Finite Group Databasebeta

← C43×#25108 #24945125

Subgroups — C43×#25108 #24945125

Order 11008.

1388 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#466C211yesmaximal, characteristic, complemented
2C2×C43×#447C211yesmaximal, characteristic, complemented
3C2×C8×D4×C43C211yesmaximal, characteristic, complemented
4C22×#102×C43C211yesmaximal, characteristic, complemented
5C43×#2416C211yesmaximal, characteristic, complemented
6C43×#2408C211yesmaximal, characteristic, complemented
7C43×#2067C211yesmaximal, characteristic, complemented
8C43×#2054C211yesmaximal, characteristic, complemented
9C43×#2033C211yesmaximal, characteristic, complemented
10C43×#1999C211yesmaximal, characteristic, complemented
11C43×#1970C211yesmaximal, characteristic, complemented
12C43×#1934C211yesmaximal, characteristic, complemented
13C43×#1893C211yesmaximal, characteristic, complemented
14C43×#1893C211yesmaximal, characteristic, complemented
15C43×#1852C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C22×D8×C43C2211yescharacteristic
18C22×D8×C43C2211yescharacteristic
19C23×C8×C43C2211yescharacteristic
20C23×C8×C43C2211yescharacteristic, complemented
21C2×#121×C43—21no—
22C2×#121×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×#121×C43C2211yescharacteristic
25C2×#121×C43C2211yescharacteristic, complemented
26C2×#120×C43—21no—
27C2×C4×D4×C43C2211yescharacteristic
28C22×C4⋊C4×C43C2211yescharacteristic
29C43×#466—24no—
30C43×#447—24no—
31C8×D4×C43—24no—
32C2×#107×C43C2211yescharacteristic, complemented
33C2×#107×C43C2211yescharacteristic, complemented
34C2×C4⋊C8×C43C2211yescharacteristic, complemented
35C2×#102×C43—24no—
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×#102×C43C2211yescharacteristic
39C2×#102×C43C2211yescharacteristic
40C2×#102×C43C2211yescharacteristic
41C2×#102×C43C2211yescharacteristic
42C2×#102×C43C2211yescharacteristic, complemented
43C2×#102×C43C2211yescharacteristic, complemented
44C2×C22⋊C8×C43C2211yescharacteristic
45C2×C22⋊C8×C43C2211yescharacteristic, complemented
46C2×C4×C8×C43C2211yescharacteristic, complemented
47C43×#396—21no—
48C43×#394—21no—
49C43×#394—21no—
50C43×#392—21no—
51C43×#390C2211yescharacteristic
52C43×#390C2211yescharacteristic
53C43×#390C2211yescharacteristic, complemented
54C43×#389C2211yescharacteristic, complemented
55C43×#386—21no—
56C43×#380C2211yescharacteristic
57C43×#380C2211yescharacteristic, complemented
58C43×#379—21no—
59C43×#340C2211yescharacteristic, complemented
60C43×#340C2211yescharacteristic, complemented
61C43×#340C2211yescharacteristic, complemented
62C43×#340C2211yescharacteristic, complemented
63C25×C43—21no—
64C22×D4×C43—22no—
65C22×D4×C43—22no—
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43—21no—
70C22×D4×C43—22no—
71C22×D4×C43—21no—
72C22×D4×C43—22no—
73C22×D4×C43—41no—
74C22×D4×C43—41no—
75C22×D4×C43D411yescharacteristic
76C22×D4×C43C2311yescharacteristic
77C22×D4×C43C2311yescharacteristic
78C22×D4×C43C2311yescharacteristic
79C23×C4×C43—21no—
80C23×C4×C43C2311yescharacteristic
81C23×C4×C43C2311yescharacteristic
82C2×D8×C43—22no—
83C2×D8×C43—22no—
84C2×D8×C43—22no—
85C2×D8×C43—22no—
86C2×D8×C43—41no—
87C2×D8×C43—41no—
88C22×C8×C43—22no—
89C22×C8×C43—22no—
90C22×C8×C43—22no—
91C22×C8×C43—22no—
92C22×C8×C43—41no—
93C22×C8×C43—41no—
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96C22×C8×C43C2311yescharacteristic
97C22×C8×C43C2311yescharacteristic
98#121×C43—22no—
99#121×C43—22no—
100#121×C43—22no—
101#121×C43—22no—
102#121×C43—22no—
103#121×C43—41no—
104#121×C43—41no—
105#121×C43—41no—
106#121×C43—44no—
107#120×C43—44no—
108C4×D4×C43—22no—
