Finite Group Databasebeta

← #67×C4⋊Dic3 #11805439

Subgroups — #67×C4⋊Dic3 #11805439

Order 1152.

1669 conjugacy classes of subgroups.

The subgroup lattice has 733 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C22×C3×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×Dic3×#67C212yesmaximal
4C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#10592911C211yesmaximal, characteristic, complemented
6#10591718C212yesmaximal, complemented
7#10591377C212yesmaximal, complemented
8#10591349C211yesmaximal, characteristic, complemented
9#10591313C211yesmaximal, characteristic, complemented
10Dic3×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#10591265C212yesmaximal, complemented
12D4×C4⋊Dic3—31nomaximal
13C4⋊C4×#67—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C23×C3×Dic3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C22×D3×Dic3C2212yes—
19C2×#3757C2212yes—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23C3×C4×#67C418yescomplemented
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×C4⋊Dic3—24no—
26C2×C3×C4⋊Dic3C2212yes—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31Dic3×#67—28no—
32C2×Dic3⋊Dic3C2212yes—
33C2×Dic3⋊Dic3C2212yes—
34C2×Dic3⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×Dic32C2212yes—
37D3×C4⋊Dic3—24no—
38#63658C2212yes—
39#63579C2212yes—
40#63579C2212yes—
41C2×C3×C4×D4—31no—
42C22×C3×C4⋊C4—31no—
43C2×D4×Dic3—32no—
44C2×C4×#67—32no—
45C2×C4×#67D311yescharacteristic
46C22×C4⋊Dic3—31no—
47C22×C4⋊Dic3D311yescharacteristic, complemented
48C2×D3×C4⋊C4—31no—
49#5212—31no—
50#5212—31no—
51#5212—31no—
52#5212—61no—
53#5210—32no—
54#4989—32no—
55#4987—31no—
56#4984—32no—
57#4976—32no—
58#4975—31no—
59Dic3×C4⋊C4—31no—
60#4950—32no—
61#4950—32no—
62#4935—31no—
63C4×C4⋊Dic3—31no—
64C24×C32C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C22×C32×C4—22no—
67C22×C32×C4—22no—
68C22×C32×C4C2×C414yescomplemented
69C22×C32×C4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3C2312yes—
72C22×C3⋊Dic3C2312yes—
73C2×C3×#67C2×C414yes—
74C2×C3×#67D414yes—
75C2×C3×#67Q814yes—
76C22×C3×Dic3—24no—
77C22×C3×Dic3—24no—
78C22×C3×Dic3—42no—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2312yes—
83C22×C3×Dic3C2311yescharacteristic
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3C2×C414yescomplemented
87C2×D3×Dic3—24no—
88C2×D3×Dic3—24no—
89C2×D3×Dic3—42no—
90#3757—24no—
91C4⋊(C3⋊Dic3)—22no—
92C4⋊(C3⋊Dic3)—22no—
93C3×#217C2×C414yescomplemented
94C3×(C2×D3)⋊C4C2×C414yescomplemented
95C3×C4⋊Dic3—22no—
96C3×C4⋊Dic3—24no—
97C3×C4⋊Dic3D414yescomplemented
98C3×Dic3⋊C4C2×C414yescomplemented
99C3×C4×Dic3C2×C414yescomplemented
100Dic3⋊Dic3—24no—
101Dic3⋊Dic3—24no—
102Dic3⋊Dic3—42no—
103(C2×D3)⋊Dic3—24no—
104Dic32—24no—
105D4×C4⋊C4—91noSylow
106C22×C3×D4—31no—
107C23×C3×C4—21no—
108C23×C3×C4—31no—
109C23×C3×C4—32no—
