Finite Group Databasebeta

← #25064133

Subgroups — #25064133

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#19143630C211yesmaximal, characteristic, complemented
3#19133170C211yesmaximal, characteristic, complemented
4#19133166C211yesmaximal, characteristic, complemented
5#19133158C211yesmaximal, characteristic, complemented
6#19133149C211yesmaximal, characteristic, complemented
7#19133145C211yesmaximal, characteristic, complemented
8#19133136C211yesmaximal, characteristic, complemented
9#19133131C211yesmaximal, characteristic, complemented
10#19133127C211yesmaximal, characteristic, complemented
11#19133114C211yesmaximal, characteristic, complemented
12#19133097C211yesmaximal, characteristic, complemented
13#19133084C211yesmaximal, characteristic, complemented
14C2×#14582635C211yesmaximal, characteristic, complemented
15C43×#2318C211yesmaximal, 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#14582977—21no—
39#14582971—21no—
40#14582971—21no—
41D4×C43⋊C8—21no—
42#14582956C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582863C2211yescharacteristic
45#14582863C2211yescharacteristic
46C2×C22⋊(C43⋊C8)C2211yescharacteristic
47C2×C22⋊(C43⋊C8)C2211yescharacteristic
48#14582635C2211yescharacteristic
49#14582635C2211yescharacteristic
50#14582635C2211yescharacteristic
51#14582635C2211yescharacteristic
52#14582635C2211yescharacteristic
53#14582635C2211yescharacteristic
54#14582635C2211yescharacteristic
55#14582635C2211yescharacteristic
56#14582635C2211yescharacteristic
57#14582635C2211yescharacteristic
58#14582635C2211yescharacteristic
59#14582635C2211yescharacteristic
60#14582632C2211yescharacteristic
61#14582632C2211yescharacteristic
62#14582632C2211yescharacteristic
63#14582632C2211yescharacteristic
64C2×C4×D4×C43C2211yescharacteristic
65C43×#388—21no—
66C43×#387—21no—
67C43×#386—21no—
68C43×#385—21no—
69C43×#383C2211yescharacteristic
70C43×#382C2211yescharacteristic
71C43×#381C2211yescharacteristic
72C43×#380C2211yescharacteristic
73C4×C22⋊C4×C43C2211yescharacteristic
74C2×#95×C43C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic
76C2×#10621898C2×C411yescharacteristic, complemented
77C2×#10621900—21no—
78C22×Dic86C2×C411yescharacteristic
79C22×Dic86C2×C411yescharacteristic, complemented
80C2×#10621877—21no—
81C2×#10621877—21no—
82C22×C43⋊C8—21no—
83C22×C43⋊C8—21no—
84#13063325C2×C411yescharacteristic, complemented
85#13063325C2×C411yescharacteristic, complemented
86#13063324—21no—
87#13063319—21no—
88#13063318—21no—
89#13063318—21no—
90#13063318—21no—
91#13063318—21no—
92#13063317—21no—
93#13063317C2×C411yescharacteristic, complemented
94#13063315—21no—
95#13063315—21no—
96#13063313C2×C411yescharacteristic, complemented
97#13063312—21no—
98#13063311—21no—
99#13063311—21no—
100#13063309—21no—
101#13063309—21no—
102#13063308—21no—
103#13063308—21no—
104#13063308—21no—
105#13063307—21no—
106#13063307—21no—
107#13063306—21no—
108#13063306—21no—
109#13063305—21no—
110#13063304—21no—
111#13063304—21no—
112#13063304—21no—
113#13063304—21no—
114#13063304—21no—
115#13063304C2×C411yescharacteristic
116#13063304C2×C411yescharacteristic
117#13063304C2×C411yescharacteristic
118#13063304C2×C411yescharacteristic, complemented
119#13063304C2×C411yescharacteristic, complemented
120#13063304C2×C411yescharacteristic, complemented
121#13063304C2311yescharacteristic
122#13063304C2311yescharacteristic
123#13063304C2311yescharacteristic
124#13063303—21no—
125#13063303—21no—
126#13063302—21no—
127#13063302—21no—
128#13063299C2×C411yescharacteristic
129#13063299C2×C411yescharacteristic, complemented
130#13063299C2311yescharacteristic
131#13063297—21no—
132#13063297—21no—
133#13063296—21no—
134#13063294—21no—
135#13063294—21no—
136C4×Dic86—21no—
137C4×Dic86C2×C411yescharacteristic, complemented
138C4×Dic86C2×C411yescharacteristic, complemented
139C4×Dic86C2×C411yescharacteristic, complemented
140#13063290—21no—
141C4×D172C2×C411yescharacteristic, complemented
142D4×Dic43—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146C4×C22⋊D43—21no—
147C4×C22⋊D43—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150#13063284—21no—
151#13063284C2×C411yescharacteristic
152#13063284C2×C411yescharacteristic, complemented
153#13063282—21no—
154#13063281—21no—
155#13063281—21no—
156C2×C4⋊Dic43C2×C411yescharacteristic
157C2×C4⋊Dic43C2×C411yescharacteristic, complemented
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C4⋊C4×D43—21no—
161C2×C22⋊Dic43—21no—
162C2×C22⋊Dic43—21no—
