Finite Group Databasebeta

← C3×#82161 #11805630

Subgroups — C3×#82161 #11805630

Order 1152.

1529 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic
3C2×C3×#892C211yesmaximal, characteristic, complemented
4C3×#5213C212yesmaximal
5C3×#5212C211yesmaximal, characteristic, complemented
6C3×C4×#217C212yesmaximal, complemented
7C3×#4990C212yesmaximal, complemented
8C3×#4987C211yesmaximal, characteristic, complemented
9C3×#4978C212yesmaximal, complemented
10C3×#4977C211yesmaximal, characteristic, complemented
11C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
12C3×#2352—31nomaximal
13#82161C311yesmaximal, characteristic, direct product factor
14C23×C32×C4C2212yes—
15C23×C32×C4C2211yescharacteristic
16C22×C3×#67C2211yescharacteristic
17C22×C3×C4×D3C2211yescharacteristic
18C2×C32×C4⋊C4—24no—
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2212yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2211yescharacteristic
24C3×C4×#67C418yescomplemented
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2212yes—
32C2×C3×C4×Dic3C2212yes—
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×#892—24no—
35C3×C3⋊#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—21no—
43C22×C3×C4⋊C4D311yescharacteristic, complemented
44C22×C3×C4⋊C4C2×C311yescharacteristic, complemented
45C2×C4×#67C2×C311yescharacteristic
46C2×#892C2×C311yescharacteristic, complemented
47C3×#388—32no—
48C3×#387—32no—
49C3×#386—32no—
50C3×#382—31no—
51C3×#380—31no—
52C3×#380—31no—
53C3×C4×C4⋊C4—31no—
54C3×C4×C22⋊C4—32no—
55#5213C2×C312yes—
56#5212C2×C311yescharacteristic, complemented
57C4×#217C2×C312yescomplemented
58#4990C2×C312yescomplemented
59#4987C2×C311yescharacteristic, complemented
60#4978C2×C312yescomplemented
61#4977C2×C311yescharacteristic, complemented
62Dic3×C4⋊C4C2×C311yescharacteristic, complemented
63C24×C32C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C22×C32×C4—22no—
66C22×C32×C4—22no—
67C22×C32×C4—24no—
68C22×C32×C4—24no—
69C22×C32×C4—42no—
70C22×C32×C4C2×C414yes—
71C22×C32×C4C2312yes—
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2312yes—
74C22×C32×C4C2311yescharacteristic
75C2×C3×#67—22no—
76C2×C3×#67—22no—
77C2×C3×#67C2×C414yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2311yescharacteristic
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2311yescharacteristic
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3C2×C414yescomplemented
86C32×C4⋊C4—24no—
87C32×C4⋊C4—22no—
88C32×C4⋊C4D414yescomplemented
89C3×#217—24no—
90C3×#217C2×C414yes—
91C3×(C2×D3)⋊C4—24no—
92C3×(C2×D3)⋊C4—42no—
93C3×(C2×D3)⋊C4C2×C414yescomplemented
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3—22no—
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—22no—
104C23×C3×C4—31no—
105C23×C3×C4C2×D312yes—
106C23×C3×C4C2×D311yescharacteristic
107C23×C3×C4C22×C312yes—
108C23×C3×C4C22×C311yescharacteristic
109C22×#67C22×C311yescharacteristic
110C22×C4×D3C22×C311yescharacteristic
111C3×C4×D4—38no—
112C3×#117—64no—
113C2×C3×C4⋊C4—28no—
114C2×C3×C4⋊C4—24no—
115C2×C3×C4⋊C4—24no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4—22no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—31no—
121C2×C3×C4⋊C4—31no—
122C2×C3×C4⋊C4C2×D311yescharacteristic
123C2×C3×C4⋊C4C2×D312yes—
