Finite Group Databasebeta

← #25064213

Subgroups — #25064213

Order 11008.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148332C211yesmaximal, characteristic
2#19143249C211yesmaximal, characteristic, complemented
3#19137457C211yesmaximal, characteristic, complemented
4#19133171C211yesmaximal, characteristic, complemented
5#19133153C211yesmaximal, characteristic, complemented
6#19133140C211yesmaximal, characteristic, complemented
7#19133132C211yesmaximal, characteristic, complemented
8#19133123C211yesmaximal, characteristic, complemented
9#19133119C211yesmaximal, characteristic, complemented
10#19133101C211yesmaximal, characteristic, complemented
11#19133099C211yesmaximal, characteristic, complemented
12#19133088C211yesmaximal, characteristic, complemented
13#19133080C211yesmaximal, characteristic, complemented
14C2×#14582634C211yesmaximal, characteristic, complemented
15C43×#1516C211yesmaximal, characteristic, complemented
16#14583614—21no—
17#14583595—21no—
18#14583595—21no—
19#14583572—21no—
20#14583572—21no—
21#14583553—21no—
22#14583536—21no—
23#14583536—21no—
24#14583527C411yescharacteristic, complemented
25#14583522C411yescharacteristic, complemented
26#14583522C411yescharacteristic, complemented
27#14583502C411yescharacteristic, complemented
28#14583502C411yescharacteristic, complemented
29#14583463C411yescharacteristic, complemented
30#14583444C2211yescharacteristic
31#14583444C2211yescharacteristic
32#14583435C2211yescharacteristic
33#14583435C2211yescharacteristic
34C2×#13063299C2211yescharacteristic
35#14583382C411yescharacteristic, complemented
36#14583373C411yescharacteristic, complemented
37C2×#13063284C2211yescharacteristic
38#14582957—21no—
39#14582957—21no—
40#14582953C2211yescharacteristic, complemented
41#14582953C2211yescharacteristic, complemented
42#14582949C2211yescharacteristic, complemented
43#14582949C2211yescharacteristic, complemented
44#14582925—21no—
45#14582863C2211yescharacteristic
46#14582854—21no—
47#14582784—21no—
48#14582782—21no—
49#14582771—21no—
50#14582766C2211yescharacteristic, complemented
51#14582763C2211yescharacteristic, complemented
52#14582750C2211yescharacteristic, complemented
53C22⋊C4×Dic43—21no—
54#14582744C2211yescharacteristic, complemented
55C2×C43⋊#95C2211yescharacteristic
56#14582636C2211yescharacteristic, complemented
57#14582636C2211yescharacteristic, complemented
58#14582634C2211yescharacteristic
59#14582634C2211yescharacteristic
60#14582634C2211yescharacteristic
61#14582634C2211yescharacteristic
62#14582633C2211yescharacteristic, complemented
63#14582633C2211yescharacteristic, complemented
64#14582632C2211yescharacteristic
65#14582632C2211yescharacteristic
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C43×#525C2211yescharacteristic
69C2×C22⋊C8×C43C2211yescharacteristic
70C43×#381C2211yescharacteristic
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic, complemented
74C43×#327C2211yescharacteristic, complemented
75C2×#10621900—21no—
76C2×#10621900—21no—
77C22×D172C2×C411yescharacteristic
78C22×C22⋊D43—21no—
79C23×Dic43—21no—
80C2×#10621877—21no—
81#13063325—21no—
82#13063324C2×C411yescharacteristic, complemented
83#13063324C2×C411yescharacteristic, complemented
84#13063321C2×C411yescharacteristic, complemented
85#13063321C2×C411yescharacteristic, complemented
86#13063320—21no—
87#13063320—21no—
88#13063320—21no—
89#13063320—21no—
90#13063317—21no—
91#13063316C2×C411yescharacteristic, complemented
92#13063316C2×C411yescharacteristic, complemented
