Finite Group Databasebeta

← C3×#76306 #11806880

Subgroups — C3×#76306 #11806880

Order 1152.

1793 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#67⋊C4C212yesmaximal, complemented
4C2×C3×C4×D12C211yesmaximal, characteristic, complemented
5C32×#390C211yesmaximal, characteristic, complemented
6C3×#4988C211yesmaximal, characteristic, complemented
7C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
8C3×#4958C212yesmaximal, complemented
9C3×#4957C212yesmaximal, complemented
10C3×#4956C212yesmaximal, complemented
11C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12C3×#2366—31nomaximal
13#76306C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×#67C2212yes—
17C23×C3×Dic3C2212yes—
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2212yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C22⋊C4C2212yes—
22C2×C32×C22⋊C4C2212yes—
23C2×C32×C42C2211yescharacteristic
24C2×C3×#217C2212yes—
25C3×#940C418yescomplemented
26C3×D4×Dic3—24no—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×C3×C4×Dic3C2212yes—
35C2×C3×C4×Dic3C2211yescharacteristic
36C3×#67⋊C4—28no—
37C3×C4×D12—24no—
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2212yes—
41C2×C3×#127—31no—
42C2×C3×C4×D4—31no—
43C2×C3×C4×D4—32no—
44C2×C3×C4×D4—31no—
45C2×#940C2×C311yescharacteristic
46C2×D4×Dic3C2×C311yescharacteristic, complemented
47C2×#67⋊C4C2×C312yescomplemented
48C2×C4×D12C2×C311yescharacteristic, complemented
49C3×#390—21no—
50C3×#390—31no—
51C3×#390—32no—
52C3×#390D311yescharacteristic, complemented
53C3×#390C2×C311yescharacteristic, complemented
54C3×#386—32no—
55C3×#386—32no—
56C3×C4×C4⋊C4—31no—
57C3×C4×C4⋊C4—31no—
58#4988C2×C311yescharacteristic, complemented
59Dic3×C4⋊C4C2×C311yescharacteristic, complemented
60#4958C2×C312yescomplemented
61#4957C2×C312yescomplemented
62#4956C2×C312yescomplemented
63C4×Dic3⋊C4C2×C311yescharacteristic, complemented
64C24×C32C2312yes—
65C23×C3×D3C2312yes—
66C2×C32×D4—22no—
67C2×C32×D4—22no—
68C2×C32×D4C2×C414yescomplemented
69C22×C32×C4C2312yes—
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C2×C3×#67—24no—
74C2×C3×#67—24no—
75C2×C3×#67—42no—
76C2×C3×#67—42no—
77C2×C3×#67C2×C418yescomplemented
78C2×C3×#67C2×C418yescomplemented
79C22×C3×Dic3—24no—
80C22×C3×Dic3—24no—
81C22×C3×Dic3—42no—
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2311yescharacteristic
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2311yescharacteristic
87C2×C3×D12—22no—
88C2×C3×D12—22no—
89C2×C3×D12C2×C414yescomplemented
90C2×C3×C4×D3—24no—
91C2×C3×C4×D3—24no—
92C2×C3×C4×D3—42no—
93C32×C4⋊C4—22no—
94C32×C22⋊C4—24no—
95C32×C22⋊C4—42no—
96C32×C42—22no—
97C3×#217—24no—
98C3×(C2×D3)⋊C4—24no—
99C3×(C2×D3)⋊C4—24no—
100C3×(C2×D3)⋊C4—42no—
101C3×C4⋊Dic3D414yescomplemented
102C3×Dic3⋊C4—22no—
103C3×Dic3⋊C4D414yescomplemented
104C3×C4×Dic3—22no—
