Finite Group Databasebeta

← C43×#15776 #24935793

Subgroups — C43×#15776 #24935793

Order 11008.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C43×#399C211yesmaximal, characteristic, complemented
2C2×C43×#396C211yesmaximal, characteristic, complemented
3C2×C43×#394C211yesmaximal, characteristic, complemented
4C2×C43×#392C211yesmaximal, characteristic
5C2×C43×#390C211yesmaximal, characteristic, complemented
6C2×C43×#390C211yesmaximal, characteristic, complemented
7C2×C43×#388C211yesmaximal, characteristic, complemented
8C2×C43×#387C211yesmaximal, characteristic, complemented
9C43×#1439C211yesmaximal, characteristic, complemented
10C43×#1439C211yesmaximal, characteristic, complemented
11C43×#1438C211yesmaximal, characteristic, complemented
12C43×#1438C211yesmaximal, characteristic, complemented
13C43×#1438C211yesmaximal, characteristic, complemented
14C43×#1437C211yesmaximal, characteristic, complemented
15C43×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C43C2211yescharacteristic
17C23×D4×C43C2211yescharacteristic
18C23×D4×C43C2211yescharacteristic
19C22×C4⋊C4×C43C2211yescharacteristic
20C22×C4⋊C4×C43C2211yescharacteristic
21C22×C4⋊C4×C43C2211yescharacteristic
22C22×C4⋊C4×C43C2211yescharacteristic
23C22×C4⋊C4×C43C2211yescharacteristic
24C22×C22⋊C4×C43C2211yescharacteristic
25C22×C22⋊C4×C43C2211yescharacteristic
26C22×C22⋊C4×C43C2211yescharacteristic
27C22×C22⋊C4×C43C2211yescharacteristic
28C22×C22⋊C4×C43C2211yescharacteristic
29C22×C22⋊C4×C43C2211yescharacteristic
30C22×C22⋊C4×C43C2211yescharacteristic
31C22×C22⋊C4×C43C2211yescharacteristic
32C22×C22⋊C4×C43C2211yescharacteristic
33C22×C22⋊C4×C43C2211yescharacteristic
34C22×C22⋊C4×C43C2211yescharacteristic
35C22×C22⋊C4×C43C2211yescharacteristic
36C22×C22⋊C4×C43C2211yescharacteristic
37C22×C22⋊C4×C43C2211yescharacteristic
38C22×C22⋊C4×C43C2211yescharacteristic
39C22×C42×C43C2211yescharacteristic
40C22×C42×C43C2211yescharacteristic
41C43×#399—24no—
42C43×#396—24no—
43C43×#394—24no—
44C43×#392—24no—
45C43×#390—24no—
46C43×#390—24no—
47C43×#388—24no—
48C43×#387—24no—
49C2×#95×C43C2211yescharacteristic
50C2×#95×C43C2211yescharacteristic
51C2×#95×C43C2211yescharacteristic
52C2×#95×C43C2211yescharacteristic
53C2×#95×C43C2211yescharacteristic
54C2×#95×C43C2211yescharacteristic
55C2×#95×C43C2211yescharacteristic
56C2×#95×C43C2211yescharacteristic
57C2×#95×C43C2211yescharacteristic
58C2×#95×C43C2211yescharacteristic
59C25×C43C2311yescharacteristic
60C25×C43C2311yescharacteristic
61C25×C43C2311yescharacteristic
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—22no—
65C22×D4×C43—22no—
66C22×D4×C43—22no—
67C22×D4×C43—22no—
68C22×D4×C43—22no—
69C22×D4×C43—22no—
70C22×D4×C43—22no—
71C22×D4×C43—22no—
72C22×D4×C43—22no—
73C22×D4×C43—22no—
74C22×D4×C43—22no—
75C22×D4×C43—41no—
76C22×D4×C43—41no—
77C22×D4×C43—41no—
78C22×D4×C43—41no—
79C22×D4×C43—41no—
80C22×D4×C43—41no—
81C22×D4×C43—41no—
82C22×D4×C43—41no—
