic, complemented
4#19133171C211yesmaximal, characteristic, complemented
5#19133169C211yesmaximal, characteristic, complemented
6#19133139C211yesmaximal, characteristic, complemented
7#19133138C211yesmaximal, characteristic, complemented
8#19133126C211yesmaximal, characteristic, complemented
9#19133122C211yesmaximal, characteristic, complemented
10#19133113C211yesmaximal, characteristic, complemented
11#19133109C211yesmaximal, characteristic, complemented
12#19133097C211yesmaximal, characteristic, complemented
13#19133080C211yesmaximal, characteristic, complemented
14#19133078C211yesmaximal, characteristic, complemented
15C43×#1504C211yesmaximal, characteristic, complemented
16#14583599—21no—
17#14583596C411yescharacteristic, complemented
18#14583594—21no—
19#14583593C411yescharacteristic, complemented
20#14583588C411yescharacteristic, complemented
21#14583583C411yescharacteristic, complemented
22#14583578—21no—
23#14583577—21no—
24#14583559C411yescharacteristic, complemented
25#14583556C411yescharacteristic, complemented
26#14583546C411yescharacteristic, complemented
27#14583537C411yescharacteristic, complemented
28#14583491—21no—
29#14583484—21no—
30#14583459—21no—
31#14583435C2211yescharacteristic
32#14583430C2211yescharacteristic
33#14583410C2211yescharacteristic
34C22⋊Q8×D43C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583371—21no—
37C2×C4×C22⋊D43C2211yescharacteristic
38#14582975—21no—
39#14582975—21no—
40#14582974—21no—
41#14582974—21no—
42#14582949C2211yescharacteristic, complemented
43#14582949C2211yescharacteristic, complemented
44#14582863C2211yescharacteristic, complemented
45#14582861C2211yescharacteristic
46#14582861C2211yescharacteristic
47#14582791—21no—
48#14582786—21no—
49#14582778—21no—
50#14582766C2211yescharacteristic, complemented
51#14582761C2211yescharacteristic
52#14582759C2211yescharacteristic, complemented
53C4×C22⋊Dic43—21no—
54#14582746C2211yescharacteristic
55#14582744C2211yescharacteristic, complemented
56#14582637C2211yescharacteristic, complemented
57#14582637C2211yescharacteristic, complemented
58#14582636C2211yescharacteristic, complemented
59#14582636C2211yescharacteristic, complemented
60#14582635C2211yescharacteristic, complemented
61#14582635C2211yescharacteristic, complemented
62#14582634C2211yescharacteristic
63#14582634C2211yescharacteristic
64#14582633C2211yescharacteristic
65#14582633C2211yescharacteristic
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C43×#525C2211yescharacteristic
69C43×#407C2211yescharacteristic, complemented
70C2×#95×C43C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic
76C2×Q8×D43C2×C411yescharacteristic, complemented
77C22×C22⋊D43D411yescharacteristic
78C2×D4×D43—21no—
79C2×D4×D43C2×C411yescharacteristic, complemented
80C22×C4×D43C2311yescharacteristic
81C2×#10621877—21no—
82C2×#10621872—21no—
83C2×#10621872—21no—
84#13063320—21no—
85#13063319—21no—
86#13063318—21no—
87#13063318—21no—
88#13063318—21no—
89#13063318—21no—
90#13063317—21no—
91#13063316C2×C411yescharacteristic, complemented
92#13063316C2×C411yescharacteristic, complemented
93#13063315—21no—
94#13063314C2×C411yescharacteristic, complemented
95#13063312—21no—
96#13063312C2×C411yescharacteristic, complemented
97#13063311—21no—
98#13063309—21no—
99#13063308—21no—
100#13063308—21no—
101#13063307—21no—
102#13063307—21no—
103#13063307—21no—
104#13063307—21no—
105#13063306—21no—
106#13063306—21no—
