Finite Group Databasebeta

← #25062910

Subgroups — #25062910

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×#14583592C211yesmaximal, characteristic
2#19143631C211yesmaximal, characteristic, complemented
3#19143626C211yesmaximal, characteristic, complemented
4#19132961C211yesmaximal, characteristic, complemented
5#19132961C211yesmaximal, characteristic, complemented
6#19132955C211yesmaximal, characteristic, complemented
7#19132940C211yesmaximal, characteristic, complemented
8#19132940C211yesmaximal, characteristic, complemented
9#19132930C211yesmaximal, characteristic, complemented
10#19132926C211yesmaximal, characteristic, complemented
11#19132924C211yesmaximal, characteristic, complemented
12#19132910C211yesmaximal, characteristic, complemented
13#19132906C211yesmaximal, characteristic, complemented
14C2×#14582624C211yesmaximal, characteristic, complemented
15C43×#1471C211yesmaximal, characteristic, complemented
16#14583592—21no—
17#14583592—21no—
18#14583592—21no—
19#14583592—21no—
20#14583592—21no—
21#14583592—21no—
22#14583592—21no—
23#14583592—21no—
24C2×#13063320C411yescharacteristic
25C2×#13063318C2211yescharacteristic
26C2×#13063315C411yescharacteristic
27C2×#13063307C2211yescharacteristic
28C2×#13063306C411yescharacteristic
29C2×#13063297C411yescharacteristic
30C2×#13063297C411yescharacteristic
31C2×#13063297C411yescharacteristic
32C2×D4×Dic43C411yescharacteristic
33C2×D4×Dic43C411yescharacteristic
34C2×C4×C22⋊D43C2211yescharacteristic
35C2×(C22⋊D43)⋊C4C2211yescharacteristic
36C2×#13063281C2211yescharacteristic
37C22×Dic43⋊C4C2211yescharacteristic
38#14582975—21no—
39#14582974—21no—
40#14582973—21no—
41#14582970—21no—
42#14582968—21no—
43#14582967—21no—
44C8×C22⋊D43—21no—
45(C22⋊D43)⋊C8—21no—
46#14582953C2211yescharacteristic
47#14582953C2211yescharacteristic
48#14582949C2211yescharacteristic
49#14582949C2211yescharacteristic
50#14582863C2211yescharacteristic
51#14582861C2211yescharacteristic
52#14582861C2211yescharacteristic
53C2×C22⋊(C43⋊C8)C2211yescharacteristic
54C22⋊C8×D43C2211yescharacteristic
55C22⋊C8×D43C2211yescharacteristic
56#14582624C2211yescharacteristic
57#14582624C2211yescharacteristic
58#14582624C2211yescharacteristic
59#14582624C2211yescharacteristic
60#14582624C2211yescharacteristic
61#14582624C2211yescharacteristic
62#14582624C2211yescharacteristic
63#14582624C2211yescharacteristic
64#14582623C2211yescharacteristic
65#14582623C2211yescharacteristic
66#14582623C2211yescharacteristic
67#14582623C2211yescharacteristic
68C2×#121×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic
70C2×C22⋊C8×C43C2211yescharacteristic
71C43×#323C2211yescharacteristic
72C43×#323C2211yescharacteristic
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C22×C22⋊D43C2×C411yescharacteristic
76C22×C22⋊D43C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic
78C23×Dic43C2×C411yescharacteristic
79C23×Dic43C2×C411yescharacteristic
80C23×Dic43C2×C411yescharacteristic
81C23×Dic43C2×C411yescharacteristic
82C22×C4×D43C2311yescharacteristic
83C2×#10621877—21no—
84C2×#10621872—21no—
85C2×#10621872—21no—
