Finite Group Databasebeta

← #25064178

Subgroups — #25064178

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148678C211yesmaximal, characteristic
2#19143685C211yesmaximal, characteristic, complemented
3#19137243C211yesmaximal, characteristic, complemented
4#19133172C211yesmaximal, characteristic, complemented
5#19133171C211yesmaximal, characteristic, complemented
6#19133154C211yesmaximal, characteristic, complemented
7#19133153C211yesmaximal, characteristic, complemented
8#19133143C211yesmaximal, characteristic, complemented
9#19133140C211yesmaximal, characteristic, complemented
10#19133132C211yesmaximal, characteristic, complemented
11#19133119C211yesmaximal, characteristic, complemented
12#19133101C211yesmaximal, characteristic, complemented
13#19133088C211yesmaximal, characteristic, complemented
14#19133080C211yesmaximal, characteristic, complemented
15C43×#1512C211yesmaximal, characteristic, complemented
16#14583634C411yescharacteristic, complemented
17#14583631C411yescharacteristic, complemented
18#14583631C411yescharacteristic, complemented
19Q8×Dic86C411yescharacteristic, complemented
20#14583606C411yescharacteristic, complemented
21#14583605C411yescharacteristic, complemented
22#14583605C411yescharacteristic, complemented
23#14583570C411yescharacteristic, complemented
24#14583558—21no—
25#14583553—21no—
26#14583547—21no—
27#14583547—21no—
28#14583520—21no—
29#14583515—21no—
30#14583515—21no—
31#14583449C2211yescharacteristic
32#14583444C2211yescharacteristic
33#14583444C2211yescharacteristic
34#14583435C2211yescharacteristic
35#14583435C2211yescharacteristic
36#14583379—21no—
37C2×C4×Dic86C2211yescharacteristic
38#14583027—21no—
39#14583027—21no—
40#14583026—21no—
41#14583023—21no—
42#14582953C2211yescharacteristic
43#14582953C2211yescharacteristic
44#14582952C2211yescharacteristic
45#14582949C2211yescharacteristic
46#14582949C2211yescharacteristic
47#14582803—21no—
48#14582794—21no—
49#14582782—21no—
50#14582780—21no—
51#14582767C2211yescharacteristic
52#14582766C2211yescharacteristic
53#14582763C2211yescharacteristic
54#14582750C2211yescharacteristic
55#14582744C2211yescharacteristic
56#14582636C2211yescharacteristic
57#14582636C2211yescharacteristic
58#14582634C2211yescharacteristic
59#14582634C2211yescharacteristic
60#14582634C2211yescharacteristic
61#14582634C2211yescharacteristic
62#14582633C2211yescharacteristic
63#14582633C2211yescharacteristic
64#14582632C2211yescharacteristic
65#14582632C2211yescharacteristic
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#382C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621898—21no—
76C2×#10621898—21no—
77C2×#10621900—21no—
78C2×#10621900—21no—
79C22×Dic86D411yescharacteristic
80#13063325—21no—
81#13063325C2×C411yescharacteristic
82#13063324—21no—
83#13063324—21no—
84#13063324C2×C411yescharacteristic
85#13063324C2×C411yescharacteristic
86#13063322C2×C411yescharacteristic
87#13063321C2×C411yescharacteristic
88#13063321C2×C411yescharacteristic
89#13063320—21no—
90#13063320—21no—
91#13063316C2×C411yescharacteristic
92#13063316C2×C411yescharacteristic
93#13063314C2×C411yescharacteristic
94#13063314C2×C411yescharacteristic
95#13063313—21no—
96#13063313—21no—
97#13063311—21no—
98#13063311—21no—
99#13063311—21no—
