Finite Group Databasebeta

← #25062908

Subgroups — #25062908

Order 11008.

1022 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583598C211yesmaximal, characteristic
2#19143630C211yesmaximal, characteristic, complemented
3#19132965C211yesmaximal, characteristic, complemented
4#19132962C211yesmaximal, characteristic, complemented
5#19132956C211yesmaximal, characteristic, complemented
6#19132954C211yesmaximal, characteristic, complemented
7#19132944C211yesmaximal, characteristic, complemented
8#19132941C211yesmaximal, characteristic, complemented
9#19132931C211yesmaximal, characteristic, complemented
10#19132927C211yesmaximal, characteristic, complemented
11#19132924C211yesmaximal, characteristic, complemented
12#19132911C211yesmaximal, characteristic, complemented
13#19132907C211yesmaximal, characteristic, complemented
14C2×#14582624C211yesmaximal, characteristic, complemented
15C43×#2974C211yesmaximal, characteristic, complemented
16#14583598—21no—
17#14583598—21no—
18#14583598—21no—
19#14583598—21no—
20#14583598—21no—
21#14583598—21no—
22#14583598—21no—
23#14583598—21no—
24C2×#13063319C2211yescharacteristic
25C2×#13063318C411yescharacteristic
26C2×#13063315C411yescharacteristic
27C2×#13063310C411yescharacteristic
28C2×#13063308C2211yescharacteristic
29C2×#13063299C2211yescharacteristic
30C2×#13063298C411yescharacteristic
31C2×#13063297C411yescharacteristic
32C2×#13063297C411yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×(C22⋊D43)⋊C4C411yescharacteristic
35C2×(C22⋊D43)⋊C4C411yescharacteristic
36C2×#13063282C2211yescharacteristic
37C22×Dic43⋊C4C2211yescharacteristic
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#14582624C2211yescharacteristic
49#14582624C2211yescharacteristic
50#14582624C2211yescharacteristic
51#14582624C2211yescharacteristic
52#14582624C2211yescharacteristic
53#14582624C2211yescharacteristic
54#14582624C2211yescharacteristic
55#14582624C2211yescharacteristic
56#14582622C2211yescharacteristic
57#14582622C2211yescharacteristic
58#14582622C2211yescharacteristic
59#14582622C2211yescharacteristic
60#14582622C2211yescharacteristic
61#14582622C2211yescharacteristic
62#14582622C2211yescharacteristic
63#14582622C2211yescharacteristic
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
75C22×D172C2×C411yescharacteristic
76C22×C22⋊D43C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C22×C22⋊D43C2×C411yescharacteristic
80C23×Dic43C2×C411yescharacteristic
81C23×Dic43C2×C411yescharacteristic
82C22×C4×D43C2×C411yescharacteristic
83C22×C4×D43C2×C411yescharacteristic
84C2×#10621877—21no—
85C2×#10621877—21no—
86C22×C43⋊C8—21no—
87C22×C43⋊C8—21no—
88#13063319—21no—
89#13063319—21no—
90#13063319—21no—
91#13063319—21no—
92#13063318—21no—
93#13063318—21no—
94#13063318—21no—
95#13063318—21no—
96#13063315—21no—
97#13063315—21no—
98#13063315—21no—
99#13063315—21no—
100#13063310—21no—
101#13063310—21no—
