Finite Group Databasebeta

← C43×#29897 #24949914

Subgroups — C43×#29897 #24949914

Order 11008.

978 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2848C211yesmaximal, characteristic
2C43×#2280C211yesmaximal, characteristic
3C43×#2077C211yesmaximal, characteristic, complemented
4C43×#2077C211yesmaximal, characteristic, complemented
5C43×#2076C211yesmaximal, characteristic, complemented
6C43×#2075C211yesmaximal, characteristic, complemented
7C43×#2036C211yesmaximal, characteristic, complemented
8C43×#2036C211yesmaximal, characteristic, complemented
9C43×#2035C211yesmaximal, characteristic, complemented
10C43×#2035C211yesmaximal, characteristic, complemented
11C43×#1873C211yesmaximal, characteristic, complemented
12C43×#1873C211yesmaximal, characteristic, complemented
13C43×#1854C211yesmaximal, characteristic, complemented
14C43×#1854C211yesmaximal, characteristic, complemented
15C43×#1779C211yesmaximal, characteristic
16C24×C4×C43C2211yescharacteristic
17C2×C22⋊Q8×C43C2211yescharacteristic
18C2×C22⋊Q8×C43C2211yescharacteristic
19C2×C22⋊Q8×C43C2211yescharacteristic
20C2×#117×C43C2211yescharacteristic
21C2×#117×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic, complemented
23C2×#107×C43C2211yescharacteristic, complemented
24C2×#106×C43C2211yescharacteristic, complemented
25C2×#106×C43C2211yescharacteristic, complemented
26C2×#103×C43C2211yescharacteristic, complemented
27C2×#103×C43C2211yescharacteristic, complemented
28C2×#103×C43C2211yescharacteristic, complemented
29C2×#103×C43C2211yescharacteristic, complemented
30C2×C22⋊C8×C43C2211yescharacteristic
31C2×C22⋊C8×C43C2211yescharacteristic
32C2×C22⋊C8×C43C2211yescharacteristic
33C2×C22⋊C8×C43C2211yescharacteristic
34C2×C22⋊C8×C43C2211yescharacteristic
35C2×C22⋊C8×C43C2211yescharacteristic
36C43×#385—21no—
37C43×#385—21no—
38C43×#385—21no—
39C43×#381—21no—
40C43×#380C2211yescharacteristic
41C43×#380C2211yescharacteristic
42C43×#380C2211yescharacteristic
43C43×#380C2211yescharacteristic
44C43×#380C2211yescharacteristic
45C43×#380C2211yescharacteristic
46C43×#380C2211yescharacteristic
47C43×#379—21no—
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×Q8×C43C2311yescharacteristic
61C23×C4×C43—22no—
62C23×C4×C43—22no—
63C23×C4×C43—41no—
64C23×C4×C43—41no—
65C23×C4×C43—41no—
66C23×C4×C43—41no—
67C23×C4×C43D411yescharacteristic
68C23×C4×C43D411yescharacteristic
69C23×C4×C43D411yescharacteristic
70C23×C4×C43C2311yescharacteristic
71C23×C4×C43C2311yescharacteristic
72C23×C4×C43C2311yescharacteristic
73C22×C8×C43C2311yescharacteristic
74C22×C8×C43C2311yescharacteristic
75C22×C8×C43C2311yescharacteristic
76C22×C8×C43C2311yescharacteristic
77C22⋊Q8×C43—22no—
78C22⋊Q8×C43—22no—
79C22⋊Q8×C43—41no—
80C22⋊Q8×C43—41no—
81C22⋊Q8×C43—41no—
82C22⋊Q8×C43—41no—
83#117×C43—41no—
84#117×C43—41no—
85#117×C43—41no—
86#117×C43—41no—
87C2×C4⋊C4×C43—21no—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43C2311yescharacteristic
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×C22⋊C4×C43—21no—
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×C42×C43—21no—
110C2×C42×C43—21no—
111#107×C43—41no—
112#107×C43—41no—
113#106×C43—41no—
114#106×C43—41no—
115#103×C43—41no—
116#103×C43—41no—
117#103×C43—41no—
118#103×C43—41no—
119C22⋊C8×C43—22no—
120C22⋊C8×C43—22no—
121C22⋊C8×C43—41no—
122C22⋊C8×C43—41no—
123C22⋊C8×C43—41no—
124C22⋊C8×C43—41no—
125#95×C43—21no—
126#95×C43—21no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132C24×C43—22no—
133C24×C43—22no—
134C24×C43—22no—
135C24×C43—41no—
136C24×C43—41no—
137C24×C43—41no—
