Finite Group Databasebeta

← #25113300

Subgroups — #25113300

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#19148173C211yesmaximal, characteristic
2#19143546C211yesmaximal, characteristic, complemented
3#19137067C211yesmaximal, characteristic, complemented
4#19135574C211yesmaximal, characteristic, complemented
5#19135570C211yesmaximal, characteristic, complemented
6#19135540C211yesmaximal, characteristic, complemented
7#19135537C211yesmaximal, characteristic, complemented
8#19135537C211yesmaximal, characteristic, complemented
9#19134614C211yesmaximal, characteristic
10#19134614C211yesmaximal, characteristic
11#19134612C211yesmaximal, characteristic
12#19134406C211yesmaximal, characteristic
13#19134404C211yesmaximal, characteristic
14#19134399C211yesmaximal, characteristic
15C43×#1995C211yesmaximal, characteristic, complemented
16#14583629C411yescharacteristic, complemented
17#14583626C411yescharacteristic, complemented
18#14583626C411yescharacteristic, complemented
19#14583624C411yescharacteristic, complemented
20#14583610C411yescharacteristic, complemented
21#14583607—21no—
22#14583605C411yescharacteristic, complemented
23#14583605C411yescharacteristic, complemented
24#14583603—21no—
25#14583603—21no—
26#14583564C411yescharacteristic, complemented
27#14583562—21no—
28#14583453—21no—
29#14583453—21no—
30#14583453—21no—
31#14583452C2211yescharacteristic
32#14583452C2211yescharacteristic
33C4×#10621898C2211yescharacteristic
34#14583367C2211yescharacteristic
35#14583367C2211yescharacteristic
36C2×C4×Dic86C2211yescharacteristic
37C4×Q8×D43—21no—
38#14583028—21no—
39#14583028—21no—
40#14583026—21no—
41#14583023—21no—
42#14582922C2211yescharacteristic
43#14582922C2211yescharacteristic
44C2×#13063253C2211yescharacteristic
45C2×#13063253C2211yescharacteristic
46C2×#13063251C2211yescharacteristic
47C2×#13063251C2211yescharacteristic
48C4×#10621877C2211yescharacteristic
49M16×Dic43C2211yescharacteristic
50M16×Dic43C2211yescharacteristic
51#14582803—21no—
52#14582796—21no—
53#14582786—21no—
54#14582782—21no—
55C4×Dic43⋊C4C2211yescharacteristic
56C4×Dic43⋊C4C2211yescharacteristic
57C4×C4⋊Dic43C2211yescharacteristic
58#14582745C2211yescharacteristic
59C42×Dic43C2211yescharacteristic
60#14582660C2211yescharacteristic
61#14582660C2211yescharacteristic
62#14582659C2211yescharacteristic
63#14582659C2211yescharacteristic
64#14582658C2211yescharacteristic
65#14582658C2211yescharacteristic
66#14582658C2211yescharacteristic
67#14582658C2211yescharacteristic
68C43×#533C2211yescharacteristic
69C43×#423C2211yescharacteristic
70C43×#376C2211yescharacteristic
71C43×#339C2211yescharacteristic
72C43×#339C2211yescharacteristic
73C43×#339C2211yescharacteristic
74C43×#339C2211yescharacteristic
75C2×#10621898C2311yescharacteristic
76C22×Dic86D411yescharacteristic
77C2×Q8×D43—21no—
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80#13063324—21no—
81#13063324—21no—
82#13063324—21no—
83#13063324C2×C411yescharacteristic
84#13063324C2×C411yescharacteristic
85#13063324C2×C411yescharacteristic
86#13063324C2×C411yescharacteristic
87#13063323—21no—
88#13063323—21no—
89#13063323—21no—
90#13063316C2×C411yescharacteristic
91#13063316C2×C411yescharacteristic
92#13063316C2×C411yescharacteristic
93#13063316C2×C411yescharacteristic
94#13063315—21no—
95#13063315—21no—
96#13063315—21no—
97#13063315—21no—
98#13063315—21no—
99#13063315—21no—
100#13063305—21no—
101#13063305—21no—
102#13063305—21no—
103#13063303—21no—
104#13063303—21no—
