Finite Group Databasebeta

← C3×#79865 #11860274

Subgroups — C3×#79865 #11860274

Order 1152.

1162 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#911C211yesmaximal, characteristic
2C3×C4×D3×D4C211yesmaximal, characteristic, complemented
3C3×C4×#237C211yesmaximal, characteristic, complemented
4C32×#442C211yesmaximal, characteristic, complemented
5C3×Dic3×D8C211yesmaximal, characteristic, complemented
6C3×#5018C211yesmaximal, characteristic, complemented
7C3×#5014C211yesmaximal, characteristic, complemented
8C3×#4861C211yesmaximal, characteristic, complemented
9C3×#4852C211yesmaximal, characteristic, complemented
10C3×#4771C211yesmaximal, characteristic, complemented
11C3×#4770C211yesmaximal, characteristic, complemented
12C3×#4758C211yesmaximal, characteristic, complemented
13C3×#4756C211yesmaximal, characteristic, complemented
14C3×#4710C211yesmaximal, characteristic, complemented
15C3×#4707C211yesmaximal, characteristic, complemented
16C3×C4×AGL(1,ℤ/8)—31nomaximal
17#79865C311yesmaximal, characteristic, direct product factor
18C2×C3×#237C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×C3×C4×D3—21no—
21C2×C32×D8C2211yescharacteristic
22C32×C4×D4C2211yescharacteristic
23C32×C4×D4C2211yescharacteristic, complemented
24C3×D4×Dic3C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic, complemented
26C2×C3×#214C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C3×C4×#67—21no—
29C3×C4×#67—21no—
30C2×C3×C4×Dic3—21no—
31C3×#911C418yescomplemented
32C2×C3×#204C2211yescharacteristic
33C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
34C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
35C3×#893C2211yescharacteristic
36C3×#892C2211yescharacteristic
37C3×D3×C4⋊C4C2211yescharacteristic
38C3×#887C2211yescharacteristic, complemented
39C3×#67⋊C4—21no—
40C3×#67⋊C4—21no—
41C3×D3×C22⋊C4—21no—
42C3×#877—21no—
43C3×C4×D12C2211yescharacteristic
44C3×C42×D3C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic, complemented
46C32×#106C2211yescharacteristic, complemented
47C32×#102C2211yescharacteristic
48C32×#102C2211yescharacteristic, complemented
49C32×#97C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic
51C3×#832C2211yescharacteristic, complemented
52C3×#821C2211yescharacteristic
53C3×#818C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55C3×C8×Dic3C2211yescharacteristic, complemented
56C3×C8×Dic3C2211yescharacteristic, complemented
57C3×#810C2211yescharacteristic, complemented
58C3×#809C2211yescharacteristic
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×#911C2×C311yescharacteristic
66C4×D3×D4C2×C311yescharacteristic, complemented
67C4×#237C2×C311yescharacteristic, complemented
68C3×#442—21no—
69C3×#442—31no—
70C3×#442D311yescharacteristic, complemented
71C3×#442C2×C311yescharacteristic, complemented
72C3×#440—31no—
73C3×#440—31no—
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×D8C2×C311yescharacteristic, complemented
83#5018C2×C311yescharacteristic, complemented
84#5014C2×C311yescharacteristic, complemented
85#4861C2×C311yescharacteristic, complemented
