Finite Group Databasebeta

← C2×C3×#4957 #11801607

Subgroups — C2×C3×#4957 #11801607

Order 1152.

3057 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×#67C211yesmaximal, characteristic
2C22×C32×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×C3×#217C211yesmaximal, characteristic, complemented
4C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C22×C3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C22×C3×Dic3⋊C4C211yesmaximal, characteristic, complemented
7C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
8C3×#4957C218yesmaximal, direct product factor
9C2×C3×#390—31nomaximal
10C2×#4957C311yesmaximal, characteristic, direct product factor
11C25×C32C2211yescharacteristic
12C24×C3×D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C32×C4C2211yescharacteristic
15C22×C3×#67—24no—
16C22×C3×#67—24no—
17C22×C3×#67C418yescomplemented
18C22×C3×#67C2214yes—
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C23×C3×Dic3C2211yescharacteristic
22C2×C32×C22⋊C4—24no—
23C2×C32×C22⋊C4C2214yescomplemented
24C2×C3×#217—24no—
25C2×C3×#217C2214yescomplemented
26C2×C3×(C2×D3)⋊C4—24no—
27C2×C3×(C2×D3)⋊C4—24no—
28C2×C3×(C2×D3)⋊C4C2214yescomplemented
29C2×C3×(C2×D3)⋊C4C2214yescomplemented
30C2×C3×Dic3⋊C4—24no—
31C2×C3×Dic3⋊C4C2214yescomplemented
32C2×C3×C4×Dic3—24no—
33C2×C3×C4×Dic3C2214yescomplemented
34C23×C3×D4—31no—
35C23×#67C2×C311yescharacteristic
36C22×C3×C4⋊C4—31no—
37C22×C3×C22⋊C4—21no—
38C22×C3×C22⋊C4—31no—
39C22×C3×C22⋊C4—31no—
40C22×C3×C22⋊C4—31no—
41C22×C3×C22⋊C4D311yescharacteristic, complemented
42C22×C3×C22⋊C4C2×C311yescharacteristic, complemented
43C22×C3×C42—31no—
44C22×#217C2×C311yescharacteristic, complemented
45C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
46C22×(C2×D3)⋊C4C2×C311yescharacteristic, complemented
47C22×Dic3⋊C4C2×C311yescharacteristic, complemented
48C22×C4×Dic3C2×C311yescharacteristic, complemented
49C3×#390—38no—
50#4957C2×C318yesdirect product factor
51C24×C32—22no—
52C24×C32—22no—
53C24×C32—22no—
54C24×C32—22no—
55C24×C32—22no—
56C24×C32—22no—
57C24×C32C2×C414yes—
58C24×C32C2312yes—
59C24×C32C2311yescharacteristic
60C23×C3×D3—22no—
61C23×C3×D3—22no—
62C23×C3×D3—22no—
63C23×C3×D3—22no—
64C23×C3×D3—22no—
65C23×C3×D3—22no—
66C23×C3×D3C2×C414yes—
67C23×C3×D3C2312yes—
68C22×C32×C4—22no—
69C22×C32×C4—22no—
70C22×C32×C4—22no—
71C22×C32×C4—22no—
72C22×C32×C4—22no—
73C22×C32×C4D414yescomplemented
74C22×C32×C4C2312yes—
75C22×C32×C4C2312yes—
76C2×C3×#67—232no—
77C2×C3×#67—28no—
78C2×C3×#67—28no—
79C2×C3×#67C2×C4116yescomplemented
80C22×C3×Dic3—22no—
81C22×C3×Dic3—22no—
82C22×C3×Dic3—22no—
83C22×C3×Dic3—22no—
84C22×C3×Dic3—22no—
85C22×C3×Dic3C2×C414yes—
86C22×C3×Dic3D414yes—
87C22×C3×Dic3D414yes—
88C22×C3×Dic3D414yescomplemented