100#13063311—21no—
101#13063310—21no—
102#13063310—21no—
103#13063309—21no—
104#13063309—21no—
105#13063309—21no—
106#13063309—21no—
107#13063307—21no—
108#13063307—21no—
109#13063305—21no—
110#13063305—21no—
111#13063304—21no—
112#13063303—21no—
113#13063303—21no—
114#13063303—21no—
115#13063303—21no—
116#13063302—21no—
117#13063302—21no—
118#13063299—21no—
119#13063299—21no—
120#13063299C2311yescharacteristic
121#13063299C2311yescharacteristic
122#13063298—21no—
123#13063298—21no—
124#13063297—21no—
125#13063297—21no—
126Q8×Dic43C2×C411yescharacteristic
127Q8×Dic43C2×C411yescharacteristic
128C4×Dic86—21no—
129C4×Dic86C2×C411yescharacteristic
130C4×Dic86C2×C411yescharacteristic
131C4×Dic86C2×C411yescharacteristic
132C4×Dic86C2×C411yescharacteristic
133C4×Dic86D411yescharacteristic
134C4×Dic86D411yescharacteristic
135C4×Dic86D411yescharacteristic
136C4×Dic86D411yescharacteristic
137C4×D172—21no—
138C4×D172—21no—
139C4×D172C2×C411yescharacteristic
140C4×D172C2×C411yescharacteristic
141D4×Dic43C2×C411yescharacteristic
142D4×Dic43C2×C411yescharacteristic
143#13063287C2×C411yescharacteristic
144#13063287C2×C411yescharacteristic
145#13063287C2×C411yescharacteristic
146#13063287C2×C411yescharacteristic
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153#13063283—21no—
154#13063283—21no—
155C2×C4⋊Dic43—21no—
156C2×C4⋊Dic43D411yescharacteristic
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4D411yescharacteristic
160C2×Dic43⋊C4D411yescharacteristic
161C4⋊C4×D43—21no—
162C4⋊C4×D43—21no—
163C2×C4×Dic43—21no—
164C2×C4×Dic43—21no—
165C2×C4×Dic43C2311yescharacteristic
166C2×C4×Dic43C2311yescharacteristic
167C4⋊(C43⋊C8)—21no—
168Dic43⋊C8—21no—
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172C22⋊(C43⋊C8)C2311yescharacteristic
173C22⋊(C43⋊C8)C2311yescharacteristic
174#13063235—21no—
175#13063235—21no—
176C4×C43⋊C8—21no—
177C8×Dic43—21no—
178C8×Dic43—21no—
179C43⋊#95—21no—
180C43⋊#95—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187#126×C43—21no—
188#125×C43C2×C411yescharacteristic
189#124×C43C2×C411yescharacteristic
190#123×C43—21no—
191C22⋊Q8×C43C2311yescharacteristic
192#121×C43C2311yescharacteristic
193C4×Q8×C43C2×C411yescharacteristic
194C4×D4×C43—21no—
195C4×D4×C43C2×C411yescharacteristic
196#117×C43—21no—
197C2×C4⋊C4×C43—21no—
198C2×C42×C43C2311yescharacteristic
199C4⋊C8×C43—21no—
200C22⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43C2311yescharacteristic
202#97×C43—21no—
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C2×Q8×C43C22×C411yescharacteristic
207C2×D4×C43—21no—
208C2×D4×C43C22×C411yescharacteristic
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2411yescharacteristic
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43—21no—
224C22×Dic43—21no—
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229#10621900—81no—
230#10621900—81no—
231#10621900—81no—
232#10621900—81no—
233#10621898—44no—
234#10621898—81no—
235#10621898—81no—
236C2×D172—21no—
237C2×D172—21no—
238C2×D172C22×C411yescharacteristic
239C2×D172C22×C411yescharacteristic
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×Dic86—21no—
247C2×Dic86—21no—
248C2×Dic86—21no—
249C2×Dic86—42no—
250C2×Dic86C22⋊C411yescharacteristic
251C2×Dic86C22⋊C411yescharacteristic
252C2×Dic86C22⋊C411yescharacteristic
