Finite Group Databasebeta

← #25105527

Subgroups — #25105527

Order 11008.

1426 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583446C211yesmaximal, characteristic
2C2×#14582867C211yesmaximal, characteristic, complemented
3C2×#14582864C211yesmaximal, characteristic, complemented
4#19134892C211yesmaximal, characteristic, complemented
5#19134891C211yesmaximal, characteristic, complemented
6#19134889C211yesmaximal, characteristic, complemented
7#19134888C211yesmaximal, characteristic, complemented
8#19134886C211yesmaximal, characteristic, complemented
9#19134885C211yesmaximal, characteristic, complemented
10#19134884C211yesmaximal, characteristic, complemented
11#19134662C211yesmaximal, characteristic, complemented
12#19134662C211yesmaximal, characteristic, complemented
13#19134506C211yesmaximal, characteristic, complemented
14#19134506C211yesmaximal, characteristic, complemented
15C43×#1870C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621898C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C22×C8×D43C2211yescharacteristic
21#14583446—24no—
22#14583446—24no—
23C2×#13063324C411yescharacteristic
24C2×#13063321C411yescharacteristic
25C2×#13063311C411yescharacteristic
26C2×#13063311C411yescharacteristic
27C2×#13063300C411yescharacteristic
28C2×#13063298C411yescharacteristic
29C2×#13063298C411yescharacteristic
30C2×#13063296C411yescharacteristic
31C2×C4×D172C2211yescharacteristic
32C2×C4×C22⋊D43C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×C42×D43C2211yescharacteristic
35#14582867—24no—
36#14582864—24no—
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×(C2×D43)⋊C8C2211yescharacteristic
48C2×(C2×D43)⋊C8C2211yescharacteristic
49C2×(C2×D43)⋊C8C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×M16×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C2×#10621898—41no—
70C2×#10621898—41no—
71C2×#10621898—41no—
72C2×#10621898—41no—
73C2×#10621898D414yes—
74C2×#10621898D414yes—
75C22×Dic86C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C22×D172C2×C411yescharacteristic
78C22×D172C2×C411yescharacteristic
79C22×D172C2×C411yescharacteristic
80C22×C22⋊D43C2×C411yescharacteristic
81C22×C22⋊D43C2×C411yescharacteristic
82C22×C22⋊D43C2×C411yescharacteristic
83C22×C22⋊D43C2×C411yescharacteristic
84C22×C22⋊D43C2×C411yescharacteristic
85C22×C22⋊D43C2×C411yescharacteristic
86C22×C4×D43C2×C411yescharacteristic
87C22×C4×D43C2×C411yescharacteristic
88C22×C4×D43C2311yescharacteristic
89C22×C4×D43C2311yescharacteristic
90C22×C4×D43C2311yescharacteristic
91C2×#10621872—22no—
92C2×#10621872—41no—
93C2×#10621872—41no—
94C22×C43⋊C8—22no—
95C22×C43⋊C8—41no—
96C22×C43⋊C8—41no—
97C22×C43⋊C8C2311yescharacteristic
98C22×C43⋊C8C2311yescharacteristic