102#13063310—21no—
103#13063310—21no—
104#13063308—21no—
105#13063308—21no—
106#13063308—21no—
107#13063308—21no—
108#13063299—21no—
109#13063299—21no—
110#13063299—21no—
111#13063299—21no—
112#13063298—21no—
113#13063298—21no—
114#13063298—21no—
115#13063298—21no—
116#13063297—21no—
117#13063297—21no—
118#13063297—21no—
119#13063297—21no—
120#13063297—21no—
121#13063297—21no—
122#13063297—21no—
123#13063297—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127C4×C22⋊D43—21no—
128(C22⋊D43)⋊C4—21no—
129(C22⋊D43)⋊C4—21no—
130(C22⋊D43)⋊C4—21no—
131(C22⋊D43)⋊C4—21no—
132(C22⋊D43)⋊C4—21no—
133(C22⋊D43)⋊C4—21no—
134(C22⋊D43)⋊C4—21no—
135(C22⋊D43)⋊C4—21no—
136#13063282—21no—
137#13063282—21no—
138#13063282—21no—
139#13063282—21no—
140C2×C4⋊Dic43C2×C411yescharacteristic
141C2×Dic43⋊C4—21no—
142C2×Dic43⋊C4—21no—
143C2×Dic43⋊C4—21no—
144C2×Dic43⋊C4—21no—
145C2×Dic43⋊C4C2×C411yescharacteristic
146C2×Dic43⋊C4C2×C411yescharacteristic
147C2×Dic43⋊C4C2×C411yescharacteristic
148C2×Dic43⋊C4C2×C411yescharacteristic
149C2×Dic43⋊C4C2×C411yescharacteristic
150C2×Dic43⋊C4C2×C411yescharacteristic
151C2×Dic43⋊C4C2311yescharacteristic
152C2×Dic43⋊C4C2311yescharacteristic
153C2×C22⋊Dic43C2×C411yescharacteristic
154C2×C22⋊Dic43C2×C411yescharacteristic
155C2×(C2×D43)⋊C4C2×C411yescharacteristic
156C2×(C2×D43)⋊C4C2×C411yescharacteristic
157C2×(C2×D43)⋊C4C2×C411yescharacteristic
158C2×(C2×D43)⋊C4C2×C411yescharacteristic
159C2×(C2×D43)⋊C4C2311yescharacteristic
160C2×(C2×D43)⋊C4C2311yescharacteristic
161C2×C4×Dic43C2×C411yescharacteristic
162C2×C4×Dic43C2×C411yescharacteristic
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×C43C2×C411yescharacteristic
176C23×C4×C43C2311yescharacteristic
177C23×C4×C43C2311yescharacteristic
178C2×M16×C43—21no—
179C2×M16×C43—21no—
180C22×C8×C43—21no—
181C22×C8×C43—21no—
182C4×D4×C43D411yescharacteristic
183C4×D4×C43D411yescharacteristic
184C4×D4×C43D411yescharacteristic
185C4×D4×C43D411yescharacteristic
186C4×D4×C43D411yescharacteristic
187C4×D4×C43D411yescharacteristic
188C4×D4×C43D411yescharacteristic
189C4×D4×C43D411yescharacteristic
190C2×C4⋊C4×C43C2×C411yescharacteristic
191C2×C22⋊C4×C43C2×C411yescharacteristic
192C2×C22⋊C4×C43C2×C411yescharacteristic
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×C43C22×C411yescharacteristic
207C24×C43C22×C411yescharacteristic
208C23×D43C22×C411yescharacteristic
209C23×D43C22×C411yescharacteristic
210C2×D4×C43—42no—
211C2×D4×C43C22⋊C411yescharacteristic
212C2×D4×C43C22⋊C411yescharacteristic
213C2×D4×C43C22⋊C411yescharacteristic
214C2×D4×C43C22⋊C411yescharacteristic
215C22×C4×C43—81no—
216C22×C4×C43—81no—
217C22×C4×C43C22×C411yescharacteristic
218C22×C4×C43C22×C411yescharacteristic
219C22×C4×C43C22×C411yescharacteristic
220C22×C4×C43C22×C411yescharacteristic
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×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C2×C22⋊D43—22no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—21no—
