Finite Group Databasebeta

← #25064141

Subgroups — #25064141

Order 11008.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148644C211yesmaximal, characteristic
2#19137228C211yesmaximal, characteristic, complemented
3#19133173C211yesmaximal, characteristic, complemented
4#19133168C211yesmaximal, characteristic, complemented
5#19133160C211yesmaximal, characteristic, complemented
6#19133152C211yesmaximal, characteristic, complemented
7#19133147C211yesmaximal, characteristic, complemented
8#19133139C211yesmaximal, characteristic, complemented
9#19133134C211yesmaximal, characteristic, complemented
10#19133129C211yesmaximal, characteristic, complemented
11#19133116C211yesmaximal, characteristic, complemented
12#19133100C211yesmaximal, characteristic, complemented
13#19133087C211yesmaximal, characteristic, complemented
14C2×#14582637C211yesmaximal, characteristic, complemented
15C43×#2974C211yesmaximal, characteristic, complemented
16#14583619C411yescharacteristic, complemented
17#14583604—21no—
18#14583589C411yescharacteristic, complemented
19#14583589C411yescharacteristic, complemented
20#14583575—21no—
21#14583575—21no—
22D4×Dic86C411yescharacteristic, complemented
23#14583558C411yescharacteristic, complemented
24#14583558C411yescharacteristic, complemented
25#14583554C411yescharacteristic, complemented
26#14583553C411yescharacteristic, complemented
27#14583543—21no—
28#14583514—21no—
29#14583491—21no—
30#14583491—21no—
31#14583456C2211yescharacteristic
32#14583433C2211yescharacteristic
33#14583410C2211yescharacteristic
34#14583410C2211yescharacteristic
35C2×#13063304C2211yescharacteristic
36C2×#13063304C2211yescharacteristic
37#14583378—21no—
38#14582792—21no—
39#14582785—21no—
40#14582779—21no—
41#14582774—21no—
42#14582767C2211yescharacteristic
43#14582765C2211yescharacteristic
44#14582762C2211yescharacteristic
45#14582759C2211yescharacteristic
46C4×C22⋊Dic43C2211yescharacteristic
47C2×C43⋊#95C2211yescharacteristic
48#14582637C2211yescharacteristic
49#14582637C2211yescharacteristic
50#14582637C2211yescharacteristic
51#14582637C2211yescharacteristic
52#14582637C2211yescharacteristic
53#14582637C2211yescharacteristic
54#14582637C2211yescharacteristic
55#14582637C2211yescharacteristic
56#14582637C2211yescharacteristic
57#14582637C2211yescharacteristic
58#14582637C2211yescharacteristic
59#14582637C2211yescharacteristic
60#14582634C2211yescharacteristic
61#14582634C2211yescharacteristic
62#14582634C2211yescharacteristic
63#14582634C2211yescharacteristic
64C2×C4×D4×C43C2211yescharacteristic
65C43×#436—21no—
66C43×#435—21no—
67C43×#435—21no—
68C8×D4×C43—21no—
69C43×#432C2211yescharacteristic
70C43×#431C2211yescharacteristic
71C43×#407C2211yescharacteristic
72C43×#407C2211yescharacteristic
73C2×C22⋊C8×C43C2211yescharacteristic
74C2×C22⋊C8×C43C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic
76C2×#10621898C2×C411yescharacteristic, complemented
77C2×#10621900—21no—
78C22×Dic86C2×C411yescharacteristic
79C22×Dic86C2×C411yescharacteristic, complemented
80C23×Dic43—21no—