253C2×Dic86C22⋊C411yescharacteristic
254C2×C8×C43—21no—
255C2×C8×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43—21no—
260C4⋊C4×C43—81no—
261C4⋊C4×C43C22×C411yescharacteristic
262C4⋊C4×C43C22×C411yescharacteristic
263C22⋊C4×C43—21no—
264C22⋊C4×C43—21no—
265C22⋊C4×C43—21no—
266C22⋊C4×C43—21no—
267C22⋊C4×C43—21no—
268C42×C43—21no—
269C42×C43C22×C411yescharacteristic
270C42×C43C22×C411yescharacteristic
271C42×C43C2×D411yescharacteristic
272C42×C43C2×D411yescharacteristic
273C22⋊Dic43—21no—
274C22⋊Dic43—21no—
275(C2×D43)⋊C4—21no—
276(C2×D43)⋊C4—21no—
277(C2×D43)⋊C4—21no—
278(C2×D43)⋊C4—21no—
279(C2×D43)⋊C4—21no—
280(C2×D43)⋊C4—21no—
281(C2×D43)⋊C4—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43—21no—
289C4⋊Dic43—21no—
290C4⋊Dic43—21no—
291C4⋊Dic43—21no—
292C4⋊Dic43C22⋊C411yescharacteristic
293C4⋊Dic43C22⋊C411yescharacteristic
294C4⋊Dic43C22⋊C411yescharacteristic
295C4⋊Dic43C22⋊C411yescharacteristic
296C4⋊Dic43C22×C411yescharacteristic
297C4⋊Dic43C22×C411yescharacteristic
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—42no—
303Dic43⋊C4—81no—
304Dic43⋊C4C22⋊C411yescharacteristic
305Dic43⋊C4C22⋊C411yescharacteristic
306Dic43⋊C4C22⋊C411yescharacteristic
307Dic43⋊C4C22⋊C411yescharacteristic
308Dic43⋊C4C22⋊C411yescharacteristic
309Dic43⋊C4C22⋊C411yescharacteristic
310Dic43⋊C4C22⋊C411yescharacteristic
311Dic43⋊C4C22⋊C411yescharacteristic
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43—42no—
315C4×Dic43—81no—
316C4×Dic43C22×C411yescharacteristic
317C4×Dic43C22×C411yescharacteristic
318C4×Dic43C22×C411yescharacteristic
319C4×Dic43C22×C411yescharacteristic
320C4×Dic43C2×D411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322C4×Dic43C2×D411yescharacteristic
323C4×Dic43C2×D411yescharacteristic
324C2×C43⋊C8—21no—
325C2×C43⋊C8—21no—
326C23×C43—21no—
327C23×C43C22×D411yescharacteristic
328C22×D43—21no—
329C22×D43—21no—
330Q8×C43—41no—
331D4×C43—41no—
332D4×C43—41no—
333D4×C43—41no—
334C2×C4×C43—21no—
335C2×C4×C43—21no—
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—41no—
340C2×C4×C43—41no—
341C2×C4×C43—42no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43C2×C22⋊C411yescharacteristic
349C2×C4×C43C2×C22⋊C411yescharacteristic
350C2×C4×C43C2×C22⋊C411yescharacteristic
351C2×C4×C43C2×C22⋊C411yescharacteristic
352C2×C4×C43C23×C411yescharacteristic
353C2×C4×C43C22×D411yescharacteristic
354C22⋊D43—42no—
355C22⋊D43—41no—
356C22⋊D43—41no—
357C22⋊D43—41no—
358C22⋊D43—41no—
359C22⋊D43—42no—
360C22⋊D43—81no—
361C22⋊D43—81no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—21no—
366C2×Dic43—22no—
367C2×Dic43—21no—
368C2×Dic43—21no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—41no—
373C2×Dic43—41no—
374C2×Dic43—41no—
375C2×Dic43—41no—
376C2×Dic43—81no—
377C2×Dic43—81no—
378C2×Dic43C2×C22⋊C411yescharacteristic
379C2×Dic43C2×C22⋊C411yescharacteristic
380C2×Dic43C2×C22⋊C411yescharacteristic
381C2×Dic43C2×C22⋊C411yescharacteristic
382C2×Dic43C2×C22⋊C411yescharacteristic
383C2×Dic43C2×C22⋊C411yescharacteristic
384C2×Dic43C2×C22⋊C411yescharacteristic
385C2×Dic43C2×C22⋊C411yescharacteristic
386D172—41no—
387D172—41no—
388D172—42no—
389D172—81no—
390C4×D43—42no—
391C4×D43—42no—
392C4×D43—81no—
393C4×D43—81no—
394C4×D43—81no—
395C4×D43—81no—
396Dic86—22no—
