Finite Group Databasebeta

← #25064321

Subgroups — #25064321

Order 11008.

1038 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#19143617C211yesmaximal, characteristic, complemented
3#19137532C211yesmaximal, characteristic, complemented
4#19133171C211yesmaximal, characteristic, complemented
5#19133169C211yesmaximal, characteristic, complemented
6#19133165C211yesmaximal, characteristic, complemented
7#19133161C211yesmaximal, characteristic, complemented
8#19133149C211yesmaximal, characteristic, complemented
9#19133087C211yesmaximal, characteristic, complemented
10#19133086C211yesmaximal, characteristic, complemented
11#19133080C211yesmaximal, characteristic, complemented
12#19133078C211yesmaximal, characteristic, complemented
13#328×D43C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1516C211yesmaximal, 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
38C8×C22⋊D43—21no—
39C8×C22⋊D43—21no—
40(C22⋊D43)⋊C8—21no—
41(C22⋊D43)⋊C8—21no—
42#14582949C2211yescharacteristic, complemented
43#14582949C2211yescharacteristic, complemented
44C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
45C22⋊C8×D43C2211yescharacteristic
46C22⋊C8×D43C2211yescharacteristic
47#14582793—21no—
48#14582781—21no—
49#14582775—21no—
50#14582766C2211yescharacteristic, complemented
51#14582758C2211yescharacteristic
52C4×C22⋊Dic43C2211yescharacteristic, complemented
53#14582746—21no—
54#14582744C2211yescharacteristic, complemented
55#95×D43C2211yescharacteristic
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
70C43×#381C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic, complemented
76C2×Q8×D43C2×C411yescharacteristic
77C22×C22⋊D43D411yescharacteristic
78C2×D4×D43—21no—
79C2×D4×D43C2×C411yescharacteristic
80C22×C4×D43—21no—
81C22×C4×D43C2311yescharacteristic
82C22×C43⋊C8—21no—
83C2×C8×D43—21no—
84C2×C8×D43—21no—
85#13063320—21no—
86#13063319—21no—
87#13063318—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063317—21no—
92#13063316C2×C411yescharacteristic, complemented
93#13063316C2×C411yescharacteristic, complemented
94#13063315—21no—
95#13063314C2×C411yescharacteristic, complemented
96#13063312—21no—
97#13063312C2×C411yescharacteristic, complemented
98#13063311—21no—
99#13063309—21no—
100#13063308—21no—
101#13063308—21no—
102#13063307—21no—
103#13063307—21no—
104#13063307—21no—
105#13063307—21no—
106#13063306—21no—
107#13063306—21no—
108#13063305C2×C411yescharacteristic
109#13063304—21no—
110#13063304C2×C411yescharacteristic, complemented
111#13063304C2311yescharacteristic
112#13063303—21no—
113#13063303—21no—
114#13063302—21no—
115#13063301C2×C411yescharacteristic
116#13063300C2×C411yescharacteristic
117#13063299C2×C411yescharacteristic, complemented
118#13063299C2311yescharacteristic
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063297—21no—
123#13063297—21no—
124#13063296—21no—
125#13063296—21no—
126#13063296—21no—
127#13063296C2×C411yescharacteristic
128#13063294—21no—
129#13063293—21no—
130#13063293—21no—
131Q8×Dic43C2×C411yescharacteristic, complemented
132#13063290C2×C411yescharacteristic, complemented
133C4×D172—21no—
134D4×Dic43—21no—
135D4×Dic43C2×C411yescharacteristic, complemented
136#13063287—21no—
137#13063287C2×C411yescharacteristic, complemented
138C4×C22⋊D43—21no—
139C4×C22⋊D43—21no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43C2×C411yescharacteristic
142C4×C22⋊D43C2×C411yescharacteristic
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43D411yescharacteristic
146C4×C22⋊D43D411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151#13063284C2×C411yescharacteristic, complemented
152#13063283—21no—
153#13063283—21no—
154#13063282—21no—
155#13063281—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)⋊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, 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—
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—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—22no—
231C2×C22⋊D43—22no—
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—42no—
255C2×C4×D43—42no—
256C2×C4×D43—81no—
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
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—81no—
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—
276C22⋊C4×C43—81no—
277C42×C43—21no—
278C22⋊Dic43—21no—
