Finite Group Databasebeta

← #25249358

Subgroups — #25249358

Order 11008.

1240 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148236C211yesmaximal, characteristic
2#19143071C211yesmaximal, characteristic, complemented
3#19143053C211yesmaximal, characteristic, complemented
4#19136247C212yesmaximal, complemented
5#19136241C211yesmaximal, characteristic, complemented
6#19136238C212yesmaximal, complemented
7#19136233C212yesmaximal, complemented
8C2×#14582690C211yesmaximal, characteristic, complemented
9C2×#14582688C211yesmaximal, characteristic, complemented
10#352×D43C212yesmaximal, complemented
11C43×#2121C211yesmaximal, characteristic, complemented
12C2×#13063370C2211yescharacteristic
13C22×#10621900C411yescharacteristic, complemented
14#14583665—21no—
15#14583549—21no—
16#14583549—21no—
17#14583547—21no—
18#14583547—21no—
19#14583538—21no—
20#14583538—21no—
21#14583536—21no—
22#14583536—21no—
23#14583471C411yescharacteristic, complemented
24#14583471C2211yescharacteristic
25#14583459C411yescharacteristic, complemented
26#14583459C2211yescharacteristic
27#14583458C411yescharacteristic, complemented
28#14583405C411yescharacteristic, complemented
29#14583405C2211yescharacteristic
30C2×#13063309C411yescharacteristic, complemented
31C2×#13063306C2211yescharacteristic
32#123×D43C411yescharacteristic, complemented
33#123×D43C2211yescharacteristic
34#14583372—21no—
35#14583372C411yescharacteristic, complemented
36#14582881—21no—
37#14582880—21no—
38#14582880C2212yes—
39C2×#13063242C2211yescharacteristic
40#100×D43—21no—
41#100×D43C2212yes—
42#14582871—21no—
43#14582871C2212yes—
44C2×#13063240C2211yescharacteristic
45C2×#13063239—21no—
46#99×D43—21no—
47#99×D43C2212yes—
48#14582690C2212yescomplemented
49#14582690C2212yescomplemented
50#14582689C2212yescomplemented
51#14582688C2212yescomplemented
52#14582688C2212yescomplemented
53#14582686C2212yescomplemented
54C43×#534C2211yescharacteristic
55C2×#100×C43C2211yescharacteristic
56C2×#99×C43C2211yescharacteristic
57C43×#352C2212yescomplemented
58C43×AΣL(1,𝔽16)C2212yescomplemented
59#13063370—42no—
60#13063370—42no—
61C2×#10621898D411yescharacteristic
62C2×#10621898D411yescharacteristic
63C2×#10621900—21no—
64C2×#10621900—21no—
65C2×#10621900—21no—
66C2×#10621900—21no—
67C2×#10621900—42no—
68C2×#10621900—42no—
69C2×#10621900C2×C411yescharacteristic
70C2×#10621900D411yescharacteristic
71C2×#10621900D411yescharacteristic
72C2×#10621900C2311yescharacteristic
73C22×Dic86C2×C411yescharacteristic, complemented
74C22×C22⋊D43C2×C411yescharacteristic
75C22×C22⋊D43C2×C411yescharacteristic
76C22×C22⋊D43C2×C411yescharacteristic, complemented
77C22×C22⋊D43D411yescharacteristic
78C22×C22⋊D43D411yescharacteristic
79C2×D4×D43C2×C411yescharacteristic
80C2×D4×D43D411yescharacteristic
81C2×D4×D43D411yescharacteristic
82C2×D4×D43C2311yescharacteristic
83C23×Dic43C2×C411yescharacteristic, complemented