81#13063325C2×C411yescharacteristic, complemented
82#13063325C2×C411yescharacteristic, complemented
83#13063324—21no—
84#13063319—21no—
85#13063318—21no—
86#13063318—21no—
87#13063318—21no—
88#13063318—21no—
89#13063317—21no—
90#13063317C2×C411yescharacteristic, complemented
91#13063315—21no—
92#13063315—21no—
93#13063313C2×C411yescharacteristic, complemented
94#13063312—21no—
95#13063311—21no—
96#13063311—21no—
97#13063309—21no—
98#13063309—21no—
99#13063308—21no—
100#13063308—21no—
101#13063308—21no—
102#13063307—21no—
103#13063307—21no—
104#13063306—21no—
105#13063306—21no—
106#13063305—21no—
107#13063304—21no—
108#13063304—21no—
109#13063304—21no—
110#13063304—21no—
111#13063304—21no—
112#13063304C2×C411yescharacteristic
113#13063304C2×C411yescharacteristic
114#13063304C2×C411yescharacteristic
115#13063304C2×C411yescharacteristic, complemented
116#13063304C2×C411yescharacteristic, complemented
117#13063304C2×C411yescharacteristic, complemented
118#13063304C2311yescharacteristic
119#13063304C2311yescharacteristic
120#13063304C2311yescharacteristic
121#13063303—21no—
122#13063303—21no—
123#13063302—21no—
124#13063302—21no—
125#13063299C2×C411yescharacteristic
126#13063299C2×C411yescharacteristic, complemented
127#13063299C2311yescharacteristic
128#13063297—21no—
129#13063297—21no—
130#13063296—21no—
131#13063294—21no—
132#13063294—21no—
133C4×Dic86—21no—
134C4×Dic86C2×C411yescharacteristic, complemented
135C4×Dic86C2×C411yescharacteristic, complemented
136C4×Dic86C2×C411yescharacteristic, complemented
137#13063290—21no—
138C4×D172C2×C411yescharacteristic, complemented
139D4×Dic43—21no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43—21no—
145(C22⋊D43)⋊C4—21no—
146(C22⋊D43)⋊C4—21no—
147#13063284—21no—
148#13063284C2×C411yescharacteristic
149#13063284C2×C411yescharacteristic, complemented
150#13063282—21no—
151#13063281—21no—
152#13063281—21no—
153C2×C4⋊Dic43—21no—
154C2×C4⋊Dic43—21no—
155C2×C4⋊Dic43C2×C411yescharacteristic
156C2×C4⋊Dic43C2×C411yescharacteristic, complemented
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4—21no—
159C4⋊C4×D43—21no—
160C2×C22⋊Dic43—21no—
161C2×C22⋊Dic43—21no—
162C2×C22⋊Dic43—21no—
163C2×C22⋊Dic43—21no—
164C2×C22⋊Dic43—21no—
165C2×C4×Dic43—21no—
166C43⋊#95—21no—
167C43⋊#95—21no—
168C43⋊#95—21no—
169C43⋊#95—21no—
170C43⋊#95—21no—
171C43⋊#95C2311yescharacteristic
172C43⋊#95C2311yescharacteristic
173C43⋊#95C2311yescharacteristic
174C43⋊#95C2311yescharacteristic
175C22×D4×C43D411yescharacteristic
176C23×C4×C43C2311yescharacteristic
177C23×C4×C43C2311yescharacteristic
178C2×M16×C43—21no—
179C2×M16×C43—21no—
180C22×C8×C43—21no—
181C22×C8×C43—21no—
182C4×D4×C43C2×C411yescharacteristic
183C4×D4×C43C2×C411yescharacteristic
184C4×D4×C43C2×C411yescharacteristic
185C4×D4×C43C2×C411yescharacteristic
186C4×D4×C43D411yescharacteristic
187C4×D4×C43D411yescharacteristic
188C4×D4×C43D411yescharacteristic
189C4×D4×C43D411yescharacteristic
190C2×C4⋊C4×C43D411yescharacteristic
191C2×C22⋊C4×C43D411yescharacteristic
192C2×C22⋊C4×C43D411yescharacteristic
193C2×C42×C43C2311yescharacteristic
