Finite Group Databasebeta

← #25965039

Subgroups — #25965039

Order 11008.

2148 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic, complemented
2C2×#14583367C211yesmaximal, characteristic
3#19144752C214yesmaximal, complemented
4#19144722C212yesmaximal, complemented
5#19144691C212yesmaximal, complemented
6#19144661C214yesmaximal, complemented
7#19144631C212yesmaximal, complemented
8#19144600C212yesmaximal, complemented
9#19144543C211yesmaximal, characteristic, complemented
10#19144408C212yesmaximal, complemented
11#19144081C212yesmaximal, complemented
12#19143857C211yesmaximal, characteristic
13#19143853C211yesmaximal, characteristic
14#19143413C212yesmaximal, complemented
15#19143410C212yesmaximal, complemented
16#19143224C211yesmaximal, characteristic, complemented
17C43×#3095C211yesmaximal, characteristic, complemented
18C22×#10621898C2211yescharacteristic
19C2×#13063358C2212yes—
20C2×#13063356C2212yes—
21#14583451—21no—
22#14583451—21no—
23#14583451—21no—
24#14583451—21no—
25#14583451C2212yes—
26#14583451C2212yes—
27#14583451C2212yescomplemented
28#14583451C2212yescomplemented
29C2×#13063324C2211yescharacteristic, complemented
30C2×#13063323C2211yescharacteristic, complemented
31C2×#13063315—21no—
32C2×#13063304C2211yescharacteristic
33C2×#13063302—21no—
34#14583367—21no—
35#14583367—21no—
36#14583367—21no—
37#14583367—21no—
38#14583367C2212yes—
39#14583367C2212yes—
40#14583367C2212yes—
41#14583367C2212yes—
42C2×Q8×Dic43C2211yescharacteristic, complemented
43C2×#13063290—21no—
44C2×#13063290C2211yescharacteristic
45C2×#13063290C2211yescharacteristic
46C2×#13063290C2211yescharacteristic, complemented
47C2×#13063287C2211yescharacteristic
48C2×#13063287C2211yescharacteristic
49C2×(C22⋊D43)⋊C4—21no—
50C2×(C22⋊D43)⋊C4—21no—
51C2×#13063282—21no—
52C2×#13063281—21no—
53C22×C4×Dic43C2211yescharacteristic
54C2×C42×D43—21no—
55#14583240C2214yescomplemented
56#14583234C2212yes—
57#14583229C2212yes—
58#14583193C2214yescomplemented
59#14583188C2214yescomplemented
60#14583183C2214yescomplemented
61#14583178C2214yescomplemented
62#14583108C2214yescomplemented
63#14583108C2214yescomplemented
64#14583103C2214yescomplemented
65#14583103C2214yescomplemented
66#14583063C2214yes—
67#14583059C2214yes—
68#14583057C2212yes—
69#14583054C2212yes—
70#14583052C2212yes—
71#14583049C2212yes—
72#14583005C2214yescomplemented
73#14583003C2214yescomplemented
74#14583002C2214yescomplemented
75#14582998C2214yescomplemented
76#14582993C2214yescomplemented
77#14582991C2214yescomplemented
78#14582986C2214yescomplemented
79#14582984C2214yescomplemented
80#14582953C2212yes—
81#14582953C2212yescomplemented
82#14582949C2212yes—
83#14582949C2212yescomplemented
84#14582942C2212yescomplemented
85#14582922C2212yescomplemented
86#14582907C2212yescomplemented
87#14582901C2212yes—
88#14582898C2212yes—
