Finite Group Databasebeta

← D3×#4861 #11858467

Subgroups — D3×#4861 #11858467

Order 1152.

1131 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×ΓL(1,𝔽25)C211yesmaximal, characteristic
2D3×#892C211yesmaximal, characteristic
3D32×C4⋊C4C211yesmaximal, characteristic
4#10592560C211yesmaximal, characteristic, complemented
5C3×#4861C211yesmaximal, characteristic, complemented
6C3×D3×#106C211yesmaximal, characteristic, complemented
7#10590688C211yesmaximal, characteristic, complemented
8#10590681C211yesmaximal, characteristic, complemented
9D3×#818C211yesmaximal, characteristic, complemented
10#10590584C211yesmaximal, characteristic, complemented
11#10590583C211yesmaximal, characteristic, complemented
12#10590581C211yesmaximal, characteristic, complemented
13D3×#808C211yesmaximal, characteristic, complemented
14D3×#807C211yesmaximal, characteristic, complemented
15#10590437C211yesmaximal, characteristic, complemented
16D3×#428—31nomaximal
17C2×#4861—31nomaximal
18C2×C4×D32—21no—
19C2×C4×D32C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21#64101C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic
25C3×#892C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29D3×(C2×D3)⋊C4—21no—
30#63900C2211yescharacteristic
31D3×C4⋊Dic3C2211yescharacteristic
32D3×C4⋊Dic3C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63883—21no—
35#63878—21no—
36D3×Dic3⋊C4—21no—
37D3×Dic3⋊C4—21no—
38C4×D3×Dic3—21no—
39#63849C2211yescharacteristic
40#63841C2211yescharacteristic
41#63836—21no—
42C2×#3712C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45D3×ΓL(1,𝔽25)C418yescomplemented
46C32×#106C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49#63634C2211yescharacteristic, complemented
50C3×#818C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#808C2211yescharacteristic, complemented
53C3×#808C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55C3×#807C2211yescharacteristic, complemented
56#63576C2211yescharacteristic, complemented
57#63575C2211yescharacteristic, complemented
58#63575C2211yescharacteristic, complemented
59#63575C2211yescharacteristic, complemented
60#63574C2211yescharacteristic, complemented
61#63573C2211yescharacteristic, complemented
62C2×D3×M16—31no—
63C22×ΓL(1,𝔽25)—31no—
64D3×#117—31no—
65C2×#892—31no—
66C2×D3×C4⋊C4—31no—
67C2×D3×C4⋊C4—31no—
68C3×#428—31no—
69C2×C3×#106—31no—
70#5121—31no—
71C2×#818—31no—
72#4995—31no—
73#4964—31no—
74C2×#808—31no—
75C2×#807—31no—
76#4881—31no—
77#4881—31no—
78D3×#107—31no—
79D3×#107—31no—
80#4861—31no—
81#4861—31no—
82#4861—31no—
83#4861—31no—
84#4861—31no—
85#4861—31no—
86#4861—31no—
87#4861—31no—
88#4861—31no—
89#4861—61no—
90#4861D311yescharacteristic, direct product factor
91D3×#106—31no—
92D3×#106D311yescharacteristic, complemented
93C22×D32D411yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×C4×D3—21no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×#624—21no—
102C2×#624D411yescharacteristic
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3D411yescharacteristic
107C2×D3×Dic3D411yescharacteristic
108C4×D32—44no—
109C4×D32C2×C414yes—
110C4×D32Q814yes—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113C32×C4⋊C4C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3—21no—
