Finite Group Databasebeta

← C3×#74012 #11805621

Subgroups — C3×#74012 #11805621

Order 1152.

1437 conjugacy classes of subgroups.

The subgroup lattice has 709 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
4C32×#380C211yesmaximal, characteristic, complemented
5C3×#4987C211yesmaximal, characteristic, complemented
6C3×#4977C211yesmaximal, characteristic, complemented
7C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
8C3×#4956C212yesmaximal
9C3×#4944C212yesmaximal, complemented
10C3×#4666C212yesmaximal, complemented
11C3×#4652C212yesmaximal, complemented
12C3×#2352—31nomaximal
13#74012C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67C2211yescharacteristic
16C22×C3×C4×D3C2212yes—
17C22×C3×C4×D3C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C22⋊C4C2212yes—
21C2×C3×#217C2212yes—
22C2×C3×#217C2211yescharacteristic
23C3×C4×#67C418yescomplemented
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C3×#926—24no—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2212yes—
32C2×C3×C4×Dic3C2212yes—
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×D3×C4⋊C4—24no—
35C32×#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38C3×C3⋊#95C2212yes—
39C3×C3⋊#95C2212yes—
40C2×C3×C4×D4—31no—
41C2×C3×#117—31no—
42C22×C3×C4⋊C4—31no—
43C2×C4×#67C2×C311yescharacteristic
44C2×#926C2×C311yescharacteristic, complemented
45C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
46C3×#388—32no—
47C3×#387—32no—
48C3×#386—32no—
49C3×#382—31no—
50C3×#380—21no—
51C3×#380—31no—
52C3×#380D311yescharacteristic, complemented
53C3×#380C2×C311yescharacteristic, complemented
54C3×C4×C4⋊C4—31no—
55C3×C4×C22⋊C4—32no—
56#4987C2×C311yescharacteristic, complemented
57#4977C2×C311yescharacteristic, complemented
58Dic3×C4⋊C4C2×C311yescharacteristic, complemented
59#4956C2×C312yes—
60#4944C2×C312yescomplemented
61#4666C2×C312yescomplemented
62#4652C2×C312yescomplemented
63C24×C32C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4C2×C414yescomplemented
68C22×C32×C4C2312yes—
69C22×C32×C4C2312yes—
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C2×C3×#67—22no—
73C2×C3×#67—22no—
74C2×C3×#67C2×C414yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C22×C3×Dic3C2312yes—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—22no—
82C2×C3×C4×D3—24no—
83C2×C3×C4×D3—24no—
84C2×C3×C4×D3—42no—
85C2×C3×C4×D3C2×C414yes—
86C32×C4⋊C4—22no—
87C32×C4⋊C4—22no—
88C32×C22⋊C4—42no—
89C3×#217—24no—
90C3×#217C2×C414yescomplemented
91C3×(C2×D3)⋊C4—24no—
92C3×(C2×D3)⋊C4C2×C414yes—
93C3×C4⋊Dic3—22no—
94C3×C4⋊Dic3D414yescomplemented
95C3×Dic3⋊C4—24no—
96C3×Dic3⋊C4C2×C414yescomplemented
97C3×C4×Dic3—24no—
98C3×C4×Dic3—42no—
99C3×C4×Dic3C2×C414yescomplemented
100#2352—31noSylow
101C22×C3×D4—31no—
102C23×C3×C4—21no—
103C23×C3×C4—31no—
104C23×C3×C4—32no—
105C23×C3×C4C2×D311yescharacteristic
106C23×C3×C4C22×C311yescharacteristic
107C22×#67C22×C311yescharacteristic
108C22×C4×D3C22×C312yes—
109C22×C4×D3C22×C311yescharacteristic
110C3×C4×D4—38no—
111C3×#117—64no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—31no—
116C2×C3×C4⋊C4—32no—
117C2×C3×C4⋊C4—31no—