86#4852C2×C311yescharacteristic, complemented
87#4771C2×C311yescharacteristic, complemented
88#4770C2×C311yescharacteristic, complemented
89#4758C2×C311yescharacteristic, complemented
90#4756C2×C311yescharacteristic, complemented
91#4710C2×C311yescharacteristic, complemented
92#4707C2×C311yescharacteristic, complemented
93C23×C3×D3—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C22×C32×C4—21no—
97C22×C32×C4—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237C2×C414yescomplemented
105C3×D3×D4—22no—
106C3×D3×D4C2×C414yescomplemented
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—21no—
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3—44no—
112C2×C3×C4×D3D411yescharacteristic
113C2×C3×C4×D3D411yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C32×D8C2×C414yescomplemented
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C32×C4⋊C4C2311yescharacteristic
120C32×C4⋊C4C2311yescharacteristic
121C32×C22⋊C4—21no—
122C32×C22⋊C4—21no—
123C32×C42C2311yescharacteristic
124C3×#217—21no—
125C3×#217—21no—
126C3×#214C2×C414yescomplemented
127C3×#213C2×C414yescomplemented
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×C4×Dic3—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×#204C2×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×#237C22×C311yescharacteristic
152C2×D3×D4C22×C311yescharacteristic
153C22×C4×D3—21no—
154C3×AGL(1,ℤ/8)—38no—
155C2×C3×SD16—31no—
156C2×C3×SD16—31no—
157C2×C3×D8—21no—
158C2×C3×D8—31no—
159C2×C3×D8C2×D311yescharacteristic
160C2×C3×D8C22×C311yescharacteristic
161C2×C3×M16—31no—
162C2×C3×M16—31no—
163C3×C4×Q8—31no—
164C3×C4×Q8—31no—
165C3×C4×D4—21no—
166C3×C4×D4—21no—
167C3×C4×D4—31no—
168C3×C4×D4—31no—
169C3×C4×D4—31no—
170C3×C4×D4—31no—
171C3×C4×D4—61no—
172C3×C4×D4—61no—
173C3×C4×D4—61no—
174C3×C4×D4—61no—
175C3×C4×D4C2×D311yescharacteristic
176C3×C4×D4C2×D311yescharacteristic, complemented
177C3×C4×D4C22×C311yescharacteristic
178C3×C4×D4C22×C311yescharacteristic, complemented
179C3×#117—31no—
180C3×#117—61no—
181C2×C3×C4⋊C4—31no—
182C2×C3×C22⋊C4—61no—
183C2×C3×C42—31no—
184C2×C3×C42—61no—
185D4×Dic3C22×C311yescharacteristic
186D4×Dic3C22×C311yescharacteristic, complemented
187C2×#214C22×C311yescharacteristic
188C2×#213C22×C311yescharacteristic
189C4×#67—21no—
190C4×#67—21no—
191C2×C4×Dic3—21no—
192#911C3×C418yescomplemented
193C2×#204C22×C311yescharacteristic
194C2×ΓL(1,𝔽25)C22×C311yescharacteristic
195C2×ΓL(1,𝔽25)C22×C311yescharacteristic
196#893C22×C311yescharacteristic
197#892C22×C311yescharacteristic
198D3×C4⋊C4C22×C311yescharacteristic
199#887C22×C311yescharacteristic, complemented
200#67⋊C4—21no—
201#67⋊C4—21no—
202D3×C22⋊C4—21no—
203#877—21no—
204C4×D12C22×C311yescharacteristic
205C42×D3C22×C311yescharacteristic
206C4×Dic6C22×C311yescharacteristic, complemented
207C3×#107—31no—
208C3×#107—31no—
209C3×#106—21no—
210C3×#106—31no—
211C3×#106C2×D311yescharacteristic, complemented
212C3×#106C22×C311yescharacteristic, complemented
213C3×#103—31no—
214C3×#103—31no—
215C3×#102—21no—
216C3×#102—21no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#102—31no—