124C2×C3×C4⋊C4C2×D311yescharacteristic
125C2×C3×C4⋊C4C22×C311yescharacteristic
126C2×C3×C4⋊C4C22×C312yes—
127C2×C3×C4⋊C4C22×C311yescharacteristic
128C2×C3×C22⋊C4—31no—
129C2×C3×C22⋊C4—31no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C22⋊C4—32no—
133C2×C3×C42—31no—
134C2×C3×C42—32no—
135C2×C3×C42—32no—
136C2×#217C22×C312yes—
137C2×#217C22×C311yescharacteristic
138C4×#67C3×C418yescomplemented
139C2×(C2×D3)⋊C4C22×C312yes—
140C2×(C2×D3)⋊C4C22×C312yes—
141C2×(C2×D3)⋊C4C22×C311yescharacteristic
142C2×C4⋊Dic3C22×C311yescharacteristic
143C2×C4⋊Dic3C22×C311yescharacteristic
144C2×Dic3⋊C4C22×C311yescharacteristic
145C2×C4×Dic3C22×C312yes—
146C2×C4×Dic3C22×C312yes—
147C2×C4×Dic3C22×C311yescharacteristic
148#892—24no—
149C3×#95—32no—
150C3×#95—32no—
151C3×#95—32no—
152C3×#95—32no—
153C3×#95—32no—
154C3⋊#95C22×C312yes—
155C3⋊#95C22×C312yes—
156C3⋊#95C22×C312yes—
157C3⋊#95C22×C312yes—
158C3⋊#95C22×C312yes—
159C23×C32—21no—
160C23×C32—21no—
161C23×C32—21no—
162C23×C32—21no—
163C23×C32C22×C412yes—
164C23×C32#4112yes—
165C23×C32#4112yes—
166C23×C32C2411yescharacteristic
167C22×C3×D3—21no—
168C22×C3×D3—21no—
169C22×C3×D3—21no—
170C22×C3×D3—21no—
171C22×C3×D3—21no—
172C22×C3×D3—21no—
173C22×C3×D3C22×C412yes—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—28no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4—22no—
181C2×C32×C4—22no—
182C2×C32×C4—48no—
183C2×C32×C4C22×C412yes—
184C2×C32×C4C22×C412yes—
185C2×C32×C4C2×D414yes—
186C2×C32×C4C2×D412yes—
187C2×C32×C4#4112yes—
188C3×#67—28no—
189C2×C3×Dic3—21no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—21no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3C22×C412yes—
202C2×C3×Dic3C22×C412yes—
203C2×C3×Dic3C22×C412yes—
204C3×C4×D3—28no—
205C2×C4×D4—31no—
206C2×#117—31no—
207C22×C4⋊C4C3×D311yescharacteristic, complemented
208#388—32no—
209#387—32no—
210#386—32no—
211#382—31no—
212#380—31no—
213#380—31no—
214C4×C4⋊C4—31no—
215C4×C22⋊C4—32no—
216C24×C3—21no—
217C24×C3—31no—
218C24×C3C22×D311yescharacteristic
219C24×C3C23×C311yescharacteristic
220C23×D3C23×C311yescharacteristic
221C2×C3×D4—34no—
222C2×C3×D4—62no—
223C2×C3×D4—62no—
224C22×C3×C4—24no—
225C22×C3×C4—24no—
226C22×C3×C4—22no—
227C22×C3×C4—22no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—28no—
231C22×C3×C4—24no—
232C22×C3×C4—24no—
233C22×C3×C4—24no—
234C22×C3×C4—24no—
235C22×C3×C4—24no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—22no—
239C22×C3×C4—22no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—31no—
243C22×C3×C4—34no—
244C22×C3×C4—32no—
245C22×C3×C4—32no—
246C22×C3×C4—44no—
247C22×C3×C4—42no—
248C22×C3×C4—42no—
249C22×C3×C4—44no—
250C22×C3×C4—62no—
251C22×C3×C4—62no—
252C22×C3×C4C4×D314yes—
253C22×C3×C4C2×C3×C414yes—
254C22×C3×C4C22×D312yes—
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D312yes—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C23×C312yes—
259C22×C3×C4C23×C311yescharacteristic
260C22×C3×C4C23×C312yes—
261C22×C3×C4C23×C311yescharacteristic
262C2×#67—22no—
263C2×#67—22no—
264C2×#67C2×C3×C414yes—
265C22×Dic3C23×C312yes—
266C22×Dic3C23×C312yes—
267C22×Dic3C23×C311yescharacteristic
268C22×Dic3C23×C311yescharacteristic
269C22×Dic3C23×C311yescharacteristic
270C2×C4×D3—22no—
271C2×C4×D3—22no—