84C23×Dic43C2×C411yescharacteristic, complemented
85C22×C4×D43C2×C411yescharacteristic, complemented
86#13063333—42no—
87#13063331—42no—
88C2×#10621877—21no—
89M16×D43—22no—
90M16×D43—22no—
91#13063324—21no—
92#13063324—21no—
93#13063311—21no—
94#13063311—21no—
95#13063310—21no—
96#13063310—21no—
97#13063309—21no—
98#13063309—21no—
99#13063309C2×C411yescharacteristic, complemented
100#13063309C2×C411yescharacteristic, complemented
101#13063309C2×C411yescharacteristic, complemented
102#13063309C2×C411yescharacteristic, complemented
103#13063308C2×C411yescharacteristic, complemented
104#13063308C2×C411yescharacteristic, complemented
105#13063307—21no—
106#13063307—21no—
107#13063307—21no—
108#13063307—21no—
109#13063306—21no—
110#13063306—21no—
111#13063306—21no—
112#13063306C2×C411yescharacteristic, complemented
113#13063306C2×C411yescharacteristic, complemented
114#13063306C2311yescharacteristic
115#13063306C2311yescharacteristic
116#13063303—21no—
117#13063303—21no—
118#13063302—21no—
119#13063302—21no—
120#13063302—21no—
121#13063302—21no—
122#13063298—21no—
123#13063298—21no—
124#13063297—21no—
125#13063297—21no—
126#13063297—21no—
127#13063297—21no—
128#13063296—21no—
129#13063296—21no—
130#13063294C2×C411yescharacteristic, complemented
131#13063294C2×C411yescharacteristic, complemented
132#13063293—21no—
133#13063293—21no—
134#13063293—21no—
135D4×Dic43—21no—
136D4×Dic43—21no—
137C4×C22⋊D43—21no—
138C4×C22⋊D43—21no—
139C4×C22⋊D43—42no—
140(C22⋊D43)⋊C4—21no—
141(C22⋊D43)⋊C4—21no—
142(C22⋊D43)⋊C4—21no—
143(C22⋊D43)⋊C4—21no—
144(C22⋊D43)⋊C4—42no—
145#13063281—22no—
146#13063281C2×C411yescharacteristic, complemented
147#13063281C2×C411yescharacteristic, complemented
148C2×C4⋊Dic43—21no—
149C2×Dic43⋊C4—21no—
150C4⋊C4×D43—21no—
151C4⋊C4×D43—21no—
152C2×C22⋊Dic43—21no—
153C2×C22⋊Dic43—21no—
154C2×C22⋊Dic43C2×C411yescharacteristic, complemented
155C2×(C2×D43)⋊C4—21no—
156C22⋊C4×D43—21no—
157C22⋊C4×D43—21no—
158C22⋊C4×D43—22no—
159C22⋊C4×D43C2×C411yescharacteristic, complemented
160C22⋊C4×D43C2×C411yescharacteristic, complemented
161#13063243—22no—
162#13063242—21no—
163#13063242C2312yes—
164#13063241—22no—
165#13063240—21no—
166#13063240C2312yes—
167#13063239—22no—
168#13063239—22no—
169C22×D4×C43C2×C411yescharacteristic, complemented
170C22×D4×C43C2311yescharacteristic
171C2×M16×C43—21no—
172#123×C43—21no—
173#123×C43C2×C411yescharacteristic, complemented
174#123×C43C2311yescharacteristic
175#121×C43—21no—
176#121×C43—21no—
177#120×C43—21no—
178#120×C43C2×C411yescharacteristic, complemented
179#120×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43C2×C411yescharacteristic, complemented
182#100×C43—21no—
183#100×C43C2312yes—
184#99×C43—21no—
185#99×C43C2312yes—
186C24×C43C22×C411yescharacteristic
187C24×C43C22×C411yescharacteristic
188C24×C43C2×D411yescharacteristic
189C23×D43C22⋊C411yescharacteristic
190C23×D43C22⋊C411yescharacteristic
