Finite Group Databasebeta

← #25967374

Subgroups — #25967374

Order 11008.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583411C211yesmaximal, characteristic, complemented
2C2×#14583409C211yesmaximal, characteristic, complemented
3#19145435C214yesmaximal, complemented
4#19145424C212yesmaximal, complemented
5#19145408C212yesmaximal, complemented
6#19145386C214yesmaximal, complemented
7#19145375C212yesmaximal, complemented
8#19145359C212yesmaximal, complemented
9#19144543C211yesmaximal, characteristic, complemented
10#19144529C212yesmaximal, complemented
11#19144226C212yesmaximal, complemented
12#19144212C212yesmaximal, complemented
13#19143857C211yesmaximal, characteristic, complemented
14#19143845C211yesmaximal, characteristic, complemented
15#19143839C212yesmaximal, complemented
16#407×D43C211yesmaximal, characteristic, complemented
17C43×#3094C211yesmaximal, characteristic, complemented
18C22×#10621898C2211yescharacteristic
19C22×#10621900C2211yescharacteristic, complemented
20C23×C4×D43C2211yescharacteristic
21C2×#13063358C2212yescomplemented
22C2×#13063351C2212yescomplemented
23C2×M16×D43C2212yescomplemented
24#14583411—21no—
25#14583411—21no—
26#14583411—21no—
27#14583411—21no—
28#14583411C2212yes—
29#14583411C2212yes—
30#14583411C2212yescomplemented
31#14583411C2212yescomplemented
32#14583409—21no—
33#14583409—21no—
34#14583409—21no—
35#14583409—21no—
36#14583409C2212yes—
37#14583409C2212yes—
38#14583409C2212yescomplemented
39#14583409C2212yescomplemented
40C2×#13063309—21no—
41C2×#13063307—21no—
42C2×#13063305C2211yescharacteristic, complemented
43C2×#13063305C2211yescharacteristic, complemented
44C2×#13063305C2211yescharacteristic, complemented
45C2×#13063304C2211yescharacteristic
46C2×#13063300C2211yescharacteristic, complemented
47C2×#13063300C2211yescharacteristic, complemented
48C2×#13063296C2211yescharacteristic, complemented
49C2×#13063295—21no—
50C2×#13063293—21no—
51C2×C4×D172—21no—
52C2×C4×D172—21no—
53C2×D4×Dic43—21no—
54C2×(C22⋊D43)⋊C4—21no—
55C2×#13063283C2211yescharacteristic, complemented
56#14583243C2214yescomplemented
57#14583242C2214yescomplemented
58#14583240C2214yescomplemented
59#14583234C2212yescomplemented
60#14583229C2212yescomplemented
61#14583226C2214yescomplemented
62#14583225C2214yescomplemented
63#14583158C2214yescomplemented
64#14583151C2214yescomplemented
65#14583146C2214yescomplemented
66#14583144C2214yescomplemented
67#14583141C2214yescomplemented
68#14583134C2214yescomplemented
69#14583129C2214yescomplemented
70#14583127C2214yescomplemented
71#14583063C2214yescomplemented
72#14583062C2214yescomplemented
73#14583062C2214yescomplemented
74#14583057C2212yescomplemented
75#14583052C2212yescomplemented
76#14583045C2214yescomplemented
77#14583045C2214yescomplemented
78#14583042C2214yescomplemented
79#14583037C2212yescomplemented
80#14583032C2212yescomplemented
81#14582942C2212yescomplemented
82#14582907C2212yescomplemented
83#14582901C2212yescomplemented
84#14582898C2212yescomplemented
85#14582863C2211yescharacteristic
86#14582862C2212yescomplemented
87#14582861C2212yescomplemented
88#14582861C2212yescomplemented
89C22⋊C8×D43C2212yescomplemented
90C22⋊C8×D43C2212yescomplemented
91C2×#121×C43C2211yescharacteristic
92C2×#117×C43C2211yescharacteristic
93C43×#482C2214yescomplemented
94C43×#481C2212yescomplemented
95C43×#480C2212yescomplemented
96C43×#428C2212yescomplemented
97C43×#418C2212yescomplemented
98C43×#407C2211yescharacteristic