105C3×C4×Dic3—24no—
106C3×C4×Dic3C2×C414yescomplemented
107#2366—31noSylow
108C22×C3×D4—21no—
109C22×C3×D4—32no—
110C22×C3×D4—32no—
111C22×C3×D4—31no—
112C22×C3×D4C2×D311yescharacteristic
113C22×C3×D4C22×C311yescharacteristic
114C23×C3×C4—32no—
115C23×C3×C4—32no—
116C22×#67C22×C312yes—
117C22×#67C22×C312yes—
118C23×Dic3C22×C312yes—
119C22×D12C22×C311yescharacteristic
120C22×C4×D3C22×C312yes—
121C3×#127—38no—
122C3×C4×D4—64no—
123C3×C4×D4—68no—
124C3×C4×D4—64no—
125C2×C3×C4⋊C4—21no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—31no—
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4C2×D311yescharacteristic
130C2×C3×C4⋊C4C22×C311yescharacteristic
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—32no—
134C2×C3×C22⋊C4—32no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C22⋊C4—32no—
137C2×C3×C22⋊C4C2×D312yes—
138C2×C3×C22⋊C4C2×D312yes—
139C2×C3×C22⋊C4C22×C312yes—
140C2×C3×C22⋊C4C22×C312yes—
141C2×C3×C42—21no—
142C2×C3×C42—31no—
143C2×C3×C42—32no—
144C2×C3×C42—31no—
145C2×C3×C42C2×D311yescharacteristic
146C2×C3×C42C22×C311yescharacteristic
147C2×#217C22×C312yes—
148#940C3×C418yescomplemented
149D4×Dic3—24no—
150C2×(C2×D3)⋊C4C22×C312yes—
151C2×(C2×D3)⋊C4C22×C312yes—
152C2×(C2×D3)⋊C4C22×C312yes—
153C2×C4⋊Dic3C22×C311yescharacteristic
154C2×Dic3⋊C4C22×C311yescharacteristic
155C2×Dic3⋊C4C22×C311yescharacteristic
156C2×C4×Dic3C22×C311yescharacteristic
157C2×C4×Dic3C22×C312yes—
158C2×C4×Dic3C22×C311yescharacteristic
159#67⋊C4—28no—
160C4×D12—24no—
161C3×#95—32no—
162C3×#95—31no—
163C3×#95—31no—
164C3⋊#95C22×C311yescharacteristic
165C3⋊#95C22×C311yescharacteristic
166C3⋊#95C22×C312yes—
167C23×C32—22no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—22no—
173C23×C32C22×C414yes—
174C23×C32C2411yescharacteristic
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3C22×C414yes—
182C32×D4—28no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—22no—
187C2×C32×C4—21no—
188C2×C32×C4—21no—
189C2×C32×C4—22no—
190C2×C32×C4—22no—
191C2×C32×C4C22×C412yes—
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2×D412yes—
194C2×C32×C4#4112yes—
195C3×#67—216no—
196C3×#67—48no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—48no—
207C2×C3×Dic3C22×C412yes—
208C2×C3×Dic3C22×C412yes—
209C2×C3×Dic3C2×D412yes—
210C2×C3×Dic3C2×D414yes—
211C2×C3×Dic3C2×D412yes—
212C2×C3×Dic3#4112yes—
213C3×D12—28no—
214C3×C4×D3—48no—
215C2×#127—31no—
216C2×C4×D4—31no—
217C2×C4×D4—32no—
218C2×C4×D4—31no—
219#390—31no—
220#390—32no—
221#390C3×D311yescharacteristic, complemented
222#386—32no—
223#386—32no—
224C4×C4⋊C4—31no—
225C4×C4⋊C4—31no—
226C24×C3—22no—
227C24×C3—32no—
228C24×C3C22×D312yes—
229C24×C3C23×C312yes—
230C23×D3C23×C312yes—
231C2×C3×D4—22no—
232C2×C3×D4—22no—
233C2×C3×D4—22no—
234C2×C3×D4—22no—
235C2×C3×D4—24no—
236C2×C3×D4—38no—
237C2×C3×D4—38no—
238C2×C3×D4—34no—