89C22×C3×Dic3C2312yes—
90C22×C3×Dic3C2312yes—
91C22×C3×Dic3C2312yes—
92C32×C22⋊C4—28no—
93C3×#217—28no—
94C3×(C2×D3)⋊C4—28no—
95C3×(C2×D3)⋊C4—28no—
96C3×Dic3⋊C4—28no—
97C3×C4×Dic3—28no—
98C2×#390—31noSylow
99C25×C3—21no—
100C25×C3—31no—
101C25×C3C2×D311yescharacteristic
102C25×C3C22×C311yescharacteristic
103C24×D3C22×C311yescharacteristic
104C22×C3×D4—38no—
105C22×C3×D4—34no—
106C22×C3×D4—64no—
107C22×C3×D4—64no—
108C23×C3×C4—21no—
109C23×C3×C4—21no—
110C23×C3×C4—31no—
111C23×C3×C4—31no—
112C23×C3×C4—31no—
113C23×C3×C4C2×D311yescharacteristic
114C23×C3×C4C2×D311yescharacteristic
115C23×C3×C4C22×C311yescharacteristic
116C23×C3×C4C22×C311yescharacteristic
117C22×#67—24no—
118C22×#67—24no—
119C22×#67C3×C418yescomplemented
120C22×#67C22×C314yes—
121C23×Dic3C22×C311yescharacteristic
122C23×Dic3C22×C311yescharacteristic
123C23×Dic3C22×C311yescharacteristic
124C2×C3×C4⋊C4—34no—
125C2×C3×C4⋊C4—64no—
126C2×C3×C22⋊C4—28no—
127C2×C3×C22⋊C4—24no—
128C2×C3×C22⋊C4—24no—
129C2×C3×C22⋊C4—24no—
130C2×C3×C22⋊C4—34no—
131C2×C3×C22⋊C4—34no—
132C2×C3×C22⋊C4—34no—
133C2×C3×C22⋊C4—64no—
134C2×C3×C22⋊C4—64no—
135C2×C3×C22⋊C4—64no—
136C2×C3×C22⋊C4C2×D314yescomplemented
137C2×C3×C22⋊C4C22×C314yescomplemented
138C2×C3×C42—34no—
139C2×C3×C42—64no—
140C2×#217—24no—
141C2×#217C22×C314yescomplemented
142C2×(C2×D3)⋊C4—24no—
143C2×(C2×D3)⋊C4—24no—
144C2×(C2×D3)⋊C4C22×C314yescomplemented
145C2×(C2×D3)⋊C4C22×C314yescomplemented
146C2×Dic3⋊C4—24no—
147C2×Dic3⋊C4C22×C314yescomplemented
148C2×C4×Dic3—24no—
149C2×C4×Dic3C22×C314yescomplemented
150C23×C32—28no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32—28no—
154C23×C32—28no—
155C23×C32—22no—
156C23×C32—22no—
157C23×C32—22no—
158C23×C32—22no—
159C23×C32—44no—
160C23×C32—44no—
161C23×C32—44no—
162C23×C32—44no—
163C23×C32C22×C414yes—
164C23×C32C22×C412yes—
165C23×C32C2×D412yes—
166C23×C32C2×D412yes—
167C23×C32C2×D412yes—
168C23×C32C2×D412yes—
169C23×C32#4112yes—
170C23×C32#4112yes—
171C23×C32C2411yescharacteristic
172C22×C3×D3—28no—
173C22×C3×D3—28no—
174C22×C3×D3—28no—
175C22×C3×D3—22no—
176C22×C3×D3—22no—
177C22×C3×D3—22no—
178C22×C3×D3—22no—
179C22×C3×D3—22no—
180C22×C3×D3—22no—
181C22×C3×D3—44no—
182C22×C3×D3—44no—
183C22×C3×D3—44no—
184C22×C3×D3—44no—
185C22×C3×D3C22×C414yes—
186C2×C32×C4—22no—
187C2×C32×C4—28no—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4—22no—
191C2×C32×C4—22no—
192C2×C32×C4—44no—
193C2×C32×C4C2×D414yescomplemented
194C3×#67—232no—
195C2×C3×Dic3—28no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—44no—
202C2×C3×Dic3C22⋊C4116yescomplemented
203C2×C3×Dic3C22×C414yes—
204C2×C3×Dic3C2×D414yes—
205C2×C3×Dic3C2×D414yes—
206C2×C3×Dic3C2×D414yescomplemented
207C23×D4—31no—
208C22×C4⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4—31no—