99C24×D43D411yescharacteristic
100C2×#10621898—21no—
101C2×#10621898—21no—
102C2×#10621898—44no—
103C2×#10621898C2312yes—
104C2×#10621898C2312yes—
105C2×#10621900—21no—
106C2×#10621900—21no—
107C2×#10621900—44no—
108C2×#10621900C2312yes—
109C2×#10621900C2312yes—
110C22×Dic86C2311yescharacteristic
111C22×Dic86C2311yescharacteristic
112C22×D172—21no—
113C22×D172—21no—
114C22×D172C2311yescharacteristic
115C22×C22⋊D43—21no—
116C22×C22⋊D43—21no—
117C22×C22⋊D43—21no—
118C23×Dic43—21no—
119C23×Dic43D411yescharacteristic
120C22×C4×D43—21no—
121C22×C4×D43—44no—
122C22×C4×D43D411yescharacteristic
123C22×C4×D43D411yescharacteristic
124C22×C4×D43D411yescharacteristic
125C22×C4×D43D411yescharacteristic
126C22×C4×D43D411yescharacteristic
127C22×C4×D43D411yescharacteristic
128C22×C4×D43C2311yescharacteristic
129C22×C4×D43C2311yescharacteristic
130C22×C4×D43C2311yescharacteristic
131C22×C4×D43C2311yescharacteristic
132C22×C4×D43C2311yescharacteristic
133C22×C4×D43C2311yescharacteristic
134#13063358—44no—
135#13063351—44no—
136C2×Dic172C2314yescomplemented
137C2×#10621873C2314yescomplemented
138C2×#10621883C2314yescomplemented
139C2×#10621882C2314yescomplemented
140C2×#10621877C2312yes—
141C2×#10621872C2314yes—
142M16×D43—44no—
143C2×C8×D43C2314yes—
144#13063309—22no—
145#13063309—22no—
146#13063309—22no—
147#13063309—22no—
148#13063307—22no—
149#13063307—22no—
150#13063307—22no—
151#13063307—22no—
152#13063305—21no—
153#13063305—21no—
154#13063305—21no—
155#13063305—21no—
156#13063305—21no—
157#13063305—21no—
158#13063305C2312yes—
159#13063305C2312yes—
160#13063305C2312yes—
161#13063305C2312yes—
162#13063305C2312yes—
163#13063305C2312yes—
164#13063304—21no—
165#13063304—21no—
166#13063304C2312yes—
167#13063304C2312yes—
168#13063300—21no—
169#13063300—21no—
170#13063300—21no—
171#13063300—21no—
172#13063300C2312yes—
173#13063300C2312yes—
174#13063300C2312yes—
175#13063300C2312yes—
176#13063296—21no—
177#13063296—21no—
178#13063296C2312yes—
179#13063296C2312yes—
180#13063295—22no—
181#13063295—22no—
182#13063295—22no—
183#13063295—22no—
184#13063293—22no—
185#13063293—22no—
186#13063293—22no—
187#13063293—22no—
188C4×D172—22no—
189C4×D172—22no—
190C4×D172—22no—
191C4×D172—22no—
192C4×D172—22no—
193C4×D172—22no—
194C4×D172—22no—
195C4×D172—22no—
196D4×Dic43—22no—
197D4×Dic43—22no—
198D4×Dic43—22no—
199D4×Dic43—22no—
200(C22⋊D43)⋊C4—22no—
201(C22⋊D43)⋊C4—22no—
202(C22⋊D43)⋊C4—22no—
203(C22⋊D43)⋊C4—22no—
204#13063283—21no—
205#13063283—21no—
206#13063283C2312yes—
207#13063283C2312yes—
208C2×C4⋊Dic43—21no—
209C2×C4⋊Dic43—21no—
210C2×C4⋊Dic43—21no—
211C2×C4⋊Dic43C2311yescharacteristic
212C2×Dic43⋊C4—21no—
213C2×C22⋊Dic43—21no—
214C2×C22⋊Dic43—21no—
215C2×(C2×D43)⋊C4—21no—
216C2×(C2×D43)⋊C4—21no—
217C2×(C2×D43)⋊C4—21no—
218C2×(C2×D43)⋊C4—21no—
219C2×(C2×D43)⋊C4—21no—
220C2×(C2×D43)⋊C4—21no—
221C2×C4×Dic43—21no—
222#13063258C2314yescomplemented
223#13063256C2314yescomplemented
224#13063250C2314yescomplemented
225#13063248C2314yescomplemented
226#13063248C2314yescomplemented
227#13063248C2314yescomplemented
228#13063247C2314yescomplemented
229#13063245C2314yescomplemented
230C22⋊(C43⋊C8)C2312yes—
231C22⋊(C43⋊C8)C2312yes—
232(C2×D43)⋊C8C2314yes—
233(C2×D43)⋊C8C2314yes—
234C22×D4×C43—21no—
235C22×D4×C43C2311yescharacteristic
236C23×C4×C43C2311yescharacteristic
237C2×M16×C43C2312yes—
238#121×C43—21no—
239#121×C43—21no—
240#121×C43C2312yes—
241#121×C43C2312yes—
242#117×C43—21no—
