Finite Group Databasebeta

← D43×#2635 #25262988

Subgroups — D43×#2635 #25262988

Order 11008.

3606 conjugacy classes of subgroups.

The subgroup lattice has 1282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×D43C211yesmaximal, characteristic, complemented
2C2×C4×D4×D43C211yesmaximal, characteristic, complemented
3#19140488C211yesmaximal, characteristic, complemented
4#19140487C211yesmaximal, characteristic, complemented
5#19140486C212yesmaximal, complemented
6#19140485C211yesmaximal, characteristic, complemented
7#19140484C211yesmaximal, characteristic, complemented
8#19140483C212yesmaximal, complemented
9#19140482C211yesmaximal, characteristic, complemented
10#19140481C212yesmaximal, complemented
11#19140480C211yesmaximal, characteristic, complemented
12#19140479C211yesmaximal, characteristic, complemented
13#19140478C212yesmaximal, complemented
14#400×D43C211yesmaximal, characteristic, complemented
15#399×D43C211yesmaximal, characteristic, complemented
16#394×D43C212yesmaximal, complemented
17#394×D43C211yesmaximal, characteristic, complemented
18#392×D43C212yesmaximal, complemented
19#392×D43C211yesmaximal, characteristic, complemented
20#388×D43C212yesmaximal, complemented
21#386×D43C212yesmaximal, complemented
22#381×D43C211yesmaximal, characteristic, complemented
23C43×#2635C211yesmaximal, characteristic, complemented
24C22×D4×D43C2211yescharacteristic
25C22×D4×D43C2211yescharacteristic
26C22×D4×D43C2212yes—
27C22×D4×D43C2212yes—
28C23×C4×D43C2211yescharacteristic
29C23×C4×D43C2211yescharacteristic
30C2×#13063300C2211yescharacteristic, complemented
31C2×#13063299C2211yescharacteristic, complemented
32C2×#13063298C2212yescomplemented
33C2×#13063297C2212yescomplemented
34C2×#13063296C2211yescharacteristic, complemented
35#121×D43—28no—
36C2×C4×D172C2211yescharacteristic, complemented
37C2×D4×Dic43C2211yescharacteristic, complemented
38C2×#13063287C2211yescharacteristic, complemented
39C2×C4×C22⋊D43C2211yescharacteristic, complemented
40C2×C4×C22⋊D43C2211yescharacteristic, complemented
41C2×(C22⋊D43)⋊C4C2211yescharacteristic, complemented
42C2×(C22⋊D43)⋊C4C2211yescharacteristic, complemented
43C4×D4×D43—28no—
44C2×C4⋊C4×D43C2211yescharacteristic
45C2×C4⋊C4×D43C2211yescharacteristic
46C2×C4⋊C4×D43C2212yes—
47C2×C22⋊C4×D43C2211yescharacteristic
48C2×C22⋊C4×D43C2212yes—
49C2×C22⋊C4×D43C2212yes—
50C2×C22⋊C4×D43C2211yescharacteristic
51C2×C22⋊C4×D43C2212yes—
52C2×C22⋊C4×D43C2212yes—
53C2×C22⋊C4×D43C2212yes—
54C2×C22⋊C4×D43C2212yes—
55C2×C42×D43C2211yescharacteristic
56#14582841C2212yescomplemented
57#14582840C2212yescomplemented
58#14582839C2211yescharacteristic, complemented
59#14582838C2211yescharacteristic, complemented
60#14582837C2211yescharacteristic, complemented
61#14582836C2211yescharacteristic, complemented
62#14582835C2212yescomplemented
63#14582835C2211yescharacteristic, complemented
64#14582834C2211yescharacteristic, complemented
65#14582834C2212yescomplemented
66#14582817C2211yescharacteristic, complemented
67#14582817C2212yescomplemented
68#14582816C2211yescharacteristic, complemented
69#14582816C2212yescomplemented
70#14582815C2212yescomplemented
71#14582815C2212yescomplemented
72#14582815C2212yescomplemented
73#14582814C2212yescomplemented
74#14582814C2212yescomplemented
75#14582814C2212yescomplemented
76#14582813C2212yescomplemented
77#14582813C2211yescharacteristic, complemented
78#14582809C2211yescharacteristic, complemented
79#14582809C2212yescomplemented
80#14582808C2211yescharacteristic, complemented
81#14582808C2212yescomplemented
82#14582808C2212yescomplemented
83#14582808C2212yescomplemented
84#14582808C2212yescomplemented
85#14582807C2212yescomplemented
86#14582807C2212yescomplemented
87#14582807C2212yescomplemented
88#14582807C2211yescharacteristic, complemented
89#14582807C2212yescomplemented
90#14582793C2212yescomplemented
91#14582792C2212yescomplemented
92#14582791C2212yescomplemented