221C3×#102C2×D311yescharacteristic
222C3×#102C2×D311yescharacteristic, complemented
223C3×#102C22×C311yescharacteristic
224C3×#102C22×C311yescharacteristic, complemented
225C3×#97—21no—
226C3×#97—31no—
227C3×#97C2×D311yescharacteristic, complemented
228C3×#97C22×C311yescharacteristic, complemented
229C3×C4×C8—31no—
230C3×C4×C8—31no—
231#832C22×C311yescharacteristic
232#832C22×C311yescharacteristic, complemented
233#821C22×C311yescharacteristic
234#818C22×C311yescharacteristic, complemented
235#816C22×C311yescharacteristic, complemented
236C8×Dic3C22×C311yescharacteristic, complemented
237C8×Dic3C22×C311yescharacteristic, complemented
238#810C22×C311yescharacteristic, complemented
239#809C22×C311yescharacteristic
240#808C22×C311yescharacteristic, complemented
241#807C22×C311yescharacteristic, complemented
242#803C22×C311yescharacteristic, complemented
243C23×C32—21no—
244C23×C32—21no—
245C22×C3×D3—21no—
246C22×C3×D3—24no—
247C22×C3×D3—42no—
248C22×C3×D3—42no—
249C22×C3×D3C2×D411yescharacteristic
250C32×D4—21no—
251C32×D4—21no—
252C32×D4C22×C412yes—
253C32×D4C22×C412yescomplemented
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—42no—
257C2×C32×C4—42no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2×D411yescharacteristic
260C2×C32×C4C2411yescharacteristic
261C3×#67—24no—
262C3×#67—24no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—24no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—42no—
268C2×C3×Dic3—42no—
269C2×C3×Dic3C2×D411yescharacteristic
270C2×C3×Dic3C2×D411yescharacteristic
271C2×C3×Dic3C2×D411yescharacteristic
272C3×D12—21no—
273C3×D12C22×C412yes—
274C3×C4×D3—22no—
275C3×C4×D3—41no—
276C3×C4×D3—42no—
277C3×C4×D3—42no—
278C3×C4×D3—42no—
279C3×C4×D3C22×C412yes—
280C3×C4×D3#4112yes—
281C3×Dic6—21no—
282C3×Dic6C22×C412yescomplemented
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#442C3×D311yescharacteristic, complemented
292#440—31no—
293#440—31no—
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—31no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—34no—
310C2×C3×D4—31no—
311C2×C3×D4—62no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4C22×D311yescharacteristic
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C23×C311yescharacteristic
317C2×C3×D4C23×C311yescharacteristic
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—41no—
326C22×C3×C4—41no—
327C22×C3×C4—61no—
328C22×C3×C4—61no—
329C22×C3×C4—61no—
330C22×C3×C4—61no—
331C22×C3×C4—61no—
332C22×C3×C4—61no—
333C22×C3×C4—124no—
334C2×#67—21no—
335C2×#67—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339#237—22no—
340#237C2×C3×C414yescomplemented
341D3×D4—22no—
342D3×D4C2×C3×C414yescomplemented
343C2×D12C23×C311yescharacteristic
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
351C2×Dic6C23×C311yescharacteristic
352C3×SD16—34no—
353C3×SD16—34no—
354C3×D8—24no—
355C3×D8—34no—
356C3×D8C4×D314yescomplemented
357C3×D8C2×C3×C414yescomplemented
358C3×M16—34no—
359C3×M16—62no—
360C2×C3×C8—21no—
361C2×C3×C8—21no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C2×C3×C8C22×D311yescharacteristic