191C23×D43C22×C411yescharacteristic
192C23×D43C2×D411yescharacteristic
193C2×D4×C43—21no—
194C2×D4×C43—21no—
195C2×D4×C43—21no—
196C2×D4×C43—21no—
197C2×D4×C43—41no—
198C2×D4×C43—41no—
199C2×D4×C43—41no—
200C2×D4×C43—41no—
201C2×D4×C43C22×C411yescharacteristic
202C2×D4×C43C2×D411yescharacteristic
203C2×D4×C43C2×D411yescharacteristic
204C2×D4×C43C2411yescharacteristic
205C22×C4×C43—21no—
206C22×C4×C43—41no—
207C22×C4×C43C22×C411yescharacteristic
208C22×C4×C43C2×D411yescharacteristic
209C2×C22⋊D43—22no—
210C2×C22⋊D43—22no—
211C2×C22⋊D43—22no—
212C2×C22⋊D43—22no—
213C2×C22⋊D43—21no—
214C2×C22⋊D43—21no—
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C2×C22⋊D43—42no—
218C2×C22⋊D43—41no—
219C2×C22⋊D43—41no—
220C2×C22⋊D43—41no—
221C2×C22⋊D43—41no—
222C2×C22⋊D43C22⋊C411yescharacteristic
223C2×C22⋊D43C22⋊C411yescharacteristic
224C2×C22⋊D43C22⋊C411yescharacteristic
225C2×C22⋊D43C22⋊C411yescharacteristic
226C2×C22⋊D43C22⋊C411yescharacteristic
227C2×C22⋊D43C22⋊C411yescharacteristic
228C2×C22⋊D43C22⋊C411yescharacteristic
229C2×C22⋊D43C22⋊C411yescharacteristic
230C2×C22⋊D43C22×C411yescharacteristic
231C2×C22⋊D43C22×C411yescharacteristic
232C2×C22⋊D43C2×D411yescharacteristic
233C2×C22⋊D43C2×D411yescharacteristic
234C22×Dic43—21no—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43—41no—
240C22×Dic43—41no—
241C22×Dic43—41no—
242C22×Dic43—42no—
243C22×Dic43C22⋊C411yescharacteristic
244C22×Dic43C22⋊C411yescharacteristic
245C22×Dic43C22×C411yescharacteristic
246C22×Dic43C22×C411yescharacteristic
247C22×Dic43C22×C411yescharacteristic
248C22×Dic43C2×D411yescharacteristic
249#10621900—42no—
250#10621900—42no—
251#10621900—42no—
252#10621900—42no—
253#10621900—42no—
254#10621900—42no—
255#10621900—44no—
256#10621900—44no—
257#10621900—42no—
258#10621900—42no—
259D4×D43—42no—
260D4×D43—42no—
261D4×D43—42no—
262D4×D43—42no—
263#10621898—22no—
264#10621898—22no—
265#10621898—41no—
266#10621898—41no—
267C2×D172C22⋊C411yescharacteristic
268C2×D172C2×D411yescharacteristic
269C2×C4×D43—21no—
270C2×C4×D43—21no—
271C2×C4×D43—21no—
272C2×C4×D43—21no—
273C2×C4×D43—42no—
274C2×C4×D43—42no—
275C2×C4×D43C22⋊C411yescharacteristic
276C2×C4×D43C22⋊C411yescharacteristic
277C2×C4×D43C2×D411yescharacteristic
278C2×C4×D43C2×D411yescharacteristic
279C2×Dic86—21no—
280C2×Dic86—21no—
281C2×Dic86—42no—
282C2×Dic86C22⋊C411yescharacteristic
283C2×Dic86C2×D411yescharacteristic
284M16×C43—22no—
285M16×C43—41no—
286C2×C8×C43—41no—
287C4⋊C4×C43—21no—
288C4⋊C4×C43—21no—
289C22⋊C4×C43—21no—
290C22⋊C4×C43—21no—
291C22⋊C4×C43—21no—
292C22⋊C4×C43—21no—
293C22⋊C4×C43—21no—
294C22⋊C4×C43—22no—
295C22⋊C4×C43—41no—
296C22⋊C4×C43C22×C411yescharacteristic
297C22⋊C4×C43C22×C411yescharacteristic
298C22⋊Dic43—21no—
299C22⋊Dic43—21no—
300C22⋊Dic43—21no—
301C22⋊Dic43—21no—
302C22⋊Dic43—21no—
303C22⋊Dic43—21no—
304C22⋊Dic43—21no—
305C22⋊Dic43—22no—
306C22⋊Dic43—41no—