93#14582790C2212yescomplemented
94#14582789C2212yescomplemented
95#14582788C2212yescomplemented
96#14582787C2212yescomplemented
97#14582779C2212yescomplemented
98#14582778C2212yescomplemented
99#14582777C2212yescomplemented
100#14582777C2212yescomplemented
101#14582776C2212yescomplemented
102#14582775C2212yescomplemented
103#14582775C2212yescomplemented
104#14582762C2211yescharacteristic, complemented
105#14582761C2212yescomplemented
106#14582761C2211yescharacteristic, complemented
107#14582761C2211yescharacteristic, complemented
108#14582760C2212yescomplemented
109#95×D43C2211yescharacteristic
110#95×D43C2212yes—
111#95×D43C2211yescharacteristic
112#95×D43C2212yes—
113#95×D43C2212yes—
114C2×#121×C43C2211yescharacteristic, complemented
115C2×C4×D4×C43C2211yescharacteristic, complemented
116C43×#400C2211yescharacteristic, complemented
117C43×#399C2211yescharacteristic, complemented
118C43×#394C2212yescomplemented
119C43×#394C2211yescharacteristic, complemented
120C43×#392C2212yescomplemented
121C43×#392C2211yescharacteristic, complemented
122C43×#388C2212yescomplemented
123C43×#386C2212yescomplemented
124C43×#381C2211yescharacteristic, complemented
125C24×D43C2312yes—
126C24×D43C2311yescharacteristic
127C24×D43C2311yescharacteristic
128C22×D172C2311yescharacteristic
129C22×D172C2312yes—
130C22×D172C2312yes—
131C22×D172C2311yescharacteristic
132C22×C22⋊D43C2311yescharacteristic
133C22×C22⋊D43C2311yescharacteristic
134C22×C22⋊D43C2312yes—
135C22×C22⋊D43C2312yes—
136C22×C22⋊D43C2312yes—
137C22×C22⋊D43C2312yes—
138C22×C22⋊D43C2312yes—
139C2×D4×D43—24no—
140C2×D4×D43—24no—
141C2×D4×D43—28no—
142C2×D4×D43—28no—
143C2×D4×D43—24no—
144C2×D4×D43—24no—
145C2×D4×D43—44no—
146C2×D4×D43—44no—
147C2×D4×D43—44no—
148C2×D4×D43—44no—
149C2×D4×D43—44no—
150C23×Dic43C2311yescharacteristic
151C23×Dic43C2311yescharacteristic
152C22×C4×D43—24no—
153C22×C4×D43—44no—
154C22×C4×D43—44no—
155C22×C4×D43D418yescomplemented
156C22×C4×D43C2311yescharacteristic
157C22×C4×D43C2312yes—
158C22×C4×D43C2311yescharacteristic
159C22×C4×D43C2312yes—
160C22×C4×D43C2312yes—
161C22×C4×D43C2311yescharacteristic
162C22×C4×D43C2311yescharacteristic
163C22×C4×D43C2311yescharacteristic
164C22×C4×D43C2311yescharacteristic
165C22×C4×D43C2311yescharacteristic
166C22×C4×D43C2311yescharacteristic
167C22×C4×D43C2311yescharacteristic
168#13063300—24no—
169#13063299—24no—
170#13063298—28no—
171#13063297—28no—
172#13063296—24no—
173C4×D172—24no—
174D4×Dic43—24no—
175#13063287—24no—
176C4×C22⋊D43—24no—
177C4×C22⋊D43—24no—
178(C22⋊D43)⋊C4—24no—
179(C22⋊D43)⋊C4—24no—
180C2×C4⋊Dic43C2311yescharacteristic
181C2×C4⋊Dic43C2311yescharacteristic
182C2×C4⋊Dic43C2312yes—
183C2×Dic43⋊C4C2311yescharacteristic
184C2×Dic43⋊C4C2311yescharacteristic
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2312yes—
188C4⋊C4×D43—24no—
189C4⋊C4×D43—24no—
190C4⋊C4×D43—44no—
191C2×C22⋊Dic43C2312yes—
192C2×C22⋊Dic43C2312yes—
193C2×C22⋊Dic43C2311yescharacteristic
194C2×C22⋊Dic43C2311yescharacteristic
195C2×C22⋊Dic43C2312yes—
196C2×C22⋊Dic43C2312yes—
197C2×C22⋊Dic43C2312yes—
198C2×C22⋊Dic43C2312yes—
199C2×(C2×D43)⋊C4C2312yes—
200C2×(C2×D43)⋊C4C2312yes—
201C2×(C2×D43)⋊C4C2312yes—
202C2×(C2×D43)⋊C4C2312yes—
203C2×(C2×D43)⋊C4C2311yescharacteristic
204C2×(C2×D43)⋊C4C2311yescharacteristic
205C2×(C2×D43)⋊C4C2311yescharacteristic
206C2×(C2×D43)⋊C4C2311yescharacteristic
207C2×(C2×D43)⋊C4C2312yes—
208C2×(C2×D43)⋊C4C2312yes—
209C2×(C2×D43)⋊C4C2312yes—
210C2×(C2×D43)⋊C4C2312yes—
211C2×(C2×D43)⋊C4C2312yes—
212C2×(C2×D43)⋊C4C2312yes—
213C2×(C2×D43)⋊C4C2312yes—
214C2×(C2×D43)⋊C4C2312yes—
215C22⋊C4×D43—24no—
216C22⋊C4×D43—24no—
217C22⋊C4×D43—28no—
218C22⋊C4×D43—28no—
219C22⋊C4×D43—44no—
220C22⋊C4×D43—44no—
221C22⋊C4×D43—44no—
222C22⋊C4×D43—44no—
223C2×C4×Dic43C2311yescharacteristic
224C2×C4×Dic43C2311yescharacteristic
225C2×C4×Dic43C2311yescharacteristic
226C42×D43—24no—
227C43⋊#95C2312yes—
228C43⋊#95C2312yes—
