Finite Group Databasebeta

← C3×#80534 #11865839

Subgroups — C3×#80534 #11865839

Order 1152.

1158 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
1C2×C3×#914C211yesmaximal, characteristic, complemented
2C2×C3×#911C211yesmaximal, characteristic, complemented
3C3×#5668C211yesmaximal, characteristic, complemented
4C3×C4×D3×D4C211yesmaximal, characteristic, complemented
5C32×#463C211yesmaximal, characteristic, complemented
6C3×#5162C211yesmaximal, characteristic, complemented
7C3×#5150C211yesmaximal, characteristic, complemented
8C3×#5057C211yesmaximal, characteristic, complemented
9C3×#5016C211yesmaximal, characteristic, complemented
10C3×#4844C211yesmaximal, characteristic, complemented
11C3×#4837C211yesmaximal, characteristic, complemented
12C3×#4818C211yesmaximal, characteristic, complemented
13C3×#4803C211yesmaximal, characteristic, complemented
14C3×#4786C211yesmaximal, characteristic, complemented
15C3×#4771C211yesmaximal, characteristic, complemented
16C3×#3036—31nomaximal
17#80534C311yesmaximal, characteristic, direct product factor
18C2×C3×#239C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20C2×C3×D3×D4C2211yescharacteristic
21C22×C3×C4×D3—21no—
22C2×C32×SD16C2211yescharacteristic
23C2×C32×D8C2211yescharacteristic
24C32×#124C2211yescharacteristic, complemented
25C32×C4×D4C2211yescharacteristic
26C3×#944C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic
28C3×#940C2211yescharacteristic, complemented
29C3×D4×Dic3C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C2×C3×#213C2211yescharacteristic
33C3×C4×#67—21no—
34C3×#914—24no—
35C3×#911—24no—
36C2×C3×D24C2211yescharacteristic
37C2×C3×#204C2211yescharacteristic
38C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
39C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
40C3×#893C2211yescharacteristic
41C3×D3×C4⋊C4C2211yescharacteristic
42C3×#884—21no—
43C3×#884—21no—
44C3×#67⋊C4—21no—
45C3×#67⋊C4—21no—
46C3×#67⋊C4—21no—
47C3×D3×C22⋊C4—21no—
48C3×#875C2211yescharacteristic, complemented
49C3×C4×D12C2211yescharacteristic
50C3×C42×D3C2211yescharacteristic
51C32×C4⋊C8C2211yescharacteristic, complemented
52C32×#103C2211yescharacteristic, complemented
53C32×#102C2211yescharacteristic, complemented
54C3×#835C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#816C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59C3×Dic3⋊C8C2211yescharacteristic, complemented
60C3×#810C2211yescharacteristic, complemented
61C3×#809C2211yescharacteristic, complemented
62C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64C2×C3×AGL(1,ℤ/8)—31no—
65C3×#532—31no—
66C2×C3×C4×D4—31no—
67C2×#914C2×C311yescharacteristic, complemented
68C2×#911C2×C311yescharacteristic, complemented
69#5668C2×C311yescharacteristic, complemented
70C4×D3×D4C2×C311yescharacteristic, complemented
71C3×#463—21no—
72C3×#463—31no—
73C3×#463—31no—
74C3×#463—31no—
75C3×#463D311yescharacteristic, complemented
76C3×#463C2×C311yescharacteristic, complemented
77C3×#461—31no—
78C3×#461—31no—
79C3×#459—31no—
80C3×#459—31no—
81C3×#423—31no—
82C3×#417—31no—
83C3×#417—31no—
84#5162C2×C311yescharacteristic, complemented
