Finite Group Databasebeta

← C3×#74229 #11805633

Subgroups — C3×#74229 #11805633

Order 1152.

1397 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic, complemented
2C2×C3×D3×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×C4×D12C211yesmaximal, characteristic
4C32×#382C211yesmaximal, characteristic, complemented
5C3×#4987C211yesmaximal, characteristic, complemented
6C3×#4987C211yesmaximal, characteristic, complemented
7C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
8C3×#4669C212yesmaximal, complemented
9C3×#4666C212yesmaximal, complemented
10C3×#4665C212yesmaximal
11C3×#4654C212yesmaximal, complemented
12C3×#2352—31nomaximal
13#74229C311yesmaximal, characteristic, direct product factor
14C22×C3×D12C2211yescharacteristic
15C22×C3×C4×D3C2212yes—
16C22×C3×C4×D3C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×C32×C4⋊C4C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C42C2211yescharacteristic
21C2×C3×(C2×D3)⋊C4C2212yes—
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×C4×Dic3C2212yes—
31C2×C3×C4×Dic3C2212yes—
32C3×#892—24no—
33C3×D3×C4⋊C4—24no—
34C3×C4×D12C418yescomplemented
35C32×#95C2212yes—
36C32×#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×#892C2×C311yescharacteristic, complemented
44C2×D3×C4⋊C4C2×C311yescharacteristic, complemented
45C2×C4×D12C2×C311yescharacteristic
46C3×#388—32no—
47C3×#387—32no—
48C3×#386—32no—
49C3×#382—21no—
50C3×#382D311yescharacteristic, complemented
51C3×#382C2×C311yescharacteristic, complemented
52C3×#380—31no—
53C3×#380—31no—
54C3×C4×C4⋊C4—31no—
55C3×C4×C22⋊C4—32no—
56#4987C2×C311yescharacteristic, complemented
57#4987C2×C311yescharacteristic, complemented
58C4×C4⋊Dic3C2×C311yescharacteristic, complemented
59#4669C2×C312yescomplemented
60#4666C2×C312yescomplemented
61#4665C2×C312yes—
62#4654C2×C312yescomplemented
63C23×C3×D3C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4C2312yes—
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C32×C4C2311yescharacteristic
69C22×C32×C4C2311yescharacteristic
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2311yescharacteristic
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2312yes—
74C2×C3×D12—22no—
75C2×C3×D12—22no—
76C2×C3×D12C2×C414yes—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3—24no—
82C2×C3×C4×D3—24no—
83C2×C3×C4×D3—42no—
84C2×C3×C4×D3C2×C414yes—
85C2×C3×C4×D3C2×C414yescomplemented
86C32×C4⋊C4—22no—
87C32×C4⋊C4—22no—
88C32×C42C2×C414yescomplemented
89C3×(C2×D3)⋊C4—24no—
90C3×(C2×D3)⋊C4—24no—
91C3×(C2×D3)⋊C4—42no—
92C3×(C2×D3)⋊C4C2×C414yes—
93C3×(C2×D3)⋊C4C2×C414yescomplemented
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3C2×C414yescomplemented
96C3×C4⋊Dic3D414yescomplemented
97C3×Dic3⋊C4—24no—
98C3×C4×Dic3—24no—
99C3×C4×Dic3—42no—
100#2352—31noSylow
101C22×C3×D4—31no—
102C23×C3×C4—31no—
103C23×C3×C4—31no—
104C23×C3×C4—32no—
105C22×D12C22×C311yescharacteristic
106C22×C4×D3C22×C312yes—
107C22×C4×D3C22×C311yescharacteristic
108C22×C4×D3C22×C311yescharacteristic
109C3×C4×D4—38no—
110C3×#117—64no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4—21no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C4⋊C4—31no—
115C2×C3×C4⋊C4—32no—
116C2×C3×C4⋊C4—31no—
