Finite Group Databasebeta

← #25063451

Subgroups — #25063451

Order 11008.

890 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148022C211yesmaximal, characteristic
2#19143714C211yesmaximal, characteristic, complemented
3#19143559C211yesmaximal, characteristic, complemented
4#19133066C211yesmaximal, characteristic, complemented
5#19133057C211yesmaximal, characteristic, complemented
6#19133052C211yesmaximal, characteristic, complemented
7#19133048C211yesmaximal, characteristic, complemented
8#19133041C211yesmaximal, characteristic, complemented
9#19133034C211yesmaximal, characteristic, complemented
10#19133025C211yesmaximal, characteristic, complemented
11#19133014C211yesmaximal, characteristic, complemented
12#19133005C211yesmaximal, characteristic, complemented
13#19133000C211yesmaximal, characteristic, complemented
14#19132996C211yesmaximal, characteristic, complemented
15C43×#1488C211yesmaximal, characteristic, complemented
16#14583527C411yescharacteristic
17#14583520—21no—
18#14583514C411yescharacteristic
19#14583514C411yescharacteristic
20#14583511—21no—
21#14583507C411yescharacteristic
22#14583507C411yescharacteristic
23#14583491—21no—
24#14583491—21no—
25#14583477C411yescharacteristic
26#14583475C411yescharacteristic
27#14583470C411yescharacteristic
28#14583456—21no—
29#14583453C2211yescharacteristic
30#14583453C2211yescharacteristic
31#14583433—21no—
32#14583431C2211yescharacteristic
33#14583431C2211yescharacteristic
34#14583429—21no—
35#14583429—21no—
36C4×#10621898C2211yescharacteristic
37C2×C4×Dic86C2211yescharacteristic
38#14583028—21no—
39#14583027—21no—
40#14582974—21no—
41#14582974—21no—
42#14582973—21no—
43#14582973—21no—
44#14582972—21no—
45#14582969—21no—
46#14582955C2211yescharacteristic
47#14582951C2211yescharacteristic
48#14582950C2211yescharacteristic
49#14582950C2211yescharacteristic
50#14582923C2211yescharacteristic
51#14582921C2211yescharacteristic
52C4⋊C8×D43C2211yescharacteristic
53C4×#10621877C2211yescharacteristic
54C4×#10621872C2211yescharacteristic
55C4×C8×D43C2211yescharacteristic
56#14582631C2211yescharacteristic
57#14582631C2211yescharacteristic
58#14582631C2211yescharacteristic
59#14582631C2211yescharacteristic
60Q8⋊(C43⋊C8)C2211yescharacteristic
61Q8⋊(C43⋊C8)C2211yescharacteristic
62#14582629C2211yescharacteristic
63#14582629C2211yescharacteristic
64#14582629C2211yescharacteristic
65#14582629C2211yescharacteristic
66D4⋊(C43⋊C8)C2211yescharacteristic
67D4⋊(C43⋊C8)C2211yescharacteristic
68C4×#41×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic
70C43×#431C2211yescharacteristic
71C43×Q8⋊C8C2211yescharacteristic
72C43×Q8⋊C8C2211yescharacteristic
73C43×D4⋊C8C2211yescharacteristic
74C43×D4⋊C8C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic
76C22×Dic86C2×C411yescharacteristic
77C2×#10621877—21no—
78C2×#10621877—21no—
79C2×#10621872—21no—
80C2×#10621872—21no—
81C2×C8×D43—21no—
82C2×C8×D43—21no—
83#13063325—21no—
84#13063325—21no—
85#13063324C2×C411yescharacteristic
86#13063324C2×C411yescharacteristic
87#13063323C2×C411yescharacteristic
88#13063323C2×C411yescharacteristic
