Finite Group Databasebeta

← #25969642

Subgroups — #25969642

Order 11008.

1822 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147980C211yesmaximal, characteristic, complemented
2C2×#14583523C211yesmaximal, characteristic, complemented
3#19146067C212yesmaximal, complemented
4#19146064C212yesmaximal, complemented
5#19146058C212yesmaximal, complemented
6#19146055C212yesmaximal, complemented
7#19146028C212yesmaximal, complemented
8#19146020C212yesmaximal, complemented
9#19146013C212yesmaximal, complemented
10#19146005C212yesmaximal, complemented
11#19144404C211yesmaximal, characteristic, complemented
12#19144399C211yesmaximal, characteristic, complemented
13#19144391C211yesmaximal, characteristic, complemented
14#19144228C211yesmaximal, characteristic, complemented
15#19144226C211yesmaximal, characteristic, complemented
16#19144217C211yesmaximal, characteristic, complemented
17#19144215C211yesmaximal, characteristic, complemented
18#19144090C211yesmaximal, characteristic, complemented
19#19144089C211yesmaximal, characteristic, complemented
20#19144066C211yesmaximal, characteristic, complemented
21#19144058C211yesmaximal, characteristic, complemented
22#19143157C211yesmaximal, characteristic, complemented
23C43×#3079C211yesmaximal, characteristic, complemented
24C2×#13063358C2211yescharacteristic
25C2×#13063355C2211yescharacteristic
26C2×#13063353C2211yescharacteristic
27C2×#13063350C2211yescharacteristic
28C2×M16×D43C2211yescharacteristic
29C2×M16×D43C2211yescharacteristic
30#14583523—21no—
31#14583523—21no—
32#14583523—21no—
33#14583523—21no—
34#14583523C2212yes—
35#14583523C2212yes—
36#14583523C2212yes—
37#14583523C2212yes—
38#14583521C2211yescharacteristic, complemented
39#14583521C2211yescharacteristic, complemented
40#14583514C2211yescharacteristic, complemented
41#14583514C2211yescharacteristic, complemented
42#14583507C2211yescharacteristic, complemented
43#14583507C2211yescharacteristic, complemented
44#14583500C2211yescharacteristic, complemented
45#14583500C2211yescharacteristic, complemented
46#14583491—21no—
47#14583491—21no—
48#14583482—21no—
49#14583482—21no—
50#14583452C2211yescharacteristic
51#14583445C2211yescharacteristic
52#14583433—21no—
53#14583433—21no—
54#14583427—21no—
55#14583427—21no—
56C2×#13063320—21no—
57C2×#13063314—21no—
58C2×#13063313C2211yescharacteristic
59#14583411C2211yescharacteristic
60#14583406C2211yescharacteristic
61C2×#13063310—21no—
62C2×#13063305C2211yescharacteristic
63C2×#13063301—21no—
64C2×#13063300C2211yescharacteristic
65C4×#10621898C2211yescharacteristic
66C2×#13063290C2211yescharacteristic
67C2×#13063287C2211yescharacteristic
68C2×#13063282C2211yescharacteristic
69#14583209C2212yescomplemented
70#14583205C2212yescomplemented
71#14583202C2212yescomplemented
72#14583198C2212yescomplemented
73#14583193C2212yescomplemented
74#14583191C2212yescomplemented
75#14583188C2212yescomplemented
76#14583186C2212yescomplemented
77#14583183C2212yescomplemented
78#14583181C2212yescomplemented
79#14583178C2212yescomplemented
80#14583176C2212yescomplemented
81#14583158C2212yescomplemented
82#14583156C2212yescomplemented
83#14583153C2212yes—
84#14583151C2212yes—
85#14583148C2212yes—
86#14583146C2212yes—
87#14583146C2212yescomplemented
88#14583144C2212yescomplemented
89#14583141C2212yescomplemented
90#14583139C2212yescomplemented
91#14583136C2212yes—
92#14583134C2212yes—
93#14583131C2212yes—
94#14583129C2212yes—
95#14583129C2212yescomplemented
96#14583127C2212yescomplemented
97#14583124C2212yescomplemented
98#14583122C2212yescomplemented
99#14583122C2212yescomplemented
100#14583121C2212yescomplemented
101#14583121C2212yescomplemented
102#14583120C2212yescomplemented
103#14583117C2212yescomplemented
104#14583115C2212yescomplemented
105#14583115C2212yescomplemented
106#14583114C2212yescomplemented
107#14583114C2212yescomplemented