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43—21no—
285C22⋊Dic43—42no—
286C22⋊Dic43C22⋊C411yescharacteristic
287C22⋊Dic43C22⋊C411yescharacteristic
288C22⋊Dic43C22⋊C411yescharacteristic
289C22⋊Dic43C22⋊C411yescharacteristic
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—21no—
298(C2×D43)⋊C4—42no—
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⋊Dic43C22×C411yescharacteristic
308C4⋊Dic43C22×C411yescharacteristic
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—81no—
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—
334C8×D43—81no—
335C8×D43—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—41no—
346C22×D43—41no—
347C22×D43—42no—
348C22×D43—81no—
349C22×D43—81no—
350C22×D43C2×C22⋊C411yescharacteristic
351C22×D43C2×C22⋊C411yescharacteristic
352C22×D43#13512yes—
353C22×D43#13512yes—
354Q8×C43—41no—
355D4×C43—41no—
356D4×C43—41no—
357D4×C43—41no—
358D4×C43—81no—
359D4×C43—81no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—21no—
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—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—22no—
381C22⋊D43—22no—
382C22⋊D43—22no—
383C22⋊D43—22no—
384C22⋊D43—41no—
385C22⋊D43—41no—
386C22⋊D43—42no—
387C22⋊D43—81no—
388C22⋊D43—81no—
389C22⋊D43—81no—
390C2×Dic43—21no—
391C2×Dic43—21no—
392C2×Dic43—22no—
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—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—
421C4×D43—84no—
422Dic86—41no—
423Dic86—81no—
424C8×C43—41no—
425C8×C43—41no—
426C43⋊C8—41no—
427C43⋊C8—41no—
428#17615—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×C43C2×#13511yescharacteristic
444C22×C43C2×#13511yescharacteristic
445C2×D43—21no—
446C2×D43—21no—
447C2×D43—21no—
448C2×D43—21no—
449C2×D43—42no—
450C2×D43—42no—
451C2×D43—41no—
452C2×D43—41no—
453C2×D43—41no—
454C2×D43—162no—
455C2×D43#41612yes—
456C2×D43#41612yes—
457C4×C43—21no—
458C4×C43—21no—
459C4×C43—21no—
460C4×C43—21no—
461C4×C43—41no—
462C4×C43—41no—
463C4×C43—41no—
464C4×C43—81no—
465C4×C43—81no—
466Dic43—21no—
467Dic43—21no—
468Dic43—21no—
469Dic43—21no—
470Dic43—21no—
471Dic43—21no—
472Dic43—42no—
473Dic43—41no—
474Dic43—41no—
475Dic43—41no—
476Dic43—81no—
477#3505—431no—
478#2972—431no—
479#2353—431no—
480#1521—431no—
481#1521—431no—
482#1520—431no—
483#1519—431no—
484#1516—431no—
485#1516D4311yescharacteristic, complemented
486#1501—431no—
487#1501—431no—
488#1500—431no—
489#1500—431no—
490C2×#328—431no—
491C2×#327—431no—
492C2×C43—21no—
493C2×C43—21no—
494C2×C43—41no—
495C2×C43—41no—
496C2×C43—81no—
497C2×C43#288311yescharacteristic
498C2×C43C2×#41611yescharacteristic
499C2×C43#290111yescharacteristic
500D43—22no—
501D43—22no—
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—
526C8×D4—861no—
527C8×D4—861no—
528C8×D4—861no—
529C8×D4—861no—
530#431—431no—
531#431—431no—
532C2×C22⋊C8—431no—
533C2×C22⋊C8—431no—
534C2×C22⋊C8—431no—
535C2×C22⋊C8C2×D4311yescharacteristic, complemented
536#388—861no—
537#387—861no—
538#386—861no—
539#383—431no—
540#381C2×D4311yescharacteristic, complemented
541#380—431no—
542C4×C22⋊C4—431no—
543C4×C22⋊C4—861no—
544#376—431no—
545C2×#95—431no—
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#1761511yescharacteristic, complemented, Sylow
563C2×#41—431no—
564C2×#41C4×D4311yescharacteristic, complemented
565C22×Q8—431no—
566C22×D4—431no—
567C22×D4—431no—
568C22×D4—861no—
569C23×C4—431no—
570C23×C4—861no—
571C23×C4C22×D4311yescharacteristic
572C22×C8—21no—
573C22×C8—861no—
574C22×C8—861no—
575C22×C8—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, complemented
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, complemented
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, complemented
656C2×C4⋊C4—431no—
657C2×C4⋊C4—431no—
658C2×C4⋊C4—431no—
659C2×C4⋊C4—861no—
660C2×C4⋊C4—861no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—431no—
663C2×C22⋊C4—431no—
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—862no—
714C2×D4—862no—
715C2×D4—861no—
716C2×D4—861no—
717C2×D4—861no—
718C2×D4—861no—
719C2×D4—3441no—
720C2×D4—1722no—
721C2×D4—1722no—
722C2×D4C2×C4×D4311yescharacteristic
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—81no—
727C22×C4—431no—
728C22×C4—431no—
729C22×C4—431no—
730C22×C4—431no—
731C22×C4—431no—
732C22×C4—431no—
733C22×C4—431no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—861no—
