Finite Group Databasebeta

← C43×#22588 #24942605

Subgroups — C43×#22588 #24942605

Order 11008.

888 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
1C43×#2924C211yesmaximal, characteristic, complemented
2C43×#2896C211yesmaximal, characteristic
3C43×#2880C211yesmaximal, characteristic
4C43×#1938C211yesmaximal, characteristic, complemented
5C43×#1937C211yesmaximal, characteristic, complemented
6C43×#1929C211yesmaximal, characteristic, complemented
7C43×#1929C211yesmaximal, characteristic, complemented
8C43×#1866C211yesmaximal, characteristic, complemented
9C43×#1866C211yesmaximal, characteristic, complemented
10C43×#1826C211yesmaximal, characteristic, complemented
11C43×#1811C211yesmaximal, characteristic, complemented
12C43×#1789C211yesmaximal, characteristic
13C43×#1765C211yesmaximal, characteristic, complemented
14C43×#1764C211yesmaximal, characteristic, complemented
15C43×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C43C2211yescharacteristic
17C2×#131×C43C2211yescharacteristic
18C2×#131×C43C2211yescharacteristic
19C22×M16×C43C2211yescharacteristic
20C2×#117×C43C2211yescharacteristic
21C43×#433—21no—
22C43×#433—21no—
23C43×#432—21no—
24C43×#431—21no—
25C2×#108×C43C2211yescharacteristic, complemented
26C2×#108×C43C2211yescharacteristic, complemented
27C43×#424C2211yescharacteristic, complemented
28C43×#424C2211yescharacteristic, complemented
29C2×#104×C43C2211yescharacteristic
30C2×#104×C43C2211yescharacteristic
31C2×#104×C43C2211yescharacteristic
32C2×#104×C43C2211yescharacteristic
33C43×#419C411yescharacteristic, complemented
34C43×#419C411yescharacteristic, complemented
35C43×#418C411yescharacteristic, complemented
36C43×#418C411yescharacteristic, complemented
37C43×#417C411yescharacteristic, complemented
38C43×#417C411yescharacteristic, complemented
39C43×#417C411yescharacteristic, complemented
40C43×#417C411yescharacteristic, complemented
41C43×#416C2211yescharacteristic
42C43×#416C2211yescharacteristic
43C43×#416C2211yescharacteristic
44C43×#416C2211yescharacteristic
45C43×#408—21no—
46C43×#408—21no—
47C43×#408C2211yescharacteristic
48C43×#408C2211yescharacteristic
49C43×#407—21no—
50C43×#407C2211yescharacteristic
51C43×#407C2211yescharacteristic
52C2×C22⋊C8×C43—21no—
53C2×C22⋊C8×C43C2211yescharacteristic
54C43×#405C2211yescharacteristic, complemented
55C43×#405C2211yescharacteristic, complemented
56C2×#97×C43C2211yescharacteristic, complemented
57C2×C4×C8×C43C2211yescharacteristic, complemented
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#341C2211yescharacteristic, complemented
60C43×#341C2211yescharacteristic, complemented
61C43×#339C2211yescharacteristic, complemented
62C43×#339C2211yescharacteristic, complemented
63C43×#339C2211yescharacteristic, complemented
64C43×#339C2211yescharacteristic, complemented
65C43×#336C2211yescharacteristic, complemented
66C43×#336C2211yescharacteristic, complemented
67C2×#41×C43—21no—
68C2×#41×C43—21no—
69C2×#41×C43—22no—
70C2×#41×C43—22no—
71C2×#41×C43—41no—
72C2×#41×C43—41no—
73C2×#41×C43C2×C411yescharacteristic
74C2×#41×C43C2×C411yescharacteristic
75C2×#41×C43C2311yescharacteristic
76C2×#41×C43C2311yescharacteristic
77C22×Q8×C43C2×C411yescharacteristic
78C22×D4×C43—21no—
79C22×D4×C43C2×C411yescharacteristic
80C23×C4×C43—21no—
81C23×C4×C43C2311yescharacteristic
82#131×C43—22no—