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120#3743C2×C414yescomplemented
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×ΓL(1,𝔽25)C2×C414yescomplemented
133C3×D3×C8C2×C414yescomplemented
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3712C2×C414yescomplemented
143#3711C2×C414yescomplemented
144D3×C3⋊C8C2×C414yescomplemented
145C2×#428—91noSylow
146C22×C4×D3—31no—
147C22×C4×D3—31no—
148C22×C4×D3—61no—
149C22×C4×D3—61no—
150C2×C3×M16—31no—
151C22×C3×C8—31no—
152C3×#117—31no—
153C2×C3×C4⋊C4—31no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4—31no—
156C2×(C2×D3)⋊C4—61no—
157#926—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×Dic3⋊C4—61no—
162C2×Dic3⋊C4—61no—
163C2×C4×Dic3—61no—
164C2×#208—31no—
165C22×C3⋊C8—31no—
166D3×M16—38no—
167C2×ΓL(1,𝔽25)—31no—
168C2×ΓL(1,𝔽25)—31no—
169C2×ΓL(1,𝔽25)—31no—
170C2×ΓL(1,𝔽25)—31no—
171C2×ΓL(1,𝔽25)—31no—
172C2×ΓL(1,𝔽25)—38no—
173C2×ΓL(1,𝔽25)—61no—
174C2×ΓL(1,𝔽25)C2×D311yescharacteristic
175C2×D3×C8—31no—
176C2×D3×C8C2×D311yescharacteristic
177#892—31no—
178#892—31no—
179#892—31no—
180#892—31no—
181#892—31no—
182#892—61no—
183#892—61no—
184#892—61no—
185#892C2×D311yescharacteristic
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—31no—
191D3×C4⋊C4—31no—
192D3×C4⋊C4—31no—
193D3×C4⋊C4—61no—
194D3×C4⋊C4—61no—
195D3×C4⋊C4—61no—
196D3×C4⋊C4—61no—
197D3×C4⋊C4—61no—
198D3×C4⋊C4C2×D311yescharacteristic
199D3×C4⋊C4C2×D311yescharacteristic
200D3×C4⋊C4C2×D311yescharacteristic
201D3×C22⋊C4—61no—
202#877—61no—
203#872—61no—
204C42×D3—61no—
205C3×#107—31no—
206C3×#107—31no—
207C3×#106—21no—
208C3×#106—31no—
209C3×#106—31no—
210C3×#106—31no—
211C3×#106—31no—
212C3×#106C2×D311yescharacteristic, complemented
213C3×#106C2×D311yescharacteristic, complemented
214#818—31no—
215#818—31no—
216#818—31no—
217#818—31no—
218#818—31no—
219#818—61no—
220#818C2×D311yescharacteristic, complemented
221#817—31no—
222#817C2×D311yescharacteristic, complemented
223#808—31no—
224#808—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—61no—
229#808C2×D311yescharacteristic, complemented
230#808C2×D311yescharacteristic, complemented
231#808C2×D311yescharacteristic, complemented
232#807—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236#807—31no—
237#807—31no—
238#807—31no—
239#807—61no—
240#807C2×D311yescharacteristic, complemented
241C22×C3⋊D3C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C2×D32—22no—
245C2×D32—22no—
246C2×D32C4⋊C414yes—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—42no—
254C4×C3⋊D3C22×C412yes—
255C4×C3⋊D3C2×Q812yes—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—42no—
263C3×C4×D3—42no—
264C3×C4×D3—42no—
265C3×C4×D3C22×C412yes—
266C3×C4×D3C22×C412yes—
267C3×C4×D3C2×Q812yes—
268C3×C4×D3C2×Q812yes—
269#624—42no—
270#624C4⋊C414yes—
271D3×Dic3—42no—
272D3×Dic3—42no—
273D3×Dic3—42no—
274D3×Dic3C4⋊C414yes—
275D3×Dic3C4⋊C414yes—
276C32×C8C22×C412yescomplemented
277C3⋊(C3⋊C8)C22×C412yescomplemented
278C3×C3⋊C8C22×C412yescomplemented
279C3×C3⋊C8C22×C412yescomplemented
280C22×M16—91no—
281C2×#117—91no—
282C22×C4⋊C4—91no—
283#428—31no—
284#428—91no—
285#428—91no—
286#428—91no—
