Finite Group Databasebeta

← #25064404

Subgroups — #25064404

Order 11008.

1002 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#19148423C211yesmaximal, characteristic
2#19143621C211yesmaximal, characteristic, complemented
3#19137569C211yesmaximal, characteristic, complemented
4#19133152C211yesmaximal, characteristic, complemented
5#19133151C211yesmaximal, characteristic, complemented
6#19133132C211yesmaximal, characteristic, complemented
7#19133130C211yesmaximal, characteristic, complemented
8#19133126C211yesmaximal, characteristic, complemented
9#19133122C211yesmaximal, characteristic, complemented
10#19133119C211yesmaximal, characteristic, complemented
11#19133117C211yesmaximal, characteristic, complemented
12#19133113C211yesmaximal, characteristic, complemented
13#19133109C211yesmaximal, characteristic, complemented
14#19133084C211yesmaximal, characteristic, complemented
15C43×#1501C211yesmaximal, 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#14582970—21no—
39#14582970—21no—
40#14582967—21no—
41#14582967—21no—
42#14582953C2211yescharacteristic, complemented
43#14582953C2211yescharacteristic, complemented
44#14582861C2211yescharacteristic
45#14582861C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
47#14582799—21no—
48#14582793—21no—
49#14582790—21no—
50#14582763C2211yescharacteristic, complemented
51#14582762C2211yescharacteristic, complemented
52#14582761C2211yescharacteristic
53C4×Dic43⋊C4—21no—
54#14582750C2211yescharacteristic, complemented
55#14582746C2211yescharacteristic
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
69C2×C22⋊C8×C43C2211yescharacteristic, complemented
70C4×C22⋊C4×C43C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic
76C2×Q8×D43C2×C411yescharacteristic
77C22×C22⋊D43D411yescharacteristic
78C2×D4×D43—21no—
79C2×D4×D43C2×C411yescharacteristic
80C22×C4×D43C2311yescharacteristic
81C2×#10621872—21no—
82C2×#10621872—21no—
83C22×C43⋊C8—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
92#13063316C2×C411yescharacteristic
93#13063315—21no—
94#13063314C2×C411yescharacteristic
95#13063312—21no—
96#13063312C2×C411yescharacteristic
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
108#13063304—21no—
109#13063304C2×C411yescharacteristic
110#13063304C2311yescharacteristic
111#13063303—21no—
112#13063303—21no—
113#13063302—21no—
114#13063301C2×C411yescharacteristic
115#13063300C2×C411yescharacteristic
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
127#13063294—21no—
128#13063293—21no—
129#13063293—21no—
130Q8×Dic43C2×C411yescharacteristic
131#13063290C2×C411yescharacteristic
132C4×D172—21no—
133D4×Dic43—21no—
134D4×Dic43C2×C411yescharacteristic
135#13063287—21no—
136#13063287C2×C411yescharacteristic
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×Dic43⋊C4—21no—
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4D411yescharacteristic
158C4⋊C4×D43—21no—
159C4⋊C4×D43C2×C411yescharacteristic
160C4⋊C4×D43C2×C411yescharacteristic
161C2×C22⋊Dic43—21no—
162C2×C22⋊Dic43D411yescharacteristic
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4D411yescharacteristic
167C22⋊C4×D43—21no—
168C22⋊C4×D43—21no—
169C22⋊C4×D43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43C2311yescharacteristic
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175C22⋊(C43⋊C8)—21no—
176C22⋊(C43⋊C8)C2311yescharacteristic
177C22⋊(C43⋊C8)C2311yescharacteristic
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180#13063235—21no—
181#13063235—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187C2×#41×C43C2×C411yescharacteristic
188C23×C4×C43C2311yescharacteristic
189C22×C8×C43—21no—
190#123×C43—21no—
191C22⋊Q8×C43C2×C411yescharacteristic
192C22⋊Q8×C43C2311yescharacteristic
193#121×C43C2×C411yescharacteristic
194#121×C43C2311yescharacteristic
195#120×C43—21no—
196C4×D4×C43—21no—
197C4×D4×C43—21no—
198#117×C43C2×C411yescharacteristic
