Finite Group Databasebeta

← #25064433

Subgroups — #25064433

Order 11008.

942 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148451C211yesmaximal, characteristic
2#19143679C211yesmaximal, characteristic, complemented
3#19137512C211yesmaximal, characteristic, complemented
4#19133157C211yesmaximal, characteristic, complemented
5#19133153C211yesmaximal, characteristic
6#19133132C211yesmaximal, characteristic, complemented
7#19133131C211yesmaximal, characteristic, complemented
8#19133130C211yesmaximal, characteristic, complemented
9#19133121C211yesmaximal, characteristic, complemented
10#19133120C211yesmaximal, characteristic, complemented
11#19133119C211yesmaximal, characteristic, complemented
12#19133117C211yesmaximal, characteristic, complemented
13#19133092C211yesmaximal, characteristic, complemented
14#19133088C211yesmaximal, characteristic
15C43×#1512C211yesmaximal, characteristic, complemented
16#14583632C411yescharacteristic, complemented
17#14583631C411yescharacteristic, complemented
18#14583626C411yescharacteristic, complemented
19#14583625C411yescharacteristic, complemented
20#14583621C411yescharacteristic, complemented
21#14583618C411yescharacteristic, complemented
22#14583617—21no—
23#14583616—21no—
24#14583608C411yescharacteristic, complemented
25#14583605C411yescharacteristic, complemented
26#14583585—21no—
27#14583582—21no—
28#14583493—21no—
29#14583491—21no—
30#14583471—21no—
31#14583451C2211yescharacteristic
32#14583444C2211yescharacteristic
33#14583435C2211yescharacteristic
34#14583433C2211yescharacteristic
35#14583430C2211yescharacteristic
36#14583378—21no—
37C2×C4×Dic86C2211yescharacteristic
38C2×#13063290—21no—
39#14583028—21no—
40#14583028—21no—
41#14583027—21no—
42#14583027—21no—
43#14582956C2211yescharacteristic
44#14582953C2211yescharacteristic
45#14582953C2211yescharacteristic
46#14582949C2211yescharacteristic
47#14582949C2211yescharacteristic
48#14582796—21no—
49#14582796—21no—
50#14582795—21no—
51#14582763C2211yescharacteristic
52#14582763C2211yescharacteristic
53C4×C4⋊Dic43C2211yescharacteristic
54#14582750C2211yescharacteristic
55#14582750C2211yescharacteristic
56#14582637C2211yescharacteristic
57#14582637C2211yescharacteristic
58#14582636C2211yescharacteristic
59#14582636C2211yescharacteristic
60#14582635C2211yescharacteristic
61#14582635C2211yescharacteristic
62#14582634C2211yescharacteristic
63#14582634C2211yescharacteristic
64#14582633C2211yescharacteristic
65#14582633C2211yescharacteristic
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C43×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#382C2211yescharacteristic
71C43×#328C2211yescharacteristic
72C43×#328C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621900—21no—
76C22×Dic86D411yescharacteristic
77#13063324—21no—
78#13063324—21no—
79#13063324C2×C411yescharacteristic
80#13063324C2×C411yescharacteristic
81#13063323C2×C411yescharacteristic
82#13063321C2×C411yescharacteristic
83#13063320—21no—
84#13063320—21no—
85#13063319—21no—
86#13063319—21no—
87#13063318—21no—
88#13063318—21no—
89#13063318—21no—
90#13063317—21no—
91#13063317C2×C411yescharacteristic
92#13063316—21no—
93#13063316C2×C411yescharacteristic