107#13063305C2×C411yescharacteristic, complemented
108#13063304—21no—
109#13063304C2×C411yescharacteristic
110#13063304C2311yescharacteristic
111#13063303—21no—
112#13063303—21no—
113#13063302—21no—
114#13063301C2×C411yescharacteristic, complemented
115#13063300C2×C411yescharacteristic, complemented
116#13063299C2×C411yescharacteristic
117#13063299C2311yescharacteristic
118#13063298—21no—
119#13063298—21no—
120#13063298—21no—
121#13063297—21no—
122#13063297—21no—
123#13063296—21no—
124#13063296—21no—
125#13063296—21no—
126#13063296C2×C411yescharacteristic, complemented
127#13063294—21no—
128#13063293—21no—
129#13063293—21no—
130Q8×Dic43C2×C411yescharacteristic, complemented
131#13063290C2×C411yescharacteristic, complemented
132C4×D172—21no—
133D4×Dic43—21no—
134D4×Dic43C2×C411yescharacteristic, complemented
135#13063287—21no—
136#13063287C2×C411yescharacteristic, complemented
137C4×C22⋊D43—21no—
138C4×C22⋊D43—21no—
139C4×C22⋊D43—21no—
140C4×C22⋊D43C2×C411yescharacteristic
141C4×C22⋊D43C2×C411yescharacteristic
142C4×C22⋊D43C2×C411yescharacteristic
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43D411yescharacteristic
145C4×C22⋊D43D411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150#13063284C2×C411yescharacteristic
151#13063283—21no—
152#13063283—21no—
153#13063282—21no—
154#13063281—21no—
155C2×C4⋊Dic43—21no—
156C2×Dic43⋊C4D411yescharacteristic
157C4⋊C4×D43—21no—
158C4⋊C4×D43C2×C411yescharacteristic, complemented
159C4⋊C4×D43C2×C411yescharacteristic, complemented
160C2×C22⋊Dic43—21no—
161C2×C22⋊Dic43D411yescharacteristic
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4D411yescharacteristic
166C22⋊C4×D43—21no—
167C22⋊C4×D43—21no—
168C22⋊C4×D43—21no—
169C2×C4×Dic43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43C2311yescharacteristic
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174C22⋊(C43⋊C8)—21no—
175C22⋊(C43⋊C8)C2311yescharacteristic
176C22⋊(C43⋊C8)C2311yescharacteristic
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179C8×Dic43—21no—
180C8×Dic43—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187C2×#41×C43C2×C411yescharacteristic
188C23×C4×C43—21no—
189C23×C4×C43C2311yescharacteristic
190C2×M16×C43—21no—
191#123×C43—21no—
192C22⋊Q8×C43C2×C411yescharacteristic
193C22⋊Q8×C43C2311yescharacteristic
194#121×C43C2×C411yescharacteristic
195#121×C43C2311yescharacteristic
196#120×C43—21no—
197C4×D4×C43—21no—
198C4×D4×C43—21no—
199#117×C43C2×C411yescharacteristic
200C22⋊C8×C43—21no—
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43C2×D411yescharacteristic
207C23×D43—21no—
208C23×D43C2×D411yescharacteristic
209#41×C43—81no—
210C2×Q8×C43C22×C411yescharacteristic
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43C22×C411yescharacteristic
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—42no—
219C22×C4×C43—42no—
220C22×C4×C43—81no—
221C22×C4×C43—81no—
222C22×C4×C43C22×C411yescharacteristic
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2411yescharacteristic
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—41no—
234C2×C22⋊D43—41no—
235C2×C22⋊D43C22⋊C411yescharacteristic
236C2×C22⋊D43C22⋊C411yescharacteristic
237C2×C22⋊D43C22⋊C411yescharacteristic
238C2×C22⋊D43C22⋊C411yescharacteristic
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43C2×D411yescharacteristic
243C22×Dic43C2×D411yescharacteristic
244C22×Dic43C2×D411yescharacteristic
245Q8×D43—81no—
246D4×D43—42no—
247D4×D43—42no—
248D4×D43—81no—
249#10621898—81no—
