Finite Group Databasebeta

← #25130720

Subgroups — #25130720

Order 11008.

1238 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583196C211yesmaximal, characteristic, complemented
2C2×#14583009C211yesmaximal, characteristic, complemented
3#19139508C211yesmaximal, characteristic, complemented
4#19135781C211yesmaximal, characteristic, complemented
5#19135774C211yesmaximal, characteristic, complemented
6#19135591C211yesmaximal, characteristic, complemented
7#19135591C211yesmaximal, characteristic, complemented
8#19135565C211yesmaximal, characteristic, complemented
9#19135394C211yesmaximal, characteristic, complemented
10#19134917C211yesmaximal, characteristic, complemented
11#19134912C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134788C211yesmaximal, characteristic, complemented
14#19134595C211yesmaximal, characteristic, complemented
15C2×C43×#553C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×#13063296—21no—
20C2×C4×D172C2211yescharacteristic
21#14583196—24no—
22#14583009—24no—
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×#13063245C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×#13063236C2211yescharacteristic
38#14582815—21no—
39#14582815—21no—
40#14582769C2211yescharacteristic
41#14582759C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582756—21no—
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50C43×#553—24no—
51C43×#553—24no—
52C2×#126×C43—21no—
53C2×#125×C43C2211yescharacteristic
54C2×#123×C43—21no—
55C2×#121×C43—21no—
56C2×#121×C43C2211yescharacteristic
57C2×#121×C43C2211yescharacteristic
58C2×C4×D4×C43—21no—
59C2×C4×D4×C43C2211yescharacteristic
60C2×C4×D4×C43C2211yescharacteristic
61C2×#117×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×D172C2311yescharacteristic
64C22×C22⋊D43—21no—
65C22×C22⋊D43—21no—
66C22×C4×D43—21no—
67C2×#10621882—22no—
68C2×#10621882—22no—
69C2×#10621882—22no—
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74#13063299—22no—
75#13063299—22no—
76#13063299—41no—
77#13063299—41no—
78#13063296—44no—
79C4×D172—22no—
80C4×D172—22no—
81C2×C4⋊Dic43—21no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43C2311yescharacteristic
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91#13063258—22no—
92#13063256—22no—
93#13063256—22no—
94C4⋊(C43⋊C8)—22no—
95#13063246—22no—
96#13063246—41no—
97#13063246—41no—
98#13063245—22no—
99#13063245—22no—
100#13063245—22no—
101C22⋊(C43⋊C8)—22no—
102C22⋊(C43⋊C8)—22no—
103C22⋊(C43⋊C8)—41no—
104C22⋊(C43⋊C8)—41no—
105#13063236—22no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×D4×C43—21no—
109C22×D4×C43—21no—
110C22×D4×C43D411yescharacteristic
111C22×D4×C43C2311yescharacteristic
112C23×C4×C43—21no—
113C23×C4×C43—21no—
114C23×C4×C43C2311yescharacteristic
115C23×C4×C43C2311yescharacteristic
116#126×C43—28no—
117#125×C43—22no—
118#125×C43D414yescomplemented
119#123×C43—28no—
120#121×C43—28no—
121#121×C43—22no—
122#121×C43—22no—
123#121×C43—22no—
124#121×C43—22no—
125C4×D4×C43—28no—
126C4×D4×C43—22no—
127C4×D4×C43—22no—
128C4×D4×C43—22no—
129C4×D4×C43D414yescomplemented
130#117×C43—22no—
131#117×C43—22no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—21no—
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43—22no—
137C2×C4⋊C4×C43D411yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43—21no—
144C2×C22⋊C4×C43—21no—
145C2×C22⋊C4×C43D411yescharacteristic
146C2×C22⋊C4×C43D411yescharacteristic
147C2×C42×C43—21no—
148C2×C42×C43C2311yescharacteristic
149C24×C43—21no—
150C24×C43C2×D411yescharacteristic
151C24×C43C2×D411yescharacteristic
152C23×D43—21no—
153C2×D4×C43—24no—
154C2×D4×C43—24no—
155C2×D4×C43—22no—
156C2×D4×C43—21no—
157C2×D4×C43—22no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—41no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43—81no—