243#117×C43—21no—
244#117×C43C2312yes—
245#117×C43C2312yes—
246C2×C4⋊C4×C43C2311yescharacteristic
247C2×C4⋊C4×C43C2311yescharacteristic
248C2×C4⋊C4×C43C2311yescharacteristic
249C2×C22⋊C4×C43—21no—
250C2×C22⋊C4×C43—21no—
251C2×C42×C43—21no—
252#107×C43C2314yescomplemented
253#106×C43C2314yescomplemented
254#102×C43C2314yescomplemented
255#102×C43C2314yescomplemented
256C22⋊C8×C43C2312yes—
257C22⋊C8×C43C2312yes—
258C24×C43—21no—
259C24×C43C2×D411yescharacteristic
260C23×D43—21no—
261C23×D43—42no—
262C23×D43—42no—
263C23×D43—42no—
264C23×D43C2×D411yescharacteristic
265C23×D43C2×D411yescharacteristic
266C23×D43C2×D411yescharacteristic
267C23×D43C2×D411yescharacteristic
268C23×D43C2×D411yescharacteristic
269C23×D43C2×D411yescharacteristic
270C2×D4×C43—21no—
271C2×D4×C43—22no—
272C2×D4×C43—22no—
273C2×D4×C43—24no—
274C2×D4×C43—44no—
275C2×D4×C43C2412yes—
276C22×C4×C43—24no—
277C22×C4×C43—21no—
278C22×C4×C43—21no—
279C22×C4×C43—21no—
280C22×C4×C43C2×D411yescharacteristic
281C22×C4×C43C2×D411yescharacteristic
282C22×C4×C43C2×D411yescharacteristic
283C22×C4×C43C2411yescharacteristic
284C22×C4×C43C2411yescharacteristic
285C22×C4×C43C2411yescharacteristic
286C2×C22⋊D43—22no—
287C2×C22⋊D43—22no—
288C2×C22⋊D43—22no—
289C2×C22⋊D43—22no—
290C2×C22⋊D43—22no—
291C2×C22⋊D43—22no—
292C2×C22⋊D43—44no—
293C2×C22⋊D43—44no—
294C2×C22⋊D43—44no—
295C22×Dic43—22no—
296C22×Dic43—22no—
297C22×Dic43—21no—
298C22×Dic43—21no—
299C22×Dic43—21no—
300C22×Dic43—42no—
301C22×Dic43—44no—
302C22×Dic43C2×D411yescharacteristic
303C22×Dic43C2×D411yescharacteristic
304C22×Dic43C2×D411yescharacteristic
305C22×Dic43C2×D411yescharacteristic
306C22×Dic43C2×D411yescharacteristic
307C22×Dic43C2×D411yescharacteristic
308#10621900—44no—
309#10621900—44no—
310#10621900—44no—
311#10621900—44no—
312#10621898—24no—
313#10621898—24no—
314#10621898—42no—
315#10621898—42no—
316#10621898—44no—
317#10621898—44no—
318C2×D172—21no—
319C2×D172—22no—
320C2×D172—22no—
321C2×D172—22no—
322C2×D172—22no—
323C2×D172—44no—
324C2×D172—44no—
325C2×D172—42no—
326C2×D172C2412yes—
327C2×C4×D43—24no—
328C2×C4×D43—24no—
329C2×C4×D43—22no—
330C2×C4×D43—22no—
331C2×C4×D43—42no—
332C2×C4×D43—42no—
333C2×C4×D43—42no—
334C2×C4×D43—42no—
335C2×C4×D43—42no—
336C2×C4×D43—42no—
337C2×C4×D43—42no—
338C2×C4×D43—42no—
339C2×C4×D43—42no—
340C2×C4×D43—42no—
341C2×C4×D43—44no—
342C2×C4×D43C2×D411yescharacteristic
343C2×C4×D43C2×D411yescharacteristic
344C2×C4×D43C2×D411yescharacteristic
345C2×C4×D43C2×D411yescharacteristic
346C2×C4×D43C2×D411yescharacteristic
347C2×C4×D43C2×D411yescharacteristic
348C2×C4×D43C2×D411yescharacteristic
349C2×C4×D43C2×D411yescharacteristic
350C2×C4×D43C2×D411yescharacteristic
351C2×C4×D43C2×D411yescharacteristic
352C2×C4×D43C2×D411yescharacteristic
353C2×C4×D43C2×D411yescharacteristic
354C2×C4×D43C2411yescharacteristic
355C2×C4×D43C2411yescharacteristic
356C2×C4×D43C2411yescharacteristic
357C2×C4×D43C2411yescharacteristic
358C2×Dic86—24no—
359C2×Dic86—21no—
360C2×Dic86—21no—
361C2×Dic86—42no—
362C2×Dic86C2412yes—
363C2×Dic86C2412yes—
364M16×C43—24no—
365C2×C8×C43C2414yes—
366C4⋊C4×C43—21no—
367C4⋊C4×C43—21no—
368C4⋊C4×C43—21no—
369C4⋊C4×C43C2412yes—
370C4⋊C4×C43C2412yes—
371C4⋊C4×C43C2412yes—
372C22⋊C4×C43—22no—
373C22⋊C4×C43—22no—
374C22⋊C4×C43—22no—
375C22⋊C4×C43—22no—
376C42×C43—22no—
377C42×C43—22no—
378C22⋊Dic43—22no—
379C22⋊Dic43—22no—
380C22⋊Dic43—22no—
381C22⋊Dic43—22no—
382#10621883—44no—
383#10621882—44no—