93#13063314C2×C411yescharacteristic, complemented
94#13063314C2×C411yescharacteristic, complemented
95#13063311—21no—
96#13063311—21no—
97#13063311—21no—
98#13063311—21no—
99#13063309—21no—
100#13063309—21no—
101#13063309—21no—
102#13063309—21no—
103#13063307—21no—
104#13063307—21no—
105#13063307—21no—
106#13063307—21no—
107#13063305—21no—
108#13063305—21no—
109#13063302—21no—
110#13063302—21no—
111#13063299—21no—
112#13063299—21no—
113#13063299—21no—
114#13063299—21no—
115#13063299C2×C411yescharacteristic
116#13063299C2×C411yescharacteristic
117#13063299C2311yescharacteristic
118#13063299C2311yescharacteristic
119#13063297—21no—
120#13063297—21no—
121#13063297—21no—
122#13063297—21no—
123#13063296—21no—
124#13063296—21no—
125#13063293—21no—
126#13063293—21no—
127Q8×Dic43C2×C411yescharacteristic, complemented
128Q8×Dic43C2×C411yescharacteristic, complemented
129C4×D172—21no—
130C4×D172—21no—
131D4×Dic43—21no—
132D4×Dic43—21no—
133D4×Dic43C2×C411yescharacteristic, complemented
134D4×Dic43C2×C411yescharacteristic, complemented
135#13063287C2×C411yescharacteristic, complemented
136#13063287C2×C411yescharacteristic, complemented
137#13063287C2×C411yescharacteristic, complemented
138#13063287C2×C411yescharacteristic, complemented
139(C22⋊D43)⋊C4—21no—
140(C22⋊D43)⋊C4—21no—
141(C22⋊D43)⋊C4—21no—
142(C22⋊D43)⋊C4—21no—
143#13063284—21no—
144#13063284C2×C411yescharacteristic
145#13063284C2×C411yescharacteristic
146#13063284C2×C411yescharacteristic
147#13063284C2×C411yescharacteristic
148#13063284D411yescharacteristic
149#13063284D411yescharacteristic
150#13063284D411yescharacteristic
151#13063284D411yescharacteristic
152#13063283—21no—
153#13063283—21no—
154C2×C4⋊Dic43—21no—
155C2×C4⋊Dic43C2×C411yescharacteristic
156C2×C4⋊Dic43D411yescharacteristic
157C2×C4⋊Dic43D411yescharacteristic
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C2×C22⋊Dic43D411yescharacteristic
161C2×C22⋊Dic43D411yescharacteristic
162C2×(C2×D43)⋊C4—21no—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—21no—
165C2×C4×Dic43—21no—
166C2×C4×Dic43—21no—
167C2×C4×Dic43C2311yescharacteristic
168C2×C4×Dic43C2311yescharacteristic
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)C2311yescharacteristic
175C22⋊(C43⋊C8)C2311yescharacteristic
176#13063235—21no—
177#13063235—21no—
178C8×Dic43—21no—
179C8×Dic43—21no—
180C43⋊#95—21no—
181C43⋊#95—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—
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—
208#41×C43—42no—
209C2×Q8×C43C22×C411yescharacteristic
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43C22×C411yescharacteristic
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—42no—
218C22×C4×C43C22×C411yescharacteristic
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2411yescharacteristic
224C2×C22⋊D43—21no—
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—81no—
233C2×C22⋊D43—81no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—42no—
240C22×Dic43—42no—
241C22×Dic43—81no—
242C22×Dic43C2×D411yescharacteristic
243C22×Dic43C2×D411yescharacteristic
244C22×Dic43C2×D411yescharacteristic
245C22×Dic43C2×D411yescharacteristic
246#10621900—81no—
247#10621900—81no—
248#10621900—81no—
249#10621900—81no—
250C2×D172—21no—
251C2×D172—42no—
252C2×D172C22×C411yescharacteristic
253C2×D172C22×C411yescharacteristic
254C2×C4×D43—21no—
255C2×C4×D43—21no—
256C2×C4×D43—21no—
257C2×C4×D43—21no—
258C2×Dic86—21no—
259C2×Dic86—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—42no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43C22×C411yescharacteristic
