Finite Group Databasebeta

← D43×#2821 #25303156

Subgroups — D43×#2821 #25303156

Order 11008.

2370 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
2C2×#126×D43C211yesmaximal, characteristic
3#19142660C212yesmaximal, complemented
4#19142659C212yesmaximal, complemented
5#19142658C212yesmaximal, complemented
6#19142657C212yesmaximal, complemented
7#19142656C211yesmaximal, characteristic, complemented
8#19142655C212yesmaximal, complemented
9#19142654C211yesmaximal, characteristic, complemented
10#19142653C211yesmaximal, characteristic, complemented
11#19142652C212yesmaximal, complemented
12#400×D43C212yesmaximal, complemented
13#399×D43C212yesmaximal
14#398×D43C212yesmaximal, complemented
15#397×D43C212yesmaximal
16#395×D43C212yesmaximal, complemented
17#393×D43C212yesmaximal
18#383×D43C211yesmaximal, characteristic, complemented
19C43×#2821C211yesmaximal, characteristic, complemented
20C22×Q8×D43C2212yes—
21C2×#13063325C2211yescharacteristic, complemented
22C2×#13063324C2212yescomplemented
23C2×#13063324C2212yescomplemented
24C2×#13063323C2212yescomplemented
25C4⋊Q8×D43—28no—
26C2×#13063320C2211yescharacteristic
27C2×#13063320C2211yescharacteristic
28C2×#13063320C2211yescharacteristic
29C2×#13063319C2211yescharacteristic
30C2×#13063318C2211yescharacteristic
31C2×#13063318C2211yescharacteristic
32C2×#13063318C2211yescharacteristic
33#126×D43—28no—
34C2×C4⋊C4×D43C2211yescharacteristic
35C2×C4⋊C4×D43C2212yes—
36C2×C4⋊C4×D43C2211yescharacteristic
37C2×C4⋊C4×D43C2212yes—
38C2×C4⋊C4×D43C2211yescharacteristic
39C2×C4⋊C4×D43C2214yes—
40C2×C22⋊C4×D43C2211yescharacteristic
41C2×C22⋊C4×D43C2211yescharacteristic
42C2×C22⋊C4×D43C2211yescharacteristic
43C2×C22⋊C4×D43C2214yes—
44C2×C42×D43C2211yescharacteristic
45#14582841C2214yescomplemented
46#14582840C2214yescomplemented
47#14582839C2212yescomplemented
48#14582838C2212yescomplemented
49#14582837C2212yescomplemented
50#14582836C2212yes—
51#14582835C2214yes—
52#14582835C2212yes—
53#14582834C2214yes—
54#14582834C2212yes—
55#14582833C2214yescomplemented
56#14582832C2214yescomplemented
57#14582831C2212yescomplemented
58#14582830C2212yescomplemented
59#14582829C2212yescomplemented
60#14582828C2214yes—
61#14582827C2214yes—
62#14582826C2212yes—
63#14582825C2212yes—
64#14582824C2212yes—
65#14582820C2212yescomplemented
66#14582820C2214yescomplemented
67#14582819C2214yescomplemented
68#14582819C2212yescomplemented
69#14582818C2212yescomplemented
70#14582812C2212yes—
71#14582812C2214yes—
72#14582811C2212yes—
73#14582811C2214yes—
74#14582810C2212yes—
75#14582767C2211yescharacteristic, complemented
76#14582766C2212yescomplemented