307C22⋊Dic43C22×C411yescharacteristic
308C22⋊Dic43C22×C411yescharacteristic
309(C2×D43)⋊C4—21no—
310(C2×D43)⋊C4—21no—
311(C2×D43)⋊C4—21no—
312(C2×D43)⋊C4—21no—
313(C2×D43)⋊C4—21no—
314(C2×D43)⋊C4—21no—
315(C2×D43)⋊C4—21no—
316(C2×D43)⋊C4—21no—
317(C2×D43)⋊C4—42no—
318C4⋊Dic43—21no—
319C4⋊Dic43—21no—
320C4⋊Dic43—21no—
321C4⋊Dic43—21no—
322Dic43⋊C4—21no—
323Dic43⋊C4—21no—
324Dic43⋊C4—21no—
325Dic43⋊C4—21no—
326Dic43⋊C4—21no—
327Dic43⋊C4—21no—
328Dic43⋊C4—21no—
329Dic43⋊C4—21no—
330Dic43⋊C4—42no—
331C4×Dic43—21no—
332C4×Dic43—21no—
333C4×Dic43—42no—
334#10621877—22no—
335#10621877—41no—
336C2×C43⋊C8—41no—
337#10621872—42no—
338#10621872—42no—
339C8×D43—42no—
340C8×D43—42no—
341C23×C43—21no—
342C23×C43—21no—
343C23×C43—21no—
344C23×C43—21no—
345C23×C43—21no—
346C23×C43—41no—
347C23×C43—81no—
348C23×C43—81no—
349C23×C43—81no—
350C23×C43C2×C22⋊C411yescharacteristic
351C23×C43C2×C22⋊C411yescharacteristic
352C23×C43C2×C22⋊C411yescharacteristic
353C23×C43C23×C411yescharacteristic
354C23×C43C22×D411yescharacteristic
355C22×D43—22no—
356C22×D43—22no—
357C22×D43—41no—
358C22×D43—41no—
359C22×D43—81no—
360C22×D43—81no—
361C22×D43—81no—
362C22×D43—81no—
363C22×D43C2×C22⋊C411yescharacteristic
364C22×D43C2×C22⋊C411yescharacteristic
365C22×D43C2×C22⋊C411yescharacteristic
366C22×D43C2×C22⋊C411yescharacteristic
367D4×C43—41no—
368D4×C43—41no—
369D4×C43—41no—
370D4×C43—41no—
371D4×C43—42no—
372D4×C43—41no—
373D4×C43—41no—
374D4×C43—81no—
375D4×C43—81no—
376C2×C4×C43—21no—
377C2×C4×C43—21no—
378C2×C4×C43—21no—
379C2×C4×C43—21no—
380C2×C4×C43—21no—
381C2×C4×C43—41no—
382C2×C4×C43—42no—
383C2×C4×C43—81no—
384C2×C4×C43—161no—
385C2×C4×C43C2×C22⋊C411yescharacteristic
386C2×C4×C43C22×D411yescharacteristic
387C22⋊D43—21no—
388C22⋊D43—21no—
389C22⋊D43—21no—
390C22⋊D43—21no—
391C22⋊D43—21no—
392C22⋊D43—21no—
393C22⋊D43—22no—
394C22⋊D43—22no—
395C22⋊D43—22no—
396C22⋊D43—22no—
397C22⋊D43—41no—
398C22⋊D43—41no—
399C22⋊D43—41no—
400C22⋊D43—41no—
401C22⋊D43—42no—
402C22⋊D43—42no—
403C22⋊D43—81no—
404C22⋊D43—81no—
405C22⋊D43#9912yes—
406C22⋊D43#9912yes—
407C2×Dic43—22no—
408C2×Dic43—22no—
409C2×Dic43—21no—
410C2×Dic43—21no—
411C2×Dic43—21no—
412C2×Dic43—21no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—42no—
416C2×Dic43—42no—
417C2×Dic43—41no—
418C2×Dic43—41no—
419C2×Dic43—42no—
420C2×Dic43—41no—
421C2×Dic43—41no—
422C2×Dic43—42no—
423C2×Dic43—81no—
424C2×Dic43—161no—
425C2×Dic43C2×C22⋊C411yescharacteristic
426C2×Dic43C2×C22⋊C411yescharacteristic
427C2×Dic43C2×C22⋊C411yescharacteristic
428C2×Dic43C2×C22⋊C411yescharacteristic
429D172—22no—
430D172—41no—
431C4×D43—22no—
432C4×D43—22no—
433C4×D43—41no—
434C4×D43—41no—
435C4×D43—42no—
436C4×D43—42no—
437C4×D43—81no—
438C4×D43—81no—
439C4×D43—162no—
440Dic86—22no—
441Dic86—41no—
442Dic86—42no—
443Dic86—42no—
444C8×C43—42no—
445C43⋊C8—42no—
446#33350—431nomaximal, Sylow
447C22×C43—21no—
448C22×C43—21no—
449C22×C43—21no—