138C24×C43—41no—
139C24×C43C2×D411yescharacteristic
140C24×C43C2×D411yescharacteristic
141C24×C43C2×D411yescharacteristic
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—22no—
153C22×C4×C43—22no—
154C22×C4×C43—21no—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—22no—
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—41no—
176C22×C4×C43—41no—
177C22×C4×C43—41no—
178C22×C4×C43—41no—
179C22×C4×C43—41no—
180C22×C4×C43—41no—
181C22×C4×C43—44no—
182C22×C4×C43—44no—
183C22×C4×C43—44no—
184C22×C4×C43—44no—
185C22×C4×C43C2×D411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C22×C4×C43#4112yes—
189C22×C4×C43#4112yes—
190C22×C4×C43C2411yescharacteristic
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—21no—
208C4⋊C4×C43—21no—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—42no—
218C4⋊C4×C43—42no—
219C4⋊C4×C43—42no—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—42no—
223C22⋊C4×C43—42no—
224C22⋊C4×C43—42no—
225C22⋊C4×C43—42no—
226C22⋊C4×C43—42no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—42no—
231C22⋊C4×C43—42no—
232C42×C43—42no—
233C42×C43—42no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
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—44no—
253C23×C43—44no—
254C23×C43—44no—
255C23×C43—44no—
256C23×C43—44no—
257C23×C43—44no—
258C23×C43—44no—
259C23×C43#12312yes—
260C23×C43#13512yes—
261C23×C43#13712yes—
262C23×C43C22×D411yescharacteristic
263Q8×C43—41no—
264Q8×C43—41no—
265Q8×C43—41no—
266Q8×C43—41no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—44no—
280C2×C4×C43—44no—
281C2×C4×C43—44no—
282C2×C4×C43—41no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—41no—
297C2×C4×C43—41no—
298C2×C4×C43—41no—
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#12312yes—
315C2×C4×C43C2×#4111yescharacteristic
316C2×C4×C43C2×#4111yescharacteristic
317C2×C4×C43H(5,𝔽2)11yescharacteristic
318C2×C4×C43H(5,𝔽2)11yescharacteristic
319C2×C4×C43H(5,𝔽2)11yescharacteristic
320C2×C4×C43H(5,𝔽2)11yescharacteristic
321C8×C43—41no—
322C8×C43—41no—
323C8×C43—41no—
324C8×C43—41no—
325#29897C4311yesmaximal, characteristic, direct product factor, Sylow
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—22no—
329C22×C43—22no—
330C22×C43—22no—
331C22×C43—22no—
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—416no—
336C22×C43—41no—
337C22×C43—41no—
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×C43C2×#12311yescharacteristic
349C22×C43#53411yescharacteristic
350C22×C43#53411yescharacteristic
351C22×C43C2×#13511yescharacteristic
352C22×C43C2×#13711yescharacteristic
353C22×C43#57511yescharacteristic
354C22×C43#57511yescharacteristic
355C4×C43—22no—
356C4×C43—41no—
357C4×C43—41no—
358C4×C43—81no—
359C4×C43—81no—
360C4×C43—81no—
361C4×C43—81no—
362C4×C43—81no—
363C4×C43—81no—
364C4×C43—81no—
365C4×C43—81no—
366C4×C43#53811yescharacteristic
367C4×C43#53811yescharacteristic
368C4×C43#53811yescharacteristic
369C4×C43#53811yescharacteristic
370#2848C2×C4311yescharacteristic
371#2280C2×C4311yescharacteristic
372#2077C2×C4311yescharacteristic, complemented
373#2077C2×C4311yescharacteristic, complemented
374#2076C2×C4311yescharacteristic, complemented
375#2075C2×C4311yescharacteristic, complemented
376#2036C2×C4311yescharacteristic, complemented
377#2036C2×C4311yescharacteristic, complemented
378#2035C2×C4311yescharacteristic, complemented
379#2035C2×C4311yescharacteristic, complemented
380#1873C2×C4311yescharacteristic, complemented
381#1873C2×C4311yescharacteristic, complemented
382#1854C2×C4311yescharacteristic, complemented
