Finite Group Databasebeta

← C2×C3×#5598 #11902573

Subgroups — C2×C3×#5598 #11902573

Order 1152.

3453 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C23×C3×Dic6C211yesmaximal, characteristic, complemented
3C2×C32×#121C211yesmaximal, characteristic, complemented
4C2×C3×#939C212yesmaximal, complemented
5C2×C3×#936C211yesmaximal, characteristic, complemented
6C2×C3×D4×Dic3C212yesmaximal, complemented
7C2×C3×C4×#67C211yesmaximal, characteristic, complemented
8C3×#5598C2116yesmaximal, direct product factor
9C2×C3×#897C211yesmaximal, characteristic, complemented
10C2×C3×#887C211yesmaximal, characteristic, complemented
11C2×C3×#885C212yesmaximal, complemented
12C2×C3×#878C212yesmaximal, complemented
13C2×C3×#548—31nomaximal
14C2×#5598C311yesmaximal, characteristic, direct product factor
15C22×C32×D4C2212yes—
16C22×C32×D4C2211yescharacteristic
17C23×C32×C4C2211yescharacteristic
18C22×C3×#67C2212yes—
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2212yes—
21C23×C3×Dic3C2212yes—
22C2×C3×#237—28no—
23C2×C3×#237C2218yescomplemented
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×Dic6—28no—
26C22×C3×Dic6C2212yes—
27C22×C3×Dic6C2211yescharacteristic
28C22×C3×Dic6C2211yescharacteristic
29C22×C3×Dic6C2218yescomplemented
30C32×#121C2218yescomplemented
31C2×C32×C4⋊C4C2211yescharacteristic
32C2×C32×C22⋊C4C2212yes—
33C2×C3×#217C2212yes—
34C2×C3×#217C2211yescharacteristic
35C2×C3×#217C2212yes—
36C3×#939C22116yescomplemented
37C3×#936C2218yescomplemented
38C3×D4×Dic3C22116yescomplemented
39C3×C4×#67C2218yescomplemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic
41C2×C3×(C2×D3)⋊C4C2212yes—
42C2×C3×C4⋊Dic3C2212yes—
43C2×C3×Dic3⋊C4C2212yes—
44C2×C3×Dic3⋊C4C2211yescharacteristic
45C2×C3×C4×Dic3C2212yes—
46C2×C3×C4×Dic3C2211yescharacteristic
47C3×#897C2218yescomplemented
48C3×#887C2218yescomplemented
49C3×#885C22116yescomplemented
50C3×#878C22116yescomplemented
51C22×C3×#41—31no—
52C23×C3×Q8—31no—
53C22×#237C2×C311yescharacteristic, complemented
54C23×Dic6C2×C311yescharacteristic, complemented
55C3×#548—316no—
56C2×C3×#124—31no—
57C2×C3×#124—32no—
58C2×C3×C22⋊Q8—31no—
59C2×C3×C22⋊Q8—32no—
60C2×C3×#121—21no—
61C2×C3×#121—32no—
62C2×C3×#121D311yescharacteristic, complemented
63C2×C3×#121C2×C311yescharacteristic, complemented
64C2×C3×C4×Q8—31no—
65C2×C3×C4×D4—32no—
66C2×C3×C4×D4—31no—
67C2×#939C2×C312yescomplemented
68C2×#936C2×C311yescharacteristic, complemented
69C2×D4×Dic3C2×C312yescomplemented
70C2×C4×#67C2×C311yescharacteristic, complemented
71#5598C2×C3116yesdirect product factor
72C2×#897C2×C311yescharacteristic, complemented
73C2×#887C2×C311yescharacteristic, complemented
74C2×#885C2×C312yescomplemented
75C2×#878C2×C312yescomplemented
76C24×C32C2312yes—
77C24×C32C2311yescharacteristic
78C23×C3×D3C2311yescharacteristic
79C2×C32×D4—28no—
80C2×C32×D4—24no—
81C2×C32×D4C2318yes—
82C2×C32×D4C2314yes—
83C22×C32×C4—24no—
84C22×C32×C4C2312yes—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2314yes—