229C43⋊#95C2312yes—
230C43⋊#95C2312yes—
231C43⋊#95C2312yes—
232C43⋊#95C2312yes—
233C43⋊#95C2311yescharacteristic
234C43⋊#95C2312yes—
235C43⋊#95C2311yescharacteristic
236C43⋊#95C2312yes—
237C43⋊#95C2312yes—
238C43⋊#95C2312yes—
239C43⋊#95C2312yes—
240C22×D4×C43C2311yescharacteristic
241C22×D4×C43C2312yes—
242C22×D4×C43C2311yescharacteristic
243C22×D4×C43C2312yes—
244C23×C4×C43C2311yescharacteristic
245C23×C4×C43C2311yescharacteristic
246#121×C43—24no—
247C4×D4×C43—24no—
248C2×C4⋊C4×C43C2311yescharacteristic
249C2×C4⋊C4×C43C2311yescharacteristic
250C2×C4⋊C4×C43C2312yes—
251C2×C22⋊C4×C43C2312yes—
252C2×C22⋊C4×C43C2312yes—
253C2×C22⋊C4×C43C2311yescharacteristic
254C2×C22⋊C4×C43C2311yescharacteristic
255C2×C22⋊C4×C43C2312yes—
256C2×C22⋊C4×C43C2312yes—
257C2×C22⋊C4×C43C2312yes—
258C2×C22⋊C4×C43C2312yes—
259C2×C42×C43C2311yescharacteristic
260#95×C43C2312yes—
261#95×C43C2312yes—
262#95×C43C2311yescharacteristic
263#95×C43C2311yescharacteristic
264#95×C43C2312yes—
265C24×C43C2412yes—
266C24×C43C2411yescharacteristic
267C24×C43C2411yescharacteristic
268C23×D43—22no—
269C23×D43—22no—
270C23×D43—22no—
271C23×D43—22no—
272C23×D43—24no—
273C23×D43—24no—
274C23×D43—24no—
275C23×D43—24no—
276C23×D43—24no—
277C23×D43—24no—
278C23×D43—24no—
279C23×D43—24no—
280C23×D43—24no—
281C23×D43—24no—
282C23×D43—24no—
283C23×D43C2×D414yes—
284C23×D43#4114yes—
285C23×D43C2412yes—
286C23×D43C2411yescharacteristic
287C23×D43C2411yescharacteristic
288C23×D43C2411yescharacteristic
289C2×D4×C43—22no—
290C2×D4×C43—22no—
291C2×D4×C43—22no—
292C2×D4×C43—24no—
293C2×D4×C43—22no—
294C2×D4×C43—24no—
295C2×D4×C43—42no—
296C2×D4×C43—42no—
297C2×D4×C43—42no—
298C2×D4×C43—42no—
299C2×D4×C43—42no—
300C22×C4×C43—22no—
301C22×C4×C43—42no—
302C22×C4×C43—42no—
303C22×C4×C43C2×D414yescomplemented
304C22×C4×C43C2412yes—
305C22×C4×C43C2412yes—
306C22×C4×C43C2411yescharacteristic
307C22×C4×C43C2412yes—
308C22×C4×C43C2411yescharacteristic
309C22×C4×C43C2411yescharacteristic
310C22×C4×C43C2411yescharacteristic
311C22×C4×C43C2411yescharacteristic
312C2×C22⋊D43—24no—
313C2×C22⋊D43—22no—
314C2×C22⋊D43—22no—
315C2×C22⋊D43—22no—
316C2×C22⋊D43—24no—
317C2×C22⋊D43—22no—
318C2×C22⋊D43—24no—
319C2×C22⋊D43—22no—
320C2×C22⋊D43—24no—
321C2×C22⋊D43—22no—
322C2×C22⋊D43—24no—
323C2×C22⋊D43—42no—
324C2×C22⋊D43—42no—
325C2×C22⋊D43—42no—
326C2×C22⋊D43—42no—
327C2×C22⋊D43—42no—
328C2×C22⋊D43—42no—
329C2×C22⋊D43—42no—
330C2×C22⋊D43—42no—
331C2×C22⋊D43—42no—
332C2×C22⋊D43—42no—
333C22×Dic43—22no—
334C22×Dic43—42no—
335C22×Dic43—42no—
336C22×Dic43C2×D414yescomplemented
337C22×Dic43C2412yes—
338C22×Dic43C2412yes—
339C22×Dic43C2411yescharacteristic
340C22×Dic43C2412yes—
341C22×Dic43C2411yescharacteristic
342C22×Dic43C2411yescharacteristic
343C22×Dic43C2411yescharacteristic
344C22×Dic43C2411yescharacteristic
345D4×D43—232no—
346D4×D43—432no—
347D4×D43—432no—
348D4×D43—416no—
349C2×D172—22no—
350C2×D172—22no—
351C2×D172—22no—
352C2×D172—24no—
353C2×D172—22no—
354C2×D172—24no—
355C2×D172—42no—
356C2×D172—42no—
357C2×D172—42no—
358C2×D172—42no—
359C2×D172—42no—
360C2×C4×D43—22no—
361C2×C4×D43—22no—
362C2×C4×D43—22no—
363C2×C4×D43—22no—
364C2×C4×D43—22no—
365C2×C4×D43—24no—
366C2×C4×D43—22no—
367C2×C4×D43—24no—
368C2×C4×D43—24no—
369C2×C4×D43—24no—
370C2×C4×D43—24no—
371C2×C4×D43—24no—
372C2×C4×D43—24no—
373C2×C4×D43—24no—
374C2×C4×D43—24no—
375C2×C4×D43—24no—
376C2×C4×D43—24no—
377C2×C4×D43—24no—
378C2×C4×D43—24no—
379C2×C4×D43—416no—
380C2×C4×D43—42no—
381C2×C4×D43—42no—
382C2×C4×D43—42no—
383C2×C4×D43—42no—
384C2×C4×D43—416no—
385C2×C4×D43C2×D414yes—
386C2×C4×D43C2×D414yes—
387C2×C4×D43C2×D414yescomplemented
388C2×C4×D43C2×D414yescomplemented
389C2×C4×D43#4114yes—
390C4⋊C4×C43—22no—
391C4⋊C4×C43—22no—
392C4⋊C4×C43—42no—
393C22⋊C4×C43—22no—
394C22⋊C4×C43—24no—
395C22⋊C4×C43—24no—
396C22⋊C4×C43—22no—
397C22⋊C4×C43—42no—
398C22⋊C4×C43—42no—
399C22⋊C4×C43—42no—
400C22⋊C4×C43—42no—
401C42×C43—22no—
402C22⋊Dic43—22no—