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×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—81no—
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—41no—
231C2×C22⋊D43—41no—
232C2×C22⋊D43C22⋊C411yescharacteristic
233C2×C22⋊D43C22⋊C411yescharacteristic
234C2×C22⋊D43C22⋊C411yescharacteristic
235C2×C22⋊D43C22⋊C411yescharacteristic
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43C2×D411yescharacteristic
240C22×Dic43C2×D411yescharacteristic
241C22×Dic43C2×D411yescharacteristic
242Q8×D43—81no—
243D4×D43—42no—
244D4×D43—42no—
245D4×D43—81no—
246#10621898—81no—
247C2×D172—21no—
248C2×D172C22×C411yescharacteristic
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—21no—
254C2×C4×D43—81no—
255C2×C4×D43C22×C411yescharacteristic
256C2×C4×D43C22×C411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×C4×D43C2×D411yescharacteristic
259C2×Dic86—21no—
260C2×Dic86C22×C411yescharacteristic
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—81no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43C22×C411yescharacteristic
267C4⋊C4×C43C22×C411yescharacteristic
268C22⋊C4×C43—21no—
269C22⋊C4×C43—21no—
270C22⋊C4×C43—21no—
271C22⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C22⋊C4×C43—42no—
274C42×C43—21no—
275C42×C43—81no—
276C22⋊Dic43—21no—
277C22⋊Dic43—21no—
278C22⋊Dic43—21no—
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282C22⋊Dic43—21no—
283C22⋊Dic43—81no—
284C22⋊Dic43C22⋊C411yescharacteristic
285C22⋊Dic43C22⋊C411yescharacteristic
286C22⋊Dic43C22⋊C411yescharacteristic
287C22⋊Dic43C22⋊C411yescharacteristic
288(C2×D43)⋊C4—21no—
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—42no—
297(C2×D43)⋊C4—81no—
298(C2×D43)⋊C4C22⋊C411yescharacteristic
299(C2×D43)⋊C4C22⋊C411yescharacteristic
300(C2×D43)⋊C4C22⋊C411yescharacteristic
301(C2×D43)⋊C4C22⋊C411yescharacteristic
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
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—42no—
317Dic43⋊C4—42no—
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
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×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×C43C2×C22⋊C411yescharacteristic
377C2×C4×C43C2×C22⋊C411yescharacteristic
378C2×C4×C43C23×C411yescharacteristic
379C2×C4×C43C22×D411yescharacteristic
380C22⋊D43—41no—
381C22⋊D43—41no—
382C22⋊D43—41no—
383C22⋊D43—41no—
384C22⋊D43—42no—
385C22⋊D43—41no—
386C22⋊D43—41no—
387C22⋊D43—81no—
388C22⋊D43—81no—
389C22⋊D43—81no—
390C2×Dic43—21no—
391C2×Dic43—21no—
392C2×Dic43—21no—
393C2×Dic43—21no—
394C2×Dic43—21no—
395C2×Dic43—41no—
396C2×Dic43—41no—
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—42no—
412C4×D43—41no—
413C4×D43—41no—
414C4×D43—41no—
415C4×D43—41no—
416C4×D43—42no—
417C4×D43—81no—
418C4×D43—81no—
419C4×D43—81no—
420C4×D43—81no—
421Dic86—41no—
422Dic86—81no—
423C8×C43—41no—
424C8×C43—41no—
425C43⋊C8—41no—
426C43⋊C8—41no—
427#17625—431nomaximal, Sylow
428C22×C43—21no—
429C22×C43—21no—
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—21no—
433C22×C43—21no—
434C22×C43—21no—
435C22×C43—21no—
436C22×C43—41no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—81no—
440C22×C43—81no—
441C22×C43C22×C22⋊C411yescharacteristic
442C22×C43#57511yescharacteristic
443C22×C43#57511yescharacteristic
444C2×D43—21no—
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—21no—
450C2×D43—41no—
451C2×D43—41no—
452C2×D43—41no—
453C2×D43—81no—
454C2×D43—81no—
455C2×D43—162no—
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#3505—431no—
477#2973—431no—
478#2357—431no—
479#1516—431no—
480#1516—431no—
481#1512—431no—
482#1512—431no—
483#1511—431no—
484#1510—431no—
485#1509—431no—
486#1509—431no—
487#1508—431no—
488#1507—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#553—431no—
503#553—431no—
504#553—861no—
505#553—861no—
506#552—431no—
507#552—431no—
508#551—861no—
509#551—861no—
510#548—431no—
511#548—431no—
