Finite Group Databasebeta

← C43×#17505 #24937522

Subgroups — C43×#17505 #24937522

Order 11008.

954 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43×#3460C211yesmaximal, characteristic
2C43×#2989C211yesmaximal, characteristic, complemented
3C43×#2965C211yesmaximal, characteristic, complemented
4C43×#1496C211yesmaximal, characteristic, complemented
5C43×#1495C211yesmaximal, characteristic, complemented
6C43×#1494C211yesmaximal, characteristic, complemented
7C43×#1492C211yesmaximal, characteristic, complemented
8C43×#1490C211yesmaximal, characteristic, complemented
9C43×#1489C211yesmaximal, characteristic, complemented
10C43×#1488C211yesmaximal, characteristic, complemented
11C43×#1486C211yesmaximal, characteristic, complemented
12C43×#1484C211yesmaximal, characteristic, complemented
13C43×#1483C211yesmaximal, characteristic, complemented
14C43×#1482C211yesmaximal, characteristic, complemented
15C43×#1480C211yesmaximal, characteristic, complemented
16C43×#544C411yescharacteristic
17C43×#542—21no—
18C43×#542C411yescharacteristic
19C43×#542C411yescharacteristic
20C43×#540—21no—
21C43×#540C411yescharacteristic
22C43×#540C411yescharacteristic
23C43×#538—21no—
24C43×#538—21no—
25C43×#537C411yescharacteristic
26C43×#535C411yescharacteristic
27C43×#535C411yescharacteristic
28C43×#532—21no—
29C43×#532C2211yescharacteristic
30C43×#532C2211yescharacteristic
31C43×#529—21no—
32C43×#529C2211yescharacteristic
33C43×#529C2211yescharacteristic
34C43×#525—21no—
35C43×#525—21no—
36C4×#41×C43C2211yescharacteristic
37C4×#41×C43C2211yescharacteristic
38C2×C4×D4×C43C2211yescharacteristic
39C43×#446—21no—
40C43×#446—21no—
41C43×#436—21no—
42C43×#436—21no—
43C43×#435—21no—
44C43×#435—21no—
45C43×#435—21no—
46C43×#435—21no—
47C43×#432C2211yescharacteristic
48C43×#432C2211yescharacteristic, complemented
49C43×#431C2211yescharacteristic
50C43×#431C2211yescharacteristic, complemented
51C43×#431C2211yescharacteristic, complemented
52C43×#431C2211yescharacteristic, complemented
53C43×#423C2211yescharacteristic
54C43×#423C2211yescharacteristic, complemented
55C2×C4⋊C8×C43C2211yescharacteristic, complemented
56C4×M16×C43C2211yescharacteristic
57C4×M16×C43C2211yescharacteristic, complemented
58C2×C4×C8×C43C2211yescharacteristic, complemented
59C43×Q8⋊C8C2211yescharacteristic, complemented
60C43×Q8⋊C8C2211yescharacteristic, complemented
61C43×Q8⋊C8C2211yescharacteristic, complemented
62C43×Q8⋊C8C2211yescharacteristic, complemented
63C43×D4⋊C8C2211yescharacteristic
64C43×D4⋊C8C2211yescharacteristic
65C43×D4⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C43×D4⋊C8C2211yescharacteristic
68C43×D4⋊C8C2211yescharacteristic
69C43×D4⋊C8C2211yescharacteristic
70C43×D4⋊C8C2211yescharacteristic
71C43×D4⋊C8C2211yescharacteristic, complemented
72C43×D4⋊C8C2211yescharacteristic, complemented
73C43×D4⋊C8C2211yescharacteristic, complemented
