Finite Group Databasebeta

← #25106606

Subgroups — #25106606

Order 11008.

1106 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147888C211yesmaximal, characteristic
2#19143227C211yesmaximal, characteristic, complemented
3#19136999C211yesmaximal, characteristic, complemented
4#19135537C212yesmaximal, complemented
5#19135512C212yesmaximal, complemented
6#19135042C212yesmaximal, complemented
7#19135040C212yesmaximal, complemented
8#19134616C211yesmaximal, characteristic, complemented
9#19134615C211yesmaximal, characteristic, complemented
10#19134612C211yesmaximal, characteristic, complemented
11C43×#1806C211yesmaximal, characteristic, complemented
12#14583453C411yescharacteristic, complemented
13#14583453C411yescharacteristic, complemented
14#14583452C2211yescharacteristic
15#14583446C411yescharacteristic, complemented
16#14583446C411yescharacteristic, complemented
17#14583445C2211yescharacteristic
18#14583436C411yescharacteristic, complemented
19#14583436C411yescharacteristic, complemented
20#14583431C411yescharacteristic, complemented
21#14583431C411yescharacteristic, complemented
22#14583429—21no—
23#14583429—21no—
24#14583427—21no—
25#14583427—21no—
26#14583411C2211yescharacteristic
27#14583408—21no—
28#14583408—21no—
29#14583406C2211yescharacteristic
30C4×#10621898—21no—
31C4×#10621898—21no—
32C4×#10621898C2211yescharacteristic
33C2×#13063282C2212yes—
34C2×C42×D43C2211yescharacteristic
35#14582955—21no—
36#14582955—21no—
37#14582951—21no—
38#14582951—21no—
39#14582923C2211yescharacteristic
40C2×#13063253C2212yes—
41C2×#13063252C2212yes—
42C2×#13063251C2212yes—
43#14582862C2212yes—
44M16×Dic43C2212yes—
45#14582768—21no—
46#14582763—21no—
47#14582758—21no—
48#14582756—21no—
49C4×Dic43⋊C4C2212yes—
50C4×C4⋊Dic43C2211yescharacteristic
51#14582660C2212yes—
52#14582659C2212yes—
53#14582658C2212yes—
54C4×#41×C43C2211yescharacteristic
55C43×#423C2211yescharacteristic
56C2×#104×C43C2212yes—
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#339C2212yes—
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898C2311yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43C2311yescharacteristic
65C2×#10621877C2312yes—
66#13063324C2×C411yescharacteristic
67#13063324C2×C411yescharacteristic
68#13063323C2×C411yescharacteristic
69#13063321C2×C411yescharacteristic
70#13063320—21no—
71#13063320—21no—
72#13063318—21no—
73#13063318—21no—
74#13063316C2×C411yescharacteristic
75#13063316C2×C411yescharacteristic
76#13063315—21no—
77#13063315—21no—
78#13063314C2×C411yescharacteristic
79#13063312C2×C411yescharacteristic
80#13063311—21no—
81#13063311—21no—
82#13063310—21no—
83#13063310—21no—
84#13063309—21no—
85#13063307—21no—
86#13063307—21no—
87#13063306—21no—
88#13063305C2×C411yescharacteristic
89#13063305C2×C411yescharacteristic
90#13063303—21no—
91#13063303—21no—
92#13063302—21no—
93#13063302—21no—
94#13063301C2×C411yescharacteristic
95#13063301C2×C411yescharacteristic
96#13063300C2×C411yescharacteristic
97#13063300C2×C411yescharacteristic
98#13063298—21no—
99#13063298—21no—
100#13063297—21no—
101#13063297—21no—
102#13063296C2×C411yescharacteristic
103#13063296C2×C411yescharacteristic
104#13063295—21no—
105#13063293—21no—