85#5150C2×C311yescharacteristic, complemented
86#5057C2×C311yescharacteristic, complemented
87#5016C2×C311yescharacteristic, complemented
88#4844C2×C311yescharacteristic, complemented
89#4837C2×C311yescharacteristic, complemented
90#4818C2×C311yescharacteristic, complemented
91#4803C2×C311yescharacteristic, complemented
92#4786C2×C311yescharacteristic, complemented
93#4771C2×C311yescharacteristic, complemented
94C23×C3×D3—21no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4C2311yescharacteristic
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C22×C3×Dic3—21no—
104C22×C3×Dic3—21no—
105C3×#239—22no—
106C3×#239—22no—
107C3×#237—22no—
108C3×#237—22no—
109C3×D3×D4—22no—
110C3×D3×D4D414yescomplemented
111C2×C3×D12—21no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3—21no—
116C2×C3×C4×D3—21no—
117C2×C3×C4×D3—21no—
118C2×C3×C4×D3—44no—
119C2×C3×C4×D3D411yescharacteristic
120C2×C3×C4×D3D411yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×Dic6C2311yescharacteristic
123C32×SD16—22no—
124C32×D8—22no—
125C2×C32×C8C2311yescharacteristic
126C2×C32×C8C2311yescharacteristic
127C32×C4⋊C4C2311yescharacteristic
128C32×C22⋊C4—21no—
129C32×C22⋊C4—21no—
130C32×C22⋊C4—21no—
131C32×C42C2311yescharacteristic
132C3×#217—21no—
133C3×#215—22no—
134C3×#214—22no—
135C3×#213—22no—
136C3×#213—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4—21no—
144C3×Dic3⋊C4—21no—
145C3×C4×Dic3D411yescharacteristic
146C3×C4×Dic3D411yescharacteristic
147C3×C4×Dic3C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149C2×C3×C3⋊C8C2311yescharacteristic
150C3×D24—22no—
151C3×#204—22no—
152C3×ΓL(1,𝔽25)—22no—
153C3×ΓL(1,𝔽25)—22no—
154#3036—31noSylow
155C2×C3×#41—31no—
156C2×C3×#41—31no—
157C22×C3×D4—31no—
158C23×C3×C4—61no—
159C2×#239C22×C311yescharacteristic
160C2×#237C22×C311yescharacteristic
161C2×D3×D4C22×C311yescharacteristic
162C22×C4×D3—21no—
163C3×AGL(1,ℤ/8)—64no—
164C3×AGL(1,ℤ/8)—64no—
165C2×C3×SD16—21no—
166C2×C3×SD16—31no—
167C2×C3×SD16—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16C2×D311yescharacteristic
170C2×C3×SD16C22×C311yescharacteristic
171C2×C3×D8—21no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C2×C3×D8C2×D311yescharacteristic
176C2×C3×D8C22×C311yescharacteristic
177C2×C3×M16—31no—
178C2×C3×M16—31no—
179C3×C4⋊Q8—31no—
180C3×#127—31no—
181C3×#124—21no—
182C3×#124—31no—
183C3×#124C2×D311yescharacteristic, complemented
184C3×#124C22×C311yescharacteristic, complemented
185C3×#121—61no—
186C3×#121—61no—
187C3×C4×D4—21no—
188C3×C4×D4—31no—
189C3×C4×D4—31no—
190C3×C4×D4—31no—
191C3×C4×D4—61no—
192C3×C4×D4—61no—
193C3×C4×D4—61no—
194C3×C4×D4—61no—
195C3×C4×D4C2×D311yescharacteristic
196C3×C4×D4C22×C311yescharacteristic
197C2×C3×C4⋊C4—31no—
198C2×C3×C22⋊C4—61no—
199C2×C3×C42—31no—
200#944C22×C311yescharacteristic, complemented
201C2×#215C22×C311yescharacteristic
202#940C22×C311yescharacteristic, complemented
203D4×Dic3C22×C311yescharacteristic
204C2×#214C22×C311yescharacteristic
205C2×#213C22×C311yescharacteristic
206C2×#213C22×C311yescharacteristic
207C4×#67—21no—
208#914—24no—
209#911—24no—
210C2×D24C22×C311yescharacteristic