89#14582863C2211yescharacteristic
90M16×Dic43C2212yescomplemented
91C2×C22⋊Q8×C43C2211yescharacteristic
92C2×#117×C43C2211yescharacteristic
93C43×#485C2214yescomplemented
94C43×#484C2212yes—
95C43×#483C2212yes—
96C43×#428C2212yescomplemented
97C43×#419C2212yescomplemented
98C43×#407C2211yescharacteristic
99C2×#10621898—21no—
100C2×#10621898—21no—
101C2×#10621898—28no—
102C2×#10621898C2312yes—
103C2×#10621898C2312yes—
104C22×Dic86—21no—
105C22×Dic86C2311yescharacteristic
106C22×Dic86C2311yescharacteristic
107C22×D172C2311yescharacteristic
108C22×C22⋊D43—21no—
109C23×Dic43D411yescharacteristic
110C23×Dic43D411yescharacteristic
111C22×C4×D43—21no—
112C22×C4×D43—21no—
113C22×C4×D43—21no—
114#13063358—28no—
115#13063356—28no—
116C2×Dic172C2314yes—
117C2×#10621885C2314yes—
118C2×#10621873C2314yes—
119C2×#10621884C2314yes—
120C2×#10621877C2312yes—
121#13063324—21no—
122#13063324—21no—
123#13063324C2312yes—
124#13063324C2312yes—
125#13063323—21no—
126#13063323—21no—
127#13063323C2312yes—
128#13063323C2312yes—
129#13063315—22no—
130#13063315—22no—
131#13063315—22no—
132#13063315—22no—
133#13063304—21no—
134#13063304—21no—
135#13063304C2312yes—
136#13063304C2312yes—
137#13063302—22no—
138#13063302—22no—
139#13063302—22no—
140#13063302—22no—
141Q8×Dic43—21no—
142Q8×Dic43—21no—
143Q8×Dic43C2312yes—
144Q8×Dic43C2312yes—
145#13063290—22no—
146#13063290—22no—
147#13063290—22no—
148#13063290—22no—
149#13063290—21no—
150#13063290—21no—
151#13063290—21no—
152#13063290—21no—
153#13063290—21no—
154#13063290—21no—
155#13063290C2312yes—
156#13063290C2312yes—
157#13063290C2312yes—
158#13063290C2312yes—
159#13063290C2312yes—
160#13063290C2312yes—
161#13063287—21no—
162#13063287—21no—
163#13063287—21no—
164#13063287—21no—
165#13063287C2312yes—
166#13063287C2312yes—
167#13063287C2312yes—
168#13063287C2312yes—
169(C22⋊D43)⋊C4—22no—
170(C22⋊D43)⋊C4—22no—
171(C22⋊D43)⋊C4—22no—
172(C22⋊D43)⋊C4—22no—
173(C22⋊D43)⋊C4—22no—
174(C22⋊D43)⋊C4—22no—
175(C22⋊D43)⋊C4—22no—
176(C22⋊D43)⋊C4—22no—
177#13063282—22no—
178#13063282—22no—
179#13063282—22no—
180#13063282—22no—
181#13063281—22no—
182#13063281—22no—
183#13063281—22no—
184#13063281—22no—
185C2×C4⋊Dic43—21no—
186C2×C4⋊Dic43C2311yescharacteristic
187C2×Dic43⋊C4—21no—
188C2×Dic43⋊C4—21no—
189C2×Dic43⋊C4—21no—
190C2×Dic43⋊C4—21no—
191C2×Dic43⋊C4—21no—
192C2×Dic43⋊C4—21no—
193C2×Dic43⋊C4—21no—
194C2×C22⋊Dic43—21no—
195C2×(C2×D43)⋊C4—21no—
196C2×(C2×D43)⋊C4—21no—
197C2×C4×Dic43—21no—
198C2×C4×Dic43—21no—
199C2×C4×Dic43—21no—
200C2×C4×Dic43—21no—
201C2×C4×Dic43D411yescharacteristic
202C2×C4×Dic43D411yescharacteristic
203C2×C4×Dic43D411yescharacteristic
204C2×C4×Dic43D411yescharacteristic
205C2×C4×Dic43D411yescharacteristic
206C2×C4×Dic43D411yescharacteristic
207C2×C4×Dic43C2311yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2311yescharacteristic
211C2×C4×Dic43C2311yescharacteristic
