Finite Group Databasebeta

← C43×#61860 #24981877

Subgroups — C43×#61860 #24981877

Order 11008.

1706 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3554C211yesmaximal, characteristic, complemented
2C43×#3503C211yesmaximal, characteristic, complemented
3C43×#3388C212yesmaximal, complemented
4C43×#3387C211yesmaximal, characteristic, complemented
5C43×#3384C212yesmaximal, complemented
6C43×#3384C211yesmaximal, characteristic, complemented
7C43×#3381C211yesmaximal, characteristic, complemented
8Q8×SD16×C43C211yesmaximal, characteristic, complemented
9C43×#3375C211yesmaximal, characteristic, complemented
10C43×#3373C212yesmaximal, complemented
11C43×#3371C212yesmaximal, complemented
12C43×#3366C211yesmaximal, characteristic, complemented
13C43×#3362C211yesmaximal, characteristic, complemented
14C43×#3361C211yesmaximal, characteristic, complemented
15C43×#3244C212yesmaximal, complemented
16C43×#3241C212yesmaximal, complemented
17C43×#3238C211yesmaximal, characteristic, complemented
18C43×#3227C211yesmaximal, characteristic, complemented
19C43×#3125C212yesmaximal, complemented
20C43×#3119C212yesmaximal, complemented
21C43×#3115C211yesmaximal, characteristic, complemented
22C43×#3102C211yesmaximal, characteristic, complemented
23C43×#2985C211yesmaximal, characteristic, complemented
24C43×#562—22no—
25C43×#559C2211yescharacteristic
26C43×#559C2212yes—
27Q82×C43C2211yescharacteristic
28Q82×C43C2211yescharacteristic
29C43×#557C2212yes—
30C43×#557C2211yescharacteristic
31C43×#554—21no—
32C43×#554—21no—
33C43×#554C2211yescharacteristic
34C43×#554C2211yescharacteristic
35C43×#554C2212yes—
36C43×#550C2211yescharacteristic
37D4×Q8×C43—22no—
38D4×Q8×C43C2212yes—
39D4×Q8×C43C2211yescharacteristic
40C43×#548—21no—
41C43×#547—21no—
42C43×#544—22no—
43C43×#544C2212yes—
44C43×#542—21no—
45C43×#542C2212yes—
46C43×#540C2212yes—
47C43×#539—22no—
48C43×#536—21no—
49C43×#533—21no—
50C43×#533C2211yescharacteristic
51C43×#532C2211yescharacteristic
52C2×C4⋊Q8×C43—21no—
53C2×C4⋊Q8×C43C2211yescharacteristic
54C43×#529C2211yescharacteristic
55C43×#520C2212yes—
56C4×#41×C43C2211yescharacteristic
57C43×#501C2212yes—
58C43×#501C2212yes—
59C43×#501C2212yes—
60C43×#499C2212yes—
61C43×#498C2211yescharacteristic
62C43×#498C2212yes—
63C43×#498C2211yescharacteristic
64C43×#490C2212yes—
65C43×#489C2212yes—
66C43×#489C2212yes—
67C43×#488C2212yes—
68C43×#486C2211yescharacteristic
69C43×#486C2212yes—
70C43×#486C2211yescharacteristic
71C43×#485C2211yescharacteristic
72C43×#483C2212yes—
73C43×#482C2211yescharacteristic
74C43×#482C2212yes—
75C43×#481C2212yes—
76C43×#481C2212yes—
77C43×#480C2212yes—
78C43×#479C2211yescharacteristic
79C43×#479C2212yes—
80C43×#479C2212yes—
81C43×#478C2211yescharacteristic
82C43×#478C2212yes—
83C43×#478C2212yes—
84C43×#478C2212yes—
85C43×#478C2212yes—
86C43×#477C2211yescharacteristic
87C43×#477C2211yescharacteristic
88C43×#476C2211yescharacteristic
89C43×#476C2212yes—
90C43×#476C2211yescharacteristic
91C43×#476C2212yes—
92C43×#476C2212yes—
93C43×#476C2212yes—
94C43×#476C2212yes—
95C43×#475C2211yescharacteristic
96C43×#475C2212yes—
97C43×#475C2212yes—
98C43×#474C2211yescharacteristic
99C43×#474C2212yes—
100C43×#464C2211yescharacteristic
101C43×#464C2212yes—
102C43×#463C2211yescharacteristic
103C43×#463C2212yes—
104C43×#460C2211yescharacteristic
105C43×#460C2212yes—
106C43×#459C2211yescharacteristic
107C43×#459C2212yes—
108C43×#452C2211yescharacteristic