110C23×C3×C4C2×D311yescharacteristic
111C23×C3×C4C2×D311yescharacteristic
112C22×#67C2×D311yescharacteristic
113C23×Dic3—32no—
114C23×Dic3C2×D312yes—
115C22×C4×D3—32no—
116C22×C4×D3C2×D311yescharacteristic
117C3×C4×D4—38no—
118C2×C3×C4⋊C4—31no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—32no—
122C2×C3×C4⋊C4—64no—
123C2×C3×C22⋊C4—31no—
124C2×C3×C22⋊C4—31no—
125C2×C3×C42—31no—
126C2×#217—32no—
127C2×#217—32no—
128C2×#217—32no—
129C2×#217—62no—
130C2×#217C2×D311yescharacteristic
131D4×Dic3—68no—
132C4×#67—68no—
133C4×#67Dic318yescomplemented
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4C2×D311yescharacteristic
136C2×C4⋊Dic3—24no—
137C2×C4⋊Dic3—31no—
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—31no—
140C2×C4⋊Dic3—31no—
141C2×C4⋊Dic3—32no—
142C2×C4⋊Dic3—32no—
143C2×C4⋊Dic3—32no—
144C2×C4⋊Dic3—61no—
145C2×C4⋊Dic3—61no—
146C2×C4⋊Dic3—64no—
147C2×C4⋊Dic3C2×D311yescharacteristic
148C2×C4⋊Dic3C2×D312yes—
149C2×C4⋊Dic3C2×D311yescharacteristic
150C2×Dic3⋊C4—32no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4C2×D311yescharacteristic
154C2×C4×Dic3—32no—
155C2×C4×Dic3—32no—
156C2×C4×Dic3C2×D311yescharacteristic
157D3×C4⋊C4—64no—
158C3⋊#95—32no—
159C3⋊#95—32no—
160C3⋊#95—32no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95—32no—
164C3⋊#95—62no—
165C23×C32—21no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—21no—
169C23×C32C22×C412yes—
170C23×C32C2×D412yes—
171C23×C32C2×Q812yes—
172C23×C32C2411yescharacteristic
173C22×C3×D3—21no—
174C22×C3×D3—21no—
175C22×C3×D3—21no—
176C22×C3×D3—21no—
177C22×C3×D3C22×C412yes—
178C22×C3×D3C2×D412yes—
179C22×C3×D3C2×Q812yes—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—28no—
183C2×C32×C4C22×C412yes—
184C2×C32×C4C22×C412yes—
185C2×C32×C4C2×D412yes—
186C2×C32×C4#4112yes—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—22no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—22no—
192C2×C3⋊Dic3—22no—
193C3×#67C4⋊C4116yescomplemented
194C2×C3×Dic3—22no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—48no—
204C2×C3×Dic3C22×C412yes—
205C2×C3×Dic3C22×C412yes—
206C2×C3×Dic3C22×C412yes—
207C2×C3×Dic3C2×D412yes—
208C2×C3×Dic3C2×D414yes—
209C2×C3×Dic3C2×Q812yes—
210C3×C4×D3—28no—
211D3×Dic3—48no—
212C2×C4×D4—31no—
213C2×C4×D4—92no—
214C22×C4⋊C4—31no—
215C22×C4⋊C4—91no—
216#389—92no—
217#385—92no—
218#385—92no—
219#384—91no—
220#380—91no—
221#380—91no—
222C4×C4⋊C4—91no—
223C24×C3—21no—
224C24×C3—31no—
225C24×C3C22×D311yescharacteristic
226C24×C3C22×D311yescharacteristic
227C23×D3C22×D311yescharacteristic
228C2×C3×D4—34no—
229C2×C3×D4—34no—
230C2×C3×D4—34no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—22no—
234C22×C3×C4—22no—
235C22×C3×C4—24no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—32no—
242C22×C3×C4—34no—
243C22×C3×C4—32no—
244C22×C3×C4—42no—
