Finite Group Databasebeta

← C3⋊D3×#914 #13176732

Subgroups — C3⋊D3×#914 #13176732

Order 1728.

2060 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#239C211yesmaximal, characteristic, complemented
2D3×D4×C3⋊D3C211yesmaximal, characteristic, complemented
3#11723955C211yesmaximal, characteristic, complemented
4C3×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
5C32×#914C211yesmaximal, characteristic, complemented
6#11723572C211yesmaximal, characteristic, complemented
7C3⋊D3×#215C211yesmaximal, characteristic, complemented
8#11723568C211yesmaximal, characteristic, complemented
9#11723564C211yesmaximal, characteristic, complemented
10#11723557C211yesmaximal, characteristic, complemented
11C3⋊D3×#213C211yesmaximal, characteristic, complemented
12#11723324C211yesmaximal, characteristic, complemented
13C3⋊D3×D24C211yesmaximal, characteristic, complemented
14#11723315C211yesmaximal, characteristic, complemented
15C3⋊D3×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
16C3⋊D3×AGL(1,ℤ/8)—31nomaximal
17D3×#914—34nomaximal
18C22×D3×C3⋊D3—21no—
19#89080C2211yescharacteristic, complemented
20D4×C3⋊(C3⋊D3)C2211yescharacteristic, complemented
21C3×Q8×C3⋊D3C2211yescharacteristic, complemented
22C3×D4×C3⋊D3C2211yescharacteristic
23C32×#239C2211yescharacteristic, complemented
24C32×D3×D4C2211yescharacteristic, complemented
25#89039—21no—
26C3⋊D3×#67—21no—
27D3×#638—21no—
28#89026C2211yescharacteristic, complemented
29C3⋊D3×D12—21no—
30C3⋊D3×D12C2211yescharacteristic
31C3⋊D3×D12C2211yescharacteristic, complemented
32D3×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
33C4×D3×C3⋊D3—21no—
34C4×D3×C3⋊D3C2211yescharacteristic
35#89022—21no—
36#89022C2211yescharacteristic, complemented
37#89015—21no—
38#89015C2211yescharacteristic, complemented
39C33×SD16C2211yescharacteristic, complemented
40#88862C2211yescharacteristic, complemented
41#88860C2211yescharacteristic, complemented
42#88852C2211yescharacteristic, complemented
43#88850C2211yescharacteristic, complemented
44C3×#3755C2211yescharacteristic, complemented
45C3×#3754C2211yescharacteristic, complemented
46C3×#3744C2211yescharacteristic, complemented
47C3×C8×C3⋊D3C2211yescharacteristic, complemented
48C32×#215C2211yescharacteristic, complemented
49C32×#213C2211yescharacteristic, complemented
50C32×D24C2211yescharacteristic, complemented
51C32×ΓL(1,𝔽25)C2211yescharacteristic, complemented
52#88797C2211yescharacteristic, complemented
53#88792C2211yescharacteristic, complemented
54#88791C2211yescharacteristic, complemented
55#88790C2211yescharacteristic, complemented
56#88790C2211yescharacteristic, complemented
57#88789C2211yescharacteristic, complemented
58#88788C2211yescharacteristic, complemented