109C4×D4×C43—22no—
110C2×C4⋊C4×C43—22no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—21no—
113C2×C4⋊C4×C43—41no—
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
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×C43—21no—
129C2×C22⋊C4×C43—21no—
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43D411yescharacteristic
133C2×C22⋊C4×C43D411yescharacteristic
134C2×C42×C43C2311yescharacteristic
135#107×C43—22no—
136#107×C43—41no—
137C4⋊C8×C43—22no—
138#102×C43—22no—
139#102×C43—22no—
140#102×C43—22no—
141#102×C43—22no—
142#102×C43—22no—
143#102×C43—22no—
144#102×C43—41no—
145#102×C43D414yescomplemented
146C22⋊C8×C43—22no—
147C22⋊C8×C43D414yescomplemented
148C4×C8×C43—22no—
149#95×C43—21no—
150#95×C43—21no—
151#95×C43—21no—
152C24×C43—21no—
153C24×C43—21no—
154C24×C43—21no—
155C24×C43—42no—
156C24×C43—42no—
157C24×C43—42no—
158C24×C43—42no—
159C24×C43—42no—
160C24×C43—81no—
161C24×C43—81no—
162C24×C43C2×D411yescharacteristic
163C24×C43C2×D411yescharacteristic
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—22no—
167C2×D4×C43—22no—
168C2×D4×C43—28no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—21no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—21no—
179C2×D4×C43—21no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—42no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43—42no—
187C2×D4×C43—42no—
188C2×D4×C43—44no—
189C2×D4×C43—44no—
190C2×D4×C43—44no—
191C2×D4×C43—42no—
192C2×D4×C43—42no—
193C2×D4×C43—42no—
194C2×D4×C43—42no—
195C2×D4×C43—42no—
196C2×D4×C43—42no—
197C2×D4×C43—42no—
198C2×D4×C43—81no—
199C2×D4×C43—81no—
200C2×D4×C43—81no—
201C2×D4×C43D814yescomplemented
202C2×D4×C43C2×D412yes—
203C2×D4×C43#4112yes—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—42no—
220C22×C4×C43—42no—
221C22×C4×C43—81no—
222C22×C4×C43C2×D412yes—
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43#4112yes—
228C22×C4×C43C2411yescharacteristic
229D8×C43—44no—
230D8×C43—44no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—44no—
241C2×C8×C43—44no—
242C2×C8×C43C2×D412yes—
243C2×C8×C43C2×D412yes—
244C2×C8×C43C2×D412yes—
245C4⋊C4×C43—22no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43—21no—
251C4⋊C4×C43—21no—
252C4⋊C4×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—42no—
256C4⋊C4×C43—42no—
257C4⋊C4×C43C2×D412yes—
258C22⋊C4×C43—22no—
259C22⋊C4×C43—22no—
260C22⋊C4×C43—42no—
261C22⋊C4×C43—42no—
262C22⋊C4×C43—42no—
263C22⋊C4×C43—42no—
264C22⋊C4×C43—42no—
265C22⋊C4×C43—42no—
266C22⋊C4×C43—42no—
267C22⋊C4×C43—42no—
268C22⋊C4×C43—42no—
269C22⋊C4×C43—81no—
270C22⋊C4×C43—81no—
271C22⋊C4×C43—81no—
272C42×C43—21no—
273C42×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—21no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—48no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—41no—
302C23×C43—41no—
303C23×C43—41no—
304C23×C43—41no—
305C23×C43—41no—
306C23×C43—84no—
307C23×C43—84no—
308C23×C43—84no—
309C23×C43—84no—
310C23×C43—84no—
311C23×C43—84no—
312C23×C43#12112yes—
313C23×C43C2×D812yes—
314C23×C43C2×D812yes—
315C23×C43#13512yes—
316C23×C43C22×D411yescharacteristic
317D4×C43—28no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—22no—
322D4×C43—48no—
323D4×C43—41no—
324D4×C43—41no—
325D4×C43—41no—
326D4×C43—41no—
327D4×C43—41no—
328D4×C43—41no—
329D4×C43—41no—
330D4×C43—41no—
331D4×C43—84no—
332D4×C43—84no—
333D4×C43—84no—
334D4×C43—84no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—22no—
343C2×C4×C43—21no—
344C2×C4×C43—21no—
345C2×C4×C43—21no—
346C2×C4×C43—22no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—41no—
351C2×C4×C43—41no—