108#14583113C2212yescomplemented
109#14583108C2212yescomplemented
110#14583103C2212yescomplemented
111#14583098C2212yescomplemented
112#14583093C2212yescomplemented
113#14582939C2211yescharacteristic
114#14582939C2211yescharacteristic
115#14582924C2212yescomplemented
116#14582924C2212yescomplemented
117#14582924C2212yescomplemented
118#14582924C2212yescomplemented
119#14582923C2211yescharacteristic
120#14582922C2211yescharacteristic
121#14582922C2211yescharacteristic
122#14582909C2211yescharacteristic
123#14582907C2211yescharacteristic
124#14582905C2211yescharacteristic
125#14582903C2211yescharacteristic
126#14582898C2211yescharacteristic
127#14582898C2211yescharacteristic
128C2×C4⋊Q8×C43C2211yescharacteristic
129C4×#41×C43C2211yescharacteristic
130C43×#477C2212yescomplemented
131C43×#476C2212yescomplemented
132C43×#475C2212yescomplemented
133C43×#474C2212yescomplemented
134C43×#428C2211yescharacteristic
135C43×#428C2211yescharacteristic
136C43×#423C2211yescharacteristic
137C43×#417C2211yescharacteristic
138C43×#417C2211yescharacteristic
139C2×#10621898C2311yescharacteristic
140C22×Dic86C2311yescharacteristic
141C22×D172—21no—
142C22×D172C2311yescharacteristic
143C22×C4×D43—21no—
144C22×C4×D43C2311yescharacteristic
145#13063358—42no—
146#13063355—42no—
147#13063353—42no—
148#13063350—42no—
149C2×Dic172C2312yes—
150C2×#10621885C2312yes—
151C2×#10621873C2312yes—
152C2×#10621873C2312yes—
153C2×#10621883C2312yes—
154C2×#10621884C2312yes—
155C2×D344C2312yes—
156C2×#10621882C2312yes—
157C2×#10621877C2311yescharacteristic
158C2×#10621877C2311yescharacteristic
159C2×#10621872C2312yes—
160C2×#10621872C2312yes—
161M16×D43—42no—
162M16×D43—42no—
163C2×C8×D43C2312yes—
164C2×C8×D43C2312yes—
165#13063324C2311yescharacteristic
166#13063324C2311yescharacteristic
167#13063323C2311yescharacteristic
168#13063321C2311yescharacteristic
169#13063320—21no—
170#13063320—21no—
171#13063320—22no—
172#13063320—22no—
173#13063320—22no—
174#13063320—22no—
175#13063319—21no—
176#13063319—21no—
177#13063319—21no—
178#13063319—21no—
179#13063318—21no—
180#13063318—21no—
181#13063317—21no—
182#13063317—21no—
183#13063316C2311yescharacteristic
184#13063316C2311yescharacteristic
185#13063315—21no—
186#13063315—21no—
187#13063314—22no—
188#13063314—22no—
189#13063314—22no—
190#13063314—22no—
191#13063314C2311yescharacteristic
192#13063313—21no—
193#13063313—21no—
194#13063313—21no—
195#13063313—21no—
196#13063313C2312yes—
197#13063313C2312yes—
198#13063312C2311yescharacteristic
199#13063311—21no—
200#13063311—21no—
201#13063310—22no—
202#13063310—22no—
203#13063310—22no—
204#13063310—22no—
205#13063310—21no—
206#13063310—21no—
207#13063309—21no—
208#13063308—21no—
209#13063308—21no—
210#13063308—21no—
211#13063308—21no—
212#13063307—21no—
213#13063307—21no—
214#13063306—21no—
215#13063305—21no—
216#13063305—21no—
217#13063305C2312yes—
218#13063305C2311yescharacteristic
219#13063305C2312yes—
220#13063305C2311yescharacteristic
221#13063304—21no—
222#13063304—21no—
223#13063303—21no—
224#13063303—21no—
225#13063302—21no—
226#13063302—21no—
227#13063301—22no—
228#13063301—22no—
229#13063301—22no—
230#13063301—22no—
231#13063301C2311yescharacteristic
232#13063301C2311yescharacteristic
233#13063300—21no—
234#13063300—21no—
235#13063300C2312yes—
236#13063300C2311yescharacteristic
237#13063300C2312yes—
238#13063300C2311yescharacteristic
239#13063299—21no—
240#13063299—21no—
241#13063298—21no—
242#13063298—21no—
243#13063297—21no—
244#13063297—21no—
245#13063296C2311yescharacteristic
246#13063296C2311yescharacteristic
247#13063295—21no—
248#13063293—21no—
249C4×Dic86—21no—
250C4×Dic86—21no—
251C4×Dic86C2311yescharacteristic
252C4×Dic86C2311yescharacteristic
253#13063290—21no—
254#13063290—21no—
255#13063290C2312yes—
256#13063290C2312yes—
257C4×D172—21no—
258C4×D172—21no—
259C4×D172C2311yescharacteristic
260C4×D172C2311yescharacteristic