83C23×C4×C43C2311yescharacteristic
84C23×C4×C43C2311yescharacteristic
85C23×C4×C43C2311yescharacteristic
86C23×C4×C43C2311yescharacteristic
87C23×C4×C43C2311yescharacteristic
88C23×C4×C43C2311yescharacteristic
89C23×C4×C43C2311yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2311yescharacteristic
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2311yescharacteristic
95C2×C4⋊C4×C43—22no—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—22no—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—22no—
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43—22no—
102C2×C4⋊C4×C43—22no—
103C2×C4⋊C4×C43—22no—
104C2×C4⋊C4×C43—41no—
105C2×C4⋊C4×C43—41no—
106C2×C4⋊C4×C43—41no—
107C2×C4⋊C4×C43—41no—
108C2×C4⋊C4×C43D414yescomplemented
109C2×C4⋊C4×C43D414yescomplemented
110C2×C22⋊C4×C43—22no—
111C2×C22⋊C4×C43—22no—
112C2×C22⋊C4×C43—22no—
113C2×C22⋊C4×C43—22no—
114C2×C22⋊C4×C43—22no—
115C2×C22⋊C4×C43—22no—
116C2×C22⋊C4×C43—22no—
117C2×C22⋊C4×C43—22no—
118C2×C22⋊C4×C43—22no—
119C2×C22⋊C4×C43—22no—
120C2×C22⋊C4×C43—22no—
121C2×C22⋊C4×C43—22no—
122C2×C22⋊C4×C43—22no—
123C2×C22⋊C4×C43—22no—
124C2×C22⋊C4×C43—22no—
125C2×C22⋊C4×C43—22no—
126C2×C22⋊C4×C43—22no—
127C2×C22⋊C4×C43—22no—
128C2×C22⋊C4×C43—22no—
129C2×C22⋊C4×C43—22no—
130C2×C22⋊C4×C43—22no—
131C2×C22⋊C4×C43—22no—
132C2×C22⋊C4×C43—22no—
133C2×C22⋊C4×C43—22no—
134C2×C22⋊C4×C43—22no—
135C2×C22⋊C4×C43—22no—
136C2×C22⋊C4×C43—22no—
137C2×C22⋊C4×C43—22no—
138C2×C22⋊C4×C43—22no—
139C2×C22⋊C4×C43—22no—
140C2×C22⋊C4×C43—22no—
141C2×C22⋊C4×C43—41no—
142C2×C22⋊C4×C43—41no—
143C2×C22⋊C4×C43—41no—
144C2×C22⋊C4×C43—41no—
145C2×C22⋊C4×C43—41no—
146C2×C22⋊C4×C43—41no—
147C2×C22⋊C4×C43—41no—
148C2×C22⋊C4×C43—41no—
149C2×C22⋊C4×C43—41no—
150C2×C22⋊C4×C43—41no—
151C2×C22⋊C4×C43—41no—
152C2×C22⋊C4×C43—41no—
153C2×C22⋊C4×C43—41no—
154C2×C22⋊C4×C43—41no—
155C2×C42×C43—22no—
156C2×C42×C43—22no—
157C2×C42×C43—22no—
158C2×C42×C43—22no—
159C2×C42×C43—41no—
160C2×C42×C43—41no—
161#95×C43—22no—
162#95×C43—22no—
163#95×C43—22no—
164#95×C43—22no—
165#95×C43—22no—
166#95×C43—22no—
167#95×C43—41no—
168#95×C43—41no—
169#95×C43D414yes—
170#95×C43D414yescomplemented
171C24×C43—21no—
172C24×C43—21no—
173C24×C43—21no—
174C24×C43—21no—
175C24×C43—21no—
176C24×C43—21no—
177C24×C43—21no—
178C24×C43—21no—
179C24×C43—21no—
180C24×C43—21no—
181C24×C43—21no—
182C24×C43—21no—
183C24×C43—21no—
184C24×C43—21no—
185C24×C43—21no—
186C24×C43—21no—
187C24×C43—21no—
188C24×C43—21no—
189C24×C43—21no—
190C24×C43—21no—
191C24×C43—21no—
192C24×C43—21no—
193C24×C43—21no—
194C24×C43—21no—
195C24×C43—21no—
196C24×C43—21no—
197C24×C43—21no—
198C24×C43—21no—
199C24×C43—21no—
200C24×C43—21no—
201C24×C43—21no—
202C24×C43—21no—
203C24×C43—21no—
204C24×C43—21no—
205C24×C43—21no—
206C24×C43—21no—
207C24×C43—21no—
208C24×C43—21no—
209C24×C43—21no—
210C24×C43—21no—
211C24×C43—21no—
212C24×C43—21no—
213C24×C43#4112yes—
214C24×C43#4112yes—
215C24×C43#4112yes—