266C4⋊C4×C43C22×C411yescharacteristic
267C22⋊C4×C43—21no—
268C22⋊C4×C43—21no—
269C22⋊C4×C43—21no—
270C22⋊C4×C43—21no—
271C22⋊C4×C43—21no—
272C22⋊C4×C43—42no—
273C42×C43—21no—
274C22⋊Dic43—21no—
275C22⋊Dic43—21no—
276C22⋊Dic43C22⋊C411yescharacteristic
277C22⋊Dic43C22⋊C411yescharacteristic
278C22⋊Dic43C22⋊C411yescharacteristic
279C22⋊Dic43C22⋊C411yescharacteristic
280C22⋊Dic43C22⋊C411yescharacteristic
281C22⋊Dic43C22⋊C411yescharacteristic
282C22⋊Dic43C22⋊C411yescharacteristic
283C22⋊Dic43C22⋊C411yescharacteristic
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
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—
296C4⋊Dic43—21no—
297C4⋊Dic43—21no—
298C4⋊Dic43—21no—
299C4⋊Dic43—21no—
300C4⋊Dic43—21no—
301C4⋊Dic43C22⋊C411yescharacteristic
302C4⋊Dic43C22⋊C411yescharacteristic
303C4⋊Dic43C22⋊C411yescharacteristic
304C4⋊Dic43C22⋊C411yescharacteristic
305C4⋊Dic43C22⋊C411yescharacteristic
306C4⋊Dic43C22⋊C411yescharacteristic
307C4⋊Dic43C22⋊C411yescharacteristic
308C4⋊Dic43C22⋊C411yescharacteristic
309C4⋊Dic43C22×C411yescharacteristic
310C4⋊Dic43C22×C411yescharacteristic
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—42no—
316Dic43⋊C4—81no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43—42no—
320C4×Dic43—81no—
321C4×Dic43C22×C411yescharacteristic
322C4×Dic43C22×C411yescharacteristic
323C4×Dic43C22×C411yescharacteristic
324C4×Dic43C22×C411yescharacteristic
325C4×Dic43C2×D411yescharacteristic
326C4×Dic43C2×D411yescharacteristic
327C4×Dic43C2×D411yescharacteristic
328C4×Dic43C2×D411yescharacteristic
329#10621877—42no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—21no—
332C23×C43—21no—
333C23×C43—21no—
334C23×C43—22no—
335C23×C43—21no—
336C23×C43—41no—
337C23×C43C2×C22⋊C411yescharacteristic
338C23×C43C2×C22⋊C411yescharacteristic
339C23×C43C22×D411yescharacteristic
340C22×D43—21no—
341C22×D43—21no—
342C22×D43—42no—
343C22×D43—81no—
344C22×D43—81no—
345Q8×C43—41no—
346D4×C43—41no—
347D4×C43—41no—
348D4×C43—41no—
349D4×C43—42no—
350D4×C43—81no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—42no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43C2×C22⋊C411yescharacteristic
368C2×C4×C43C2×C22⋊C411yescharacteristic
369C2×C4×C43C23×C411yescharacteristic
370C2×C4×C43C22×D411yescharacteristic
371C22⋊D43—41no—
372C22⋊D43—41no—
373C22⋊D43—41no—
374C22⋊D43—41no—
375C22⋊D43—81no—
376C22⋊D43—81no—
377C22⋊D43—81no—
378C22⋊D43—81no—
379C22⋊D43—81no—
380C22⋊D43—81no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—22no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—41no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—81no—
396C2×Dic43—81no—
397C2×Dic43—81no—
398C2×Dic43—84no—
399C2×Dic43C2×C22⋊C411yescharacteristic
400C2×Dic43C2×C22⋊C411yescharacteristic
401C2×Dic43C2×C22⋊C411yescharacteristic
402C2×Dic43C2×C22⋊C411yescharacteristic
403C2×Dic43C2×C22⋊C411yescharacteristic
404C2×Dic43C2×C22⋊C411yescharacteristic
405C2×Dic43C2×C22⋊C411yescharacteristic
406C2×Dic43C2×C22⋊C411yescharacteristic
407D172—41no—
408D172—41no—
409D172—42no—
410C4×D43—81no—
411C4×D43—81no—
412C4×D43—81no—
413C4×D43—81no—
414Dic86—81no—
415Dic86—81no—
416C8×C43—41no—
417C8×C43—41no—
418C43⋊C8—41no—
419C43⋊C8—41no—
420#17604—431nomaximal, Sylow
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—21no—
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—42no—
429C22×C43—42no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43#41012yes—
