Finite Group Databasebeta

← C43×#29896 #24949913

Subgroups — C43×#29896 #24949913

Order 11008.

1056 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2847C211yesmaximal, characteristic
2C43×#2280C211yesmaximal, characteristic, complemented
3C43×#2077C211yesmaximal, characteristic, complemented
4C43×#2077C211yesmaximal, characteristic, complemented
5C43×#2076C211yesmaximal, characteristic, complemented
6C43×#2075C211yesmaximal, characteristic, complemented
7C43×#2034C211yesmaximal, characteristic, complemented
8C43×#2034C211yesmaximal, characteristic, complemented
9C43×#2033C211yesmaximal, characteristic, complemented
10C43×#2033C211yesmaximal, characteristic, complemented
11C43×#1875C211yesmaximal, characteristic, complemented
12C43×#1875C211yesmaximal, characteristic, complemented
13C43×#1854C211yesmaximal, characteristic, complemented
14C43×#1854C211yesmaximal, characteristic, complemented
15C43×#1779C211yesmaximal, characteristic, complemented
16C24×C4×C43C2211yescharacteristic
17C2×#121×C43C2211yescharacteristic
18C2×#121×C43C2211yescharacteristic
19C2×#121×C43C2211yescharacteristic
20C2×#120×C43—21no—
21C2×#117×C43C2211yescharacteristic
22C2×#117×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic, complemented
24C2×#107×C43C2211yescharacteristic, complemented
25C2×#106×C43C2211yescharacteristic, complemented
26C2×#106×C43C2211yescharacteristic, complemented
27C2×#102×C43C2211yescharacteristic, complemented
28C2×#102×C43C2211yescharacteristic, complemented
29C2×#102×C43C2211yescharacteristic, complemented
30C2×#102×C43C2211yescharacteristic, complemented
31C2×C22⋊C8×C43C2211yescharacteristic
32C2×C22⋊C8×C43C2211yescharacteristic
33C2×C22⋊C8×C43C2211yescharacteristic
34C2×C22⋊C8×C43C2211yescharacteristic
35C2×C22⋊C8×C43C2211yescharacteristic
36C2×C22⋊C8×C43C2211yescharacteristic
37C43×#386—21no—
38C43×#386—21no—
39C43×#386—21no—
40C43×#381—21no—
41C43×#380C2211yescharacteristic
42C43×#380C2211yescharacteristic
43C43×#380C2211yescharacteristic
44C43×#380C2211yescharacteristic
45C43×#380C2211yescharacteristic
46C43×#380C2211yescharacteristic
47C43×#380C2211yescharacteristic
48C43×#379—21no—
49C4×C22⋊C4×C43—21no—
50C4×C22⋊C4×C43—21no—
51C43×#340C2211yescharacteristic, complemented
52C43×#340C2211yescharacteristic, complemented
53C43×#340C2211yescharacteristic, complemented
54C43×#340C2211yescharacteristic, complemented
55C43×#340C2211yescharacteristic, complemented
56C43×#340C2211yescharacteristic, complemented
57C43×#340C2211yescharacteristic, complemented
58C43×#340C2211yescharacteristic, complemented
59C25×C43D411yescharacteristic
60C22×D4×C43—21no—
61C22×D4×C43—21no—
62C22×D4×C43—21no—
63C22×D4×C43C2311yescharacteristic
64C23×C4×C43—22no—
65C23×C4×C43—22no—
66C23×C4×C43—41no—
67C23×C4×C43—41no—
68C23×C4×C43—41no—
69C23×C4×C43—41no—
70C23×C4×C43D411yescharacteristic
71C23×C4×C43D411yescharacteristic
72C23×C4×C43D411yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C23×C4×C43C2311yescharacteristic
76C22×C8×C43C2311yescharacteristic
77C22×C8×C43C2311yescharacteristic
78C22×C8×C43C2311yescharacteristic
79C22×C8×C43C2311yescharacteristic
80#121×C43—22no—
81#121×C43—22no—
82#121×C43—41no—
83#121×C43—41no—
84#121×C43—41no—
85#121×C43—41no—
86#120×C43—44no—
87#117×C43—41no—
88#117×C43—41no—
89#117×C43—41no—
90#117×C43—41no—
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C4⋊C4×C43C2311yescharacteristic
94C2×C4⋊C4×C43C2311yescharacteristic
95C2×C4⋊C4×C43C2311yescharacteristic
96C2×C4⋊C4×C43C2311yescharacteristic
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C22⋊C4×C43—21no—
99C2×C22⋊C4×C43—21no—
100C2×C22⋊C4×C43—21no—
101C2×C22⋊C4×C43—21no—
102C2×C22⋊C4×C43—21no—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C22⋊C4×C43—21no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C42×C43—21no—
111C2×C42×C43—21no—
112#107×C43—41no—
113#107×C43—41no—
114#106×C43—41no—
115#106×C43—41no—
116#102×C43—41no—
117#102×C43—41no—
118#102×C43—41no—
