Finite Group Databasebeta

← #25062812

Subgroups — #25062812

Order 11008.

1008 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583600C211yesmaximal, characteristic
2#19143254C211yesmaximal, characteristic, complemented
3#19143248C211yesmaximal, characteristic, complemented
4#19132964C211yesmaximal, characteristic, complemented
5#19132963C211yesmaximal, characteristic, complemented
6#19132963C211yesmaximal, characteristic, complemented
7#19132953C211yesmaximal, characteristic, complemented
8#19132953C211yesmaximal, characteristic, complemented
9#19132935C211yesmaximal, characteristic, complemented
10#19132934C211yesmaximal, characteristic, complemented
11#19132932C211yesmaximal, characteristic, complemented
12#19132915C211yesmaximal, characteristic, complemented
13#19132914C211yesmaximal, characteristic, complemented
14#19132912C211yesmaximal, characteristic, complemented
15C43×#1473C211yesmaximal, characteristic, complemented
16#14583600—21no—
17#14583600—21no—
18#14583600—21no—
19#14583600—21no—
20#14583600—21no—
21#14583600—21no—
22#14583600—21no—
23#14583600—21no—
24C2×#13063320C2211yescharacteristic
25C2×#13063315C411yescharacteristic
26C2×#13063310C411yescharacteristic
27C2×#13063309C411yescharacteristic
28C2×#13063300C411yescharacteristic
29C2×#13063298C411yescharacteristic
30C2×#13063298C411yescharacteristic
31C2×#13063298C2211yescharacteristic
32C2×C4×D172C2211yescharacteristic
33C2×#13063287C2211yescharacteristic
34C2×(C22⋊D43)⋊C4C411yescharacteristic
35C2×(C22⋊D43)⋊C4C2211yescharacteristic
36C2×#13063282C2211yescharacteristic
37C2×C4⋊C4×D43C411yescharacteristic
38#14582961—21no—
39#14582959—21no—
40#14582959—21no—
41#14582958—21no—
42#14582956C2211yescharacteristic
43#14582953C2211yescharacteristic
44#14582953C2211yescharacteristic
45#14582952C2211yescharacteristic
46#14582949C2211yescharacteristic
47#14582949C2211yescharacteristic
48#14582924—21no—
49#14582924—21no—
50#14582861C2211yescharacteristic
51#14582861C2211yescharacteristic
52C22⋊C8×D43C2211yescharacteristic
53C22⋊C8×D43C2211yescharacteristic
54#14582856—21no—
55#14582853—21no—
56#14582625C2211yescharacteristic
57#14582625C2211yescharacteristic
58#14582623C2211yescharacteristic
59#14582623C2211yescharacteristic
60#14582622C2211yescharacteristic
61#14582622C2211yescharacteristic
62#14582622C2211yescharacteristic
63#14582622C2211yescharacteristic
64#14582622C2211yescharacteristic
65#14582622C2211yescharacteristic
66#14582622C2211yescharacteristic
67#14582622C2211yescharacteristic
68C2×#126×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#431C2211yescharacteristic
71C43×#324C2211yescharacteristic
72C43×#324C2211yescharacteristic
73C43×#323C2211yescharacteristic
74C43×#323C2211yescharacteristic
75C22×D172C2×C411yescharacteristic
76C22×D172C2×C411yescharacteristic
77C22×D172C2×C411yescharacteristic