403C22⋊Dic43—24no—
404C22⋊Dic43—24no—
405C22⋊Dic43—22no—
406C22⋊Dic43—42no—
407C22⋊Dic43—42no—
408C22⋊Dic43—42no—
409C22⋊Dic43—42no—
410(C2×D43)⋊C4—22no—
411(C2×D43)⋊C4—24no—
412(C2×D43)⋊C4—24no—
413(C2×D43)⋊C4—22no—
414(C2×D43)⋊C4—24no—
415(C2×D43)⋊C4—24no—
416(C2×D43)⋊C4—22no—
417(C2×D43)⋊C4—22no—
418(C2×D43)⋊C4—42no—
419(C2×D43)⋊C4—42no—
420(C2×D43)⋊C4—42no—
421(C2×D43)⋊C4—42no—
422(C2×D43)⋊C4—42no—
423(C2×D43)⋊C4—42no—
424(C2×D43)⋊C4—42no—
425(C2×D43)⋊C4—42no—
426C4⋊Dic43—22no—
427C4⋊Dic43—22no—
428C4⋊Dic43—42no—
429Dic43⋊C4—22no—
430Dic43⋊C4—22no—
431Dic43⋊C4—24no—
432Dic43⋊C4—42no—
433Dic43⋊C4—42no—
434C4×Dic43—22no—
435C4×Dic43—22no—
436C4×Dic43—22no—
437C23×C43—21no—
438C23×C43—21no—
439C23×C43—21no—
440C23×C43—21no—
441C23×C43—22no—
442C23×C43—22no—
443C23×C43—22no—
444C23×C43—22no—
445C23×C43—22no—
446C23×C43—22no—
447C23×C43—22no—
448C23×C43—22no—
449C23×C43—22no—
450C23×C43—22no—
451C23×C43—22no—
452C23×C43C22×D412yes—
453C23×C43C2×#4112yes—
454C23×C43C2511yescharacteristic
455C22×D43—21no—
456C22×D43—21no—
457C22×D43—21no—
458C22×D43—21no—
459C22×D43—22no—
460C22×D43—22no—
461C22×D43—22no—
462C22×D43—22no—
463C22×D43—28no—
464C22×D43—28no—
465C22×D43—28no—
466C22×D43—28no—
467C22×D43—216no—
468C22×D43—22no—
469C22×D43—22no—
470C22×D43—22no—
471C22×D43—22no—
472C22×D43—22no—
473C22×D43—22no—
474C22×D43—22no—
475C22×D43—44no—
476C22×D43—44no—
477C22×D43—48no—
478C22×D43—48no—
479C22×D43—48no—
480C22×D43—48no—
481C22×D43—48no—
482C22×D43—48no—
483C22×D43—48no—
484C22×D43—48no—
485C22×D43—48no—
486C22×D43—48no—
487C22×D43C22×D412yes—
488C22×D43C22×D412yes—
489C22×D43C2×#4112yes—
490C22×D43C2×#4112yes—
491C22×D43C2×#4112yes—
492C22×D43H(5,𝔽2)14yes—
493C22×D43H(5,𝔽2)14yes—
494D4×C43—28no—
495D4×C43—44no—
496D4×C43—48no—
497D4×C43—48no—
498C2×C4×C43—21no—
499C2×C4×C43—21no—
500C2×C4×C43—22no—
501C2×C4×C43—22no—
502C2×C4×C43—21no—
503C2×C4×C43—21no—
504C2×C4×C43—22no—
505C2×C4×C43—22no—
506C2×C4×C43—22no—
507C2×C4×C43—22no—
508C2×C4×C43—22no—
509C2×C4×C43—22no—
510C2×C4×C43—22no—
511C2×C4×C43—22no—
512C2×C4×C43—22no—
513C2×C4×C43—22no—
514C2×C4×C43—22no—
515C2×C4×C43—44no—
516C2×C4×C43—44no—
517C2×C4×C43C22×D412yes—
518C2×C4×C43C22×D412yes—
519C2×C4×C43C2×#4112yes—
520C22⋊D43—28no—
521C22⋊D43—28no—
522C22⋊D43—48no—
523C22⋊D43—48no—
524C22⋊D43—48no—
525C22⋊D43—48no—
526C22⋊D43—48no—
527C2×Dic43—21no—
528C2×Dic43—21no—
529C2×Dic43—22no—
530C2×Dic43—22no—
531C2×Dic43—21no—
532C2×Dic43—21no—
533C2×Dic43—22no—
534C2×Dic43—22no—
535C2×Dic43—22no—
536C2×Dic43—22no—
537C2×Dic43—22no—
538C2×Dic43—22no—
539C2×Dic43—22no—
540C2×Dic43—22no—
541C2×Dic43—22no—
542C2×Dic43—22no—
543C2×Dic43—22no—
544C2×Dic43—44no—
545C2×Dic43—44no—
546C2×Dic43C22×D412yes—
547C2×Dic43C22×D412yes—
548C2×Dic43C2×#4112yes—
549D172—28no—
550D172—44no—
551D172—48no—
552D172—48no—
553C4×D43—28no—
554C4×D43—28no—
555C4×D43—28no—
556C4×D43—44no—
557C4×D43—44no—
558C4×D43—44no—
559C4×D43—44no—
560C4×D43—44no—
561C4×D43—44no—
562C4×D43—48no—
563C4×D43—48no—
564C4×D43—48no—
565C2×#2635—431nomaximal, Sylow
566C22×C43—22no—
567C22×C43—22no—
568C22×C43—22no—
569C22×C43—22no—
570C22×C43—24no—
571C22×C43—41no—
572C22×C43—41no—
573C22×C43—42no—
574C22×C43—42no—
575C22×C43—42no—
576C22×C43—42no—
577C22×C43—42no—
578C22×C43—42no—
579C22×C43—42no—
580C22×C43—42no—
581C22×C43—42no—
582C22×C43—42no—
583C22×C43C23×D411yescharacteristic
584C22×C43C22×#4111yescharacteristic
585C22×C43C22×#4111yescharacteristic
586C22×C43C2×H(5,𝔽2)12yes—
587C22×C43C2×H(5,𝔽2)12yes—
588C2×D43—22no—
589C2×D43—22no—
590C2×D43—22no—
591C2×D43—22no—
592C2×D43—24no—
593C2×D43—41no—
594C2×D43—41no—
595C2×D43—42no—
596C2×D43—42no—
597C2×D43—42no—
598C2×D43—416no—
599C2×D43—416no—
600C2×D43—42no—
601C2×D43—42no—
602C2×D43—42no—
603C2×D43—42no—
604C2×D43—42no—
605C2×D43—42no—
606C2×D43—42no—
607C2×D43—816no—
608C2×D43#52514yes—
609C2×D43#53414yes—
610C2×D43#53514yes—
611C2×D43#53818yes—
612C2×D43#54018yes—