211C2×#204C22×C311yescharacteristic
212C2×ΓL(1,𝔽25)C22×C311yescharacteristic
213C2×ΓL(1,𝔽25)C22×C311yescharacteristic
214#893C22×C311yescharacteristic
215D3×C4⋊C4C22×C311yescharacteristic
216#884—21no—
217#884—21no—
218#67⋊C4—21no—
219#67⋊C4—21no—
220#67⋊C4—21no—
221D3×C22⋊C4—21no—
222#875C22×C311yescharacteristic, complemented
223C4×D12C22×C311yescharacteristic
224C42×D3C22×C311yescharacteristic
225C3×C4⋊C8—21no—
226C3×C4⋊C8—31no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8—31no—
229C3×C4⋊C8C2×D311yescharacteristic, complemented
230C3×C4⋊C8C22×C311yescharacteristic, complemented
231C3×#103—21no—
232C3×#103—31no—
233C3×#103—31no—
234C3×#103—31no—
235C3×#103C2×D311yescharacteristic, complemented
236C3×#103C22×C311yescharacteristic, complemented
237C3×#102—21no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102C2×D311yescharacteristic, complemented
242C3×#102C22×C311yescharacteristic, complemented
243#835C22×C311yescharacteristic, complemented
244#832C22×C311yescharacteristic, complemented
245#821C22×C311yescharacteristic, complemented
246#816C22×C311yescharacteristic, complemented
247Dic3⋊C8C22×C311yescharacteristic, complemented
248Dic3⋊C8C22×C311yescharacteristic, complemented
249#810C22×C311yescharacteristic, complemented
250#809C22×C311yescharacteristic, complemented
251C4⋊(C3⋊C8)C22×C311yescharacteristic, complemented
252C23×C32—21no—
253C23×C32—21no—
254C22×C3×D3—21no—
255C22×C3×D3—24no—
256C22×C3×D3—21no—
257C22×C3×D3—42no—
258C22×C3×D3—42no—
259C22×C3×D3C2×D411yescharacteristic
260C32×Q8—21no—
261C32×Q8—21no—
262C32×D4—21no—
263C32×D4—21no—
264C32×D4—21no—
265C32×D4C2×D412yes—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—42no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2411yescharacteristic
272C3×#67—24no—
273C3×#67—42no—
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—42no—
279C2×C3×Dic3—42no—
280C2×C3×Dic3C2×D411yescharacteristic
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—42no—
287C3×D12C2×D412yes—
288C3×C4×D3—22no—
289C3×C4×D3—41no—
290C3×C4×D3—42no—
291C3×C4×D3—42no—
292C3×C4×D3—42no—
293C3×C4×D3—42no—
294C3×C4×D3C2×D412yes—
295C3×C4×D3#4112yes—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C32×C8—21no—
299C32×C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—31no—
303C2×AGL(1,ℤ/8)—31no—
304#532—31no—
305C2×C4×D4—31no—
306#463—31no—
307#463—31no—
308#463—31no—
309#463C3×D311yescharacteristic, complemented
310#461—31no—
311#461—31no—
312#459—31no—
313#459—31no—
314#423—31no—
315#417—31no—
316#417—31no—
317C24×C3—61no—
318C23×D3—21no—
319C3×#41—62no—
320C3×#41—62no—
321C3×#41—62no—
322C3×#41—62no—
323C2×C3×Q8—21no—
324C2×C3×Q8—31no—
325C2×C3×Q8C22×D311yescharacteristic
326C2×C3×Q8C23×C311yescharacteristic
327C2×C3×D4—21no—
328C2×C3×D4—21no—
329C2×C3×D4—34no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—61no—
333C2×C3×D4—62no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C2×C3×D4C23×C311yescharacteristic
341C2×C3×D4C23×C311yescharacteristic
342C22×C3×C4—21no—
343C22×C3×C4—21no—
344C22×C3×C4—31no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—41no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C22×C3×C4—61no—
