Finite Group Databasebeta

← #25249355

Subgroups — #25249355

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#19148233C211yesmaximal, characteristic
2#19143071C211yesmaximal, characteristic, complemented
3#19143053C211yesmaximal, characteristic, complemented
4#19136247C212yesmaximal, complemented
5#19136242C211yesmaximal, characteristic, complemented
6#19136240C212yesmaximal, complemented
7#19136239C211yesmaximal, characteristic, complemented
8#19136235C212yesmaximal, complemented
9C2×#14582689C211yesmaximal, characteristic, complemented
10#352×D43C212yesmaximal, complemented
11C2×C43×#352C211yesmaximal, characteristic, complemented
12C2×#13063370C2211yescharacteristic
13C22×#10621898C411yescharacteristic, complemented
14#14583665—21no—
15#14583550—21no—
16#14583550—21no—
17#14583547—21no—
18#14583547—21no—
19#14583541—21no—
20#14583541—21no—
21#14583539—21no—
22#14583539—21no—
23#14583471C411yescharacteristic, complemented
24#14583471C2211yescharacteristic
25#14583461C411yescharacteristic, complemented
26#14583460C411yescharacteristic, complemented
27#14583460C2211yescharacteristic
28#14583458C2211yescharacteristic
29#14583407C411yescharacteristic, complemented
30#14583407C2211yescharacteristic
31C2×#13063308C411yescharacteristic, complemented
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#14582689C2212yescomplemented
50#14582689C2212yescomplemented
51#14582688C2212yescomplemented
52#14582687C2212yescomplemented
53#14582685C2212yescomplemented
54C2×#123×C43C2211yescharacteristic
55C2×#100×C43C2211yescharacteristic
56C2×#99×C43C2211yescharacteristic
57C43×#352C2212yescomplemented
58C43×#352C2212yescomplemented
59#13063370—42no—
60#13063370—42no—
61C2×#10621898—21no—
62C2×#10621898—21no—
63C2×#10621898—21no—
64C2×#10621898—21no—
65C2×#10621898—42no—
66C2×#10621898—42no—
67C2×#10621898D411yescharacteristic
68C2×#10621898D411yescharacteristic
69C2×#10621900C2×C411yescharacteristic
70C2×#10621900D411yescharacteristic
71C2×#10621900D411yescharacteristic
72C2×#10621900C2311yescharacteristic
73C22×Dic86C2×C411yescharacteristic, complemented
74C22×D172C2×C411yescharacteristic, complemented
75C22×C22⋊D43C2×C411yescharacteristic
76C22×C22⋊D43C2×C411yescharacteristic
77C22×C22⋊D43C2×C411yescharacteristic, complemented
78C22×C22⋊D43D411yescharacteristic
79C22×C22⋊D43D411yescharacteristic
80C2×D4×D43C2×C411yescharacteristic
81C2×D4×D43D411yescharacteristic
82C2×D4×D43D411yescharacteristic
83C2×D4×D43C2311yescharacteristic
84C22×C4×D43C2×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#13063310—21no—
98#13063310—21no—
99#13063309—21no—
100#13063309C2×C411yescharacteristic, complemented
101#13063309C2×C411yescharacteristic, complemented
102#13063308—21no—
103#13063308—21no—
104#13063308—21no—
105#13063308C2×C411yescharacteristic, complemented
106#13063308C2×C411yescharacteristic, complemented
107#13063308C2×C411yescharacteristic, complemented
108#13063308C2×C411yescharacteristic, complemented
109#13063307—21no—
110#13063307—21no—
111#13063306C2×C411yescharacteristic, complemented
112#13063306C2311yescharacteristic
113#13063303—21no—
114#13063303—21no—
115#13063303—21no—
116#13063303—21no—
117#13063302—21no—
118#13063302—21no—
119#13063300—21no—
