Finite Group Databasebeta

← D43×#2364 #25256173

Subgroups — D43×#2364 #25256173

Order 11008.

4262 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#121×D43C211yesmaximal, characteristic
2C2×C4×D4×D43C212yesmaximal, complemented
3#19137647C211yesmaximal, characteristic, complemented
4#19137646C212yesmaximal, complemented
5#19137645C211yesmaximal, characteristic, complemented
6#19137644C212yesmaximal, complemented
7#19137643C212yesmaximal, complemented
8#19137642C211yesmaximal, characteristic, complemented
9#19137641C212yesmaximal, complemented
10#19137640C212yesmaximal, complemented
11#19137639C212yesmaximal, complemented
12#388×D43C212yesmaximal, complemented
13#387×D43C212yesmaximal, complemented
14#386×D43C212yesmaximal, complemented
15#386×D43C212yesmaximal, complemented
16C4×C22⋊C4×D43C212yesmaximal, complemented
17C4×C22⋊C4×D43C211yesmaximal, characteristic, complemented
18C2×#95×D43C211yesmaximal, characteristic, complemented
19C43×#2364C211yesmaximal, characteristic, complemented
20C22×D4×D43C2212yes—
21C22×D4×D43C2211yescharacteristic
22C23×C4×D43C2212yes—
23C23×C4×D43C2212yes—
24C23×C4×D43C2211yescharacteristic
25C2×#13063300C2211yescharacteristic
26C2×#13063299C2211yescharacteristic
27C2×#13063298C2212yes—
28C2×#13063297C2212yes—
29C2×#13063296C2211yescharacteristic
30#121×D43C4116yescomplemented
31C2×C4×D172C2212yescomplemented
32C2×D4×Dic43C2212yescomplemented
33C2×#13063287C2212yescomplemented
34C2×C4×C22⋊D43C2212yescomplemented
35C2×C4×C22⋊D43C2212yescomplemented
36C2×(C22⋊D43)⋊C4C2212yescomplemented
37C2×(C22⋊D43)⋊C4C2212yescomplemented
38C4×D4×D43—216no—
39C2×C4⋊C4×D43C2212yes—
40C2×C4⋊C4×D43C2211yescharacteristic
41C2×C22⋊C4×D43C2212yes—
42C2×C22⋊C4×D43C2211yescharacteristic
43C2×C22⋊C4×D43C2212yes—
44C2×C22⋊C4×D43C2212yes—
45C2×C22⋊C4×D43C2212yes—
46C2×C22⋊C4×D43C2211yescharacteristic
47C2×C42×D43C2212yes—
48C2×C42×D43C2212yes—
49#14582793C2212yescomplemented
50#14582792C2212yescomplemented
51#14582791C2212yescomplemented
52#14582790C2212yescomplemented
53#14582789C2212yescomplemented
54#14582788C2212yescomplemented
55#14582787C2212yescomplemented
56#14582786C2212yescomplemented
57#14582785C2212yescomplemented
58#14582784C2212yescomplemented
59#14582783C2212yescomplemented
60#14582782C2212yescomplemented
61#14582781C2212yescomplemented
62#14582780C2212yescomplemented
63#14582779C2212yescomplemented
64#14582779C2212yescomplemented
65#14582778C2212yescomplemented
66#14582778C2212yescomplemented
67#14582777C2212yescomplemented
68#14582777C2212yescomplemented
69#14582777C2212yescomplemented
70#14582777C2212yescomplemented
71#14582776C2212yescomplemented
72#14582776C2212yescomplemented
73#14582775C2212yescomplemented
74#14582775C2212yescomplemented
75#14582775C2212yescomplemented
76#14582775C2212yescomplemented
77C22⋊C4×Dic43C2212yescomplemented
78C22⋊C4×Dic43C2211yescharacteristic, complemented
79C22⋊C4×Dic43C2211yescharacteristic, complemented
80C22⋊C4×Dic43C2212yescomplemented
81C4×(C2×D43)⋊C4C2212yescomplemented
82C4×(C2×D43)⋊C4C2212yescomplemented
83C4×(C2×D43)⋊C4C2212yescomplemented
84C4×C22⋊Dic43C2212yescomplemented
85C4×C22⋊Dic43C2211yescharacteristic, complemented
86#14582746C2212yescomplemented
87#14582746C2212yescomplemented
88#14582746C2212yescomplemented
89C2×C43⋊#95C2212yescomplemented
90C2×C43⋊#95C2211yescharacteristic, complemented
91#95×D43C2211yescharacteristic
92#95×D43C2212yes—