365C2×C3×C8C22×D311yescharacteristic
366C2×C3×C8C23×C311yescharacteristic
367C2×C3×C8C23×C311yescharacteristic
368C3×C4⋊C4—21no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—31no—
371C3×C4⋊C4—31no—
372C3×C4⋊C4—61no—
373C3×C4⋊C4—61no—
374C3×C4⋊C4—61no—
375C3×C4⋊C4C22×D311yescharacteristic
376C3×C4⋊C4C22×D311yescharacteristic
377C3×C4⋊C4C23×C311yescharacteristic
378C3×C4⋊C4C23×C311yescharacteristic
379C3×C22⋊C4—21no—
380C3×C22⋊C4—21no—
381C3×C22⋊C4—21no—
382C3×C22⋊C4—21no—
383C3×C22⋊C4—41no—
384C3×C22⋊C4—41no—
385C3×C22⋊C4—61no—
386C3×C22⋊C4—61no—
387C3×C22⋊C4—61no—
388C3×C22⋊C4—61no—
389C3×C22⋊C4—61no—
390C3×C42—21no—
391C3×C42—31no—
392C3×C42—31no—
393C3×C42—31no—
394C3×C42—61no—
395C3×C42—61no—
396C3×C42—61no—
397C3×C42C22×D311yescharacteristic
398C3×C42C23×C311yescharacteristic
399#217—21no—
400#217—21no—
401#214C2×C3×C414yescomplemented
402#213C2×C3×C414yescomplemented
403(C2×D3)⋊C4—21no—
404(C2×D3)⋊C4—21no—
405(C2×D3)⋊C4—21no—
406C4⋊Dic3C23×C311yescharacteristic
407C4⋊Dic3C23×C311yescharacteristic
408Dic3⋊C4—21no—
409Dic3⋊C4—21no—
410Dic3⋊C4—21no—
411C4×Dic3—21no—
412C4×Dic3—21no—
413C4×Dic3—21no—
414C4×Dic3C3×D411yescharacteristic
415C4×Dic3C3×D411yescharacteristic
416C4×Dic3C23×C311yescharacteristic
417C2×C3⋊C8C23×C311yescharacteristic
418C2×C3⋊C8C23×C311yescharacteristic
419#204C2×C3×C414yescomplemented
420ΓL(1,𝔽25)—22no—
421ΓL(1,𝔽25)C2×C3×C414yescomplemented
422C22×C32—22no—
423C22×C32—22no—
424C22×C32—41no—
425C22×C32—41no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32C22×D411yescharacteristic
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—22no—
432C2×C3×D3—48no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3C4×D412yes—
436C32×C4—21no—
437C32×C4—21no—
438C32×C4—41no—
439C32×C4—41no—
440C32×C4C23×C411yescharacteristic
441C32×C4C2×#4111yescharacteristic
442C3×Dic3—22no—
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×SD16—31no—
454C2×D8—31no—
455C2×D8C2×C3×D311yescharacteristic
456C2×M16—31no—
457C2×M16—31no—
458C4×Q8—31no—
459C4×Q8—31no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—31no—
463C4×D4—31no—
464C4×D4—61no—
465C4×D4—61no—
466C4×D4—61no—
467C4×D4—61no—
468C4×D4C2×C3×D311yescharacteristic
469C4×D4C2×C3×D311yescharacteristic, complemented
470#117—31no—
471#117—61no—
472C2×C4⋊C4—31no—
473C2×C22⋊C4—61no—
474C2×C42—31no—
475C2×C42—61no—
476#107—31no—
477#107—31no—
478#106—31no—
479#106C2×C3×D311yescharacteristic, complemented
480#103—31no—
481#103—31no—
482#102—31no—
483#102—31no—
484#102—31no—
485#102—31no—
486#102C2×C3×D311yescharacteristic
487#102C2×C3×D311yescharacteristic, complemented
488#97—31no—
489#97C2×C3×D311yescharacteristic, complemented
490C4×C8—31no—
491C4×C8—31no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3—21no—
495C23×C3—21no—
496C23×C3—31no—
497C23×C3—41no—
498C23×C3—41no—
499C23×C3—64no—
500C23×C3—61no—
501C23×C3—122no—
502C23×C3—122no—
503C22×D3—21no—
504C22×D3—24no—
505C22×D3—42no—
506C22×D3—42no—
507C22×D3C2×C3×D411yescharacteristic
508C3×Q8—32no—
509C3×Q8—61no—
