Finite Group Databasebeta

← #13167775

Subgroups — #13167775

Order 1728.

1298 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11724398C211yesmaximal, characteristic
2#11723652C211yesmaximal, characteristic, complemented
3#11723312C212yesmaximal, complemented
4D3×C8×C3⋊D3C211yesmaximal, characteristic, complemented
5C3×#63805C211yesmaximal, characteristic, complemented
6C3×#63804C212yesmaximal, complemented
7#11722826C211yesmaximal, characteristic, complemented
8#11722822C212yesmaximal, complemented
9#11722821C211yesmaximal, characteristic, complemented
10#11722819C211yesmaximal, characteristic, complemented
11D3×#3710C212yesmaximal, complemented
12#10594707—32nomaximal
13#10594669—31nomaximal
14#89042C2211yescharacteristic
15C4×D3×C3⋊D3C2211yescharacteristic
16C4×D3×C3⋊D3C2212yes—
17C3×#3798C2211yescharacteristic
18C3×#3798C2212yes—
19#88964C412yes—
20#88964C411yescharacteristic
21#88963C411yescharacteristic
22#88958C411yescharacteristic
23#88954C411yescharacteristic
24#88954C412yes—
25C8×C3⋊(C3⋊D3)C2211yescharacteristic
26C3×#3743C2212yescomplemented
27C3×C8×C3⋊D3C2211yescharacteristic, complemented
28C32×ΓL(1,𝔽25)C2212yescomplemented
29C32×D3×C8C2211yescharacteristic, complemented
30#88809C2211yescharacteristic, complemented
31#88808C2212yescomplemented
32#88787C2212yescomplemented
33#88786C2212yescomplemented
34#88785C2211yescharacteristic
35#88785C2212yes—
36C3⋊D3×C3⋊C8C2211yescharacteristic, complemented
37D3×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
38C3×#3712C2211yescharacteristic, complemented
39C3×#3711C2212yescomplemented
40C3×#3710C2212yescomplemented
41C3×D3×C3⋊C8C2212yescomplemented
42C3×D3×C3⋊C8C2212yescomplemented
43#64306—31no—
44#64306—32no—
45M16×C3⋊D3—32no—
46C2×C8×C3⋊D3—31no—
47C3×#907—32no—
48C3×#907—32no—
49C3×#901—32no—
50#63818—31no—
51C2×#3710—32no—
52#63815—32no—
53#63814—32no—
54#63814—32no—
55#63805—31no—
56#63805D311yescharacteristic, complemented
57#63804—32no—
58#63804—32no—
59#63804—32no—
60#63804D312yescomplemented
61#63803—31no—
62#63803—31no—
63#63791—32no—
64#63791—32no—
65#63791—32no—
66#63791—62no—
67D32×C8—32no—
68D32×C8—32no—
69D32×C8—32no—
70D32×C8—61no—
71C2×D3×C3⋊D3C2×C411yescharacteristic
72C2×D3×C3⋊D3C2×C412yes—
73C4×C3⋊(C3⋊D3)C2311yescharacteristic
74C3×C4×C3⋊D3C2311yescharacteristic
75C3×C4×C3⋊D3C2312yes—
76C32×C4×D3C2312yes—