99C22×C43⋊C8C2311yescharacteristic
100C22×C43⋊C8C2311yescharacteristic
101C2×C8×D43—22no—
102C2×C8×D43—41no—
103C2×C8×D43—41no—
104#13063324—24no—
105#13063321—24no—
106#13063311—24no—
107#13063311—24no—
108#13063300—24no—
109#13063298—24no—
110#13063298—24no—
111#13063296—24no—
112C4×D172—22no—
113C4×D172—22no—
114C4×C22⋊D43—22no—
115C4×C22⋊D43—22no—
116C4×C22⋊D43—22no—
117C4×C22⋊D43—22no—
118C2×C4⋊Dic43C2×C411yescharacteristic
119C2×Dic43⋊C4C2×C411yescharacteristic
120C2×Dic43⋊C4C2×C411yescharacteristic
121C2×C22⋊Dic43C2×C411yescharacteristic
122C2×C22⋊Dic43C2×C411yescharacteristic
123C2×(C2×D43)⋊C4C2×C411yescharacteristic
124C2×(C2×D43)⋊C4C2×C411yescharacteristic
125C2×(C2×D43)⋊C4C2×C411yescharacteristic
126C2×(C2×D43)⋊C4C2×C411yescharacteristic
127C2×C4×Dic43C2×C411yescharacteristic
128C2×C4×Dic43C2×C411yescharacteristic
129C2×C4×Dic43C2311yescharacteristic
130C42×D43—22no—
131C42×D43—22no—
132C22⋊(C43⋊C8)—22no—
133C22⋊(C43⋊C8)—41no—
134C22⋊(C43⋊C8)—41no—
135(C2×D43)⋊C8—22no—
136(C2×D43)⋊C8—22no—
137(C2×D43)⋊C8—22no—
138(C2×D43)⋊C8—22no—
139(C2×D43)⋊C8—22no—
140(C2×D43)⋊C8—22no—
141(C2×D43)⋊C8—41no—
142(C2×D43)⋊C8—41no—
143(C2×D43)⋊C8—41no—
144(C2×D43)⋊C8—41no—
145C22×D4×C43C2×C411yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C2×M16×C43—22no—
149C2×M16×C43—41no—
150C2×M16×C43—41no—
151C22×C8×C43C2311yescharacteristic
152C22×C8×C43C2311yescharacteristic
153C22×C8×C43C2311yescharacteristic
154C22×C8×C43C2311yescharacteristic
155C4×D4×C43—22no—
156C4×D4×C43—22no—
157C2×C4⋊C4×C43C2×C411yescharacteristic
158C2×C22⋊C4×C43C2×C411yescharacteristic
159C2×C22⋊C4×C43C2×C411yescharacteristic
160C2×C42×C43C2311yescharacteristic
161C22⋊C8×C43—22no—
162C22⋊C8×C43—41no—
163C22⋊C8×C43—41no—
164C24×C43C22×C411yescharacteristic
165C24×C43C22×C411yescharacteristic
166C23×D43C22×C411yescharacteristic
167C23×D43C22×C411yescharacteristic
168C23×D43C22×C411yescharacteristic
169C2×D4×C43—22no—
170C2×D4×C43—22no—
171C2×D4×C43—41no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43C22×C411yescharacteristic
183C22×C4×C43C22×C411yescharacteristic
184C22×C4×C43C22×C411yescharacteristic
185C22×C4×C43C22×C411yescharacteristic
186C22×C4×C43C2×D412yes—
187C22×C4×C43C2×D412yes—
188C22×C4×C43C2411yescharacteristic
189C2×C22⋊D43—22no—
190C2×C22⋊D43—22no—
191C2×C22⋊D43—22no—
192C2×C22⋊D43—22no—
193C2×C22⋊D43—22no—
194C2×C22⋊D43—22no—
195C2×C22⋊D43—41no—
196C2×C22⋊D43—41no—
197C2×C22⋊D43—41no—
198C2×C22⋊D43—41no—
199C2×C22⋊D43—41no—
200C2×C22⋊D43—41no—
201C2×C22⋊D43—41no—
202C2×C22⋊D43—41no—
203C2×C22⋊D43—41no—
204C2×C22⋊D43—41no—
205C2×C22⋊D43C22⋊C414yes—
206C2×C22⋊D43C22⋊C414yes—
207C22×Dic43C22×C411yescharacteristic
208C22×Dic43C22×C411yescharacteristic
209C22×Dic43C22×C411yescharacteristic