86C22×C43⋊C8—21no—
87C2×C8×D43—21no—
88C2×C8×D43—21no—
89#13063320—21no—
90#13063320—21no—
91#13063320—21no—
92#13063320—21no—
93#13063318—21no—
94#13063318—21no—
95#13063318—21no—
96#13063318—21no—
97#13063315—21no—
98#13063315—21no—
99#13063315—21no—
100#13063315—21no—
101#13063307—21no—
102#13063307—21no—
103#13063307—21no—
104#13063307—21no—
105#13063306—21no—
106#13063306—21no—
107#13063306—21no—
108#13063306—21no—
109#13063297—21no—
110#13063297—21no—
111#13063297—21no—
112#13063297—21no—
113#13063297—21no—
114#13063297—21no—
115#13063297—21no—
116#13063297—21no—
117#13063297—21no—
118#13063297—21no—
119#13063297—21no—
120#13063297—21no—
121D4×Dic43—21no—
122D4×Dic43—21no—
123D4×Dic43—21no—
124D4×Dic43—21no—
125D4×Dic43—21no—
126D4×Dic43—21no—
127D4×Dic43—21no—
128D4×Dic43—21no—
129C4×C22⋊D43D411yescharacteristic
130C4×C22⋊D43D411yescharacteristic
131C4×C22⋊D43D411yescharacteristic
132C4×C22⋊D43D411yescharacteristic
133C4×C22⋊D43D411yescharacteristic
134C4×C22⋊D43D411yescharacteristic
135C4×C22⋊D43D411yescharacteristic
136C4×C22⋊D43D411yescharacteristic
137(C22⋊D43)⋊C4—21no—
138(C22⋊D43)⋊C4—21no—
139(C22⋊D43)⋊C4—21no—
140(C22⋊D43)⋊C4—21no—
141#13063281—21no—
142#13063281—21no—
143#13063281—21no—
144#13063281—21no—
145C2×C4⋊Dic43C2×C411yescharacteristic
146C2×C4⋊Dic43C2×C411yescharacteristic
147C2×Dic43⋊C4—21no—
148C2×Dic43⋊C4—21no—
149C2×Dic43⋊C4—21no—
150C2×Dic43⋊C4—21no—
151C2×Dic43⋊C4C2×C411yescharacteristic
152C2×Dic43⋊C4C2×C411yescharacteristic
153C2×Dic43⋊C4C2×C411yescharacteristic
154C2×Dic43⋊C4C2×C411yescharacteristic
155C2×Dic43⋊C4C2×C411yescharacteristic
156C2×Dic43⋊C4C2311yescharacteristic
157C2×Dic43⋊C4C2311yescharacteristic
158C2×C22⋊Dic43C2×C411yescharacteristic
159C2×C22⋊Dic43C2×C411yescharacteristic
160C2×C22⋊Dic43C2×C411yescharacteristic
161C2×C22⋊Dic43C2×C411yescharacteristic
162C2×C22⋊Dic43C2×C411yescharacteristic
163C2×(C2×D43)⋊C4C2×C411yescharacteristic
164C2×(C2×D43)⋊C4C2×C411yescharacteristic
165C2×(C2×D43)⋊C4C2×C411yescharacteristic
166C2×C4×Dic43C2×C411yescharacteristic
167C2×C4×Dic43C2×C411yescharacteristic
168C2×C4×Dic43C2311yescharacteristic
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)—21no—
175C22⋊(C43⋊C8)C2311yescharacteristic
176C22⋊(C43⋊C8)C2311yescharacteristic
177C22⋊(C43⋊C8)C2311yescharacteristic
178C22⋊(C43⋊C8)C2311yescharacteristic
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182(C2×D43)⋊C8—21no—
183#13063235—21no—
184#13063235—21no—
185C8×Dic43—21no—
186C8×Dic43—21no—
187C22×D4×C43C2×C411yescharacteristic
188C22×D4×C43C2×C411yescharacteristic
189C22×D4×C43C2×C411yescharacteristic
190C23×C4×C43C2311yescharacteristic
191C2×M16×C43—21no—
192C22×C8×C43—21no—
193#121×C43—21no—
194#121×C43—21no—
195#121×C43—21no—
196#121×C43—21no—
197C2×C4⋊C4×C43C2×C411yescharacteristic
198C2×C22⋊C4×C43C2311yescharacteristic
199C2×C22⋊C4×C43C2311yescharacteristic
200C22⋊C8×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204C22⋊C8×C43C2311yescharacteristic
205C22⋊C8×C43C2311yescharacteristic
206C24×C43C22×C411yescharacteristic
207C24×C43C22×C411yescharacteristic
208C24×C43C22×C411yescharacteristic