74C43×D4⋊C8C2211yescharacteristic, complemented
75C2×#41×C43—21no—
76C2×#41×C43—21no—
77C2×#41×C43C2×C411yescharacteristic
78C2×#41×C43C2×C411yescharacteristic
79C22×D4×C43C2×C411yescharacteristic
80C23×C4×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43—21no—
83C2×M16×C43—21no—
84C2×M16×C43—21no—
85C22×C8×C43—21no—
86C22×C8×C43—21no—
87C4⋊Q8×C43—21no—
88C4⋊Q8×C43C2×C411yescharacteristic
89C4⋊Q8×C43C2×C411yescharacteristic
90#127×C43—21no—
91#127×C43C2×C411yescharacteristic
92#127×C43C2×C411yescharacteristic
93#126×C43—21no—
94#126×C43—21no—
95#126×C43—21no—
96#126×C43—21no—
97#125×C43—21no—
98#125×C43C2×C411yescharacteristic
99#125×C43C2×C411yescharacteristic
100#124×C43—21no—
101#124×C43—21no—
102#124×C43—21no—
103#124×C43—21no—
104#124×C43—21no—
105#124×C43C2×C411yescharacteristic
106#124×C43C2×C411yescharacteristic
107#123×C43—21no—
108#123×C43—21no—
109#123×C43—21no—
110#123×C43—21no—
111#123×C43—21no—
112#123×C43—21no—
113#123×C43—21no—
114#123×C43—21no—
115C22⋊Q8×C43—21no—
116C22⋊Q8×C43—21no—
117C22⋊Q8×C43—21no—
118C22⋊Q8×C43—21no—
119C22⋊Q8×C43—21no—
120C22⋊Q8×C43C2×C411yescharacteristic
121C22⋊Q8×C43C2×C411yescharacteristic
122#121×C43—21no—
123#121×C43—21no—
124#121×C43—21no—
125#121×C43—21no—
126#121×C43—21no—
127#121×C43—21no—
128#121×C43—21no—
129#121×C43—21no—
130#121×C43—21no—
131#121×C43—21no—
132#121×C43—21no—
133#121×C43C2×C411yescharacteristic
134#121×C43C2×C411yescharacteristic
135#121×C43C2×C411yescharacteristic
136#121×C43C2×C411yescharacteristic
137#121×C43C2×C411yescharacteristic
138#121×C43C2×C411yescharacteristic
139#120×C43—21no—
140#120×C43—21no—
141#120×C43—21no—
142#120×C43—21no—
143C4×Q8×C43C2×C411yescharacteristic
144C4×Q8×C43D411yescharacteristic
145C4×Q8×C43D411yescharacteristic
146C4×Q8×C43C2311yescharacteristic
147C4×D4×C43—21no—
148C4×D4×C43—21no—
149C4×D4×C43—21no—
150C4×D4×C43—21no—
151C4×D4×C43—21no—
152C4×D4×C43—21no—
153C4×D4×C43—21no—
154C4×D4×C43—21no—
155C4×D4×C43C2×C411yescharacteristic
156C4×D4×C43C2×C411yescharacteristic
157C4×D4×C43C2×C411yescharacteristic
158C4×D4×C43D411yescharacteristic
159C4×D4×C43D411yescharacteristic
160C4×D4×C43D411yescharacteristic
161C4×D4×C43D411yescharacteristic
162C4×D4×C43D411yescharacteristic
163C4×D4×C43D411yescharacteristic
164C4×D4×C43C2311yescharacteristic
165C4×D4×C43C2311yescharacteristic
166C4×D4×C43C2311yescharacteristic
167#117×C43—21no—
168#117×C43—21no—
169#117×C43—21no—
170#117×C43C2×C411yescharacteristic
171#117×C43C2×C411yescharacteristic
172#117×C43C2×C411yescharacteristic
173#117×C43C2×C411yescharacteristic
174C2×C4⋊C4×C43C2×C411yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C42×C43—21no—
177C2×C42×C43C2311yescharacteristic
178C2×C42×C43C2311yescharacteristic
179C2×C42×C43C2311yescharacteristic
180C4⋊C8×C43—21no—
181C4⋊C8×C43—21no—
182C4⋊C8×C43—21no—
183C4⋊C8×C43—21no—
184C4⋊C8×C43—21no—