194C4⋊C8×C43—21no—
195C4⋊C8×C43—21no—
196C22⋊C8×C43—21no—
197C22⋊C8×C43—21no—
198C22⋊C8×C43—21no—
199C22⋊C8×C43—21no—
200C22⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204#97×C43—21no—
205C4×C8×C43—21no—
206C24×C43C2×D411yescharacteristic
207C24×C43C2×D411yescharacteristic
208C2×D4×C43—42no—
209C2×D4×C43C22⋊C411yescharacteristic
210C2×D4×C43C22⋊C411yescharacteristic
211C2×D4×C43C22⋊C411yescharacteristic
212C2×D4×C43C22⋊C411yescharacteristic
213C22×C4×C43—81no—
214C22×C4×C43—81no—
215C22×C4×C43C22×C411yescharacteristic
216C22×C4×C43C22×C411yescharacteristic
217C22×C4×C43C22×C411yescharacteristic
218C22×C4×C43C22×C411yescharacteristic
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2411yescharacteristic
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C22×Dic43—21no—
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—42no—
242C22×Dic43—81no—
243C22×Dic43—81no—
244#10621900—44no—
245#10621898—81no—
246#10621898—81no—
247C2×D172C22×C411yescharacteristic
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×Dic86—21no—
252C2×Dic86—21no—
253C2×Dic86—21no—
254C2×Dic86—81no—
255C2×Dic86—81no—
256C2×Dic86C22×C411yescharacteristic
257C2×Dic86C22×C411yescharacteristic
258C2×Dic86C22×C411yescharacteristic
259M16×C43—81no—
260M16×C43—81no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—81no—
266C2×C8×C43—81no—
267C4⋊C4×C43C22⋊C411yescharacteristic
268C4⋊C4×C43C22⋊C411yescharacteristic
269C4⋊C4×C43C22⋊C411yescharacteristic
270C4⋊C4×C43C22⋊C411yescharacteristic
271C22⋊C4×C43C22⋊C411yescharacteristic
272C22⋊C4×C43C22⋊C411yescharacteristic
273C22⋊C4×C43C22⋊C411yescharacteristic
274C22⋊C4×C43C22⋊C411yescharacteristic
275C22⋊C4×C43C22⋊C411yescharacteristic
276C22⋊C4×C43C22⋊C411yescharacteristic
277C22⋊C4×C43C22⋊C411yescharacteristic
278C22⋊C4×C43C22⋊C411yescharacteristic
279C42×C43C22×C411yescharacteristic
280C42×C43C22×C411yescharacteristic
281C42×C43C2×D411yescharacteristic
282C42×C43C2×D411yescharacteristic
283C22⋊Dic43—21no—
284C22⋊Dic43—21no—
285C22⋊Dic43—21no—
286C22⋊Dic43—21no—
287C22⋊Dic43—21no—
288C22⋊Dic43—21no—
289C22⋊Dic43—21no—
290C22⋊Dic43—21no—
291C22⋊Dic43—21no—
292C22⋊Dic43—21no—
293C22⋊Dic43—21no—
294C22⋊Dic43—42no—
295C22⋊Dic43—81no—
296C22⋊Dic43—81no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43—21no—
305C4⋊Dic43—21no—
306C4⋊Dic43—21no—
307C4⋊Dic43—21no—
308C4⋊Dic43—81no—
309C4⋊Dic43—81no—
310C4⋊Dic43C22×C411yescharacteristic
311C4⋊Dic43C22×C411yescharacteristic
312C4⋊Dic43C22×C411yescharacteristic
313C4⋊Dic43C22×C411yescharacteristic
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—21no—
323Dic43⋊C4—21no—
324Dic43⋊C4—21no—
325Dic43⋊C4—21no—
326Dic43⋊C4—21no—
327Dic43⋊C4—21no—
328C4×Dic43—21no—
329C4×Dic43—21no—
330C4×Dic43—21no—
331C4×Dic43—21no—
332C4×Dic43—21no—
333C4×Dic43—81no—
334C23×C43—21no—
335C23×C43—21no—
336C23×C43—22no—
337C23×C43—21no—
338C23×C43—21no—
339C23×C43—41no—
340C23×C43—41no—
341C23×C43—41no—
342C23×C43C2×C22⋊C411yescharacteristic
343C23×C43C2×C22⋊C411yescharacteristic
344C23×C43C2×C22⋊C411yescharacteristic