434C22×C43C22×C22⋊C411yescharacteristic
435C22×C43#57611yescharacteristic
436C22×C43#57711yescharacteristic
437C2×D43—41no—
438C2×D43—41no—
439C2×D43—41no—
440C2×D43—41no—
441C2×D43—41no—
442C2×D43—41no—
443C2×D43—162no—
444C4×C43—21no—
445C4×C43—21no—
446C4×C43—21no—
447C4×C43—21no—
448C4×C43—41no—
449C4×C43—41no—
450C4×C43—41no—
451C4×C43—81no—
452C4×C43—81no—
453Dic43—21no—
454Dic43—21no—
455Dic43—21no—
456Dic43—21no—
457Dic43—21no—
458Dic43—21no—
459Dic43—21no—
460Dic43—21no—
461Dic43—42no—
462Dic43—41no—
463Dic43—41no—
464Dic43—81no—
465#3494—431no—
466#2924—431no—
467#2343—431no—
468#1521—431no—
469#1517—431no—
470#1516D4311yescharacteristic, complemented
471#1514—431no—
472#1512—431no—
473#1510—431no—
474#1509—431no—
475#1505—431no—
476#1504—431no—
477#1502—431no—
478#1500—431no—
479C2×#327—431no—
480C2×C43—21no—
481C2×C43—21no—
482C2×C43—22no—
483C2×C43—41no—
484C2×C43—81no—
485C2×C43C2×#41011yescharacteristic
486C2×C43#289711yescharacteristic
487C2×C43#290111yescharacteristic
488D43—81no—
489D43—81no—
490#555—861no—
491#553—861no—
492#553—861no—
493#551—861no—
494#551—861no—
495#547—861no—
496#546—861no—
497#546—861no—
498#544—431no—
499#542—431no—
500#542—431no—
501#540—431no—
502#540—431no—
503#535—431no—
504#532—431no—
505#532—431no—
506#529—431no—
507#529—431no—
508#525C2×D4311yescharacteristic
509C2×#121—431no—
510#520—431no—
511#518—431no—
512C2×#117—431no—
513#433—861no—
514#433—861no—
515#432—431no—
516#432—431no—
517#431—431no—
518#431—431no—
519#424—861no—
520#407—431no—
521C2×C22⋊C8C2×D4311yescharacteristic
522#405—861no—
523#387—861no—
524#387—861no—
525#385—861no—
526#383—431no—
527#382—431no—
528#381C2×D4311yescharacteristic
529C4×C4⋊C4—431no—
530C4×C22⋊C4—861no—
531#376—431no—
532C2×#95—431no—
533#328—431no—
534#328—431no—
535#328C2×D4311yescharacteristic, complemented
536#328C2×D4311yescharacteristic, complemented
537#327—431no—
538#327—431no—
539#327—431no—
540#327—431no—
541#327—431no—
542#327—431no—
543#327—431no—
544#327—431no—
545#327—431no—
546#327—431no—
547#327C2×D4311yescharacteristic, complemented
548#327C2×D4311yescharacteristic, complemented
549C43#1760411yescharacteristic, complemented, Sylow
550C2×#41—861no—
551C2×#41—861no—
552C2×#41C4×D4311yescharacteristic
553C22×D4—431no—
554C22×D4—861no—
555C23×C4—861no—
556C23×C4C22×D4311yescharacteristic
557C2×M16—861no—
558C22×C8—21no—
559C4⋊Q8—431no—
560C4⋊Q8—431no—
561C4⋊Q8—861no—
562#127—431no—
563#127—431no—
564#126—861no—
565#126—861no—
566#126—861no—
567#126—861no—
568#125—431no—
569#125—431no—
570#125—861no—
571#124—431no—
572#124—431no—
573#124—861no—
574#124—861no—
575#124—861no—
576#124—861no—
577#123—21no—
578#123—861no—
579#123—861no—
580#123—861no—
581#123—861no—
582#123—861no—
583#123—861no—
584#123—861no—
585#123—861no—
586C22⋊Q8—861no—
587C22⋊Q8—861no—
588C22⋊Q8—861no—
589C22⋊Q8—861no—
590C22⋊Q8C4×D4311yescharacteristic
591C22⋊Q8C22×D4311yescharacteristic
592#121—431no—
593#121—431no—
594#121—431no—
595#121—431no—
596#121—861no—
597#121—861no—
598#121—861no—
599#121—861no—
600#121—861no—
601#121—861no—
602#121—861no—
603#121—861no—
604#121—861no—
605#121—861no—
606#121C4×D4311yescharacteristic
607#121C22×D4311yescharacteristic
608#120—21no—
609#120—861no—
610#120—861no—
611C4×Q8—431no—
612C4×Q8—431no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—431no—
616C4×D4—431no—
617C4×D4—431no—
618C4×D4—431no—
619C4×D4—431no—
620C4×D4—431no—
621C4×D4—861no—
622C4×D4—861no—
623C4×D4—861no—
624C4×D4—861no—
625C4×D4—861no—