78C22×C22⋊D43C2×C411yescharacteristic
79C22×C22⋊D43C2×C411yescharacteristic
80C22×C22⋊D43C2×C411yescharacteristic
81C23×Dic43C2×C411yescharacteristic
82C22×C4×D43C2×C411yescharacteristic
83C22×C4×D43C2×C411yescharacteristic
84C22×C4×D43C2×C411yescharacteristic
85C22×C4×D43C2×C411yescharacteristic
86C22×C4×D43C2311yescharacteristic
87C2×#10621872—21no—
88C2×#10621872—21no—
89C2×C8×D43—21no—
90C2×C8×D43—21no—
91#13063320—21no—
92#13063320—21no—
93#13063320—21no—
94#13063320—21no—
95#13063315—21no—
96#13063315—21no—
97#13063315—21no—
98#13063315—21no—
99#13063310—21no—
100#13063310—21no—
101#13063310—21no—
102#13063310—21no—
103#13063309—21no—
104#13063309—21no—
105#13063309—21no—
106#13063309—21no—
107#13063300—21no—
108#13063300—21no—
109#13063300—21no—
110#13063300—21no—
111#13063298—21no—
112#13063298—21no—
113#13063298—21no—
114#13063298—21no—
115#13063298—21no—
116#13063298—21no—
117#13063298—21no—
118#13063298—21no—
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063298—21no—
123C4×D172—21no—
124C4×D172—21no—
125C4×D172—21no—
126C4×D172—21no—
127#13063287—21no—
128#13063287—21no—
129#13063287—21no—
130#13063287—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(C22⋊D43)⋊C4—21no—
137(C22⋊D43)⋊C4—21no—
138(C22⋊D43)⋊C4—21no—
139#13063282D411yescharacteristic
140#13063282D411yescharacteristic
141#13063282D411yescharacteristic
142#13063282D411yescharacteristic
143#13063282D411yescharacteristic
144#13063282D411yescharacteristic
145#13063282D411yescharacteristic
146#13063282D411yescharacteristic
147C2×C4⋊Dic43C2×C411yescharacteristic
148C2×C4⋊Dic43C2×C411yescharacteristic
149C2×Dic43⋊C4C2×C411yescharacteristic
150C2×Dic43⋊C4C2×C411yescharacteristic
151C2×Dic43⋊C4C2×C411yescharacteristic
152C2×Dic43⋊C4C2×C411yescharacteristic
153C2×Dic43⋊C4C2×C411yescharacteristic
154C4⋊C4×D43—21no—
155C4⋊C4×D43—21no—
156C4⋊C4×D43—21no—
157C4⋊C4×D43—21no—
158C2×(C2×D43)⋊C4C2×C411yescharacteristic
159C2×(C2×D43)⋊C4C2×C411yescharacteristic
160C2×(C2×D43)⋊C4C2×C411yescharacteristic
161C2×(C2×D43)⋊C4C2×C411yescharacteristic
162C2×(C2×D43)⋊C4C2×C411yescharacteristic
163C2×(C2×D43)⋊C4C2311yescharacteristic
164C2×(C2×D43)⋊C4C2311yescharacteristic
165C2×C4×Dic43C2×C411yescharacteristic
166C2×C4×Dic43C2311yescharacteristic
167C4⋊(C43⋊C8)—21no—
168C4⋊(C43⋊C8)—21no—
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)C2311yescharacteristic
174C22⋊(C43⋊C8)C2311yescharacteristic
175C22⋊(C43⋊C8)C2311yescharacteristic
176C22⋊(C43⋊C8)C2311yescharacteristic
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181#13063236—21no—
182#13063235—21no—
183#13063235—21no—
184C4×C43⋊C8—21no—
185C8×Dic43—21no—
186C8×Dic43—21no—
187#126×C43—21no—
188#126×C43—21no—
189#126×C43—21no—
190#126×C43—21no—
191C2×C4⋊C4×C43C2×C411yescharacteristic
192C2×C4⋊C4×C43C2×C411yescharacteristic
193C2×C4⋊C4×C43C2311yescharacteristic
