Finite Group Databasebeta

← D43×#2429 #25264609

Subgroups — D43×#2429 #25264609

Order 11008.

3246 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
2C2×C22⋊Q8×D43C211yesmaximal, characteristic
3C2×C22⋊Q8×D43C211yesmaximal, characteristic
4C2×C4×Q8×D43C211yesmaximal, characteristic, complemented
5#19138197C211yesmaximal, characteristic, complemented
6#19138196C211yesmaximal, characteristic, complemented
7#19138195C211yesmaximal, characteristic, complemented
8#19138194C211yesmaximal, characteristic, complemented
9#19138193C212yesmaximal, complemented
10#19138192C211yesmaximal, characteristic, complemented
11#19138191C212yesmaximal, complemented
12#19138190C211yesmaximal, characteristic, complemented
13#19138189C212yesmaximal, complemented
14#19138188C211yesmaximal, characteristic, complemented
15#19138187C212yesmaximal, complemented
16#398×D43C212yesmaximal, complemented
17#396×D43C212yesmaximal
18#391×D43C211yesmaximal, characteristic, complemented
19#389×D43C211yesmaximal, characteristic, complemented
20#389×D43C212yesmaximal, complemented
21#388×D43C212yesmaximal
22C4×C22⋊C4×D43C211yesmaximal, characteristic
23C43×#2429C211yesmaximal, characteristic, complemented
24C22×Q8×D43C2211yescharacteristic
25C22×Q8×D43C2211yescharacteristic
26C23×C4×D43C2211yescharacteristic
27C2×#13063325C2211yescharacteristic, complemented
28C2×#13063324C2212yescomplemented
29C2×#13063324C2212yescomplemented
30C2×#13063323C2211yescharacteristic, complemented
31C2×#13063323C2211yescharacteristic, complemented
32C4⋊Q8×D43—28no—
33C2×#13063305C2211yescharacteristic
34C2×#13063305C2211yescharacteristic
35C2×#13063304C2211yescharacteristic
36C2×#13063304C2211yescharacteristic
37C2×#13063303C2212yes—
38C2×#13063303C2212yes—
39C2×#13063302C2212yes—
40C2×#13063302C2212yes—
41C2×#13063301C2211yescharacteristic
42C2×#13063301C2211yescharacteristic
43C22⋊Q8×D43—28no—
44C22⋊Q8×D43—28no—
45C2×Q8×Dic43C2211yescharacteristic, complemented
46C2×C4×Dic86C2212yescomplemented
47C2×C4×Dic86C2211yescharacteristic, complemented
48C2×#13063290C2212yescomplemented
49C2×#13063290C2211yescharacteristic, complemented
50C4×Q8×D43—28no—
51C2×C4⋊C4×D43C2212yes—
52C2×C4⋊C4×D43C2212yes—
53C2×C4⋊C4×D43C2212yes—
54C2×C4⋊C4×D43C2212yes—
55C2×C4⋊C4×D43C2211yescharacteristic
56C2×C4⋊C4×D43C2212yes—
57C2×C4⋊C4×D43C2212yes—
58C2×C4⋊C4×D43C2211yescharacteristic
59C2×C22⋊C4×D43C2211yescharacteristic
60C2×C22⋊C4×D43C2212yes—
61C2×C22⋊C4×D43C2212yes—
62C2×C22⋊C4×D43C2211yescharacteristic
63C2×C42×D43C2211yescharacteristic
64C2×C42×D43C2212yes—
65C2×C42×D43C2211yescharacteristic
66#14582833C2212yescomplemented
67#14582833C2212yescomplemented
68#14582832C2212yescomplemented
69#14582832C2212yescomplemented
70#14582831C2212yescomplemented
71#14582830C2212yescomplemented
72#14582829C2212yescomplemented
73#14582823C2212yes—
74#14582822C2212yes—
75#14582822C2212yes—
76#14582822C2212yes—
77#14582821C2212yes—
78#14582821C2212yes—
79#14582821C2212yes—
80#14582806C2211yescharacteristic, complemented
81#14582805C2211yescharacteristic, complemented
82#14582804C2211yescharacteristic, complemented
83#14582803C2212yescomplemented
84#14582803C2212yescomplemented
85#14582798C2212yescomplemented
86#14582798C2211yescharacteristic, complemented
87#14582797C2212yescomplemented
88#14582797C2211yescharacteristic, complemented
89#14582796C2212yescomplemented
90#14582796C2212yescomplemented
91#14582796C2212yescomplemented
92#14582795C2212yescomplemented
93#14582795C2211yescharacteristic, complemented
94#14582794C2212yescomplemented