210C22×Dic43C22×C411yescharacteristic
211C22×Dic43C22×C411yescharacteristic
212#10621898—44no—
213#10621898—44no—
214#10621898—44no—
215#10621898—44no—
216#10621898—44no—
217#10621898—44no—
218#10621898—44no—
219#10621898—44no—
220C2×D172—22no—
221C2×D172—22no—
222C2×D172—22no—
223C2×D172—41no—
224C2×D172—41no—
225C2×D172—41no—
226C2×D172—41no—
227C2×D172—41no—
228C2×D172C22⋊C414yes—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×C4×D43—22no—
238C2×C4×D43—21no—
239C2×C4×D43—21no—
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—22no—
245C2×C4×D43—22no—
246C2×C4×D43—22no—
247C2×C4×D43—41no—
248C2×C4×D43—41no—
249C2×C4×D43C2×D412yes—
250C2×C4×D43C2×D412yes—
251C2×C4×D43C2×D412yes—
252C2×C4×D43C2×D412yes—
253C2×Dic86—22no—
254C2×Dic86—41no—
255C2×Dic86—41no—
256C2×Dic86—41no—
257C2×Dic86—41no—
258C2×Dic86C22⋊C414yes—
259M16×C43—44no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—21no—
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C2×C8×C43—21no—
271C2×C8×C43—21no—
272C4⋊C4×C43—22no—
273C22⋊C4×C43—22no—
274C22⋊C4×C43—22no—
275C42×C43—21no—
276C42×C43—21no—
277C22⋊Dic43—22no—
278C22⋊Dic43—22no—
279(C2×D43)⋊C4—22no—
280(C2×D43)⋊C4—22no—
281(C2×D43)⋊C4—22no—
282(C2×D43)⋊C4—22no—
283C4⋊Dic43—22no—
284Dic43⋊C4—22no—
285Dic43⋊C4—22no—
286C4×Dic43—21no—
287C4×Dic43—21no—
288C4×Dic43—22no—
289C4×Dic43—22no—
290C2×C43⋊C8—21no—
291C2×C43⋊C8—21no—
292C2×C43⋊C8—21no—
293C2×C43⋊C8—21no—
294C2×C43⋊C8—21no—
295C2×C43⋊C8—21no—
296C2×C43⋊C8—21no—
297C2×C43⋊C8—21no—
298C2×C43⋊C8—21no—
299C2×C43⋊C8—21no—
300C2×C43⋊C8—21no—
301C2×C43⋊C8—21no—
302C2×C43⋊C8—44no—
303#10621872—44no—
304C8×D43—44no—
305C23×C43—21no—
306C23×C43—21no—
307C23×C43—21no—
308C23×C43—21no—
309C23×C43—21no—
310C23×C43—21no—
311C23×C43—21no—
312C23×C43—21no—
313C23×C43—21no—
314C23×C43—21no—
315C23×C43—21no—
316C23×C43—21no—
317C23×C43—21no—
318C23×C43C2×C22⋊C412yes—
319C23×C43C23×C411yescharacteristic
320C22×D43—21no—
321C22×D43—21no—
322C22×D43—21no—
323C22×D43—21no—
324C22×D43—21no—
325C22×D43—21no—
326C22×D43—21no—
327C22×D43—21no—
328C22×D43—21no—
329C22×D43—21no—
330C22×D43—21no—
331C22×D43—21no—
332C22×D43—21no—
333C22×D43—21no—
334C22×D43—21no—
335C22×D43—21no—
336C22×D43—21no—
337C22×D43—21no—
338C22×D43—21no—
339C22×D43C2×C22⋊C412yes—
340C22×D43C2×C22⋊C412yes—
341D4×C43—44no—
342C2×C4×C43—21no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43C2×C22⋊C412yes—
361C2×C4×C43#13112yes—
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43H(5,𝔽2)11yescharacteristic
365C2×C4×C43H(5,𝔽2)11yescharacteristic
366C2×C4×C43H(5,𝔽2)11yescharacteristic
367C2×C4×C43H(5,𝔽2)11yescharacteristic
368C22⋊D43—44no—
369C22⋊D43—44no—
370C22⋊D43—44no—
371C22⋊D43—44no—
372C22⋊D43—44no—
373C22⋊D43—44no—
