Finite Group Databasebeta

← #25965505

Subgroups — #25965505

Order 11008.

2084 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148330C211yesmaximal, characteristic, complemented
2#19144886C212yesmaximal, complemented
3#19144838C212yesmaximal, complemented
4#19144824C212yesmaximal, complemented
5#19144779C212yesmaximal, complemented
6#19144746C212yesmaximal, complemented
7#19144704C212yesmaximal, complemented
8#19144655C212yesmaximal, complemented
9#19144613C212yesmaximal, complemented
10#19144526C211yesmaximal, characteristic, complemented
11C2×#14583223C211yesmaximal, characteristic, complemented
12#19144457C211yesmaximal, characteristic, complemented
13#19144446C211yesmaximal, characteristic, complemented
14#19144134C211yesmaximal, characteristic, complemented
15#19144134C211yesmaximal, characteristic, complemented
16#19143847C211yesmaximal, characteristic, complemented
17#19143813C211yesmaximal, characteristic, complemented
18#19143476C211yesmaximal, characteristic, complemented
19#19143468C211yesmaximal, characteristic, complemented
20#19143423C211yesmaximal, characteristic, complemented
21#19143423C211yesmaximal, characteristic, complemented
22#19143253C211yesmaximal, characteristic, complemented
23C43×#3428C211yesmaximal, characteristic, complemented
24C2×#13063350C2211yescharacteristic
25C2×#13063350C2211yescharacteristic
26C2×#13063345C2211yescharacteristic
27C2×#13063345C2211yescharacteristic
28#14583612—21no—
29#14583597—21no—
30#14583593—21no—
31#14583573—22no—
32#14583550—21no—
33#14583539—22no—
34#14583527C2211yescharacteristic, complemented
35#14583520C2212yes—
36#14583504C2212yes—
37#14583468C2211yescharacteristic, complemented
38#14583449C2212yescomplemented
39#14583433C2212yescomplemented
40#14583410C2211yescharacteristic
41C2×#13063299C2211yescharacteristic
42#14583379C2211yescharacteristic, complemented
43#14583373C2211yescharacteristic, complemented
44#14583240C2212yescomplemented
45#14583240C2212yescomplemented
46#14583223C2212yes—
47#14583223C2212yes—
48#14583223C2212yescomplemented
49#14583223C2212yescomplemented
50#14583223C2212yescomplemented
51#14583223C2212yescomplemented
52#14583206C2212yescomplemented
53#14583206C2212yescomplemented
54#14583199C2212yescomplemented
55#14583199C2212yescomplemented
56#14583194C2212yescomplemented
57#14583189C2212yescomplemented
58#14583184C2212yescomplemented
59#14583179C2212yescomplemented
60#14583121C2212yescomplemented
61#14583121C2212yescomplemented
62#14583114C2212yescomplemented
63#14583114C2212yescomplemented
64#14583099C2212yescomplemented
65#14583099C2212yescomplemented
66#14583094C2212yescomplemented
67#14583094C2212yescomplemented
68#14583061C2211yescharacteristic, complemented
69#14583061C2211yescharacteristic, complemented
70#14583055C2211yescharacteristic, complemented
71#14583050C2211yescharacteristic, complemented
72#14583044C2212yes—
73#14583044C2212yes—
74#14583044C2211yescharacteristic, complemented
75#14583044C2211yescharacteristic, complemented
76#14583038C2212yes—
77#14583038C2211yescharacteristic, complemented
78#14583033C2212yes—
79#14583033C2211yescharacteristic, complemented
80#14583009C2212yescomplemented
81#14583009C2212yescomplemented
82#14583009C2212yescomplemented
83#14583004C2212yescomplemented
84#14582999C2212yescomplemented
85#14582997C2212yescomplemented
86#14582997C2212yescomplemented
87#14582997C2212yescomplemented
88C4×#10621885C2212yescomplemented
89C4×#10621884C2212yescomplemented
90C4×#10621884C2212yescomplemented
91C4×#10621884C2212yescomplemented
92C4×#10621883C2212yescomplemented
93C4×#10621882C2212yescomplemented
94C4×#10621882C2212yescomplemented
95C4×#10621882C2212yescomplemented
96#14582960C2212yescomplemented
97#14582960C2212yescomplemented