166C2×D4×C43—81no—
167C2×D4×C43C2×D412yes—
168C22×C4×C43—24no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
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—24no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—81no—
186C22×C4×C43—81no—
187C22×C4×C43—81no—
188C22×C4×C43—81no—
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2411yescharacteristic
194C2×C22⋊D43—42no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—42no—
197C2×C22⋊D43—42no—
198C2×C22⋊D43—81no—
199C2×C22⋊D43—81no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—21no—
207C2×D172—21no—
208C2×D172#4112yes—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×C4×D43—42no—
212C4⋊C4×C43—24no—
213C4⋊C4×C43—24no—
214C4⋊C4×C43—24no—
215C4⋊C4×C43—22no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43C2×D412yes—
220C4⋊C4×C43C2×D412yes—
221C4⋊C4×C43C2×D412yes—
222C22⋊C4×C43—24no—
223C22⋊C4×C43—24no—
224C22⋊C4×C43—24no—
225C22⋊C4×C43—24no—
226C22⋊C4×C43—22no—
227C22⋊C4×C43—22no—
228C42×C43—24no—
229C42×C43C2×D412yes—
230C42×C43C2×D412yes—
231C22⋊Dic43—42no—
232C22⋊Dic43—42no—
233#10621882—28no—
234(C2×D43)⋊C4—42no—
235(C2×D43)⋊C4—42no—
236(C2×D43)⋊C4—42no—
237C4⋊Dic43—21no—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43—21no—
241C4⋊Dic43—21no—
242C4⋊Dic43—21no—
243C4⋊Dic43—42no—
244C4⋊Dic43—81no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8#4112yes—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—22no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43—41no—
274C23×C43—41no—
275C23×C43—41no—
276C23×C43—41no—
277C23×C43AGL(1,ℤ/8)12yes—
278C23×C43C22×D411yescharacteristic
279C22×D43—22no—
280C22×D43—41no—
281C22×D43—41no—
282C22×D43—41no—
283C22×D43—41no—
284C22×D43—41no—
285C22×D43—41no—
286D4×C43—22no—
287D4×C43—22no—
288D4×C43—44no—
289D4×C43—48no—
290D4×C43—41no—
291D4×C43—41no—
292D4×C43—84no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—21no—
301C2×C4×C43—22no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—41no—
307C2×C4×C43—41no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—41no—
311C2×C4×C43—41no—
312C2×C4×C43—41no—
313C2×C4×C43—41no—
314C2×C4×C43—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—41no—
320C2×C4×C43—84no—
321C2×C4×C43—84no—
322C2×C4×C43#12012yes—
323C2×C4×C43#12012yes—
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C22×D411yescharacteristic
326C2×C4×C43C2×#4111yescharacteristic
327C2×C4×C43C2×#4111yescharacteristic
328C2×C4×C43H(5,𝔽2)11yescharacteristic
329C2×C4×C432−1+411yescharacteristic
330C22⋊D43—84no—
331C22⋊D43—84no—
332C2×Dic43—41no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337C2×Dic43—41no—
338C2×Dic43—41no—
339C2×Dic43—41no—
340C2×Dic43—41no—
341D172—22no—
342D172—22no—
343D172—41no—
344D172—41no—
345C4×D43—84no—
346C43⋊C8—22no—
347C43⋊C8—41no—
348C43⋊C8—41no—
349C43⋊C8—41no—
350#24136—431nomaximal, Sylow
351C22×C43—22no—
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—42no—
362C22×C43—41no—
363C22×C43—42no—
364C22×C43—41no—
365C22×C43—42no—
366C22×C43—41no—
367C22×C43—41no—
368C22×C43—81no—
369C22×C43—81no—
370C22×C43—81no—
371C22×C43—81no—
372C22×C43C2×#12011yescharacteristic
373C22×C43#54611yescharacteristic
374C22×C43#54711yescharacteristic
375C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C43#57511yescharacteristic
377C22×C43#57611yescharacteristic
378C22×C43#57711yescharacteristic
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—81no—
383C2×D43—81no—
384C2×D43—81no—
385C2×D43—81no—
386C4×C43—22no—
387C4×C43—22no—
388C4×C43—41no—
389C4×C43—41no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43#52511yescharacteristic
394C4×C43#53711yescharacteristic
395C4×C43#54811yescharacteristic
396C4×C43#55011yescharacteristic
397Dic43—81no—
398Dic43—81no—
