Finite Group Databasebeta

← #25113298

Subgroups — #25113298

Order 11008.

1004 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic86C211yesmaximal, characteristic
2#19143546C211yesmaximal, characteristic, complemented
3#19137071C211yesmaximal, characteristic, complemented
4#19135575C211yesmaximal, characteristic, complemented
5#19135574C211yesmaximal, characteristic, complemented
6#19135570C211yesmaximal, characteristic, complemented
7#19135538C211yesmaximal, characteristic, complemented
8#19135537C211yesmaximal, characteristic, complemented
9#19135537C211yesmaximal, characteristic, complemented
10#19134613C211yesmaximal, characteristic
11#19134613C211yesmaximal, characteristic
12#19134407C211yesmaximal, characteristic
13#19134405C211yesmaximal, characteristic
14#104×Dic43C211yesmaximal, characteristic
15C43×#1806C211yesmaximal, characteristic
16Q8×Dic86C411yescharacteristic, complemented
17#14583628C411yescharacteristic, complemented
18#14583625C411yescharacteristic, complemented
19#14583625C411yescharacteristic, complemented
20#14583608—21no—
21#14583608—21no—
22#14583608C411yescharacteristic, complemented
23#14583608C411yescharacteristic, complemented
24#14583606—21no—
25#14583606C411yescharacteristic, complemented
26D4×Dic86—21no—
27D4×Dic86C411yescharacteristic, complemented
28#14583456—21no—
29#14583456C2211yescharacteristic
30#14583452—21no—
31#14583452—21no—
32#14583452C2211yescharacteristic
33#14583452C2211yescharacteristic
34#41×Dic43C2211yescharacteristic
35#41×Dic43C2211yescharacteristic
36C2×C4×Dic86—21no—
37C2×C4×Dic86C2211yescharacteristic
38#14583028—21no—
39#14583028—21no—
40#14583026—21no—
41#14583023—21no—
42#14582922C2211yescharacteristic
43#14582922C2211yescharacteristic
44C2×#13063252C2211yescharacteristic
45C2×#13063252C2211yescharacteristic
46C4×#10621877C2211yescharacteristic
47M16×Dic43C2211yescharacteristic
48M16×Dic43C2211yescharacteristic
49#14582803—21no—
50#14582794—21no—
51#14582784—21no—
52#14582780—21no—
53C4×Dic43⋊C4C2211yescharacteristic
54C4×Dic43⋊C4C2211yescharacteristic
55#14582745C2211yescharacteristic
56#14582745C2211yescharacteristic
57C42×Dic43C2211yescharacteristic
58#14582660C2211yescharacteristic
59#14582660C2211yescharacteristic
60#14582660C2211yescharacteristic
61#14582660C2211yescharacteristic
62#14582659C2211yescharacteristic
63#14582659C2211yescharacteristic
64#14582659C2211yescharacteristic
65#14582659C2211yescharacteristic
66#14582658C2211yescharacteristic
67#14582658C2211yescharacteristic
68C4×#41×C43C2211yescharacteristic
69C43×#423C2211yescharacteristic
70C2×#104×C43C2211yescharacteristic
71C2×#104×C43C2211yescharacteristic
72C4×C4⋊C4×C43C2211yescharacteristic
73C43×#339C2211yescharacteristic
74C43×#339C2211yescharacteristic
75C22×Dic86—21no—
76C22×Dic86D411yescharacteristic
77C2×#10621877C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79#13063325—21no—