98#14582956C2212yescomplemented
99#14582952C2212yescomplemented
100#14582939C2211yescharacteristic, complemented
101#14582939C2211yescharacteristic, complemented
102C2×#13063258C2211yescharacteristic, complemented
103C2×#13063256C2211yescharacteristic, complemented
104#14582926C2211yescharacteristic, complemented
105#14582926C2211yescharacteristic, complemented
106#14582900C2211yescharacteristic
107#14582900C2211yescharacteristic
108#14582898C2211yescharacteristic, complemented
109#14582898C2211yescharacteristic, complemented
110#14582895C2211yescharacteristic
111#14582895C2211yescharacteristic
112C2×#13063245C2211yescharacteristic, complemented
113C2×#13063245C2211yescharacteristic, complemented
114#14582863C2211yescharacteristic
115C2×C22⋊(C43⋊C8)C2211yescharacteristic
116#14582855C2211yescharacteristic, complemented
117#14582855C2211yescharacteristic, complemented
118C22×#41×C43C2211yescharacteristic
119C43×#520—21no—
120C43×#520—21no—
121C43×#520C2211yescharacteristic
122C43×#520C2211yescharacteristic
123C43×#520C2211yescharacteristic
124C43×#520C2211yescharacteristic
125C43×#519C2212yescomplemented
126C43×#518—22no—
127C43×#518C2212yescomplemented
128C4×#41×C43—22no—
129C4×#41×C43C2212yescomplemented
130C4×#41×C43C2212yescomplemented
131C2×#117×C43—21no—
132C2×#117×C43—21no—
133C2×#117×C43C2211yescharacteristic
134C2×#117×C43C2211yescharacteristic
135C2×#10621898—22no—
136C2×#10621898C2311yescharacteristic
137C22×D172C2311yescharacteristic
138C22×C22⋊D43—21no—
139#13063350—24no—
140#13063350—24no—
141#13063345—24no—
142#13063345—24no—
143C2×#10621885C2311yescharacteristic
144C2×#10621885C2311yescharacteristic
145C2×#10621883C2311yescharacteristic
146C2×#10621883C2311yescharacteristic
147C2×#10621884C2312yes—
148C2×#10621884C2312yes—
149C2×#10621884C2311yescharacteristic
150C2×#10621884C2311yescharacteristic
151C2×#10621882C2312yes—
152C2×#10621882C2312yes—
153C2×#10621882C2311yescharacteristic
154C2×#10621882C2311yescharacteristic
155C2×#10621877C2311yescharacteristic
156C2×#10621877C2311yescharacteristic
157C22×C43⋊C8C2311yescharacteristic
158C22×C43⋊C8C2311yescharacteristic
159#13063325C2312yes—
160#13063324—21no—
161#13063322C2312yes—
162#13063320—22no—
163#13063319—22no—
164#13063317C2312yes—
165#13063316—21no—
166#13063313—22no—
167#13063313C2312yes—
168#13063311—22no—
169#13063310—22no—
170#13063310—22no—
171#13063308—21no—
172#13063308—22no—
173#13063307—22no—
174#13063304C2311yescharacteristic
175#13063304C2311yescharacteristic
176#13063303—22no—
177#13063302—22no—
178#13063300—21no—
179#13063300—21no—
180#13063299—21no—
181#13063299—21no—
182#13063299—22no—
183#13063299C2312yes—
184#13063299C2311yescharacteristic
185#13063299C2312yes—
186#13063299C2311yescharacteristic
187#13063298—22no—
188#13063298—22no—
189#13063295—22no—
190#13063294—21no—
191C4×Dic86C2312yes—
192C4×D172—22no—
193C4×D172C2312yes—
194C4×D172C2312yes—
195C4×D172C2312yes—
196#13063287—21no—
197#13063287—21no—
198C4×C22⋊D43—21no—
199C4×C22⋊D43—21no—
200C4×C22⋊D43—22no—
201(C22⋊D43)⋊C4—22no—
202#13063284C2311yescharacteristic
203#13063283—21no—
204#13063282—22no—
205C2×C4⋊Dic43C2311yescharacteristic
206C4⋊C4×D43—21no—
207C2×(C2×D43)⋊C4—21no—
208C22⋊C4×D43—22no—
209#13063258C2312yes—
210#13063258C2312yes—
211#13063258C2312yes—
212#13063258C2312yes—
213#13063256C2312yes—
214#13063256C2312yes—
215#13063256C2312yes—
216#13063256C2312yes—
217C4⋊(C43⋊C8)C2312yes—
218C4⋊(C43⋊C8)C2312yes—
219C4⋊(C43⋊C8)C2312yes—
220C4⋊(C43⋊C8)C2312yes—
221#13063249C2312yes—
222#13063249C2312yes—
223#13063249C2311yescharacteristic
224#13063249C2311yescharacteristic
225#13063249C2311yescharacteristic
226#13063249C2311yescharacteristic
227#13063248C2312yes—
228#13063248C2312yes—
229#13063246C2312yes—