216C24×C43C2411yescharacteristic
217C2×D4×C43—28no—
218C2×D4×C43—28no—
219C2×D4×C43—44no—
220C2×D4×C43—44no—
221C2×D4×C43—44no—
222C2×D4×C43—44no—
223C2×D4×C43—44no—
224C2×D4×C43—44no—
225C2×D4×C43—44no—
226C2×D4×C43—44no—
227C2×D4×C43—44no—
228C2×D4×C43—44no—
229C2×D4×C43—44no—
230C2×D4×C43—44no—
231C2×D4×C43—44no—
232C2×D4×C43—44no—
233C2×D4×C43—44no—
234C2×D4×C43—44no—
235C2×D4×C43—44no—
236C2×D4×C43—44no—
237C2×D4×C43—44no—
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—21no—
245C22×C4×C43—21no—
246C22×C4×C43—21no—
247C22×C4×C43—21no—
248C22×C4×C43—21no—
249C22×C4×C43—21no—
250C22×C4×C43—21no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—21no—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43—21no—
258C22×C4×C43—21no—
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43—21no—
266C22×C4×C43—21no—
267C22×C4×C43—21no—
268C22×C4×C43—21no—
269C22×C4×C43—21no—
270C22×C4×C43—21no—
271C22×C4×C43—21no—
272C22×C4×C43—21no—
273C22×C4×C43—21no—
274C22×C4×C43—21no—
275C22×C4×C43—21no—
276C22×C4×C43—21no—
277C22×C4×C43—21no—
278C22×C4×C43—21no—
279C22×C4×C43—21no—
280C22×C4×C43—21no—
281C22×C4×C43—21no—
282C22×C4×C43—21no—
283C22×C4×C43—21no—
284C22×C4×C43—21no—
285C22×C4×C43—21no—
286C22×C4×C43—21no—
287C22×C4×C43—21no—
288C22×C4×C43—21no—
289C22×C4×C43—21no—
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×C43C2×D412yes—
309C22×C4×C43C2×D412yes—
310C22×C4×C43C2×D412yes—
311C22×C4×C43C2×D412yes—
312C22×C4×C43C2×D412yes—
313C22×C4×C43C2×D412yes—
314C22×C4×C43C2×D412yes—
315C22×C4×C43C2×D412yes—
316C22×C4×C43C2×D412yes—
317C22×C4×C43C2×D412yes—
318C22×C4×C43C2×D412yes—
319C22×C4×C43C2×D412yes—
320C22×C4×C43#4112yes—
321C22×C4×C43#4112yes—
322C4⋊C4×C43—28no—
323C4⋊C4×C43—44no—
324C4⋊C4×C43—44no—
325C4⋊C4×C43—44no—
326C4⋊C4×C43—44no—
327C22⋊C4×C43—28no—
328C22⋊C4×C43—44no—
329C22⋊C4×C43—44no—
330C22⋊C4×C43—44no—
331C22⋊C4×C43—44no—
332C22⋊C4×C43—44no—
333C22⋊C4×C43—44no—
334C22⋊C4×C43—44no—
335C22⋊C4×C43—44no—
336C22⋊C4×C43—44no—
337C22⋊C4×C43—44no—
338C22⋊C4×C43—44no—
339C22⋊C4×C43—44no—
340C22⋊C4×C43—44no—
341C22⋊C4×C43—44no—
342C42×C43—44no—
343C42×C43—44no—
344C23×C43—22no—
345C23×C43—22no—
346C23×C43—22no—
347C23×C43—22no—
348C23×C43—22no—
349C23×C43—22no—
350C23×C43—22no—
351C23×C43—22no—
352C23×C43—22no—
353C23×C43—22no—
354C23×C43—22no—
355C23×C43—22no—
356C23×C43—22no—
357C23×C43—22no—
358C23×C43—22no—
359C23×C43—22no—
360C23×C43—22no—
361C23×C43—22no—
362C23×C43—22no—
363C23×C43—22no—
364C23×C43—22no—
365C23×C43—41no—
366C23×C43—41no—
367C23×C43—41no—
368C23×C43—41no—
369C23×C43—41no—
370C23×C43—41no—
371C23×C43—41no—
372C23×C43—41no—
373C23×C43—41no—
374C23×C43—41no—
375C23×C43—41no—
376C23×C43—41no—
377C23×C43—41no—
378C23×C43—41no—
379C23×C43—41no—
380C23×C43—41no—
381C23×C43—41no—
382C23×C43—41no—
383C23×C43—41no—
384C23×C43—41no—
385C23×C43—41no—
386C23×C43—41no—
387C23×C43—41no—
388C23×C43—41no—
389C23×C43—41no—
390C23×C43—41no—