89#13063320—21no—
90#13063320—21no—
91#13063319—21no—
92#13063319—21no—
93#13063318—21no—
94#13063318—21no—
95#13063318—21no—
96#13063318—21no—
97#13063317—21no—
98#13063317—21no—
99#13063317—21no—
100#13063316C2×C411yescharacteristic
101#13063316C2×C411yescharacteristic
102#13063315—21no—
103#13063315—21no—
104#13063315—21no—
105#13063315—21no—
106#13063313—21no—
107#13063312C2×C411yescharacteristic
108#13063312C2×C411yescharacteristic
109#13063311—21no—
110#13063311—21no—
111#13063309—21no—
112#13063309—21no—
113#13063308—21no—
114#13063308—21no—
115#13063307—21no—
116#13063307—21no—
117#13063306—21no—
118#13063306—21no—
119#13063305C2×C411yescharacteristic
120#13063305C2×C411yescharacteristic
121#13063305C2×C411yescharacteristic
122#13063305C2×C411yescharacteristic
123#13063304—21no—
124#13063304—21no—
125#13063304—21no—
126#13063304—21no—
127#13063304—21no—
128#13063303—21no—
129#13063303—21no—
130#13063302—21no—
131#13063302—21no—
132#13063301C2×C411yescharacteristic
133#13063301C2×C411yescharacteristic
134#13063299—21no—
135#13063297—21no—
136#13063297—21no—
137#13063296C2×C411yescharacteristic
138#13063296C2×C411yescharacteristic
139C4×Dic86—21no—
140C4×Dic86—21no—
141C4×Dic86—21no—
142C4×Dic86—21no—
143C4×Dic86C2×C411yescharacteristic
144C4×Dic86C2×C411yescharacteristic
145C4×Dic86D411yescharacteristic
146C4×Dic86D411yescharacteristic
147C4×Dic86C2311yescharacteristic
148C4×Dic86C2311yescharacteristic
149C4×D172D411yescharacteristic
150C4×D172D411yescharacteristic
151C4×C22⋊D43—21no—
152C4×C22⋊D43—21no—
153C4×C22⋊D43D411yescharacteristic
154C4×C22⋊D43D411yescharacteristic
155C4×C22⋊D43D411yescharacteristic
156C4×C22⋊D43D411yescharacteristic
157#13063284—21no—
158#13063284—21no—
159#13063284C2×C411yescharacteristic
160#13063282—21no—
161#13063282—21no—
162#13063282C2×C411yescharacteristic
163#13063282C2×C411yescharacteristic
164C2×C4⋊Dic43C2×C411yescharacteristic
165C2×Dic43⋊C4—21no—
166C2×C4×Dic43—21no—
167C42×D43C2311yescharacteristic
168C42×D43C2311yescharacteristic
169C4⋊(C43⋊C8)—21no—
170C4⋊(C43⋊C8)C2311yescharacteristic
171C4⋊(C43⋊C8)C2311yescharacteristic
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180#13063236—21no—
181#13063235—21no—
182#13063235—21no—
183C4×C43⋊C8C2311yescharacteristic
184C4×C43⋊C8C2311yescharacteristic
185C8×Dic43—21no—
186C8×Dic43—21no—
187C2×#41×C43C2×C411yescharacteristic
188C4×Q8×C43C2×C411yescharacteristic
189C4×Q8×C43C2311yescharacteristic
190C4×D4×C43—21no—
191C4×D4×C43—21no—
192C4×D4×C43C2×C411yescharacteristic
193C4×D4×C43C2311yescharacteristic
194#117×C43—21no—
195#117×C43C2×C411yescharacteristic
196C2×C42×C43—21no—
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C4⋊C8×C43C2311yescharacteristic
200C4⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43—21no—
202C22⋊C8×C43—21no—
203#97×C43—21no—
204C4×C8×C43C2311yescharacteristic
205C4×C8×C43C2311yescharacteristic
206#41×C43—42no—
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×C43C22×C411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43C22⋊C411yescharacteristic
