Finite Group Databasebeta

← #25128766

Subgroups — #25128766

Order 11008.

1338 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583042C211yesmaximal, characteristic, complemented
2C2×#14582893C211yesmaximal, characteristic, complemented
3#19137940C211yesmaximal, characteristic, complemented
4#19135743C211yesmaximal, characteristic, complemented
5#19135738C211yesmaximal, characteristic, complemented
6#19135598C211yesmaximal, characteristic, complemented
7#19135591C211yesmaximal, characteristic, complemented
8#19135024C211yesmaximal, characteristic, complemented
9#19134943C211yesmaximal, characteristic, complemented
10#19134929C211yesmaximal, characteristic, complemented
11#19134912C211yesmaximal, characteristic, complemented
12#19134902C211yesmaximal, characteristic, complemented
13#19134888C211yesmaximal, characteristic, complemented
14#19134690C211yesmaximal, characteristic, complemented
15C2×C43×#553C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621883C2211yescharacteristic
18C22×#10621882C2211yescharacteristic
19C23×C43⋊C8C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063299C2211yescharacteristic
22#14583042—24no—
23#14582893—24no—
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063246C2211yescharacteristic
29C2×#13063245C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×#13063245C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35#14582814—21no—
36#14582807—21no—
37#14582805C2211yescharacteristic
38#14582801C2211yescharacteristic
39#14582775—21no—
40#14582770—21no—
41#14582759C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
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
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C22×Dic86C2311yescharacteristic
70C22×D172C2311yescharacteristic
71C22×C22⋊D43—21no—
72C22×C22⋊D43—21no—
73C22×C4×D43—21no—
74C2×#10621883—22no—
75C2×#10621883—22no—
76C2×#10621883—41no—
77C2×#10621882—22no—
78C2×#10621882—22no—
79C2×#10621882—41no—
80C22×C43⋊C8—22no—
81C22×C43⋊C8—41no—
82C22×C43⋊C8—41no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C22×C43⋊C8C2311yescharacteristic
86C22×C43⋊C8C2311yescharacteristic
87#13063304—22no—
88#13063304—41no—
89#13063299—22no—
90#13063299—41no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×C22⋊Dic43—21no—
95C2×C22⋊Dic43—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99#13063248—22no—
100#13063248—22no—
101#13063248—22no—
102#13063246—41no—
103#13063246—41no—
104#13063245—22no—
105#13063245—22no—
106#13063245—22no—
107C22⋊(C43⋊C8)—22no—
108C22⋊(C43⋊C8)—41no—
109C22⋊(C43⋊C8)—41no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×D4×C43—21no—
114C22×D4×C43—21no—
115C22×D4×C43D411yescharacteristic
116C22×D4×C43C2311yescharacteristic
117C23×C4×C43—21no—
118C23×C4×C43—21no—
119C23×C4×C43C2311yescharacteristic
120C23×C4×C43C2311yescharacteristic
121#126×C43—28no—
122#125×C43—22no—
123#125×C43—22no—
124#123×C43—28no—
125#121×C43—28no—
126#121×C43—22no—
127#121×C43—22no—
128#121×C43—22no—
129#121×C43D414yescomplemented
130C4×D4×C43—28no—
131C4×D4×C43—22no—
132C4×D4×C43—22no—
133C4×D4×C43—22no—
134C4×D4×C43—22no—
135#117×C43—22no—
136#117×C43D414yescomplemented
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43—21no—