94#13063316C2×C411yescharacteristic
95#13063315—21no—
96#13063315—21no—
97#13063315—21no—
98#13063314C2×C411yescharacteristic
99#13063313C2×C411yescharacteristic
100#13063312C2×C411yescharacteristic
101#13063311—21no—
102#13063311—21no—
103#13063311—21no—
104#13063309—21no—
105#13063309—21no—
106#13063308—21no—
107#13063308—21no—
108#13063307—21no—
109#13063307—21no—
110#13063306—21no—
111#13063305—21no—
112#13063304—21no—
113#13063304C2311yescharacteristic
114#13063303—21no—
115#13063303—21no—
116#13063303—21no—
117#13063302—21no—
118#13063302—21no—
119#13063302—21no—
120#13063302—21no—
121#13063299C2311yescharacteristic
122#13063297—21no—
123Q8×Dic43C2×C411yescharacteristic
124Q8×Dic43C2×C411yescharacteristic
125C4×Dic86—21no—
126C4×Dic86C2×C411yescharacteristic
127C4×Dic86C2×C411yescharacteristic
128C4×Dic86C2×C411yescharacteristic
129C4×Dic86C2×C411yescharacteristic
130C4×Dic86C2×C411yescharacteristic
131C4×Dic86D411yescharacteristic
132C4×Dic86D411yescharacteristic
133C4×Dic86D411yescharacteristic
134C4×Dic86D411yescharacteristic
135#13063290—21no—
136#13063290—21no—
137#13063290—44no—
138#13063290C2×C411yescharacteristic
139#13063290C2×C411yescharacteristic
140C4×D172C2×C411yescharacteristic
141D4×Dic43—21no—
142D4×Dic43C2×C411yescharacteristic
143D4×Dic43C2×C411yescharacteristic
144#13063287C2×C411yescharacteristic
145#13063287C2×C411yescharacteristic
146C4×C22⋊D43—21no—
147C4×C22⋊D43—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151#13063283—21no—
152#13063282—21no—
153#13063282—21no—
154#13063281—21no—
155#13063281—21no—
156#13063281—21no—
157C2×C4⋊Dic43—21no—
158C2×C4⋊Dic43D411yescharacteristic
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4—21no—
162C2×Dic43⋊C4—21no—
163C2×Dic43⋊C4—21no—
164C2×Dic43⋊C4D411yescharacteristic
165C2×Dic43⋊C4D411yescharacteristic
166C4⋊C4×D43—21no—
167C2×C4×Dic43—21no—
168C2×C4×Dic43—21no—
169C2×C4×Dic43—21no—
170C2×C4×Dic43C2311yescharacteristic
171C2×C4×Dic43C2311yescharacteristic
172C4⋊(C43⋊C8)—21no—
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176Dic43⋊C8—21no—
177C22⋊(C43⋊C8)C2311yescharacteristic
178C22⋊(C43⋊C8)C2311yescharacteristic
179#13063236—21no—
180#13063235—21no—
181#13063235—21no—
182C8×Dic43—21no—
183C8×Dic43—21no—
184C43⋊#95—21no—
185C43⋊#95—21no—
186C43⋊#95C2311yescharacteristic
187C43⋊#95C2311yescharacteristic
188#126×C43—21no—
189#125×C43C2×C411yescharacteristic
190#124×C43C2×C411yescharacteristic
191#123×C43—21no—
192C22⋊Q8×C43C2311yescharacteristic
193#121×C43C2311yescharacteristic
194C4×Q8×C43C2×C411yescharacteristic
195C4×D4×C43—21no—
196C4×D4×C43C2×C411yescharacteristic
197#117×C43—21no—
198C2×C4⋊C4×C43—21no—
199C2×C42×C43C2311yescharacteristic
200C4⋊C8×C43—21no—
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203#97×C43—21no—
204#95×C43—21no—
205#95×C43C2311yescharacteristic
206#95×C43C2311yescharacteristic
207C2×Q8×C43C22×C411yescharacteristic
208C2×D4×C43—21no—
209C2×D4×C43C22×C411yescharacteristic
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2411yescharacteristic
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C22×Dic43—21no—
220C22×Dic43—21no—
221C22×Dic43—21no—
222C22×Dic43—21no—
223C22×Dic43C2×D411yescharacteristic