384(C2×D43)⋊C4—22no—
385(C2×D43)⋊C4—22no—
386(C2×D43)⋊C4—22no—
387(C2×D43)⋊C4—22no—
388(C2×D43)⋊C4—22no—
389(C2×D43)⋊C4—22no—
390(C2×D43)⋊C4—22no—
391(C2×D43)⋊C4—22no—
392(C2×D43)⋊C4—22no—
393(C2×D43)⋊C4—22no—
394(C2×D43)⋊C4—22no—
395(C2×D43)⋊C4—22no—
396C4⋊Dic43—21no—
397C4⋊Dic43—22no—
398C4⋊Dic43—22no—
399C4⋊Dic43—22no—
400C4⋊Dic43—22no—
401C4⋊Dic43—22no—
402C4⋊Dic43—22no—
403C4⋊Dic43C2412yes—
404Dic43⋊C4—22no—
405Dic43⋊C4—22no—
406C4×Dic43—22no—
407C4×Dic43—22no—
408#10621877—24no—
409C2×C43⋊C8C2414yes—
410Dic172—44no—
411#10621873—44no—
412#10621872—44no—
413C8×D43—44no—
414C23×C43—22no—
415C23×C43—22no—
416C23×C43—22no—
417C23×C43—41no—
418C23×C43—42no—
419C23×C43—42no—
420C23×C43—42no—
421C23×C43C22×D411yescharacteristic
422C23×C43C22×D411yescharacteristic
423C23×C43C22×D411yescharacteristic
424C22×D43—22no—
425C22×D43—22no—
426C22×D43—22no—
427C22×D43—22no—
428C22×D43—22no—
429C22×D43—22no—
430C22×D43—22no—
431C22×D43—22no—
432C22×D43—41no—
433C22×D43—41no—
434C22×D43—41no—
435C22×D43—41no—
436C22×D43—41no—
437C22×D43—41no—
438C22×D43—41no—
439C22×D43—41no—
440C22×D43—41no—
441C22×D43—41no—
442C22×D43—41no—
443C22×D43—416no—
444C22×D43—42no—
445C22×D43—42no—
446C22×D43—42no—
447C22×D43C22×D411yescharacteristic
448C22×D43C22×D411yescharacteristic
449C22×D43C22×D411yescharacteristic
450C22×D43C22×D411yescharacteristic
451D4×C43—24no—
452D4×C43—44no—
453D4×C43—44no—
454D4×C43—42no—
455C2×C4×C43—22no—
456C2×C4×C43—22no—
457C2×C4×C43—22no—
458C2×C4×C43—22no—
459C2×C4×C43—22no—
460C2×C4×C43—22no—
461C2×C4×C43—22no—
462C2×C4×C43—22no—
463C2×C4×C43—42no—
464C2×C4×C43—42no—
465C2×C4×C43—42no—
466C2×C4×C43C22×D411yescharacteristic
467C2×C4×C43C22×D411yescharacteristic
468C2×C4×C43C22×D411yescharacteristic
469C2×C4×C43H(5,𝔽2)14yes—
470C2×C4×C43C2511yescharacteristic
471C22⋊D43—44no—
472C22⋊D43—44no—
473C22⋊D43—44no—
474C22⋊D43—44no—
475C22⋊D43—44no—
476C22⋊D43—44no—
477C2×Dic43—22no—
478C2×Dic43—22no—
479C2×Dic43—22no—
480C2×Dic43—22no—
481C2×Dic43—22no—
482C2×Dic43—41no—
483C2×Dic43—41no—
484C2×Dic43—41no—
485C2×Dic43—41no—
486C2×Dic43—44no—
487C2×Dic43—44no—
488C2×Dic43—42no—
489C2×Dic43—42no—
490C2×Dic43—42no—
491C2×Dic43C22×D411yescharacteristic
492C2×Dic43C22×D411yescharacteristic
493C2×Dic43C22×D411yescharacteristic
494C2×Dic43C22×D411yescharacteristic
495D172—22no—
496D172—22no—
497D172—42no—
498D172—44no—
499D172—44no—
500D172—44no—
501D172—44no—
502C4×D43—22no—
503C4×D43—22no—
504C4×D43—22no—
505C4×D43—22no—
506C4×D43—22no—
507C4×D43—22no—
508C4×D43—22no—
509C4×D43—22no—
510C4×D43—41no—
511C4×D43—41no—
512C4×D43—41no—
513C4×D43—41no—
514C4×D43—41no—
515C4×D43—41no—
516C4×D43—41no—
517C4×D43—41no—
518C4×D43—44no—
519C4×D43—44no—
520Dic86—24no—
521Dic86—22no—
522Dic86—22no—
523Dic86—42no—
524Dic86—42no—
525C8×C43—24no—
526C43⋊C8—24no—
527#60752—431nomaximal, Sylow
528C22×C43—21no—
529C22×C43—21no—
530C22×C43—21no—
531C22×C43—21no—
532C22×C43—21no—
533C22×C43—21no—
534C22×C43—21no—
535C22×C43—44no—
536C22×C43—42no—
537C22×C43—42no—
538C22×C43—42no—
539C22×C43—84no—
540C22×C43#53412yes—
541C22×C43#57512yes—
542C22×C43C23×D411yescharacteristic
543C2×D43—21no—
544C2×D43—21no—
545C2×D43—21no—
546C2×D43—21no—
547C2×D43—21no—
548C2×D43—21no—
549C2×D43—21no—
550C2×D43—21no—
551C2×D43—21no—
552C2×D43—21no—
553C2×D43—21no—
554C2×D43—44no—
555C2×D43—44no—
556C2×D43—44no—
557C2×D43—44no—
558C2×D43—44no—
559C2×D43—44no—
560C2×D43—42no—
561C2×D43—42no—
562C2×D43—42no—