83#131×C43—22no—
84#131×C43—41no—
85#131×C43—41no—
86C2×M16×C43—21no—
87C2×M16×C43—21no—
88C2×M16×C43—41no—
89C2×M16×C43—41no—
90C2×M16×C43C2×C411yescharacteristic
91C2×M16×C43C2×C411yescharacteristic
92C2×M16×C43C2×C411yescharacteristic
93C2×M16×C43C2×C411yescharacteristic
94C2×M16×C43C2311yescharacteristic
95C2×M16×C43C2311yescharacteristic
96C2×M16×C43C2311yescharacteristic
97C2×M16×C43C2311yescharacteristic
98C22×C8×C43—21no—
99C22×C8×C43—21no—
100C22×C8×C43C2311yescharacteristic
101C22×C8×C43C2311yescharacteristic
102C22×C8×C43C2311yescharacteristic
103C22×C8×C43C2311yescharacteristic
104#117×C43—21no—
105#117×C43—21no—
106#117×C43C2×C411yescharacteristic
107#117×C43C2×C411yescharacteristic
108#117×C43C2311yescharacteristic
109#117×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2×C411yescharacteristic
111C2×C4⋊C4×C43C2×C411yescharacteristic
112C2×C22⋊C4×C43—21no—
113C2×C22⋊C4×C43—21no—
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116C2×C42×C43C2311yescharacteristic
117#108×C43—41no—
118#108×C43—41no—
119C4⋊C8×C43—21no—
120C4⋊C8×C43—21no—
121C4⋊C8×C43—21no—
122C4⋊C8×C43—21no—
123#104×C43—22no—
124#104×C43—22no—
125#104×C43—41no—
126#104×C43—41no—
127#103×C43C2×C411yescharacteristic
128#103×C43C2×C411yescharacteristic
129#103×C43C2×C411yescharacteristic
130#103×C43C2×C411yescharacteristic
131#103×C43C2×C411yescharacteristic
132#103×C43C2×C411yescharacteristic
133#103×C43C2×C411yescharacteristic
134#103×C43C2×C411yescharacteristic
135#102×C43C2×C411yescharacteristic
136#102×C43C2×C411yescharacteristic
137#102×C43C2×C411yescharacteristic
138#102×C43C2×C411yescharacteristic
139#102×C43C2×C411yescharacteristic
140#102×C43C2×C411yescharacteristic
141#102×C43C2×C411yescharacteristic
142#102×C43C2×C411yescharacteristic
143C22⋊C8×C43—21no—
144C22⋊C8×C43—21no—
145C22⋊C8×C43—21no—
146C22⋊C8×C43—21no—
147C22⋊C8×C43—21no—
148C22⋊C8×C43—21no—
149C22⋊C8×C43—21no—
150C22⋊C8×C43—21no—
151C22⋊C8×C43D411yescharacteristic
152C22⋊C8×C43D411yescharacteristic
153C22⋊C8×C43D411yescharacteristic
154C22⋊C8×C43D411yescharacteristic
155#97×C43—21no—
156#97×C43—21no—
157#97×C43—41no—
158C4×C8×C43—21no—
159C4×C8×C43—21no—
160C4×C8×C43—41no—
161#95×C43—21no—
162C24×C43—21no—
163C24×C43#4111yescharacteristic
164#41×C43—21no—
165#41×C43—21no—
166#41×C43—22no—
167#41×C43—22no—
168#41×C43—21no—
169#41×C43—21no—
170#41×C43—21no—
171#41×C43—21no—
172#41×C43—42no—
173#41×C43—42no—
174#41×C43—41no—
175#41×C43—41no—
176#41×C43—42no—
177#41×C43—42no—
178#41×C43#4112yes—
179#41×C43#4112yes—
180C2×Q8×C43—21no—
181C2×Q8×C43—22no—
182C2×Q8×C43—41no—
183C2×Q8×C43C22×C411yescharacteristic
184C2×Q8×C43C22×C411yescharacteristic
185C2×D4×C43—21no—
186C2×D4×C43—21no—
187C2×D4×C43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—22no—
191C2×D4×C43—42no—
192C2×D4×C43—42no—
193C2×D4×C43—41no—
194C2×D4×C43C22×C411yescharacteristic
195C2×D4×C43C22×C411yescharacteristic
196C22×C4×C43—21no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—42no—
210C22×C4×C43—42no—
211C22×C4×C43C22×C411yescharacteristic
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43#4111yescharacteristic
216C22×C4×C43C2411yescharacteristic
217M16×C43—21no—
218M16×C43—21no—
219M16×C43—21no—
220M16×C43—21no—
221M16×C43—21no—
222M16×C43—21no—
223M16×C43—21no—
224M16×C43—21no—
225M16×C43—41no—
226M16×C43—41no—
