Finite Group Databasebeta

← #25063798

Subgroups — #25063798

Order 11008.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148615C211yesmaximal, characteristic
2#19143626C211yesmaximal, characteristic, complemented
3#19136954C211yesmaximal, characteristic, complemented
4#19133119C211yesmaximal, characteristic, complemented
5#19133110C211yesmaximal, characteristic, complemented
6#19133109C211yesmaximal, characteristic, complemented
7#19133101C211yesmaximal, characteristic, complemented
8#19133099C211yesmaximal, characteristic, complemented
9#19133098C211yesmaximal, characteristic, complemented
10#19133088C211yesmaximal, characteristic, complemented
11#19133085C211yesmaximal, characteristic, complemented
12#19133080C211yesmaximal, characteristic, complemented
13C2×#14582634C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1501C211yesmaximal, characteristic, complemented
16#14583612C411yescharacteristic, complemented
17#14583607C411yescharacteristic, complemented
18#14583601C411yescharacteristic, complemented
19#14583598—21no—
20#14583593C411yescharacteristic, complemented
21#14583568C411yescharacteristic, complemented
22#14583544—21no—
23#14583540C411yescharacteristic, complemented
24#14583537C411yescharacteristic, complemented
25#14583536—21no—
26#14583533C411yescharacteristic, complemented
27#14583531—21no—
28#14583501—21no—
29#14583485—21no—
30#14583482—21no—
31#14583444C2211yescharacteristic
32#14583435C2211yescharacteristic
33#14583412C2211yescharacteristic
34C2×#13063299C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583371—21no—
37C2×C4×C22⋊D43C2211yescharacteristic
38C2×(C22⋊D43)⋊C4—21no—
39#14582974—21no—
40#14582973—21no—
41#14582970—21no—
42C8×C22⋊D43—21no—
43#14582953C2211yescharacteristic, complemented
44#14582949C2211yescharacteristic, complemented
45#14582863C2211yescharacteristic, complemented
46#14582861C2211yescharacteristic, complemented
47C22⋊C8×D43C2211yescharacteristic, complemented
48C4×Dic43⋊C4—21no—
49#14582750C2211yescharacteristic, complemented
50C22⋊C4×Dic43—21no—
51C4×(C2×D43)⋊C4—21no—
52#14582746C2211yescharacteristic, complemented
53#14582744C2211yescharacteristic, complemented
54C2×C43⋊#95C2211yescharacteristic, complemented
55#95×D43C2211yescharacteristic, complemented
56#14582636C2211yescharacteristic, complemented
57#14582636C2211yescharacteristic, complemented
58#14582634C2211yescharacteristic
59#14582634C2211yescharacteristic
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic, complemented
63#14582633C2211yescharacteristic, complemented
64#14582632C2211yescharacteristic
65#14582632C2211yescharacteristic
66#14582632C2211yescharacteristic, complemented
67#14582632C2211yescharacteristic, complemented
68C43×#525C2211yescharacteristic
69C2×C22⋊C8×C43C2211yescharacteristic, complemented
70C4×C22⋊C4×C43C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic, complemented
74C43×#327C2211yescharacteristic, complemented
75C2×#10621902C2×C411yescharacteristic, complemented
76C2×#10621900—21no—