250C2×D172—21no—
251C2×D172C22×C411yescharacteristic
252C2×C4×D43—21no—
253C2×C4×D43—21no—
254C2×C4×D43—21no—
255C2×C4×D43—21no—
256C2×C4×D43—21no—
257C2×C4×D43—81no—
258C2×C4×D43C22×C411yescharacteristic
259C2×C4×D43C22×C411yescharacteristic
260C2×C4×D43C2×D411yescharacteristic
261C2×C4×D43C2×D411yescharacteristic
262C2×Dic86—21no—
263C2×Dic86C22×C411yescharacteristic
264M16×C43—81no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43C22×C411yescharacteristic
270C4⋊C4×C43C22×C411yescharacteristic
271C22⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C42×C43—21no—
277C22⋊Dic43—21no—
278C22⋊Dic43—21no—
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43—42no—
285C22⋊Dic43C22⋊C411yescharacteristic
286C22⋊Dic43C22⋊C411yescharacteristic
287C22⋊Dic43C22⋊C411yescharacteristic
288C22⋊Dic43C22⋊C411yescharacteristic
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
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—42no—
298(C2×D43)⋊C4—81no—
299(C2×D43)⋊C4C22⋊C411yescharacteristic
300(C2×D43)⋊C4C22⋊C411yescharacteristic
301(C2×D43)⋊C4C22⋊C411yescharacteristic
302(C2×D43)⋊C4C22⋊C411yescharacteristic
303C4⋊Dic43—21no—
304C4⋊Dic43—21no—
305C4⋊Dic43—21no—
306C4⋊Dic43—21no—
307C4⋊Dic43—81no—
308C4⋊Dic43C22×C411yescharacteristic
309C4⋊Dic43C22×C411yescharacteristic
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4C22⋊C411yescharacteristic
319Dic43⋊C4C22⋊C411yescharacteristic
320Dic43⋊C4C22⋊C411yescharacteristic
321Dic43⋊C4C22⋊C411yescharacteristic
322C4×Dic43—21no—
323C4×Dic43—21no—
324C4×Dic43—21no—
325C4×Dic43—42no—
326C4×Dic43—81no—
327C4×Dic43C22×C411yescharacteristic
328C4×Dic43C22×C411yescharacteristic
329C4×Dic43C2×D411yescharacteristic
330C4×Dic43C2×D411yescharacteristic
331#10621877—81no—
332C2×C43⋊C8—21no—
333C2×C43⋊C8—21no—
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×D43—42no—
350C22×D43—81no—
351C22×D43—81no—
352C22×D43C2×C22⋊C411yescharacteristic
353C22×D43C2×C22⋊C411yescharacteristic
354Q8×C43—41no—
355D4×C43—41no—
356D4×C43—41no—
357D4×C43—41no—
358D4×C43—81no—
359D4×C43—81no—
360C2×C4×C43—22no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
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—41no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—81no—
376C2×C4×C43—84no—
377C2×C4×C43C2×C22⋊C411yescharacteristic
378C2×C4×C43C2×C22⋊C411yescharacteristic
379C2×C4×C43C23×C411yescharacteristic
380C2×C4×C43C22×D411yescharacteristic
381C22⋊D43—41no—
382C22⋊D43—41no—
383C22⋊D43—41no—
384C22⋊D43—41no—
385C22⋊D43—42no—
386C22⋊D43—41no—
387C22⋊D43—41no—
388C22⋊D43—81no—
389C22⋊D43—81no—
390C22⋊D43—81no—
391C2×Dic43—21no—
392C2×Dic43—21no—
393C2×Dic43—21no—
394C2×Dic43—21no—
395C2×Dic43—21no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403C2×Dic43—41no—
404C2×Dic43—81no—
405C2×Dic43C2×C22⋊C411yescharacteristic
406C2×Dic43C2×C22⋊C411yescharacteristic
407C2×Dic43C2×C22⋊C411yescharacteristic
408C2×Dic43C2×C22⋊C411yescharacteristic
409C2×Dic43C2×C22⋊C411yescharacteristic
410C2×Dic43C2×C22⋊C411yescharacteristic
411D172—41no—
412D172—42no—
413C4×D43—41no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—41no—
417C4×D43—42no—
418C4×D43—81no—
419C4×D43—81no—
420C4×D43—81no—
421C4×D43—81no—
422Dic86—41no—
423Dic86—81no—
424C8×C43—41no—
425C8×C43—41no—
426C43⋊C8—41no—
427C43⋊C8—41no—
428#17623—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—42no—
438C22×C43—42no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43—41no—