239C2×C3×D4—42no—
240C2×C3×D4—42no—
241C2×C3×D4—64no—
242C2×C3×D4—64no—
243C2×C3×D4—62no—
244C2×C3×D4—62no—
245C2×C3×D4—122no—
246C2×C3×D4—122no—
247C2×C3×D4C4×D314yescomplemented
248C2×C3×D4C2×C3×C414yescomplemented
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—22no—
253C22×C3×C4—31no—
254C22×C3×C4—31no—
255C22×C3×C4—32no—
256C22×C3×C4—31no—
257C22×C3×C4—31no—
258C22×C3×C4—64no—
259C22×C3×C4—64no—
260C22×C3×C4—64no—
261C22×C3×C4—64no—
262C22×C3×C4—122no—
263C22×C3×C4—122no—
264C22×C3×C4C22×D312yes—
265C22×C3×C4C22×D311yescharacteristic
266C22×C3×C4C22×D311yescharacteristic
267C22×C3×C4C22×D311yescharacteristic
268C22×C3×C4C23×C312yes—
269C22×C3×C4C23×C311yescharacteristic
270C22×C3×C4C23×C311yescharacteristic
271C22×C3×C4C23×C311yescharacteristic
272C2×#67—24no—
273C2×#67—24no—
274C2×#67—42no—
275C2×#67—42no—
276C2×#67C2×C3×C418yescomplemented
277C2×#67C2×C3×C418yescomplemented
278C22×Dic3—24no—
279C22×Dic3—24no—
280C22×Dic3—42no—
281C22×Dic3C23×C311yescharacteristic
282C22×Dic3C23×C311yescharacteristic
283C22×Dic3C23×C311yescharacteristic
284C22×Dic3C23×C312yes—
285C22×Dic3C23×C311yescharacteristic
286C2×D12—22no—
287C2×D12—22no—
288C2×D12C2×C3×C414yescomplemented
289C2×C4×D3—24no—
290C2×C4×D3—24no—
291C2×C4×D3—42no—
292C3×C4⋊C4—22no—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—34no—
295C3×C4⋊C4—34no—
296C3×C4⋊C4—42no—
297C3×C4⋊C4—62no—
298C3×C22⋊C4—24no—
299C3×C22⋊C4—24no—
300C3×C22⋊C4—44no—
301C3×C22⋊C4—42no—
302C3×C22⋊C4—42no—
303C3×C22⋊C4—44no—
304C3×C22⋊C4—64no—
305C3×C22⋊C4—64no—
306C3×C22⋊C4—64no—
307C3×C22⋊C4—122no—
308C3×C42—22no—
309C3×C42—22no—
310C3×C42—34no—
311C3×C42—42no—
312C3×C42—64no—
313C3×C42—62no—
314#217—24no—
315(C2×D3)⋊C4—24no—
316(C2×D3)⋊C4—24no—
317(C2×D3)⋊C4—42no—
318C4⋊Dic3C3×D414yescomplemented
319Dic3⋊C4—22no—
320Dic3⋊C4C3×D414yescomplemented
321C4×Dic3—22no—
322C4×Dic3—24no—
323C4×Dic3C2×C3×C414yescomplemented
324C22×C32—24no—
325C22×C32—24no—
326C22×C32—24no—
327C22×C32—42no—
328C22×C32—42no—
329C22×C32—42no—
330C22×C32—42no—
331C22×C32C23×C411yescharacteristic
332C22×C32C22×D411yescharacteristic
333C22×C32C22×D411yescharacteristic
334C22×C32C2×#4111yescharacteristic
335C22×C32C2×#4111yescharacteristic
336C22×C32H(5,𝔽2)11yescharacteristic
337C22×C32H(5,𝔽2)11yescharacteristic
338C2×C3×D3—24no—
339C2×C3×D3—24no—
340C2×C3×D3—24no—
341C2×C3×D3—42no—
342C2×C3×D3—42no—
343C2×C3×D3—42no—
344C2×C3×D3—42no—
345C32×C4—22no—
346C32×C4—41no—
347C32×C4—42no—
348C32×C4C4×D414yescomplemented
349C3×Dic3—22no—
350C3×Dic3—24no—
351C3×Dic3—22no—
352C3×Dic3—41no—
353C3×Dic3C4×D414yescomplemented
354C22×D4—32no—
355C22×D4—32no—
356C22×D4—31no—
357C22×D4C2×C3×D311yescharacteristic
358C23×C4—32no—
359C23×C4—32no—
360#127—38no—
361C4×D4—64no—
362C4×D4—68no—
363C4×D4—64no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4C2×C3×D311yescharacteristic