397Dic86—22no—
398Dic86—41no—
399Dic86—41no—
400Dic86—81no—
401Dic86—81no—
402Dic86—81no—
403C8×C43—41no—
404C8×C43—41no—
405C43⋊C8—41no—
406C43⋊C8—41no—
407#17602—431nomaximal, Sylow
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—41no—
411C22×C43—41no—
412C22×C43—41no—
413C22×C43C22×C22⋊C411yescharacteristic
414C22×C43#57611yescharacteristic
415C22×C43#57711yescharacteristic
416C2×D43—41no—
417C2×D43—41no—
418C2×D43—41no—
419C2×D43—41no—
420C2×D43—41no—
421C2×D43—41no—
422C4×C43—21no—
423C4×C43—21no—
424C4×C43—21no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—21no—
428C4×C43—41no—
429C4×C43—41no—
430C4×C43—41no—
431C4×C43—81no—
432C4×C43—81no—
433Dic43—21no—
434Dic43—21no—
435Dic43—21no—
436Dic43—21no—
437Dic43—21no—
438Dic43—21no—
439Dic43—21no—
440Dic43—41no—
441Dic43—41no—
442Dic43—81no—
443Dic43—81no—
444Dic43#42112yes—
445#3522—431no—
446#2984—431no—
447#2320—431no—
448#1521—431no—
449#1521—431no—
450#1517—431no—
451#1517—431no—
452#1514—431no—
453#1514—431no—
454#1512—431no—
455#1512D4311yescharacteristic, complemented
456#1509—431no—
457#1505—431no—
458#1502—431no—
459#1500—431no—
460C2×C43—21no—
461C2×C43—21no—
462C2×C43—81no—
463C2×C43#288411yescharacteristic
464C2×C43#289711yescharacteristic
465C2×C43C2×#42111yescharacteristic
466D43—81no—
467D43—81no—
468#559—431no—
469#559—431no—
470#559—431no—
471Q82—431no—
472#554—431no—
473#554—431no—
474#554—431no—
475#550—431no—
476#548—861no—
477#547—861no—
478#547—861no—
479#547—861no—
480#542—861no—
481#542—861no—
482#542—861no—
483#532—431no—
484#532—431no—
485#532—431no—
486#529—431no—
487#529—431no—
488#529C2×D4311yescharacteristic
489#520—861no—
490C2×C4×Q8—431no—
491#446—861no—
492#446—861no—
493#446—861no—
494C8×Q8—861no—
495#432—431no—
496#432—431no—
497#432C2×D4311yescharacteristic
498#431—431no—
499#431—431no—
500#431—431no—
501#391—861no—
502#389—861no—
503#387—861no—
504#387—861no—
505#383—431no—
506#383—431no—
507#382—431no—
508#382C2×D4311yescharacteristic
509C4×C4⋊C4—431no—
510#376—431no—
511#328—431no—
512#328—431no—
513#328C2×D4311yescharacteristic
514#328C2×D4311yescharacteristic
515#327—431no—
516#327—431no—
517#327—431no—
518#327—431no—
519#327—431no—
520#327—431no—
521#327—431no—
522#327—431no—
523#327—431no—
524#327—431no—
525#327C2×D4311yescharacteristic
526#327C2×D4311yescharacteristic
527C43#1760211yescharacteristic, complemented, Sylow
528C2×#41—861no—
529C2×#41—861no—
530C2×#41—861no—
531C2×#41—861no—
532C22×Q8—431no—
533C4⋊Q8—431no—
534C4⋊Q8—431no—
535C4⋊Q8—431no—
536C4⋊Q8—861no—
537C4⋊Q8—861no—
538C4⋊Q8—861no—
539#127—431no—
540#127—431no—
541#127—431no—
542#126—21no—
543#126—861no—
544#126—861no—
545#125—431no—
546#125—431no—
547#125C4×D4311yescharacteristic
548#124—431no—
549#124—431no—
550#124—861no—
551#124—861no—
552#124—861no—
553#124—861no—
554#124—861no—
555#124—861no—
556#124C4×D4311yescharacteristic
557#123—21no—
558#123—861no—
559#123—861no—
560#123—861no—
561#123—861no—
562#123—861no—
563#123—861no—
564#123—861no—
565#123—861no—
566C22⋊Q8—861no—
567C22⋊Q8—861no—
568C22⋊Q8—861no—
569C22⋊Q8—861no—
570C22⋊Q8—861no—
571C22⋊Q8—861no—
572C22⋊Q8—861no—
573C22⋊Q8—861no—
574C22⋊Q8—861no—
575C22⋊Q8C22×D4311yescharacteristic
576#121—431no—
577#121—431no—
578#121—861no—
579#121—861no—
580#121—861no—