351C22×C3×C4—61no—
352C22×C3×C4—61no—
353C22×C3×C4—61no—
354C22×C3×C4—124no—
355C2×#67—21no—
356C2×#67—21no—
357C2×#67—21no—
358C2×#67—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361#239—22no—
362#239—22no—
363#237—22no—
364#237—22no—
365D3×D4—22no—
366D3×D4C3×D414yescomplemented
367C2×D12—21no—
368C2×D12C23×C311yescharacteristic
369C2×D12C23×C311yescharacteristic
370C2×C4×D3—21no—
371C2×C4×D3—21no—
372C2×C4×D3—21no—
373C2×C4×D3—21no—
374C2×C4×D3—44no—
375C2×C4×D3C3×D411yescharacteristic
376C2×C4×D3C3×D411yescharacteristic
377C2×C4×D3C23×C311yescharacteristic
378C2×Dic6C23×C311yescharacteristic
379C3×SD16—22no—
380C3×SD16—22no—
381C3×SD16—42no—
382C3×SD16—62no—
383C3×SD16—62no—
384C3×SD16—62no—
385C3×D8—22no—
386C3×D8—22no—
387C3×D8—42no—
388C3×D8—62no—
389C3×D8—62no—
390C3×D8—62no—
391C3×M16—62no—
392C3×M16—62no—
393C2×C3×C8—21no—
394C2×C3×C8—21no—
395C2×C3×C8—31no—
396C2×C3×C8—31no—
397C2×C3×C8C22×D311yescharacteristic
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C23×C311yescharacteristic
400C2×C3×C8C23×C311yescharacteristic
401C3×C4⋊C4—21no—
402C3×C4⋊C4—31no—
403C3×C4⋊C4—61no—
404C3×C4⋊C4—61no—
405C3×C4⋊C4—61no—
406C3×C4⋊C4C22×D311yescharacteristic
407C3×C4⋊C4C23×C311yescharacteristic
408C3×C22⋊C4—21no—
409C3×C22⋊C4—21no—
410C3×C22⋊C4—21no—
411C3×C22⋊C4—21no—
412C3×C22⋊C4—21no—
413C3×C22⋊C4—21no—
414C3×C22⋊C4—41no—
415C3×C22⋊C4—41no—
416C3×C22⋊C4—41no—
417C3×C22⋊C4—61no—
418C3×C22⋊C4—61no—
419C3×C22⋊C4—61no—
420C3×C22⋊C4—61no—
421C3×C22⋊C4—61no—
422C3×C42—21no—
423C3×C42—31no—
424C3×C42—31no—
425C3×C42—31no—
426C3×C42C22×D311yescharacteristic
427C3×C42C23×C311yescharacteristic
428#217—21no—
429#215—22no—
430#214—22no—
431#213—22no—
432#213—22no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—21no—
437C4⋊Dic3C23×C311yescharacteristic
438Dic3⋊C4—21no—
439Dic3⋊C4—21no—
440Dic3⋊C4—21no—
441C4×Dic3C3×D411yescharacteristic
442C4×Dic3C3×D411yescharacteristic
443C4×Dic3C23×C311yescharacteristic
444C2×C3⋊C8C23×C311yescharacteristic
445C2×C3⋊C8C23×C311yescharacteristic
446D24—22no—
447#204—22no—
448ΓL(1,𝔽25)—22no—
449ΓL(1,𝔽25)—22no—
450C22×C32—22no—
451C22×C32—41no—
452C22×C32—41no—
453C22×C32—41no—
454C22×C32—41no—
455C22×C32—41no—
456C22×C32C22×D411yescharacteristic
457C2×C3×D3—21no—
458C2×C3×D3—21no—
459C2×C3×D3—22no—
460C2×C3×D3—48no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3#12112yes—
467C32×C4—21no—
468C32×C4—21no—
469C32×C4—41no—
470C32×C4—41no—
471C32×C4C22×D411yescharacteristic
472C32×C4C2×#4111yescharacteristic
473C3×Dic3—21no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C3×Dic3#12112yes—
477C3×Dic3AGL(1,ℤ/8)12yescomplemented
478C2×#41—31no—
479C2×#41—31no—
480C22×D4—31no—
481C23×C4—61no—
482AGL(1,ℤ/8)—64no—
483AGL(1,ℤ/8)—64no—
484C2×SD16—31no—
485C2×SD16—31no—
486C2×SD16—31no—
487C2×SD16C2×C3×D311yescharacteristic
488C2×D8—31no—
489C2×D8—31no—
490C2×D8—31no—
491C2×D8C2×C3×D311yescharacteristic
492C2×M16—31no—
493C2×M16—31no—
494C4⋊Q8—31no—
495#127—31no—
496#124—31no—
497#124C2×C3×D311yescharacteristic, complemented
498#121—61no—