212C2×C4×Dic43C2311yescharacteristic
213C42×D43—22no—
214C42×D43—22no—
215C42×D43—22no—
216C42×D43—22no—
217#13063258C2314yes—
218#13063256C2314yes—
219Dic43⋊C8C2314yes—
220Dic43⋊C8C2314yes—
221#13063250C2314yes—
222#13063248C2314yes—
223#13063248C2314yes—
224#13063248C2314yes—
225#13063247C2314yes—
226#13063245C2314yes—
227C22⋊(C43⋊C8)C2312yes—
228C22⋊(C43⋊C8)C2312yes—
229#13063235C2314yes—
230C8×Dic43C2314yes—
231C22×Q8×C43C2311yescharacteristic
232C23×C4×C43C2311yescharacteristic
233C2×M16×C43C2312yes—
234C22⋊Q8×C43—21no—
235C22⋊Q8×C43—21no—
236C22⋊Q8×C43C2312yes—
237C22⋊Q8×C43C2312yes—
238#117×C43—21no—
239#117×C43—21no—
240#117×C43C2312yes—
241#117×C43C2312yes—
242C2×C4⋊C4×C43—21no—
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C4⋊C4×C43C2311yescharacteristic
245C2×C4⋊C4×C43C2311yescharacteristic
246C2×C22⋊C4×C43—21no—
247C2×C22⋊C4×C43—21no—
248C2×C42×C43—21no—
249#107×C43C2314yes—
250#106×C43C2314yes—
251#103×C43C2314yes—
252#103×C43C2314yes—
253C22⋊C8×C43C2312yes—
254C22⋊C8×C43C2312yes—
255C24×C43C2×D411yescharacteristic
256C23×D43—21no—
257C2×Q8×C43—21no—
258C2×Q8×C43—24no—
259C2×Q8×C43C2412yes—
260C22×C4×C43—24no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43C2×D411yescharacteristic
266C22×C4×C43C2×D411yescharacteristic
267C22×C4×C43C2×D411yescharacteristic
268C22×C4×C43C2411yescharacteristic
269C22×C4×C43C2411yescharacteristic
270C22×C4×C43C2411yescharacteristic
271C2×C22⋊D43—28no—
272C2×C22⋊D43—22no—
273C2×C22⋊D43—22no—
274C22×Dic43—24no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278C22×Dic43—42no—
279C22×Dic43C2×D411yescharacteristic
280C22×Dic43C2×D411yescharacteristic
281C22×Dic43C2×D411yescharacteristic
282C22×Dic43C2×D411yescharacteristic
283C22×Dic43C2×D411yescharacteristic
284C22×Dic43C2×D411yescharacteristic
285C22×Dic43C2×D411yescharacteristic
286C22×Dic43C2×D411yescharacteristic
287C22×Dic43C2×D411yescharacteristic
288C22×Dic43C2×D411yescharacteristic
289C22×Dic43C2×D411yescharacteristic
290C22×Dic43C2×D411yescharacteristic
291#10621898—28no—
292#10621898—28no—
293#10621898—24no—
294#10621898—24no—
295#10621898—24no—
296#10621898#4118yes—
297C2×D172—21no—
298C2×D172—24no—
299C2×D172C2412yes—
300C2×C4×D43—28no—
301C2×C4×D43—22no—
302C2×C4×D43—22no—
303C2×C4×D43—22no—
304C2×C4×D43—22no—
305C2×C4×D43—22no—
306C2×C4×D43—22no—
307C2×C4×D43—44no—
308C2×C4×D43—44no—
309C2×Dic86—21no—
310C2×Dic86—24no—
311C2×Dic86—24no—
312C2×Dic86—21no—
313C2×Dic86—22no—
314C2×Dic86—22no—
315C2×Dic86—44no—
316C2×Dic86C2412yes—
317C2×Dic86C2412yes—
318M16×C43—24no—
319C2×C8×C43C2414yes—
320C4⋊C4×C43—22no—
321C4⋊C4×C43—22no—
322C4⋊C4×C43—21no—
323C4⋊C4×C43—21no—
324C4⋊C4×C43—21no—
325C4⋊C4×C43C2412yes—
326C4⋊C4×C43C2412yes—
327C4⋊C4×C43C2412yes—
328C22⋊C4×C43—22no—
329C22⋊C4×C43—22no—
330C22⋊C4×C43—22no—
331C22⋊C4×C43—22no—
332C42×C43—22no—
333C42×C43—22no—