106C4×Dic86—21no—
107C4×Dic86—21no—
108C4×Dic86—21no—
109C4×Dic86—21no—
110C4×Dic86C2×C411yescharacteristic
111C4×Dic86C2×C411yescharacteristic
112C4×D172—21no—
113C4×D172—21no—
114C4×D172—21no—
115C4×D172—21no—
116C4×D172C2×C411yescharacteristic
117C4×D172C2×C411yescharacteristic
118C4×C22⋊D43—21no—
119C4×C22⋊D43—21no—
120C4×C22⋊D43—21no—
121C4×C22⋊D43—21no—
122C4×C22⋊D43—21no—
123C4×C22⋊D43—21no—
124C4×C22⋊D43—21no—
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127C4×C22⋊D43—21no—
128#13063284—21no—
129#13063284—21no—
130#13063284C2311yescharacteristic
131#13063282—21no—
132#13063282—21no—
133#13063282—21no—
134#13063282—21no—
135#13063282—21no—
136#13063282—42no—
137#13063282—42no—
138C2×C4⋊Dic43—21no—
139C2×Dic43⋊C4—22no—
140C2×Dic43⋊C4—22no—
141C2×(C2×D43)⋊C4—22no—
142C2×C4×Dic43D411yescharacteristic
143C2×C4×Dic43D411yescharacteristic
144C2×C4×Dic43C2312yes—
145C2×C4×Dic43C2311yescharacteristic
146C42×D43—21no—
147C42×D43C2×C411yescharacteristic
148C42×D43C2×C411yescharacteristic
149C42×D43C2×C411yescharacteristic
150C42×D43C2×C411yescharacteristic
151C42×D43D411yescharacteristic
152C42×D43D411yescharacteristic
153C42×D43D411yescharacteristic
154C42×D43D411yescharacteristic
155C4⋊(C43⋊C8)—21no—
156C4⋊(C43⋊C8)—21no—
157#13063253—42no—
158#13063252—42no—
159#13063251—42no—
160(C2×D43)⋊C8—22no—
161(C2×D43)⋊C8—22no—
162#13063235—22no—
163C8×Dic43—22no—
164C43⋊#95—21no—
165C43⋊#95—22no—
166C2×#41×C43C2311yescharacteristic
167C2×M16×C43C2312yes—
168C4×Q8×C43C2×C411yescharacteristic
169C4×Q8×C43C2×C411yescharacteristic
170C4×D4×C43—21no—
171C4×D4×C43—21no—
172C4×D4×C43C2×C411yescharacteristic
173C4×D4×C43C2×C411yescharacteristic
174#117×C43—21no—
175#117×C43C2311yescharacteristic
176C2×C4⋊C4×C43—21no—
177C2×C42×C43—21no—
178C2×C42×C43C2312yes—
179C2×C42×C43C2311yescharacteristic
180C4⋊C8×C43—21no—
181C4⋊C8×C43—21no—
182#104×C43—42no—
183#95×C43—21no—
184C23×D43C2×D411yescharacteristic
185#41×C43—21no—
186#41×C43—21no—
187#41×C43—21no—
188#41×C43—21no—
189C2×Q8×C43C22×C411yescharacteristic
190C2×D4×C43—21no—
191C2×D4×C43C22×C411yescharacteristic
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—22no—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—21no—
200C2×C22⋊D43—21no—
201C2×C22⋊D43—21no—
202C2×C22⋊D43—21no—
203C2×C22⋊D43—21no—
204C22×Dic43—22no—
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208#10621898—21no—
209#10621898—21no—
210#10621898—21no—
211#10621898—21no—
212#10621898—44no—
213#10621898—44no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172C22×C411yescharacteristic
217C2×C4×D43—21no—
218C2×C4×D43—21no—
219C2×C4×D43—21no—
220C2×C4×D43—21no—
221C2×C4×D43—21no—
222C2×C4×D43—21no—
223C2×C4×D43—21no—
224C2×C4×D43—42no—
225C2×C4×D43—42no—
226C2×C4×D43C22⋊C411yescharacteristic
227C2×C4×D43C22⋊C411yescharacteristic
228C2×C4×D43C22⋊C411yescharacteristic
229C2×C4×D43C22⋊C411yescharacteristic
230C2×C4×D43C22⋊C411yescharacteristic
231C2×C4×D43C22⋊C411yescharacteristic
232C2×C4×D43C22⋊C411yescharacteristic
233C2×C4×D43C22⋊C411yescharacteristic
234C2×C4×D43C22×C411yescharacteristic
235C2×C4×D43C22×C411yescharacteristic
236C2×C4×D43C2×D411yescharacteristic
237C2×C4×D43C2×D411yescharacteristic