80#13063325—21no—
81#13063325C2×C411yescharacteristic
82#13063325C2×C411yescharacteristic
83#13063324—21no—
84#13063324—21no—
85#13063324—21no—
86#13063324—21no—
87#13063324C2×C411yescharacteristic
88#13063324C2×C411yescharacteristic
89#13063324C2×C411yescharacteristic
90#13063324C2×C411yescharacteristic
91#13063317—21no—
92#13063317—21no—
93#13063317C2×C411yescharacteristic
94#13063317C2×C411yescharacteristic
95#13063316—21no—
96#13063316—21no—
97#13063316—21no—
98#13063316—21no—
99#13063316C2×C411yescharacteristic
100#13063316C2×C411yescharacteristic
101#13063316C2×C411yescharacteristic
102#13063316C2×C411yescharacteristic
103#13063304—21no—
104#13063304—21no—
105#13063304—21no—
106#13063304—21no—
107#13063304—21no—
108#13063304—21no—
109#13063302—21no—
110#13063302—21no—
111#13063302—21no—
112#13063302—21no—
113#13063302—21no—
114#13063302—21no—
115#13063302—21no—
116#13063302—21no—
117#13063302—21no—
118#13063302—21no—
119#13063302—21no—
120#13063302—21no—
121Q8×Dic43C2×C411yescharacteristic
122Q8×Dic43C2×C411yescharacteristic
123Q8×Dic43C2×C411yescharacteristic
124Q8×Dic43C2×C411yescharacteristic
125C4×Dic86—21no—
126C4×Dic86—21no—
127C4×Dic86—21no—
128C4×Dic86—21no—
129C4×Dic86—21no—
130C4×Dic86—21no—
131C4×Dic86—21no—
132C4×Dic86—21no—
133C4×Dic86—21no—
134C4×Dic86—21no—
135C4×Dic86C2×C411yescharacteristic
136C4×Dic86C2×C411yescharacteristic
137C4×Dic86C2×C411yescharacteristic
138C4×Dic86C2×C411yescharacteristic
139C4×Dic86D411yescharacteristic
140C4×Dic86D411yescharacteristic
141C4×Dic86D411yescharacteristic
142C4×Dic86D411yescharacteristic
143D4×Dic43—21no—
144D4×Dic43—21no—
145D4×Dic43—21no—
146D4×Dic43—21no—
147D4×Dic43C2×C411yescharacteristic
148D4×Dic43C2×C411yescharacteristic
149D4×Dic43C2×C411yescharacteristic
150D4×Dic43C2×C411yescharacteristic
151#13063284—21no—
152#13063284—21no—
153#13063284C2311yescharacteristic
154#13063284C2311yescharacteristic
155C2×C4⋊Dic43—21no—
156C2×C4⋊Dic43D411yescharacteristic
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4D411yescharacteristic
162C2×Dic43⋊C4D411yescharacteristic
163C2×C4×Dic43—21no—
164C2×C4×Dic43—21no—
165C2×C4×Dic43—21no—
166C2×C4×Dic43—21no—
167C2×C4×Dic43C2311yescharacteristic
168C2×C4×Dic43C2311yescharacteristic
169C2×C4×Dic43C2311yescharacteristic
170C2×C4×Dic43C2311yescharacteristic
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175#13063252—22no—
176#13063252Q814yescomplemented
177#13063236—21no—
178#13063235—21no—
179#13063235—21no—
180C4×C43⋊C8—21no—
181C8×Dic43—21no—
182C8×Dic43—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95—21no—
186C43⋊#95—21no—
187C43⋊#95—21no—
188C43⋊#95—21no—
189C2×#41×C43C2311yescharacteristic
190C2×M16×C43C2311yescharacteristic
191C2×M16×C43C2311yescharacteristic
192C4×Q8×C43C2×C411yescharacteristic
193C4×Q8×C43C2×C411yescharacteristic