117C2×C3×C4⋊C4—64no—
118C2×C3×C4⋊C4C2×D311yescharacteristic
119C2×C3×C4⋊C4C2×D311yescharacteristic
120C2×C3×C4⋊C4C22×C311yescharacteristic
121C2×C3×C4⋊C4C22×C311yescharacteristic
122C2×C3×C22⋊C4—31no—
123C2×C3×C22⋊C4—31no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4—32no—
126C2×C3×C22⋊C4—32no—
127C2×C3×C42—21no—
128C2×C3×C42—32no—
129C2×C3×C42—32no—
130C2×C3×C42C2×D311yescharacteristic
131C2×C3×C42C22×C311yescharacteristic
132C2×(C2×D3)⋊C4C22×C312yes—
133C2×(C2×D3)⋊C4C22×C312yes—
134C2×(C2×D3)⋊C4C22×C312yes—
135C2×(C2×D3)⋊C4C22×C311yescharacteristic
136C2×(C2×D3)⋊C4C22×C311yescharacteristic
137C2×C4⋊Dic3C22×C311yescharacteristic
138C2×C4⋊Dic3C22×C311yescharacteristic
139C2×C4⋊Dic3C22×C311yescharacteristic
140C2×Dic3⋊C4C22×C312yes—
141C2×C4×Dic3C22×C312yes—
142C2×C4×Dic3C22×C312yes—
143#892—24no—
144D3×C4⋊C4—24no—
145C4×D12C3×C418yescomplemented
146C3×#95—22no—
147C3×#95—22no—
148C3×#95—32no—
149C3×#95—32no—
150C3×#95—32no—
151C3×#95C2×D312yes—
152C3×#95C2×D312yes—
153C3×#95C22×C312yes—
154C3×#95C22×C312yes—
155C3⋊#95C22×C312yes—
156C3⋊#95C22×C312yes—
157C3⋊#95C22×C312yes—
158C23×C32C2411yescharacteristic
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C22×C3×D3—21no—
162C22×C3×D3—21no—
163C22×C3×D3—21no—
164C22×C3×D3—21no—
165C22×C3×D3—21no—
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3C22×C412yes—
170C22×C3×D3C22×C412yes—
171C22×C3×D3#4112yes—
172C22×C3×D3#4112yes—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4C22×C412yes—
184C2×C32×C4C22×C412yes—
185C2×C32×C4C22×C412yes—
186C2×C32×C4C2×D412yes—
187C2×C32×C4#4112yes—
188C2×C3×Dic3—21no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—22no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3C22×C412yes—
198C2×C3×Dic3C22×C412yes—
199C2×C3×Dic3C2×D414yes—
200C3×D12—28no—
201C3×C4×D3—28no—
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#382C3×D311yescharacteristic, complemented
211#380—31no—
212#380—31no—
213C4×C4⋊C4—31no—
214C4×C22⋊C4—32no—
215C24×C3—31no—
216C24×C3—31no—
217C23×D3C23×C311yescharacteristic
218C23×D3C23×C311yescharacteristic
219C2×C3×D4—34no—
220C2×C3×D4—62no—
221C2×C3×D4—62no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—22no—
226C22×C3×C4—22no—
227C22×C3×C4—31no—
228C22×C3×C4—31no—
229C22×C3×C4—32no—
230C22×C3×C4—34no—
231C22×C3×C4—34no—
232C22×C3×C4—32no—
233C22×C3×C4—64no—
234C22×C3×C4—64no—
235C22×C3×C4—62no—
236C22×C3×C4—62no—
237C22×C3×C4—62no—
238C22×C3×C4—62no—
239C22×C3×C4—122no—
240C22×C3×C4C22×D312yes—
241C22×C3×C4C22×D312yes—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C23×C312yes—
246C22×C3×C4C23×C312yes—
247C22×C3×C4C23×C311yescharacteristic
248C22×C3×C4C23×C311yescharacteristic
249C22×C3×C4C23×C311yescharacteristic
250C22×Dic3C23×C312yes—
251C22×Dic3C23×C311yescharacteristic
252C22×Dic3C23×C311yescharacteristic
253C22×Dic3C23×C312yes—
254C2×D12—22no—
255C2×D12—22no—
256C2×D12C2×C3×C414yes—
257C2×C4×D3—22no—
258C2×C4×D3—22no—
259C2×C4×D3—22no—
260C2×C4×D3—22no—
261C2×C4×D3—24no—
262C2×C4×D3—24no—
263C2×C4×D3—42no—
264C2×C4×D3C2×C3×C414yes—
265C2×C4×D3C2×C3×C414yescomplemented
266C3×C4⋊C4—22no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—22no—