120#13063300—21no—
121#13063299—21no—
122#13063299—21no—
123#13063298—21no—
124#13063298—21no—
125#13063298—21no—
126#13063298—21no—
127#13063297—21no—
128#13063297—21no—
129#13063295—21no—
130#13063295—21no—
131#13063295—21no—
132#13063295C2×C411yescharacteristic, complemented
133#13063295C2×C411yescharacteristic, complemented
134#13063294—21no—
135#13063293C2×C411yescharacteristic, complemented
136#13063293C2311yescharacteristic
137#13063287—21no—
138#13063287—21no—
139C4×C22⋊D43—21no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43—42no—
142(C22⋊D43)⋊C4—21no—
143(C22⋊D43)⋊C4—21no—
144(C22⋊D43)⋊C4—21no—
145(C22⋊D43)⋊C4—21no—
146(C22⋊D43)⋊C4—42no—
147#13063281—22no—
148#13063281C2×C411yescharacteristic, complemented
149#13063281C2×C411yescharacteristic, complemented
150C2×Dic43⋊C4—21no—
151C4⋊C4×D43—21no—
152C4⋊C4×D43—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×C43C2311yescharacteristic
170C23×C4×C43C2×C411yescharacteristic, complemented
171C2×M16×C43—21no—
172#123×C43—21no—
173#123×C43—21no—
174#123×C43C2×C411yescharacteristic, complemented
175#123×C43C2×C411yescharacteristic, complemented
176#123×C43C2311yescharacteristic
177#123×C43C2311yescharacteristic
178C2×C4⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
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×C43C2×D411yescharacteristic
188C23×D43C22⋊C411yescharacteristic
189C23×D43C22⋊C411yescharacteristic
190C23×D43C22×C411yescharacteristic
191C23×D43C22×C411yescharacteristic
192C23×D43C2×D411yescharacteristic
193C2×D4×C43—41no—
194C2×D4×C43—41no—
195C2×D4×C43C22×C411yescharacteristic
196C2×D4×C43C2×D411yescharacteristic
197C2×D4×C43C2×D411yescharacteristic
198C2×D4×C43C2411yescharacteristic
199C22×C4×C43—21no—
200C22×C4×C43—21no—
201C22×C4×C43—21no—
202C22×C4×C43—41no—
203C22×C4×C43—41no—
204C22×C4×C43—41no—
205C22×C4×C43C22×C411yescharacteristic
206C22×C4×C43C22×C411yescharacteristic
207C22×C4×C43C2×D411yescharacteristic
208C2×C22⋊D43—22no—
209C2×C22⋊D43—22no—
210C2×C22⋊D43—22no—
211C2×C22⋊D43—22no—
212C2×C22⋊D43—21no—
213C2×C22⋊D43—21no—
214C2×C22⋊D43—21no—
215C2×C22⋊D43—21no—
216C2×C22⋊D43—41no—
217C2×C22⋊D43—41no—
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—41no—
236C22×Dic43C22⋊C411yescharacteristic
237C22×Dic43C22⋊C411yescharacteristic
238C22×Dic43C22×C411yescharacteristic
239C22×Dic43C22×C411yescharacteristic
240C22×Dic43C2×D411yescharacteristic
241#10621900—42no—
242#10621900—42no—
243#10621900—42no—
244#10621900—42no—
245D4×D43—42no—
246D4×D43—42no—
247D4×D43—42no—
248D4×D43—42no—
249#10621898—22no—
250#10621898—22no—
251#10621898—41no—
252#10621898—41no—
253#10621898—42no—
254#10621898—42no—
255#10621898—44no—
256#10621898—44no—
257#10621898—42no—
258#10621898—42no—
259C2×D172—21no—
260C2×D172—21no—
261C2×D172—21no—
262C2×D172—21no—
263C2×D172—42no—
264C2×D172C22⋊C411yescharacteristic
265C2×D172C2×D411yescharacteristic
266C2×C4×D43—21no—
267C2×C4×D43—21no—
268C2×C4×D43—21no—
269C2×C4×D43—21no—
270C2×C4×D43—21no—
271C2×C4×D43—21no—
272C2×C4×D43—42no—
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—
289C4⋊C4×C43—21no—
290C4⋊C4×C43—21no—
291C22⋊C4×C43—21no—
292C22⋊C4×C43—21no—
293C22⋊C4×C43—21no—
294C22⋊C4×C43—21no—
295C22⋊C4×C43—21no—
