Finite Group Databasebeta

← C3×#79773 #11860256

Subgroups — C3×#79773 #11860256

Order 1152.

1156 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#914C211yesmaximal, characteristic
2C3×C4×#239C211yesmaximal, characteristic, complemented
3C3×C4×D3×D4C211yesmaximal, characteristic, complemented
4C32×#440C211yesmaximal, characteristic, complemented
5C3×Dic3×SD16C211yesmaximal, characteristic, complemented
6C3×#5026C211yesmaximal, characteristic, complemented
7C3×#5014C211yesmaximal, characteristic, complemented
8C3×#4881C211yesmaximal, characteristic, complemented
9C3×#4872C211yesmaximal, characteristic, complemented
10C3×#4803C211yesmaximal, characteristic, complemented
11C3×#4788C211yesmaximal, characteristic, complemented
12C3×#4770C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic, complemented
14C3×#4711C211yesmaximal, characteristic, complemented
15C3×#4707C211yesmaximal, characteristic, complemented
16C3×C4×AGL(1,ℤ/8)—31nomaximal
17#79773C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×C3×C4×D3—21no—
21C2×C32×SD16C2211yescharacteristic
22C32×C4×Q8C2211yescharacteristic, complemented
23C32×C4×D4C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic, complemented
25C2×C3×#215C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C3×C4×#67—21no—
29C3×#914C418yescomplemented
30C2×C3×D24C2211yescharacteristic
31C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
32C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
33C3×#893—21no—
34C3×#893C2211yescharacteristic
35C3×#893C2211yescharacteristic, complemented
36C3×#892—21no—
37C3×#892C2211yescharacteristic
38C3×D3×C4⋊C4C2211yescharacteristic
39C3×#67⋊C4—21no—
40C3×D3×C22⋊C4—21no—
41C3×C4×D12—21no—
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic, complemented
44C3×C42×D3—21no—
45C3×C42×D3C2211yescharacteristic
46C32×#107C2211yescharacteristic, complemented
47C32×#103C2211yescharacteristic, complemented
48C32×#102C2211yescharacteristic
49C32×#97C2211yescharacteristic, complemented
50C3×#835C2211yescharacteristic, complemented
51C3×#832C2211yescharacteristic
52C3×#821C2211yescharacteristic
53C3×#821C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55C3×C8×Dic3C2211yescharacteristic, complemented
56C3×C8×Dic3C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic
58C3×#809C2211yescharacteristic, complemented
59C3×#808C2211yescharacteristic, complemented
60C3×#807C2211yescharacteristic, complemented
61C3×#803C2211yescharacteristic, complemented
62C2×C3×AGL(1,ℤ/8)—31no—
63C3×C4×#41—31no—
64C2×C3×C4×D4—31no—
65C2×#914C2×C311yescharacteristic
66C4×#239C2×C311yescharacteristic, complemented
67C4×D3×D4C2×C311yescharacteristic, complemented
68C3×#442—31no—
69C3×#442—31no—
70C3×#440—21no—
71C3×#440—31no—
72C3×#440D311yescharacteristic, complemented
73C3×#440C2×C311yescharacteristic, complemented
74C3×C4×SD16—31no—
75C3×C4×SD16—31no—
76C3×C4×D8—31no—
77C3×C4×D8—31no—
78C3×#428—31no—
79C3×#418—31no—
80C3×#417—31no—
81C3×C4×M16—31no—
82Dic3×SD16C2×C311yescharacteristic, complemented
83#5026C2×C311yescharacteristic, complemented
84#5014C2×C311yescharacteristic, complemented