245C22×C3×C4—42no—
246C22×C3×C4—64no—
247C22×C3×C4—62no—
248C22×C3×C4—62no—
249C22×C3×C4—64no—
250C22×C3×C4—122no—
251C22×C3×C4C4×D314yescomplemented
252C22×C3×C4C2×Dic314yescomplemented
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D311yescharacteristic
257C2×#67Dic614yes—
258C2×#67D1214yes—
259C2×#67C2×Dic314yes—
260C22×Dic3—24no—
261C22×Dic3—24no—
262C22×Dic3—32no—
263C22×Dic3—32no—
264C22×Dic3—32no—
265C22×Dic3—32no—
266C22×Dic3—42no—
267C22×Dic3—62no—
268C22×Dic3—62no—
269C22×Dic3—64no—
270C22×Dic3—64no—
271C22×Dic3—122no—
272C22×Dic3C22×D312yes—
273C22×Dic3C22×D311yescharacteristic
274C22×Dic3C22×D311yescharacteristic
275C22×Dic3C22×D312yes—
276C22×Dic3C22×D311yescharacteristic
277C2×C4×D3—22no—
278C2×C4×D3—22no—
279C2×C4×D3—64no—
280C2×C4×D3—64no—
281C2×C4×D3—122no—
282C2×C4×D3C2×Dic314yescomplemented
283C3×C4⋊C4—34no—
284C3×C4⋊C4—34no—
285C3×C4⋊C4—64no—
286C3×C4⋊C4—62no—
287C3×C22⋊C4—34no—
288C3×C22⋊C4—34no—
289C3×C42—34no—
290#217—64no—
291#217—64no—
292#217—64no—
293#217—124no—
294#217C2×Dic314yescomplemented
295(C2×D3)⋊C4—64no—
296(C2×D3)⋊C4C2×Dic314yescomplemented
297C4⋊Dic3—22no—
298C4⋊Dic3—24no—
299C4⋊Dic3—64no—
300C4⋊Dic3—62no—
301C4⋊Dic3—62no—
302C4⋊Dic3—62no—
303C4⋊Dic3—62no—
304C4⋊Dic3—64no—
305C4⋊Dic3—122no—
306C4⋊Dic3—122no—
307C4⋊Dic3—122no—
308C4⋊Dic3#6714yesdirect product factor
309Dic3⋊C4—64no—
310Dic3⋊C4—64no—
311Dic3⋊C4—122no—
312Dic3⋊C4C2×Dic314yescomplemented
313C4×Dic3—64no—
314C4×Dic3—64no—
315C4×Dic3C2×Dic314yescomplemented
316C22×C32—22no—
317C22×C32—22no—
318C22×C32—22no—
319C22×C32—22no—
320C22×C32—22no—
321C22×C32—22no—
322C22×C32C2×C4⋊C414yescomplemented
323C22×C32C23×C411yescharacteristic
324C22×C32C22×D411yescharacteristic
325C22×C32C22×D411yescharacteristic
326C22×C32C22×Q811yescharacteristic
327C22×C32C2×#4111yescharacteristic
328C22×C32H(5,𝔽2)11yescharacteristic
329C22×C322−1+411yescharacteristic
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—22no—
333C2×C3×D3—22no—
334C2×C3×D3—22no—
335C2×C3×D3—22no—
336C2×C3×D3C2×C4⋊C414yescomplemented
337C32×C4—22no—
338C32×C4C4×D414yescomplemented
339C3⋊Dic3—42no—
340C3⋊Dic3—42no—
341C3×Dic3—22no—
342C3×Dic3—22no—
343C3×Dic3—24no—
344C3×Dic3—42no—
345C3×Dic3C2×C4⋊C414yescomplemented
346C22×D4—31no—
347C23×C4—31no—
348C23×C4—32no—
349C23×C4—92no—
350C23×C4D3211yescharacteristic
351C4×D4—38no—
352C4×D4—188no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—31no—
355C2×C4⋊C4—31no—
356C2×C4⋊C4—32no—
357C2×C4⋊C4—64no—
358C2×C4⋊C4—92no—
359C2×C4⋊C4—92no—
360C2×C4⋊C4—91no—
361C2×C4⋊C4—91no—
362C2×C4⋊C4—92no—
363C2×C4⋊C4—184no—
364C2×C22⋊C4—31no—
365C2×C22⋊C4—31no—
366C2×C22⋊C4—92no—
367C2×C22⋊C4—92no—
368C2×C42—31no—
369C2×C42—92no—
370#95—92no—
371#95—92no—
372#95—92no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—21no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—32no—