234C2×C22⋊D43—21no—
235C2×C22⋊D43—21no—
236C2×C22⋊D43—21no—
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43—41no—
240C2×C22⋊D43—42no—
241C2×C22⋊D43—42no—
242C2×C22⋊D43—81no—
243C22×Dic43—22no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—41no—
249C22×Dic43—81no—
250C22×Dic43C22×C411yescharacteristic
251C22×Dic43C22×C411yescharacteristic
252C22×Dic43C22×C411yescharacteristic
253C22×Dic43C22×C411yescharacteristic
254C22×Dic43C22×C411yescharacteristic
255C22×Dic43C22×C411yescharacteristic
256C2×D172—21no—
257C2×D172—21no—
258C2×D172—81no—
259C2×C4×D43—21no—
260C2×C4×D43—21no—
261C2×C4×D43—22no—
262C2×C4×D43—21no—
263C2×C4×D43—21no—
264C2×C4×D43—41no—
265C2×C4×D43—81no—
266M16×C43—81no—
267M16×C43—81no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—21no—
272C2×C8×C43—81no—
273C2×C8×C43—81no—
274C4⋊C4×C43C22⋊C411yescharacteristic
275C4⋊C4×C43C22⋊C411yescharacteristic
276C4⋊C4×C43C22⋊C411yescharacteristic
277C4⋊C4×C43C22⋊C411yescharacteristic
278C22⋊C4×C43C22⋊C411yescharacteristic
279C22⋊C4×C43C22⋊C411yescharacteristic
280C22⋊C4×C43C22⋊C411yescharacteristic
281C22⋊C4×C43C22⋊C411yescharacteristic
282C22⋊C4×C43C22⋊C411yescharacteristic
283C22⋊C4×C43C22⋊C411yescharacteristic
284C22⋊C4×C43C22⋊C411yescharacteristic
285C22⋊C4×C43C22⋊C411yescharacteristic
286C42×C43C2×D411yescharacteristic
287C42×C43C2×D411yescharacteristic
288C42×C43C2×D411yescharacteristic
289C42×C43C2×D411yescharacteristic
290C22⋊Dic43—21no—
291C22⋊Dic43—21no—
292C22⋊Dic43—21no—
293C22⋊Dic43—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
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—
306C4⋊Dic43—21no—
307C4⋊Dic43—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—
321Dic43⋊C4—21no—
322Dic43⋊C4—21no—
323Dic43⋊C4—21no—
324C4×Dic43—21no—
325C4×Dic43—21no—
326C4×Dic43—21no—
327C4×Dic43—21no—
328#10621877—81no—
329#10621877—81no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—21no—
332C2×C43⋊C8—21no—
333C2×C43⋊C8—21no—
334C2×C43⋊C8—81no—
335C2×C43⋊C8—81no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—22no—
339C23×C43—21no—
340C23×C43—21no—
341C23×C43—41no—
342C23×C43—41no—
343C23×C43—41no—
344C23×C43C2×C22⋊C411yescharacteristic
345C23×C43C2×C22⋊C411yescharacteristic
346C23×C43C2×C22⋊C411yescharacteristic
347C23×C43C2×C22⋊C411yescharacteristic
348C23×C43C23×C411yescharacteristic
349C22×D43—21no—
350C22×D43—21no—
351C22×D43—21no—
352C22×D43—21no—
353C22×D43—21no—
354C22×D43—21no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—41no—
358C22×D43—41no—
359D4×C43—22no—
360D4×C43—22no—
361D4×C43—41no—
362D4×C43—41no—
363C2×C4×C43—21no—
364C2×C4×C43—21no—
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×C43C2×C22⋊C411yescharacteristic
378C2×C4×C43C2×C22⋊C411yescharacteristic
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×C43C22×D411yescharacteristic