194C2×C22⋊C4×C43C2×C411yescharacteristic
195C2×C22⋊C4×C43C2×C411yescharacteristic
196C2×C22⋊C4×C43C2311yescharacteristic
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C4⋊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
207C23×D43C22×C411yescharacteristic
208C23×D43C22×C411yescharacteristic
209C23×D43C22×C411yescharacteristic
210C22×C4×C43C22×C411yescharacteristic
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C22×C411yescharacteristic
215C22×C4×C43C2411yescharacteristic
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—22no—
223C2×C22⋊D43—41no—
224C2×C22⋊D43—42no—
225C2×C22⋊D43—81no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—81no—
229C22×Dic43C22×C411yescharacteristic
230C22×Dic43C22×C411yescharacteristic
231C22×Dic43C22×C411yescharacteristic
232C22×Dic43C22×C411yescharacteristic
233C22×Dic43C22×C411yescharacteristic
234C2×D172—21no—
235C2×D172—21no—
236C2×D172—21no—
237C2×D172—21no—
238C2×D172—21no—
239C2×D172—21no—
240C2×D172—22no—
241C2×D172—22no—
242C2×D172—41no—
243C2×D172—41no—
244C2×D172—81no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—21no—
250C2×C4×D43—21no—
251C2×C4×D43—21no—
252C2×C4×D43—21no—
253C2×C4×D43—42no—
254C2×C4×D43—42no—
255C2×C4×D43—81no—
256C2×C4×D43—81no—
257C2×C4×D43—81no—
258C2×C4×D43C2×D411yescharacteristic
259C2×C4×D43C2×D411yescharacteristic
260C2×C4×D43C2×D411yescharacteristic
261C2×C4×D43C2×D411yescharacteristic
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C22⋊C4×C43—21no—
277C22⋊C4×C43—21no—
278C42×C43C2×D411yescharacteristic
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2×D411yescharacteristic
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4C22⋊C411yescharacteristic
293(C2×D43)⋊C4C22⋊C411yescharacteristic
294(C2×D43)⋊C4C22⋊C411yescharacteristic
295(C2×D43)⋊C4C22⋊C411yescharacteristic
296(C2×D43)⋊C4C22⋊C411yescharacteristic
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298(C2×D43)⋊C4C22⋊C411yescharacteristic
299(C2×D43)⋊C4C22⋊C411yescharacteristic
300C4⋊Dic43—21no—
301C4⋊Dic43—21no—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4C22⋊C411yescharacteristic
311Dic43⋊C4C22⋊C411yescharacteristic
312Dic43⋊C4C22⋊C411yescharacteristic
313Dic43⋊C4C22⋊C411yescharacteristic
314Dic43⋊C4C22⋊C411yescharacteristic
315Dic43⋊C4C22⋊C411yescharacteristic
316Dic43⋊C4C22⋊C411yescharacteristic
317Dic43⋊C4C22⋊C411yescharacteristic
318C4×Dic43—21no—
319C4×Dic43—21no—
320C4×Dic43C2×D411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322C4×Dic43C2×D411yescharacteristic
323C4×Dic43C2×D411yescharacteristic
324C2×C43⋊C8—21no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—21no—
328#10621872—42no—
329#10621872—42no—
330C8×D43—42no—
331C8×D43—42no—
332C23×C43—21no—
333C23×C43—21no—
334C23×C43—21no—
335C23×C43—41no—
336C23×C43—41no—
337C23×C43C23×C411yescharacteristic
338C22×D43—21no—
339C22×D43—21no—