238C2×Dic86—21no—
239C2×Dic86—21no—
240C2×Dic86C22×C411yescharacteristic
241M16×C43—22no—
242M16×C43—22no—
243C2×C8×C43—22no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—42no—
247C4⋊C4×C43C22×C411yescharacteristic
248C4⋊C4×C43C22×C411yescharacteristic
249C22⋊C4×C43—21no—
250C22⋊C4×C43—21no—
251C22⋊C4×C43—21no—
252C42×C43—21no—
253C42×C43—21no—
254C42×C43—21no—
255C42×C43—22no—
256C42×C43—22no—
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—
274(C2×D43)⋊C4—21no—
275(C2×D43)⋊C4—21no—
276(C2×D43)⋊C4—44no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43—42no—
282C4⋊Dic43C22×C411yescharacteristic
283C4⋊Dic43C22×C411yescharacteristic
284Dic43⋊C4—21no—
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—44no—
295Dic43⋊C4—44no—
296C4×Dic43—21no—
297C4×Dic43—21no—
298C4×Dic43—21no—
299C4×Dic43—22no—
300C4×Dic43—22no—
301C4×Dic43C22⋊C411yescharacteristic
302C4×Dic43C22⋊C411yescharacteristic
303C4×Dic43C22⋊C411yescharacteristic
304C4×Dic43C22⋊C411yescharacteristic
305C4×Dic43C22⋊C411yescharacteristic
306C4×Dic43C22⋊C411yescharacteristic
307C4×Dic43C22⋊C411yescharacteristic
308C4×Dic43C22⋊C411yescharacteristic
309C4×Dic43C22×C411yescharacteristic
310C4×Dic43C22×C411yescharacteristic
311C4×Dic43C2×D411yescharacteristic
312C4×Dic43C2×D411yescharacteristic
313#10621877—22no—
314#10621877—22no—
315C2×C43⋊C8—22no—
316C23×C43—21no—
317C23×C43C22×D411yescharacteristic
318C22×D43—21no—
319C22×D43—21no—
320C22×D43—21no—
321C22×D43—41no—
322C22×D43—41no—
323C22×D43C2×C22⋊C411yescharacteristic
324C22×D43C2×C22⋊C411yescharacteristic
325Q8×C43—21no—
326Q8×C43—21no—
327D4×C43—21no—
328D4×C43—21no—
329D4×C43—41no—
330D4×C43—41no—
331C2×C4×C43—22no—
332C2×C4×C43—21no—
333C2×C4×C43—21no—
334C2×C4×C43—21no—
335C2×C4×C43—41no—
336C2×C4×C43—42no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—42no—
340C2×C4×C43—42no—
341C2×C4×C43—42no—
342C2×C4×C43—42no—
343C2×C4×C43C2×C22⋊C411yescharacteristic
344C2×C4×C43C2×C22⋊C411yescharacteristic
345C2×C4×C43C2×C22⋊C411yescharacteristic
346C2×C4×C43C2×C22⋊C411yescharacteristic
347C2×C4×C43C23×C411yescharacteristic
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43H(5,𝔽2)11yescharacteristic
350C2×C4×C43H(5,𝔽2)11yescharacteristic
351C2×C4×C432−1+411yescharacteristic
352C2×C4×C432−1+411yescharacteristic
353C22⋊D43—42no—
354C22⋊D43—42no—
355C22⋊D43—42no—
356C22⋊D43—41no—
357C22⋊D43—41no—
358C22⋊D43—42no—
359C2×Dic43—21no—
360C2×Dic43—21no—
361C2×Dic43—22no—
362C2×Dic43—21no—
363C2×Dic43—21no—
364C2×Dic43—21no—
365C2×Dic43—41no—
366C2×Dic43—42no—
367C2×Dic43—42no—
368C2×Dic43—42no—
369C2×Dic43C2×C22⋊C411yescharacteristic
370C2×Dic43C2×C22⋊C411yescharacteristic
371C2×Dic43C2×C22⋊C411yescharacteristic
372C2×Dic43C2×C22⋊C411yescharacteristic
373C2×Dic43C2×C22⋊C411yescharacteristic
374C2×Dic43C2×C22⋊C411yescharacteristic
375D172—21no—
376D172—21no—
377D172—42no—
378D172—42no—
379C4×D43—21no—
380C4×D43—21no—
381C4×D43—21no—
382C4×D43—21no—
383C4×D43—21no—
384C4×D43—21no—
385C4×D43—21no—
386C4×D43—21no—
387C4×D43—22no—
388C4×D43—22no—
389C4×D43—22no—
390C4×D43—22no—
391C4×D43—41no—
392C4×D43—41no—
393C4×D43—41no—
394C4×D43—41no—
395C4×D43—42no—
396C4×D43—41no—
397C4×D43—41no—