219C2×C22⋊D43C22⋊C411yescharacteristic
220C22×Dic43—21no—
221C22×Dic43—21no—
222#10621898—42no—
223C2×D172C22⋊C411yescharacteristic
224C2×C4×D43C22×C411yescharacteristic
225C2×C4×D43C22×C411yescharacteristic
226C2×C4×D43C2×D411yescharacteristic
227C2×C4×D43C2×D411yescharacteristic
228C2×C4×D43C2×D411yescharacteristic
229C2×C4×D43C2×D411yescharacteristic
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86—42no—
234C2×Dic86C22⋊C411yescharacteristic
235C2×Dic86C22×C411yescharacteristic
236C2×Dic86C22×C411yescharacteristic
237C2×C8×C43—21no—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43C22×C411yescharacteristic
244C4⋊C4×C43C22×C411yescharacteristic
245C22⋊C4×C43—21no—
246C22⋊C4×C43—21no—
247C22⋊C4×C43—21no—
248C42×C43—21no—
249C42×C43—21no—
250C42×C43—21no—
251C42×C43C22×C411yescharacteristic
252C42×C43C2×D411yescharacteristic
253C42×C43C2×D411yescharacteristic
254C42×C43C2411yescharacteristic
255C22⋊Dic43—21no—
256C22⋊Dic43—21no—
257C22⋊Dic43—21no—
258C22⋊Dic43—21no—
259C22⋊Dic43—21no—
260C22⋊Dic43—21no—
261C22⋊Dic43C22⋊C411yescharacteristic
262C22⋊Dic43C22⋊C411yescharacteristic
263(C2×D43)⋊C4—21no—
264(C2×D43)⋊C4—21no—
265(C2×D43)⋊C4—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—21no—
268(C2×D43)⋊C4—21no—
269(C2×D43)⋊C4C22⋊C411yescharacteristic
270(C2×D43)⋊C4C22⋊C411yescharacteristic
271(C2×D43)⋊C4C22⋊C411yescharacteristic
272(C2×D43)⋊C4C22⋊C411yescharacteristic
273C4⋊Dic43—21no—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43C22⋊C411yescharacteristic
281C4⋊Dic43C22⋊C411yescharacteristic
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—21no—
295Dic43⋊C4—21no—
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4C22⋊C411yescharacteristic
299Dic43⋊C4C22⋊C411yescharacteristic
300Dic43⋊C4C22⋊C411yescharacteristic
301Dic43⋊C4C22⋊C411yescharacteristic
302C4×Dic43—21no—
303C4×Dic43—21no—
304C4×Dic43—21no—
305C4×Dic43—21no—
306C4×Dic43C22×C411yescharacteristic
307C4×Dic43C22×C411yescharacteristic
308C4×Dic43C2×D411yescharacteristic
309C4×Dic43C2×D411yescharacteristic
310C4×Dic43C2×D411yescharacteristic
311C4×Dic43C2×D411yescharacteristic
312#10621877—42no—
313#10621877—81no—
314C2×C43⋊C8—21no—
315C2×C43⋊C8—21no—
316C2×C43⋊C8—21no—
317C2×C43⋊C8—21no—
318#10621872—42no—
319#10621872—81no—
320C8×D43—42no—
321C8×D43—81no—
322C23×C43—21no—
323C23×C43C2×C22⋊C411yescharacteristic
324C22×D43C2×C22⋊C411yescharacteristic
325C22×D43C2×C22⋊C411yescharacteristic
326Q8×C43—22no—
327D4×C43—22no—
328D4×C43—42no—
329C2×C4×C43—22no—
330C2×C4×C43—21no—
331C2×C4×C43—21no—
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—81no—
340C2×C4×C43C2×C22⋊C411yescharacteristic
341C2×C4×C43C2×C22⋊C411yescharacteristic
342C2×C4×C43C2×C22⋊C411yescharacteristic
343C2×C4×C43C23×C411yescharacteristic
344C2×C4×C43C22×D411yescharacteristic
345C2×C4×C43C22×D411yescharacteristic
346C22⋊D43—41no—
347C22⋊D43—41no—
348C22⋊D43—81no—
349C22⋊D43—81no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—42no—
355C2×Dic43—81no—
356C2×Dic43C2×C22⋊C411yescharacteristic
357C2×Dic43C2×C22⋊C411yescharacteristic
358C2×Dic43C2×C22⋊C411yescharacteristic