194C4×D4×C43—21no—
195C4×D4×C43—21no—
196C4×D4×C43C2×C411yescharacteristic
197C4×D4×C43C2×C411yescharacteristic
198#117×C43—21no—
199#117×C43C2311yescharacteristic
200C2×C4⋊C4×C43—21no—
201C2×C42×C43—21no—
202C2×C42×C43C2311yescharacteristic
203C2×C42×C43C2311yescharacteristic
204C2×C42×C43C2311yescharacteristic
205C4⋊C8×C43—21no—
206C4⋊C8×C43—21no—
207#104×C43—22no—
208#104×C43—22no—
209#95×C43—21no—
210#41×C43—21no—
211#41×C43—21no—
212#41×C43C2×Q812yes—
213#41×C43#4112yes—
214C2×Q8×C43C22×C411yescharacteristic
215C2×D4×C43—21no—
216C2×D4×C43C22×C411yescharacteristic
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2411yescharacteristic
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43—21no—
231C22×Dic43C2×D411yescharacteristic
232C22×Dic43C2×D411yescharacteristic
233C22×Dic43C2×D411yescharacteristic
234C22×Dic43C2×D411yescharacteristic
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—42no—
242C2×Dic86—44no—
243C2×Dic86C22⋊C411yescharacteristic
244C2×Dic86C22⋊C411yescharacteristic
245C2×Dic86C22⋊C411yescharacteristic
246C2×Dic86C22⋊C411yescharacteristic
247M16×C43—21no—
248M16×C43—21no—
249M16×C43—21no—
250M16×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C4⋊C4×C43—21no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—42no—
256C4⋊C4×C43C22×C411yescharacteristic
257C4⋊C4×C43C22×C411yescharacteristic
258C22⋊C4×C43—21no—
259C22⋊C4×C43—21no—
260C22⋊C4×C43—21no—
261C42×C43—21no—
262C42×C43—21no—
263C42×C43—21no—
264C42×C43—21no—
265C42×C43—21no—
266C42×C43—21no—
267C42×C43—21no—
268C42×C43C22×C411yescharacteristic
269C42×C43C22×C411yescharacteristic
270C42×C43C2×D411yescharacteristic
271C42×C43C2×D411yescharacteristic
272C22⋊Dic43—21no—
273C22⋊Dic43—21no—
274C22⋊Dic43—21no—
275C22⋊Dic43—21no—
276C22⋊Dic43—21no—
277C22⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43—21no—
287C4⋊Dic43—21no—
288C4⋊Dic43C22⋊C411yescharacteristic
289C4⋊Dic43C22⋊C411yescharacteristic
290C4⋊Dic43C22⋊C411yescharacteristic
291C4⋊Dic43C22⋊C411yescharacteristic
292C4⋊Dic43C22×C411yescharacteristic
293C4⋊Dic43C22×C411yescharacteristic
294C4⋊Dic43C22×C411yescharacteristic
295C4⋊Dic43C22×C411yescharacteristic
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—42no—
309Dic43⋊C4—42no—
310Dic43⋊C4C22⋊C411yescharacteristic
311Dic43⋊C4C22⋊C411yescharacteristic
312Dic43⋊C4C22⋊C411yescharacteristic
313Dic43⋊C4C22⋊C411yescharacteristic
314Dic43⋊C4C22⋊C411yescharacteristic
315Dic43⋊C4C22⋊C411yescharacteristic
316Dic43⋊C4C22⋊C411yescharacteristic
317Dic43⋊C4C22⋊C411yescharacteristic
318C4×Dic43—21no—
319C4×Dic43—21no—
320C4×Dic43—21no—
321C4×Dic43—21no—
322C4×Dic43—21no—
323C4×Dic43—21no—
324C4×Dic43—21no—
325C4×Dic43—21no—
326C4×Dic43—21no—
327C4×Dic43—42no—
328C4×Dic43—42no—
329C4×Dic43C22×C411yescharacteristic
330C4×Dic43C22×C411yescharacteristic
331C4×Dic43C22×C411yescharacteristic