118C2×C3×C4⋊C4—64no—
119C2×C3×C4⋊C4C2×D311yescharacteristic
120C2×C3×C4⋊C4C2×D311yescharacteristic
121C2×C3×C4⋊C4C22×C311yescharacteristic
122C2×C3×C4⋊C4C22×C311yescharacteristic
123C2×C3×C22⋊C4—22no—
124C2×C3×C22⋊C4—31no—
125C2×C3×C22⋊C4—31no—
126C2×C3×C22⋊C4—32no—
127C2×C3×C22⋊C4—32no—
128C2×C3×C22⋊C4C2×D312yes—
129C2×C3×C22⋊C4C22×C312yes—
130C2×C3×C42—31no—
131C2×C3×C42—32no—
132C2×C3×C42—32no—
133C2×#217C22×C312yes—
134C2×#217C22×C311yescharacteristic
135C4×#67C3×C418yescomplemented
136C2×(C2×D3)⋊C4C22×C312yes—
137C2×(C2×D3)⋊C4C22×C311yescharacteristic
138#926—24no—
139C2×C4⋊Dic3C22×C311yescharacteristic
140C2×C4⋊Dic3C22×C311yescharacteristic
141C2×Dic3⋊C4C22×C312yes—
142C2×Dic3⋊C4C22×C311yescharacteristic
143C2×C4×Dic3C22×C312yes—
144C2×C4×Dic3C22×C312yes—
145C2×C4×Dic3C22×C311yescharacteristic
146D3×C4⋊C4—24no—
147C3×#95—22no—
148C3×#95—32no—
149C3×#95—32no—
150C3×#95—32no—
151C3×#95—32no—
152C3×#95C2×D312yes—
153C3×#95C22×C312yes—
154C3⋊#95C22×C312yes—
155C3⋊#95C22×C312yes—
156C3⋊#95C22×C312yes—
157C3⋊#95C22×C312yes—
158C23×C32—21no—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32—21no—
164C23×C32C22×C412yes—
165C23×C32C2411yescharacteristic
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3C22×C412yes—
171C22×C3×D3#4112yes—
172C22×C3×D3#4112yes—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—28no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4C22×C412yes—
183C2×C32×C4C22×C412yes—
184C2×C32×C4C2×D412yes—
185C2×C32×C4#4112yes—
186C3×#67—28no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3C22×C412yes—
199C2×C3×Dic3C22×C412yes—
200C2×C3×Dic3C22×C412yes—
201C2×C3×Dic3C2×D414yes—
202C3×C4×D3—28no—
203C3×C4×D3—48no—
204C2×C4×D4—31no—
205C2×#117—31no—
206C22×C4⋊C4—31no—
207#388—32no—
208#387—32no—
209#386—32no—
210#382—31no—
211#380—31no—
212#380C3×D311yescharacteristic, complemented
213C4×C4⋊C4—31no—
214C4×C22⋊C4—32no—
215C24×C3—21no—
216C24×C3—31no—
217C24×C3C22×D311yescharacteristic
218C24×C3C23×C311yescharacteristic
219C23×D3C23×C311yescharacteristic
220C2×C3×D4—34no—
221C2×C3×D4—62no—
222C2×C3×D4—62no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—24no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—31no—
235C22×C3×C4—32no—
236C22×C3×C4—34no—
237C22×C3×C4—32no—
238C22×C3×C4—42no—
239C22×C3×C4—42no—
240C22×C3×C4—64no—
241C22×C3×C4—64no—
242C22×C3×C4—62no—
243C22×C3×C4—62no—
244C22×C3×C4—122no—
245C22×C3×C4C4×D314yescomplemented
246C22×C3×C4C2×C3×C414yescomplemented
247C22×C3×C4C22×D312yes—
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C23×C312yes—
252C22×C3×C4C23×C312yes—
253C22×C3×C4C23×C311yescharacteristic
254C22×C3×C4C23×C311yescharacteristic
255C2×#67—22no—
256C2×#67—22no—
257C2×#67C2×C3×C414yes—
258C22×Dic3C23×C312yes—
259C22×Dic3C23×C311yescharacteristic
260C22×Dic3C23×C311yescharacteristic
261C22×Dic3C23×C311yescharacteristic
262C22×Dic3C23×C312yes—
263C2×C4×D3—22no—
264C2×C4×D3—22no—
265C2×C4×D3—24no—
266C2×C4×D3—24no—
267C2×C4×D3—42no—
268C2×C4×D3C2×C3×C414yes—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—22no—
271C3×C4⋊C4—22no—
272C3×C4⋊C4—22no—
273C3×C4⋊C4—34no—