359C2×Dic43C2×C22⋊C411yescharacteristic
360C2×Dic43C2×C22⋊C411yescharacteristic
361C2×Dic43C2×C22⋊C411yescharacteristic
362D172—41no—
363C4×D43—22no—
364C4×D43—22no—
365C4×D43—21no—
366C4×D43—21no—
367C4×D43—21no—
368C4×D43—21no—
369C4×D43—41no—
370C4×D43—41no—
371Dic86—22no—
372Dic86—22no—
373Dic86—41no—
374Dic86—42no—
375Dic86—81no—
376Dic86—81no—
377C8×C43—41no—
378C8×C43—41no—
379C8×C43—41no—
380C8×C43—41no—
381C43⋊C8—22no—
382C43⋊C8—41no—
383C43⋊C8—41no—
384C43⋊C8—41no—
385#17506—431nomaximal, Sylow
386C22×C43—21no—
387C22×C43—21no—
388C22×C43—21no—
389C22×C43—41no—
390C22×C43—41no—
391C22×C43—41no—
392C22×C43C22×C22⋊C411yescharacteristic
393C2×D43—21no—
394C2×D43—21no—
395C2×D43—21no—
396C2×D43—21no—
397C2×D43—21no—
398C2×D43—21no—
399C4×C43—21no—
400C4×C43—21no—
401C4×C43—21no—
402C4×C43—21no—
403C4×C43—41no—
404C4×C43—41no—
405C4×C43—41no—
406C4×C43#56812yes—
407C4×C43#57711yescharacteristic
408C4×C43#57811yescharacteristic
409Dic43—21no—
410Dic43—21no—
411Dic43—21no—
412Dic43—21no—
413Dic43—21no—
414Dic43—21no—
415Dic43—41no—
416Dic43—41no—
417Dic43—41no—
418Dic43—41no—
419#3461—431no—
420#2989—431no—
421#2965—431no—
422#1497—431no—
423#1495—431no—
424#1494—431no—
425#1493—431no—
426#1491—431no—
427#1489—431no—
428#1488D4311yescharacteristic, complemented
429#1487—431no—
430#1485—431no—
431#1483—431no—
432#1482—431no—
433#1481—431no—
434C2×C43—41no—
435C2×C43—81no—
436C2×C43#287911yescharacteristic
437C2×C43#289811yescharacteristic
438C2×C43#290111yescharacteristic
439D43—41no—
440D43—41no—
441#544—431no—
442#542—431no—
443#542—431no—
444#542—861no—
445#541—431no—
446#541—431no—
447#541—861no—
448#539—861no—
449#539—861no—
450#537—431no—
451#536—431no—
452#536—431no—
453#533—431no—
454#533—431no—
455#533—861no—
456#529—431no—
457#529—431no—
458#529—861no—
459#529—861no—
460#529—861no—
461C4×#41—431no—
462C4×#41C2×D4311yescharacteristic
463C2×C4×Q8—431no—
464#446—861no—
465#446—861no—
466#436—861no—
467#436—861no—
468#435—861no—
469#435—861no—
470#435—861no—
471#435—861no—
472#432—431no—
473#432C2×D4311yescharacteristic
474#431—431no—
475#431—431no—
476#431—431no—
477#431C2×D4311yescharacteristic
478#423—431no—
479#423—431no—
480C2×C4⋊C8—431no—
481C4×M16—431no—
482C4×M16—431no—
483C2×C4×C8—431no—
484Q8⋊C8—431no—
485Q8⋊C8—431no—
486Q8⋊C8—431no—
487Q8⋊C8—431no—
488Q8⋊C8—431no—
489Q8⋊C8—431no—
490Q8⋊C8—431no—
491Q8⋊C8—431no—
492Q8⋊C8—431no—
493Q8⋊C8—431no—
494Q8⋊C8C2×D4311yescharacteristic
495Q8⋊C8C2×D4311yescharacteristic
496D4⋊C8—431no—
497D4⋊C8—431no—
498D4⋊C8C2×D4311yescharacteristic
499D4⋊C8C2×D4311yescharacteristic
500C43#1750611yescharacteristic, complemented, Sylow
501C2×#41—431no—
502C2×#41C4×D4311yescharacteristic
503C22×Q8—431no—
504C2×M16—861no—
505C2×M16—861no—
506C2×M16—861no—
507C2×M16—861no—
508C22×C8—861no—
509C22×C8—861no—
510C4⋊Q8—431no—
511C4⋊Q8—431no—
512C4⋊Q8—431no—
513C4⋊Q8—431no—
514C4⋊Q8—861no—
515C4⋊Q8—861no—
516#126—861no—
517#126—861no—
518#126—861no—
519#126—861no—
520#126—861no—
521#126—861no—
522#126—861no—
523#126—861no—
524#125—431no—
525#125—431no—
526#125—861no—
527#125—861no—