185C4⋊C8×C43—21no—
186C4⋊C8×C43C2311yescharacteristic
187C4⋊C8×C43C2311yescharacteristic
188C4⋊C8×C43C2311yescharacteristic
189C4⋊C8×C43C2311yescharacteristic
190C22⋊C8×C43—21no—
191C22⋊C8×C43—21no—
192C22⋊C8×C43—21no—
193C22⋊C8×C43—21no—
194C22⋊C8×C43—21no—
195C22⋊C8×C43—21no—
196#97×C43—21no—
197#97×C43—21no—
198#97×C43—21no—
199#97×C43—21no—
200C4×C8×C43—21no—
201C4×C8×C43—21no—
202C4×C8×C43C2311yescharacteristic
203C4×C8×C43C2311yescharacteristic
204C4×C8×C43C2311yescharacteristic
205C4×C8×C43C2311yescharacteristic
206C24×C43—21no—
207#41×C43—42no—
208#41×C43—42no—
209#41×C43—81no—
210#41×C43—81no—
211#41×C43—81no—
212#41×C43—81no—
213C2×Q8×C43—21no—
214C2×Q8×C43—21no—
215C2×Q8×C43C22⋊C411yescharacteristic
216C2×Q8×C43C22×C411yescharacteristic
217C2×D4×C43—21no—
218C2×D4×C43—21no—
219C2×D4×C43—21no—
220C2×D4×C43—21no—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—21no—
224C2×D4×C43—21no—
225C2×D4×C43—21no—
226C2×D4×C43—21no—
227C2×D4×C43—21no—
228C2×D4×C43—21no—
229C2×D4×C43—42no—
230C2×D4×C43C22⋊C411yescharacteristic
231C2×D4×C43C22⋊C411yescharacteristic
232C2×D4×C43C22⋊C411yescharacteristic
233C2×D4×C43C22×C411yescharacteristic
234C2×D4×C43C22×C411yescharacteristic
235C2×D4×C43C22×C411yescharacteristic
236C22×C4×C43—21no—
237C22×C4×C43—21no—
238C22×C4×C43—21no—
239C22×C4×C43—21no—
240C22×C4×C43—21no—
241C22×C4×C43—21no—
242C22×C4×C43—21no—
243C22×C4×C43—21no—
244C22×C4×C43—81no—
245C22×C4×C43—81no—
246C22×C4×C43C22×C411yescharacteristic
247C22×C4×C43C22×C411yescharacteristic
248C22×C4×C43C22×C411yescharacteristic
249C22×C4×C43C2×D411yescharacteristic
250C22×C4×C43C2×D411yescharacteristic
251C22×C4×C43C2×D411yescharacteristic
252C22×C4×C43C2×D411yescharacteristic
253C22×C4×C43C2×D411yescharacteristic
254C22×C4×C43C2×D411yescharacteristic
255M16×C43—42no—
256M16×C43—42no—
257M16×C43—81no—
258M16×C43—81no—
259C2×C8×C43—21no—
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C2×C8×C43—21no—
267C2×C8×C43—42no—
268C2×C8×C43—81no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43—21no—
275C4⋊C4×C43—21no—
276C4⋊C4×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43C22⋊C411yescharacteristic
281C4⋊C4×C43C22⋊C411yescharacteristic
282C4⋊C4×C43C22⋊C411yescharacteristic
283C4⋊C4×C43C22⋊C411yescharacteristic
284C4⋊C4×C43C22⋊C411yescharacteristic
285C4⋊C4×C43C22⋊C411yescharacteristic
286C4⋊C4×C43C22×C411yescharacteristic
287C4⋊C4×C43C22×C411yescharacteristic
288C4⋊C4×C43C22×C411yescharacteristic
289C4⋊C4×C43C22×C411yescharacteristic
290C22⋊C4×C43—21no—
291C22⋊C4×C43—21no—
292C22⋊C4×C43—21no—
293C22⋊C4×C43—21no—
294C22⋊C4×C43—21no—
295C22⋊C4×C43—21no—
296C22⋊C4×C43—21no—
297C22⋊C4×C43—21no—
298C22⋊C4×C43—21no—
299C22⋊C4×C43—21no—
300C22⋊C4×C43—21no—
301C22⋊C4×C43—21no—
302C22⋊C4×C43—21no—
303C22⋊C4×C43—21no—
304C22⋊C4×C43—21no—
305C22⋊C4×C43—21no—
306C22⋊C4×C43—21no—
307C22⋊C4×C43—21no—
308C22⋊C4×C43—21no—