510C3×D4—21no—
511C3×D4—21no—
512C3×D4—21no—
513C3×D4—21no—
514C3×D4—22no—
515C3×D4—22no—
516C3×D4—32no—
517C3×D4—41no—
518C3×D4—41no—
519C3×D4—64no—
520C3×D4—64no—
521C3×D4—61no—
522C3×D4C2×C4×D312yes—
523C3×D4C2×C4×D312yescomplemented
524C3×D4C22×C3×C412yes—
525C3×D4C22×C3×C412yescomplemented
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—31no—
534C2×C3×C4—31no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—31no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—42no—
541C2×C3×C4—42no—
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—61no—
549C2×C3×C4—82no—
550C2×C3×C4—82no—
551C2×C3×C4—121no—
552C2×C3×C4—122no—
553C2×C3×C4—122no—
554C2×C3×C4—122no—
555C2×C3×C4—122no—
556C2×C3×C4—122no—
557C2×C3×C4D3×D411yescharacteristic
558C2×C3×C4D3×D411yescharacteristic
559C2×C3×C4C2×C3×D411yescharacteristic
560C2×C3×C4C2×C3×D411yescharacteristic
561C2×C3×C4C23×D311yescharacteristic
562C2×C3×C4C24×C311yescharacteristic
563#67—24no—
564#67—24no—
565C2×Dic3—21no—
566C2×Dic3—24no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—42no—
570C2×Dic3—42no—
571C2×Dic3C2×C3×D411yescharacteristic
572C2×Dic3C2×C3×D411yescharacteristic
573C2×Dic3C2×C3×D411yescharacteristic
574D12—21no—
575D12C22×C3×C412yes—
576C4×D3—22no—
577C4×D3—41no—
578C4×D3—42no—
579C4×D3—42no—
580C4×D3—42no—
581C4×D3C22×C3×C412yes—
582C4×D3C3×#4112yes—
583Dic6—21no—
584Dic6C22×C3×C412yescomplemented
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—22no—
588C3×C8—32no—
589C3×C8—41no—
590C3×C8—61no—
591C3×C8C2×C4×D312yescomplemented
592C3×C8C22×C3×C412yescomplemented
593C3⋊C8—21no—
594C3⋊C8C22×C3×C412yescomplemented
595C2×C32—42no—
596C2×C32—42no—
597C2×C32C2×C4×D411yescharacteristic
598C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
599C2×C32#57511yescharacteristic
600C3×D3—22no—
601C3×D3—42no—
602C24—61no—
603#41—34no—
604#41—62no—
605C2×Q8—31no—
606C2×D4—34no—
607C2×D4—31no—
608C2×D4—62no—
609C2×D4—61no—
610C2×D4—61no—
611C2×D4C22×C3×D311yescharacteristic
612C2×D4C22×C3×D311yescharacteristic
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—31no—
618C22×C4—61no—
619C22×C4—61no—
620C22×C4—61no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—61no—
624C22×C4—124no—
625SD16—34no—
626SD16—34no—
627D8—34no—
628D8C3×C4×D314yescomplemented
629M16—34no—
630M16—62no—
631C2×C8—31no—
632C2×C8—31no—
633C2×C8C22×C3×D311yescharacteristic
634C2×C8C22×C3×D311yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4C22×C3×D311yescharacteristic
641C4⋊C4C22×C3×D311yescharacteristic
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—61no—
647C22⋊C4—61no—
648C22⋊C4—61no—
649C42—31no—
650C42—31no—
651C42—31no—
652C42—61no—
653C42—61no—
654C42—61no—
655C42C22×C3×D311yescharacteristic
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—21no—
661C22×C3—32no—
662C22×C3—42no—
663C22×C3—42no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3—41no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—62no—
675C22×C3—81no—
676C22×C3—81no—
677C22×C3—81no—
678C22×C3—81no—