87C22×C32×C4C2311yescharacteristic
88C2×C3×#67—24no—
89C2×C3×#67—28no—
90C2×C3×#67C2318yes—
91C2×C3×#67C2314yes—
92C22×C3×Dic3—28no—
93C22×C3×Dic3—28no—
94C22×C3×Dic3C2318yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2312yes—
99C22×C3×Dic3C2318yes—
100C22×C3×Dic3C2312yes—
101C3×#237—232no—
102C2×C3×C4×D3—24no—
103C2×C3×C4×D3C2314yes—
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⋊C4C2318yes—
113C3×#217C2318yes—
114C3×#217C2318yes—
115C3×#217C2314yes—
116C3×(C2×D3)⋊C4C2314yes—
117C3×(C2×D3)⋊C4C2318yes—
118C3×C4⋊Dic3C2318yes—
119C3×Dic3⋊C4C2314yes—
120C3×Dic3⋊C4C2318yes—
121C3×C4×Dic3C2318yes—
122C3×C4×Dic3C2314yes—
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—22no—
132C22×C3×D4—21no—
133C22×C3×D4—32no—
134C22×C3×D4—31no—
135C22×C3×D4C2×D311yescharacteristic
136C22×C3×D4C2×D312yes—
137C22×C3×D4C22×C311yescharacteristic
138C22×C3×D4C22×C312yes—
139C23×C3×C4—21no—
140C23×C3×C4—32no—
141C23×C3×C4—32no—
142C23×C3×C4—31no—
143C23×C3×C4C2×D311yescharacteristic
144C23×C3×C4C22×C311yescharacteristic
145C22×#67C22×C312yes—
146C22×#67C22×C311yescharacteristic
147C23×Dic3C22×C312yes—
148C23×Dic3C22×C312yes—
149C2×#237—28no—
150C2×#237C22×C318yescomplemented
151C22×C4×D3C22×C311yescharacteristic
152C22×Dic6—28no—
153C22×Dic6C22×C312yes—
154C22×Dic6C22×C311yescharacteristic
155C22×Dic6C22×C311yescharacteristic
156C22×Dic6C22×C318yescomplemented
157C3×#124—38no—
158C3×#124—316no—
159C3×C22⋊Q8—38no—
160C3×C22⋊Q8—316no—
161C3×#121—28no—
162C3×#121—316no—
163C3×#121C2×D318yescomplemented
164C3×#121C22×C318yescomplemented
165C3×C4×Q8—38no—
166C3×C4×D4—316no—
167C3×C4×D4—38no—
168C2×C3×C4⋊C4—21no—
169C2×C3×C4⋊C4—31no—
170C2×C3×C4⋊C4—32no—
171C2×C3×C4⋊C4—32no—
172C2×C3×C4⋊C4C2×D311yescharacteristic
173C2×C3×C4⋊C4C22×C311yescharacteristic
174C2×C3×C22⋊C4—22no—
175C2×C3×C22⋊C4—31no—
176C2×C3×C22⋊C4—32no—
177C2×C3×C22⋊C4—32no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—32no—
180C2×C3×C22⋊C4C2×D312yes—
181C2×C3×C22⋊C4C22×C312yes—
182C2×C3×C42—32no—
183C2×C3×C42—31no—
184C2×#217C22×C312yes—
185C2×#217C22×C312yes—
186C2×#217C22×C311yescharacteristic
187#939C22×C3116yescomplemented
188#936C22×C318yescomplemented
189D4×Dic3C22×C3116yescomplemented
190C4×#67C22×C318yescomplemented
191C2×(C2×D3)⋊C4C22×C311yescharacteristic
192C2×(C2×D3)⋊C4C22×C312yes—
193C2×C4⋊Dic3C22×C312yes—
194C2×Dic3⋊C4C22×C311yescharacteristic
195C2×Dic3⋊C4C22×C312yes—
196C2×C4×Dic3C22×C312yes—
197C2×C4×Dic3C22×C311yescharacteristic
198#897C22×C318yescomplemented
199#887C22×C318yescomplemented
200#885C22×C3116yescomplemented
201#878C22×C3116yescomplemented
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—24no—
205C23×C32—24no—
206C23×C32—24no—
207C23×C32#4114yescomplemented
208C23×C32C2414yes—
209C23×C32C2412yes—
210C23×C32C2411yescharacteristic
211C22×C3×D3—22no—
212C22×C3×D3—22no—
213C22×C3×D3—22no—
214C22×C3×D3C2412yes—
215C32×D4—216no—
216C32×D4—28no—
217C2×C32×C4—22no—
218C2×C32×C4—24no—
219C2×C32×C4—28no—
220C2×C32×C4C2×D414yes—
221C2×C32×C4C2414yes—