626C4×D4—861no—
627C4×D4—861no—
628C4×D4—861no—
629#117—431no—
630#117—431no—
631#117—431no—
632#117—431no—
633#117—431no—
634#117—431no—
635#117—431no—
636#117—431no—
637#117—861no—
638#117—861no—
639#117—861no—
640#117C4×D4311yescharacteristic
641C2×C4⋊C4—431no—
642C2×C4⋊C4—431no—
643C2×C4⋊C4—431no—
644C2×C4⋊C4—861no—
645C2×C4⋊C4—861no—
646C2×C4⋊C4—861no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—431no—
649C2×C22⋊C4—431no—
650C2×C22⋊C4—861no—
651C2×C22⋊C4—861no—
652C2×C22⋊C4—861no—
653C2×C42—431no—
654C2×C42—431no—
655C2×C42—861no—
656C2×C42—861no—
657C4⋊C8—861no—
658C4⋊C8—861no—
659C4⋊C8—861no—
660C4⋊C8—861no—
661C22⋊C8—21no—
662C22⋊C8—431no—
663C22⋊C8—431no—
664C22⋊C8—861no—
665C22⋊C8C22×D4311yescharacteristic
666C22⋊C8C22×D4311yescharacteristic
667#97—861no—
668#97—861no—
669C4×C8—861no—
670C4×C8—861no—
671#95—21no—
672#95—431no—
673#95—431no—
674#95—861no—
675#95—861no—
676#95—861no—
677#95—861no—
678#95—861no—
679#95C22×D4311yescharacteristic
680#95C22×D4311yescharacteristic
681C24—861no—
682C24D4×D4311yescharacteristic
683#41—42no—
684#41—3441no—
685#41—3441no—
686#41—3441no—
687#41—3441no—
688C2×Q8—861no—
689C2×Q8—861no—
690C2×Q8C2×C4×D4311yescharacteristic
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—431no—
695C2×D4—431no—
696C2×D4—861no—
697C2×D4—861no—
698C2×D4—861no—
699C2×D4—861no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—861no—
705C2×D4—3441no—
706C2×D4—3441no—
707C2×D4—1722no—
708C2×D4C2×C4×D4311yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—42no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—431no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—3441no—
727C22×C4—1722no—
728C22×C4—1722no—
729C22×C4C2×C4×D4311yescharacteristic
730C22×C4C2×C4×D4311yescharacteristic
731C22×C4D4×D4311yescharacteristic
732C22×C4D4×D4311yescharacteristic
733C22×C4D4×D4311yescharacteristic
734C22×C4C23×D4311yescharacteristic
735M16—1722no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—42no—
739C2×C8—861no—
740C2×C8—861no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—431no—
744C4⋊C4—431no—
745C4⋊C4—431no—
746C4⋊C4—431no—
747C4⋊C4—431no—
748C4⋊C4—431no—
749C4⋊C4—431no—
750C4⋊C4—431no—
751C4⋊C4—431no—
752C4⋊C4—431no—
753C4⋊C4—861no—
754C4⋊C4—861no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4—3441no—
763C4⋊C4—1722no—
764C4⋊C4C2×C4×D4311yescharacteristic
765C4⋊C4C2×C4×D4311yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—42no—
772C22⋊C4—431no—
773C22⋊C4—431no—
774C22⋊C4—431no—
775C22⋊C4—431no—
776C22⋊C4—431no—
777C22⋊C4—431no—
778C22⋊C4—431no—
779C22⋊C4—431no—
780C22⋊C4—861no—
781C22⋊C4—861no—
782C22⋊C4—861no—
783C22⋊C4—861no—
784C22⋊C4—861no—
785C22⋊C4—861no—
786C22⋊C4—861no—
787C22⋊C4—861no—
788C22⋊C4—861no—
789C22⋊C4—861no—
790C22⋊C4—861no—
791C22⋊C4—861no—
792C22⋊C4—861no—
793C22⋊C4—861no—
794C42—21no—
795C42—431no—
796C42—431no—
797C42—431no—
798C42—431no—
799C42—431no—
800C42—431no—
801C42—431no—
802C42—431no—
803C42—861no—
804C42—861no—
805C42—3441no—
806C42—1722no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—41no—
812C23—861no—
813C23—861no—
814C23—3441no—
815C23—3441no—
816C23—1722no—
817C23C22⋊C4×D4311yescharacteristic
818C23C22⋊C4×D4311yescharacteristic
819C23C2×D4×D4311yescharacteristic
820Q8—41no—
821Q8—3441no—
822Q8—3441no—
823D4—41no—
824D4—42no—
825D4—41no—
826D4—41no—
827D4—81no—
828D4—3441no—
829D4—3441no—
830D4—3441no—
831D4—3441no—
832D4—3441no—
833D4—3441no—
834D4—1721no—
835D4—1721no—
836D4—1722no—
837D4—1721no—
838D4—1721no—