287#428—91no—
288#428—91no—
289#428—91no—
290#428—91no—
291C2×#107—91no—
292C2×#107—91no—
293C2×#106—31no—
294C2×#106—91no—
295C23×D3—31no—
296C23×D3—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—61no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—31no—
315C2×C4×D3—31no—
316C2×C4×D3—34no—
317C2×C4×D3—34no—
318C2×C4×D3—34no—
319C2×C4×D3—34no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—121no—
329C2×C4×D3—124no—
330C2×C4×D3—124no—
331C2×C4×D3C22×D311yescharacteristic
332C2×C4×D3C22×D311yescharacteristic
333C3×M16—34no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—34no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C4⋊C4C22×D311yescharacteristic
353C3×C22⋊C4—61no—
354C3×C42—61no—
355#217—61no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—121no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3C22×D311yescharacteristic
373C4⋊Dic3C22×D311yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—121no—
387C4×Dic3—21no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—121no—
395#208—34no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—34no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402ΓL(1,𝔽25)—34no—
403ΓL(1,𝔽25)—34no—
404ΓL(1,𝔽25)—34no—
405ΓL(1,𝔽25)—34no—
406ΓL(1,𝔽25)—34no—
407ΓL(1,𝔽25)—64no—
408ΓL(1,𝔽25)C4×D314yescomplemented
409D3×C8—34no—
410D3×C8C4×D314yescomplemented
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3C2×C4⋊C412yes—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3C2×C4⋊C412yes—
418C2×C3×D3C2×C4⋊C412yes—
419C2×C3×D3AGL(1,ℤ/8)12yes—
420C2×C3×D3#13712yes—
421D32—28no—
422C32×C4—41no—
423C32×C4—41no—
424C32×C4C23×C411yescharacteristic
425C32×C4C22×Q811yescharacteristic
426C3⋊Dic3—41no—
427C3⋊Dic3—41no—
428C3⋊Dic3C2×C4⋊C412yes—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3C2×C4⋊C412yes—
434C3×Dic3C2×C4⋊C412yes—
435C23×C4—91no—
436C23×C4—181no—
437C2×M16—31no—
438C2×M16—91no—
439C2×M16—98no—
440C2×M16—91no—
441C2×M16—91no—
442C22×C8—31no—
443C22×C8—91no—
444#117—31no—
445#117—91no—
446#117—91no—
447#117—91no—
448#117—181no—
449#117—181no—
450C2×C4⋊C4—31no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—91no—
454C2×C4⋊C4—91no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4—91no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—181no—
459C2×C4⋊C4—181no—
460C2×C4⋊C4—181no—
461C2×C22⋊C4—181no—
462C2×C42—181no—
463#107—31no—
464#107—31no—
465#107—91no—
466#107—91no—
467#107—91no—
468#107—91no—
469#107—91no—
470#107—91no—
471#106—31no—
472#106—31no—
473#106—31no—
474#106—31no—
475#106—91no—
476#106—91no—
477#106—91no—
478#106D3211yescharacteristic, complemented
479C23×C3—31no—
480C23×C3—31no—
481C22×D3—31no—
482C22×D3—31no—
483C22×D3—34no—
484C22×D3—34no—
485C22×D3—61no—
486C22×D3—62no—
487C22×D3—62no—
488C22×D3—62no—
489C22×D3—62no—
490C22×D3D3×D411yescharacteristic
491C22×D3D3×D411yescharacteristic
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—32no—
500C2×C3×C4—32no—
501C2×C3×C4—32no—
502C2×C3×C4—32no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—122no—
510C2×C3×C4—122no—
511C2×C3×C4—122no—
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—34no—
521C2×Dic3—34no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—122no—