581#121—861no—
582#121—861no—
583#121—861no—
584#121C22×D4311yescharacteristic
585C4×Q8—431no—
586C4×Q8—431no—
587C4×Q8—431no—
588C4×Q8—431no—
589C4×Q8—431no—
590C4×Q8—431no—
591C4×Q8—431no—
592C4×Q8—431no—
593C4×Q8—431no—
594C4×Q8—431no—
595C4×Q8—861no—
596C4×Q8C4×D4311yescharacteristic
597C4×D4—21no—
598C4×D4—431no—
599C4×D4—431no—
600C4×D4—431no—
601C4×D4—431no—
602C4×D4—431no—
603C4×D4—431no—
604C4×D4—431no—
605C4×D4—431no—
606C4×D4—861no—
607C4×D4—861no—
608C4×D4—861no—
609C4×D4—861no—
610C4×D4—861no—
611C4×D4—861no—
612C4×D4—861no—
613C4×D4—861no—
614C4×D4C4×D4311yescharacteristic
615#117—21no—
616#117—861no—
617#117—861no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—431no—
620C2×C4⋊C4—431no—
621C2×C4⋊C4—431no—
622C2×C4⋊C4—861no—
623C2×C4⋊C4—861no—
624C2×C4⋊C4—861no—
625C2×C4⋊C4—861no—
626C2×C4⋊C4—861no—
627C2×C42—431no—
628C2×C42—431no—
629C2×C42—861no—
630C2×C42—861no—
631C2×C42C22×D4311yescharacteristic
632C4⋊C8—21no—
633C4⋊C8—861no—
634C4⋊C8—861no—
635C4⋊C8—861no—
636C4⋊C8—861no—
637C4⋊C8—861no—
638C22⋊C8—431no—
639C22⋊C8—431no—
640C22⋊C8C22×D4311yescharacteristic
641C22⋊C8C22×D4311yescharacteristic
642#97—21no—
643#97—861no—
644#97—861no—
645C4×C8—861no—
646C4×C8—861no—
647C4×C8—861no—
648#95—21no—
649#95—431no—
650#95—431no—
651#95—861no—
652#95—861no—
653#95—861no—
654#95—861no—
655#95—861no—
656#95—861no—
657#95C22×D4311yescharacteristic
658#95C22×D4311yescharacteristic
659#41—3441no—
660#41—3441no—
661#41—3441no—
662#41—3441no—
663#41—3441no—
664#41—3441no—
665#41—1724no—
666C2×Q8—431no—
667C2×Q8—431no—
668C2×Q8—431no—
669C2×Q8—431no—
670C2×Q8—861no—
671C2×Q8—861no—
672C2×Q8—861no—
673C2×Q8—1722no—
674C2×Q8C2×C4×D4311yescharacteristic
675C2×D4—21no—
676C2×D4—431no—
677C2×D4—431no—
678C2×D4—861no—
679C2×D4—861no—
680C2×D4—861no—
681C2×D4—861no—
682C2×D4—861no—
683C2×D4—861no—
684C2×D4—861no—
685C2×D4—861no—
686C2×D4C2×C4×D4311yescharacteristic
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—431no—
691C22×C4—431no—
692C22×C4—431no—
693C22×C4—431no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—861no—
697C22×C4—861no—
698C22×C4—861no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4—861no—
704C22×C4D4×D4311yescharacteristic
705C22×C4D4×D4311yescharacteristic
706C22×C4C23×D4311yescharacteristic
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—861no—
710C2×C8—861no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—81no—
716C4⋊C4—431no—
717C4⋊C4—431no—
718C4⋊C4—431no—
719C4⋊C4—431no—
720C4⋊C4—431no—
721C4⋊C4—431no—
722C4⋊C4—431no—
723C4⋊C4—431no—
724C4⋊C4—431no—
725C4⋊C4—431no—
726C4⋊C4—431no—
727C4⋊C4—431no—
728C4⋊C4—431no—
729C4⋊C4—431no—
730C4⋊C4—861no—
731C4⋊C4—861no—
732C4⋊C4—861no—
733C4⋊C4—861no—
734C4⋊C4—861no—
735C4⋊C4—861no—
736C4⋊C4—861no—
737C4⋊C4—861no—
738C4⋊C4—861no—
739C4⋊C4—3441no—
740C4⋊C4—1722no—
741C4⋊C4C2×C4×D4311yescharacteristic
742C4⋊C4C2×C4×D4311yescharacteristic
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—861no—
749C22⋊C4—861no—
750C22⋊C4—861no—
751C22⋊C4—861no—
752C22⋊C4—861no—
753C22⋊C4—861no—
754C22⋊C4—861no—
755C22⋊C4—861no—
756C22⋊C4—861no—
757C22⋊C4—861no—
758C22⋊C4—861no—
759C22⋊C4—861no—
760C22⋊C4—861no—
761C22⋊C4—861no—
762C42—21no—
763C42—431no—
764C42—431no—
765C42—431no—
766C42—431no—
767C42—431no—
