Finite Group Databasebeta

← C3×#82343 #11806883

Subgroups — C3×#82343 #11806883

Order 1152.

1877 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic
3C2×C3×C4×#67C212yesmaximal, complemented
4C2×C3×#893C211yesmaximal, characteristic, complemented
5C3×#5221C211yesmaximal, characteristic, complemented
6C3×#5213C212yesmaximal, complemented
7C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
8C3×#4957C212yesmaximal, complemented
9C3×#4956C212yesmaximal, complemented
10C3×#4939C211yesmaximal, characteristic, complemented
11C3×C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12C3×#2366—31nomaximal
13#82343C311yesmaximal, characteristic, direct product factor
14C22×C32×D4C2211yescharacteristic
15C23×C32×C4C2212yes—
16C22×C3×#67C2212yes—
17C22×C3×#67C2212yes—
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2212yes—
20C32×C4×D4—24no—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C32×C22⋊C4C2212yes—
23C2×C32×C42C2211yescharacteristic
24C2×C3×#217C2212yes—
25C2×C3×#217C2212yes—
26C3×#940C418yescomplemented
27C3×C4×#67—28no—
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×C3×C4×Dic3C2212yes—
36C2×C3×C4×Dic3C2211yescharacteristic
37C3×#893—24no—
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2212yes—
41C2×C3×#127—31no—
42C2×C3×C4×D4—21no—
43C2×C3×C4×D4—32no—
44C2×C3×C4×D4—31no—
45C2×C3×C4×D4D311yescharacteristic, complemented
46C2×C3×C4×D4C2×C311yescharacteristic, complemented
47C2×#940C2×C311yescharacteristic
48C2×C4×#67C2×C312yescomplemented
49C2×#893C2×C311yescharacteristic, complemented
50C3×#390—31no—
51C3×#390—32no—
52C3×#390—31no—
53C3×#386—32no—
54C3×#386—32no—
55C3×C4×C4⋊C4—31no—
56C3×C4×C4⋊C4—31no—
57#5221C2×C311yescharacteristic, complemented
58#5213C2×C312yescomplemented
59Dic3×C4⋊C4C2×C311yescharacteristic, complemented
60#4957C2×C312yescomplemented
61#4956C2×C312yescomplemented
62#4939C2×C311yescharacteristic, complemented
63C4×Dic3⋊C4C2×C311yescharacteristic, complemented
64C24×C32C2312yes—
65C23×C3×D3C2312yes—
66C2×C32×D4—22no—
67C2×C32×D4—22no—
68C2×C32×D4C2×C414yescomplemented
69C22×C32×C4—24no—
70C22×C32×C4—24no—
71C22×C32×C4—42no—
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2312yes—
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C2×C3×#67—24no—
77C2×C3×#67—24no—
78C2×C3×#67—42no—
79C2×C3×#67—42no—
80C2×C3×#67C2×C418yescomplemented
81C2×C3×#67C2×C418yescomplemented
82C22×C3×Dic3C2311yescharacteristic
83C22×C3×Dic3C2312yes—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
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⋊C4D414yescomplemented
94C32×C22⋊C4—24no—
95C32×C42—22no—
96C3×#217—24no—
97C3×#217—42no—
98C3×(C2×D3)⋊C4—24no—
99C3×(C2×D3)⋊C4—24no—
100C3×(C2×D3)⋊C4—42no—
101C3×C4⋊Dic3—22no—
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—22no—