139C2×C4⋊C4×C43—21no—
140C2×C4⋊C4×C43—22no—
141C2×C4⋊C4×C43—22no—
142C2×C4⋊C4×C43D411yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C4⋊C4×C43C2311yescharacteristic
145C2×C4⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43—21no—
147C2×C22⋊C4×C43—21no—
148C2×C22⋊C4×C43—21no—
149C2×C22⋊C4×C43—21no—
150C2×C22⋊C4×C43D411yescharacteristic
151C2×C22⋊C4×C43D411yescharacteristic
152C2×C42×C43—21no—
153C2×C42×C43C2311yescharacteristic
154C24×C43—21no—
155C24×C43C2×D411yescharacteristic
156C24×C43C2×D411yescharacteristic
157C23×D43—21no—
158C2×D4×C43—24no—
159C2×D4×C43—21no—
160C2×D4×C43—22no—
161C2×D4×C43—24no—
162C2×D4×C43—22no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—41no—
168C2×D4×C43—42no—
169C2×D4×C43—42no—
170C2×D4×C43—81no—
171C2×D4×C43—81no—
172C2×D4×C43C2×D412yes—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—24no—
178C22×C4×C43—24no—
179C22×C4×C43—21no—
180C22×C4×C43—21no—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—81no—
189C22×C4×C43—81no—
190C22×C4×C43—81no—
191C22×C4×C43—81no—
192C22×C4×C43C2×D412yes—
193C22×C4×C43C2×D412yes—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—42no—
200C2×C22⋊D43—42no—
201C2×C22⋊D43—42no—
202C2×C22⋊D43—42no—
203C2×C22⋊D43—42no—
204C2×C22⋊D43—81no—
205C22×Dic43—21no—
206C22×Dic43—21no—
207C22×Dic43—21no—
208#10621898—28no—
209#10621898—44no—
210#10621898—44no—
211#10621898—44no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—21no—
217C2×D172#4112yes—
218C2×C4×D43—42no—
219C2×C4×D43—42no—
220C2×C4×D43—42no—
221C2×Dic86—21no—
222C2×Dic86—21no—
223C2×Dic86—21no—
224C2×Dic86—21no—
225C2×Dic86—21no—
226C2×Dic86#4112yes—
227C4⋊C4×C43—24no—
228C4⋊C4×C43—24no—
229C4⋊C4×C43—24no—
230C4⋊C4×C43—22no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C2×D412yes—
235C4⋊C4×C43C2×D412yes—
236C4⋊C4×C43C2×D412yes—
237C22⋊C4×C43—24no—
238C22⋊C4×C43—24no—
239C22⋊C4×C43—24no—
240C22⋊C4×C43—22no—
241C22⋊C4×C43—24no—
242C22⋊C4×C43—22no—
243C42×C43—24no—
244C42×C43—21no—
245C42×C43—21no—
246C22⋊Dic43—42no—
247C22⋊Dic43—81no—
248#10621883—44no—
249#10621882—44no—
250(C2×D43)⋊C4—42no—
251(C2×D43)⋊C4—42no—
252(C2×D43)⋊C4—81no—
253C4⋊Dic43—21no—
254C4⋊Dic43—21no—
255C4⋊Dic43—21no—
256C4⋊Dic43—21no—
257Dic43⋊C4—42no—
258C2×C43⋊C8—21no—
259C2×C43⋊C8—21no—
260C2×C43⋊C8—21no—
261C2×C43⋊C8—21no—
262C2×C43⋊C8—21no—
263C2×C43⋊C8—21no—
264C2×C43⋊C8—21no—
265C2×C43⋊C8—21no—
266C2×C43⋊C8—21no—
267C2×C43⋊C8—21no—
268C2×C43⋊C8—21no—
269C2×C43⋊C8—21no—
270C2×C43⋊C8—44no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—21no—
277C23×C43—21no—
278C23×C43—21no—
279C23×C43—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—22no—
284C23×C43—41no—
285C23×C43—41no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43#12012yes—
291C23×C43#13512yes—
292C23×C43C22×D411yescharacteristic
293C22×D43—22no—
294C22×D43—41no—
295C22×D43—41no—
296C22×D43—41no—
297C22×D43—41no—
298C22×D43—41no—
299C22×D43—41no—
300D4×C43—22no—
301D4×C43—22no—
302D4×C43—44no—
303D4×C43—48no—
304D4×C43—41no—
305D4×C43—41no—
306D4×C43—84no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—21no—
314C2×C4×C43—22no—
315C2×C4×C43—21no—
316C2×C4×C43—22no—
317C2×C4×C43—21no—