512#546—431no—
513#546—431no—
514#539—861no—
515#538—861no—
516#534—861no—
517#529—431no—
518#529—431no—
519#525—431no—
520#525C2×D4311yescharacteristic
521C2×C22⋊Q8—431no—
522C2×#121—431no—
523#518—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, complemented
535#390—861no—
536#388—861no—
537#388—861no—
538#382—431no—
539#381—431no—
540#381—431no—
541C4×C4⋊C4—431no—
542C4×C4⋊C4—861no—
543C4×C22⋊C4—431no—
544C4×C22⋊C4C2×D4311yescharacteristic, complemented
545#328—431no—
546#328—431no—
547#328—431no—
548#328—431no—
549#328—431no—
550#328—431no—
551#328C2×D4311yescharacteristic, complemented
552#328C2×D4311yescharacteristic, complemented
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#1762511yescharacteristic, complemented, Sylow
562C2×#41—431no—
563C2×#41C4×D4311yescharacteristic
564C22×Q8—431no—
565C22×D4—431no—
566C22×D4—431no—
567C22×D4—861no—
568C23×C4—431no—
569C23×C4C22×D4311yescharacteristic
570C2×M16—861no—
571C2×M16—861no—
572C22×C8—21no—
573C22×C8—861no—
574#126—861no—
575#126—861no—
576#126—861no—
577#126—861no—
578#126—861no—
579#126—861no—
580#125—431no—
581#125—431no—
582#125—861no—
583#125—861no—
584#124—431no—
585#124—431no—
586#124—861no—
587#124—861no—
588#123—21no—
589#123—861no—
590#123—861no—
591#123—861no—
592#123—861no—
593#123—861no—
594#123—861no—
595#123—861no—
596#123—861no—
597#123—861no—
598C22⋊Q8—431no—
599C22⋊Q8—431no—
600C22⋊Q8—431no—
601C22⋊Q8—431no—
602C22⋊Q8—861no—
603C22⋊Q8—861no—
604C22⋊Q8—861no—
605C22⋊Q8—861no—
606C22⋊Q8C4×D4311yescharacteristic
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#121C4×D4311yescharacteristic
621#121C22×D4311yescharacteristic
622#120—21no—
623#120—861no—
624#120—861no—
625#120—861no—
626C4×Q8—431no—
627C4×Q8—431no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—431no—
631C4×D4—431no—
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—861no—
641C4×D4—861no—
642C4×D4—861no—
643C4×D4—861no—
644C4×D4—861no—
645C4×D4—861no—
646C4×D4—861no—
647C4×D4—861no—
648#117—431no—
649#117—861no—
650#117—861no—
651#117—861no—
652#117—861no—
653#117C4×D4311yescharacteristic
654C2×C4⋊C4—431no—
655C2×C4⋊C4—431no—
656C2×C4⋊C4—431no—
657C2×C4⋊C4—861no—
658C2×C4⋊C4—861no—
659C2×C4⋊C4—861no—
660C2×C22⋊C4—21no—
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—21no—
671C2×C42—431no—
672C2×C42—861no—
673C2×C42—861no—
674C4⋊C8—861no—
675C4⋊C8—861no—
676C22⋊C8—21no—
677C22⋊C8—431no—
678C22⋊C8—431no—
679C22⋊C8—861no—
680C22⋊C8—861no—
681C22⋊C8—861no—
682C22⋊C8C22×D4311yescharacteristic
683C22⋊C8C22×D4311yescharacteristic
684#97—861no—
685#97—861no—
686#95—431no—
687#95—431no—
688#95—861no—
689#95—861no—
690#95—861no—
691#95C22×D4311yescharacteristic
692#95C22×D4311yescharacteristic
693C24—431no—
694C24—861no—
695C24D4×D4311yescharacteristic
696#41—81no—
697#41—3441no—
698C2×Q8—431no—
699C2×Q8—861no—
700C2×Q8—3441no—
701C2×Q8C2×C4×D4311yescharacteristic
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—431no—
706C2×D4—431no—
707C2×D4—431no—
708C2×D4—431no—
709C2×D4—431no—
710C2×D4—861no—
711C2×D4—861no—
712C2×D4—861no—
713C2×D4—861no—
714C2×D4—861no—
715C2×D4—861no—
716C2×D4—3441no—
717C2×D4—1721no—
718C2×D4—1721no—
719C2×D4—1722no—
720C2×D4—1722no—
721C2×D4C2×C4×D4311yescharacteristic
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—81no—
726C22×C4—431no—
727C22×C4—431no—
728C22×C4—431no—
729C22×C4—431no—
730C22×C4—431no—
731C22×C4—431no—
732C22×C4—431no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—3441no—
742C22×C4C2×C4×D4311yescharacteristic
743C22×C4C2×C4×D4311yescharacteristic
744C22×C4D4×D4311yescharacteristic
745C22×C4D4×D4311yescharacteristic
746C22×C4D4×D4311yescharacteristic
747C22×C4C23×D4311yescharacteristic
748M16—3441no—
749M16—3441no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—81no—
753C2×C8—861no—
754C2×C8—861no—
755C2×C8—3441no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—431no—