95#14582794C2212yescomplemented
96#14582794C2212yescomplemented
97#14582793C2212yes—
98#14582792C2212yes—
99#14582791C2212yes—
100#14582790C2212yes—
101#14582789C2212yes—
102#14582788C2212yes—
103#14582787C2212yes—
104C22⋊C4×Dic43C2211yescharacteristic
105C22⋊C4×Dic43C2211yescharacteristic
106C4×(C2×D43)⋊C4C2211yescharacteristic
107C4×(C2×D43)⋊C4C2211yescharacteristic
108C4×C22⋊Dic43C2211yescharacteristic
109#14582746C2211yescharacteristic
110#14582746C2211yescharacteristic
111#95×D43C2211yescharacteristic
112#95×D43C2212yes—
113#95×D43C2212yes—
114#95×D43C2212yes—
115#95×D43C2211yescharacteristic
116C2×C4⋊Q8×C43C2211yescharacteristic, complemented
117C2×C22⋊Q8×C43C2211yescharacteristic
118C2×C22⋊Q8×C43C2211yescharacteristic
119C2×C4×Q8×C43C2211yescharacteristic, complemented
120C43×#398C2212yescomplemented
121C43×#396C2212yes—
122C43×#391C2211yescharacteristic, complemented
123C43×#389C2211yescharacteristic, complemented
124C43×#389C2212yescomplemented
125C43×#388C2212yes—
126C4×C22⋊C4×C43C2211yescharacteristic
127C24×D43C2311yescharacteristic
128C22×Dic86C2312yes—
129C22×Dic86C2311yescharacteristic
130C22×Dic86C2312yes—
131C22×Dic86C2311yescharacteristic
132C2×Q8×D43—24no—
133C2×Q8×D43—24no—
134C2×Q8×D43—24no—
135C2×Q8×D43—24no—
136C2×Q8×D43—24no—
137C2×Q8×D43D418yes—
138C23×Dic43C2311yescharacteristic
139C22×C4×D43—24no—
140C22×C4×D43—24no—
141C22×C4×D43—24no—
142C22×C4×D43C2311yescharacteristic
143C22×C4×D43C2312yes—
144C22×C4×D43C2312yes—
145C22×C4×D43C2311yescharacteristic
146C22×C4×D43C2311yescharacteristic
147C22×C4×D43C2311yescharacteristic
148C22×C4×D43C2312yes—
149C22×C4×D43C2312yes—
150C22×C4×D43C2311yescharacteristic
151C22×C4×D43C2311yescharacteristic
152C22×C4×D43C2311yescharacteristic
153C22×C4×D43C2311yescharacteristic
154#13063325—24no—
155#13063324—28no—
156#13063324—28no—
157#13063323—24no—
158#13063323—24no—
159#13063305—24no—
160#13063305—24no—
161#13063304—24no—
162#13063304—24no—
163#13063303—28no—
164#13063303—28no—
165#13063302—28no—
166#13063302—28no—
167#13063301—24no—
168#13063301—24no—
169Q8×Dic43—24no—
170C4×Dic86—24no—
171C4×Dic86—28no—
172#13063290—24no—
173#13063290—28no—
174C2×C4⋊Dic43C2312yes—
175C2×C4⋊Dic43C2312yes—
176C2×C4⋊Dic43C2312yes—
177C2×C4⋊Dic43C2312yes—
178C2×C4⋊Dic43C2311yescharacteristic
179C2×C4⋊Dic43C2312yes—
180C2×C4⋊Dic43C2312yes—
181C2×C4⋊Dic43C2311yescharacteristic
182C2×Dic43⋊C4C2312yes—
183C2×Dic43⋊C4C2312yes—
184C2×Dic43⋊C4C2312yes—
185C2×Dic43⋊C4C2312yes—
186C2×Dic43⋊C4C2312yes—
187C2×Dic43⋊C4C2312yes—
188C2×Dic43⋊C4C2312yes—
189C2×Dic43⋊C4C2312yes—
190C2×Dic43⋊C4C2312yes—
191C2×Dic43⋊C4C2312yes—
192C2×Dic43⋊C4C2312yes—
193C2×Dic43⋊C4C2312yes—
194C2×Dic43⋊C4C2312yes—
195C2×Dic43⋊C4C2312yes—
196C4⋊C4×D43—28no—
197C4⋊C4×D43—28no—
198C4⋊C4×D43—28no—
199C4⋊C4×D43—24no—
200C4⋊C4×D43—28no—
201C4⋊C4×D43—28no—
202C4⋊C4×D43—28no—
203C4⋊C4×D43D418yes—
204C2×C22⋊Dic43C2312yes—
205C2×C22⋊Dic43C2312yes—
206C2×C22⋊Dic43C2311yescharacteristic
207C2×C22⋊Dic43C2311yescharacteristic
208C2×(C2×D43)⋊C4C2312yes—
209C2×(C2×D43)⋊C4C2312yes—
210C2×(C2×D43)⋊C4C2312yes—
211C2×(C2×D43)⋊C4C2312yes—
212C2×(C2×D43)⋊C4C2311yescharacteristic
213C2×(C2×D43)⋊C4C2311yescharacteristic
214C2×(C2×D43)⋊C4C2311yescharacteristic
215C2×(C2×D43)⋊C4C2311yescharacteristic
216C22⋊C4×D43—28no—
217C22⋊C4×D43—28no—
218C22⋊C4×D43—24no—
219C22⋊C4×D43Q818yescomplemented
220C2×C4×Dic43C2312yes—
221C2×C4×Dic43C2312yes—
222C2×C4×Dic43C2312yes—
223C2×C4×Dic43C2311yescharacteristic
224C2×C4×Dic43C2311yescharacteristic
225C2×C4×Dic43C2311yescharacteristic