93#95×D43C2211yescharacteristic
94#95×D43C2212yes—
95#95×D43C2212yes—
96#95×D43C2212yes—
97#95×D43C2211yescharacteristic, complemented
98#95×D43C2212yescomplemented
99#95×D43C2211yescharacteristic, complemented
100C2×#121×C43C2211yescharacteristic
101C2×C4×D4×C43C2212yescomplemented
102C43×#388C2212yescomplemented
103C43×#387C2212yescomplemented
104C43×#386C2212yescomplemented
105C43×#386C2212yescomplemented
106C4×C22⋊C4×C43C2211yescharacteristic, complemented
107C4×C22⋊C4×C43C2212yescomplemented
108C2×#95×C43C2211yescharacteristic, complemented
109C24×D43C2312yes—
110C24×D43C2311yescharacteristic
111C22×D172C2312yes—
112C22×D172C2311yescharacteristic
113C22×C22⋊D43C2312yes—
114C22×C22⋊D43C2312yes—
115C22×C22⋊D43C2312yes—
116C2×D4×D43—28no—
117C2×D4×D43—28no—
118C2×D4×D43—44no—
119C2×D4×D43C2×C4116yescomplemented
120C2×D4×D43C2×C418yescomplemented
121C23×Dic43C2312yes—
122C23×Dic43C2312yes—
123C23×Dic43C2311yescharacteristic
124C22×C4×D43—28no—
125C22×C4×D43—28no—
126C22×C4×D43—28no—
127C22×C4×D43—28no—
128C22×C4×D43—44no—
129C22×C4×D43—44no—
130C22×C4×D43—44no—
131C22×C4×D43C2×C418yescomplemented
132C22×C4×D43C2312yes—
133C22×C4×D43C2312yes—
134C22×C4×D43C2312yes—
135C22×C4×D43C2312yes—
136C22×C4×D43C2312yes—
137C22×C4×D43C2312yes—
138C22×C4×D43C2311yescharacteristic
139C22×C4×D43C2312yes—
140C22×C4×D43C2311yescharacteristic
141C22×C4×D43C2312yes—
142C22×C4×D43C2312yes—
143C22×C4×D43C2311yescharacteristic
144C22×C4×D43C2311yescharacteristic
145#13063300C2×C418yescomplemented
146#13063299C2×C418yescomplemented
147#13063298C2×C4116yescomplemented
148#13063297C2×C4116yescomplemented
149#13063296C2×C418yescomplemented
150C4×D172—28no—
151D4×Dic43—28no—
152#13063287—28no—
153C4×C22⋊D43—28no—
154C4×C22⋊D43—28no—
155(C22⋊D43)⋊C4—28no—
156(C22⋊D43)⋊C4—28no—
157C2×C4⋊Dic43C2312yes—
158C2×C4⋊Dic43C2311yescharacteristic
159C2×Dic43⋊C4C2312yes—
160C2×Dic43⋊C4C2312yes—
161C2×Dic43⋊C4C2312yes—
162C4⋊C4×D43—28no—
163C4⋊C4×D43C2×C418yescomplemented
164C2×C22⋊Dic43C2312yes—
165C2×C22⋊Dic43C2312yes—
166C2×C22⋊Dic43C2311yescharacteristic
167C2×C22⋊Dic43C2312yes—
168C2×C22⋊Dic43C2312yes—
169C2×C22⋊Dic43C2311yescharacteristic
170C2×(C2×D43)⋊C4C2312yes—
171C2×(C2×D43)⋊C4C2312yes—
172C2×(C2×D43)⋊C4C2312yes—
173C2×(C2×D43)⋊C4C2312yes—
174C2×(C2×D43)⋊C4C2312yes—
175C2×(C2×D43)⋊C4C2312yes—
176C2×(C2×D43)⋊C4C2312yes—
177C2×(C2×D43)⋊C4C2312yes—
178C2×(C2×D43)⋊C4C2312yes—
179C2×(C2×D43)⋊C4C2312yes—
180C22⋊C4×D43—24no—
181C22⋊C4×D43—28no—
182C22⋊C4×D43—28no—
183C22⋊C4×D43—44no—
184C22⋊C4×D43C2×C4116yescomplemented
185C22⋊C4×D43D418yescomplemented
186C2×C4×Dic43C2312yes—
187C2×C4×Dic43C2312yes—
188C2×C4×Dic43C2312yes—
189C2×C4×Dic43C2312yes—
190C2×C4×Dic43C2312yes—
191C2×C4×Dic43C2312yes—
192C42×D43—28no—
193C42×D43—44no—
194C43⋊#95C2312yes—
195C43⋊#95C2312yes—
196C43⋊#95C2312yes—
197C43⋊#95C2312yes—
198C43⋊#95C2312yes—
199C43⋊#95C2312yes—
200C43⋊#95C2312yes—
201C43⋊#95C2312yes—
202C43⋊#95C2312yes—
203C43⋊#95C2312yes—
204C43⋊#95C2311yescharacteristic
205C43⋊#95C2312yes—
206C43⋊#95C2311yescharacteristic
207C43⋊#95C2312yes—
208C43⋊#95C2312yes—
209C43⋊#95C2312yes—
210C22×D4×C43C2312yes—
211C22×D4×C43C2311yescharacteristic
212C23×C4×C43C2312yes—
213C23×C4×C43C2312yes—
214C23×C4×C43C2311yescharacteristic
215#121×C43C2×C418yescomplemented
216C4×D4×C43—28no—
217C2×C4⋊C4×C43C2312yes—
218C2×C4⋊C4×C43C2311yescharacteristic
219C2×C22⋊C4×C43C2312yes—
220C2×C22⋊C4×C43C2312yes—