269C3×C4⋊C4—22no—
270C3×C4⋊C4—34no—
271C3×C4⋊C4—34no—
272C3×C4⋊C4—42no—
273C3×C4⋊C4—42no—
274C3×C4⋊C4—64no—
275C3×C4⋊C4—62no—
276C3×C22⋊C4—34no—
277C3×C22⋊C4—34no—
278C3×C22⋊C4—64no—
279C3×C22⋊C4—64no—
280C3×C22⋊C4—122no—
281C3×C42—24no—
282C3×C42—64no—
283C3×C42—122no—
284C3×C42C4×D314yescomplemented
285C3×C42C2×C3×C414yescomplemented
286(C2×D3)⋊C4—24no—
287(C2×D3)⋊C4—24no—
288(C2×D3)⋊C4—42no—
289(C2×D3)⋊C4C2×C3×C414yes—
290(C2×D3)⋊C4C2×C3×C414yescomplemented
291C4⋊Dic3—22no—
292C4⋊Dic3C2×C3×C414yescomplemented
293C4⋊Dic3C3×D414yescomplemented
294Dic3⋊C4—24no—
295C4×Dic3—24no—
296C4×Dic3—42no—
297C22×C32C23×C411yescharacteristic
298C22×C32C22×D411yescharacteristic
299C22×C32C2×#4111yescharacteristic
300C22×C32C2×#4111yescharacteristic
301C22×C32C2×#4111yescharacteristic
302C22×C32H(5,𝔽2)11yescharacteristic
303C22×C322−1+411yescharacteristic
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C2×C3×D3—22no—
307C2×C3×D3—22no—
308C2×C3×D3—22no—
309C2×C3×D3—22no—
310C2×C3×D3—22no—
311C2×C3×D3—22no—
312C2×C3×D3—22no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C2×C3×D3#11714yescomplemented
318C32×C4—22no—
319C32×C4—22no—
320C32×C4—42no—
321C32×C4—42no—
322C32×C4C4×D414yes—
323C3×Dic3—22no—
324C3×Dic3—22no—
325C3×Dic3—24no—
326C3×Dic3—42no—
327C22×D4—31no—
328C23×C4—31no—
329C23×C4—31no—
330C23×C4—32no—
331C4×D4—38no—
332#117—64no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—32no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—64no—
338C2×C4⋊C4C2×C3×D311yescharacteristic
339C2×C4⋊C4C2×C3×D311yescharacteristic
340C2×C22⋊C4—31no—
341C2×C22⋊C4—31no—
342C2×C22⋊C4—32no—
343C2×C22⋊C4—32no—
344C2×C22⋊C4—32no—
345C2×C42—32no—
346C2×C42—32no—
347C2×C42C2×C3×D311yescharacteristic
348#95—32no—
349#95—32no—
350#95—32no—
351#95C2×C3×D312yes—
352#95C2×C3×D312yes—
353C23×C3—21no—
354C23×C3—32no—
355C23×C3—32no—
356C23×C3—32no—
357C23×C3—32no—
358C23×C3—61no—
359C23×C3—61no—
360C23×C3—61no—
361C23×C3—61no—
362C23×C3—61no—
363C23×C3—61no—
364C23×C3—61no—
365C23×C3—61no—
366C23×C3—61no—
367C23×C3—61no—
368C23×C3C23×D311yescharacteristic
369C23×C3C24×C311yescharacteristic
370C22×D3—21no—
371C22×D3—21no—
372C22×D3—21no—
373C22×D3—21no—
374C22×D3—21no—
375C22×D3—21no—
376C22×D3—21no—
377C22×D3—21no—
378C22×D3—21no—
379C22×D3—21no—
380C22×D3C22×C3×C412yes—
381C22×D3C22×C3×C412yes—
382C22×D3C3×#4112yes—
383C22×D3C3×#4112yes—
384C3×D4—68no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
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—32no—
411C2×C3×C4—32no—
412C2×C3×C4—34no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—42no—
421C2×C3×C4—42no—
422C2×C3×C4—42no—
423C2×C3×C4—61no—
424C2×C3×C4—61no—
425C2×C3×C4—61no—
426C2×C3×C4—61no—
427C2×C3×C4—62no—
428C2×C3×C4—62no—
429C2×C3×C4—68no—
430C2×C3×C4—68no—
431C2×C3×C4—62no—
432C2×C3×C4—62no—
433C2×C3×C4—62no—
434C2×C3×C4—128no—
435C2×C3×C4C2×C4×D312yes—
436C2×C3×C4C2×C4×D312yes—
437C2×C3×C4C2×C4×D312yes—
438C2×C3×C4D3×D412yes—
439C2×C3×C4#23912yes—
440C2×C3×C4C22×C3×C412yes—
441C2×C3×C4C22×C3×C412yes—
442C2×C3×C4C22×C3×C412yes—
443C2×C3×C4C2×C3×D412yes—
444C2×C3×C4C3×#4112yes—
445C2×Dic3—21no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—22no—