226C2×C4×Dic43C2311yescharacteristic
227C2×C4×Dic43C2311yescharacteristic
228C2×C4×Dic43C2311yescharacteristic
229C42×D43—28no—
230C42×D43—24no—
231C42×D43—24no—
232C43⋊#95C2312yes—
233C43⋊#95C2312yes—
234C43⋊#95C2312yes—
235C43⋊#95C2312yes—
236C43⋊#95C2312yes—
237C43⋊#95C2312yes—
238C43⋊#95C2311yescharacteristic
239C43⋊#95C2311yescharacteristic
240C43⋊#95C2311yescharacteristic
241C43⋊#95C2312yes—
242C43⋊#95C2312yes—
243C43⋊#95C2312yes—
244C43⋊#95C2311yescharacteristic
245C43⋊#95C2311yescharacteristic
246C43⋊#95C2311yescharacteristic
247C22×Q8×C43C2311yescharacteristic
248C22×Q8×C43C2311yescharacteristic
249C23×C4×C43C2311yescharacteristic
250C4⋊Q8×C43—24no—
251C22⋊Q8×C43—24no—
252C22⋊Q8×C43—24no—
253C4×Q8×C43—24no—
254C2×C4⋊C4×C43C2312yes—
255C2×C4⋊C4×C43C2312yes—
256C2×C4⋊C4×C43C2312yes—
257C2×C4⋊C4×C43C2312yes—
258C2×C4⋊C4×C43C2311yescharacteristic
259C2×C4⋊C4×C43C2312yes—
260C2×C4⋊C4×C43C2312yes—
261C2×C4⋊C4×C43C2311yescharacteristic
262C2×C22⋊C4×C43C2312yes—
263C2×C22⋊C4×C43C2312yes—
264C2×C22⋊C4×C43C2311yescharacteristic
265C2×C22⋊C4×C43C2311yescharacteristic
266C2×C42×C43C2312yes—
267C2×C42×C43C2311yescharacteristic
268C2×C42×C43C2311yescharacteristic
269#95×C43C2312yes—
270#95×C43C2312yes—
271#95×C43C2311yescharacteristic
272#95×C43C2312yes—
273#95×C43C2311yescharacteristic
274C24×C43C2411yescharacteristic
275C23×D43—22no—
276C23×D43—22no—
277C23×D43—22no—
278C23×D43—22no—
279C23×D43—22no—
280C23×D43—22no—
281C23×D43C2×Q814yes—
282C23×D43C2411yescharacteristic
283C23×D43C2411yescharacteristic
284C2×Q8×C43—22no—
285C2×Q8×C43—22no—
286C2×Q8×C43—22no—
287C2×Q8×C43—22no—
288C2×Q8×C43—22no—
289C2×Q8×C43C2×D414yes—
290C22×C4×C43—22no—
291C22×C4×C43—22no—
292C22×C4×C43—22no—
293C22×C4×C43C2411yescharacteristic
294C22×C4×C43C2412yes—
295C22×C4×C43C2412yes—
296C22×C4×C43C2411yescharacteristic
297C22×C4×C43C2412yes—
298C22×C4×C43C2412yes—
299C22×C4×C43C2411yescharacteristic
300C22×C4×C43C2411yescharacteristic
301C22×C4×C43C2411yescharacteristic
302C22×C4×C43C2411yescharacteristic
303C22×Dic43—22no—
304C22×Dic43—22no—
305C22×Dic43—22no—
306C22×Dic43C2411yescharacteristic
307C22×Dic43C2412yes—
308C22×Dic43C2412yes—
309C22×Dic43C2411yescharacteristic
310C22×Dic43C2412yes—
311C22×Dic43C2412yes—
312C22×Dic43C2411yescharacteristic
313C22×Dic43C2411yescharacteristic
314C22×Dic43C2411yescharacteristic
315C22×Dic43C2411yescharacteristic
316Q8×D43—232no—
317Q8×D43—416no—
318C2×C4×D43—22no—
319C2×C4×D43—22no—
320C2×C4×D43—22no—
321C2×C4×D43—22no—
322C2×C4×D43—22no—
323C2×C4×D43—22no—
324C2×C4×D43—22no—
325C2×C4×D43—22no—
326C2×C4×D43—22no—
327C2×C4×D43—24no—
328C2×C4×D43—22no—
329C2×C4×D43—24no—
330C2×C4×D43—24no—
331C2×C4×D43—22no—
332C2×C4×D43—22no—
333C2×C4×D43—24no—
334C2×C4×D43—24no—
335C2×C4×D43—24no—
336C2×C4×D43—22no—
337C2×C4×D43—24no—
338C2×C4×D43—22no—
339C2×C4×D43—24no—
340C2×C4×D43—24no—
341C2×C4×D43—22no—
342C2×C4×D43—22no—
343C2×C4×D43—22no—
344C2×C4×D43—22no—
345C2×C4×D43—24no—
346C2×C4×D43—416no—
347C2×C4×D43C2×D418yes—
348C2×C4×D43C2×D418yes—
349C2×C4×D43C2×D414yes—
350C2×C4×D43C2×D414yes—
351C2×C4×D43C2×Q814yes—
352C2×C4×D43C2×Q814yes—
353C2×C4×D43#4114yes—
354C2×C4×D43#4114yes—
355C2×Dic86—22no—
356C2×Dic86—22no—
357C2×Dic86—24no—
358C2×Dic86—24no—
359C2×Dic86—22no—
360C2×Dic86—22no—
361C2×Dic86—22no—
362C2×Dic86—24no—
363C2×Dic86—24no—
364C2×Dic86—24no—
365C2×Dic86C2×D418yes—
366C2×Dic86C2×D414yes—
367C4⋊C4×C43—24no—
368C4⋊C4×C43—24no—
369C4⋊C4×C43—24no—
370C4⋊C4×C43—22no—
371C4⋊C4×C43—24no—
372C4⋊C4×C43—24no—
373C4⋊C4×C43—24no—