230#13063246C2312yes—
231#13063246C2311yescharacteristic
232#13063246C2311yescharacteristic
233#13063246C2311yescharacteristic
234#13063246C2311yescharacteristic
235#13063245C2312yes—
236#13063245C2312yes—
237#13063245C2312yes—
238#13063245C2312yes—
239#13063245C2312yes—
240#13063245C2312yes—
241C22⋊(C43⋊C8)C2312yes—
242C22⋊(C43⋊C8)C2311yescharacteristic
243C22⋊(C43⋊C8)C2311yescharacteristic
244C22⋊(C43⋊C8)C2311yescharacteristic
245C22⋊(C43⋊C8)C2311yescharacteristic
246C22⋊(C43⋊C8)C2312yes—
247#13063236C2312yes—
248#13063236C2312yes—
249C4×C43⋊C8C2312yes—
250C4×C43⋊C8C2312yes—
251C2×#41×C43—24no—
252C2×#41×C43—24no—
253C2×#41×C43—21no—
254C2×#41×C43—21no—
255C2×#41×C43C2311yescharacteristic
256C2×#41×C43C2311yescharacteristic
257C2×#41×C43C2311yescharacteristic
258C2×#41×C43C2311yescharacteristic
259C22×Q8×C43C2311yescharacteristic
260C22×D4×C43—21no—
261C22×D4×C43C2311yescharacteristic
262C23×C4×C43—21no—
263C23×C4×C43C2311yescharacteristic
264C4×Q8×C43—22no—
265C4×Q8×C43—22no—
266C4×Q8×C43C2312yes—
267C4×Q8×C43C2312yes—
268C4×Q8×C43C2312yes—
269C4×Q8×C43C2312yes—
270C4×D4×C43—22no—
271C4×D4×C43—22no—
272C4×D4×C43—22no—
273C4×D4×C43—22no—
274C4×D4×C43—22no—
275C4×D4×C43—22no—
276C4×D4×C43—22no—
277C4×D4×C43—22no—
278C4×D4×C43—22no—
279C4×D4×C43—22no—
280C4×D4×C43C2312yes—
281C4×D4×C43C2312yes—
282C4×D4×C43C2312yes—
283C4×D4×C43C2312yes—
284#117×C43—21no—
285#117×C43—21no—
286#117×C43—21no—
287#117×C43—21no—
288#117×C43—21no—
289#117×C43—21no—
290#117×C43—22no—
291#117×C43—22no—
292#117×C43—22no—
293#117×C43—22no—
294#117×C43D411yescharacteristic
295#117×C43D411yescharacteristic
296#117×C43D412yes—
297#117×C43C2312yes—
298#117×C43C2312yes—
299#117×C43C2312yes—
300#117×C43C2311yescharacteristic
301#117×C43C2311yescharacteristic
302C2×C4⋊C4×C43—21no—
303C2×C4⋊C4×C43—21no—
304C2×C4⋊C4×C43—21no—
305C2×C4⋊C4×C43—21no—
306C2×C4⋊C4×C43D411yescharacteristic
307C2×C4⋊C4×C43D411yescharacteristic
308C2×C4⋊C4×C43C2311yescharacteristic
309C2×C4⋊C4×C43C2311yescharacteristic
310C2×C22⋊C4×C43—21no—
311C2×C22⋊C4×C43—22no—
312C2×C22⋊C4×C43—22no—
313C2×C22⋊C4×C43D412yes—
314C2×C42×C43—21no—
315C2×C42×C43—22no—
316C2×C42×C43—22no—
317C2×C42×C43C2312yes—
318C24×C43—21no—
319C24×C43C2×D411yescharacteristic
320C23×D43—21no—
321#41×C43—28no—
322#41×C43—28no—
323#41×C43—22no—
324#41×C43—22no—
325#41×C43—22no—
326#41×C43—22no—
327#41×C43—22no—
328#41×C43—22no—
329#41×C43#4114yescomplemented
330#41×C43#4114yescomplemented
331C2×Q8×C43—22no—
332C2×Q8×C43—22no—
333C2×Q8×C43—21no—
334C2×Q8×C43C2411yescharacteristic
335C2×Q8×C43C2411yescharacteristic
336C2×D4×C43—28no—
337C2×D4×C43—22no—
338C2×D4×C43—22no—
339C2×D4×C43—21no—
340C2×D4×C43—21no—
341C2×D4×C43—21no—
342C2×D4×C43—21no—
343C2×D4×C43—21no—
344C2×D4×C43C2411yescharacteristic
345C2×D4×C43C2411yescharacteristic
346C22×C4×C43—28no—
347C22×C4×C43—21no—
348C22×C4×C43—21no—
349C22×C4×C43—21no—
350C22×C4×C43—21no—
351C22×C4×C43—22no—
352C22×C4×C43—22no—
353C22×C4×C43—22no—
354C22×C4×C43—22no—
355C22×C4×C43—22no—
356C22×C4×C43—22no—
357C22×C4×C43—21no—
358C22×C4×C43—21no—
359C22×C4×C43—21no—
360C22×C4×C43C2×D411yescharacteristic
361C22×C4×C43C2×D411yescharacteristic
362C22×C4×C43C2×D411yescharacteristic
363C22×C4×C43C2×D412yes—
364C22×C4×C43C2×D412yes—
365C22×C4×C43C2411yescharacteristic
366C22×C4×C43C2411yescharacteristic
367C22×C4×C43C2411yescharacteristic
368C2×C22⋊D43—21no—
369C2×C22⋊D43—21no—
370C2×C22⋊D43—22no—
371C2×C22⋊D43—21no—
372C2×C22⋊D43—22no—
373C2×C22⋊D43—82no—
374C22×Dic43—21no—
375#10621898—22no—
376#10621898—22no—
377#10621898—84no—
378C2×D172—21no—
379C2×D172—22no—
380C2×D172—22no—
381C2×D172—22no—
382C2×D172—22no—
383C2×D172C2412yes—
384C2×D172C2411yescharacteristic
385C2×C4×D43—21no—
386C2×C4×D43—22no—
387C2×C4×D43—22no—