499#121—61no—
500C4×D4—31no—
501C4×D4—31no—
502C4×D4—31no—
503C4×D4—61no—
504C4×D4—61no—
505C4×D4—61no—
506C4×D4—61no—
507C4×D4C2×C3×D311yescharacteristic
508C2×C4⋊C4—31no—
509C2×C22⋊C4—61no—
510C2×C42—31no—
511C4⋊C8—31no—
512C4⋊C8—31no—
513C4⋊C8—31no—
514C4⋊C8C2×C3×D311yescharacteristic, complemented
515#103—31no—
516#103—31no—
517#103—31no—
518#103C2×C3×D311yescharacteristic, complemented
519#102—31no—
520#102—31no—
521#102—31no—
522#102C2×C3×D311yescharacteristic, complemented
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—31no—
528C23×C3—41no—
529C23×C3—41no—
530C23×C3—64no—
531C23×C3—61no—
532C23×C3—61no—
533C23×C3—122no—
534C23×C3—122no—
535C22×D3—21no—
536C22×D3—24no—
537C22×D3—21no—
538C22×D3—42no—
539C22×D3—42no—
540C22×D3C2×C3×D411yescharacteristic
541C3×Q8—21no—
542C3×Q8—21no—
543C3×Q8—21no—
544C3×Q8—21no—
545C3×Q8—41no—
546C3×Q8—41no—
547C3×Q8—61no—
548C3×Q8—61no—
549C3×D4—21no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—22no—
556C3×D4—32no—
557C3×D4—41no—
558C3×D4—41no—
559C3×D4—41no—
560C3×D4—64no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—122no—
565C3×D4—122no—
566C3×D4—122no—
567C3×D4—122no—
568C3×D4D3×D412yes—
569C3×D4C2×C3×D412yes—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—31no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—42no—
585C2×C3×C4—42no—
586C2×C3×C4—62no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—82no—
590C2×C3×C4—121no—
591C2×C3×C4—122no—
592C2×C3×C4—122no—
593C2×C3×C4—122no—
594C2×C3×C4—122no—
595C2×C3×C4—122no—
596C2×C3×C4—122no—
597C2×C3×C4D3×D411yescharacteristic
598C2×C3×C4D3×D411yescharacteristic
599C2×C3×C4C2×C3×D411yescharacteristic
600C2×C3×C4C2×C3×D411yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C24×C311yescharacteristic
603#67—24no—
604#67—42no—
605#67—42no—
606#67—42no—
607C2×Dic3—21no—
608C2×Dic3—21no—
609C2×Dic3—42no—
610C2×Dic3—42no—
611C2×Dic3C2×C3×D411yescharacteristic
612C2×Dic3C2×C3×D411yescharacteristic
613C2×Dic3C2×C3×D411yescharacteristic
614D12—21no—
615D12—21no—
616D12—21no—
617D12—42no—
618D12C2×C3×D412yes—
619C4×D3—22no—
620C4×D3—41no—
621C4×D3—42no—
622C4×D3—42no—
623C4×D3—42no—
624C4×D3—42no—
625C4×D3C2×C3×D412yes—
626C4×D3C3×#4112yes—
627Dic6—21no—
628Dic6—21no—
629C3×C8—21no—
630C3×C8—21no—
631C3×C8—21no—
632C3×C8—21no—
633C3×C8—41no—
634C3×C8—41no—
635C3×C8—61no—
636C3×C8—61no—
637C3⋊C8—21no—
638C3⋊C8—21no—
639C2×C32—42no—
640C2×C32—81no—
641C2×C32C2×#12111yescharacteristic
642C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
643C2×C32#57511yescharacteristic
644C3×D3—22no—
645C3×D3—42no—
646C3×D3—81no—
647C24—61no—
648#41—62no—
649#41—62no—
650#41—62no—
651#41—62no—
652C2×Q8—31no—
653C2×Q8C22×C3×D311yescharacteristic
654C2×D4—34no—
655C2×D4—31no—
656C2×D4—31no—
657C2×D4—61no—
658C2×D4—62no—
659C2×D4—61no—
660C2×D4—61no—
661C2×D4—61no—
662C2×D4—61no—
663C2×D4C22×C3×D311yescharacteristic
664C2×D4C22×C3×D311yescharacteristic
665C22×C4—21no—
666C22×C4—31no—
667C22×C4—31no—
668C22×C4—31no—
669C22×C4—61no—
670C22×C4—61no—
671C22×C4—61no—
672C22×C4—61no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—124no—
