Finite Group Databasebeta

← C2×C3×#5552 #11902582

Subgroups — C2×C3×#5552 #11902582

Order 1152.

3453 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C23×C3×Dic6C211yesmaximal, characteristic, complemented
3C2×C32×C4×D4C211yesmaximal, characteristic, complemented
4C2×C3×#939C212yesmaximal, complemented
5C2×C3×#930C211yesmaximal, characteristic, complemented
6C2×C3×#924C211yesmaximal, characteristic, complemented
7C3×#5552C2116yesmaximal, direct product factor
8C2×C3×#896C212yesmaximal, complemented
9C2×C3×#885C212yesmaximal, complemented
10C2×C3×#67⋊C4C212yesmaximal, complemented
11C2×C3×#875C211yesmaximal, characteristic, complemented
12C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
13C2×C3×#548—31nomaximal
14C2×#5552C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C23×C32×C4C2211yescharacteristic
18C22×C3×#67C2212yes—
19C22×C3×#67C2212yes—
20C23×C3×Dic3C2212yes—
21C2×C3×#235—28no—
22C2×C3×#235C2218yescomplemented
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2212yes—
25C22×C3×Dic6—28no—
26C22×C3×Dic6C2212yes—
27C22×C3×Dic6C2211yescharacteristic
28C22×C3×Dic6C2211yescharacteristic
29C22×C3×Dic6C2218yescomplemented
30C32×C4×D4C2218yescomplemented
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×C32×C22⋊C4C2211yescharacteristic
33C2×C32×C22⋊C4C2211yescharacteristic
34C2×C32×C42C2211yescharacteristic
35C2×C3×#217C2212yes—
36C3×#939C22116yescomplemented
37C3×#930C2218yescomplemented
38C2×C3×(C2×D3)⋊C4C2212yes—
39C2×C3×(C2×D3)⋊C4C2212yes—
40C2×C3×(C2×D3)⋊C4C2212yes—
41C2×C3×C4⋊Dic3C2211yescharacteristic
42C3×#924C2218yescomplemented
43C2×C3×Dic3⋊C4C2212yes—
44C2×C3×Dic3⋊C4C2212yes—
45C2×C3×C4×Dic3C2212yes—
46C3×#896C22116yescomplemented
47C3×#885C22116yescomplemented
48C3×#67⋊C4C22116yescomplemented
49C3×#875C2218yescomplemented
50C3×C4×Dic6C2218yescomplemented
51C22×C3×#41—31no—
52C23×C3×Q8—31no—
53C22×#235C2×C311yescharacteristic, complemented
54C23×Dic6C2×C311yescharacteristic, complemented
55C3×#548—316no—
56C2×C3×#124—32no—
57C2×C3×#124—31no—
58C2×C3×C22⋊Q8—31no—
59C2×C3×C22⋊Q8—32no—
60C2×C3×#121—32no—
61C2×C3×#121—31no—
62C2×C3×C4×Q8—31no—
63C2×C3×C4×D4—21no—
64C2×C3×C4×D4—32no—
65C2×C3×C4×D4D311yescharacteristic, complemented
66C2×C3×C4×D4C2×C311yescharacteristic, complemented
67C2×#939C2×C312yescomplemented
68C2×#930C2×C311yescharacteristic, complemented
69C2×#924C2×C311yescharacteristic, complemented
70#5552C2×C3116yesdirect product factor
71C2×#896C2×C312yescomplemented
72C2×#885C2×C312yescomplemented
73C2×#67⋊C4C2×C312yescomplemented
74C2×#875C2×C311yescharacteristic, complemented
75C2×C4×Dic6C2×C311yescharacteristic, complemented