332C4×Dic43C22×C411yescharacteristic
333C4×Dic43C2×D411yescharacteristic
334C4×Dic43C2×D411yescharacteristic
335C4×Dic43C2×D411yescharacteristic
336C4×Dic43C2×D411yescharacteristic
337C4×Dic43C2×Q812yescomplemented
338#10621877—21no—
339#10621877—21no—
340#10621877—21no—
341#10621877C2×Q812yescomplemented
342C2×C43⋊C8—21no—
343C2×C43⋊C8—21no—
344C23×C43—21no—
345C23×C43C22×D411yescharacteristic
346Q8×C43—21no—
347Q8×C43C4×Q812yes—
348D4×C43—22no—
349D4×C43—22no—
350D4×C43—21no—
351D4×C43C4×Q812yes—
352C2×C4×C43—21no—
353C2×C4×C43—22no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—42no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—81no—
367C2×C4×C43C2×C22⋊C411yescharacteristic
368C2×C4×C43C2×C22⋊C411yescharacteristic
369C2×C4×C43C2×C22⋊C411yescharacteristic
370C2×C4×C43C2×C22⋊C411yescharacteristic
371C2×C4×C43C23×C411yescharacteristic
372C2×C4×C43C22×D411yescharacteristic
373C2×C4×C43C22×Q811yescharacteristic
374C2×C4×C43C2×#4111yescharacteristic
375C2×C4×C432−1+411yescharacteristic
376C2×C4×C432−1+411yescharacteristic
377C2×Dic43—22no—
378C2×Dic43—21no—
379C2×Dic43—21no—
380C2×Dic43—21no—
381C2×Dic43—21no—
382C2×Dic43—22no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43—41no—
386C2×Dic43—42no—
387C2×Dic43—41no—
388C2×Dic43—41no—
389C2×Dic43—42no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—81no—
394C2×Dic43—81no—
395C2×Dic43C2×C22⋊C411yescharacteristic
396C2×Dic43C2×C22⋊C411yescharacteristic
397C2×Dic43C2×C22⋊C411yescharacteristic
398C2×Dic43C2×C22⋊C411yescharacteristic
399C2×Dic43C2×C22⋊C411yescharacteristic
400C2×Dic43C2×C22⋊C411yescharacteristic
401C2×Dic43C2×C22⋊C411yescharacteristic
402C2×Dic43C2×C22⋊C411yescharacteristic
403Dic86—22no—
404Dic86—22no—
405Dic86—41no—
406Dic86—41no—
407Dic86—42no—
408Dic86—42no—
409Dic86—42no—
410Dic86—81no—
411Dic86—81no—
412Dic86—81no—
413C8×C43—41no—
414C8×C43—41no—
415C43⋊C8—22no—
416C43⋊C8—41no—
417#22529—431nomaximal, Sylow
418C22×C43—21no—
419C22×C43—21no—
420C22×C43—22no—
421C22×C43—41no—
422C22×C43—41no—
423C22×C43C22×C22⋊C411yescharacteristic
424C22×C43#54811yescharacteristic
425C22×C43D4×Q811yescharacteristic
426C4×C43—22no—
427C4×C43—21no—
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—21no—
431C4×C43—42no—
432C4×C43—41no—
433C4×C43—41no—
434C4×C43—81no—
435C4×C43C2×C4×Q811yescharacteristic
436C4×C43#51911yescharacteristic
437C4×C43#54811yescharacteristic
438C4×C43D4×Q811yescharacteristic
439Dic43—21no—
440Dic43—21no—
441Dic43—21no—
442Dic43—21no—
443Dic43—21no—
444Dic43—21no—
445Dic43—21no—
446Dic43—42no—
447Dic43—41no—
448Dic43—41no—
449Dic43—41no—
450Dic43—41no—
451Dic43—81no—
452Dic43#42112yes—
453Q8×#41—431no—
454Q8×M16—431no—
455#2295—431no—
456#1995—431no—
457#1995—431no—
458#1994—431no—
459#1986—431no—
460#1986—431no—
461#1986—431no—
462#1806—431no—
463#1806—431no—