613C4×C43—22no—
614C4×C43—22no—
615C4×C43—22no—
616C4×C43—41no—
617C4×C43—42no—
618C4×C43—41no—
619C4×C43—42no—
620C4×C43—42no—
621Dic43—22no—
622Dic43—22no—
623Dic43—22no—
624Dic43—41no—
625Dic43—41no—
626Dic43—42no—
627Dic43—42no—
628Dic43—42no—
629C22×#121—431no—
630C22×C4×D4—431no—
631#2635—431no—
632#2635—431no—
633#2635—432no—
634#2635—431no—
635#2635—432no—
636#2635—431no—
637#2635—432no—
638#2635—432no—
639#2635—431no—
640#2635—431no—
641#2635—431no—
642#2635D4311yescharacteristic, direct product factor
643C2×#400—431no—
644C2×#399—431no—
645C2×#394—431no—
646C2×#394—432no—
647C2×#392—432no—
648C2×#392—431no—
649C2×#388—432no—
650C2×#386—432no—
651C2×#381—431no—
652C2×C43—42no—
653C2×C43—42no—
654C2×C43—82no—
655C2×C43C2×#52511yescharacteristic
656C2×C43C2×#53411yescharacteristic
657C2×C43C2×#53511yescharacteristic
658C2×C43C2×#53812yes—
659C2×C43C2×#54012yes—
660D43—42no—
661D43—42no—
662D43—82no—
663D43#263518yesdirect product factor
664C23×D4—431no—
665C23×D4—432no—
666C23×D4—431no—
667C23×D4—432no—
668C24×C4—431no—
669C24×C4—431no—
670C2×#121—431no—
671C2×#121—432no—
672C2×#121—431no—
673C2×#121—431no—
674C2×#121—432no—
675C2×#121—868no—
676C2×#121C2×D4311yescharacteristic, complemented
677C2×C4×D4—431no—
678C2×C4×D4—431no—
679C2×C4×D4—431no—
680C2×C4×D4—431no—
681C2×C4×D4—431no—
682C2×C4×D4—431no—
683C2×C4×D4—431no—
684C2×C4×D4—868no—
685C2×C4×D4C2×D4311yescharacteristic, complemented
686C22×C4⋊C4—431no—
687C22×C4⋊C4—431no—
688C22×C4⋊C4—432no—
689C22×C22⋊C4—432no—
690C22×C22⋊C4—431no—
691C22×C22⋊C4—431no—
692C22×C22⋊C4—432no—
693C22×C22⋊C4—432no—
694C22×C22⋊C4—432no—
695C22×C22⋊C4—432no—
696C22×C22⋊C4—432no—
697C22×C42—431no—
698#400—431no—
699#400—431no—
700#400—431no—
701#400—432no—
702#400—432no—
703#400C2×D4311yescharacteristic, complemented
704#399—432no—
705#399—431no—
706#399—432no—
707#399—431no—
708#399—431no—
709#399C2×D4311yescharacteristic, complemented
710#394—431no—
711#394—432no—
712#394—431no—
713#394—432no—
714#394—432no—
715#394—432no—
716#394—432no—
717#394—432no—
718#394—432no—
719#394—432no—
720#394—431no—
721#394—432no—
722#394C2×D4311yescharacteristic, complemented
723#394C2×D4312yescomplemented
724#392—432no—
725#392—431no—
726#392—432no—
727#392—432no—
728#392—432no—
729#392—432no—
730#392—431no—
731#392—432no—
732#392—432no—
733#392—432no—
734#392—431no—
735#392—432no—
736#392C2×D4311yescharacteristic, complemented
737#392C2×D4312yescomplemented
738#388—432no—
739#388—432no—
740#388—432no—
741#388—432no—
742#388—432no—
743#388—432no—
744#388—432no—
745#388C2×D4312yescomplemented
746#386—432no—
747#386—432no—
748#386—432no—
749#386—432no—
750#386—432no—
751#386—432no—
752#386—432no—
753#386C2×D4312yescomplemented
754#381—431no—
755#381—432no—
756#381—431no—
757#381—431no—
758#381—432no—
759#381C2×D4311yescharacteristic, complemented
760C2×#95—431no—
761C2×#95—432no—
762C2×#95—431no—
763C2×#95—432no—
764C2×#95—432no—
765C43C2×#263511yescharacteristic, complemented, Sylow
766C25—431no—
767C25—431no—
768C25—432no—
769C22×D4—431no—
770C22×D4—431no—
771C22×D4—432no—
772C22×D4—432no—
773C22×D4—432no—
774C22×D4—432no—
775C22×D4—432no—
776C22×D4—431no—
777C22×D4—432no—
778C22×D4—431no—
779C22×D4—432no—
780C22×D4—864no—
781C22×D4—864no—
782C22×D4—864no—
783C22×D4—864no—
784C22×D4—868no—
785C22×D4—868no—
786C22×D4—1724no—
787C22×D4—1724no—
788C22×D4—1724no—
789C22×D4—1724no—
790C22×D4—1724no—
791C22×D4C22×D4311yescharacteristic
792C22×D4C22×D4312yes—
793C22×D4C22×D4311yescharacteristic
794C22×D4C22×D4312yes—
795C23×C4—431no—
796C23×C4—431no—
797C23×C4—431no—
798C23×C4—431no—
799C23×C4—438no—
800C23×C4—431no—
801C23×C4—431no—
802C23×C4—431no—
803C23×C4—431no—
804C23×C4—432no—
805C23×C4—431no—
806C23×C4—432no—
807C23×C4—432no—
808C23×C4—431no—
809C23×C4—431no—
810C23×C4—864no—
811C23×C4—1724no—
812C23×C4—1724no—
813C23×C4C22×D4311yescharacteristic
814C23×C4C22×D4311yescharacteristic