345C23×C43C2×C22⋊C411yescharacteristic
346C23×C43C22×D411yescharacteristic
347C22×D43—21no—
348D4×C43—22no—
349D4×C43—22no—
350D4×C43—41no—
351D4×C43—41no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43C2×C22⋊C411yescharacteristic
367C2×C4×C43C2×C22⋊C411yescharacteristic
368C2×C4×C43C2×C22⋊C411yescharacteristic
369C2×C4×C43C2×C22⋊C411yescharacteristic
370C2×C4×C43C2×C22⋊C411yescharacteristic
371C2×C4×C43C2×C22⋊C411yescharacteristic
372C2×C4×C43C2×C22⋊C411yescharacteristic
373C2×C4×C43C2×C22⋊C411yescharacteristic
374C2×C4×C43C23×C411yescharacteristic
375C2×C4×C43C22×D411yescharacteristic
376C22⋊D43—42no—
377C22⋊D43—41no—
378C22⋊D43—41no—
379C22⋊D43—42no—
380C22⋊D43—81no—
381C22⋊D43—81no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—21no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—21no—
389C2×Dic43—42no—
390C2×Dic43—42no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
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×Dic43—81no—
405C2×Dic43—84no—
406D172—41no—
407C4×D43—42no—
408C4×D43—81no—
409C4×D43—81no—
410Dic86—42no—
411Dic86—41no—
412Dic86—41no—
413Dic86—41no—
414Dic86—81no—
415Dic86—81no—
416C8×C43—41no—
417C8×C43—41no—
418C8×C43—41no—
419C8×C43—41no—
420#17598—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—21no—
429C22×C43—21no—
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—21no—
433C22×C43—21no—
434C22×C43—42no—
435C22×C43—42no—
436C22×C43—81no—
437C22×C43—81no—
438C22×C43#42112yes—
439C22×C43C22×C22⋊C411yescharacteristic
440C22×C43#57711yescharacteristic
441C22×C43#57811yescharacteristic
442C2×D43—41no—
443C2×D43—41no—
444C2×D43—41no—
445C4×C43—21no—
446C4×C43—21no—
447C4×C43—21no—
448C4×C43—21no—
449C4×C43—21no—
450C4×C43—21no—
451C4×C43—21no—
452C4×C43—21no—
453C4×C43—21no—
454C4×C43—21no—
455Dic43—41no—
456Dic43—41no—
457Dic43—41no—
458Dic43—41no—
459Dic43—41no—
460Dic43—41no—
461Dic43—41no—
462Dic43—81no—
463Dic43—81no—
464Dic43—81no—
465Dic43—81no—
466#3520—431no—
467#2974D4311yescharacteristic, complemented
468#2318—431no—
469#1521—431no—
470#1520—431no—
471#1518—431no—
472#1516—431no—
473#1515—431no—
474#1513—431no—
475#1512—431no—
476#1511—431no—
477#1508—431no—
478#1504—431no—
479#1501—431no—
480C2×#328—431no—
481C2×C43—21no—
482C2×C43—21no—
483C2×C43—22no—
484C2×C43—41no—
485C2×C43—41no—
486C2×C43—41no—
487C2×C43#288311yescharacteristic
488C2×C43#289811yescharacteristic
489C2×C43C2×#42111yescharacteristic
490D43—81no—
491#556—431no—
492#554—861no—
493#552—431no—
494#552—431no—
495#551—861no—
496#551—861no—
497D4×Q8—431no—
498#548—431no—
499#548—431no—
500#547—431no—
501#547—431no—
502#546—861no—
503#542—861no—
504#539—861no—
505#539—861no—
506#533—431no—
507#529—431no—
508#525—431no—
509#525—431no—
510C2×C22⋊Q8—431no—
511C2×C22⋊Q8—431no—
512#520—861no—
513C2×C4×D4C2×D4311yescharacteristic
514#436—21no—
515#435—21no—
516#435—21no—
517C8×D4—21no—
518#432C2×D4311yescharacteristic
519#431C2×D4311yescharacteristic
520#407C2×D4311yescharacteristic
521#407C2×D4311yescharacteristic
522C2×C22⋊C8C2×D4311yescharacteristic