386C2×C4×C43C22×D411yescharacteristic
387C22⋊D43—42no—
388C22⋊D43—42no—
389C22⋊D43—42no—
390C22⋊D43—42no—
391C22⋊D43—42no—
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—21no—
403C2×Dic43—21no—
404C2×Dic43—42no—
405C2×Dic43—42no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—81no—
411C2×Dic43—81no—
412C2×Dic43#13112yes—
413D172—81no—
414D172—81no—
415C4×D43—42no—
416C4×D43—42no—
417C4×D43—81no—
418C4×D43—81no—
419C8×C43—41no—
420C8×C43—41no—
421C8×C43—41no—
422C8×C43—41no—
423C43⋊C8—41no—
424C43⋊C8—41no—
425C43⋊C8—41no—
426C43⋊C8—41no—
427#17427—431nomaximal, Sylow
428C22×C43—21no—
429C22×C43—21no—
430C22×C43—21no—
431C22×C43—21no—
432C22×C43—21no—
433C22×C43—21no—
434C22×C43—21no—
435C22×C43—21no—
436C22×C43—21no—
437C22×C43—21no—
438C22×C43—21no—
439C22×C43—21no—
440C22×C43—21no—
441C22×C43—42no—
442C22×C43—42no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43#41312yes—
446C22×C43C22×C22⋊C411yescharacteristic
447C22×C43C2×#13111yescharacteristic
448C22×C43#56811yescharacteristic
449C2×D43—41no—
450C2×D43—41no—
451C2×D43—41no—
452C2×D43—41no—
453C2×D43—41no—
454C2×D43—41no—
455C2×D43—81no—
456C2×D43—81no—
457C2×D43—81no—
458C2×D43—81no—
459C4×C43—21no—
460C4×C43—21no—
461C4×C43—21no—
462C4×C43—21no—
463C4×C43—21no—
464C4×C43—21no—
465C4×C43—21no—
466C4×C43—21no—
467C4×C43—21no—
468C4×C43—21no—
469Dic43—22no—
470Dic43—41no—
471Dic43—41no—
472Dic43—41no—
473Dic43—41no—
474Dic43—41no—
475C2×#553—431no—
476#2974—431no—
477#2974D4311yescharacteristic, complemented
478#1473—431no—
479#1473—431no—
480#1471—431no—
481#1471—431no—
482#1468—431no—
483#1468—431no—
484#1465—431no—
485#1464—431no—
486#1463—431no—
487#1459—431no—
488#1458—431no—
489C2×#324—431no—
490C2×C43—21no—
491C2×C43—21no—
492C2×C43—22no—
493C2×C43—41no—
494C2×C43—41no—
495C2×C43—41no—
496C2×C43#288011yescharacteristic
497C2×C43#288311yescharacteristic
498C2×C43C2×#41311yescharacteristic
499D43—81no—
500D43—81no—
501#553—861no—
502#553—861no—
503#553—861no—
504#553—861no—
505#553—861no—
506#553—861no—
507#553—861no—
508#553—861no—
509C2×#126—431no—
510C2×#126—431no—
511C2×#125—431no—
512C2×#123—431no—
513C2×#123—431no—
514C2×#121—431no—
515C2×#121—431no—
516C2×#121—431no—
517C2×#121—431no—
518C2×C4×D4—431no—
519C2×C4×D4—431no—
520C2×C4×D4—431no—
521C2×C4×D4C2×D4311yescharacteristic
522C2×#117—431no—
523C22×C4⋊C4—431no—
524#436—21no—
525#436—861no—
526#435—21no—
527#435—21no—
528#435—861no—
529#435—861no—
530C8×D4—21no—
531C8×D4—861no—
532#432—431no—
533#432C2×D4311yescharacteristic
534#431—431no—
535#431C2×D4311yescharacteristic
536#407—431no—
537#407—431no—
538#407C2×D4311yescharacteristic
539#407C2×D4311yescharacteristic
540C2×C22⋊C8—431no—
541C2×C22⋊C8—431no—
542C2×C22⋊C8C2×D4311yescharacteristic
543C2×C22⋊C8C2×D4311yescharacteristic
544#324—431no—
545#324—431no—
546#324—431no—
547#324—431no—
548#324—431no—
549#324—431no—
550#324—431no—
551#324—431no—