77#14582766C2212yescomplemented
78#14582766C2212yescomplemented
79#95×D43C2212yes—
80#95×D43C2214yes—
81#95×D43C2214yes—
82#95×D43C2212yes—
83#95×D43C2212yes—
84C2×C4⋊Q8×C43C2211yescharacteristic, complemented
85C2×#126×C43C2211yescharacteristic
86C43×#400C2212yescomplemented
87C43×#399C2212yes—
88C43×#398C2212yescomplemented
89C43×#397C2212yes—
90C43×#395C2212yescomplemented
91C43×#393C2212yes—
92C43×#383C2211yescharacteristic, complemented
93C24×D43C2311yescharacteristic
94C22×Dic86C2312yes—
95C22×Dic86C2314yes—
96C2×Q8×D43—28no—
97C2×Q8×D43—48no—
98C22×C4×D43C2311yescharacteristic
99C22×C4×D43C2314yes—
100C22×C4×D43C2311yescharacteristic
101C22×C4×D43C2311yescharacteristic
102C22×C4×D43C2314yes—
103C22×C4×D43C2311yescharacteristic
104C22×C4×D43C2311yescharacteristic
105C22×C4×D43C2311yescharacteristic
106#13063325—24no—
107#13063324—28no—
108#13063324—28no—
109#13063323—28no—
110#13063320—24no—
111#13063320—24no—
112#13063320—24no—
113#13063319—24no—
114#13063318—24no—
115#13063318—24no—
116#13063318—24no—
117C2×C4⋊Dic43C2311yescharacteristic
118C2×C4⋊Dic43C2312yes—
119C2×C4⋊Dic43C2311yescharacteristic
120C2×C4⋊Dic43C2312yes—
121C2×C4⋊Dic43C2311yescharacteristic
122C2×C4⋊Dic43C2314yes—
123C2×Dic43⋊C4C2311yescharacteristic
124C2×Dic43⋊C4C2311yescharacteristic
125C2×Dic43⋊C4C2314yes—
126C2×Dic43⋊C4C2311yescharacteristic
127C2×Dic43⋊C4C2311yescharacteristic
128C2×Dic43⋊C4C2314yes—
129C2×Dic43⋊C4C2311yescharacteristic
130C2×Dic43⋊C4C2311yescharacteristic
131C2×Dic43⋊C4C2314yes—
132C2×Dic43⋊C4C2314yes—
133C4⋊C4×D43—24no—
134C4⋊C4×D43—24no—
135C4⋊C4×D43—24no—
136C4⋊C4×D43—28no—
137C4⋊C4×D43—28no—
138C4⋊C4×D43—48no—
139C2×C22⋊Dic43C2311yescharacteristic
140C2×C22⋊Dic43C2311yescharacteristic
141C2×C22⋊Dic43C2311yescharacteristic
142C2×C22⋊Dic43C2314yes—
143C2×(C2×D43)⋊C4C2311yescharacteristic
144C2×(C2×D43)⋊C4C2311yescharacteristic
145C2×(C2×D43)⋊C4C2311yescharacteristic
146C2×(C2×D43)⋊C4C2311yescharacteristic
147C2×(C2×D43)⋊C4C2311yescharacteristic
148C2×(C2×D43)⋊C4C2311yescharacteristic
149C2×(C2×D43)⋊C4C2314yes—
150C2×(C2×D43)⋊C4C2314yes—
151C22⋊C4×D43—24no—
152C22⋊C4×D43—24no—
153C22⋊C4×D43—24no—
154C22⋊C4×D43—48no—
155C2×C4×Dic43C2311yescharacteristic
156C2×C4×Dic43C2311yescharacteristic
157C2×C4×Dic43C2311yescharacteristic
158C42×D43D418yes—
159C43⋊#95C2312yes—
160C43⋊#95C2314yes—
161C43⋊#95C2314yes—
162C43⋊#95C2314yes—
163C43⋊#95C2314yes—
164C43⋊#95C2314yes—
165C43⋊#95C2314yes—
166C43⋊#95C2314yes—
167C43⋊#95C2312yes—
168C43⋊#95C2314yes—
169C43⋊#95C2312yes—
170C43⋊#95C2314yes—
171C22×Q8×C43C2312yes—
172C4⋊Q8×C43—24no—
173#126×C43—24no—
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2312yes—