296C22⋊C4×C43—22no—
297C22⋊C4×C43—41no—
298C22⋊C4×C43C22×C411yescharacteristic
299C22⋊C4×C43C22×C411yescharacteristic
300C22⋊Dic43—21no—
301C22⋊Dic43—21no—
302C22⋊Dic43—21no—
303C22⋊Dic43—22no—
304C22⋊Dic43—41no—
305C22⋊Dic43C22×C411yescharacteristic
306C22⋊Dic43C22×C411yescharacteristic
307(C2×D43)⋊C4—21no—
308(C2×D43)⋊C4—21no—
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—21no—
318(C2×D43)⋊C4—21no—
319(C2×D43)⋊C4—42no—
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—81no—
346C23×C43—81no—
347C23×C43C2×C22⋊C411yescharacteristic
348C23×C43C2×C22⋊C411yescharacteristic
349C23×C43C2×C22⋊C411yescharacteristic
350C23×C43C23×C411yescharacteristic
351C23×C43C22×D411yescharacteristic
352C22×D43—22no—
353C22×D43—22no—
354C22×D43—21no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—41no—
358C22×D43—81no—
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—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—42no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
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—41no—
403C22⋊D43—41no—
404C22⋊D43—81no—
405C22⋊D43—81no—
406C22⋊D43#9912yes—
407C22⋊D43#9912yes—
408C2×Dic43—22no—
409C2×Dic43—22no—
410C2×Dic43—21no—
411C2×Dic43—21no—
412C2×Dic43—21no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—42no—
417C2×Dic43—81no—
418C2×Dic43—161no—
419C2×Dic43C2×C22⋊C411yescharacteristic
420C2×Dic43C2×C22⋊C411yescharacteristic
421C2×Dic43C2×C22⋊C411yescharacteristic
422C2×Dic43C2×C22⋊C411yescharacteristic
423D172—22no—
424D172—41no—
425D172—42no—
426D172—42no—
427D172—81no—
428D172—81no—
429C4×D43—22no—
430C4×D43—22no—
431C4×D43—41no—
432C4×D43—41no—
433C4×D43—42no—
434C4×D43—42no—
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—81no—
457C22×C43—81no—
458C22×C43—81no—
459C22×C43—81no—
460C22×C43C2×#9911yescharacteristic
461C22×C43C2×#9911yescharacteristic
462C22×C43C22×C22⋊C411yescharacteristic
463C2×D43—21no—
464C2×D43—21no—
465C2×D43—21no—
466C2×D43—41no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C2×D43—41no—
471C2×D43—41no—
472C2×D43—41no—
473C2×D43—82no—
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—41no—
485C4×C43—82no—
486Dic43—21no—
487Dic43—21no—
488Dic43—21no—
489Dic43—41no—
490Dic43—41no—
491Dic43—41no—
492Dic43—82no—
493Dic43C2×#9912yes—
494#3485—431no—
495#2888—431no—
496#2883—431no—
497#2123—432no—
498#2121—431no—
499#2121—431no—
500#2121—432no—
501#2120—432no—
502C2×#352—432no—
503C2×#352—431no—
504C2×#352D4311yescharacteristic, complemented
505C2×C43—21no—
506C2×C43—21no—
507C2×C43—21no—
508C2×C43—41no—
509C2×C43—41no—
510C2×C43—41no—
511C2×C43—41no—
512C2×C43C22×#9911yescharacteristic
513D43—22no—
514D43—41no—
515D43—41no—
516D43—41no—
517D43—81no—
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#534—431no—
535#525—431no—
536#525—431no—
537C2×#123—431no—
538C2×#123—431no—
539C2×#123—431no—
540C2×#123C2×D4311yescharacteristic
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#352C2×D4312yescomplemented
562#352C2×D4312yescomplemented
563AΣL(1,𝔽16)—432no—
564AΣL(1,𝔽16)—432no—
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×D4—431no—
591C22×D4C22×D4311yescharacteristic
592C23×C4—431no—
593C23×C4—431no—
594C23×C4C4×D4311yescharacteristic, complemented