391C23×C43—41no—
392C23×C43—41no—
393C23×C43—41no—
394C23×C43—41no—
395C23×C43—41no—
396C23×C43—41no—
397C23×C43—41no—
398C23×C43—41no—
399C23×C43—41no—
400C23×C43—41no—
401C23×C43—41no—
402C23×C43—41no—
403C23×C43—41no—
404C23×C43—41no—
405C23×C43—41no—
406C23×C43—41no—
407C23×C43—41no—
408C23×C43—41no—
409C23×C43—41no—
410C23×C43—41no—
411C23×C43—41no—
412C23×C43—41no—
413C23×C43—41no—
414C23×C43—41no—
415C23×C43—41no—
416C23×C43—41no—
417C23×C43—41no—
418C23×C43—41no—
419C23×C43—41no—
420C23×C43—41no—
421C23×C43—41no—
422C23×C43—41no—
423C23×C43—41no—
424C23×C43—41no—
425C23×C43—41no—
426C23×C43—41no—
427C23×C43—41no—
428C23×C43—41no—
429C23×C43—41no—
430C23×C43—41no—
431C23×C43—41no—
432C23×C43—41no—
433C23×C43—41no—
434C23×C43—41no—
435C23×C43—41no—
436C23×C43—41no—
437C23×C43—41no—
438C23×C43—41no—
439C23×C43—41no—
440C23×C43—41no—
441C23×C43—41no—
442C23×C43—41no—
443C23×C43—41no—
444C23×C43—41no—
445C23×C43—41no—
446C23×C43—41no—
447C23×C43—41no—
448C23×C43—41no—
449C23×C43C22×D411yescharacteristic
450C23×C43C22×D411yescharacteristic
451C23×C43C22×D411yescharacteristic
452C23×C43C22×D411yescharacteristic
453C23×C43C2×#4111yescharacteristic
454C23×C43C2×#4111yescharacteristic
455C23×C43C2×#4111yescharacteristic
456C23×C43C2×#4111yescharacteristic
457C23×C43C2×#4111yescharacteristic
458C23×C43H(5,𝔽2)11yescharacteristic
459C23×C43H(5,𝔽2)11yescharacteristic
460C23×C43H(5,𝔽2)11yescharacteristic
461C23×C43H(5,𝔽2)11yescharacteristic
462C23×C43H(5,𝔽2)11yescharacteristic
463C23×C432−1+411yescharacteristic
464D4×C43—416no—
465D4×C43—416no—
466D4×C43—416no—
467C2×C4×C43—22no—
468C2×C4×C43—22no—
469C2×C4×C43—22no—
470C2×C4×C43—22no—
471C2×C4×C43—22no—
472C2×C4×C43—22no—
473C2×C4×C43—22no—
474C2×C4×C43—22no—
475C2×C4×C43—22no—
476C2×C4×C43—22no—
477C2×C4×C43—22no—
478C2×C4×C43—22no—
479C2×C4×C43—22no—
480C2×C4×C43—22no—
481C2×C4×C43—22no—
482C2×C4×C43—22no—
483C2×C4×C43—22no—
484C2×C4×C43—22no—
485C2×C4×C43—22no—
486C2×C4×C43—22no—
487C2×C4×C43—22no—
488C2×C4×C43—22no—
489C2×C4×C43—22no—
490C2×C4×C43—22no—
491C2×C4×C43—22no—
492C2×C4×C43—22no—
493C2×C4×C43—22no—
494C2×C4×C43—22no—
495C2×C4×C43—22no—
496C2×C4×C43—22no—
497C2×C4×C43—22no—
498C2×C4×C43—22no—
499C2×C4×C43—22no—
500C2×C4×C43—22no—
501C2×C4×C43—22no—
502C2×C4×C43—22no—
503C2×C4×C43—41no—
504C2×C4×C43—41no—
505C2×C4×C43—41no—
506C2×C4×C43—41no—
507C2×C4×C43—41no—
508C2×C4×C43—41no—
509C2×C4×C43—41no—
510C2×C4×C43—41no—
511C2×C4×C43—41no—
512C2×C4×C43—41no—
513C2×C4×C43—41no—
514C2×C4×C43—41no—
515C2×C4×C43—41no—
516C2×C4×C43—41no—
517C2×C4×C43—41no—
518C2×C4×C43—41no—
519C2×C4×C43—41no—
520C2×C4×C43—41no—
521C2×C4×C43—41no—
522C2×C4×C43—41no—
523C2×C4×C43—41no—
524C2×C4×C43—41no—
525C2×C4×C43—41no—
526C2×C4×C43—41no—
527C2×C4×C43—41no—
528C2×C4×C43—41no—
529C2×C4×C43—41no—
530C2×C4×C43—41no—
531C2×C4×C43—41no—
532C2×C4×C43—41no—
533C2×C4×C43—41no—
534C2×C4×C43—41no—
535C2×C4×C43—41no—
536C2×C4×C43—41no—