105#13063303—21no—
106#13063303—21no—
107#13063303—21no—
108#13063303—21no—
109#13063302—21no—
110#13063302—21no—
111#13063302—21no—
112#13063302—21no—
113#13063301—21no—
114#13063301—21no—
115#13063301—21no—
116Q8×Dic43—21no—
117C4×Dic86—21no—
118C4×Dic86—21no—
119C4×Dic86—21no—
120C4×Dic86—21no—
121C4×Dic86C2×C411yescharacteristic
122C4×Dic86C2×C411yescharacteristic
123C4×Dic86C2×C411yescharacteristic
124C4×Dic86C2×C411yescharacteristic
125C4×Dic86C2×C411yescharacteristic
126C4×Dic86C2×C411yescharacteristic
127C4×Dic86D411yescharacteristic
128C4×Dic86D411yescharacteristic
129C4×Dic86D411yescharacteristic
130C4×Dic86D411yescharacteristic
131#13063290—21no—
132#13063290—21no—
133#13063290—21no—
134#13063290C2×C411yescharacteristic
135#13063290C2×C411yescharacteristic
136#13063290C2×C411yescharacteristic
137#13063290C2×C411yescharacteristic
138C4×D172C2×C411yescharacteristic
139C4×D172C2×C411yescharacteristic
140#13063287C2×C411yescharacteristic
141#13063287C2×C411yescharacteristic
142#13063287C2×C411yescharacteristic
143#13063287C2×C411yescharacteristic
144C4×C22⋊D43—21no—
145C4×C22⋊D43—21no—
146(C22⋊D43)⋊C4—21no—
147(C22⋊D43)⋊C4—21no—
148(C22⋊D43)⋊C4—21no—
149(C22⋊D43)⋊C4—21no—
150#13063284C2311yescharacteristic
151#13063282—21no—
152#13063282—21no—
153#13063282—21no—
154C2×C4⋊Dic43—21no—
155C2×C4⋊Dic43D411yescharacteristic
156C2×Dic43⋊C4—21no—
157C2×Dic43⋊C4—21no—
158C2×Dic43⋊C4D411yescharacteristic
159C2×Dic43⋊C4D411yescharacteristic
160C4⋊C4×D43—21no—
161C4⋊C4×D43—21no—
162C4⋊C4×D43—21no—
163C2×C4×Dic43—21no—
164C2×C4×Dic43—21no—
165C2×C4×Dic43C2311yescharacteristic
166C2×C4×Dic43C2311yescharacteristic
167C2×C4×Dic43C2311yescharacteristic
168C2×C4×Dic43C2311yescharacteristic
169C42×D43—21no—
170C42×D43—21no—
171C42×D43—21no—
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176#13063253—22no—
177#13063253Q814yescomplemented
178#13063251—22no—
179#13063251—22no—
180#13063236—21no—
181#13063235—21no—
182#13063235—21no—
183C4×C43⋊C8—21no—
184C8×Dic43—21no—
185C8×Dic43—21no—
186C43⋊#95—21no—
187C43⋊#95—21no—
188C43⋊#95—21no—
189C43⋊#95—21no—
190C43⋊#95—21no—
191C2×M16×C43C2311yescharacteristic
192C2×M16×C43C2311yescharacteristic
193C4⋊Q8×C43C2×C411yescharacteristic
194C4⋊Q8×C43C2×C411yescharacteristic
195#125×C43C2×C411yescharacteristic
196#125×C43C2×C411yescharacteristic
197C22⋊Q8×C43—21no—
198C22⋊Q8×C43—21no—
199C4×Q8×C43—21no—
200C4×Q8×C43—21no—
201#117×C43C2311yescharacteristic
202#117×C43C2311yescharacteristic
203C2×C42×C43C2311yescharacteristic
204C2×C42×C43C2311yescharacteristic
205C2×C42×C43C2311yescharacteristic
206C4⋊C8×C43—21no—
207C4⋊C8×C43—21no—
208#95×C43—21no—
209#95×C43—21no—
210C2×Q8×C43—21no—
211C2×Q8×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—21no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224Q8×D43—44no—
225#10621898—21no—
226#10621898—21no—
227#10621898C2×Q812yes—
228#10621898#4112yes—
229C2×D172C22×C411yescharacteristic
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—21no—
235C2×C4×D43—21no—
236C2×C4×D43—21no—
237C2×Dic86—21no—
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86—21no—
241C2×Dic86—42no—
242C2×Dic86C22⋊C411yescharacteristic
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—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43C22×C411yescharacteristic
260C4⋊C4×C43C22×C411yescharacteristic
261C4⋊C4×C43C22×C411yescharacteristic
262C4⋊C4×C43C22×C411yescharacteristic
263C22⋊C4×C43—21no—
264C22⋊C4×C43—21no—
265C42×C43—21no—
266C42×C43—21no—