227M16×C43—41no—
228M16×C43—41no—
229M16×C43—42no—
230M16×C43—42no—
231C2×C8×C43—21no—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—42no—
244C2×C8×C43—42no—
245C2×C8×C43C22×C411yescharacteristic
246C2×C8×C43C22×C411yescharacteristic
247C2×C8×C43C22×C411yescharacteristic
248C2×C8×C43C22×C411yescharacteristic
249C2×C8×C43C2×D411yescharacteristic
250C2×C8×C43C2×D411yescharacteristic
251C2×C8×C43C2×D411yescharacteristic
252C2×C8×C43C2×D411yescharacteristic
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43C22×C411yescharacteristic
256C4⋊C4×C43C22×C411yescharacteristic
257C4⋊C4×C43C22×C411yescharacteristic
258C4⋊C4×C43C22×C411yescharacteristic
259C22⋊C4×C43—21no—
260C22⋊C4×C43—21no—
261C22⋊C4×C43—21no—
262C22⋊C4×C43—21no—
263C22⋊C4×C43—42no—
264C42×C43—21no—
265C42×C43—21no—
266C42×C43—21no—
267C42×C43—21no—
268C42×C43—21no—
269C42×C43—21no—
270C42×C43—21no—
271C42×C43—21no—
272C23×C43—21no—
273C23×C43—21no—
274C23×C43—21no—
275C23×C43—21no—
276C23×C43—41no—
277C23×C43—41no—
278C23×C43—42no—
279C23×C43—42no—
280C23×C43—81no—
281C23×C43C4×D411yescharacteristic
282C23×C43C4×D411yescharacteristic
283C23×C43C2×#4111yescharacteristic
284Q8×C43—21no—
285Q8×C43—21no—
286Q8×C43—21no—
287Q8×C43—42no—
288Q8×C43#11712yes—
289D4×C43—22no—
290D4×C43—22no—
291D4×C43—21no—
292D4×C43—21no—
293D4×C43—21no—
294D4×C43—42no—
295D4×C43—42no—
296D4×C43—42no—
297D4×C43—41no—
298D4×C43—41no—
299D4×C43#11712yes—
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—22no—
308C2×C4×C43—22no—
309C2×C4×C43—21no—
310C2×C4×C43—21no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—22no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—21no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43—41no—
323C2×C4×C43—42no—
324C2×C4×C43—41no—
325C2×C4×C43—41no—
326C2×C4×C43—41no—
327C2×C4×C43—41no—
328C2×C4×C43—41no—
329C2×C4×C43—41no—
330C2×C4×C43—81no—
331C2×C4×C43C4×D411yescharacteristic
332C2×C4×C43C4×D411yescharacteristic
333C2×C4×C43C23×C411yescharacteristic
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C2×#4111yescharacteristic
336C2×C4×C43C2×#4111yescharacteristic
337C2×C4×C43H(5,𝔽2)11yescharacteristic
338C2×C4×C43H(5,𝔽2)11yescharacteristic
339C8×C43—21no—
340C8×C43—21no—
341C8×C43—21no—
342C8×C43—21no—
343C8×C43—21no—
344C8×C43—21no—
345C8×C43—21no—
346C8×C43—21no—
347C8×C43—41no—
348C8×C43—41no—
349C8×C43—41no—
350C8×C43—41no—
351#22588C4311yesmaximal, characteristic, direct product factor, Sylow
352C22×C43—21no—
353C22×C43—21no—
354C22×C43—21no—
355C22×C43—21no—
356C22×C43—22no—
357C22×C43—21no—
358C22×C43—21no—
359C22×C43—21no—
360C22×C43—21no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43—41no—
364C22×C43—41no—
365C22×C43—41no—
366C22×C43—81no—
367C22×C43—81no—
368C22×C43—84no—
369C22×C43C2×C4×D411yescharacteristic
370C22×C43#55111yescharacteristic
371C22×C43#55111yescharacteristic
372C4×C43—21no—
373C4×C43—21no—
374C4×C43—22no—
375C4×C43—42no—
376C4×C43—41no—
377C4×C43—41no—
378C4×C43—41no—
379C4×C43—41no—
380C4×C43—41no—
381C4×C43—81no—
382C4×C43C2×#11711yescharacteristic
383C4×C43#51811yescharacteristic
384C4×C43#54611yescharacteristic
385C4×C43#54611yescharacteristic
386#2924C2×C4311yescharacteristic, complemented
387#2896C2×C4311yescharacteristic
388#2880C2×C4311yescharacteristic
389#1938C2×C4311yescharacteristic, complemented