309C22⋊C4×C43C22⋊C411yescharacteristic
310C22⋊C4×C43C22⋊C411yescharacteristic
311C22⋊C4×C43C22⋊C411yescharacteristic
312C22⋊C4×C43C22⋊C411yescharacteristic
313C22⋊C4×C43C22⋊C411yescharacteristic
314C22⋊C4×C43C22⋊C411yescharacteristic
315C42×C43—21no—
316C42×C43—21no—
317C42×C43—21no—
318C42×C43C22×C411yescharacteristic
319C42×C43C22×C411yescharacteristic
320C42×C43C22×C411yescharacteristic
321C42×C43C2×D411yescharacteristic
322C42×C43C2×D411yescharacteristic
323C42×C43C2×D411yescharacteristic
324C42×C43C2×D411yescharacteristic
325C42×C43C2×D411yescharacteristic
326C42×C43C2×D411yescharacteristic
327C42×C43C2411yescharacteristic
328C23×C43—21no—
329C23×C43—21no—
330C23×C43—21no—
331C23×C43—42no—
332C23×C43—81no—
333C23×C43—81no—
334C23×C43C2×C22⋊C411yescharacteristic
335C23×C43C2×C22⋊C411yescharacteristic
336C23×C43C2×C22⋊C411yescharacteristic
337Q8×C43—22no—
338Q8×C43—41no—
339Q8×C43—81no—
340Q8×C43—81no—
341D4×C43—22no—
342D4×C43—22no—
343D4×C43—22no—
344D4×C43—41no—
345D4×C43—41no—
346D4×C43—41no—
347D4×C43—42no—
348D4×C43—42no—
349D4×C43—81no—
350D4×C43—81no—
351D4×C43—81no—
352D4×C43—81no—
353D4×C43—81no—
354D4×C43—81no—
355D4×C43—81no—
356D4×C43—81no—
357D4×C43—81no—
358D4×C43—81no—
359C2×C4×C43—22no—
360C2×C4×C43—22no—
361C2×C4×C43—22no—
362C2×C4×C43—21no—
363C2×C4×C43—21no—
364C2×C4×C43—21no—
365C2×C4×C43—21no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
373C2×C4×C43—41no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—42no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—81no—
384C2×C4×C43—81no—
385C2×C4×C43—81no—
386C2×C4×C43—81no—
387C2×C4×C43C2×C22⋊C411yescharacteristic
388C2×C4×C43C2×C22⋊C411yescharacteristic
389C2×C4×C43C2×C22⋊C411yescharacteristic
390C2×C4×C43C2×C22⋊C411yescharacteristic
391C2×C4×C43C2×C22⋊C411yescharacteristic
392C2×C4×C43C2×C22⋊C411yescharacteristic
393C2×C4×C43C2×C22⋊C411yescharacteristic
394C2×C4×C43C2×C22⋊C411yescharacteristic
395C2×C4×C43C2×C22⋊C411yescharacteristic
396C2×C4×C43C23×C411yescharacteristic
397C2×C4×C43C22×D411yescharacteristic
398C2×C4×C43C22×D411yescharacteristic
399C8×C43—22no—
400C8×C43—41no—
401C8×C43—41no—
402C8×C43—41no—
403C8×C43—41no—
404C8×C43—41no—
405C8×C43—41no—
406C8×C43—41no—
407#17505C4311yesmaximal, characteristic, direct product factor, Sylow
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—21no—
411C22×C43—21no—
412C22×C43—21no—
413C22×C43—21no—
414C22×C43—21no—
415C22×C43—21no—
416C22×C43—21no—
417C22×C43—41no—
418C22×C43—41no—
419C22×C43—41no—
420C22×C43—41no—
421C22×C43—41no—
422C22×C43—41no—
423C22×C43—41no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43—84no—
427C22×C43C22×C22⋊C411yescharacteristic
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—21no—
431C4×C43—21no—
432C4×C43—21no—
433C4×C43—21no—
434C4×C43—21no—
435C4×C43—21no—
436C4×C43—21no—
437C4×C43—21no—
438C4×C43—41no—
439C4×C43—41no—
