Finite Group Databasebeta

← C43×#29720 #24949737

Subgroups — C43×#29720 #24949737

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#452C211yesmaximal, characteristic, complemented
2C2×C43×#449C211yesmaximal, characteristic
3C43×#2850C211yesmaximal, characteristic, complemented
4C43×#2297C211yesmaximal, characteristic, complemented
5C43×#2074C211yesmaximal, characteristic, complemented
6C43×#2073C211yesmaximal, characteristic, complemented
7C43×#2056C211yesmaximal, characteristic, complemented
8C43×#2055C211yesmaximal, characteristic, complemented
9C43×#2055C211yesmaximal, characteristic, complemented
10C43×#2054C211yesmaximal, characteristic, complemented
11C43×#2015C211yesmaximal, characteristic, complemented
12C43×#2012C211yesmaximal, characteristic, complemented
13C43×#1875C211yesmaximal, characteristic, complemented
14C43×#1873C211yesmaximal, characteristic, complemented
15C43×#1797C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C22×Q16×C43C2211yescharacteristic
18C22×SD16×C43C2211yescharacteristic
19C22×SD16×C43C2211yescharacteristic
20C22×D8×C43C2211yescharacteristic
21C2×#124×C43C2211yescharacteristic
22C2×C22⋊Q8×C43C2211yescharacteristic
23C2×#121×C43C2211yescharacteristic
24C2×#117×C43C2211yescharacteristic
25C22×C42×C43C2211yescharacteristic
26C43×#452—24no—
27C43×#449—24no—
28C2×C4⋊C8×C43C2211yescharacteristic
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×#103×C43C2211yescharacteristic
31C2×#103×C43C2211yescharacteristic
32C2×#103×C43C2211yescharacteristic
33C2×#103×C43C2211yescharacteristic
34C2×#102×C43C2211yescharacteristic
35C2×#102×C43C2211yescharacteristic
36C2×#102×C43C2211yescharacteristic
37C2×#102×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C2×C22⋊C8×C43C2211yescharacteristic
40C43×#391C2211yescharacteristic
41C43×#391C2211yescharacteristic
42C43×#391C2211yescharacteristic
43C43×#390C2211yescharacteristic
44C43×#390C2211yescharacteristic
45C43×#390C2211yescharacteristic
46C43×#388—21no—
47C43×#388—21no—
48C43×#386—21no—
49C43×#386—21no—
50C43×#386—21no—
51C43×#386—21no—
52C43×#382C2211yescharacteristic
53C4×C22⋊C4×C43—21no—
54C4×C22⋊C4×C43—21no—
55C43×#340C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#41×C43—22no—
62C2×#41×C43—41no—
63C2×#41×C43—41no—
64C2×#41×C43—41no—
65C2×#41×C43—41no—
66C2×#41×C43D414yes—
67C22×Q8×C43C2311yescharacteristic
68C22×Q8×C43C2311yescharacteristic
69C22×D4×C43—21no—
70C22×D4×C43—21no—
71C22×D4×C43C2311yescharacteristic
72C22×D4×C43C2311yescharacteristic
73C23×C4×C43—21no—
74C23×C4×C43D411yescharacteristic
75C23×C4×C43D411yescharacteristic
76C23×C4×C43C2311yescharacteristic
77C2×Q16×C43—22no—
78C2×Q16×C43—41no—
79C2×Q16×C43—41no—
80C2×SD16×C43—22no—
81C2×SD16×C43—22no—
82C2×SD16×C43—41no—
83C2×SD16×C43—41no—
84C2×SD16×C43—41no—
85C2×SD16×C43—41no—
86C2×D8×C43—22no—
87C2×D8×C43—41no—
88C2×D8×C43—41no—
89C22×C8×C43C2311yescharacteristic
90C22×C8×C43C2311yescharacteristic
91C22×C8×C43C2311yescharacteristic
92C22×C8×C43C2311yescharacteristic
93#124×C43—41no—
94#124×C43—41no—
95C22⋊Q8×C43—22no—
96C22⋊Q8×C43—22no—
97#121×C43—22no—
98#121×C43—22no—
99#117×C43—41no—
100#117×C43—41no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C4⋊C4×C43C2311yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C22⋊C4×C43—21no—
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43—21no—
116C2×C22⋊C4×C43—21no—
117C2×C42×C43—21no—
118C2×C42×C43—41no—
119C2×C42×C43—41no—
120C2×C42×C43D411yescharacteristic
121C2×C42×C43D411yescharacteristic
122C2×C42×C43C2311yescharacteristic
123C2×C42×C43C2311yescharacteristic
124C4⋊C8×C43—41no—
125C4⋊C8×C43—41no—
126#103×C43—22no—
127#103×C43—22no—
128#103×C43—41no—
129#103×C43—41no—
130#102×C43—22no—
131#102×C43—22no—
132#102×C43—41no—
133#102×C43—41no—
134C22⋊C8×C43—22no—
135C22⋊C8×C43—22no—
136#95×C43—21no—
137#95×C43—21no—