221C2×C22⋊C4×C43C2311yescharacteristic
222C2×C22⋊C4×C43C2312yes—
223C2×C22⋊C4×C43C2312yes—
224C2×C22⋊C4×C43C2311yescharacteristic
225C2×C42×C43C2312yes—
226C2×C42×C43C2312yes—
227#95×C43C2312yes—
228#95×C43C2312yes—
229#95×C43C2311yescharacteristic
230#95×C43C2312yes—
231#95×C43C2311yescharacteristic
232#95×C43C2312yes—
233C24×C43C2412yes—
234C24×C43C2411yescharacteristic
235C23×D43—24no—
236C23×D43—24no—
237C23×D43—24no—
238C23×D43—24no—
239C23×D43—24no—
240C23×D43—24no—
241C23×D43—24no—
242C23×D43—24no—
243C23×D43C22×C418yes—
244C23×D43C22×C414yes—
245C23×D43C2×D414yes—
246C23×D43#4114yes—
247C23×D43C2412yes—
248C23×D43C2411yescharacteristic
249C23×D43C2411yescharacteristic
250C2×D4×C43—24no—
251C2×D4×C43—24no—
252C2×D4×C43—42no—
253C2×D4×C43C22×C418yescomplemented
254C2×D4×C43C22×C414yescomplemented
255C22×C4×C43—24no—
256C22×C4×C43—24no—
257C22×C4×C43—24no—
258C22×C4×C43—24no—
259C22×C4×C43—42no—
260C22×C4×C43—42no—
261C22×C4×C43—42no—
262C22×C4×C43C22×C414yescomplemented
263C22×C4×C43C2412yes—
264C22×C4×C43C2412yes—
265C22×C4×C43C2411yescharacteristic
266C22×C4×C43C2411yescharacteristic
267C22×C4×C43C2412yes—
268C22×C4×C43C2412yes—
269C22×C4×C43C2412yes—
270C2×C22⋊D43—24no—
271C2×C22⋊D43—24no—
272C2×C22⋊D43—24no—
273C2×C22⋊D43—24no—
274C2×C22⋊D43—42no—
275C2×C22⋊D43—42no—
276C2×C22⋊D43C22×C418yescomplemented
277C2×C22⋊D43C22×C418yescomplemented
278C2×C22⋊D43C22×C418yescomplemented
279C22×Dic43—24no—
280C22×Dic43—24no—
281C22×Dic43—24no—
282C22×Dic43—24no—
283C22×Dic43—42no—
284C22×Dic43—42no—
285C22×Dic43—42no—
286C22×Dic43C22×C414yescomplemented
287C22×Dic43C2412yes—
288C22×Dic43C2412yes—
289C22×Dic43C2411yescharacteristic
290C22×Dic43C2411yescharacteristic
291C22×Dic43C2412yes—
292C22×Dic43C2412yes—
293C22×Dic43C2412yes—
294D4×D43—264no—
295D4×D43—416no—
296C2×D172—24no—
297C2×D172—24no—
298C2×D172—42no—
299C2×D172C22×C418yescomplemented
300C2×D172C22×C414yescomplemented
301C2×C4×D43—24no—
302C2×C4×D43—24no—
303C2×C4×D43—24no—
304C2×C4×D43—24no—
305C2×C4×D43—24no—
306C2×C4×D43—24no—
307C2×C4×D43—24no—
308C2×C4×D43—24no—
309C2×C4×D43—24no—
310C2×C4×D43—24no—
311C2×C4×D43—24no—
312C2×C4×D43—24no—
313C2×C4×D43—24no—
314C2×C4×D43—24no—
315C2×C4×D43—24no—
316C2×C4×D43—24no—
317C2×C4×D43—24no—
318C2×C4×D43—24no—
319C2×C4×D43—24no—
320C2×C4×D43—24no—
321C2×C4×D43—24no—
322C2×C4×D43—24no—
323C2×C4×D43—416no—
324C2×C4×D43—432no—
325C2×C4×D43—42no—
326C2×C4×D43—42no—
327C2×C4×D43—42no—
328C2×C4×D43—42no—
329C2×C4×D43—42no—
330C2×C4×D43—42no—
331C2×C4×D43—432no—
332C2×C4×D43C22×C414yes—
333C2×C4×D43C22×C418yes—
334C2×C4×D43C22×C414yes—
335C2×C4×D43C22×C414yescomplemented
336C2×C4×D43C22×C414yescomplemented
337C2×C4×D43C2×D418yes—
338C2×C4×D43#4118yes—
339C4⋊C4×C43—24no—
340C4⋊C4×C43C22×C414yescomplemented
341C22⋊C4×C43—24no—
342C22⋊C4×C43—24no—
343C22⋊C4×C43—22no—
344C22⋊C4×C43—42no—
345C22⋊C4×C43C22×C418yescomplemented
346C22⋊C4×C43C2×D414yescomplemented
347C42×C43—24no—
348C42×C43—42no—
349C22⋊Dic43—24no—
350C22⋊Dic43—24no—
351C22⋊Dic43—22no—
352C22⋊Dic43—42no—
353C22⋊Dic43C22×C418yescomplemented
354C22⋊Dic43C2×D414yescomplemented
355(C2×D43)⋊C4—24no—
356(C2×D43)⋊C4—24no—
357(C2×D43)⋊C4—24no—
358(C2×D43)⋊C4—24no—
359(C2×D43)⋊C4—24no—
360(C2×D43)⋊C4—42no—
361(C2×D43)⋊C4—42no—
362(C2×D43)⋊C4C22×C418yescomplemented
363(C2×D43)⋊C4C22×C418yescomplemented
364(C2×D43)⋊C4C2×D418yescomplemented
365C4⋊Dic43—24no—
366C4⋊Dic43C22×C414yescomplemented