383#1854C2×C4311yescharacteristic, complemented
384#1779C2×C4311yescharacteristic
385C2×C43—42no—
386C2×C43—42no—
387C2×C43—42no—
388C2×C43#262211yescharacteristic
389C2×C43#309111yescharacteristic
390C2×C43#309511yescharacteristic
391C2×C43#319011yescharacteristic
392C2×C43#319111yescharacteristic
393C2×C43#319611yescharacteristic
394C2×C43#319711yescharacteristic
395C24×C4C22×C4311yescharacteristic
396C2×C22⋊Q8C22×C4311yescharacteristic
397C2×C22⋊Q8C22×C4311yescharacteristic
398C2×C22⋊Q8C22×C4311yescharacteristic
399C2×#117C22×C4311yescharacteristic
400C2×#117C22×C4311yescharacteristic
401C2×#107C22×C4311yescharacteristic, complemented
402C2×#107C22×C4311yescharacteristic, complemented
403C2×#106C22×C4311yescharacteristic, complemented
404C2×#106C22×C4311yescharacteristic, complemented
405C2×#103C22×C4311yescharacteristic, complemented
406C2×#103C22×C4311yescharacteristic, complemented
407C2×#103C22×C4311yescharacteristic, complemented
408C2×#103C22×C4311yescharacteristic, complemented
409C2×C22⋊C8C22×C4311yescharacteristic
410C2×C22⋊C8C22×C4311yescharacteristic
411C2×C22⋊C8C22×C4311yescharacteristic
412C2×C22⋊C8C22×C4311yescharacteristic
413C2×C22⋊C8C22×C4311yescharacteristic
414C2×C22⋊C8C22×C4311yescharacteristic
415#385—21no—
416#385—21no—
417#385—21no—
418#381—21no—
419#380C22×C4311yescharacteristic
420#380C22×C4311yescharacteristic
421#380C22×C4311yescharacteristic
422#380C22×C4311yescharacteristic
423#380C22×C4311yescharacteristic
424#380C22×C4311yescharacteristic
425#380C22×C4311yescharacteristic
426#379—21no—
427#379—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430#340C22×C4311yescharacteristic, complemented
431#340C22×C4311yescharacteristic, complemented
432#340C22×C4311yescharacteristic, complemented
433#340C22×C4311yescharacteristic, complemented
434#340C22×C4311yescharacteristic, complemented
435#340C22×C4311yescharacteristic, complemented
436#340C22×C4311yescharacteristic, complemented
437#340C22×C4311yescharacteristic, complemented
438C43#2989711yescharacteristic, direct product factor, Sylow
439C25D4×C4311yescharacteristic
440C22×Q8C23×C4311yescharacteristic
441C23×C4—22no—
442C23×C4—22no—
443C23×C4—41no—
444C23×C4—41no—
445C23×C4—41no—
446C23×C4—41no—
447C23×C4D4×C4311yescharacteristic
448C23×C4D4×C4311yescharacteristic
449C23×C4D4×C4311yescharacteristic
450C23×C4C23×C4311yescharacteristic
451C23×C4C23×C4311yescharacteristic
452C23×C4C23×C4311yescharacteristic
453C22×C8C23×C4311yescharacteristic
454C22×C8C23×C4311yescharacteristic
455C22×C8C23×C4311yescharacteristic
456C22×C8C23×C4311yescharacteristic
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—41no—
460C22⋊Q8—41no—
461C22⋊Q8—41no—
462C22⋊Q8—41no—
463#117—41no—
464#117—41no—
465#117—41no—
466#117—41no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4C23×C4311yescharacteristic
471C2×C4⋊C4C23×C4311yescharacteristic
472C2×C4⋊C4C23×C4311yescharacteristic
473C2×C4⋊C4C23×C4311yescharacteristic
474C2×C4⋊C4C23×C4311yescharacteristic
475C2×C4⋊C4C23×C4311yescharacteristic
476C2×C4⋊C4C23×C4311yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C42—21no—
490C2×C42—21no—
491#107—41no—
492#107—41no—
493#106—41no—
494#106—41no—
495#103—41no—
496#103—41no—
497#103—41no—
498#103—41no—
499C22⋊C8—22no—
500C22⋊C8—22no—
501C22⋊C8—41no—
502C22⋊C8—41no—
503C22⋊C8—41no—
504C22⋊C8—41no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95—21no—
510#95—21no—
511#95—21no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—41no—
516C24—41no—
517C24—41no—
518C24—41no—
519C24C2×D4×C4311yescharacteristic
520C24C2×D4×C4311yescharacteristic
