Finite Group Databasebeta

← C43×#28915 #24948932

Subgroups — C43×#28915 #24948932

Order 11008.

884 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#489C211yesmaximal, characteristic, complemented
2C2×C43×#468C211yesmaximal, characteristic
3C43×#2492C211yesmaximal, characteristic, complemented
4C43×#2427C211yesmaximal, characteristic
5C43×#2057C211yesmaximal, characteristic, complemented
6C43×#2033C211yesmaximal, characteristic
7C43×#2015C211yesmaximal, characteristic, complemented
8C43×#2001C211yesmaximal, characteristic, complemented
9C43×#1969C211yesmaximal, characteristic, complemented
10C43×#1935C211yesmaximal, characteristic, complemented
11C43×#1928C211yesmaximal, characteristic, complemented
12C43×#1894C211yesmaximal, characteristic, complemented
13C43×#1877C211yesmaximal, characteristic, complemented
14C4×#102×C43C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C22×Q16×C43C2211yescharacteristic
17C22×SD16×C43C2211yescharacteristic
18C22×M16×C43C2211yescharacteristic
19C2×C4⋊Q8×C43C2211yescharacteristic
20C2×#124×C43C2211yescharacteristic
21C2×C22⋊Q8×C43C2211yescharacteristic
22C2×C22⋊Q8×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×C4×D4×C43C2211yescharacteristic
25C43×#489—24no—
26C43×#468—24no—
27C2×#107×C43C2211yescharacteristic
28C2×#107×C43C2211yescharacteristic
29C2×#103×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#103×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×C22⋊C8×C43C2211yescharacteristic
38C2×#97×C43C2211yescharacteristic
39C2×C4×C8×C43C2211yescharacteristic
40C43×#400—21no—
41C43×#397—21no—
42C43×#394—21no—
43C43×#393—21no—
44C43×#391—21no—
45C43×#391C2211yescharacteristic
46C43×#391C2211yescharacteristic
47C43×#391C2211yescharacteristic
48C43×#389C2211yescharacteristic
49C43×#388—21no—
50C43×#386—21no—
51C43×#380—21no—
52C43×#380C2211yescharacteristic
53C4×C4⋊C4×C43C2211yescharacteristic
54C4×C22⋊C4×C43C2211yescharacteristic
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C22×Q8×C43—21no—
62C22×Q8×C43C2311yescharacteristic
63C22×Q8×C43C2311yescharacteristic
64C22×D4×C43—21no—
65C22×D4×C43C2311yescharacteristic
66C23×C4×C43—21no—
67C23×C4×C43C2311yescharacteristic
68C2×Q16×C43—22no—
69C2×Q16×C43—41no—
70C2×Q16×C43—41no—
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
81C4⋊Q8×C43—22no—
82C4⋊Q8×C43—41no—
83#124×C43—22no—
84#124×C43—41no—
85C22⋊Q8×C43—22no—
86C22⋊Q8×C43—22no—
87C22⋊Q8×C43—41no—
88C22⋊Q8×C43—41no—
89#121×C43—22no—
90#121×C43—41no—
91C4×D4×C43—22no—
92C4×D4×C43—41no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43C2311yescharacteristic
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
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×C43D411yescharacteristic
110C2×C22⋊C4×C43D411yescharacteristic
111C2×C42×C43—21no—
112C2×C42×C43C2311yescharacteristic
113C2×C42×C43C2311yescharacteristic
114#107×C43—22no—
115#107×C43—41no—
116#103×C43—22no—
117#103×C43—22no—
118#103×C43—22no—
119#103×C43—22no—
120#103×C43—22no—
121#102×C43—22no—
122#102×C43—22no—
123#102×C43D414yes—
124C22⋊C8×C43—22no—
125#97×C43—22no—
126C4×C8×C43—41no—
127#95×C43—21no—
128#95×C43—21no—
129#95×C43—21no—
130#95×C43—21no—
131#95×C43—21no—
132#95×C43—21no—
133#95×C43—21no—
134#95×C43—21no—
135#95×C43—21no—
136#95×C43D411yescharacteristic
137#95×C43D411yescharacteristic
138C24×C43—21no—
139C24×C43C2×D411yescharacteristic
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—42no—
153C2×Q8×C43—42no—