209C23×D43C22×C411yescharacteristic
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—21no—
216C2×D4×C43—42no—
217C2×D4×C43—42no—
218C2×D4×C43—81no—
219C22×C4×C43—81no—
220C22×C4×C43C22×C411yescharacteristic
221C22×C4×C43C22×C411yescharacteristic
222C22×C4×C43C22×C411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2411yescharacteristic
228C2×C22⋊D43—22no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43—41no—
234C2×C22⋊D43—42no—
235C2×C22⋊D43—81no—
236C2×C22⋊D43C22⋊C411yescharacteristic
237C2×C22⋊D43C22⋊C411yescharacteristic
238C2×C22⋊D43C22⋊C411yescharacteristic
239C2×C22⋊D43C22⋊C411yescharacteristic
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43—22no—
243C22×Dic43—22no—
244C22×Dic43—21no—
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—41no—
251C22×Dic43—41no—
252C22×Dic43—81no—
253C22×Dic43—81no—
254C22×Dic43C22×C411yescharacteristic
255C22×Dic43C22×C411yescharacteristic
256C22×Dic43C22×C411yescharacteristic
257C22×Dic43C22×C411yescharacteristic
258C22×Dic43C22×C411yescharacteristic
259C22×Dic43C22×C411yescharacteristic
260C22×Dic43C22×C411yescharacteristic
261C2×C4×D43—81no—
262C2×C4×D43C2×D411yescharacteristic
263C2×C4×D43C2×D411yescharacteristic
264C2×C4×D43C2×D411yescharacteristic
265C2×C4×D43C2×D411yescharacteristic
266M16×C43—81no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—81no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C22⋊C4×C43—21no—
277C22⋊C4×C43—21no—
278C22⋊Dic43—21no—
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43—21no—
285C22⋊Dic43—21no—
286C22⋊Dic43C22⋊C411yescharacteristic
287C22⋊Dic43C22⋊C411yescharacteristic
288C22⋊Dic43C22⋊C411yescharacteristic
289C22⋊Dic43C22⋊C411yescharacteristic
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4C22⋊C411yescharacteristic
295(C2×D43)⋊C4C22⋊C411yescharacteristic
296(C2×D43)⋊C4C22⋊C411yescharacteristic
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298C4⋊Dic43—21no—
299C4⋊Dic43—21no—
300C4⋊Dic43—21no—
301C4⋊Dic43—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4C22⋊C411yescharacteristic
315Dic43⋊C4C22⋊C411yescharacteristic
316Dic43⋊C4C22⋊C411yescharacteristic
317Dic43⋊C4C22⋊C411yescharacteristic
318C4×Dic43—21no—
319C4×Dic43—21no—
320C4×Dic43—21no—
321C4×Dic43—21no—
322C4×Dic43C2×D411yescharacteristic
323C4×Dic43C2×D411yescharacteristic
324C4×Dic43C2×D411yescharacteristic
325C4×Dic43C2×D411yescharacteristic
326#10621877—81no—
327C2×C43⋊C8—21no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—81no—
332#10621872—81no—
333#10621872—81no—
334C8×D43—81no—
335C8×D43—81no—
336C23×C43—21no—
337C23×C43—21no—
338C23×C43—22no—
339C23×C43—21no—
340C23×C43—21no—
341C23×C43—21no—
342C23×C43—21no—
343C23×C43—21no—
344C23×C43—21no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—41no—
348C23×C43—41no—
349C23×C43—41no—
350C23×C43C2×C22⋊C411yescharacteristic
351C23×C43C2×C22⋊C411yescharacteristic
352C23×C43C23×C411yescharacteristic
353C22×D43—21no—
354C22×D43—21no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43C2×C22⋊C411yescharacteristic
358C22×D43C2×C22⋊C411yescharacteristic
359D4×C43—42no—