59#88786C2211yescharacteristic, complemented
60C3⋊D3×C3⋊C8C2211yescharacteristic, complemented
61#41×C3⋊D3—31no—
62C2×D4×C3⋊D3—31no—
63D3×#239—34no—
64D32×D4—34no—
65C32×AGL(1,ℤ/8)—31no—
66#64158—31no—
67#64141—31no—
68#64123—31no—
69#64123—31no—
70#64123—34no—
71#64123—64no—
72SD16×C3⋊D3—31no—
73SD16×C3⋊D3D311yescharacteristic, complemented
74#64120—31no—
75#64120—31no—
76D8×C3⋊D3—31no—
77D8×C3⋊D3—31no—
78#64117—31no—
79M16×C3⋊D3—31no—
80C3×#914D314yescomplemented
81C3×D3×SD16—34no—
82#63941—34no—
83#63939—34no—
84D3×#215—34no—
85#63937—34no—
86#63934—34no—
87D3×#213—34no—
88#63798—34no—
89#63794—34no—
90D3×D24—34no—
91D3×ΓL(1,𝔽25)—34no—
92C22×C3⋊(C3⋊D3)—21no—
93C22×C3×C3⋊D3—21no—
94C22×C32×D3—21no—
95C2×D3×C3⋊D3—21no—
96C2×D3×C3⋊D3—21no—
97C2×D3×C3⋊D3—21no—
98C2×D3×C3⋊D3—21no—
99C2×D3×C3⋊D3—44no—
100C2×D3×C3⋊D3D411yescharacteristic
101C33×Q8C2311yescharacteristic, complemented
102C33×D4C2311yescharacteristic
103#6312—21no—
104C4⋊(C3⋊(C3⋊D3))—21no—
105C4⋊(C3⋊(C3⋊D3))C2311yescharacteristic
106C4⋊(C3⋊(C3⋊D3))C2311yescharacteristic, complemented
107C4×C3⋊(C3⋊D3)—21no—
108C4×C3⋊(C3⋊D3)C2311yescharacteristic
109C3×#638—21no—
110C3×C4⋊(C3⋊D3)C2311yescharacteristic
111C3×C4×C3⋊D3—21no—
112C3×C4×C3⋊D3C2311yescharacteristic
113C3×#634—21no—
114C3×#634C2311yescharacteristic, complemented
115C32×#67—21no—
116C32×D12—21no—
117C32×D12C2311yescharacteristic
118C32×D12C2311yescharacteristic, complemented
119C32×C4×D3—21no—
120C32×C4×D3C2311yescharacteristic
121#6292—21no—
122#6291—21no—
123#6291—21no—
124#6291—21no—
125#6291—21no—
126#6290—21no—
127#6289—21no—
128#6289D411yescharacteristic
129Dic3×C3⋊D3D411yescharacteristic
130D3×C3⋊Dic3—21no—
131D3×C3⋊Dic3D411yescharacteristic
132C33×C8C2311yescharacteristic, complemented
133C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic, complemented
134C3×C3⋊(C3⋊C8)C2311yescharacteristic, complemented
135C32×C3⋊C8C2311yescharacteristic, complemented
136D3×AGL(1,ℤ/8)—94no—
137C2×#914—91no—
138C23×C3⋊D3—61no—
139C22×D32—64no—
140C32×#41—31no—
141C2×C32×D4—31no—
142C2×#638—61no—
143#3832—31no—
144#3832—34no—
145#3832—64no—
146Q8×C3⋊D3C2×D311yescharacteristic, complemented
147#3830—31no—
148#3830—61no—
149D4×C3⋊D3—31no—
150D4×C3⋊D3—34no—
151D4×C3⋊D3—31no—
152D4×C3⋊D3—31no—
153D4×C3⋊D3—31no—
154D4×C3⋊D3—61no—
155D4×C3⋊D3—61no—
156D4×C3⋊D3—61no—
157D4×C3⋊D3—64no—
158D4×C3⋊D3C2×D311yescharacteristic
159#3828—31no—
160#3828—61no—
161C2×C4⋊(C3⋊D3)—31no—
162C2×C4×C3⋊D3—31no—
163C2×C4×C3⋊D3—61no—
164C3×#239C2×D314yescomplemented
165C3×D3×Q8—34no—
166C3×D3×D4—34no—
167C3×D3×D4C2×D314yescomplemented
168#3811—64no—
169D3×#67—64no—
170D3×#67—64no—
171#3802—34no—
172D3×D12—34no—
173D3×D12—34no—
174D3×D12—34no—
175D3×D12—64no—
176C4×D32—34no—
177C4×D32—64no—
178#3799—34no—