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—41no—
452C2×D43—41no—
453C2×D43—41no—
454C2×D43—81no—
455C2×D43—81no—
456C2×D43—162no—
457C4×C43—21no—
458C4×C43—21no—
459C4×C43—21no—
460C4×C43—21no—
461C4×C43—42no—
462C4×C43—41no—
463C4×C43—41no—
464C4×C43—41no—
465C4×C43—81no—
466Dic43—21no—
467Dic43—21no—
468Dic43—21no—
469Dic43—21no—
470Dic43—21no—
471Dic43—21no—
472Dic43—41no—
473Dic43—41no—
474Dic43—41no—
475Dic43—81no—
476Dic43—81no—
477#3505—431no—
478#2975—431no—
479#2353—431no—
480#1521—431no—
481#1521—431no—
482#1513—431no—
483#1513—431no—
484#1511—431no—
485#1510—431no—
486#1508—431no—
487#1507—431no—
488#1504—431no—
489#1504D4311yescharacteristic, complemented
490#1500—431no—
491#1500—431no—
492C2×C43—21no—
493C2×C43—21no—
494C2×C43—41no—
495C2×C43—41no—
496C2×C43—81no—
497C2×C43#288311yescharacteristic
498C2×C43#289611yescharacteristic
499C2×C43#290111yescharacteristic
500D43—41no—
501D43—41no—
502D43—81no—
503#553—431no—
504#553—431no—
505#553—861no—
506#553—861no—
507#552—431no—
508#552—431no—
509#551—861no—
510#551—861no—
511#548—431no—
512#548—431no—
513#546—431no—
514#546—431no—
515#539—861no—
516#538—861no—
517#534—861no—
518#529—431no—
519#529—431no—
520#525—431no—
521#525C2×D4311yescharacteristic
522C2×C22⋊Q8—431no—
523C2×#121—431no—
524#518—861no—
525C2×C4×D4—431no—
526#436—861no—
527#436—861no—
528#436—861no—
529#436—861no—
530#431—431no—
531#431—431no—
532#407—431no—
533#407—431no—
534#407—431no—
535#407C2×D4311yescharacteristic, complemented
536#388—861no—
537#387—861no—
538#386—861no—
539#383—431no—
540#381—431no—
541#380—431no—
542C4×C22⋊C4—431no—
543C4×C22⋊C4—861no—
544#376—431no—
545C2×#95C2×D4311yescharacteristic, complemented
546#328—431no—
547#328—431no—
548#328—431no—
549#328—431no—
550#328—431no—
551#328—431no—
552#328C2×D4311yescharacteristic, complemented
553#328C2×D4311yescharacteristic, complemented
554#327—431no—
555#327—431no—
556#327—431no—
557#327—431no—
558#327—431no—
559#327—431no—
560#327C2×D4311yescharacteristic
561#327C2×D4311yescharacteristic
562C43#1762311yescharacteristic, complemented, Sylow
563C2×#41—431no—
564C2×#41C4×D4311yescharacteristic
565C22×Q8—431no—
566C22×D4—431no—
567C22×D4—431no—
568C22×D4—861no—
569C23×C4—21no—
570C23×C4—431no—
571C23×C4C22×D4311yescharacteristic
572C2×M16—21no—
573C2×M16—861no—
574C2×M16—861no—
575C2×M16—861no—
576#126—861no—
577#126—861no—
578#126—861no—
579#126—861no—
580#126—861no—
581#126—861no—
582#125—431no—
583#125—431no—
584#125—861no—
585#125—861no—
586#124—431no—
587#124—431no—
588#124—861no—
589#124—861no—
590#123—21no—
591#123—861no—
592#123—861no—
593#123—861no—
594#123—861no—
595#123—861no—
596#123—861no—
597#123—861no—
598#123—861no—
599#123—861no—
600C22⋊Q8—431no—
601C22⋊Q8—431no—
602C22⋊Q8—431no—
603C22⋊Q8—431no—
604C22⋊Q8—861no—
605C22⋊Q8—861no—
606C22⋊Q8—861no—
607C22⋊Q8—861no—
608C22⋊Q8C4×D4311yescharacteristic
609C22⋊Q8C22×D4311yescharacteristic
610#121—431no—
611#121—431no—
612#121—431no—
613#121—431no—
614#121—861no—
615#121—861no—
616#121—861no—
617#121—861no—
618#121—861no—
619#121—861no—
620#121—861no—
621#121—861no—
622#121C4×D4311yescharacteristic
623#121C22×D4311yescharacteristic
624#120—21no—
625#120—861no—
626#120—861no—
627#120—861no—
628C4×Q8—431no—
629C4×Q8—431no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—431no—
633C4×D4—431no—
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—861no—
643C4×D4—861no—
644C4×D4—861no—
645C4×D4—861no—