115C23×C3×C4—32no—
116C23×C3×C4C2×D312yes—
117C23×C3×C4C22×C312yes—
118C22×#67C22×C312yes—
119C22×#67C22×C312yes—
120C22×D12C22×C311yescharacteristic
121C22×C4×D3C22×C312yes—
122C3×#127—38no—
123C3×C4×D4—28no—
124C3×C4×D4—24no—
125C3×C4×D4—24no—
126C3×C4×D4—68no—
127C3×C4×D4—64no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C4⋊C4C22×C311yescharacteristic
134C2×C3×C22⋊C4—22no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C22⋊C4—32no—
137C2×C3×C22⋊C4—32no—
138C2×C3×C22⋊C4—32no—
139C2×C3×C22⋊C4—32no—
140C2×C3×C22⋊C4C2×D312yes—
141C2×C3×C22⋊C4C22×C312yes—
142C2×C3×C42—21no—
143C2×C3×C42—31no—
144C2×C3×C42—32no—
145C2×C3×C42—31no—
146C2×C3×C42C2×D311yescharacteristic
147C2×C3×C42C22×C311yescharacteristic
148C2×#217C22×C312yes—
149C2×#217C22×C312yes—
150#940C3×C418yescomplemented
151C4×#67—28no—
152C2×(C2×D3)⋊C4C22×C312yes—
153C2×(C2×D3)⋊C4C22×C312yes—
154C2×(C2×D3)⋊C4C22×C312yes—
155C2×C4⋊Dic3C22×C311yescharacteristic
156C2×Dic3⋊C4C22×C311yescharacteristic
157C2×Dic3⋊C4C22×C311yescharacteristic
158C2×C4×Dic3C22×C311yescharacteristic
159C2×C4×Dic3C22×C312yes—
160C2×C4×Dic3C22×C311yescharacteristic
161#893—24no—
162C3×#95—31no—
163C3×#95—31no—
164C3×#95—32no—
165C3⋊#95C22×C311yescharacteristic
166C3⋊#95C22×C311yescharacteristic
167C3⋊#95C22×C312yes—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—22no—
173C23×C32—22no—
174C23×C32C22×C414yes—
175C23×C32C2411yescharacteristic
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—22no—
182C22×C3×D3C22×C414yes—
183C32×D4—28no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4—21no—
190C2×C32×C4—21no—
191C2×C32×C4—48no—
192C2×C32×C4C22×C412yes—
193C2×C32×C4C2×D412yes—
194C2×C32×C4C2×D414yes—
195C2×C32×C4C2×D412yes—
196C2×C32×C4#4112yes—
197C3×#67—216no—
198C3×#67—48no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3C22×C412yes—
210C2×C3×Dic3C22×C412yes—
211C2×C3×Dic3C2×D412yes—
212C2×C3×Dic3C2×D412yes—
213C2×C3×Dic3#4112yes—
214C3×D12—28no—
215C3×C4×D3—48no—
216C2×#127—31no—
217C2×C4×D4—32no—
218C2×C4×D4—31no—
219C2×C4×D4C3×D311yescharacteristic, complemented
220#390—31no—
221#390—32no—
222#390—31no—
223#386—32no—
224#386—32no—
225C4×C4⋊C4—31no—
226C4×C4⋊C4—31no—
227C24×C3—22no—
228C24×C3—32no—
229C24×C3C22×D312yes—
230C24×C3C23×C312yes—
231C23×D3C23×C312yes—
232C2×C3×D4—24no—
233C2×C3×D4—24no—
234C2×C3×D4—22no—
235C2×C3×D4—22no—
236C2×C3×D4—22no—
237C2×C3×D4—22no—
238C2×C3×D4—24no—
239C2×C3×D4—38no—
240C2×C3×D4—38no—
241C2×C3×D4—34no—
242C2×C3×D4—64no—
243C2×C3×D4—64no—
244C2×C3×D4—62no—
245C2×C3×D4—62no—
246C2×C3×D4—122no—
247C2×C3×D4—122no—
248C2×C3×D4C4×D314yescomplemented
249C2×C3×D4C2×C3×C414yescomplemented
250C22×C3×C4—28no—
251C22×C3×C4—24no—
252C22×C3×C4—24no—
253C22×C3×C4—24no—
254C22×C3×C4—24no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—22no—