367Dic43⋊C4—24no—
368Dic43⋊C4—24no—
369Dic43⋊C4C22×C418yescomplemented
370C4×Dic43—24no—
371C4×Dic43—24no—
372C4×Dic43—24no—
373C4×Dic43—42no—
374C4×Dic43—42no—
375C4×Dic43—42no—
376C23×C43—22no—
377C23×C43—22no—
378C23×C43—22no—
379C23×C43—22no—
380C23×C43—22no—
381C23×C43—22no—
382C23×C43—22no—
383C23×C43—22no—
384C23×C43C23×C414yes—
385C23×C43C23×C412yes—
386C23×C43C22×D412yes—
387C23×C43C2×#4112yes—
388C23×C43C2511yescharacteristic
389C22×D43—22no—
390C22×D43—22no—
391C22×D43—28no—
392C22×D43—28no—
393C22×D43—216no—
394C22×D43—216no—
395C22×D43—22no—
396C22×D43—22no—
397C22×D43—22no—
398C22×D43—22no—
399C22×D43—22no—
400C22×D43—22no—
401C22×D43—216no—
402C22×D43—216no—
403C22×D43—216no—
404C22×D43—48no—
405C22×D43—48no—
406C22×D43—48no—
407C22×D43—48no—
408C22×D43C4×D4116yes—
409C22×D43C23×C414yes—
410C22×D43C23×C412yes—
411C22×D43C23×C412yes—
412C22×D43C22×D412yes—
413C22×D43C22×D412yes—
414C22×D43C2×#4112yes—
415C22×D43C2×#4112yes—
416C22×D43C2×#4114yes—
417C22×D43H(5,𝔽2)14yes—
418D4×C43—216no—
419D4×C43—44no—
420C2×C4×C43—22no—
421C2×C4×C43—22no—
422C2×C4×C43—22no—
423C2×C4×C43—22no—
424C2×C4×C43—22no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—22no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—22no—
434C2×C4×C43—44no—
435C2×C4×C43—48no—
436C2×C4×C43—48no—
437C2×C4×C43C23×C414yes—
438C2×C4×C43C23×C412yes—
439C2×C4×C43C23×C412yes—
440C2×C4×C43C22×D414yes—
441C2×C4×C43C2×#4114yes—
442C22⋊D43—216no—
443C22⋊D43—216no—
444C22⋊D43—48no—
445C2×Dic43—22no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—22no—
453C2×Dic43—22no—
454C2×Dic43—22no—
455C2×Dic43—22no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—44no—
460C2×Dic43—48no—
461C2×Dic43—48no—
462C2×Dic43C23×C412yes—
463C2×Dic43C23×C414yes—
464C2×Dic43C23×C412yes—
465C2×Dic43C22×D414yes—
466C2×Dic43C2×#4114yes—
467D172—216no—
468D172—44no—
469C4×D43—216no—
470C4×D43—28no—
471C4×D43—28no—
472C4×D43—216no—
473C4×D43—216no—
474C4×D43—44no—
475C4×D43—44no—
476C4×D43—48no—
477C4×D43—48no—
478C4×D43—48no—
479C4×D43—48no—
480C4×D43—48no—
481C4×D43—48no—
482C2×#2364—431nomaximal, Sylow
483C22×C43—22no—
484C22×C43—22no—
485C22×C43—24no—
486C22×C43—24no—
487C22×C43—24no—
488C22×C43—24no—
489C22×C43—24no—
490C22×C43—42no—
491C22×C43—42no—
492C22×C43—42no—
493C22×C43—42no—
494C22×C43C2×C4×D414yes—
495C22×C43C24×C411yescharacteristic
496C22×C43C23×D411yescharacteristic
497C22×C43C22×#4111yescharacteristic
498C22×C43C22×#4112yes—
499C22×C43C2×H(5,𝔽2)12yes—
500C2×D43—22no—
501C2×D43—22no—
502C2×D43—24no—
503C2×D43—24no—
504C2×D43—232no—
505C2×D43—24no—
506C2×D43—24no—
507C2×D43—24no—
508C2×D43—42no—
509C2×D43—42no—
510C2×D43—42no—
511C2×D43—42no—
512C2×D43—432no—
513C2×D43C2×C4×D414yes—
514C2×D43C2×C4×D414yes—
515C2×D43C4×#4114yes—
516C2×D43#51814yes—
517C2×D43#54618yes—
518C2×D43#55318yes—
519C4×C43—24no—
520C4×C43—22no—
521C4×C43—22no—
522C4×C43—24no—
523C4×C43—24no—
524C4×C43—42no—
525C4×C43—42no—
526Dic43—24no—
527Dic43—22no—
528Dic43—22no—
529Dic43—24no—
530Dic43—24no—
531Dic43—42no—
532Dic43—42no—
533C22×#121—431no—
534C22×C4×D4—432no—
535#2364—432no—
536#2364—432no—
537#2364—432no—
538#2364—432no—
539#2364—431no—
540#2364—432no—
541#2364—431no—
542#2364—431no—
543#2364—432no—
544#2364D4311yescharacteristic, direct product factor
545C2×#388—432no—
546C2×#387—432no—
547C2×#386—432no—
548C2×#386—432no—
549C2×C4×C22⋊C4—431no—
550C2×C4×C22⋊C4—432no—
551C22×#95—431no—