440C4×C43—41no—
441C4×C43—41no—
442C4×C43—41no—
443C4×C43#56812yes—
444C4×C43#57611yescharacteristic
445C4×C43#57711yescharacteristic
446#3460C2×C4311yescharacteristic
447#2989C2×C4311yescharacteristic, complemented
448#2965C2×C4311yescharacteristic, complemented
449#1496C2×C4311yescharacteristic, complemented
450#1495C2×C4311yescharacteristic, complemented
451#1494C2×C4311yescharacteristic, complemented
452#1492C2×C4311yescharacteristic, complemented
453#1490C2×C4311yescharacteristic, complemented
454#1489C2×C4311yescharacteristic, complemented
455#1488C2×C4311yescharacteristic, complemented
456#1486C2×C4311yescharacteristic, complemented
457#1484C2×C4311yescharacteristic, complemented
458#1483C2×C4311yescharacteristic, complemented
459#1482C2×C4311yescharacteristic, complemented
460#1480C2×C4311yescharacteristic, complemented
461C2×C43—41no—
462C2×C43—41no—
463C2×C43—41no—
464C2×C43—81no—
465C2×C43—81no—
466C2×C43—81no—
467C2×C43#287911yescharacteristic
468C2×C43#289711yescharacteristic
469C2×C43#290111yescharacteristic
470#544C4×C4311yescharacteristic
471#542—21no—
472#542C4×C4311yescharacteristic
473#542C4×C4311yescharacteristic
474#540—21no—
475#540C4×C4311yescharacteristic
476#540C4×C4311yescharacteristic
477#538—21no—
478#538—21no—
479#537C4×C4311yescharacteristic
480#535C4×C4311yescharacteristic
481#535C4×C4311yescharacteristic
482#532—21no—
483#532C22×C4311yescharacteristic
484#532C22×C4311yescharacteristic
485#529—21no—
486#529C22×C4311yescharacteristic
487#529C22×C4311yescharacteristic
488#525—21no—
489#525—21no—
490C4×#41C22×C4311yescharacteristic
491C4×#41C22×C4311yescharacteristic
492C2×C4×D4C22×C4311yescharacteristic
493#446—21no—
494#446—21no—
495#436—21no—
496#436—21no—
497#435—21no—
498#435—21no—
499#435—21no—
500#435—21no—
501#432C22×C4311yescharacteristic
502#432C22×C4311yescharacteristic, complemented
503#431C22×C4311yescharacteristic
504#431C22×C4311yescharacteristic, complemented
505#431C22×C4311yescharacteristic, complemented
506#431C22×C4311yescharacteristic, complemented
507#423C22×C4311yescharacteristic
508#423C22×C4311yescharacteristic, complemented
509C2×C4⋊C8C22×C4311yescharacteristic, complemented
510C4×M16C22×C4311yescharacteristic
511C4×M16C22×C4311yescharacteristic, complemented
512C2×C4×C8C22×C4311yescharacteristic, complemented
513Q8⋊C8C22×C4311yescharacteristic, complemented
514Q8⋊C8C22×C4311yescharacteristic, complemented
515Q8⋊C8C22×C4311yescharacteristic, complemented
516Q8⋊C8C22×C4311yescharacteristic, complemented
517D4⋊C8C22×C4311yescharacteristic
518D4⋊C8C22×C4311yescharacteristic
519D4⋊C8C22×C4311yescharacteristic
520D4⋊C8C22×C4311yescharacteristic
521D4⋊C8C22×C4311yescharacteristic
522D4⋊C8C22×C4311yescharacteristic
523D4⋊C8C22×C4311yescharacteristic
524D4⋊C8C22×C4311yescharacteristic
525D4⋊C8C22×C4311yescharacteristic, complemented
526D4⋊C8C22×C4311yescharacteristic, complemented