259C22×C3×C4—31no—
260C22×C3×C4—31no—
261C22×C3×C4—31no—
262C22×C3×C4—32no—
263C22×C3×C4—31no—
264C22×C3×C4—44no—
265C22×C3×C4—42no—
266C22×C3×C4—42no—
267C22×C3×C4—44no—
268C22×C3×C4—64no—
269C22×C3×C4—64no—
270C22×C3×C4—122no—
271C22×C3×C4C22×D311yescharacteristic
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C22×D312yes—
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C23×C311yescharacteristic
276C22×C3×C4C23×C312yes—
277C22×C3×C4C23×C311yescharacteristic
278C22×C3×C4C23×C311yescharacteristic
279C2×#67—24no—
280C2×#67—24no—
281C2×#67—42no—
282C2×#67—42no—
283C2×#67C2×C3×C418yescomplemented
284C2×#67C2×C3×C418yescomplemented
285C22×Dic3C23×C311yescharacteristic
286C22×Dic3C23×C312yes—
287C22×Dic3C23×C311yescharacteristic
288C22×Dic3C23×C311yescharacteristic
289C22×Dic3C23×C311yescharacteristic
290C2×D12—22no—
291C2×D12—22no—
292C2×D12C2×C3×C414yescomplemented
293C2×C4×D3—24no—
294C2×C4×D3—24no—
295C2×C4×D3—42no—
296C3×C4⋊C4—24no—
297C3×C4⋊C4—34no—
298C3×C4⋊C4—62no—
299C3×C4⋊C4—62no—
300C3×C4⋊C4#6714yescomplemented
301C3×C4⋊C4C3×D414yescomplemented
302C3×C22⋊C4—28no—
303C3×C22⋊C4—24no—
304C3×C22⋊C4—24no—
305C3×C22⋊C4—64no—
306C3×C22⋊C4—64no—
307C3×C22⋊C4—64no—
308C3×C22⋊C4—122no—
309C3×C22⋊C4—122no—
310C3×C42—24no—
311C3×C42—22no—
312C3×C42—22no—
313C3×C42—34no—
314C3×C42—64no—
315C3×C42—62no—
316#217—24no—
317#217—42no—
318(C2×D3)⋊C4—24no—
319(C2×D3)⋊C4—24no—
320(C2×D3)⋊C4—42no—
321C4⋊Dic3—22no—
322Dic3⋊C4—22no—
323Dic3⋊C4C3×D414yescomplemented
324C4×Dic3—22no—
325C4×Dic3—24no—
326C4×Dic3C2×C3×C414yescomplemented
327C22×C32—24no—
328C22×C32—24no—
329C22×C32—24no—
330C22×C32—42no—
331C22×C32—42no—
332C22×C32—42no—
333C22×C32—42no—
334C22×C32C23×C411yescharacteristic
335C22×C32C22×D411yescharacteristic
336C22×C32C22×D411yescharacteristic
337C22×C32C2×#4111yescharacteristic
338C22×C32C2×#4111yescharacteristic
339C22×C32H(5,𝔽2)11yescharacteristic
340C22×C32H(5,𝔽2)11yescharacteristic
341C2×C3×D3—24no—
342C2×C3×D3—24no—
343C2×C3×D3—24no—
344C2×C3×D3—42no—
345C2×C3×D3—42no—
346C2×C3×D3—42no—
347C2×C3×D3—42no—
348C32×C4—22no—
349C32×C4—24no—
350C32×C4—41no—
351C32×C4C4×D414yescomplemented
352C3×Dic3—22no—
353C3×Dic3—22no—
354C3×Dic3—42no—
355C3×Dic3—41no—
356C3×Dic3C4×D414yescomplemented
357C22×D4—32no—
358C22×D4—32no—
359C22×D4—31no—
360C22×D4C2×C3×D311yescharacteristic
361C23×C4—32no—
362C23×C4C2×C3×D312yes—
363#127—38no—
364C4×D4—24no—
365C4×D4—68no—
366C4×D4—64no—
367C2×C4⋊C4—31no—
368C2×C4⋊C4—31no—
369C2×C4⋊C4—31no—
370C2×C4⋊C4C2×C3×D311yescharacteristic
371C2×C22⋊C4—32no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—32no—
374C2×C22⋊C4—32no—
375C2×C22⋊C4—32no—
376C2×C22⋊C4C2×C3×D312yes—
377C2×C42—31no—
378C2×C42—32no—
379C2×C42—31no—
380C2×C42C2×C3×D311yescharacteristic
381#95—31no—
382#95—31no—