77C32×C4×D3C2311yescharacteristic
78#6296C2×C411yescharacteristic
79#6295C2×C411yescharacteristic
80#6295C2×C412yes—
81#6289C2×C411yescharacteristic
82#6289C2×C412yes—
83Dic3×C3⋊D3C2×C411yescharacteristic
84Dic3×C3⋊D3C2×C412yes—
85D3×C3⋊Dic3C2×C411yescharacteristic
86D3×C3⋊Dic3C2×C412yes—
87C3×#627C2×C411yescharacteristic
88C3×#627C2×C412yes—
89C3×#626C2×C412yes—
90C3×#626C2×C412yes—
91C3×#626C2×C412yes—
92C3×#625C2×C411yescharacteristic
93C3×#625C2×C412yes—
94C33×C8C2311yescharacteristic
95C3⋊(C3⋊(C3⋊C8))C2311yescharacteristic
96C3×C3⋊(C3⋊C8)C2311yescharacteristic
97C3×C3⋊(C3⋊C8)C2312yes—
98C32×C3⋊C8C2311yescharacteristic
99C32×C3⋊C8C2312yes—
100D3×#131—92no—
101D3×#131—91no—
102C2×C4×C3⋊D3—32no—
103C2×C4×C3⋊D3—31no—
104C3×#235—32no—
105C3×#235—32no—
106C3×#235—32no—
107#3811—32no—
108#3811—32no—
109#3811—32no—
110#3805—31no—
111#3805—32no—
112#3805—31no—
113#3805—32no—
114#3802—31no—
115#3802—32no—
116C4×D32—32no—
117C4×D32—32no—
118C4×D32—32no—
119C4×D32—61no—
120C4×D32—62no—
121#3798—31no—
122#3798—32no—
123#3798C2×D311yescharacteristic
124#3798C2×D312yes—
125#3797—31no—
126#3797—32no—
127#3796—32no—
128#3796—32no—
129#3796—32no—
130C32×M16—32no—
131C2×C32×C8—31no—
132#3748—32no—
133C2×C3⋊(C3⋊C8)—31no—
134#3743—32no—
135#3743C2×D312yescomplemented
136C8×C3⋊D3—31no—
137C8×C3⋊D3—32no—
138C8×C3⋊D3—31no—
139C8×C3⋊D3—31no—
140C8×C3⋊D3—32no—
141C8×C3⋊D3—61no—
142C8×C3⋊D3—62no—
143C8×C3⋊D3—121no—
144C8×C3⋊D3C2×D311yescharacteristic, complemented
145C3×#208—32no—
146C2×C3×C3⋊C8—32no—
147C2×C3×C3⋊C8—32no—
148C3×ΓL(1,𝔽25)—22no—
149C3×ΓL(1,𝔽25)—32no—
150C3×ΓL(1,𝔽25)—32no—
151C3×ΓL(1,𝔽25)—32no—
152C3×ΓL(1,𝔽25)—32no—
153C3×ΓL(1,𝔽25)—62no—
154C3×ΓL(1,𝔽25)C2×D312yescomplemented
155C3×ΓL(1,𝔽25)C2×D312yescomplemented
156C3×D3×C8—21no—
157C3×D3×C8—32no—
158C3×D3×C8—32no—
159C3×D3×C8—32no—
160C3×D3×C8—32no—
161C3×D3×C8—32no—
162C3×D3×C8—61no—
163C3×D3×C8C2×D312yescomplemented
164#3712—31no—
165#3712C2×D311yescharacteristic, complemented
166#3711—32no—
167#3711—32no—
168#3711—32no—
169#3711—32no—
170#3711—32no—
171#3711—62no—
172#3711—62no—
173#3711C2×D312yescomplemented
174#3710—32no—
175#3710—32no—
176#3710—32no—
177#3710—32no—
178#3710—61no—
179#3710—62no—
180#3710C2×D312yescomplemented
181D3×C3⋊C8—32no—
182D3×C3⋊C8—32no—
183D3×C3⋊C8—32no—
184D3×C3⋊C8—32no—
185D3×C3⋊C8—61no—
186D3×C3⋊C8—61no—
187D3×C3⋊C8C2×D312yescomplemented