85#4881C2×C311yescharacteristic, complemented
86#4872C2×C311yescharacteristic, complemented
87#4803C2×C311yescharacteristic, complemented
88#4788C2×C311yescharacteristic, complemented
89#4770C2×C311yescharacteristic, complemented
90#4756C2×C311yescharacteristic, complemented
91#4711C2×C311yescharacteristic, complemented
92#4707C2×C311yescharacteristic, complemented
93C23×C3×D3—21no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×#239—22no—
100C3×#239C2×C414yescomplemented
101C3×D3×D4—22no—
102C3×D3×D4C2×C414yescomplemented
103C2×C3×D12—21no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3—21no—
107C2×C3×C4×D3—21no—
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—44no—
113C2×C3×C4×D3D411yescharacteristic
114C2×C3×C4×D3D411yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C32×SD16C2×C414yescomplemented
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C32×C4⋊C4—21no—
120C32×C4⋊C4C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122C32×C22⋊C4—21no—
123C32×C42—21no—
124C32×C42C2311yescharacteristic
125C3×#217—21no—
126C3×#215C2×C414yescomplemented
127C3×#213C2×C414yescomplemented
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4—21no—
132C3×(C2×D3)⋊C4—21no—
133C3×C4⋊Dic3—21no—
134C3×C4⋊Dic3C2311yescharacteristic
135C3×C4⋊Dic3C2311yescharacteristic
136C3×Dic3⋊C4—21no—
137C3×C4×Dic3—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3D411yescharacteristic
140C3×C4×Dic3D411yescharacteristic
141C3×C4×Dic3C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C3×D24C2×C414yescomplemented
145C3×ΓL(1,𝔽25)—22no—
146C3×ΓL(1,𝔽25)C2×C414yescomplemented
147C4×AGL(1,ℤ/8)—31noSylow
148C2×C3×#41—31no—
149C22×C3×D4—31no—
150C23×C3×C4—61no—
151C2×#239C22×C311yescharacteristic
152C2×D3×D4C22×C311yescharacteristic
153C22×C4×D3—21no—
154C3×AGL(1,ℤ/8)—38no—
155C2×C3×SD16—21no—
156C2×C3×SD16—31no—
157C2×C3×SD16C2×D311yescharacteristic
158C2×C3×SD16C22×C311yescharacteristic
159C2×C3×D8—31no—
160C2×C3×D8—31no—
161C2×C3×M16—31no—
162C2×C3×M16—31no—
163C3×C4×Q8—21no—
164C3×C4×Q8—31no—
165C3×C4×Q8C2×D311yescharacteristic, complemented
166C3×C4×Q8C22×C311yescharacteristic, complemented
167C3×C4×D4—21no—
168C3×C4×D4—31no—
169C3×C4×D4—31no—
170C3×C4×D4—31no—
171C3×C4×D4—31no—
172C3×C4×D4—31no—
173C3×C4×D4—61no—
174C3×C4×D4—61no—
175C3×C4×D4—61no—
176C3×C4×D4—61no—
177C3×C4×D4C2×D311yescharacteristic
178C3×C4×D4C22×C311yescharacteristic
179C3×#117—31no—
180C3×#117—61no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C22⋊C4—61no—
183C2×C3×C42—31no—
184C2×C3×C42—61no—
185Q8×Dic3C22×C311yescharacteristic, complemented
186C2×#215C22×C311yescharacteristic
187D4×Dic3C22×C311yescharacteristic
188C2×#213C22×C311yescharacteristic
189C4×#67—21no—
190#914C3×C418yescomplemented
191C2×D24C22×C311yescharacteristic
192C2×ΓL(1,𝔽25)C22×C311yescharacteristic
193C2×ΓL(1,𝔽25)C22×C311yescharacteristic
194#893—21no—
195#893C22×C311yescharacteristic
196#893C22×C311yescharacteristic, complemented
197#892—21no—
198#892C22×C311yescharacteristic
199D3×C4⋊C4C22×C311yescharacteristic
200#67⋊C4—21no—
201D3×C22⋊C4—21no—
202C4×D12—21no—
203C4×D12C22×C311yescharacteristic
204C4×D12C22×C311yescharacteristic, complemented