450C22×C43—21no—
451C22×C43—41no—
452C22×C43—41no—
453C22×C43—41no—
454C22×C43—41no—
455C22×C43—41no—
456C22×C43—41no—
457C22×C43—41no—
458C22×C43—41no—
459C22×C43—81no—
460C22×C43—81no—
461C22×C43—81no—
462C22×C43—81no—
463C22×C43—82no—
464C22×C43C2×#9911yescharacteristic
465C22×C43C2×#9911yescharacteristic
466C22×C43C22×C22⋊C411yescharacteristic
467C2×D43—21no—
468C2×D43—21no—
469C2×D43—21no—
470C2×D43—41no—
471C2×D43—41no—
472C2×D43—41no—
473C2×D43—41no—
474C2×D43—82no—
475C2×D43—82no—
476C2×D43—161no—
477C2×D43—161no—
478C2×D43C2×#9912yes—
479C4×C43—21no—
480C4×C43—21no—
481C4×C43—41no—
482C4×C43—41no—
483C4×C43—41no—
484C4×C43—82no—
485Dic43—21no—
486Dic43—21no—
487Dic43—21no—
488Dic43—41no—
489Dic43—41no—
490Dic43—41no—
491Dic43—41no—
492Dic43—82no—
493Dic43C2×#9912yes—
494#3485—431no—
495#2888—431no—
496#2883—431no—
497#2123—432no—
498#2121—432no—
499#2121—431no—
500#2121D4311yescharacteristic, complemented
501#2120—432no—
502C2×#352—431no—
503C2×#352—431no—
504C2×#352—432no—
505C2×C43—21no—
506C2×C43—21no—
507C2×C43—21no—
508C2×C43—41no—
509C2×C43—41no—
510C2×C43—41no—
511C2×C43—41no—
512C2×C43—81no—
513C2×C43C22×#9911yescharacteristic
514D43—22no—
515D43—41no—
516D43—41no—
517D43—41no—
518C2×H(5,𝔽2)—431no—
519C22×#41—431no—
520#568—861no—
521#547—861no—
522#547—861no—
523#547—861no—
524#547—861no—
525#546—861no—
526#546—861no—
527#546—861no—
528#546—861no—
529#536—431no—
530#536—431no—
531#534—431no—
532#534—431no—
533#534—431no—
534#534C2×D4311yescharacteristic
535#525—431no—
536#525—431no—
537C2×#123—431no—
538C2×#123—431no—
539C2×#123—431no—
540C2×#123—431no—
541#518—431no—
542#518—861no—
543#413—432no—
544#413—861no—
545#413—861no—
546C2×#100—431no—
547C2×#100—432no—
548C2×#100—861no—
549C2×#100C2×D4311yescharacteristic
550#410—432no—
551#410—861no—
552C2×#99—431no—
553C2×#99—432no—
554C2×#99—861no—
555C2×#99—861no—
556C2×#99C2×D4311yescharacteristic
557#352—432no—
558#352—432no—
559#352—432no—
560#352—432no—
561#352—432no—
562#352C2×D4312yescomplemented
563AΣL(1,𝔽16)—432no—
564AΣL(1,𝔽16)C2×D4312yescomplemented
565C43#3335011yescharacteristic, complemented, Sylow
566H(5,𝔽2)—1722no—
567H(5,𝔽2)—1722no—
568C2×#41—431no—
569C2×#41—431no—
570C2×#41—431no—
571C2×#41—431no—
572C2×#41—431no—
573C2×#41—431no—
574C2×#41—861no—
575C2×#41—861no—
576C2×#41—861no—
577C2×#41—861no—
578C2×#41—1722no—
579C2×#41—1722no—
580C22×Q8—431no—
581C22×D4—431no—
582C22×D4—431no—
583C22×D4—431no—
584C22×D4—431no—
585C22×D4—431no—
586C22×D4—431no—
587C22×D4—431no—
588C22×D4—431no—
589C22×D4—431no—
590C22×D4C4×D4311yescharacteristic, complemented
591C22×D4C22×D4311yescharacteristic
592C23×C4—431no—
593C23×C4—431no—
594C23×C4—431no—
595#131—1722no—
596#131—1722no—
597C2×M16—21no—
598C2×M16—862no—
599C2×M16—862no—
600C2×M16—861no—
601C4⋊Q8—861no—
602C4⋊Q8—861no—
603#124—861no—
604#124—861no—
605#123—21no—
606#123—431no—
607#123—431no—
608#123—431no—