77C22×D172C2×C411yescharacteristic, complemented
78C22×C22⋊D43—21no—
79C22×C22⋊D43D411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43—21no—
82C2×D4×D43C2×C411yescharacteristic, complemented
83C23×Dic43—21no—
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C2×#10621877—21no—
87C2×#10621872—21no—
88C2×C8×D43—21no—
89#13063324C2×C411yescharacteristic, complemented
90#13063321—21no—
91#13063321C2×C411yescharacteristic, complemented
92#13063320—21no—
93#13063319—21no—
94#13063318—21no—
95#13063316C2×C411yescharacteristic, complemented
96#13063315—21no—
97#13063314C2×C411yescharacteristic, complemented
98#13063313—21no—
99#13063311—21no—
100#13063311—21no—
101#13063310—21no—
102#13063310—21no—
103#13063309—21no—
104#13063309—21no—
105#13063308—21no—
106#13063307—21no—
107#13063305—21no—
108#13063302—21no—
109#13063301C2×C411yescharacteristic, complemented
110#13063300—21no—
111#13063300C2×C411yescharacteristic, complemented
112#13063300C2×C411yescharacteristic, complemented
113#13063299—21no—
114#13063299—21no—
115#13063299—21no—
116#13063299C2×C411yescharacteristic, complemented
117#13063299C2×C411yescharacteristic, complemented
118#13063299C2311yescharacteristic
119#13063299C2311yescharacteristic
120#13063298—21no—
121#13063298—21no—
122#13063298—21no—
123#13063298—21no—
124#13063297—21no—
125#13063297—21no—
126#13063297—21no—
127#13063297—21no—
128#13063296—21no—
129#13063296C2×C411yescharacteristic, complemented
130#13063295—21no—
131#13063295—21no—
132#13063295—21no—
133#13063293—21no—
134#13063293—21no—
135Q8×Dic43C2×C411yescharacteristic, complemented
136C4×D172—21no—
137D4×Dic43—21no—
138D4×Dic43C2×C411yescharacteristic, complemented
139#13063287—21no—
140#13063287C2×C411yescharacteristic, complemented
141#13063287C2×C411yescharacteristic, complemented
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—28no—
152(C22⋊D43)⋊C4—21no—
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155(C22⋊D43)⋊C4—21no—
156#13063283—21no—
157#13063283C2×C411yescharacteristic, complemented
158#13063282—21no—
159C2×C4⋊Dic43C2×C411yescharacteristic, complemented
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4D411yescharacteristic
162C4⋊C4×D43C2×C411yescharacteristic, complemented
163C2×C22⋊Dic43D411yescharacteristic
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4D411yescharacteristic
168C22⋊C4×D43—21no—
169C22⋊C4×D43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43C2311yescharacteristic
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176C22⋊(C43⋊C8)—21no—
177C22⋊(C43⋊C8)C2311yescharacteristic
178C22⋊(C43⋊C8)C2311yescharacteristic
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181#13063235—21no—
182C8×Dic43—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95—21no—
186C43⋊#95C2311yescharacteristic
187C43⋊#95C2311yescharacteristic
188C2×#41×C43C2×C411yescharacteristic, complemented
189C23×C4×C43C2311yescharacteristic
190C22×C8×C43—21no—
191#123×C43—21no—
192C22⋊Q8×C43C2×C411yescharacteristic, complemented