178C2×C4⋊C4×C43C2312yes—
179C2×C4⋊C4×C43C2314yes—
180C2×C22⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43C2311yescharacteristic
182C2×C22⋊C4×C43C2311yescharacteristic
183C2×C22⋊C4×C43C2314yes—
184C2×C42×C43C2311yescharacteristic
185#95×C43C2312yes—
186#95×C43C2314yes—
187#95×C43C2314yes—
188#95×C43C2312yes—
189#95×C43C2312yes—
190C24×C43C2411yescharacteristic
191C23×D43—22no—
192C23×D43—24no—
193C23×D43—24no—
194C23×D43—24no—
195C23×D43C2411yescharacteristic
196C23×D43C2411yescharacteristic
197C2×Q8×C43—24no—
198C2×Q8×C43—44no—
199C22×C4×C43C2414yes—
200C22×C4×C43C2411yescharacteristic
201C22×C4×C43C2411yescharacteristic
202C22×C4×C43C2414yes—
203C22×C4×C43C2411yescharacteristic
204C22×C4×C43C2411yescharacteristic
205C22×C4×C43C2411yescharacteristic
206C22×C4×C43C2411yescharacteristic
207C22×Dic43C2414yes—
208C22×Dic43C2411yescharacteristic
209C22×Dic43C2411yescharacteristic
210C22×Dic43C2414yes—
211C22×Dic43C2411yescharacteristic
212C22×Dic43C2411yescharacteristic
213C22×Dic43C2411yescharacteristic
214C22×Dic43C2411yescharacteristic
215Q8×D43—432no—
216C2×C4×D43—22no—
217C2×C4×D43—22no—
218C2×C4×D43—22no—
219C2×C4×D43—28no—
220C2×C4×D43—24no—
221C2×C4×D43—28no—
222C2×C4×D43—28no—
223C2×C4×D43—24no—
224C2×C4×D43—28no—
225C2×C4×D43—24no—
226C2×C4×D43—24no—
227C2×C4×D43—24no—
228C2×C4×D43—24no—
229C2×C4×D43—28no—
230C2×C4×D43—28no—
231C2×C4×D43C2×D414yes—
232C2×C4×D43C2×D414yes—
233C2×C4×D43C2×D414yes—
234C2×Dic86—24no—
235C2×Dic86—28no—
236C2×Dic86—44no—
237C2×Dic86—44no—
238C2×Dic86—44no—
239C4⋊C4×C43—22no—
240C4⋊C4×C43—22no—
241C4⋊C4×C43—22no—
242C4⋊C4×C43—24no—
243C4⋊C4×C43—24no—
244C4⋊C4×C43—44no—
245C22⋊C4×C43—22no—
246C22⋊C4×C43—22no—
247C22⋊C4×C43—22no—
248C22⋊C4×C43—44no—
249C42×C43C2×D414yes—
250C22⋊Dic43—22no—
251C22⋊Dic43—22no—
252C22⋊Dic43—22no—
253C22⋊Dic43—44no—
254(C2×D43)⋊C4—22no—
255(C2×D43)⋊C4—22no—
256(C2×D43)⋊C4—22no—
257(C2×D43)⋊C4—22no—
258(C2×D43)⋊C4—22no—
259(C2×D43)⋊C4—22no—
260(C2×D43)⋊C4—44no—
261(C2×D43)⋊C4—44no—
262C4⋊Dic43—24no—
263C4⋊Dic43—24no—
264C4⋊Dic43—22no—
265C4⋊Dic43—22no—
266C4⋊Dic43—22no—
267C4⋊Dic43—44no—
268Dic43⋊C4—22no—
269Dic43⋊C4—22no—
270Dic43⋊C4—22no—
271Dic43⋊C4—22no—
272Dic43⋊C4—22no—
273Dic43⋊C4—22no—
274Dic43⋊C4—28no—
275Dic43⋊C4—28no—
276Dic43⋊C4—44no—
277Dic43⋊C4—44no—
278C4×Dic43C2×D414yes—
279C4×Dic43C2×D414yes—
280C4×Dic43C2×D414yes—
281C23×C43—21no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43C2511yescharacteristic
286C22×D43—21no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—44no—
291C22×D43—44no—
292C22×D43—44no—
293C22×D43—416no—
294C22×D43C22×D412yes—