398C4×D43—42no—
399Dic86—21no—
400Dic86—21no—
401Dic86—42no—
402Dic86—42no—
403C8×C43—42no—
404C43⋊C8—42no—
405#21900—431nomaximal, Sylow
406C22×C43—21no—
407C22×C43—21no—
408C22×C43—41no—
409C22×C43—41no—
410C22×C43—41no—
411C22×C43C22×C22⋊C411yescharacteristic
412C22×C43#53511yescharacteristic
413C22×C43#53611yescharacteristic
414C2×D43—21no—
415C2×D43—21no—
416C2×D43—21no—
417C2×D43—21no—
418C2×D43—21no—
419C2×D43—21no—
420C2×D43—42no—
421C2×D43—42no—
422C2×D43—41no—
423C2×D43—41no—
424C2×D43—41no—
425C4×C43—21no—
426C4×C43—21no—
427C4×C43—21no—
428C4×C43—41no—
429C4×C43—41no—
430C4×C43—41no—
431C4×C43—82no—
432C4×C43#42112yes—
433C4×C43#52011yescharacteristic
434C4×C43#52011yescharacteristic
435C4×C43#53711yescharacteristic
436C4×C43#53711yescharacteristic
437Dic43—21no—
438Dic43—21no—
439Dic43—21no—
440Dic43—21no—
441Dic43—21no—
442Dic43—41no—
443Dic43—41no—
444Dic43—41no—
445Dic43—82no—
446Dic43#42112yes—
447#3444—431no—
448#2920—431no—
449#2285—431no—
450#1986—432no—
451#1980—432no—
452#1897—432no—
453#1897—432no—
454#1806—431no—
455#1806—431no—
456#1806—431no—
457#1806D4311yescharacteristic, complemented
458C2×C43—21no—
459C2×C43—21no—
460C2×C43—81no—
461C2×C43#231111yescharacteristic
462C2×C43C2×#42111yescharacteristic
463C2×C43C2×#42111yescharacteristic
464D43—41no—
465D43—41no—
466D43—81no—
467#533—431no—
468#533—431no—
469#533—431no—
470#532—431no—
471#532—431no—
472#532—431no—
473#529—431no—
474#529—431no—
475#529—431no—
476#529—431no—
477#529—861no—
478#529—861no—
479#529—861no—
480#529—861no—
481#525—431no—
482#525—431no—
483#525—861no—
484#525—861no—
485C4×#41—431no—
486C4×#41—861no—
487C4×#41—861no—
488C4×#41C2×D4311yescharacteristic
489C2×#117—432no—
490C22×C42—431no—
491#432—861no—
492#432—861no—
493#431—861no—
494#431—861no—
495#423—431no—
496#423C2×D4311yescharacteristic
497C2×#104—432no—
498C2×#104—432no—
499C2×#104—432no—
500C2×#104C2×D4312yes—
501#407—432no—
502C4×M16—432no—
503#384—861no—
504#382—861no—
505#380—861no—
506#380—861no—
507C4×C4⋊C4—432no—
508C4×C4⋊C4—431no—
509C4×C4⋊C4C2×D4311yescharacteristic
510#339—432no—
511#339—432no—
512#339—432no—
513#339C2×D4312yes—
514C43#2190011yescharacteristic, complemented, Sylow
515C2×#41—431no—
516C2×#41—861no—
517C2×#41—861no—
518C2×#41C22×D4311yescharacteristic
519C23×C4—431no—
520C23×C4—431no—
521C23×C4—431no—
522C2×M16—432no—
523C2×M16C22×D4312yes—
524C4⋊Q8—431no—
525C4⋊Q8—431no—
526C4⋊Q8—431no—
527#127—431no—
528#126—861no—
529#126—861no—
530#126—861no—
531#126—861no—
532#125—431no—
533#125—431no—
534#125—861no—
535#125—861no—
536#124—431no—
537#124—431no—
538#124—861no—
539#124—861no—
540#123—861no—
541#123—861no—
542#123—861no—
543#123—861no—
544#123—861no—
545#123—861no—
546C22⋊Q8—431no—
547C22⋊Q8—431no—
548C22⋊Q8—431no—
549C22⋊Q8—431no—
550C22⋊Q8—861no—
551C22⋊Q8—861no—
552C22⋊Q8—861no—
553C22⋊Q8—861no—
554#121—431no—
555#121—431no—
556#121—431no—
557#121—431no—
558#121—861no—
559#121—861no—
560#121—861no—
561#121—861no—
562#120—861no—
563#120—861no—
564C4×Q8—431no—
565C4×Q8—431no—
566C4×Q8—861no—
567C4×Q8—861no—
568C4×Q8—861no—
569C4×Q8—861no—
570C4×Q8C4×D4311yescharacteristic
571C4×Q8C4×D4311yescharacteristic
572C4×D4—21no—