76C24×C32C2311yescharacteristic
77C24×C32C2311yescharacteristic
78C23×C3×D3C2312yes—
79C2×C32×D4—24no—
80C2×C32×D4C2314yes—
81C22×C32×C4—24no—
82C22×C32×C4—24no—
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2314yes—
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2314yes—
89C22×C32×C4C2311yescharacteristic
90C2×C3×#67—28no—
91C2×C3×#67—28no—
92C2×C3×#67C2318yes—
93C2×C3×#67C2318yes—
94C22×C3×Dic3—28no—
95C22×C3×Dic3C2318yes—
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2312yes—
98C22×C3×Dic3C2312yes—
99C3×#235—232no—
100C2×C3×D12—24no—
101C2×C3×D12C2314yes—
102C2×C3×C4×D3—28no—
103C2×C3×C4×D3C2318yes—
104C2×C3×Dic6—24no—
105C2×C3×Dic6—28no—
106C2×C3×Dic6—232no—
107C2×C3×Dic6D418yescomplemented
108C2×C3×Dic6C2318yes—
109C2×C3×Dic6C2314yes—
110C2×C3×Dic6C2314yes—
111C32×C4⋊C4C2314yes—
112C32×C22⋊C4C2314yes—
113C32×C22⋊C4C2314yes—
114C32×C42C2314yes—
115C3×#217C2318yes—
116C3×(C2×D3)⋊C4C2318yes—
117C3×(C2×D3)⋊C4C2318yes—
118C3×(C2×D3)⋊C4C2318yes—
119C3×C4⋊Dic3C2314yes—
120C3×Dic3⋊C4C2318yes—
121C3×Dic3⋊C4C2318yes—
122C3×C4×Dic3C2318yes—
123C2×#548—31noSylow
124C2×C3×#41—38no—
125C2×C3×#41—68no—
126C22×C3×Q8—31no—
127C22×C3×Q8—32no—
128C22×C3×Q8—31no—
129C22×C3×Q8—38no—
130C22×C3×Q8—68no—
131C22×C3×D4—21no—
132C22×C3×D4—32no—
133C22×C3×D4—32no—
134C22×C3×D4—31no—
135C22×C3×D4C2×D311yescharacteristic
136C22×C3×D4C22×C311yescharacteristic
137C23×C3×C4—21no—
138C23×C3×C4—21no—
139C23×C3×C4—32no—
140C23×C3×C4—32no—
141C23×C3×C4C2×D311yescharacteristic
142C23×C3×C4C2×D311yescharacteristic
143C23×C3×C4C22×C311yescharacteristic
144C23×C3×C4C22×C311yescharacteristic
145C22×#67C22×C312yes—
146C22×#67C22×C312yes—
147C23×Dic3C22×C312yes—
148C2×#235—28no—
149C2×#235C22×C318yescomplemented
150C22×D12C22×C311yescharacteristic
151C22×C4×D3C22×C312yes—
152C22×Dic6—28no—
153C22×Dic6C22×C311yescharacteristic
154C22×Dic6C22×C312yes—
155C22×Dic6C22×C311yescharacteristic
156C22×Dic6C22×C318yescomplemented
157C3×#124—316no—
158C3×#124—38no—
159C3×C22⋊Q8—38no—
160C3×C22⋊Q8—316no—
161C3×#121—316no—
162C3×#121—38no—
163C3×C4×Q8—38no—
164C3×C4×D4—28no—
165C3×C4×D4—316no—
166C3×C4×D4C2×D318yescomplemented
167C3×C4×D4C22×C318yescomplemented
168C2×C3×C4⋊C4—21no—
169C2×C3×C4⋊C4—32no—
170C2×C3×C4⋊C4—32no—
171C2×C3×C4⋊C4—31no—
172C2×C3×C4⋊C4C2×D311yescharacteristic
173C2×C3×C4⋊C4C22×C311yescharacteristic
174C2×C3×C22⋊C4—21no—
175C2×C3×C22⋊C4—21no—
176C2×C3×C22⋊C4—32no—
177C2×C3×C22⋊C4—32no—
178C2×C3×C22⋊C4—32no—
179C2×C3×C22⋊C4—32no—
180C2×C3×C22⋊C4C2×D311yescharacteristic
181C2×C3×C22⋊C4C2×D311yescharacteristic
182C2×C3×C22⋊C4C22×C311yescharacteristic
183C2×C3×C22⋊C4C22×C311yescharacteristic
184C2×C3×C42—21no—