295C22×D43H(5,𝔽2)14yes—
296C22×D432−1+414yes—
297C22×D432−1+414yes—
298Q8×C43—48no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—24no—
303C2×C4×C43—21no—
304C2×C4×C43—21no—
305C2×C4×C43—21no—
306C2×C4×C43—22no—
307C2×C4×C43—24no—
308C2×C4×C43—24no—
309C2×C4×C43—24no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—24no—
313C2×C4×C43—24no—
314C2×C4×C43C22×D412yes—
315C2×C4×C43C22×D412yes—
316C2×C4×C43C22×D412yes—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—21no—
321C2×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—24no—
324C2×Dic43—22no—
325C2×Dic43—24no—
326C2×Dic43—24no—
327C2×Dic43—24no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—24no—
331C2×Dic43—24no—
332C2×Dic43C22×D412yes—
333C2×Dic43C22×D412yes—
334C2×Dic43C22×D412yes—
335C4×D43—28no—
336C4×D43—28no—
337C4×D43—28no—
338C4×D43—44no—
339C4×D43—416no—
340C4×D43—44no—
341C4×D43—44no—
342C4×D43—416no—
343Dic86—416no—
344Dic86—48no—
345C2×#2821—431nomaximal, Sylow
346C22×C43—41no—
347C22×C43—41no—
348C22×C43—41no—
349C22×C43—44no—
350C22×C43C23×D411yescharacteristic
351C22×C43C2×H(5,𝔽2)12yes—
352C22×C43C2×2−1+412yes—
353C22×C43C2×2−1+412yes—
354C2×D43—41no—
355C2×D43—41no—
356C2×D43—41no—
357C2×D43—44no—
358C2×D43—88no—
359C2×D43#53514yes—
360C2×D43#53614yes—
361C2×D43#53614yes—
362C2×D43#563116yes—
363C4×C43—22no—
364C4×C43—22no—
365C4×C43—22no—
366C4×C43—44no—
367C4×C43—41no—
368C4×C43—41no—
369C4×C43—41no—
370C4×C43—44no—
371Dic43—22no—
372Dic43—22no—
373Dic43—22no—
374Dic43—44no—
375Dic43—41no—
376Dic43—41no—
377Dic43—41no—
378Dic43—44no—
379C22×C4⋊Q8—431no—
380C22×#126—431no—
381#2821—432no—
382#2821—432no—
383#2821—432no—
384#2821—432no—
385#2821—432no—
386#2821—432no—
387#2821—431no—
388#2821—431no—
389#2821—431no—
390#2821D4311yescharacteristic, direct product factor
391C2×#400—432no—
392C2×#399—432no—
393C2×#398—432no—
394C2×#397—432no—
395C2×#395—432no—
396C2×#393—432no—
397C2×#383—431no—
398C2×C43—81no—
399C2×C43C2×#53511yescharacteristic
400C2×C43C2×#53611yescharacteristic
401C2×C43C2×#53611yescharacteristic
402C2×C43C2×#56314yes—
403D43—81no—
404D43#282118yesdirect product factor
405C23×Q8—432no—
406C2×C4⋊Q8—432no—
407C2×C4⋊Q8—432no—
408C2×C4⋊Q8—432no—
409C2×C4⋊Q8—431no—
410C2×C4⋊Q8—868no—
411C2×C4⋊Q8C2×D4311yescharacteristic, complemented
412C2×#126—431no—
413C2×#126—431no—
414C2×#126—431no—
415C2×#126—431no—
416C2×#126—431no—
417C2×#126—431no—
418C2×#126—431no—
419C2×#126—868no—
420C2×#126C2×D4311yescharacteristic
421C22×C4⋊C4—431no—
422C22×C4⋊C4—432no—
423C22×C4⋊C4—431no—
424C22×C4⋊C4—432no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4—434no—
427C22×C22⋊C4—431no—