154C2×Q8×C43—81no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43—21no—
159C2×D4×C43—21no—
160C2×D4×C43—42no—
161C2×D4×C43—42no—
162C2×D4×C43—81no—
163C2×D4×C43C2×D412yes—
164C22×C4×C43—21no—
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—42no—
178C22×C4×C43—42no—
179C22×C4×C43—81no—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2×D411yescharacteristic
183C22×C4×C43C2×D411yescharacteristic
184C22×C4×C43C2×D411yescharacteristic
185C22×C4×C43C2411yescharacteristic
186Q16×C43—44no—
187SD16×C43—44no—
188M16×C43—44no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
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×C43C2×D412yes—
199C2×C8×C43#4112yes—
200C2×C8×C43#4112yes—
201C4⋊C4×C43—21no—
202C4⋊C4×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—42no—
210C4⋊C4×C43—42no—
211C4⋊C4×C43—42no—
212C4⋊C4×C43—81no—
213C4⋊C4×C43C2×D412yes—
214C4⋊C4×C43#4112yes—
215C22⋊C4×C43—22no—
216C22⋊C4×C43—41no—
217C22⋊C4×C43—42no—
218C22⋊C4×C43—42no—
219C22⋊C4×C43—42no—
220C22⋊C4×C43—42no—
221C22⋊C4×C43—42no—
222C22⋊C4×C43—42no—
223C22⋊C4×C43—81no—
224C42×C43—21no—
225C42×C43—21no—
226C42×C43—21no—
227C42×C43—21no—
228C42×C43—81no—
229C23×C43—21no—
230C23×C43—22no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—41no—
238C23×C43—41no—
239C23×C43—41no—
240C23×C43—41no—
241C23×C43—41no—
242C23×C43—41no—
243C23×C43C22×D411yescharacteristic
244Q8×C43—41no—
245Q8×C43—41no—
246Q8×C43—41no—
247Q8×C43—41no—
248Q8×C43—41no—
249Q8×C43—41no—
250Q8×C43—41no—
251Q8×C43—41no—
252Q8×C43—84no—
253D4×C43—22no—
254D4×C43—22no—
255D4×C43—41no—
256D4×C43—41no—
257D4×C43—84no—
258C2×C4×C43—21no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—22no—
265C2×C4×C43—21no—
266C2×C4×C43—22no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—41no—
275C2×C4×C43—41no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
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—84no—
298C2×C4×C43#13712yes—
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43C2×#4111yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C2×C4×C43H(5,𝔽2)11yescharacteristic
305C8×C43—22no—
306C8×C43—22no—
307C8×C43—22no—
308C8×C43—41no—
309#28915C4311yesmaximal, characteristic, direct product factor, Sylow
310C22×C43—41no—
311C22×C43—41no—
312C22×C43—41no—
313C22×C43—42no—
314C22×C43—41no—
315C22×C43—42no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43—42no—
320C22×C43—81no—
321C22×C43—81no—
322C22×C43—81no—
323C22×C43—81no—
324C22×C43#53211yescharacteristic
325C22×C43D4211yescharacteristic
326C22×C43#54611yescharacteristic
327C22×C43C2×#13711yescharacteristic
328C22×C43#57511yescharacteristic
329C22×C43#57611yescharacteristic
330C22×C43#57811yescharacteristic
331C4×C43—22no—
332C4×C43—41no—
333C4×C43—42no—
334C4×C43—41no—
335C4×C43—41no—
336C4×C43—42no—
337C4×C43—41no—
338C4×C43—81no—
339C4×C43—81no—
340C4×C43—81no—
341C4×C43—81no—
342C4×C43—81no—
343C4×C43#53211yescharacteristic
344C4×C43#53811yescharacteristic
345C4×C43#54611yescharacteristic
346C4×C43#55511yescharacteristic
347C2×#489C2×C4311yescharacteristic, complemented
348C2×#468C2×C4311yescharacteristic
349#2492C2×C4311yescharacteristic, complemented
350#2427C2×C4311yescharacteristic
351#2057C2×C4311yescharacteristic, complemented
352#2033C2×C4311yescharacteristic
353#2015C2×C4311yescharacteristic, complemented
354#2001C2×C4311yescharacteristic, complemented
355#1969C2×C4311yescharacteristic, complemented
356#1935C2×C4311yescharacteristic, complemented