185C2×C3×C42—32no—
186C2×C3×C42C2×D311yescharacteristic
187C2×C3×C42C22×C311yescharacteristic
188C2×#217C22×C312yes—
189#939C22×C3116yescomplemented
190#930C22×C318yescomplemented
191C2×(C2×D3)⋊C4C22×C312yes—
192C2×(C2×D3)⋊C4C22×C312yes—
193C2×(C2×D3)⋊C4C22×C312yes—
194C2×C4⋊Dic3C22×C311yescharacteristic
195#924C22×C318yescomplemented
196C2×Dic3⋊C4C22×C312yes—
197C2×Dic3⋊C4C22×C312yes—
198C2×C4×Dic3C22×C312yes—
199#896C22×C3116yescomplemented
200#885C22×C3116yescomplemented
201#67⋊C4C22×C3116yescomplemented
202#875C22×C318yescomplemented
203C4×Dic6C22×C318yescomplemented
204C23×C32—22no—
205C23×C32—22no—
206C23×C32—22no—
207C23×C32—22no—
208C23×C32—22no—
209C23×C32#4114yescomplemented
210C23×C32C2412yes—
211C23×C32C2412yes—
212C23×C32C2411yescharacteristic
213C22×C3×D3—24no—
214C22×C3×D3—24no—
215C22×C3×D3—24no—
216C22×C3×D3C2414yes—
217C32×D4—28no—
218C2×C32×C4—22no—
219C2×C32×C4—22no—
220C2×C32×C4—22no—
221C2×C32×C4—22no—
222C2×C32×C4—28no—
223C2×C32×C4—28no—
224C2×C32×C4C2×D414yes—
225C2×C32×C4C2412yes—
226C2×C32×C4C2412yes—
227C2×C32×C4C2412yes—
228C2×C32×C4C2412yes—
229C2×C32×C4C2412yes—
230C3×#67—216no—
231C3×#67—216no—
232C2×C3×Dic3—24no—
233C2×C3×Dic3—24no—
234C2×C3×Dic3—216no—
235C2×C3×Dic3C2×D418yes—
236C2×C3×Dic3C2414yes—
237C2×C3×Dic3C2414yes—
238C2×C3×Dic3C2414yes—
239C3×D12—28no—
240C3×C4×D3—216no—
241C3×Dic6—28no—
242C3×Dic6—216no—
243C3×Dic6C2×D4116yescomplemented
244C22×#41—31no—
245C23×Q8—31no—
246#548—316no—
247C2×#124—32no—
248C2×#124—31no—
249C2×C22⋊Q8—31no—
250C2×C22⋊Q8—32no—
251C2×#121—32no—
252C2×#121—31no—
253C2×C4×Q8—31no—
254C2×C4×D4—32no—
255C2×C4×D4C3×D311yescharacteristic, complemented
256C24×C3—21no—
257C24×C3—21no—
258C24×C3—32no—
259C24×C3C22×D311yescharacteristic
260C24×C3C22×D311yescharacteristic
261C24×C3C23×C311yescharacteristic
262C24×C3C23×C311yescharacteristic
263C23×D3C23×C312yes—
264C3×#41—632no—
265C2×C3×Q8—38no—
266C2×C3×Q8—34no—
267C2×C3×Q8—38no—
268C2×C3×Q8—34no—
269C2×C3×Q8—68no—
270C2×C3×Q8—632no—
271C2×C3×Q8—64no—
272C2×C3×D4—28no—
273C2×C3×D4—24no—
274C2×C3×D4—24no—
275C2×C3×D4—24no—
276C2×C3×D4—38no—
277C2×C3×D4—38no—
278C2×C3×D4—34no—
279C2×C3×D4—68no—
280C2×C3×D4—68no—
281C2×C3×D4—64no—
282C2×C3×D4C22×D314yes—
283C2×C3×D4C23×C314yes—
284C22×C3×C4—24no—
285C22×C3×C4—24no—
286C22×C3×C4—24no—
287C22×C3×C4—24no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—24no—
294C22×C3×C4—24no—
295C22×C3×C4—32no—
296C22×C3×C4—38no—
297C22×C3×C4—32no—
298C22×C3×C4—32no—
299C22×C3×C4—38no—
300C22×C3×C4—44no—
301C22×C3×C4—44no—
302C22×C3×C4—68no—
303C22×C3×C4—68no—
304C22×C3×C4C22×D314yes—