138#95×C43—21no—
139#95×C43—21no—
140#95×C43—21no—
141#95×C43—21no—
142#95×C43—21no—
143#95×C43—21no—
144C24×C43—21no—
145C24×C43—21no—
146C24×C43C2×D411yescharacteristic
147#41×C43—44no—
148#41×C43—44no—
149#41×C43—44no—
150#41×C43—44no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43—21no—
157C2×Q8×C43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×Q8×C43—21no—
161C2×Q8×C43—21no—
162C2×Q8×C43C2×D412yes—
163C2×D4×C43—21no—
164C2×D4×C43—24no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43—21no—
168C2×D4×C43—21no—
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—42no—
176C2×D4×C43—42no—
177C2×D4×C43—42no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43C2×D412yes—
181C22×C4×C43—21no—
182C22×C4×C43—21no—
183C22×C4×C43—21no—
184C22×C4×C43—21no—
185C22×C4×C43—24no—
186C22×C4×C43—22no—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—41no—
194C22×C4×C43—41no—
195C22×C4×C43—41no—
196C22×C4×C43—41no—
197C22×C4×C43—41no—
198C22×C4×C43—42no—
199C22×C4×C43—42no—
200C22×C4×C43C2×D412yes—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43#4112yes—
207C22×C4×C43C2411yescharacteristic
208Q16×C43—44no—
209SD16×C43—44no—
210SD16×C43—44no—
211D8×C43—44no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43—21no—
218C2×C8×C43—21no—
219C2×C8×C43—21no—
220C2×C8×C43—21no—
221C2×C8×C43—21no—
222C2×C8×C43—21no—
223C2×C8×C43—21no—
224C4⋊C4×C43—21no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊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—
239C22⋊C4×C43—42no—
240C22⋊C4×C43—42no—
241C22⋊C4×C43—42no—
242C22⋊C4×C43—42no—
243C22⋊C4×C43—42no—
244C42×C43—21no—
245C42×C43—21no—
246C42×C43—21no—
247C42×C43—21no—
248C42×C43—41no—
249C42×C43—41no—
250C42×C43—42no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43—22no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43—41no—
263C23×C43—41no—
264C23×C43—41no—
265C23×C43—41no—
266C23×C43—41no—
267C23×C43—41no—
268C23×C43—41no—
269C23×C43—41no—
270C23×C43—41no—
271C23×C43#12112yes—
272C23×C43C22×D411yescharacteristic
273Q8×C43—22no—
274Q8×C43—22no—
275Q8×C43—41no—
276Q8×C43—41no—
277Q8×C43—41no—
278Q8×C43—41no—
279Q8×C43—41no—
280Q8×C43—41no—
281D4×C43—22no—
282D4×C43—22no—
283D4×C43—48no—
284D4×C43—41no—
285D4×C43—41no—
286D4×C43—41no—
287D4×C43—41no—
288D4×C43—41no—
289D4×C43—41no—
290D4×C43—84no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—21no—
309C2×C4×C43—44no—
310C2×C4×C43—48no—
311C2×C4×C43—44no—
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—41no—
329C2×C4×C43#12112yes—
330C2×C4×C43#13512yes—
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4111yescharacteristic
333C2×C4×C43H(5,𝔽2)11yescharacteristic
334C2×C4×C43H(5,𝔽2)11yescharacteristic
335C2×C4×C43H(5,𝔽2)11yescharacteristic
336C2×C4×C43H(5,𝔽2)11yescharacteristic
337C8×C43—41no—
338C8×C43—41no—
339C8×C43—41no—
340C8×C43—41no—
341#29720C4311yesmaximal, characteristic, direct product factor, Sylow
342C22×C43—22no—
343C22×C43—22no—
344C22×C43—22no—
345C22×C43—41no—
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—81no—
353C22×C43—81no—
354C22×C43—81no—
355C22×C43—81no—
356C22×C43—81no—
357C22×C43—81no—
358C22×C43—81no—
359C22×C43—81no—
360C22×C43—81no—
361C22×C43—81no—
362C22×C43—81no—
363C22×C43C2×#12111yescharacteristic
364C22×C43#53411yescharacteristic
365C22×C43#53511yescharacteristic
366C22×C43C2×#13511yescharacteristic
367C22×C43#57511yescharacteristic
368C22×C43#57511yescharacteristic
369C22×C43#57511yescharacteristic
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—42no—
373C4×C43—41no—
374C4×C43—41no—
375C4×C43—41no—
376C4×C43—81no—
377C4×C43—81no—
378C4×C43—81no—
379C4×C43—81no—
380C4×C43—81no—
381C4×C43#53411yescharacteristic
382C4×C43#53411yescharacteristic
383C4×C43#53811yescharacteristic
384C4×C43#53811yescharacteristic
385C2×#452C2×C4311yescharacteristic, complemented