676SD16—22no—
677SD16—62no—
678SD16—62no—
679SD16—62no—
680D8—22no—
681D8—62no—
682D8—62no—
683D8—62no—
684M16—62no—
685M16—62no—
686C2×C8—31no—
687C2×C8—31no—
688C2×C8C22×C3×D311yescharacteristic
689C2×C8C22×C3×D311yescharacteristic
690C4⋊C4—31no—
691C4⋊C4—61no—
692C4⋊C4—61no—
693C4⋊C4—61no—
694C4⋊C4C22×C3×D311yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C42—31no—
704C42—31no—
705C42—31no—
706C42C22×C3×D311yescharacteristic
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—21no—
710C22×C3—32no—
711C22×C3—42no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—62no—
725C22×C3—81no—
726C22×C3—81no—
727C22×C3—81no—
728C22×C3—81no—
729C22×C3—81no—
730C22×C3—128no—
731C22×C3—121no—
732C22×C3—121no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3C2×D3×D411yescharacteristic
737C22×C3C22×C3×D411yescharacteristic
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—22no—
741C2×D3—48no—
742C2×D3—41no—
743C2×D3—41no—
744C2×D3—41no—
745C2×D3—41no—
746C2×D3—41no—
747C2×D3C3×#12112yes—
748C3×C4—21no—
749C3×C4—21no—
750C3×C4—21no—
751C3×C4—21no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—32no—
755C3×C4—32no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4—41no—
760C3×C4—41no—
761C3×C4—41no—
762C3×C4—61no—
763C3×C4—81no—
764C3×C4—81no—
765C3×C4—121no—
766C3×C4—121no—
767C3×C4C2×D3×D411yescharacteristic
768C3×C4D3×#4111yescharacteristic
769C3×C4C22×C3×D411yescharacteristic
770C3×C4C2×C3×#4111yescharacteristic
771Dic3—21no—
772Dic3—41no—
773Dic3—41no—
774Dic3C3×#12112yes—
775Dic3C3×AGL(1,ℤ/8)12yescomplemented
776C32#303611yescharacteristic, complemented, Sylow
777C23—21no—
778C23—21no—
779C23—31no—
780C23—64no—
781C23—61no—
782C23—61no—
783C23—122no—
784C23—122no—
785Q8—21no—
786Q8—21no—
787Q8—61no—
788Q8—61no—
789D4—21no—
790D4—21no—
791D4—21no—
792D4—32no—
793D4—64no—
794D4—61no—
795D4—61no—
796D4—61no—
797D4—122no—
798D4—122no—
799D4—122no—
800D4—122no—
801D4C3×D3×D412yes—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—31no—
805C2×C4—31no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—31no—
809C2×C4—42no—
810C2×C4—62no—
811C2×C4—61no—
812C2×C4—61no—
813C2×C4—121no—
814C2×C4—122no—
815C2×C4—122no—
816C2×C4—122no—
817C2×C4—122no—
818C2×C4—122no—
819C2×C4—122no—
820C2×C4C3×D3×D411yescharacteristic
821C2×C4C3×D3×D411yescharacteristic
822C2×C4C23×C3×D311yescharacteristic
823C8—21no—
824C8—21no—
825C8—61no—
826C8—61no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—42no—
831C2×C3—42no—
832C2×C3—62no—
833C2×C3—82no—
834C2×C3—81no—
835C2×C3—81no—
836C2×C3—122no—
837C2×C3—161no—
838C2×C3—241no—
839C2×C3D3×#12111yescharacteristic
840C2×C3#576811yescharacteristic
841C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
842C2×C3C2×C3×#12111yescharacteristic
843C2×C3C2×C3×AGL(1,ℤ/8)11yescharacteristic
844C2×C3C3×#57511yescharacteristic
845D3—22no—
846D3—42no—
847D3—81no—
848C22—22no—
849C22—32no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—61no—
856C22—61no—
857C22—62no—
858C22—128no—
859C22—121no—
860C22—121no—
861C22—121no—
862C22—121no—
863C22—121no—
864C22C2×C3×D3×D411yescharacteristic
865C4—21no—
866C4—21no—