109C43×#449C2211yescharacteristic
110C43×#449C2212yes—
111C43×#446C2211yescharacteristic
112C43×#446C2212yes—
113C43×#446C2212yes—
114C43×#446C2211yescharacteristic
115C8×Q8×C43C2211yescharacteristic
116C8×Q8×C43C2211yescharacteristic
117C43×#442C2212yes—
118C43×#442C2212yes—
119C43×#442C2212yes—
120C43×#441C2212yes—
121C43×#440C2212yes—
122C43×#440C2212yes—
123C4×Q16×C43C2211yescharacteristic
124C4×SD16×C43C2211yescharacteristic
125C4×SD16×C43C2211yescharacteristic
126C4×SD16×C43C2212yes—
127C4×SD16×C43C2212yes—
128C4×SD16×C43C2212yes—
129C4×D8×C43C2211yescharacteristic
130C4×D8×C43C2212yes—
131C43×#433C2212yes—
132C43×#433C2212yes—
133C43×#432C2211yescharacteristic
134C43×#431C2211yescharacteristic
135C2×#41×C43—21no—
136C2×#41×C43—21no—
137C2×#41×C43C2311yescharacteristic
138C22×Q8×C43—22no—
139C22×Q8×C43—21no—
140C22×Q8×C43—21no—
141C2×Q16×C43C2311yescharacteristic
142C2×SD16×C43C2311yescharacteristic
143C2×SD16×C43C2311yescharacteristic
144C2×SD16×C43C2312yes—
145C2×D8×C43C2311yescharacteristic
146C2×D8×C43C2312yes—
147C4⋊Q8×C43—22no—
148C4⋊Q8×C43—21no—
149C4⋊Q8×C43—22no—
150C4⋊Q8×C43—21no—
151C4⋊Q8×C43—21no—
152C4⋊Q8×C43—22no—
153C4⋊Q8×C43—22no—
154C4⋊Q8×C43—21no—
155C4⋊Q8×C43—21no—
156C4⋊Q8×C43D411yescharacteristic
157C4⋊Q8×C43D411yescharacteristic
158C4⋊Q8×C43C2311yescharacteristic
159C4⋊Q8×C43C2312yes—
160C4⋊Q8×C43C2311yescharacteristic
161C4⋊Q8×C43C2311yescharacteristic
162C4⋊Q8×C43C2312yes—
163C4⋊Q8×C43C2312yes—
164C4⋊Q8×C43C2312yes—
165#127×C43C2311yescharacteristic
166#127×C43C2312yes—
167#126×C43—22no—
168#126×C43—21no—
169#125×C43—22no—
170#125×C43—22no—
171#125×C43—22no—
172#125×C43—22no—
173#125×C43D412yes—
174#125×C43C2312yes—
175#125×C43C2312yes—
176#125×C43C2311yescharacteristic
177#125×C43C2312yes—
178#124×C43—21no—
179#124×C43—22no—
180#124×C43—22no—
181#124×C43—21no—
182#124×C43C2311yescharacteristic
183#124×C43C2312yes—
184#123×C43—21no—
185#123×C43—22no—
186#123×C43—22no—
187#123×C43—22no—
188#123×C43—22no—
189#123×C43—22no—
190#123×C43—22no—
191C22⋊Q8×C43—21no—
192C22⋊Q8×C43—21no—
193C22⋊Q8×C43—22no—
194C22⋊Q8×C43—22no—
195C22⋊Q8×C43—22no—
196C22⋊Q8×C43—22no—
197C22⋊Q8×C43—22no—
198C22⋊Q8×C43—22no—
199C22⋊Q8×C43—21no—
200C22⋊Q8×C43—22no—
201C22⋊Q8×C43—22no—
202C22⋊Q8×C43—22no—
203C22⋊Q8×C43—22no—
204C22⋊Q8×C43—22no—
205C22⋊Q8×C43—22no—
206C22⋊Q8×C43D411yescharacteristic
207C22⋊Q8×C43D411yescharacteristic
208C22⋊Q8×C43D412yes—
209C22⋊Q8×C43C2311yescharacteristic
210#121×C43—21no—
211#121×C43—22no—
212#121×C43—21no—
213#121×C43—22no—
214#121×C43—22no—
215#121×C43C2311yescharacteristic
216#121×C43C2312yes—
217C4×Q8×C43—21no—
218C4×Q8×C43—21no—
219C4×Q8×C43—22no—
220C4×Q8×C43—21no—
221C4×Q8×C43C2311yescharacteristic
222C4×Q8×C43C2311yescharacteristic
223C4×Q8×C43C2312yes—
224C4×Q8×C43C2312yes—
225C4×Q8×C43C2311yescharacteristic
226C4×Q8×C43C2312yes—
227C4×Q8×C43C2312yes—
228C4×Q8×C43C2311yescharacteristic
229C4×Q8×C43C2311yescharacteristic
230C4×D4×C43—21no—
231C4×D4×C43—21no—
232C4×D4×C43—21no—
233C4×D4×C43—22no—
234C4×D4×C43—21no—
235C4×D4×C43—22no—
236C4×D4×C43—22no—
237C4×D4×C43—21no—
238C4×D4×C43C2311yescharacteristic
239C4×D4×C43C2311yescharacteristic
240C4×D4×C43C2312yes—
241C4×D4×C43C2312yes—
242C4×D4×C43C2311yescharacteristic
243C4×D4×C43C2312yes—
244C4×D4×C43C2312yes—
245C4×D4×C43C2312yes—
246C4×D4×C43C2312yes—
247#117×C43—22no—
248#117×C43—21no—
249#117×C43—21no—
250#117×C43C2311yescharacteristic