179#3799—64no—
180#3796—34no—
181#3796—64no—
182C32×SD16—24no—
183C32×SD16—31no—
184C32×SD16C2×D314yescomplemented
185C32×SD16C2×D311yescharacteristic, complemented
186C32×D8—31no—
187C32×D8—31no—
188C32×M16—31no—
189#3755—31no—
190#3755—34no—
191#3755—64no—
192#3755C2×D311yescharacteristic, complemented
193#3754—31no—
194#3754C2×D311yescharacteristic, complemented
195#3753—31no—
196#3753—34no—
197#3753—31no—
198#3753—31no—
199#3753—31no—
200#3753—64no—
201#3748—31no—
202#3745—31no—
203#3745—31no—
204#3745—34no—
205#3745—64no—
206#3744—31no—
207#3744C2×D311yescharacteristic, complemented
208#3743—31no—
209#3743—34no—
210#3743—31no—
211#3743—64no—
212C8×C3⋊D3—31no—
213C8×C3⋊D3C2×D311yescharacteristic, complemented
214C3×#215—34no—
215C3×#215C2×D314yescomplemented
216C3×#214—34no—
217C3×#213C2×D314yescomplemented
218C3×D24C2×D314yescomplemented
219C3×#204—34no—
220C3×ΓL(1,𝔽25)C2×D314yescomplemented
221C3×D3×C8—34no—
222#3717—34no—
223#3715—34no—
224#3714—34no—
225#3714—34no—
226#3714—34no—
227#3713—34no—
228#3712—34no—
229#3711—34no—
230D3×C3⋊C8—34no—
231C22×C33—21no—
232C2×C3⋊(C3⋊D3)—21no—
233C2×C3⋊(C3⋊D3)—21no—
234C2×C3⋊(C3⋊D3)—42no—
235C2×C3⋊(C3⋊D3)C2×D411yescharacteristic
236C2×C3×C3⋊D3—21no—
237C2×C3×C3⋊D3—42no—
238C2×C3×C3⋊D3C2×D411yescharacteristic
239C2×C32×D3—21no—
240C2×C32×D3—21no—
241C2×C32×D3—42no—
242C2×C32×D3C2×D411yescharacteristic
243D3×C3⋊D3—22no—
244D3×C3⋊D3—42no—
245D3×C3⋊D3—42no—
246D3×C3⋊D3—42no—
247D3×C3⋊D3—42no—
248C33×C4—21no—
249C33×C4C2411yescharacteristic
250C3⋊(C3⋊Dic3)C2×D411yescharacteristic
251C3×C3⋊Dic3—21no—
252C3×C3⋊Dic3C2×D411yescharacteristic
253C32×Dic3C2×D411yescharacteristic
254D3×#41—94no—
255C2×#239—91no—
256C2×D3×D4—94no—
257C2×D3×D4—91no—
258C3×AGL(1,ℤ/8)—34no—
259C2×C3×SD16—91no—
260#949—94no—
261C2×#215—91no—
262#932—94no—
263C2×#213—91no—
264#914—94no—
265#914—91no—
266#914—91no—
267#914—94no—
268#914—91no—
269#914—91no—
270#914—91no—
271#914—91no—
272#914—91no—
273#914—184no—
274#914C3⋊D311yescharacteristic, direct product factor
275D3×SD16—34no—
276D3×SD16—94no—
277#911—94no—
278#911—94no—
279D3×D8—94no—
280D3×D8—94no—
281#908—94no—
282D3×M16—94no—
283C2×D24—91no—
284C2×ΓL(1,𝔽25)—91no—
285C23×C32—61no—
286C22×C3⋊D3—21no—
287C22×C3⋊D3—31no—
288C22×C3⋊D3—61no—
289C22×C3⋊D3—61no—
290C22×C3⋊D3—61no—
291C22×C3⋊D3—61no—
292C22×C3⋊D3—61no—
293C22×C3⋊D3—64no—
294C22×C3⋊D3—124no—
295C22×C3⋊D3—124no—
296C22×C3×D3—24no—
297C22×C3×D3—64no—
298C2×D32—34no—
299C2×D32—64no—
300C2×D32—64no—
301C2×D32—64no—
302C2×D32—64no—
303C2×D32—1216no—
304C32×Q8—24no—
305C32×Q8C22×D314yescomplemented
306C32×Q8C22×D311yescharacteristic, complemented
307C32×D4—24no—
308C32×D4—31no—
309C32×D4—31no—
310C32×D4—61no—
311C32×D4—61no—
312C32×D4C22×D314yes—