390#1937C2×C4311yescharacteristic, complemented
391#1929C2×C4311yescharacteristic, complemented
392#1929C2×C4311yescharacteristic, complemented
393#1866C2×C4311yescharacteristic, complemented
394#1866C2×C4311yescharacteristic, complemented
395#1826C2×C4311yescharacteristic, complemented
396#1811C2×C4311yescharacteristic, complemented
397#1789C2×C4311yescharacteristic
398#1765C2×C4311yescharacteristic, complemented
399#1764C2×C4311yescharacteristic, complemented
400#1753C2×C4311yescharacteristic, complemented
401C2×C43—21no—
402C2×C43—21no—
403C2×C43—41no—
404C2×C43—41no—
405C2×C43—42no—
406C2×C43—81no—
407C2×C43#234211yescharacteristic
408C2×C43#295511yescharacteristic
409C2×C43#295611yescharacteristic
410C22×#41C22×C4311yescharacteristic
411C2×#131C22×C4311yescharacteristic
412C2×#131C22×C4311yescharacteristic
413C22×M16C22×C4311yescharacteristic
414C2×#117C22×C4311yescharacteristic
415#433—21no—
416#433—21no—
417#432—21no—
418#431—21no—
419C2×#108C22×C4311yescharacteristic, complemented
420C2×#108C22×C4311yescharacteristic, complemented
421#424C22×C4311yescharacteristic, complemented
422#424C22×C4311yescharacteristic, complemented
423C2×#104C22×C4311yescharacteristic
424C2×#104C22×C4311yescharacteristic
425C2×#104C22×C4311yescharacteristic
426C2×#104C22×C4311yescharacteristic
427#419C4×C4311yescharacteristic, complemented
428#419C4×C4311yescharacteristic, complemented
429#418C4×C4311yescharacteristic, complemented
430#418C4×C4311yescharacteristic, complemented
431#417C4×C4311yescharacteristic, complemented
432#417C4×C4311yescharacteristic, complemented
433#417C4×C4311yescharacteristic, complemented
434#417C4×C4311yescharacteristic, complemented
435#416C22×C4311yescharacteristic
436#416C22×C4311yescharacteristic
437#416C22×C4311yescharacteristic
438#416C22×C4311yescharacteristic
439#408—21no—
440#408—21no—
441#408C22×C4311yescharacteristic
442#408C22×C4311yescharacteristic
443#407—21no—
444#407C22×C4311yescharacteristic
445#407C22×C4311yescharacteristic
446C2×C22⋊C8—21no—
447C2×C22⋊C8C22×C4311yescharacteristic
448#405C22×C4311yescharacteristic, complemented
449#405C22×C4311yescharacteristic, complemented
450C2×#97C22×C4311yescharacteristic, complemented
451C2×C4×C8C22×C4311yescharacteristic, complemented
452C4×C22⋊C4C22×C4311yescharacteristic
453#341C22×C4311yescharacteristic, complemented
454#341C22×C4311yescharacteristic, complemented
455#339C22×C4311yescharacteristic, complemented
456#339C22×C4311yescharacteristic, complemented
457#339C22×C4311yescharacteristic, complemented
458#339C22×C4311yescharacteristic, complemented
459#336C22×C4311yescharacteristic, complemented
460#336C22×C4311yescharacteristic, complemented
461C43#2258811yescharacteristic, direct product factor, Sylow
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×C4×C4311yescharacteristic
469C2×#41C2×C4×C4311yescharacteristic
470C2×#41C23×C4311yescharacteristic
471C2×#41C23×C4311yescharacteristic
472C22×Q8C2×C4×C4311yescharacteristic
473C22×D4—21no—
474C22×D4C2×C4×C4311yescharacteristic
475C23×C4—21no—
476C23×C4C23×C4311yescharacteristic
477#131—22no—
478#131—22no—
479#131—41no—
480#131—41no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—41no—
484C2×M16—41no—
485C2×M16C2×C4×C4311yescharacteristic
486C2×M16C2×C4×C4311yescharacteristic
487C2×M16C2×C4×C4311yescharacteristic