388C2×C4×D43—22no—
389C2×Dic86—22no—
390C2×Dic86C2411yescharacteristic
391C4⋊C4×C43—21no—
392C4⋊C4×C43—21no—
393C4⋊C4×C43—22no—
394C4⋊C4×C43—22no—
395C4⋊C4×C43—22no—
396C4⋊C4×C43—22no—
397C4⋊C4×C43C2×D411yescharacteristic
398C4⋊C4×C43C2×D411yescharacteristic
399C4⋊C4×C43C2×D411yescharacteristic
400C4⋊C4×C43C2×D411yescharacteristic
401C4⋊C4×C43C2×D412yes—
402C4⋊C4×C43C2×D412yes—
403C4⋊C4×C43C2412yes—
404C4⋊C4×C43C2412yes—
405C22⋊C4×C43—22no—
406C22⋊C4×C43—22no—
407C22⋊C4×C43—22no—
408C22⋊C4×C43—22no—
409C22⋊C4×C43—22no—
410C22⋊C4×C43—22no—
411C22⋊C4×C43C2×D412yes—
412C22⋊C4×C43C2×D412yes—
413C22⋊C4×C43C2×D412yes—
414C22⋊C4×C43C2×D412yes—
415C42×C43—22no—
416C42×C43—22no—
417C42×C43—22no—
418C42×C43—22no—
419C42×C43—22no—
420C42×C43—22no—
421C42×C43C2×D412yes—
422C42×C43C2×D412yes—
423C42×C43C2412yes—
424C42×C43C2412yes—
425C22⋊Dic43—21no—
426C22⋊Dic43—21no—
427C22⋊Dic43—21no—
428#10621885—22no—
429#10621885—22no—
430#10621884—22no—
431#10621884—22no—
432#10621884—24no—
433#10621884—24no—
434#10621883—22no—
435#10621883—22no—
436#10621882—22no—
437#10621882—22no—
438#10621882—24no—
439#10621882—24no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—22no—
442(C2×D43)⋊C4—22no—
443(C2×D43)⋊C4—22no—
444(C2×D43)⋊C4—22no—
445(C2×D43)⋊C4—22no—
446(C2×D43)⋊C4—21no—
447(C2×D43)⋊C4—22no—
448(C2×D43)⋊C4—21no—
449C4⋊Dic43—21no—
450C4⋊Dic43—22no—
451C4⋊Dic43C2412yes—
452C4⋊Dic43C2411yescharacteristic
453C4⋊Dic43C2411yescharacteristic
454Dic43⋊C4—22no—
455Dic43⋊C4—21no—
456Dic43⋊C4—22no—
457Dic43⋊C4—22no—
458Dic43⋊C4—21no—
459C4×Dic43—22no—
460C4×Dic43—21no—
461#10621877—22no—
462#10621877—22no—
463C2×C43⋊C8—22no—
464C2×C43⋊C8—22no—
465C2×C43⋊C8C2411yescharacteristic
466C2×C43⋊C8C2411yescharacteristic
467C2×C43⋊C8C2412yes—
468C2×C43⋊C8C2412yes—
469C2×C43⋊C8C2411yescharacteristic
470C2×C43⋊C8C2411yescharacteristic
471C23×C43—24no—
472C23×C43—21no—
473C23×C43—21no—
474C23×C43—22no—
475C23×C43—41no—
476C23×C43—41no—
477C23×C43—81no—
478C23×C43—81no—
479C23×C43C22×D411yescharacteristic
480C23×C43C22×D411yescharacteristic
481C23×C43C22×D411yescharacteristic
482C22×D43—22no—
483C22×D43—21no—
484C22×D43—42no—
485C22×D43—81no—
486C22×D43—81no—
487Q8×C43—24no—
488Q8×C43—21no—
489Q8×C43—21no—
490Q8×C43C2×#4112yes—
491Q8×C43C2×#4112yes—
492D4×C43—24no—
493D4×C43—24no—
494D4×C43—24no—
495D4×C43—24no—
496D4×C43—24no—
497D4×C43—21no—
498D4×C43—21no—
499D4×C43C2×#4112yes—
500D4×C43C2×#4112yes—
501C2×C4×C43—24no—
502C2×C4×C43—24no—
503C2×C4×C43—24no—
504C2×C4×C43—22no—
505C2×C4×C43—21no—
506C2×C4×C43—21no—
507C2×C4×C43—22no—
508C2×C4×C43—24no—
509C2×C4×C43—24no—
510C2×C4×C43—22no—
511C2×C4×C43—21no—
512C2×C4×C43—21no—
513C2×C4×C43—21no—
514C2×C4×C43—21no—
515C2×C4×C43—22no—
516C2×C4×C43—22no—
517C2×C4×C43—42no—
518C2×C4×C43—42no—
519C2×C4×C43—82no—
520C2×C4×C43—82no—
521C2×C4×C43—82no—
522C2×C4×C43—82no—
523C2×C4×C43—81no—
524C2×C4×C43—81no—
525C2×C4×C43C22×D412yes—
526C2×C4×C43C22×D412yes—
527C2×C4×C43C22×D411yescharacteristic
528C2×C4×C43C22×D411yescharacteristic
529C2×C4×C43C22×D412yes—
530C2×C4×C43C22×D412yes—
531C2×C4×C43C22×D411yescharacteristic
532C2×C4×C43C2×#4112yes—
533C2×C4×C43C2×#4112yes—
534C2×C4×C43C2511yescharacteristic
535C22⋊D43—42no—
536C22⋊D43—44no—
537C22⋊D43—42no—
538C22⋊D43—81no—
539C22⋊D43—82no—
540C2×Dic43—21no—
541C2×Dic43—21no—
542C2×Dic43—22no—
543C2×Dic43—21no—
544C2×Dic43—81no—
545D172—22no—
546D172—22no—
547D172—21no—
548D172—21no—
549D172—42no—
550D172—82no—
551D172—82no—
552C4×D43—42no—
553C4×D43—82no—
554C4×D43—82no—
555C4×D43—82no—
556Dic86—21no—
557Dic86—21no—
558Dic86—82no—
559C43⋊C8—21no—
560C43⋊C8—21no—
561C43⋊C8—21no—
562C43⋊C8—21no—
563C43⋊C8—22no—
564C43⋊C8—22no—
565#60587—431nomaximal, Sylow
566C22×C43—21no—
567C22×C43—21no—