352C2×C4×C43—41no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—84no—
369C2×C4×C43#12112yes—
370C2×C4×C43C2×D812yes—
371C2×C4×C43C22×D411yescharacteristic
372C2×C4×C43C22×D411yescharacteristic
373C2×C4×C43C2×#4111yescharacteristic
374C2×C4×C43C2×#4111yescharacteristic
375C2×C4×C43H(5,𝔽2)11yescharacteristic
376C2×C4×C43H(5,𝔽2)11yescharacteristic
377C8×C43—22no—
378C8×C43—22no—
379C8×C43—22no—
380C8×C43—41no—
381#25108C4311yesmaximal, characteristic, direct product factor, Sylow
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—22no—
388C22×C43—22no—
389C22×C43—22no—
390C22×C43—22no—
391C22×C43—41no—
392C22×C43—41no—
393C22×C43—41no—
394C22×C43—41no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—42no—
401C22×C43—816no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43—81no—
406C22×C43—81no—
407C22×C43—81no—
408C22×C43—81no—
409C22×C43—81no—
410C22×C43—81no—
411C22×C43—81no—
412C22×C43—81no—
413C22×C43—81no—
414C22×C43—81no—
415C22×C43—81no—
416C22×C43—81no—
417C22×C43#46614yescomplemented
418C22×C43C2×#12111yescharacteristic
419C22×C43D4211yescharacteristic
420C22×C43#54611yescharacteristic
421C22×C43C22×D811yescharacteristic
422C22×C43C2×#13511yescharacteristic
423C22×C43#57611yescharacteristic
424C22×C43#57711yescharacteristic
425C4×C43—22no—
426C4×C43—22no—
427C4×C43—41no—
428C4×C43—42no—
429C4×C43—41no—
430C4×C43—81no—
431C4×C43—81no—
432C4×C43—81no—
433C4×C43—81no—
434C4×C43#52511yescharacteristic
435C4×C43#53811yescharacteristic
436C4×C43D4211yescharacteristic
437C4×C43#54611yescharacteristic
438C2×#466C2×C4311yescharacteristic, complemented
439C2×#447C2×C4311yescharacteristic, complemented
440C2×C8×D4C2×C4311yescharacteristic, complemented
441C22×#102C2×C4311yescharacteristic, complemented
442#2416C2×C4311yescharacteristic, complemented
443#2408C2×C4311yescharacteristic, complemented
444#2067C2×C4311yescharacteristic, complemented
445#2054C2×C4311yescharacteristic, complemented
446#2033C2×C4311yescharacteristic, complemented
447#1999C2×C4311yescharacteristic, complemented
448#1970C2×C4311yescharacteristic, complemented
449#1934C2×C4311yescharacteristic, complemented
450#1893C2×C4311yescharacteristic, complemented
451#1893C2×C4311yescharacteristic, complemented
452#1852C2×C4311yescharacteristic, complemented
453C2×C43—24no—
454C2×C43—42no—
455C2×C43—82no—
456C2×C43—82no—
457C2×C43—161no—
458C2×C43#242411yescharacteristic
459C2×C43C2×#46611yescharacteristic
460C2×C43#306211yescharacteristic
461C2×C43D4×D811yescharacteristic
462C2×C43#328211yescharacteristic
463C2×C43#329411yescharacteristic
464C2×C43#329711yescharacteristic
465C23×D4C22×C4311yescharacteristic
466C22×D8C22×C4311yescharacteristic
467C22×D8C22×C4311yescharacteristic
468C23×C8C22×C4311yescharacteristic
469C23×C8C22×C4311yescharacteristic, complemented
470C2×#121—21no—
471C2×#121C22×C4311yescharacteristic
472C2×#121C22×C4311yescharacteristic
473C2×#121C22×C4311yescharacteristic
474C2×#121C22×C4311yescharacteristic, complemented
475C2×#120—21no—
476C2×C4×D4C22×C4311yescharacteristic
477C22×C4⋊C4C22×C4311yescharacteristic
478#466—24no—
479#447—24no—
480C8×D4—24no—
481C2×#107C22×C4311yescharacteristic, complemented
482C2×#107C22×C4311yescharacteristic, complemented
483C2×C4⋊C8C22×C4311yescharacteristic, complemented
484C2×#102—24no—
485C2×#102C22×C4311yescharacteristic
486C2×#102C22×C4311yescharacteristic
487C2×#102C22×C4311yescharacteristic
488C2×#102C22×C4311yescharacteristic
489C2×#102C22×C4311yescharacteristic
490C2×#102C22×C4311yescharacteristic
491C2×#102C22×C4311yescharacteristic, complemented
492C2×#102C22×C4311yescharacteristic, complemented