368C2×C22⋊C4—32no—
369C2×C22⋊C4—32no—
370C2×C22⋊C4—32no—
371C2×C22⋊C4—32no—
372C2×C22⋊C4C2×C3×D312yes—
373C2×C22⋊C4C2×C3×D312yes—
374C2×C42—31no—
375C2×C42—32no—
376C2×C42—31no—
377C2×C42C2×C3×D311yescharacteristic
378#95—32no—
379#95—31no—
380#95—31no—
381C23×C3—22no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—21no—
394C23×C3—24no—
395C23×C3—34no—
396C23×C3—42no—
397C23×C3—42no—
398C23×C3—42no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—42no—
402C23×C3—62no—
403C23×C3—62no—
404C23×C3—62no—
405C23×C3—62no—
406C23×C3—62no—
407C23×C3—62no—
408C23×C3C2×C4×D314yes—
409C23×C3C22×C3×C414yes—
410C23×C3C23×D311yescharacteristic
411C23×C3C24×C311yescharacteristic
412C22×D3—22no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3C22×C3×C414yes—
419C3×D4—28no—
420C3×D4—28no—
421C3×D4—48no—
422C3×D4—616no—
423C3×D4—68no—
424C3×D4—128no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—21no—
436C2×C3×C4—22no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—32no—
447C2×C3×C4—32no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—34no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—42no—
457C2×C3×C4—42no—
458C2×C3×C4—42no—
459C2×C3×C4—62no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—62no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—128no—
469C2×C3×C4—128no—
470C2×C3×C4C2×C4×D312yes—
471C2×C3×C4D3×D412yes—
472C2×C3×C4D3×D412yes—
473C2×C3×C4#23712yes—
474C2×C3×C4C22×C3×C412yes—
475C2×C3×C4C2×C3×D412yes—
476C2×C3×C4C2×C3×D412yes—
477C2×C3×C4C3×#4112yes—
478#67—216no—
479#67—48no—
480C2×Dic3—22no—
481C2×Dic3—21no—
482C2×Dic3—22no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—48no—
490C2×Dic3C22×C3×C412yes—
491C2×Dic3C22×C3×C412yes—
492C2×Dic3C2×C3×D412yes—
493C2×Dic3C2×C3×D414yes—
494C2×Dic3C2×C3×D412yes—
495C2×Dic3C3×#4112yes—
496D12—28no—
497C4×D3—48no—
498C2×C32—44no—
499C2×C32C2×C4×D411yescharacteristic
500C2×C32C2×C4×D411yescharacteristic
501C2×C32#51811yescharacteristic
502C2×C32D4211yescharacteristic
503C2×C32#55011yescharacteristic
504C2×C32#55011yescharacteristic
505C2×C32#55911yescharacteristic
506C3×D3—44no—
507C24—32no—
508C24C22×C3×D312yes—
509C2×D4—22no—
510C2×D4—22no—
511C2×D4—38no—
512C2×D4—38no—
513C2×D4—34no—
514C2×D4—64no—
515C2×D4—64no—
516C2×D4—62no—
517C2×D4—62no—
518C2×D4—122no—
519C2×D4—122no—
520C2×D4C3×C4×D314yescomplemented
521C22×C4—31no—
522C22×C4—31no—
523C22×C4—32no—
524C22×C4—31no—
525C22×C4—31no—
526C22×C4—64no—
527C22×C4—64no—
528C22×C4—64no—
529C22×C4—64no—
530C22×C4—122no—
531C22×C4—122no—
532C22×C4C22×C3×D312yes—
533C22×C4C22×C3×D311yescharacteristic
534C22×C4C22×C3×D311yescharacteristic
535C22×C4C22×C3×D311yescharacteristic
536C4⋊C4—22no—
537C4⋊C4—34no—
538C4⋊C4—34no—
539C4⋊C4—62no—
540C22⋊C4—24no—
541C22⋊C4—42no—
542C22⋊C4—64no—
543C22⋊C4—64no—