768C42—431no—
769C42—431no—
770C42—431no—
771C42—861no—
772C42—861no—
773C42—3441no—
774C42—1722no—
775C42C2×C4×D4311yescharacteristic
776C42C2×C4×D4311yescharacteristic
777C42D4×D4311yescharacteristic
778C42D4×D4311yescharacteristic
779C23—21no—
780C23—861no—
781C23—861no—
782C23C2×D4×D4311yescharacteristic
783Q8—41no—
784Q8—862no—
785Q8—862no—
786Q8—3441no—
787Q8—3441no—
788Q8—3441no—
789Q8—1721no—
790Q8—1721no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—3441no—
795D4—3441no—
796D4—3441no—
797D4—1721no—
798D4—1721no—
799D4—1722no—
800D4—1722no—
801D4—1722no—
802D4—1721no—
803D4—1721no—
804D4—1721no—
805D4—1721no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—431no—
821C2×C4—431no—
822C2×C4—431no—
823C2×C4—431no—
824C2×C4—431no—
825C2×C4—431no—
826C2×C4—431no—
827C2×C4—431no—
828C2×C4—862no—
829C2×C4—861no—
830C2×C4—861no—
831C2×C4—861no—
832C2×C4—861no—
833C2×C4—861no—
834C2×C4—861no—
835C2×C4—3441no—
836C2×C4—3441no—
837C2×C4—3441no—
838C2×C4—3441no—
839C2×C4—3441no—
840C2×C4—3441no—
841C2×C4—1722no—
842C2×C4—1722no—
843C2×C4—1721no—
844C2×C4—1721no—
845C2×C4—1721no—
846C2×C4—1721no—
847C2×C4—1721no—
848C2×C4—1721no—
849C2×C4—1721no—
850C2×C4C22⋊C4×D4311yescharacteristic
851C2×C4C22⋊C4×D4311yescharacteristic
852C2×C4C22⋊C4×D4311yescharacteristic
853C2×C4C22⋊C4×D4311yescharacteristic
854C2×C4C22×C4×D4311yescharacteristic
855C2×C4C2×D4×D4311yescharacteristic
856C8—41no—
857C8—41no—
858C8—1721no—
859C8—1721no—
860C22—21no—
861C22—21no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—1721no—
866C22—1721no—
867C22—1721no—
868C22—1721no—
869C22—1721no—
870C22—1721no—
871C22C2×C22⋊C4×D4311yescharacteristic
872C22#1458370311yescharacteristic
873C22#1458370811yescharacteristic
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—432no—
886C4—861no—
887C4—861no—
888C4—861no—
889C4—861no—
890C4—861no—
891C4—861no—
892C4—861no—
893C4—3441no—
894C4—3441no—
895C4—1721no—
896C4—1721no—
897C2—21no—
898C2—21no—
899C2—81no—
900C2—3441no—
901C2—3441no—
902C2#1914305711yescharacteristic
903C2#1914311911yescharacteristic
904C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1512C2
socleC22×C43C22×C22⋊C4
prime radical#19148678C2
cosocleC22×C4×C43C24
hypercenter#1512D43
hypocenterC43#17602
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1512

Complements

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

NH ≅ G/Ntype
2. #19143685C2semidirect
3. #19137243C2semidirect
4. #19133172C2semidirect
5. #19133171C2semidirect
6. #19133154C2semidirect
7. #19133153C2semidirect
8. #19133143C2semidirect
9. #19133140C2semidirect
10. #19133132C2semidirect
11. #19133119C2semidirect
12. #19133101C2semidirect
13. #19133088C2semidirect
14. #19133080C2semidirect
15. C43×#1512C2semidirect
16. #14583634C4semidirect
17. #14583631C4semidirect
18. #14583631C4semidirect
19. Q8×Dic86C4semidirect
20. #14583606C4semidirect
21. #14583605C4semidirect
22. #14583605C4semidirect
23. #14583570C4semidirect
455. #1512D43semidirect
527. C43#17602semidirect

Maximal subgroups

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

subgroupindex
#191486782
#191436852
#191372432
#191331722
#191331712
#191331542
#191331532
#191331432
#191331402
#191331322
#191331192
#191331012
#191330882
#191330802
C43×#15122
#1760243