537C2×C4×C43—41no—
538C2×C4×C43—41no—
539C2×C4×C43—41no—
540C2×C4×C43—41no—
541C2×C4×C43—41no—
542C2×C4×C43—41no—
543C2×C4×C43—41no—
544C2×C4×C43—41no—
545C2×C4×C43—41no—
546C2×C4×C43—41no—
547C2×C4×C43—41no—
548C2×C4×C43—41no—
549C2×C4×C43#12114yes—
550C2×C4×C43#12714yes—
551#15776C4311yesmaximal, characteristic, direct product factor, Sylow
552C22×C43—42no—
553C22×C43—42no—
554C22×C43—42no—
555C22×C43—42no—
556C22×C43—42no—
557C22×C43—42no—
558C22×C43—42no—
559C22×C43—42no—
560C22×C43—42no—
561C22×C43—42no—
562C22×C43—42no—
563C22×C43—42no—
564C22×C43—42no—
565C22×C43—42no—
566C22×C43—42no—
567C22×C43—42no—
568C22×C43—42no—
569C22×C43—42no—
570C22×C43—42no—
571C22×C43—42no—
572C22×C43—42no—
573C22×C43—81no—
574C22×C43—81no—
575C22×C43—81no—
576C22×C43—81no—
577C22×C43—81no—
578C22×C43—81no—
579C22×C43—81no—
580C22×C43—81no—
581C22×C43—81no—
582C22×C43—81no—
583C22×C43—81no—
584C22×C43—81no—
585C22×C43—81no—
586C22×C43—81no—
587C22×C43—81no—
588C22×C43—81no—
589C22×C43—81no—
590C22×C43—81no—
591C22×C43—81no—
592C22×C43—81no—
593C22×C43—81no—
594C22×C43—81no—
595C22×C43—81no—
596C22×C43—81no—
597C22×C43C2×#12111yescharacteristic
598C22×C43#52511yescharacteristic
599C22×C43#52511yescharacteristic
600C22×C43#52511yescharacteristic
601C22×C43#52911yescharacteristic
602C22×C43C2×#12711yescharacteristic
603C22×C43#53411yescharacteristic
604C22×C43#53511yescharacteristic
605C22×C43#53511yescharacteristic
606C22×C43#53711yescharacteristic
607C22×C43#53811yescharacteristic
608C22×C43#53811yescharacteristic
609C22×C43#53911yescharacteristic
610C22×C43#54011yescharacteristic
611C22×C43#54211yescharacteristic
612C22×C43D4211yescharacteristic
613C22×C43D4211yescharacteristic
614C22×C43#54611yescharacteristic
615C22×C43#54611yescharacteristic
616C22×C43#54611yescharacteristic
617C22×C43#54611yescharacteristic
618C22×C43#54611yescharacteristic
619C22×C43#54611yescharacteristic
620C22×C43#54811yescharacteristic
621C22×C43#54811yescharacteristic
622C22×C43#54811yescharacteristic
623C22×C43#55011yescharacteristic
624C22×C43#55011yescharacteristic
625C22×C43#55011yescharacteristic
626C22×C43#55111yescharacteristic
627C22×C43#55111yescharacteristic
628C22×C43#55111yescharacteristic
629C22×C43#55311yescharacteristic
630C22×C43#56011yescharacteristic
631C22×C43#56211yescharacteristic
632C4×C43—24no—
633C4×C43—24no—
634C4×C43—42no—
635C4×C43—42no—
636C4×C43—42no—
637C4×C43—42no—
638C4×C43—42no—
639C4×C43—42no—
640C4×C43—42no—
641C4×C43—42no—
642C4×C43—81no—
643C4×C43—81no—
644C2×#399C2×C4311yescharacteristic, complemented
645C2×#396C2×C4311yescharacteristic, complemented
646C2×#394C2×C4311yescharacteristic, complemented
647C2×#392C2×C4311yescharacteristic
648C2×#390C2×C4311yescharacteristic, complemented
649C2×#390C2×C4311yescharacteristic, complemented
650C2×#388C2×C4311yescharacteristic, complemented
651C2×#387C2×C4311yescharacteristic, complemented