530C2×Dic3—122no—
531C2×Dic3—122no—
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534C4×D3—34no—
535C4×D3—34no—
536C4×D3—32no—
537C4×D3—32no—
538C4×D3—32no—
539C4×D3—32no—
540C4×D3—34no—
541C4×D3—34no—
542C4×D3—42no—
543C4×D3—42no—
544C4×D3—42no—
545C4×D3—62no—
546C4×D3—62no—
547C4×D3—122no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—242no—
555C4×D3C2×C4×D312yes—
556C4×D3C2×C4×D312yes—
557C4×D3D3×Q812yes—
558C4×D3D3×Q812yes—
559C3×C8—22no—
560C3×C8—32no—
561C3×C8—32no—
562C3×C8C2×C4×D312yescomplemented
563C3×C8C2×C4×D312yescomplemented
564C3⋊C8—32no—
565C3⋊C8—32no—
566C3⋊C8—62no—
567C3⋊C8C2×C4×D312yescomplemented
568C3⋊C8C2×C4×D312yescomplemented
569C2×C32C22×C4⋊C411yescharacteristic
570C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
571C2×C32C2×#13711yescharacteristic
572C3⋊D3—22no—
573C3×D3—22no—
574C3×D3#42814yescomplemented
575C24—91no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—61no—
581C22×C4—91no—
582C22×C4—94no—
583C22×C4—94no—
584C22×C4—91no—
585C22×C4—91no—
586C22×C4—91no—
587C22×C4—181no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4—364no—
593M16—34no—
594M16—94no—
595M16—94no—
596M16—94no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—34no—
600C2×C8—94no—
601C2×C8—91no—
602C2×C8C2×D3211yescharacteristic
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—91no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4C2×D3211yescharacteristic
618C4⋊C4C2×D3211yescharacteristic
619C22⋊C4—61no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C42—61no—
624C42—181no—
625C42—181no—
626C42—181no—
627C22×C3—21no—
628C22×C3—32no—
629C22×C3—32no—
630C22×C3—32no—
631C22×C3—32no—
632C22×C3—61no—
633C22×C3—61no—
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C2×D3×D411yescharacteristic
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—32no—
639C2×D3—32no—
640C2×D3—62no—
641C2×D3—68no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—68no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3D3×C4⋊C412yes—
650C2×D3D3×C4⋊C412yes—
651C2×D3#91412yes—
652C2×D3#91512yes—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—32no—
656C3×C4—32no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—81no—
662C3×C4—81no—
663C3×C4—121no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4C22×C4×D311yescharacteristic
668C3×C4C22×C4×D311yescharacteristic
669C3×C4C2×D3×Q811yescharacteristic
670C3×C4C2×D3×Q811yescharacteristic
671Dic3—32no—
672Dic3—32no—
673Dic3—41no—
674Dic3—41no—
675Dic3—41no—
676Dic3—41no—
677Dic3—62no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—241no—
683Dic3—241no—
684Dic3D3×C4⋊C412yes—
685Dic3D3×C4⋊C412yes—
686C32C2×#42811yescharacteristic, complemented, Sylow
687C23—31no—
688C23—31no—
689C23—94no—
690C23—91no—
691C23—182no—
692C23—182no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—32no—
700C2×C4—32no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—94no—
706C2×C4—94no—
707C2×C4—94no—
708C2×C4—91no—
709C2×C4—92no—
710C2×C4—92no—
711C2×C4—122no—
712C2×C4—122no—
713C2×C4—122no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—362no—
717C2×C4—362no—
718C2×C4—362no—
719C2×C4—362no—
720C2×C4—362no—