267C42×C43—21no—
268C42×C43—21no—
269C42×C43—21no—
270C42×C43C22×C411yescharacteristic
271C42×C43C22×C411yescharacteristic
272C42×C43C2×D411yescharacteristic
273C42×C43C2×D411yescharacteristic
274C42×C43C2×Q812yescomplemented
275C22⋊Dic43—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—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43—42no—
287C4⋊Dic43C22⋊C411yescharacteristic
288C4⋊Dic43C22⋊C411yescharacteristic
289C4⋊Dic43C22⋊C411yescharacteristic
290C4⋊Dic43C22⋊C411yescharacteristic
291C4⋊Dic43C22×C411yescharacteristic
292C4⋊Dic43C22×C411yescharacteristic
293Dic43⋊C4—21no—
294Dic43⋊C4—21no—
295Dic43⋊C4—21no—
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—42no—
308Dic43⋊C4—42no—
309Dic43⋊C4C22⋊C411yescharacteristic
310Dic43⋊C4C22⋊C411yescharacteristic
311Dic43⋊C4C22⋊C411yescharacteristic
312Dic43⋊C4C22⋊C411yescharacteristic
313Dic43⋊C4C22⋊C411yescharacteristic
314Dic43⋊C4C22⋊C411yescharacteristic
315Dic43⋊C4C22⋊C411yescharacteristic
316Dic43⋊C4C22⋊C411yescharacteristic
317C4×Dic43—21no—
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—21no—
328C4×Dic43—42no—
329C4×Dic43—42no—
330C4×Dic43C22×C411yescharacteristic
331C4×Dic43C22×C411yescharacteristic
332C4×Dic43C22×C411yescharacteristic
333C4×Dic43C22×C411yescharacteristic
334C4×Dic43C2×D411yescharacteristic
335C4×Dic43C2×D411yescharacteristic
336C4×Dic43C2×D411yescharacteristic
337C4×Dic43C2×D411yescharacteristic
338#10621877—21no—
339#10621877—21no—
340#10621877—21no—
341#10621877C2×Q812yescomplemented
342C2×C43⋊C8—21no—
343C2×C43⋊C8—21no—
344C23×C43C22×D411yescharacteristic
345C22×D43—21no—
346Q8×C43—42no—
347Q8×C43—81no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—22no—
353C2×C4×C43—41no—
354C2×C4×C43—41no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43C2×C22⋊C411yescharacteristic
361C2×C4×C43C2×C22⋊C411yescharacteristic
362C2×C4×C43C2×C22⋊C411yescharacteristic
363C2×C4×C43C2×C22⋊C411yescharacteristic
364C2×C4×C43C23×C411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C22×Q811yescharacteristic
367C2×C4×C43C2×#4111yescharacteristic
368C2×C4×C432−1+411yescharacteristic
369C2×C4×C432−1+411yescharacteristic
370C22⋊D43—22no—
371C22⋊D43—22no—
372C2×Dic43—21no—
373C2×Dic43—22no—
374C2×Dic43—22no—
375C2×Dic43—21no—
376C2×Dic43—21no—
377C2×Dic43—41no—
378C2×Dic43—41no—
379C2×Dic43—41no—
380C2×Dic43—41no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—41no—
385C2×Dic43C2×C22⋊C411yescharacteristic
386C2×Dic43C2×C22⋊C411yescharacteristic
387C2×Dic43C2×C22⋊C411yescharacteristic
388C2×Dic43C2×C22⋊C411yescharacteristic
389C2×Dic43C2×C22⋊C411yescharacteristic
390C2×Dic43C2×C22⋊C411yescharacteristic
391C2×Dic43C2×C22⋊C411yescharacteristic
392C2×Dic43C2×C22⋊C411yescharacteristic
393D172—21no—
394D172C4×Q812yes—
395C4×D43—22no—
396C4×D43—22no—
397C4×D43—42no—
398C4×D43—42no—
399C4×D43—42no—
400C4×D43—81no—
401C4×D43—81no—
402C4×D43—81no—
403Dic86—21no—
404Dic86—22no—
405Dic86—22no—
406Dic86—41no—
407Dic86—41no—
408Dic86—42no—
409Dic86—42no—
410Dic86—81no—
411Dic86—81no—
412Dic86C4×Q812yes—
413C8×C43—41no—
414C8×C43—41no—
415C43⋊C8—22no—
416C43⋊C8—41no—
417#22529—431nomaximal, Sylow
418C22×C43—21no—
419C22×C43—21no—
420C22×C43C22×C22⋊C411yescharacteristic
421C22×C43#54811yescharacteristic
422C22×C43D4×Q811yescharacteristic
423C2×D43—22no—
424C2×D43—41no—
425C2×D43—41no—
426C4×C43—21no—
427C4×C43—21no—
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—42no—
431C4×C43—41no—
432C4×C43—41no—
433C4×C43—41no—
434C4×C43—41no—