193C22⋊Q8×C43C2311yescharacteristic
194#121×C43C2×C411yescharacteristic, complemented
195#121×C43C2311yescharacteristic
196#120×C43—21no—
197C4×D4×C43—21no—
198C4×D4×C43—21no—
199#117×C43C2×C411yescharacteristic, complemented
200C2×C22⋊C4×C43—21no—
201C2×C42×C43—21no—
202C22⋊C8×C43—21no—
203C22⋊C8×C43C2311yescharacteristic
204C22⋊C8×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206#95×C43C2311yescharacteristic
207C24×C43C2×D411yescharacteristic
208C23×D43—21no—
209C23×D43—21no—
210C23×D43C2×D411yescharacteristic
211#41×C43—81no—
212C2×Q8×C43C22×C411yescharacteristic
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—21no—
216C2×D4×C43C22×C411yescharacteristic
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—81no—
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C22×C411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2411yescharacteristic
227C2×C22⋊D43—24no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43—21no—
235C2×C22⋊D43—21no—
236C2×C22⋊D43—81no—
237C2×C22⋊D43—81no—
238C2×C22⋊D43C22⋊C411yescharacteristic
239C2×C22⋊D43C22⋊C411yescharacteristic
240C2×C22⋊D43C22⋊C411yescharacteristic
241C2×C22⋊D43C22⋊C411yescharacteristic
242C22×Dic43—24no—
243C22×Dic43—21no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—81no—
248C22×Dic43—81no—
249C22×Dic43C2×D411yescharacteristic
250C22×Dic43C2×D411yescharacteristic
251C22×Dic43C2×D411yescharacteristic
252#10621902—81no—
253#10621900—81no—
254#10621900—81no—
255D4×D43—44no—
256D4×D43—81no—
257D4×D43—81no—
258D4×D43—81no—
259C2×D172—21no—
260C2×D172—21no—
261C2×D172—21no—
262C2×D172—21no—
263C2×D172—81no—
264C2×D172C22×C411yescharacteristic
265C2×D172C22×C411yescharacteristic
266C2×C4×D43—21no—
267C2×C4×D43—24no—
268C2×C4×D43—21no—
269C2×C4×D43—21no—
270C2×C4×D43—21no—
271C2×C4×D43—81no—
272C2×C4×D43—81no—
273C2×C4×D43—81no—
274C2×C4×D43C22×C411yescharacteristic
275C2×C4×D43C22×C411yescharacteristic
276C2×C4×D43C2×D411yescharacteristic
277C2×C4×D43C2×D411yescharacteristic
278C2×Dic86—21no—
279C2×C8×C43—21no—
280C2×C8×C43—21no—
281C2×C8×C43—81no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43—21no—
284C4⋊C4×C43C22×C411yescharacteristic
285C4⋊C4×C43C22×C411yescharacteristic
286C22⋊C4×C43—24no—
287C22⋊C4×C43—21no—
288C22⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C22⋊C4×C43—21no—
292C42×C43—21no—
293C42×C43—81no—
294C22⋊Dic43—21no—
295C22⋊Dic43—21no—
296C22⋊Dic43C22⋊C411yescharacteristic
297C22⋊Dic43C22⋊C411yescharacteristic
298C22⋊Dic43C22⋊C411yescharacteristic
299C22⋊Dic43C22⋊C411yescharacteristic
300(C2×D43)⋊C4—24no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—21no—
308(C2×D43)⋊C4—21no—
309(C2×D43)⋊C4—21no—
310(C2×D43)⋊C4—21no—
311(C2×D43)⋊C4—21no—
312(C2×D43)⋊C4—21no—
313(C2×D43)⋊C4C22⋊C411yescharacteristic
314(C2×D43)⋊C4C22⋊C411yescharacteristic
315(C2×D43)⋊C4C22⋊C411yescharacteristic
316(C2×D43)⋊C4C22⋊C411yescharacteristic
317C4⋊Dic43—21no—
318C4⋊Dic43—21no—
319C4⋊Dic43—21no—
320C4⋊Dic43C22×C411yescharacteristic
321C4⋊Dic43C22×C411yescharacteristic