205C42×D3—21no—
206C42×D3C22×C311yescharacteristic
207C3×#107—21no—
208C3×#107—31no—
209C3×#107C2×D311yescharacteristic, complemented
210C3×#107C22×C311yescharacteristic, complemented
211C3×#106—31no—
212C3×#106—31no—
213C3×#103—21no—
214C3×#103—31no—
215C3×#103C2×D311yescharacteristic, complemented
216C3×#103C22×C311yescharacteristic, complemented
217C3×#102—21no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#102—31no—
222C3×#102—31no—
223C3×#102C2×D311yescharacteristic
224C3×#102C22×C311yescharacteristic
225C3×#97—21no—
226C3×#97—31no—
227C3×#97C2×D311yescharacteristic, complemented
228C3×#97C22×C311yescharacteristic, complemented
229C3×C4×C8—31no—
230C3×C4×C8—31no—
231#835C22×C311yescharacteristic, complemented
232#832C22×C311yescharacteristic
233#821C22×C311yescharacteristic
234#821C22×C311yescharacteristic, complemented
235#817C22×C311yescharacteristic, complemented
236C8×Dic3C22×C311yescharacteristic, complemented
237C8×Dic3C22×C311yescharacteristic, complemented
238#809C22×C311yescharacteristic
239#809C22×C311yescharacteristic, complemented
240#808C22×C311yescharacteristic, complemented
241#807C22×C311yescharacteristic, complemented
242#803C22×C311yescharacteristic, complemented
243C23×C32—21no—
244C22×C3×D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—24no—
247C22×C3×D3—42no—
248C22×C3×D3—42no—
249C22×C3×D3C2×D411yescharacteristic
250C32×Q8—21no—
251C32×Q8C22×C412yescomplemented
252C32×D4—21no—
253C32×D4C22×C412yes—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—42no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C3×#67—24no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—42no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×D12—24no—
269C3×D12—21no—
270C3×D12—21no—
271C3×D12C22×C412yes—
272C3×D12C22×C412yescomplemented
273C3×C4×D3—24no—
274C3×C4×D3—22no—
275C3×C4×D3—41no—
276C3×C4×D3—42no—
277C3×C4×D3—42no—
278C3×C4×D3—42no—
279C3×C4×D3—42no—
280C3×C4×D3—42no—
281C3×C4×D3C22×C412yes—
282C3×C4×D3#4112yes—
283C32×C8—21no—
284C32×C8C22×C412yescomplemented
285C3×C3⋊C8—21no—
286C3×C3⋊C8C22×C412yescomplemented
287C2×AGL(1,ℤ/8)—31no—
288C4×#41—31no—
289C2×C4×D4—31no—
290#442—31no—
291#442—31no—
292#440—31no—
293#440C3×D311yescharacteristic, complemented
294C4×SD16—31no—
295C4×SD16—31no—
296C4×D8—31no—
297C4×D8—31no—
298#428—31no—
299#418—31no—
300#417—31no—
301C4×M16—31no—
302C24×C3—61no—
303C23×D3—21no—
304C3×#41—34no—
305C3×#41—62no—
306C2×C3×Q8—21no—
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C23×C311yescharacteristic
309C2×C3×D4—21no—
310C2×C3×D4—34no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—61no—
314C2×C3×D4—62no—
315C2×C3×D4—61no—
316C2×C3×D4C22×D311yescharacteristic
317C2×C3×D4C23×C311yescharacteristic
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—41no—
324C22×C3×C4—61no—
325C22×C3×C4—61no—
326C22×C3×C4—61no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4—124no—
332C2×#67—21no—
333C22×Dic3—21no—
334#239—22no—
335#239C2×C3×C414yescomplemented
336D3×D4—22no—
337D3×D4C2×C3×C414yescomplemented
338C2×D12—21no—
339C2×D12C23×C311yescharacteristic
340C2×D12C23×C311yescharacteristic
341C2×C4×D3—21no—