212C22×C22⋊C4C3×D311yescharacteristic, complemented
213C22×C42—31no—
214#390—38no—
215C24×C3—24no—
216C24×C3—24no—
217C24×C3—22no—
218C24×C3—22no—
219C24×C3—22no—
220C24×C3—22no—
221C24×C3—22no—
222C24×C3—22no—
223C24×C3—22no—
224C24×C3—22no—
225C24×C3—22no—
226C24×C3—22no—
227C24×C3—22no—
228C24×C3—22no—
229C24×C3—24no—
230C24×C3—21no—
231C24×C3—22no—
232C24×C3—34no—
233C24×C3—32no—
234C24×C3—42no—
235C24×C3—42no—
236C24×C3—42no—
237C24×C3—42no—
238C24×C3—62no—
239C24×C3—62no—
240C24×C3—62no—
241C24×C3—62no—
242C24×C3—62no—
243C24×C3—62no—
244C24×C3C4×D314yes—
245C24×C3C2×C3×C414yes—
246C24×C3C22×D312yes—
247C24×C3C22×D311yescharacteristic
248C24×C3C23×C312yes—
249C24×C3C23×C311yescharacteristic
250C23×D3—22no—
251C23×D3—22no—
252C23×D3—22no—
253C23×D3—22no—
254C23×D3—22no—
255C23×D3—22no—
256C23×D3C2×C3×C414yes—
257C23×D3C23×C312yes—
258C2×C3×D4—316no—
259C2×C3×D4—632no—
260C2×C3×D4—68no—
261C2×C3×D4—68no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—24no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—22no—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4—24no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—34no—
277C22×C3×C4—34no—
278C22×C3×C4—34no—
279C22×C3×C4—32no—
280C22×C3×C4—34no—
281C22×C3×C4—32no—
282C22×C3×C4—32no—
283C22×C3×C4—42no—
284C22×C3×C4—42no—
285C22×C3×C4—42no—
286C22×C3×C4—42no—
287C22×C3×C4—62no—
288C22×C3×C4—62no—
289C22×C3×C4—62no—
290C22×C3×C4—62no—
291C22×C3×C4—62no—
292C22×C3×C4#6714yescomplemented
293C22×C3×C4C3×D414yescomplemented
294C22×C3×C4C22×D312yes—
295C22×C3×C4C22×D312yes—
296C22×C3×C4C23×C312yes—
297C22×C3×C4C23×C312yes—
298C2×#67—232no—
299C2×#67—28no—
300C2×#67—28no—
301C2×#67C2×C3×C4116yescomplemented
302C22×Dic3—22no—
303C22×Dic3—22no—
304C22×Dic3—22no—
305C22×Dic3—22no—
306C22×Dic3—22no—
307C22×Dic3C2×C3×C414yes—
308C22×Dic3C3×D414yes—
309C22×Dic3C3×D414yes—
310C22×Dic3C3×D414yescomplemented
311C22×Dic3C23×C312yes—
312C22×Dic3C23×C312yes—
313C22×Dic3C23×C312yes—
314C3×C4⋊C4—68no—
315C3×C22⋊C4—216no—
316C3×C22⋊C4—28no—
317C3×C22⋊C4—28no—
318C3×C22⋊C4—68no—
319C3×C22⋊C4—68no—
320C3×C22⋊C4—68no—
321C3×C42—68no—
322#217—28no—
323(C2×D3)⋊C4—28no—
324(C2×D3)⋊C4—28no—
325Dic3⋊C4—28no—
326C4×Dic3—28no—
327C22×C32—24no—
328C22×C32—24no—
329C22×C32—24no—
330C22×C32—42no—
331C22×C32—42no—
332C22×C32—42no—
333C22×C32—42no—
334C22×C32—416no—
335C22×C32C2×C22⋊C414yes—
336C22×C32C4×D414yes—
337C22×C32C4×D414yes—
338C22×C32#12114yes—
339C22×C32#12114yes—
340C22×C32#12414yes—
341C22×C32#12714yes—
342C22×C32C23×C411yescharacteristic
343C22×C32C22×D411yescharacteristic
344C22×C32C22×D411yescharacteristic
345C22×C32C22×D411yescharacteristic
346C22×C32C22×D411yescharacteristic
347C22×C32C2×#4111yescharacteristic