609#123—431no—
610#123—431no—
611#123—431no—
612#123—431no—
613#123—431no—
614#123—431no—
615#123—431no—
616#123—861no—
617#123—861no—
618#123—861no—
619#123—861no—
620#123—861no—
621#123—861no—
622#123—861no—
623#123—861no—
624#123—861no—
625#123—861no—
626#123—861no—
627#123C4×D4311yescharacteristic, complemented
628#123C22×D4311yescharacteristic
629C22⋊Q8—861no—
630C22⋊Q8—861no—
631C22⋊Q8—861no—
632C22⋊Q8—861no—
633C22⋊Q8—861no—
634C22⋊Q8—861no—
635#121—21no—
636#121—21no—
637#121—861no—
638#121—861no—
639#121—861no—
640#121—861no—
641#121—861no—
642#121—861no—
643#121—861no—
644#121—861no—
645#120—21no—
646#120—431no—
647#120—431no—
648#120—861no—
649#120—861no—
650#120—861no—
651#120C4×D4311yescharacteristic, complemented
652#120C22×D4311yescharacteristic
653C4×D4—861no—
654C4×D4—861no—
655C4×D4—861no—
656C4×D4—861no—
657C4×D4—861no—
658C4×D4—861no—
659C4×D4—861no—
660C4×D4—861no—
661C4×D4—1722no—
662C4×D4—1722no—
663#117—431no—
664#117—431no—
665#117—862no—
666C2×C4⋊C4—861no—
667C2×C4⋊C4—861no—
668C2×C4⋊C4—861no—
669C2×C4⋊C4—861no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—431no—
672C2×C22⋊C4—431no—
673C2×C22⋊C4—431no—
674C2×C22⋊C4—861no—
675C2×C22⋊C4—861no—
676C2×C22⋊C4—862no—
677C2×C22⋊C4—861no—
678C2×C22⋊C4—861no—
679C2×C22⋊C4—861no—
680C2×C22⋊C4C4×D4311yescharacteristic, complemented
681#101—862no—
682#100—21no—
683#100—432no—
684#100—862no—
685#100—861no—
686#100C22×D4312yes—
687#99—21no—
688#99—432no—
689#99—862no—
690#99—862no—
691#99—861no—
692#99C22×D4312yes—
693C24—431no—
694C24—431no—
695C24—431no—
696C24—431no—
697C24C2×C4×D4311yescharacteristic
698C24C2×C4×D4311yescharacteristic
699C24D4×D4311yescharacteristic
700#41—862no—
701#41—862no—
702#41—1721no—
703#41—1721no—
704#41—1722no—
705#41—1722no—
706#41—1722no—
707#41—1722no—
708#41—1722no—
709#41—1722no—
710#41—1724no—
711#41—1724no—
712#41—1722no—
713#41—1722no—
714C2×Q8—431no—
715C2×Q8—431no—
716C2×Q8—861no—
717C2×Q8—861no—
718C2×Q8—1722no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—41no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4—41no—
727C2×D4—431no—
728C2×D4—431no—
729C2×D4—431no—
730C2×D4—431no—
731C2×D4—431no—
732C2×D4—431no—
733C2×D4—431no—
734C2×D4—431no—
735C2×D4—431no—
736C2×D4—431no—
737C2×D4—431no—
738C2×D4—431no—
739C2×D4—431no—
740C2×D4—431no—
741C2×D4—862no—
742C2×D4—862no—
743C2×D4—862no—
744C2×D4—862no—
745C2×D4—861no—
746C2×D4—861no—
747C2×D4—861no—
748C2×D4—861no—
749C2×D4—1722no—
750C2×D4—1722no—
751C2×D4—1722no—
752C2×D4—1722no—
753C2×D4—1721no—
754C2×D4—1721no—
755C2×D4—1721no—
756C2×D4—1721no—
757C2×D4—1722no—
758C2×D4C2×C4×D4311yescharacteristic
759C2×D4D4×D4311yescharacteristic
760C2×D4D4×D4311yescharacteristic
761C2×D4C23×D4311yescharacteristic
762C22×C4—21no—
763C22×C4—41no—
764C22×C4—431no—
765C22×C4—431no—
766C22×C4—431no—
767C22×C4—431no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—431no—