374C4⋊C4×C43C2×D414yes—
375C22⋊C4×C43—24no—
376C22⋊C4×C43—24no—
377C22⋊C4×C43—22no—
378C22⋊C4×C43C2×Q814yescomplemented
379C42×C43—24no—
380C42×C43—22no—
381C42×C43—22no—
382C22⋊Dic43—24no—
383C22⋊Dic43—24no—
384C22⋊Dic43—22no—
385C22⋊Dic43C2×Q814yescomplemented
386(C2×D43)⋊C4—24no—
387(C2×D43)⋊C4—24no—
388(C2×D43)⋊C4—22no—
389(C2×D43)⋊C4—24no—
390(C2×D43)⋊C4—24no—
391(C2×D43)⋊C4—22no—
392(C2×D43)⋊C4C2×Q814yescomplemented
393(C2×D43)⋊C4C2×Q814yescomplemented
394C4⋊Dic43—22no—
395C4⋊Dic43—24no—
396C4⋊Dic43—24no—
397C4⋊Dic43—24no—
398C4⋊Dic43—24no—
399C4⋊Dic43—24no—
400C4⋊Dic43—24no—
401C4⋊Dic43C2×D414yes—
402Dic43⋊C4—24no—
403Dic43⋊C4—24no—
404Dic43⋊C4—24no—
405Dic43⋊C4—24no—
406Dic43⋊C4—24no—
407Dic43⋊C4—24no—
408Dic43⋊C4—24no—
409Dic43⋊C4—24no—
410Dic43⋊C4—24no—
411Dic43⋊C4—24no—
412Dic43⋊C4—24no—
413Dic43⋊C4—24no—
414Dic43⋊C4—24no—
415Dic43⋊C4C2×D418yes—
416C4×Dic43—24no—
417C4×Dic43—22no—
418C4×Dic43—22no—
419C4×Dic43—22no—
420C4×Dic43—24no—
421C4×Dic43—24no—
422C4×Dic43—22no—
423C4×Dic43—22no—
424C4×Dic43—22no—
425C23×C43—21no—
426C23×C43—21no—
427C23×C43—21no—
428C23×C43—21no—
429C23×C43—21no—
430C23×C43—21no—
431C23×C43C22×Q812yes—
432C23×C43C2511yescharacteristic
433C22×D43—21no—
434C22×D43—21no—
435C22×D43—21no—
436C22×D43—21no—
437C22×D43—21no—
438C22×D43—21no—
439C22×D43—28no—
440C22×D43—28no—
441C22×D43—28no—
442C22×D43—44no—
443C22×D43—44no—
444C22×D43—44no—
445C22×D43—44no—
446C22×D43C22×D412yes—
447C22×D43C22×D412yes—
448C22×D43C22×Q812yes—
449C22×D43C22×Q812yes—
450C22×D43C2×#4112yes—
451C22×D43C2×#4112yes—
452C22×D432−1+412yes—
453C22×D432−1+412yes—
454Q8×C43—28no—
455Q8×C43—44no—
456C2×C4×C43—21no—
457C2×C4×C43—21no—
458C2×C4×C43—21no—
459C2×C4×C43—22no—
460C2×C4×C43—22no—
461C2×C4×C43—22no—
462C2×C4×C43—22no—
463C2×C4×C43—21no—
464C2×C4×C43—21no—
465C2×C4×C43—21no—
466C2×C4×C43—21no—
467C2×C4×C43—22no—
468C2×C4×C43—21no—
469C2×C4×C43—21no—
470C2×C4×C43—22no—
471C2×C4×C43—22no—
472C2×C4×C43—22no—
473C2×C4×C43—21no—
474C2×C4×C43—22no—
475C2×C4×C43—21no—
476C2×C4×C43—21no—
477C2×C4×C43—22no—
478C2×C4×C43—44no—
479C2×C4×C43C22×D414yes—
480C2×C4×C43C22×D414yes—
481C2×C4×C43C22×D412yes—
482C2×C4×C43C22×D412yes—
483C2×C4×C43C22×Q812yes—
484C2×C4×C43C22×Q812yes—
485C2×C4×C43C2×#4112yes—
486C2×C4×C43C2×#4112yes—
487C2×Dic43—21no—
488C2×Dic43—21no—
489C2×Dic43—21no—
490C2×Dic43—22no—
491C2×Dic43—22no—
492C2×Dic43—22no—
493C2×Dic43—22no—
494C2×Dic43—21no—
495C2×Dic43—21no—
496C2×Dic43—21no—
497C2×Dic43—21no—
498C2×Dic43—22no—
499C2×Dic43—22no—
500C2×Dic43—21no—
501C2×Dic43—21no—
502C2×Dic43—22no—
503C2×Dic43—22no—
504C2×Dic43—21no—
505C2×Dic43—22no—
506C2×Dic43—21no—
507C2×Dic43—21no—
508C2×Dic43—22no—
509C2×Dic43—44no—
510C2×Dic43C22×D414yes—
511C2×Dic43C22×D414yes—
512C2×Dic43C22×D412yes—
513C2×Dic43C22×D412yes—
514C2×Dic43C22×Q812yes—
515C2×Dic43C22×Q812yes—
516C2×Dic43C2×#4112yes—
517C2×Dic43C2×#4112yes—
518C4×D43—216no—
519C4×D43—216no—
520C4×D43—28no—
521C4×D43—28no—
522C4×D43—28no—
523C4×D43—44no—
524C4×D43—48no—
525C4×D43—44no—
526C4×D43—48no—
527C4×D43—44no—
528C4×D43—44no—
529C4×D43#121116yes—
530Dic86—28no—
531Dic86—216no—
532Dic86—44no—
533Dic86—48no—
534C2×#2429—431nomaximal, Sylow
535C22×C43—22no—
536C22×C43—22no—
537C22×C43—22no—
538C22×C43—41no—
539C22×C43—41no—
540C22×C43—41no—
541C22×C43—41no—
542C22×C43C23×D411yescharacteristic
543C22×C43C23×D411yescharacteristic
544C22×C43C23×Q811yescharacteristic
545C22×C43C22×#4111yescharacteristic
546C22×C43C22×#4111yescharacteristic
547C22×C43C2×2−1+411yescharacteristic
548C22×C43C2×2−1+411yescharacteristic