348C22×C32C2×#4111yescharacteristic
349C2×C3×D3—24no—
350C2×C3×D3—24no—
351C2×C3×D3—24no—
352C2×C3×D3—42no—
353C2×C3×D3—42no—
354C2×C3×D3—42no—
355C2×C3×D3—42no—
356C2×C3×D3—416no—
357C32×C4—24no—
358C32×C4—42no—
359C3×Dic3—24no—
360C3×Dic3—42no—
361C3×Dic3C2×C22⋊C418yescomplemented
362C25—31no—
363C25C2×C3×D311yescharacteristic
364C22×D4—38no—
365C22×D4—34no—
366C22×D4—64no—
367C22×D4—64no—
368C23×C4—31no—
369C23×C4—31no—
370C23×C4—31no—
371C23×C4C2×C3×D311yescharacteristic
372C23×C4C2×C3×D311yescharacteristic
373C2×C4⋊C4—34no—
374C2×C4⋊C4—64no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—34no—
377C2×C22⋊C4—34no—
378C2×C22⋊C4—34no—
379C2×C22⋊C4—64no—
380C2×C22⋊C4—64no—
381C2×C22⋊C4—64no—
382C2×C22⋊C4C2×C3×D314yescomplemented
383C2×C42—34no—
384C2×C42—64no—
385C23×C3—24no—
386C23×C3—216no—
387C23×C3—24no—
388C23×C3—28no—
389C23×C3—28no—
390C23×C3—28no—
391C23×C3—28no—
392C23×C3—28no—
393C23×C3—28no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—22no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—21no—
407C23×C3—22no—
408C23×C3—24no—
409C23×C3—22no—
410C23×C3—22no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—34no—
416C23×C3—48no—
417C23×C3—48no—
418C23×C3—42no—
419C23×C3—42no—
420C23×C3—42no—
421C23×C3—42no—
422C23×C3—48no—
423C23×C3—48no—
424C23×C3—48no—
425C23×C3—48no—
426C23×C3—44no—
427C23×C3—44no—
428C23×C3—44no—
429C23×C3—44no—
430C23×C3—44no—
431C23×C3—44no—
432C23×C3—44no—
433C23×C3—44no—
434C23×C3—68no—
435C23×C3—68no—
436C23×C3—68no—
437C23×C3—62no—
438C23×C3—62no—
439C23×C3—62no—
440C23×C3—62no—
441C23×C3—62no—
442C23×C3—62no—
443C23×C3—124no—
444C23×C3—124no—
445C23×C3—124no—
446C23×C3—124no—
447C23×C3C2×C4×D314yes—
448C23×C3C2×C4×D312yes—
449C23×C3#23512yes—
450C23×C3D3×D412yes—
451C23×C3D3×D412yes—
452C23×C3D3×D412yes—
453C23×C3#23712yes—
454C23×C3C2×#6712yes—
455C23×C3C22×C3×C414yes—
456C23×C3C22×C3×C412yes—
457C23×C3C2×C3×D412yes—
458C23×C3C2×C3×D412yes—
459C23×C3C2×C3×D412yes—
460C23×C3C2×C3×D412yes—
461C23×C3C3×#4112yes—
462C23×C3C3×#4112yes—
463C23×C3C23×D311yescharacteristic
464C23×C3C24×C311yescharacteristic
465C22×D3—28no—
466C22×D3—28no—
467C22×D3—28no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—22no—
473C22×D3—22no—
474C22×D3—44no—
475C22×D3—44no—
476C22×D3—44no—
477C22×D3—44no—
478C22×D3C22×C3×C414yes—
479C3×D4—632no—
480C2×C3×C4—28no—
481C2×C3×C4—28no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—24no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—22no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—24no—
494C2×C3×C4—316no—
495C2×C3×C4—34no—
496C2×C3×C4—34no—
497C2×C3×C4—34no—
498C2×C3×C4—34no—
499C2×C3×C4—48no—
500C2×C3×C4—42no—
501C2×C3×C4—42no—
502C2×C3×C4—42no—
503C2×C3×C4—42no—
504C2×C3×C4—48no—