322Dic43⋊C4—24no—
323Dic43⋊C4—21no—
324Dic43⋊C4—21no—
325Dic43⋊C4—21no—
326Dic43⋊C4—21no—
327Dic43⋊C4C22⋊C411yescharacteristic
328Dic43⋊C4C22⋊C411yescharacteristic
329Dic43⋊C4C22⋊C411yescharacteristic
330Dic43⋊C4C22⋊C411yescharacteristic
331C4×Dic43—24no—
332C4×Dic43—21no—
333C4×Dic43—21no—
334C4×Dic43—81no—
335C4×Dic43—81no—
336C4×Dic43C22×C411yescharacteristic
337C4×Dic43C22×C411yescharacteristic
338C4×Dic43C2×D411yescharacteristic
339C4×Dic43C2×D411yescharacteristic
340#10621877—81no—
341C2×C43⋊C8—21no—
342C2×C43⋊C8—21no—
343#10621872—81no—
344C8×D43—81no—
345C23×C43—21no—
346C23×C43—21no—
347C23×C43—22no—
348C23×C43—21no—
349C23×C43—41no—
350C23×C43C2×C22⋊C411yescharacteristic
351C23×C43C2×C22⋊C411yescharacteristic
352C23×C43C22×D411yescharacteristic
353C22×D43—21no—
354C22×D43—21no—
355C22×D43—22no—
356C22×D43—21no—
357C22×D43—21no—
358C22×D43—41no—
359C22×D43—42no—
360C22×D43—42no—
361C22×D43—81no—
362C22×D43—81no—
363C22×D43—81no—
364C22×D43—81no—
365C22×D43C2×C22⋊C411yescharacteristic
366C22×D43C2×C22⋊C411yescharacteristic
367Q8×C43—41no—
368D4×C43—41no—
369D4×C43—41no—
370D4×C43—41no—
371D4×C43—42no—
372D4×C43—81no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—21no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—41no—
386C2×C4×C43—41no—
387C2×C4×C43—41no—
388C2×C4×C43—81no—
389C2×C4×C43C2×C22⋊C411yescharacteristic
390C2×C4×C43C2×C22⋊C411yescharacteristic
391C2×C4×C43C23×C411yescharacteristic
392C2×C4×C43C22×D411yescharacteristic
393C22⋊D43—22no—
394C22⋊D43—22no—
395C22⋊D43—22no—
396C22⋊D43—41no—
397C22⋊D43—41no—
398C22⋊D43—41no—
399C22⋊D43—41no—
400C22⋊D43—42no—
401C22⋊D43—81no—
402C22⋊D43—81no—
403C22⋊D43—81no—
404C22⋊D43—81no—
405C22⋊D43—81no—
406C22⋊D43#10414yes—
407C2×Dic43—21no—
408C2×Dic43—21no—
409C2×Dic43—22no—
410C2×Dic43—22no—
411C2×Dic43—22no—
412C2×Dic43—21no—
413C2×Dic43—21no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—81no—
420C2×Dic43—81no—
421C2×Dic43—84no—
422C2×Dic43C2×C22⋊C411yescharacteristic
423C2×Dic43C2×C22⋊C411yescharacteristic
424C2×Dic43C2×C22⋊C411yescharacteristic
425C2×Dic43C2×C22⋊C411yescharacteristic
426C2×Dic43C2×C22⋊C411yescharacteristic
427C2×Dic43C2×C22⋊C411yescharacteristic
428D172—41no—
429D172—41no—
430D172—42no—
431D172—81no—
432D172—81no—
433D172—81no—
434C4×D43—41no—
435C4×D43—41no—
436C4×D43—41no—
437C4×D43—41no—
438C4×D43—42no—
439C4×D43—81no—
440C4×D43—81no—
441C4×D43—81no—
442C4×D43—84no—
443Dic86—81no—
444C8×C43—41no—
445C8×C43—41no—
446C43⋊C8—41no—
447C43⋊C8—41no—
448#17547—431nomaximal, Sylow
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—21no—
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—21no—
456C22×C43—42no—
457C22×C43—42no—
458C22×C43—41no—
459C22×C43—41no—
460C22×C43—41no—
461C22×C43C2×#10412yes—
462C22×C43C22×C22⋊C411yescharacteristic
463C22×C43#57611yescharacteristic
464C22×C43#57711yescharacteristic
465C2×D43—21no—
466C2×D43—21no—
467C2×D43—21no—
468C2×D43—21no—
469C2×D43—21no—
470C2×D43—42no—
471C2×D43—42no—
472C2×D43—41no—
473C2×D43—41no—