251#117×C43C2312yes—
252C2×C4⋊C4×C43—21no—
253C2×C4⋊C4×C43—22no—
254C2×C4⋊C4×C43—21no—
255C2×C4⋊C4×C43—21no—
256C2×C4⋊C4×C43—22no—
257C2×C4⋊C4×C43C2312yes—
258C2×C42×C43—21no—
259C2×C42×C43C2311yescharacteristic
260#107×C43C2312yes—
261#107×C43C2312yes—
262#107×C43C2312yes—
263#107×C43C2311yescharacteristic
264#107×C43C2311yescharacteristic
265#106×C43C2311yescharacteristic
266#106×C43C2312yes—
267#106×C43C2312yes—
268#106×C43C2312yes—
269#106×C43C2312yes—
270#106×C43C2312yes—
271#106×C43C2312yes—
272#106×C43C2311yescharacteristic
273#106×C43C2312yes—
274C4⋊C8×C43C2311yescharacteristic
275C4⋊C8×C43C2311yescharacteristic
276C4⋊C8×C43C2311yescharacteristic
277C4⋊C8×C43C2311yescharacteristic
278C4⋊C8×C43C2312yes—
279C4⋊C8×C43C2312yes—
280C4⋊C8×C43C2312yes—
281C4⋊C8×C43C2312yes—
282#103×C43C2311yescharacteristic
283#103×C43C2312yes—
284#103×C43C2312yes—
285#103×C43C2311yescharacteristic
286#103×C43C2311yescharacteristic
287#103×C43C2311yescharacteristic
288#103×C43C2312yes—
289#102×C43C2311yescharacteristic
290#102×C43C2311yescharacteristic
291#102×C43C2312yes—
292#102×C43C2311yescharacteristic
293#102×C43C2312yes—
294#102×C43C2312yes—
295#102×C43C2311yescharacteristic
296#102×C43C2312yes—
297#102×C43C2312yes—
298#102×C43C2312yes—
299#102×C43C2312yes—
300#102×C43C2312yes—
301#102×C43C2312yes—
302C22⋊C8×C43C2311yescharacteristic
303C22⋊C8×C43C2311yescharacteristic
304C22⋊C8×C43C2312yes—
305#97×C43C2312yes—
306#97×C43C2312yes—
307#97×C43C2312yes—
308C4×C8×C43C2311yescharacteristic
309C4×C8×C43C2311yescharacteristic
310C4×C8×C43C2312yes—
311C4×C8×C43C2312yes—
312#41×C43—22no—
313#41×C43—22no—
314#41×C43—82no—
315#41×C43—82no—
316C2×Q8×C43—21no—
317C2×Q8×C43—22no—
318C2×Q8×C43—22no—
319C2×Q8×C43—22no—
320C2×Q8×C43—22no—
321C2×Q8×C43—21no—
322C2×Q8×C43—21no—
323C2×Q8×C43—82no—
324C2×Q8×C43—82no—
325C2×Q8×C43—84no—
326C2×Q8×C43C2×D411yescharacteristic
327C2×Q8×C43C2×D411yescharacteristic
328C2×Q8×C43C2×D412yes—
329C2×Q8×C43C2411yescharacteristic
330C2×Q8×C43C2411yescharacteristic
331C2×D4×C43—21no—
332C2×D4×C43—21no—
333C2×D4×C43—22no—
334C2×D4×C43—22no—
335C2×D4×C43—21no—
336C2×D4×C43—21no—
337C2×D4×C43—22no—
338C2×D4×C43C2412yes—
339C2×D4×C43C2411yescharacteristic
340C2×D4×C43C2411yescharacteristic
341C22×C4×C43—21no—
342C22×C4×C43—21no—
343C22×C4×C43—21no—
344C22×C4×C43—21no—
345C22×C4×C43—22no—
346C22×C4×C43—22no—
347C22×C4×C43—22no—
348C22×C4×C43—22no—
349C22×C4×C43—22no—
350C22×C4×C43—22no—
351C22×C4×C43—22no—
352C22×C4×C43C2×D411yescharacteristic
353C22×C4×C43C2×D411yescharacteristic
354C22×C4×C43C2411yescharacteristic
355Q16×C43—22no—
356SD16×C43—22no—
357SD16×C43—24no—
358SD16×C43—22no—
359D8×C43—22no—
360D8×C43—24no—
361C2×C8×C43C2411yescharacteristic
362C2×C8×C43C2411yescharacteristic
363C2×C8×C43C2411yescharacteristic
364C2×C8×C43C2412yes—
365C2×C8×C43C2411yescharacteristic
366C2×C8×C43C2412yes—
367C4⋊C4×C43—21no—
368C4⋊C4×C43—21no—
369C4⋊C4×C43—21no—
370C4⋊C4×C43—22no—
371C4⋊C4×C43—22no—
372C4⋊C4×C43—22no—
373C4⋊C4×C43—22no—
374C4⋊C4×C43—22no—
375C4⋊C4×C43—22no—
376C4⋊C4×C43—22no—
377C4⋊C4×C43—22no—
378C4⋊C4×C43—21no—
379C4⋊C4×C43—21no—
380C4⋊C4×C43—21no—
381C4⋊C4×C43—21no—
382C4⋊C4×C43—21no—
383C4⋊C4×C43—22no—
384C4⋊C4×C43—22no—
385C4⋊C4×C43—22no—
386C4⋊C4×C43—22no—
387C4⋊C4×C43—22no—
388C4⋊C4×C43—22no—
389C4⋊C4×C43—21no—
390C4⋊C4×C43C2×D412yes—
391C4⋊C4×C43C2×D411yescharacteristic
392C4⋊C4×C43C2×D411yescharacteristic