222C2×C32×C4C2412yes—
223C2×C32×C4C2412yes—
224C3×#67—28no—
225C3×#67—216no—
226C2×C3×Dic3—24no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—216no—
231C2×C3×Dic3—216no—
232C2×C3×Dic3C2×D418yes—
233C2×C3×Dic3C2412yes—
234C2×C3×Dic3C2412yes—
235C2×C3×Dic3C2412yes—
236C2×C3×Dic3C2414yes—
237C2×C3×Dic3C2414yes—
238C3×C4×D3—28no—
239C3×Dic6—28no—
240C3×Dic6—216no—
241C3×Dic6C2×D4116yescomplemented
242C22×#41—31no—
243C23×Q8—31no—
244#548—316no—
245C2×#124—31no—
246C2×#124—32no—
247C2×C22⋊Q8—31no—
248C2×C22⋊Q8—32no—
249C2×#121—32no—
250C2×#121C3×D311yescharacteristic, complemented
251C2×C4×Q8—31no—
252C2×C4×D4—32no—
253C2×C4×D4—31no—
254C24×C3—21no—
255C24×C3—22no—
256C24×C3—31no—
257C24×C3C22×D312yes—
258C24×C3C22×D311yescharacteristic
259C24×C3C23×C312yes—
260C24×C3C23×C311yescharacteristic
261C23×D3C23×C311yescharacteristic
262C3×#41—632no—
263C2×C3×Q8—38no—
264C2×C3×Q8—34no—
265C2×C3×Q8—38no—
266C2×C3×Q8—34no—
267C2×C3×Q8—68no—
268C2×C3×Q8—632no—
269C2×C3×Q8—64no—
270C2×C3×D4—28no—
271C2×C3×D4—28no—
272C2×C3×D4—24no—
273C2×C3×D4—24no—
274C2×C3×D4—28no—
275C2×C3×D4—24no—
276C2×C3×D4—34no—
277C2×C3×D4—38no—
278C2×C3×D4—44no—
279C2×C3×D4—48no—
280C2×C3×D4—68no—
281C2×C3×D4—64no—
282C2×C3×D4C22×D318yes—
283C2×C3×D4C22×D314yes—
284C2×C3×D4C23×C318yes—
285C2×C3×D4C23×C314yes—
286C22×C3×C4—24no—
287C22×C3×C4—24no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—22no—
291C22×C3×C4—24no—
292C22×C3×C4—32no—
293C22×C3×C4—38no—
294C22×C3×C4—38no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—32no—
298C22×C3×C4—31no—
299C22×C3×C4—34no—
300C22×C3×C4—44no—
301C22×C3×C4—68no—
302C22×C3×C4—68no—
303C22×C3×C4—64no—
304C22×C3×C4C22×D314yes—
305C22×C3×C4C22×D312yes—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C23×C312yes—
309C22×C3×C4C23×C311yescharacteristic
310C22×C3×C4C23×C314yes—
311C22×C3×C4C23×C311yescharacteristic
312C2×#67—24no—
313C2×#67—28no—
314C2×#67C23×C318yes—
315C2×#67C23×C314yes—
316C22×Dic3—28no—
317C22×Dic3—28no—
318C22×Dic3C23×C318yes—
319C22×Dic3C23×C311yescharacteristic
320C22×Dic3C23×C311yescharacteristic
321C22×Dic3C23×C311yescharacteristic
322C22×Dic3C23×C312yes—
323C22×Dic3C23×C318yes—
324C22×Dic3C23×C312yes—
325#237—232no—
326C2×C4×D3—24no—
327C2×C4×D3C23×C314yes—
328C2×Dic6—24no—
329C2×Dic6—28no—
330C2×Dic6—232no—
331C2×Dic6C3×D418yescomplemented
332C2×Dic6C23×C318yes—
333C2×Dic6C23×C314yes—
334C2×Dic6C23×C314yes—
335C3×C4⋊C4—24no—
336C3×C4⋊C4—34no—
337C3×C4⋊C4—38no—
338C3×C4⋊C4—38no—
339C3×C4⋊C4C22×D314yes—
340C3×C4⋊C4C23×C314yes—
341C3×C22⋊C4—28no—
342C3×C22⋊C4—34no—
343C3×C22⋊C4—38no—
344C3×C22⋊C4—38no—
345C3×C22⋊C4—34no—
346C3×C22⋊C4—38no—
347C3×C22⋊C4C22×D318yes—
348C3×C22⋊C4C23×C318yes—
349C3×C42—38no—
350C3×C42—34no—
351#217C23×C318yes—
352#217C23×C318yes—
353#217C23×C314yes—
354(C2×D3)⋊C4C23×C314yes—
355(C2×D3)⋊C4C23×C318yes—
356C4⋊Dic3C23×C318yes—
357Dic3⋊C4C23×C314yes—
358Dic3⋊C4C23×C318yes—
359C4×Dic3C23×C318yes—
360C4×Dic3C23×C314yes—