568C22×C43—21no—
569C22×C43—21no—
570C22×C43—21no—
571C22×C43—21no—
572C22×C43—21no—
573C22×C43—22no—
574C22×C43—22no—
575C22×C43—21no—
576C22×C43—41no—
577C22×C43—41no—
578C22×C43—41no—
579C22×C43—41no—
580C22×C43—82no—
581C22×C43—84no—
582C22×C43#52512yes—
583C22×C43C23×D411yescharacteristic
584C2×D43—42no—
585C2×D43—41no—
586C2×D43—42no—
587C2×D43—41no—
588C2×D43—42no—
589C2×D43—41no—
590C2×D43—162no—
591C4×C43—22no—
592C4×C43—22no—
593C4×C43—22no—
594C4×C43—22no—
595C4×C43—21no—
596C4×C43—22no—
597C4×C43—22no—
598C4×C43—21no—
599C4×C43—42no—
600C4×C43—42no—
601C4×C43#52512yes—
602C4×C43C22×#4111yescharacteristic
603C4×C43C22×#4111yescharacteristic
604Dic43—41no—
605Dic43—41no—
606Dic43—42no—
607Dic43—41no—
608#3494—431no—
609#3428D4311yescharacteristic, complemented
610#3126—432no—
611#3122—432no—
612#3121—432no—
613#3118—432no—
614#3115—432no—
615#3111—432no—
616#3106—432no—
617#3102—432no—
618#3093—431no—
619C2×#482—431no—
620#3084—431no—
621#3083—431no—
622#3045—431no—
623#3045—431no—
624#3006—431no—
625#3002—431no—
626#2952—431no—
627#2951—431no—
628#2946—431no—
629#2946—431no—
630#2924—431no—
631C2×C43—22no—
632C2×C43—41no—
633C2×C43—41no—
634C2×C43—42no—
635C2×C43—42no—
636C2×C43C2×#52511yescharacteristic
637C2×C43#358411yescharacteristic
638C2×C43#358511yescharacteristic
639D43—81no—
640D43—82no—
641C22×#41C2×D4311yescharacteristic
642C2×AGL(1,ℤ/8)—431no—
643C2×AGL(1,ℤ/8)—431no—
644C2×#135—431no—
645C2×#135—431no—
646#555—861no—
647#553—861no—
648#553—861no—
649#551—862no—
650#547—861no—
651#546—862no—
652#544—431no—
653#542—432no—
654#540—432no—
655#535—431no—
656#532—432no—
657#529—432no—
658#525—431no—
659C2×#121—431no—
660#520—21no—
661#520—21no—
662#520—431no—
663#520C2×D4311yescharacteristic
664#520C2×D4311yescharacteristic
665#520C2×D4311yescharacteristic
666#520C2×D4311yescharacteristic
667#519C2×D4312yescomplemented
668#518—22no—
669#518—431no—
670#518C2×D4312yescomplemented
671C4×#41—22no—
672C4×#41C2×D4312yescomplemented
673C4×#41C2×D4312yescomplemented
674C2×#117—21no—
675C2×#117—21no—
676C2×#117C2×D4311yescharacteristic
677C2×#117C2×D4311yescharacteristic
678#485—432no—
679#485—432no—
680#482—432no—
681#482—432no—
682#482—432no—
683#482—432no—
684#482—432no—
685#482—432no—
686#479—432no—
687#479—432no—
688#478—432no—
689#478—432no—
690#477—432no—
691#476—432no—
692#475—432no—
693#474—432no—
694#464—432no—
695#464—432no—
696#463—432no—
697#463—432no—
698#460—432no—
699#460—432no—
700#459—432no—
701#459—432no—
702#452—431no—
703#452—431no—
704#451—431no—
705#450—431no—
706#449—432no—
707#449—432no—
708#449—431no—
709#449—431no—
710#448—432no—
711#448—431no—
712#447—432no—
713#447—431no—
714#442—432no—
715#442—432no—
716#442—432no—
717#441—432no—
718#440—432no—
719#440—432no—
720#440—432no—
721#440—432no—
722C4×Q16—432no—
723C4×SD16—432no—
724C4×SD16—432no—
725C4×SD16—432no—
726C4×SD16—432no—
727C4×D8—432no—
728C4×D8—432no—
729C4×D8—432no—
730#433—432no—
731#433—432no—
732#432—432no—
733#431—432no—
734#428—431no—
735#428—431no—
736C2×#107—431no—
737C2×#106—431no—
738#424—431no—
739#424—431no—
740#417—431no—
741#417—431no—
742#417—431no—
743#417—431no—
744#416—431no—
745#416—431no—
746C2×#102—431no—
747C2×#102—431no—
748#407—431no—
749C2×C22⋊C8—431no—
750#405—431no—
751#405—431no—
752C43#6058711yescharacteristic, complemented, Sylow
753C2×#41—24no—
754C2×#41—24no—
755C2×#41—21no—
756C2×#41—21no—
757C2×#41—431no—
758C2×#41—862no—
759C2×#41C22×D4311yescharacteristic
760C2×#41C22×D4311yescharacteristic
761C2×#41C22×D4311yescharacteristic
762C2×#41C22×D4311yescharacteristic
763C22×Q8C22×D4311yescharacteristic
764C22×D4—21no—
765C22×D4—431no—
766C22×D4—861no—
767C22×D4C22×D4311yescharacteristic
768C23×C4—21no—
769C23×C4C22×D4311yescharacteristic