393C4⋊C4×C43C2×D412yes—
394C4⋊C4×C43C2×D412yes—
395C4⋊C4×C43C2×D412yes—
396C4⋊C4×C43C2×D412yes—
397C4⋊C4×C43C2×D412yes—
398C4⋊C4×C43C2×D412yes—
399C4⋊C4×C43C2412yes—
400C4⋊C4×C43C2412yes—
401C4⋊C4×C43C2411yescharacteristic
402C4⋊C4×C43C2411yescharacteristic
403C4⋊C4×C43C2411yescharacteristic
404C4⋊C4×C43C2412yes—
405C4⋊C4×C43C2411yescharacteristic
406C22⋊C4×C43—21no—
407C22⋊C4×C43—21no—
408C22⋊C4×C43—22no—
409C22⋊C4×C43—22no—
410C22⋊C4×C43—21no—
411C22⋊C4×C43—21no—
412C22⋊C4×C43—21no—
413C22⋊C4×C43—22no—
414C22⋊C4×C43—22no—
415C22⋊C4×C43—22no—
416C22⋊C4×C43—21no—
417C22⋊C4×C43—22no—
418C22⋊C4×C43—22no—
419C22⋊C4×C43—22no—
420C22⋊C4×C43—22no—
421C22⋊C4×C43—21no—
422C22⋊C4×C43—21no—
423C22⋊C4×C43C2×D412yes—
424C22⋊C4×C43C2×D412yes—
425C42×C43—21no—
426C42×C43—21no—
427C42×C43—21no—
428C42×C43—21no—
429C42×C43—22no—
430C42×C43—22no—
431C42×C43—22no—
432C42×C43C2×D411yescharacteristic
433C42×C43C2×D411yescharacteristic
434C42×C43C2411yescharacteristic
435C42×C43C2412yes—
436C42×C43C2412yes—
437C42×C43C2411yescharacteristic
438C23×C43—21no—
439C23×C43—22no—
440C23×C43—21no—
441C23×C43C22×D411yescharacteristic
442Q8×C43—22no—
443Q8×C43—22no—
444Q8×C43—21no—
445Q8×C43—21no—
446Q8×C43—21no—
447Q8×C43—42no—
448Q8×C43—44no—
449Q8×C43—42no—
450Q8×C43—81no—
451Q8×C43—81no—
452Q8×C43—82no—
453Q8×C43—82no—
454Q8×C43—82no—
455Q8×C432−1+412yes—
456D4×C43—24no—
457D4×C43—21no—
458D4×C43—22no—
459D4×C43—21no—
460D4×C43—21no—
461D4×C43—22no—
462D4×C43—42no—
463D4×C43—81no—
464D4×C43—82no—
465D4×C43—82no—
466D4×C43—81no—
467D4×C43—82no—
468D4×C432−1+412yes—
469C2×C4×C43—24no—
470C2×C4×C43—21no—
471C2×C4×C43—22no—
472C2×C4×C43—21no—
473C2×C4×C43—21no—
474C2×C4×C43—21no—
475C2×C4×C43—21no—
476C2×C4×C43—21no—
477C2×C4×C43—21no—
478C2×C4×C43—22no—
479C2×C4×C43—22no—
480C2×C4×C43—22no—
481C2×C4×C43—21no—
482C2×C4×C43—41no—
483C2×C4×C43—42no—
484C2×C4×C43—42no—
485C2×C4×C43—42no—
486C2×C4×C43—82no—
487C2×C4×C43—82no—
488C2×C4×C43—82no—
489C2×C4×C43—82no—
490C2×C4×C43—82no—
491C2×C4×C43—82no—
492C2×C4×C43—82no—
493C2×C4×C43C22×D411yescharacteristic
494C2×C4×C43C22×D411yescharacteristic
495C2×C4×C43C22×D412yes—
496C2×C4×C43C22×D412yes—
497C2×C4×C43C22×D412yes—
498C2×C4×C43C22×D411yescharacteristic
499C2×C4×C43C22×D411yescharacteristic
500C2×C4×C43C22×D412yes—
501C2×C4×C43C22×D411yescharacteristic
502C2×C4×C43C2511yescharacteristic
503C8×C43—21no—
504C8×C43—22no—
505C8×C43—21no—
506C8×C43—22no—
507C8×C43—21no—
508C8×C43—21no—
509#61860C4311yesmaximal, characteristic, direct product factor, Sylow
510C22×C43—21no—
511C22×C43—22no—
512C22×C43—21no—
513C22×C43—21no—
514C22×C43—41no—
515C22×C43—41no—
516C22×C43—42no—
517C22×C43—41no—
518C22×C43—42no—
519C22×C43—41no—
520C22×C43—41no—
521C22×C43—42no—
522C22×C43C23×D411yescharacteristic
523C4×C43—21no—
524C4×C43—21no—
525C4×C43—22no—
526C4×C43—22no—
527C4×C43—21no—
528C4×C43—22no—
529C4×C43—21no—
530C4×C43—22no—
531C4×C43—22no—
532C4×C43—41no—
533C4×C43—41no—
534C4×C43—42no—
535C4×C43—42no—
536C4×C43—41no—
537C4×C43—41no—
538C4×C43—41no—
539C4×C43—42no—
540C4×C43#57712yes—
541C4×C43C2×2−1+411yescharacteristic
542C4×C43C2×2−1+411yescharacteristic
543#3554C2×C4311yescharacteristic, complemented
544#3503C2×C4311yescharacteristic, complemented
545#3388C2×C4312yescomplemented
546#3387C2×C4311yescharacteristic, complemented
547#3384C2×C4312yescomplemented
548#3384C2×C4311yescharacteristic, complemented