464#1806D4311yescharacteristic
465#1759—431no—
466#1759—431no—
467C4×#104—431no—
468C2×C43—21no—
469C2×C43—21no—
470C2×C43—42no—
471C2×C43Q8×C22⋊C411yescharacteristic
472C2×C43C2×#42111yescharacteristic
473C2×C43#290111yescharacteristic
474Q82—431no—
475#557—431no—
476#557—431no—
477#557—431no—
478#554—431no—
479#554—431no—
480#554—431no—
481#554—861no—
482#554—861no—
483#554—861no—
484D4×Q8—431no—
485D4×Q8—861no—
486#533—431no—
487#533—431no—
488#533—431no—
489#533—861no—
490#533—861no—
491#533—861no—
492C4×#41—431no—
493C4×#41—431no—
494C4×#41C2×D4311yescharacteristic
495C2×C4×Q8—431no—
496C2×C4×Q8—861no—
497#446—861no—
498#446—861no—
499#446—861no—
500C8×Q8—861no—
501#423—431no—
502#423—431no—
503#423C2×D4311yescharacteristic
504C2×#104—431no—
505C2×#104—431no—
506C2×#104C2×D4311yescharacteristic
507C2×#104C2×D4311yescharacteristic
508C4×M16—431no—
509C4×M16—431no—
510C4×M16—431no—
511#391—861no—
512#389—861no—
513#387—861no—
514#387—861no—
515C4×C4⋊C4—431no—
516C4×C4⋊C4—431no—
517C4×C4⋊C4C2×D4311yescharacteristic
518#376—431no—
519#376—431no—
520C43—431no—
521#339—431no—
522#339—431no—
523#339—431no—
524#339—431no—
525#339—431no—
526#339—431no—
527#339—431no—
528#339—431no—
529#339—431no—
530#339—431no—
531#339C2×D4311yescharacteristic
532#339C2×D4311yescharacteristic
533C43#2252911yescharacteristic, complemented, Sylow
534C2×#41C22×D4311yescharacteristic
535C22×Q8—431no—
536C22×Q8—861no—
537C2×M16—431no—
538C2×M16—431no—
539C2×M16C22×D4311yescharacteristic
540C2×M16C22×D4311yescharacteristic
541C4⋊Q8—431no—
542C4⋊Q8—431no—
543C4⋊Q8—431no—
544C4⋊Q8—431no—
545C4⋊Q8—431no—
546C4⋊Q8—431no—
547C4⋊Q8—861no—
548C4⋊Q8—861no—
549C4⋊Q8—861no—
550C4⋊Q8—861no—
551C4⋊Q8—861no—
552C4⋊Q8—861no—
553#125—431no—
554#125—431no—
555#125—431no—
556#125—431no—
557#125—431no—
558#125—431no—
559#125—861no—
560#125—861no—
561#125—861no—
562#125—861no—
563#125—861no—
564#125—861no—
565C22⋊Q8—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⋊Q8—861no—
576C22⋊Q8—861no—
577C22⋊Q8—861no—
578C22⋊Q8—861no—
579C22⋊Q8—861no—
580C22⋊Q8—861no—
581C22⋊Q8—861no—
582C22⋊Q8—861no—
583C4×Q8—431no—
584C4×Q8—431no—
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×Q8—861no—
597C4×Q8—861no—
598C4×Q8—861no—
599C4×Q8—861no—
600C4×Q8—861no—
601C4×Q8—861no—
602C4×Q8—861no—
603C4×Q8—861no—
604C4×Q8—861no—
605C4×Q8C4×D4311yescharacteristic
606C4×Q8C4×D4311yescharacteristic
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—431no—
610C4×D4—431no—
611C4×D4—431no—
612C4×D4—431no—
613C4×D4—861no—
614C4×D4—861no—
615C4×D4—861no—
616C4×D4—861no—
617C4×D4C4×D4311yescharacteristic
618C4×D4C4×D4311yescharacteristic
619#117—21no—
620#117—431no—
621#117—431no—
622#117—861no—
623#117—861no—
624#117C22×D4311yescharacteristic
625C2×C4⋊C4—21no—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—861no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4—861no—