360D4×C43—42no—
361D4×C43—42no—
362D4×C43—42no—
363D4×C43—81no—
364D4×C43—81no—
365C2×C4×C43—21no—
366C2×C4×C43—21no—
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×C43C2×C22⋊C411yescharacteristic
376C2×C4×C43C2×C22⋊C411yescharacteristic
377C2×C4×C43C22×D411yescharacteristic
378C2×C4×C43C22×D411yescharacteristic
379C22⋊D43—22no—
380C22⋊D43—22no—
381C22⋊D43—41no—
382C22⋊D43—41no—
383C22⋊D43—42no—
384C22⋊D43—42no—
385C22⋊D43—81no—
386C22⋊D43—81no—
387C2×Dic43—21no—
388C2×Dic43—21no—
389C2×Dic43—21no—
390C2×Dic43—21no—
391C2×Dic43—21no—
392C2×Dic43—21no—
393C2×Dic43—21no—
394C2×Dic43—21no—
395C2×Dic43—21no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—42no—
399C2×Dic43—42no—
400C2×Dic43—42no—
401C2×Dic43—42no—
402C2×Dic43—41no—
403C2×Dic43—41no—
404C2×Dic43—81no—
405C2×Dic43—81no—
406C2×Dic43—81no—
407C2×Dic43—81no—
408C2×Dic43C2×C22⋊C411yescharacteristic
409C2×Dic43C2×C22⋊C411yescharacteristic
410C2×Dic43C2×C22⋊C411yescharacteristic
411C2×Dic43C2×C22⋊C411yescharacteristic
412C2×Dic43C2×C22⋊C411yescharacteristic
413C2×Dic43C2×C22⋊C411yescharacteristic
414C2×Dic43#13112yes—
415C4×D43—41no—
416C4×D43—41no—
417C4×D43—41no—
418C4×D43—41no—
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—42no—
436C22×C43—42no—
437C22×C43—41no—
438C22×C43—41no—
439C22×C43—41no—
440C22×C43—41no—
441C22×C43—41no—
442C22×C43—41no—
443C22×C43—81no—
444C22×C43—81no—
445C22×C43—81no—
446C22×C43—81no—
447C22×C43#41312yes—
448C22×C43C22×C22⋊C411yescharacteristic
449C22×C43C2×#13111yescharacteristic
450C22×C43#56811yescharacteristic
451C2×D43—21no—
452C2×D43—21no—
453C2×D43—21no—
454C2×D43—21no—
455C2×D43—21no—
456C2×D43—21no—
457C2×D43—81no—
458C2×D43—81no—
459C4×C43—21no—
460C4×C43—21no—
461C4×C43—21no—
462C4×C43—21no—
463C4×C43—41no—
464C4×C43—41no—
465Dic43—22no—
466Dic43—21no—
467Dic43—21no—
468Dic43—21no—
469Dic43—21no—
470Dic43—21no—
471Dic43—21no—
472Dic43—41no—
473Dic43—41no—
474Dic43—41no—
475C2×#553—431no—
476#2974—431no—
477#2974—431no—
478#1473—431no—
479#1473—431no—
480#1471—431no—
481#1471D4311yescharacteristic, complemented
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—81no—
495C2×C43—81no—
496C2×C43#288011yescharacteristic
497C2×C43#288311yescharacteristic
498C2×C43C2×#41311yescharacteristic
499D43—41no—
500D43—41no—
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×#121C2×D4311yescharacteristic
518C2×C4×D4—431no—
519C2×C4×D4—431no—
520C2×C4×D4—431no—
521C2×C4×D4—431no—
522C2×#117—431no—
523C22×C4⋊C4—431no—
524#436—861no—
525#436—861no—
526#435—861no—
527#435—861no—
528#435—861no—
529#435—861no—
530C8×D4—861no—
531C8×D4—861no—
532#432—431no—
533#432—431no—
534#431—431no—
535#431—431no—
536#407—431no—
537#407—431no—
538#407—431no—
539#407C2×D4311yescharacteristic
540C2×C22⋊C8—431no—
541C2×C22⋊C8—431no—
542C2×C22⋊C8—431no—
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#323C2×D4311yescharacteristic
557#323C2×D4311yescharacteristic
558#323C2×D4311yescharacteristic
559#323C2×D4311yescharacteristic
560C43#1742711yescharacteristic, complemented, Sylow
561C22×D4—431no—
562C22×D4—431no—
563C22×D4—431no—