261#13063287—21no—
262#13063287—21no—
263#13063287C2312yes—
264#13063287C2312yes—
265C4×C22⋊D43—21no—
266C4×C22⋊D43—21no—
267C4×C22⋊D43—21no—
268C4×C22⋊D43—21no—
269C4×C22⋊D43—21no—
270C4×C22⋊D43—21no—
271#13063284C2311yescharacteristic
272#13063282—21no—
273#13063282D411yescharacteristic
274#13063282D411yescharacteristic
275#13063282D411yescharacteristic
276#13063282D411yescharacteristic
277#13063282C2311yescharacteristic
278#13063282C2311yescharacteristic
279#13063282C2311yescharacteristic
280#13063282C2311yescharacteristic
281C2×C4⋊Dic43—21no—
282C2×Dic43⋊C4—21no—
283C2×Dic43⋊C4D411yescharacteristic
284C2×Dic43⋊C4D411yescharacteristic
285C2×(C2×D43)⋊C4—21no—
286C2×(C2×D43)⋊C4—21no—
287C2×(C2×D43)⋊C4—21no—
288C2×(C2×D43)⋊C4—21no—
289C2×(C2×D43)⋊C4—21no—
290C2×(C2×D43)⋊C4D411yescharacteristic
291C2×(C2×D43)⋊C4D411yescharacteristic
292C2×C4×Dic43—21no—
293C2×C4×Dic43C2311yescharacteristic
294C42×D43—21no—
295#13063258C2312yes—
296#13063258C2312yes—
297#13063256C2312yes—
298#13063256C2312yes—
299C4⋊(C43⋊C8)C2312yes—
300C4⋊(C43⋊C8)C2312yes—
301Dic43⋊C8C2312yes—
302Dic43⋊C8C2312yes—
303Dic43⋊C8C2312yes—
304Dic43⋊C8C2312yes—
305#13063250C2312yes—
306#13063250C2312yes—
307#13063248C2312yes—
308#13063248C2312yes—
309#13063248C2312yes—
310#13063248C2312yes—
311#13063247C2312yes—
312#13063247C2312yes—
313#13063245C2312yes—
314#13063245C2312yes—
315#13063245C2312yes—
316#13063245C2312yes—
317C2×#41×C43C2311yescharacteristic
318C22×Q8×C43—21no—
319C2×M16×C43C2311yescharacteristic
320C2×M16×C43C2311yescharacteristic
321C4⋊Q8×C43—21no—
322C4⋊Q8×C43—21no—
323C4⋊Q8×C43C2312yes—
324C4⋊Q8×C43C2312yes—
325C4×Q8×C43C2311yescharacteristic
326C4×Q8×C43C2311yescharacteristic
327C4×D4×C43—21no—
328C4×D4×C43—21no—
329C4×D4×C43C2311yescharacteristic
330C4×D4×C43C2311yescharacteristic
331#117×C43—21no—
332#117×C43C2311yescharacteristic
333C2×C4⋊C4×C43—21no—
334C2×C4⋊C4×C43C2311yescharacteristic
335C2×C4⋊C4×C43C2311yescharacteristic
336C2×C42×C43—21no—
337C2×C42×C43C2311yescharacteristic
338#107×C43C2312yes—
339#107×C43C2312yes—
340#106×C43C2312yes—
341#106×C43C2312yes—
342C4⋊C8×C43C2312yes—
343C4⋊C8×C43C2312yes—
344#103×C43C2312yes—
345#103×C43C2312yes—
346#102×C43C2312yes—
347#102×C43C2312yes—
348C23×D43—21no—
349C23×D43C2×D411yescharacteristic
350#41×C43—22no—
351#41×C43—22no—
352C2×Q8×C43—22no—
353C2×Q8×C43—22no—
354C2×Q8×C43—82no—
355C2×Q8×C43C2411yescharacteristic
356C2×D4×C43—21no—
357C2×D4×C43C2411yescharacteristic
358C22×C4×C43—21no—
359C22×C4×C43—21no—
360C22×C4×C43—21no—
361C22×C4×C43—21no—
362C22×C4×C43—21no—
363C22×C4×C43C2×D411yescharacteristic
364C22×C4×C43C2×D411yescharacteristic
365C22×C4×C43C2411yescharacteristic
366C2×C22⋊D43—21no—
367C2×C22⋊D43—21no—
368C2×C22⋊D43—21no—
369C2×C22⋊D43—21no—
370C2×C22⋊D43—21no—
371C22×Dic43—21no—
372C22×Dic43C2×D411yescharacteristic
373C22×Dic43C2×D411yescharacteristic
374C22×Dic43C2×D411yescharacteristic
375#10621898—22no—
376#10621898—22no—
377C2×D172—21no—
378C2×D172—21no—
379C2×D172—21no—
380C2×D172—22no—
381C2×D172—22no—
382C2×D172—22no—
383C2×D172—22no—
384C2×D172—82no—
385C2×D172C2411yescharacteristic
386C2×D172C2412yes—
387C2×C4×D43—22no—
388C2×C4×D43—22no—
389C2×C4×D43—21no—
390C2×C4×D43—21no—
391C2×C4×D43—21no—
392C2×C4×D43—22no—
393C2×C4×D43—22no—
394C2×C4×D43—82no—
395C2×C4×D43C2×D411yescharacteristic
396C2×C4×D43C2×D411yescharacteristic
397C2×C4×D43C2411yescharacteristic
398C2×C4×D43C2411yescharacteristic
399C2×Dic86—22no—
400C2×Dic86—22no—
401C2×Dic86—21no—
402C2×Dic86—21no—
403C2×Dic86—21no—
404C2×Dic86C2411yescharacteristic
405C2×Dic86C2412yes—
406M16×C43—22no—
407M16×C43—22no—
408C2×C8×C43C2412yes—
409C2×C8×C43C2412yes—
410C4⋊C4×C43—22no—
411C4⋊C4×C43—22no—
412C4⋊C4×C43—21no—
413C4⋊C4×C43—21no—
414C4⋊C4×C43—21no—
415C4⋊C4×C43—21no—
416C4⋊C4×C43C2412yes—
417C4⋊C4×C43C2412yes—
418C4⋊C4×C43C2411yescharacteristic
419C4⋊C4×C43C2411yescharacteristic