652#1439C2×C4311yescharacteristic, complemented
653#1439C2×C4311yescharacteristic, complemented
654#1438C2×C4311yescharacteristic, complemented
655#1438C2×C4311yescharacteristic, complemented
656#1438C2×C4311yescharacteristic, complemented
657#1437C2×C4311yescharacteristic, complemented
658#1436C2×C4311yescharacteristic, complemented
659C2×C43—82no—
660C2×C43—82no—
661C2×C43—82no—
662C2×C43#241111yescharacteristic
663C2×C43#242611yescharacteristic
664C2×C43#245611yescharacteristic
665C2×C43#246311yescharacteristic
666C2×C43#246711yescharacteristic
667C2×C43#247111yescharacteristic
668C2×C43#253911yescharacteristic
669C2×C43#254011yescharacteristic
670C2×C43#254111yescharacteristic
671C2×C43#267311yescharacteristic
672C2×C43#267611yescharacteristic
673C2×C43#268511yescharacteristic
674C2×C43#270511yescharacteristic
675C2×C43#271111yescharacteristic
676C2×C43#273011yescharacteristic
677C23×D4C22×C4311yescharacteristic
678C23×D4C22×C4311yescharacteristic
679C23×D4C22×C4311yescharacteristic
680C22×C4⋊C4C22×C4311yescharacteristic
681C22×C4⋊C4C22×C4311yescharacteristic
682C22×C4⋊C4C22×C4311yescharacteristic
683C22×C4⋊C4C22×C4311yescharacteristic
684C22×C4⋊C4C22×C4311yescharacteristic
685C22×C22⋊C4C22×C4311yescharacteristic
686C22×C22⋊C4C22×C4311yescharacteristic
687C22×C22⋊C4C22×C4311yescharacteristic
688C22×C22⋊C4C22×C4311yescharacteristic
689C22×C22⋊C4C22×C4311yescharacteristic
690C22×C22⋊C4C22×C4311yescharacteristic
691C22×C22⋊C4C22×C4311yescharacteristic
692C22×C22⋊C4C22×C4311yescharacteristic
693C22×C22⋊C4C22×C4311yescharacteristic
694C22×C22⋊C4C22×C4311yescharacteristic
695C22×C22⋊C4C22×C4311yescharacteristic
696C22×C22⋊C4C22×C4311yescharacteristic
697C22×C22⋊C4C22×C4311yescharacteristic
698C22×C22⋊C4C22×C4311yescharacteristic
699C22×C22⋊C4C22×C4311yescharacteristic
700C22×C42C22×C4311yescharacteristic
701C22×C42C22×C4311yescharacteristic
702#399—24no—
703#396—24no—
704#394—24no—
705#392—24no—
706#390—24no—
707#390—24no—
708#388—24no—
709#387—24no—
710C2×#95C22×C4311yescharacteristic
711C2×#95C22×C4311yescharacteristic
712C2×#95C22×C4311yescharacteristic
713C2×#95C22×C4311yescharacteristic
714C2×#95C22×C4311yescharacteristic
715C2×#95C22×C4311yescharacteristic
716C2×#95C22×C4311yescharacteristic
717C2×#95C22×C4311yescharacteristic
718C2×#95C22×C4311yescharacteristic
719C2×#95C22×C4311yescharacteristic
720C43#1577611yescharacteristic, direct product factor, Sylow
721C25C23×C4311yescharacteristic
722C25C23×C4311yescharacteristic
723C25C23×C4311yescharacteristic
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—41no—
738C22×D4—41no—
739C22×D4—41no—
740C22×D4—41no—
741C22×D4—41no—
742C22×D4—41no—
743C22×D4—41no—
744C22×D4—41no—
745C23×C4C23×C4311yescharacteristic
746C23×C4C23×C4311yescharacteristic
747C23×C4C23×C4311yescharacteristic
748C23×C4C23×C4311yescharacteristic
749C23×C4C23×C4311yescharacteristic
750C23×C4C23×C4311yescharacteristic
751C23×C4C23×C4311yescharacteristic