770AGL(1,ℤ/8)—864no—
771AGL(1,ℤ/8)—864no—
772#135—864no—
773#135—864no—
774C2×Q16—431no—
775C2×Q16—431no—
776C2×SD16—431no—
777C2×SD16—431no—
778C2×SD16—432no—
779C2×SD16—432no—
780C2×SD16—431no—
781C2×SD16—431no—
782C2×D8—431no—
783C2×D8—431no—
784C2×D8—432no—
785C2×D8—432no—
786C2×M16—431no—
787C2×M16—431no—
788C22×C8—431no—
789C22×C8—431no—
790C4⋊Q8—432no—
791C4⋊Q8—861no—
792#127—432no—
793#126—862no—
794#126—862no—
795#125—432no—
796#125—861no—
797#124—432no—
798#124—862no—
799#124—862no—
800#123—861no—
801#123—862no—
802#123—862no—
803#123—862no—
804#123—862no—
805C22⋊Q8—431no—
806C22⋊Q8—431no—
807C22⋊Q8—862no—
808C22⋊Q8—862no—
809#121—432no—
810#121—432no—
811#121—431no—
812#121—431no—
813#121—861no—
814#121—861no—
815#121—862no—
816#121—861no—
817#121—861no—
818#121—862no—
819#121—862no—
820#120—861no—
821#120—862no—
822C4×Q8—22no—
823C4×Q8—22no—
824C4×Q8—432no—
825C4×Q8C22×D4312yes—
826C4×Q8C22×D4312yes—
827C4×Q8C22×D4312yes—
828C4×Q8C22×D4312yes—
829C4×D4—22no—
830C4×D4—22no—
831C4×D4—22no—
832C4×D4—22no—
833C4×D4—22no—
834C4×D4—22no—
835C4×D4—22no—
836C4×D4—22no—
837C4×D4—22no—
838C4×D4—22no—
839C4×D4—432no—
840C4×D4—432no—
841C4×D4—432no—
842C4×D4—861no—
843C4×D4—861no—
844C4×D4—862no—
845C4×D4—861no—
846C4×D4—861no—
847C4×D4—862no—
848C4×D4—862no—
849C4×D4C22×D4312yes—
850C4×D4C22×D4312yes—
851C4×D4C22×D4312yes—
852C4×D4C22×D4312yes—
853#117—21no—
854#117—21no—
855#117—21no—
856#117—21no—
857#117—21no—
858#117—21no—
859#117—22no—
860#117—22no—
861#117—22no—
862#117—22no—
863#117—431no—
864#117—861no—
865#117—862no—
866#117C22⋊D4311yescharacteristic
867#117C22⋊D4311yescharacteristic
868#117C22⋊D4312yes—
869#117C22×D4312yes—
870#117C22×D4312yes—
871#117C22×D4311yescharacteristic
872#117C22×D4312yes—
873#117C22×D4311yescharacteristic
874C2×C4⋊C4—21no—
875C2×C4⋊C4—21no—
876C2×C4⋊C4—21no—
877C2×C4⋊C4—21no—
878C2×C4⋊C4—431no—
879C2×C4⋊C4—861no—
880C2×C4⋊C4C22⋊D4311yescharacteristic
881C2×C4⋊C4C22⋊D4311yescharacteristic
882C2×C4⋊C4C22×D4311yescharacteristic
883C2×C4⋊C4C22×D4311yescharacteristic
884C2×C22⋊C4—21no—
885C2×C22⋊C4—22no—
886C2×C22⋊C4—22no—
887C2×C22⋊C4—861no—
888C2×C22⋊C4—862no—
889C2×C22⋊C4C22⋊D4312yes—
890C2×C42—21no—
891C2×C42—22no—
892C2×C42—22no—
893C2×C42C22×D4312yes—
894#107—432no—
895#107—432no—
896#107—432no—
897#107—432no—
898#106—432no—
899#106—432no—
900#106—432no—
901#106—432no—
902C4⋊C8—432no—
903C4⋊C8—432no—
904C4⋊C8—432no—
905C4⋊C8—432no—
906#103—431no—
907#103—431no—
908#103—431no—
909#103—431no—
910#103—432no—
911#103—432no—
912#103—432no—
913#103—432no—
914#102—431no—
915#102—431no—
916#102—431no—
917#102—431no—
918#102—432no—
919#102—432no—
920#102—432no—
921#102—432no—
922#102—432no—
923#102—432no—
924#102—432no—
925#102—432no—
926C22⋊C8—431no—
927C22⋊C8—431no—
928C22⋊C8—431no—
929C22⋊C8—431no—
930C22⋊C8—432no—
931C22⋊C8—432no—
932#97—432no—
933#97—432no—
934C4×C8—432no—
935C4×C8—432no—
936C24—21no—
937C24—861no—
938C24C2×C22⋊D4311yescharacteristic
939#41—28no—
940#41—28no—
941#41—22no—
942#41—22no—
943#41—22no—
944#41—22no—
945#41—22no—
946#41—22no—
947#41—862no—
948#41—862no—
949#41—3444no—
950#41#1062189814yescomplemented
951#41#1062189814yescomplemented
952C2×Q8—22no—
953C2×Q8—22no—
954C2×Q8—21no—
955C2×Q8—431no—
956C2×Q8—862no—
957C2×Q8C23×D4311yescharacteristic
958C2×Q8C23×D4311yescharacteristic
959C2×D4—28no—
960C2×D4—21no—
961C2×D4—21no—
962C2×D4—21no—
963C2×D4—21no—
964C2×D4—22no—
965C2×D4—22no—
966C2×D4—21no—
967C2×D4—432no—
968C2×D4—431no—
969C2×D4—861no—
970C2×D4—862no—
971C2×D4—861no—
972C2×D4—861no—
973C2×D4—862no—
974C2×D4—862no—
975C2×D4—862no—
976C2×D4—861no—
977C2×D4—862no—
978C2×D4—862no—
979C2×D4—3442no—
980C2×D4C23×D4311yescharacteristic
981C2×D4C23×D4311yescharacteristic
