Finite Group Databasebeta

← C43×#25555 #24945572

Subgroups — C43×#25555 #24945572

Order 11008.

1136 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#552C211yesmaximal, characteristic, complemented
2C2×C43×#481C211yesmaximal, characteristic, complemented
3C2×C43×#468C211yesmaximal, characteristic, complemented
4C43×#2414C211yesmaximal, characteristic
5C43×#2059C211yesmaximal, characteristic, complemented
6C43×#2035C211yesmaximal, characteristic, complemented
7C43×#2025C211yesmaximal, characteristic, complemented
8C43×#2000C211yesmaximal, characteristic, complemented
9C43×#1880C211yesmaximal, characteristic, complemented
10C43×#1875C211yesmaximal, characteristic, complemented
11C43×#1873C211yesmaximal, characteristic, complemented
12C43×#1870C211yesmaximal, characteristic, complemented
13C43×#1865C211yesmaximal, characteristic, complemented
14C43×#1854C211yesmaximal, characteristic, complemented
15C43×#1736C211yesmaximal, characteristic, complemented
16C22×SD16×C43C2211yescharacteristic
17C22×M16×C43C2211yescharacteristic
18C43×#552—24no—
19C43×#552—24no—
20C2×#126×C43—21no—
21C2×#125×C43—21no—
22C2×#125×C43C2211yescharacteristic
23C2×#123×C43—21no—
24C2×C22⋊Q8×C43C2211yescharacteristic
25C2×C22⋊Q8×C43C2211yescharacteristic
26C2×#121×C43C2211yescharacteristic
27C2×#121×C43C2211yescharacteristic
28C2×C4×Q8×C43C2211yescharacteristic
29C2×C4×D4×C43C2211yescharacteristic
30C2×#117×C43—21no—
31C2×#117×C43C2211yescharacteristic
32C2×#117×C43C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C43×#481—24no—
35C43×#468—24no—
36C2×#107×C43C2211yescharacteristic
37C2×#106×C43C2211yescharacteristic
38C2×#106×C43C2211yescharacteristic
39C2×#103×C43C2211yescharacteristic
40C2×#103×C43C2211yescharacteristic
41C2×#103×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic
43C2×#102×C43C2211yescharacteristic
44C2×#102×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic
46C2×C22⋊C8×C43C2211yescharacteristic
47C2×C22⋊C8×C43C2211yescharacteristic
48C43×#394—21no—
49C43×#392—21no—
50C43×#390—21no—
51C43×#390C2211yescharacteristic
52C43×#389C2211yescharacteristic
53C43×#388—21no—
54C43×#380C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Q8×C43C2311yescharacteristic
64C22×D4×C43—21no—
65C22×D4×C43—21no—
66C22×D4×C43D411yescharacteristic
67C22×D4×C43C2311yescharacteristic
68C23×C4×C43—21no—
69C23×C4×C43C2311yescharacteristic
70C23×C4×C43C2311yescharacteristic
71C2×SD16×C43—22no—
72C2×SD16×C43—22no—
73C2×SD16×C43—41no—
74C2×M16×C43—22no—
75C2×M16×C43—22no—
76C2×M16×C43—41no—
77C22×C8×C43C2311yescharacteristic
78C22×C8×C43C2311yescharacteristic
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81#126×C43—28no—
82#125×C43—28no—
83#125×C43—22no—
84#125×C43—22no—
85#123×C43—28no—
86C22⋊Q8×C43—22no—
87C22⋊Q8×C43—22no—
88C22⋊Q8×C43—22no—
89C22⋊Q8×C43D414yescomplemented
90#121×C43—22no—
91#121×C43—22no—
92#121×C43—22no—
93#121×C43—41no—
94C4×Q8×C43—22no—
95C4×Q8×C43—22no—
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98#117×C43—28no—
99#117×C43—22no—
100#117×C43—22no—
101#117×C43—22no—
102#117×C43—41no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—22no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43—21no—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43D411yescharacteristic
112C2×C4⋊C4×C43D414yescomplemented
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C22⋊C4×C43—21no—
125C2×C22⋊C4×C43—21no—
126C2×C22⋊C4×C43—21no—
127C2×C22⋊C4×C43—21no—
128C2×C22⋊C4×C43D411yescharacteristic
129C2×C22⋊C4×C43D411yescharacteristic
130C2×C42×C43—21no—
131C2×C42×C43—21no—
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—22no—
135#106×C43—22no—
136#106×C43—22no—
137#103×C43—22no—
138#103×C43—22no—