752C23×C4C23×C4311yescharacteristic
753C23×C4C23×C4311yescharacteristic
754C23×C4C23×C4311yescharacteristic
755C23×C4C23×C4311yescharacteristic
756C23×C4C23×C4311yescharacteristic
757C2×C4⋊C4—22no—
758C2×C4⋊C4—22no—
759C2×C4⋊C4—22no—
760C2×C4⋊C4—22no—
761C2×C4⋊C4—22no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—22no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4—41no—
767C2×C4⋊C4—41no—
768C2×C4⋊C4—41no—
769C2×C4⋊C4—41no—
770C2×C4⋊C4D4×C4314yescomplemented
771C2×C4⋊C4D4×C4314yescomplemented
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
802C2×C22⋊C4—22no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C42—22no—
818C2×C42—22no—
819C2×C42—22no—
820C2×C42—22no—
821C2×C42—41no—
822C2×C42—41no—
823#95—22no—
824#95—22no—
825#95—22no—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—41no—
830#95—41no—
831#95D4×C4314yes—
832#95D4×C4314yescomplemented
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24#41×C4312yes—
876C24#41×C4312yes—
877C24#41×C4312yes—
878C24C24×C4311yescharacteristic
879C2×D4—28no—
880C2×D4—28no—
881C2×D4—44no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—44no—
888C2×D4—44no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4C2×D4×C4312yes—
971C22×C4C2×D4×C4312yes—
972C22×C4C2×D4×C4312yes—
973C22×C4C2×D4×C4312yes—
974C22×C4C2×D4×C4312yes—
975C22×C4C2×D4×C4312yes—
976C22×C4C2×D4×C4312yes—
977C22×C4C2×D4×C4312yes—
978C22×C4C2×D4×C4312yes—
979C22×C4C2×D4×C4312yes—
980C22×C4C2×D4×C4312yes—
981C22×C4C2×D4×C4312yes—
982C22×C4#41×C4312yes—
983C22×C4#41×C4312yes—
984C4⋊C4—28no—
985C4⋊C4—44no—
986C4⋊C4—44no—
987C4⋊C4—44no—
988C4⋊C4—44no—
989C22⋊C4—28no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—44no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C42—44no—
1005C42—44no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23C22×D4×C4311yescharacteristic
1112C23C22×D4×C4311yescharacteristic
1113C23C22×D4×C4311yescharacteristic
1114C23C22×D4×C4311yescharacteristic
1115C23C2×#41×C4311yescharacteristic
1116C23C2×#41×C4311yescharacteristic
1117C23C2×#41×C4311yescharacteristic
1118C23C2×#41×C4311yescharacteristic
1119C23C2×#41×C4311yescharacteristic
1120C23H(5,𝔽2)×C4311yescharacteristic
1121C23H(5,𝔽2)×C4311yescharacteristic
1122C23H(5,𝔽2)×C4311yescharacteristic
1123C23H(5,𝔽2)×C4311yescharacteristic
1124C23H(5,𝔽2)×C4311yescharacteristic
1125C232−1+4×C4311yescharacteristic
1126D4—416no—
1127D4—416no—
1128D4—416no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4#121×C4314yes—
1212C2×C4#127×C4314yes—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22C2×#121×C4311yescharacteristic
1259C22C43×#52511yescharacteristic
1260C22C43×#52511yescharacteristic
1261C22C43×#52511yescharacteristic
1262C22C43×#52911yescharacteristic
1263C22C2×#127×C4311yescharacteristic
1264C22C43×#53411yescharacteristic
1265C22C43×#53511yescharacteristic
1266C22C43×#53511yescharacteristic
1267C22C43×#53711yescharacteristic
