Finite Group Databasebeta

← C2×C3×#5824 #11902491

Subgroups — C2×C3×#5824 #11902491

Order 1152.

3709 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#41C211yesmaximal, characteristic, complemented
2C22×C3×#237C211yesmaximal, characteristic, complemented
3C3×#5824C2116yesmaximal, direct product factor
4C2×C3×#946C211yesmaximal, characteristic, complemented
5C2×C3×#944C211yesmaximal, characteristic, complemented
6C2×C3×#939C212yesmaximal, complemented
7C2×C3×#935C212yesmaximal, complemented
8C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
9C2×C3×#929C212yesmaximal, complemented
10C2×C3×C4×#67C211yesmaximal, characteristic, complemented
11C2×C3×#924C211yesmaximal, characteristic, complemented
12C22×C3×Dic3⋊C4C212yesmaximal, complemented
13C2×C3×#547—31nomaximal
14C2×#5824C311yesmaximal, characteristic, direct product factor
15C2×C32×#41—28no—
16C2×C32×#41C2218yescomplemented
17C22×C32×Q8C2211yescharacteristic
18C22×C32×D4C2212yes—
19C22×C32×D4C2211yescharacteristic
20C23×C32×C4C2212yes—
21C23×C32×C4C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C22×C3×#67C2212yes—
24C23×C3×Dic3C2212yes—
25C23×C3×Dic3C2212yes—
26C2×C3×#237—28no—
27C2×C3×#237C2218yescomplemented
28C22×C3×C4×D3C2211yescharacteristic
29C22×C3×Dic6C2211yescharacteristic
30C2×C3×#217C2212yes—
31C2×C3×#217C2211yescharacteristic
32C2×C3×#217C2212yes—
33C3×#946C2218yescomplemented
34C3×#944C2218yescomplemented
35C3×#939C22116yescomplemented
36C3×#935C22116yescomplemented
37C3×D4×Dic3C2218yescomplemented
38C3×#929C22116yescomplemented
39C3×C4×#67C2218yescomplemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2212yes—
42C2×C3×C4⋊Dic3C2211yescharacteristic
43C3×#924C2218yescomplemented
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×Dic3⋊C4C2212yes—
46C2×C3×Dic3⋊C4C2212yes—
47C2×C3×Dic3⋊C4C2212yes—
48C2×C3×Dic3⋊C4C2212yes—
49C2×C3×Dic3⋊C4C22116yescomplemented
50C2×C3×C4×Dic3C2211yescharacteristic
51C22×C3×#41—21no—
52C22×C3×#41—31no—
53C22×C3×#41D311yescharacteristic, complemented
54C22×C3×#41C2×C311yescharacteristic, complemented
55C22×#237C2×C311yescharacteristic, complemented
56C3×#547—316no—
57C2×C3×C4⋊Q8—31no—
58C2×C3×#123—32no—
59C2×C3×#123—32no—
60C2×C3×C22⋊Q8—31no—
61C2×C3×C22⋊Q8—31no—
62C2×C3×#121—32no—
63C2×C3×C4×D4—31no—
64C2×C3×C4×D4—31no—
65C22×C3×C4⋊C4—32no—
66#5824C2×C3116yesdirect product factor
67C2×#946C2×C311yescharacteristic, complemented
68C2×#944C2×C311yescharacteristic, complemented
69C2×#939C2×C312yescomplemented
70C2×#935C2×C312yescomplemented
71C2×D4×Dic3C2×C311yescharacteristic, complemented
72C2×#929C2×C312yescomplemented
73C2×C4×#67C2×C311yescharacteristic, complemented
74C2×#924C2×C311yescharacteristic, complemented
75C22×Dic3⋊C4C2×C312yescomplemented