552C2×C43—24no—
553C2×C43—44no—
554C2×C43C22×C4×D411yescharacteristic
555C2×C43C2×C4×#4111yescharacteristic
556C2×C43C2×#51811yescharacteristic
557C2×C43C2×#54612yes—
558C2×C43C2×#55312yes—
559D43—24no—
560D43—44no—
561D43#236418yesdirect product factor
562C23×D4—432no—
563C23×D4—431no—
564C24×C4—431no—
565C24×C4—432no—
566C24×C4—432no—
567C2×#121—431no—
568C2×#121—432no—
569C2×#121—431no—
570C2×#121—4316no—
571C2×#121—431no—
572C2×#121—432no—
573C2×#121C2×D4311yescharacteristic
574C2×C4×D4—432no—
575C2×C4×D4—432no—
576C2×C4×D4—432no—
577C2×C4×D4—432no—
578C2×C4×D4—432no—
579C2×C4×D4—432no—
580C2×C4×D4—432no—
581C2×C4×D4—8616no—
582C2×C4×D4C2×D4312yescomplemented
583C22×C4⋊C4—431no—
584C22×C4⋊C4—432no—
585C22×C22⋊C4—431no—
586C22×C22⋊C4—432no—
587C22×C22⋊C4—432no—
588C22×C22⋊C4—432no—
589C22×C22⋊C4—431no—
590C22×C22⋊C4—432no—
591C22×C42—432no—
592C22×C42—432no—
593#388—432no—
594#388—432no—
595#388—432no—
596#388—432no—
597#388—432no—
598#388—432no—
599#388—432no—
600#388C2×D4312yescomplemented
601#387—432no—
602#387—432no—
603#387—432no—
604#387—432no—
605#387—432no—
606#387—432no—
607#387—432no—
608#387C2×D4312yescomplemented
609#386—432no—
610#386—432no—
611#386—432no—
612#386—432no—
613#386—432no—
614#386—432no—
615#386—432no—
616#386—432no—
617#386—432no—
618#386—432no—
619#386—432no—
620#386—432no—
621#386—432no—
622#386—432no—
623#386C2×D4312yescomplemented
624#386C2×D4312yescomplemented
625C4×C22⋊C4—432no—
626C4×C22⋊C4—431no—
627C4×C22⋊C4—432no—
628C4×C22⋊C4—432no—
629C4×C22⋊C4—431no—
630C4×C22⋊C4—431no—
631C4×C22⋊C4—432no—
632C4×C22⋊C4—432no—
633C4×C22⋊C4—432no—
634C4×C22⋊C4—432no—
635C4×C22⋊C4—432no—
636C4×C22⋊C4—432no—
637C4×C22⋊C4C2×D4312yescomplemented
638C4×C22⋊C4C2×D4311yescharacteristic, complemented
639C2×#95—432no—
640C2×#95—431no—
641C2×#95—431no—
642C2×#95—432no—
643C2×#95—431no—
644C2×#95—431no—
645C2×#95—432no—
646C2×#95—431no—
647C2×#95—432no—
648C2×#95—432no—
649C2×#95—432no—
650C2×#95C2×D4311yescharacteristic, complemented
651C43C2×#236411yescharacteristic, complemented, Sylow
652C25—431no—
653C25—432no—
654C22×D4—432no—
655C22×D4—432no—
656C22×D4—432no—
657C22×D4—4316no—
658C22×D4—438no—
659C22×D4—432no—
660C22×D4—431no—
661C22×D4—868no—
662C22×D4—868no—
663C22×D4—1724no—
664C22×D4C22×D4312yes—
665C22×D4C22×D4311yescharacteristic
666C23×C4—431no—
667C23×C4—432no—
668C23×C4—431no—
669C23×C4—432no—
670C23×C4—432no—
671C23×C4—431no—
672C23×C4—438no—
673C23×C4—431no—
674C23×C4—431no—
675C23×C4—432no—
676C23×C4—432no—
677C23×C4—432no—
678C23×C4—432no—
679C23×C4—432no—
680C23×C4—432no—
681C23×C4—432no—
682C23×C4—432no—
683C23×C4—868no—
684C23×C4—868no—
685C23×C4—868no—
686C23×C4—868no—
687C23×C4—1724no—
688C23×C4—1724no—
689C23×C4—1724no—
690C23×C4C22×D4312yes—
691C23×C4C22×D4312yes—
692C23×C4C22×D4311yescharacteristic
693#121—438no—
694#121—4316no—
695#121—438no—
696#121—438no—
697#121—4316no—
698#121C4×D4318yescomplemented
699C4×D4—28no—
700C4×D4—868no—
701C4×D4—868no—
702C4×D4—868no—
703C4×D4—868no—
704C4×D4—868no—
705C4×D4—868no—
706C4×D4—868no—
707C2×C4⋊C4—432no—
708C2×C4⋊C4—431no—
709C2×C4⋊C4—438no—
710C2×C4⋊C4—432no—
711C2×C4⋊C4—432no—
712C2×C4⋊C4—432no—
713C2×C4⋊C4—868no—
714C2×C4⋊C4C22×D4312yes—
715C2×C4⋊C4C22×D4311yescharacteristic
716C2×C22⋊C4—431no—
717C2×C22⋊C4—432no—
718C2×C22⋊C4—432no—
719C2×C22⋊C4—432no—
720C2×C22⋊C4—432no—
721C2×C22⋊C4—4316no—
722C2×C22⋊C4—438no—
723C2×C22⋊C4—432no—
724C2×C22⋊C4—432no—