357#1928C2×C4311yescharacteristic, complemented
358#1894C2×C4311yescharacteristic, complemented
359#1877C2×C4311yescharacteristic, complemented
360C4×#102C2×C4311yescharacteristic, complemented
361#1753C2×C4311yescharacteristic, complemented
362C2×C43—81no—
363C2×C43—82no—
364C2×C43#255511yescharacteristic
365C2×C43#317211yescharacteristic
366C2×C43#317511yescharacteristic
367C2×C43#327311yescharacteristic
368C2×C43#327611yescharacteristic
369C2×C43#331311yescharacteristic
370C2×C43#331411yescharacteristic
371C22×Q16C22×C4311yescharacteristic
372C22×SD16C22×C4311yescharacteristic
373C22×M16C22×C4311yescharacteristic
374C2×C4⋊Q8C22×C4311yescharacteristic
375C2×#124C22×C4311yescharacteristic
376C2×C22⋊Q8C22×C4311yescharacteristic
377C2×C22⋊Q8C22×C4311yescharacteristic
378C2×#121C22×C4311yescharacteristic
379C2×C4×D4C22×C4311yescharacteristic
380#489—24no—
381#468—24no—
382C2×#107C22×C4311yescharacteristic
383C2×#107C22×C4311yescharacteristic
384C2×#103C22×C4311yescharacteristic
385C2×#103C22×C4311yescharacteristic
386C2×#103C22×C4311yescharacteristic
387C2×#103C22×C4311yescharacteristic
388C2×#103C22×C4311yescharacteristic
389C2×#102C22×C4311yescharacteristic
390C2×#102C22×C4311yescharacteristic
391C2×#102C22×C4311yescharacteristic
392C2×C22⋊C8C22×C4311yescharacteristic
393C2×#97C22×C4311yescharacteristic
394C2×C4×C8C22×C4311yescharacteristic
395#400—21no—
396#397—21no—
397#394—21no—
398#393—21no—
399#391—21no—
400#391C22×C4311yescharacteristic
401#391C22×C4311yescharacteristic
402#391C22×C4311yescharacteristic
403#389C22×C4311yescharacteristic
404#388—21no—
405#386—21no—
406#380—21no—
407#380C22×C4311yescharacteristic
408C4×C4⋊C4C22×C4311yescharacteristic
409C4×C22⋊C4C22×C4311yescharacteristic
410#340C22×C4311yescharacteristic
411#340C22×C4311yescharacteristic
412#340C22×C4311yescharacteristic
413#340C22×C4311yescharacteristic
414#336C22×C4311yescharacteristic
415#336C22×C4311yescharacteristic
416C43#2891511yescharacteristic, direct product factor, Sylow
417C22×Q8—21no—
418C22×Q8C23×C4311yescharacteristic
419C22×Q8C23×C4311yescharacteristic
420C22×D4—21no—
421C22×D4C23×C4311yescharacteristic
422C23×C4—21no—
423C23×C4C23×C4311yescharacteristic
424C2×Q16—22no—
425C2×Q16—41no—
426C2×Q16—41no—
427C2×SD16—22no—
428C2×SD16—22no—
429C2×SD16—41no—
430C2×M16—22no—
431C2×M16—22no—
432C2×M16—41no—
433C22×C8C23×C4311yescharacteristic
434C22×C8C23×C4311yescharacteristic
435C22×C8C23×C4311yescharacteristic
436C22×C8C23×C4311yescharacteristic
437C4⋊Q8—22no—
438C4⋊Q8—41no—
439#124—22no—
440#124—41no—
441C22⋊Q8—22no—
442C22⋊Q8—22no—
443C22⋊Q8—41no—
444C22⋊Q8—41no—
445#121—22no—
446#121—41no—
447C4×D4—22no—
448C4×D4—41no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4C23×C4311yescharacteristic
454C2×C4⋊C4C23×C4311yescharacteristic
455C2×C4⋊C4C23×C4311yescharacteristic
456C2×C4⋊C4C23×C4311yescharacteristic
457C2×C4⋊C4C23×C4311yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4D4×C4311yescharacteristic
466C2×C22⋊C4D4×C4311yescharacteristic
467C2×C42—21no—
468C2×C42C23×C4311yescharacteristic
469C2×C42C23×C4311yescharacteristic
470#107—22no—
471#107—41no—
472#103—22no—
473#103—22no—
474#103—22no—
475#103—22no—
476#103—22no—
477#102—22no—
478#102—22no—
479#102D4×C4314yes—
480C22⋊C8—22no—
481#97—22no—
482C4×C8—41no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95D4×C4311yescharacteristic
493#95D4×C4311yescharacteristic
494C24—21no—
495C24C2×D4×C4311yescharacteristic