528#125—861no—
529#125—861no—
530#125—861no—
531#125—861no—
532#125—861no—
533#124—431no—
534#124—431no—
535#124—861no—
536#124—861no—
537#124—861no—
538#123—861no—
539#123—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—431no—
551C22⋊Q8—431no—
552C22⋊Q8—861no—
553C22⋊Q8—861no—
554C22⋊Q8—861no—
555C22⋊Q8—861no—
556C22⋊Q8—861no—
557C22⋊Q8—861no—
558C22⋊Q8—861no—
559C22⋊Q8—861no—
560C22⋊Q8—861no—
561#121—431no—
562#121—431no—
563#121—861no—
564#121—861no—
565#121—861no—
566C4×Q8—431no—
567C4×Q8—431no—
568C4×Q8—431no—
569C4×Q8—431no—
570C4×Q8—431no—
571C4×Q8—431no—
572C4×Q8—861no—
573C4×Q8—861no—
574C4×Q8—861no—
575C4×Q8—861no—
576C4×Q8C4×D4311yescharacteristic
577C4×Q8C22×D4311yescharacteristic
578C4×D4—21no—
579C4×D4—21no—
580C4×D4—431no—
581C4×D4—431no—
582C4×D4—431no—
583C4×D4—431no—
584C4×D4—431no—
585C4×D4—431no—
586C4×D4—861no—
587C4×D4—861no—
588C4×D4C4×D4311yescharacteristic
589C4×D4C22×D4311yescharacteristic
590#117—21no—
591#117—431no—
592#117—431no—
593#117—431no—
594#117—861no—
595#117—861no—
596#117—861no—
597#117—861no—
598#117C4×D4311yescharacteristic
599C2×C4⋊C4—431no—
600C2×C4⋊C4—861no—
601C2×C42—21no—
602C2×C42—431no—
603C2×C42—431no—
604C2×C42—861no—
605C2×C42C22×D4311yescharacteristic
606C4⋊C8—21no—
607C4⋊C8—431no—
608C4⋊C8—431no—
609C4⋊C8—861no—
610C4⋊C8—861no—
611C4⋊C8—861no—
612C4⋊C8—861no—
613C4⋊C8—861no—
614C4⋊C8C22×D4311yescharacteristic
615C4⋊C8C22×D4311yescharacteristic
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—861no—
619C22⋊C8—861no—
620C22⋊C8—861no—
621C22⋊C8—861no—
622#97—21no—
623#97—861no—
624#97—861no—
625#97—861no—
626C4×C8—431no—
627C4×C8—431no—
628C4×C8—861no—
629C4×C8—861no—
630C4×C8C22×D4311yescharacteristic
631C4×C8C22×D4311yescharacteristic
632#41—42no—
633#41—1722no—
634C2×Q8—431no—
635C2×Q8—431no—
636C2×Q8—431no—
637C2×Q8—861no—
638C2×Q8—861no—
639C2×Q8—861no—
640C2×Q8—1722no—
641C2×Q8C2×C4×D4311yescharacteristic
642C2×D4—21no—
643C2×D4—431no—
644C2×D4—431no—
645C2×D4—431no—
646C2×D4—861no—
647C2×D4—861no—
648C2×D4C2×C4×D4311yescharacteristic
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—431no—
653C22×C4—431no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4C2×C4×D4311yescharacteristic
661C22×C4D4×D4311yescharacteristic
662C22×C4D4×D4311yescharacteristic
663M16—3441no—
664M16—3441no—
665M16—1722no—
666M16—1722no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—861no—
672C2×C8—861no—
673C2×C8—861no—
674C2×C8—861no—
675C2×C8—3441no—
676C2×C8—1722no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—431no—
680C4⋊C4—431no—
681C4⋊C4—431no—
682C4⋊C4—431no—
683C4⋊C4—431no—
684C4⋊C4—431no—
685C4⋊C4—431no—
686C4⋊C4—431no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4—861no—
690C4⋊C4—861no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—861no—
700C4⋊C4—861no—
701C4⋊C4—861no—
702C4⋊C4—861no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C4⋊C4—861no—
708C4⋊C4C2×C4×D4311yescharacteristic
709C4⋊C4C2×C4×D4311yescharacteristic
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—431no—
714C22⋊C4—431no—
715C22⋊C4—431no—