549#3381C2×C4311yescharacteristic, complemented
550Q8×SD16C2×C4311yescharacteristic, complemented
551#3375C2×C4311yescharacteristic, complemented
552#3373C2×C4312yescomplemented
553#3371C2×C4312yescomplemented
554#3366C2×C4311yescharacteristic, complemented
555#3362C2×C4311yescharacteristic, complemented
556#3361C2×C4311yescharacteristic, complemented
557#3244C2×C4312yescomplemented
558#3241C2×C4312yescomplemented
559#3238C2×C4311yescharacteristic, complemented
560#3227C2×C4311yescharacteristic, complemented
561#3125C2×C4312yescomplemented
562#3119C2×C4312yescomplemented
563#3115C2×C4311yescharacteristic, complemented
564#3102C2×C4311yescharacteristic, complemented
565#2985C2×C4311yescharacteristic, complemented
566C2×C43—41no—
567C2×C43—42no—
568C2×C43—82no—
569C2×C43—81no—
570C2×C43#348611yescharacteristic
571C2×C43C2×#57711yescharacteristic
572C2×C43#358511yescharacteristic
573#562—22no—
574#559C22×C4311yescharacteristic
575#559C22×C4312yes—
576Q82C22×C4311yescharacteristic
577Q82C22×C4311yescharacteristic
578#557C22×C4312yes—
579#557C22×C4311yescharacteristic
580#554—21no—
581#554—21no—
582#554C22×C4311yescharacteristic
583#554C22×C4311yescharacteristic
584#554C22×C4312yes—
585#550C22×C4311yescharacteristic
586D4×Q8—22no—
587D4×Q8C22×C4312yes—
588D4×Q8C22×C4311yescharacteristic
589#548—21no—
590#547—21no—
591#544—22no—
592#544C22×C4312yes—
593#542—21no—
594#542C22×C4312yes—
595#540C22×C4312yes—
596#539—22no—
597#536—21no—
598#533—21no—
599#533C22×C4311yescharacteristic
600#532C22×C4311yescharacteristic
601C2×C4⋊Q8—21no—
602C2×C4⋊Q8C22×C4311yescharacteristic
603#529C22×C4311yescharacteristic
604#520C22×C4312yes—
605C4×#41C22×C4311yescharacteristic
606#501C22×C4312yes—
607#501C22×C4312yes—
608#501C22×C4312yes—
609#499C22×C4312yes—
610#498C22×C4311yescharacteristic
611#498C22×C4312yes—
612#498C22×C4311yescharacteristic
613#490C22×C4312yes—
614#489C22×C4312yes—
615#489C22×C4312yes—
616#488C22×C4312yes—
617#486C22×C4311yescharacteristic
618#486C22×C4312yes—
619#486C22×C4311yescharacteristic
620#485C22×C4311yescharacteristic
621#483C22×C4312yes—
622#482C22×C4311yescharacteristic
623#482C22×C4312yes—
624#481C22×C4312yes—
625#481C22×C4312yes—
626#480C22×C4312yes—
627#479C22×C4311yescharacteristic
628#479C22×C4312yes—
629#479C22×C4312yes—
630#478C22×C4311yescharacteristic
631#478C22×C4312yes—
632#478C22×C4312yes—
633#478C22×C4312yes—
634#478C22×C4312yes—
635#477C22×C4311yescharacteristic
636#477C22×C4311yescharacteristic
637#476C22×C4311yescharacteristic
638#476C22×C4312yes—
639#476C22×C4311yescharacteristic
640#476C22×C4312yes—
641#476C22×C4312yes—
642#476C22×C4312yes—
643#476C22×C4312yes—
644#475C22×C4311yescharacteristic
645#475C22×C4312yes—
646#475C22×C4312yes—
647#474C22×C4311yescharacteristic
648#474C22×C4312yes—
649#464C22×C4311yescharacteristic
650#464C22×C4312yes—
651#463C22×C4311yescharacteristic
652#463C22×C4312yes—
653#460C22×C4311yescharacteristic
654#460C22×C4312yes—
655#459C22×C4311yescharacteristic
656#459C22×C4312yes—
657#452C22×C4311yescharacteristic
658#449C22×C4311yescharacteristic
659#449C22×C4312yes—
660#446C22×C4311yescharacteristic
661#446C22×C4312yes—
662#446C22×C4312yes—
663#446C22×C4311yescharacteristic
664C8×Q8C22×C4311yescharacteristic
665C8×Q8C22×C4311yescharacteristic
666#442C22×C4312yes—
667#442C22×C4312yes—
668#442C22×C4312yes—
669#441C22×C4312yes—
670#440C22×C4312yes—
671#440C22×C4312yes—
672C4×Q16C22×C4311yescharacteristic