474C2×D43—41no—
475C2×D43—41no—
476C2×D43—41no—
477C2×D43—41no—
478C2×D43—162no—
479C2×D43—162no—
480C2×D43C2×#10412yes—
481C4×C43—21no—
482C4×C43—21no—
483C4×C43—21no—
484C4×C43—21no—
485C4×C43—42no—
486C4×C43—42no—
487C4×C43—41no—
488C4×C43—41no—
489C4×C43—41no—
490Dic43—21no—
491Dic43—21no—
492Dic43—21no—
493Dic43—21no—
494Dic43—21no—
495Dic43—42no—
496Dic43—42no—
497Dic43—41no—
498Dic43—41no—
499Dic43C2×#10412yes—
500#3519—431no—
501#2974—431no—
502#2275—431no—
503#1509—431no—
504#1507—431no—
505#1507—431no—
506#1505—431no—
507#1504—431no—
508#1504—431no—
509#1502—431no—
510#1501—431no—
511#1501D4311yescharacteristic, complemented
512#1500—431no—
513C2×#327—431no—
514C2×#327—431no—
515C2×C43—21no—
516C2×C43—21no—
517C2×C43—22no—
518C2×C43—41no—
519C2×C43—81no—
520C2×C43#288311yescharacteristic
521C2×C43#289711yescharacteristic
522C2×C43C22×#10411yescharacteristic
523D43—22no—
524D43—41no—
525D43—81no—
526D43—81no—
527#555—431no—
528#554—431no—
529#553—431no—
530#553—431no—
531#553—861no—
532#550—431no—
533#546—431no—
534#546—431no—
535#546—861no—
536#546—861no—
537D42—431no—
538D42—861no—
539#540—861no—
540#538—861no—
541#538—861no—
542#532—431no—
543#529—431no—
544#525—431no—
545#525C2×D4311yescharacteristic
546C2×#121—431no—
547C2×#121—431no—
548#518—861no—
549C2×C4×D4—431no—
550C2×C4×D4—861no—
551#436—861no—
552#435—861no—
553#435—861no—
554C8×D4—861no—
555#432—431no—
556#431—431no—
557#407—431no—
558#407—431no—
559C2×C22⋊C8—431no—
560C2×C22⋊C8C2×D4311yescharacteristic, complemented
561C4×C4⋊C4—431no—
562C4×C4⋊C4—861no—
563C4×C22⋊C4—431no—
564C4×C22⋊C4—861no—
565C4×C22⋊C4—861no—
566C4×C22⋊C4C2×D4311yescharacteristic, complemented
567#376—431no—
568C2×#95—431no—
569C2×#95—431no—
570#328—431no—
571#328—431no—
572#328C2×D4311yescharacteristic, complemented
573#328C2×D4311yescharacteristic, complemented
574#327—431no—
575#327—431no—
576#327—431no—
577#327—431no—
578#327—431no—
579#327—431no—
580#327—431no—
581#327—431no—
582#327—431no—
583#327—431no—
584#327C2×D4311yescharacteristic, complemented
585#327C2×D4311yescharacteristic, complemented
586C43#1754711yescharacteristic, complemented, Sylow
587C2×#41—431no—
588C2×#41—861no—
589C2×#41C4×D4311yescharacteristic, complemented
590C22×D4—431no—
591C22×D4—431no—
592C22×D4—431no—
593C22×D4—861no—
594C22×D4—861no—
595C22×D4—861no—
596C23×C4—431no—
597C23×C4—861no—
598C23×C4—861no—
599C23×C4C22×D4311yescharacteristic
600C2×M16—861no—
601C2×M16—861no—
602C22×C8—21no—
603C22×C8—861no—
604C4⋊Q8—431no—
605#127—431no—
606#127—861no—
607#126—861no—
608#126—861no—
609#126—861no—
610#125—431no—
611#125—861no—
612#124—431no—
613#124—861no—
614#124—861no—
615#124—861no—
616#123—21no—
617#123—861no—
618#123—861no—
619#123—861no—
620#123—861no—
621#123—861no—
622#123—861no—
623C22⋊Q8—431no—
624C22⋊Q8—861no—
625C22⋊Q8—861no—
626C22⋊Q8C4×D4311yescharacteristic, complemented
627C22⋊Q8C22×D4311yescharacteristic
628#121—431no—
629#121—431no—
630#121—431no—
631#121—431no—
632#121—431no—
633#121—431no—
634#121—431no—