549C2×D43—22no—
550C2×D43—22no—
551C2×D43—22no—
552C2×D43—41no—
553C2×D43—41no—
554C2×D43—41no—
555C2×D43—41no—
556C2×D43—416no—
557C2×D43C2×#12114yes—
558C2×D43#53314yes—
559C2×D43#54114yes—
560C2×D43#54714yes—
561C2×D43#54814yes—
562C2×D43D4×Q814yes—
563C2×D43D4×Q814yes—
564C4×C43—24no—
565C4×C43—24no—
566C4×C43—22no—
567C4×C43—22no—
568C4×C43—22no—
569C4×C43—42no—
570C4×C43—41no—
571C4×C43—41no—
572C4×C43—42no—
573C4×C43C2×#12114yes—
574Dic43—24no—
575Dic43—24no—
576Dic43—22no—
577Dic43—22no—
578Dic43—22no—
579Dic43—42no—
580Dic43—41no—
581Dic43—41no—
582Dic43—42no—
583Dic43C2×#12114yes—
584C22×C4⋊Q8—431no—
585C22×C22⋊Q8—431no—
586C22×C22⋊Q8—431no—
587C22×C4×Q8—431no—
588#2429—432no—
589#2429—432no—
590#2429—431no—
591#2429—431no—
592#2429—432no—
593#2429—432no—
594#2429—431no—
595#2429—431no—
596#2429—431no—
597#2429—431no—
598#2429—431no—
599#2429D4311yescharacteristic, direct product factor
600C2×#398—432no—
601C2×#396—432no—
602C2×#391—431no—
603C2×#389—431no—
604C2×#389—432no—
605C2×#388—432no—
606C2×C4×C22⋊C4—431no—
607C2×C43—42no—
608C2×C43C22×#12111yescharacteristic
609C2×C43C2×#53311yescharacteristic
610C2×C43C2×#54111yescharacteristic
611C2×C43C2×#54711yescharacteristic
612C2×C43C2×#54811yescharacteristic
613C2×C43C2×D4×Q811yescharacteristic
614C2×C43C2×D4×Q811yescharacteristic
615D43—42no—
616D43#242918yesdirect product factor
617C23×Q8—431no—
618C23×Q8—431no—
619C24×C4—431no—
620C2×C4⋊Q8—431no—
621C2×C4⋊Q8—431no—
622C2×C4⋊Q8—432no—
623C2×C4⋊Q8—432no—
624C2×C4⋊Q8—431no—
625C2×C4⋊Q8—868no—
626C2×C4⋊Q8C2×D4311yescharacteristic, complemented
627C2×C22⋊Q8—431no—
628C2×C22⋊Q8—431no—
629C2×C22⋊Q8—431no—
630C2×C22⋊Q8—431no—
631C2×C22⋊Q8—432no—
632C2×C22⋊Q8—432no—
633C2×C22⋊Q8—431no—
634C2×C22⋊Q8—431no—
635C2×C22⋊Q8—432no—
636C2×C22⋊Q8—432no—
637C2×C22⋊Q8—868no—
638C2×C22⋊Q8—868no—
639C2×C22⋊Q8C2×D4311yescharacteristic
640C2×C22⋊Q8C2×D4311yescharacteristic
641C2×C4×Q8—431no—
642C2×C4×Q8—432no—
643C2×C4×Q8—431no—
644C2×C4×Q8—432no—
645C2×C4×Q8—431no—
646C2×C4×Q8—868no—
647C2×C4×Q8C2×D4311yescharacteristic, complemented
648C22×C4⋊C4—431no—
649C22×C4⋊C4—432no—
650C22×C4⋊C4—432no—
651C22×C4⋊C4—432no—
652C22×C4⋊C4—432no—
653C22×C4⋊C4—432no—
654C22×C4⋊C4—432no—
655C22×C4⋊C4—431no—
656C22×C22⋊C4—431no—
657C22×C22⋊C4—431no—
658C22×C22⋊C4—432no—
659C22×C22⋊C4—432no—
660C22×C42—431no—
661C22×C42—432no—
662C22×C42—431no—
663#398—432no—
664#398—432no—
665#398—432no—
666#398—432no—
667#398—432no—
668#398—432no—
669#398—432no—
670#398C2×D4312yescomplemented
671#396—432no—
672#396—432no—
673#396—432no—
674#396—432no—
675#396—432no—
676#396—432no—
677#396—432no—
678#396C2×D4312yes—
679#391—431no—
680#391—431no—
681#391—431no—
682#391—432no—
683#391—432no—
684#391C2×D4311yescharacteristic, complemented
685#389—432no—
686#389—432no—
687#389—432no—
688#389—432no—
689#389—431no—
690#389—432no—
691#389—431no—
692#389—432no—
693#389—431no—
694#389—432no—
695#389—432no—
696#389—432no—
697#389C2×D4312yescomplemented
698#389C2×D4311yescharacteristic, complemented
699#388—432no—
700#388—432no—
701#388—432no—
702#388—432no—
703#388—432no—
704#388—432no—
705#388—432no—
706#388C2×D4312yes—
707C4×C22⋊C4—431no—
708C4×C22⋊C4—431no—
709C4×C22⋊C4—431no—
710C4×C22⋊C4—431no—
711C4×C22⋊C4—431no—
712C4×C22⋊C4—431no—
713C4×C22⋊C4—431no—
714C4×C22⋊C4C2×D4311yescharacteristic
715C2×#95—432no—
716C2×#95—431no—
717C2×#95—432no—
718C2×#95—431no—
719C2×#95—432no—
720C43C2×#242911yescharacteristic, complemented, Sylow
721C25—431no—
722C22×Q8—438no—
723C22×Q8—432no—
724C22×Q8—431no—