318C2×C4×C43—22no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—21no—
323C2×C4×C43—21no—
324C2×C4×C43—21no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—84no—
336C2×C4×C43—84no—
337C2×C4×C43#12012yes—
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43C2×#4111yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C2×C4×C43H(5,𝔽2)11yescharacteristic
344C22⋊D43—48no—
345C22⋊D43—84no—
346C2×Dic43—22no—
347C2×Dic43—41no—
348C2×Dic43—41no—
349C2×Dic43—41no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—41no—
353C2×Dic43—41no—
354C2×Dic43—41no—
355D172—22no—
356D172—22no—
357D172—41no—
358D172—41no—
359C4×D43—48no—
360Dic86—22no—
361Dic86—22no—
362Dic86—41no—
363Dic86—41no—
364C43⋊C8—41no—
365C43⋊C8—41no—
366C43⋊C8—41no—
367C43⋊C8—41no—
368#23962—431nomaximal, Sylow
369C22×C43—22no—
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—41no—
376C22×C43—41no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43—41no—
381C22×C43—41no—
382C22×C43—41no—
383C22×C43—42no—
384C22×C43—42no—
385C22×C43—42no—
386C22×C43—81no—
387C22×C43—81no—
388C22×C43—81no—
389C22×C43—81no—
390C22×C43C2×#12011yescharacteristic
391C22×C43#54611yescharacteristic
392C22×C43#54611yescharacteristic
393C22×C43C2×#13511yescharacteristic
394C22×C43#57511yescharacteristic
395C22×C43#57611yescharacteristic
396C22×C43#57711yescharacteristic
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—81no—
401C2×D43—81no—
402C2×D43—81no—
403C2×D43—81no—
404C4×C43—22no—
405C4×C43—41no—
406C4×C43—41no—
407C4×C43—42no—
408C4×C43—41no—
409C4×C43—42no—
410C4×C43—42no—
411C4×C43#52511yescharacteristic
412C4×C43#53511yescharacteristic
413C4×C43#54611yescharacteristic
414C4×C43#54611yescharacteristic
415Dic43—42no—
416Dic43—81no—
417Dic43—81no—
418C2×#553D4311yescharacteristic, complemented
419C2×#449—431no—
420C2×#416—431no—
421#2407—431no—
422#2026—431no—
423#2025—431no—
424#2000—431no—
425#1999—431no—
426#1893—431no—
427#1879—431no—
428#1877—431no—
429#1874—431no—
430#1872—431no—
431#1869—431no—
432#1825—431no—
433C2×C43—42no—
434C2×C43—42no—
435C2×C43—82no—
436C2×C43#240411yescharacteristic
437C2×C43#300211yescharacteristic
438C2×C43#301211yescharacteristic
439C2×C43#329711yescharacteristic
440C2×C43#330111yescharacteristic
441C2×C43#330711yescharacteristic
442C2×C43#330911yescharacteristic
443D43—82no—
444C22×#41—431no—
445C22×SD16—431no—
446C22×D8—431no—
447C23×C8—431no—
448#553—24no—
449#553—24no—
450C2×#126—21no—
451C2×#125C2×D4311yescharacteristic
452C2×#123—21no—
453C2×C22⋊Q8—431no—
454C2×#121—21no—
455C2×#121—431no—
456C2×#121C2×D4311yescharacteristic
457C2×#121C2×D4311yescharacteristic
458C2×C4×D4—21no—
459C2×C4×D4C2×D4311yescharacteristic
460C2×C4×D4C2×D4311yescharacteristic
461C2×#117C2×D4311yescharacteristic
462C22×C4⋊C4C2×D4311yescharacteristic
463#449—864no—
464#416—864no—
465C2×#103—431no—
466C2×#103—431no—
467C2×#103—431no—
468C2×#102—431no—
469C2×#102—431no—
470C2×#102—431no—
471C2×#102—431no—
472C2×#102—431no—
473C2×C22⋊C8—431no—
474C2×C22⋊C8—431no—
475C2×C22⋊C8—431no—
476#394—861no—
477#392—861no—
478#391—431no—
479#390—431no—
480#386—861no—
481#385—861no—
482#380—431no—
483#340—431no—
484#340—431no—
485#340—431no—
486#340—431no—
487#340—431no—