635#121—861no—
636#121—861no—
637#121—861no—
638#121—861no—
639#121—861no—
640#121—861no—
641#121—861no—
642#121—861no—
643#121—861no—
644#121—861no—
645#121—861no—
646#121—861no—
647#121—861no—
648#121C4×D4311yescharacteristic, complemented
649#121C22×D4311yescharacteristic
650#120—21no—
651#120—861no—
652#120—861no—
653#120—861no—
654#120—861no—
655#120—861no—
656C4×Q8—431no—
657C4×D4—21no—
658C4×D4—21no—
659C4×D4—431no—
660C4×D4—431no—
661C4×D4—431no—
662C4×D4—431no—
663C4×D4—431no—
664C4×D4—431no—
665C4×D4—431no—
666C4×D4—431no—
667C4×D4—431no—
668C4×D4—431no—
669C4×D4—431no—
670C4×D4—861no—
671C4×D4—861no—
672C4×D4—861no—
673C4×D4—861no—
674C4×D4—861no—
675C4×D4—868no—
676C4×D4—861no—
677C4×D4—861no—
678C4×D4—861no—
679#117—431no—
680#117—861no—
681#117—861no—
682#117C4×D4311yescharacteristic, complemented
683C2×C4⋊C4—431no—
684C2×C4⋊C4—431no—
685C2×C4⋊C4—431no—
686C2×C4⋊C4—861no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—431no—
689C2×C22⋊C4—431no—
690C2×C22⋊C4—861no—
691C2×C22⋊C4—861no—
692C2×C22⋊C4—861no—
693C2×C22⋊C4—861no—
694C2×C22⋊C4—861no—
695C2×C42—21no—
696C2×C42—431no—
697C2×C42—861no—
698C2×C42—861no—
699C2×C42—861no—
700C4⋊C8—861no—
701C4⋊C8—861no—
702C22⋊C8—21no—
703C22⋊C8—431no—
704C22⋊C8—431no—
705C22⋊C8—861no—
706C22⋊C8—861no—
707C22⋊C8—861no—
708C22⋊C8C22×D4311yescharacteristic
709C22⋊C8C22×D4311yescharacteristic
710#97—861no—
711C4×C8—861no—
712#95—431no—
713#95—431no—
714#95—861no—
715#95—861no—
716#95—861no—
717#95C22×D4311yescharacteristic
718#95C22×D4311yescharacteristic
719C24—431no—
720C24—861no—
721C24—861no—
722C24D4×D4311yescharacteristic
723#41—81no—
724#41—3441no—
725#41—3441no—
726#41—3441no—
727C2×Q8—861no—
728C2×Q8C2×C4×D4311yescharacteristic
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—431no—
733C2×D4—431no—
734C2×D4—431no—
735C2×D4—431no—
736C2×D4—431no—
737C2×D4—431no—
738C2×D4—861no—
739C2×D4—861no—
740C2×D4—861no—
741C2×D4—861no—
742C2×D4—861no—
743C2×D4—861no—
744C2×D4—864no—
745C2×D4—861no—
746C2×D4—861no—
747C2×D4—861no—
748C2×D4—861no—
749C2×D4—861no—
750C2×D4—861no—
751C2×D4—3441no—
752C2×D4—3441no—
753C2×D4—3441no—
754C2×D4—3441no—
755C2×D4—3441no—
756C2×D4—3441no—
757C2×D4—1724no—
758C2×D4C2×C4×D4311yescharacteristic
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—81no—
763C22×C4—431no—
764C22×C4—431no—
765C22×C4—431no—
766C22×C4—431no—
767C22×C4—431no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—864no—
775C22×C4—861no—
776C22×C4—864no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—3441no—
781C22×C4—3441no—
782C22×C4—3441no—
783C22×C4—3441no—
784C22×C4—3441no—
785C22×C4C2×C4×D4311yescharacteristic
786C22×C4C2×C4×D4311yescharacteristic
787C22×C4D4×D4311yescharacteristic
788C22×C4D4×D4311yescharacteristic
789C22×C4D4×D4311yescharacteristic
790C22×C4C23×D4311yescharacteristic
791M16—3441no—
792M16—3441no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—81no—
796C2×C8—861no—
797C2×C8—861no—
798C2×C8—3441no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—431no—