725C22×Q8—432no—
726C22×Q8—431no—
727C22×Q8—864no—
728C22×Q8—864no—
729C22×Q8—864no—
730C22×Q8—864no—
731C22×Q8—864no—
732C22×Q8C22×D4311yescharacteristic
733C22×Q8C22×D4311yescharacteristic
734C23×C4—431no—
735C23×C4—432no—
736C23×C4—432no—
737C23×C4—431no—
738C23×C4—431no—
739C23×C4—431no—
740C23×C4—431no—
741C23×C4—432no—
742C23×C4—432no—
743C23×C4—431no—
744C23×C4—431no—
745C23×C4—431no—
746C23×C4—431no—
747C23×C4—864no—
748C23×C4—864no—
749C23×C4—864no—
750C23×C4C22×D4311yescharacteristic
751C4⋊Q8—24no—
752C4⋊Q8—864no—
753C4⋊Q8—868no—
754C4⋊Q8—868no—
755C4⋊Q8—864no—
756C4⋊Q8—864no—
757C22⋊Q8—24no—
758C22⋊Q8—24no—
759C22⋊Q8—868no—
760C22⋊Q8—868no—
761C22⋊Q8—868no—
762C22⋊Q8—868no—
763C22⋊Q8—864no—
764C22⋊Q8—864no—
765C22⋊Q8—864no—
766C22⋊Q8—864no—
767C22⋊Q8—864no—
768C22⋊Q8—864no—
769C4×Q8—24no—
770C4×Q8—868no—
771C4×Q8—864no—
772C4×Q8—868no—
773C4×Q8—864no—
774C4×Q8—864no—
775C2×C4⋊C4—432no—
776C2×C4⋊C4—431no—
777C2×C4⋊C4—438no—
778C2×C4⋊C4—432no—
779C2×C4⋊C4—432no—
780C2×C4⋊C4—432no—
781C2×C4⋊C4—432no—
782C2×C4⋊C4—432no—
783C2×C4⋊C4—432no—
784C2×C4⋊C4—432no—
785C2×C4⋊C4—432no—
786C2×C4⋊C4—431no—
787C2×C4⋊C4—432no—
788C2×C4⋊C4—432no—
789C2×C4⋊C4—432no—
790C2×C4⋊C4—432no—
791C2×C4⋊C4—432no—
792C2×C4⋊C4—432no—
793C2×C4⋊C4—432no—
794C2×C4⋊C4—432no—
795C2×C4⋊C4—432no—
796C2×C4⋊C4—432no—
797C2×C4⋊C4—432no—
798C2×C4⋊C4—868no—
799C2×C4⋊C4—864no—
800C2×C4⋊C4—868no—
801C2×C4⋊C4—868no—
802C2×C4⋊C4—868no—
803C2×C4⋊C4—868no—
804C2×C4⋊C4—868no—
805C2×C4⋊C4C22×D4312yes—
806C2×C4⋊C4C22×D4311yescharacteristic
807C2×C4⋊C4C22×D4312yes—
808C2×C4⋊C4C22×D4312yes—
809C2×C4⋊C4C22×D4312yes—
810C2×C4⋊C4C22×D4312yes—
811C2×C4⋊C4C22×D4312yes—
812C2×C4⋊C4C22×D4311yescharacteristic
813C2×C22⋊C4—431no—
814C2×C22⋊C4—431no—
815C2×C22⋊C4—431no—
816C2×C22⋊C4—438no—
817C2×C22⋊C4—432no—
818C2×C22⋊C4—432no—
819C2×C22⋊C4—431no—
820C2×C22⋊C4—432no—
821C2×C22⋊C4—432no—
822C2×C22⋊C4—432no—
823C2×C22⋊C4—432no—
824C2×C22⋊C4—431no—
825C2×C22⋊C4—431no—
826C2×C22⋊C4—868no—
827C2×C22⋊C4—868no—
828C2×C22⋊C4—864no—
829C2×C22⋊C4C22×D4312yes—
830C2×C22⋊C4C22×D4312yes—
831C2×C22⋊C4C22×D4311yescharacteristic
832C2×C22⋊C4C22×D4311yescharacteristic
833C2×C42—431no—
834C2×C42—431no—
835C2×C42—431no—
836C2×C42—432no—
837C2×C42—432no—
838C2×C42—432no—
839C2×C42—431no—
840C2×C42—431no—
841C2×C42—431no—
842C2×C42—864no—
843C2×C42—868no—
844C2×C42—864no—
845C2×C42C22×D4311yescharacteristic
846C2×C42C22×D4312yes—
847C2×C42C22×D4311yescharacteristic
848#95—431no—
849#95—431no—
850#95—431no—
851#95—431no—
852#95—431no—
853#95—431no—
854#95—432no—
855#95—432no—
856#95—432no—
857#95—432no—
858#95—432no—
859#95—432no—
860#95—432no—
861#95—432no—
862#95—432no—
863#95C22×D4311yescharacteristic
864#95C22×D4311yescharacteristic
865#95C22×D4312yes—
866#95C22×D4312yes—
867#95C22×D4312yes—
868C24—431no—
869C24—434no—
870C24—431no—
871C24—862no—
872C24—862no—
873C24—862no—
874C24—862no—
875C24—862no—
876C24—862no—
877C24C23×D4311yescharacteristic
878C2×Q8—22no—
879C2×Q8—22no—
880C2×Q8—22no—
881C2×Q8—22no—
882C2×Q8—22no—
883C2×Q8—438no—
884C2×Q8—434no—
885C2×Q8—864no—
886C2×Q8—864no—
887C2×Q8—864no—
888C2×Q8—864no—
889C2×Q8—864no—
890C2×Q8—8632no—
891C2×Q8—862no—
892C2×Q8—862no—
893C2×Q8—862no—
894C2×Q8—862no—
895C2×Q8—862no—
896C2×Q8—17216no—
897C2×Q8D4×D4314yes—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—431no—
902C22×C4—434no—
903C22×C4—434no—
904C22×C4—434no—
905C22×C4—431no—
906C22×C4—431no—
907C22×C4—432no—
908C22×C4—431no—
909C22×C4—432no—
910C22×C4—438no—
911C22×C4—438no—
912C22×C4—434no—
913C22×C4—434no—