383#95—32no—
384C23×C3—24no—
385C23×C3—24no—
386C23×C3—22no—
387C23×C3—22no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—21no—
399C23×C3—24no—
400C23×C3—34no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—62no—
406C23×C3—62no—
407C23×C3—62no—
408C23×C3—62no—
409C23×C3—62no—
410C23×C3—62no—
411C23×C3C2×C4×D314yes—
412C23×C3C22×C3×C414yes—
413C23×C3C23×D311yescharacteristic
414C23×C3C24×C311yescharacteristic
415C22×D3—22no—
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—22no—
419C22×D3—22no—
420C22×D3—22no—
421C22×D3C22×C3×C414yes—
422C3×D4—216no—
423C3×D4—28no—
424C3×D4—28no—
425C3×D4—616no—
426C3×D4—68no—
427C3×D4—128no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—21no—
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—22no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—24no—
450C2×C3×C4—32no—
451C2×C3×C4—32no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—32no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—42no—
458C2×C3×C4—42no—
459C2×C3×C4—48no—
460C2×C3×C4—48no—
461C2×C3×C4—416no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—61no—
469C2×C3×C4—62no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—128no—
473C2×C3×C4C2×C4×D312yes—
474C2×C3×C4#23512yes—
475C2×C3×C4D3×D412yes—
476C2×C3×C4C2×#6714yes—
477C2×C3×C4C2×#6712yes—
478C2×C3×C4C22×C3×C412yes—
479C2×C3×C4C2×C3×D412yes—
480C2×C3×C4C2×C3×D414yes—
481C2×C3×C4C2×C3×D412yes—
482C2×C3×C4C3×#4112yes—
483#67—216no—
484#67—48no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—22no—
491C2×Dic3—21no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—21no—
495C2×Dic3C22×C3×C412yes—
496C2×Dic3C22×C3×C412yes—
497C2×Dic3C2×C3×D412yes—
498C2×Dic3C2×C3×D412yes—
499C2×Dic3C3×#4112yes—
500D12—28no—
501C4×D3—48no—
502C2×C32—44no—
503C2×C32C2×C4×D411yescharacteristic
504C2×C32C2×C4×D411yescharacteristic
505C2×C32#51811yescharacteristic
506C2×C32D4211yescharacteristic
507C2×C32#55011yescharacteristic
508C2×C32#55011yescharacteristic
509C2×C32#55911yescharacteristic
510C3×D3—44no—
511C24—32no—
512C24C22×C3×D312yes—
513C2×D4—22no—
514C2×D4—22no—
515C2×D4—38no—
516C2×D4—38no—
517C2×D4—34no—
518C2×D4—64no—
519C2×D4—64no—
520C2×D4—62no—
521C2×D4—62no—
522C2×D4—122no—
523C2×D4—122no—
524C2×D4C3×C4×D314yescomplemented
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—31no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—32no—
531C22×C4—31no—
532C22×C4—42no—
533C22×C4—64no—
534C22×C4—64no—
535C22×C4—122no—
536C22×C4C22×C3×D311yescharacteristic
537C22×C4C22×C3×D311yescharacteristic
538C22×C4C22×C3×D312yes—
539C22×C4C22×C3×D311yescharacteristic
540C4⋊C4—34no—
541C4⋊C4—62no—
542C4⋊C4—62no—
543C4⋊C4C3×#6714yescomplemented
544C22⋊C4—24no—
545C22⋊C4—64no—
546C22⋊C4—64no—
547C22⋊C4—64no—
548C22⋊C4—122no—
549C22⋊C4—122no—
550C42—22no—