272C2×C4×D3C2×C3×C414yescomplemented
273C3×C4⋊C4—28no—
274C3×C4⋊C4—24no—
275C3×C4⋊C4—24no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—24no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—24no—
280C3×C4⋊C4—34no—
281C3×C4⋊C4—62no—
282C3×C4⋊C4—62no—
283C3×C4⋊C4#6714yescomplemented
284C3×C4⋊C4C3×D414yescomplemented
285C3×C22⋊C4—34no—
286C3×C22⋊C4—34no—
287C3×C22⋊C4—64no—
288C3×C22⋊C4—64no—
289C3×C22⋊C4—122no—
290C3×C42—34no—
291C3×C42—64no—
292C3×C42—122no—
293#217—24no—
294#217C2×C3×C414yes—
295(C2×D3)⋊C4—24no—
296(C2×D3)⋊C4—42no—
297(C2×D3)⋊C4C2×C3×C414yescomplemented
298C4⋊Dic3—22no—
299C4⋊Dic3—22no—
300Dic3⋊C4C2×C3×C414yescomplemented
301C4×Dic3—24no—
302C4×Dic3—42no—
303C4×Dic3C2×C3×C414yescomplemented
304C22×C32—22no—
305C22×C32—22no—
306C22×C32—22no—
307C22×C32—22no—
308C22×C32—22no—
309C22×C32—22no—
310C22×C32#11714yescomplemented
311C22×C32C23×C411yescharacteristic
312C22×C32C22×D411yescharacteristic
313C22×C32C2×#4111yescharacteristic
314C22×C32C2×#4111yescharacteristic
315C22×C32C2×#4111yescharacteristic
316C22×C32H(5,𝔽2)11yescharacteristic
317C22×C322−1+411yescharacteristic
318C2×C3×D3—22no—
319C2×C3×D3—22no—
320C2×C3×D3—22no—
321C2×C3×D3—41no—
322C2×C3×D3—41no—
323C2×C3×D3—41no—
324C2×C3×D3—41no—
325C32×C4—22no—
326C32×C4—24no—
327C32×C4—42no—
328C32×C4C4×D414yes—
329C3×Dic3—22no—
330C3×Dic3—22no—
331C3×Dic3—22no—
332C3×Dic3—42no—
333C3×Dic3—42no—
334C22×D4—31no—
335C23×C4—31no—
336C23×C4C2×C3×D312yes—
337C23×C4C2×C3×D311yescharacteristic
338C4×D4—38no—
339#117—64no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4C2×C3×D311yescharacteristic
345C2×C4⋊C4C2×C3×D312yes—
346C2×C4⋊C4C2×C3×D311yescharacteristic
347C2×C22⋊C4—31no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—32no—
350C2×C22⋊C4—32no—
351C2×C22⋊C4—32no—
352C2×C42—31no—
353C2×C42—32no—
354C2×C42—32no—
355#95—32no—
356#95—32no—
357#95—32no—
358#95—32no—
359#95—32no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—21no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—32no—
377C23×C3—61no—
378C23×C3—61no—
379C23×C3—61no—
380C23×C3—61no—
381C23×C3—61no—
382C23×C3—61no—
383C23×C3C2×C4×D312yes—
384C23×C3#23712yes—
385C23×C3#23912yes—
386C23×C3C22×C3×C412yes—
387C23×C3C3×#4112yes—
388C23×C3C3×#4112yes—
389C23×C3C23×D311yescharacteristic
390C23×C3C24×C311yescharacteristic
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3C22×C3×C412yes—
398C3×D4—68no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—216no—
402C2×C3×C4—21no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—28no—
411C2×C3×C4—28no—
412C2×C3×C4—24no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—24no—
424C2×C3×C4—32no—
425C2×C3×C4—32no—
426C2×C3×C4—32no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—48no—
432C2×C3×C4—48no—
433C2×C3×C4—416no—
434C2×C3×C4—61no—
435C2×C3×C4—61no—
436C2×C3×C4—61no—
437C2×C3×C4—61no—
438C2×C3×C4—61no—
439C2×C3×C4—61no—
440C2×C3×C4—68no—
441C2×C3×C4—62no—
442C2×C3×C4—62no—
443C2×C3×C4—62no—
444C2×C3×C4—62no—
445C2×C3×C4—62no—
446C2×C3×C4—62no—
447C2×C3×C4C2×C4×D312yes—
448C2×C3×C4C2×C4×D312yes—
449C2×C3×C4#23512yes—
450C2×C3×C4C2×#6714yes—
451C2×C3×C4C2×#6712yes—
452C2×C3×C4C22×C3×C412yes—
453C2×C3×C4C22×C3×C412yes—
454C2×C3×C4C2×C3×D414yes—