224C22×Dic43C2×D411yescharacteristic
225C22×Dic43C2×D411yescharacteristic
226C22×Dic43C2×D411yescharacteristic
227#10621900—42no—
228#10621900—42no—
229C2×D172C22×C411yescharacteristic
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×Dic86—22no—
234C2×Dic86—22no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86C22⋊C411yescharacteristic
238C2×Dic86C22⋊C411yescharacteristic
239C2×Dic86C22⋊C411yescharacteristic
240C2×Dic86C22⋊C411yescharacteristic
241C2×Dic86C22×C411yescharacteristic
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—42no—
249C4⋊C4×C43C22×C411yescharacteristic
250C4⋊C4×C43C22×C411yescharacteristic
251C22⋊C4×C43—21no—
252C22⋊C4×C43—21no—
253C22⋊C4×C43—21no—
254C22⋊C4×C43—21no—
255C22⋊C4×C43—21no—
256C42×C43—21no—
257C42×C43C22×C411yescharacteristic
258C42×C43C22×C411yescharacteristic
259C42×C43C2×D411yescharacteristic
260C42×C43C2×D411yescharacteristic
261C22⋊Dic43—21no—
262C22⋊Dic43—21no—
263C22⋊Dic43—21no—
264C22⋊Dic43—21no—
265C22⋊Dic43—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4—21no—
270(C2×D43)⋊C4—21no—
271(C2×D43)⋊C4—21no—
272(C2×D43)⋊C4—21no—
273(C2×D43)⋊C4—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—42no—
279C4⋊Dic43C22⋊C411yescharacteristic
280C4⋊Dic43C22⋊C411yescharacteristic
281C4⋊Dic43C22⋊C411yescharacteristic
282C4⋊Dic43C22⋊C411yescharacteristic
283C4⋊Dic43C22×C411yescharacteristic
284C4⋊Dic43C22×C411yescharacteristic
285Dic43⋊C4—21no—
286Dic43⋊C4—21no—
287Dic43⋊C4—21no—
288Dic43⋊C4—21no—
289Dic43⋊C4—21no—
290Dic43⋊C4—21no—
291Dic43⋊C4—21no—
292Dic43⋊C4—21no—
293Dic43⋊C4—21no—
294Dic43⋊C4—21no—
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4—42no—
298Dic43⋊C4—42no—
299Dic43⋊C4—42no—
300Dic43⋊C4—42no—
301Dic43⋊C4C22⋊C411yescharacteristic
302Dic43⋊C4C22⋊C411yescharacteristic
303Dic43⋊C4C22⋊C411yescharacteristic
304Dic43⋊C4C22⋊C411yescharacteristic
305Dic43⋊C4C22⋊C411yescharacteristic
306Dic43⋊C4C22⋊C411yescharacteristic
307Dic43⋊C4C22⋊C411yescharacteristic
308Dic43⋊C4C22⋊C411yescharacteristic
309C4×Dic43—21no—
310C4×Dic43—21no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43—42no—
315C4×Dic43—42no—
316C4×Dic43—42no—
317C4×Dic43C22×C411yescharacteristic
318C4×Dic43C22×C411yescharacteristic
319C4×Dic43C22×C411yescharacteristic
320C4×Dic43C22×C411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322C4×Dic43C2×D411yescharacteristic
323C4×Dic43C2×D411yescharacteristic
324C4×Dic43C2×D411yescharacteristic
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327C23×C43—21no—
328C23×C43C22×D411yescharacteristic
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—41no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—81no—
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—41no—
355C22⋊D43—41no—
356C22⋊D43—42no—
357C22⋊D43—81no—
358C2×Dic43—21no—
359C2×Dic43—21no—
360C2×Dic43—22no—
361C2×Dic43—21no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—41no—
365C2×Dic43—41no—
366C2×Dic43—41no—
367C2×Dic43—41no—
368C2×Dic43—42no—
369C2×Dic43—41no—
370C2×Dic43—41no—
371C2×Dic43—41no—
372C2×Dic43—81no—
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377C2×Dic43C2×C22⋊C411yescharacteristic
378C2×Dic43C2×C22⋊C411yescharacteristic