386C23×C3—32no—
387C23×C3—32no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3—41no—
391C23×C3—41no—
392C23×C3—61no—
393C23×C3—61no—
394C23×C3—61no—
395C23×C3—61no—
396C23×C3C2×Dic612yes—
397C23×C3C2×C4×D312yes—
398C23×C3C2×D1212yes—
399C23×C3D3×D412yes—
400C23×C3D3×Q812yes—
401C23×C3C22×Dic312yes—
402C23×C3C23×D311yescharacteristic
403C23×C3C23×D311yescharacteristic
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3C2×Dic612yes—
409C22×D3C2×D1212yes—
410C22×D3C22×Dic312yes—
411C3×D4—316no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—28no—
417C2×C3×C4—28no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—32no—
423C2×C3×C4—32no—
424C2×C3×C4—32no—
425C2×C3×C4—32no—
426C2×C3×C4—32no—
427C2×C3×C4—34no—
428C2×C3×C4—48no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—62no—
432C2×C3×C4—61no—
433C2×C3×C4—61no—
434C2×C3×C4—61no—
435C2×C3×C4—62no—
436C2×C3×C4—61no—
437C2×C3×C4—68no—
438C2×C3×C4—62no—
439C2×C3×C4—62no—
440C2×C3×C4—62no—
441C2×C3×C4—128no—
442C2×C3×C4C2×C4×D312yes—
443C2×C3×C4C2×C4×D312yes—
444C2×C3×C4#23512yes—
445C2×C3×C4D3×D412yes—
446C2×C3×C4#23712yes—
447C2×C3×C4C22×Dic312yes—
448C2×C3×C4C22×Dic312yes—
449C2×C3×C4C2×#6712yes—
450#67C4⋊Dic3116yesdirect product factor
451C2×Dic3—22no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—22no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—22no—
458C2×Dic3—22no—
459C2×Dic3—22no—
460C2×Dic3—48no—
461C2×Dic3—62no—
462C2×Dic3—62no—
463C2×Dic3—62no—
464C2×Dic3—62no—
465C2×Dic3—62no—
466C2×Dic3—62no—
467C2×Dic3—62no—
468C2×Dic3—62no—
469C2×Dic3—62no—
470C2×Dic3—62no—
471C2×Dic3—62no—
472C2×Dic3—62no—
473C2×Dic3—122no—
474C2×Dic3—122no—
475C2×Dic3—122no—
476C2×Dic3—122no—
477C2×Dic3—122no—
478C2×Dic3—122no—
479C2×Dic3—128no—
480C2×Dic3C2×Dic612yes—
481C2×Dic3C2×D1212yes—
482C2×Dic3C22×Dic312yes—
483C2×Dic3C22×Dic312yes—
484C2×Dic3C22×Dic312yes—
485C2×Dic3C2×#6714yes—
486C4×D3—28no—
487C4×D3—128no—
488C2×C32—24no—
489C2×C32C22×C4⋊C411yescharacteristic
490C2×C32C2×C4×D411yescharacteristic
491C2×C32#52011yescharacteristic
492C2×C32D4211yescharacteristic
493C2×C32#54711yescharacteristic
494C2×C32D4×Q811yescharacteristic
495C2×C32#55411yescharacteristic
496C3×D3—24no—
497C24—31no—
498C24C2×D3211yescharacteristic
499C2×D4—34no—
500C2×D4—34no—
501C2×D4—34no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—31no—
507C22×C4—32no—
508C22×C4—34no—
509C22×C4—32no—
510C22×C4—64no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—64no—
514C22×C4—92no—
515C22×C4—92no—
516C22×C4—122no—
517C22×C4—184no—
518C22×C4—184no—
519C22×C4—362no—
520C22×C4D3×Dic314yescomplemented
521C22×C4C2×D3211yescharacteristic
522C22×C4C2×D3211yescharacteristic
523C4⋊C4—34no—
524C4⋊C4—34no—
525C4⋊C4—64no—
526C4⋊C4—62no—
527C4⋊C4—184no—
528C4⋊C4—184no—
529C4⋊C4—182no—
530C4⋊C4—182no—