815#121—24no—
816#121—868no—
817#121—864no—
818#121—864no—
819#121—868no—
820#121—864no—
821C4×D4—24no—
822C4×D4—864no—
823C4×D4—864no—
824C4×D4—864no—
825C4×D4—864no—
826C4×D4—864no—
827C4×D4—864no—
828C4×D4—864no—
829C2×C4⋊C4—431no—
830C2×C4⋊C4—431no—
831C2×C4⋊C4—431no—
832C2×C4⋊C4—432no—
833C2×C4⋊C4—431no—
834C2×C4⋊C4—432no—
835C2×C4⋊C4—432no—
836C2×C4⋊C4—432no—
837C2×C4⋊C4—864no—
838C2×C4⋊C4—864no—
839C2×C4⋊C4—1724no—
840C2×C4⋊C4C22×D4311yescharacteristic
841C2×C4⋊C4C22×D4311yescharacteristic
842C2×C4⋊C4C22×D4312yes—
843C2×C22⋊C4—431no—
844C2×C22⋊C4—431no—
845C2×C22⋊C4—432no—
846C2×C22⋊C4—432no—
847C2×C22⋊C4—431no—
848C2×C22⋊C4—431no—
849C2×C22⋊C4—431no—
850C2×C22⋊C4—431no—
851C2×C22⋊C4—432no—
852C2×C22⋊C4—432no—
853C2×C22⋊C4—432no—
854C2×C22⋊C4—432no—
855C2×C22⋊C4—432no—
856C2×C22⋊C4—432no—
857C2×C22⋊C4—432no—
858C2×C22⋊C4—432no—
859C2×C22⋊C4—432no—
860C2×C22⋊C4—432no—
861C2×C22⋊C4—432no—
862C2×C22⋊C4—432no—
863C2×C22⋊C4—432no—
864C2×C22⋊C4—432no—
865C2×C22⋊C4—432no—
866C2×C22⋊C4—432no—
867C2×C22⋊C4—864no—
868C2×C22⋊C4—868no—
869C2×C22⋊C4—868no—
870C2×C22⋊C4—864no—
871C2×C22⋊C4—1724no—
872C2×C22⋊C4—1724no—
873C2×C22⋊C4—1724no—
874C2×C22⋊C4—1724no—
875C2×C22⋊C4C22×D4311yescharacteristic
876C2×C22⋊C4C22×D4311yescharacteristic
877C2×C22⋊C4C22×D4312yes—
878C2×C22⋊C4C22×D4312yes—
879C2×C22⋊C4C22×D4312yes—
880C2×C22⋊C4C22×D4312yes—
881C2×C22⋊C4C22×D4312yes—
882C2×C22⋊C4C22×D4312yes—
883C2×C42—431no—
884C2×C42—431no—
885C2×C42—431no—
886C2×C42—864no—
887C2×C42C22×D4311yescharacteristic
888#95—432no—
889#95—432no—
890#95—432no—
891#95—432no—
892#95—431no—
893#95—432no—
894#95—431no—
895#95—432no—
896#95—432no—
897#95—432no—
898#95—432no—
899#95—432no—
900#95—432no—
901#95C22×D4312yes—
902#95C22×D4311yescharacteristic
903#95C22×D4311yescharacteristic
904#95C22×D4312yes—
905#95C22×D4312yes—
906C24—431no—
907C24—434no—
908C24—434no—
909C24—431no—
910C24—431no—
911C24—432no—
912C24—862no—
913C24—864no—
914C24—864no—
915C24—864no—
916C24—862no—
917C24—862no—
918C24—862no—
919C24—864no—
920C24—864no—
921C24—864no—
922C24—864no—
923C24—864no—
924C24—864no—
925C24—864no—
926C24—864no—
927C24C23×D4312yes—
928C24C23×D4311yescharacteristic
929C24C23×D4311yescharacteristic
930C2×D4—22no—
931C2×D4—22no—
932C2×D4—24no—
933C2×D4—24no—
934C2×D4—22no—
935C2×D4—22no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—862no—
942C2×D4—862no—
943C2×D4—864no—
944C2×D4—864no—
945C2×D4—862no—
946C2×D4—862no—
947C2×D4—864no—
948C2×D4—8632no—
949C2×D4—862no—
950C2×D4—862no—
951C2×D4—862no—
952C2×D4—862no—
953C2×D4—864no—
954C2×D4—864no—
955C2×D4—864no—
956C2×D4—864no—
957C2×D4—862no—
958C2×D4—862no—
959C2×D4—1722no—
960C2×D4—1722no—
961C2×D4—1722no—
962C2×D4—1722no—
963C2×D4—1722no—
964C2×D4—17216no—
965C2×D4—1722no—
966C2×D4—1722no—
967C2×D4—1722no—
968C2×D4—1722no—
969C2×D4—1722no—
970C2×D4—1722no—
971C2×D4—1722no—
972C2×D4—1722no—
973C2×D4—1722no—
974C2×D4—1722no—
975C2×D4—17232no—
976C2×D4—17232no—
977C22×C4—22no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—431no—
981C22×C4—431no—
982C22×C4—431no—
983C22×C4—434no—
984C22×C4—434no—
985C22×C4—434no—
986C22×C4—434no—
987C22×C4—434no—
988C22×C4—434no—
989C22×C4—432no—
990C22×C4—432no—
991C22×C4—431no—
992C22×C4—432no—
993C22×C4—431no—
994C22×C4—862no—
995C22×C4—862no—
996C22×C4—864no—
997C22×C4—864no—
998C22×C4—862no—
999C22×C4—862no—
1000C22×C4—862no—
1001C22×C4—864no—
1002C22×C4—864no—
1003C22×C4—864no—
1004C22×C4—864no—
1005C22×C4—864no—
1006C22×C4—864no—
1007C22×C4—864no—
1008C22×C4—864no—
1009C22×C4—864no—
1010C22×C4—864no—
1011C22×C4—864no—
1012C22×C4—862no—
1013C22×C4—862no—
1014C22×C4—1722no—
1015C22×C4—1722no—
1016C22×C4—1722no—
1017C22×C4—1722no—
1018C22×C4—17216no—
1019C22×C4—17216no—
1020C22×C4—1722no—
1021C22×C4—1722no—
1022C22×C4D4×D4314yescomplemented
1023C22×C4C23×D4312yes—
1024C22×C4C23×D4312yes—
1025C22×C4C23×D4311yescharacteristic
1026C22×C4C23×D4312yes—
1027C22×C4C23×D4311yescharacteristic