455C2×C3×C4C2×C3×D412yes—
456C2×C3×C4C3×#4112yes—
457#67—28no—
458C2×Dic3—21no—
459C2×Dic3—21no—
460C2×Dic3—21no—
461C2×Dic3—21no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3C22×C3×C412yes—
471C2×Dic3C22×C3×C412yes—
472C2×Dic3C22×C3×C412yes—
473C4×D3—28no—
474C2×C32—24no—
475C2×C32C2×#11711yescharacteristic
476C2×C32C2×C4×D411yescharacteristic
477C2×C32#52011yescharacteristic
478C2×C32#54611yescharacteristic
479C2×C32#54811yescharacteristic
480C2×C32#55211yescharacteristic
481C2×C32#55311yescharacteristic
482C3×D3—42no—
483C24—31no—
484C24C22×C3×D311yescharacteristic
485C2×D4—34no—
486C2×D4—62no—
487C2×D4—62no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—31no—
493C22×C4—31no—
494C22×C4—31no—
495C22×C4—34no—
496C22×C4—32no—
497C22×C4—32no—
498C22×C4—42no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4C3×C4×D314yes—
502C22×C4C22×C3×D312yes—
503C22×C4C22×C3×D311yescharacteristic
504C22×C4C22×C3×D312yes—
505C22×C4C22×C3×D311yescharacteristic
506C4⋊C4—24no—
507C4⋊C4—22no—
508C4⋊C4—34no—
509C4⋊C4—62no—
510C4⋊C4—62no—
511C4⋊C4C3×#6714yescomplemented
512C22⋊C4—34no—
513C22⋊C4—34no—
514C22⋊C4—64no—
515C22⋊C4—64no—
516C22⋊C4—122no—
517C42—34no—
518C42—64no—
519C42—122no—
520C22×C3—24no—
521C22×C3—24no—
522C22×C3—24no—
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—24no—
526C22×C3—22no—
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—22no—
538C22×C3—24no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—21no—
544C22×C3—21no—
545C22×C3—21no—
546C22×C3—62no—
547C22×C3—62no—
548C22×C3—62no—
549C22×C3—121no—
550C22×C3—121no—
551C22×C3—121no—
552C22×C3—121no—
553C22×C3#89214yescomplemented
554C22×C3C3×#11714yescomplemented
555C22×C3C22×C4×D311yescharacteristic
556C22×C3C2×#23511yescharacteristic
557C22×C3C2×#23711yescharacteristic
558C22×C3#100411yescharacteristic
559C22×C3C2×#23911yescharacteristic
560C22×C3#100711yescharacteristic
561C22×C3C22×#6711yescharacteristic
562C22×C3C23×C3×C411yescharacteristic
563C22×C3C22×C3×D411yescharacteristic
564C22×C3C2×C3×#4111yescharacteristic
565C22×C3C2×C3×#4111yescharacteristic
566C22×C3C2×C3×#4111yescharacteristic
567C22×C3C3×H(5,𝔽2)11yescharacteristic
568C22×C3C3×2−1+411yescharacteristic
569C2×D3—22no—
570C2×D3—22no—
571C2×D3—22no—
572C2×D3—41no—
573C2×D3—41no—
574C2×D3—41no—
575C2×D3—41no—
576C3×C4—24no—
577C3×C4—22no—
578C3×C4—24no—
579C3×C4—22no—
580C3×C4—24no—
581C3×C4—24no—
582C3×C4—44no—
583C3×C4—44no—
584C3×C4—42no—
585C3×C4—42no—
586C3×C4—62no—
587C3×C4—62no—
588C3×C4—62no—
589C3×C4—122no—
590C3×C4—122no—
591C3×C4C4×#6714yes—
592C3×C4C3×C4×D414yes—
593Dic3—22no—
594Dic3—22no—
595Dic3—22no—
596Dic3—42no—
597Dic3—42no—
598C32#235211yescharacteristic, complemented, Sylow
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—32no—
604C23—61no—
605C23—61no—
606C23—61no—
607C23—61no—
608C23—61no—
609C23—61no—
610C23C2×C3×C4×D312yes—
611C23C3×#23712yes—
612C23C3×#23912yes—
613C23C23×C3×D311yescharacteristic
614D4—68no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—32no—
624C2×C4—32no—
625C2×C4—32no—
626C2×C4—48no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—68no—
634C2×C4—62no—
635C2×C4—62no—
636C2×C4—62no—
637C2×C4—62no—
638C2×C4—62no—
639C2×C4—62no—
640C2×C4C2×C3×C4×D312yes—