523C2×C22⋊C8C2×D4311yescharacteristic
524#388—861no—
525#387—861no—
526#386—861no—
527#385—861no—
528#383—431no—
529#382—431no—
530#381—431no—
531#380—431no—
532C4×C22⋊C4—431no—
533C2×#95—431no—
534#328—431no—
535#328—431no—
536#328—431no—
537#328—431no—
538#328—431no—
539#328—431no—
540#328—431no—
541#328—431no—
542#328—431no—
543#328—431no—
544#328—431no—
545#328—431no—
546#327—431no—
547#327—431no—
548#327—431no—
549#327—431no—
550C43#1759811yescharacteristic, complemented, Sylow
551C2×#41—431no—
552C2×#41—431no—
553C2×#41—861no—
554C22×Q8—431no—
555C22×Q8—431no—
556C22×D4D17211yescharacteristic
557C23×C4—861no—
558C23×C4C22×D4311yescharacteristic
559C23×C4C22×D4311yescharacteristic
560C2×M16—21no—
561C2×M16—21no—
562C22×C8—21no—
563C22×C8—21no—
564C4⋊Q8—431no—
565C4⋊Q8—431no—
566C4⋊Q8—861no—
567#126—861no—
568#126—861no—
569#126—861no—
570#126—861no—
571#126—861no—
572#125—431no—
573#125—861no—
574#125—861no—
575#125—861no—
576#124—431no—
577#124—861no—
578#124—861no—
579#124—861no—
580#123—861no—
581#123—861no—
582#123—861no—
583#123—861no—
584#123—861no—
585#123—861no—
586#123—861no—
587#123—861no—
588#123—861no—
589C22⋊Q8—431no—
590C22⋊Q8—431no—
591C22⋊Q8—431no—
592C22⋊Q8—431no—
593C22⋊Q8—431no—
594C22⋊Q8—431no—
595C22⋊Q8—431no—
596C22⋊Q8—431no—
597C22⋊Q8—431no—
598C22⋊Q8—861no—
599C22⋊Q8—861no—
600C22⋊Q8—861no—
601C22⋊Q8—861no—
602C22⋊Q8—861no—
603C22⋊Q8—861no—
604C22⋊Q8—861no—
605C22⋊Q8—861no—
606C22⋊Q8—861no—
607C22⋊Q8—861no—
608#121—431no—
609#121—431no—
610#121—431no—
611#121—861no—
612#121—861no—
613#121—861no—
614#120—861no—
615#120—861no—
616C4×Q8—431no—
617C4×Q8—431no—
618C4×Q8—431no—
619C4×Q8—861no—
620C4×Q8—861no—
621C4×D4—431no—
622C4×D4—861no—
623C4×D4—861no—
624C4×D4—861no—
625C4×D4—861no—
626C4×D4—861no—
627C4×D4—861no—
628C4×D4—861no—
629C4×D4—861no—
630C4×D4C4×D4311yescharacteristic
631C4×D4C4×D4311yescharacteristic
632C4×D4C4×D4311yescharacteristic
633C4×D4C4×D4311yescharacteristic
634C4×D4C22⋊D4311yescharacteristic
635C4×D4C22⋊D4311yescharacteristic
636C4×D4C22⋊D4311yescharacteristic
637C4×D4C22⋊D4311yescharacteristic
638#117—431no—
639#117—431no—
640#117—861no—
641#117—861no—
642#117—861no—
643#117—861no—
644C2×C4⋊C4—431no—
645C2×C4⋊C4—431no—
646C2×C4⋊C4—861no—
647C2×C4⋊C4—861no—
648C2×C4⋊C4—861no—
649C2×C4⋊C4—861no—
650C2×C4⋊C4—861no—
651C2×C4⋊C4D17211yescharacteristic
652C2×C22⋊C4—861no—
653C2×C22⋊C4—861no—
654C2×C22⋊C4—861no—
655C2×C22⋊C4—861no—
656C2×C22⋊C4—861no—
657C2×C22⋊C4D17211yescharacteristic
658C2×C22⋊C4D17211yescharacteristic
659C2×C42—861no—
660C2×C42C22×D4311yescharacteristic
661C4⋊C8—21no—
662C4⋊C8—21no—
663C22⋊C8—21no—
664C22⋊C8—21no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8C22×D4311yescharacteristic
668C22⋊C8C22×D4311yescharacteristic
669C22⋊C8C22×D4311yescharacteristic
670C22⋊C8C22×D4311yescharacteristic
671#97—21no—
672C4×C8—21no—
673#95—431no—
674#95—431no—
675#95—431no—
676#95—431no—
677#95—861no—
678#95—861no—
679#95—861no—
680#95—861no—
681#95—861no—
682C24C2×D17211yescharacteristic
683C24C2×D17211yescharacteristic
684#41—3441no—