342C2×C4×D3—21no—
343C2×C4×D3—21no—
344C2×C4×D3—21no—
345C2×C4×D3—21no—
346C2×C4×D3—21no—
347C2×C4×D3—44no—
348C2×C4×D3C3×D411yescharacteristic
349C2×C4×D3C3×D411yescharacteristic
350C2×C4×D3C23×C311yescharacteristic
351C3×SD16—24no—
352C3×SD16—34no—
353C3×SD16C4×D314yescomplemented
354C3×SD16C2×C3×C414yescomplemented
355C3×D8—34no—
356C3×D8—34no—
357C3×M16—34no—
358C3×M16—62no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8C22×D311yescharacteristic
364C2×C3×C8C22×D311yescharacteristic
365C2×C3×C8C23×C311yescharacteristic
366C2×C3×C8C23×C311yescharacteristic
367C3×C4⋊C4—21no—
368C3×C4⋊C4—21no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—21no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—41no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4—61no—
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C4⋊C4C22×D311yescharacteristic
378C3×C4⋊C4C23×C311yescharacteristic
379C3×C4⋊C4C23×C311yescharacteristic
380C3×C22⋊C4—21no—
381C3×C22⋊C4—21no—
382C3×C22⋊C4—41no—
383C3×C22⋊C4—61no—
384C3×C22⋊C4—61no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C42—21no—
390C3×C42—21no—
391C3×C42—21no—
392C3×C42—31no—
393C3×C42—31no—
394C3×C42—31no—
395C3×C42—41no—
396C3×C42—61no—
397C3×C42—61no—
398C3×C42C22×D311yescharacteristic
399C3×C42C23×C311yescharacteristic
400#217—21no—
401#215C2×C3×C414yescomplemented
402#213C2×C3×C414yescomplemented
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406(C2×D3)⋊C4—21no—
407(C2×D3)⋊C4—21no—
408C4⋊Dic3—21no—
409C4⋊Dic3C23×C311yescharacteristic
410C4⋊Dic3C23×C311yescharacteristic
411Dic3⋊C4—21no—
412C4×Dic3—21no—
413C4×Dic3—21no—
414C4×Dic3C3×D411yescharacteristic
415C4×Dic3C3×D411yescharacteristic
416C4×Dic3C23×C311yescharacteristic
417C2×C3⋊C8C23×C311yescharacteristic
418C2×C3⋊C8C23×C311yescharacteristic
419D24C2×C3×C414yescomplemented
420ΓL(1,𝔽25)—22no—
421ΓL(1,𝔽25)C2×C3×C414yescomplemented
422C22×C32—22no—
423C22×C32—41no—
424C22×C32—41no—
425C22×C32C22×D411yescharacteristic
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—22no—
430C2×C3×D3—48no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3C4×D412yes—
436C32×C4—22no—
437C32×C4—21no—
438C32×C4—21no—
439C32×C4—41no—
440C32×C4—41no—
441C32×C4C23×C411yescharacteristic
442C32×C4C2×#4111yescharacteristic
443C3×Dic3—21no—
444C3×Dic3—41no—
445C3×Dic3—41no—
446C3×Dic3C4×D412yes—
447C3×Dic3AGL(1,ℤ/8)12yescomplemented
448C2×#41—31no—
449C22×D4—31no—
450C23×C4—61no—
451AGL(1,ℤ/8)—38no—
452C2×SD16—31no—
453C2×SD16C2×C3×D311yescharacteristic
454C2×D8—31no—
455C2×D8—31no—
456C2×M16—31no—
457C2×M16—31no—
458C4×Q8—31no—
459C4×Q8C2×C3×D311yescharacteristic, complemented
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—31no—
465C4×D4—61no—
466C4×D4—61no—
467C4×D4—61no—
468C4×D4—61no—
469C4×D4C2×C3×D311yescharacteristic
470#117—31no—
471#117—61no—
472C2×C4⋊C4—31no—
473C2×C22⋊C4—61no—
474C2×C42—31no—
475C2×C42—61no—
476#107—31no—
477#107C2×C3×D311yescharacteristic, complemented
478#106—31no—
479#106—31no—
480#103—31no—
481#103C2×C3×D311yescharacteristic, complemented
482#102—31no—
483#102—31no—
484#102—31no—
485#102—31no—
486#102—31no—
487#102C2×C3×D311yescharacteristic