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—21no—
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—861no—
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#123C4×D4311yescharacteristic, complemented
626#123C4×D4311yescharacteristic, complemented
627#123C22×D4311yescharacteristic
628#123C22×D4311yescharacteristic
629C22⋊Q8—861no—
630C22⋊Q8—861no—
631C22⋊Q8—861no—
632C22⋊Q8—861no—
633C22⋊Q8—861no—
634C22⋊Q8—861no—
635#121—861no—
636#121—861no—
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—431no—
646#120—431no—
647#120—431no—
648#120—431no—
649#120—861no—
650#120—861no—
651#120—861no—
652#120—861no—
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—21no—
667C2×C4⋊C4—861no—
668C2×C4⋊C4—861no—
669C2×C4⋊C4—861no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—431no—
673C2×C22⋊C4—431no—
674C2×C22⋊C4—431no—
675C2×C22⋊C4—861no—
676C2×C22⋊C4—861no—
677C2×C22⋊C4—862no—
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—
697C24—431no—
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—1724no—
707#41—1724no—
708#41—1722no—
709#41—1722no—
710#41—1722no—
711#41—1722no—
712#41—1722no—
713#41—1722no—
714C2×Q8—431no—
715C2×Q8—431no—
716C2×Q8—861no—
717C2×Q8—861no—
718C2×Q8—1722no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—431no—
722C2×D4—431no—
723C2×D4—431no—
724C2×D4—431no—
725C2×D4—431no—
726C2×D4—431no—
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—861no—
736C2×D4—861no—
737C2×D4—861no—
738C2×D4—861no—
739C2×D4—862no—
740C2×D4—862no—
741C2×D4—862no—
742C2×D4—862no—
743C2×D4—861no—
744C2×D4—861no—
745C2×D4—861no—
746C2×D4—861no—
747C2×D4—1722no—
748C2×D4—1722no—
749C2×D4—1722no—
750C2×D4—1722no—
751C2×D4—1722no—
752C2×D4—1721no—
753C2×D4—1721no—
754C2×D4—1721no—
755C2×D4—1721no—
756C2×D4—1721no—
757C2×D4—1721no—
758C2×D4C2×C4×D4311yescharacteristic
759C2×D4D4×D4311yescharacteristic
760C2×D4D4×D4311yescharacteristic
761C2×D4C23×D4311yescharacteristic
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—41no—
766C22×C4—41no—
767C22×C4—41no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—431no—
771C22×C4—431no—
772C22×C4—431no—
773C22×C4—431no—
774C22×C4—431no—
775C22×C4—431no—
776C22×C4—431no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—861no—
783C22×C4—861no—
784C22×C4—1722no—
785C22×C4—1722no—
786C22×C4—1722no—
787C22×C4—1721no—
788C22×C4C2×C4×D4311yescharacteristic
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—21no—
804C4⋊C4—21no—
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—81no—
853C23—81no—
854C23—431no—
855C23—431no—
856C23—431no—
857C23—431no—
858C23—862no—
859C23—862no—
860C23—861no—
861C23—3441no—
862C23—3441no—
863C23—3441no—
864C23—3441no—
865C23—3441no—
866C23—1721no—
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—432no—
883D4—432no—
884D4—862no—
885D4—862no—
886D4—862no—
887D4—862no—
888D4—862no—
889D4—861no—
890D4—861no—
891D4—861no—
892D4—861no—
893D4—861no—
894D4—861no—
895D4—3441no—
896D4—3441no—
897D4—3441no—
898D4—3441no—
899D4—1721no—
900D4—1722no—
901D4—1722no—
902D4—1721no—
903D4—1721no—
904D4—1721no—
905D4—1721no—
906D4—1722no—
907D4—1721no—
908D4—1721no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—42no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—42no—