313C32×D4C22×D311yescharacteristic
314C2×C32×C4—31no—
315C2×C32×C4—61no—
316#638—21no—
317#638—61no—
318#638—61no—
319#638—61no—
320#638—61no—
321#638—61no—
322#638—61no—
323#638—64no—
324#638—124no—
325C2×C3⋊Dic3—31no—
326C2×C3⋊Dic3—61no—
327C4⋊(C3⋊D3)—31no—
328C4⋊(C3⋊D3)—31no—
329C4⋊(C3⋊D3)—34no—
330C4⋊(C3⋊D3)—34no—
331C4⋊(C3⋊D3)—64no—
332C4⋊(C3⋊D3)—64no—
333C4⋊(C3⋊D3)—61no—
334C4⋊(C3⋊D3)—61no—
335C4⋊(C3⋊D3)—64no—
336C4⋊(C3⋊D3)—124no—
337C4⋊(C3⋊D3)C22×D311yescharacteristic
338C4×C3⋊D3—21no—
339C4×C3⋊D3—31no—
340C4×C3⋊D3—31no—
341C4×C3⋊D3—31no—
342C4×C3⋊D3—34no—
343C4×C3⋊D3—64no—
344C4×C3⋊D3—61no—
345C4×C3⋊D3—61no—
346C4×C3⋊D3—64no—
347C4×C3⋊D3—124no—
348C4×C3⋊D3C22×D311yescharacteristic
349#634—21no—
350#634C22×D311yescharacteristic, complemented
351C3×#67—24no—
352C3×#67—64no—
353C3×D12—24no—
354C3×D12—34no—
355C3×D12C22×D314yes—
356C3×D12C22×D314yescomplemented
357C3×C4×D3—24no—
358C3×C4×D3—34no—
359C3×C4×D3—64no—
360C3×C4×D3C22×D314yes—
361C3×Dic6—34no—
362C3×Dic6—64no—
363#626—64no—
364#626—64no—
365#626—64no—
366#626—64no—
367#626—64no—
368#625—64no—
369#624—34no—
370#624—64no—
371D3×Dic3—34no—
372D3×Dic3—34no—
373D3×Dic3—64no—
374C32×C8—24no—
375C32×C8—31no—
376C32×C8C22×D314yescomplemented
377C32×C8C22×D311yescharacteristic, complemented
378C3⋊(C3⋊C8)—31no—
379C3⋊(C3⋊C8)—34no—
380C3⋊(C3⋊C8)—64no—
381C3⋊(C3⋊C8)C22×D311yescharacteristic, complemented
382C3×C3⋊C8—34no—
383C3×C3⋊C8C22×D314yescomplemented
384C2×AGL(1,ℤ/8)—271noSylow
385C2×C33—41no—
386C2×C33C22×D411yescharacteristic
387C3⋊(C3⋊D3)—21no—
388C3⋊(C3⋊D3)—41no—
389C3⋊(C3⋊D3)—41no—
390C3×C3⋊D3—41no—
391C3×C3⋊D3AGL(1,ℤ/8)12yescomplemented
392C32×D3—21no—
393C32×D3—41no—
394C32×D3—41no—
395C23×D3—181no—
396C23×D3—184no—
397C3×#41—34no—
398C2×C3×Q8—91no—
399C2×C3×D4—34no—
400C2×C3×D4—91no—
401C2×#67—181no—
402C2×#67—184no—
403#239—94no—
404#239—91no—
405#239—91no—
406#239—91no—
407#239—184no—
408#239—181no—
409#239—181no—
410#239C2×C3⋊D311yescharacteristic, complemented
411D3×Q8—34no—
412#237—94no—
413#237—184no—
414D3×D4—34no—
415D3×D4—94no—
416D3×D4—94no—
417D3×D4—94no—
418D3×D4—94no—
419D3×D4—91no—
420D3×D4—91no—
421D3×D4—91no—
422D3×D4—184no—
423D3×D4—184no—
424D3×D4—181no—
425D3×D4—184no—
426D3×D4—184no—
427D3×D4—181no—
428D3×D4C2×C3⋊D311yescharacteristic, complemented
429#235—94no—
430#235—184no—
431C2×D12—94no—
432C2×D12—91no—
433C2×D12—91no—
434C2×D12—181no—
435C2×C4×D3—94no—
436C2×C4×D3—91no—
437C2×C4×D3—181no—
438C2×C4×D3—184no—
439C3×SD16—24no—
440C3×SD16—34no—
441C3×SD16—91no—
442C3×SD16—91no—
443C3×SD16—91no—
444C3×SD16D3214yescomplemented
445C3×SD16C2×C3⋊D311yescharacteristic, complemented
446C3×D8—34no—
447C3×D8—34no—
448C3×M16—34no—
449C2×C3×C8—91no—
450#215—34no—
451#215—94no—
452#215—91no—