521C24C2×D4×C4311yescharacteristic
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4C2×D4×C4311yescharacteristic
566C22×C4C2×D4×C4311yescharacteristic
567C22×C4C2×D4×C4311yescharacteristic
568C22×C4#41×C4312yes—
569C22×C4#41×C4312yes—
570C22×C4C24×C4311yescharacteristic
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—42no—
607C22⋊C4—42no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C42—42no—
613C42—42no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23#123×C4312yes—
640C23#135×C4312yes—
641C23#137×C4312yes—
642C23C22×D4×C4311yescharacteristic
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4#123×C4312yes—
695C2×C4C2×#41×C4311yescharacteristic
696C2×C4C2×#41×C4311yescharacteristic
697C2×C4H(5,𝔽2)×C4311yescharacteristic
698C2×C4H(5,𝔽2)×C4311yescharacteristic
699C2×C4H(5,𝔽2)×C4311yescharacteristic
700C2×C4H(5,𝔽2)×C4311yescharacteristic
701C8—41no—
702C8—41no—
703C8—41no—
704C8—41no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—416no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—41no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22C2×#123×C4311yescharacteristic
728C22C43×#53411yescharacteristic
729C22C43×#53411yescharacteristic
730C22C2×#135×C4311yescharacteristic
731C22C2×#137×C4311yescharacteristic
732C22C43×#57511yescharacteristic
733C22C43×#57511yescharacteristic
734C4—22no—
735C4—41no—
736C4—41no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4—81no—
743C4—81no—
744C4—81no—
745C4C43×#53811yescharacteristic
746C4C43×#53811yescharacteristic
747C4C43×#53811yescharacteristic
748C4C43×#53811yescharacteristic
749C2—42no—
750C2—42no—
751C2—42no—
752C2C43×#262211yescharacteristic
753C2C43×#309111yescharacteristic
754C2C43×#309511yescharacteristic
755C2C43×#319011yescharacteristic
756C2C43×#319111yescharacteristic
757C2C43×#319611yescharacteristic
758C2C43×#319711yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC25×C43D4
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
3. C43×#2077C2semidirect
4. C43×#2077C2semidirect
5. C43×#2076C2semidirect
6. C43×#2075C2semidirect
7. C43×#2036C2semidirect
8. C43×#2036C2semidirect
9. C43×#2035C2semidirect
10. C43×#2035C2semidirect
11. C43×#1873C2semidirect
12. C43×#1873C2semidirect
13. C43×#1854C2semidirect
14. C43×#1854C2semidirect
22. C2×#107×C43C22semidirect
23. C2×#107×C43C22semidirect
24. C2×#106×C43C22semidirect
25. C2×#106×C43C22semidirect
26. C2×#103×C43C22semidirect
27. C2×#103×C43C22semidirect
28. C2×#103×C43C22semidirect
29. C2×#103×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
325. #29897C43direct (N × H)
372. #2077C2×C43semidirect
373. #2077C2×C43semidirect
374. #2076C2×C43semidirect
375. #2075C2×C43semidirect
376. #2036C2×C43semidirect
377. #2036C2×C43semidirect
378. #2035C2×C43semidirect
379. #2035C2×C43semidirect
380. #1873C2×C43semidirect
381. #1873C2×C43semidirect
382. #1854C2×C43semidirect
383. #1854C2×C43semidirect
401. C2×#107C22×C43semidirect
402. C2×#107C22×C43semidirect
403. C2×#106C22×C43semidirect
404. C2×#106C22×C43semidirect
405. C2×#103C22×C43semidirect
406. C2×#103C22×C43semidirect
407. C2×#103C22×C43semidirect
408. C2×#103C22×C43semidirect
430. #340C22×C43semidirect
431. #340C22×C43semidirect
432. #340C22×C43semidirect
433. #340C22×C43semidirect
434. #340C22×C43semidirect
435. #340C22×C43semidirect
436. #340C22×C43semidirect
437. #340C22×C43semidirect
438. C43#29897direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#28482
C43×#22802
C43×#20772
C43×#20762
C43×#20752
C43×#20362
C43×#20352
C43×#18732
C43×#18542
C43×#17792
#2989743