188D3×C3⋊C8C2×D312yescomplemented
189C2×C3⋊(C3⋊D3)C22×C411yescharacteristic
190C2×C3×C3⋊D3C22×C411yescharacteristic
191C2×C3×C3⋊D3C22×C412yes—
192C2×C32×D3C22×C411yescharacteristic
193C2×C32×D3C22×C412yes—
194D3×C3⋊D3—22no—
195D3×C3⋊D3—24no—
196C33×C4C2411yescharacteristic
197C3⋊(C3⋊Dic3)C22×C411yescharacteristic
198C3×C3⋊Dic3C22×C411yescharacteristic
199C3×C3⋊Dic3C22×C412yes—
200C32×Dic3C22×C412yes—
201C32×Dic3C22×C411yescharacteristic
202D3×#41—92no—
203D3×#41—91no—
204C3×#131—92no—
205C3×#131—91no—
206#948—91no—
207#948—92no—
208#907—32no—
209#907—32no—
210#907—91no—
211#907—92no—
212#907—92no—
213D3×M16—91no—
214D3×M16—92no—
215D3×M16—92no—
216D3×M16—92no—
217D3×M16—92no—
218D3×M16—182no—
219#901—32no—
220#901—92no—
221#901—92no—
222#901—91no—
223#901—92no—
224C2×D3×C8—92no—
225C2×D3×C8—92no—
226C2×D3×C8—92no—
227C2×D3×C8—92no—
228C2×D3×C8—91no—
229C2×D3×C8—181no—
230C22×C3⋊D3—31no—
231C22×C3⋊D3—32no—
232C2×D32—32no—
233C2×D32—32no—
234C2×D32—32no—
235C2×D32—61no—
236C2×D32—62no—
237C2×C32×C4—32no—
238C2×C32×C4—31no—
239C2×C3⋊Dic3—32no—
240C2×C3⋊Dic3—31no—
241C4×C3⋊D3—32no—
242C4×C3⋊D3—31no—
243C4×C3⋊D3—32no—
244C4×C3⋊D3—31no—
245C4×C3⋊D3—32no—
246C4×C3⋊D3—31no—
247C4×C3⋊D3—61no—
248C4×C3⋊D3—62no—
249C4×C3⋊D3—121no—
250C4×C3⋊D3C22×D312yes—
251C4×C3⋊D3C22×D311yescharacteristic
252C3×#67—32no—
253C3×#67—32no—
254C3×#67—32no—
255C3×#67—32no—
256C3×#67—32no—
257C3×#67—32no—
258C3×D12—32no—
259C3×D12—32no—
260C3×D12—32no—
261C3×C4×D3—21no—
262C3×C4×D3—22no—
263C3×C4×D3—32no—
264C3×C4×D3—32no—
265C3×C4×D3—32no—
266C3×C4×D3—61no—
267C3×C4×D3—62no—
268C3×C4×D3C22×D312yes—
269C3×C4×D3C22×D312yes—
270C3×C4×D3C22×D312yes—
271C3×Dic6—32no—
272C3×Dic6—32no—
273C3×Dic6—32no—
274#627—31no—
275#627—32no—
276#627C4×D311yescharacteristic
277#627C4×D312yes—
278#626—32no—
279#626—32no—
280#626—32no—
281#626C4×D312yes—
282#626C4×D312yes—
283#626C4×D312yes—
284#625—31no—
285#625—32no—
286#625C4×D311yescharacteristic
287#625C4×D312yes—
288#624—32no—
289#624—32no—
290#624—32no—
291#624—61no—
292#624—62no—
293D3×Dic3—32no—
294D3×Dic3—32no—
295D3×Dic3—32no—
296D3×Dic3—32no—
297D3×Dic3—32no—
298D3×Dic3—32no—
299D3×Dic3—61no—
300D3×Dic3—62no—
301D3×Dic3—61no—
302D3×Dic3—62no—
303C32×C8—21no—
304C32×C8—22no—
305C32×C8—31no—
306C32×C8—32no—
307C32×C8—41no—
308C32×C8C22×D312yes—
309C32×C8C22×D311yescharacteristic