505C2×C3×C4—44no—
506C2×C3×C4—44no—
507C2×C3×C4—68no—
508C2×C3×C4—62no—
509C2×C3×C4—62no—
510C2×C3×C4—62no—
511C2×C3×C4—62no—
512C2×C3×C4—62no—
513C2×C3×C4—124no—
514C2×C3×C4C2×#6714yescomplemented
515C2×C3×C4C2×C3×D414yescomplemented
516#67—232no—
517C2×Dic3—28no—
518C2×Dic3—22no—
519C2×Dic3—22no—
520C2×Dic3—22no—
521C2×Dic3—22no—
522C2×Dic3—22no—
523C2×Dic3—44no—
524C2×Dic3C3×C22⋊C4116yescomplemented
525C2×Dic3C22×C3×C414yes—
526C2×Dic3C2×C3×D414yes—
527C2×Dic3C2×C3×D414yes—
528C2×Dic3C2×C3×D414yescomplemented
529C2×C32—44no—
530C2×C32#39018yescomplemented
531C2×C32C22×C22⋊C411yescharacteristic
532C2×C32C2×C4×D411yescharacteristic
533C2×C32C2×C4×D411yescharacteristic
534C2×C32C2×#12111yescharacteristic
535C2×C32C2×#12111yescharacteristic
536C2×C32C2×#12411yescharacteristic
537C2×C32C2×#12711yescharacteristic
538C3×D3—44no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—32no—
546C24—34no—
547C24—62no—
548C24—62no—
549C24—62no—
550C24—62no—
551C24—62no—
552C24—62no—
553C24C3×C4×D314yes—
554C24C22×C3×D312yes—
555C24C22×C3×D311yescharacteristic
556C2×D4—316no—
557C2×D4—632no—
558C2×D4—68no—
559C2×D4—68no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—32no—
566C22×C4—34no—
567C22×C4—34no—
568C22×C4—34no—
569C22×C4—32no—
570C22×C4—34no—
571C22×C4—32no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—62no—
577C22×C4C3×#6714yescomplemented
578C22×C4C22×C3×D312yes—
579C22×C4C22×C3×D312yes—
580C4⋊C4—68no—
581C22⋊C4—28no—
582C22⋊C4—68no—
583C22⋊C4—68no—
584C22⋊C4—68no—
585C42—68no—
586C22×C3—28no—
587C22×C3—24no—
588C22×C3—24no—
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—24no—
593C22×C3—24no—
594C22×C3—24no—
595C22×C3—24no—
596C22×C3—24no—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—24no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—44no—
608C22×C3—44no—
609C22×C3—44no—
610C22×C3—44no—
611C22×C3—432no—
612C22×C3—44no—
613C22×C3—44no—
614C22×C3—416no—
615C22×C3—42no—
616C22×C3—42no—
617C22×C3—416no—
618C22×C3—42no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—42no—
623C22×C3—42no—
624C22×C3—64no—
625C22×C3—64no—
626C22×C3—64no—
627C22×C3—1216no—
628C22×C3—122no—
629C22×C3—122no—
630C22×C3—122no—
631C22×C3—122no—
632C22×C3D3×C22⋊C414yes—
633C22×C3#67⋊C414yes—
634C22×C3#88414yes—
635C22×C3#88514yes—
636C22×C3C4×#6714yes—
637C22×C3#93914yes—
638C22×C3#94014yes—
639C22×C3C2×C3×C22⋊C414yes—
640C22×C3C3×C4×D414yes—
641C22×C3C3×C4×D414yes—
642C22×C3C3×#12114yes—
643C22×C3C3×#12114yes—
644C22×C3C3×#12414yes—
645C22×C3C3×#12714yes—
646C22×C3C22×C4×D311yescharacteristic
647C22×C3C2×#23511yescharacteristic
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×#23711yescharacteristic
652C22×C3C22×#6711yescharacteristic
653C22×C3C23×C3×C411yescharacteristic