551C42—34no—
552C42—64no—
553C42—62no—
554C22×C3—28no—
555C22×C3—24no—
556C22×C3—24no—
557C22×C3—24no—
558C22×C3—24no—
559C22×C3—24no—
560C22×C3—24no—
561C22×C3—21no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—44no—
569C22×C3—44no—
570C22×C3—44no—
571C22×C3—44no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—64no—
583C22×C3—64no—
584C22×C3—64no—
585C22×C3—122no—
586C22×C3—122no—
587C22×C3—122no—
588C22×C3—122no—
589C22×C3C22×C4×D311yescharacteristic
590C22×C3C2×#23511yescharacteristic
591C22×C3C2×D3×D411yescharacteristic
592C22×C3#100411yescharacteristic
593C22×C3D3×#4111yescharacteristic
594C22×C3#100911yescharacteristic
595C22×C3C22×#6711yescharacteristic
596C22×C3C23×C3×C411yescharacteristic
597C22×C3C22×C3×D411yescharacteristic
598C22×C3C22×C3×D411yescharacteristic
599C22×C3C2×C3×#4111yescharacteristic
600C22×C3C2×C3×#4111yescharacteristic
601C22×C3C3×H(5,𝔽2)11yescharacteristic
602C22×C3C3×H(5,𝔽2)11yescharacteristic
603C2×D3—24no—
604C2×D3—24no—
605C2×D3—24no—
606C2×D3—42no—
607C2×D3—42no—
608C2×D3—42no—
609C2×D3—42no—
610C3×C4—24no—
611C3×C4—22no—
612C3×C4—24no—
613C3×C4—24no—
614C3×C4—22no—
615C3×C4—24no—
616C3×C4—34no—
617C3×C4—44no—
618C3×C4—42no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—62no—
622C3×C4—62no—
623C3×C4—122no—
624C3×C4—121no—
625C3×C4C4×#6714yescomplemented
626C3×C4C3×C4×D414yescomplemented
627Dic3—22no—
628Dic3—22no—
629Dic3—42no—
630Dic3—41no—
631Dic3C3×C4×D414yescomplemented
632C32#236611yescharacteristic, complemented, Sylow
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—34no—
640C23—62no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—62no—
645C23—62no—
646C23C2×C3×C4×D314yes—
647C23C23×C3×D311yescharacteristic
648D4—28no—
649D4—616no—
650D4—68no—
651D4—128no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—32no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—48no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—61no—
672C2×C4—62no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—128no—
676C2×C4C2×C3×C4×D312yes—
677C2×C4C3×#23512yes—
678C2×C4C3×D3×D412yes—
679C2×C4C2×C3×#6714yes—
680C2×C4C2×C3×#6712yes—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—21no—
685C2×C3—21no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—48no—
689C2×C3—44no—
690C2×C3—44no—
691C2×C3—124no—
692C2×C3C4×D3×D411yescharacteristic
693C2×C3#554511yescharacteristic
694C2×C3#555311yescharacteristic
695C2×C3#555911yescharacteristic
696C2×C3C2×C4×#6711yescharacteristic
697C2×C3D4×#6711yescharacteristic
698C2×C3#583411yescharacteristic
699C2×C3C2×C3×C4×D411yescharacteristic
700C2×C3C2×C3×C4×D411yescharacteristic
701C2×C3C3×#51811yescharacteristic
702C2×C3C3×D4211yescharacteristic
703C2×C3C3×#55011yescharacteristic
704C2×C3C3×#55011yescharacteristic