488#340—431no—
489#336—431no—
490#336—431no—
491C43#2396211yescharacteristic, complemented, Sylow
492C2×#41—862no—
493C2×#41—862no—
494C2×#41—862no—
495C2×#41—862no—
496C2×#41—1721no—
497C2×#41—1721no—
498C22×Q8—431no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—431no—
502C22×D4—861no—
503C22×D4—861no—
504C22×D4C22⋊D4311yescharacteristic
505C22×D4C22×D4311yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—861no—
509C23×C4C22×D4311yescharacteristic
510C23×C4C22×D4311yescharacteristic
511C2×SD16—862no—
512C2×SD16—862no—
513C2×SD16—1721no—
514C2×D8—862no—
515C2×D8—862no—
516C2×D8—1721no—
517C22×C8—431no—
518C22×C8—431no—
519C22×C8—431no—
520C22×C8—431no—
521C22×C8—862no—
522C22×C8—1721no—
523C22×C8—1721no—
524#126—28no—
525#125—22no—
526#125—22no—
527#123—28no—
528C22⋊Q8—862no—
529C22⋊Q8—1721no—
530#121—28no—
531#121—22no—
532#121—22no—
533#121—22no—
534#121—862no—
535#121—1721no—
536#121C22⋊D4314yescomplemented
537C4×D4—28no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—22no—
543#117C22⋊D4314yescomplemented
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—431no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—861no—
552C2×C4⋊C4C22⋊D4311yescharacteristic
553C2×C4⋊C4C22×D4311yescharacteristic
554C2×C4⋊C4C22×D4311yescharacteristic
555C2×C4⋊C4C22×D4311yescharacteristic
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4C22⋊D4311yescharacteristic
566C2×C22⋊C4C22⋊D4311yescharacteristic
567C2×C42—21no—
568C2×C42C22×D4311yescharacteristic
569#103—862no—
570#103—862no—
571#103—862no—
572#102—862no—
573#102—862no—
574#102—862no—
575#102—1721no—
576#102—1721no—
577C22⋊C8—862no—
578C22⋊C8—1721no—
579C22⋊C8—1721no—
580#95—861no—
581#95—861no—
582#95—861no—
583C24—21no—
584C24—861no—
585C24C2×C22⋊D4311yescharacteristic
586C24C2×C22⋊D4311yescharacteristic
587#41—868no—
588#41—1724no—
589#41—1724no—
590#41—1724no—
591C2×Q8—432no—
592C2×Q8—861no—
593C2×Q8—861no—
594C2×Q8—861no—
595C2×Q8—861no—
596C2×Q8—861no—
597C2×D4—24no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—24no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—41no—
607C2×D4—42no—
608C2×D4—42no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—432no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4—3441no—
618C2×D4—1722no—
619C2×D4—1722no—
620C2×D4—1722no—
621C2×D4—1722no—
622C2×D4—1722no—
623C2×D4C2×C22⋊D4312yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4—81no—
642C22×C4—81no—
643C22×C4—861no—
644C22×C4—861no—
645C22×C4—861no—
646C22×C4—1722no—
647C22×C4—1722no—
648C22×C4—1722no—
649C22×C4C2×C22⋊D4311yescharacteristic
650C22×C4C2×C22⋊D4311yescharacteristic
651C22×C4C2×C22⋊D4311yescharacteristic
652C22×C4C2×C22⋊D4311yescharacteristic
653C22×C4C2×C22⋊D4312yes—
654C22×C4C2×C22⋊D4312yes—
655C22×C4C23×D4311yescharacteristic
656SD16—1724no—
657D8—1724no—
658C2×C8—861no—
659C2×C8—861no—
660C2×C8—861no—
661C2×C8—861no—
662C2×C8—861no—
663C2×C8—861no—
664C2×C8—861no—
665C2×C8—861no—
666C2×C8—861no—
667C2×C8—861no—
668C2×C8—861no—
669C2×C8—861no—
670C2×C8—1724no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—22no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—861no—
681C4⋊C4—861no—
682C4⋊C4—1722no—
683C4⋊C4C2×C22⋊D4312yes—