453#215—91no—
454#215—91no—
455#215—184no—
456#215C2×C3⋊D311yescharacteristic, complemented
457#214—34no—
458#214—94no—
459#213—94no—
460#213—94no—
461#213—94no—
462#213—94no—
463#213—91no—
464#213—91no—
465#213—91no—
466#213—184no—
467#213C2×C3⋊D311yescharacteristic, complemented
468#208—94no—
469C2×C3⋊C8—91no—
470D24—94no—
471D24—91no—
472D24—91no—
473D24—94no—
474D24—91no—
475D24—184no—
476D24C2×C3⋊D311yescharacteristic, complemented
477#204—34no—
478#204—94no—
479ΓL(1,𝔽25)—94no—
480ΓL(1,𝔽25)—91no—
481ΓL(1,𝔽25)—94no—
482ΓL(1,𝔽25)—91no—
483ΓL(1,𝔽25)—91no—
484ΓL(1,𝔽25)—184no—
485ΓL(1,𝔽25)C2×C3⋊D311yescharacteristic, complemented
486D3×C8—34no—
487D3×C8—94no—
488C22×C32—21no—
489C22×C32—24no—
490C22×C32—31no—
491C22×C32—44no—
492C22×C32—61no—
493C22×C32—61no—
494C22×C32—122no—
495C2×C3⋊D3—21no—
496C2×C3⋊D3—31no—
497C2×C3⋊D3—34no—
498C2×C3⋊D3—42no—
499C2×C3⋊D3—64no—
500C2×C3⋊D3—62no—
501C2×C3⋊D3—61no—
502C2×C3⋊D3—61no—
503C2×C3⋊D3—64no—
504C2×C3⋊D3—64no—
505C2×C3⋊D3—124no—
506C2×C3⋊D3—124no—
507C2×C3⋊D3—122no—
508C2×C3⋊D3—122no—
509C2×C3⋊D3—122no—
510C2×C3⋊D3—122no—
511C2×C3⋊D3—122no—
512C2×C3⋊D3—128no—
513C2×C3⋊D3—248no—
514C2×C3⋊D3D3×D411yescharacteristic
515C2×C3×D3—24no—
516C2×C3×D3—24no—
517C2×C3×D3—34no—
518C2×C3×D3—48no—
519C2×C3×D3—64no—
520C2×C3×D3—128no—
521C2×C3×D3D3×D414yes—
522D32—68no—
523D32—128no—
524D32—128no—
525D32—128no—
526D32—128no—
527C32×C4—21no—
528C32×C4—24no—
529C32×C4—24no—
530C32×C4—31no—
531C32×C4—44no—
532C32×C4C23×D314yes—
533C32×C4C23×D311yescharacteristic
534C3⋊Dic3—21no—
535C3⋊Dic3—31no—
536C3⋊Dic3—34no—
537C3⋊Dic3—64no—
538C3⋊Dic3D3×D411yescharacteristic
539C3×Dic3—34no—
540C3×Dic3—64no—
541C3×Dic3D3×D414yes—
542C2×#41—271no—
543C22×D4—271no—
544AGL(1,ℤ/8)—31no—
545AGL(1,ℤ/8)—271no—
546AGL(1,ℤ/8)—271no—
547AGL(1,ℤ/8)—271no—
548AGL(1,ℤ/8)—271no—
549AGL(1,ℤ/8)—271no—
550AGL(1,ℤ/8)—271no—
551AGL(1,ℤ/8)—271no—
552C2×SD16—91no—
553C2×SD16—271no—
554C2×D8—271no—
555C2×D8—271no—
556C2×M16—271no—
557C33C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
558C23×C3—64no—
559C23×C3—181no—
560C22×D3—21no—
561C22×D3—64no—
562C22×D3—94no—
563C22×D3—91no—
564C22×D3—181no—
565C22×D3—181no—
566C22×D3—181no—
567C22×D3—184no—
568C22×D3—184no—
569C22×D3—184no—
570C22×D3—184no—
571C22×D3—181no—
572C22×D3—184no—
573C22×D3—181no—
574C22×D3—364no—
575C22×D3—364no—
576C22×D3—3616no—
577C3×Q8—24no—
578C3×Q8—91no—
579C3×Q8—181no—
580C3×Q8C2×D3214yescomplemented
581C3×Q8C22×C3⋊D311yescharacteristic, complemented
582C3×D4—24no—
583C3×D4—34no—
584C3×D4—34no—
585C3×D4—64no—
586C3×D4—64no—
587C3×D4—91no—
588C3×D4—181no—
589C3×D4C2×D3214yes—
590C3×D4C22×C3⋊D311yescharacteristic
591C2×C3×C4—34no—
592C2×C3×C4—64no—
593C2×C3×C4—91no—
594C2×C3×C4—181no—
595#67—21no—