646C4×D4—861no—
647C4×D4—861no—
648C4×D4—861no—
649C4×D4—861no—
650#117—431no—
651#117—861no—
652#117—861no—
653#117—861no—
654#117—861no—
655#117C4×D4311yescharacteristic
656C2×C4⋊C4—431no—
657C2×C4⋊C4—431no—
658C2×C4⋊C4—431no—
659C2×C4⋊C4—861no—
660C2×C4⋊C4—861no—
661C2×C22⋊C4—431no—
662C2×C22⋊C4—431no—
663C2×C22⋊C4—861no—
664C2×C22⋊C4—861no—
665C2×C22⋊C4—861no—
666C2×C22⋊C4—861no—
667C2×C22⋊C4—861no—
668C2×C22⋊C4—861no—
669C2×C22⋊C4—861no—
670C2×C42—431no—
671C2×C42—861no—
672C2×C42—861no—
673C4⋊C8—861no—
674C4⋊C8—861no—
675C22⋊C8—21no—
676C22⋊C8—431no—
677C22⋊C8—431no—
678C22⋊C8—861no—
679C22⋊C8—861no—
680C22⋊C8—861no—
681C22⋊C8C22×D4311yescharacteristic
682C22⋊C8C22×D4311yescharacteristic
683C4×C8—861no—
684C4×C8—861no—
685#95—21no—
686#95—431no—
687#95—431no—
688#95—861no—
689#95—861no—
690#95—861no—
691#95—861no—
692#95C22×D4311yescharacteristic
693#95C22×D4311yescharacteristic
694C24—431no—
695C24—861no—
696C24D4×D4311yescharacteristic
697#41—81no—
698#41—3441no—
699C2×Q8—431no—
700C2×Q8—861no—
701C2×Q8—3441no—
702C2×Q8C2×C4×D4311yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—431no—
707C2×D4—431no—
708C2×D4—431no—
709C2×D4—431no—
710C2×D4—431no—
711C2×D4—861no—
712C2×D4—861no—
713C2×D4—861no—
714C2×D4—861no—
715C2×D4—861no—
716C2×D4—861no—
717C2×D4—3441no—
718C2×D4—1721no—
719C2×D4—1721no—
720C2×D4—1722no—
721C2×D4—1722no—
722C2×D4C2×C4×D4311yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4—431no—
731C22×C4—431no—
732C22×C4—431no—
733C22×C4—431no—
734C22×C4—431no—
735C22×C4—431no—
736C22×C4—431no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—861no—
743C22×C4—861no—
744C22×C4—861no—
745C22×C4—3441no—
746C22×C4C2×C4×D4311yescharacteristic
747C22×C4C2×C4×D4311yescharacteristic
748C22×C4D4×D4311yescharacteristic
749C22×C4D4×D4311yescharacteristic
750C22×C4D4×D4311yescharacteristic
751C22×C4C23×D4311yescharacteristic
752M16—81no—
753M16—3441no—
754M16—3441no—
755M16—3441no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—861no—
759C2×C8—861no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—431no—
763C4⋊C4—431no—
764C4⋊C4—431no—
765C4⋊C4—431no—
766C4⋊C4—431no—
767C4⋊C4—431no—
768C4⋊C4—861no—
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—861no—
780C4⋊C4—3441no—
781C4⋊C4C2×C4×D4311yescharacteristic
782C4⋊C4C2×C4×D4311yescharacteristic
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
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—861no—
810C22⋊C4—861no—
811C22⋊C4—3441no—
812C22⋊C4—1722no—
813C22⋊C4—1722no—
814C42—21no—
815C42—431no—
816C42—431no—
817C42—431no—
818C42—431no—
819C42—861no—
820C42—861no—
821C42—861no—
822C42—3441no—
823C42—1722no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—41no—
828C23—41no—
829C23—431no—
830C23—431no—
831C23—861no—
832C23—861no—
833C23—861no—
834C23—3441no—
835C23—3441no—
836C23—1721no—
837C23—1721no—
838C23—1722no—
839C23C22⋊C4×D4311yescharacteristic
840C23C22⋊C4×D4311yescharacteristic
841C23C2×D4×D4311yescharacteristic
842Q8—41no—
843Q8—3441no—
844Q8—1721no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—81no—
849D4—81no—
850D4—3441no—
851D4—3441no—
852D4—3441no—
853D4—1721no—
854D4—1722no—
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—84no—
879C2×C4—431no—
880C2×C4—431no—
881C2×C4—431no—
882C2×C4—431no—
883C2×C4—431no—
884C2×C4—431no—
885C2×C4—861no—
886C2×C4—861no—
887C2×C4—861no—
888C2×C4—861no—
889C2×C4—861no—
890C2×C4—3441no—
891C2×C4—3441no—