527D4⋊C8C22×C4311yescharacteristic, complemented
528D4⋊C8C22×C4311yescharacteristic, complemented
529C43#1750511yescharacteristic, direct product factor, Sylow
530C2×#41—21no—
531C2×#41—21no—
532C2×#41C2×C4×C4311yescharacteristic
533C2×#41C2×C4×C4311yescharacteristic
534C22×D4C2×C4×C4311yescharacteristic
535C23×C4—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—21no—
539C2×M16—21no—
540C22×C8—21no—
541C22×C8—21no—
542C4⋊Q8—21no—
543C4⋊Q8C2×C4×C4311yescharacteristic
544C4⋊Q8C2×C4×C4311yescharacteristic
545#127—21no—
546#127C2×C4×C4311yescharacteristic
547#127C2×C4×C4311yescharacteristic
548#126—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#125—21no—
553#125C2×C4×C4311yescharacteristic
554#125C2×C4×C4311yescharacteristic
555#124—21no—
556#124—21no—
557#124—21no—
558#124—21no—
559#124—21no—
560#124C2×C4×C4311yescharacteristic
561#124C2×C4×C4311yescharacteristic
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8C2×C4×C4311yescharacteristic
576C22⋊Q8C2×C4×C4311yescharacteristic
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121C2×C4×C4311yescharacteristic
589#121C2×C4×C4311yescharacteristic
590#121C2×C4×C4311yescharacteristic
591#121C2×C4×C4311yescharacteristic
592#121C2×C4×C4311yescharacteristic
593#121C2×C4×C4311yescharacteristic
594#120—21no—
595#120—21no—
596#120—21no—
597#120—21no—
598C4×Q8C2×C4×C4311yescharacteristic
599C4×Q8D4×C4311yescharacteristic
600C4×Q8D4×C4311yescharacteristic
601C4×Q8C23×C4311yescharacteristic
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4C2×C4×C4311yescharacteristic
611C4×D4C2×C4×C4311yescharacteristic
612C4×D4C2×C4×C4311yescharacteristic
613C4×D4D4×C4311yescharacteristic
614C4×D4D4×C4311yescharacteristic
615C4×D4D4×C4311yescharacteristic
616C4×D4D4×C4311yescharacteristic
617C4×D4D4×C4311yescharacteristic
618C4×D4D4×C4311yescharacteristic
619C4×D4C23×C4311yescharacteristic
620C4×D4C23×C4311yescharacteristic
621C4×D4C23×C4311yescharacteristic
622#117—21no—
623#117—21no—
624#117—21no—
625#117C2×C4×C4311yescharacteristic
626#117C2×C4×C4311yescharacteristic
627#117C2×C4×C4311yescharacteristic
628#117C2×C4×C4311yescharacteristic
629C2×C4⋊C4C2×C4×C4311yescharacteristic
630C2×C22⋊C4—21no—
631C2×C42—21no—
632C2×C42C23×C4311yescharacteristic
633C2×C42C23×C4311yescharacteristic
634C2×C42C23×C4311yescharacteristic
635C4⋊C8—21no—
636C4⋊C8—21no—
637C4⋊C8—21no—
638C4⋊C8—21no—
639C4⋊C8—21no—
640C4⋊C8—21no—
641C4⋊C8C23×C4311yescharacteristic
642C4⋊C8C23×C4311yescharacteristic
643C4⋊C8C23×C4311yescharacteristic
644C4⋊C8C23×C4311yescharacteristic
645C22⋊C8—21no—
646C22⋊C8—21no—
647C22⋊C8—21no—
648C22⋊C8—21no—
649C22⋊C8—21no—
650C22⋊C8—21no—
651#97—21no—
652#97—21no—
653#97—21no—
654#97—21no—
655C4×C8—21no—
656C4×C8—21no—
657C4×C8C23×C4311yescharacteristic
658C4×C8C23×C4311yescharacteristic
659C4×C8C23×C4311yescharacteristic
660C4×C8C23×C4311yescharacteristic