1268C22C43×#53811yescharacteristic
1269C22C43×#53811yescharacteristic
1270C22C43×#53911yescharacteristic
1271C22C43×#54011yescharacteristic
1272C22C43×#54211yescharacteristic
1273C22D42×C4311yescharacteristic
1274C22D42×C4311yescharacteristic
1275C22C43×#54611yescharacteristic
1276C22C43×#54611yescharacteristic
1277C22C43×#54611yescharacteristic
1278C22C43×#54611yescharacteristic
1279C22C43×#54611yescharacteristic
1280C22C43×#54611yescharacteristic
1281C22C43×#54811yescharacteristic
1282C22C43×#54811yescharacteristic
1283C22C43×#54811yescharacteristic
1284C22C43×#55011yescharacteristic
1285C22C43×#55011yescharacteristic
1286C22C43×#55011yescharacteristic
1287C22C43×#55111yescharacteristic
1288C22C43×#55111yescharacteristic
1289C22C43×#55111yescharacteristic
1290C22C43×#55311yescharacteristic
1291C22C43×#56011yescharacteristic
1292C22C43×#56211yescharacteristic
1293C4—24no—
1294C4—24no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—81no—
1304C4—81no—
1305C2—82no—
1306C2—82no—
1307C2—82no—
1308C2C43×#241111yescharacteristic
1309C2C43×#242611yescharacteristic
1310C2C43×#245611yescharacteristic
1311C2C43×#246311yescharacteristic
1312C2C43×#246711yescharacteristic
1313C2C43×#247111yescharacteristic
1314C2C43×#253911yescharacteristic
1315C2C43×#254011yescharacteristic
1316C2C43×#254111yescharacteristic
1317C2C43×#267311yescharacteristic
1318C2C43×#267611yescharacteristic
1319C2C43×#268511yescharacteristic
1320C2C43×#270511yescharacteristic
1321C2C43×#271111yescharacteristic
1322C2C43×#273011yescharacteristic
subgroupG/H
center, socleC24×C43C24
commutator, Frattini, cosocleC24C24×C43
prime radicalC2×C43×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C43×#399C2semidirect
2. C2×C43×#396C2semidirect
3. C2×C43×#394C2semidirect
5. C2×C43×#390C2semidirect
6. C2×C43×#390C2semidirect
7. C2×C43×#388C2semidirect
8. C2×C43×#387C2semidirect
9. C43×#1439C2semidirect
10. C43×#1439C2semidirect
11. C43×#1438C2semidirect
12. C43×#1438C2semidirect
13. C43×#1438C2semidirect
14. C43×#1437C2semidirect
15. C43×#1436C2semidirect
108. C2×C4⋊C4×C43D4semidirect
109. C2×C4⋊C4×C43D4semidirect
170. #95×C43D4semidirect
551. #15776C43direct (N × H)
644. C2×#399C2×C43semidirect
645. C2×#396C2×C43semidirect
646. C2×#394C2×C43semidirect
648. C2×#390C2×C43semidirect
649. C2×#390C2×C43semidirect
650. C2×#388C2×C43semidirect
651. C2×#387C2×C43semidirect
652. #1439C2×C43semidirect
653. #1439C2×C43semidirect
654. #1438C2×C43semidirect
655. #1438C2×C43semidirect
656. #1438C2×C43semidirect
657. #1437C2×C43semidirect
658. #1436C2×C43semidirect
720. C43#15776direct (N × H)
770. C2×C4⋊C4D4×C43semidirect
771. C2×C4⋊C4D4×C43semidirect
832. #95D4×C43semidirect

Maximal subgroups

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

subgroupindex
C2×C43×#3992
C2×C43×#3962
C2×C43×#3942
C2×C43×#3922
C2×C43×#3902
C2×C43×#3882
C2×C43×#3872
C43×#14392
C43×#14382
C43×#14372
C43×#14362
#1577643