163C4⋊(C43⋊C8)—21no—
164C4⋊(C43⋊C8)—21no—
165C22⋊(C43⋊C8)—21no—
166C22⋊(C43⋊C8)—21no—
167C22⋊(C43⋊C8)—21no—
168C22⋊(C43⋊C8)—21no—
169C22⋊(C43⋊C8)C2311yescharacteristic
170C22⋊(C43⋊C8)C2311yescharacteristic
171C22⋊(C43⋊C8)C2311yescharacteristic
172C22⋊(C43⋊C8)C2311yescharacteristic
173#13063236—21no—
174C4×C43⋊C8—21no—
175C22×D4×C43D411yescharacteristic
176C23×C4×C43—21no—
177C23×C4×C43C2311yescharacteristic
178C23×C4×C43C2311yescharacteristic
179C4×D4×C43C2×C411yescharacteristic
180C4×D4×C43C2×C411yescharacteristic
181C4×D4×C43C2×C411yescharacteristic
182C4×D4×C43C2×C411yescharacteristic
183C4×D4×C43D411yescharacteristic
184C4×D4×C43D411yescharacteristic
185C4×D4×C43D411yescharacteristic
186C4×D4×C43D411yescharacteristic
187C2×C4⋊C4×C43—21no—
188C2×C4⋊C4×C43—21no—
189C2×C4⋊C4×C43D411yescharacteristic
190C2×C22⋊C4×C43—21no—
191C2×C22⋊C4×C43—21no—
192C2×C22⋊C4×C43—21no—
193C2×C22⋊C4×C43D411yescharacteristic
194C2×C22⋊C4×C43D411yescharacteristic
195C2×C42×C43—21no—
196C2×C42×C43C2311yescharacteristic
197#95×C43—21no—
198#95×C43—21no—
199#95×C43—21no—
200#95×C43—21no—
201#95×C43—21no—
202#95×C43C2311yescharacteristic
203#95×C43C2311yescharacteristic
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
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—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—42no—
218C22×C4×C43—81no—
219C22×C4×C43—81no—
220C22×C4×C43—81no—
221C22×C4×C43—81no—
222C22×C4×C43C22×C411yescharacteristic
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C22×C411yescharacteristic
225C22×C4×C43C22×C411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2×D411yescharacteristic
230C22×C4×C43C2×D411yescharacteristic
231C22×C4×C43C2×D411yescharacteristic
232C22×C4×C43C2×D411yescharacteristic
233C22×C4×C43C2×D411yescharacteristic
234C22×C4×C43C2411yescharacteristic
235C2×C22⋊D43—21no—
236C2×C22⋊D43—21no—
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—21no—
243C22×Dic43—21no—
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
259C4⋊C4×C43—81no—
260C4⋊C4×C43—81no—
261C4⋊C4×C43C22⋊C411yescharacteristic
262C4⋊C4×C43C22⋊C411yescharacteristic
263C4⋊C4×C43C22⋊C411yescharacteristic
264C4⋊C4×C43C22⋊C411yescharacteristic
265C22⋊C4×C43—42no—
266C22⋊C4×C43—81no—
267C22⋊C4×C43—81no—
268C22⋊C4×C43C22⋊C411yescharacteristic
269C22⋊C4×C43C22⋊C411yescharacteristic
270C22⋊C4×C43C22⋊C411yescharacteristic
271C22⋊C4×C43C22⋊C411yescharacteristic
272C22⋊C4×C43C22⋊C411yescharacteristic
273C22⋊C4×C43C22⋊C411yescharacteristic
274C22⋊C4×C43C22⋊C411yescharacteristic
275C22⋊C4×C43C22⋊C411yescharacteristic
276C42×C43—81no—
277C42×C43C22×C411yescharacteristic
278C42×C43C22×C411yescharacteristic
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C22⋊Dic43—21no—
282C22⋊Dic43—21no—
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—
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—
298C4⋊Dic43—21no—
299C4⋊Dic43—21no—
300C4⋊Dic43—21no—
301C4⋊Dic43—21no—
302C4⋊Dic43—21no—
303C4⋊Dic43C22×C411yescharacteristic
304C4⋊Dic43C22×C411yescharacteristic
305C4⋊Dic43C22×C411yescharacteristic
306C4⋊Dic43C22×C411yescharacteristic
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4—21no—
315Dic43⋊C4—21no—
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321C4×Dic43—21no—
322C4×Dic43—21no—
323C4×Dic43—21no—
324C4×Dic43—21no—
325C4×Dic43—21no—
326#10621877—81no—
327#10621877—81no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—21no—
332C2×C43⋊C8—81no—
333C2×C43⋊C8—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×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—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—84no—
379C2×C4×C43C2×C22⋊C411yescharacteristic
380C2×C4×C43C2×C22⋊C411yescharacteristic
381C2×C4×C43C2×C22⋊C411yescharacteristic
382C2×C4×C43C2×C22⋊C411yescharacteristic
383C2×C4×C43C2×C22⋊C411yescharacteristic
384C2×C4×C43C2×C22⋊C411yescharacteristic
385C2×C4×C43C2×C22⋊C411yescharacteristic
386C2×C4×C43C2×C22⋊C411yescharacteristic
387C2×C4×C43C23×C411yescharacteristic
388C2×C4×C43C22×D411yescharacteristic
389C22⋊D43—42no—
390C22⋊D43—41no—
391C22⋊D43—41no—
392C22⋊D43—42no—
393C22⋊D43—81no—
394C22⋊D43—81no—
395C2×Dic43—21no—
396C2×Dic43—21no—
397C2×Dic43—21no—
398C2×Dic43—21no—
399C2×Dic43—21no—
400C2×Dic43—21no—
401C2×Dic43—21no—
402C2×Dic43—42no—
403C2×Dic43—42no—
404C2×Dic43—81no—
405C2×Dic43—81no—
406D172—41no—
407C4×D43—42no—
408C4×D43—81no—
409C4×D43—81no—
410Dic86—42no—
411Dic86—41no—
412Dic86—41no—
413Dic86—41no—
414Dic86—81no—