679C22×C3—128no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3C2×D3×D411yescharacteristic
683C22×C3C22×C3×D411yescharacteristic
684C2×D3—21no—
685C2×D3—21no—
686C2×D3—22no—
687C2×D3—48no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3C3×C4×D412yes—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—32no—
698C3×C4—32no—
699C3×C4—41no—
700C3×C4—41no—
701C3×C4—41no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—61no—
706C3×C4—62no—
707C3×C4—81no—
708C3×C4—81no—
709C3×C4—121no—
710C3×C4—121no—
711C3×C4C22×C4×D311yescharacteristic
712C3×C4D3×#4111yescharacteristic
713C3×C4C23×C3×C411yescharacteristic
714C3×C4C2×C3×#4111yescharacteristic
715Dic3—21no—
716Dic3—22no—
717Dic3—41no—
718Dic3—41no—
719Dic3C3×C4×D412yes—
720Dic3C3×AGL(1,ℤ/8)12yescomplemented
721C32C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
722C23—21no—
723C23—21no—
724C23—31no—
725C23—64no—
726C23—61no—
727C23—122no—
728C23—122no—
729Q8—32no—
730Q8—61no—
731D4—21no—
732D4—21no—
733D4—32no—
734D4—64no—
735D4—64no—
736D4—61no—
737D4C2×C3×C4×D312yes—
738D4C2×C3×C4×D312yescomplemented
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—32no—
744C2×C4—32no—
745C2×C4—31no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—62no—
749C2×C4—64no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—121no—
754C2×C4—122no—
755C2×C4—122no—
756C2×C4—122no—
757C2×C4—122no—
758C2×C4—122no—
759C2×C4C3×D3×D411yescharacteristic
760C2×C4C3×D3×D411yescharacteristic
761C2×C4C23×C3×D311yescharacteristic
762C8—21no—
763C8—32no—
764C8—61no—
765C8C2×C3×C4×D312yescomplemented
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—42no—
770C2×C3—42no—
771C2×C3—42no—
772C2×C3—42no—
773C2×C3—62no—
774C2×C3—82no—
775C2×C3—82no—
776C2×C3—122no—
777C2×C3C4×D3×D411yescharacteristic
778C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
779C2×C3#577311yescharacteristic
780C2×C3C2×C3×C4×D411yescharacteristic
781C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
782C2×C3C3×#57511yescharacteristic
783D3—22no—
784D3—42no—
785C22—22no—
786C22—22no—
787C22—32no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—61no—
793C22—61no—
794C22—62no—
795C22—128no—
796C22—121no—
797C22—121no—
798C22C2×C3×D3×D411yescharacteristic
799C4—21no—
800C4—21no—
801C4—32no—
802C4—32no—
803C4—41no—
804C4—41no—
805C4—61no—
806C4—62no—
807C4—121no—
808C4—121no—
809C4C22×C3×C4×D311yescharacteristic
810C4C3×D3×#4111yescharacteristic
811C3—21no—
812C3#7986511yescharacteristic, direct product factor
813C3C3×C4×AGL(1,ℤ/8)11yescharacteristic, complemented
814C2—42no—
815C2—42no—
816C2—62no—
817C2—122no—
818C2C3×C4×D3×D411yescharacteristic
819C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
820C2C3×#577311yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutatorC3×C4C23×C3×C4
FrattiniC2×C4C23×C3×D3
FittingC32×#442C2
socleC22×C32C22×D4
prime radicalC2×C3×#911C2
cosocleC2×C3×C4C24×C3
hypercenterC3×#442D3
hypocenterC3C3×C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#442

Complements

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

NH ≅ G/Ntype
2. C3×C4×D3×D4C2semidirect