633C2×C4⋊C4—861no—
634C2×C42—21no—
635C2×C42—431no—
636C2×C42—431no—
637C2×C42—431no—
638C2×C42—431no—
639C2×C42—861no—
640C2×C42—861no—
641C2×C42—861no—
642C2×C42—861no—
643C2×C42C22×D4311yescharacteristic
644C2×C42C22×D4311yescharacteristic
645C2×C42C22×D4311yescharacteristic
646C4⋊C8—21no—
647C4⋊C8—21no—
648C4⋊C8—861no—
649C4⋊C8—861no—
650C4⋊C8—861no—
651C4⋊C8—861no—
652#104—22no—
653#104—22no—
654#104—434no—
655#104—862no—
656#97—861no—
657#97—861no—
658#97—861no—
659C4×C8—861no—
660C4×C8—861no—
661C4×C8—861no—
662#95—21no—
663#95—861no—
664#95—861no—
665#95—861no—
666#95—861no—
667#95—861no—
668#95—861no—
669#41—21no—
670#41—21no—
671#41#1062190012yes—
672#41Q8×D4312yes—
673C2×Q8—431no—
674C2×Q8—431no—
675C2×Q8—431no—
676C2×Q8—431no—
677C2×Q8—861no—
678C2×Q8—861no—
679C2×Q8—861no—
680C2×Q8—861no—
681C2×Q8—861no—
682C2×Q8—861no—
683C2×Q8—1722no—
684C2×Q8—1724no—
685C2×Q8C2×C4×D4311yescharacteristic
686C2×D4—21no—
687C2×D4C2×C4×D4311yescharacteristic
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—431no—
694C22×C4—431no—
695C22×C4—431no—
696C22×C4—431no—
697C22×C4—861no—
698C22×C4—861no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—861no—
703C22×C4D4×D4311yescharacteristic
704C22×C4D4×D4311yescharacteristic
705C22×C4C23×D4311yescharacteristic
706M16—21no—
707M16—21no—
708M16—21no—
709M16—21no—
710M16—432no—
711M16—861no—
712M16—861no—
713M16—861no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—861no—
717C2×C8—861no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—42no—
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—431no—
731C4⋊C4—431no—
732C4⋊C4—431no—
733C4⋊C4—431no—
734C4⋊C4—431no—
735C4⋊C4—431no—
736C4⋊C4—431no—
737C4⋊C4—861no—
738C4⋊C4—861no—
739C4⋊C4—861no—
740C4⋊C4—861no—
741C4⋊C4—861no—
742C4⋊C4—861no—
743C4⋊C4—861no—
744C4⋊C4—861no—
745C4⋊C4—861no—
746C4⋊C4—861no—
747C4⋊C4—861no—
748C4⋊C4—861no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C4⋊C4—861no—
752C4⋊C4—861no—
753C4⋊C4—861no—
754C4⋊C4—861no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—1722no—
760C4⋊C4—1722no—
761C4⋊C4C2×C4×D4311yescharacteristic
762C4⋊C4C2×C4×D4311yescharacteristic
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—861no—
767C22⋊C4—861no—
768C22⋊C4—861no—
769C22⋊C4—861no—
770C22⋊C4—861no—
771C22⋊C4—861no—
772C42—21no—
773C42—21no—
774C42—21no—
775C42—21no—
776C42—21no—
777C42—21no—
778C42—21no—
779C42—431no—
780C42—431no—
781C42—431no—
782C42—431no—
783C42—431no—
784C42—431no—
785C42—431no—
786C42—431no—
787C42—432no—
788C42—861no—
789C42—861no—
790C42—861no—
791C42—861no—
792C42—861no—
793C42—861no—
794C42—861no—
795C42—861no—
796C42—861no—
797C42—1722no—
798C42—1722no—
799C42C2×C4×D4311yescharacteristic
800C42C2×C4×D4311yescharacteristic
801C42D4×D4311yescharacteristic
802C42D4×D4311yescharacteristic
803C23—21no—