982C22×C4—28no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—861no—
997C22×C4—862no—
998C22×C4—862no—
999C22×C4—862no—
1000C22×C4—861no—
1001C22×C4C2×C22⋊D4311yescharacteristic
1002C22×C4C2×C22⋊D4311yescharacteristic
1003C22×C4C2×C22⋊D4311yescharacteristic
1004C22×C4C2×C22⋊D4312yes—
1005C22×C4C2×C22⋊D4312yes—
1006C22×C4C23×D4311yescharacteristic
1007C22×C4C23×D4311yescharacteristic
1008C22×C4C23×D4311yescharacteristic
1009Q16—862no—
1010Q16—862no—
1011SD16—862no—
1012SD16—862no—
1013SD16—864no—
1014SD16—864no—
1015SD16—862no—
1016SD16—862no—
1017D8—862no—
1018D8—862no—
1019D8—864no—
1020D8—864no—
1021M16—862no—
1022M16—862no—
1023C2×C8—431no—
1024C2×C8—431no—
1025C2×C8—432no—
1026C2×C8—432no—
1027C2×C8—431no—
1028C2×C8—431no—
1029C2×C8—862no—
1030C2×C8—862no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—22no—
1037C4⋊C4—432no—
1038C4⋊C4—431no—
1039C4⋊C4—431no—
1040C4⋊C4—861no—
1041C4⋊C4—862no—
1042C4⋊C4—861no—
1043C4⋊C4—862no—
1044C4⋊C4—862no—
1045C4⋊C4—862no—
1046C4⋊C4—861no—
1047C4⋊C4C2×C22⋊D4311yescharacteristic
1048C4⋊C4C2×C22⋊D4311yescharacteristic
1049C4⋊C4C2×C22⋊D4311yescharacteristic
1050C4⋊C4C2×C22⋊D4311yescharacteristic
1051C4⋊C4C2×C22⋊D4312yes—
1052C4⋊C4C2×C22⋊D4312yes—
1053C4⋊C4C23×D4312yes—
1054C4⋊C4C23×D4312yes—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—861no—
1062C22⋊C4—861no—
1063C22⋊C4—861no—
1064C22⋊C4—862no—
1065C22⋊C4—862no—
1066C22⋊C4—862no—
1067C22⋊C4—862no—
1068C22⋊C4—862no—
1069C22⋊C4—862no—
1070C22⋊C4—861no—
1071C22⋊C4—862no—
1072C22⋊C4—861no—
1073C22⋊C4C2×C22⋊D4312yes—
1074C22⋊C4C2×C22⋊D4312yes—
1075C22⋊C4C2×C22⋊D4312yes—
1076C22⋊C4C2×C22⋊D4312yes—
1077C42—22no—
1078C42—22no—
1079C42—22no—
1080C42—22no—
1081C42—22no—
1082C42—22no—
1083C42—861no—
1084C42—862no—
1085C42C2×C22⋊D4312yes—
1086C42C2×C22⋊D4312yes—
1087C42C23×D4312yes—
1088C42C23×D4312yes—
1089C23—24no—
1090C23—21no—
1091C23—21no—
1092C23—22no—
1093C23—41no—
1094C23—41no—
1095C23—81no—
1096C23—81no—
1097C23—862no—
1098C23—861no—
1099C23—3441no—
1100C23—3441no—
1101C23—1722no—
1102C23C22×C22⋊D4311yescharacteristic
1103C23C22×C22⋊D4311yescharacteristic
1104C23C22×C22⋊D4311yescharacteristic
1105Q8—24no—
1106Q8—21no—
1107Q8—21no—
1108Q8—861no—
1109Q8—861no—
1110Q8—3442no—
1111Q8C2×#1062189812yes—
1112Q8C2×#1062189812yes—
1113D4—24no—
1114D4—24no—
1115D4—24no—
1116D4—24no—
1117D4—24no—
1118D4—21no—
1119D4—21no—
1120D4—862no—
1121D4—862no—
1122D4—861no—
1123D4—861no—
1124D4—3442no—
1125D4—3442no—
1126D4—3442no—
1127D4—3441no—
1128D4—1724no—
1129D4—1722no—
1130D4—1722no—
1131D4—1722no—
1132D4C2×#1062189812yes—
1133D4C2×#1062189812yes—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—82no—
1153C2×C4—82no—
1154C2×C4—82no—
1155C2×C4—82no—
1156C2×C4—81no—
1157C2×C4—81no—
1158C2×C4—861no—
1159C2×C4—861no—
1160C2×C4—861no—
1161C2×C4—862no—
1162C2×C4—3442no—
1163C2×C4—3442no—
1164C2×C4—3442no—
1165C2×C4—3441no—
1166C2×C4—1722no—
1167C2×C4C22×C22⋊D4311yescharacteristic
1168C2×C4C22×C22⋊D4311yescharacteristic
1169C2×C4C22×C22⋊D4312yes—
1170C2×C4C22×C22⋊D4312yes—
1171C2×C4C22×C22⋊D4312yes—
1172C2×C4C22×C22⋊D4312yes—
1173C2×C4C22×C22⋊D4311yescharacteristic
1174C2×C4C2×#1062189812yes—
1175C2×C4C2×#1062189812yes—
1176C2×C4C24×D4311yescharacteristic
1177C8—861no—
1178C8—861no—
1179C8—861no—
1180C8—861no—
1181C8—862no—
1182C8—862no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—22no—
1190C22—22no—
1191C22—21no—
1192C22—21no—
1193C22—41no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—82no—
1198C22—84no—
1199C22—1722no—
1200C22—1721no—
1201C22—1721no—
1202C22—1722no—
1203C22—1721no—
1204C22—1722no—
1205C22—6882no—
1206C22#1458341012yes—
1207C22C23×C22⋊D4311yescharacteristic
1208C4—22no—
1209C4—22no—
1210C4—21no—
1211C4—22no—
1212C4—22no—
1213C4—21no—
1214C4—22no—
1215C4—22no—