361C22×C32—28no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32—24no—
365C22×C32—24no—
366C22×C32—24no—
367C22×C32—48no—
368C22×C32C22×D412yes—
369C22×C32C2×#4112yes—
370C22×C32C2×#4114yescomplemented
371C22×C322−1+412yes—
372C22×C32C2511yescharacteristic
373C2×C3×D3—22no—
374C2×C3×D3—22no—
375C2×C3×D3—22no—
376C2×C3×D3—44no—
377C32×C4—22no—
378C32×C4—24no—
379C32×C4C22×D414yes—
380C3×Dic3—24no—
381C3×Dic3—22no—
382C3×Dic3—22no—
383C3×Dic3—22no—
384C3×Dic3C22×D418yes—
385C2×#41—38no—
386C2×#41—68no—
387C22×Q8—31no—
388C22×Q8—32no—
389C22×Q8—31no—
390C22×Q8—38no—
391C22×Q8—68no—
392C22×D4—31no—
393C22×D4—32no—
394C22×D4C2×C3×D312yes—
395C22×D4C2×C3×D311yescharacteristic
396C23×C4—32no—
397C23×C4—32no—
398C23×C4—31no—
399C23×C4C2×C3×D311yescharacteristic
400#124—38no—
401#124—316no—
402C22⋊Q8—38no—
403C22⋊Q8—316no—
404#121—316no—
405#121C2×C3×D318yescomplemented
406C4×Q8—38no—
407C4×D4—316no—
408C4×D4—38no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—32no—
411C2×C4⋊C4—32no—
412C2×C4⋊C4C2×C3×D311yescharacteristic
413C2×C22⋊C4—31no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—31no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4C2×C3×D312yes—
419C2×C42—32no—
420C2×C42—31no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—24no—
426C23×C3—24no—
427C23×C3—24no—
428C23×C3—24no—
429C23×C3—24no—
430C23×C3—24no—
431C23×C3—21no—
432C23×C3—22no—
433C23×C3—24no—
434C23×C3—24no—
435C23×C3—32no—
436C23×C3—42no—
437C23×C3—42no—
438C23×C3—44no—
439C23×C3—44no—
440C23×C3—44no—
441C23×C3—62no—
442C23×C3—62no—
443C23×C3—62no—
444C23×C3#23714yescomplemented
445C23×C3C3×#4114yescomplemented
446C23×C3C23×D314yes—
447C23×C3C23×D312yes—
448C23×C3C23×D311yescharacteristic
449C23×C3C24×C314yes—
450C23×C3C24×C312yes—
451C23×C3C24×C311yescharacteristic
452C22×D3—22no—
453C22×D3—22no—
454C22×D3—22no—
455C22×D3C24×C312yes—
456C3×Q8—316no—
457C3×Q8—616no—
458C3×Q8—68no—
459C3×D4—216no—
460C3×D4—216no—
461C3×D4—28no—
462C3×D4—28no—
463C3×D4—48no—
464C3×D4—416no—
465C3×D4—616no—
466C3×D4—68no—
467C2×C3×C4—22no—
468C2×C3×C4—24no—
469C2×C3×C4—22no—
470C2×C3×C4—24no—
471C2×C3×C4—28no—
472C2×C3×C4—28no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—24no—
476C2×C3×C4—24no—
477C2×C3×C4—38no—
478C2×C3×C4—34no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—34no—
482C2×C3×C4—32no—
483C2×C3×C4—48no—
484C2×C3×C4—42no—
485C2×C3×C4—44no—
486C2×C3×C4—616no—
487C2×C3×C4—616no—
488C2×C3×C4—62no—
489C2×C3×C4—64no—
490C2×C3×C4—62no—
491C2×C3×C4—62no—
492C2×C3×C4—68no—
493C2×C3×C4D3×D414yes—
494C2×C3×C4C2×C3×D414yes—
495C2×C3×C4C23×D314yes—
496C2×C3×C4C23×D312yes—
497C2×C3×C4C23×D312yes—
498C2×C3×C4C24×C314yes—
499C2×C3×C4C24×C312yes—
500C2×C3×C4C24×C312yes—
501#67—28no—
502#67—216no—
503C2×Dic3—24no—
504C2×Dic3—22no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—216no—
508C2×Dic3—216no—
509C2×Dic3C2×C3×D418yes—
510C2×Dic3C24×C312yes—
511C2×Dic3C24×C312yes—
512C2×Dic3C24×C312yes—
513C2×Dic3C24×C314yes—
514C2×Dic3C24×C314yes—
515C4×D3—28no—
516Dic6—28no—