420C22⋊C4×C43—21no—
421C22⋊C4×C43—21no—
422C22⋊C4×C43—21no—
423C42×C43—21no—
424C42×C43—21no—
425C42×C43—21no—
426C42×C43C2×D411yescharacteristic
427C42×C43C2×D411yescharacteristic
428C42×C43C2411yescharacteristic
429C42×C43C2411yescharacteristic
430C22⋊Dic43—21no—
431C22⋊Dic43—21no—
432C22⋊Dic43—21no—
433C22⋊Dic43—21no—
434C22⋊Dic43—21no—
435#10621885—42no—
436#10621884—42no—
437#10621883—42no—
438#10621882—42no—
439(C2×D43)⋊C4—22no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—22no—
442(C2×D43)⋊C4—22no—
443(C2×D43)⋊C4—21no—
444(C2×D43)⋊C4—21no—
445(C2×D43)⋊C4—22no—
446(C2×D43)⋊C4—22no—
447(C2×D43)⋊C4—22no—
448(C2×D43)⋊C4—22no—
449(C2×D43)⋊C4—21no—
450(C2×D43)⋊C4—21no—
451(C2×D43)⋊C4—21no—
452(C2×D43)⋊C4—21no—
453(C2×D43)⋊C4—22no—
454(C2×D43)⋊C4—22no—
455(C2×D43)⋊C4—21no—
456(C2×D43)⋊C4—21no—
457(C2×D43)⋊C4—21no—
458(C2×D43)⋊C4—21no—
459(C2×D43)⋊C4C2×D411yescharacteristic
460(C2×D43)⋊C4C2×D411yescharacteristic
461(C2×D43)⋊C4C2×D411yescharacteristic
462(C2×D43)⋊C4C2×D411yescharacteristic
463(C2×D43)⋊C4C2×D411yescharacteristic
464(C2×D43)⋊C4C2×D411yescharacteristic
465(C2×D43)⋊C4C2×D411yescharacteristic
466(C2×D43)⋊C4C2×D411yescharacteristic
467C4⋊Dic43—22no—
468C4⋊Dic43—22no—
469C4⋊Dic43—21no—
470C4⋊Dic43—21no—
471C4⋊Dic43—21no—
472C4⋊Dic43—21no—
473C4⋊Dic43C2411yescharacteristic
474C4⋊Dic43C2411yescharacteristic
475Dic43⋊C4—21no—
476Dic43⋊C4—21no—
477Dic43⋊C4—22no—
478Dic43⋊C4—22no—
479Dic43⋊C4—21no—
480Dic43⋊C4—21no—
481Dic43⋊C4—21no—
482Dic43⋊C4—21no—
483Dic43⋊C4—21no—
484Dic43⋊C4—21no—
485Dic43⋊C4—21no—
486Dic43⋊C4—21no—
487Dic43⋊C4C2×D411yescharacteristic
488Dic43⋊C4C2×D411yescharacteristic
489Dic43⋊C4C2×D411yescharacteristic
490Dic43⋊C4C2×D411yescharacteristic
491Dic43⋊C4C2×D411yescharacteristic
492Dic43⋊C4C2×D411yescharacteristic
493Dic43⋊C4C2×D411yescharacteristic
494Dic43⋊C4C2×D411yescharacteristic
495C4×Dic43—21no—
496C4×Dic43—21no—
497C4×Dic43—21no—
498C4×Dic43—22no—
499C4×Dic43—22no—
500C4×Dic43C2×D411yescharacteristic
501C4×Dic43C2×D411yescharacteristic
502C4×Dic43C2411yescharacteristic
503C4×Dic43C2411yescharacteristic
504#10621877—22no—
505#10621877—22no—
506C2×C43⋊C8C2412yes—
507C2×C43⋊C8C2412yes—
508Dic172—42no—
509D344—42no—
510#10621873—42no—
511#10621873—42no—
512#10621872—42no—
513#10621872—42no—
514C8×D43—42no—
515C8×D43—42no—
516C23×C43—21no—
517C23×C43C22×D411yescharacteristic
518C22×D43—22no—
519C22×D43—22no—
520C22×D43—21no—
521C22×D43—41no—
522C22×D43—41no—
523C22×D43—42no—
524C22×D43—42no—
525C22×D43—42no—
526C22×D43C22×D411yescharacteristic
527C22×D43C22×D411yescharacteristic
528Q8×C43—21no—
529Q8×C43—21no—
530Q8×C43—82no—
531Q8×C43—82no—
532D4×C43—21no—
533D4×C43—21no—
534D4×C43—42no—
535C2×C4×C43—22no—
536C2×C4×C43—21no—
537C2×C4×C43—21no—
538C2×C4×C43—21no—
539C2×C4×C43—22no—
540C2×C4×C43—41no—
541C2×C4×C43—41no—
542C2×C4×C43—42no—
543C2×C4×C43—42no—
544C2×C4×C43—42no—
545C2×C4×C43—81no—
546C2×C4×C43—81no—
547C2×C4×C43C22×D411yescharacteristic
548C2×C4×C43C22×D411yescharacteristic
549C2×C4×C43C22×D411yescharacteristic
550C2×C4×C43C22×D411yescharacteristic
551C2×C4×C43C22×D411yescharacteristic
552C2×C4×C43H(5,𝔽2)12yes—
553C2×C4×C432−1+412yes—
554C2×C4×C43C2511yescharacteristic
555C22⋊D43—42no—
556C22⋊D43—81no—
557C22⋊D43—81no—
558C22⋊D43—81no—
559C22⋊D43—81no—
560C2×Dic43—22no—
561C2×Dic43—21no—
562C2×Dic43—21no—
563C2×Dic43—21no—
564C2×Dic43—22no—
565C2×Dic43—41no—
566C2×Dic43—41no—
567C2×Dic43—42no—
568C2×Dic43C22×D411yescharacteristic
569C2×Dic43C22×D411yescharacteristic
570C2×Dic43C22×D411yescharacteristic
571C2×Dic43C22×D411yescharacteristic
572C2×Dic43C22×D411yescharacteristic
573C2×Dic43C22×D411yescharacteristic
574D172—21no—
575D172—22no—
576D172—22no—
577D172—21no—
578D172—42no—
579D172—81no—
580D172—81no—
581D172—82no—
582D172—82no—
583C4×D43—22no—
584C4×D43—22no—
585C4×D43—21no—
586C4×D43—21no—
587C4×D43—21no—