415Dic86—81no—
416C43⋊C8—41no—
417C43⋊C8—41no—
418C43⋊C8—41no—
419C43⋊C8—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—
455C4×C43—81no—
456C4×C43—81no—
457C4×C43—81no—
458C4×C43—81no—
459Dic43—41no—
460Dic43—41no—
461Dic43—41no—
462Dic43—41no—
463Dic43—41no—
464Dic43—41no—
465Dic43—41no—
466#3520—431no—
467#2974—431no—
468#2318D4311yescharacteristic, complemented
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—861no—
515#435—861no—
516#435—861no—
517C8×D4—861no—
518#432—431no—
519#431—431no—
520#407—431no—
521#407—431no—
522C2×C22⋊C8—431no—
523C2×C22⋊C8—431no—
524#388—21no—
525#387—21no—
526#386—21no—
527#385—21no—
528#383C2×D4311yescharacteristic
529#382C2×D4311yescharacteristic
530#381C2×D4311yescharacteristic
531#380C2×D4311yescharacteristic
532C4×C22⋊C4C2×D4311yescharacteristic
533C2×#95C2×D4311yescharacteristic
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×D4C22⋊D4311yescharacteristic
557C23×C4—21no—
558C23×C4C22×D4311yescharacteristic
559C23×C4C22×D4311yescharacteristic
560C2×M16—861no—
561C2×M16—861no—
562C22×C8—861no—
563C22×C8—861no—
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×D4D17211yescharacteristic
635C4×D4D17211yescharacteristic
636C4×D4D17211yescharacteristic
637C4×D4D17211yescharacteristic
638#117—431no—
639#117—431no—
640#117—861no—
641#117—861no—
642#117—861no—
643#117—861no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—431no—
647C2×C4⋊C4—431no—
648C2×C4⋊C4—861no—
649C2×C4⋊C4—861no—
650C2×C4⋊C4—861no—
651C2×C4⋊C4C22⋊D4311yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—861no—
656C2×C22⋊C4—861no—
657C2×C22⋊C4C22⋊D4311yescharacteristic
658C2×C22⋊C4C22⋊D4311yescharacteristic
659C2×C42—21no—
660C2×C42C22×D4311yescharacteristic
661C4⋊C8—861no—
662C4⋊C8—861no—
663C22⋊C8—431no—
664C22⋊C8—431no—
665C22⋊C8—431no—
666C22⋊C8—431no—
667C22⋊C8—861no—
668C22⋊C8—861no—
669C22⋊C8—861no—
670C22⋊C8—861no—
671#97—861no—
672C4×C8—861no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
678#95C22×D4311yescharacteristic
679#95C22×D4311yescharacteristic
680#95C22×D4311yescharacteristic
681#95C22×D4311yescharacteristic
682C24C2×C22⋊D4311yescharacteristic
683C24C2×C22⋊D4311yescharacteristic
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—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—81no—
712C22×C4—81no—
713C22×C4—81no—
714C22×C4—81no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
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—3441no—
736M16—3441no—
737C2×C8—861no—
738C2×C8—861no—
739C2×C8—861no—
740C2×C8—861no—
741C2×C8—3441no—
742C2×C8—3441no—
743C4⋊C4—81no—
744C4⋊C4—81no—
745C4⋊C4—431no—
746C4⋊C4—431no—
747C4⋊C4—431no—
748C4⋊C4—431no—
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—861no—
767C4⋊C4—861no—
768C4⋊C4(C2×D43)⋊C411yescharacteristic
769C4⋊C4(C2×D43)⋊C411yescharacteristic
770C4⋊C4(C2×D43)⋊C411yescharacteristic
771C4⋊C4(C2×D43)⋊C411yescharacteristic
772C22⋊C4—42no—
773C22⋊C4—81no—
774C22⋊C4—81no—
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—861no—
790C22⋊C4—861no—
791C22⋊C4—861no—
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—81no—
801C42—861no—
802C42—861no—
803C42—861no—
804C42—861no—
805C42—861no—
806C42C2×C4×D4311yescharacteristic
807C42C2×C4×D4311yescharacteristic
808C42C2×D17211yescharacteristic
809C42C2×D17211yescharacteristic
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×C22⋊D4311yescharacteristic
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—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—84no—
868C2×C4—861no—
869C2×C4—861no—
870C2×C4—861no—
871C2×C4—861no—
872C2×C4—861no—
873C2×C4—861no—
874C2×C4—861no—
875C2×C4—3441no—
876C2×C4—3441no—
877C2×C4—3441no—
878C2×C4—3441no—
879C2×C4—1722no—
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×D17211yescharacteristic
892C8—1721no—
893C8—1721no—
894C8—1721no—
895C8—1721no—
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#1458291712yes—
917C22C22×(C2×D43)⋊C411yescharacteristic
918C22#1458371011yescharacteristic
919C22#1458371411yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—21no—
929C4—21no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
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#1914312511yescharacteristic
950C2C2×#1458291711yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2318C2
socleC22×C43C22×C22⋊C4
prime radical#19148644C2
cosocleC22×C4×C43C24
hypercenter#2318D43
hypocenterC43#17598
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2318