564C22×D4C4×D4311yescharacteristic
565C22×D4C4×D4311yescharacteristic
566C22×D4C4×D4311yescharacteristic
567C23×C4—431no—
568C23×C4—431no—
569C23×C4—431no—
570C23×C4—431no—
571C23×C4—431no—
572C23×C4C22×D4311yescharacteristic
573C2×M16—21no—
574C2×M16—861no—
575C2×M16—861no—
576C2×M16—861no—
577C22×C8—21no—
578C22×C8—861no—
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—21no—
602#121—21no—
603#121—21no—
604#121—21no—
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—431no—
618C4×D4—431no—
619C4×D4—431no—
620C4×D4—431no—
621C4×D4—431no—
622C4×D4—431no—
623C4×D4—431no—
624C4×D4—431no—
625C4×D4—861no—
626C4×D4—861no—
627C4×D4—861no—
628C4×D4—861no—
629C4×D4—861no—
630C4×D4—861no—
631C4×D4—861no—
632C4×D4—861no—
633C4×D4—861no—
634C4×D4—861no—
635C4×D4—861no—
636C4×D4—861no—
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⋊C4C22×D4311yescharacteristic
664C2×C22⋊C4C22×D4311yescharacteristic
665C2×C42—431no—
666C2×C42—431no—
667C2×C42—431no—
668C4⋊C8—861no—
669C4⋊C8—861no—
670C4⋊C8—861no—
671C4⋊C8—861no—
672C22⋊C8—21no—
673C22⋊C8—21no—
674C22⋊C8—431no—
675C22⋊C8—431no—
676C22⋊C8—431no—
677C22⋊C8—431no—
678C22⋊C8—861no—
679C22⋊C8—861no—
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—861no—
689#97—861no—
690C4×C8—861no—
691C4×C8—861no—
692C24—431no—
693C24C2×C4×D4311yescharacteristic
694C24C2×C4×D4311yescharacteristic
695C24C2×C4×D4311yescharacteristic
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—81no—
705C2×D4—431no—
706C2×D4—431no—
707C2×D4—431no—
708C2×D4—431no—
709C2×D4—862no—
710C2×D4—861no—
711C2×D4—861no—
712C2×D4—861no—
713C2×D4—861no—
714C2×D4—3441no—
715C2×D4—1721no—
716C2×D4—1722no—
717C22×C4—81no—
718C22×C4—431no—
719C22×C4—431no—
720C22×C4—431no—
721C22×C4—431no—
722C22×C4—431no—
723C22×C4—431no—
724C22×C4—431no—
725C22×C4—431no—
726C22×C4—431no—
727C22×C4—431no—
728C22×C4—431no—
729C22×C4—861no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—862no—
734C22×C4—862no—
735C22×C4—861no—
736C22×C4—861no—
737C22×C4—861no—
738C22×C4—861no—
739C22×C4—3441no—
740C22×C4—3441no—
741C22×C4—3441no—
742C22×C4—1721no—
743C22×C4—1721no—
744C22×C4C2×C4×D4311yescharacteristic
745C22×C4C2×C4×D4311yescharacteristic
746C22×C4C2×C4×D4311yescharacteristic
747C22×C4D4×D4311yescharacteristic
748C22×C4D4×D4311yescharacteristic
749C22×C4D4×D4311yescharacteristic
750C22×C4D4×D4311yescharacteristic
751C22×C4C23×D4311yescharacteristic
752M16—81no—
753M16—3441no—
754M16—3441no—
755M16—3441no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C2×C8—861no—
762C2×C8—861no—
763C2×C8—861no—
764C2×C8—861no—
765C2×C8—3441no—
766C2×C8—3441no—
767C2×C8—3441no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—431no—
771C4⋊C4—431no—
772C4⋊C4—431no—
773C4⋊C4—431no—
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—861no—
787C4⋊C4—861no—
788C4⋊C4—861no—
789C4⋊C4—861no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—431no—
795C22⋊C4—431no—
796C22⋊C4—431no—
797C22⋊C4—431no—
798C22⋊C4—431no—
799C22⋊C4—431no—
800C22⋊C4—431no—
801C22⋊C4—431no—
802C22⋊C4—861no—
803C22⋊C4—861no—
804C22⋊C4—861no—
805C22⋊C4—861no—