596#67—64no—
597#67—184no—
598#67—184no—
599#67—184no—
600#67—184no—
601#67—181no—
602#67—184no—
603#67—181no—
604#67—184no—
605#67—181no—
606#67—364no—
607C2×Dic3—94no—
608C2×Dic3—91no—
609C2×Dic3—184no—
610D12—21no—
611D12—34no—
612D12—94no—
613D12—94no—
614D12—91no—
615D12—91no—
616D12—184no—
617D12—184no—
618D12—181no—
619D12—184no—
620D12—184no—
621D12—181no—
622D12—181no—
623D12—181no—
624D12—181no—
625D12—364no—
626D12C22×C3⋊D311yescharacteristic
627D12C22×C3⋊D311yescharacteristic, complemented
628C4×D3—21no—
629C4×D3—34no—
630C4×D3—64no—
631C4×D3—94no—
632C4×D3—94no—
633C4×D3—91no—
634C4×D3—94no—
635C4×D3—91no—
636C4×D3—91no—
637C4×D3—184no—
638C4×D3—184no—
639C4×D3—181no—
640C4×D3—184no—
641C4×D3—181no—
642C4×D3—181no—
643C4×D3—364no—
644C4×D3C22×C3⋊D311yescharacteristic
645Dic6—34no—
646Dic6—64no—
647C3×C8—24no—
648C3×C8—34no—
649C3×C8—91no—
650C3×C8C2×D3214yescomplemented
651C3×C8C22×C3⋊D311yescharacteristic, complemented
652C3⋊C8—34no—
653C3⋊C8—94no—
654C3⋊C8—91no—
655C3⋊C8—184no—
656C3⋊C8C22×C3⋊D311yescharacteristic, complemented
657C2×C32—24no—
658C2×C32—41no—
659C2×C32—44no—
660C2×C32—61no—
661C2×C32—84no—
662C2×C32—121no—
663C2×C32—121no—
664C2×C32C2×D3×D414yes—
665C2×C32C2×D3×D411yescharacteristic
666C3⋊D3—41no—
667C3⋊D3—61no—
668C3⋊D3—64no—
669C3⋊D3—124no—
670C3⋊D3—121no—
671C3⋊D3—121no—
672C3⋊D3—124no—
673C3⋊D3—124no—
674C3⋊D3—244no—
675C3⋊D3—244no—
676C3⋊D3#91412yesdirect product factor
677C3×D3—24no—
678C3×D3—38no—
679C3×D3—44no—
680C3×D3—44no—
681C3×D3—124no—
682C24—541no—
683#41—31no—
684#41—271no—
685#41—271no—
686#41—271no—
687#41—541no—
688#41—541no—
689C2×Q8—91no—
690C2×D4—31no—
691C2×D4—91no—
692C2×D4—271no—
693C2×D4—271no—
694C2×D4—271no—
695C2×D4—271no—
696C2×D4—271no—
697C2×D4—541no—
698C2×D4—541no—
699C2×D4—541no—
700C2×D4—541no—
701C22×C4—271no—
702C22×C4—541no—
703SD16—31no—
704SD16—91no—
705SD16—91no—
706SD16—91no—
707SD16—271no—
708SD16—271no—
709SD16—271no—
710SD16D3×C3⋊D311yescharacteristic, complemented
711D8—31no—
712D8—31no—
713D8—271no—
714D8—271no—
715D8—271no—
716D8—271no—
717D8—271no—
718D8—271no—
719M16—31no—
720M16—271no—
721M16—271no—
722M16—271no—
723C2×C8—91no—
724C2×C8—271no—
725C22×C3—24no—
726C22×C3—21no—
727C22×C3—34no—
728C22×C3—44no—
729C22×C3—64no—
730C22×C3—64no—
731C22×C3—91no—
732C22×C3—128no—
733C22×C3—181no—
734C22×C3—362no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—34no—
738C2×D3—42no—
739C2×D3—64no—
740C2×D3—94no—
741C2×D3—91no—
742C2×D3—128no—
743C2×D3—184no—
744C2×D3—182no—
745C2×D3—188no—
746C2×D3—184no—
747C2×D3—184no—
748C2×D3—181no—
749C2×D3—181no—
750C2×D3—364no—
751C2×D3—364no—
752C2×D3—362no—
753C2×D3—368no—
754C2×D3—368no—
755C2×D3—362no—
756C2×D3—362no—
757C2×D3—362no—
758C2×D3—368no—