305C22×C3×C4C22×D314yes—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C23×C311yescharacteristic
312C22×C3×C4C23×C311yescharacteristic
313C22×C3×C4C23×C311yescharacteristic
314C22×C3×C4C23×C314yes—
315C22×C3×C4C23×C311yescharacteristic
316C22×C3×C4C23×C314yes—
317C22×C3×C4C23×C311yescharacteristic
318C2×#67—28no—
319C2×#67—28no—
320C2×#67C23×C318yes—
321C2×#67C23×C318yes—
322C22×Dic3—28no—
323C22×Dic3C23×C318yes—
324C22×Dic3C23×C312yes—
325C22×Dic3C23×C312yes—
326C22×Dic3C23×C312yes—
327#235—232no—
328C2×D12—24no—
329C2×D12C23×C314yes—
330C2×C4×D3—28no—
331C2×C4×D3C23×C318yes—
332C2×Dic6—24no—
333C2×Dic6—28no—
334C2×Dic6—232no—
335C2×Dic6C3×D418yescomplemented
336C2×Dic6C23×C314yes—
337C2×Dic6C23×C318yes—
338C2×Dic6C23×C314yes—
339C3×C4⋊C4—24no—
340C3×C4⋊C4—38no—
341C3×C4⋊C4—38no—
342C3×C4⋊C4—34no—
343C3×C4⋊C4C22×D314yes—
344C3×C4⋊C4C23×C314yes—
345C3×C22⋊C4—24no—
346C3×C22⋊C4—24no—
347C3×C22⋊C4—38no—
348C3×C22⋊C4—38no—
349C3×C22⋊C4—38no—
350C3×C22⋊C4—38no—
351C3×C22⋊C4C22×D314yes—
352C3×C22⋊C4C22×D314yes—
353C3×C22⋊C4C23×C314yes—
354C3×C22⋊C4C23×C314yes—
355C3×C42—24no—
356C3×C42—38no—
357C3×C42C22×D314yes—
358C3×C42C23×C314yes—
359#217C23×C318yes—
360(C2×D3)⋊C4C23×C318yes—
361(C2×D3)⋊C4C23×C318yes—
362(C2×D3)⋊C4C23×C318yes—
363C4⋊Dic3C23×C314yes—
364Dic3⋊C4C23×C318yes—
365Dic3⋊C4C23×C318yes—
366C4×Dic3C23×C318yes—
367C22×C32—22no—
368C22×C32—28no—
369C22×C32—22no—
370C22×C32—22no—
371C22×C32—22no—
372C22×C32—22no—
373C22×C32—44no—
374C22×C32C22×D412yes—
375C22×C32C2×#4112yes—
376C22×C32C2×#4114yescomplemented
377C22×C322−1+412yes—
378C22×C32C2511yescharacteristic
379C2×C3×D3—24no—
380C2×C3×D3—24no—
381C2×C3×D3—24no—
382C2×C3×D3—48no—
383C32×C4—22no—
384C32×C4—22no—
385C32×C4—22no—
386C32×C4—22no—
387C32×C4C22×D414yes—
388C3×Dic3—24no—
389C3×Dic3—24no—
390C3×Dic3C22×D418yes—
391C2×#41—38no—
392C2×#41—68no—
393C22×Q8—31no—
394C22×Q8—32no—
395C22×Q8—31no—
396C22×Q8—38no—
397C22×Q8—68no—
398C22×D4—32no—
399C22×D4—32no—
400C22×D4—31no—
401C22×D4C2×C3×D311yescharacteristic
402C23×C4—32no—
403C23×C4—32no—
404C23×C4C2×C3×D311yescharacteristic
405C23×C4C2×C3×D311yescharacteristic
406#124—316no—
407#124—38no—
408C22⋊Q8—38no—
409C22⋊Q8—316no—
410#121—316no—
411#121—38no—
412C4×Q8—38no—
413C4×D4—316no—
414C4×D4C2×C3×D318yescomplemented
415C2×C4⋊C4—32no—
416C2×C4⋊C4—32no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4C2×C3×D311yescharacteristic
419C2×C22⋊C4—32no—
420C2×C22⋊C4—32no—
421C2×C22⋊C4—32no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4C2×C3×D311yescharacteristic
424C2×C22⋊C4C2×C3×D311yescharacteristic
425C2×C42—32no—
426C2×C42C2×C3×D311yescharacteristic