76C24×C32C2311yescharacteristic
77C24×C32C2312yes—
78C23×C3×D3C2311yescharacteristic
79C32×#41—232no—
80C2×C32×Q8—24no—
81C2×C32×Q8C2314yes—
82C2×C32×D4—28no—
83C2×C32×D4D418yescomplemented
84C2×C32×D4C2318yes—
85C2×C32×D4C2314yes—
86C22×C32×C4—28no—
87C22×C32×C4—24no—
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2312yes—
90C22×C32×C4C2318yes—
91C22×C32×C4C2314yes—
92C22×C32×C4C2311yescharacteristic
93C2×C3×#67—28no—
94C2×C3×#67—24no—
95C2×C3×#67C2314yes—
96C2×C3×#67C2318yes—
97C22×C3×Dic3—28no—
98C22×C3×Dic3—28no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2312yes—
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2312yes—
103C22×C3×Dic3C2318yes—
104C22×C3×Dic3C2318yes—
105C22×C3×Dic3C2311yescharacteristic
106C3×#237—232no—
107C2×C3×C4×D3—24no—
108C2×C3×C4×D3C2314yes—
109C2×C3×Dic6—24no—
110C2×C3×Dic6C2314yes—
111C3×#217C2318yes—
112C3×#217C2314yes—
113C3×#217C2318yes—
114C3×(C2×D3)⋊C4C2314yes—
115C3×(C2×D3)⋊C4C2318yes—
116C3×C4⋊Dic3C2314yes—
117C3×Dic3⋊C4C2314yes—
118C3×Dic3⋊C4C2318yes—
119C3×Dic3⋊C4C2318yes—
120C3×Dic3⋊C4C2318yes—
121C3×Dic3⋊C4C2318yes—
122C3×C4×Dic3C2314yes—
123C2×#547—31noSylow
124C2×C3×#41—216no—
125C2×C3×#41—28no—
126C2×C3×#41—28no—
127C2×C3×#41—28no—
128C2×C3×#41—38no—
129C2×C3×#41—68no—
130C2×C3×#41C2×D318yescomplemented
131C2×C3×#41C22×C318yescomplemented
132C22×C3×Q8—21no—
133C22×C3×Q8—31no—
134C22×C3×Q8C2×D311yescharacteristic
135C22×C3×Q8C22×C311yescharacteristic
136C22×C3×D4—22no—
137C22×C3×D4—21no—
138C22×C3×D4—32no—
139C22×C3×D4—31no—
140C22×C3×D4C2×D312yes—
141C22×C3×D4C2×D311yescharacteristic
142C22×C3×D4C22×C312yes—
143C22×C3×D4C22×C311yescharacteristic
144C23×C3×C4—22no—
145C23×C3×C4—21no—
146C23×C3×C4—32no—
147C23×C3×C4—32no—
148C23×C3×C4—31no—
149C23×C3×C4C2×D312yes—
150C23×C3×C4C2×D311yescharacteristic
151C23×C3×C4C22×C312yes—
152C23×C3×C4C22×C311yescharacteristic
153C22×#67C22×C312yes—
154C22×#67C22×C311yescharacteristic
155C23×Dic3C22×C312yes—
156C23×Dic3C22×C312yes—
157C2×#237—28no—
158C2×#237C22×C318yescomplemented
159C22×C4×D3C22×C311yescharacteristic
160C22×Dic6C22×C311yescharacteristic
161C3×C4⋊Q8—38no—
162C3×#123—316no—
163C3×#123—316no—
164C3×C22⋊Q8—38no—
165C3×C22⋊Q8—38no—
166C3×#121—316no—
167C3×C4×D4—38no—
168C3×C4×D4—38no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—32no—
171C2×C3×C4⋊C4—32no—
172C2×C3×C4⋊C4—32no—
173C2×C3×C4⋊C4—32no—
174C2×C3×C4⋊C4—316no—
175C2×C3×C4⋊C4—31no—
176C2×C3×C22⋊C4—32no—
177C2×C3×C22⋊C4—31no—
178C2×C3×C22⋊C4—32no—
179C2×C3×C22⋊C4—31no—
180C2×C3×C22⋊C4—32no—
181C2×C3×C42—31no—
182C2×#217C22×C312yes—
183C2×#217C22×C311yescharacteristic
184C2×#217C22×C312yes—
185#946C22×C318yescomplemented
186#944C22×C318yescomplemented