1028C22×C4C23×D4311yescharacteristic
1029C22×C4C23×D4311yescharacteristic
1030C22×C4C23×D4311yescharacteristic
1031C4⋊C4—22no—
1032C4⋊C4—22no—
1033C4⋊C4—42no—
1034C4⋊C4—862no—
1035C4⋊C4—862no—
1036C4⋊C4—864no—
1037C4⋊C4—862no—
1038C4⋊C4—862no—
1039C4⋊C4—1722no—
1040C4⋊C4—1722no—
1041C4⋊C4—1722no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—24no—
1045C22⋊C4—24no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—862no—
1051C22⋊C4—864no—
1052C22⋊C4—864no—
1053C22⋊C4—862no—
1054C22⋊C4—862no—
1055C22⋊C4—862no—
1056C22⋊C4—864no—
1057C22⋊C4—864no—
1058C22⋊C4—862no—
1059C22⋊C4—862no—
1060C22⋊C4—864no—
1061C22⋊C4—864no—
1062C22⋊C4—1722no—
1063C22⋊C4—1722no—
1064C22⋊C4—1722no—
1065C22⋊C4—1722no—
1066C22⋊C4—1722no—
1067C22⋊C4—1722no—
1068C22⋊C4—1722no—
1069C22⋊C4—1722no—
1070C22⋊C4—1722no—
1071C22⋊C4—1722no—
1072C22⋊C4—1722no—
1073C22⋊C4—1722no—
1074C42—22no—
1075C42—862no—
1076C42—862no—
1077C42—862no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—22no—
1083C23—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—22no—
1092C23—22no—
1093C23—432no—
1094C23—432no—
1095C23—432no—
1096C23—434no—
1097C23—434no—
1098C23—432no—
1099C23—432no—
1100C23—868no—
1101C23—868no—
1102C23—868no—
1103C23—868no—
1104C23—8616no—
1105C23—861no—
1106C23—861no—
1107C23—861no—
1108C23—861no—
1109C23—862no—
1110C23—862no—
1111C23—862no—
1112C23—862no—
1113C23—862no—
1114C23—862no—
1115C23—862no—
1116C23—862no—
1117C23—862no—
1118C23—862no—
1119C23—862no—
1120C23—1728no—
1121C23—1728no—
1122C23—1728no—
1123C23—1728no—
1124C23—1728no—
1125C23—1728no—
1126C23—1728no—
1127C23—1724no—
1128C23—1724no—
1129C23—1728no—
1130C23—1728no—
1131C23—1728no—
1132C23C2×D4×D4312yes—
1133C23#41×D4312yes—
1134C23C24×D4311yescharacteristic
1135D4—28no—
1136D4—44no—
1137D4—48no—
1138D4—48no—
1139D4—868no—
1140D4—868no—
1141D4—868no—
1142D4—1724no—
1143D4—1728no—
1144D4—1728no—
1145D4—1728no—
1146D4—1728no—
1147D4—1728no—
1148D4—1728no—
1149D4—1728no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—21no—
1155C2×C4—21no—
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—22no—
1166C2×C4—22no—
1167C2×C4—44no—
1168C2×C4—44no—
1169C2×C4—432no—
1170C2×C4—432no—
1171C2×C4—432no—
1172C2×C4—868no—
1173C2×C4—868no—
1174C2×C4—868no—
1175C2×C4—861no—
1176C2×C4—861no—
1177C2×C4—862no—
1178C2×C4—862no—
1179C2×C4—861no—
1180C2×C4—861no—
1181C2×C4—862no—
1182C2×C4—862no—
1183C2×C4—862no—
1184C2×C4—862no—
1185C2×C4—862no—
1186C2×C4—862no—
1187C2×C4—862no—
1188C2×C4—862no—
1189C2×C4—862no—
1190C2×C4—862no—
1191C2×C4—862no—
1192C2×C4—1724no—
1193C2×C4—1724no—
1194C2×C4—1724no—
1195C2×C4—1724no—
1196C2×C4—1724no—
1197C2×C4—1728no—
1198C2×C4—1728no—
1199C2×C4—1724no—
1200C2×C4—1728no—
1201C2×C4—1724no—
1202C2×C4—1724no—
1203C2×C4C2×D4×D4312yes—
1204C2×C4C2×D4×D4312yes—
1205C2×C4#41×D4312yes—
1206C22—22no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—24no—
1211C22—41no—
1212C22—41no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—42no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—434no—
1224C22—434no—
1225C22—434no—
1226C22—438no—
1227C22—438no—
1228C22—862no—
1229C22—862no—
1230C22—862no—
1231C22—862no—
1232C22—864no—
1233C22—34416no—
1234C22—17216no—
1235C22—17216no—
1236C22—1722no—
1237C22—1722no—
1238C22—1722no—
1239C22—1722no—
1240C22—1722no—
1241C22—1722no—
1242C22—1722no—
1243C22—1721no—
1244C22—1721no—
1245C22—1722no—
1246C22—1722no—
1247C22—1722no—
1248C22C22×D4×D4311yescharacteristic
1249C22C2×#41×D4311yescharacteristic
1250C22C2×#41×D4311yescharacteristic
1251C22H(5,𝔽2)×D4312yes—
1252C22H(5,𝔽2)×D4312yes—
1253C4—22no—
1254C4—22no—
1255C4—22no—
1256C4—41no—
1257C4—42no—
1258C4—41no—
1259C4—42no—
1260C4—42no—
1261C4—862no—
1262C4—862no—
1263C4—862no—
1264C4—1721no—
1265C4—1722no—
1266C4—1721no—
1267C4—1722no—
1268C4—1722no—
1269C2—42no—
1270C2—42no—
1271C2—82no—
1272C2—438no—
1273C2—3442no—
1274C2—1722no—
1275C2—1722no—