892C2×C4—3441no—
893C2×C4—3441no—
894C2×C4—3441no—
895C2×C4—1721no—
896C2×C4—1721no—
897C2×C4—1721no—
898C2×C4—1721no—
899C2×C4—1722no—
900C2×C4—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4—1721no—
907C2×C4—1721no—
908C2×C4C22⋊C4×D4311yescharacteristic
909C2×C4C22⋊C4×D4311yescharacteristic
910C2×C4C22×C4×D4311yescharacteristic
911C2×C4C2×D4×D4311yescharacteristic
912C8—41no—
913C8—41no—
914C8—1721no—
915C8—1721no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—42no—
925C22—42no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—861no—
930C22—861no—
931C22—861no—
932C22—861no—
933C22—861no—
934C22—861no—
935C22—3441no—
936C22—3441no—
937C22—1721no—
938C22—1721no—
939C22—1721no—
940C22—6882no—
941C22C2×C22⋊C4×D4311yescharacteristic
942C22#1458369511yescharacteristic
943C22#1458369811yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—42no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—81no—
953C4—861no—
954C4—861no—
955C4—861no—
956C4—861no—
957C4—861no—
958C4—861no—
959C4—3441no—
960C4—3441no—
961C4—1721no—
962C4—1721no—
963C4—1721no—
964C2—21no—
965C2—21no—
966C2—41no—
967C2—41no—
968C2—81no—
969C2—3441no—
970C2—1721no—
971C2—1721no—
972C2#1914305311yescharacteristic
973C2#1914311111yescharacteristic
974C2#1914313911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1504C2
socleC22×C43C22×C22⋊C4
prime radical#19148423C2
cosocleC22×C4×C43C24
hypercenter#1504D43
hypocenterC43#17623
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1504

Complements

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

NH ≅ G/Ntype
2. #19143634C2semidirect
3. #19137531C2semidirect
4. #19133171C2semidirect
5. #19133169C2semidirect
6. #19133139C2semidirect
7. #19133138C2semidirect
8. #19133126C2semidirect
9. #19133122C2semidirect
10. #19133113C2semidirect
11. #19133109C2semidirect
12. #19133097C2semidirect
13. #19133080C2semidirect
14. #19133078C2semidirect
15. C43×#1504C2semidirect
17. #14583596C4semidirect
19. #14583593C4semidirect
20. #14583588C4semidirect
21. #14583583C4semidirect
24. #14583559C4semidirect
25. #14583556C4semidirect
26. #14583546C4semidirect
27. #14583537C4semidirect
42. #14582949C22semidirect
43. #14582949C22semidirect
44. #14582863C22semidirect
50. #14582766C22semidirect
52. #14582759C22semidirect
55. #14582744C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582636C22semidirect
59. #14582636C22semidirect
60. #14582635C22semidirect
61. #14582635C22semidirect
69. C43×#407C22semidirect
70. C2×#95×C43C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
76. C2×Q8×D43C2×C4semidirect
79. C2×D4×D43C2×C4semidirect
91. #13063316C2×C4semidirect
92. #13063316C2×C4semidirect
94. #13063314C2×C4semidirect
96. #13063312C2×C4semidirect
107. #13063305C2×C4semidirect
114. #13063301C2×C4semidirect
115. #13063300C2×C4semidirect
126. #13063296C2×C4semidirect
130. Q8×Dic43C2×C4semidirect
131. #13063290C2×C4semidirect
134. D4×Dic43C2×C4semidirect
136. #13063287C2×C4semidirect
158. C4⋊C4×D43C2×C4semidirect
159. C4⋊C4×D43C2×C4semidirect
489. #1504D43semidirect
535. #407C2×D43semidirect
545. C2×#95C2×D43semidirect
552. #328C2×D43semidirect
553. #328C2×D43semidirect
562. C43#17623semidirect

Maximal subgroups

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

subgroupindex
#191484232
#191436342
#191375312
#191331712
#191331692
#191331392
#191331382
#191331262
#191331222
#191331132
#191331092
#191330972
#191330802
#191330782
C43×#15042
#1762343