544C22⋊C4—64no—
545C22⋊C4—122no—
546C42—22no—
547C42—34no—
548C42—64no—
549C42—62no—
550C22×C3—24no—
551C22×C3—24no—
552C22×C3—24no—
553C22×C3—24no—
554C22×C3—24no—
555C22×C3—24no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—44no—
564C22×C3—44no—
565C22×C3—44no—
566C22×C3—42no—
567C22×C3—42no—
568C22×C3—42no—
569C22×C3—42no—
570C22×C3—42no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—64no—
575C22×C3—64no—
576C22×C3—64no—
577C22×C3—82no—
578C22×C3—82no—
579C22×C3—82no—
580C22×C3—82no—
581C22×C3—122no—
582C22×C3—122no—
583C22×C3—122no—
584C22×C3—122no—
585C22×C3C22×C4×D311yescharacteristic
586C22×C3C2×D3×D411yescharacteristic
587C22×C3C2×D3×D411yescharacteristic
588C22×C3C2×#23711yescharacteristic
589C22×C3#100411yescharacteristic
590C22×C3D3×#4111yescharacteristic
591C22×C3#100911yescharacteristic
592C22×C3C23×C3×C411yescharacteristic
593C22×C3C22×C3×D411yescharacteristic
594C22×C3C22×C3×D411yescharacteristic
595C22×C3C2×C3×#4111yescharacteristic
596C22×C3C2×C3×#4111yescharacteristic
597C22×C3C3×H(5,𝔽2)11yescharacteristic
598C22×C3C3×H(5,𝔽2)11yescharacteristic
599C2×D3—24no—
600C2×D3—24no—
601C2×D3—24no—
602C2×D3—42no—
603C2×D3—42no—
604C2×D3—42no—
605C2×D3—42no—
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—24no—
609C3×C4—34no—
610C3×C4—42no—
611C3×C4—42no—
612C3×C4—42no—
613C3×C4—41no—
614C3×C4—41no—
615C3×C4—42no—
616C3×C4—62no—
617C3×C4—64no—
618C3×C4—62no—
619C3×C4—82no—
620C3×C4—121no—
621C3×C4#67⋊C414yescomplemented
622C3×C4C3×C4×D414yescomplemented
623Dic3—22no—
624Dic3—24no—
625Dic3—22no—
626Dic3—41no—
627Dic3C3×C4×D414yescomplemented
628C32#236611yescharacteristic, complemented, Sylow
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—34no—
636C23—62no—
637C23—62no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23—62no—
642C23C2×C3×C4×D314yes—
643C23C23×C3×D311yescharacteristic
644D4—28no—
645D4—616no—
646D4—68no—
647D4—128no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—32no—
657C2×C4—32no—
658C2×C4—32no—
659C2×C4—32no—
660C2×C4—32no—
661C2×C4—34no—
662C2×C4—62no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—62no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—61no—
671C2×C4—128no—
672C2×C4—128no—
673C2×C4C2×C3×C4×D312yes—
674C2×C4C3×D3×D412yes—
675C2×C4C3×D3×D412yes—
676C2×C4C3×#23712yes—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—21no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—44no—
685C2×C3—44no—
686C2×C3—84no—
687C2×C3—124no—
688C2×C3C2×#67⋊C411yescharacteristic
689C2×C3C4×D3×D411yescharacteristic
690C2×C3#554511yescharacteristic
691C2×C3#559911yescharacteristic
692C2×C3#560911yescharacteristic
693C2×C3#568111yescharacteristic
694C2×C3#571811yescharacteristic
695C2×C3C2×C3×C4×D411yescharacteristic
696C2×C3C2×C3×C4×D411yescharacteristic
697C2×C3C3×#51811yescharacteristic