310C3⋊(C3⋊C8)—32no—
311C3⋊(C3⋊C8)—31no—
312C3⋊(C3⋊C8)—61no—
313C3⋊(C3⋊C8)—62no—
314C3⋊(C3⋊C8)—121no—
315C3⋊(C3⋊C8)C22×D311yescharacteristic
316C3⋊(C3⋊C8)C22×D312yes—
317C3×C3⋊C8—21no—
318C3×C3⋊C8—22no—
319C3×C3⋊C8—32no—
320C3×C3⋊C8—32no—
321C3×C3⋊C8—32no—
322C3×C3⋊C8—61no—
323C3×C3⋊C8—62no—
324C3×C3⋊C8C22×D312yes—
325C3×C3⋊C8C22×D312yes—
326C3×C3⋊C8C22×D312yes—
327C2×#131—271noSylow
328C2×C33C23×C411yescharacteristic
329C3⋊(C3⋊D3)#13112yescomplemented
330C3×C3⋊D3—21no—
331C3×C3⋊D3—22no—
332C32×D3—21no—
333C32×D3—22no—
334C3×#41—91no—
335C3×#41—92no—
336#239—92no—
337#239—91no—
338D3×Q8—92no—
339D3×Q8—91no—
340#237—92no—
341#237—92no—
342#237—92no—
343#237—92no—
344#237—91no—
345D3×D4—92no—
346D3×D4—92no—
347D3×D4—92no—
348D3×D4—92no—
349D3×D4—91no—
350#235—32no—
351#235—32no—
352#235—32no—
353#235—92no—
354#235—91no—
355C2×C4×D3—92no—
356C2×C4×D3—92no—
357C2×C4×D3—92no—
358C2×C4×D3—92no—
359C2×C4×D3—91no—
360C2×C4×D3—181no—
361C2×C4×D3—182no—
362C3×M16—32no—
363C3×M16—32no—
364C3×M16—62no—
365C3×M16—91no—
366C3×M16—92no—
367C3×M16—92no—
368C2×C3×C8—32no—
369C2×C3×C8—61no—
370C2×C3×C8—92no—
371C2×C3×C8—92no—
372C2×C3×C8—92no—
373C2×C3×C8—91no—
374#208—32no—
375#208—91no—
376#208—92no—
377#208—92no—
378#208—92no—
379#208—182no—
380C2×C3⋊C8—32no—
381C2×C3⋊C8—32no—
382C2×C3⋊C8—92no—
383C2×C3⋊C8—92no—
384C2×C3⋊C8—91no—
385C2×C3⋊C8—181no—
386ΓL(1,𝔽25)—32no—
387ΓL(1,𝔽25)—32no—
388ΓL(1,𝔽25)—32no—
389ΓL(1,𝔽25)—32no—
390ΓL(1,𝔽25)—62no—
391ΓL(1,𝔽25)—92no—
392ΓL(1,𝔽25)—92no—
393ΓL(1,𝔽25)—92no—
394ΓL(1,𝔽25)—92no—
395ΓL(1,𝔽25)—182no—
396ΓL(1,𝔽25)D3212yescomplemented
397D3×C8—32no—
398D3×C8—32no—
399D3×C8—32no—
400D3×C8—32no—
401D3×C8—32no—
402D3×C8—61no—
403D3×C8—92no—
404D3×C8—92no—
405D3×C8—92no—
406D3×C8—92no—
407D3×C8—92no—
408D3×C8—92no—
409D3×C8—91no—
410D3×C8—92no—
411D3×C8—91no—
412D3×C8—91no—
413D3×C8—92no—
414D3×C8—181no—
415D3×C8—182no—
416D3×C8—181no—
417D3×C8—182no—
418D3×C8—181no—
419D3×C8—361no—
420D3×C8D3211yescharacteristic, complemented
421C22×C32—31no—
422C22×C32—32no—
423C2×C3⋊D3—32no—
424C2×C3⋊D3—31no—
425C2×C3⋊D3—61no—
426C2×C3⋊D3—62no—
427C2×C3⋊D3—62no—
428C2×C3⋊D3—64no—
429C2×C3⋊D3—121no—
430C2×C3⋊D3C2×C4×D311yescharacteristic
431C2×C3⋊D3C2×C4×D312yes—
432C2×C3×D3—21no—
433C2×C3×D3—22no—
434C2×C3×D3—32no—
435C2×C3×D3—32no—
436C2×C3×D3—32no—
437C2×C3×D3—61no—
438C2×C3×D3—62no—