488#97—31no—
489#97C2×C3×D311yescharacteristic, complemented
490C4×C8—31no—
491C4×C8—31no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—41no—
496C23×C3—64no—
497C23×C3—61no—
498C23×C3—61no—
499C23×C3—122no—
500C23×C3—122no—
501C22×D3—21no—
502C22×D3—21no—
503C22×D3—24no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3C2×C3×D411yescharacteristic
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—22no—
510C3×Q8—41no—
511C3×Q8C2×C4×D312yescomplemented
512C3×Q8C22×C3×C412yescomplemented
513C3×D4—21no—
514C3×D4—21no—
515C3×D4—22no—
516C3×D4—32no—
517C3×D4—32no—
518C3×D4—41no—
519C3×D4—64no—
520C3×D4—64no—
521C3×D4—61no—
522C3×D4—61no—
523C3×D4C2×C4×D312yes—
524C3×D4C22×C3×C412yes—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—31no—
535C2×C3×C4—31no—
536C2×C3×C4—32no—
537C2×C3×C4—32no—
538C2×C3×C4—31no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—42no—
543C2×C3×C4—42no—
544C2×C3×C4—62no—
545C2×C3×C4—64no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—82no—
549C2×C3×C4—121no—
550C2×C3×C4—122no—
551C2×C3×C4—122no—
552C2×C3×C4—122no—
553C2×C3×C4—122no—
554C2×C3×C4—122no—
555C2×C3×C4—122no—
556C2×C3×C4D3×D411yescharacteristic
557C2×C3×C4D3×D411yescharacteristic
558C2×C3×C4C2×C3×D411yescharacteristic
559C2×C3×C4C2×C3×D411yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561C2×C3×C4C24×C311yescharacteristic
562#67—24no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—42no—
566C2×Dic3C2×C3×D411yescharacteristic
567C2×Dic3C2×C3×D411yescharacteristic
568C2×Dic3C2×C3×D411yescharacteristic
569D12—24no—
570D12—21no—
571D12—21no—
572D12C22×C3×C412yes—
573D12C22×C3×C412yescomplemented
574C4×D3—24no—
575C4×D3—22no—
576C4×D3—41no—
577C4×D3—42no—
578C4×D3—42no—
579C4×D3—42no—
580C4×D3—42no—
581C4×D3—42no—
582C4×D3C22×C3×C412yes—
583C4×D3C3×#4112yes—
584C3×C8—21no—
585C3×C8—21no—
586C3×C8—22no—
587C3×C8—32no—
588C3×C8—41no—
589C3×C8—61no—
590C3×C8C2×C4×D312yescomplemented
591C3×C8C22×C3×C412yescomplemented
592C3⋊C8—21no—
593C3⋊C8C22×C3×C412yescomplemented
594C2×C32—42no—
595C2×C32C2×C4×D411yescharacteristic
596C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
597C2×C32#57511yescharacteristic
598C3×D3—22no—
599C3×D3—42no—
600C3×D3—42no—
601C24—61no—
602#41—34no—
603#41—62no—
604C2×Q8C22×C3×D311yescharacteristic
605C2×D4—34no—
606C2×D4—31no—
607C2×D4—31no—
608C2×D4—61no—
609C2×D4—62no—
610C2×D4—61no—
611C2×D4C22×C3×D311yescharacteristic
612C22×C4—21no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—31no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—124no—
624SD16—34no—
625SD16C3×C4×D314yescomplemented
626D8—34no—
627D8—34no—
628M16—34no—
629M16—62no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8C22×C3×D311yescharacteristic
633C2×C8C22×C3×D311yescharacteristic
634C4⋊C4—21no—
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4C22×C3×D311yescharacteristic
640C4⋊C4C22×C3×D311yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C42—21no—
649C42—31no—
650C42—31no—
651C42—31no—
652C42—61no—
653C42—61no—
654C42C22×C3×D311yescharacteristic
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—42no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—61no—