914C22×C4—434no—
915C22×C4—431no—
916C22×C4—432no—
917C22×C4—432no—
918C22×C4—431no—
919C22×C4—862no—
920C22×C4—862no—
921C22×C4—862no—
922C22×C4—862no—
923C22×C4—862no—
924C22×C4—862no—
925C22×C4—864no—
926C22×C4—864no—
927C22×C4—864no—
928C22×C4—864no—
929C22×C4—862no—
930C22×C4—862no—
931C22×C4—862no—
932C22×C4—862no—
933C22×C4—864no—
934C22×C4—864no—
935C22×C4—862no—
936C22×C4—862no—
937C22×C4—862no—
938C22×C4—864no—
939C22×C4—864no—
940C22×C4—862no—
941C22×C4—864no—
942C22×C4—864no—
943C22×C4—862no—
944C22×C4—862no—
945C22×C4—862no—
946C22×C4—862no—
947C22×C4—862no—
948C22×C4—862no—
949C22×C4—862no—
950C22×C4—17216no—
951C22×C4C23×D4311yescharacteristic
952C22×C4C23×D4312yes—
953C22×C4C23×D4312yes—
954C22×C4C23×D4311yescharacteristic
955C22×C4C23×D4312yes—
956C22×C4C23×D4312yes—
957C22×C4C23×D4311yescharacteristic
958C22×C4C23×D4311yescharacteristic
959C22×C4C23×D4311yescharacteristic
960C22×C4C23×D4311yescharacteristic
961C4⋊C4—24no—
962C4⋊C4—22no—
963C4⋊C4—24no—
964C4⋊C4—24no—
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—24no—
968C4⋊C4—438no—
969C4⋊C4—434no—
970C4⋊C4—864no—
971C4⋊C4—864no—
972C4⋊C4—864no—
973C4⋊C4—864no—
974C4⋊C4—864no—
975C4⋊C4—864no—
976C4⋊C4—864no—
977C4⋊C4—864no—
978C4⋊C4—864no—
979C4⋊C4—864no—
980C4⋊C4—864no—
981C4⋊C4—864no—
982C4⋊C4—864no—
983C4⋊C4—864no—
984C4⋊C4—864no—
985C4⋊C4—862no—
986C4⋊C4—864no—
987C4⋊C4—864no—
988C4⋊C4—864no—
989C4⋊C4—864no—
990C4⋊C4D4×D4314yes—
991C22⋊C4—24no—
992C22⋊C4—24no—
993C22⋊C4—22no—
994C22⋊C4—434no—
995C22⋊C4—434no—
996C22⋊C4—434no—
997C22⋊C4—864no—
998C22⋊C4—864no—
999C22⋊C4—862no—
1000C22⋊C4—864no—
1001C22⋊C4—864no—
1002C22⋊C4—862no—
1003C22⋊C4—864no—
1004C22⋊C4—864no—
1005C22⋊C4—862no—
1006C22⋊C4Q8×D4314yescomplemented
1007C42—24no—
1008C42—22no—
1009C42—22no—
1010C42—862no—
1011C42—864no—
1012C42—864no—
1013C42—862no—
1014C42—862no—
1015C42—862no—
1016C42—864no—
1017C42—862no—
1018C42—862no—
1019C23—21no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—432no—
1026C23—432no—
1027C23—432no—
1028C23—432no—
1029C23—432no—
1030C23—432no—
1031C23—432no—
1032C23—432no—
1033C23—868no—
1034C23—868no—
1035C23—868no—
1036C23—861no—
1037C23—861no—
1038C23—861no—
1039C23—861no—
1040C23—861no—
1041C23—861no—
1042C23—1724no—
1043C23—1724no—
1044C23—1724no—
1045C23—1724no—
1046C23C2×Q8×D4312yes—
1047C23C24×D4311yescharacteristic
1048Q8—28no—
1049Q8—44no—
1050Q8—8616no—
1051Q8—868no—
1052Q8—1728no—
1053Q8—1724no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—44no—
1077C2×C4—432no—
1078C2×C4—432no—
1079C2×C4—432no—
1080C2×C4—4316no—
1081C2×C4—434no—
1082C2×C4—434no—
1083C2×C4—432no—
1084C2×C4—432no—
1085C2×C4—432no—
1086C2×C4—8616no—
1087C2×C4—8616no—
1088C2×C4—868no—
1089C2×C4—868no—
1090C2×C4—868no—
1091C2×C4—861no—
1092C2×C4—861no—
1093C2×C4—861no—
1094C2×C4—862no—
1095C2×C4—862no—
1096C2×C4—862no—
1097C2×C4—862no—
1098C2×C4—861no—
1099C2×C4—861no—
1100C2×C4—861no—
1101C2×C4—861no—
1102C2×C4—862no—
1103C2×C4—862no—
1104C2×C4—861no—
1105C2×C4—861no—
1106C2×C4—862no—
1107C2×C4—861no—
1108C2×C4—862no—
1109C2×C4—861no—
1110C2×C4—862no—
1111C2×C4—861no—
1112C2×C4—862no—
1113C2×C4—1724no—
1114C2×C4—1724no—
1115C2×C4—1728no—
1116C2×C4—1724no—
1117C2×C4—1728no—
1118C2×C4—1724no—
1119C2×C4—1724no—
1120C2×C4C2×D4×D4314yes—
1121C2×C4C2×D4×D4314yes—
1122C2×C4C2×D4×D4312yes—
1123C2×C4C2×D4×D4312yes—
1124C2×C4C2×Q8×D4312yes—
1125C2×C4C2×Q8×D4312yes—
1126C2×C4#41×D4312yes—
1127C2×C4#41×D4312yes—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—41no—
1135C22—434no—
1136C22—434no—