334C22⋊Dic43—22no—
335C22⋊Dic43—22no—
336#10621885—28no—
337#10621884—28no—
338(C2×D43)⋊C4—22no—
339(C2×D43)⋊C4—22no—
340(C2×D43)⋊C4—22no—
341(C2×D43)⋊C4—22no—
342C4⋊Dic43—21no—
343C4⋊Dic43—22no—
344C4⋊Dic43—22no—
345C4⋊Dic43C2412yes—
346Dic43⋊C4—22no—
347Dic43⋊C4—22no—
348Dic43⋊C4—22no—
349Dic43⋊C4—22no—
350Dic43⋊C4—22no—
351Dic43⋊C4—22no—
352Dic43⋊C4—22no—
353Dic43⋊C4—22no—
354Dic43⋊C4—22no—
355Dic43⋊C4—22no—
356Dic43⋊C4—22no—
357Dic43⋊C4—22no—
358Dic43⋊C4—22no—
359Dic43⋊C4—22no—
360C4×Dic43—22no—
361C4×Dic43—22no—
362C4×Dic43—22no—
363C4×Dic43—22no—
364C4×Dic43—22no—
365C4×Dic43—22no—
366C4×Dic43—22no—
367C4×Dic43—22no—
368C4×Dic43C2×D411yescharacteristic
369C4×Dic43C2×D411yescharacteristic
370C4×Dic43C2×D411yescharacteristic
371C4×Dic43C2×D411yescharacteristic
372C4×Dic43C2×D411yescharacteristic
373C4×Dic43C2×D411yescharacteristic
374C4×Dic43C2×D411yescharacteristic
375C4×Dic43C2×D411yescharacteristic
376C4×Dic43C2×D411yescharacteristic
377C4×Dic43C2×D411yescharacteristic
378C4×Dic43C2×D411yescharacteristic
379C4×Dic43C2×D411yescharacteristic
380C4×Dic43C2411yescharacteristic
381C4×Dic43C2411yescharacteristic
382C4×Dic43C2411yescharacteristic
383C4×Dic43C2411yescharacteristic
384#10621877—24no—
385C2×C43⋊C8C2414yes—
386Dic172—28no—
387#10621873—28no—
388C23×C43—22no—
389C23×C43—22no—
390C23×C43—41no—
391C23×C43C22×D411yescharacteristic
392C23×C43C22×D411yescharacteristic
393C23×C43C22×D411yescharacteristic
394C22×D43—24no—
395C22×D43—22no—
396C22×D43—42no—
397C22×D43—42no—
398Q8×C43—24no—
399Q8×C43—42no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43—22no—
404C2×C4×C43—22no—
405C2×C4×C43—22no—
406C2×C4×C43—22no—
407C2×C4×C43—22no—
408C2×C4×C43—22no—
409C2×C4×C43—42no—
410C2×C4×C43—42no—
411C2×C4×C43—42no—
412C2×C4×C43—42no—
413C2×C4×C43C22×D411yescharacteristic
414C2×C4×C43C22×D411yescharacteristic
415C2×C4×C43C22×D411yescharacteristic
416C2×C4×C43C2×#4114yes—
417C2×C4×C43C2511yescharacteristic
418C22⋊D43—28no—
419C22⋊D43—28no—
420C2×Dic43—24no—
421C2×Dic43—22no—
422C2×Dic43—22no—
423C2×Dic43—22no—
424C2×Dic43—22no—
425C2×Dic43—22no—
426C2×Dic43—22no—
427C2×Dic43—22no—
428C2×Dic43—22no—
429C2×Dic43—22no—
430C2×Dic43—22no—
431C2×Dic43—22no—
432C2×Dic43—41no—
433C2×Dic43—41no—
434C2×Dic43—41no—
435C2×Dic43—42no—
436C2×Dic43—42no—
437C2×Dic43#13714yescomplemented
438C2×Dic43C22×D411yescharacteristic
439C2×Dic43C22×D411yescharacteristic
440C2×Dic43C22×D411yescharacteristic
441C2×Dic43C22×D411yescharacteristic
442C2×Dic43C22×D411yescharacteristic
443C2×Dic43C22×D411yescharacteristic
444C2×Dic43C22×D411yescharacteristic
445C2×Dic43C22×D411yescharacteristic
446D172—24no—
447D172—22no—
448D172C2×#4114yes—
449C4×D43—28no—
450C4×D43—28no—
451C4×D43—44no—
452C4×D43—44no—
453C4×D43—44no—
454C4×D43—44no—
455Dic86—24no—
456Dic86—22no—
457Dic86—24no—
458Dic86—44no—
459Dic86—42no—