654C22×C3C22×C3×D411yescharacteristic
655C22×C3C22×C3×D411yescharacteristic
656C22×C3C22×C3×D411yescharacteristic
657C22×C3C22×C3×D411yescharacteristic
658C22×C3C2×C3×#4111yescharacteristic
659C22×C3C2×C3×#4111yescharacteristic
660C2×D3—24no—
661C2×D3—24no—
662C2×D3—24no—
663C2×D3—416no—
664C2×D3—42no—
665C2×D3—42no—
666C2×D3—42no—
667C2×D3—42no—
668C3×C4—24no—
669C3×C4—24no—
670C3×C4—38no—
671C3×C4—44no—
672C3×C4—44no—
673C3×C4—42no—
674C3×C4—42no—
675C3×C4—64no—
676C3×C4—122no—
677Dic3—24no—
678Dic3—42no—
679Dic3C2×C3×C22⋊C418yescomplemented
680C32C2×#39011yescharacteristic, complemented, Sylow
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—34no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—68no—
696C23—68no—
697C23—68no—
698C23—62no—
699C23—62no—
700C23—62no—
701C23—62no—
702C23—62no—
703C23—62no—
704C23—124no—
705C23—124no—
706C23—124no—
707C23—124no—
708C23C2×C3×C4×D314yes—
709C23C2×C3×C4×D312yes—
710C23C3×#23512yes—
711C23C3×D3×D412yes—
712C23C3×D3×D412yes—
713C23C3×D3×D412yes—
714C23C3×#23712yes—
715C23C2×C3×#6712yes—
716C23C23×C3×D311yescharacteristic
717D4—632no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—316no—
725C2×C4—34no—
726C2×C4—34no—
727C2×C4—34no—
728C2×C4—34no—
729C2×C4—44no—
730C2×C4—68no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—124no—
737C2×C4C2×C3×#6714yescomplemented
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—28no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—48no—
747C2×C3—44no—
748C2×C3—44no—
749C2×C3—124no—
750C2×C3#495718yesdirect product factor
751C2×C3C3×#39018yescomplemented
752C2×C3C2×D3×C22⋊C411yescharacteristic
753C2×C3C2×#67⋊C411yescharacteristic
754C2×C3C2×#88411yescharacteristic
755C2×C3C2×#88511yescharacteristic
756C2×C3C2×C4×#6711yescharacteristic
757C2×C3C2×#93911yescharacteristic
758C2×C3C2×#94011yescharacteristic
759C2×C3C22×C3×C22⋊C411yescharacteristic
760C2×C3C2×C3×C4×D411yescharacteristic
761C2×C3C2×C3×C4×D411yescharacteristic
762C2×C3C2×C3×#12111yescharacteristic
763C2×C3C2×C3×#12111yescharacteristic
764C2×C3C2×C3×#12411yescharacteristic
765C2×C3C2×C3×#12711yescharacteristic
766D3—44no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—42no—
771C22—42no—
772C22—416no—
773C22—42no—
774C22—42no—
775C22—64no—
776C22—64no—
777C22—64no—
778C22—122no—
779C22—122no—
780C22—1216no—
781C22—122no—
782C22—122no—
783C22C3×D3×C22⋊C414yes—
784C22C3×#67⋊C414yes—
785C22C3×#88414yes—
786C22C3×#88514yes—
787C22C3×C4×#6714yes—
788C22C3×#93914yes—
789C22C3×#94014yes—
790C22C22×C3×C4×D311yescharacteristic
791C22C2×C3×#23511yescharacteristic
792C22C2×C3×D3×D411yescharacteristic
793C22C2×C3×D3×D411yescharacteristic
794C22C2×C3×D3×D411yescharacteristic
795C22C2×C3×#23711yescharacteristic