684C4⋊C4C2×C22⋊D4312yes—
685C4⋊C4C2×C22⋊D4312yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—22no—
690C22⋊C4—24no—
691C22⋊C4—22no—
692C22⋊C4—3441no—
693C22⋊C4—3441no—
694C22⋊C4—1722no—
695C22⋊C4—1722no—
696C22⋊C4—1722no—
697C42—24no—
698C42—21no—
699C42—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—22no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—862no—
720C23—1721no—
721C23—1721no—
722C23—1721no—
723C23—1721no—
724C23—1721no—
725C23—1721no—
726C23#1306329412yes—
727C23#1306334512yes—
728C23C22×C22⋊D4311yescharacteristic
729Q8—862no—
730Q8—862no—
731Q8—1721no—
732Q8—1721no—
733D4—22no—
734D4—22no—
735D4—44no—
736D4—48no—
737D4—41no—
738D4—41no—
739D4—84no—
740D4—862no—
741D4—862no—
742D4—3444no—
743D4—1728no—
744D4—1721no—
745D4—1721no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—84no—
775C2×C4—84no—
776C2×C4—862no—
777C2×C4—1728no—
778C2×C4—1721no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4—1721no—
782C2×C4—1721no—
783C2×C4—1721no—
784C2×C4—1721no—
785C2×C4—1721no—
786C2×C4#1306329412yes—
787C2×C4C22×C22⋊D4311yescharacteristic
788C2×C4C22×C22⋊D4311yescharacteristic
789C2×C4#41×D4311yescharacteristic
790C2×C4#41×D4311yescharacteristic
791C2×C4#1306337111yescharacteristic
792C2×C4#1306337111yescharacteristic
793C8—1721no—
794C8—1721no—
795C8—1721no—
796C8—1721no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—3441no—
819C22—3441no—
820C22—3441no—
821C22—3441no—
822C22—1722no—
823C22—1722no—
824C22—1722no—
825C22C2×#1306329411yescharacteristic
826C22#1458353711yescharacteristic
827C22#1458353711yescharacteristic
828C22C2×#1306334511yescharacteristic
829C22#1458369711yescharacteristic
830C22#1458370211yescharacteristic
831C22#1458371011yescharacteristic
832C4—22no—
833C4—41no—
834C4—41no—
835C4—42no—
836C4—41no—
837C4—42no—
838C4—42no—
839C4—3441no—
840C4—3441no—
841C4—1722no—
842C4#1458340611yescharacteristic
843C4#1458346311yescharacteristic
844C4#1458353711yescharacteristic
845C4#1458353711yescharacteristic
846C2—42no—
847C2—42no—
848C2—82no—
849C2—3442no—
850C2#1913791011yescharacteristic
851C2#1914381311yescharacteristic
852C2#1914389911yescharacteristic
853C2#1914643911yescharacteristic
854C2#1914649111yescharacteristic
855C2#1914656511yescharacteristic
856C2#1914659511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#553C2
socleC23×C43C22×D4
hypercenterC2×#553D43
hypocenterC43#23962
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×#14583042C2semidirect
2. C2×#14582893C2semidirect
3. #19137940C2semidirect
4. #19135743C2semidirect
5. #19135738C2semidirect
6. #19135598C2semidirect
7. #19135591C2semidirect
8. #19135024C2semidirect
9. #19134943C2semidirect
10. #19134929C2semidirect
11. #19134912C2semidirect
12. #19134902C2semidirect
13. #19134888C2semidirect
14. #19134690C2semidirect
15. C2×C43×#553C2semidirect
129. #121×C43D4semidirect
136. #117×C43D4semidirect
418. C2×#553D43semidirect
491. C43#23962semidirect
536. #121C22⋊D43semidirect
543. #117C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830422
C2×#145828932
#191379402
#191357432
#191357382
#191355982
#191355912
#191350242
#191349432
#191349292
#191349122
#191349022
#191348882
#191346902
C2×C43×#5532
#2396243