Finite Group Databasebeta

← C43×#29898 #24949915

Subgroups — C43×#29898 #24949915

Order 11008.

922 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#2615C211yesmaximal, characteristic
2C43×#2311C211yesmaximal, characteristic, complemented
3C43×#2077C211yesmaximal, characteristic, complemented
4C43×#2076C211yesmaximal, characteristic, complemented
5C43×#2076C211yesmaximal, characteristic, complemented
6C43×#2075C211yesmaximal, characteristic, complemented
7C43×#2034C211yesmaximal, characteristic, complemented
8C43×#2033C211yesmaximal, characteristic, complemented
9C43×#2033C211yesmaximal, characteristic, complemented
10C43×#2033C211yesmaximal, characteristic, complemented
11C43×#1875C211yesmaximal, characteristic, complemented
12C43×#1874C211yesmaximal, characteristic, complemented
13C43×#1854C211yesmaximal, characteristic, complemented
14C43×#1852C211yesmaximal, characteristic, complemented
15C43×#1780C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C2×#121×C43C2211yescharacteristic
18C2×#121×C43C2211yescharacteristic
19C2×#121×C43C2211yescharacteristic
20C2×#117×C43C2211yescharacteristic
21C22×C4⋊C4×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C2×#107×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C2×#106×C43C2211yescharacteristic
26C2×#102×C43C2211yescharacteristic
27C2×#102×C43C2211yescharacteristic
28C2×#102×C43C2211yescharacteristic
29C2×#102×C43C2211yescharacteristic
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×#393—21no—
37C43×#392—21no—
38C43×#392—21no—
39C43×#392—21no—
40C43×#391—21no—
41C43×#390—21no—
42C43×#386—21no—
43C43×#386—21no—
44C43×#380C2211yescharacteristic
45C43×#380C2211yescharacteristic
46C43×#380C2211yescharacteristic
47C43×#380C2211yescharacteristic
48C43×#380C2211yescharacteristic
49C43×#380C2211yescharacteristic
50C43×#380C2211yescharacteristic
51C43×#340C2211yescharacteristic
52C43×#340C2211yescharacteristic
53C43×#340C2211yescharacteristic
54C43×#340C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C2×#41×C43—22no—
60C2×#41×C43—22no—
61C2×#41×C43—41no—
62C2×#41×C43—41no—
63C2×#41×C43—41no—
64C2×#41×C43—41no—
65C22×Q8×C43D411yescharacteristic
66C22×D4×C43—21no—
67C22×D4×C43—21no—
68C22×D4×C43—21no—
69C22×D4×C43D411yescharacteristic
70C22×D4×C43D411yescharacteristic
71C22×D4×C43D411yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C23×C4×C43—21no—
74C23×C4×C43C2311yescharacteristic
75C23×C4×C43C2311yescharacteristic
76C23×C4×C43C2311yescharacteristic
77C22×C8×C43C2311yescharacteristic
78C22×C8×C43C2311yescharacteristic
79C22×C8×C43C2311yescharacteristic
80C22×C8×C43C2311yescharacteristic
81#121×C43—22no—
82#121×C43—22no—
83#121×C43—41no—
84#121×C43—41no—
85#121×C43—41no—
86#121×C43—41no—
87#117×C43—41no—
88#117×C43—41no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43—41no—
91C2×C4⋊C4×C43—41no—
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×C4⋊C4×C43C2311yescharacteristic
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—
111#107×C43—41no—
112#107×C43—41no—
113#107×C43—41no—
114#106×C43—41no—
115#102×C43—41no—
116#102×C43—41no—
117#102×C43—41no—
118#102×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—21no—
133C24×C43C2×D411yescharacteristic
134C24×C43C2×D411yescharacteristic
135C24×C43C2×D411yescharacteristic
136#41×C43—44no—
137#41×C43—44no—
138#41×C43—44no—
139#41×C43—44no—
140C2×Q8×C43—22no—
141C2×Q8×C43—41no—
142C2×Q8×C43—41no—
143C2×D4×C43—22no—
144C2×D4×C43—22no—