665C22×C3—61no—
666C22×C3—62no—
667C22×C3—62no—
668C22×C3—81no—
669C22×C3—81no—
670C22×C3—128no—
671C22×C3—121no—
672C22×C3—121no—
673C22×C3—121no—
674C22×C3—121no—
675C22×C3C2×D3×D411yescharacteristic
676C22×C3C22×C3×D411yescharacteristic
677C2×D3—21no—
678C2×D3—21no—
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—48no—
682C2×D3—41no—
683C2×D3—41no—
684C2×D3—41no—
685C2×D3—41no—
686C2×D3C3×C4×D412yes—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—22no—
692C3×C4—22no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—32no—
696C3×C4—32no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—42no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—61no—
705C3×C4—81no—
706C3×C4—81no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4C22×C4×D311yescharacteristic
710C3×C4D3×#4111yescharacteristic
711C3×C4C23×C3×C411yescharacteristic
712C3×C4C2×C3×#4111yescharacteristic
713Dic3—21no—
714Dic3—41no—
715Dic3—41no—
716Dic3C3×C4×D412yes—
717Dic3C3×AGL(1,ℤ/8)12yescomplemented
718C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
719C23—21no—
720C23—31no—
721C23—64no—
722C23—61no—
723C23—61no—
724C23—122no—
725C23—122no—
726Q8—21no—
727Q8C2×C3×C4×D312yescomplemented
728D4—21no—
729D4—32no—
730D4—32no—
731D4—64no—
732D4—64no—
733D4—61no—
734D4—61no—
735D4C2×C3×C4×D312yes—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—32no—
742C2×C4—32no—
743C2×C4—31no—
744C2×C4—42no—
745C2×C4—62no—
746C2×C4—64no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—121no—
750C2×C4—122no—
751C2×C4—122no—
752C2×C4—122no—
753C2×C4—122no—
754C2×C4—122no—
755C2×C4—122no—
756C2×C4C3×D3×D411yescharacteristic
757C2×C4C3×D3×D411yescharacteristic
758C2×C4C23×C3×D311yescharacteristic
759C8—21no—
760C8—32no—
761C8—61no—
762C8C2×C3×C4×D312yescomplemented
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—42no—
767C2×C3—42no—
768C2×C3—62no—
769C2×C3—82no—
770C2×C3—122no—
771C2×C3—122no—
772C2×C3C4×D3×D411yescharacteristic
773C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
774C2×C3#577711yescharacteristic
775C2×C3C2×C3×C4×D411yescharacteristic
776C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
777C2×C3C3×#57511yescharacteristic
778D3—22no—
779D3—42no—
780D3—42no—
781C22—22no—
782C22—32no—
783C22—41no—
784C22—41no—
785C22—61no—
786C22—61no—
787C22—62no—
788C22—62no—
789C22—128no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22C2×C3×D3×D411yescharacteristic
795C4—21no—
796C4—21no—
797C4—22no—
798C4—32no—
799C4—32no—
800C4—41no—
801C4—41no—
802C4—61no—
803C4—121no—
804C4—121no—
805C4C22×C3×C4×D311yescharacteristic
806C4C3×D3×#4111yescharacteristic
807C3—21no—
808C3#7977311yescharacteristic, direct product factor
809C3C3×C4×AGL(1,ℤ/8)11yescharacteristic, complemented
810C2—42no—
811C2—62no—
812C2—122no—
813C2—122no—
814C2C3×C4×D3×D411yescharacteristic
815C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
816C2C3×#577711yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#440C2
socleC22×C32C22×D4
prime radicalC2×C3×#914C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#440D3
hypocenterC3C3×C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