340C22×D43—21no—
341C22×D43—21no—
342C22×D43—21no—
343C22×D43—21no—
344C22×D43—21no—
345C22×D43—41no—
346C22×D43—41no—
347C22×D43—41no—
348C22×D43—41no—
349C22×D43—41no—
350C22×D43—41no—
351C22×D43C2×C22⋊C411yescharacteristic
352C22×D43C2×C22⋊C411yescharacteristic
353C22×D43#13112yes—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43C2×C22⋊C411yescharacteristic
366C2×C4×C43C2×C22⋊C411yescharacteristic
367C2×C4×C43C2×C22⋊C411yescharacteristic
368C2×C4×C43C2×C22⋊C411yescharacteristic
369C2×C4×C43C22×D411yescharacteristic
370C2×C4×C43C22×D411yescharacteristic
371C22⋊D43—42no—
372C22⋊D43—42no—
373C22⋊D43—42no—
374C22⋊D43—42no—
375C22⋊D43—81no—
376C22⋊D43—81no—
377C2×Dic43—21no—
378C2×Dic43—21no—
379C2×Dic43—22no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—81no—
386C2×Dic43—81no—
387C2×Dic43C2×C22⋊C411yescharacteristic
388C2×Dic43C2×C22⋊C411yescharacteristic
389C2×Dic43C2×C22⋊C411yescharacteristic
390C2×Dic43C2×C22⋊C411yescharacteristic
391C2×Dic43C2×C22⋊C411yescharacteristic
392C2×Dic43C2×C22⋊C411yescharacteristic
393D172—42no—
394D172—42no—
395D172—42no—
396D172—42no—
397D172—81no—
398D172—81no—
399C4×D43—22no—
400C4×D43—22no—
401C4×D43—41no—
402C4×D43—41no—
403C4×D43—42no—
404C4×D43—42no—
405C4×D43—81no—
406C4×D43—81no—
407C4×D43—81no—
408C4×D43—81no—
409C4×D43—81no—
410C4×D43—81no—
411C8×C43—41no—
412C8×C43—41no—
413C8×C43—41no—
414C8×C43—41no—
415C43⋊C8—41no—
416C43⋊C8—41no—
417C43⋊C8—41no—
418C43⋊C8—41no—
419#17415—431nomaximal, Sylow
420C22×C43—21no—
421C22×C43—21no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—81no—
426C22×C43—81no—
427C22×C43C22×C22⋊C411yescharacteristic
428C22×C43C2×#13111yescharacteristic
429C22×C43#56811yescharacteristic
430C2×D43—21no—
431C2×D43—21no—
432C2×D43—22no—
433C2×D43—21no—
434C2×D43—21no—
435C2×D43—21no—
436C2×D43—21no—
437C2×D43—42no—
438C2×D43—41no—
439C2×D43—41no—
440C2×D43—42no—
441C2×D43—41no—
442C2×D43—41no—
443C2×D43—41no—
444C2×D43—81no—
445C2×D43—81no—
446C2×D43—81no—
447C2×D43—81no—
448C4×C43—21no—
449C4×C43—21no—
450C4×C43—21no—
451C4×C43—21no—
452C4×C43—21no—
453C4×C43—21no—
454C4×C43—41no—
455C4×C43—41no—
456C4×C43—41no—
457Dic43—21no—
458Dic43—21no—
459Dic43—21no—
460Dic43—21no—
461Dic43—21no—
462Dic43—41no—
463Dic43—41no—
464Dic43#41012yes—
465C2×#553—431no—
466#2924—431no—
467#2924—431no—
468#1473—431no—
469#1473—431no—
470#1473—431no—
471#1473D4311yescharacteristic, complemented
472#1471—431no—
473#1471—431no—
474#1466—431no—
475#1466—431no—
476#1465—431no—
477#1460—431no—
478#1460—431no—
479#1459—431no—
480C2×C43—21no—
481C2×C43—21no—
482C2×C43—81no—
483C2×C43#288011yescharacteristic
484C2×C43C2×#41011yescharacteristic
485C2×C43#288811yescharacteristic
486D43—41no—
487D43—41no—
488D43—42no—
489D43—81no—
490#553—861no—
491#553—861no—
492#553—861no—
493#553—861no—
494#553—861no—
495#553—861no—
496#553—861no—