493C2×C22⋊C8C22×C4311yescharacteristic
494C2×C22⋊C8C22×C4311yescharacteristic, complemented
495C2×C4×C8C22×C4311yescharacteristic, complemented
496#396—21no—
497#394—21no—
498#394—21no—
499#392—21no—
500#390C22×C4311yescharacteristic
501#390C22×C4311yescharacteristic
502#390C22×C4311yescharacteristic, complemented
503#389C22×C4311yescharacteristic, complemented
504#386—21no—
505#380C22×C4311yescharacteristic
506#380C22×C4311yescharacteristic, complemented
507#379—21no—
508#340C22×C4311yescharacteristic, complemented
509#340C22×C4311yescharacteristic, complemented
510#340C22×C4311yescharacteristic, complemented
511#340C22×C4311yescharacteristic, complemented
512C43#2510811yescharacteristic, direct product factor, Sylow
513C25—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4D4×C4311yescharacteristic
526C22×D4C23×C4311yescharacteristic
527C22×D4C23×C4311yescharacteristic
528C22×D4C23×C4311yescharacteristic
529C23×C4—21no—
530C23×C4C23×C4311yescharacteristic
531C23×C4C23×C4311yescharacteristic
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—41no—
537C2×D8—41no—
538C22×C8—22no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8—22no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8C23×C4311yescharacteristic
545C22×C8C23×C4311yescharacteristic
546C22×C8C23×C4311yescharacteristic
547C22×C8C23×C4311yescharacteristic
548#121—22no—
549#121—22no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—44no—
557#120—44no—
558C4×D4—22no—
559C4×D4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4D4×C4311yescharacteristic
565C2×C4⋊C4C23×C4311yescharacteristic
566C2×C4⋊C4C23×C4311yescharacteristic
567C2×C4⋊C4C23×C4311yescharacteristic
568C2×C4⋊C4C23×C4311yescharacteristic
569C2×C4⋊C4C23×C4311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4D4×C4311yescharacteristic
583C2×C22⋊C4D4×C4311yescharacteristic
584C2×C42C23×C4311yescharacteristic
585#107—22no—
586#107—41no—
587C4⋊C8—22no—
588#102—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102D4×C4314yescomplemented
596C22⋊C8—22no—
597C22⋊C8D4×C4314yescomplemented
598C4×C8—22no—
599#95—21no—
600#95—21no—
601#95—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—81no—
611C24—81no—
612C24C2×D4×C4311yescharacteristic
613C24C2×D4×C4311yescharacteristic
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—28no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—44no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—81no—
649C2×D4—81no—
650C2×D4—81no—
651C2×D4D8×C4314yescomplemented
652C2×D4C2×D4×C4312yes—
653C2×D4#41×C4312yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4C2×D4×C4311yescharacteristic
673C22×C4C2×D4×C4311yescharacteristic
674C22×C4C2×D4×C4311yescharacteristic
675C22×C4C2×D4×C4312yes—
676C22×C4C2×D4×C4311yescharacteristic
677C22×C4#41×C4312yes—
678C22×C4C24×C4311yescharacteristic
679D8—44no—
680D8—44no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—44no—
691C2×C8—44no—
692C2×C8C2×D4×C4312yes—
693C2×C8C2×D4×C4312yes—
694C2×C8C2×D4×C4312yes—
695C4⋊C4—22no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—42no—
707C4⋊C4C2×D4×C4312yes—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—81no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C42—21no—
723C42—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—22no—
735C23—22no—
736C23—48no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23#121×C4312yes—
763C23C2×D8×C4312yes—
764C23C2×D8×C4312yes—
765C23#135×C4312yes—
766C23C22×D4×C4311yescharacteristic
767D4—28no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—84no—
782D4—84no—
783D4—84no—