705C2×C3C3×#55911yescharacteristic
706D3—44no—
707C22—24no—
708C22—24no—
709C22—24no—
710C22—42no—
711C22—42no—
712C22—42no—
713C22—42no—
714C22—64no—
715C22—64no—
716C22—64no—
717C22—122no—
718C22—122no—
719C22—122no—
720C22—122no—
721C22C22×C3×C4×D311yescharacteristic
722C22C2×C3×#23511yescharacteristic
723C22C2×C3×D3×D411yescharacteristic
724C22C3×#100411yescharacteristic
725C22C3×D3×#4111yescharacteristic
726C22C3×#100911yescharacteristic
727C22C22×C3×#6711yescharacteristic
728C4—22no—
729C4—24no—
730C4—34no—
731C4—41no—
732C4—62no—
733C4—62no—
734C4—122no—
735C4—121no—
736C4C3×C4×#6714yescomplemented
737C3—21no—
738C3#8234311yescharacteristic, direct product factor
739C3C3×#236611yescharacteristic, complemented
740C2—44no—
741C2—124no—
742C2C3×C4×D3×D411yescharacteristic
743C2C3×#554511yescharacteristic
744C2C3×#555311yescharacteristic
745C2C3×#555911yescharacteristic
746C2C2×C3×C4×#6711yescharacteristic
747C2C3×D4×#6711yescharacteristic
748C2C3×#583411yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
prime radicalC2×C3×#940C2
cosocleC23×C3C24×C3
hypercenterC2×C3×C4×D4D3
hypocenterC3C3×#2366
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×D4C2semidirect
3. C2×C3×C4×#67C2semidirect
4. C2×C3×#893C2semidirect
5. C3×#5221C2semidirect
6. C3×#5213C2semidirect
7. C3×Dic3×C4⋊C4C2semidirect
8. C3×#4957C2semidirect
9. C3×#4956C2semidirect
10. C3×#4939C2semidirect
11. C3×C4×Dic3⋊C4C2semidirect
13. #82343C3direct (N × H)
26. C3×#940C4semidirect
45. C2×C3×C4×D4D3semidirect
46. C2×C3×C4×D4C2×C3semidirect
48. C2×C4×#67C2×C3semidirect
49. C2×#893C2×C3semidirect
57. #5221C2×C3semidirect
58. #5213C2×C3semidirect
59. Dic3×C4⋊C4C2×C3semidirect
60. #4957C2×C3semidirect
61. #4956C2×C3semidirect
62. #4939C2×C3semidirect
63. C4×Dic3⋊C4C2×C3semidirect
68. C2×C32×D4C2×C4semidirect
80. C2×C3×#67C2×C4semidirect
81. C2×C3×#67C2×C4semidirect
89. C2×C3×D12C2×C4semidirect
93. C32×C4⋊C4D4semidirect
103. C3×Dic3⋊C4D4semidirect
106. C3×C4×Dic3C2×C4semidirect
150. #940C3×C4semidirect
219. C2×C4×D4C3×D3semidirect
248. C2×C3×D4C4×D3semidirect
249. C2×C3×D4C2×C3×C4semidirect
283. C2×#67C2×C3×C4semidirect
284. C2×#67C2×C3×C4semidirect
292. C2×D12C2×C3×C4semidirect
300. C3×C4⋊C4#67semidirect
301. C3×C4⋊C4C3×D4semidirect
323. Dic3⋊C4C3×D4semidirect
326. C4×Dic3C2×C3×C4semidirect
351. C32×C4C4×D4semidirect
356. C3×Dic3C4×D4semidirect
524. C2×D4C3×C4×D3semidirect
543. C4⋊C4C3×#67semidirect
625. C3×C4C4×#67semidirect
626. C3×C4C3×C4×D4semidirect
631. Dic3C3×C4×D4semidirect
632. C32#2366semidirect
736. C4C3×C4×#67semidirect
738. C3#82343direct (N × H)
739. C3C3×#2366semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×D42
C2×C3×#9402
C2×C3×C4×#672
C2×C3×#8932
C3×#52212
C3×#52132
C3×Dic3×C4⋊C42
C3×#49572
C3×#49562
C3×#49392
C3×C4×Dic3⋊C42
C3×#23663
#823433