Complements

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

NH ≅ G/Ntype
2. #19143630C2semidirect
3. #19133170C2semidirect
4. #19133166C2semidirect
5. #19133158C2semidirect
6. #19133149C2semidirect
7. #19133145C2semidirect
8. #19133136C2semidirect
9. #19133131C2semidirect
10. #19133127C2semidirect
11. #19133114C2semidirect
12. #19133097C2semidirect
13. #19133084C2semidirect
14. C2×#14582635C2semidirect
15. C43×#2318C2semidirect
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
84. #13063325C2×C4semidirect
85. #13063325C2×C4semidirect
93. #13063317C2×C4semidirect
96. #13063313C2×C4semidirect
118. #13063304C2×C4semidirect
119. #13063304C2×C4semidirect
120. #13063304C2×C4semidirect
129. #13063299C2×C4semidirect
137. C4×Dic86C2×C4semidirect
138. C4×Dic86C2×C4semidirect
139. C4×Dic86C2×C4semidirect
141. C4×D172C2×C4semidirect
152. #13063284C2×C4semidirect
157. C2×C4⋊Dic43C2×C4semidirect
468. #2318D43semidirect
550. C43#17598semidirect

Maximal subgroups

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

subgroupindex
#191486442
#191436302
#191331702
#191331662
#191331582
#191331492
#191331452
#191331362
#191331312
#191331272
#191331142
#191330972
#191330842
C2×#145826352
C43×#23182
#1759843