588C4×D43—21no—
589C4×D43—42no—
590C4×D43—82no—
591C4×D43—82no—
592C4×D43—81no—
593C4×D43—81no—
594Dic86—21no—
595Dic86—22no—
596Dic86—22no—
597Dic86—21no—
598Dic86—42no—
599Dic86—81no—
600Dic86—81no—
601C8×C43—22no—
602C8×C43—22no—
603C43⋊C8—22no—
604C43⋊C8—22no—
605#60919—431nomaximal, Sylow
606C22×C43—21no—
607C22×C43—21no—
608C22×C43—41no—
609C22×C43—41no—
610C22×C43—41no—
611C22×C43#53712yes—
612C22×C43C23×D411yescharacteristic
613C2×D43—21no—
614C2×D43—21no—
615C2×D43—21no—
616C2×D43—21no—
617C2×D43—21no—
618C2×D43—21no—
619C2×D43—42no—
620C2×D43—41no—
621C2×D43—42no—
622C2×D43—41no—
623C2×D43—42no—
624C2×D43—41no—
625C2×D43—82no—
626C2×D43—84no—
627C4×C43—21no—
628C4×C43—21no—
629C4×C43—21no—
630C4×C43—21no—
631C4×C43—41no—
632C4×C43—42no—
633C4×C43—42no—
634C4×C43—41no—
635C4×C43—41no—
636C4×C43#53712yes—
637C4×C43C2×H(5,𝔽2)11yescharacteristic
638C4×C43C2×2−1+411yescharacteristic
639Dic43—21no—
640Dic43—21no—
641Dic43—21no—
642Dic43—21no—
643Dic43—21no—
644Dic43—21no—
645Dic43—41no—
646Dic43—41no—
647Dic43—42no—
648Dic43—41no—
649#3455—431no—
650C2×#542—431no—
651#3263—432no—
652#3263—432no—
653#3262—432no—
654#3262—432no—
655#3258—432no—
656#3258—432no—
657#3257—432no—
658#3257—432no—
659#3079—431no—
660#3079D4311yescharacteristic, complemented
661#3078—431no—
662#3077—431no—
663#3056—431no—
664#3056—431no—
665#3055—431no—
666#3055—431no—
667#3040—431no—
668#3040—431no—
669#3037—431no—
670#3036—431no—
671#2905—431no—
672C2×C43—22no—
673C2×C43—81no—
674C2×C43C2×#53711yescharacteristic
675C2×C43#358511yescharacteristic
676C2×C43#358611yescharacteristic
677D43—41no—
678D43—41no—
679D43—81no—
680D43—82no—
681C2×#137—431no—
682C2×#137—431no—
683C2×AGL(1,ℤ/8)—431no—
684C2×AGL(1,ℤ/8)—431no—
685C22×M16—431no—
686C22×M16—431no—
687#542—432no—
688#542—432no—
689#542—432no—
690#542—432no—
691#542—431no—
692#542—431no—
693#542—431no—
694#542—431no—
695#542—861no—
696#542—861no—
697#542—861no—
698#542—861no—
699#541—431no—
700#541—431no—
701#540—431no—
702#540—431no—
703#539—861no—
704#539—861no—
705#538—861no—
706#538—861no—
707#533—431no—
708#532—431no—
709C2×C4⋊Q8C2×D4311yescharacteristic
710#529—861no—
711#529—861no—
712#529—861no—
713#529—861no—
714C2×#126—861no—
715C2×#124—431no—
716C2×#124—861no—
717#525—431no—
718#525—431no—
719C2×#123—861no—
720C2×C22⋊Q8—431no—
721C2×C22⋊Q8—861no—
722C2×#121—431no—
723C4×#41—431no—
724C4×#41C2×D4311yescharacteristic
725C2×C4×Q8—431no—
726C2×C4×D4—431no—
727C2×#117—431no—
728#479—432no—
729#479—432no—
730#478—432no—
731#478—432no—
732#477—432no—
733#477—432no—
734#477C2×D4312yescomplemented
735#476—432no—
736#476—432no—
737#476C2×D4312yescomplemented
738#475—432no—
739#475—432no—
740#475C2×D4312yescomplemented
741#474—432no—
742#474—432no—
743#474C2×D4312yescomplemented
744#470—432no—
745#470—432no—
746#469—432no—
747#469—432no—
748#468—432no—
749#468—432no—
750#468—432no—
751#468—432no—
752#467—432no—
753#467—432no—
754#466—432no—
755#466—432no—
756#465—432no—
757#465—432no—
758#465—432no—
759#465—432no—
760#464—432no—
761#464—432no—
762#464—432no—
763#464—432no—
764#464—432no—
765#464—432no—
766#463—432no—
767#463—432no—
768#463—432no—
769#463—432no—
770#463—432no—
771#463—432no—
772#462—432no—
773#461—432no—
774#460—432no—
775#459—432no—
776#428—431no—
777#428—431no—
778#428C2×D4311yescharacteristic
779#428C2×D4311yescharacteristic
780#424—432no—
781#424—432no—
782#424—432no—
783#424—432no—
784#423—431no—
785#423—431no—
786#423—431no—
787#423C2×D4311yescharacteristic
788#419—431no—
789#419—431no—
790#418—431no—
791#418—431no—
792#417—431no—
793#417—431no—
794#417C2×D4311yescharacteristic
795#417C2×D4311yescharacteristic
796C43#6091911yescharacteristic, complemented, Sylow
797C2×#41—431no—
798C2×#41C22×D4311yescharacteristic
799C22×Q8—21no—
800C22×Q8—431no—
801C22×D4—431no—
802C22×D4—861no—
803C23×C4—431no—
804C23×C4—861no—
805#137—1722no—