379C2×Dic43C2×C22⋊C411yescharacteristic
380C2×Dic43C2×C22⋊C411yescharacteristic
381C2×Dic43AGL(1,ℤ/8)12yes—
382C2×Dic43#13712yes—
383D172—41no—
384C4×D43—42no—
385C4×D43—81no—
386C4×D43—81no—
387Dic86—22no—
388Dic86—22no—
389Dic86—22no—
390Dic86—22no—
391Dic86—42no—
392Dic86—41no—
393Dic86—81no—
394C8×C43—41no—
395C8×C43—41no—
396C43⋊C8—41no—
397C43⋊C8—41no—
398#17628—431nomaximal, Sylow
399C22×C43—21no—
400C22×C43—21no—
401C22×C43—41no—
402C22×C43—41no—
403C22×C43—41no—
404C22×C43C22×C22⋊C411yescharacteristic
405C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
406C22×C43C2×#13711yescharacteristic
407C2×D43—41no—
408C2×D43—41no—
409C2×D43—41no—
410C4×C43—21no—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—21no—
414C4×C43—21no—
415C4×C43—21no—
416C4×C43—41no—
417C4×C43—41no—
418C4×C43—41no—
419C4×C43—81no—
420C4×C43—81no—
421Dic43—21no—
422Dic43—21no—
423Dic43—21no—
424Dic43—21no—
425Dic43—21no—
426Dic43—21no—
427Dic43—42no—
428Dic43—41no—
429Dic43—41no—
430Dic43—41no—
431Dic43—81no—
432Dic43#41712yes—
433Dic43#41712yes—
434#3507—431no—
435#2983—431no—
436#2351—431no—
437#1518—431no—
438#1517—431no—
439#1512—431no—
440#1512—431no—
441#1512—431no—
442#1512D4311yescharacteristic, complemented
443#1509—431no—
444#1509—431no—
445#1509—431no—
446#1509—431no—
447#1503—431no—
448#1502—431no—
449C2×C43—21no—
450C2×C43—21no—
451C2×C43—81no—
452C2×C43#288411yescharacteristic
453C2×C43C2×#41711yescharacteristic
454C2×C43#290111yescharacteristic
455D43—81no—
456#559—431no—
457#559—431no—
458#557—431no—
459#557—431no—
460#556—431no—
461#556—431no—
462#556—861no—
463#556—861no—
464#554—431no—
465#554—431no—
466#552—861no—
467#552—861no—
468#539—861no—
469#539—861no—
470#536—861no—
471#533—431no—
472#532—431no—
473#529—431no—
474#529—431no—
475#529—431no—
476#529C2×D4311yescharacteristic
477#520—861no—
478C2×C4×Q8—431no—
479C2×C4×Q8—861no—
480#446—861no—
481#446—861no—
482#446—861no—
483#446—861no—
484#432—431no—
485#432—431no—
486#432—431no—
487#432C2×D4311yescharacteristic
488#431—431no—
489#431—431no—
490#389—861no—
491#389—861no—
492#389—861no—
493#382—431no—
494#382—431no—
495#382C2×D4311yescharacteristic
496C4×C4⋊C4—431no—
497C4×C4⋊C4—431no—
498C4×C4⋊C4—431no—
499#328—431no—
500#328—431no—
501#328—431no—
502#328—431no—
503#328—431no—
504#328—431no—
505#328C2×D4311yescharacteristic
506#328C2×D4311yescharacteristic
507#327—431no—
508#327—431no—
509#327—431no—
510#327—431no—
511#327—431no—
512#327—431no—
513#327C2×D4311yescharacteristic
514#327C2×D4311yescharacteristic
515C43#1762811yescharacteristic, complemented, Sylow
516C2×#41—861no—
517C22×Q8—431no—
518C4⋊Q8—431no—
519C4⋊Q8—431no—
520C4⋊Q8—431no—
521C4⋊Q8—861no—
522C4⋊Q8—861no—
523#127—431no—
524#126—21no—
525#126—861no—
526#126—861no—
527#126—861no—
528#126—861no—
529#126—861no—
530#126—861no—
531#126—861no—
532#125—431no—
533#125—431no—
534#125—431no—
535#125—861no—
536#125—861no—
537#125—861no—
538#125—861no—
539#125—861no—
540#125C4×D4311yescharacteristic
541#124—431no—
542#124—431no—
543#124—431no—
544#124—861no—
545#124—861no—
546#124—861no—
547#124C4×D4311yescharacteristic
548#123—21no—
549#123—861no—
550#123—861no—
551#123—861no—
552#123—861no—
553#123—861no—