139#103×C43—41no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143C22⋊C8×C43—22no—
144C22⋊C8×C43—22no—
145C22⋊C8×C43—41no—
146#95×C43—21no—
147#95×C43—21no—
148C24×C43—21no—
149C24×C43C2×D411yescharacteristic
150C24×C43C2×D411yescharacteristic
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43C2×D412yes—
157C2×D4×C43—22no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—41no—
165C2×D4×C43—41no—
166C2×D4×C43—42no—
167C2×D4×C43—42no—
168C2×D4×C43—42no—
169C2×D4×C43—81no—
170C2×D4×C43—81no—
171C2×D4×C43—81no—
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×C43—24no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—42no—
191C22×C4×C43—42no—
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
199SD16×C43—44no—
200M16×C43—44no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43#4112yes—
213C4⋊C4×C43—24no—
214C4⋊C4×C43—24no—
215C4⋊C4×C43—24no—
216C4⋊C4×C43—24no—
217C4⋊C4×C43—24no—
218C4⋊C4×C43—24no—
219C4⋊C4×C43—22no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—21no—
222C4⋊C4×C43—21no—
223C4⋊C4×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—81no—
229C4⋊C4×C43C2×D412yes—
230C4⋊C4×C43C2×D412yes—
231C4⋊C4×C43C2×D412yes—
232C4⋊C4×C43#4112yes—
233C22⋊C4×C43—24no—
234C22⋊C4×C43—24no—
235C22⋊C4×C43—22no—
236C22⋊C4×C43—24no—
237C22⋊C4×C43—22no—
238C22⋊C4×C43—42no—
239C22⋊C4×C43—42no—
240C22⋊C4×C43—42no—
241C22⋊C4×C43—42no—
242C22⋊C4×C43—81no—
243C22⋊C4×C43—81no—
244C42×C43—24no—
245C42×C43—24no—
246C42×C43—21no—
247C42×C43—21no—
248C42×C43—42no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—21no—
259C23×C43—21no—
260C23×C43—21no—
261C23×C43—21no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43#12012yes—
270C23×C43C22×D411yescharacteristic
271Q8×C43—22no—
272Q8×C43—22no—
273Q8×C43—41no—
274Q8×C43—41no—
275D4×C43—44no—
276D4×C43—41no—
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—84no—
281D4×C43—84no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—22no—
291C2×C4×C43—22no—
292C2×C4×C43—22no—
293C2×C4×C43—21no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—48no—
303C2×C4×C43—41no—
304C2×C4×C43—41no—
305C2×C4×C43—41no—
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—41no—
321C2×C4×C43—41no—
322C2×C4×C43—41no—
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
330C8×C43—22no—
331C8×C43—41no—
332C8×C43—41no—
333C8×C43—41no—
334#25555C4311yesmaximal, characteristic, direct product factor, Sylow
335C22×C43—22no—
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—41no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—41no—
344C22×C43—41no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—81no—
350C22×C43—81no—
351C22×C43—81no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43C2×#12011yescharacteristic
357C22×C43#54611yescharacteristic
358C22×C43#54711yescharacteristic
359C22×C43#57511yescharacteristic
360C22×C43#57511yescharacteristic
361C22×C43#57711yescharacteristic
362C22×C43#57711yescharacteristic
363C4×C43—22no—
364C4×C43—41no—
365C4×C43—42no—
366C4×C43—41no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—41no—
370C4×C43—42no—
371C4×C43—42no—
372C4×C43—81no—
373C4×C43—81no—
374C4×C43#53211yescharacteristic
375C4×C43#53711yescharacteristic
376C4×C43#54611yescharacteristic
377C4×C43#54711yescharacteristic
378C2×#552C2×C4311yescharacteristic, complemented
379C2×#481C2×C4311yescharacteristic, complemented
380C2×#468C2×C4311yescharacteristic, complemented
381#2414C2×C4311yescharacteristic
382#2059C2×C4311yescharacteristic, complemented
383#2035C2×C4311yescharacteristic, complemented
384#2025C2×C4311yescharacteristic, complemented
385#2000C2×C4311yescharacteristic, complemented
386#1880C2×C4311yescharacteristic, complemented
387#1875C2×C4311yescharacteristic, complemented
388#1873C2×C4311yescharacteristic, complemented