488C2×M16C2×C4×C4311yescharacteristic
489C2×M16C23×C4311yescharacteristic
490C2×M16C23×C4311yescharacteristic
491C2×M16C23×C4311yescharacteristic
492C2×M16C23×C4311yescharacteristic
493C22×C8—21no—
494C22×C8—21no—
495C22×C8C23×C4311yescharacteristic
496C22×C8C23×C4311yescharacteristic
497C22×C8C23×C4311yescharacteristic
498C22×C8C23×C4311yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×C4×C4311yescharacteristic
502#117C2×C4×C4311yescharacteristic
503#117C23×C4311yescharacteristic
504#117C23×C4311yescharacteristic
505C2×C4⋊C4C2×C4×C4311yescharacteristic
506C2×C4⋊C4C2×C4×C4311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C42—21no—
510C2×C42C23×C4311yescharacteristic
511C2×C42C23×C4311yescharacteristic
512#108—41no—
513#108—41no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518#104—22no—
519#104—22no—
520#104—41no—
521#104—41no—
522#103C2×C4×C4311yescharacteristic
523#103C2×C4×C4311yescharacteristic
524#103C2×C4×C4311yescharacteristic
525#103C2×C4×C4311yescharacteristic
526#103C2×C4×C4311yescharacteristic
527#103C2×C4×C4311yescharacteristic
528#103C2×C4×C4311yescharacteristic
529#103C2×C4×C4311yescharacteristic
530#102C2×C4×C4311yescharacteristic
531#102C2×C4×C4311yescharacteristic
532#102C2×C4×C4311yescharacteristic
533#102C2×C4×C4311yescharacteristic
534#102C2×C4×C4311yescharacteristic
535#102C2×C4×C4311yescharacteristic
536#102C2×C4×C4311yescharacteristic
537#102C2×C4×C4311yescharacteristic
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546C22⋊C8D4×C4311yescharacteristic
547C22⋊C8D4×C4311yescharacteristic
548C22⋊C8D4×C4311yescharacteristic
549C22⋊C8D4×C4311yescharacteristic
550#97—21no—
551#97—21no—
552#97—41no—
553C4×C8—21no—
554C4×C8—21no—
555C4×C8—41no—
556#95—21no—
557C24—21no—
558C24#41×C4311yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#41×C4312yes—
574#41#41×C4312yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×C4×C4311yescharacteristic
579C2×Q8C22×C4×C4311yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×C4×C4311yescharacteristic
590C2×D4C22×C4×C4311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C22×C4×C4311yescharacteristic
607C22×C4C22×C4×C4311yescharacteristic
608C22×C4C2×D4×C4311yescharacteristic
609C22×C4C2×D4×C4311yescharacteristic
610C22×C4#41×C4311yescharacteristic
611C22×C4C24×C4311yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—41no—
621M16—41no—
622M16—41no—
623M16—41no—
624M16—42no—
625M16—42no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8C22×C4×C4311yescharacteristic
641C2×C8C22×C4×C4311yescharacteristic
642C2×C8C22×C4×C4311yescharacteristic
643C2×C8C22×C4×C4311yescharacteristic
644C2×C8C2×D4×C4311yescharacteristic
645C2×C8C2×D4×C4311yescharacteristic
646C2×C8C2×D4×C4311yescharacteristic
647C2×C8C2×D4×C4311yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×C4×C4311yescharacteristic
651C4⋊C4C22×C4×C4311yescharacteristic
652C4⋊C4C22×C4×C4311yescharacteristic
653C4⋊C4C22×C4×C4311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—42no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23C4×D4×C4311yescharacteristic
677C23C4×D4×C4311yescharacteristic
678C23C2×#41×C4311yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#117×C4312yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#117×C4312yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—81no—