740C22×C4—861no—
741C22×C4—861no—
742C22×C4—3441no—
743C22×C4—3441no—
744C22×C4—1722no—
745C22×C4—1722no—
746C22×C4C2×C4×D4311yescharacteristic
747C22×C4C2×C4×D4311yescharacteristic
748C22×C4D4×D4311yescharacteristic
749C22×C4D4×D4311yescharacteristic
750C22×C4D4×D4311yescharacteristic
751C22×C4C23×D4311yescharacteristic
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—81no—
755C2×C8—861no—
756C2×C8—861no—
757C2×C8—3441no—
758C2×C8—3441no—
759C2×C8—3441no—
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—81no—
789C22⋊C4—431no—
790C22⋊C4—431no—
791C22⋊C4—431no—
792C22⋊C4—431no—
793C22⋊C4—431no—
794C22⋊C4—431no—
795C22⋊C4—431no—
796C22⋊C4—431no—
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—861no—
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—432no—
832C23—432no—
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—862no—
851D4—862no—
852D4—862no—
853D4—862no—
854D4—3441no—
855D4—3441no—
856D4—3441no—
857D4—1721no—
858D4—1722no—
859D4—1722no—
860D4—1721no—
861D4—1721no—
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—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—862no—
887C2×C4—861no—
888C2×C4—861no—
889C2×C4—861no—
890C2×C4—3441no—
891C2×C4—3441no—
892C2×C4—3441no—
893C2×C4—3441no—
894C2×C4—3444no—
895C2×C4—3441no—
896C2×C4—1721no—
897C2×C4—1721no—
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×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—41no—
925C22—41no—
926C22—41no—
927C22—81no—
928C22—81no—
929C22—432no—
930C22—432no—
931C22—861no—
932C22—861no—
933C22—861no—
934C22—861no—
935C22—1722no—
936C22—1722no—
937C22—1721no—
938C22—1721no—
939C22—1721no—
940C22—6882no—
941C22C2×C22⋊C4×D4311yescharacteristic
942C22#135×D4311yescharacteristic
943C22#135×D4311yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C4—861no—
954C4—861no—
955C4—861no—
956C4—861no—
957C4—861no—
958C4—861no—
959C4—3441no—
960C4—1722no—
961C4—1721no—
962C4—1721no—
963C4—1721no—
964C2—21no—
965C2—21no—
966C2—41no—
967C2—41no—
968C2—81no—
969C2—862no—
970C2—862no—
971C2—3441no—
972C2#1914305311yescharacteristic
973C2#416×D4311yescharacteristic
974C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1516C2
socleC22×C43C22×C22⋊C4
prime radical#19148423C2
cosocleC22×C4×C43C24
hypercenter#1516D43
hypocenterC43#17615
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. #19143617C2semidirect
3. #19137532C2semidirect
4. #19133171C2semidirect
5. #19133169C2semidirect
6. #19133165C2semidirect
7. #19133161C2semidirect
8. #19133149C2semidirect
9. #19133087C2semidirect
10. #19133086C2semidirect
11. #19133080C2semidirect
12. #19133078C2semidirect
13. #328×D43C2semidirect
14. #327×D43C2semidirect
15. C43×#1516C2semidirect
17. #14583596C4semidirect
19. #14583593C4semidirect
20. #14583588C4semidirect
21. #14583583C4semidirect
24. #14583559C4semidirect
25. #14583556C4semidirect
26. #14583546C4semidirect
27. #14583537C4semidirect
42. #14582949C22semidirect
43. #14582949C22semidirect
44. C2×C22⋊(C43⋊C8)C22semidirect
50. #14582766C22semidirect
52. C4×C22⋊Dic43C22semidirect
54. #14582744C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582636C22semidirect
59. #14582636C22semidirect
60. #14582635C22semidirect
61. #14582635C22semidirect
69. C2×C22⋊C8×C43C22semidirect
70. C43×#381C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
75. C2×#10621898C2×C4semidirect
92. #13063316C2×C4semidirect
93. #13063316C2×C4semidirect
95. #13063314C2×C4semidirect
97. #13063312C2×C4semidirect
110. #13063304C2×C4semidirect
117. #13063299C2×C4semidirect
131. Q8×Dic43C2×C4semidirect
132. #13063290C2×C4semidirect
135. D4×Dic43C2×C4semidirect
137. #13063287C2×C4semidirect
151. #13063284C2×C4semidirect
187. C2×#41×C43C2×C4semidirect
191. C22⋊Q8×C43C2×C4semidirect
193. #121×C43C2×C4semidirect
198. #117×C43C2×C4semidirect
485. #1516D43semidirect
535. C2×C22⋊C8C2×D43semidirect
540. #381C2×D43semidirect
552. #328C2×D43semidirect
553. #328C2×D43semidirect
562. C43#17615semidirect
564. C2×#41C4×D43semidirect
608. C22⋊Q8C4×D43semidirect
622. #121C4×D43semidirect
655. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191484232
#191436172
#191375322
#191331712
#191331692
#191331652
#191331612
#191331492
#191330872
#191330862
#191330802
#191330782
#328×D432
#327×D432
C43×#15162
#1761543