187#939C22×C3116yescomplemented
188#935C22×C3116yescomplemented
189D4×Dic3C22×C318yescomplemented
190#929C22×C3116yescomplemented
191C4×#67C22×C318yescomplemented
192C2×(C2×D3)⋊C4C22×C311yescharacteristic
193C2×(C2×D3)⋊C4C22×C312yes—
194C2×C4⋊Dic3C22×C311yescharacteristic
195#924C22×C318yescomplemented
196C2×Dic3⋊C4C22×C311yescharacteristic
197C2×Dic3⋊C4C22×C312yes—
198C2×Dic3⋊C4C22×C312yes—
199C2×Dic3⋊C4C22×C312yes—
200C2×Dic3⋊C4C22×C312yes—
201C2×Dic3⋊C4C22×C3116yescomplemented
202C2×C4×Dic3C22×C311yescharacteristic
203C23×C32—22no—
204C23×C32—24no—
205C23×C32—24no—
206C23×C32—22no—
207C23×C32—22no—
208C23×C32C2×D418yes—
209C23×C32C2412yes—
210C23×C32C2414yes—
211C23×C32C2411yescharacteristic
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3—22no—
215C22×C3×D3C2412yes—
216C32×Q8—28no—
217C32×D4—216no—
218C32×D4C2×D4116yescomplemented
219C2×C32×C4—22no—
220C2×C32×C4—24no—
221C2×C32×C4—216no—
222C2×C32×C4—28no—
223C2×C32×C4C2×D414yes—
224C2×C32×C4C2412yes—
225C2×C32×C4C2414yes—
226C2×C32×C4C2412yes—
227C3×#67—216no—
228C3×#67—28no—
229C2×C3×Dic3—24no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—216no—
232C2×C3×Dic3—24no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—216no—
235C2×C3×Dic3#4114yescomplemented
236C2×C3×Dic3C2412yes—
237C2×C3×Dic3C2414yes—
238C2×C3×Dic3C2412yes—
239C2×C3×Dic3C2414yes—
240C2×C3×Dic3C2412yes—
241C3×C4×D3—28no—
242C3×Dic6—28no—
243C22×#41—31no—
244C22×#41C3×D311yescharacteristic, complemented
245#547—316no—
246C2×C4⋊Q8—31no—
247C2×#123—32no—
248C2×#123—32no—
249C2×C22⋊Q8—31no—
250C2×C22⋊Q8—31no—
251C2×#121—32no—
252C2×C4×D4—31no—
253C2×C4×D4—31no—
254C22×C4⋊C4—32no—
255C24×C3—21no—
256C24×C3—22no—
257C24×C3—31no—
258C24×C3C22×D311yescharacteristic
259C24×C3C22×D312yes—
260C24×C3C23×C311yescharacteristic
261C24×C3C23×C312yes—
262C23×D3C23×C311yescharacteristic
263C3×#41—264no—
264C3×#41—232no—
265C3×#41—232no—
266C3×#41—632no—
267C2×C3×Q8—28no—
268C2×C3×Q8—24no—
269C2×C3×Q8—24no—
270C2×C3×Q8—24no—
271C2×C3×Q8—34no—
272C2×C3×Q8—64no—
273C2×C3×Q8C22×D314yes—
274C2×C3×Q8C23×C314yes—
275C2×C3×D4—216no—
276C2×C3×D4—28no—
277C2×C3×D4—28no—
278C2×C3×D4—28no—
279C2×C3×D4—28no—
280C2×C3×D4—24no—
281C2×C3×D4—34no—
282C2×C3×D4—38no—
283C2×C3×D4—64no—
284C2×C3×D4—68no—
285C2×C3×D4#6718yescomplemented
286C2×C3×D4C3×D418yescomplemented
287C2×C3×D4C22×D318yes—
288C2×C3×D4C22×D314yes—
289C2×C3×D4C23×C318yes—
290C2×C3×D4C23×C314yes—
291C22×C3×C4—216no—
292C22×C3×C4—28no—
293C22×C3×C4—28no—
294C22×C3×C4—28no—
295C22×C3×C4—24no—
296C22×C3×C4—24no—
297C22×C3×C4—21no—
298C22×C3×C4—22no—
299C22×C3×C4—21no—
300C22×C3×C4—28no—
301C22×C3×C4—24no—
302C22×C3×C4—31no—
303C22×C3×C4—38no—
304C22×C3×C4—38no—
305C22×C3×C4—31no—
306C22×C3×C4—32no—