439C2×C3×D3C2×C4×D312yes—
440C2×C3×D3C2×C4×D312yes—
441C2×C3×D3C2×C4×D312yes—
442D32—64no—
443D32—64no—
444D32—64no—
445D32—64no—
446D32—124no—
447C32×C4—21no—
448C32×C4—22no—
449C32×C4—32no—
450C32×C4—31no—
451C32×C4—41no—
452C32×C4C23×D312yes—
453C32×C4C23×D311yescharacteristic
454C3⋊Dic3—32no—
455C3⋊Dic3—31no—
456C3⋊Dic3—61no—
457C3⋊Dic3—62no—
458C3⋊Dic3—121no—
459C3⋊Dic3C2×C4×D312yes—
460C3⋊Dic3C2×C4×D311yescharacteristic
461C3×Dic3—21no—
462C3×Dic3—22no—
463C3×Dic3—32no—
464C3×Dic3—32no—
465C3×Dic3—32no—
466C3×Dic3—61no—
467C3×Dic3—62no—
468C3×Dic3C2×C4×D312yes—
469C3×Dic3C2×C4×D312yes—
470C3×Dic3C2×C4×D312yes—
471C2×#41—271no—
472#131—92no—
473#131—91no—
474#131—271no—
475#131—271no—
476#131—271no—
477#131—272no—
478C2×M16—272no—
479C2×M16—271no—
480C22×C8—271no—
481C22×C8—272no—
482C33C2×#13111yescharacteristic, complemented, Sylow
483C22×D3—92no—
484C22×D3—92no—
485C22×D3—92no—
486C22×D3—91no—
487C22×D3—92no—
488C22×D3—181no—
489C22×D3—182no—
490C3×Q8—91no—
491C3×Q8—92no—
492C3×D4—92no—
493C3×D4—92no—
494C3×D4—92no—
495C3×D4—91no—
496C3×D4—92no—
497C2×C3×C4—32no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—61no—
501C2×C3×C4—62no—
502C2×C3×C4—91no—
503C2×C3×C4—92no—
504#67—32no—
505#67—32no—
506#67—32no—
507#67—32no—
508#67—32no—
509#67—32no—
510#67—92no—
511#67—92no—
512#67—92no—
513C2×Dic3—92no—
514C2×Dic3—92no—
515C2×Dic3—92no—
516C2×Dic3—91no—
517C2×Dic3—92no—
518C2×Dic3—181no—
519C2×Dic3—182no—
520D12—32no—
521D12—32no—
522D12—32no—
523D12—91no—
524D12—92no—
525C4×D3—32no—
526C4×D3—32no—
527C4×D3—32no—
528C4×D3—61no—
529C4×D3—62no—
530C4×D3—92no—
531C4×D3—92no—
532C4×D3—92no—
533C4×D3—92no—
534C4×D3—92no—
535C4×D3—92no—
536C4×D3—91no—
537C4×D3—92no—
538C4×D3—92no—
539C4×D3—91no—
540C4×D3—91no—
541C4×D3—92no—
542C4×D3—181no—
543C4×D3—182no—
544C4×D3—181no—
545C4×D3—182no—
546C4×D3—181no—
547C4×D3—182no—
548C4×D3—361no—
549C4×D3C2×D3212yes—
550C4×D3C2×D3211yescharacteristic
551Dic6—32no—
552Dic6—32no—
553Dic6—32no—
554Dic6—91no—
555Dic6—92no—
556C3×C8—21no—
557C3×C8—22no—
558C3×C8—32no—
559C3×C8—32no—
560C3×C8—32no—
561C3×C8—41no—
562C3×C8—61no—
563C3×C8—62no—
564C3×C8—91no—
565C3×C8—92no—
566C3×C8C2×D3212yes—
567C3×C8C2×D3211yescharacteristic
568C3⋊C8—32no—
569C3⋊C8—32no—
570C3⋊C8—32no—
571C3⋊C8—61no—
572C3⋊C8—62no—
573C3⋊C8—91no—
574C3⋊C8—92no—
575C3⋊C8—181no—
576C3⋊C8—182no—