661C24—21no—
662#41—42no—
663#41—42no—
664#41—81no—
665#41—81no—
666#41—81no—
667#41—81no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8C22⋊C4×C4311yescharacteristic
671C2×Q8C22×C4×C4311yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4C22⋊C4×C4311yescharacteristic
686C2×D4C22⋊C4×C4311yescharacteristic
687C2×D4C22⋊C4×C4311yescharacteristic
688C2×D4C22×C4×C4311yescharacteristic
689C2×D4C22×C4×C4311yescharacteristic
690C2×D4C22×C4×C4311yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—81no—
700C22×C4—81no—
701C22×C4C22×C4×C4311yescharacteristic
702C22×C4C22×C4×C4311yescharacteristic
703C22×C4C22×C4×C4311yescharacteristic
704C22×C4C2×D4×C4311yescharacteristic
705C22×C4C2×D4×C4311yescharacteristic
706C22×C4C2×D4×C4311yescharacteristic
707C22×C4C2×D4×C4311yescharacteristic
708C22×C4C2×D4×C4311yescharacteristic
709C22×C4C2×D4×C4311yescharacteristic
710M16—42no—
711M16—42no—
712M16—81no—
713M16—81no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—42no—
723C2×C8—81no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4C22⋊C4×C4311yescharacteristic
736C4⋊C4C22⋊C4×C4311yescharacteristic
737C4⋊C4C22⋊C4×C4311yescharacteristic
738C4⋊C4C22⋊C4×C4311yescharacteristic
739C4⋊C4C22⋊C4×C4311yescharacteristic
740C4⋊C4C22⋊C4×C4311yescharacteristic
741C4⋊C4C22×C4×C4311yescharacteristic
742C4⋊C4C22×C4×C4311yescharacteristic
743C4⋊C4C22×C4×C4311yescharacteristic
744C4⋊C4C22×C4×C4311yescharacteristic
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4C22⋊C4×C4311yescharacteristic
765C22⋊C4C22⋊C4×C4311yescharacteristic
766C22⋊C4C22⋊C4×C4311yescharacteristic
767C22⋊C4C22⋊C4×C4311yescharacteristic
768C22⋊C4C22⋊C4×C4311yescharacteristic
769C22⋊C4C22⋊C4×C4311yescharacteristic
770C42—21no—
771C42—21no—
772C42—21no—
773C42C22×C4×C4311yescharacteristic
774C42C22×C4×C4311yescharacteristic
775C42C22×C4×C4311yescharacteristic
776C42C2×D4×C4311yescharacteristic
777C42C2×D4×C4311yescharacteristic
778C42C2×D4×C4311yescharacteristic
779C42C2×D4×C4311yescharacteristic
780C42C2×D4×C4311yescharacteristic
781C42C2×D4×C4311yescharacteristic
782C42C24×C4311yescharacteristic
783C23—21no—
784C23—21no—
785C23—21no—
786C23—42no—
787C23—81no—
788C23—81no—
789C23C2×C22⋊C4×C4311yescharacteristic
790C23C2×C22⋊C4×C4311yescharacteristic
791C23C2×C22⋊C4×C4311yescharacteristic
792Q8—22no—
793Q8—41no—
794Q8—81no—
795Q8—81no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—81no—
813D4—81no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4C2×C22⋊C4×C4311yescharacteristic
843C2×C4C2×C22⋊C4×C4311yescharacteristic
844C2×C4C2×C22⋊C4×C4311yescharacteristic
845C2×C4C2×C22⋊C4×C4311yescharacteristic
846C2×C4C2×C22⋊C4×C4311yescharacteristic
847C2×C4C2×C22⋊C4×C4311yescharacteristic
848C2×C4C2×C22⋊C4×C4311yescharacteristic
849C2×C4C2×C22⋊C4×C4311yescharacteristic
850C2×C4C2×C22⋊C4×C4311yescharacteristic
851C2×C4C23×C4×C4311yescharacteristic