759C2×D3—368no—
760C2×D3—362no—
761C2×D3—368no—
762C2×D3—728no—
763C2×D3D4×C3⋊D311yescharacteristic
764C3×C4—24no—
765C3×C4—21no—
766C3×C4—24no—
767C3×C4—34no—
768C3×C4—44no—
769C3×C4—91no—
770C3×C4—181no—
771C3×C4C22×D3214yes—
772C3×C4C23×C3⋊D311yescharacteristic
773Dic3—34no—
774Dic3—64no—
775Dic3—94no—
776Dic3—91no—
777Dic3—184no—
778Dic3D4×C3⋊D311yescharacteristic
779C32—24no—
780C32C2×#91411yescharacteristic, complemented
781C32D3×AGL(1,ℤ/8)14yescomplemented
782C23—61no—
783C23—181no—
784C23—271no—
785C23—541no—
786C23—541no—
787C23—541no—
788C23—541no—
789C23—541no—
790C23—1084no—
791Q8—91no—
792Q8—181no—
793Q8C2×D3×C3⋊D311yescharacteristic, complemented
794D4—31no—
795D4—31no—
796D4—61no—
797D4—61no—
798D4—91no—
799D4—181no—
800D4—271no—
801D4—271no—
802D4—541no—
803D4—541no—
804D4—541no—
805D4—541no—
806D4—541no—
807D4—541no—
808D4—541no—
809D4—541no—
810D4C2×D3×C3⋊D311yescharacteristic
811C2×C4—31no—
812C2×C4—61no—
813C2×C4—91no—
814C2×C4—181no—
815C2×C4—271no—
816C2×C4—271no—
817C2×C4—271no—
818C2×C4—271no—
819C2×C4—541no—
820C2×C4—541no—
821C2×C4—541no—
822C8—31no—
823C8—91no—
824C8—271no—
825C8C2×D3×C3⋊D311yescharacteristic, complemented
826C2×C3—24no—
827C2×C3—41no—
828C2×C3—44no—
829C2×C3—64no—
830C2×C3—84no—
831C2×C3—92no—
832C2×C3—124no—
833C2×C3—124no—
834C2×C3—361no—
835C2×C3D32×D414yes—
836C2×C3C2×D4×C3⋊D311yescharacteristic
837D3—21no—
838D3—38no—
839D3—41no—
840D3—41no—
841D3—124no—
842D3—181no—
843D3—184no—
844D3—364no—
845D3—361no—
846D3—361no—
847D3—364no—
848D3—364no—
849D3—724no—
850D3—724no—
851C22—21no—
852C22—31no—
853C22—61no—
854C22—61no—
855C22—91no—
856C22—122no—
857C22—181no—
858C22—271no—
859C22—362no—
860C22—542no—
861C22—541no—
862C22—541no—
863C22—1082no—
864C22—1082no—
865C22—1082no—
866C22—1082no—
867C22—1082no—
868C4—21no—
869C4—31no—
870C4—91no—
871C4—181no—
872C4—271no—
873C4C22×D3×C3⋊D311yescharacteristic
874C3—24no—
875C3D3×#91414yescomplemented
876C3C3⋊D3×AGL(1,ℤ/8)11yescharacteristic, complemented
877C2—41no—
878C2—61no—
879C2—92no—
880C2—121no—
881C2—121no—
882C2—361no—
883C2—541no—
884C2—1081no—
885C2—1081no—
886C2D3×D4×C3⋊D311yescharacteristic
subgroupG/H
centerC2D3×D4×C3⋊D3
commutator, cosocleC33×C4C24
FrattiniC4C22×D3×C3⋊D3
FittingC33×SD16C22
socleC2×C33C22×D4
hypercenterSD16D3×C3⋊D3
hypocenterC33C2×AGL(1,ℤ/8)
LCSG ▷ C33×C4 ▷ C2×C33 ▷ C33
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#239C2semidirect
2. D3×D4×C3⋊D3C2semidirect
3. #11723955C2semidirect
4. C3×SD16×C3⋊D3C2semidirect
5. C32×#914C2semidirect
6. #11723572C2semidirect
7. C3⋊D3×#215C2semidirect
8. #11723568C2semidirect
9. #11723564C2semidirect
10. #11723557C2semidirect
11. C3⋊D3×#213C2semidirect
12. #11723324C2semidirect
13. C3⋊D3×D24C2semidirect