428C22×C22⋊C4—431no—
429C22×C22⋊C4—431no—
430C22×C22⋊C4—434no—
431C22×C42—431no—
432#400—432no—
433#400—432no—
434#400—432no—
435#400—434no—
436#400—434no—
437#400C2×D4312yescomplemented
438#399—434no—
439#399—432no—
440#399—434no—
441#399—432no—
442#399—432no—
443#399C2×D4312yes—
444#398—432no—
445#398—432no—
446#398—434no—
447#398—432no—
448#398—434no—
449#398C2×D4312yescomplemented
450#397—432no—
451#397—432no—
452#397—434no—
453#397—432no—
454#397—434no—
455#397C2×D4312yes—
456#395—432no—
457#395—434no—
458#395—432no—
459#395—434no—
460#395—432no—
461#395C2×D4312yescomplemented
462#393—432no—
463#393—434no—
464#393—432no—
465#393—434no—
466#393—432no—
467#393C2×D4312yes—
468#383—431no—
469#383—432no—
470#383—432no—
471#383—432no—
472#383C2×D4311yescharacteristic, complemented
473C2×#95—432no—
474C2×#95—434no—
475C2×#95—434no—
476C2×#95—432no—
477C2×#95—432no—
478C43C2×#282111yescharacteristic, complemented, Sylow
479C25—431no—
480C22×Q8—434no—
481C22×Q8—432no—
482C22×Q8—868no—
483C22×Q8—1728no—
484C22×Q8C22×D4312yes—
485C23×C4—431no—
486C23×C4—431no—
487C23×C4—431no—
488C23×C4—431no—
489C23×C4—434no—
490C23×C4—431no—
491C23×C4—431no—
492C23×C4—434no—
493C4⋊Q8—24no—
494C4⋊Q8—868no—
495C4⋊Q8—868no—
496C4⋊Q8—868no—
497C4⋊Q8—864no—
498#126—24no—
499#126—864no—
500#126—864no—
501#126—864no—
502#126—864no—
503#126—864no—
504#126—864no—
505#126—864no—
506C2×C4⋊C4—431no—
507C2×C4⋊C4—431no—
508C2×C4⋊C4—431no—
509C2×C4⋊C4—431no—
510C2×C4⋊C4—431no—
511C2×C4⋊C4—431no—
512C2×C4⋊C4—431no—
513C2×C4⋊C4—431no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—434no—
516C2×C4⋊C4—434no—
517C2×C4⋊C4—432no—
518C2×C4⋊C4—432no—
519C2×C4⋊C4—434no—
520C2×C4⋊C4—434no—
521C2×C4⋊C4—434no—
522C2×C4⋊C4—864no—
523C2×C4⋊C4—864no—
524C2×C4⋊C4—864no—
525C2×C4⋊C4—868no—
526C2×C4⋊C4—868no—
527C2×C4⋊C4—1728no—
528C2×C4⋊C4C22×D4311yescharacteristic
529C2×C4⋊C4C22×D4311yescharacteristic
530C2×C4⋊C4C22×D4311yescharacteristic
531C2×C4⋊C4C22×D4312yes—
532C2×C4⋊C4C22×D4312yes—
533C2×C4⋊C4C22×D4314yes—
534C2×C22⋊C4—431no—
535C2×C22⋊C4—431no—
536C2×C22⋊C4—431no—
537C2×C22⋊C4—431no—
538C2×C22⋊C4—431no—
539C2×C22⋊C4—431no—
540C2×C22⋊C4—431no—
541C2×C22⋊C4—431no—
542C2×C22⋊C4—431no—
543C2×C22⋊C4—434no—
544C2×C22⋊C4—434no—
545C2×C22⋊C4—434no—
546C2×C22⋊C4—864no—
547C2×C22⋊C4—864no—
548C2×C22⋊C4—864no—
549C2×C22⋊C4—1728no—
550C2×C22⋊C4C22×D4311yescharacteristic
551C2×C22⋊C4C22×D4311yescharacteristic
552C2×C22⋊C4C22×D4311yescharacteristic
553C2×C22⋊C4C22×D4314yes—
554C2×C42—431no—
555C2×C42—431no—
556C2×C42—431no—
557C2×C42—438no—
558C2×C42C22×D4311yescharacteristic
559#95—434no—
560#95—432no—
561#95—434no—
562#95—432no—