3. C3×C4×#237C2semidirect
4. C32×#442C2semidirect
5. C3×Dic3×D8C2semidirect
6. C3×#5018C2semidirect
7. C3×#5014C2semidirect
8. C3×#4861C2semidirect
9. C3×#4852C2semidirect
10. C3×#4771C2semidirect
11. C3×#4770C2semidirect
12. C3×#4758C2semidirect
13. C3×#4756C2semidirect
14. C3×#4710C2semidirect
15. C3×#4707C2semidirect
17. #79865C3direct (N × H)
23. C32×C4×D4C22semidirect
25. C3×D4×Dic3C22semidirect
31. C3×#911C4semidirect
38. C3×#887C22semidirect
45. C3×C4×Dic6C22semidirect
46. C32×#106C22semidirect
48. C32×#102C22semidirect
49. C32×#97C22semidirect
51. C3×#832C22semidirect
53. C3×#818C22semidirect
54. C3×#816C22semidirect
55. C3×C8×Dic3C22semidirect
56. C3×C8×Dic3C22semidirect
57. C3×#810C22semidirect
59. C3×#808C22semidirect
60. C3×#807C22semidirect
61. C3×#803C22semidirect
66. C4×D3×D4C2×C3semidirect
67. C4×#237C2×C3semidirect
70. C3×#442D3semidirect
71. C3×#442C2×C3semidirect
82. Dic3×D8C2×C3semidirect
83. #5018C2×C3semidirect
84. #5014C2×C3semidirect
85. #4861C2×C3semidirect
86. #4852C2×C3semidirect
87. #4771C2×C3semidirect
88. #4770C2×C3semidirect
89. #4758C2×C3semidirect
90. #4756C2×C3semidirect
91. #4710C2×C3semidirect
92. #4707C2×C3semidirect
104. C3×#237C2×C4semidirect
106. C3×D3×D4C2×C4semidirect
116. C32×D8C2×C4semidirect
126. C3×#214C2×C4semidirect
127. C3×#213C2×C4semidirect
144. C3×#204C2×C4semidirect
146. C3×ΓL(1,𝔽25)C2×C4semidirect
176. C3×C4×D4C2×D3semidirect
178. C3×C4×D4C22×C3semidirect
186. D4×Dic3C22×C3semidirect
192. #911C3×C4semidirect
199. #887C22×C3semidirect
206. C4×Dic6C22×C3semidirect
211. C3×#106C2×D3semidirect
212. C3×#106C22×C3semidirect
222. C3×#102C2×D3semidirect
224. C3×#102C22×C3semidirect
227. C3×#97C2×D3semidirect
228. C3×#97C22×C3semidirect
232. #832C22×C3semidirect
234. #818C22×C3semidirect
235. #816C22×C3semidirect
236. C8×Dic3C22×C3semidirect
237. C8×Dic3C22×C3semidirect
238. #810C22×C3semidirect
240. #808C22×C3semidirect
241. #807C22×C3semidirect
242. #803C22×C3semidirect
253. C32×D4C22×C4semidirect
282. C3×Dic6C22×C4semidirect
284. C32×C8C22×C4semidirect
286. C3×C3⋊C8C22×C4semidirect
291. #442C3×D3semidirect
340. #237C2×C3×C4semidirect
342. D3×D4C2×C3×C4semidirect
356. C3×D8C4×D3semidirect
357. C3×D8C2×C3×C4semidirect
401. #214C2×C3×C4semidirect
402. #213C2×C3×C4semidirect
419. #204C2×C3×C4semidirect
421. ΓL(1,𝔽25)C2×C3×C4semidirect
447. C3×Dic3AGL(1,ℤ/8)semidirect
469. C4×D4C2×C3×D3semidirect
479. #106C2×C3×D3semidirect
487. #102C2×C3×D3semidirect
489. #97C2×C3×D3semidirect
523. C3×D4C2×C4×D3semidirect
525. C3×D4C22×C3×C4semidirect
584. Dic6C22×C3×C4semidirect
591. C3×C8C2×C4×D3semidirect
592. C3×C8C22×C3×C4semidirect
594. C3⋊C8C22×C3×C4semidirect
628. D8C3×C4×D3semidirect
720. Dic3C3×AGL(1,ℤ/8)semidirect
721. C32C4×AGL(1,ℤ/8)semidirect
738. D4C2×C3×C4×D3semidirect
765. C8C2×C3×C4×D3semidirect
812. C3#79865direct (N × H)
813. 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×#9112
C3×C4×D3×D42
C3×C4×#2372
C32×#4422
C3×Dic3×D82
C3×#50182
C3×#50142
C3×#48612
C3×#48522
C3×#47712
C3×#47702
C3×#47582
C3×#47562
C3×#47102
C3×#47072
C3×C4×AGL(1,ℤ/8)3
#798653