552#323—431no—
553#323—431no—
554#323—431no—
555#323—431no—
556#323—431no—
557#323—431no—
558#323—431no—
559#323—431no—
560C43#1742711yescharacteristic, complemented, Sylow
561C22×D4—431no—
562C22×D4—431no—
563C22×D4—431no—
564C22×D4—431no—
565C22×D4—431no—
566C22×D4C4×D4311yescharacteristic
567C23×C4—431no—
568C23×C4—431no—
569C23×C4—431no—
570C23×C4—431no—
571C23×C4C22×D4311yescharacteristic
572C23×C4C22×D4311yescharacteristic
573C2×M16—21no—
574C2×M16—21no—
575C2×M16—861no—
576C2×M16—861no—
577C22×C8—21no—
578C22×C8—21no—
579C22×C8—861no—
580C22×C8—861no—
581#126—861no—
582#126—861no—
583#126—861no—
584#126—861no—
585#126—861no—
586#126—861no—
587#126—861no—
588#126—861no—
589#125—861no—
590#125—861no—
591#125—861no—
592#125—861no—
593#123—861no—
594#123—861no—
595#123—861no—
596#123—861no—
597#123—861no—
598#123—861no—
599#123—861no—
600#123—861no—
601#121—861no—
602#121—861no—
603#121—861no—
604#121—861no—
605#121—861no—
606#121—861no—
607#121—861no—
608#121—861no—
609#121—861no—
610#121—861no—
611#121—861no—
612#121—861no—
613#121—861no—
614#121—861no—
615#121—861no—
616#121—861no—
617C4×D4—861no—
618C4×D4—861no—
619C4×D4—861no—
620C4×D4—861no—
621C4×D4—861no—
622C4×D4—861no—
623C4×D4—861no—
624C4×D4—861no—
625C4×D4—861no—
626C4×D4—861no—
627C4×D4—861no—
628C4×D4—861no—
629C4×D4D17211yescharacteristic
630C4×D4D17211yescharacteristic
631C4×D4D17211yescharacteristic
632C4×D4D17211yescharacteristic
633C4×D4C22⋊D4311yescharacteristic
634C4×D4C22⋊D4311yescharacteristic
635C4×D4C22⋊D4311yescharacteristic
636C4×D4C22⋊D4311yescharacteristic
637#117—861no—
638#117—861no—
639#117—861no—
640#117—861no—
641C2×C4⋊C4—431no—
642C2×C4⋊C4—431no—
643C2×C4⋊C4—431no—
644C2×C4⋊C4—431no—
645C2×C4⋊C4—431no—
646C2×C4⋊C4—431no—
647C2×C4⋊C4—431no—
648C2×C4⋊C4—431no—
649C2×C4⋊C4—431no—
650C2×C4⋊C4—861no—
651C2×C4⋊C4—861no—
652C2×C4⋊C4—861no—
653C2×C4⋊C4—861no—
654C2×C4⋊C4C4×D4311yescharacteristic
655C2×C22⋊C4—431no—
656C2×C22⋊C4—431no—
657C2×C22⋊C4—431no—
658C2×C22⋊C4—431no—
659C2×C22⋊C4—431no—
660C2×C22⋊C4—431no—
661C2×C22⋊C4—431no—
662C2×C22⋊C4—431no—
663C2×C22⋊C4C4×D4311yescharacteristic
664C2×C22⋊C4C4×D4311yescharacteristic
665C2×C42—431no—
666C2×C42—431no—
667C2×C42C22×D4311yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670C4⋊C8—861no—
671C4⋊C8—861no—
672C22⋊C8—21no—
673C22⋊C8—21no—
674C22⋊C8—21no—
675C22⋊C8—21no—
676C22⋊C8—431no—
677C22⋊C8—431no—
678C22⋊C8—431no—
679C22⋊C8—431no—
680C22⋊C8—861no—
681C22⋊C8—861no—
682C22⋊C8—861no—
683C22⋊C8—861no—
684C22⋊C8C22×D4311yescharacteristic
685C22⋊C8C22×D4311yescharacteristic
686C22⋊C8C22×D4311yescharacteristic
687C22⋊C8C22×D4311yescharacteristic
688#97—21no—
689#97—861no—
690C4×C8—21no—
691C4×C8—861no—
692C24—431no—
693C24—431no—
694C24C2×C4×D4311yescharacteristic
695C24C2×C4×D4311yescharacteristic
696C2×D4—42no—
697C2×D4—862no—
698C2×D4—861no—
699C2×D4—861no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—861no—