399Dic43—81no—
400C2×#553D4311yescharacteristic, complemented
401C2×#478—431no—
402C2×#442—431no—
403#2537—431no—
404#2034—431no—
405#2033—431no—
406#1999—431no—
407#1999—431no—
408#1992—431no—
409#1955—431no—
410#1875—431no—
411#1874—431no—
412#1854—431no—
413#1853—431no—
414#1802—431no—
415C2×C43—42no—
416C2×C43—81no—
417C2×C43—82no—
418C2×C43#240711yescharacteristic
419C2×C43#300611yescharacteristic
420C2×C43#301211yescharacteristic
421C2×C43#330711yescharacteristic
422C2×C43#331811yescharacteristic
423C2×C43#334511yescharacteristic
424C2×C43#334711yescharacteristic
425D43—82no—
426C22×D8—431no—
427#553—24no—
428#553—24no—
429C2×#126—21no—
430C2×#125C2×D4311yescharacteristic
431C2×#123—21no—
432C2×#121—21no—
433C2×#121—431no—
434C2×#121—431no—
435C2×#121—861no—
436C2×#121C2×D4311yescharacteristic
437C2×#121C2×D4311yescharacteristic
438C2×C4×D4—21no—
439C2×C4×D4—431no—
440C2×C4×D4C2×D4311yescharacteristic
441C2×C4×D4C2×D4311yescharacteristic
442C2×#117C2×D4311yescharacteristic
443C22×C4⋊C4C2×D4311yescharacteristic
444#478—864no—
445#442—864no—
446C2×#107—431no—
447C2×#106—431no—
448C2×#106—431no—
449C2×C4⋊C8—431no—
450C2×#102—431no—
451C2×#102—431no—
452C2×#102—431no—
453C2×#102—431no—
454C2×#102—431no—
455C2×#102—431no—
456C2×C22⋊C8—431no—
457C2×C22⋊C8—431no—
458C2×C22⋊C8—431no—
459C2×C22⋊C8—431no—
460C2×#97—431no—
461#394—861no—
462#394—861no—
463#384—431no—
464#380—431no—
465#380—431no—
466#380—861no—
467#340—431no—
468#340—431no—
469#340—431no—
470#340—431no—
471#340—431no—
472#340—431no—
473C43#2413611yescharacteristic, complemented, Sylow
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—431no—
477C22×D4—861no—
478C22×D4—861no—
479C22×D4C22⋊D4311yescharacteristic
480C22×D4C22×D4311yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—861no—
484C23×C4C22×D4311yescharacteristic
485C23×C4C22×D4311yescharacteristic
486C2×D8—862no—
487C2×D8—862no—
488C2×D8—862no—
489C22×C8—431no—
490C22×C8—431no—
491C22×C8—431no—
492C22×C8—431no—
493#126—28no—
494#125—22no—
495#125C22⋊D4314yescomplemented
496#123—28no—
497#121—28no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—862no—
503#121—862no—
504#121—1721no—
505#121—1721no—
506#121—1724no—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—862no—
512C4×D4—862no—
513C4×D4C22⋊D4314yescomplemented
514#117—22no—
515#117—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—431no—
524C2×C4⋊C4—861no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4C22⋊D4311yescharacteristic
527C2×C4⋊C4C22×D4311yescharacteristic
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C4⋊C4C22×D4311yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—861no—
535C2×C22⋊C4—861no—
536C2×C22⋊C4—861no—
537C2×C22⋊C4—861no—
538C2×C22⋊C4—861no—
539C2×C22⋊C4C22⋊D4311yescharacteristic
540C2×C22⋊C4C22⋊D4311yescharacteristic
541C2×C42—21no—
542C2×C42C22×D4311yescharacteristic
543#107—862no—
544#106—862no—
545#106—862no—
546C4⋊C8—862no—
547#102—862no—
548#102—862no—
549#102—862no—
550#102—862no—
551#102—1721no—
552#102—1721no—
553C22⋊C8—862no—
554C22⋊C8—862no—
555C22⋊C8—1721no—
556C22⋊C8—1721no—
557#97—862no—
558#95—861no—
559#95—861no—
560C24—21no—
561C24—861no—
562C24C2×C22⋊D4311yescharacteristic
563C24C2×C22⋊D4311yescharacteristic
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—24no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—41no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—81no—
577C2×D4—81no—
578C2×D4—432no—
579C2×D4—861no—
580C2×D4—861no—
581C2×D4—861no—
582C2×D4—861no—
583C2×D4—861no—
584C2×D4—3441no—
585C2×D4—3441no—
586C2×D4—1722no—
587C2×D4—1722no—
588C2×D4—1722no—
589C2×D4—1722no—
590C2×D4C2×C22⋊D4312yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—81no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—861no—