806#137—1722no—
807AGL(1,ℤ/8)—1722no—
808AGL(1,ℤ/8)—1722no—
809C2×Q16—432no—
810C2×Q16—432no—
811C2×SD16—432no—
812C2×SD16—432no—
813C2×SD16—432no—
814C2×SD16—432no—
815C2×D8—432no—
816C2×D8—432no—
817C2×M16—431no—
818C2×M16—431no—
819C2×M16—432no—
820C2×M16—432no—
821C2×M16—1722no—
822C2×M16—1722no—
823C2×M16C22×D4311yescharacteristic
824C2×M16C22×D4311yescharacteristic
825C22×C8—432no—
826C22×C8—432no—
827C4⋊Q8—21no—
828C4⋊Q8—21no—
829C4⋊Q8—431no—
830C4⋊Q8—431no—
831C4⋊Q8—431no—
832C4⋊Q8C22×D4312yes—
833C4⋊Q8C22×D4312yes—
834#127—431no—
835#126—861no—
836#126—861no—
837#126—861no—
838#126—861no—
839#126—861no—
840#126—861no—
841#126—861no—
842#126—861no—
843#126—862no—
844#126—862no—
845#126—862no—
846#126—862no—
847#125—431no—
848#125—431no—
849#125—861no—
850#125—861no—
851#125—861no—
852#125—861no—
853#124—431no—
854#124—431no—
855#124—432no—
856#124—432no—
857#124—861no—
858#124—861no—
859#124—861no—
860#124—861no—
861#124—862no—
862#124—862no—
863#124—862no—
864#124—862no—
865#124—861no—
866#124—861no—
867#123—861no—
868#123—861no—
869#123—861no—
870#123—862no—
871#123—862no—
872#123—862no—
873#123—862no—
874#123—861no—
875#123—861no—
876#123—861no—
877#123—861no—
878#123—861no—
879#123—861no—
880#123—861no—
881C22⋊Q8—431no—
882C22⋊Q8—431no—
883C22⋊Q8—432no—
884C22⋊Q8—432no—
885C22⋊Q8—431no—
886C22⋊Q8—431no—
887C22⋊Q8—861no—
888C22⋊Q8—861no—
889C22⋊Q8—861no—
890C22⋊Q8—861no—
891C22⋊Q8—861no—
892C22⋊Q8—861no—
893C22⋊Q8—861no—
894C22⋊Q8—861no—
895C22⋊Q8—862no—
896C22⋊Q8—862no—
897C22⋊Q8—862no—
898C22⋊Q8—862no—
899#121—431no—
900#121—431no—
901#121—432no—
902#121—432no—
903#121—431no—
904#121—431no—
905#121—861no—
906#121—861no—
907#121—861no—
908#121—861no—
909#121—861no—
910#121—861no—
911#121—861no—
912#121—861no—
913#120—861no—
914#120—861no—
915C4×Q8—432no—
916C4×Q8—432no—
917C4×Q8—431no—
918C4×Q8—431no—
919C4×Q8—861no—
920C4×Q8—861no—
921C4×Q8—861no—
922C4×Q8—861no—
923C4×Q8C22×D4311yescharacteristic
924C4×Q8C22×D4311yescharacteristic
925C4×D4—21no—
926C4×D4—21no—
927C4×D4—432no—
928C4×D4—432no—
929C4×D4—431no—
930C4×D4—431no—
931C4×D4—861no—
932C4×D4—861no—
933C4×D4—861no—
934C4×D4—861no—
935C4×D4—861no—
936C4×D4—861no—
937C4×D4—861no—
938C4×D4—861no—
939C4×D4—861no—
940C4×D4—861no—
941C4×D4C22×D4311yescharacteristic
942C4×D4C22×D4311yescharacteristic
943#117—21no—
944#117—431no—
945#117—431no—
946#117—431no—
947#117—431no—
948#117—431no—
949#117—431no—
950#117—431no—
951#117—431no—
952#117—431no—
953#117—861no—
954#117C22×D4311yescharacteristic
955C2×C4⋊C4—21no—
956C2×C4⋊C4—431no—
957C2×C4⋊C4—431no—
958C2×C4⋊C4—861no—
959C2×C4⋊C4—861no—
960C2×C4⋊C4C22×D4311yescharacteristic
961C2×C4⋊C4C22×D4311yescharacteristic
962C2×C22⋊C4—431no—
963C2×C22⋊C4—431no—
964C2×C22⋊C4—861no—
965C2×C22⋊C4—861no—
966C2×C22⋊C4—861no—
967C2×C22⋊C4—861no—
968C2×C22⋊C4—861no—
969C2×C42—21no—
970C2×C42—431no—
971C2×C42—861no—
972C2×C42—861no—
973C2×C42C22×D4311yescharacteristic
974#107—432no—
975#107—432no—
976#107C22×D4312yes—
977#107C22×D4312yes—
978#106—432no—
979#106—432no—
980#106C22×D4312yes—
981#106C22×D4312yes—
982C4⋊C8—432no—
983C4⋊C8—432no—
984C4⋊C8—432no—
985C4⋊C8—432no—
986C4⋊C8—432no—
987C4⋊C8—432no—
988C4⋊C8C22×D4312yes—
989C4⋊C8C22×D4312yes—
990#103—432no—
991#103—432no—
992#103—432no—
993#103—432no—
994#103—432no—
995#103—432no—
996#103C22×D4312yes—
997#103C22×D4312yes—
998#102—432no—
999#102—432no—
1000#102—432no—
1001#102—432no—
1002#102—432no—
1003#102—432no—
1004#102C22×D4312yes—
1005#102C22×D4312yes—
1006C24—431no—
1007C24—861no—
1008#41—22no—
1009#41—22no—
1010#41—862no—
1011#41—862no—
1012C2×Q8—22no—
1013C2×Q8—22no—
1014C2×Q8—82no—
1015C2×Q8—432no—
1016C2×Q8—431no—
1017C2×Q8—861no—
1018C2×Q8—861no—
1019C2×Q8—861no—
1020C2×Q8—862no—
1021C2×Q8—862no—
1022C2×Q8C23×D4311yescharacteristic
1023C2×D4—21no—
1024C2×D4—432no—
1025C2×D4—431no—
1026C2×D4—861no—
1027C2×D4—861no—