771C22×C4—431no—
772C22×C4—431no—
773C22×C4—431no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—861no—
783C22×C4—1722no—
784C22×C4—1722no—
785C22×C4—1722no—
786C22×C4—1721no—
787C22×C4—1721no—
788C22×C4—1721no—
789C22×C4C2×C4×D4311yescharacteristic
790C22×C4D4×D4311yescharacteristic
791M16—22no—
792M16—41no—
793M16—862no—
794M16—1722no—
795M16—1722no—
796M16—1721no—
797C2×C8—41no—
798C2×C8—1722no—
799C2×C8—1722no—
800C2×C8—1721no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—861no—
804C4⋊C4—861no—
805C4⋊C4—861no—
806C4⋊C4—861no—
807C4⋊C4—861no—
808C4⋊C4—861no—
809C4⋊C4—861no—
810C4⋊C4—861no—
811C4⋊C4—861no—
812C4⋊C4—861no—
813C4⋊C4—861no—
814C4⋊C4—861no—
815C4⋊C4—1722no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—22no—
822C22⋊C4—41no—
823C22⋊C4—431no—
824C22⋊C4—431no—
825C22⋊C4—861no—
826C22⋊C4—861no—
827C22⋊C4—861no—
828C22⋊C4—861no—
829C22⋊C4—861no—
830C22⋊C4—861no—
831C22⋊C4—861no—
832C22⋊C4—861no—
833C22⋊C4—861no—
834C22⋊C4—861no—
835C22⋊C4—861no—
836C22⋊C4—861no—
837C22⋊C4—861no—
838C22⋊C4—861no—
839C22⋊C4—861no—
840C22⋊C4—862no—
841C22⋊C4—1722no—
842C22⋊C4—1721no—
843C22⋊C4C2×C4×D4311yescharacteristic
844C22⋊C4C2×C4×D4311yescharacteristic
845C42—861no—
846C42—861no—
847C42—1722no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—41no—
854C23—81no—
855C23—81no—
856C23—81no—
857C23—431no—
858C23—431no—
859C23—431no—
860C23—431no—
861C23—862no—
862C23—862no—
863C23—3441no—
864C23—3441no—
865C23—3441no—
866C23—3441no—
867C23—1721no—
868C23—1721no—
869C23C22⋊C4×D4311yescharacteristic
870C23C22⋊C4×D4311yescharacteristic
871C23C22⋊C4×D4311yescharacteristic
872C23C22×C4×D4311yescharacteristic
873C23C2×D4×D4311yescharacteristic
874Q8—862no—
875Q8—1721no—
876Q8—1722no—
877Q8—1722no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—41no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—81no—
886D4—81no—
887D4—432no—
888D4—432no—
889D4—862no—
890D4—862no—
891D4—862no—
892D4—862no—
893D4—862no—
894D4—861no—
895D4—861no—
896D4—861no—
897D4—861no—
898D4—861no—
899D4—861no—
900D4—3441no—
901D4—3441no—
902D4—1721no—
903D4—1721no—
904D4—1721no—
905D4—1721no—
906D4—1721no—
907D4—1722no—
908D4—1722no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—41no—
915C2×C4—42no—
916C2×C4—81no—
917C2×C4—161no—
918C2×C4—431no—
919C2×C4—431no—
920C2×C4—431no—
921C2×C4—431no—
922C2×C4—862no—
923C2×C4—862no—
924C2×C4—862no—
925C2×C4—862no—
926C2×C4—861no—
927C2×C4—861no—
928C2×C4—861no—
929C2×C4—861no—
930C2×C4—3441no—
931C2×C4—3441no—
932C2×C4—3441no—
933C2×C4—1721no—
934C2×C4—1721no—
935C2×C4—1722no—
936C2×C4—1722no—
937C2×C4—1722no—
938C2×C4—1721no—
939C2×C4—1721no—
940C2×C4—1722no—
941C2×C4—1722no—
942C2×C4—1722no—
943C2×C4—1721no—
944C2×C4—1721no—
945C2×C4—1721no—
946C2×C4—1721no—
947C2×C4—6882no—
948C2×C4—6881no—
949C2×C4C22⋊C4×D4311yescharacteristic
950C2×C4C2×D4×D4311yescharacteristic
951C8—42no—