2. C3×C4×#239C2semidirect
3. C3×C4×D3×D4C2semidirect
4. C32×#440C2semidirect
5. C3×Dic3×SD16C2semidirect
6. C3×#5026C2semidirect
7. C3×#5014C2semidirect
8. C3×#4881C2semidirect
9. C3×#4872C2semidirect
10. C3×#4803C2semidirect
11. C3×#4788C2semidirect
12. C3×#4770C2semidirect
13. C3×#4756C2semidirect
14. C3×#4711C2semidirect
15. C3×#4707C2semidirect
17. #79773C3direct (N × H)
22. C32×C4×Q8C22semidirect
24. C3×Q8×Dic3C22semidirect
29. C3×#914C4semidirect
35. C3×#893C22semidirect
43. C3×C4×D12C22semidirect
46. C32×#107C22semidirect
47. C32×#103C22semidirect
49. C32×#97C22semidirect
50. C3×#835C22semidirect
53. C3×#821C22semidirect
54. C3×#817C22semidirect
55. C3×C8×Dic3C22semidirect
56. C3×C8×Dic3C22semidirect
58. C3×#809C22semidirect
59. C3×#808C22semidirect
60. C3×#807C22semidirect
61. C3×#803C22semidirect
66. C4×#239C2×C3semidirect
67. C4×D3×D4C2×C3semidirect
72. C3×#440D3semidirect
73. C3×#440C2×C3semidirect
82. Dic3×SD16C2×C3semidirect
83. #5026C2×C3semidirect
84. #5014C2×C3semidirect
85. #4881C2×C3semidirect
86. #4872C2×C3semidirect
87. #4803C2×C3semidirect
88. #4788C2×C3semidirect
89. #4770C2×C3semidirect
90. #4756C2×C3semidirect
91. #4711C2×C3semidirect
92. #4707C2×C3semidirect
100. C3×#239C2×C4semidirect
102. C3×D3×D4C2×C4semidirect
116. C32×SD16C2×C4semidirect
126. C3×#215C2×C4semidirect
127. C3×#213C2×C4semidirect
144. C3×D24C2×C4semidirect
146. C3×ΓL(1,𝔽25)C2×C4semidirect
165. C3×C4×Q8C2×D3semidirect
166. C3×C4×Q8C22×C3semidirect
185. Q8×Dic3C22×C3semidirect
190. #914C3×C4semidirect
196. #893C22×C3semidirect
204. C4×D12C22×C3semidirect
209. C3×#107C2×D3semidirect
210. C3×#107C22×C3semidirect
215. C3×#103C2×D3semidirect
216. C3×#103C22×C3semidirect
227. C3×#97C2×D3semidirect
228. C3×#97C22×C3semidirect
231. #835C22×C3semidirect
234. #821C22×C3semidirect
235. #817C22×C3semidirect
236. C8×Dic3C22×C3semidirect
237. C8×Dic3C22×C3semidirect
239. #809C22×C3semidirect
240. #808C22×C3semidirect
241. #807C22×C3semidirect
242. #803C22×C3semidirect
251. C32×Q8C22×C4semidirect
272. C3×D12C22×C4semidirect
284. C32×C8C22×C4semidirect
286. C3×C3⋊C8C22×C4semidirect
293. #440C3×D3semidirect
335. #239C2×C3×C4semidirect
337. D3×D4C2×C3×C4semidirect
353. C3×SD16C4×D3semidirect
354. C3×SD16C2×C3×C4semidirect
401. #215C2×C3×C4semidirect
402. #213C2×C3×C4semidirect
419. D24C2×C3×C4semidirect
421. ΓL(1,𝔽25)C2×C3×C4semidirect
447. C3×Dic3AGL(1,ℤ/8)semidirect
459. C4×Q8C2×C3×D3semidirect
477. #107C2×C3×D3semidirect
481. #103C2×C3×D3semidirect
489. #97C2×C3×D3semidirect
511. C3×Q8C2×C4×D3semidirect
512. C3×Q8C22×C3×C4semidirect
573. D12C22×C3×C4semidirect
590. C3×C8C2×C4×D3semidirect
591. C3×C8C22×C3×C4semidirect
593. C3⋊C8C22×C3×C4semidirect
625. SD16C3×C4×D3semidirect
717. Dic3C3×AGL(1,ℤ/8)semidirect
718. C32C4×AGL(1,ℤ/8)semidirect
727. Q8C2×C3×C4×D3semidirect
762. C8C2×C3×C4×D3semidirect
808. C3#79773direct (N × H)
809. C3C3×C4×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
C2×C3×#9142
C3×C4×#2392
C3×C4×D3×D42
C32×#4402
C3×Dic3×SD162
C3×#50262
C3×#50142
C3×#48812
C3×#48722
C3×#48032
C3×#47882
C3×#47702
C3×#47562
C3×#47112
C3×#47072
C3×C4×AGL(1,ℤ/8)3
#797733