698C2×C3C3×D4211yescharacteristic
699C2×C3C3×#55011yescharacteristic
700C2×C3C3×#55011yescharacteristic
701C2×C3C3×#55911yescharacteristic
702D3—44no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—64no—
711C22—64no—
712C22—64no—
713C22—122no—
714C22—122no—
715C22—122no—
716C22—122no—
717C22C22×C3×C4×D311yescharacteristic
718C22C2×C3×D3×D411yescharacteristic
719C22C2×C3×D3×D411yescharacteristic
720C22C2×C3×#23711yescharacteristic
721C22C3×#100411yescharacteristic
722C22C3×D3×#4111yescharacteristic
723C22C3×#100911yescharacteristic
724C4—22no—
725C4—34no—
726C4—41no—
727C4—42no—
728C4—62no—
729C4—64no—
730C4—62no—
731C4—121no—
732C4C3×#67⋊C414yescomplemented
733C3—21no—
734C3#7630611yescharacteristic, direct product factor
735C3C3×#236611yescharacteristic, complemented
736C2—44no—
737C2—124no—
738C2C2×C3×#67⋊C411yescharacteristic
739C2C3×C4×D3×D411yescharacteristic
740C2C3×#554511yescharacteristic
741C2C3×#559911yescharacteristic
742C2C3×#560911yescharacteristic
743C2C3×#568111yescharacteristic
744C2C3×#571811yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#390C2
socleC23×C32C24
prime radicalC2×C3×#940C2
cosocleC23×C3C24×C3
hypercenterC3×#390D3
hypocenterC3C3×#2366
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic3C2semidirect
3. C2×C3×#67⋊C4C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C32×#390C2semidirect
6. C3×#4988C2semidirect
7. C3×Dic3×C4⋊C4C2semidirect
8. C3×#4958C2semidirect
9. C3×#4957C2semidirect
10. C3×#4956C2semidirect
11. C3×C4×Dic3⋊C4C2semidirect
13. #76306C3direct (N × H)
25. C3×#940C4semidirect
46. C2×D4×Dic3C2×C3semidirect
47. C2×#67⋊C4C2×C3semidirect
48. C2×C4×D12C2×C3semidirect
52. C3×#390D3semidirect
53. C3×#390C2×C3semidirect
58. #4988C2×C3semidirect
59. Dic3×C4⋊C4C2×C3semidirect
60. #4958C2×C3semidirect
61. #4957C2×C3semidirect
62. #4956C2×C3semidirect
63. C4×Dic3⋊C4C2×C3semidirect
68. C2×C32×D4C2×C4semidirect
77. C2×C3×#67C2×C4semidirect
78. C2×C3×#67C2×C4semidirect
89. C2×C3×D12C2×C4semidirect
101. C3×C4⋊Dic3D4semidirect
103. C3×Dic3⋊C4D4semidirect
106. C3×C4×Dic3C2×C4semidirect
148. #940C3×C4semidirect
221. #390C3×D3semidirect
247. C2×C3×D4C4×D3semidirect
248. C2×C3×D4C2×C3×C4semidirect
276. C2×#67C2×C3×C4semidirect
277. C2×#67C2×C3×C4semidirect
288. C2×D12C2×C3×C4semidirect
318. C4⋊Dic3C3×D4semidirect
320. Dic3⋊C4C3×D4semidirect
323. C4×Dic3C2×C3×C4semidirect
348. C32×C4C4×D4semidirect
353. C3×Dic3C4×D4semidirect
520. C2×D4C3×C4×D3semidirect
621. C3×C4#67⋊C4semidirect
622. C3×C4C3×C4×D4semidirect
627. Dic3C3×C4×D4semidirect
628. C32#2366semidirect
732. C4C3×#67⋊C4semidirect
734. C3#76306direct (N × H)
735. C3C3×#2366semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×C3×D4×Dic32
C2×C3×#67⋊C42
C2×C3×C4×D122
C32×#3902
C3×#49882
C3×Dic3×C4⋊C42
C3×#49582
C3×#49572
C3×#49562
C3×C4×Dic3⋊C42
C3×#23663
#763063