641C2×C4C2×C3×C4×D312yes—
642C2×C4C3×#23512yes—
643C2×C4C2×C3×#6714yes—
644C2×C4C2×C3×#6712yes—
645C2×C3—28no—
646C2×C3—24no—
647C2×C3—24no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—122no—
656C2×C3C2×#89211yescharacteristic
657C2×C3#550411yescharacteristic
658C2×C3#551311yescharacteristic
659C2×C3#551411yescharacteristic
660C2×C3C2×C4×#6711yescharacteristic
661C2×C3#580611yescharacteristic
662C2×C3#581711yescharacteristic
663C2×C3C2×C3×#11711yescharacteristic
664C2×C3C2×C3×C4×D411yescharacteristic
665C2×C3C3×#52011yescharacteristic
666C2×C3C3×#54611yescharacteristic
667C2×C3C3×#54811yescharacteristic
668C2×C3C3×#55211yescharacteristic
669C2×C3C3×#55311yescharacteristic
670D3—42no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—62no—
678C22—62no—
679C22—62no—
680C22—121no—
681C22—121no—
682C22—121no—
683C22—121no—
684C22C3×#89214yescomplemented
685C22C22×C3×C4×D311yescharacteristic
686C22C2×C3×#23511yescharacteristic
687C22C2×C3×#23711yescharacteristic
688C22C3×#100411yescharacteristic
689C22C2×C3×#23911yescharacteristic
690C22C3×#100711yescharacteristic
691C22C22×C3×#6711yescharacteristic
692C4—22no—
693C4—24no—
694C4—42no—
695C4—62no—
696C4—62no—
697C4—62no—
698C4—122no—
699C4—122no—
700C4C3×C4×#6714yes—
701C3—21no—
702C3#8216111yescharacteristic, direct product factor
703C3C3×#235211yescharacteristic, complemented
704C2—24no—
705C2—122no—
706C2C2×C3×#89211yescharacteristic
707C2C3×#550411yescharacteristic
708C2C3×#551311yescharacteristic
709C2C3×#551411yescharacteristic
710C2C2×C3×C4×#6711yescharacteristic
711C2C3×#580611yescharacteristic
712C2C3×#581711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC22×C32×C4⋊C4C2
socleC23×C32C24
prime radicalC22×C3×#67C22
cosocleC23×C3C24×C3
hypercenterC22×C3×C4⋊C4D3
hypocenterC3C3×#2352
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C32×C4⋊C4C2semidirect
3. C2×C3×#892C2semidirect
5. C3×#5212C2semidirect
6. C3×C4×#217C2semidirect
7. C3×#4990C2semidirect
8. C3×#4987C2semidirect
9. C3×#4978C2semidirect
10. C3×#4977C2semidirect
11. C3×Dic3×C4⋊C4C2semidirect
13. #82161C3direct (N × H)
24. C3×C4×#67C4semidirect
43. C22×C3×C4⋊C4D3semidirect
44. C22×C3×C4⋊C4C2×C3semidirect
46. C2×#892C2×C3semidirect
56. #5212C2×C3semidirect
57. C4×#217C2×C3semidirect
58. #4990C2×C3semidirect
59. #4987C2×C3semidirect
60. #4978C2×C3semidirect
61. #4977C2×C3semidirect
62. Dic3×C4⋊C4C2×C3semidirect
85. C2×C3×C4×D3C2×C4semidirect
88. C32×C4⋊C4D4semidirect
93. C3×(C2×D3)⋊C4C2×C4semidirect
96. C3×Dic3⋊C4C2×C4semidirect
99. C3×C4×Dic3C2×C4semidirect
138. C4×#67C3×C4semidirect
207. C22×C4⋊C4C3×D3semidirect
272. C2×C4×D3C2×C3×C4semidirect
283. C3×C4⋊C4#67semidirect
284. C3×C4⋊C4C3×D4semidirect
297. (C2×D3)⋊C4C2×C3×C4semidirect
300. Dic3⋊C4C2×C3×C4semidirect
303. C4×Dic3C2×C3×C4semidirect
310. C22×C32#117semidirect
511. C4⋊C4C3×#67semidirect
553. C22×C3#892semidirect
554. C22×C3C3×#117semidirect
598. C32#2352semidirect
684. C22C3×#892semidirect
702. C3#82161direct (N × H)
703. C3C3×#2352semidirect

Maximal subgroups

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

subgroupindex
C22×C32×C4⋊C42
C2×C3×C4×#672
C2×C3×#8922
C3×#52132
C3×#52122
C3×C4×#2172
C3×#49902
C3×#49872
C3×#49782
C3×#49772
C3×Dic3×C4⋊C42
C3×#23523
#821613