1028C2×D4—862no—
1029C2×D4—862no—
1030C2×D4—861no—
1031C2×D4—861no—
1032C2×D4—861no—
1033C2×D4—861no—
1034C2×D4—861no—
1035C2×D4—861no—
1036C2×D4—862no—
1037C2×D4—862no—
1038C2×D4—3442no—
1039C2×D4C23×D4311yescharacteristic
1040C22×C4—21no—
1041C22×C4—21no—
1042C22×C4—21no—
1043C22×C4—21no—
1044C22×C4—21no—
1045C22×C4—431no—
1046C22×C4—431no—
1047C22×C4—431no—
1048C22×C4—431no—
1049C22×C4—431no—
1050C22×C4—431no—
1051C22×C4—431no—
1052C22×C4—862no—
1053C22×C4—862no—
1054C22×C4—862no—
1055C22×C4—862no—
1056C22×C4—861no—
1057C22×C4—861no—
1058C22×C4—861no—
1059C22×C4—861no—
1060C22×C4—3442no—
1061C22×C4D4×D4311yescharacteristic
1062C22×C4D4×D4311yescharacteristic
1063C22×C4C23×D4311yescharacteristic
1064Q16—1722no—
1065Q16—1722no—
1066SD16—1722no—
1067SD16—1722no—
1068SD16—1722no—
1069SD16—1722no—
1070D8—1722no—
1071D8—1722no—
1072M16—22no—
1073M16—22no—
1074M16—862no—
1075M16—862no—
1076M16—1722no—
1077M16—1722no—
1078C2×C8—432no—
1079C2×C8—432no—
1080C2×C8—1722no—
1081C2×C8—1722no—
1082C2×C8C23×D4312yes—
1083C2×C8C23×D4312yes—
1084C4⋊C4—22no—
1085C4⋊C4—22no—
1086C4⋊C4—21no—
1087C4⋊C4—21no—
1088C4⋊C4—21no—
1089C4⋊C4—21no—
1090C4⋊C4—431no—
1091C4⋊C4—431no—
1092C4⋊C4—431no—
1093C4⋊C4—431no—
1094C4⋊C4—431no—
1095C4⋊C4—431no—
1096C4⋊C4—431no—
1097C4⋊C4—431no—
1098C4⋊C4—431no—
1099C4⋊C4—431no—
1100C4⋊C4—862no—
1101C4⋊C4—862no—
1102C4⋊C4—862no—
1103C4⋊C4—862no—
1104C4⋊C4—861no—
1105C4⋊C4—861no—
1106C4⋊C4—861no—
1107C4⋊C4—861no—
1108C4⋊C4—861no—
1109C4⋊C4—861no—
1110C4⋊C4—861no—
1111C4⋊C4—861no—
1112C4⋊C4—861no—
1113C4⋊C4—861no—
1114C4⋊C4—861no—
1115C4⋊C4—861no—
1116C4⋊C4—861no—
1117C4⋊C4—861no—
1118C4⋊C4C23×D4311yescharacteristic
1119C4⋊C4C23×D4311yescharacteristic
1120C4⋊C4C23×D4312yes—
1121C4⋊C4C23×D4312yes—
1122C22⋊C4—21no—
1123C22⋊C4—21no—
1124C22⋊C4—21no—
1125C22⋊C4—431no—
1126C22⋊C4—431no—
1127C22⋊C4—431no—
1128C22⋊C4—431no—
1129C22⋊C4—431no—
1130C22⋊C4—431no—
1131C22⋊C4—431no—
1132C22⋊C4—431no—
1133C22⋊C4—862no—
1134C22⋊C4—862no—
1135C22⋊C4—862no—
1136C22⋊C4—862no—
1137C22⋊C4—861no—
1138C22⋊C4—861no—
1139C22⋊C4—861no—
1140C22⋊C4—861no—
1141C22⋊C4—862no—
1142C22⋊C4—862no—
1143C22⋊C4—861no—
1144C22⋊C4—861no—
1145C22⋊C4—861no—
1146C22⋊C4—861no—
1147C22⋊C4—861no—
1148C22⋊C4—861no—
1149C22⋊C4—861no—
1150C22⋊C4—861no—
1151C22⋊C4—861no—
1152C22⋊C4—862no—
1153C22⋊C4—862no—
1154C22⋊C4—862no—
1155C22⋊C4—862no—
1156C22⋊C4—861no—
1157C22⋊C4—861no—
1158C42—21no—
1159C42—21no—
1160C42—21no—
1161C42—431no—
1162C42—431no—
1163C42—431no—
1164C42—431no—
1165C42—862no—
1166C42—862no—
1167C42—861no—
1168C42—861no—
1169C42—861no—
1170C42D4×D4311yescharacteristic
1171C42D4×D4311yescharacteristic
1172C42C23×D4311yescharacteristic
1173C42C23×D4311yescharacteristic
1174C23—21no—
1175C23—431no—
1176C23—431no—
1177C23—862no—
1178C23—862no—
1179C23—861no—
1180C23—1721no—
1181C23—1721no—
1182C23—1722no—
1183C23—1722no—
1184C23—1722no—
1185C23C2×D4×D4311yescharacteristic
1186Q8—21no—
1187Q8—21no—
1188Q8—82no—
1189Q8—82no—
1190Q8—862no—
1191Q8—861no—
1192Q8—862no—
1193Q8—861no—
1194Q8—3441no—
1195Q8—3441no—
1196Q8—1722no—
1197D4—21no—
1198D4—21no—
1199D4—42no—
1200D4—862no—
1201D4—861no—
1202D4—862no—
1203D4—861no—
1204D4—3442no—
1205D4—3442no—
1206D4—3441no—
1207D4—3441no—
1208D4—3441no—
1209D4—3441no—
1210D4—3441no—
1211D4—3441no—
1212D4—1722no—
1213D4—1722no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—81no—
1225C2×C4—81no—
1226C2×C4—431no—
1227C2×C4—431no—
1228C2×C4—431no—
1229C2×C4—431no—
1230C2×C4—431no—
1231C2×C4—431no—
1232C2×C4—862no—
1233C2×C4—861no—
1234C2×C4—861no—
1235C2×C4—861no—
1236C2×C4—861no—
1237C2×C4—862no—
1238C2×C4—862no—
1239C2×C4—862no—
1240C2×C4—861no—
1241C2×C4—861no—
1242C2×C4—861no—
1243C2×C4—3441no—
1244C2×C4—3441no—
1245C2×C4—3442no—
1246C2×C4—3442no—
1247C2×C4—1721no—
1248C2×C4—1721no—
1249C2×C4—1722no—
1250C2×C4—1722no—
1251C2×C4C2×D4×D4311yescharacteristic