563C2×D43—84no—
564C2×D43#57512yes—
565C4×C43—21no—
566C4×C43—21no—
567C4×C43—42no—
568C4×C43—42no—
569C4×C43—42no—
570C4×C43#53412yes—
571C4×C43C2×H(5,𝔽2)12yes—
572Dic43—21no—
573Dic43—21no—
574Dic43—21no—
575Dic43—21no—
576Dic43—42no—
577Dic43—42no—
578Dic43—42no—
579C2×#525—431no—
580C2×#525—431no—
581#3197—434no—
582#3196—432no—
583#3194—432no—
584#3191—434no—
585#3190—432no—
586#3188—432no—
587#3095—431no—
588#3094D4311yescharacteristic, complemented
589#3093—432no—
590#3056—432no—
591#3055—432no—
592#3007—431no—
593#3006—431no—
594#3005—432no—
595C2×#407—431no—
596C2×C43—22no—
597C2×C43—22no—
598C2×C43—41no—
599C2×C43—82no—
600C2×C43C2×#53411yescharacteristic
601C2×C43C2×#57511yescharacteristic
602C2×C43C2×#57511yescharacteristic
603D43—22no—
604D43—41no—
605D43—41no—
606D43—41no—
607D43—82no—
608C22×#41—431no—
609C22×#41—431no—
610C24×C4—431no—
611C2×#137—432no—
612C2×AGL(1,ℤ/8)—432no—
613C22×M16—432no—
614#525—432no—
615#525—432no—
616#525—432no—
617#525—432no—
618#525—432no—
619#525—432no—
620#525—432no—
621#525—432no—
622#525—861no—
623#525—861no—
624#525—861no—
625#525—861no—
626#525—861no—
627#525—861no—
628#525—861no—
629#525—861no—
630C2×#123—861no—
631C2×#123—861no—
632C2×C22⋊Q8—431no—
633C2×C22⋊Q8—431no—
634C2×C22⋊Q8—431no—
635C2×C22⋊Q8—431no—
636C2×#121—431no—
637C2×#121—431no—
638C2×#121—431no—
639C2×#121C2×D4311yescharacteristic
640C2×#120—861no—
641C2×#120—861no—
642C2×C4×D4—861no—
643C2×C4×D4—861no—
644C2×C4×D4—861no—
645C2×C4×D4—861no—
646C2×#117—431no—
647C2×#117C2×D4311yescharacteristic
648#485—434no—
649#485—434no—
650#485—434no—
651#484—432no—
652#483—432no—
653#482—434no—
654#482—434no—
655#482C2×D4314yescomplemented
656#481C2×D4312yescomplemented
657#480C2×D4312yescomplemented
658#470—434no—
659#469—434no—
660#468—434no—
661#468—434no—
662#467—434no—
663#466—434no—
664#465—434no—
665#465—434no—
666#452—434no—
667#452—434no—
668#452—434no—
669#451—432no—
670#450—432no—
671#449—434no—
672#449—434no—
673#449—434no—
674#448—432no—
675#447—432no—
676#428—432no—
677#428C2×D4312yescomplemented
678#419—432no—
679#418C2×D4312yescomplemented
680#417—432no—
681#417—432no—
682#407—431no—
683#407—432no—
684#407—432no—
685#407—432no—
686#407C2×D4311yescharacteristic
687C2×C22⋊C8—432no—
688C2×C22⋊C8—432no—
689C43#6075211yescharacteristic, complemented, Sylow
690C25—431no—
691C2×#41—432no—
692C2×#41—432no—
693C2×#41—432no—
694C2×#41—432no—
695C2×#41—861no—
696C2×#41—861no—
697C2×#41—861no—
698C2×#41—861no—
699C2×#41—1724no—
700C2×#41—1724no—
701C22×Q8—431no—
702C22×Q8—431no—
703C22×D4—21no—
704C22×D4—431no—
705C22×D4—861no—
706C22×D4—861no—
707C22×D4—861no—
708C22×D4—861no—
709C22×D4—861no—
710C22×D4C22×D4311yescharacteristic
711C23×C4—431no—
712C23×C4—431no—
713C23×C4—431no—
714C23×C4—431no—
715C23×C4—431no—
716C23×C4—431no—
717C23×C4—431no—
718C23×C4—431no—
719C23×C4—431no—
720C23×C4—431no—
721C23×C4—431no—
722C23×C4—431no—
723C23×C4—431no—
724C23×C4—861no—
725C23×C4—861no—
726C23×C4—1724no—
727C23×C4C22×D4311yescharacteristic
728#137—1724no—
729AGL(1,ℤ/8)—1724no—
730C2×Q16—434no—
731C2×SD16—434no—
732C2×SD16—434no—
733C2×D8—434no—
734C2×M16—432no—
735C2×M16—434no—
736C2×M16—1724no—
737C2×M16C22×D4312yes—
738C22×C8—434no—
739#123—862no—
740#123—862no—
741#123—862no—
742#123—862no—
743#123—862no—
744#123—862no—
745#123—862no—
746#123—862no—
747C22⋊Q8—432no—
748C22⋊Q8—432no—
749C22⋊Q8—432no—
750C22⋊Q8—432no—
751C22⋊Q8—432no—
752C22⋊Q8—432no—
753C22⋊Q8—432no—