145C2×D4×C43—22no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43—41no—
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43—41no—
158C2×D4×C43—42no—
159C2×D4×C43—42no—
160C2×D4×C43—42no—
161C2×D4×C43—81no—
162C2×D4×C43—81no—
163C2×D4×C43—81no—
164C2×D4×C43—81no—
165C2×D4×C43—81no—
166C2×D4×C43—81no—
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—21no—
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—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—42no—
191C22×C4×C43—81no—
192C22×C4×C43—81no—
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43#4112yes—
197C22×C4×C43#4112yes—
198C22×C4×C43C2411yescharacteristic
199C2×C8×C43—21no—
200C2×C8×C43—21no—
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—
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—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—42no—
226C22⋊C4×C43—42no—
227C22⋊C4×C43—42no—
228C22⋊C4×C43—42no—
229C22⋊C4×C43—42no—
230C22⋊C4×C43—81no—
231C22⋊C4×C43—81no—
232C22⋊C4×C43—81no—
233C22⋊C4×C43—81no—
234C22⋊C4×C43—81no—
235C22⋊C4×C43—81no—
236C22⋊C4×C43—81no—
237C42×C43—42no—
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—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—21no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43#12312yes—
266C23×C43C22×D411yescharacteristic
267Q8×C43—44no—
268D4×C43—44no—
269D4×C43—44no—
270D4×C43—44no—
271D4×C43—41no—
272D4×C43—41no—
273D4×C43—41no—
274D4×C43—41no—
275D4×C43—84no—
276D4×C43—84no—
277D4×C43—84no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
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—41no—
315C2×C4×C43—41no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43—84no—
320C2×C4×C43#12312yes—
321C2×C4×C43C2×#4111yescharacteristic
322C2×C4×C43C2×#4111yescharacteristic
323C2×C4×C43H(5,𝔽2)11yescharacteristic
324C2×C4×C43H(5,𝔽2)11yescharacteristic
325C2×C4×C43H(5,𝔽2)11yescharacteristic
326C2×C4×C43H(5,𝔽2)11yescharacteristic
327C8×C43—41no—
328C8×C43—41no—
329C8×C43—41no—
330C8×C43—41no—
331#29898C4311yesmaximal, characteristic, direct product factor, Sylow
332C22×C43—22no—
333C22×C43—22no—
334C22×C43—22no—
335C22×C43—41no—
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×C43—41no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43—41no—
352C22×C43—41no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43C2×#12311yescharacteristic
361C22×C43#53411yescharacteristic
362C22×C43#53411yescharacteristic
363C22×C43#57611yescharacteristic
364C22×C43#57611yescharacteristic
365C22×C43#57711yescharacteristic
366C22×C43#57811yescharacteristic
367C4×C43—22no—
368C4×C43—41no—
369C4×C43—41no—
370C4×C43—81no—
371C4×C43—81no—
372C4×C43—81no—
373C4×C43—81no—
374C4×C43—81no—
375C4×C43—81no—
376C4×C43—81no—
377C4×C43#53811yescharacteristic
378C4×C43#53811yescharacteristic
379C4×C43#53811yescharacteristic
380C4×C43#53811yescharacteristic
381#2615C2×C4311yescharacteristic
382#2311C2×C4311yescharacteristic, complemented
383#2077C2×C4311yescharacteristic, complemented
384#2076C2×C4311yescharacteristic, complemented
385#2076C2×C4311yescharacteristic, complemented
386#2075C2×C4311yescharacteristic, complemented
387#2034C2×C4311yescharacteristic, complemented
388#2033C2×C4311yescharacteristic, complemented
389#2033C2×C4311yescharacteristic, complemented
390#2033C2×C4311yescharacteristic, complemented
391#1875C2×C4311yescharacteristic, complemented
392#1874C2×C4311yescharacteristic, complemented