374C2×Dic43—21no—
375C2×Dic43—21no—
376C2×Dic43—21no—
377C2×Dic43—21no—
378C2×Dic43—21no—
379C2×Dic43—21no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—21no—
386C2×Dic43C2×C22⋊C412yes—
387C2×Dic43C2×C22⋊C412yes—
388C2×Dic43#13112yes—
389D172—44no—
390D172—44no—
391D172—44no—
392C4×D43—22no—
393C4×D43—22no—
394C4×D43—22no—
395C4×D43—22no—
396C4×D43—22no—
397C4×D43—22no—
398C4×D43—22no—
399C4×D43—22no—
400C4×D43—44no—
401C4×D43—44no—
402C4×D43—41no—
403C4×D43—41no—
404C4×D43—41no—
405C4×D43—41no—
406Dic86—44no—
407Dic86—44no—
408C8×C43—41no—
409C8×C43—41no—
410C8×C43—41no—
411C8×C43—41no—
412C43⋊C8—41no—
413C43⋊C8—41no—
414C43⋊C8—41no—
415C43⋊C8—41no—
416#21745—431nomaximal, Sylow
417C22×C43—22no—
418C22×C43—22no—
419C22×C43—22no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43—41no—
427C22×C43—41no—
428C22×C43—41no—
429C22×C43—41no—
430C22×C43—41no—
431C22×C43C22×C22⋊C411yescharacteristic
432C22×C43#51811yescharacteristic
433C22×C43#51811yescharacteristic
434C22×C43C2×#13111yescharacteristic
435C22×C43C2×#13111yescharacteristic
436C22×C43#56811yescharacteristic
437C22×C43#56811yescharacteristic
438C2×D43—22no—
439C2×D43—22no—
440C2×D43—22no—
441C2×D43—22no—
442C2×D43—22no—
443C2×D43—22no—
444C2×D43—41no—
445C2×D43—41no—
446C2×D43—41no—
447C2×D43—41no—
448C2×D43—41no—
449C2×D43—41no—
450C2×D43—41no—
451C2×D43—41no—
452C2×D43—41no—
453C2×D43—41no—
454C2×D43—41no—
455C2×D43—41no—
456C2×D43—41no—
457C2×D43—41no—
458C2×D43—41no—
459C4×C43—22no—
460C4×C43—22no—
461C4×C43—41no—
462C4×C43—41no—
463C4×C43#53411yescharacteristic
464C4×C43#53411yescharacteristic
465C4×C43#53411yescharacteristic
466C4×C43#53411yescharacteristic
467Dic43—22no—
468Dic43—22no—
469Dic43—22no—
470Dic43—41no—
471Dic43—41no—
472C2×#532—431no—
473C2×#408—431no—
474C2×#408—431no—
475#1870—431no—
476#1870—431no—
477#1870—431no—
478#1870D4311yescharacteristic, complemented
479#1869—431no—
480#1869—431no—
481#1869—431no—
482#1869—431no—
483#1817—431no—
484#1817—431no—
485#1780—431no—
486#1780—431no—
487C2×C43—42no—
488C2×C43—81no—
489C2×C43#230811yescharacteristic
490C2×C43#288011yescharacteristic
491C2×C43#288011yescharacteristic
492C2×C43#297911yescharacteristic
493C2×C43#298011yescharacteristic
494C2×C43#298111yescharacteristic
495C2×C43#298111yescharacteristic
496D43—42no—
497D43—42no—
498D43—81no—
499C22×#41—431no—
500C22×#41—431no—
501C22×M16—431no—
502C22×M16C2×D4311yescharacteristic
503C23×C8—431no—
504C23×C8—431no—
505#532—864no—
506#532—864no—
507C2×C4⋊Q8—431no—
508C2×#127—431no—
509C2×#124—431no—
510C2×#124—431no—
511C2×#121—431no—
512C2×#121—431no—
513C2×#121—431no—
514C2×#121—431no—
515C2×C4×D4—431no—
516C2×C4×D4—431no—
517C2×C4×D4—431no—
518C2×C4×D4C2×D4311yescharacteristic