497#553—861no—
498C2×#126—431no—
499C2×#126C2×D4311yescharacteristic
500C2×#125—431no—
501C2×#123—431no—
502C2×#123—431no—
503C2×#121—431no—
504C2×#121—431no—
505C2×#121—431no—
506C2×#121—431no—
507C2×C4×D4—431no—
508C2×C4×D4—431no—
509C2×C4×D4—431no—
510C2×C4×D4—431no—
511C2×#117—431no—
512C22×C4⋊C4—431no—
513#433—861no—
514#433—861no—
515#433—861no—
516#433—861no—
517#432—431no—
518#432—431no—
519#432—431no—
520#432C2×D4311yescharacteristic
521#431—431no—
522#431—431no—
523#431—431no—
524#431C2×D4311yescharacteristic
525#424—861no—
526#424—861no—
527#407—431no—
528#407—431no—
529C2×C22⋊C8—431no—
530C2×C22⋊C8—431no—
531#405—861no—
532#405—861no—
533#324—431no—
534#324—431no—
535#324C2×D4311yescharacteristic
536#324C2×D4311yescharacteristic
537#323—431no—
538#323—431no—
539#323—431no—
540#323—431no—
541#323—431no—
542#323—431no—
543#323—431no—
544#323—431no—
545#323—431no—
546#323—431no—
547#323C2×D4311yescharacteristic
548#323C2×D4311yescharacteristic
549C43#1741511yescharacteristic, complemented, Sylow
550C22×D4—431no—
551C22×D4—431no—
552C22×D4—431no—
553C22×D4—431no—
554C22×D4—431no—
555C22×D4—431no—
556C23×C4—431no—
557C23×C4—431no—
558C23×C4—431no—
559C23×C4—431no—
560C23×C4—431no—
561C23×C4—431no—
562C2×M16—861no—
563C2×M16—861no—
564C22×C8—861no—
565C22×C8—861no—
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—861no—
571#126—861no—
572#126—861no—
573#126—861no—
574#125—861no—
575#125—861no—
576#125—861no—
577#125—861no—
578#123—861no—
579#123—861no—
580#123—861no—
581#123—861no—
582#123—861no—
583#123—861no—
584#123—861no—
585#123—861no—
586#121—861no—
587#121—861no—
588#121—861no—
589#121—861no—
590#121—861no—
591#121—861no—
592#121—861no—
593#121—861no—
594#121—861no—
595#121—861no—
596#121—861no—
597#121—861no—
598#121—861no—
599#121—861no—
600#121—861no—
601#121—861no—
602C4×D4—861no—
603C4×D4—861no—
604C4×D4—861no—
605C4×D4—861no—
606C4×D4—861no—
607C4×D4—861no—
608C4×D4—861no—
609C4×D4—861no—
610C4×D4—861no—
611C4×D4—861no—
612C4×D4—861no—
613C4×D4—861no—
614C4×D4—861no—
615C4×D4—861no—
616C4×D4—861no—
617C4×D4—861no—
618#117—431no—
619#117—431no—
620#117—431no—
621#117—431no—
622#117—431no—
623#117—431no—
624#117—431no—
625#117—431no—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—431no—
630C2×C4⋊C4—431no—
631C2×C4⋊C4—431no—
632C2×C4⋊C4—431no—
633C2×C4⋊C4—861no—
634C2×C4⋊C4—861no—
635C2×C4⋊C4—861no—
636C2×C4⋊C4—861no—
637C2×C4⋊C4C4×D4311yescharacteristic
638C2×C4⋊C4C4×D4311yescharacteristic
639C2×C4⋊C4C22×D4311yescharacteristic
640C2×C22⋊C4—431no—
641C2×C22⋊C4—431no—
642C2×C22⋊C4—431no—
643C2×C22⋊C4—431no—
644C2×C22⋊C4—431no—
645C2×C22⋊C4—431no—
646C2×C22⋊C4—431no—
647C2×C22⋊C4C4×D4311yescharacteristic
648C2×C22⋊C4C4×D4311yescharacteristic
649C2×C22⋊C4C22×D4311yescharacteristic
650C2×C42—431no—
651C2×C42—431no—
652C2×C42C22×D4311yescharacteristic