307C22×C3×C4—31no—
308C22×C3×C4—32no—
309C22×C3×C4—34no—
310C22×C3×C4—68no—
311C22×C3×C4—68no—
312C22×C3×C4—64no—
313C22×C3×C4C22×D318yes—
314C22×C3×C4C22×D314yes—
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D312yes—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C23×C311yescharacteristic
319C22×C3×C4C23×C312yes—
320C22×C3×C4C23×C318yes—
321C22×C3×C4C23×C314yes—
322C22×C3×C4C23×C311yescharacteristic
323C2×#67—28no—
324C2×#67—24no—
325C2×#67C23×C314yes—
326C2×#67C23×C318yes—
327C22×Dic3—28no—
328C22×Dic3—28no—
329C22×Dic3C23×C311yescharacteristic
330C22×Dic3C23×C312yes—
331C22×Dic3C23×C311yescharacteristic
332C22×Dic3C23×C312yes—
333C22×Dic3C23×C318yes—
334C22×Dic3C23×C318yes—
335C22×Dic3C23×C311yescharacteristic
336#237—232no—
337C2×C4×D3—24no—
338C2×C4×D3C23×C314yes—
339C2×Dic6—24no—
340C2×Dic6C23×C314yes—
341C3×C4⋊C4—34no—
342C3×C4⋊C4—38no—
343C3×C4⋊C4—38no—
344C3×C4⋊C4—38no—
345C3×C4⋊C4—38no—
346C3×C4⋊C4—34no—
347C3×C22⋊C4—38no—
348C3×C22⋊C4—34no—
349C3×C22⋊C4—38no—
350C3×C22⋊C4—34no—
351C3×C22⋊C4—38no—
352C3×C42—34no—
353#217C23×C318yes—
354#217C23×C314yes—
355#217C23×C318yes—
356(C2×D3)⋊C4C23×C314yes—
357(C2×D3)⋊C4C23×C318yes—
358C4⋊Dic3C23×C314yes—
359Dic3⋊C4C23×C314yes—
360Dic3⋊C4C23×C318yes—
361Dic3⋊C4C23×C318yes—
362Dic3⋊C4C23×C318yes—
363Dic3⋊C4C23×C318yes—
364C4×Dic3C23×C314yes—
365C22×C32—22no—
366C22×C32—216no—
367C22×C32—24no—
368C22×C32—24no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—44no—
372C22×C32C22×D418yes—
373C22×C32C22×D412yes—
374C22×C32C2×#4112yes—
375C22×C322−1+412yes—
376C22×C32C2511yescharacteristic
377C2×C3×D3—22no—
378C2×C3×D3—22no—
379C2×C3×D3—22no—
380C2×C3×D3—44no—
381C32×C4—22no—
382C32×C4—24no—
383C32×C4C22×D414yes—
384C3×Dic3—24no—
385C3×Dic3—22no—
386C3×Dic3—24no—
387C3×Dic3—22no—
388C3×Dic3C2×#4114yescomplemented
389C2×#41—28no—
390C2×#41—38no—
391C2×#41—68no—
392C2×#41C2×C3×D318yescomplemented
393C22×Q8—31no—
394C22×Q8C2×C3×D311yescharacteristic
395C22×D4—31no—
396C22×D4—32no—
397C22×D4C2×C3×D312yes—
398C22×D4C2×C3×D311yescharacteristic
399C23×C4—32no—
400C23×C4—32no—
401C23×C4—31no—
402C23×C4C2×C3×D312yes—
403C23×C4C2×C3×D311yescharacteristic
404C4⋊Q8—38no—
405#123—316no—
406#123—316no—
407C22⋊Q8—38no—
408C22⋊Q8—38no—
409#121—316no—
410C4×D4—38no—
411C4×D4—38no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—32no—
414C2×C4⋊C4—32no—
415C2×C4⋊C4—32no—
416C2×C4⋊C4—316no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—32no—
419C2×C22⋊C4—32no—
420C2×C22⋊C4—31no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—31no—
423C2×C22⋊C4—32no—
424C2×C42—31no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—24no—
428C23×C3—24no—
429C23×C3—24no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—21no—