754C22⋊Q8—432no—
755C22⋊Q8—861no—
756C22⋊Q8—861no—
757C22⋊Q8—861no—
758C22⋊Q8—861no—
759C22⋊Q8—861no—
760C22⋊Q8—861no—
761C22⋊Q8—861no—
762C22⋊Q8—861no—
763#121—21no—
764#121—21no—
765#121—432no—
766#121—432no—
767#121—432no—
768#121—432no—
769#121—432no—
770#121—432no—
771#121—861no—
772#121—861no—
773#121—861no—
774#121—861no—
775#121—861no—
776#121—861no—
777#121C22×D4312yes—
778#121C22×D4312yes—
779#120—862no—
780#120—862no—
781#120—862no—
782#120—862no—
783#120—862no—
784#120—862no—
785#120—862no—
786#120—862no—
787C4×D4—862no—
788C4×D4—862no—
789C4×D4—862no—
790C4×D4—862no—
791C4×D4—862no—
792C4×D4—862no—
793C4×D4—862no—
794C4×D4—862no—
795C4×D4—862no—
796C4×D4—862no—
797C4×D4—862no—
798C4×D4—862no—
799C4×D4—862no—
800C4×D4—862no—
801C4×D4—862no—
802C4×D4—862no—
803#117—21no—
804#117—21no—
805#117—432no—
806#117—432no—
807#117—861no—
808#117—861no—
809#117C22×D4312yes—
810#117C22×D4312yes—
811C2×C4⋊C4—431no—
812C2×C4⋊C4—861no—
813C2×C4⋊C4—861no—
814C2×C4⋊C4—861no—
815C2×C4⋊C4—861no—
816C2×C4⋊C4C22×D4311yescharacteristic
817C2×C4⋊C4C22×D4311yescharacteristic
818C2×C4⋊C4C22×D4311yescharacteristic
819C2×C22⋊C4—21no—
820C2×C22⋊C4—21no—
821C2×C22⋊C4—861no—
822C2×C22⋊C4—861no—
823C2×C22⋊C4—861no—
824C2×C22⋊C4—861no—
825C2×C22⋊C4—861no—
826C2×C22⋊C4—861no—
827C2×C22⋊C4—861no—
828C2×C22⋊C4—861no—
829C2×C42—21no—
830C2×C42—861no—
831#107—434no—
832#107C22×D4314yescomplemented
833#106—434no—
834#106C22×D4314yescomplemented
835#103—434no—
836#103—434no—
837#103—434no—
838#103—434no—
839#102—434no—
840#102—434no—
841#102C22×D4314yescomplemented
842#102C22×D4314yescomplemented
843C22⋊C8—432no—
844C22⋊C8—432no—
845C22⋊C8—434no—
846C22⋊C8—434no—
847C22⋊C8C22×D4312yes—
848C22⋊C8C22×D4312yes—
849C24—21no—
850C24—431no—
851C24—431no—
852C24—431no—
853C24—431no—
854C24—431no—
855C24—431no—
856C24—861no—
857C24—1722no—
858C24—1722no—
859C24—1722no—
860C24D4×D4311yescharacteristic
861#41—864no—
862#41—864no—
863#41—1722no—
864#41—1722no—
865#41—1724no—
866#41—1724no—
867#41—1724no—
868#41—1724no—
869#41—1724no—
870#41—1724no—
871C2×Q8—432no—
872C2×Q8—432no—
873C2×Q8—861no—
874C2×Q8—861no—
875C2×Q8—864no—
876C2×Q8—1722no—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—21no—
880C2×D4—24no—
881C2×D4—44no—
882C2×D4—432no—
883C2×D4—862no—
884C2×D4—862no—
885C2×D4—862no—
886C2×D4—862no—
887C2×D4—862no—
888C2×D4—862no—
889C2×D4—862no—
890C2×D4—862no—
891C2×D4—862no—
892C2×D4—862no—
893C2×D4—861no—
894C2×D4—1722no—
895C2×D4—1724no—
896C2×D4—1724no—
897C2×D4—1724no—
898C2×D4—1724no—
899C2×D4—1724no—
900C2×D4C23×D4312yes—
901C22×C4—24no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—431no—
906C22×C4—431no—
907C22×C4—431no—
908C22×C4—431no—
909C22×C4—431no—
910C22×C4—431no—
911C22×C4—431no—
912C22×C4—431no—
913C22×C4—431no—
914C22×C4—431no—
915C22×C4—431no—
916C22×C4—431no—
917C22×C4—431no—
918C22×C4—431no—
919C22×C4—431no—
920C22×C4—431no—
921C22×C4—431no—
922C22×C4—431no—
923C22×C4—431no—
924C22×C4—431no—
925C22×C4—431no—
926C22×C4—431no—
927C22×C4—862no—
928C22×C4—862no—
929C22×C4—864no—
930C22×C4—864no—
931C22×C4—861no—
932C22×C4—861no—
933C22×C4—861no—
934C22×C4—862no—
935C22×C4—862no—
936C22×C4—1722no—
937C22×C4—1722no—
938C22×C4—1722no—
939C22×C4—1722no—
940C22×C4—1722no—
941C22×C4—1722no—
942C22×C4—1722no—
943C22×C4—1722no—
944C22×C4—1722no—
945C22×C4—1722no—
946C22×C4—1724no—
947C22×C4—1722no—
948C22×C4—1724no—
949C22×C4D4×D4311yescharacteristic