716C22⋊C4—431no—
717C22⋊C4—431no—
718C22⋊C4—431no—
719C22⋊C4—861no—
720C22⋊C4—861no—
721C22⋊C4—861no—
722C22⋊C4—861no—
723C22⋊C4—861no—
724C22⋊C4—861no—
725C22⋊C4—861no—
726C22⋊C4—861no—
727C22⋊C4—861no—
728C22⋊C4—861no—
729C22⋊C4—861no—
730C22⋊C4—861no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—431no—
735C42—431no—
736C42—431no—
737C42—431no—
738C42—431no—
739C42—431no—
740C42—861no—
741C42—861no—
742C42—861no—
743C42—861no—
744C42C2×C4×D4311yescharacteristic
745C42D4×D4311yescharacteristic
746C42D4×D4311yescharacteristic
747C42C23×D4311yescharacteristic
748C23—21no—
749C23—431no—
750C23—431no—
751C23C22⋊C4×D4311yescharacteristic
752Q8—22no—
753Q8—862no—
754Q8—862no—
755Q8—3441no—
756Q8—3441no—
757Q8—1721no—
758Q8—1722no—
759D4—22no—
760D4—42no—
761D4—3441no—
762D4—3441no—
763D4—1721no—
764D4—1721no—
765D4—1721no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—81no—
777C2×C4—431no—
778C2×C4—431no—
779C2×C4—431no—
780C2×C4—431no—
781C2×C4—431no—
782C2×C4—431no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—861no—
786C2×C4—861no—
787C2×C4—861no—
788C2×C4—861no—
789C2×C4—861no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—861no—
793C2×C4—3441no—
794C2×C4—1721no—
795C2×C4—1721no—
796C2×C4—1722no—
797C2×C4C22⋊C4×D4311yescharacteristic
798C2×C4C22⋊C4×D4311yescharacteristic
799C2×C4C22⋊C4×D4311yescharacteristic
800C2×C4C22×C4×D4311yescharacteristic
801C2×C4C2×D4×D4311yescharacteristic
802C2×C4C2×D4×D4311yescharacteristic
803C8—41no—
804C8—41no—
805C8—41no—
806C8—41no—
807C8—862no—
808C8—1721no—
809C8—1721no—
810C8—1721no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—41no—
815C22—41no—
816C22—41no—
817C22—861no—
818C22—861no—
819C22—861no—
820C22—861no—
821C22—861no—
822C22—861no—
823C22C2×C22⋊C4×D4311yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—41no—
829C4—41no—
830C4—41no—
831C4—861no—
832C4—861no—
833C4—861no—
834C4—861no—
835C4—861no—
836C4—861no—
837C4—1721no—
838C4—1721no—
839C4—1721no—
840C4—1721no—
841C4#1458366512yes—
842C4#1458370611yescharacteristic
843C4#1458371311yescharacteristic
844C2—41no—
845C2—81no—
846C2—1721no—
847C2—1721no—
848C2#1914303811yescharacteristic
849C2#1914312411yescharacteristic
850C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1488C2
socleC22×C43C22×C22⋊C4
prime radical#14583477C4
cosocleC42×C43C24
hypercenter#1488D43
hypocenterC43#17506
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #19143714C2semidirect
3. #19143559C2semidirect
4. #19133066C2semidirect
5. #19133057C2semidirect
6. #19133052C2semidirect
7. #19133048C2semidirect
8. #19133041C2semidirect
9. #19133034C2semidirect
10. #19133025C2semidirect
11. #19133014C2semidirect
12. #19133005C2semidirect
13. #19133000C2semidirect
14. #19132996C2semidirect
15. C43×#1488C2semidirect
428. #1488D43semidirect
500. C43#17506semidirect

Maximal subgroups

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

subgroupindex
#191480222
#191437142
#191435592
#191330662
#191330572
#191330522
#191330482
#191330412
#191330342
#191330252
#191330142
#191330052
#191330002
#191329962
C43×#14882
#1750643