531C4⋊C4—362no—
532C22⋊C4—34no—
533C22⋊C4—34no—
534C22⋊C4—184no—
535C22⋊C4—184no—
536C42—34no—
537C42—184no—
538C22×C3—22no—
539C22×C3—22no—
540C22×C3—22no—
541C22×C3—22no—
542C22×C3—22no—
543C22×C3—22no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—24no—
558C22×C3—34no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—42no—
563C22×C3—42no—
564C22×C3—42no—
565C22×C3—62no—
566C22×C3—62no—
567C22×C3—62no—
568C22×C3—62no—
569C22×C3—62no—
570C22×C3—62no—
571C22×C3D3×C4⋊C414yescomplemented
572C22×C3C2×C4⋊Dic314yescomplemented
573C22×C3C22×Dic611yescharacteristic
574C22×C3C22×C4×D311yescharacteristic
575C22×C3C22×D1211yescharacteristic
576C22×C3C2×#23511yescharacteristic
577C22×C3C2×D3×D411yescharacteristic
578C22×C3C2×D3×D411yescharacteristic
579C22×C3C2×#23711yescharacteristic
580C22×C3#100411yescharacteristic
581C22×C3C2×D3×Q811yescharacteristic
582C22×C3#100711yescharacteristic
583C22×C3#100911yescharacteristic
584C22×C3#101011yescharacteristic
585C22×C3C23×Dic311yescharacteristic
586C22×C3C22×#6711yescharacteristic
587C2×D3—22no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—22no—
591C2×D3—22no—
592C2×D3—22no—
593C2×D3C2×C4⋊Dic314yescomplemented
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—24no—
597C3×C4—34no—
598C3×C4—42no—
599C3×C4—62no—
600C3×C4—62no—
601C3×C4—64no—
602C3×C4—122no—
603C3×C4C4×#6714yescomplemented
604C3×C4D4×Dic314yescomplemented
605Dic3—22no—
606Dic3—24no—
607Dic3—22no—
608Dic3—42no—
609Dic3—122no—
610Dic3—122no—
611Dic3—122no—
612Dic3—122no—
613Dic3—242no—
614Dic3—242no—
615Dic3C2×C4⋊Dic314yescomplemented
616C32D4×C4⋊C411yescharacteristic, complemented, Sylow
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—32no—
622C23—32no—
623C23—32no—
624C23—61no—
625C23—61no—
626C23—61no—
627C23—61no—
628C23D3×Dic612yes—
629C23D3×D1212yes—
630C23C2×D3×Dic312yes—
631C23C22×D3211yescharacteristic
632D4—316no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—28no—
636C2×C4—32no—
637C2×C4—32no—
638C2×C4—32no—
639C2×C4—32no—
640C2×C4—32no—
641C2×C4—34no—
642C2×C4—61no—
643C2×C4—62no—
644C2×C4—61no—
645C2×C4—62no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—68no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—128no—
653C2×C4—182no—
654C2×C4—182no—
655C2×C4—182no—
656C2×C4—182no—
657C2×C4—182no—
658C2×C4—182no—
659C2×C4—368no—
660C2×C4C2×D3×Dic312yes—
661C2×C4C2×D3×Dic312yes—
662C2×C4#380412yes—
663C2×C4D3×#6712yes—
664C2×C3—24no—
665C2×C3—24no—
666C2×C3—21no—
667C2×C3—21no—
668C2×C3—21no—
669C2×C3—21no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—44no—
674C2×C3—64no—
675C2×C3C2×D3×C4⋊C411yescharacteristic
676C2×C3#550411yescharacteristic
677C2×C3#550711yescharacteristic
678C2×C3#551111yescharacteristic
679C2×C3D4×Dic611yescharacteristic
680C2×C3#554311yescharacteristic