563#95—434no—
564#95—432no—
565#95—434no—
566#95—434no—
567#95—434no—
568#95—434no—
569#95—434no—
570#95—434no—
571#95C22×D4312yes—
572#95C22×D4312yes—
573#95C22×D4312yes—
574#95C22×D4314yes—
575#95C22×D4314yes—
576C24—431no—
577C24—431no—
578C24—862no—
579C24—864no—
580C24—864no—
581C24—864no—
582C24C23×D4311yescharacteristic
583C2×Q8—24no—
584C2×Q8—44no—
585C2×Q8—868no—
586C2×Q8—864no—
587C2×Q8—1724no—
588C2×Q8—1724no—
589C2×Q8—1724no—
590C2×Q8—17232no—
591C22×C4—431no—
592C22×C4—431no—
593C22×C4—431no—
594C22×C4—434no—
595C22×C4—434no—
596C22×C4—434no—
597C22×C4—434no—
598C22×C4—431no—
599C22×C4—431no—
600C22×C4—434no—
601C22×C4—431no—
602C22×C4—864no—
603C22×C4—864no—
604C22×C4—864no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—868no—
609C22×C4—868no—
610C22×C4—868no—
611C22×C4—864no—
612C22×C4—868no—
613C22×C4—864no—
614C22×C4—864no—
615C22×C4—868no—
616C22×C4—868no—
617C22×C4C23×D4314yes—
618C22×C4C23×D4311yescharacteristic
619C22×C4C23×D4311yescharacteristic
620C22×C4C23×D4314yes—
621C22×C4C23×D4311yescharacteristic
622C22×C4C23×D4311yescharacteristic
623C22×C4C23×D4311yescharacteristic
624C22×C4C23×D4311yescharacteristic
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—24no—
629C4⋊C4—24no—
630C4⋊C4—44no—
631C4⋊C4—862no—
632C4⋊C4—862no—
633C4⋊C4—862no—
634C4⋊C4—862no—
635C4⋊C4—862no—
636C4⋊C4—862no—
637C4⋊C4—868no—
638C4⋊C4—868no—
639C4⋊C4—862no—
640C4⋊C4—862no—
641C4⋊C4—862no—
642C4⋊C4—864no—
643C4⋊C4—864no—
644C4⋊C4—1724no—
645C4⋊C4—1724no—
646C4⋊C4—1724no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—44no—
651C22⋊C4—862no—
652C22⋊C4—862no—
653C22⋊C4—862no—
654C22⋊C4—862no—
655C22⋊C4—862no—
656C22⋊C4—862no—
657C22⋊C4—862no—
658C22⋊C4—862no—
659C22⋊C4—862no—
660C22⋊C4—1724no—
661C22⋊C4—1724no—
662C22⋊C4—1724no—
663C42—434no—
664C42—434no—
665C42—434no—
666C42D4×D4314yes—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—432no—
672C23—434no—
673C23—434no—
674C23—434no—
675C23—861no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23—1724no—
680C23—1724no—
681C23—1724no—
682C23—17216no—
683C23C24×D4311yescharacteristic
684Q8—48no—
685Q8—1728no—
686Q8—17216no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—432no—
703C2×C4—432no—
704C2×C4—432no—
705C2×C4—868no—
706C2×C4—868no—
707C2×C4—868no—
708C2×C4—862no—
709C2×C4—862no—
710C2×C4—862no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—864no—
715C2×C4—864no—
716C2×C4—864no—
717C2×C4—862no—
718C2×C4—864no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—864no—
722C2×C4—864no—
723C2×C4—17216no—
724C2×C4—1724no—
725C2×C4—1724no—
726C2×C4—1724no—
727C2×C4—17216no—
728C2×C4C2×D4×D4312yes—