452C2×Dic3—22no—
453C2×Dic3—22no—
454C2×Dic3C22×C3×C412yes—
455C2×Dic3C22×C3×C412yes—
456C2×Dic3C2×C3×D414yes—
457D12—28no—
458C4×D3—28no—
459C4×D3—28no—
460C4×D3—48no—
461C2×C32C2×#11711yescharacteristic
462C2×C32C2×C4×D411yescharacteristic
463C2×C32#52011yescharacteristic
464C2×C32#54611yescharacteristic
465C2×C32#54811yescharacteristic
466C2×C32#55211yescharacteristic
467C2×C32#55311yescharacteristic
468C3×D3—24no—
469C3×D3—42no—
470C24—31no—
471C24—31no—
472C2×D4—34no—
473C2×D4—62no—
474C2×D4—62no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—32no—
478C22×C4—34no—
479C22×C4—34no—
480C22×C4—32no—
481C22×C4—64no—
482C22×C4—64no—
483C22×C4—62no—
484C22×C4—62no—
485C22×C4—62no—
486C22×C4—62no—
487C22×C4—122no—
488C22×C4C22×C3×D312yes—
489C22×C4C22×C3×D312yes—
490C22×C4C22×C3×D311yescharacteristic
491C22×C4C22×C3×D311yescharacteristic
492C22×C4C22×C3×D311yescharacteristic
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—34no—
496C4⋊C4—34no—
497C4⋊C4—64no—
498C4⋊C4—62no—
499C22⋊C4—34no—
500C22⋊C4—34no—
501C22⋊C4—64no—
502C22⋊C4—64no—
503C22⋊C4—122no—
504C42—64no—
505C42—122no—
506C42C3×C4×D314yescomplemented
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—34no—
515C22×C3—62no—
516C22×C3—62no—
517C22×C3—62no—
518C22×C3—62no—
519C22×C3—62no—
520C22×C3—62no—
521C22×C3—62no—
522C22×C3—62no—
523C22×C3—62no—
524C22×C3—121no—
525C22×C3—121no—
526C22×C3—121no—
527C22×C3—121no—
528C22×C3C22×C4×D311yescharacteristic
529C22×C3C2×D3×D411yescharacteristic
530C22×C3C2×#23911yescharacteristic
531C22×C3D3×#4111yescharacteristic
532C22×C3D3×#4111yescharacteristic
533C22×C3#100911yescharacteristic
534C22×C3#101011yescharacteristic
535C22×C3C23×C3×C411yescharacteristic
536C22×C3C22×C3×D411yescharacteristic
537C22×C3C2×C3×#4111yescharacteristic
538C22×C3C2×C3×#4111yescharacteristic
539C22×C3C2×C3×#4111yescharacteristic
540C22×C3C3×H(5,𝔽2)11yescharacteristic
541C22×C3C3×2−1+411yescharacteristic
542C2×D3—22no—
543C2×D3—22no—
544C2×D3—22no—
545C2×D3—22no—
546C2×D3—22no—
547C2×D3—22no—
548C2×D3—22no—
549C2×D3—22no—
550C2×D3—22no—
551C2×D3—41no—
552C2×D3—41no—
553C2×D3—41no—
554C2×D3—41no—
555C2×D3C3×#11714yescomplemented
556C3×C4—22no—
557C3×C4—22no—
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—24no—
561C3×C4—42no—
562C3×C4—42no—
563C3×C4—42no—
564C3×C4—42no—
565C3×C4—42no—
566C3×C4—42no—
567C3×C4—64no—
568C3×C4—62no—
569C3×C4—62no—
570C3×C4—82no—
571C3×C4—82no—
572C3×C4—122no—
573C3×C4#89314yes—
574C3×C4C3×C4×D414yes—
575Dic3—22no—
576Dic3—22no—
577Dic3—24no—
578Dic3—42no—
579C32#235211yescharacteristic, complemented, Sylow
580C23—32no—
581C23—32no—
582C23—32no—
583C23—32no—
584C23—61no—
585C23—61no—
586C23—61no—
587C23—61no—
588C23—61no—
589C23—61no—
590C23—61no—
591C23—61no—
592C23—61no—
593C23—61no—
594C23C23×C3×D311yescharacteristic
595D4—68no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—32no—
607C2×C4—32no—
608C2×C4—34no—
609C2×C4—61no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—61no—
613C2×C4—62no—
614C2×C4—62no—
615C2×C4—68no—
616C2×C4—68no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—62no—
620C2×C4—128no—
621C2×C4C2×C3×C4×D312yes—
622C2×C4C2×C3×C4×D312yes—