950C22×C4D4×D4311yescharacteristic
951C22×C4D4×D4311yescharacteristic
952C22×C4C23×D4311yescharacteristic
953C22×C4C23×D4311yescharacteristic
954C22×C4C23×D4311yescharacteristic
955Q16—1724no—
956SD16—1724no—
957SD16—1724no—
958D8—1724no—
959M16—24no—
960M16—864no—
961M16—1724no—
962C2×C8—434no—
963C2×C8—1724no—
964C2×C8C23×D4314yes—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—432no—
969C4⋊C4—862no—
970C4⋊C4—862no—
971C4⋊C4—862no—
972C4⋊C4—862no—
973C4⋊C4—862no—
974C4⋊C4—862no—
975C4⋊C4—861no—
976C4⋊C4—862no—
977C4⋊C4—862no—
978C4⋊C4C23×D4312yes—
979C4⋊C4C23×D4312yes—
980C4⋊C4C23×D4312yes—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—862no—
986C22⋊C4—862no—
987C22⋊C4—862no—
988C22⋊C4—862no—
989C22⋊C4—862no—
990C22⋊C4—862no—
991C22⋊C4—862no—
992C22⋊C4—862no—
993C22⋊C4—862no—
994C22⋊C4—862no—
995C22⋊C4—862no—
996C22⋊C4—862no—
997C22⋊C4—862no—
998C22⋊C4—862no—
999C22⋊C4—862no—
1000C22⋊C4—862no—
1001C42—22no—
1002C42—22no—
1003C42—862no—
1004C42—862no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—41no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—431no—
1013C23—431no—
1014C23—431no—
1015C23—431no—
1016C23—862no—
1017C23—862no—
1018C23—862no—
1019C23—862no—
1020C23—862no—
1021C23—862no—
1022C23—862no—
1023C23—862no—
1024C23—1721no—
1025C23—1721no—
1026C23—1721no—
1027C23—1721no—
1028C23—1721no—
1029C23—1721no—
1030C23—1721no—
1031C23—1721no—
1032C23—1721no—
1033C23—1721no—
1034C23—1721no—
1035C23—1722no—
1036C23—1722no—
1037C23—17216no—
1038C23—1722no—
1039C23C2×D4×D4311yescharacteristic
1040C23C2×D4×D4311yescharacteristic
1041C23C2×D4×D4311yescharacteristic
1042Q8—862no—
1043Q8—864no—
1044Q8—862no—
1045Q8—1722no—
1046Q8—1722no—
1047D4—24no—
1048D4—44no—
1049D4—44no—
1050D4—42no—
1051D4—862no—
1052D4—862no—
1053D4—1722no—
1054D4—1724no—
1055D4—1724no—
1056D4—1724no—
1057D4—1724no—
1058D4—1724no—
1059D4—1724no—
1060D4—1724no—
1061D4—1724no—
1062D4—1724no—
1063D4—1724no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—42no—
1073C2×C4—42no—
1074C2×C4—42no—
1075C2×C4—431no—
1076C2×C4—431no—
1077C2×C4—431no—
1078C2×C4—431no—
1079C2×C4—862no—
1080C2×C4—862no—
1081C2×C4—862no—
1082C2×C4—862no—
1083C2×C4—862no—
1084C2×C4—862no—
1085C2×C4—862no—
1086C2×C4—862no—
1087C2×C4—862no—
1088C2×C4—862no—
1089C2×C4—862no—
1090C2×C4—862no—
1091C2×C4—862no—
1092C2×C4—1721no—
1093C2×C4—1721no—
1094C2×C4—1721no—
1095C2×C4—1721no—
1096C2×C4—1721no—
1097C2×C4—1721no—
1098C2×C4—1721no—
1099C2×C4—1721no—
1100C2×C4—1724no—
1101C2×C4—1721no—
1102C2×C4—1721no—
1103C2×C4—1721no—
1104C2×C4—1721no—
1105C2×C4—1724no—
1106C2×C4—1724no—
1107C2×C4—1722no—
1108C2×C4—1722no—
1109C2×C4—1722no—
1110C2×C4—1724no—
1111C2×C4C2×D4×D4311yescharacteristic
1112C2×C4C2×D4×D4311yescharacteristic
1113C2×C4C2×D4×D4311yescharacteristic
1114C2×C4#1306337114yes—
1115C2×C4C24×D4311yescharacteristic
1116C8—24no—
1117C8—864no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—44no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—84no—
1130C22—432no—
1131C22—861no—
1132C22—861no—
1133C22—861no—
1134C22—861no—
1135C22—861no—
1136C22—861no—
1137C22—861no—
1138C22—861no—
1139C22—861no—
1140C22—861no—
1141C22—861no—
1142C22—3444no—
1143C22—1724no—
1144C22—1724no—
1145C22—1724no—
1146C22—1724no—
1147C22—1724no—
1148C22—1724no—
1149C22—1722no—
1150C22—1722no—
1151C22—1722no—
1152C22#1458346012yes—
1153C22#1458369512yes—
1154C22C22×D4×D4311yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—861no—