802C4⋊C4—431no—
803C4⋊C4—431no—
804C4⋊C4—431no—
805C4⋊C4—431no—
806C4⋊C4—431no—
807C4⋊C4—861no—
808C4⋊C4—861no—
809C4⋊C4—861no—
810C4⋊C4—861no—
811C4⋊C4—861no—
812C4⋊C4—861no—
813C4⋊C4—864no—
814C4⋊C4—861no—
815C4⋊C4C2×C4×D4311yescharacteristic
816C4⋊C4C2×C4×D4311yescharacteristic
817C22⋊C4—24no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—431no—
824C22⋊C4—431no—
825C22⋊C4—431no—
826C22⋊C4—431no—
827C22⋊C4—431no—
828C22⋊C4—431no—
829C22⋊C4—431no—
830C22⋊C4—431no—
831C22⋊C4—861no—
832C22⋊C4—861no—
833C22⋊C4—861no—
834C22⋊C4—861no—
835C22⋊C4—861no—
836C22⋊C4—861no—
837C22⋊C4—861no—
838C22⋊C4—861no—
839C22⋊C4—864no—
840C22⋊C4—861no—
841C22⋊C4—861no—
842C22⋊C4—861no—
843C22⋊C4—861no—
844C22⋊C4—861no—
845C22⋊C4—861no—
846C42—21no—
847C42—81no—
848C42—431no—
849C42—431no—
850C42—431no—
851C42—431no—
852C42—861no—
853C42—861no—
854C42—864no—
855C42—3441no—
856C42—3441no—
857C23—22no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—41no—
862C23—431no—
863C23—431no—
864C23—862no—
865C23—861no—
866C23—861no—
867C23—861no—
868C23—861no—
869C23—3441no—
870C23—3441no—
871C23—3441no—
872C23—3441no—
873C23—1721no—
874C23—1722no—
875C23—1722no—
876C23C22⋊C4×D4311yescharacteristic
877C23C22⋊C4×D4311yescharacteristic
878C23C2×D4×D4311yescharacteristic
879Q8—41no—
880Q8—3441no—
881D4—41no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—81no—
886D4—434no—
887D4—862no—
888D4—862no—
889D4—862no—
890D4—3441no—
891D4—3441no—
892D4—3441no—
893D4—3441no—
894D4—3441no—
895D4—3441no—
896D4—3441no—
897D4—3441no—
898D4—1721no—
899D4—1721no—
900D4—1722no—
901D4—1722no—
902D4—1721no—
903D4—1721no—
904D4—1721no—
905D4—1721no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—81no—
922C2×C4—431no—
923C2×C4—431no—
924C2×C4—431no—
925C2×C4—431no—
926C2×C4—431no—
927C2×C4—431no—
928C2×C4—862no—
929C2×C4—861no—
930C2×C4—861no—
931C2×C4—862no—
932C2×C4—862no—
933C2×C4—861no—
934C2×C4—861no—
935C2×C4—3441no—
936C2×C4—3441no—
937C2×C4—3441no—
938C2×C4—3444no—
939C2×C4—3441no—
940C2×C4—3441no—
941C2×C4—3444no—
942C2×C4—1721no—
943C2×C4—1721no—
944C2×C4—1721no—
945C2×C4—1721no—
946C2×C4—1722no—
947C2×C4—1721no—
948C2×C4—1721no—
949C2×C4—1721no—
950C2×C4—1721no—
951C2×C4—1721no—
952C2×C4C22⋊C4×D4311yescharacteristic
953C2×C4C22⋊C4×D4311yescharacteristic
954C2×C4C22×C4×D4311yescharacteristic
955C2×C4C2×D4×D4311yescharacteristic
956C8—41no—
957C8—41no—
958C8—1721no—
959C8—1721no—
960C22—21no—
961C22—21no—
962C22—21no—
963C22—21no—
964C22—21no—
965C22—21no—
966C22—21no—
967C22—42no—
968C22—42no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—432no—
973C22—861no—
974C22—861no—
975C22—861no—
976C22—861no—
977C22—861no—
978C22—1722no—
979C22—1722no—
980C22—1721no—
981C22—1721no—
982C22—1721no—
983C22—1721no—
984C22—1721no—
985C22—1721no—
986C22—6882no—
987C22—6882no—
988C22#104×D4312yes—
989C22C2×C22⋊C4×D4311yescharacteristic
990C22#1458370111yescharacteristic
991C22#1458370611yescharacteristic
992C4—21no—
993C4—21no—
994C4—21no—
995C4—21no—