435C4×C43—81no—
436C4×C43C2×C4×Q811yescharacteristic
437C4×C43#51911yescharacteristic
438C4×C43#54811yescharacteristic
439C4×C43D4×Q811yescharacteristic
440Dic43—22no—
441Dic43—21no—
442Dic43—21no—
443Dic43—21no—
444Dic43—21no—
445Dic43—21no—
446Dic43—21no—
447Dic43—21no—
448Dic43—42no—
449Dic43—41no—
450Dic43—41no—
451Dic43—81no—
452Dic43#42112yes—
453Q8×#41—431no—
454Q8×M16—431no—
455#2295—431no—
456#1995—431no—
457#1995D4311yescharacteristic, complemented
458#1994—431no—
459#1986—431no—
460#1986—431no—
461#1986—431no—
462#1806—431no—
463#1806—431no—
464#1806—431no—
465#1759—431no—
466#1759—431no—
467C4×#104—431no—
468C2×C43—21no—
469C2×C43—21no—
470C2×C43Q8×C22⋊C411yescharacteristic
471C2×C43C2×#42111yescharacteristic
472C2×C43#290111yescharacteristic
473D43—42no—
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—861no—
489#533—861no—
490#533—861no—
491#533C2×D4311yescharacteristic
492C4×#41—431no—
493C4×#41—431no—
494C4×#41—431no—
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×#104—431no—
507C2×#104—431no—
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⋊C4—431no—
518#376—431no—
519#376C2×D4311yescharacteristic
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#339C2×D4311yescharacteristic
530#339C2×D4311yescharacteristic
531#339C2×D4311yescharacteristic
532#339C2×D4311yescharacteristic
533C43#2252911yescharacteristic, complemented, Sylow
534C2×#41—431no—
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—861no—
546C4⋊Q8—861no—
547C4⋊Q8—861no—
548C4⋊Q8—861no—
549C4⋊Q8—861no—
550C4⋊Q8—861no—
551C4⋊Q8C4×D4311yescharacteristic
552C4⋊Q8C4×D4311yescharacteristic
553#125—431no—
554#125—431no—
555#125—431no—
556#125—431no—
557#125—861no—
558#125—861no—
559#125—861no—
560#125—861no—
561#125—861no—
562#125—861no—
563#125C4×D4311yescharacteristic
564#125C4×D4311yescharacteristic
565C22⋊Q8—21no—
566C22⋊Q8—21no—
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—21no—
584C4×Q8—21no—
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—431no—
596C4×Q8—431no—
597C4×Q8—431no—
598C4×Q8—431no—
599C4×Q8—861no—
600C4×Q8—861no—
601C4×Q8—861no—
602C4×Q8—861no—
603C4×Q8—861no—
604C4×Q8—861no—
605C4×Q8—861no—
606C4×Q8—861no—
607C4×D4—431no—
608C4×D4—431no—
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×D4—861no—
618C4×D4—861no—
619#117—431no—
620#117—861no—
621#117—861no—
622#117—861no—
623#117C22×D4311yescharacteristic
624#117C22×D4311yescharacteristic
625C2×C4⋊C4—431no—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—431no—
628C2×C4⋊C4—861no—
629C2×C4⋊C4—861no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4—861no—
633C2×C4⋊C4—861no—
634C2×C42—431no—
635C2×C42—431no—
636C2×C42—431no—
637C2×C42—431no—
638C2×C42—861no—
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—434no—
653#104—862no—
654#104—862no—
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—21no—
664#95—861no—
665#95—861no—
666#95—861no—
667#95—861no—
668#95—861no—
669#41—432no—
670#41—432no—
671#41—861no—
672#41—861no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—431no—
676C2×Q8—431no—
677C2×Q8—431no—
678C2×Q8—431no—
679C2×Q8—431no—
680C2×Q8—861no—
681C2×Q8—861no—
682C2×Q8—861no—
683C2×Q8—861no—
684C2×Q8—1722no—
685C2×Q8—1724no—
686C2×D4—431no—
687C2×D4—861no—
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×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—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
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—431no—