274C3×C4⋊C4—34no—
275C3×C4⋊C4—42no—
276C3×C4⋊C4—42no—
277C3×C4⋊C4—64no—
278C3×C4⋊C4—62no—
279C3×C22⋊C4—34no—
280C3×C22⋊C4—34no—
281C3×C22⋊C4—42no—
282C3×C22⋊C4—42no—
283C3×C22⋊C4—44no—
284C3×C22⋊C4—64no—
285C3×C22⋊C4—64no—
286C3×C42—34no—
287C3×C42—64no—
288C3×C42—122no—
289#217—24no—
290#217C2×C3×C414yescomplemented
291(C2×D3)⋊C4—24no—
292(C2×D3)⋊C4C2×C3×C414yes—
293C4⋊Dic3—22no—
294C4⋊Dic3C3×D414yescomplemented
295Dic3⋊C4—24no—
296Dic3⋊C4C2×C3×C414yescomplemented
297C4×Dic3—24no—
298C4×Dic3—42no—
299C4×Dic3C2×C3×C414yescomplemented
300C22×C32—22no—
301C22×C32—22no—
302C22×C32—22no—
303C22×C32—41no—
304C22×C32—41no—
305C22×C32—41no—
306C22×C32—41no—
307C22×C32C23×C411yescharacteristic
308C22×C32C22×D411yescharacteristic
309C22×C32C2×#4111yescharacteristic
310C22×C32C2×#4111yescharacteristic
311C22×C32C2×#4111yescharacteristic
312C22×C32H(5,𝔽2)11yescharacteristic
313C22×C322−1+411yescharacteristic
314C2×C3×D3—22no—
315C2×C3×D3—22no—
316C2×C3×D3—22no—
317C2×C3×D3—22no—
318C2×C3×D3—22no—
319C2×C3×D3—22no—
320C2×C3×D3#11714yescomplemented
321C32×C4—22no—
322C32×C4—42no—
323C32×C4—42no—
324C32×C4C4×D414yes—
325C3×Dic3—22no—
326C3×Dic3—22no—
327C3×Dic3—22no—
328C3×Dic3—24no—
329C3×Dic3—42no—
330C22×D4—31no—
331C23×C4—31no—
332C23×C4—32no—
333C23×C4C2×C3×D311yescharacteristic
334C4×D4—38no—
335#117—64no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—32no—
339C2×C4⋊C4—31no—
340C2×C4⋊C4—64no—
341C2×C4⋊C4C2×C3×D311yescharacteristic
342C2×C4⋊C4C2×C3×D311yescharacteristic
343C2×C22⋊C4—31no—
344C2×C22⋊C4—31no—
345C2×C22⋊C4—32no—
346C2×C22⋊C4—32no—
347C2×C22⋊C4C2×C3×D312yes—
348C2×C42—31no—
349C2×C42—32no—
350C2×C42—32no—
351#95—32no—
352#95—32no—
353#95—32no—
354#95—32no—
355#95C2×C3×D312yes—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—22no—
372C23×C3—32no—
373C23×C3—32no—
374C23×C3—32no—
375C23×C3—41no—
376C23×C3—41no—
377C23×C3—41no—
378C23×C3—41no—
379C23×C3—61no—
380C23×C3—61no—
381C23×C3—61no—
382C23×C3—61no—
383C23×C3C2×C4×D312yes—
384C23×C3C22×C3×C412yes—
385C23×C3C23×D311yescharacteristic
386C23×C3C24×C311yescharacteristic
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3C22×C3×C412yes—
392C22×D3C3×#4112yes—
393C22×D3C3×#4112yes—
394C3×D4—68no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—28no—
400C2×C3×C4—28no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—32no—
418C2×C3×C4—32no—
419C2×C3×C4—32no—
420C2×C3×C4—34no—
421C2×C3×C4—48no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—61no—
431C2×C3×C4—61no—
432C2×C3×C4—61no—
433C2×C3×C4—62no—
434C2×C3×C4—61no—
435C2×C3×C4—62no—
436C2×C3×C4—61no—
437C2×C3×C4—61no—
438C2×C3×C4—68no—
439C2×C3×C4—62no—
440C2×C3×C4—62no—
441C2×C3×C4—62no—
442C2×C3×C4—128no—
443C2×C3×C4C2×C4×D312yes—
444C2×C3×C4C2×C4×D312yes—
445C2×C3×C4D3×D412yes—
446C2×C3×C4#23712yes—
447C2×C3×C4C22×C3×C412yes—
448C2×C3×C4C22×C3×C412yes—
449C2×C3×C4C2×C3×D412yes—
450C2×C3×C4C3×#4112yes—
451#67—28no—
452C2×Dic3—21no—
453C2×Dic3—21no—
454C2×Dic3—22no—
455C2×Dic3—21no—
456C2×Dic3—21no—
457C2×Dic3—21no—
458C2×Dic3—22no—
459C2×Dic3—21no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3C22×C3×C412yes—