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—24no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—21no—
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—24no—
442C23×C3—34no—
443C23×C3—42no—
444C23×C3—42no—
445C23×C3—42no—
446C23×C3—42no—
447C23×C3—64no—
448C23×C3—64no—
449C23×C3—64no—
450C23×C3#23514yescomplemented
451C23×C3C3×#4114yescomplemented
452C23×C3C23×D312yes—
453C23×C3C23×D312yes—
454C23×C3C23×D311yescharacteristic
455C23×C3C24×C312yes—
456C23×C3C24×C312yes—
457C23×C3C24×C311yescharacteristic
458C22×D3—24no—
459C22×D3—24no—
460C22×D3—24no—
461C22×D3C24×C314yes—
462C3×Q8—316no—
463C3×Q8—616no—
464C3×Q8—68no—
465C3×D4—216no—
466C3×D4—28no—
467C3×D4—28no—
468C3×D4—616no—
469C3×D4—616no—
470C3×D4—68no—
471C2×C3×C4—24no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—28no—
481C2×C3×C4—28no—
482C2×C3×C4—28no—
483C2×C3×C4—28no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—24no—
490C2×C3×C4—38no—
491C2×C3×C4—34no—
492C2×C3×C4—34no—
493C2×C3×C4—34no—
494C2×C3×C4—48no—
495C2×C3×C4—48no—
496C2×C3×C4—42no—
497C2×C3×C4—42no—
498C2×C3×C4—42no—
499C2×C3×C4—616no—
500C2×C3×C4—616no—
501C2×C3×C4—64no—
502C2×C3×C4—64no—
503C2×C3×C4D3×D414yes—
504C2×C3×C4C2×C3×D414yes—
505C2×C3×C4C23×D312yes—
506C2×C3×C4C23×D312yes—
507C2×C3×C4C23×D312yes—
508C2×C3×C4C23×D312yes—
509C2×C3×C4C23×D312yes—
510C2×C3×C4C24×C312yes—
511C2×C3×C4C24×C312yes—
512C2×C3×C4C24×C312yes—
513C2×C3×C4C24×C312yes—
514C2×C3×C4C24×C312yes—
515#67—216no—
516#67—216no—
517C2×Dic3—24no—
518C2×Dic3—24no—
519C2×Dic3—216no—
520C2×Dic3C2×C3×D418yes—
521C2×Dic3C24×C314yes—
522C2×Dic3C24×C314yes—
523C2×Dic3C24×C314yes—
524D12—28no—
525C4×D3—216no—
526Dic6—28no—
527Dic6—216no—
528Dic6C2×C3×D4116yescomplemented
529C2×C32—24no—
530C2×C32—42no—
531C2×C32#54814yescomplemented
532C2×C32C23×D411yescharacteristic
533C2×C32C22×#4111yescharacteristic
534C2×C32C2×2−1+411yescharacteristic
535C3×D3—44no—
536C24—32no—
537C24C22×C3×D311yescharacteristic
538C24C22×C3×D311yescharacteristic
539#41—632no—
540C2×Q8—34no—
541C2×Q8—38no—
542C2×Q8—34no—
543C2×Q8—38no—
544C2×Q8—68no—
545C2×Q8—632no—
546C2×Q8—64no—
547C2×D4—24no—
548C2×D4—38no—
549C2×D4—38no—
550C2×D4—34no—
551C2×D4—68no—
552C2×D4—68no—
553C2×D4—64no—
554C2×D4C22×C3×D314yes—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—32no—
560C22×C4—38no—
561C22×C4—38no—
562C22×C4—68no—
563C22×C4—68no—
564C22×C4C22×C3×D311yescharacteristic
565C22×C4C22×C3×D311yescharacteristic
566C22×C4C22×C3×D311yescharacteristic
567C22×C4C22×C3×D311yescharacteristic
568C22×C4C22×C3×D314yes—
569C22×C4C22×C3×D314yes—
570C22×C4C22×C3×D311yescharacteristic
571C4⋊C4—38no—
572C4⋊C4—38no—
573C4⋊C4—34no—
574C4⋊C4C22×C3×D314yes—
575C22⋊C4—38no—