554#123—861no—
555#123—861no—
556C22⋊Q8—431no—
557C22⋊Q8—861no—
558C22⋊Q8—861no—
559C22⋊Q8—861no—
560C22⋊Q8—861no—
561C22⋊Q8—861no—
562C22⋊Q8—861no—
563C22⋊Q8—861no—
564C22⋊Q8—861no—
565C22⋊Q8—861no—
566C22⋊Q8C22×D4311yescharacteristic
567#121—431no—
568#121—861no—
569#121C22×D4311yescharacteristic
570C4×Q8—431no—
571C4×Q8—431no—
572C4×Q8—431no—
573C4×Q8—431no—
574C4×Q8—431no—
575C4×Q8—431no—
576C4×Q8—431no—
577C4×Q8—431no—
578C4×Q8—431no—
579C4×Q8—431no—
580C4×Q8—431no—
581C4×Q8—431no—
582C4×Q8—431no—
583C4×Q8—861no—
584C4×Q8—861no—
585C4×Q8—861no—
586C4×Q8—1724no—
587C4×Q8C4×D4311yescharacteristic
588C4×D4—21no—
589C4×D4—431no—
590C4×D4—431no—
591C4×D4—431no—
592C4×D4—431no—
593C4×D4—431no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4—861no—
599C4×D4—861no—
600C4×D4C4×D4311yescharacteristic
601#117—21no—
602#117—861no—
603#117—861no—
604#117—861no—
605#117—861no—
606#117—861no—
607#117—861no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—431no—
610C2×C4⋊C4—431no—
611C2×C4⋊C4—431no—
612C2×C4⋊C4—861no—
613C2×C4⋊C4—861no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4—861no—
617C2×C4⋊C4—861no—
618C2×C4⋊C4—861no—
619C2×C42—431no—
620C2×C42—431no—
621C2×C42—861no—
622C2×C42—861no—
623C2×C42—861no—
624C2×C42C22×D4311yescharacteristic
625C4⋊C8—21no—
626C4⋊C8—861no—
627C4⋊C8—861no—
628C4⋊C8—861no—
629C4⋊C8—861no—
630C4⋊C8—861no—
631C22⋊C8—431no—
632C22⋊C8—431no—
633C22⋊C8C22×D4311yescharacteristic
634C22⋊C8C22×D4311yescharacteristic
635#97—21no—
636#97—861no—
637#97—861no—
638#97—861no—
639C4×C8—861no—
640C4×C8—861no—
641#95—21no—
642#95—431no—
643#95—431no—
644#95—861no—
645#95—861no—
646#95C22×D4311yescharacteristic
647#95C22×D4311yescharacteristic
648#41—1722no—
649#41—1722no—
650C2×Q8—431no—
651C2×Q8—431no—
652C2×Q8—431no—
653C2×Q8—431no—
654C2×Q8—431no—
655C2×Q8—862no—
656C2×Q8—862no—
657C2×Q8—861no—
658C2×Q8—861no—
659C2×Q8C2×C4×D4311yescharacteristic
660C2×D4—21no—
661C2×D4—431no—
662C2×D4—861no—
663C2×D4—861no—
664C2×D4—861no—
665C2×D4C2×C4×D4311yescharacteristic
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—861no—
678C22×C4—861no—
679C22×C4—861no—
680C22×C4D4×D4311yescharacteristic
681C22×C4D4×D4311yescharacteristic
682C22×C4C23×D4311yescharacteristic
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—861no—
686C2×C8—861no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—42no—
692C4⋊C4—431no—
693C4⋊C4—431no—
694C4⋊C4—431no—
695C4⋊C4—431no—
696C4⋊C4—431no—
697C4⋊C4—431no—
698C4⋊C4—431no—
699C4⋊C4—431no—
700C4⋊C4—431no—
701C4⋊C4—431no—
702C4⋊C4—431no—
703C4⋊C4—431no—
704C4⋊C4—431no—
705C4⋊C4—431no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4—861no—
709C4⋊C4—861no—
710C4⋊C4—861no—
711C4⋊C4—861no—
712C4⋊C4—861no—
713C4⋊C4—861no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—861no—
717C4⋊C4—861no—
718C4⋊C4—861no—
719C4⋊C4—861no—
720C4⋊C4—861no—
721C4⋊C4—861no—
722C4⋊C4—1722no—
723C4⋊C4—1722no—
724C4⋊C4—1722no—
725C4⋊C4—1722no—
726C4⋊C4—1722no—
727C4⋊C4C2×C4×D4311yescharacteristic
728C4⋊C4C2×C4×D4311yescharacteristic
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—861no—
735C22⋊C4—861no—
736C22⋊C4—861no—
737C22⋊C4—861no—
738C22⋊C4—861no—
739C22⋊C4—861no—
740C22⋊C4—861no—