996C4—42no—
997C4—42no—
998C4—41no—
999C4—41no—
1000C4—41no—
1001C4—432no—
1002C4—861no—
1003C4—861no—
1004C4—861no—
1005C4—861no—
1006C4—861no—
1007C4—1722no—
1008C4—1722no—
1009C4—1721no—
1010C4—1721no—
1011C2—21no—
1012C2—21no—
1013C2—22no—
1014C2—41no—
1015C2—81no—
1016C2—862no—
1017C2—3441no—
1018C2—3441no—
1019C2—1721no—
1020C2#1914305311yescharacteristic
1021C2#1914311711yescharacteristic
1022C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1501C2
socleC22×C43C22×C22⋊C4
prime radical#19148615C2
cosocleC22×C4×C43C24
hypercenter#1501D43
hypocenterC43#17547
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. #19143626C2semidirect
3. #19136954C2semidirect
4. #19133119C2semidirect
5. #19133110C2semidirect
6. #19133109C2semidirect
7. #19133101C2semidirect
8. #19133099C2semidirect
9. #19133098C2semidirect
10. #19133088C2semidirect
11. #19133085C2semidirect
12. #19133080C2semidirect
13. C2×#14582634C2semidirect
14. #327×D43C2semidirect
15. C43×#1501C2semidirect
16. #14583612C4semidirect
17. #14583607C4semidirect
18. #14583601C4semidirect
20. #14583593C4semidirect
21. #14583568C4semidirect
23. #14583540C4semidirect
24. #14583537C4semidirect
26. #14583533C4semidirect
43. #14582953C22semidirect
44. #14582949C22semidirect
45. #14582863C22semidirect
46. #14582861C22semidirect
47. C22⋊C8×D43C22semidirect
49. #14582750C22semidirect
52. #14582746C22semidirect
53. #14582744C22semidirect
54. C2×C43⋊#95C22semidirect
55. #95×D43C22semidirect
56. #14582636C22semidirect
57. #14582636C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
62. #14582633C22semidirect
63. #14582633C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C2×C22⋊C8×C43C22semidirect
70. C4×C22⋊C4×C43C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
75. C2×#10621902C2×C4semidirect
77. C22×D172C2×C4semidirect
82. C2×D4×D43C2×C4semidirect
89. #13063324C2×C4semidirect
91. #13063321C2×C4semidirect
95. #13063316C2×C4semidirect
97. #13063314C2×C4semidirect
109. #13063301C2×C4semidirect
111. #13063300C2×C4semidirect
112. #13063300C2×C4semidirect
116. #13063299C2×C4semidirect
117. #13063299C2×C4semidirect
129. #13063296C2×C4semidirect
135. Q8×Dic43C2×C4semidirect
138. D4×Dic43C2×C4semidirect
140. #13063287C2×C4semidirect
141. #13063287C2×C4semidirect
157. #13063283C2×C4semidirect
159. C2×C4⋊Dic43C2×C4semidirect
162. C4⋊C4×D43C2×C4semidirect
188. C2×#41×C43C2×C4semidirect
192. C22⋊Q8×C43C2×C4semidirect
194. #121×C43C2×C4semidirect
199. #117×C43C2×C4semidirect
511. #1501D43semidirect
560. C2×C22⋊C8C2×D43semidirect
566. C4×C22⋊C4C2×D43semidirect
572. #328C2×D43semidirect
573. #328C2×D43semidirect
584. #327C2×D43semidirect
585. #327C2×D43semidirect
586. C43#17547semidirect
589. C2×#41C4×D43semidirect
626. C22⋊Q8C4×D43semidirect
648. #121C4×D43semidirect
682. #117C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191486152
#191436262
#191369542
#191331192
#191331102
#191331092
#191331012
#191330992
#191330982
#191330882
#191330852
#191330802
C2×#145826342
#327×D432
C43×#15012
#1754743