784D4—84no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—22no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—84no—
819C2×C4#121×C4312yes—
820C2×C4C2×D8×C4312yes—
821C2×C4C22×D4×C4311yescharacteristic
822C2×C4C22×D4×C4311yescharacteristic
823C2×C4C2×#41×C4311yescharacteristic
824C2×C4C2×#41×C4311yescharacteristic
825C2×C4H(5,𝔽2)×C4311yescharacteristic
826C2×C4H(5,𝔽2)×C4311yescharacteristic
827C8—22no—
828C8—22no—
829C8—22no—
830C8—41no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22C43×#46614yescomplemented
867C22C2×#121×C4311yescharacteristic
868C22D42×C4311yescharacteristic
869C22C43×#54611yescharacteristic
870C22C22×D8×C4311yescharacteristic
871C22C2×#135×C4311yescharacteristic
872C22C43×#57611yescharacteristic
873C22C43×#57711yescharacteristic
874C4—22no—
875C4—22no—
876C4—41no—
877C4—42no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4C43×#52511yescharacteristic
884C4C43×#53811yescharacteristic
885C4D42×C4311yescharacteristic
886C4C43×#54611yescharacteristic
887C2—24no—
888C2—42no—
889C2—82no—
890C2—82no—
891C2—161no—
892C2C43×#242411yescharacteristic
893C2C2×C43×#46611yescharacteristic
894C2C43×#306211yescharacteristic
895C2D4×D8×C4311yescharacteristic
896C2C43×#328211yescharacteristic
897C2C43×#329411yescharacteristic
898C2C43×#329711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
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×#466C2semidirect
2. C2×C43×#447C2semidirect
3. C2×C8×D4×C43C2semidirect
4. C22×#102×C43C2semidirect
5. C43×#2416C2semidirect
6. C43×#2408C2semidirect
7. C43×#2067C2semidirect
8. C43×#2054C2semidirect
9. C43×#2033C2semidirect
10. C43×#1999C2semidirect
11. C43×#1970C2semidirect
12. C43×#1934C2semidirect
13. C43×#1893C2semidirect
14. C43×#1893C2semidirect
15. C43×#1852C2semidirect
20. C23×C8×C43C22semidirect
25. C2×#121×C43C22semidirect
32. C2×#107×C43C22semidirect
33. C2×#107×C43C22semidirect
34. C2×C4⋊C8×C43C22semidirect
42. C2×#102×C43C22semidirect
43. C2×#102×C43C22semidirect
45. C2×C22⋊C8×C43C22semidirect
46. C2×C4×C8×C43C22semidirect
53. C43×#390C22semidirect
54. C43×#389C22semidirect
57. C43×#380C22semidirect
59. C43×#340C22semidirect
60. C43×#340C22semidirect
61. C43×#340C22semidirect
62. C43×#340C22semidirect
145. #102×C43D4semidirect
147. C22⋊C8×C43D4semidirect
201. C2×D4×C43D8semidirect
381. #25108C43direct (N × H)
417. C22×C43#466semidirect
438. C2×#466C2×C43semidirect
439. C2×#447C2×C43semidirect
440. C2×C8×D4C2×C43semidirect
441. C22×#102C2×C43semidirect
442. #2416C2×C43semidirect
443. #2408C2×C43semidirect
444. #2067C2×C43semidirect
445. #2054C2×C43semidirect
446. #2033C2×C43semidirect
447. #1999C2×C43semidirect
448. #1970C2×C43semidirect
449. #1934C2×C43semidirect
450. #1893C2×C43semidirect
451. #1893C2×C43semidirect
452. #1852C2×C43semidirect
469. C23×C8C22×C43semidirect
474. C2×#121C22×C43semidirect
481. C2×#107C22×C43semidirect
482. C2×#107C22×C43semidirect
483. C2×C4⋊C8C22×C43semidirect
491. C2×#102C22×C43semidirect
492. C2×#102C22×C43semidirect
494. C2×C22⋊C8C22×C43semidirect
495. C2×C4×C8C22×C43semidirect
502. #390C22×C43semidirect
503. #389C22×C43semidirect
506. #380C22×C43semidirect
508. #340C22×C43semidirect
509. #340C22×C43semidirect
510. #340C22×C43semidirect
511. #340C22×C43semidirect
512. C43#25108direct (N × H)
595. #102D4×C43semidirect
597. C22⋊C8D4×C43semidirect
651. C2×D4D8×C43semidirect
866. C22C43×#466semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#4662
C2×C43×#4472
C2×C8×D4×C432
C22×#102×C432
C43×#24162
C43×#24082
C43×#20672
C43×#20542
C43×#20332
C43×#19992
C43×#19702
C43×#19342
C43×#18932
C43×#18522
#2510843