623C2×C4C2×C3×C4×D312yes—
624C2×C4C3×D3×D412yes—
625C2×C4C3×#23912yes—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—21no—
633C2×C3—64no—
634C2×C3—122no—
635C2×C3C2×#89311yescharacteristic
636C2×C3D3×#11711yescharacteristic
637C2×C3#552311yescharacteristic
638C2×C3#567611yescharacteristic
639C2×C3#567711yescharacteristic
640C2×C3#569411yescharacteristic
641C2×C3#569511yescharacteristic
642C2×C3C2×C3×#11711yescharacteristic
643C2×C3C2×C3×C4×D411yescharacteristic
644C2×C3C3×#52011yescharacteristic
645C2×C3C3×#54611yescharacteristic
646C2×C3C3×#54811yescharacteristic
647C2×C3C3×#55211yescharacteristic
648C2×C3C3×#55311yescharacteristic
649D3—24no—
650D3—42no—
651C22—34no—
652C22—62no—
653C22—62no—
654C22—62no—
655C22—62no—
656C22—62no—
657C22—62no—
658C22—62no—
659C22—62no—
660C22—62no—
661C22—121no—
662C22—121no—
663C22—121no—
664C22—121no—
665C22C22×C3×C4×D311yescharacteristic
666C22C2×C3×D3×D411yescharacteristic
667C22C2×C3×#23911yescharacteristic
668C22C3×D3×#4111yescharacteristic
669C22C3×D3×#4111yescharacteristic
670C22C3×#100911yescharacteristic
671C22C3×#101011yescharacteristic
672C4—22no—
673C4—22no—
674C4—42no—
675C4—42no—
676C4—62no—
677C4—62no—
678C4—64no—
679C4—122no—
680C4C3×#89314yes—
681C3—21no—
682C3#7422911yescharacteristic, direct product factor
683C3C3×#235211yescharacteristic, complemented
684C2—64no—
685C2—122no—
686C2C2×C3×#89311yescharacteristic
687C2C3×D3×#11711yescharacteristic
688C2C3×#552311yescharacteristic
689C2C3×#567611yescharacteristic
690C2C3×#567711yescharacteristic
691C2C3×#569411yescharacteristic
692C2C3×#569511yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC32×#382C2
socleC23×C32C24
prime radicalC22×C3×D12C22
cosocleC23×C3C24×C3
hypercenterC3×#382D3
hypocenterC3C3×#2352
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C3×#382

Complements

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

NH ≅ G/Ntype
1. C2×C3×#892C2semidirect
2. C2×C3×D3×C4⋊C4C2semidirect
4. C32×#382C2semidirect
5. C3×#4987C2semidirect
6. C3×#4987C2semidirect
7. C3×C4×C4⋊Dic3C2semidirect
8. C3×#4669C2semidirect
9. C3×#4666C2semidirect
11. C3×#4654C2semidirect
13. #74229C3direct (N × H)
34. C3×C4×D12C4semidirect
43. C2×#892C2×C3semidirect
44. C2×D3×C4⋊C4C2×C3semidirect
50. C3×#382D3semidirect
51. C3×#382C2×C3semidirect
56. #4987C2×C3semidirect
57. #4987C2×C3semidirect
58. C4×C4⋊Dic3C2×C3semidirect
59. #4669C2×C3semidirect
60. #4666C2×C3semidirect
62. #4654C2×C3semidirect
85. C2×C3×C4×D3C2×C4semidirect
88. C32×C42C2×C4semidirect
93. C3×(C2×D3)⋊C4C2×C4semidirect
95. C3×C4⋊Dic3C2×C4semidirect
96. C3×C4⋊Dic3D4semidirect
145. C4×D12C3×C4semidirect
210. #382C3×D3semidirect
265. C2×C4×D3C2×C3×C4semidirect
284. C3×C42C4×D3semidirect
285. C3×C42C2×C3×C4semidirect
290. (C2×D3)⋊C4C2×C3×C4semidirect
292. C4⋊Dic3C2×C3×C4semidirect
293. C4⋊Dic3C3×D4semidirect
317. C2×C3×D3#117semidirect
506. C42C3×C4×D3semidirect
555. C2×D3C3×#117semidirect
579. C32#2352semidirect
682. C3#74229direct (N × H)
683. C3C3×#2352semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×C3×D3×C4⋊C42
C2×C3×C4×D122
C32×#3822
C3×#49872
C3×C4×C4⋊Dic32
C3×#46692
C3×#46662
C3×#46652
C3×#46542
C3×#23523
#742293