705C2×D4—861no—
706C2×D4—861no—
707C2×D4—861no—
708C2×D4—3441no—
709C2×D4—3441no—
710C2×D4—1721no—
711C2×D4—1722no—
712C2×D4—1722no—
713C2×D4(C2×D43)⋊C411yescharacteristic
714C2×D4(C2×D43)⋊C411yescharacteristic
715C2×D4(C2×D43)⋊C411yescharacteristic
716C2×D4(C2×D43)⋊C411yescharacteristic
717C22×C4—81no—
718C22×C4—81no—
719C22×C4—431no—
720C22×C4—431no—
721C22×C4—431no—
722C22×C4—431no—
723C22×C4—431no—
724C22×C4—431no—
725C22×C4—862no—
726C22×C4—862no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—861no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—3441no—
736C22×C4—3441no—
737C22×C4—1721no—
738C22×C4—1721no—
739C22×C4C2×C4×D4311yescharacteristic
740C22×C4C2×C4×D4311yescharacteristic
741C22×C4C2×C4×D4311yescharacteristic
742C22×C4C2×C4×D4311yescharacteristic
743C22×C4C2×D17211yescharacteristic
744C22×C4C2×D17211yescharacteristic
745C22×C4C2×D17211yescharacteristic
746C22×C4C2×D17211yescharacteristic
747C22×C4C2×C22⋊D4311yescharacteristic
748C22×C4C2×C22⋊D4311yescharacteristic
749C22×C4C2×C22⋊D4311yescharacteristic
750C22×C4C2×C22⋊D4311yescharacteristic
751C22×C4C23×D4311yescharacteristic
752M16—81no—
753M16—81no—
754M16—3441no—
755M16—3441no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C2×C8—81no—
762C2×C8—861no—
763C2×C8—861no—
764C2×C8—861no—
765C2×C8—861no—
766C2×C8—3441no—
767C2×C8—3441no—
768C4⋊C4—861no—
769C4⋊C4—861no—
770C4⋊C4—861no—
771C4⋊C4—861no—
772C4⋊C4—861no—
773C4⋊C4—861no—
774C4⋊C4—861no—
775C4⋊C4—861no—
776C4⋊C4—861no—
777C4⋊C4—861no—
778C4⋊C4—861no—
779C4⋊C4—861no—
780C4⋊C4—861no—
781C4⋊C4—861no—
782C4⋊C4—861no—
783C4⋊C4—861no—
784C4⋊C4—861no—
785C4⋊C4—861no—
786C4⋊C4(C2×D43)⋊C411yescharacteristic
787C4⋊C4(C2×D43)⋊C411yescharacteristic
788C4⋊C4(C2×D43)⋊C411yescharacteristic
789C4⋊C4(C2×D43)⋊C411yescharacteristic
790C22⋊C4—861no—
791C22⋊C4—861no—
792C22⋊C4—861no—
793C22⋊C4—861no—
794C22⋊C4—861no—
795C22⋊C4—861no—
796C22⋊C4—861no—
797C22⋊C4—861no—
798C22⋊C4—861no—
799C22⋊C4—861no—
800C22⋊C4—861no—
801C22⋊C4—861no—
802C22⋊C4—861no—
803C22⋊C4—861no—
804C22⋊C4—861no—
805C22⋊C4—861no—
806C22⋊C4(C2×D43)⋊C411yescharacteristic
807C22⋊C4(C2×D43)⋊C411yescharacteristic
808C22⋊C4(C2×D43)⋊C411yescharacteristic
809C22⋊C4(C2×D43)⋊C411yescharacteristic
810C22⋊C4(C2×D43)⋊C411yescharacteristic
811C22⋊C4(C2×D43)⋊C411yescharacteristic
812C22⋊C4(C2×D43)⋊C411yescharacteristic
813C22⋊C4(C2×D43)⋊C411yescharacteristic
814C42—861no—
815C42—861no—
816C42—861no—
817C42—861no—
818C42C2×D17211yescharacteristic
819C42C2×D17211yescharacteristic
820C42C2×C22⋊D4311yescharacteristic
821C42C2×C22⋊D4311yescharacteristic
822C23—22no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—861no—
831C23—861no—
832C23—861no—
833C23—861no—
834C23—861no—
835C23—861no—
836C23—1721no—
837C23—1721no—
838C23—1721no—
839C23—1721no—
840C23C2×(C2×D43)⋊C411yescharacteristic
841C23C2×(C2×D43)⋊C411yescharacteristic