576C22⋊C4—38no—
577C22⋊C4—38no—
578C22⋊C4—38no—
579C22⋊C4C22×C3×D314yes—
580C22⋊C4C22×C3×D314yes—
581C42—38no—
582C42C22×C3×D314yes—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—28no—
588C22×C3—28no—
589C22×C3—24no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—24no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—21no—
601C22×C3—42no—
602C22×C3—42no—
603C22×C3—48no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—48no—
607C22×C3—44no—
608C22×C3—44no—
609C22×C3—64no—
610C22×C3—64no—
611C22×C3—64no—
612C22×C3—128no—
613C22×C3C2×#23512yes—
614C22×C3C2×#23514yescomplemented
615C22×C3C2×D3×D412yes—
616C22×C3#101012yes—
617C22×C3C22×C3×D412yes—
618C22×C3C2×C3×#4112yes—
619C22×C3C2×C3×#4114yescomplemented
620C22×C3C3×2−1+412yes—
621C22×C3C24×D311yescharacteristic
622C22×C3C25×C311yescharacteristic
623C2×D3—24no—
624C2×D3—24no—
625C2×D3—24no—
626C2×D3—48no—
627C3×C4—24no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—22no—
631C3×C4—22no—
632C3×C4—22no—
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—24no—
637C3×C4—38no—
638C3×C4—42no—
639C3×C4—42no—
640C3×C4—42no—
641C3×C4—64no—
642C3×C4—64no—
643C3×C4C2×D3×D414yes—
644C3×C4C22×C3×D414yes—
645Dic3—24no—
646Dic3—24no—
647Dic3C22×C3×D418yes—
648C32C2×#54811yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—34no—
655C23—64no—
656C23—64no—
657C23—64no—
658C23C3×#23514yescomplemented
659C23C23×C3×D312yes—
660C23C23×C3×D312yes—
661C23C23×C3×D311yescharacteristic
662Q8—316no—
663Q8—616no—
664Q8—68no—
665D4—28no—
666D4—616no—
667D4—616no—
668D4—68no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—38no—
676C2×C4—34no—
677C2×C4—34no—
678C2×C4—34no—
679C2×C4—616no—
680C2×C4—616no—
681C2×C4—64no—
682C2×C4—64no—
683C2×C4C3×D3×D414yes—
684C2×C4C23×C3×D312yes—
685C2×C4C23×C3×D312yes—
686C2×C4C23×C3×D312yes—
687C2×C4C23×C3×D312yes—
688C2×C4C23×C3×D312yes—
689C2×C3—24no—
690C2×C3—24no—
691C2×C3—24no—
692C2×C3—21no—
693C2×C3—21no—
694C2×C3—21no—
695C2×C3—44no—
696C2×C3—44no—
697C2×C3—42no—
698C2×C3—42no—
699C2×C3—124no—
700C2×C3#555214yesdirect product factor
701C2×C3C3×#54814yescomplemented
702C2×C3C22×#23511yescharacteristic
703C2×C3C22×D3×D411yescharacteristic
704C2×C3C2×#101011yescharacteristic
705C2×C3C23×C3×D411yescharacteristic
706C2×C3C22×C3×#4111yescharacteristic
707C2×C3C2×C3×2−1+411yescharacteristic
708D3—44no—
709C22—28no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—44no—
716C22—64no—
717C22—64no—
718C22—64no—
719C22—128no—
720C22C2×C3×#23512yes—
721C22C2×C3×#23514yescomplemented
722C22C2×C3×D3×D412yes—
723C22C3×#101012yes—
724C22C24×C3×D311yescharacteristic
725C4—22no—
726C4—22no—
727C4—22no—