721C2×C4C22×D3211yescharacteristic
722C8—32no—
723C8—32no—
724C8—92no—
725C8C4×D3212yescomplemented
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—34no—
730C2×C3—62no—
731C2×C3C2×D3×C4⋊C411yescharacteristic
732C2×C3C2×D3×C4⋊C411yescharacteristic
733C2×C3C2×#91411yescharacteristic
734C2×C3C2×#91511yescharacteristic
735C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
736C2×C3D3×#13711yescharacteristic
737D3—22no—
738D3—62no—
739D3—62no—
740D3—122no—
741D3#486114yesdirect product factor
742C22—32no—
743C22—32no—
744C22—32no—
745C22—32no—
746C22—61no—
747C22—61no—
748C22—92no—
749C22—188no—
750C22—181no—
751C22—181no—
752C22D32×D411yescharacteristic
753C4—32no—
754C4—32no—
755C4—41no—
756C4—41no—
757C4—92no—
758C4—121no—
759C4—121no—
760C4—121no—
761C4—121no—
762C4—361no—
763C4—361no—
764C4C2×C4×D3211yescharacteristic
765C4D32×Q811yescharacteristic
766C3—21no—
767C3C2×#486111yescharacteristic, complemented
768C3D3×#42811yescharacteristic, complemented
769C2—34no—
770C2—62no—
771C2—182no—
772C2D32×C4⋊C411yescharacteristic
773C2D3×#91411yescharacteristic
774C2D3×#91511yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×D32D4
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32C2×#428
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
4. #10592560C2semidirect
5. C3×#4861C2semidirect
6. C3×D3×#106C2semidirect
7. #10590688C2semidirect
8. #10590681C2semidirect
9. D3×#818C2semidirect
10. #10590584C2semidirect
11. #10590583C2semidirect
12. #10590581C2semidirect
13. D3×#808C2semidirect
14. D3×#807C2semidirect
15. #10590437C2semidirect
45. D3×ΓL(1,𝔽25)C4semidirect
46. C32×#106C22semidirect
47. #63645C22semidirect
48. #63635C22semidirect
49. #63634C22semidirect
50. C3×#818C22semidirect
51. C3×#817C22semidirect
52. C3×#808C22semidirect
53. C3×#808C22semidirect
54. C3×#808C22semidirect
55. C3×#807C22semidirect
56. #63576C22semidirect
57. #63575C22semidirect
58. #63575C22semidirect
59. #63575C22semidirect
60. #63574C22semidirect
61. #63573C22semidirect
90. #4861D3direct (N × H)
92. D3×#106D3semidirect
120. #3743C2×C4semidirect
132. C3×ΓL(1,𝔽25)C2×C4semidirect
133. C3×D3×C8C2×C4semidirect
142. #3712C2×C4semidirect
143. #3711C2×C4semidirect
144. D3×C3⋊C8C2×C4semidirect
212. C3×#106C2×D3semidirect
213. C3×#106C2×D3semidirect
220. #818C2×D3semidirect
222. #817C2×D3semidirect
229. #808C2×D3semidirect
230. #808C2×D3semidirect
231. #808C2×D3semidirect
240. #807C2×D3semidirect
276. C32×C8C22×C4semidirect
277. C3⋊(C3⋊C8)C22×C4semidirect
278. C3×C3⋊C8C22×C4semidirect
279. C3×C3⋊C8C22×C4semidirect
408. ΓL(1,𝔽25)C4×D3semidirect
410. D3×C8C4×D3semidirect
478. #106D32semidirect
562. C3×C8C2×C4×D3semidirect
563. C3×C8C2×C4×D3semidirect
567. C3⋊C8C2×C4×D3semidirect
568. C3⋊C8C2×C4×D3semidirect
574. C3×D3#428semidirect
686. C32C2×#428semidirect
725. C8C4×D32semidirect
741. D3#4861direct (N × H)
767. C3C2×#4861semidirect
768. C3D3×#428semidirect

Maximal subgroups

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

subgroupindex
C2×D3×ΓL(1,𝔽25)2
D3×#8922
D32×C4⋊C42
#105925602
C3×#48612
C3×D3×#1062
#105906882
#105906812
D3×#8182
#105905842
#105905832
#105905812
D3×#8082
D3×#8072
#105904372
D3×#4283
C2×#48613