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—1722no—
757C4⋊C4—1722no—
758C4⋊C4—1722no—
759C4⋊C4C2×C4×D4311yescharacteristic
760C4⋊C4C2×C4×D4311yescharacteristic
761C4⋊C4C2×C4×D4311yescharacteristic
762C4⋊C4C2×C4×D4311yescharacteristic
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—861no—
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—431no—
778C42—431no—
779C42—431no—
780C42—431no—
781C42—431no—
782C42—431no—
783C42—431no—
784C42—431no—
785C42—861no—
786C42—861no—
787C42—861no—
788C42—861no—
789C42—861no—
790C42—861no—
791C42—861no—
792C42—861no—
793C42—861no—
794C42—861no—
795C42—861no—
796C42—1722no—
797C42—1722no—
798C42C2×C4×D4311yescharacteristic
799C42C2×C4×D4311yescharacteristic
800C42D4×D4311yescharacteristic
801C42D4×D4311yescharacteristic
802C42Q8×D4312yescomplemented
803C23—861no—
804C23C2×D4×D4311yescharacteristic
805Q8—42no—
806Q8—81no—
807Q8—432no—
808Q8—862no—
809Q8—862no—
810Q8—861no—
811Q8—3441no—
812Q8—3441no—
813Q8—1721no—
814Q8—1721no—
815Q8—1722no—
816Q8—1722no—
817D4—432no—
818D4—862no—
819D4—862no—
820D4—861no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—431no—
834C2×C4—431no—
835C2×C4—431no—
836C2×C4—431no—
837C2×C4—431no—
838C2×C4—431no—
839C2×C4—431no—
840C2×C4—431no—
841C2×C4—862no—
842C2×C4—861no—
843C2×C4—862no—
844C2×C4—862no—
845C2×C4—862no—
846C2×C4—861no—
847C2×C4—861no—
848C2×C4—3441no—
849C2×C4—3441no—
850C2×C4—3441no—
851C2×C4—1722no—
852C2×C4—1722no—
853C2×C4—1722no—
854C2×C4—1721no—
855C2×C4—1721no—
856C2×C4—1721no—
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×C4#41×D4311yescharacteristic
870C2×C4#1306337211yescharacteristic
871C2×C4#1306337311yescharacteristic
872C8—41no—
873C8—41no—
874C8—862no—
875C8—1721no—
876C22—21no—
877C22—21no—
878C22—862no—
879C22—1721no—
880C22—1721no—
881C22C2×C22⋊C4×D4311yescharacteristic
882C22#1458355911yescharacteristic
883C22#1458356211yescharacteristic
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—42no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—81no—
894C4—432no—
895C4—862no—
896C4—861no—
897C4—861no—
898C4—861no—
899C4—861no—
900C4—861no—
901C4—861no—
902C4—861no—
903C4—3441no—
904C4—1722no—
905C4—1721no—
906C4—1721no—
907C4C4×Q8×D4311yescharacteristic
908C4#1458337511yescharacteristic
909C4#1458355711yescharacteristic
910C4#1458356411yescharacteristic
911C2—21no—
912C2—21no—
913C2—1722no—
914C2#1913742911yescharacteristic
915C2#421×D4311yescharacteristic
916C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1995C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#10621898C23
cosocleC22×C4×C43C24
hypercenter#1995D43
hypocenterC43#22529
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
2. #19143546C2semidirect
3. #19137067C2semidirect
4. #19135574C2semidirect
5. #19135570C2semidirect
6. #19135540C2semidirect
7. #19135537C2semidirect
8. #19135537C2semidirect
15. C43×#1995C2semidirect
16. #14583629C4semidirect
17. #14583626C4semidirect
18. #14583626C4semidirect
19. #14583624C4semidirect
20. #14583610C4semidirect
22. #14583605C4semidirect
23. #14583605C4semidirect
26. #14583564C4semidirect
177. #13063253Q8semidirect
274. C42×C43C2×Q8semidirect
341. #10621877C2×Q8semidirect
457. #1995D43semidirect
533. C43#22529semidirect
802. C42Q8×D43semidirect

Maximal subgroups

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

subgroupindex
#191481732
#191435462
#191370672
#191355742
#191355702
#191355402
#191355372
#191346142
#191346122
#191344062
#191344042
#191343992
C43×#19952
#2252943