681C2×C3D4×D1211yescharacteristic
682C2×C3#555511yescharacteristic
683C2×C3C22×C4⋊Dic311yescharacteristic
684C2×C3C2×C4×#6711yescharacteristic
685C2×C3C2×D4×Dic311yescharacteristic
686C2×C3D4×#6711yescharacteristic
687C2×C3Q8×#6711yescharacteristic
688C2×C3#582711yescharacteristic
689D3—24no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—34no—
697C22—62no—
698C22—62no—
699C22—62no—
700C22—62no—
701C22—62no—
702C22—62no—
703C22D3×C4⋊Dic314yescomplemented
704C22C2×D3×Dic611yescharacteristic
705C22#6429711yescharacteristic
706C22C2×D3×D1211yescharacteristic
707C22#6430711yescharacteristic
708C22C22×D3×Dic311yescharacteristic
709C22C2×#380411yescharacteristic
710C22C2×D3×#6711yescharacteristic
711C4—22no—
712C4—34no—
713C4—62no—
714C4—62no—
715C4—64no—
716C4—122no—
717C4—362no—
718C4—362no—
719C4Dic3×#6714yescomplemented
720C3—21no—
721C3C4⋊C4×#6711yescharacteristic, complemented
722C3D4×C4⋊Dic311yescharacteristic, complemented
723C2—24no—
724C2—64no—
725C2Dic6×#6711yescharacteristic
726C2C2×D3×C4⋊Dic311yescharacteristic
727C2#1059490611yescharacteristic
728C2#1059498611yescharacteristic
729C2#1059498811yescharacteristic
730C2D12×#6711yescharacteristic
731C2C2×Dic3×#6711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×C3×#67C22
hypercenterC23×C4D32
hypocenterC32D4×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4⋊Dic3C2semidirect
4. C2×D3×C4⋊Dic3C2semidirect
5. #10592911C2semidirect
6. #10591718C2semidirect
7. #10591377C2semidirect
8. #10591349C2semidirect
9. #10591313C2semidirect
10. Dic3×C4⋊Dic3C2semidirect
11. #10591265C2semidirect
23. C3×C4×#67C4semidirect
47. C22×C4⋊Dic3D3semidirect
68. C22×C32×C4C2×C4semidirect
86. C2×C3×C4×D3C2×C4semidirect
93. C3×#217C2×C4semidirect
94. C3×(C2×D3)⋊C4C2×C4semidirect
97. C3×C4⋊Dic3D4semidirect
98. C3×Dic3⋊C4C2×C4semidirect
99. C3×C4×Dic3C2×C4semidirect
133. C4×#67Dic3semidirect
193. C3×#67C4⋊C4semidirect
251. C22×C3×C4C4×D3semidirect
252. C22×C3×C4C2×Dic3semidirect
282. C2×C4×D3C2×Dic3semidirect
294. #217C2×Dic3semidirect
296. (C2×D3)⋊C4C2×Dic3semidirect
308. C4⋊Dic3#67direct (N × H)
312. Dic3⋊C4C2×Dic3semidirect
315. C4×Dic3C2×Dic3semidirect
322. C22×C32C2×C4⋊C4semidirect
336. C2×C3×D3C2×C4⋊C4semidirect
338. C32×C4C4×D4semidirect
345. C3×Dic3C2×C4⋊C4semidirect
450. #67C4⋊Dic3direct (N × H)
520. C22×C4D3×Dic3semidirect
571. C22×C3D3×C4⋊C4semidirect
572. C22×C3C2×C4⋊Dic3semidirect
593. C2×D3C2×C4⋊Dic3semidirect
603. C3×C4C4×#67semidirect
604. C3×C4D4×Dic3semidirect
615. Dic3C2×C4⋊Dic3semidirect
616. C32D4×C4⋊C4semidirect
703. C22D3×C4⋊Dic3semidirect
719. C4Dic3×#67semidirect
721. C3C4⋊C4×#67semidirect
722. C3D4×C4⋊Dic3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C22×C3×C4⋊Dic32
C2×Dic3×#672
C2×D3×C4⋊Dic32
#105929112
#105917182
#105913772
#105913492
#105913132
Dic3×C4⋊Dic32
#105912652
D4×C4⋊Dic33
C4⋊C4×#673