741C22⋊C4—861no—
742C22⋊C4—861no—
743C22⋊C4—861no—
744C22⋊C4—861no—
745C22⋊C4—861no—
746C22⋊C4—861no—
747C42—21no—
748C42—431no—
749C42—431no—
750C42—431no—
751C42—431no—
752C42—431no—
753C42—431no—
754C42—431no—
755C42—431no—
756C42—861no—
757C42—861no—
758C42—861no—
759C42—861no—
760C42—861no—
761C42—1722no—
762C42—1722no—
763C42—1722no—
764C42C2×C4×D4311yescharacteristic
765C42C2×C4×D4311yescharacteristic
766C42D4×D4311yescharacteristic
767C42D4×D4311yescharacteristic
768C23—21no—
769C23—861no—
770C23C2×D4×D4311yescharacteristic
771Q8—41no—
772Q8—862no—
773Q8—862no—
774Q8—862no—
775Q8—862no—
776Q8—3441no—
777Q8—1721no—
778Q8—1722no—
779D4—41no—
780D4—41no—
781D4—41no—
782D4—3441no—
783D4—1721no—
784D4—1722no—
785D4—1721no—
786D4—1721no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—81no—
801C2×C4—431no—
802C2×C4—431no—
803C2×C4—432no—
804C2×C4—432no—
805C2×C4—431no—
806C2×C4—431no—
807C2×C4—431no—
808C2×C4—431no—
809C2×C4—431no—
810C2×C4—431no—
811C2×C4—861no—
812C2×C4—861no—
813C2×C4—862no—
814C2×C4—861no—
815C2×C4—861no—
816C2×C4—861no—
817C2×C4—3441no—
818C2×C4—3441no—
819C2×C4—3441no—
820C2×C4—1722no—
821C2×C4—1722no—
822C2×C4—1721no—
823C2×C4—1721no—
824C2×C4—1721no—
825C2×C4—1721no—
826C2×C4—1721no—
827C2×C4—1721no—
828C2×C4—1721no—
829C2×C4C22⋊C4×D4311yescharacteristic
830C2×C4C22⋊C4×D4311yescharacteristic
831C2×C4C22⋊C4×D4311yescharacteristic
832C2×C4C22⋊C4×D4311yescharacteristic
833C2×C4C22×C4×D4311yescharacteristic
834C2×C4C2×D4×D4311yescharacteristic
835C8—41no—
836C8—41no—
837C8—1721no—
838C8—1721no—
839C22—21no—
840C22—21no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—1721no—
845C22—1721no—
846C22—1721no—
847C22C2×C22⋊C4×D4311yescharacteristic
848C22AGL(1,ℤ/8)×D4311yescharacteristic
849C22#137×D4311yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—81no—
860C4—81no—
861C4—432no—
862C4—432no—
863C4—861no—
864C4—861no—
865C4—861no—
866C4—861no—
867C4—861no—
868C4—861no—
869C4—3441no—
870C4—1722no—
871C4—1721no—
872C4—1721no—
873C4—1721no—
874C2—21no—
875C2—21no—
876C2—81no—
877C2—3441no—
878C2#1914305711yescharacteristic
879C2#417×D4311yescharacteristic
880C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1512C2
socleC22×C43C22×C22⋊C4
prime radical#14583444C22
cosocleC22×C4×C43C24
hypercenter#1512D43
hypocenterC43#17628
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. #19143679C2semidirect
3. #19137512C2semidirect
4. #19133157C2semidirect
6. #19133132C2semidirect
7. #19133131C2semidirect
8. #19133130C2semidirect
9. #19133121C2semidirect
10. #19133120C2semidirect
11. #19133119C2semidirect
12. #19133117C2semidirect
13. #19133092C2semidirect
15. C43×#1512C2semidirect
16. #14583632C4semidirect
17. #14583631C4semidirect
18. #14583626C4semidirect
19. #14583625C4semidirect
20. #14583621C4semidirect
21. #14583618C4semidirect
24. #14583608C4semidirect
25. #14583605C4semidirect
442. #1512D43semidirect
515. C43#17628semidirect

Maximal subgroups

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

subgroupindex
#191484512
#191436792
#191375122
#191331572
#191331532
#191331322
#191331312
#191331302
#191331212
#191331202
#191331192
#191331172
#191330922
#191330882
C43×#15122
#1762843