14. #11723315C2semidirect
15. C3⋊D3×ΓL(1,𝔽25)C2semidirect
19. #89080C22semidirect
20. D4×C3⋊(C3⋊D3)C22semidirect
21. C3×Q8×C3⋊D3C22semidirect
23. C32×#239C22semidirect
24. C32×D3×D4C22semidirect
28. #89026C22semidirect
31. C3⋊D3×D12C22semidirect
32. D3×C4⋊(C3⋊D3)C22semidirect
36. #89022C22semidirect
38. #89015C22semidirect
39. C33×SD16C22semidirect
40. #88862C22semidirect
41. #88860C22semidirect
42. #88852C22semidirect
43. #88850C22semidirect
44. C3×#3755C22semidirect
45. C3×#3754C22semidirect
46. C3×#3744C22semidirect
47. C3×C8×C3⋊D3C22semidirect
48. C32×#215C22semidirect
49. C32×#213C22semidirect
50. C32×D24C22semidirect
51. C32×ΓL(1,𝔽25)C22semidirect
52. #88797C22semidirect
53. #88792C22semidirect
54. #88791C22semidirect
55. #88790C22semidirect
56. #88790C22semidirect
57. #88789C22semidirect
58. #88788C22semidirect
59. #88786C22semidirect
60. C3⋊D3×C3⋊C8C22semidirect
73. SD16×C3⋊D3D3semidirect
80. C3×#914D3semidirect
101. C33×Q8C23semidirect
106. C4⋊(C3⋊(C3⋊D3))C23semidirect
114. C3×#634C23semidirect
118. C32×D12C23semidirect
132. C33×C8C23semidirect
133. C3⋊(C3⋊(C3⋊C8))C23semidirect
134. C3×C3⋊(C3⋊C8)C23semidirect
135. C32×C3⋊C8C23semidirect
146. Q8×C3⋊D3C2×D3semidirect
164. C3×#239C2×D3semidirect
167. C3×D3×D4C2×D3semidirect
184. C32×SD16C2×D3semidirect
185. C32×SD16C2×D3semidirect
192. #3755C2×D3semidirect
194. #3754C2×D3semidirect
207. #3744C2×D3semidirect
213. C8×C3⋊D3C2×D3semidirect
215. C3×#215C2×D3semidirect
217. C3×#213C2×D3semidirect
218. C3×D24C2×D3semidirect
220. C3×ΓL(1,𝔽25)C2×D3semidirect
274. #914C3⋊D3direct (N × H)
305. C32×Q8C22×D3semidirect
306. C32×Q8C22×D3semidirect
350. #634C22×D3semidirect
356. C3×D12C22×D3semidirect
376. C32×C8C22×D3semidirect
377. C32×C8C22×D3semidirect
381. C3⋊(C3⋊C8)C22×D3semidirect
383. C3×C3⋊C8C22×D3semidirect
391. C3×C3⋊D3AGL(1,ℤ/8)semidirect
410. #239C2×C3⋊D3semidirect
428. D3×D4C2×C3⋊D3semidirect
444. C3×SD16D32semidirect
445. C3×SD16C2×C3⋊D3semidirect
456. #215C2×C3⋊D3semidirect
467. #213C2×C3⋊D3semidirect
476. D24C2×C3⋊D3semidirect
485. ΓL(1,𝔽25)C2×C3⋊D3semidirect
557. C33C2×AGL(1,ℤ/8)semidirect
580. C3×Q8C2×D32semidirect
581. C3×Q8C22×C3⋊D3semidirect
627. D12C22×C3⋊D3semidirect
650. C3×C8C2×D32semidirect
651. C3×C8C22×C3⋊D3semidirect
656. C3⋊C8C22×C3⋊D3semidirect
676. C3⋊D3#914direct (N × H)
710. SD16D3×C3⋊D3semidirect
780. C32C2×#914semidirect
781. C32D3×AGL(1,ℤ/8)semidirect
793. Q8C2×D3×C3⋊D3semidirect
825. C8C2×D3×C3⋊D3semidirect
875. C3D3×#914semidirect
876. C3C3⋊D3×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#2392
D3×D4×C3⋊D32
#117239552
C3×SD16×C3⋊D32
C32×#9142
#117235722
C3⋊D3×#2152
#117235682
#117235642
#117235572
C3⋊D3×#2132
#117233242
C3⋊D3×D242
#117233152
C3⋊D3×ΓL(1,𝔽25)2
C3⋊D3×AGL(1,ℤ/8)3
D3×#9143