1216C4—42no—
1217C4—42no—
1218C4—1721no—
1219C4—1721no—
1220C4—1722no—
1221C4—1721no—
1222C4#1458341012yes—
1223C4C22×#1062189811yescharacteristic
1224C4C22×#1062189811yescharacteristic
1225C2—22no—
1226C2—41no—
1227C2—41no—
1228C2—42no—
1229C2—42no—
1230C2—3442no—
1231C2—3441no—
1232C2C2×#1458341011yescharacteristic
1233C2#1914936611yescharacteristic
1234C2#1914937411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3428C2
socleC22×C43C23×D4
hypercenter#3428D43
hypocenterC43#60587
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. #19148330C2semidirect
2. #19144886C2semidirect
3. #19144838C2semidirect
4. #19144824C2semidirect
5. #19144779C2semidirect
6. #19144746C2semidirect
7. #19144704C2semidirect
8. #19144655C2semidirect
9. #19144613C2semidirect
10. #19144526C2semidirect
11. C2×#14583223C2semidirect
12. #19144457C2semidirect
13. #19144446C2semidirect
14. #19144134C2semidirect
15. #19144134C2semidirect
16. #19143847C2semidirect
17. #19143813C2semidirect
18. #19143476C2semidirect
19. #19143468C2semidirect
20. #19143423C2semidirect
21. #19143423C2semidirect
22. #19143253C2semidirect
23. C43×#3428C2semidirect
34. #14583527C22semidirect
37. #14583468C22semidirect
38. #14583449C22semidirect
39. #14583433C22semidirect
42. #14583379C22semidirect
43. #14583373C22semidirect
44. #14583240C22semidirect
45. #14583240C22semidirect
48. #14583223C22semidirect
49. #14583223C22semidirect
50. #14583223C22semidirect
51. #14583223C22semidirect
52. #14583206C22semidirect
53. #14583206C22semidirect
54. #14583199C22semidirect
55. #14583199C22semidirect
56. #14583194C22semidirect
57. #14583189C22semidirect
58. #14583184C22semidirect
59. #14583179C22semidirect
60. #14583121C22semidirect
61. #14583121C22semidirect
62. #14583114C22semidirect
63. #14583114C22semidirect
64. #14583099C22semidirect
65. #14583099C22semidirect
66. #14583094C22semidirect
67. #14583094C22semidirect
68. #14583061C22semidirect
69. #14583061C22semidirect
70. #14583055C22semidirect
71. #14583050C22semidirect
74. #14583044C22semidirect
75. #14583044C22semidirect
77. #14583038C22semidirect
79. #14583033C22semidirect
80. #14583009C22semidirect
81. #14583009C22semidirect
82. #14583009C22semidirect
83. #14583004C22semidirect
84. #14582999C22semidirect
85. #14582997C22semidirect
86. #14582997C22semidirect
87. #14582997C22semidirect
88. C4×#10621885C22semidirect
89. C4×#10621884C22semidirect
90. C4×#10621884C22semidirect
91. C4×#10621884C22semidirect
92. C4×#10621883C22semidirect
93. C4×#10621882C22semidirect
94. C4×#10621882C22semidirect
95. C4×#10621882C22semidirect
96. #14582960C22semidirect
97. #14582960C22semidirect
98. #14582956C22semidirect
99. #14582952C22semidirect
100. #14582939C22semidirect
101. #14582939C22semidirect
102. C2×#13063258C22semidirect
103. C2×#13063256C22semidirect
104. #14582926C22semidirect
105. #14582926C22semidirect
108. #14582898C22semidirect
109. #14582898C22semidirect
112. C2×#13063245C22semidirect
113. C2×#13063245C22semidirect
116. #14582855C22semidirect
117. #14582855C22semidirect
125. C43×#519C22semidirect
127. C43×#518C22semidirect
129. C4×#41×C43C22semidirect
130. C4×#41×C43C22semidirect
329. #41×C43#41semidirect
330. #41×C43#41semidirect
609. #3428D43semidirect
667. #519C2×D43semidirect
670. #518C2×D43semidirect
672. C4×#41C2×D43semidirect
673. C4×#41C2×D43semidirect
752. C43#60587semidirect
950. #41#10621898semidirect
951. #41#10621898semidirect

Maximal subgroups

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

subgroupindex
#191483302
#191448862
#191448382
#191448242
#191447792
#191447462
#191447042
#191446552
#191446132
#191445262
C2×#145832232
#191444572
#191444462
#191441342
#191438472
#191438132
#191434762
#191434682
#191434232
#191432532
C43×#34282
#6058743