460Dic86—44no—
461Dic86C2×#4114yes—
462C8×C43—24no—
463C43⋊C8—24no—
464#60562—431nomaximal, Sylow
465C22×C43—21no—
466C22×C43—21no—
467C22×C43—21no—
468C22×C43—21no—
469C22×C43—21no—
470C22×C43—21no—
471C22×C43—21no—
472C22×C43—44no—
473C22×C43#52512yes—
474C22×C43C2×#13712yes—
475C22×C43C23×D411yescharacteristic
476C2×D43—24no—
477C2×D43—48no—
478C2×D43—42no—
479C2×D43—42no—
480C4×C43—21no—
481C4×C43—21no—
482C4×C43—42no—
483C4×C43—42no—
484C4×C43—42no—
485C4×C43—42no—
486C4×C43#52512yes—
487C4×C43C22×#4112yes—
488Dic43—24no—
489Dic43—21no—
490Dic43—21no—
491Dic43—21no—
492Dic43—21no—
493Dic43—21no—
494Dic43—42no—
495Dic43—42no—
496Dic43C2×#13712yes—
497Dic43C2×#13712yes—
498Dic43#57512yes—
499C2×#533—431no—
500C2×C4×#41—431no—
501#3116—434no—
502#3113—432no—
503#3110—432no—
504#3107—434no—
505#3104—432no—
506#3101—432no—
507#3095—431no—
508#3095D4311yescharacteristic, complemented
509#3079—432no—
510#3039—432no—
511#3007—431no—
512#3007—431no—
513C4×#137—432no—
514C4×#137—432no—
515#2920—431no—
516C2×C43—22no—
517C2×C43—22no—
518C2×C43—41no—
519C2×C43C2×#52511yescharacteristic
520C2×C43C22×#13711yescharacteristic
521C2×C43C2×#57511yescharacteristic
522D43—44no—
523C22×#41—431no—
524C2×#137—432no—
525C2×#137—432no—
526#533—432no—
527#533—432no—
528#533—432no—
529#533—432no—
530#533—861no—
531#533—861no—
532#533—861no—
533#533—861no—
534C2×C4⋊Q8—431no—
535C2×C4⋊Q8—431no—
536C2×#125—861no—
537C2×C22⋊Q8—431no—
538C2×C22⋊Q8—861no—
539C2×C22⋊Q8C2×D4311yescharacteristic
540C4×#41—432no—
541C4×#41—432no—
542C4×#41—432no—
543C4×#41—432no—
544C4×#41—861no—
545C4×#41—861no—
546C4×#41—861no—
547C4×#41—861no—
548C2×C4×Q8—431no—
549C2×C4×Q8—431no—
550C2×C4×Q8—431no—
551C2×C4×Q8—431no—
552C2×C4×Q8—861no—
553C2×C4×D4—431no—
554C2×C4×D4—431no—
555C2×C4×D4—861no—
556C2×C4×D4—861no—
557C2×#117—861no—
558C2×#117—861no—
559C2×#117C2×D4311yescharacteristic
560C22×C42—431no—
561C22×C42—861no—
562#485—434no—
563#485C2×D4314yescomplemented
564#484—432no—
565#484C2×D4312yes—
566#483—432no—
567#483C2×D4312yes—
568#477—434no—
569#476—434no—
570#475—434no—
571#474—434no—
572#462—434no—
573#462—434no—
574#461—434no—
575#461—434no—
576#452—434no—
577#452—434no—
578#451—432no—
579#451—432no—
580#450—432no—
581#450—432no—
582#441—434no—
583#441—434no—
584#440—434no—
585#440—434no—
586C4×Q16—434no—
587C4×Q16—434no—
588C4×SD16—434no—
589C4×SD16—434no—
590#432—432no—
591#432—432no—
592#431—432no—
593#431—432no—
594#428—432no—
595#428C2×D4312yescomplemented
596#423—432no—
597#419—432no—
598#419C2×D4312yescomplemented
599#417—432no—
600#417—432no—
601#407—431no—
602#407C2×D4311yescharacteristic
603C4×M16—432no—
604C43#6056211yescharacteristic, complemented, Sylow
605C2×#41—432no—
606C2×#41—432no—
607C2×#41—868no—
608C2×#41—861no—
609C2×#41—861no—
610C22×Q8—431no—
611C22×Q8—431no—
612C22×Q8—861no—