728C4—22no—
729C4—38no—
730C4—64no—
731C4—64no—
732C4C2×C3×D3×D414yes—
733C3—21no—
734C3C2×#555211yescharacteristic, direct product factor
735C3C2×C3×#54811yescharacteristic, complemented
736C2—24no—
737C2—42no—
738C2—124no—
739C2C3×#555214yesdirect product factor
740C2C22×C3×#23511yescharacteristic
741C2C22×C3×D3×D411yescharacteristic
742C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C4×D4C2
socleC23×C32C24
hypercenterC2×C3×C4×D4D3
hypocenterC3C2×C3×#548
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C23×C3×Dic6C2semidirect
3. C2×C32×C4×D4C2semidirect
4. C2×C3×#939C2semidirect
5. C2×C3×#930C2semidirect
6. C2×C3×#924C2semidirect
7. C3×#5552C2direct (N × H)
8. C2×C3×#896C2semidirect
9. C2×C3×#885C2semidirect
10. C2×C3×#67⋊C4C2semidirect
11. C2×C3×#875C2semidirect
12. C2×C3×C4×Dic6C2semidirect
14. C2×#5552C3direct (N × H)
22. C2×C3×#235C22semidirect
29. C22×C3×Dic6C22semidirect
30. C32×C4×D4C22semidirect
36. C3×#939C22semidirect
37. C3×#930C22semidirect
42. C3×#924C22semidirect
46. C3×#896C22semidirect
47. C3×#885C22semidirect
48. C3×#67⋊C4C22semidirect
49. C3×#875C22semidirect
50. C3×C4×Dic6C22semidirect
53. C22×#235C2×C3semidirect
54. C23×Dic6C2×C3semidirect
65. C2×C3×C4×D4D3semidirect
66. C2×C3×C4×D4C2×C3semidirect
67. C2×#939C2×C3semidirect
68. C2×#930C2×C3semidirect
69. C2×#924C2×C3semidirect
70. #5552C2×C3direct (N × H)
71. C2×#896C2×C3semidirect
72. C2×#885C2×C3semidirect
73. C2×#67⋊C4C2×C3semidirect
74. C2×#875C2×C3semidirect
75. C2×C4×Dic6C2×C3semidirect
107. C2×C3×Dic6D4semidirect
149. C2×#235C22×C3semidirect
156. C22×Dic6C22×C3semidirect
166. C3×C4×D4C2×D3semidirect
167. C3×C4×D4C22×C3semidirect
189. #939C22×C3semidirect
190. #930C22×C3semidirect
195. #924C22×C3semidirect
199. #896C22×C3semidirect
200. #885C22×C3semidirect
201. #67⋊C4C22×C3semidirect
202. #875C22×C3semidirect
203. C4×Dic6C22×C3semidirect
209. C23×C32#41semidirect
243. C3×Dic6C2×D4semidirect
255. C2×C4×D4C3×D3semidirect
335. C2×Dic6C3×D4semidirect
376. C22×C32C2×#41semidirect
414. C4×D4C2×C3×D3semidirect
450. C23×C3#235semidirect
451. C23×C3C3×#41semidirect
528. Dic6C2×C3×D4semidirect
531. C2×C32#548semidirect
614. C22×C3C2×#235semidirect
619. C22×C3C2×C3×#41semidirect
648. C32C2×#548semidirect
658. C23C3×#235semidirect
700. C2×C3#5552direct (N × H)
701. C2×C3C3×#548semidirect
721. C22C2×C3×#235semidirect
734. C3C2×#5552direct (N × H)
735. C3C2×C3×#548semidirect
739. C2C3×#5552direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C23×C3×Dic62
C2×C32×C4×D42
C2×C3×#9392
C2×C3×#9302
C2×C3×#9242
C3×#55522
C2×C3×#8962
C2×C3×#8852
C2×C3×#67⋊C42
C2×C3×#8752
C2×C3×C4×Dic62
C2×C3×#5483
C2×#55523