729C2×C4C2×D4×D4312yes—
730C2×C4C2×D4×D4312yes—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—44no—
735C22—434no—
736C22—434no—
737C22—434no—
738C22—4316no—
739C22—3448no—
740C22—1721no—
741C22—1721no—
742C22—1721no—
743C22—1724no—
744C22C22×D4×D4311yescharacteristic
745C22H(5,𝔽2)×D4312yes—
746C222−1+4×D4312yes—
747C222−1+4×D4312yes—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—44no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—44no—
756C4—862no—
757C4—862no—
758C4—862no—
759C4—1724no—
760C4—1721no—
761C4—1721no—
762C4—1721no—
763C4—1724no—
764C2—81no—
765C2—438no—
766C2—3441no—
767C2#535×D4311yescharacteristic
768C2#536×D4311yescharacteristic
769C2#536×D4311yescharacteristic
770C2#563×D4314yes—
subgroupG/H
center, FrattiniC23C24×D43
commutator, socle, cosocleC23×C43C25
FittingC43×#2821C2
prime radicalC24×D43C23
hypercenter#2821D43
hypocenterC43C2×#2821
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2821

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D43C2semidirect
3. #19142660C2semidirect
4. #19142659C2semidirect
5. #19142658C2semidirect
6. #19142657C2semidirect
7. #19142656C2semidirect
8. #19142655C2semidirect
9. #19142654C2semidirect
10. #19142653C2semidirect
11. #19142652C2semidirect
12. #400×D43C2semidirect
14. #398×D43C2semidirect
16. #395×D43C2semidirect
18. #383×D43C2semidirect
19. C43×#2821C2semidirect
21. C2×#13063325C22semidirect
22. C2×#13063324C22semidirect
23. C2×#13063324C22semidirect
24. C2×#13063323C22semidirect
45. #14582841C22semidirect
46. #14582840C22semidirect
47. #14582839C22semidirect
48. #14582838C22semidirect
49. #14582837C22semidirect
55. #14582833C22semidirect
56. #14582832C22semidirect
57. #14582831C22semidirect
58. #14582830C22semidirect
59. #14582829C22semidirect
65. #14582820C22semidirect
66. #14582820C22semidirect
67. #14582819C22semidirect
68. #14582819C22semidirect
69. #14582818C22semidirect
75. #14582767C22semidirect
76. #14582766C22semidirect
77. #14582766C22semidirect
78. #14582766C22semidirect
84. C2×C4⋊Q8×C43C22semidirect
86. C43×#400C22semidirect
88. C43×#398C22semidirect
90. C43×#395C22semidirect
92. C43×#383C22semidirect
390. #2821D43direct (N × H)
404. D43#2821direct (N × H)
411. C2×C4⋊Q8C2×D43semidirect
437. #400C2×D43semidirect
449. #398C2×D43semidirect
461. #395C2×D43semidirect
472. #383C2×D43semidirect
478. C43C2×#2821semidirect

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×#126×D432
#191426602
#191426592
#191426582
#191426572
#191426562
#191426552
#191426542
#191426532
#191426522
#400×D432
#399×D432
#398×D432
#397×D432
#395×D432
#393×D432
#383×D432
C43×#28212
C2×#282143