464C2×Dic3C22×C3×C412yes—
465C2×Dic3C22×C3×C412yes—
466C2×Dic3C2×C3×D414yes—
467C4×D3—28no—
468C4×D3—48no—
469C2×C32—42no—
470C2×C32C2×#11711yescharacteristic
471C2×C32C2×C4×D411yescharacteristic
472C2×C32#52011yescharacteristic
473C2×C32#54611yescharacteristic
474C2×C32#54811yescharacteristic
475C2×C32#55211yescharacteristic
476C2×C32#55311yescharacteristic
477C3×D3—24no—
478C24—31no—
479C24C22×C3×D311yescharacteristic
480C2×D4—34no—
481C2×D4—62no—
482C2×D4—62no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—31no—
486C22×C4—31no—
487C22×C4—31no—
488C22×C4—32no—
489C22×C4—34no—
490C22×C4—32no—
491C22×C4—64no—
492C22×C4—64no—
493C22×C4—62no—
494C22×C4—62no—
495C22×C4—122no—
496C22×C4C3×C4×D314yescomplemented
497C22×C4C22×C3×D312yes—
498C22×C4C22×C3×D312yes—
499C22×C4C22×C3×D311yescharacteristic
500C22×C4C22×C3×D311yescharacteristic
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—34no—
504C4⋊C4—34no—
505C4⋊C4—64no—
506C4⋊C4—62no—
507C22⋊C4—34no—
508C22⋊C4—34no—
509C22⋊C4—42no—
510C22⋊C4—64no—
511C22⋊C4—64no—
512C42—34no—
513C42—64no—
514C42—122no—
515C22×C3—24no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—34no—
530C22×C3—42no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—42no—
535C22×C3—42no—
536C22×C3—41no—
537C22×C3—41no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—41no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—41no—
544C22×C3—62no—
545C22×C3—62no—
546C22×C3—62no—
547C22×C3—62no—
548C22×C3—62no—
549C22×C3—62no—
550C22×C3C22×C4×D311yescharacteristic
551C22×C3C2×D3×D411yescharacteristic
552C22×C3C2×#23711yescharacteristic
553C22×C3#100411yescharacteristic
554C22×C3#100711yescharacteristic
555C22×C3D3×#4111yescharacteristic
556C22×C3D3×#4111yescharacteristic
557C22×C3C23×C3×C411yescharacteristic
558C22×C3C22×C3×D411yescharacteristic
559C22×C3C2×C3×#4111yescharacteristic
560C22×C3C2×C3×#4111yescharacteristic
561C22×C3C2×C3×#4111yescharacteristic
562C22×C3C3×H(5,𝔽2)11yescharacteristic
563C22×C3C3×2−1+411yescharacteristic
564C2×D3—22no—
565C2×D3—22no—
566C2×D3—22no—
567C2×D3—22no—
568C2×D3—22no—
569C2×D3—22no—
570C2×D3C3×#11714yescomplemented
571C3×C4—22no—
572C3×C4—22no—
573C3×C4—24no—
574C3×C4—42no—
575C3×C4—42no—
576C3×C4—42no—
577C3×C4—42no—
578C3×C4—42no—
579C3×C4—62no—
580C3×C4—62no—
581C3×C4—62no—
582C3×C4—64no—
583C3×C4—82no—
584C3×C4—82no—
585C3×C4—122no—
586C3×C4#67⋊C414yes—
587C3×C4C3×C4×D414yes—
588Dic3—22no—
589Dic3—22no—
590Dic3—22no—
591Dic3—24no—
592Dic3—42no—
593C32#235211yescharacteristic, complemented, Sylow
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—32no—
601C23—32no—
602C23—32no—
603C23—61no—
604C23—61no—
605C23—61no—
606C23—61no—
607C23C2×C3×C4×D312yes—
608C23C23×C3×D311yescharacteristic
609D4—68no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—28no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—32no—
620C2×C4—32no—
621C2×C4—32no—
622C2×C4—34no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—62no—
627C2×C4—61no—
628C2×C4—62no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—68no—
632C2×C4—62no—
633C2×C4—62no—
634C2×C4—62no—