1161C4—861no—
1162C4—861no—
1163C4—861no—
1164C4—1722no—
1165C4—1722no—
1166C4—1722no—
1167C4#1458346012yes—
1168C4C2×#1306337112yes—
1169C2—22no—
1170C2—22no—
1171C2—41no—
1172C2—82no—
1173C2—862no—
1174C2—3442no—
1175C2—1721no—
1176C2—1721no—
1177C2—1721no—
1178C2C2×#1458346011yescharacteristic
1179C2#575×D4311yescharacteristic
1180C2C2×#1458369511yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3094C2
socleC22×C43C23×D4
hypercenter#3094D43
hypocenterC43#60752
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
1. C2×#14583411C2semidirect
2. C2×#14583409C2semidirect
3. #19145435C2semidirect
4. #19145424C2semidirect
5. #19145408C2semidirect
6. #19145386C2semidirect
7. #19145375C2semidirect
8. #19145359C2semidirect
9. #19144543C2semidirect
10. #19144529C2semidirect
11. #19144226C2semidirect
12. #19144212C2semidirect
13. #19143857C2semidirect
14. #19143845C2semidirect
15. #19143839C2semidirect
16. #407×D43C2semidirect
17. C43×#3094C2semidirect
19. C22×#10621900C22semidirect
21. C2×#13063358C22semidirect
22. C2×#13063351C22semidirect
23. C2×M16×D43C22semidirect
30. #14583411C22semidirect
31. #14583411C22semidirect
38. #14583409C22semidirect
39. #14583409C22semidirect
42. C2×#13063305C22semidirect
43. C2×#13063305C22semidirect
44. C2×#13063305C22semidirect
46. C2×#13063300C22semidirect
47. C2×#13063300C22semidirect
48. C2×#13063296C22semidirect
55. C2×#13063283C22semidirect
56. #14583243C22semidirect
57. #14583242C22semidirect
58. #14583240C22semidirect
59. #14583234C22semidirect
60. #14583229C22semidirect
61. #14583226C22semidirect
62. #14583225C22semidirect
63. #14583158C22semidirect
64. #14583151C22semidirect
65. #14583146C22semidirect
66. #14583144C22semidirect
67. #14583141C22semidirect
68. #14583134C22semidirect
69. #14583129C22semidirect
70. #14583127C22semidirect
71. #14583063C22semidirect
72. #14583062C22semidirect
73. #14583062C22semidirect
74. #14583057C22semidirect
75. #14583052C22semidirect
76. #14583045C22semidirect
77. #14583045C22semidirect
78. #14583042C22semidirect
79. #14583037C22semidirect
80. #14583032C22semidirect
81. #14582942C22semidirect
82. #14582907C22semidirect
83. #14582901C22semidirect
84. #14582898C22semidirect
86. #14582862C22semidirect
87. #14582861C22semidirect
88. #14582861C22semidirect
89. C22⋊C8×D43C22semidirect
90. C22⋊C8×D43C22semidirect
93. C43×#482C22semidirect
94. C43×#481C22semidirect
95. C43×#480C22semidirect
96. C43×#428C22semidirect
97. C43×#418C22semidirect
136. C2×Dic172C23semidirect
137. C2×#10621873C23semidirect
138. C2×#10621883C23semidirect
139. C2×#10621882C23semidirect
222. #13063258C23semidirect
223. #13063256C23semidirect
224. #13063250C23semidirect
225. #13063248C23semidirect
226. #13063248C23semidirect
227. #13063248C23semidirect
228. #13063247C23semidirect
229. #13063245C23semidirect
252. #107×C43C23semidirect
253. #106×C43C23semidirect
254. #102×C43C23semidirect
255. #102×C43C23semidirect
588. #3094D43semidirect
655. #482C2×D43semidirect
656. #481C2×D43semidirect
657. #480C2×D43semidirect
677. #428C2×D43semidirect
679. #418C2×D43semidirect
689. C43#60752semidirect
832. #107C22×D43semidirect
834. #106C22×D43semidirect
841. #102C22×D43semidirect
842. #102C22×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834112
C2×#145834092
#191454352
#191454242
#191454082
#191453862
#191453752
#191453592
#191445432
#191445292
#191442262
#191442122
#191438572
#191438452
#191438392
#407×D432
C43×#30942
#6075243