119#102×C43—41no—
120C22⋊C8×C43—22no—
121C22⋊C8×C43—22no—
122C22⋊C8×C43—41no—
123C22⋊C8×C43—41no—
124C22⋊C8×C43—41no—
125C22⋊C8×C43—41no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133C24×C43—22no—
134C24×C43—22no—
135C24×C43—22no—
136C24×C43—21no—
137C24×C43—41no—
138C24×C43—41no—
139C24×C43—41no—
140C24×C43—41no—
141C24×C43C2×D411yescharacteristic
142C24×C43C2×D411yescharacteristic
143C24×C43C2×D411yescharacteristic
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—42no—
151C2×D4×C43—42no—
152C2×D4×C43—42no—
153C2×D4×C43—42no—
154C2×D4×C43—42no—
155C2×D4×C43—42no—
156C2×D4×C43—42no—
157C2×D4×C43—42no—
158C2×D4×C43—42no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
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—22no—
178C22×C4×C43—21no—
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—41no—
186C22×C4×C43—41no—
187C22×C4×C43—41no—
188C22×C4×C43—41no—
189C22×C4×C43—41no—
190C22×C4×C43—41no—
191C22×C4×C43—44no—
192C22×C4×C43—44no—
193C22×C4×C43—44no—
194C22×C4×C43—44no—
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43#4112yes—
199C22×C4×C43#4112yes—
200C22×C4×C43C2411yescharacteristic
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—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—21no—
218C4⋊C4×C43—21no—
219C4⋊C4×C43—21no—
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—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—42no—
232C22⋊C4×C43—42no—
233C22⋊C4×C43—42no—
234C22⋊C4×C43—42no—
235C22⋊C4×C43—42no—
236C22⋊C4×C43—42no—
237C22⋊C4×C43—42no—
238C22⋊C4×C43—42no—
239C42×C43—42no—
240C42×C43—42no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
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—44no—
260C23×C43—44no—
261C23×C43—44no—
262C23×C43—44no—
263C23×C43—44no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43—41no—
272C23×C43—41no—
273C23×C43#12312yes—
274C23×C43#13512yes—
275C23×C43AGL(1,ℤ/8)12yes—
276C23×C43C22×D411yescharacteristic
277D4×C43—41no—
278D4×C43—41no—
279D4×C43—41no—
280D4×C43—41no—
281D4×C43—84no—
282D4×C43—84no—
283D4×C43—84no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—44no—
297C2×C4×C43—44no—
298C2×C4×C43—44no—
299C2×C4×C43—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
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—41no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43#12312yes—
329C2×C4×C43C2×#4111yescharacteristic
330C2×C4×C43C2×#4111yescharacteristic
331C2×C4×C43H(5,𝔽2)11yescharacteristic
332C2×C4×C43H(5,𝔽2)11yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C8×C43—41no—
336C8×C43—41no—
337C8×C43—41no—
338C8×C43—41no—
339#29896C4311yesmaximal, characteristic, direct product factor, Sylow
340C22×C43—22no—
341C22×C43—22no—
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—22no—
346C22×C43—22no—
347C22×C43—22no—
348C22×C43—22no—
349C22×C43—416no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—81no—
363C22×C43—81no—
364C22×C43—81no—
365C22×C43—81no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—81no—
369C22×C43C2×#12311yescharacteristic
370C22×C43#53411yescharacteristic
371C22×C43#53411yescharacteristic
372C22×C43C2×#13511yescharacteristic
373C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
374C22×C43#57511yescharacteristic
375C22×C43#57511yescharacteristic
376C4×C43—22no—
377C4×C43—41no—
378C4×C43—41no—
379C4×C43—81no—
380C4×C43—81no—
381C4×C43—81no—
382C4×C43—81no—
383C4×C43—81no—
384C4×C43—81no—
385C4×C43—81no—
386C4×C43#53811yescharacteristic
387C4×C43#53811yescharacteristic
388C4×C43#53811yescharacteristic
389C4×C43#53811yescharacteristic
390#2847C2×C4311yescharacteristic
391#2280C2×C4311yescharacteristic, complemented
392#2077C2×C4311yescharacteristic, complemented
393#2077C2×C4311yescharacteristic, complemented
394#2076C2×C4311yescharacteristic, complemented
395#2075C2×C4311yescharacteristic, complemented
396#2034C2×C4311yescharacteristic, complemented
397#2034C2×C4311yescharacteristic, complemented