386C2×#449C2×C4311yescharacteristic
387#2850C2×C4311yescharacteristic, complemented
388#2297C2×C4311yescharacteristic, complemented
389#2074C2×C4311yescharacteristic, complemented
390#2073C2×C4311yescharacteristic, complemented
391#2056C2×C4311yescharacteristic, complemented
392#2055C2×C4311yescharacteristic, complemented
393#2055C2×C4311yescharacteristic, complemented
394#2054C2×C4311yescharacteristic, complemented
395#2015C2×C4311yescharacteristic, complemented
396#2012C2×C4311yescharacteristic, complemented
397#1875C2×C4311yescharacteristic, complemented
398#1873C2×C4311yescharacteristic, complemented
399#1797C2×C4311yescharacteristic, complemented
400C2×C43—42no—
401C2×C43—82no—
402C2×C43—161no—
403C2×C43#261711yescharacteristic
404C2×C43#303511yescharacteristic
405C2×C43#304011yescharacteristic
406C2×C43#319111yescharacteristic
407C2×C43#319711yescharacteristic
408C2×C43#321211yescharacteristic
409C2×C43#321911yescharacteristic
410C22×#41C22×C4311yescharacteristic
411C22×Q16C22×C4311yescharacteristic
412C22×SD16C22×C4311yescharacteristic
413C22×SD16C22×C4311yescharacteristic
414C22×D8C22×C4311yescharacteristic
415C2×#124C22×C4311yescharacteristic
416C2×C22⋊Q8C22×C4311yescharacteristic
417C2×#121C22×C4311yescharacteristic
418C2×#117C22×C4311yescharacteristic
419C22×C42C22×C4311yescharacteristic
420#452—24no—
421#449—24no—
422C2×C4⋊C8C22×C4311yescharacteristic
423C2×C4⋊C8C22×C4311yescharacteristic
424C2×#103C22×C4311yescharacteristic
425C2×#103C22×C4311yescharacteristic
426C2×#103C22×C4311yescharacteristic
427C2×#103C22×C4311yescharacteristic
428C2×#102C22×C4311yescharacteristic
429C2×#102C22×C4311yescharacteristic
430C2×#102C22×C4311yescharacteristic
431C2×#102C22×C4311yescharacteristic
432C2×C22⋊C8C22×C4311yescharacteristic
433C2×C22⋊C8C22×C4311yescharacteristic
434#391C22×C4311yescharacteristic
435#391C22×C4311yescharacteristic
436#391C22×C4311yescharacteristic
437#390C22×C4311yescharacteristic
438#390C22×C4311yescharacteristic
439#390C22×C4311yescharacteristic
440#388—21no—
441#388—21no—
442#386—21no—
443#386—21no—
444#386—21no—
445#386—21no—
446#382C22×C4311yescharacteristic
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449#340C22×C4311yescharacteristic
450#340C22×C4311yescharacteristic
451#340C22×C4311yescharacteristic
452#340C22×C4311yescharacteristic
453#336C22×C4311yescharacteristic
454#336C22×C4311yescharacteristic
455C43#2972011yescharacteristic, direct product factor, Sylow
456C2×#41—22no—
457C2×#41—41no—
458C2×#41—41no—
459C2×#41—41no—
460C2×#41—41no—
461C2×#41D4×C4314yes—
462C22×Q8C23×C4311yescharacteristic
463C22×Q8C23×C4311yescharacteristic
464C22×D4—21no—
465C22×D4—21no—
466C22×D4C23×C4311yescharacteristic
467C22×D4C23×C4311yescharacteristic
468C23×C4—21no—
469C23×C4D4×C4311yescharacteristic
470C23×C4D4×C4311yescharacteristic
471C23×C4C23×C4311yescharacteristic
472C2×Q16—22no—
473C2×Q16—41no—
474C2×Q16—41no—
475C2×SD16—22no—
476C2×SD16—22no—
477C2×SD16—41no—
478C2×SD16—41no—
479C2×SD16—41no—
480C2×SD16—41no—
481C2×D8—22no—
482C2×D8—41no—
483C2×D8—41no—
484C22×C8C23×C4311yescharacteristic
485C22×C8C23×C4311yescharacteristic
486C22×C8C23×C4311yescharacteristic
487C22×C8C23×C4311yescharacteristic
488#124—41no—
489#124—41no—
490C22⋊Q8—22no—
491C22⋊Q8—22no—
492#121—22no—
493#121—22no—
494#117—41no—
495#117—41no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4C23×C4311yescharacteristic
498C2×C4⋊C4C23×C4311yescharacteristic
499C2×C4⋊C4C23×C4311yescharacteristic
500C2×C4⋊C4C23×C4311yescharacteristic
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×C22⋊C4—21no—
512C2×C42—21no—
513C2×C42—41no—
514C2×C42—41no—
515C2×C42D4×C4311yescharacteristic
516C2×C42D4×C4311yescharacteristic
517C2×C42C23×C4311yescharacteristic
518C2×C42C23×C4311yescharacteristic
519C4⋊C8—41no—
520C4⋊C8—41no—
521#103—22no—
522#103—22no—