519C22×C42—431no—
520#408—864no—
521#408—864no—
522C2×C22⋊C8—431no—
523C2×C22⋊C8—431no—
524C2×C22⋊C8—431no—
525C2×C22⋊C8—431no—
526C2×C22⋊C8—431no—
527C2×C22⋊C8—431no—
528C2×C22⋊C8—431no—
529C2×C22⋊C8—431no—
530C2×C22⋊C8—431no—
531C2×C22⋊C8—431no—
532C2×C22⋊C8—431no—
533C2×C22⋊C8—431no—
534C2×C22⋊C8—431no—
535C2×C22⋊C8C2×D4311yescharacteristic
536C2×C22⋊C8C2×D4311yescharacteristic
537C2×C22⋊C8C2×D4311yescharacteristic
538#336—431no—
539#336—431no—
540#336—431no—
541#336—431no—
542#336—431no—
543#336—431no—
544#336C2×D4311yescharacteristic
545#336C2×D4311yescharacteristic
546C43#2174511yescharacteristic, complemented, Sylow
547C2×#41—434no—
548C2×#41—434no—
549C2×#41—862no—
550C2×#41—862no—
551C2×#41—1721no—
552C2×#41—1721no—
553C2×#41—1721no—
554C2×#41—1721no—
555C2×#41—1721no—
556C2×#41—1721no—
557C2×#41—1721no—
558C2×#41—1721no—
559C22×Q8—431no—
560C22×Q8—431no—
561C22×D4—431no—
562C22×D4—431no—
563C22×D4—431no—
564C22×D4—431no—
565C22×D4—431no—
566C22×D4—431no—
567C22×D4—431no—
568C22×D4—431no—
569C22×D4—431no—
570C22×D4C4×D4311yescharacteristic
571C23×C4—431no—
572C23×C4—431no—
573C23×C4—431no—
574C23×C4—431no—
575C23×C4—431no—
576C23×C4C22×D4311yescharacteristic
577C23×C4C22×D4311yescharacteristic
578C2×M16—22no—
579C2×M16—41no—
580C2×M16—41no—
581C2×M16—862no—
582C2×M16—1721no—
583C2×M16—1721no—
584C22×C8—431no—
585C22×C8—431no—
586C22×C8—431no—
587C22×C8—431no—
588C22×C8—862no—
589C22×C8—862no—
590C22×C8—1721no—
591C22×C8—1721no—
592C22×C8—1721no—
593C22×C8—1721no—
594C22×C8C22×D4311yescharacteristic
595C22×C8C22×D4311yescharacteristic
596C22×C8C22×D4311yescharacteristic
597C22×C8C22×D4311yescharacteristic
598C4⋊Q8—864no—
599#127—864no—
600#124—864no—
601#124—864no—
602#121—864no—
603#121—864no—
604#121—864no—
605#121—864no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4—862no—
609C4×D4—862no—
610C4×D4—862no—
611C4×D4—862no—
612C4×D4—862no—
613C4×D4—862no—
614C2×C4⋊C4—431no—
615C2×C4⋊C4—431no—
616C2×C4⋊C4—431no—
617C2×C4⋊C4C4×D4311yescharacteristic
618C2×C22⋊C4—431no—
619C2×C22⋊C4—431no—
620C2×C22⋊C4—431no—
621C2×C22⋊C4—431no—
622C2×C22⋊C4—431no—
623C2×C22⋊C4—431no—
624C2×C22⋊C4C4×D4311yescharacteristic
625C2×C22⋊C4C4×D4311yescharacteristic
626C2×C42—431no—
627C2×C42—431no—
628C2×C42—431no—
629C2×C42—862no—
630C2×C42—862no—
631C2×C42C22×D4311yescharacteristic
632C22⋊C8—22no—
633C22⋊C8—41no—
634C22⋊C8—41no—
635C22⋊C8—862no—
636C22⋊C8—862no—
637C22⋊C8—862no—
638C22⋊C8—862no—
639C22⋊C8—862no—
640C22⋊C8—862no—
641C22⋊C8—862no—
642C22⋊C8—1721no—
643C22⋊C8—1721no—
644C22⋊C8—1721no—
645C22⋊C8—1721no—
646C22⋊C8—1721no—
647C22⋊C8—1721no—
648C24—431no—
649C24—431no—
650C24—431no—
651C24C2×C4×D4311yescharacteristic
652C24C2×C4×D4311yescharacteristic