673C4×SD16C22×C4311yescharacteristic
674C4×SD16C22×C4311yescharacteristic
675C4×SD16C22×C4312yes—
676C4×SD16C22×C4312yes—
677C4×SD16C22×C4312yes—
678C4×D8C22×C4311yescharacteristic
679C4×D8C22×C4312yes—
680#433C22×C4312yes—
681#433C22×C4312yes—
682#432C22×C4311yescharacteristic
683#431C22×C4311yescharacteristic
684C43#6186011yescharacteristic, direct product factor, Sylow
685C2×#41—21no—
686C2×#41—21no—
687C2×#41C23×C4311yescharacteristic
688C22×Q8—22no—
689C22×Q8—21no—
690C22×Q8—21no—
691C2×Q16C23×C4311yescharacteristic
692C2×SD16C23×C4311yescharacteristic
693C2×SD16C23×C4311yescharacteristic
694C2×SD16C23×C4312yes—
695C2×D8C23×C4311yescharacteristic
696C2×D8C23×C4312yes—
697C4⋊Q8—22no—
698C4⋊Q8—21no—
699C4⋊Q8—22no—
700C4⋊Q8—21no—
701C4⋊Q8—21no—
702C4⋊Q8—22no—
703C4⋊Q8—22no—
704C4⋊Q8—21no—
705C4⋊Q8—21no—
706C4⋊Q8D4×C4311yescharacteristic
707C4⋊Q8D4×C4311yescharacteristic
708C4⋊Q8C23×C4312yes—
709C4⋊Q8C23×C4311yescharacteristic
710C4⋊Q8C23×C4311yescharacteristic
711C4⋊Q8C23×C4311yescharacteristic
712C4⋊Q8C23×C4312yes—
713C4⋊Q8C23×C4312yes—
714C4⋊Q8C23×C4312yes—
715#127C23×C4311yescharacteristic
716#127C23×C4312yes—
717#126—22no—
718#126—21no—
719#125—22no—
720#125—22no—
721#125—22no—
722#125—22no—
723#125D4×C4312yes—
724#125C23×C4311yescharacteristic
725#125C23×C4312yes—
726#125C23×C4312yes—
727#125C23×C4312yes—
728#124—21no—
729#124—22no—
730#124—22no—
731#124—21no—
732#124C23×C4311yescharacteristic
733#124C23×C4312yes—
734#123—21no—
735#123—22no—
736#123—22no—
737#123—22no—
738#123—22no—
739#123—22no—
740#123—22no—
741C22⋊Q8—21no—
742C22⋊Q8—21no—
743C22⋊Q8—22no—
744C22⋊Q8—22no—
745C22⋊Q8—22no—
746C22⋊Q8—22no—
747C22⋊Q8—22no—
748C22⋊Q8—22no—
749C22⋊Q8—21no—
750C22⋊Q8—22no—
751C22⋊Q8—22no—
752C22⋊Q8—22no—
753C22⋊Q8—22no—
754C22⋊Q8—22no—
755C22⋊Q8—22no—
756C22⋊Q8D4×C4311yescharacteristic
757C22⋊Q8D4×C4311yescharacteristic
758C22⋊Q8D4×C4312yes—
759C22⋊Q8C23×C4311yescharacteristic
760#121—21no—
761#121—22no—
762#121—21no—
763#121—22no—
764#121—22no—
765#121C23×C4311yescharacteristic
766#121C23×C4312yes—
767C4×Q8—21no—
768C4×Q8—21no—
769C4×Q8—22no—
770C4×Q8—21no—
771C4×Q8C23×C4311yescharacteristic
772C4×Q8C23×C4311yescharacteristic
773C4×Q8C23×C4312yes—
774C4×Q8C23×C4312yes—
775C4×Q8C23×C4311yescharacteristic
776C4×Q8C23×C4312yes—
777C4×Q8C23×C4312yes—
778C4×Q8C23×C4311yescharacteristic
779C4×Q8C23×C4311yescharacteristic
780C4×D4—21no—
781C4×D4—21no—
782C4×D4—21no—
783C4×D4—22no—
784C4×D4—21no—
785C4×D4—22no—
786C4×D4—22no—
787C4×D4—21no—
788C4×D4C23×C4311yescharacteristic
789C4×D4C23×C4311yescharacteristic
790C4×D4C23×C4312yes—
791C4×D4C23×C4312yes—
792C4×D4C23×C4311yescharacteristic
793C4×D4C23×C4312yes—
794C4×D4C23×C4312yes—
795C4×D4C23×C4312yes—
796C4×D4C23×C4312yes—
797#117—22no—
798#117—21no—
799#117—21no—
800#117C23×C4311yescharacteristic
801#117C23×C4312yes—
802C2×C4⋊C4—21no—
803C2×C4⋊C4—22no—
804C2×C4⋊C4—21no—
805C2×C4⋊C4—21no—
806C2×C4⋊C4—22no—
807C2×C4⋊C4C23×C4312yes—
808C2×C42—21no—
809C2×C42C23×C4311yescharacteristic
810#107C23×C4312yes—
811#107C23×C4311yescharacteristic
812#107C23×C4311yescharacteristic
813#107C23×C4312yes—
814#107C23×C4312yes—
815#106C23×C4312yes—
816#106C23×C4312yes—
817#106C23×C4311yescharacteristic
818#106C23×C4312yes—
819#106C23×C4311yescharacteristic
820#106C23×C4312yes—
821#106C23×C4312yes—
822#106C23×C4312yes—
823#106C23×C4312yes—
824C4⋊C8C23×C4311yescharacteristic
825C4⋊C8C23×C4311yescharacteristic