523#103—41no—
524#103—41no—
525#102—22no—
526#102—22no—
527#102—41no—
528#102—41no—
529C22⋊C8—22no—
530C22⋊C8—22no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539C24—21no—
540C24—21no—
541C24C2×D4×C4311yescharacteristic
542#41—44no—
543#41—44no—
544#41—44no—
545#41—44no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C2×D4×C4312yes—
558C2×D4—24no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4C2×D4×C4312yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4C2×D4×C4311yescharacteristic
596C22×C4C2×D4×C4311yescharacteristic
597C22×C4C2×D4×C4311yescharacteristic
598C22×C4C2×D4×C4311yescharacteristic
599C22×C4C2×D4×C4312yes—
600C22×C4C2×D4×C4311yescharacteristic
601C22×C4#41×C4312yes—
602C22×C4C24×C4311yescharacteristic
603Q16—44no—
604SD16—44no—
605SD16—44no—
606D8—44no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—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—42no—
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—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—41no—
644C42—41no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—22no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23#121×C4312yes—
667C23C22×D4×C4311yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676D4—22no—
677D4—22no—
678D4—48no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—84no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—48no—
705C2×C4—44no—
706C2×C4—44no—
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#121×C4312yes—
725C2×C4#135×C4312yes—
726C2×C4C22×D4×C4311yescharacteristic
727C2×C4C2×#41×C4311yescharacteristic
728C2×C4H(5,𝔽2)×C4311yescharacteristic
729C2×C4H(5,𝔽2)×C4311yescharacteristic
730C2×C4H(5,𝔽2)×C4311yescharacteristic
731C2×C4H(5,𝔽2)×C4311yescharacteristic
732C8—41no—
733C8—41no—
734C8—41no—
735C8—41no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C2×#121×C4311yescharacteristic
758C22C43×#53411yescharacteristic
759C22C43×#53511yescharacteristic
760C22C2×#135×C4311yescharacteristic
761C22C43×#57511yescharacteristic
762C22C43×#57511yescharacteristic
763C22C43×#57511yescharacteristic
764C4—22no—
765C4—22no—
766C4—42no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4—81no—
774C4—81no—
775C4C43×#53411yescharacteristic
776C4C43×#53411yescharacteristic
777C4C43×#53811yescharacteristic
778C4C43×#53811yescharacteristic
779C2—42no—
780C2—82no—
781C2—161no—
782C2C43×#261711yescharacteristic
783C2C43×#303511yescharacteristic
784C2C43×#304011yescharacteristic
785C2C43×#319111yescharacteristic
786C2C43×#319711yescharacteristic
787C2C43×#321211yescharacteristic
788C2C43×#321911yescharacteristic
subgroupG/H
center, socleC23×C43C22×D4
commutator, Frattini, cosocleC22×C4C24×C43
prime radicalC2×C43×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C43 ◁ C22×C42×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#452C2semidirect
3. C43×#2850C2semidirect
4. C43×#2297C2semidirect
5. C43×#2074C2semidirect
6. C43×#2073C2semidirect
7. C43×#2056C2semidirect
8. C43×#2055C2semidirect
9. C43×#2055C2semidirect
10. C43×#2054C2semidirect
11. C43×#2015C2semidirect
12. C43×#2012C2semidirect
13. C43×#1875C2semidirect
14. C43×#1873C2semidirect
15. C43×#1797C2semidirect
341. #29720C43direct (N × H)
385. C2×#452C2×C43semidirect
387. #2850C2×C43semidirect
388. #2297C2×C43semidirect
389. #2074C2×C43semidirect
390. #2073C2×C43semidirect
391. #2056C2×C43semidirect
392. #2055C2×C43semidirect
393. #2055C2×C43semidirect
394. #2054C2×C43semidirect
395. #2015C2×C43semidirect
396. #2012C2×C43semidirect
397. #1875C2×C43semidirect
398. #1873C2×C43semidirect
399. #1797C2×C43semidirect
455. C43#29720direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C43×#4522
C2×C43×#4492
C43×#28502
C43×#22972
C43×#20742
C43×#20732
C43×#20562
C43×#20552
C43×#20542
C43×#20152
C43×#20122
C43×#18752
C43×#18732
C43×#17972
#2972043