573C4×D4—21no—
574C4×D4—431no—
575C4×D4—431no—
576C4×D4—861no—
577C4×D4—861no—
578C4×D4—861no—
579C4×D4—861no—
580C4×D4—861no—
581C4×D4—861no—
582C4×D4—861no—
583C4×D4—861no—
584C4×D4—861no—
585C4×D4—861no—
586C4×D4—861no—
587C4×D4—861no—
588C4×D4—861no—
589C4×D4—861no—
590C4×D4C4×D4311yescharacteristic
591C4×D4C4×D4311yescharacteristic
592#117—21no—
593#117—431no—
594#117—861no—
595#117—861no—
596#117—861no—
597#117—861no—
598#117—861no—
599#117—861no—
600#117—861no—
601#117—1722no—
602#117—1722no—
603#117C22×D4311yescharacteristic
604C2×C4⋊C4—21no—
605C2×C4⋊C4—862no—
606C2×C4⋊C4—862no—
607C2×C4⋊C4—861no—
608C2×C22⋊C4—862no—
609C2×C42—21no—
610C2×C42—431no—
611C2×C42—431no—
612C2×C42—431no—
613C2×C42—431no—
614C2×C42—431no—
615C2×C42—431no—
616C2×C42—431no—
617C2×C42—431no—
618C2×C42—431no—
619C2×C42—431no—
620C2×C42—431no—
621C2×C42—432no—
622C2×C42—861no—
623C2×C42C22×D4312yes—
624C2×C42C22×D4311yescharacteristic
625C4⋊C8—21no—
626C4⋊C8—21no—
627C4⋊C8—861no—
628C4⋊C8—861no—
629#104—42no—
630#104—1722no—
631#104—1722no—
632#104—1722no—
633C22⋊C8—862no—
634C22⋊C8—862no—
635#97—862no—
636C4×C8—862no—
637#95—21no—
638#95—862no—
639#95—861no—
640C24—431no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—861no—
646#41—861no—
647#41—861no—
648#41—861no—
649#41—1724no—
650#41—1724no—
651C2×Q8—431no—
652C2×Q8—861no—
653C2×Q8—861no—
654C2×Q8C2×C4×D4311yescharacteristic
655C2×D4—21no—
656C2×D4—431no—
657C2×D4—861no—
658C2×D4—861no—
659C2×D4—861no—
660C2×D4—861no—
661C2×D4—861no—
662C2×D4—861no—
663C2×D4—861no—
664C2×D4C2×C4×D4311yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—22no—
669C22×C4—431no—
670C22×C4—431no—
671C22×C4—431no—
672C22×C4—431no—
673C22×C4—431no—
674C22×C4—431no—
675C22×C4—431no—
676C22×C4—431no—
677C22×C4—431no—
678C22×C4—431no—
679C22×C4—431no—
680C22×C4—431no—
681C22×C4—431no—
682C22×C4—431no—
683C22×C4—431no—
684C22×C4—861no—
685C22×C4—861no—
686C22×C4—861no—
687C22×C4—861no—
688C22×C4—861no—
689C22×C4—861no—
690C22×C4—861no—
691C22×C4—862no—
692C22×C4—1722no—
693C22×C4—1722no—
694C22×C4D4×D4311yescharacteristic
695C22×C4D4×D4311yescharacteristic
696C22×C4C23×D4311yescharacteristic
697M16—22no—
698M16—22no—
699M16—862no—
700M16—862no—
701C2×C8—22no—
702C2×C8—862no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—431no—
707C4⋊C4—431no—
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—1724no—
724C4⋊C4—1724no—
725C4⋊C4C2×C4×D4311yescharacteristic
726C4⋊C4C2×C4×D4311yescharacteristic
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—861no—
731C22⋊C4—861no—
732C22⋊C4—861no—
733C22⋊C4—861no—
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—1724no—
746C42—21no—
747C42—21no—
748C42—21no—
749C42—22no—
750C42—22no—
751C42—431no—
752C42—431no—
753C42—431no—
754C42—431no—
755C42—431no—
756C42—431no—
757C42—431no—
758C42—431no—
759C42—431no—
760C42—431no—
761C42—431no—
762C42—431no—
763C42—861no—
764C42—861no—
765C42—861no—
766C42—862no—
767C42—862no—
768C42C2×C4×D4311yescharacteristic
769C42C2×C4×D4311yescharacteristic
770C42D4×D4311yescharacteristic
771C42D4×D4311yescharacteristic
772C23—21no—
773C23—431no—
774C23—431no—
775C23—861no—
776C23—861no—
777C23—861no—
778C23—1721no—