1137C22—434no—
1138C22—434no—
1139C22—434no—
1140C22—434no—
1141C22—434no—
1142C22—862no—
1143C22—862no—
1144C22—862no—
1145C22—17216no—
1146C22—1721no—
1147C22—1721no—
1148C22—1721no—
1149C22—1721no—
1150C22C22×D4×D4311yescharacteristic
1151C22C22×D4×D4311yescharacteristic
1152C22C22×Q8×D4311yescharacteristic
1153C22C2×#41×D4311yescharacteristic
1154C22C2×#41×D4311yescharacteristic
1155C222−1+4×D4311yescharacteristic
1156C222−1+4×D4311yescharacteristic
1157C4—24no—
1158C4—22no—
1159C4—22no—
1160C4—22no—
1161C4—24no—
1162C4—41no—
1163C4—42no—
1164C4—41no—
1165C4—42no—
1166C4—434no—
1167C4—864no—
1168C4—862no—
1169C4—862no—
1170C4—862no—
1171C4—864no—
1172C4—1721no—
1173C4—1722no—
1174C4—1721no—
1175C4—1722no—
1176C4#121×D4314yes—
1177C2—42no—
1178C2—438no—
1179C2—1722no—
1180C2C2×#121×D4311yescharacteristic
1181C2#533×D4311yescharacteristic
1182C2#541×D4311yescharacteristic
1183C2#547×D4311yescharacteristic
1184C2#548×D4311yescharacteristic
1185C2D4×Q8×D4311yescharacteristic
1186C2D4×Q8×D4311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2429C2
prime radicalC24×D43C23
hypercenter#2429D43
hypocenterC43C2×#2429
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2429

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D43C2semidirect
4. C2×C4×Q8×D43C2semidirect
5. #19138197C2semidirect
6. #19138196C2semidirect
7. #19138195C2semidirect
8. #19138194C2semidirect
9. #19138193C2semidirect
10. #19138192C2semidirect
11. #19138191C2semidirect
12. #19138190C2semidirect
13. #19138189C2semidirect
14. #19138188C2semidirect
15. #19138187C2semidirect
16. #398×D43C2semidirect
18. #391×D43C2semidirect
19. #389×D43C2semidirect
20. #389×D43C2semidirect
23. C43×#2429C2semidirect
27. C2×#13063325C22semidirect
28. C2×#13063324C22semidirect
29. C2×#13063324C22semidirect
30. C2×#13063323C22semidirect
31. C2×#13063323C22semidirect
45. C2×Q8×Dic43C22semidirect
46. C2×C4×Dic86C22semidirect
47. C2×C4×Dic86C22semidirect
48. C2×#13063290C22semidirect
49. C2×#13063290C22semidirect
66. #14582833C22semidirect
67. #14582833C22semidirect
68. #14582832C22semidirect
69. #14582832C22semidirect
70. #14582831C22semidirect
71. #14582830C22semidirect
72. #14582829C22semidirect
80. #14582806C22semidirect
81. #14582805C22semidirect
82. #14582804C22semidirect
83. #14582803C22semidirect
84. #14582803C22semidirect
85. #14582798C22semidirect
86. #14582798C22semidirect
87. #14582797C22semidirect
88. #14582797C22semidirect
89. #14582796C22semidirect
90. #14582796C22semidirect
91. #14582796C22semidirect
92. #14582795C22semidirect
93. #14582795C22semidirect
94. #14582794C22semidirect
95. #14582794C22semidirect
96. #14582794C22semidirect
116. C2×C4⋊Q8×C43C22semidirect
119. C2×C4×Q8×C43C22semidirect
120. C43×#398C22semidirect
122. C43×#391C22semidirect
123. C43×#389C22semidirect
124. C43×#389C22semidirect
219. C22⋊C4×D43Q8semidirect
378. C22⋊C4×C43C2×Q8semidirect
385. C22⋊Dic43C2×Q8semidirect
392. (C2×D43)⋊C4C2×Q8semidirect
393. (C2×D43)⋊C4C2×Q8semidirect
599. #2429D43direct (N × H)
616. D43#2429direct (N × H)
626. C2×C4⋊Q8C2×D43semidirect
647. C2×C4×Q8C2×D43semidirect
670. #398C2×D43semidirect
684. #391C2×D43semidirect
697. #389C2×D43semidirect
698. #389C2×D43semidirect
720. C43C2×#2429semidirect
1006. C22⋊C4Q8×D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D432
C2×C22⋊Q8×D432
C2×C4×Q8×D432
#191381972
#191381962
#191381952
#191381942
#191381932
#191381922
#191381912
#191381902
#191381892
#191381882
#191381872
#398×D432
#396×D432
#391×D432
#389×D432
#388×D432
C4×C22⋊C4×D432
C43×#24292
C2×#242943