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—81no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—81no—
519C2×D4C2×D4×C4312yes—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—81no—
536C22×C4C2×D4×C4311yescharacteristic
537C22×C4C2×D4×C4311yescharacteristic
538C22×C4C2×D4×C4311yescharacteristic
539C22×C4C2×D4×C4311yescharacteristic
540C22×C4C2×D4×C4311yescharacteristic
541C22×C4C24×C4311yescharacteristic
542Q16—44no—
543SD16—44no—
544M16—44no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8C2×D4×C4312yes—
555C2×C8#41×C4312yes—
556C2×C8#41×C4312yes—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—81no—
569C4⋊C4C2×D4×C4312yes—
570C4⋊C4#41×C4312yes—
571C22⋊C4—22no—
572C22⋊C4—41no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—81no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—21no—
584C42—81no—
585C23—21no—
586C23—22no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23C22×D4×C4311yescharacteristic
600Q8—41no—
601Q8—41no—
602Q8—41no—
603Q8—41no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—84no—
609D4—22no—
610D4—22no—
611D4—41no—
612D4—41no—
613D4—84no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—84no—
654C2×C4#137×C4312yes—
655C2×C4C22×D4×C4311yescharacteristic
656C2×C4C2×#41×C4311yescharacteristic
657C2×C4C2×#41×C4311yescharacteristic
658C2×C4C2×#41×C4311yescharacteristic
659C2×C4H(5,𝔽2)×C4311yescharacteristic
660C2×C4H(5,𝔽2)×C4311yescharacteristic
661C8—22no—
662C8—22no—
663C8—22no—
664C8—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—42no—
669C22—41no—
670C22—42no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C43×#53211yescharacteristic
680C22D42×C4311yescharacteristic
681C22C43×#54611yescharacteristic
682C22C2×#137×C4311yescharacteristic
683C22C43×#57511yescharacteristic
684C22C43×#57611yescharacteristic
685C22C43×#57811yescharacteristic
686C4—22no—
687C4—41no—
688C4—42no—
689C4—41no—
690C4—41no—
691C4—42no—
692C4—41no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4C43×#53211yescharacteristic
699C4C43×#53811yescharacteristic
700C4C43×#54611yescharacteristic
701C4C43×#55511yescharacteristic
702C2—81no—
703C2—82no—
704C2C43×#255511yescharacteristic
705C2C43×#317211yescharacteristic
706C2C43×#317511yescharacteristic
707C2C43×#327311yescharacteristic
708C2C43×#327611yescharacteristic
709C2C43×#331311yescharacteristic
710C2C43×#331411yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×#121×C43C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C4×C22⋊C4×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#489C2semidirect
3. C43×#2492C2semidirect
5. C43×#2057C2semidirect
7. C43×#2015C2semidirect
8. C43×#2001C2semidirect
9. C43×#1969C2semidirect
10. C43×#1935C2semidirect
11. C43×#1928C2semidirect
12. C43×#1894C2semidirect
13. C43×#1877C2semidirect
14. C4×#102×C43C2semidirect
15. C43×#1753C2semidirect
309. #28915C43direct (N × H)
347. C2×#489C2×C43semidirect
349. #2492C2×C43semidirect
351. #2057C2×C43semidirect
353. #2015C2×C43semidirect
354. #2001C2×C43semidirect
355. #1969C2×C43semidirect
356. #1935C2×C43semidirect
357. #1928C2×C43semidirect
358. #1894C2×C43semidirect
359. #1877C2×C43semidirect
360. C4×#102C2×C43semidirect
361. #1753C2×C43semidirect
416. C43#28915direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4892
C2×C43×#4682
C43×#24922
C43×#24272
C43×#20572
C43×#20332
C43×#20152
C43×#20012
C43×#19692
C43×#19352
C43×#19282
C43×#18942
C43×#18772
C4×#102×C432
C43×#17532
#2891543