952C8—1722no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—82no—
970C22—432no—
971C22—861no—
972C22—861no—
973C22—861no—
974C22—3442no—
975C22—3442no—
976C22—1721no—
977C22—1721no—
978C22—1721no—
979C22—1721no—
980C22—6881no—
981C22—6881no—
982C22#99×D4311yescharacteristic
983C22#99×D4311yescharacteristic
984C22C2×C22⋊C4×D4311yescharacteristic
985C4—21no—
986C4—21no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—82no—
991C4—432no—
992C4—861no—
993C4—861no—
994C4—861no—
995C4—3442no—
996C4—1721no—
997C4—1721no—
998C4—1721no—
999C4—1721no—
1000C2—21no—
1001C2—21no—
1002C2—21no—
1003C2—41no—
1004C2—41no—
1005C2—41no—
1006C2—41no—
1007C2—81no—
1008C2—862no—
1009C2—1721no—
1010C2—1721no—
1011C2—1721no—
1012C2C2×#99×D4311yescharacteristic
subgroupG/H
centerC2C2×#99×D43
commutatorC23×C43C23×C4
FrattiniC2×D4C23×D43
FittingC43×#2121C2
socleC2×C43C22×#99
prime radical#19148236C2
cosocleC2×D4×C43C24
hypercenter#2121D43
hypocenterC43#33350
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ #2121

Complements

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

NH ≅ G/Ntype
2. #19143071C2semidirect
3. #19143053C2semidirect
4. #19136247C2semidirect
5. #19136241C2semidirect
6. #19136238C2semidirect
7. #19136233C2semidirect
8. C2×#14582690C2semidirect
9. C2×#14582688C2semidirect
10. #352×D43C2semidirect
11. C43×#2121C2semidirect
13. C22×#10621900C4semidirect
23. #14583471C4semidirect
25. #14583459C4semidirect
27. #14583458C4semidirect
28. #14583405C4semidirect
30. C2×#13063309C4semidirect
32. #123×D43C4semidirect
35. #14583372C4semidirect
48. #14582690C22semidirect
49. #14582690C22semidirect
50. #14582689C22semidirect
51. #14582688C22semidirect
52. #14582688C22semidirect
53. #14582686C22semidirect
57. C43×#352C22semidirect
58. C43×AΣL(1,𝔽16)C22semidirect
73. C22×Dic86C2×C4semidirect
76. C22×C22⋊D43C2×C4semidirect
83. C23×Dic43C2×C4semidirect
84. C23×Dic43C2×C4semidirect
85. C22×C4×D43C2×C4semidirect
99. #13063309C2×C4semidirect
100. #13063309C2×C4semidirect
101. #13063309C2×C4semidirect
102. #13063309C2×C4semidirect
103. #13063308C2×C4semidirect
104. #13063308C2×C4semidirect
112. #13063306C2×C4semidirect
113. #13063306C2×C4semidirect
130. #13063294C2×C4semidirect
131. #13063294C2×C4semidirect
146. #13063281C2×C4semidirect
147. #13063281C2×C4semidirect
154. C2×C22⋊Dic43C2×C4semidirect
159. C22⋊C4×D43C2×C4semidirect
160. C22⋊C4×D43C2×C4semidirect
169. C22×D4×C43C2×C4semidirect
173. #123×C43C2×C4semidirect
178. #120×C43C2×C4semidirect
181. C2×C22⋊C4×C43C2×C4semidirect
500. #2121D43semidirect
562. #352C2×D43semidirect
564. AΣL(1,𝔽16)C2×D43semidirect
565. C43#33350semidirect
590. C22×D4C4×D43semidirect
627. #123C4×D43semidirect
651. #120C4×D43semidirect
680. C2×C22⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191482362
#191430712
#191430532
#191362472
#191362412
#191362382
#191362332
C2×#145826902
C2×#145826882
#352×D432
C43×#21212
#3335043