806C22⋊C4—861no—
807C22⋊C4—861no—
808C22⋊C4—861no—
809C22⋊C4—861no—
810C22⋊C4—861no—
811C22⋊C4—861no—
812C22⋊C4—861no—
813C22⋊C4—861no—
814C42—431no—
815C42—431no—
816C42—431no—
817C42—431no—
818C42—861no—
819C42—861no—
820C42—861no—
821C42—861no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—431no—
837C23—431no—
838C23—861no—
839C23—861no—
840C23—1721no—
841C23—1721no—
842C23C22⋊C4×D4311yescharacteristic
843C23C22⋊C4×D4311yescharacteristic
844C23C22×C4×D4311yescharacteristic
845D4—42no—
846D4—42no—
847D4—42no—
848D4—42no—
849D4—81no—
850D4—81no—
851D4—862no—
852D4—862no—
853D4—3441no—
854D4—3441no—
855D4—1721no—
856D4—1721no—
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—431no—
870C2×C4—431no—
871C2×C4—431no—
872C2×C4—431no—
873C2×C4—431no—
874C2×C4—431no—
875C2×C4—432no—
876C2×C4—861no—
877C2×C4—861no—
878C2×C4—861no—
879C2×C4—861no—
880C2×C4—861no—
881C2×C4—861no—
882C2×C4—861no—
883C2×C4—861no—
884C2×C4—861no—
885C2×C4—3441no—
886C2×C4—3441no—
887C2×C4—3441no—
888C2×C4—3441no—
889C2×C4—1721no—
890C2×C4—1721no—
891C2×C4—1721no—
892C2×C4—1721no—
893C2×C4—1721no—
894C2×C4—1721no—
895C2×C4—1722no—
896C2×C4—1722no—
897C2×C4—1722no—
898C2×C4—1722no—
899C2×C4—1721no—
900C2×C4—1721no—
901C2×C4C22⋊C4×D4311yescharacteristic
902C2×C4C22⋊C4×D4311yescharacteristic
903C2×C4C2×D4×D4311yescharacteristic
904C2×C4C2×D4×D4311yescharacteristic
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—42no—
921C22—42no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—861no—
933C22—861no—
934C22—861no—
935C22—861no—
936C22—861no—
937C22—861no—
938C22—3441no—
939C22—3441no—
940C22#1458288012yes—
941C22C2×C22⋊C4×D4311yescharacteristic
942C22#131×D4311yescharacteristic
943C22#1458366411yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—41no—
949C4—41no—
950C4—862no—
951C4—861no—
952C4—861no—
953C4—861no—
954C4—861no—
955C4—861no—
956C4—861no—
957C4—1721no—
958C4—1721no—
959C4—1721no—
960C2—21no—
961C2—21no—
962C2—22no—
963C2—41no—
964C2—81no—
965C2—81no—
966C2—1721no—
967C2—1721no—
968C2#1914304311yescharacteristic
969C2#1914305311yescharacteristic
970C2C2×#1458288011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1471C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583592C2
cosocleC22×C4×C43C24
hypercenter#1471D43
hypocenterC43#17427
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1471

Complements

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

NH ≅ G/Ntype
2. #19143631C2semidirect
3. #19143626C2semidirect
4. #19132961C2semidirect
5. #19132961C2semidirect
6. #19132955C2semidirect
7. #19132940C2semidirect
8. #19132940C2semidirect
9. #19132930C2semidirect
10. #19132926C2semidirect
11. #19132924C2semidirect
12. #19132910C2semidirect
13. #19132906C2semidirect
14. C2×#14582624C2semidirect
15. C43×#1471C2semidirect
481. #1471D43semidirect
560. C43#17427semidirect

Maximal subgroups

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

subgroupindex
C2×#145835922
#191436312
#191436262
#191329612
#191329552
#191329402
#191329302
#191329262
#191329242
#191329102
#191329062
C2×#145826242
C43×#14712
#1742743