437C23×C3—22no—
438C23×C3—24no—
439C23×C3—28no—
440C23×C3—32no—
441C23×C3—44no—
442C23×C3—44no—
443C23×C3—42no—
444C23×C3—42no—
445C23×C3—62no—
446C23×C3—62no—
447C23×C3—62no—
448C23×C3C2×#6718yes—
449C23×C3C2×C3×D418yes—
450C23×C3C23×D312yes—
451C23×C3C23×D314yes—
452C23×C3C23×D311yescharacteristic
453C23×C3C24×C312yes—
454C23×C3C24×C314yes—
455C23×C3C24×C311yescharacteristic
456C22×D3—22no—
457C22×D3—22no—
458C22×D3—22no—
459C22×D3C24×C312yes—
460C3×Q8—216no—
461C3×Q8—28no—
462C3×Q8—28no—
463C3×Q8—68no—
464C3×D4—232no—
465C3×D4—216no—
466C3×D4—216no—
467C3×D4—216no—
468C3×D4—68no—
469C3×D4—616no—
470C3×D4C2×#67116yescomplemented
471C3×D4C2×C3×D4116yescomplemented
472C2×C3×C4—24no—
473C2×C3×C4—28no—
474C2×C3×C4—232no—
475C2×C3×C4—216no—
476C2×C3×C4—22no—
477C2×C3×C4—24no—
478C2×C3×C4—216no—
479C2×C3×C4—22no—
480C2×C3×C4—24no—
481C2×C3×C4—216no—
482C2×C3×C4—28no—
483C2×C3×C4—28no—
484C2×C3×C4—22no—
485C2×C3×C4—24no—
486C2×C3×C4—22no—
487C2×C3×C4—24no—
488C2×C3×C4—34no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—34no—
492C2×C3×C4—32no—
493C2×C3×C4—34no—
494C2×C3×C4—616no—
495C2×C3×C4—64no—
496C2×C3×C4—62no—
497C2×C3×C4—62no—
498C2×C3×C4—64no—
499C2×C3×C4—616no—
500C2×C3×C4—68no—
501C2×C3×C4C2×#6714yes—
502C2×C3×C4C2×C3×D414yes—
503C2×C3×C4C23×D312yes—
504C2×C3×C4C23×D314yes—
505C2×C3×C4C23×D312yes—
506C2×C3×C4C24×C312yes—
507C2×C3×C4C24×C314yes—
508C2×C3×C4C24×C312yes—
509#67—216no—
510#67—28no—
511C2×Dic3—24no—
512C2×Dic3—22no—
513C2×Dic3—216no—
514C2×Dic3—24no—
515C2×Dic3—22no—
516C2×Dic3—216no—
517C2×Dic3C3×#4114yescomplemented
518C2×Dic3C24×C312yes—
519C2×Dic3C24×C314yes—
520C2×Dic3C24×C312yes—
521C2×Dic3C24×C314yes—
522C2×Dic3C24×C312yes—
523C4×D3—28no—
524Dic6—28no—
525C2×C32—28no—
526C2×C32—42no—
527C2×C32#54714yescomplemented
528C2×C32C23×D411yescharacteristic
529C2×C32C22×#4111yescharacteristic
530C2×C32C2×2−1+411yescharacteristic
531C3×D3—42no—
532C24—31no—
533C24C22×C3×D311yescharacteristic
534C24C22×C3×D312yes—
535#41—232no—
536#41—632no—
537C2×Q8—24no—
538C2×Q8—34no—
539C2×Q8—64no—
540C2×Q8C22×C3×D314yes—
541C2×D4—28no—
542C2×D4—34no—
543C2×D4—38no—
544C2×D4—64no—
545C2×D4—68no—
546C2×D4C3×#6718yescomplemented
547C2×D4C22×C3×D318yes—
548C2×D4C22×C3×D314yes—
549C22×C4—28no—
550C22×C4—24no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—32no—
554C22×C4—31no—
555C22×C4—32no—
556C22×C4—38no—
557C22×C4—38no—
558C22×C4—34no—
559C22×C4—68no—
560C22×C4—68no—
561C22×C4—64no—
562C22×C4C22×C3×D311yescharacteristic
563C22×C4C22×C3×D312yes—
564C22×C4C22×C3×D318yes—
565C22×C4C22×C3×D314yes—
566C22×C4C22×C3×D311yescharacteristic
567C4⋊C4—34no—
568C4⋊C4—38no—
569C4⋊C4—38no—
570C4⋊C4—38no—
571C4⋊C4—34no—
572C4⋊C4—38no—
573C22⋊C4—38no—