826C4⋊C8C23×C4311yescharacteristic
827C4⋊C8C23×C4311yescharacteristic
828C4⋊C8C23×C4312yes—
829C4⋊C8C23×C4312yes—
830C4⋊C8C23×C4312yes—
831C4⋊C8C23×C4312yes—
832#103C23×C4311yescharacteristic
833#103C23×C4312yes—
834#103C23×C4312yes—
835#103C23×C4311yescharacteristic
836#103C23×C4311yescharacteristic
837#103C23×C4311yescharacteristic
838#103C23×C4312yes—
839#102C23×C4311yescharacteristic
840#102C23×C4311yescharacteristic
841#102C23×C4312yes—
842#102C23×C4311yescharacteristic
843#102C23×C4312yes—
844#102C23×C4312yes—
845#102C23×C4311yescharacteristic
846#102C23×C4312yes—
847#102C23×C4312yes—
848#102C23×C4312yes—
849#102C23×C4312yes—
850#102C23×C4312yes—
851#102C23×C4312yes—
852C22⋊C8C23×C4311yescharacteristic
853C22⋊C8C23×C4311yescharacteristic
854C22⋊C8C23×C4312yes—
855#97C23×C4312yes—
856#97C23×C4312yes—
857#97C23×C4312yes—
858C4×C8C23×C4311yescharacteristic
859C4×C8C23×C4311yescharacteristic
860C4×C8C23×C4312yes—
861C4×C8C23×C4312yes—
862#41—22no—
863#41—22no—
864#41—82no—
865#41—82no—
866C2×Q8—21no—
867C2×Q8—22no—
868C2×Q8—22no—
869C2×Q8—22no—
870C2×Q8—22no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—82no—
874C2×Q8—82no—
875C2×Q8—84no—
876C2×Q8C2×D4×C4311yescharacteristic
877C2×Q8C2×D4×C4311yescharacteristic
878C2×Q8C2×D4×C4312yes—
879C2×Q8C24×C4311yescharacteristic
880C2×Q8C24×C4311yescharacteristic
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—22no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4C24×C4312yes—
889C2×D4C24×C4311yescharacteristic
890C2×D4C24×C4311yescharacteristic
891C22×C4—21no—
892C22×C4—22no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4C2×D4×C4311yescharacteristic
903C22×C4C2×D4×C4311yescharacteristic
904C22×C4C24×C4311yescharacteristic
905Q16—22no—
906SD16—22no—
907SD16—24no—
908SD16—22no—
909D8—22no—
910D8—24no—
911C2×C8C24×C4311yescharacteristic
912C2×C8C24×C4311yescharacteristic
913C2×C8C24×C4311yescharacteristic
914C2×C8C24×C4312yes—
915C2×C8C24×C4311yescharacteristic
916C2×C8C24×C4312yes—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—22no—
921C4⋊C4—22no—
922C4⋊C4—22no—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—22no—
927C4⋊C4—22no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—22no—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—21no—
940C4⋊C4C2×D4×C4312yes—
941C4⋊C4C2×D4×C4311yescharacteristic
942C4⋊C4C2×D4×C4311yescharacteristic
943C4⋊C4C2×D4×C4312yes—
944C4⋊C4C2×D4×C4312yes—
945C4⋊C4C2×D4×C4312yes—
946C4⋊C4C2×D4×C4312yes—
947C4⋊C4C2×D4×C4312yes—
948C4⋊C4C2×D4×C4312yes—
949C4⋊C4C24×C4312yes—
950C4⋊C4C24×C4312yes—
951C4⋊C4C24×C4311yescharacteristic
952C4⋊C4C24×C4311yescharacteristic
953C4⋊C4C24×C4311yescharacteristic
954C4⋊C4C24×C4312yes—
955C4⋊C4C24×C4311yescharacteristic
956C22⋊C4—21no—
957C22⋊C4—21no—
958C22⋊C4—21no—
959C22⋊C4—21no—
960C22⋊C4—22no—
961C22⋊C4—22no—
962C22⋊C4—21no—
963C22⋊C4—21no—
964C22⋊C4—21no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—21no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4C2×D4×C4312yes—
974C22⋊C4C2×D4×C4312yes—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—22no—
980C42—22no—
981C42—22no—
982C42C2×D4×C4311yescharacteristic
983C42C2×D4×C4311yescharacteristic
984C42C24×C4311yescharacteristic
985C42C24×C4312yes—
986C42C24×C4312yes—
987C42C24×C4311yescharacteristic
988C23—21no—
989C23—21no—
990C23—22no—
991C23C22×D4×C4311yescharacteristic
992Q8—22no—
993Q8—22no—
994Q8—21no—
995Q8—21no—