393#1854C2×C4311yescharacteristic, complemented
394#1852C2×C4311yescharacteristic, complemented
395#1780C2×C4311yescharacteristic, complemented
396C2×C43—42no—
397C2×C43—81no—
398C2×C43—81no—
399C2×C43—161no—
400C2×C43#262211yescharacteristic
401C2×C43#309611yescharacteristic
402C2×C43#309811yescharacteristic
403C2×C43#319811yescharacteristic
404C2×C43#319911yescharacteristic
405C2×C43#320111yescharacteristic
406C2×C43#320311yescharacteristic
407C22×#41C22×C4311yescharacteristic
408C2×#121C22×C4311yescharacteristic
409C2×#121C22×C4311yescharacteristic
410C2×#121C22×C4311yescharacteristic
411C2×#117C22×C4311yescharacteristic
412C22×C4⋊C4C22×C4311yescharacteristic
413C2×#107C22×C4311yescharacteristic
414C2×#107C22×C4311yescharacteristic
415C2×#107C22×C4311yescharacteristic
416C2×#106C22×C4311yescharacteristic
417C2×#102C22×C4311yescharacteristic
418C2×#102C22×C4311yescharacteristic
419C2×#102C22×C4311yescharacteristic
420C2×#102C22×C4311yescharacteristic
421C2×C22⋊C8C22×C4311yescharacteristic
422C2×C22⋊C8C22×C4311yescharacteristic
423C2×C22⋊C8C22×C4311yescharacteristic
424C2×C22⋊C8C22×C4311yescharacteristic
425C2×C22⋊C8C22×C4311yescharacteristic
426C2×C22⋊C8C22×C4311yescharacteristic
427#393—21no—
428#392—21no—
429#392—21no—
430#392—21no—
431#391—21no—
432#390—21no—
433#386—21no—
434#386—21no—
435#380C22×C4311yescharacteristic
436#380C22×C4311yescharacteristic
437#380C22×C4311yescharacteristic
438#380C22×C4311yescharacteristic
439#380C22×C4311yescharacteristic
440#380C22×C4311yescharacteristic
441#380C22×C4311yescharacteristic
442#340C22×C4311yescharacteristic
443#340C22×C4311yescharacteristic
444#340C22×C4311yescharacteristic
445#340C22×C4311yescharacteristic
446#340C22×C4311yescharacteristic
447#340C22×C4311yescharacteristic
448#340C22×C4311yescharacteristic
449#340C22×C4311yescharacteristic
450C43#2989811yescharacteristic, direct product factor, Sylow
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—41no—
454C2×#41—41no—
455C2×#41—41no—
456C2×#41—41no—
457C22×Q8D4×C4311yescharacteristic
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4D4×C4311yescharacteristic
462C22×D4D4×C4311yescharacteristic
463C22×D4D4×C4311yescharacteristic
464C22×D4C23×C4311yescharacteristic
465C23×C4—21no—
466C23×C4C23×C4311yescharacteristic
467C23×C4C23×C4311yescharacteristic
468C23×C4C23×C4311yescharacteristic
469C22×C8C23×C4311yescharacteristic
470C22×C8C23×C4311yescharacteristic
471C22×C8C23×C4311yescharacteristic
472C22×C8C23×C4311yescharacteristic
473#121—22no—
474#121—22no—
475#121—41no—
476#121—41no—
477#121—41no—
478#121—41no—
479#117—41no—
480#117—41no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4C23×C4311yescharacteristic
485C2×C4⋊C4C23×C4311yescharacteristic
486C2×C4⋊C4C23×C4311yescharacteristic
487C2×C4⋊C4C23×C4311yescharacteristic
488C2×C4⋊C4C23×C4311yescharacteristic
489C2×C4⋊C4C23×C4311yescharacteristic
490C2×C4⋊C4C23×C4311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C42—21no—
503#107—41no—
504#107—41no—
505#107—41no—
506#106—41no—
507#102—41no—
508#102—41no—
509#102—41no—
510#102—41no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513C22⋊C8—41no—
514C22⋊C8—41no—
515C22⋊C8—41no—
516C22⋊C8—41no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524C24—21no—
525C24C2×D4×C4311yescharacteristic
526C24C2×D4×C4311yescharacteristic
527C24C2×D4×C4311yescharacteristic
528#41—44no—
529#41—44no—
530#41—44no—
531#41—44no—