613C22×Q8C22×D4311yescharacteristic
614C22×D4—431no—
615C22×D4—861no—
616C23×C4—431no—
617C23×C4—431no—
618C23×C4—861no—
619C23×C4—861no—
620C23×C4—861no—
621C23×C4C22×D4311yescharacteristic
622#137—868no—
623#137—868no—
624C2×Q16—434no—
625C2×Q16—434no—
626C2×SD16—434no—
627C2×SD16—434no—
628C2×M16—432no—
629C2×M16C22×D4312yes—
630C4⋊Q8—432no—
631C4⋊Q8—432no—
632C4⋊Q8—432no—
633C4⋊Q8—432no—
634C4⋊Q8—861no—
635C4⋊Q8—861no—
636C4⋊Q8—861no—
637C4⋊Q8—861no—
638#125—862no—
639#125—862no—
640#125—862no—
641#125—862no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—432no—
645C22⋊Q8—432no—
646C22⋊Q8—862no—
647C22⋊Q8—862no—
648C22⋊Q8—862no—
649C22⋊Q8—862no—
650C22⋊Q8—861no—
651C22⋊Q8—861no—
652C22⋊Q8C22×D4312yes—
653C22⋊Q8C22×D4312yes—
654C4×Q8—432no—
655C4×Q8—432no—
656C4×Q8—432no—
657C4×Q8—432no—
658C4×Q8—432no—
659C4×Q8—432no—
660C4×Q8—432no—
661C4×Q8—432no—
662C4×Q8—861no—
663C4×Q8—861no—
664C4×Q8—861no—
665C4×Q8—861no—
666C4×Q8—861no—
667C4×Q8—861no—
668C4×Q8—862no—
669C4×Q8—862no—
670C4×Q8—862no—
671C4×Q8—862no—
672C4×Q8—861no—
673C4×Q8—861no—
674C4×D4—432no—
675C4×D4—432no—
676C4×D4—432no—
677C4×D4—432no—
678C4×D4—861no—
679C4×D4—861no—
680C4×D4—861no—
681C4×D4—861no—
682C4×D4—862no—
683C4×D4—862no—
684C4×D4—862no—
685C4×D4—862no—
686C4×D4—862no—
687C4×D4—862no—
688C4×D4—862no—
689C4×D4—862no—
690#117—21no—
691#117—21no—
692#117—862no—
693#117—862no—
694#117—862no—
695#117—862no—
696#117—862no—
697#117—862no—
698#117—862no—
699#117—862no—
700#117C22×D4312yes—
701#117C22×D4312yes—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—431no—
704C2×C4⋊C4—861no—
705C2×C4⋊C4—861no—
706C2×C4⋊C4—861no—
707C2×C4⋊C4—861no—
708C2×C4⋊C4—861no—
709C2×C4⋊C4—861no—
710C2×C4⋊C4—861no—
711C2×C4⋊C4—861no—
712C2×C4⋊C4C22×D4311yescharacteristic
713C2×C4⋊C4C22×D4311yescharacteristic
714C2×C4⋊C4C22×D4311yescharacteristic
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—861no—
718C2×C22⋊C4—861no—
719C2×C22⋊C4—861no—
720C2×C42—21no—
721C2×C42—431no—
722C2×C42—431no—
723C2×C42—431no—
724C2×C42—431no—
725C2×C42—431no—
726C2×C42—431no—
727C2×C42—431no—
728C2×C42—431no—
729C2×C42—431no—
730C2×C42—431no—
731C2×C42—431no—
732C2×C42—431no—
733C2×C42—862no—
734C2×C42—862no—
735C2×C42—862no—
736C2×C42—862no—
737C2×C42—861no—
738C2×C42—861no—
739C2×C42—861no—
740C2×C42—861no—
741#107—434no—
742#107C22×D4314yes—
743#106—434no—
744#106C22×D4314yes—
745C4⋊C8—434no—
746C4⋊C8—434no—
747#103—434no—
748#103—434no—
749#103—434no—
750#103—434no—
751#103C22×D4314yes—
752#103C22×D4314yes—
753#102—434no—
754#102—434no—
755C22⋊C8—432no—
756C22⋊C8—432no—
757C22⋊C8C22×D4312yes—
758C22⋊C8C22×D4312yes—
759#97—434no—
760C4×C8—434no—
761C24—861no—
762C24D4×D4311yescharacteristic
763#41—438no—
764#41—864no—
765#41—864no—
766#41—868no—
767#41—868no—
768#41—864no—
769C2×Q8—21no—
770C2×Q8—24no—
771C2×Q8—432no—
772C2×Q8—432no—