653C4⋊C8—21no—
654C4⋊C8—21no—
655C4⋊C8—861no—
656C4⋊C8—861no—
657C4⋊C8—861no—
658C4⋊C8—861no—
659C4⋊C8—861no—
660C4⋊C8—861no—
661C22⋊C8—431no—
662C22⋊C8—431no—
663C22⋊C8—431no—
664C22⋊C8—431no—
665C22⋊C8—861no—
666C22⋊C8—861no—
667C22⋊C8—861no—
668C22⋊C8—861no—
669C22⋊C8C22×D4311yescharacteristic
670C22⋊C8C22×D4311yescharacteristic
671C22⋊C8C22×D4311yescharacteristic
672C22⋊C8C22×D4311yescharacteristic
673#97—21no—
674#97—861no—
675#97—861no—
676#97—861no—
677C4×C8—21no—
678C4×C8—861no—
679C4×C8—861no—
680C4×C8—861no—
681C24—431no—
682C24—431no—
683C24—431no—
684C24C2×C4×D4311yescharacteristic
685C2×D4—861no—
686C2×D4—861no—
687C2×D4—861no—
688C2×D4—861no—
689C2×D4—862no—
690C2×D4—862no—
691C2×D4—861no—
692C2×D4—861no—
693C2×D4—861no—
694C2×D4—861no—
695C2×D4—861no—
696C2×D4—861no—
697C2×D4—862no—
698C2×D4—861no—
699C2×D4—861no—
700C2×D4—3441no—
701C2×D4—3441no—
702C2×D4—1721no—
703C2×D4—1721no—
704C2×D4—1721no—
705C2×D4—1722no—
706C22×C4—431no—
707C22×C4—431no—
708C22×C4—431no—
709C22×C4—431no—
710C22×C4—431no—
711C22×C4—431no—
712C22×C4—431no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—3441no—
726C22×C4—3441no—
727C22×C4—3441no—
728C22×C4—3441no—
729C22×C4—1722no—
730C22×C4—1722no—
731C22×C4C2×C4×D4311yescharacteristic
732C22×C4C2×C4×D4311yescharacteristic
733C22×C4C2×C4×D4311yescharacteristic
734C22×C4C2×C4×D4311yescharacteristic
735C22×C4C2×C4×D4311yescharacteristic
736C22×C4C23×D4311yescharacteristic
737M16—1722no—
738M16—1722no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—861no—
744C2×C8—861no—
745C2×C8—861no—
746C2×C8—861no—
747C2×C8—1722no—
748C2×C8—1722no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—431no—
756C4⋊C4—431no—
757C4⋊C4—431no—
758C4⋊C4—431no—
759C4⋊C4—431no—
760C4⋊C4—431no—
761C4⋊C4—431no—
762C4⋊C4—431no—
763C4⋊C4—861no—
764C4⋊C4—861no—
765C4⋊C4—861no—
766C4⋊C4—861no—
767C4⋊C4—861no—
768C4⋊C4—861no—
769C4⋊C4—861no—
770C4⋊C4—861no—
771C4⋊C4—861no—
772C4⋊C4—861no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—431no—
780C22⋊C4—431no—
781C22⋊C4—431no—
782C22⋊C4—431no—
783C22⋊C4—431no—
784C22⋊C4—431no—
785C22⋊C4—431no—
786C22⋊C4—431no—
787C22⋊C4—861no—
788C22⋊C4—861no—
789C22⋊C4—861no—
790C22⋊C4—861no—
791C22⋊C4—861no—
792C22⋊C4—861no—
793C22⋊C4—861no—
794C22⋊C4—861no—
795C22⋊C4—861no—
796C22⋊C4—861no—
797C42—431no—
798C42—431no—
799C42—431no—
800C42—431no—
801C42—861no—
802C42—861no—
803C42D4×D4311yescharacteristic
804C42D4×D4311yescharacteristic
805C42D4×D4311yescharacteristic
806C42D4×D4311yescharacteristic
807C23—21no—
808C23—21no—
809C23—21no—
810C23—41no—
811C23—41no—
812C23—431no—
813C23—431no—
814C23—432no—
815C23—861no—
816C23—861no—
817C23—861no—
818C23—861no—
819C23—861no—
820C23—861no—
821C23—861no—
822C23—1721no—
823C23—1721no—
824C23—1721no—
825C23—1721no—
826C23—1721no—
827C23—1721no—
828C23C22×C4×D4311yescharacteristic