389#1870C2×C4311yescharacteristic, complemented
390#1865C2×C4311yescharacteristic, complemented
391#1854C2×C4311yescharacteristic, complemented
392#1736C2×C4311yescharacteristic, complemented
393C2×C43—42no—
394C2×C43—81no—
395C2×C43—161no—
396C2×C43#243011yescharacteristic
397C2×C43#300511yescharacteristic
398C2×C43#301011yescharacteristic
399C2×C43#331711yescharacteristic
400C2×C43#332311yescharacteristic
401C2×C43#334811yescharacteristic
402C2×C43#335111yescharacteristic
403C22×SD16C22×C4311yescharacteristic
404C22×M16C22×C4311yescharacteristic
405#552—24no—
406#552—24no—
407C2×#126—21no—
408C2×#125—21no—
409C2×#125C22×C4311yescharacteristic
410C2×#123—21no—
411C2×C22⋊Q8C22×C4311yescharacteristic
412C2×C22⋊Q8C22×C4311yescharacteristic
413C2×#121C22×C4311yescharacteristic
414C2×#121C22×C4311yescharacteristic
415C2×C4×Q8C22×C4311yescharacteristic
416C2×C4×D4C22×C4311yescharacteristic
417C2×#117—21no—
418C2×#117C22×C4311yescharacteristic
419C2×#117C22×C4311yescharacteristic
420C22×C4⋊C4C22×C4311yescharacteristic
421#481—24no—
422#468—24no—
423C2×#107C22×C4311yescharacteristic
424C2×#106C22×C4311yescharacteristic
425C2×#106C22×C4311yescharacteristic
426C2×#103C22×C4311yescharacteristic
427C2×#103C22×C4311yescharacteristic
428C2×#103C22×C4311yescharacteristic
429C2×#102C22×C4311yescharacteristic
430C2×#102C22×C4311yescharacteristic
431C2×#102C22×C4311yescharacteristic
432C2×C22⋊C8C22×C4311yescharacteristic
433C2×C22⋊C8C22×C4311yescharacteristic
434C2×C22⋊C8C22×C4311yescharacteristic
435#394—21no—
436#392—21no—
437#390—21no—
438#390C22×C4311yescharacteristic
439#389C22×C4311yescharacteristic
440#388—21no—
441#380C22×C4311yescharacteristic
442#340C22×C4311yescharacteristic
443#340C22×C4311yescharacteristic
444#340C22×C4311yescharacteristic
445#340C22×C4311yescharacteristic
446#340C22×C4311yescharacteristic
447#340C22×C4311yescharacteristic
448#336C22×C4311yescharacteristic
449#336C22×C4311yescharacteristic
450C43#2555511yescharacteristic, direct product factor, Sylow
451C22×Q8C23×C4311yescharacteristic
452C22×D4—21no—
453C22×D4—21no—
454C22×D4D4×C4311yescharacteristic
455C22×D4C23×C4311yescharacteristic
456C23×C4—21no—
457C23×C4C23×C4311yescharacteristic
458C23×C4C23×C4311yescharacteristic
459C2×SD16—22no—
460C2×SD16—22no—
461C2×SD16—41no—
462C2×M16—22no—
463C2×M16—22no—
464C2×M16—41no—
465C22×C8C23×C4311yescharacteristic
466C22×C8C23×C4311yescharacteristic
467C22×C8C23×C4311yescharacteristic
468C22×C8C23×C4311yescharacteristic
469#126—28no—
470#125—28no—
471#125—22no—
472#125—22no—
473#123—28no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—22no—
477C22⋊Q8D4×C4314yescomplemented
478#121—22no—
479#121—22no—
480#121—22no—
481#121—41no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×D4—22no—
485C4×D4—22no—
486#117—28no—
487#117—22no—
488#117—22no—
489#117—22no—
490#117—41no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4D4×C4311yescharacteristic
500C2×C4⋊C4D4×C4314yescomplemented
501C2×C4⋊C4C23×C4311yescharacteristic
502C2×C4⋊C4C23×C4311yescharacteristic
503C2×C4⋊C4C23×C4311yescharacteristic
504C2×C4⋊C4C23×C4311yescharacteristic
505C2×C4⋊C4C23×C4311yescharacteristic
506C2×C4⋊C4C23×C4311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4D4×C4311yescharacteristic
517C2×C22⋊C4D4×C4311yescharacteristic
518C2×C42—21no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42C23×C4311yescharacteristic
522#107—22no—
523#106—22no—
524#106—22no—
525#103—22no—
526#103—22no—
527#103—41no—
528#102—22no—
529#102—22no—
530#102—22no—
531C22⋊C8—22no—
532C22⋊C8—22no—
533C22⋊C8—41no—
534#95—21no—
535#95—21no—
536C24—21no—
537C24C2×D4×C4311yescharacteristic
538C24C2×D4×C4311yescharacteristic