532C2×Q8—22no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—81no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—81no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
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—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4C2×D4×C4311yescharacteristic
586C22×C4C2×D4×C4311yescharacteristic
587C22×C4C2×D4×C4311yescharacteristic
588C22×C4#41×C4312yes—
589C22×C4#41×C4312yes—
590C22×C4C24×C4311yescharacteristic
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—21no—
601C2×C8—21no—
602C2×C8—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
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—21no—
617C4⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C42—42no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
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#123×C4312yes—
658C23C22×D4×C4311yescharacteristic
659Q8—44no—
660D4—44no—
661D4—44no—
662D4—44no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—84no—
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—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
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—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—84no—
712C2×C4#123×C4312yes—
713C2×C4C2×#41×C4311yescharacteristic
714C2×C4C2×#41×C4311yescharacteristic
715C2×C4H(5,𝔽2)×C4311yescharacteristic
716C2×C4H(5,𝔽2)×C4311yescharacteristic
717C2×C4H(5,𝔽2)×C4311yescharacteristic
718C2×C4H(5,𝔽2)×C4311yescharacteristic
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×#123×C4311yescharacteristic
752C22C43×#53411yescharacteristic
753C22C43×#53411yescharacteristic
754C22C43×#57611yescharacteristic
755C22C43×#57611yescharacteristic
756C22C43×#57711yescharacteristic
757C22C43×#57811yescharacteristic
758C4—22no—
759C4—41no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4—81no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4C43×#53811yescharacteristic
769C4C43×#53811yescharacteristic
770C4C43×#53811yescharacteristic
771C4C43×#53811yescharacteristic
772C2—42no—
773C2—81no—
774C2—81no—
775C2—161no—
776C2C43×#262211yescharacteristic
777C2C43×#309611yescharacteristic
778C2C43×#309811yescharacteristic
779C2C43×#319811yescharacteristic
780C2C43×#319911yescharacteristic
781C2C43×#320111yescharacteristic
782C2C43×#320311yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC43×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×#41×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2311C2semidirect
3. C43×#2077C2semidirect
4. C43×#2076C2semidirect
5. C43×#2076C2semidirect
6. C43×#2075C2semidirect
7. C43×#2034C2semidirect
8. C43×#2033C2semidirect
9. C43×#2033C2semidirect
10. C43×#2033C2semidirect
11. C43×#1875C2semidirect
12. C43×#1874C2semidirect
13. C43×#1854C2semidirect
14. C43×#1852C2semidirect
15. C43×#1780C2semidirect
331. #29898C43direct (N × H)
382. #2311C2×C43semidirect
383. #2077C2×C43semidirect
384. #2076C2×C43semidirect
385. #2076C2×C43semidirect
386. #2075C2×C43semidirect
387. #2034C2×C43semidirect
388. #2033C2×C43semidirect
389. #2033C2×C43semidirect
390. #2033C2×C43semidirect
391. #1875C2×C43semidirect
392. #1874C2×C43semidirect
393. #1854C2×C43semidirect
394. #1852C2×C43semidirect
395. #1780C2×C43semidirect
450. C43#29898direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#26152
C43×#23112
C43×#20772
C43×#20762
C43×#20752
C43×#20342
C43×#20332
C43×#18752
C43×#18742
C43×#18542
C43×#18522
C43×#17802
#2989843