577C3⋊C8—361no—
578C3⋊C8C2×D3211yescharacteristic
579C3⋊C8C2×D3212yes—
580C2×C32—21no—
581C2×C32—22no—
582C2×C32—41no—
583C2×C32—61no—
584C2×C32—62no—
585C2×C32C22×C4×D312yes—
586C2×C32C22×C4×D311yescharacteristic
587C3⋊D3—21no—
588C3⋊D3—22no—
589C3⋊D3—34no—
590C3⋊D3—32no—
591C3⋊D3—62no—
592C3⋊D3—64no—
593C3⋊D3—122no—
594C3×D3—22no—
595C3×D3—22no—
596C3×D3—22no—
597C3×D3—22no—
598C3×D3—42no—
599C3×D3—62no—
600C3×D3—62no—
601C3×D3—62no—
602C3×D3—62no—
603C3×D3—122no—
604#41—92no—
605#41—91no—
606#41—271no—
607#41—271no—
608#41—272no—
609#41—271no—
610C2×Q8—271no—
611C2×D4—272no—
612C2×D4—271no—
613C22×C4—271no—
614C22×C4—272no—
615M16—32no—
616M16—91no—
617M16—92no—
618M16—92no—
619M16—272no—
620M16—271no—
621M16—272no—
622C2×C8—31no—
623C2×C8—92no—
624C2×C8—92no—
625C2×C8—92no—
626C2×C8—91no—
627C2×C8—271no—
628C2×C8—272no—
629C2×C8—271no—
630C2×C8—272no—
631C2×C8—271no—
632C2×C8—271no—
633C22×C3—32no—
634C22×C3—32no—
635C22×C3—32no—
636C22×C3—61no—
637C22×C3—62no—
638C22×C3—91no—
639C22×C3—92no—
640C2×D3—32no—
641C2×D3—32no—
642C2×D3—32no—
643C2×D3—61no—
644C2×D3—62no—
645C2×D3—91no—
646C2×D3—92no—
647C2×D3—181no—
648C2×D3—182no—
649C2×D3—182no—
650C2×D3—184no—
651C2×D3—184no—
652C2×D3—184no—
653C2×D3—184no—
654C2×D3—184no—
655C2×D3—361no—
656C2×D3—364no—
657C2×D3C4×D3211yescharacteristic
658C2×D3C4×D3212yes—
659C3×C4—21no—
660C3×C4—22no—
661C3×C4—32no—
662C3×C4—32no—
663C3×C4—32no—
664C3×C4—41no—
665C3×C4—61no—
666C3×C4—62no—
667C3×C4—91no—
668C3×C4—92no—
669C3×C4C22×D3211yescharacteristic
670C3×C4C22×D3212yes—
671Dic3—32no—
672Dic3—32no—
673Dic3—32no—
674Dic3—61no—
675Dic3—62no—
676Dic3—91no—
677Dic3—92no—
678Dic3—181no—
679Dic3—182no—
680Dic3—361no—
681Dic3C4×D3211yescharacteristic
682Dic3C4×D3212yes—
683C32—21no—
684C32—22no—
685C32—41no—
686C32D3×#13112yescomplemented
687C32D3×#13111yescharacteristic, complemented
688C23—271no—
689C23—272no—
690Q8—92no—
691Q8—91no—
692Q8—271no—
693D4—92no—
694D4—92no—
695D4—92no—
696D4—92no—
697D4—91no—
698D4—272no—
699D4—271no—
700C2×C4—31no—
701C2×C4—32no—
702C2×C4—92no—
703C2×C4—91no—
704C2×C4—271no—
705C2×C4—272no—
706C2×C4—271no—
707C2×C4—272no—
708C2×C4—271no—
709C2×C4—272no—
710C2×C4—271no—
711C8—31no—
712C8—32no—
713C8—91no—
714C8—92no—
715C8—271no—
716C8D3311yescharacteristic
717C2×C3—21no—
718C2×C3—22no—
719C2×C3—41no—
720C2×C3—62no—
721C2×C3—62no—