1252C2×C4C2×D4×D4311yescharacteristic
1253C2×C4C2×D4×D4311yescharacteristic
1254C2×C4C2×D4×D4311yescharacteristic
1255C2×C4C2×D4×D4311yescharacteristic
1256C2×C4#1306337112yes—
1257C2×C4#1306337312yes—
1258C2×C4C24×D4311yescharacteristic
1259C8—22no—
1260C8—22no—
1261C8—862no—
1262C8—862no—
1263C22—21no—
1264C22—21no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—861no—
1269C22—861no—
1270C22—861no—
1271C22—861no—
1272C22—861no—
1273C22—861no—
1274C22—3444no—
1275C22—3442no—
1276C22—1722no—
1277C22—1721no—
1278C22—1721no—
1279C22—1722no—
1280C22—1721no—
1281C22—1722no—
1282C22#1458347912yes—
1283C22C22×D4×D4311yescharacteristic
1284C4—21no—
1285C4—21no—
1286C4—21no—
1287C4—21no—
1288C4—42no—
1289C4—42no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—861no—
1294C4—861no—
1295C4—861no—
1296C4—861no—
1297C4—861no—
1298C4—861no—
1299C4—1721no—
1300C4—1721no—
1301C4—1721no—
1302C4—1722no—
1303C4#1458347912yes—
1304C4C2×#1306337111yescharacteristic
1305C4C2×#1306337311yescharacteristic
1306C2—22no—
1307C2—81no—
1308C2—3442no—
1309C2—3441no—
1310C2—1721no—
1311C2—1721no—
1312C2C2×#1458347911yescharacteristic
1313C2#1914937111yescharacteristic
1314C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3079C2
socleC22×C43C23×D4
hypercenter#3079D43
hypocenterC43#60919
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. #19147980C2semidirect
2. C2×#14583523C2semidirect
3. #19146067C2semidirect
4. #19146064C2semidirect
5. #19146058C2semidirect
6. #19146055C2semidirect
7. #19146028C2semidirect
8. #19146020C2semidirect
9. #19146013C2semidirect
10. #19146005C2semidirect
11. #19144404C2semidirect
12. #19144399C2semidirect
13. #19144391C2semidirect
14. #19144228C2semidirect
15. #19144226C2semidirect
16. #19144217C2semidirect
17. #19144215C2semidirect
18. #19144090C2semidirect
19. #19144089C2semidirect
20. #19144066C2semidirect
21. #19144058C2semidirect
22. #19143157C2semidirect
23. C43×#3079C2semidirect
38. #14583521C22semidirect
39. #14583521C22semidirect
40. #14583514C22semidirect
41. #14583514C22semidirect
42. #14583507C22semidirect
43. #14583507C22semidirect
44. #14583500C22semidirect
45. #14583500C22semidirect
69. #14583209C22semidirect
70. #14583205C22semidirect
71. #14583202C22semidirect
72. #14583198C22semidirect
73. #14583193C22semidirect
74. #14583191C22semidirect
75. #14583188C22semidirect
76. #14583186C22semidirect
77. #14583183C22semidirect
78. #14583181C22semidirect
79. #14583178C22semidirect
80. #14583176C22semidirect
81. #14583158C22semidirect
82. #14583156C22semidirect
87. #14583146C22semidirect
88. #14583144C22semidirect
89. #14583141C22semidirect
90. #14583139C22semidirect
95. #14583129C22semidirect
96. #14583127C22semidirect
97. #14583124C22semidirect
98. #14583122C22semidirect
99. #14583122C22semidirect
100. #14583121C22semidirect
101. #14583121C22semidirect
102. #14583120C22semidirect
103. #14583117C22semidirect
104. #14583115C22semidirect
105. #14583115C22semidirect
106. #14583114C22semidirect
107. #14583114C22semidirect
108. #14583113C22semidirect
109. #14583108C22semidirect
110. #14583103C22semidirect
111. #14583098C22semidirect
112. #14583093C22semidirect
115. #14582924C22semidirect
116. #14582924C22semidirect
117. #14582924C22semidirect
118. #14582924C22semidirect
130. C43×#477C22semidirect
131. C43×#476C22semidirect
132. C43×#475C22semidirect
133. C43×#474C22semidirect
660. #3079D43semidirect
734. #477C2×D43semidirect
737. #476C2×D43semidirect
740. #475C2×D43semidirect
743. #474C2×D43semidirect
796. C43#60919semidirect

Maximal subgroups

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

subgroupindex
#191479802
C2×#145835232
#191460672
#191460642
#191460582
#191460552
#191460282
#191460202
#191460132
#191460052
#191444042
#191443992
#191443912
#191442282
#191442262
#191442172
#191442152
#191440902
#191440892
#191440662
#191440582
#191431572
C43×#30792
#6091943