398#2033C2×C4311yescharacteristic, complemented
399#2033C2×C4311yescharacteristic, complemented
400#1875C2×C4311yescharacteristic, complemented
401#1875C2×C4311yescharacteristic, complemented
402#1854C2×C4311yescharacteristic, complemented
403#1854C2×C4311yescharacteristic, complemented
404#1779C2×C4311yescharacteristic, complemented
405C2×C43—42no—
406C2×C43—42no—
407C2×C43—42no—
408C2×C43—161no—
409C2×C43#262211yescharacteristic
410C2×C43#309111yescharacteristic
411C2×C43#309411yescharacteristic
412C2×C43#318811yescharacteristic
413C2×C43#319111yescharacteristic
414C2×C43#319411yescharacteristic
415C2×C43#319711yescharacteristic
416C24×C4C22×C4311yescharacteristic
417C2×#121C22×C4311yescharacteristic
418C2×#121C22×C4311yescharacteristic
419C2×#121C22×C4311yescharacteristic
420C2×#120—21no—
421C2×#117C22×C4311yescharacteristic
422C2×#117C22×C4311yescharacteristic
423C2×#107C22×C4311yescharacteristic, complemented
424C2×#107C22×C4311yescharacteristic, complemented
425C2×#106C22×C4311yescharacteristic, complemented
426C2×#106C22×C4311yescharacteristic, complemented
427C2×#102C22×C4311yescharacteristic, complemented
428C2×#102C22×C4311yescharacteristic, complemented
429C2×#102C22×C4311yescharacteristic, complemented
430C2×#102C22×C4311yescharacteristic, complemented
431C2×C22⋊C8C22×C4311yescharacteristic
432C2×C22⋊C8C22×C4311yescharacteristic
433C2×C22⋊C8C22×C4311yescharacteristic
434C2×C22⋊C8C22×C4311yescharacteristic
435C2×C22⋊C8C22×C4311yescharacteristic
436C2×C22⋊C8C22×C4311yescharacteristic
437#386—21no—
438#386—21no—
439#386—21no—
440#381—21no—
441#380C22×C4311yescharacteristic
442#380C22×C4311yescharacteristic
443#380C22×C4311yescharacteristic
444#380C22×C4311yescharacteristic
445#380C22×C4311yescharacteristic
446#380C22×C4311yescharacteristic
447#380C22×C4311yescharacteristic
448#379—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451#340C22×C4311yescharacteristic, complemented
452#340C22×C4311yescharacteristic, complemented
453#340C22×C4311yescharacteristic, complemented
454#340C22×C4311yescharacteristic, complemented
455#340C22×C4311yescharacteristic, complemented
456#340C22×C4311yescharacteristic, complemented
457#340C22×C4311yescharacteristic, complemented
458#340C22×C4311yescharacteristic, complemented
459C43#2989611yescharacteristic, direct product factor, Sylow
460C25D4×C4311yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—21no—
464C22×D4C23×C4311yescharacteristic
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—41no—
468C23×C4—41no—
469C23×C4—41no—
470C23×C4—41no—
471C23×C4D4×C4311yescharacteristic
472C23×C4D4×C4311yescharacteristic
473C23×C4D4×C4311yescharacteristic
474C23×C4C23×C4311yescharacteristic
475C23×C4C23×C4311yescharacteristic
476C23×C4C23×C4311yescharacteristic
477C22×C8C23×C4311yescharacteristic
478C22×C8C23×C4311yescharacteristic
479C22×C8C23×C4311yescharacteristic
480C22×C8C23×C4311yescharacteristic
481#121—22no—
482#121—22no—
483#121—41no—
484#121—41no—
485#121—41no—
486#121—41no—
487#120—44no—
488#117—41no—
489#117—41no—
490#117—41no—
491#117—41no—
492C2×C4⋊C4C23×C4311yescharacteristic
493C2×C4⋊C4C23×C4311yescharacteristic
494C2×C4⋊C4C23×C4311yescharacteristic
495C2×C4⋊C4C23×C4311yescharacteristic
496C2×C4⋊C4C23×C4311yescharacteristic
497C2×C4⋊C4C23×C4311yescharacteristic
498C2×C4⋊C4C23×C4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C42—21no—
512C2×C42—21no—
513#107—41no—
514#107—41no—
515#106—41no—
516#106—41no—
517#102—41no—
518#102—41no—
519#102—41no—
520#102—41no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523C22⋊C8—41no—
524C22⋊C8—41no—
525C22⋊C8—41no—
526C22⋊C8—41no—
527#95—21no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—21no—
538C24—41no—
539C24—41no—
540C24—41no—
541C24—41no—
542C24C2×D4×C4311yescharacteristic
543C24C2×D4×C4311yescharacteristic
544C24C2×D4×C4311yescharacteristic
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
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—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4C2×D4×C4311yescharacteristic