852C2×C4C22×D4×C4311yescharacteristic
853C2×C4C22×D4×C4311yescharacteristic
854C8—22no—
855C8—41no—
856C8—41no—
857C8—41no—
858C8—41no—
859C8—41no—
860C8—41no—
861C8—41no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—84no—
881C22C22×C22⋊C4×C4311yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—21no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4C43×#56812yes—
898C4C43×#57611yescharacteristic
899C4C43×#57711yescharacteristic
900C2—41no—
901C2—41no—
902C2—41no—
903C2—81no—
904C2—81no—
905C2—81no—
906C2C43×#287911yescharacteristic
907C2C43×#289711yescharacteristic
908C2C43×#290111yescharacteristic
subgroupG/H
centerC2×C4×C43C22×D4
commutatorC2×C4C23×C4×C43
Frattini, cosocleC42C24×C43
socleC22×C43C22×C22⋊C4
prime radicalC43×#3460C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C43 ◁ C4×#41×C43 ◁ G

Complements

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

NH ≅ G/Ntype
2. C43×#2989C2semidirect
3. C43×#2965C2semidirect
4. C43×#1496C2semidirect
5. C43×#1495C2semidirect
6. C43×#1494C2semidirect
7. C43×#1492C2semidirect
8. C43×#1490C2semidirect
9. C43×#1489C2semidirect
10. C43×#1488C2semidirect
11. C43×#1486C2semidirect
12. C43×#1484C2semidirect
13. C43×#1483C2semidirect
14. C43×#1482C2semidirect
15. C43×#1480C2semidirect
48. C43×#432C22semidirect
50. C43×#431C22semidirect
51. C43×#431C22semidirect
52. C43×#431C22semidirect
54. C43×#423C22semidirect
55. C2×C4⋊C8×C43C22semidirect
57. C4×M16×C43C22semidirect
58. C2×C4×C8×C43C22semidirect
59. C43×Q8⋊C8C22semidirect
60. C43×Q8⋊C8C22semidirect
61. C43×Q8⋊C8C22semidirect
62. C43×Q8⋊C8C22semidirect
71. C43×D4⋊C8C22semidirect
72. C43×D4⋊C8C22semidirect
73. C43×D4⋊C8C22semidirect
74. C43×D4⋊C8C22semidirect
407. #17505C43direct (N × H)
447. #2989C2×C43semidirect
448. #2965C2×C43semidirect
449. #1496C2×C43semidirect
450. #1495C2×C43semidirect
451. #1494C2×C43semidirect
452. #1492C2×C43semidirect
453. #1490C2×C43semidirect
454. #1489C2×C43semidirect
455. #1488C2×C43semidirect
456. #1486C2×C43semidirect
457. #1484C2×C43semidirect
458. #1483C2×C43semidirect
459. #1482C2×C43semidirect
460. #1480C2×C43semidirect
502. #432C22×C43semidirect
504. #431C22×C43semidirect
505. #431C22×C43semidirect
506. #431C22×C43semidirect
508. #423C22×C43semidirect
509. C2×C4⋊C8C22×C43semidirect
511. C4×M16C22×C43semidirect
512. C2×C4×C8C22×C43semidirect
513. Q8⋊C8C22×C43semidirect
514. Q8⋊C8C22×C43semidirect
515. Q8⋊C8C22×C43semidirect
516. Q8⋊C8C22×C43semidirect
525. D4⋊C8C22×C43semidirect
526. D4⋊C8C22×C43semidirect
527. D4⋊C8C22×C43semidirect
528. D4⋊C8C22×C43semidirect
529. C43#17505direct (N × H)

Maximal subgroups

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

subgroupindex
C43×#34602
C43×#29892
C43×#29652
C43×#14962
C43×#14952
C43×#14942
C43×#14922
C43×#14902
C43×#14892
C43×#14882
C43×#14862
C43×#14842
C43×#14832
C43×#14822
C43×#14802
#1750543