842C23C2×(C2×D43)⋊C411yescharacteristic
843C23C2×(C2×D43)⋊C411yescharacteristic
844C23C22×C4×D4311yescharacteristic
845D4—22no—
846D4—22no—
847D4—41no—
848D4—41no—
849D4—3441no—
850D4—3441no—
851D4—3441no—
852D4—3441no—
853D4—1722no—
854D4—1722no—
855D4—1722no—
856D4—1722no—
857D4—1722no—
858D4—1722no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—432no—
874C2×C4—861no—
875C2×C4—861no—
876C2×C4—861no—
877C2×C4—861no—
878C2×C4—861no—
879C2×C4—861no—
880C2×C4—861no—
881C2×C4—861no—
882C2×C4—861no—
883C2×C4—3441no—
884C2×C4—3441no—
885C2×C4—3441no—
886C2×C4—3441no—
887C2×C4—1722no—
888C2×C4—1722no—
889C2×C4—1722no—
890C2×C4—1722no—
891C2×C4—1721no—
892C2×C4—1721no—
893C2×C4—1721no—
894C2×C4—1721no—
895C2×C4C2×(C2×D43)⋊C411yescharacteristic
896C2×C4C2×(C2×D43)⋊C411yescharacteristic
897C2×C4C2×(C2×D43)⋊C411yescharacteristic
898C2×C4C2×(C2×D43)⋊C411yescharacteristic
899C2×C4C2×(C2×D43)⋊C411yescharacteristic
900C2×C4C2×(C2×D43)⋊C411yescharacteristic
901C2×C4C2×(C2×D43)⋊C411yescharacteristic
902C2×C4C2×(C2×D43)⋊C411yescharacteristic
903C2×C4C22×C22⋊D4311yescharacteristic
904C2×C4C22×D17211yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C8—1721no—
910C8—1721no—
911C8—1721no—
912C8—1721no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—42no—
927C22—42no—
928C22—81no—
929C22—81no—
930C22—3441no—
931C22—3441no—
932C22—3441no—
933C22—3441no—
934C22—1721no—
935C22—1721no—
936C22—1721no—
937C22—1721no—
938C22—1721no—
939C22—1721no—
940C22#1458288112yes—
941C22C22×(C2×D43)⋊C411yescharacteristic
942C22#131×D4311yescharacteristic
943C22#1458366411yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—21no—
949C4—21no—
950C4—21no—
951C4—21no—
952C4—21no—
953C4—21no—
954C4—862no—
955C4—1721no—
956C4—1721no—
957C4—1721no—
958C4—1721no—
959C4—1721no—
960C2—21no—
961C2—21no—
962C2—22no—
963C2—41no—
964C2—41no—
965C2—41no—
966C2—3441no—
967C2—3441no—
968C2#1914304211yescharacteristic
969C2#1914305511yescharacteristic
970C2C2×#1458288111yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2974C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583598C2
cosocleC22×C4×C43C24
hypercenter#2974D43
hypocenterC43#17427
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #19143630C2semidirect
3. #19132965C2semidirect
4. #19132962C2semidirect
5. #19132956C2semidirect
6. #19132954C2semidirect
7. #19132944C2semidirect
8. #19132941C2semidirect
9. #19132931C2semidirect
10. #19132927C2semidirect
11. #19132924C2semidirect
12. #19132911C2semidirect
13. #19132907C2semidirect
14. C2×#14582624C2semidirect
15. C43×#2974C2semidirect
477. #2974D43semidirect
560. C43#17427semidirect

Maximal subgroups

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

subgroupindex
C2×#145835982
#191436302
#191329652
#191329622
#191329562
#191329542
#191329442
#191329412
#191329312
#191329272
#191329242
#191329112
#191329072
C2×#145826242
C43×#29742
#1742743