773C2×Q8—862no—
774C2×Q8—862no—
775C2×Q8—864no—
776C2×Q8—861no—
777C2×Q8—861no—
778C2×Q8—864no—
779C2×Q8—1724no—
780C2×Q8C23×D4312yes—
781C2×D4—432no—
782C2×D4—864no—
783C2×D4—868no—
784C2×D4—862no—
785C2×D4—862no—
786C2×D4—861no—
787C22×C4—24no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—431no—
793C22×C4—431no—
794C22×C4—431no—
795C22×C4—431no—
796C22×C4—431no—
797C22×C4—431no—
798C22×C4—431no—
799C22×C4—431no—
800C22×C4—431no—
801C22×C4—431no—
802C22×C4—431no—
803C22×C4—431no—
804C22×C4—862no—
805C22×C4—862no—
806C22×C4—862no—
807C22×C4—862no—
808C22×C4—868no—
809C22×C4—864no—
810C22×C4—861no—
811C22×C4—862no—
812C22×C4—862no—
813C22×C4—861no—
814C22×C4—861no—
815C22×C4—1724no—
816C22×C4—1724no—
817C22×C4—1722no—
818C22×C4D4×D4311yescharacteristic
819C22×C4D4×D4311yescharacteristic
820C22×C4D4×D4311yescharacteristic
821C22×C4C23×D4311yescharacteristic
822C22×C4C23×D4311yescharacteristic
823C22×C4C23×D4311yescharacteristic
824Q16—868no—
825Q16—868no—
826SD16—868no—
827SD16—868no—
828M16—24no—
829M16—864no—
830C2×C8—434no—
831C2×C8C23×D4314yes—
832C4⋊C4—22no—
833C4⋊C4—22no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—432no—
838C4⋊C4—862no—
839C4⋊C4—862no—
840C4⋊C4—862no—
841C4⋊C4—862no—
842C4⋊C4—862no—
843C4⋊C4—862no—
844C4⋊C4—862no—
845C4⋊C4—862no—
846C4⋊C4—862no—
847C4⋊C4—862no—
848C4⋊C4—862no—
849C4⋊C4—862no—
850C4⋊C4—862no—
851C4⋊C4—862no—
852C4⋊C4—861no—
853C4⋊C4—862no—
854C4⋊C4—862no—
855C4⋊C4C23×D4312yes—
856C4⋊C4C23×D4312yes—
857C4⋊C4C23×D4312yes—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—862no—
863C22⋊C4—862no—
864C22⋊C4—862no—
865C22⋊C4—862no—
866C22⋊C4—862no—
867C22⋊C4—862no—
868C42—22no—
869C42—22no—
870C42—431no—
871C42—431no—
872C42—431no—
873C42—431no—
874C42—431no—
875C42—431no—
876C42—431no—
877C42—431no—
878C42—431no—
879C42—431no—
880C42—431no—
881C42—431no—
882C42—431no—
883C42—431no—
884C42—431no—
885C42—431no—
886C42—862no—
887C42—862no—
888C42—862no—
889C42—862no—
890C42—862no—
891C42—862no—
892C42—862no—
893C42—862no—
894C23—22no—
895C23—22no—
896C23—41no—
897C23—864no—
898C23—862no—
899C23—1722no—
900C23—1722no—
901C23C2×D4×D4311yescharacteristic
902C23C2×D4×D4311yescharacteristic
903C23C2×D4×D4311yescharacteristic
904Q8—24no—
905Q8—42no—
906Q8—434no—
907Q8—864no—
908Q8—862no—
909Q8—864no—
910Q8—1724no—
911Q8—1724no—
912Q8—1722no—
913D4—434no—
914D4—864no—
915D4—868no—
916D4—868no—
917D4—862no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—434no—
932C2×C4—431no—
933C2×C4—431no—
934C2×C4—431no—
935C2×C4—431no—
936C2×C4—431no—
937C2×C4—431no—
938C2×C4—431no—
939C2×C4—431no—
940C2×C4—868no—
941C2×C4—862no—
942C2×C4—862no—
943C2×C4—862no—
944C2×C4—862no—
945C2×C4—862no—
946C2×C4—862no—
947C2×C4—862no—
948C2×C4—864no—
949C2×C4—862no—
950C2×C4—862no—
951C2×C4—868no—
952C2×C4—862no—
953C2×C4—862no—
954C2×C4—1724no—
955C2×C4—1724no—