839D4—1721no—
840D4—1721no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—431no—
858C2×C4—431no—
859C2×C4—431no—
860C2×C4—431no—
861C2×C4—431no—
862C2×C4—431no—
863C2×C4—431no—
864C2×C4—431no—
865C2×C4—861no—
866C2×C4—861no—
867C2×C4—861no—
868C2×C4—861no—
869C2×C4—862no—
870C2×C4—861no—
871C2×C4—861no—
872C2×C4—3441no—
873C2×C4—3441no—
874C2×C4—3441no—
875C2×C4—3441no—
876C2×C4—3441no—
877C2×C4—3441no—
878C2×C4—3444no—
879C2×C4—3441no—
880C2×C4—1721no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4—1721no—
886C2×C4—1721no—
887C2×C4C22⋊C4×D4311yescharacteristic
888C2×C4C22⋊C4×D4311yescharacteristic
889C2×C4C22×C4×D4311yescharacteristic
890C2×C4C2×D4×D4311yescharacteristic
891C8—41no—
892C8—41no—
893C8—1721no—
894C8—1721no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—1721no—
908C22—1721no—
909C22—1721no—
910C22—1721no—
911C22—1721no—
912C22—1721no—
913C22—6882no—
914C22#1458287112yes—
915C22C2×C22⋊C4×D4311yescharacteristic
916C22#1458370111yescharacteristic
917C22#1458370611yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—41no—
923C4—41no—
924C4—41no—
925C4—81no—
926C4—81no—
927C4—861no—
928C4—861no—
929C4—861no—
930C4—861no—
931C4—861no—
932C4—861no—
933C4—861no—
934C4—861no—
935C4—3441no—
936C4—1722no—
937C4—1721no—
938C4—1721no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—81no—
944C2—3441no—
945C2—3441no—
946C2C2×#1458287111yescharacteristic
947C2#1914311711yescharacteristic
948C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1516C2
socleC22×C43C22×C22⋊C4
prime radical#19148332C2
cosocleC22×C4×C43C24
hypercenter#1516D43
hypocenterC43#17604
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. #19143249C2semidirect
3. #19137457C2semidirect
4. #19133171C2semidirect
5. #19133153C2semidirect
6. #19133140C2semidirect
7. #19133132C2semidirect
8. #19133123C2semidirect
9. #19133119C2semidirect
10. #19133101C2semidirect
11. #19133099C2semidirect
12. #19133088C2semidirect
13. #19133080C2semidirect
14. C2×#14582634C2semidirect
15. C43×#1516C2semidirect
24. #14583527C4semidirect
25. #14583522C4semidirect
26. #14583522C4semidirect
27. #14583502C4semidirect
28. #14583502C4semidirect
29. #14583463C4semidirect
35. #14583382C4semidirect
36. #14583373C4semidirect
40. #14582953C22semidirect
41. #14582953C22semidirect
42. #14582949C22semidirect
43. #14582949C22semidirect
50. #14582766C22semidirect
51. #14582763C22semidirect
52. #14582750C22semidirect
54. #14582744C22semidirect
56. #14582636C22semidirect
57. #14582636C22semidirect
62. #14582633C22semidirect
63. #14582633C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
82. #13063324C2×C4semidirect
83. #13063324C2×C4semidirect
84. #13063321C2×C4semidirect
85. #13063321C2×C4semidirect
91. #13063316C2×C4semidirect
92. #13063316C2×C4semidirect
93. #13063314C2×C4semidirect
94. #13063314C2×C4semidirect
127. Q8×Dic43C2×C4semidirect
128. Q8×Dic43C2×C4semidirect
133. D4×Dic43C2×C4semidirect
134. D4×Dic43C2×C4semidirect
135. #13063287C2×C4semidirect
136. #13063287C2×C4semidirect
137. #13063287C2×C4semidirect
138. #13063287C2×C4semidirect
470. #1516D43semidirect
535. #328C2×D43semidirect
536. #328C2×D43semidirect
547. #327C2×D43semidirect
548. #327C2×D43semidirect
549. C43#17604semidirect

Maximal subgroups

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

subgroupindex
#191483322
#191432492
#191374572
#191331712
#191331532
#191331402
#191331322
#191331232
#191331192
#191331012
#191330992
#191330882
#191330802
C2×#145826342
C43×#15162
#1760443