613C22×C4—861no—
614C22×C4—861no—
615C22×C4—1722no—
616C22×C4—1722no—
617C22×C4—1722no—
618C22×C4C2×C22⋊D4311yescharacteristic
619C22×C4C2×C22⋊D4311yescharacteristic
620C22×C4C2×C22⋊D4311yescharacteristic
621C22×C4C2×C22⋊D4311yescharacteristic
622C22×C4C23×D4311yescharacteristic
623D8—868no—
624C2×C8—432no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—861no—
631C2×C8—861no—
632C2×C8—861no—
633C2×C8—861no—
634C2×C8—861no—
635C2×C8—861no—
636C4⋊C4—24no—
637C4⋊C4—24no—
638C4⋊C4—24no—
639C4⋊C4—22no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—861no—
644C4⋊C4—861no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—861no—
648C4⋊C4—861no—
649C4⋊C4—3441no—
650C4⋊C4—1722no—
651C4⋊C4C2×C22⋊D4312yes—
652C4⋊C4C2×C22⋊D4312yes—
653C4⋊C4C2×C22⋊D4312yes—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—1722no—
661C22⋊C4—1722no—
662C22⋊C4—1722no—
663C22⋊C4—1722no—
664C22⋊C4—1722no—
665C42—24no—
666C42C2×C22⋊D4312yes—
667C42C2×C22⋊D4312yes—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—862no—
689C23—1721no—
690C23—1721no—
691C23—1721no—
692C23—1721no—
693C23—1721no—
694C23—1721no—
695C23#1306335012yes—
696C23C22×C22⋊D4311yescharacteristic
697D4—22no—
698D4—22no—
699D4—44no—
700D4—48no—
701D4—41no—
702D4—41no—
703D4—84no—
704D4—862no—
705D4—862no—
706D4—3444no—
707D4—3444no—
708D4—1721no—
709D4—1721no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4—3444no—
740C2×C4—1721no—
741C2×C4—1721no—
742C2×C4—1721no—
743C2×C4—1721no—
744C2×C4—1721no—
745C2×C4—1721no—
746C2×C4—1721no—
747C2×C4—1721no—
748C2×C4—1721no—
749C2×C4#1306329412yes—
750C2×C4#1306329412yes—
751C2×C4C22×C22⋊D4311yescharacteristic
752C2×C4C22×C22⋊D4311yescharacteristic
753C2×C4#41×D4311yescharacteristic
754C2×C4#41×D4311yescharacteristic
755C2×C4#1306337111yescharacteristic
756C2×C4#1306337211yescharacteristic
757C8—862no—
758C8—1721no—
759C8—1721no—
760C8—1721no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—3441no—
783C22—3441no—
784C22—3441no—
785C22—3441no—
786C22—1722no—
787C22—1722no—
788C22—1722no—
789C22C2×#1306329411yescharacteristic
790C22#1458353711yescharacteristic
791C22#1458354811yescharacteristic
792C22C2×#1306335011yescharacteristic
793C22#1458369711yescharacteristic
794C22#1458370211yescharacteristic
795C22#1458371011yescharacteristic
796C4—22no—
797C4—22no—
798C4—41no—
799C4—41no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—3441no—
804C4—3441no—
805C4—3441no—
806C4#1458340611yescharacteristic
807C4#1458347711yescharacteristic
808C4#1458355611yescharacteristic
809C4#1458356811yescharacteristic
810C2—42no—
811C2—81no—
812C2—82no—
813C2—3442no—
814C2#1913793411yescharacteristic
815C2#1914384711yescharacteristic
816C2#1914389911yescharacteristic
817C2#1914656511yescharacteristic
818C2#1914673011yescharacteristic
819C2#1914705911yescharacteristic
820C2#1914708911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#553C2
socleC23×C43C22×D4
hypercenterC2×#553D43
hypocenterC43#24136
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#14583196C2semidirect
2. C2×#14583009C2semidirect
3. #19139508C2semidirect
4. #19135781C2semidirect
5. #19135774C2semidirect
6. #19135591C2semidirect
7. #19135591C2semidirect
8. #19135565C2semidirect
9. #19135394C2semidirect
10. #19134917C2semidirect
11. #19134912C2semidirect
12. #19134794C2semidirect
13. #19134788C2semidirect
14. #19134595C2semidirect
15. C2×C43×#553C2semidirect
118. #125×C43D4semidirect
129. C4×D4×C43D4semidirect
400. C2×#553D43semidirect
473. C43#24136semidirect
495. #125C22⋊D43semidirect
513. C4×D4C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831962
C2×#145830092
#191395082
#191357812
#191357742
#191355912
#191355652
#191353942
#191349172
#191349122
#191347942
#191347882
#191345952
C2×C43×#5532
#2413643