685#41—3441no—
686#41—1724no—
687C2×Q8—431no—
688C2×Q8—431no—
689C2×Q8—431no—
690C2×Q8—861no—
691C2×Q8—861no—
692C2×Q8—861no—
693C2×Q8—3441no—
694C2×Q8—3441no—
695C2×D4—42no—
696C2×D4—431no—
697C2×D4—861no—
698C2×D4—861no—
699C2×D4—861no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4(C2×D43)⋊C411yescharacteristic
703C2×D4(C2×D43)⋊C411yescharacteristic
704C2×D4(C2×D43)⋊C411yescharacteristic
705C2×D4(C2×D43)⋊C411yescharacteristic
706C22×C4—81no—
707C22×C4—81no—
708C22×C4—861no—
709C22×C4—861no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—861no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—3441no—
720C22×C4—3441no—
721C22×C4—1722no—
722C22×C4C2×C4×D4311yescharacteristic
723C22×C4C2×C4×D4311yescharacteristic
724C22×C4C2×C4×D4311yescharacteristic
725C22×C4C2×C4×D4311yescharacteristic
726C22×C4C2×D17211yescharacteristic
727C22×C4C2×D17211yescharacteristic
728C22×C4C2×D17211yescharacteristic
729C22×C4C2×D17211yescharacteristic
730C22×C4C2×C22⋊D4311yescharacteristic
731C22×C4C2×C22⋊D4311yescharacteristic
732C22×C4C2×C22⋊D4311yescharacteristic
733C22×C4C2×C22⋊D4311yescharacteristic
734C22×C4C23×D4311yescharacteristic
735M16—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C2×C8—81no—
743C4⋊C4—431no—
744C4⋊C4—431no—
745C4⋊C4—431no—
746C4⋊C4—431no—
747C4⋊C4—861no—
748C4⋊C4—861no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C4⋊C4—861no—
752C4⋊C4—861no—
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—861no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4—861no—
766C4⋊C4—3441no—
767C4⋊C4—3441no—
768C4⋊C4(C2×D43)⋊C411yescharacteristic
769C4⋊C4(C2×D43)⋊C411yescharacteristic
770C4⋊C4(C2×D43)⋊C411yescharacteristic
771C4⋊C4(C2×D43)⋊C411yescharacteristic
772C22⋊C4—861no—
773C22⋊C4—861no—
774C22⋊C4—861no—
775C22⋊C4—861no—
776C22⋊C4—861no—
777C22⋊C4—861no—
778C22⋊C4—861no—
779C22⋊C4—861no—
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—3441no—
790C22⋊C4—3441no—
791C22⋊C4—1722no—
792C22⋊C4(C2×D43)⋊C411yescharacteristic
793C22⋊C4(C2×D43)⋊C411yescharacteristic
794C22⋊C4(C2×D43)⋊C411yescharacteristic
795C22⋊C4(C2×D43)⋊C411yescharacteristic
796C22⋊C4(C2×D43)⋊C411yescharacteristic
797C22⋊C4(C2×D43)⋊C411yescharacteristic
798C22⋊C4(C2×D43)⋊C411yescharacteristic
799C22⋊C4(C2×D43)⋊C411yescharacteristic
800C42—861no—
801C42—861no—
802C42—861no—
803C42—861no—
804C42—861no—
805C42—3441no—
806C42C2×C4×D4311yescharacteristic
807C42C2×C4×D4311yescharacteristic
808C42C2×C22⋊D4311yescharacteristic
809C42C2×C22⋊D4311yescharacteristic
810C23—22no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—861no—
819C23C2×(C2×D43)⋊C411yescharacteristic
820C23C2×(C2×D43)⋊C411yescharacteristic
821C23C2×(C2×D43)⋊C411yescharacteristic
822C23C2×(C2×D43)⋊C411yescharacteristic
823C23C22×D17211yescharacteristic
824Q8—3441no—
825Q8—3441no—
826Q8—1721no—
827Q8—1721no—
828Q8—1721no—
829Q8—1722no—
830D4—22no—
831D4—22no—
832D4—41no—
833D4—41no—
834D4—3441no—
835D4—3441no—
836D4—1721no—
837D4—1722no—
838D4—1722no—
839D4—1721no—
840D4—1721no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—861no—