722C2×C3—62no—
723C2×C3—62no—
724C2×C3—122no—
725C2×C3—181no—
726C2×C3—182no—
727C2×C3C2×C4×D3211yescharacteristic
728C2×C3C2×C4×D3212yes—
729D3—21no—
730D3—22no—
731D3—62no—
732D3—62no—
733D3—62no—
734D3—62no—
735D3—92no—
736D3—94no—
737D3—122no—
738D3—182no—
739D3—184no—
740D3—362no—
741C22—31no—
742C22—32no—
743C22—91no—
744C22—92no—
745C22—271no—
746C22—542no—
747C22—544no—
748C4—31no—
749C4—32no—
750C4—92no—
751C4—91no—
752C4—271no—
753C4C2×D3311yescharacteristic
754C3—21no—
755C3—22no—
756C3—41no—
757C3#1059466911yescharacteristic, complemented
758C3#1059470712yescomplemented
759C2—61no—
760C2—62no—
761C2—181no—
762C2—182no—
763C2—272no—
764C2C4×D3311yescharacteristic
subgroupG/H
center, FrattiniC4C2×D33
commutator, socleC2×C33C23×C4
FittingC33×C8C23
prime radical#11724398C2
cosocleC33×C4C24
hypercenterC8D33
hypocenterC33C2×#131
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
2. #11723652C2semidirect
3. #11723312C2semidirect
4. D3×C8×C3⋊D3C2semidirect
5. C3×#63805C2semidirect
6. C3×#63804C2semidirect
7. #11722826C2semidirect
8. #11722822C2semidirect
9. #11722821C2semidirect
10. #11722819C2semidirect
11. D3×#3710C2semidirect
26. C3×#3743C22semidirect
27. C3×C8×C3⋊D3C22semidirect
28. C32×ΓL(1,𝔽25)C22semidirect
29. C32×D3×C8C22semidirect
30. #88809C22semidirect
31. #88808C22semidirect
32. #88787C22semidirect
33. #88786C22semidirect
36. C3⋊D3×C3⋊C8C22semidirect
37. D3×C3⋊(C3⋊C8)C22semidirect
38. C3×#3712C22semidirect
39. C3×#3711C22semidirect
40. C3×#3710C22semidirect
41. C3×D3×C3⋊C8C22semidirect
42. C3×D3×C3⋊C8C22semidirect
56. #63805D3semidirect
60. #63804D3semidirect
135. #3743C2×D3semidirect
144. C8×C3⋊D3C2×D3semidirect
154. C3×ΓL(1,𝔽25)C2×D3semidirect
155. C3×ΓL(1,𝔽25)C2×D3semidirect
163. C3×D3×C8C2×D3semidirect
165. #3712C2×D3semidirect
173. #3711C2×D3semidirect
180. #3710C2×D3semidirect
187. D3×C3⋊C8C2×D3semidirect
188. D3×C3⋊C8C2×D3semidirect
329. C3⋊(C3⋊D3)#131semidirect
396. ΓL(1,𝔽25)D32semidirect
420. D3×C8D32semidirect
482. C33C2×#131semidirect
686. C32D3×#131semidirect
687. C32D3×#131semidirect
757. C3#10594669semidirect
758. C3#10594707semidirect

Maximal subgroups

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

subgroupindex
#117243982
#117236522
#117233122
D3×C8×C3⋊D32
C3×#638052
C3×#638042
#117228262
#117228222
#117228212
#117228192
D3×#37102
#105947073
#105946693