1276C2#525×D4311yescharacteristic
1277C2#534×D4311yescharacteristic
1278C2#535×D4311yescharacteristic
1279C2#538×D4312yes—
1280C2#540×D4312yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2635C2
hypercenter#2635D43
hypocenterC43C2×#2635
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2635

Complements

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

NH ≅ G/Ntype
1. C2×#121×D43C2semidirect
2. C2×C4×D4×D43C2semidirect
3. #19140488C2semidirect
4. #19140487C2semidirect
5. #19140486C2semidirect
6. #19140485C2semidirect
7. #19140484C2semidirect
8. #19140483C2semidirect
9. #19140482C2semidirect
10. #19140481C2semidirect
11. #19140480C2semidirect
12. #19140479C2semidirect
13. #19140478C2semidirect
14. #400×D43C2semidirect
15. #399×D43C2semidirect
16. #394×D43C2semidirect
17. #394×D43C2semidirect
18. #392×D43C2semidirect
19. #392×D43C2semidirect
20. #388×D43C2semidirect
21. #386×D43C2semidirect
22. #381×D43C2semidirect
23. C43×#2635C2semidirect
30. C2×#13063300C22semidirect
31. C2×#13063299C22semidirect
32. C2×#13063298C22semidirect
33. C2×#13063297C22semidirect
34. C2×#13063296C22semidirect
36. C2×C4×D172C22semidirect
37. C2×D4×Dic43C22semidirect
38. C2×#13063287C22semidirect
39. C2×C4×C22⋊D43C22semidirect
40. C2×C4×C22⋊D43C22semidirect
41. C2×(C22⋊D43)⋊C4C22semidirect
42. C2×(C22⋊D43)⋊C4C22semidirect
56. #14582841C22semidirect
57. #14582840C22semidirect
58. #14582839C22semidirect
59. #14582838C22semidirect
60. #14582837C22semidirect
61. #14582836C22semidirect
62. #14582835C22semidirect
63. #14582835C22semidirect
64. #14582834C22semidirect
65. #14582834C22semidirect
66. #14582817C22semidirect
67. #14582817C22semidirect
68. #14582816C22semidirect
69. #14582816C22semidirect
70. #14582815C22semidirect
71. #14582815C22semidirect
72. #14582815C22semidirect
73. #14582814C22semidirect
74. #14582814C22semidirect
75. #14582814C22semidirect
76. #14582813C22semidirect
77. #14582813C22semidirect
78. #14582809C22semidirect
79. #14582809C22semidirect
80. #14582808C22semidirect
81. #14582808C22semidirect
82. #14582808C22semidirect
83. #14582808C22semidirect
84. #14582808C22semidirect
85. #14582807C22semidirect
86. #14582807C22semidirect
87. #14582807C22semidirect
88. #14582807C22semidirect
89. #14582807C22semidirect
90. #14582793C22semidirect
91. #14582792C22semidirect
92. #14582791C22semidirect
93. #14582790C22semidirect
94. #14582789C22semidirect
95. #14582788C22semidirect
96. #14582787C22semidirect
97. #14582779C22semidirect
98. #14582778C22semidirect
99. #14582777C22semidirect
100. #14582777C22semidirect
101. #14582776C22semidirect
102. #14582775C22semidirect
103. #14582775C22semidirect
104. #14582762C22semidirect
105. #14582761C22semidirect
106. #14582761C22semidirect
107. #14582761C22semidirect
108. #14582760C22semidirect
114. C2×#121×C43C22semidirect
115. C2×C4×D4×C43C22semidirect
116. C43×#400C22semidirect
117. C43×#399C22semidirect
118. C43×#394C22semidirect
119. C43×#394C22semidirect
120. C43×#392C22semidirect
121. C43×#392C22semidirect
122. C43×#388C22semidirect
123. C43×#386C22semidirect
124. C43×#381C22semidirect
155. C22×C4×D43D4semidirect
303. C22×C4×C43C2×D4semidirect
336. C22×Dic43C2×D4semidirect
387. C2×C4×D43C2×D4semidirect
388. C2×C4×D43C2×D4semidirect
642. #2635D43direct (N × H)
663. D43#2635direct (N × H)
676. C2×#121C2×D43semidirect
685. C2×C4×D4C2×D43semidirect
703. #400C2×D43semidirect
709. #399C2×D43semidirect
722. #394C2×D43semidirect
723. #394C2×D43semidirect
736. #392C2×D43semidirect
737. #392C2×D43semidirect
745. #388C2×D43semidirect
753. #386C2×D43semidirect
759. #381C2×D43semidirect
765. C43C2×#2635semidirect
1022. C22×C4D4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#121×D432
C2×C4×D4×D432
#191404882
#191404872
#191404862
#191404852
#191404842
#191404832
#191404822
#191404812
#191404802
#191404792
#191404782
#400×D432
#399×D432
#394×D432
#392×D432
#388×D432
#386×D432
#381×D432
C43×#26352
C2×#263543