829D4—3441no—
830D4—3441no—
831D4—3441no—
832D4—3441no—
833D4—1722no—
834D4—1722no—
835D4—1722no—
836D4—1722no—
837D4—1722no—
838D4—1722no—
839D4—1722no—
840D4—1722no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—431no—
853C2×C4—431no—
854C2×C4—431no—
855C2×C4—431no—
856C2×C4—431no—
857C2×C4—431no—
858C2×C4—862no—
859C2×C4—862no—
860C2×C4—862no—
861C2×C4—861no—
862C2×C4—861no—
863C2×C4—861no—
864C2×C4—861no—
865C2×C4—3441no—
866C2×C4—3441no—
867C2×C4—3441no—
868C2×C4—3441no—
869C2×C4—3441no—
870C2×C4—3441no—
871C2×C4—3441no—
872C2×C4—3441no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1722no—
876C2×C4—1722no—
877C2×C4—1721no—
878C2×C4—1721no—
879C2×C4—1721no—
880C2×C4C22⋊C4×D4311yescharacteristic
881C2×C4C22⋊C4×D4311yescharacteristic
882C2×C4C22⋊C4×D4311yescharacteristic
883C2×C4C22⋊C4×D4311yescharacteristic
884C2×C4C2×D4×D4311yescharacteristic
885C2×C4C2×D4×D4311yescharacteristic
886C8—41no—
887C8—41no—
888C8—41no—
889C8—41no—
890C8—1721no—
891C8—1721no—
892C8—1721no—
893C8—1721no—
894C22—21no—
895C22—21no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—81no—
900C22—81no—
901C22—862no—
902C22—861no—
903C22—861no—
904C22—861no—
905C22—861no—
906C22—861no—
907C22—861no—
908C22—3441no—
909C22—3441no—
910C22—3441no—
911C22—3441no—
912C22—1722no—
913C22—1722no—
914C22—1721no—
915C22—1721no—
916C22—1721no—
917C22—1721no—
918C22—1721no—
919C22C2×C22⋊C4×D4311yescharacteristic
920C22#131×D4311yescharacteristic
921C22#1458366411yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—21no—
927C4—21no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—432no—
932C4—861no—
933C4—861no—
934C4—861no—
935C4—861no—
936C4—861no—
937C4—1721no—
938C4—1721no—
939C2—21no—
940C2—21no—
941C2—81no—
942C2—3441no—
943C2—1721no—
944C2—1721no—
945C2—1722no—
946C2#1914304311yescharacteristic
947C2#410×D4311yescharacteristic
948C2#1914307211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1473C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583600C2
cosocleC22×C4×C43C24
hypercenter#1473D43
hypocenterC43#17415
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1473

Complements

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

NH ≅ G/Ntype
2. #19143254C2semidirect
3. #19143248C2semidirect
4. #19132964C2semidirect
5. #19132963C2semidirect
6. #19132963C2semidirect
7. #19132953C2semidirect
8. #19132953C2semidirect
9. #19132935C2semidirect
10. #19132934C2semidirect
11. #19132932C2semidirect
12. #19132915C2semidirect
13. #19132914C2semidirect
14. #19132912C2semidirect
15. C43×#1473C2semidirect
471. #1473D43semidirect
549. C43#17415semidirect

Maximal subgroups

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

subgroupindex
C2×#145836002
#191432542
#191432482
#191329642
#191329632
#191329532
#191329352
#191329342
#191329322
#191329152
#191329142
#191329122
C43×#14732
#1741543