653#41—1724no—
654#41—1724no—
655#41—1724no—
656#41—1724no—
657#41—1724no—
658#41—1724no—
659#41—1724no—
660#41—1724no—
661C2×Q8—434no—
662C2×Q8—862no—
663C2×Q8—1721no—
664C2×Q8—1721no—
665C2×Q8—1721no—
666C2×Q8—1721no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—41no—
670C2×D4—434no—
671C2×D4—434no—
672C2×D4—434no—
673C2×D4—862no—
674C2×D4—862no—
675C2×D4—862no—
676C2×D4—862no—
677C2×D4—862no—
678C2×D4—862no—
679C2×D4—862no—
680C2×D4—862no—
681C2×D4—862no—
682C2×D4—1721no—
683C2×D4—1721no—
684C2×D4—1721no—
685C2×D4—1721no—
686C2×D4—1721no—
687C2×D4—1721no—
688C2×D4—1721no—
689C2×D4—1721no—
690C2×D4—1721no—
691C2×D4—1721no—
692C2×D4—1721no—
693C2×D4—1721no—
694C2×D4—1721no—
695C2×D4—1721no—
696C2×D4—1721no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—431no—
708C22×C4—431no—
709C22×C4—431no—
710C22×C4—432no—
711C22×C4—432no—
712C22×C4—432no—
713C22×C4—432no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—862no—
717C22×C4—862no—
718C22×C4—862no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—862no—
728C22×C4—861no—
729C22×C4—861no—
730C22×C4—861no—
731C22×C4—861no—
732C22×C4—861no—
733C22×C4—861no—
734C22×C4—1721no—
735C22×C4—1721no—
736C22×C4C2×C4×D4311yescharacteristic
737C22×C4C2×C4×D4311yescharacteristic
738C22×C4C2×C4×D4311yescharacteristic
739C22×C4C2×C4×D4311yescharacteristic
740C22×C4D4×D4312yes—
741C22×C4D4×D4312yes—
742C22×C4C23×D4311yescharacteristic
743M16—44no—
744M16—1724no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—861no—
758C2×C8—861no—
759C2×C8—861no—
760C2×C8—861no—
761C2×C8—861no—
762C2×C8—861no—
763C2×C8—861no—
764C2×C8—861no—
765C2×C8—861no—
766C2×C8—861no—
767C2×C8—861no—
768C2×C8—861no—
769C2×C8—1724no—
770C2×C8—1724no—
771C4⋊C4—22no—
772C4⋊C4—862no—
773C4⋊C4—862no—
774C4⋊C4—862no—
775C22⋊C4—22no—
776C22⋊C4—22no—
777C22⋊C4—862no—
778C22⋊C4—862no—
779C22⋊C4—862no—
780C22⋊C4—862no—
781C22⋊C4—862no—
782C22⋊C4—862no—
783C42—21no—
784C42—21no—
785C42—862no—
786C42—862no—
787C42—861no—
788C42—861no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—432no—
803C23—432no—
804C23—861no—
805C23—861no—
806C23—861no—
807C23—861no—
808C23—861no—
809C23—861no—
810C23—861no—
811C23—861no—
812C23—861no—
813C23—861no—
814C23—861no—
815C23—861no—
816C23—861no—
817C23—861no—
818C23—861no—
819C23—861no—
820C23—861no—
821C23—861no—
822C23—861no—
823C23C22⋊C4×D4312yes—
824C23C22×C4×D4311yescharacteristic
825Q8—1724no—
826Q8—1724no—
827D4—44no—
828D4—1724no—
829D4—1724no—
830D4—1724no—
831D4—1724no—
832D4—1724no—
833D4—1724no—
834D4—1724no—
835D4—1724no—
836D4—1724no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—432no—
856C2×C4—432no—
857C2×C4—432no—
858C2×C4—861no—
859C2×C4—861no—
860C2×C4—861no—
861C2×C4—861no—
862C2×C4—861no—