796C22C22×C3×#6711yescharacteristic
797C4—24no—
798C4—38no—
799C4—42no—
800C4—64no—
801C4—122no—
802C3—21no—
803C3C2×#495711yescharacteristic, direct product factor
804C3C2×C3×#39011yescharacteristic, complemented
805C2—44no—
806C2—124no—
807C2C3×#495718yesdirect product factor
808C2C2×C3×D3×C22⋊C411yescharacteristic
809C2C2×C3×#67⋊C411yescharacteristic
810C2C2×C3×#88411yescharacteristic
811C2C2×C3×#88511yescharacteristic
812C2C2×C3×C4×#6711yescharacteristic
813C2C2×C3×#93911yescharacteristic
814C2C2×C3×#94011yescharacteristic
subgroupG/H
centerC24×C3C22×D3
commutatorC22×C3C23×C3×C4
FrattiniC23C23×C3×D3
FittingC22×C32×C22⋊C4C2
socleC24×C32C23
prime radicalC23×C3×#67C2
cosocleC23×C3C24×C3
hypercenterC22×C3×C22⋊C4D3
hypocenterC3C2×C3×#390
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C32×C22⋊C4C2semidirect
3. C22×C3×#217C2semidirect
4. C22×C3×(C2×D3)⋊C4C2semidirect
5. C22×C3×(C2×D3)⋊C4C2semidirect
6. C22×C3×Dic3⋊C4C2semidirect
7. C22×C3×C4×Dic3C2semidirect
8. C3×#4957C2direct (N × H)
10. C2×#4957C3direct (N × H)
17. C22×C3×#67C4semidirect
23. C2×C32×C22⋊C4C22semidirect
25. C2×C3×#217C22semidirect
28. C2×C3×(C2×D3)⋊C4C22semidirect
29. C2×C3×(C2×D3)⋊C4C22semidirect
31. C2×C3×Dic3⋊C4C22semidirect
33. C2×C3×C4×Dic3C22semidirect
41. C22×C3×C22⋊C4D3semidirect
42. C22×C3×C22⋊C4C2×C3semidirect
44. C22×#217C2×C3semidirect
45. C22×(C2×D3)⋊C4C2×C3semidirect
46. C22×(C2×D3)⋊C4C2×C3semidirect
47. C22×Dic3⋊C4C2×C3semidirect
48. C22×C4×Dic3C2×C3semidirect
50. #4957C2×C3direct (N × H)
73. C22×C32×C4D4semidirect
79. C2×C3×#67C2×C4semidirect
88. C22×C3×Dic3D4semidirect
119. C22×#67C3×C4semidirect
136. C2×C3×C22⋊C4C2×D3semidirect
137. C2×C3×C22⋊C4C22×C3semidirect
141. C2×#217C22×C3semidirect
144. C2×(C2×D3)⋊C4C22×C3semidirect
145. C2×(C2×D3)⋊C4C22×C3semidirect
147. C2×Dic3⋊C4C22×C3semidirect
149. C2×C4×Dic3C22×C3semidirect
193. C2×C32×C4C2×D4semidirect
202. C2×C3×Dic3C22⋊C4semidirect
206. C2×C3×Dic3C2×D4semidirect
212. C22×C22⋊C4C3×D3semidirect
292. C22×C3×C4#67semidirect
293. C22×C3×C4C3×D4semidirect
301. C2×#67C2×C3×C4semidirect
310. C22×Dic3C3×D4semidirect
361. C3×Dic3C2×C22⋊C4semidirect
382. C2×C22⋊C4C2×C3×D3semidirect
514. C2×C3×C4C2×#67semidirect
515. C2×C3×C4C2×C3×D4semidirect
524. C2×Dic3C3×C22⋊C4semidirect
528. C2×Dic3C2×C3×D4semidirect
530. C2×C32#390semidirect
577. C22×C4C3×#67semidirect
679. Dic3C2×C3×C22⋊C4semidirect
680. C32C2×#390semidirect
737. C2×C4C2×C3×#67semidirect
750. C2×C3#4957direct (N × H)
751. C2×C3C3×#390semidirect
803. C3C2×#4957direct (N × H)
804. C3C2×C3×#390semidirect
807. C2C3×#4957direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×#672
C22×C32×C22⋊C42
C22×C3×#2172
C22×C3×(C2×D3)⋊C42
C22×C3×Dic3⋊C42
C22×C3×C4×Dic32
C3×#49572
C2×C3×#3903
C2×#49573