779C23—1721no—
780C23C2×D4×D4311yescharacteristic
781Q8—21no—
782Q8—21no—
783Q8—861no—
784Q8—861no—
785Q8—1722no—
786Q8—1722no—
787D4—21no—
788D4—21no—
789D4—41no—
790D4—41no—
791D4—861no—
792D4—861no—
793D4—1722no—
794D4—1722no—
795D4—1722no—
796D4—1722no—
797D4—1722no—
798D4—1722no—
799D4—1721no—
800D4—1721no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—431no—
814C2×C4—431no—
815C2×C4—431no—
816C2×C4—431no—
817C2×C4—431no—
818C2×C4—431no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—861no—
823C2×C4—861no—
824C2×C4—861no—
825C2×C4—861no—
826C2×C4—861no—
827C2×C4—861no—
828C2×C4—862no—
829C2×C4—862no—
830C2×C4—861no—
831C2×C4—861no—
832C2×C4—861no—
833C2×C4—861no—
834C2×C4—861no—
835C2×C4—861no—
836C2×C4—861no—
837C2×C4—1721no—
838C2×C4—1721no—
839C2×C4—1721no—
840C2×C4—1721no—
841C2×C4—1722no—
842C2×C4—1721no—
843C2×C4—1722no—
844C2×C4—1722no—
845C2×C4—1722no—
846C2×C4—1722no—
847C2×C4—1721no—
848C2×C4—1721no—
849C2×C4C22⋊C4×D4311yescharacteristic
850C2×C4C22⋊C4×D4311yescharacteristic
851C2×C4C22⋊C4×D4311yescharacteristic
852C2×C4C22⋊C4×D4311yescharacteristic
853C2×C4C22×C4×D4311yescharacteristic
854C2×C4C2×D4×D4311yescharacteristic
855C2×C4#1306337011yescharacteristic
856C2×C4#1306337111yescharacteristic
857C2×C4#1306337211yescharacteristic
858C2×C4#1306337311yescharacteristic
859C8—42no—
860C8—1722no—
861C22—21no—
862C22—21no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—861no—
867C22—861no—
868C22—861no—
869C22—861no—
870C22—861no—
871C22—861no—
872C22—1722no—
873C22—1722no—
874C22—1721no—
875C22—1721no—
876C22—1721no—
877C22C2×C22⋊C4×D4311yescharacteristic
878C22#1458346511yescharacteristic
879C22#1458347211yescharacteristic
880C4—21no—
881C4—21no—
882C4—21no—
883C4—41no—
884C4—41no—
885C4—41no—
886C4—82no—
887C4—432no—
888C4—861no—
889C4—861no—
890C4—861no—
891C4—861no—
892C4—861no—
893C4—3442no—
894C4—1721no—
895C4—1721no—
896C4—1721no—
897C4#1458291412yes—
898C4#1458337911yescharacteristic
899C4#1458338011yescharacteristic
900C4#1458347811yescharacteristic
901C4#1458347911yescharacteristic
902C2—21no—
903C2—21no—
904C2—81no—
905C2—3441no—
906C2—1721no—
907C2—1721no—
908C2#1913718411yescharacteristic
909C2#421×D4311yescharacteristic
910C2C2×#1458291411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1806C2
socleC22×C43C22×C22⋊C4
prime radical#19147888C2
cosocleC22×C4×C43C24
hypercenter#1806D43
hypocenterC43#21900
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. #19143227C2semidirect
3. #19136999C2semidirect
4. #19135537C2semidirect
5. #19135512C2semidirect
6. #19135042C2semidirect
7. #19135040C2semidirect
8. #19134616C2semidirect
9. #19134615C2semidirect
10. #19134612C2semidirect
11. C43×#1806C2semidirect
12. #14583453C4semidirect
13. #14583453C4semidirect
15. #14583446C4semidirect
16. #14583446C4semidirect
18. #14583436C4semidirect
19. #14583436C4semidirect
20. #14583431C4semidirect
21. #14583431C4semidirect
457. #1806D43semidirect
514. C43#21900semidirect

Maximal subgroups

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

subgroupindex
#191478882
#191432272
#191369992
#191355372
#191355122
#191350422
#191350402
#191346162
#191346152
#191346122
C43×#18062
#2190043