863C2×C4—861no—
864C2×C4—862no—
865C2×C4—862no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—862no—
869C2×C4—862no—
870C2×C4—862no—
871C2×C4—862no—
872C2×C4—861no—
873C2×C4—861no—
874C2×C4—861no—
875C2×C4—861no—
876C2×C4—861no—
877C2×C4—861no—
878C2×C4—1724no—
879C2×C4—1724no—
880C2×C4—1721no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4C22⋊C4×D4312yes—
885C2×C4#1306333312yes—
886C2×C4C2×D4×D4311yescharacteristic
887C2×C4C2×D4×D4311yescharacteristic
888C2×C4#1306337011yescharacteristic
889C2×C4#1306337011yescharacteristic
890C2×C4#1306337111yescharacteristic
891C2×C4#1306337111yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C8—1721no—
897C8—1721no—
898C8—1721no—
899C8—1721no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—862no—
915C22—862no—
916C22—862no—
917C22—862no—
918C22—862no—
919C22—862no—
920C22—1721no—
921C22—1721no—
922C22—1721no—
923C22—1721no—
924C22—1721no—
925C22—1721no—
926C22—1721no—
927C22—1721no—
928C22—1721no—
929C22—1721no—
930C22—1721no—
931C22—1721no—
932C22—1721no—
933C22—1721no—
934C22—1721no—
935C22C2×C22⋊C4×D4311yescharacteristic
936C22#1458337111yescharacteristic
937C22#1458337111yescharacteristic
938C22#131×D4311yescharacteristic
939C22C2×#1306333311yescharacteristic
940C22#1458366411yescharacteristic
941C22#1458366511yescharacteristic
942C4—22no—
943C4—22no—
944C4—41no—
945C4—41no—
946C4—862no—
947C4—862no—
948C4—862no—
949C4—1721no—
950C4—1721no—
951C4#1458345711yescharacteristic
952C4#1458345711yescharacteristic
953C4#1458345911yescharacteristic
954C4#1458346011yescharacteristic
955C2—42no—
956C2—81no—
957C2—3441no—
958C2—1722no—
959C2—1722no—
960C2#1913716911yescharacteristic
961C2#1914304311yescharacteristic
962C2#1914304511yescharacteristic
963C2#1914366011yescharacteristic
964C2#1914366311yescharacteristic
965C2#1914366711yescharacteristic
966C2#1914367211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1870C2
prime radicalC2×#14583446C2
cosocleC22×C4×C43C24
hypercenter#1870D43
hypocenterC43#21745
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#14582867C2semidirect
3. C2×#14582864C2semidirect
4. #19134892C2semidirect
5. #19134891C2semidirect
6. #19134889C2semidirect
7. #19134888C2semidirect
8. #19134886C2semidirect
9. #19134885C2semidirect
10. #19134884C2semidirect
11. #19134662C2semidirect
12. #19134662C2semidirect
13. #19134506C2semidirect
14. #19134506C2semidirect
15. C43×#1870C2semidirect
478. #1870D43semidirect
546. C43#21745semidirect

Maximal subgroups

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

subgroupindex
C2×#145834462
C2×#145828672
C2×#145828642
#191348922
#191348912
#191348892
#191348882
#191348862
#191348852
#191348842
#191346622
#191345062
C43×#18702
#2174543