725C2×C22⋊C4—431no—
726C2×C22⋊C4—432no—
727C2×C22⋊C4—432no—
728C2×C22⋊C4—432no—
729C2×C22⋊C4—432no—
730C2×C22⋊C4—432no—
731C2×C22⋊C4—432no—
732C2×C22⋊C4—432no—
733C2×C22⋊C4—432no—
734C2×C22⋊C4—868no—
735C2×C22⋊C4—868no—
736C2×C22⋊C4—864no—
737C2×C22⋊C4—1724no—
738C2×C22⋊C4C22×D4312yes—
739C2×C22⋊C4C22×D4311yescharacteristic
740C2×C22⋊C4C22×D4312yes—
741C2×C22⋊C4C22×D4312yes—
742C2×C22⋊C4C22×D4312yes—
743C2×C22⋊C4C22×D4311yescharacteristic
744C2×C42—432no—
745C2×C42—432no—
746C2×C42—432no—
747C2×C42—432no—
748C2×C42—432no—
749C2×C42—432no—
750C2×C42—868no—
751C2×C42—1724no—
752C2×C42C22×D4312yes—
753C2×C42C22×D4312yes—
754#95—431no—
755#95—432no—
756#95—432no—
757#95—432no—
758#95—432no—
759#95—432no—
760#95—431no—
761#95—432no—
762#95—432no—
763#95—432no—
764#95—432no—
765#95—432no—
766#95—432no—
767#95—432no—
768#95—432no—
769#95—432no—
770#95C22×D4311yescharacteristic
771#95C22×D4312yes—
772#95C22×D4311yescharacteristic
773#95C22×D4312yes—
774#95C22×D4312yes—
775#95C22×D4312yes—
776C24—431no—
777C24—434no—
778C24—434no—
779C24—434no—
780C24—431no—
781C24—438no—
782C24—432no—
783C24—864no—
784C24—864no—
785C24—864no—
786C24—864no—
787C24—864no—
788C24—864no—
789C24—864no—
790C24—864no—
791C24C23×D4312yes—
792C24C23×D4311yescharacteristic
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—42no—
796C2×D4—438no—
797C2×D4—438no—
798C2×D4—438no—
799C2×D4—438no—
800C2×D4—434no—
801C2×D4—864no—
802C2×D4—864no—
803C2×D4—8664no—
804C2×D4—864no—
805C2×D4—864no—
806C2×D4—864no—
807C2×D4—864no—
808C2×D4—1722no—
809C2×D4—17216no—
810C2×D4—1722no—
811C2×D4—1722no—
812C2×D4C2×C4×D4318yescomplemented
813C2×D4C2×C4×D4314yescomplemented
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—431no—
822C22×C4—432no—
823C22×C4—431no—
824C22×C4—432no—
825C22×C4—432no—
826C22×C4—434no—
827C22×C4—434no—
828C22×C4—438no—
829C22×C4—434no—
830C22×C4—438no—
831C22×C4—438no—
832C22×C4—434no—
833C22×C4—434no—
834C22×C4—432no—
835C22×C4—432no—
836C22×C4—864no—
837C22×C4—864no—
838C22×C4—864no—
839C22×C4—864no—
840C22×C4—864no—
841C22×C4—864no—
842C22×C4—864no—
843C22×C4—864no—
844C22×C4—864no—
845C22×C4—864no—
846C22×C4—864no—
847C22×C4—864no—
848C22×C4—864no—
849C22×C4—864no—
850C22×C4—864no—
851C22×C4—864no—
852C22×C4—864no—
853C22×C4—864no—
854C22×C4—864no—
855C22×C4—864no—
856C22×C4—864no—
857C22×C4—864no—
858C22×C4—864no—
859C22×C4—864no—
860C22×C4—864no—
861C22×C4—864no—
862C22×C4—1722no—
863C22×C4—1722no—
864C22×C4—1722no—
865C22×C4—1722no—
866C22×C4—1722no—
867C22×C4—1722no—
868C22×C4—17216no—
869C22×C4—17232no—
870C22×C4—17232no—
871C22×C4—1722no—
872C22×C4—1722no—
873C22×C4—1722no—
874C22×C4C2×C4×D4314yescomplemented
875C22×C4C23×D4312yes—
876C22×C4C23×D4312yes—
877C22×C4C23×D4311yescharacteristic
878C22×C4C23×D4311yescharacteristic
879C22×C4C23×D4312yes—
880C22×C4C23×D4312yes—
881C22×C4C23×D4312yes—
882C4⋊C4—24no—
883C4⋊C4—438no—
884C4⋊C4—434no—
885C4⋊C4—864no—
886C4⋊C4—864no—
887C4⋊C4—864no—
888C4⋊C4C2×C4×D4314yescomplemented
889C22⋊C4—22no—
890C22⋊C4—24no—
891C22⋊C4—24no—
892C22⋊C4—42no—
893C22⋊C4—438no—
894C22⋊C4—434no—
895C22⋊C4—438no—
896C22⋊C4—438no—
897C22⋊C4—438no—
898C22⋊C4—864no—
899C22⋊C4—864no—
900C22⋊C4—864no—
901C22⋊C4—864no—
902C22⋊C4—864no—
903C22⋊C4—862no—
904C22⋊C4—864no—
905C22⋊C4—864no—
906C22⋊C4—1722no—
907C22⋊C4—1722no—
908C22⋊C4—1722no—
909C22⋊C4C2×C4×D4318yescomplemented
910C22⋊C4D4×D4314yescomplemented
911C42—24no—
912C42—42no—