574C22⋊C4—34no—
575C22⋊C4—38no—
576C22⋊C4—34no—
577C22⋊C4—38no—
578C42—34no—
579C22×C3—24no—
580C22×C3—24no—
581C22×C3—24no—
582C22×C3—24no—
583C22×C3—216no—
584C22×C3—216no—
585C22×C3—24no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—28no—
596C22×C3—21no—
597C22×C3—416no—
598C22×C3—44no—
599C22×C3—44no—
600C22×C3—42no—
601C22×C3—42no—
602C22×C3—48no—
603C22×C3—44no—
604C22×C3—44no—
605C22×C3—62no—
606C22×C3—62no—
607C22×C3—62no—
608C22×C3—124no—
609C22×C3D3×#4112yes—
610C22×C3#101012yes—
611C22×C3C22×#6718yes—
612C22×C3C22×#6712yes—
613C22×C3C22×C3×D418yes—
614C22×C3C22×C3×D412yes—
615C22×C3C2×C3×#4112yes—
616C22×C3C3×2−1+412yes—
617C22×C3C24×D311yescharacteristic
618C22×C3C25×C311yescharacteristic
619C2×D3—22no—
620C2×D3—22no—
621C2×D3—22no—
622C2×D3—44no—
623C3×C4—24no—
624C3×C4—28no—
625C3×C4—22no—
626C3×C4—24no—
627C3×C4—22no—
628C3×C4—24no—
629C3×C4—24no—
630C3×C4—34no—
631C3×C4—64no—
632C3×C4—62no—
633C3×C4—62no—
634C3×C4—64no—
635C3×C4C22×#6714yes—
636C3×C4C22×C3×D414yes—
637Dic3—24no—
638Dic3—22no—
639Dic3—24no—
640Dic3—22no—
641Dic3C2×C3×#4114yescomplemented
642C32C2×#54711yescharacteristic, complemented, Sylow
643C23—24no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—32no—
649C23—62no—
650C23—62no—
651C23—62no—
652C23C2×C3×#6718yes—
653C23C23×C3×D312yes—
654C23C23×C3×D314yes—
655C23C23×C3×D311yescharacteristic
656Q8—28no—
657Q8—68no—
658D4—216no—
659D4—68no—
660D4—616no—
661D4C2×C3×#67116yescomplemented
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—216no—
665C2×C4—28no—
666C2×C4—34no—
667C2×C4—32no—
668C2×C4—32no—
669C2×C4—34no—
670C2×C4—32no—
671C2×C4—34no—
672C2×C4—616no—
673C2×C4—64no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—64no—
677C2×C4—616no—
678C2×C4—68no—
679C2×C4C2×C3×#6714yes—
680C2×C4C23×C3×D312yes—
681C2×C4C23×C3×D314yes—
682C2×C4C23×C3×D312yes—
683C2×C3—28no—
684C2×C3—28no—
685C2×C3—24no—
686C2×C3—21no—
687C2×C3—21no—
688C2×C3—21no—
689C2×C3—48no—
690C2×C3—44no—
691C2×C3—42no—
692C2×C3—42no—
693C2×C3—122no—
694C2×C3#582414yesdirect product factor
695C2×C3C3×#54714yescomplemented
696C2×C3C2×D3×#4111yescharacteristic
697C2×C3C2×#101011yescharacteristic
698C2×C3C23×#6711yescharacteristic
699C2×C3C23×C3×D411yescharacteristic
700C2×C3C22×C3×#4111yescharacteristic
701C2×C3C2×C3×2−1+411yescharacteristic
702D3—42no—
703C22—216no—
704C22—24no—
705C22—24no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—44no—
710C22—62no—
711C22—62no—
712C22—62no—
713C22—124no—
714C22C3×D3×#4112yes—
715C22C3×#101012yes—
716C22C22×C3×#6718yes—
717C22C22×C3×#6712yes—
718C22C24×C3×D311yescharacteristic
719C4—22no—
720C4—24no—
721C4—34no—
722C4—64no—
723C4—62no—
724C4—62no—
725C4—64no—
726C4C22×C3×#6714yes—
727C3—21no—