597C22×C4C2×D4×C4311yescharacteristic
598C22×C4C2×D4×C4311yescharacteristic
599C22×C4#41×C4312yes—
600C22×C4#41×C4312yes—
601C22×C4C24×C4311yescharacteristic
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C22⋊C4—42no—
629C22⋊C4—42no—
630C22⋊C4—42no—
631C22⋊C4—42no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C42—42no—
641C42—42no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23#123×C4312yes—
675C23#135×C4312yes—
676C23AGL(1,ℤ/8)×C4312yes—
677C23C22×D4×C4311yescharacteristic
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—84no—
683D4—84no—
684D4—84no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—44no—
699C2×C4—44no—
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—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4#123×C4312yes—
730C2×C4C2×#41×C4311yescharacteristic
731C2×C4C2×#41×C4311yescharacteristic
732C2×C4H(5,𝔽2)×C4311yescharacteristic
733C2×C4H(5,𝔽2)×C4311yescharacteristic
734C2×C4H(5,𝔽2)×C4311yescharacteristic
735C2×C4H(5,𝔽2)×C4311yescharacteristic
736C8—41no—
737C8—41no—
738C8—41no—
739C8—41no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—416no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22C2×#123×C4311yescharacteristic
770C22C43×#53411yescharacteristic
771C22C43×#53411yescharacteristic
772C22C2×#135×C4311yescharacteristic
773C22C2×AGL(1,ℤ/8)×C4311yescharacteristic
774C22C43×#57511yescharacteristic
775C22C43×#57511yescharacteristic
776C4—22no—
777C4—41no—
778C4—41no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4—81no—
785C4—81no—
786C4C43×#53811yescharacteristic
787C4C43×#53811yescharacteristic
788C4C43×#53811yescharacteristic
789C4C43×#53811yescharacteristic
790C2—42no—
791C2—42no—
792C2—42no—
793C2—161no—
794C2C43×#262211yescharacteristic
795C2C43×#309111yescharacteristic
796C2C43×#309411yescharacteristic
797C2C43×#318811yescharacteristic
798C2C43×#319111yescharacteristic
799C2C43×#319411yescharacteristic
800C2C43×#319711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C24×C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2280C2semidirect
3. C43×#2077C2semidirect
4. C43×#2077C2semidirect
5. C43×#2076C2semidirect
6. C43×#2075C2semidirect
7. C43×#2034C2semidirect
8. C43×#2034C2semidirect
9. C43×#2033C2semidirect
10. C43×#2033C2semidirect
11. C43×#1875C2semidirect
12. C43×#1875C2semidirect
13. C43×#1854C2semidirect
14. C43×#1854C2semidirect
15. C43×#1779C2semidirect
23. C2×#107×C43C22semidirect
24. C2×#107×C43C22semidirect
25. C2×#106×C43C22semidirect
26. C2×#106×C43C22semidirect
27. C2×#102×C43C22semidirect
28. C2×#102×C43C22semidirect
29. C2×#102×C43C22semidirect
30. C2×#102×C43C22semidirect
51. C43×#340C22semidirect
52. C43×#340C22semidirect
53. C43×#340C22semidirect
54. C43×#340C22semidirect
55. C43×#340C22semidirect
56. C43×#340C22semidirect
57. C43×#340C22semidirect
58. C43×#340C22semidirect
339. #29896C43direct (N × H)
391. #2280C2×C43semidirect
392. #2077C2×C43semidirect
393. #2077C2×C43semidirect
394. #2076C2×C43semidirect
395. #2075C2×C43semidirect
396. #2034C2×C43semidirect
397. #2034C2×C43semidirect
398. #2033C2×C43semidirect
399. #2033C2×C43semidirect
400. #1875C2×C43semidirect
401. #1875C2×C43semidirect
402. #1854C2×C43semidirect
403. #1854C2×C43semidirect
404. #1779C2×C43semidirect
423. C2×#107C22×C43semidirect
424. C2×#107C22×C43semidirect
425. C2×#106C22×C43semidirect
426. C2×#106C22×C43semidirect
427. C2×#102C22×C43semidirect
428. C2×#102C22×C43semidirect
429. C2×#102C22×C43semidirect
430. C2×#102C22×C43semidirect
451. #340C22×C43semidirect
452. #340C22×C43semidirect
453. #340C22×C43semidirect
454. #340C22×C43semidirect
455. #340C22×C43semidirect
456. #340C22×C43semidirect
457. #340C22×C43semidirect
458. #340C22×C43semidirect
459. C43#29896direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#28472
C43×#22802
C43×#20772
C43×#20762
C43×#20752
C43×#20342
C43×#20332
C43×#18752
C43×#18542
C43×#17792
#2989643