913C42—864no—
914C42—864no—
915C42—864no—
916C42—1722no—
917C42—1722no—
918C42—1722no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—432no—
928C23—432no—
929C23—434no—
930C23—432no—
931C23—434no—
932C23—4316no—
933C23—432no—
934C23—432no—
935C23—432no—
936C23—434no—
937C23—868no—
938C23—8616no—
939C23—8616no—
940C23—868no—
941C23—8616no—
942C23—8616no—
943C23—8616no—
944C23—862no—
945C23—862no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—862no—
950C23—862no—
951C23—862no—
952C23—1728no—
953C23—1728no—
954C23—1728no—
955C23—1728no—
956C23C22×C4×D4314yes—
957C23C22×C4×D4312yes—
958C23C2×D4×D4312yes—
959C23#41×D4312yes—
960C23C24×D4311yescharacteristic
961D4—216no—
962D4—44no—
963D4—8616no—
964D4—8616no—
965D4—8616no—
966D4—1724no—
967D4—1728no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—44no—
983C2×C4—48no—
984C2×C4—48no—
985C2×C4—432no—
986C2×C4—434no—
987C2×C4—432no—
988C2×C4—434no—
989C2×C4—434no—
990C2×C4—8616no—
991C2×C4—868no—
992C2×C4—868no—
993C2×C4—8616no—
994C2×C4—8616no—
995C2×C4—862no—
996C2×C4—862no—
997C2×C4—862no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—862no—
1002C2×C4—862no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—862no—
1006C2×C4—862no—
1007C2×C4—862no—
1008C2×C4—862no—
1009C2×C4—1724no—
1010C2×C4—1724no—
1011C2×C4—1728no—
1012C2×C4—1728no—
1013C2×C4—1728no—
1014C2×C4—1728no—
1015C2×C4—1728no—
1016C2×C4—1728no—
1017C2×C4—1724no—
1018C2×C4—1728no—
1019C2×C4—1728no—
1020C2×C4C22×C4×D4312yes—
1021C2×C4C22×C4×D4314yes—
1022C2×C4C22×C4×D4312yes—
1023C2×C4C2×D4×D4314yes—
1024C2×C4#41×D4314yes—
1025C22—22no—
1026C22—24no—
1027C22—24no—
1028C22—22no—
1029C22—24no—
1030C22—24no—
1031C22—24no—
1032C22—42no—
1033C22—42no—
1034C22—42no—
1035C22—42no—
1036C22—434no—
1037C22—438no—
1038C22—438no—
1039C22—434no—
1040C22—434no—
1041C22—434no—
1042C22—8632no—
1043C22—862no—
1044C22—864no—
1045C22—864no—
1046C22—862no—
1047C22—864no—
1048C22—864no—
1049C22—864no—
1050C22—17232no—
1051C22—1722no—
1052C22—1722no—
1053C22—1722no—
1054C22—1722no—
1055C22C4×D4×D4314yes—
1056C22C23×C4×D4311yescharacteristic
1057C22C22×D4×D4311yescharacteristic
1058C22C2×#41×D4312yes—
1059C22C2×#41×D4311yescharacteristic
1060C22H(5,𝔽2)×D4312yes—
1061C4—22no—
1062C4—22no—
1063C4—24no—
1064C4—24no—
1065C4—24no—
1066C4—42no—
1067C4—42no—
1068C4—862no—
1069C4—862no—
1070C4—864no—
1071C4—864no—
1072C4—864no—
1073C4—1722no—
1074C4—1722no—
1075C2—24no—
1076C2—44no—
1077C2—438no—
1078C2—864no—
1079C2—1724no—
1080C2C2×C4×D4×D4311yescharacteristic
1081C2C4×#41×D4311yescharacteristic
1082C2#518×D4311yescharacteristic
1083C2#546×D4312yes—
1084C2#553×D4312yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2364C2
socle, cosocleC23×C43C25
prime radicalC2×#121×D43C2
hypercenter#2364D43
hypocenterC43C2×#2364
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2364

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×D43C2semidirect
3. #19137647C2semidirect
4. #19137646C2semidirect
5. #19137645C2semidirect
6. #19137644C2semidirect
7. #19137643C2semidirect
8. #19137642C2semidirect
9. #19137641C2semidirect
10. #19137640C2semidirect
11. #19137639C2semidirect
12. #388×D43C2semidirect
13. #387×D43C2semidirect
14. #386×D43C2semidirect
15. #386×D43C2semidirect
16. C4×C22⋊C4×D43C2semidirect
17. C4×C22⋊C4×D43C2semidirect
18. C2×#95×D43C2semidirect
19. C43×#2364C2semidirect
30. #121×D43C4semidirect
31. C2×C4×D172C22semidirect