921C2×C4—81no—
922C2×C4—161no—
923C2×C4—431no—
924C2×C4—431no—
925C2×C4—431no—
926C2×C4—431no—
927C2×C4—862no—
928C2×C4—862no—
929C2×C4—862no—
930C2×C4—862no—
931C2×C4—861no—
932C2×C4—861no—
933C2×C4—861no—
934C2×C4—3441no—
935C2×C4—3441no—
936C2×C4—3441no—
937C2×C4—1721no—
938C2×C4—1721no—
939C2×C4—1722no—
940C2×C4—1722no—
941C2×C4—1722no—
942C2×C4—1722no—
943C2×C4—1721no—
944C2×C4—1721no—
945C2×C4—1722no—
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—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—432no—
967C22—861no—
968C22—861no—
969C22—861no—
970C22—3442no—
971C22—3442no—
972C22—3442no—
973C22—1721no—
974C22—1721no—
975C22—1721no—
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—41no—
991C4—82no—
992C4—432no—
993C4—861no—
994C4—861no—
995C4—861no—
996C4—3442no—
997C4—1721no—
998C4—1721no—
999C4—1721no—
1000C2—21no—
1001C2—21no—
1002C2—21no—
1003C2—41no—
1004C2—41no—
1005C2—41no—
1006C2—41no—
1007C2—862no—
1008C2—3441no—
1009C2—1721no—
1010C2—1721no—
1011C2—1721no—
1012C2C2×#99×D4311yescharacteristic
subgroupG/H
centerC2C2×#99×D43
commutatorC23×C43C23×C4
FrattiniC2×D4C23×D43
FittingC2×C43×#352C2
socleC2×C43C22×#99
prime radical#19148233C2
cosocleC2×D4×C43C24
hypercenterC2×#352D43
hypocenterC43#33350
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#352

Complements

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

NH ≅ G/Ntype
2. #19143071C2semidirect
3. #19143053C2semidirect
4. #19136247C2semidirect
5. #19136242C2semidirect
6. #19136240C2semidirect
7. #19136239C2semidirect
8. #19136235C2semidirect
9. C2×#14582689C2semidirect
10. #352×D43C2semidirect
11. C2×C43×#352C2semidirect
13. C22×#10621898C4semidirect
23. #14583471C4semidirect
25. #14583461C4semidirect
26. #14583460C4semidirect
29. #14583407C4semidirect
31. C2×#13063308C4semidirect
32. #123×D43C4semidirect
35. #14583372C4semidirect
48. #14582690C22semidirect
49. #14582689C22semidirect
50. #14582689C22semidirect
51. #14582688C22semidirect
52. #14582687C22semidirect
53. #14582685C22semidirect
57. C43×#352C22semidirect
58. C43×#352C22semidirect
73. C22×Dic86C2×C4semidirect
74. C22×D172C2×C4semidirect
77. C22×C22⋊D43C2×C4semidirect
84. C22×C4×D43C2×C4semidirect
85. C22×C4×D43C2×C4semidirect
100. #13063309C2×C4semidirect
101. #13063309C2×C4semidirect
105. #13063308C2×C4semidirect
106. #13063308C2×C4semidirect
107. #13063308C2×C4semidirect
108. #13063308C2×C4semidirect
111. #13063306C2×C4semidirect
132. #13063295C2×C4semidirect
133. #13063295C2×C4semidirect
135. #13063293C2×C4semidirect
148. #13063281C2×C4semidirect
149. #13063281C2×C4semidirect
154. C2×C22⋊Dic43C2×C4semidirect
159. C22⋊C4×D43C2×C4semidirect
160. C22⋊C4×D43C2×C4semidirect
170. C23×C4×C43C2×C4semidirect
174. #123×C43C2×C4semidirect
175. #123×C43C2×C4semidirect
181. C2×C22⋊C4×C43C2×C4semidirect
504. C2×#352D43semidirect
561. #352C2×D43semidirect
562. #352C2×D43semidirect
565. C43#33350semidirect
594. C23×C4C4×D43semidirect
625. #123C4×D43semidirect
626. #123C4×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
#191482332
#191430712
#191430532
#191362472
#191362422
#191362402
#191362392
#191362352
C2×#145826892
#352×D432
C2×C43×#3522
#3335043