726C2×C4C4×D4×C4311yescharacteristic
727C2×C4C4×D4×C4311yescharacteristic
728C2×C4C23×C4×C4311yescharacteristic
729C2×C4C22×D4×C4311yescharacteristic
730C2×C4C2×#41×C4311yescharacteristic
731C2×C4C2×#41×C4311yescharacteristic
732C2×C4H(5,𝔽2)×C4311yescharacteristic
733C2×C4H(5,𝔽2)×C4311yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—21no—
739C8—21no—
740C8—21no—
741C8—21no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—22no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×C4×D4×C4311yescharacteristic
764C22C43×#55111yescharacteristic
765C22C43×#55111yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4C2×#117×C4311yescharacteristic
777C4C43×#51811yescharacteristic
778C4C43×#54611yescharacteristic
779C4C43×#54611yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2C43×#234211yescharacteristic
787C2C43×#295511yescharacteristic
788C2C43×#295611yescharacteristic
subgroupG/H
centerC2×C4×C43C22×D4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC22×C4C24×C43
socleC22×C43C2×C4×D4
prime radicalC22×#41×C43C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C2×C22⋊C8×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#2924C2semidirect
4. C43×#1938C2semidirect
5. C43×#1937C2semidirect
6. C43×#1929C2semidirect
7. C43×#1929C2semidirect
8. C43×#1866C2semidirect
9. C43×#1866C2semidirect
10. C43×#1826C2semidirect
11. C43×#1811C2semidirect
13. C43×#1765C2semidirect
14. C43×#1764C2semidirect
15. C43×#1753C2semidirect
25. C2×#108×C43C22semidirect
26. C2×#108×C43C22semidirect
27. C43×#424C22semidirect
28. C43×#424C22semidirect
33. C43×#419C4semidirect
34. C43×#419C4semidirect
35. C43×#418C4semidirect
36. C43×#418C4semidirect
37. C43×#417C4semidirect
38. C43×#417C4semidirect
39. C43×#417C4semidirect
40. C43×#417C4semidirect
54. C43×#405C22semidirect
55. C43×#405C22semidirect
56. C2×#97×C43C22semidirect
57. C2×C4×C8×C43C22semidirect
59. C43×#341C22semidirect
60. C43×#341C22semidirect
61. C43×#339C22semidirect
62. C43×#339C22semidirect
63. C43×#339C22semidirect
64. C43×#339C22semidirect
65. C43×#336C22semidirect
66. C43×#336C22semidirect
351. #22588C43direct (N × H)
386. #2924C2×C43semidirect
389. #1938C2×C43semidirect
390. #1937C2×C43semidirect
391. #1929C2×C43semidirect
392. #1929C2×C43semidirect
393. #1866C2×C43semidirect
394. #1866C2×C43semidirect
395. #1826C2×C43semidirect
396. #1811C2×C43semidirect
398. #1765C2×C43semidirect
399. #1764C2×C43semidirect
400. #1753C2×C43semidirect
419. C2×#108C22×C43semidirect
420. C2×#108C22×C43semidirect
421. #424C22×C43semidirect
422. #424C22×C43semidirect
427. #419C4×C43semidirect
428. #419C4×C43semidirect
429. #418C4×C43semidirect
430. #418C4×C43semidirect
431. #417C4×C43semidirect
432. #417C4×C43semidirect
433. #417C4×C43semidirect
434. #417C4×C43semidirect
448. #405C22×C43semidirect
449. #405C22×C43semidirect
450. C2×#97C22×C43semidirect
451. C2×C4×C8C22×C43semidirect
453. #341C22×C43semidirect
454. #341C22×C43semidirect
455. #339C22×C43semidirect
456. #339C22×C43semidirect
457. #339C22×C43semidirect
458. #339C22×C43semidirect
459. #336C22×C43semidirect
460. #336C22×C43semidirect
461. C43#22588direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#29242
C43×#28962
C43×#28802
C43×#19382
C43×#19372
C43×#19292
C43×#18662
C43×#18262
C43×#18112
C43×#17892
C43×#17652
C43×#17642
C43×#17532
#2258843