804C23C2×D4×D4311yescharacteristic
805Q8—21no—
806Q8—862no—
807Q8—862no—
808Q8—3441no—
809Q8—3441no—
810Q8—3441no—
811Q8—1721no—
812Q8—1721no—
813Q8—1722no—
814Q8—1722no—
815Q8—1722no—
816Q8#1306329012yes—
817D4—22no—
818D4—22no—
819D4—21no—
820D4#1306329012yes—
821C2×C4—21no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—81no—
836C2×C4—431no—
837C2×C4—431no—
838C2×C4—431no—
839C2×C4—431no—
840C2×C4—431no—
841C2×C4—431no—
842C2×C4—431no—
843C2×C4—431no—
844C2×C4—862no—
845C2×C4—862no—
846C2×C4—861no—
847C2×C4—861no—
848C2×C4—861no—
849C2×C4—861no—
850C2×C4—3441no—
851C2×C4—3441no—
852C2×C4—1722no—
853C2×C4—1721no—
854C2×C4—1721no—
855C2×C4—1721no—
856C2×C4—1722no—
857C2×C4—1721no—
858C2×C4—1721no—
859C2×C4—1721no—
860C2×C4—1721no—
861C2×C4—1721no—
862C2×C4C22⋊C4×D4311yescharacteristic
863C2×C4C22⋊C4×D4311yescharacteristic
864C2×C4C22⋊C4×D4311yescharacteristic
865C2×C4C22⋊C4×D4311yescharacteristic
866C2×C4C22×C4×D4311yescharacteristic
867C2×C4C2×D4×D4311yescharacteristic
868C2×C4C2×Q8×D4311yescharacteristic
869C2×C4C2×#1062190011yescharacteristic
870C2×C4#1306337211yescharacteristic
871C2×C4#1306337211yescharacteristic
872C8—41no—
873C8—41no—
874C8—862no—
875C8—1721no—
876C22—21no—
877C22—21no—
878C22—22no—
879C22—41no—
880C22—41no—
881C22C2×C22⋊C4×D4311yescharacteristic
882C22#1458355511yescharacteristic
883C22#1458356211yescharacteristic
884C4—22no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—42no—
890C4—41no—
891C4—41no—
892C4—81no—
893C4—432no—
894C4—861no—
895C4—861no—
896C4—861no—
897C4—861no—
898C4—861no—
899C4—861no—
900C4—861no—
901C4—3441no—
902C4—1722no—
903C4—1721no—
904C4—1721no—
905C4—1721no—
906C4—1721no—
907C4C2×#1306329011yescharacteristic
908C4#1458337611yescharacteristic
909C4#1458355511yescharacteristic
910C4#1458356211yescharacteristic
911C2—21no—
912C2—21no—
913C2—42no—
914C2#1913742711yescharacteristic
915C2#421×D4311yescharacteristic
916C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#41×C43C23
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#22529
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
2. #19143546C2semidirect
3. #19137071C2semidirect
4. #19135575C2semidirect
5. #19135574C2semidirect
6. #19135570C2semidirect
7. #19135538C2semidirect
8. #19135537C2semidirect
9. #19135537C2semidirect
16. Q8×Dic86C4semidirect
17. #14583628C4semidirect
18. #14583625C4semidirect
19. #14583625C4semidirect
22. #14583608C4semidirect
23. #14583608C4semidirect
25. #14583606C4semidirect
27. D4×Dic86C4semidirect
176. #13063252Q8semidirect
337. C4×Dic43C2×Q8semidirect
341. #10621877C2×Q8semidirect
533. C43#22529semidirect

Maximal subgroups

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

subgroupindex
#41×Dic862
#191435462
#191370712
#191355752
#191355742
#191355702
#191355382
#191355372
#191346132
#191344072
#191344052
#104×Dic432
C43×#18062
#2252943