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8C2×D4×C4312yes—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—81no—
558C2×D4—81no—
559C2×D4—81no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4C2×D4×C4311yescharacteristic
581C22×C4C2×D4×C4311yescharacteristic
582C22×C4C2×D4×C4311yescharacteristic
583C22×C4C2×D4×C4311yescharacteristic
584C22×C4C2×D4×C4312yes—
585C22×C4C2×D4×C4312yes—
586C22×C4C24×C4311yescharacteristic
587SD16—44no—
588M16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8#41×C4312yes—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—22no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—81no—
617C4⋊C4C2×D4×C4312yes—
618C4⋊C4C2×D4×C4312yes—
619C4⋊C4C2×D4×C4312yes—
620C4⋊C4#41×C4312yes—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—42no—
627C22⋊C4—42no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—81no—
631C22⋊C4—81no—
632C42—24no—
633C42—24no—
634C42—21no—
635C42—21no—
636C42—42no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23#120×C4312yes—
658C23C22×D4×C4311yescharacteristic
659Q8—22no—
660Q8—22no—
661Q8—41no—
662Q8—41no—
663D4—44no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—84no—
669D4—84no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—48no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4#120×C4312yes—
712C2×C4C22×D4×C4311yescharacteristic
713C2×C4C22×D4×C4311yescharacteristic
714C2×C4C2×#41×C4311yescharacteristic
715C2×C4C2×#41×C4311yescharacteristic
716C2×C4H(5,𝔽2)×C4311yescharacteristic
717C2×C42−1+4×C4311yescharacteristic
718C8—22no—
719C8—41no—
720C8—41no—
721C8—41no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—81no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22C2×#120×C4311yescharacteristic
744C22C43×#54611yescharacteristic
745C22C43×#54711yescharacteristic
746C22C43×#57511yescharacteristic
747C22C43×#57511yescharacteristic
748C22C43×#57711yescharacteristic
749C22C43×#57711yescharacteristic
750C4—22no—
751C4—41no—
752C4—42no—
753C4—41no—
754C4—42no—
755C4—42no—
756C4—41no—
757C4—42no—
758C4—42no—
759C4—81no—
760C4—81no—
761C4C43×#53211yescharacteristic
762C4C43×#53711yescharacteristic
763C4C43×#54611yescharacteristic
764C4C43×#54711yescharacteristic
765C2—42no—
766C2—81no—
767C2—161no—
768C2C43×#243011yescharacteristic
769C2C43×#300511yescharacteristic
770C2C43×#301011yescharacteristic
771C2C43×#331711yescharacteristic
772C2C43×#332311yescharacteristic
773C2C43×#334811yescharacteristic
774C2C43×#335111yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2414C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C2×C4×D4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#552C2semidirect
2. C2×C43×#481C2semidirect
3. C2×C43×#468C2semidirect
5. C43×#2059C2semidirect
6. C43×#2035C2semidirect
7. C43×#2025C2semidirect
8. C43×#2000C2semidirect
9. C43×#1880C2semidirect
10. C43×#1875C2semidirect
11. C43×#1873C2semidirect
12. C43×#1870C2semidirect
13. C43×#1865C2semidirect
14. C43×#1854C2semidirect
15. C43×#1736C2semidirect
89. C22⋊Q8×C43D4semidirect
112. C2×C4⋊C4×C43D4semidirect
334. #25555C43direct (N × H)
378. C2×#552C2×C43semidirect
379. C2×#481C2×C43semidirect
380. C2×#468C2×C43semidirect
382. #2059C2×C43semidirect
383. #2035C2×C43semidirect
384. #2025C2×C43semidirect
385. #2000C2×C43semidirect
386. #1880C2×C43semidirect
387. #1875C2×C43semidirect
388. #1873C2×C43semidirect
389. #1870C2×C43semidirect
390. #1865C2×C43semidirect
391. #1854C2×C43semidirect
392. #1736C2×C43semidirect
450. C43#25555direct (N × H)
477. C22⋊Q8D4×C43semidirect
500. C2×C4⋊C4D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#5522
C2×C43×#4812
C2×C43×#4682
C43×#24142
C43×#20592
C43×#20352
C43×#20252
C43×#20002
C43×#18802
C43×#18752
C43×#18732
C43×#18702
C43×#18652
C43×#18542
C43×#17362
#2555543