635C2×C4—128no—
636C2×C4C2×C3×C4×D312yes—
637C2×C4C2×C3×C4×D312yes—
638C2×C4C3×D3×D412yes—
639C2×C4C3×#23712yes—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—44no—
648C2×C3—42no—
649C2×C3—42no—
650C2×C3—64no—
651C2×C3C2×#67⋊C411yescharacteristic
652C2×C3#550411yescharacteristic
653C2×C3D3×#11711yescharacteristic
654C2×C3#561211yescharacteristic
655C2×C3#561411yescharacteristic
656C2×C3#563311yescharacteristic
657C2×C3#563911yescharacteristic
658C2×C3C2×C3×#11711yescharacteristic
659C2×C3C2×C3×C4×D411yescharacteristic
660C2×C3C3×#52011yescharacteristic
661C2×C3C3×#54611yescharacteristic
662C2×C3C3×#54811yescharacteristic
663C2×C3C3×#55211yescharacteristic
664C2×C3C3×#55311yescharacteristic
665D3—24no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—34no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—62no—
675C22—62no—
676C22—62no—
677C22—62no—
678C22—62no—
679C22—62no—
680C22C22×C3×C4×D311yescharacteristic
681C22C2×C3×D3×D411yescharacteristic
682C22C2×C3×#23711yescharacteristic
683C22C3×#100411yescharacteristic
684C22C3×#100711yescharacteristic
685C22C3×D3×#4111yescharacteristic
686C22C3×D3×#4111yescharacteristic
687C4—22no—
688C4—42no—
689C4—42no—
690C4—62no—
691C4—62no—
692C4—64no—
693C4—62no—
694C4—122no—
695C4C3×#67⋊C414yes—
696C3—21no—
697C3#7401211yescharacteristic, direct product factor
698C3C3×#235211yescharacteristic, complemented
699C2—42no—
700C2—64no—
701C2C2×C3×#67⋊C411yescharacteristic
702C2C3×#550411yescharacteristic
703C2C3×D3×#11711yescharacteristic
704C2C3×#561211yescharacteristic
705C2C3×#561411yescharacteristic
706C2C3×#563311yescharacteristic
707C2C3×#563911yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#380C2
socleC23×C32C24
prime radicalC22×C3×#67C22
cosocleC23×C3C24×C3
hypercenterC3×#380D3
hypocenterC3C3×#2352
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C2×C3×D3×C4⋊C4C2semidirect
4. C32×#380C2semidirect
5. C3×#4987C2semidirect
6. C3×#4977C2semidirect
7. C3×Dic3×C4⋊C4C2semidirect
9. C3×#4944C2semidirect
10. C3×#4666C2semidirect
11. C3×#4652C2semidirect
13. #74012C3direct (N × H)
23. C3×C4×#67C4semidirect
44. C2×#926C2×C3semidirect
45. C2×D3×C4⋊C4C2×C3semidirect
52. C3×#380D3semidirect
53. C3×#380C2×C3semidirect
56. #4987C2×C3semidirect
57. #4977C2×C3semidirect
58. Dic3×C4⋊C4C2×C3semidirect
60. #4944C2×C3semidirect
61. #4666C2×C3semidirect
62. #4652C2×C3semidirect
67. C22×C32×C4C2×C4semidirect
90. C3×#217C2×C4semidirect
94. C3×C4⋊Dic3D4semidirect
96. C3×Dic3⋊C4C2×C4semidirect
99. C3×C4×Dic3C2×C4semidirect
135. C4×#67C3×C4semidirect
212. #380C3×D3semidirect
245. C22×C3×C4C4×D3semidirect
246. C22×C3×C4C2×C3×C4semidirect
290. #217C2×C3×C4semidirect
294. C4⋊Dic3C3×D4semidirect
296. Dic3⋊C4C2×C3×C4semidirect
299. C4×Dic3C2×C3×C4semidirect
320. C2×C3×D3#117semidirect
496. C22×C4C3×C4×D3semidirect
570. C2×D3C3×#117semidirect
593. C32#2352semidirect
697. C3#74012direct (N × H)
698. C3C3×#2352semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C2×C3×#9262
C2×C3×D3×C4⋊C42
C32×#3802
C3×#49872
C3×#49772
C3×Dic3×C4⋊C42
C3×#49562
C3×#49442
C3×#46662
C3×#46522
C3×#23523
#740123