759C4⋊C4—431no—
760C4⋊C4—431no—
761C4⋊C4—431no—
762C4⋊C4—431no—
763C4⋊C4—431no—
764C4⋊C4—861no—
765C4⋊C4—861no—
766C4⋊C4—861no—
767C4⋊C4—861no—
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—1722no—
777C4⋊C4—1722no—
778C4⋊C4C2×C4×D4311yescharacteristic
779C4⋊C4C2×C4×D4311yescharacteristic
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—42no—
786C22⋊C4—431no—
787C22⋊C4—431no—
788C22⋊C4—431no—
789C22⋊C4—431no—
790C22⋊C4—431no—
791C22⋊C4—431no—
792C22⋊C4—431no—
793C22⋊C4—431no—
794C22⋊C4—861no—
795C22⋊C4—861no—
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—3441no—
811C22⋊C4—1722no—
812C42—21no—
813C42—81no—
814C42—431no—
815C42—431no—
816C42—431no—
817C42—431no—
818C42—861no—
819C42—861no—
820C42—861no—
821C42—3441no—
822C42—1722no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—431no—
829C23—431no—
830C23—861no—
831C23—861no—
832C23—861no—
833C23—3441no—
834C23—3441no—
835C23—1721no—
836C23—1721no—
837C23—1722no—
838C23C22⋊C4×D4311yescharacteristic
839C23C22⋊C4×D4311yescharacteristic
840C23C2×D4×D4311yescharacteristic
841Q8—41no—
842Q8—3441no—
843Q8—1721no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—81no—
848D4—81no—
849D4—3441no—
850D4—3441no—
851D4—3441no—
852D4—1721no—
853D4—1722no—
854D4—1721no—
855D4—1721no—
856D4—1721no—
857D4—1721no—
858D4—1722no—
859D4—1721no—
860D4—1721no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—41no—
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—81no—
877C2×C4—431no—
878C2×C4—431no—
879C2×C4—431no—
880C2×C4—431no—
881C2×C4—431no—
882C2×C4—431no—
883C2×C4—861no—
884C2×C4—861no—
885C2×C4—861no—
886C2×C4—861no—
887C2×C4—861no—
888C2×C4—3441no—
889C2×C4—3441no—
890C2×C4—3441no—
891C2×C4—3441no—
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—1721no—
901C2×C4—1721no—
902C2×C4—1721no—
903C2×C4—1721no—
904C2×C4—1721no—
905C2×C4—1721no—
906C2×C4C22⋊C4×D4311yescharacteristic
907C2×C4C22⋊C4×D4311yescharacteristic
908C2×C4C22×C4×D4311yescharacteristic
909C2×C4C2×D4×D4311yescharacteristic
910C8—41no—
911C8—41no—
912C8—1721no—
913C8—1721no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—81no—
926C22—81no—
927C22—861no—
928C22—861no—
929C22—861no—
930C22—861no—
931C22—861no—
932C22—861no—
933C22—3441no—
934C22—3441no—
935C22—1721no—
936C22—1721no—
937C22—1721no—
938C22—6882no—
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#19148423C2
cosocleC22×C4×C43C24
hypercenter#1501D43
hypocenterC43#17625
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. #19137569C2semidirect
4. #19133152C2semidirect
5. #19133151C2semidirect
6. #19133132C2semidirect
7. #19133130C2semidirect
8. #19133126C2semidirect
9. #19133122C2semidirect
10. #19133119C2semidirect
11. #19133117C2semidirect
12. #19133113C2semidirect
13. #19133109C2semidirect
14. #19133084C2semidirect
15. C43×#1501C2semidirect
17. #14583596C4semidirect
19. #14583593C4semidirect
20. #14583588C4semidirect
21. #14583583C4semidirect
24. #14583559C4semidirect
25. #14583556C4semidirect
26. #14583546C4semidirect
27. #14583537C4semidirect
42. #14582953C22semidirect
43. #14582953C22semidirect
46. C2×C22⋊(C43⋊C8)C22semidirect
50. #14582763C22semidirect
51. #14582762C22semidirect
54. #14582750C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582636C22semidirect
59. #14582636C22semidirect
60. #14582635C22semidirect
61. #14582635C22semidirect
69. C2×C22⋊C8×C43C22semidirect
70. C4×C22⋊C4×C43C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
490. #1501D43semidirect
534. C2×C22⋊C8C2×D43semidirect
544. C4×C22⋊C4C2×D43semidirect
551. #328C2×D43semidirect
552. #328C2×D43semidirect
561. C43#17625semidirect

Maximal subgroups

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

subgroupindex
#191484232
#191436212
#191375692
#191331522
#191331512
#191331322
#191331302
#191331262
#191331222
#191331192
#191331172
#191331132
#191331092
#191330842
C43×#15012
#1762543