32. C2×D4×Dic43C22semidirect
33. C2×#13063287C22semidirect
34. C2×C4×C22⋊D43C22semidirect
35. C2×C4×C22⋊D43C22semidirect
36. C2×(C22⋊D43)⋊C4C22semidirect
37. C2×(C22⋊D43)⋊C4C22semidirect
49. #14582793C22semidirect
50. #14582792C22semidirect
51. #14582791C22semidirect
52. #14582790C22semidirect
53. #14582789C22semidirect
54. #14582788C22semidirect
55. #14582787C22semidirect
56. #14582786C22semidirect
57. #14582785C22semidirect
58. #14582784C22semidirect
59. #14582783C22semidirect
60. #14582782C22semidirect
61. #14582781C22semidirect
62. #14582780C22semidirect
63. #14582779C22semidirect
64. #14582779C22semidirect
65. #14582778C22semidirect
66. #14582778C22semidirect
67. #14582777C22semidirect
68. #14582777C22semidirect
69. #14582777C22semidirect
70. #14582777C22semidirect
71. #14582776C22semidirect
72. #14582776C22semidirect
73. #14582775C22semidirect
74. #14582775C22semidirect
75. #14582775C22semidirect
76. #14582775C22semidirect
77. C22⋊C4×Dic43C22semidirect
78. C22⋊C4×Dic43C22semidirect
79. C22⋊C4×Dic43C22semidirect
80. C22⋊C4×Dic43C22semidirect
81. C4×(C2×D43)⋊C4C22semidirect
82. C4×(C2×D43)⋊C4C22semidirect
83. C4×(C2×D43)⋊C4C22semidirect
84. C4×C22⋊Dic43C22semidirect
85. C4×C22⋊Dic43C22semidirect
86. #14582746C22semidirect
87. #14582746C22semidirect
88. #14582746C22semidirect
89. C2×C43⋊#95C22semidirect
90. C2×C43⋊#95C22semidirect
97. #95×D43C22semidirect
98. #95×D43C22semidirect
99. #95×D43C22semidirect
101. C2×C4×D4×C43C22semidirect
102. C43×#388C22semidirect
103. C43×#387C22semidirect
104. C43×#386C22semidirect
105. C43×#386C22semidirect
106. C4×C22⋊C4×C43C22semidirect
107. C4×C22⋊C4×C43C22semidirect
108. C2×#95×C43C22semidirect
119. C2×D4×D43C2×C4semidirect
120. C2×D4×D43C2×C4semidirect
131. C22×C4×D43C2×C4semidirect
145. #13063300C2×C4semidirect
146. #13063299C2×C4semidirect
147. #13063298C2×C4semidirect
148. #13063297C2×C4semidirect
149. #13063296C2×C4semidirect
163. C4⋊C4×D43C2×C4semidirect
184. C22⋊C4×D43C2×C4semidirect
185. C22⋊C4×D43D4semidirect
215. #121×C43C2×C4semidirect
253. C2×D4×C43C22×C4semidirect
254. C2×D4×C43C22×C4semidirect
262. C22×C4×C43C22×C4semidirect
276. C2×C22⋊D43C22×C4semidirect
277. C2×C22⋊D43C22×C4semidirect
278. C2×C22⋊D43C22×C4semidirect
286. C22×Dic43C22×C4semidirect
299. C2×D172C22×C4semidirect
300. C2×D172C22×C4semidirect
335. C2×C4×D43C22×C4semidirect
336. C2×C4×D43C22×C4semidirect
340. C4⋊C4×C43C22×C4semidirect
345. C22⋊C4×C43C22×C4semidirect
346. C22⋊C4×C43C2×D4semidirect
353. C22⋊Dic43C22×C4semidirect
354. C22⋊Dic43C2×D4semidirect
362. (C2×D43)⋊C4C22×C4semidirect
363. (C2×D43)⋊C4C22×C4semidirect
364. (C2×D43)⋊C4C2×D4semidirect
366. C4⋊Dic43C22×C4semidirect
369. Dic43⋊C4C22×C4semidirect
544. #2364D43direct (N × H)
561. D43#2364direct (N × H)
582. C2×C4×D4C2×D43semidirect
600. #388C2×D43semidirect
608. #387C2×D43semidirect
623. #386C2×D43semidirect
624. #386C2×D43semidirect
637. C4×C22⋊C4C2×D43semidirect
638. C4×C22⋊C4C2×D43semidirect
650. C2×#95C2×D43semidirect
651. C43C2×#2364semidirect
698. #121C4×D43semidirect
812. C2×D4C2×C4×D43semidirect
813. C2×D4C2×C4×D43semidirect
874. C22×C4C2×C4×D43semidirect
888. C4⋊C4C2×C4×D43semidirect
909. C22⋊C4C2×C4×D43semidirect
910. 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
#191376472
#191376462
#191376452
#191376442
#191376432
#191376422
#191376412
#191376402
#191376392
#388×D432
#387×D432
#386×D432
C4×C22⋊C4×D432
C2×#95×D432
C43×#23642
C2×#236443