956C2×C4—1724no—
957C2×C4—1724no—
958C2×C4—1721no—
959C2×C4—1721no—
960C2×C4—1721no—
961C2×C4—1722no—
962C2×C4—1722no—
963C2×C4C2×D4×D4311yescharacteristic
964C2×C4C2×D4×D4311yescharacteristic
965C2×C4C2×D4×D4311yescharacteristic
966C2×C4#41×D4314yes—
967C2×C4C24×D4311yescharacteristic
968C8—24no—
969C8—864no—
970C22—21no—
971C22—21no—
972C22—21no—
973C22—21no—
974C22—21no—
975C22—21no—
976C22—21no—
977C22—44no—
978C22—864no—
979C22—1728no—
980C22—1722no—
981C22—1722no—
982C22#1458340712yes—
983C22#137×D4312yes—
984C22C22×D4×D4311yescharacteristic
985C4—21no—
986C4—21no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—432no—
992C4—432no—
993C4—432no—
994C4—861no—
995C4—861no—
996C4—861no—
997C4—861no—
998C4—861no—
999C4—864no—
1000C4—1722no—
1001C4—1722no—
1002C4#1458340712yes—
1003C4C2×#41×D4312yes—
1004C2—22no—
1005C2—22no—
1006C2—41no—
1007C2—1724no—
1008C2C2×#1458340711yescharacteristic
1009C2C2×#137×D4311yescharacteristic
1010C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3095C2
socleC22×C43C23×D4
prime radicalC22×#10621898C22
hypercenter#3095D43
hypocenterC43#60562
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
1. C2×#14583451C2semidirect
3. #19144752C2semidirect
4. #19144722C2semidirect
5. #19144691C2semidirect
6. #19144661C2semidirect
7. #19144631C2semidirect
8. #19144600C2semidirect
9. #19144543C2semidirect
10. #19144408C2semidirect
11. #19144081C2semidirect
14. #19143413C2semidirect
15. #19143410C2semidirect
16. #19143224C2semidirect
17. C43×#3095C2semidirect
27. #14583451C22semidirect
28. #14583451C22semidirect
29. C2×#13063324C22semidirect
30. C2×#13063323C22semidirect
42. C2×Q8×Dic43C22semidirect
46. C2×#13063290C22semidirect
55. #14583240C22semidirect
58. #14583193C22semidirect
59. #14583188C22semidirect
60. #14583183C22semidirect
61. #14583178C22semidirect
62. #14583108C22semidirect
63. #14583108C22semidirect
64. #14583103C22semidirect
65. #14583103C22semidirect
72. #14583005C22semidirect
73. #14583003C22semidirect
74. #14583002C22semidirect
75. #14582998C22semidirect
76. #14582993C22semidirect
77. #14582991C22semidirect
78. #14582986C22semidirect
79. #14582984C22semidirect
81. #14582953C22semidirect
83. #14582949C22semidirect
84. #14582942C22semidirect
85. #14582922C22semidirect
86. #14582907C22semidirect
90. M16×Dic43C22semidirect
93. C43×#485C22semidirect
96. C43×#428C22semidirect
97. C43×#419C22semidirect
437. C2×Dic43#137semidirect
508. #3095D43semidirect
563. #485C2×D43semidirect
595. #428C2×D43semidirect
598. #419C2×D43semidirect
604. C43#60562semidirect

Maximal subgroups

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

subgroupindex
C2×#145834512
C2×#145833672
#191447522
#191447222
#191446912
#191446612
#191446312
#191446002
#191445432
#191444082
#191440812
#191438572
#191438532
#191434132
#191434102
#191432242
C43×#30952
#6056243