867C4—32no—
868C4—32no—
869C4—41no—
870C4—41no—
871C4—61no—
872C4—121no—
873C4—121no—
874C4C2×C3×D3×D411yescharacteristic
875C4C3×D3×#4111yescharacteristic
876C3—21no—
877C3#8053411yescharacteristic, direct product factor
878C3C3×#303611yescharacteristic, complemented
879C2—42no—
880C2—62no—
881C2—81no—
882C2—122no—
883C2—241no—
884C2C3×D3×#12111yescharacteristic
885C2C3×#576811yescharacteristic
886C2C3×D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22×C3C2×D3×D4
commutator, cosocleC2×C3×C4C24×C3
FrattiniC2×C4C23×C3×D3
FittingC32×#463C2
socleC22×C32C22×D4
hypercenterC3×#463D3
hypocenterC3C3×#3036
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#463

Complements

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

NH ≅ G/Ntype
1. C2×C3×#914C2semidirect
2. C2×C3×#911C2semidirect
3. C3×#5668C2semidirect
4. C3×C4×D3×D4C2semidirect
5. C32×#463C2semidirect
6. C3×#5162C2semidirect
7. C3×#5150C2semidirect
8. C3×#5057C2semidirect
9. C3×#5016C2semidirect
10. C3×#4844C2semidirect
11. C3×#4837C2semidirect
12. C3×#4818C2semidirect
13. C3×#4803C2semidirect
14. C3×#4786C2semidirect
15. C3×#4771C2semidirect
17. #80534C3direct (N × H)
24. C32×#124C22semidirect
26. C3×#944C22semidirect
28. C3×#940C22semidirect
48. C3×#875C22semidirect
51. C32×C4⋊C8C22semidirect
52. C32×#103C22semidirect
53. C32×#102C22semidirect
54. C3×#835C22semidirect
55. C3×#832C22semidirect
56. C3×#821C22semidirect
57. C3×#816C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. C3×Dic3⋊C8C22semidirect
60. C3×#810C22semidirect
61. C3×#809C22semidirect
62. C3×C4⋊(C3⋊C8)C22semidirect
67. C2×#914C2×C3semidirect
68. C2×#911C2×C3semidirect
69. #5668C2×C3semidirect
70. C4×D3×D4C2×C3semidirect
75. C3×#463D3semidirect
76. C3×#463C2×C3semidirect
84. #5162C2×C3semidirect
85. #5150C2×C3semidirect
86. #5057C2×C3semidirect
87. #5016C2×C3semidirect
88. #4844C2×C3semidirect
89. #4837C2×C3semidirect
90. #4818C2×C3semidirect
91. #4803C2×C3semidirect
92. #4786C2×C3semidirect
93. #4771C2×C3semidirect
110. C3×D3×D4D4semidirect
183. C3×#124C2×D3semidirect
184. C3×#124C22×C3semidirect
200. #944C22×C3semidirect
202. #940C22×C3semidirect
222. #875C22×C3semidirect
229. C3×C4⋊C8C2×D3semidirect
230. C3×C4⋊C8C22×C3semidirect
235. C3×#103C2×D3semidirect
236. C3×#103C22×C3semidirect
241. C3×#102C2×D3semidirect
242. C3×#102C22×C3semidirect
243. #835C22×C3semidirect
244. #832C22×C3semidirect
245. #821C22×C3semidirect
246. #816C22×C3semidirect
247. Dic3⋊C8C22×C3semidirect
248. Dic3⋊C8C22×C3semidirect
249. #810C22×C3semidirect
250. #809C22×C3semidirect
251. C4⋊(C3⋊C8)C22×C3semidirect
309. #463C3×D3semidirect
366. D3×D4C3×D4semidirect
477. C3×Dic3AGL(1,ℤ/8)semidirect
497. #124C2×C3×D3semidirect
514. C4⋊C8C2×C3×D3semidirect
518. #103C2×C3×D3semidirect
522. #102C2×C3×D3semidirect
775. Dic3C3×AGL(1,ℤ/8)semidirect
776. C32#3036semidirect
877. C3#80534direct (N × H)
878. C3C3×#3036semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9142
C2×C3×#9112
C3×#56682
C3×C4×D3×D42
C32×#4632
C3×#51622
C3×#51502
C3×#50572
C3×#50162
C3×#48442
C3×#48372
C3×#48182
C3×#48032
C3×#47862
C3×#47712
C3×#30363
#805343