856C2×C4—861no—
857C2×C4—861no—
858C2×C4—861no—
859C2×C4—861no—
860C2×C4—861no—
861C2×C4—861no—
862C2×C4—3441no—
863C2×C4—3441no—
864C2×C4—3444no—
865C2×C4—3441no—
866C2×C4—3441no—
867C2×C4—1722no—
868C2×C4—1721no—
869C2×C4—1721no—
870C2×C4—1721no—
871C2×C4—1721no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4—1721no—
877C2×C4—1721no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4—1722no—
881C2×C4—1722no—
882C2×C4C2×(C2×D43)⋊C411yescharacteristic
883C2×C4C2×(C2×D43)⋊C411yescharacteristic
884C2×C4C2×(C2×D43)⋊C411yescharacteristic
885C2×C4C2×(C2×D43)⋊C411yescharacteristic
886C2×C4C2×(C2×D43)⋊C411yescharacteristic
887C2×C4C2×(C2×D43)⋊C411yescharacteristic
888C2×C4C2×(C2×D43)⋊C411yescharacteristic
889C2×C4C2×(C2×D43)⋊C411yescharacteristic
890C2×C4C22×C4×D4311yescharacteristic
891C2×C4C22×C22⋊D4311yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—42no—
910C22—42no—
911C22—81no—
912C22—81no—
913C22—1721no—
914C22—1721no—
915C22—1721no—
916C22#1458291512yes—
917C22C22×(C2×D43)⋊C411yescharacteristic
918C22#1458371111yescharacteristic
919C22#1458371611yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—3441no—
931C4—3441no—
932C4—3441no—
933C4—3441no—
934C4—1721no—
935C4—1721no—
936C4—1721no—
937C4—1721no—
938C4—1721no—
939C4—1721no—
940C4—1721no—
941C2—21no—
942C2—21no—
943C2—22no—
944C2—41no—
945C2—41no—
946C2—41no—
947C2—3441no—
948C2#1914305511yescharacteristic
949C2#1914312911yescharacteristic
950C2C2×#1458291511yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2974C2
socleC22×C43C22×C22⋊C4
prime radical#19148644C2
cosocleC22×C4×C43C24
hypercenter#2974D43
hypocenterC43#17598
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #19137228C2semidirect
3. #19133173C2semidirect
4. #19133168C2semidirect
5. #19133160C2semidirect
6. #19133152C2semidirect
7. #19133147C2semidirect
8. #19133139C2semidirect
9. #19133134C2semidirect
10. #19133129C2semidirect
11. #19133116C2semidirect
12. #19133100C2semidirect
13. #19133087C2semidirect
14. C2×#14582637C2semidirect
15. C43×#2974C2semidirect
16. #14583619C4semidirect
18. #14583589C4semidirect
19. #14583589C4semidirect
22. D4×Dic86C4semidirect
23. #14583558C4semidirect
24. #14583558C4semidirect
25. #14583554C4semidirect
26. #14583553C4semidirect
76. C2×#10621898C2×C4semidirect
79. C22×Dic86C2×C4semidirect
81. #13063325C2×C4semidirect
82. #13063325C2×C4semidirect
90. #13063317C2×C4semidirect
93. #13063313C2×C4semidirect
115. #13063304C2×C4semidirect
116. #13063304C2×C4semidirect
117. #13063304C2×C4semidirect
126. #13063299C2×C4semidirect
134. C4×Dic86C2×C4semidirect
135. C4×Dic86C2×C4semidirect
136. C4×Dic86C2×C4semidirect
138. C4×D172C2×C4semidirect
149. #13063284C2×C4semidirect
156. C2×C4⋊Dic43C2×C4semidirect
467. #2974D43semidirect
550. C43#17598semidirect

Maximal subgroups

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

subgroupindex
#191486442
#191372282
#191331732
#191331682
#191331602
#191331522
#191331472
#191331392
#191331342
#191331292
#191331162
#191331002
#191330872
C2×#145826372
C43×#29742
#1759843