728C3C2×#582411yescharacteristic, direct product factor
729C3C2×C3×#54711yescharacteristic, complemented
730C2—28no—
731C2—42no—
732C2—122no—
733C2C3×#582414yesdirect product factor
734C2C2×C3×D3×#4111yescharacteristic
735C2C2×C3×#101011yescharacteristic
736C2C23×C3×#6711yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC22×C32×#41C2
socleC23×C32C24
hypercenterC22×C3×#41D3
hypocenterC3C2×C3×#547
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C22×C3×#41

Complements

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

NH ≅ G/Ntype
1. C22×C32×#41C2semidirect
2. C22×C3×#237C2semidirect
3. C3×#5824C2direct (N × H)
4. C2×C3×#946C2semidirect
5. C2×C3×#944C2semidirect
6. C2×C3×#939C2semidirect
7. C2×C3×#935C2semidirect
8. C2×C3×D4×Dic3C2semidirect
9. C2×C3×#929C2semidirect
10. C2×C3×C4×#67C2semidirect
11. C2×C3×#924C2semidirect
12. C22×C3×Dic3⋊C4C2semidirect
14. C2×#5824C3direct (N × H)
16. C2×C32×#41C22semidirect
27. C2×C3×#237C22semidirect
33. C3×#946C22semidirect
34. C3×#944C22semidirect
35. C3×#939C22semidirect
36. C3×#935C22semidirect
37. C3×D4×Dic3C22semidirect
38. C3×#929C22semidirect
39. C3×C4×#67C22semidirect
43. C3×#924C22semidirect
49. C2×C3×Dic3⋊C4C22semidirect
53. C22×C3×#41D3semidirect
54. C22×C3×#41C2×C3semidirect
55. C22×#237C2×C3semidirect
66. #5824C2×C3direct (N × H)
67. C2×#946C2×C3semidirect
68. C2×#944C2×C3semidirect
69. C2×#939C2×C3semidirect
70. C2×#935C2×C3semidirect
71. C2×D4×Dic3C2×C3semidirect
72. C2×#929C2×C3semidirect
73. C2×C4×#67C2×C3semidirect
74. C2×#924C2×C3semidirect
75. C22×Dic3⋊C4C2×C3semidirect
83. C2×C32×D4D4semidirect
130. C2×C3×#41C2×D3semidirect
131. C2×C3×#41C22×C3semidirect
158. C2×#237C22×C3semidirect
185. #946C22×C3semidirect
186. #944C22×C3semidirect
187. #939C22×C3semidirect
188. #935C22×C3semidirect
189. D4×Dic3C22×C3semidirect
190. #929C22×C3semidirect
191. C4×#67C22×C3semidirect
195. #924C22×C3semidirect
201. C2×Dic3⋊C4C22×C3semidirect
218. C32×D4C2×D4semidirect
235. C2×C3×Dic3#41semidirect
244. C22×#41C3×D3semidirect
285. C2×C3×D4#67semidirect
286. C2×C3×D4C3×D4semidirect
388. C3×Dic3C2×#41semidirect
392. C2×#41C2×C3×D3semidirect
470. C3×D4C2×#67semidirect
471. C3×D4C2×C3×D4semidirect
517. C2×Dic3C3×#41semidirect
527. C2×C32#547semidirect
546. C2×D4C3×#67semidirect
641. Dic3C2×C3×#41semidirect
642. C32C2×#547semidirect
661. D4C2×C3×#67semidirect
694. C2×C3#5824direct (N × H)
695. C2×C3C3×#547semidirect
728. C3C2×#5824direct (N × H)
729. C3C2×C3×#547semidirect
733. C2C3×#5824direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×#412
C22×C3×#2372
C3×#58242
C2×C3×#9462
C2×C3×#9442
C2×C3×#9392
C2×C3×#9352
C2×C3×D4×Dic32
C2×C3×#9292
C2×C3×C4×#672
C2×C3×#9242
C22×C3×Dic3⋊C42
C2×C3×#5473
C2×#58243