996Q8—21no—
997Q8—42no—
998Q8—44no—
999Q8—42no—
1000Q8—82no—
1001Q8—81no—
1002Q8—81no—
1003Q8—82no—
1004Q8—82no—
1005Q82−1+4×C4312yes—
1006D4—24no—
1007D4—21no—
1008D4—22no—
1009D4—21no—
1010D4—21no—
1011D4—22no—
1012D4—42no—
1013D4—82no—
1014D4—81no—
1015D4—82no—
1016D4—82no—
1017D4—81no—
1018D42−1+4×C4312yes—
1019C2×C4—24no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—41no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—82no—
1037C2×C4—82no—
1038C2×C4—82no—
1039C2×C4—82no—
1040C2×C4—82no—
1041C2×C4—82no—
1042C2×C4—82no—
1043C2×C4C22×D4×C4311yescharacteristic
1044C2×C4C22×D4×C4311yescharacteristic
1045C2×C4C22×D4×C4312yes—
1046C2×C4C22×D4×C4312yes—
1047C2×C4C22×D4×C4312yes—
1048C2×C4C22×D4×C4311yescharacteristic
1049C2×C4C22×D4×C4311yescharacteristic
1050C2×C4C22×D4×C4312yes—
1051C2×C4C22×D4×C4311yescharacteristic
1052C2×C4C25×C4311yescharacteristic
1053C8—21no—
1054C8—22no—
1055C8—21no—
1056C8—22no—
1057C8—21no—
1058C8—21no—
1059C22—21no—
1060C22—22no—
1061C22—21no—
1062C22—21no—
1063C22—41no—
1064C22—41no—
1065C22—41no—
1066C22—42no—
1067C22—41no—
1068C22—42no—
1069C22—42no—
1070C22—41no—
1071C22C23×D4×C4311yescharacteristic
1072C4—21no—
1073C4—22no—
1074C4—21no—
1075C4—22no—
1076C4—22no—
1077C4—21no—
1078C4—21no—
1079C4—22no—
1080C4—22no—
1081C4—41no—
1082C4—41no—
1083C4—41no—
1084C4—42no—
1085C4—41no—
1086C4—41no—
1087C4—42no—
1088C4—42no—
1089C4C43×#57712yes—
1090C4C2×2−1+4×C4311yescharacteristic
1091C4C2×2−1+4×C4311yescharacteristic
1092C2—41no—
1093C2—42no—
1094C2—81no—
1095C2—82no—
1096C2C43×#348611yescharacteristic
1097C2C2×C43×#57711yescharacteristic
1098C2C43×#358511yescharacteristic
subgroupG/H
center, socleC22×C43C23×D4
commutator, Frattini, cosocleC2×C4C25×C43
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C43 ◁ C43×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C43×#3554C2semidirect
2. C43×#3503C2semidirect
3. C43×#3388C2semidirect
4. C43×#3387C2semidirect
5. C43×#3384C2semidirect
6. C43×#3384C2semidirect
7. C43×#3381C2semidirect
8. Q8×SD16×C43C2semidirect
9. C43×#3375C2semidirect
10. C43×#3373C2semidirect
11. C43×#3371C2semidirect
12. C43×#3366C2semidirect
13. C43×#3362C2semidirect
14. C43×#3361C2semidirect
15. C43×#3244C2semidirect
16. C43×#3241C2semidirect
17. C43×#3238C2semidirect
18. C43×#3227C2semidirect
19. C43×#3125C2semidirect
20. C43×#3119C2semidirect
21. C43×#3115C2semidirect
22. C43×#3102C2semidirect
23. C43×#2985C2semidirect
509. #61860C43direct (N × H)
543. #3554C2×C43semidirect
544. #3503C2×C43semidirect
545. #3388C2×C43semidirect
546. #3387C2×C43semidirect
547. #3384C2×C43semidirect
548. #3384C2×C43semidirect
549. #3381C2×C43semidirect
550. Q8×SD16C2×C43semidirect
551. #3375C2×C43semidirect
552. #3373C2×C43semidirect
553. #3371C2×C43semidirect
554. #3366C2×C43semidirect
555. #3362C2×C43semidirect
556. #3361C2×C43semidirect
557. #3244C2×C43semidirect
558. #3241C2×C43semidirect
559. #3238C2×C43semidirect
560. #3227C2×C43semidirect
561. #3125C2×C43semidirect
562. #3119C2×C43semidirect
563. #3115C2×C43semidirect
564. #3102C2×C43semidirect
565. #2985C2×C43semidirect
684. C43#61860direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#35542
C43×#35032
C43×#33882
C43×#33872
C43×#33842
C43×#33812
Q8×SD16×C432
C43×#33752
C43×#33732
C43×#33712
C43×#33662
C43×#33622
C43×#33612
C43×#32442
C43×#32412
C43×#32382
C43×#32272
C43×#31252
C43×#31192
C43×#31152
C43×#31022
C43×#29852
#6186043