517Dic6—216no—
518Dic6C2×C3×D4116yescomplemented
519C2×C32—24no—
520C2×C32—44no—
521C2×C32#54814yescomplemented
522C2×C32C23×D411yescharacteristic
523C2×C32C22×#4111yescharacteristic
524C2×C32C2×2−1+411yescharacteristic
525C3×D3—42no—
526C24—31no—
527C24C22×C3×D312yes—
528C24C22×C3×D311yescharacteristic
529#41—632no—
530C2×Q8—34no—
531C2×Q8—38no—
532C2×Q8—34no—
533C2×Q8—38no—
534C2×Q8—68no—
535C2×Q8—632no—
536C2×Q8—64no—
537C2×D4—28no—
538C2×D4—24no—
539C2×D4—34no—
540C2×D4—38no—
541C2×D4—68no—
542C2×D4—64no—
543C2×D4C22×C3×D318yes—
544C2×D4C22×C3×D314yes—
545C22×C4—24no—
546C22×C4—32no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—32no—
550C22×C4—31no—
551C22×C4—38no—
552C22×C4—38no—
553C22×C4—34no—
554C22×C4—68no—
555C22×C4—68no—
556C22×C4—64no—
557C22×C4C22×C3×D312yes—
558C22×C4C22×C3×D311yescharacteristic
559C22×C4C22×C3×D314yes—
560C22×C4C22×C3×D311yescharacteristic
561C4⋊C4—34no—
562C4⋊C4—38no—
563C4⋊C4—38no—
564C4⋊C4C22×C3×D314yes—
565C22⋊C4—34no—
566C22⋊C4—38no—
567C22⋊C4—38no—
568C22⋊C4—34no—
569C22⋊C4—38no—
570C22⋊C4C22×C3×D318yes—
571C42—38no—
572C42—34no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—28no—
578C22×C3—28no—
579C22×C3—24no—
580C22×C3—24no—
581C22×C3—24no—
582C22×C3—24no—
583C22×C3—24no—
584C22×C3—24no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—24no—
588C22×C3—22no—
589C22×C3—21no—
590C22×C3—42no—
591C22×C3—48no—
592C22×C3—42no—
593C22×C3—44no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—48no—
597C22×C3—48no—
598C22×C3—62no—
599C22×C3—62no—
600C22×C3—62no—
601C22×C3—88no—
602C22×C3—124no—
603C22×C3C2×D3×D412yes—
604C22×C3C2×#23712yes—
605C22×C3C2×#23714yescomplemented
606C22×C3#101012yes—
607C22×C3C22×C3×D412yes—
608C22×C3C2×C3×#4112yes—
609C22×C3C2×C3×#4114yescomplemented
610C22×C3C3×2−1+412yes—
611C22×C3C24×D311yescharacteristic
612C22×C3C25×C311yescharacteristic
613C2×D3—22no—
614C2×D3—22no—
615C2×D3—22no—
616C2×D3—44no—
617C3×C4—22no—
618C3×C4—24no—
619C3×C4—22no—
620C3×C4—24no—
621C3×C4—24no—
622C3×C4—38no—
623C3×C4—42no—
624C3×C4—44no—
625C3×C4—62no—
626C3×C4—64no—
627C3×C4—62no—
628C3×C4—62no—
629C3×C4C2×D3×D414yes—
630C3×C4C22×C3×D414yes—
631Dic3—24no—
632Dic3—22no—
633Dic3—22no—
634Dic3—22no—
635Dic3C22×C3×D418yes—
636C32C2×#54811yescharacteristic, complemented, Sylow
637C23—22no—
638C23—22no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—32no—
643C23—62no—
644C23—62no—
645C23—62no—
646C23C3×#23714yescomplemented
647C23C23×C3×D314yes—
648C23C23×C3×D312yes—
649C23C23×C3×D311yescharacteristic
650Q8—316no—
651Q8—616no—
652Q8—68no—
653D4—216no—
654D4—28no—
655D4—616no—
656D4—68no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—28no—
660C2×C4—38no—
661C2×C4—34no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—34no—
665C2×C4—32no—
666C2×C4—616no—
667C2×C4—616no—
668C2×C4—62no—
669C2×C4—64no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—68no—
673C2×C4C3×D3×D414yes—
674C2×C4C23×C3×D314yes—
675C2×C4C23×C3×D312yes—
676C2×C4C23×C3×D312yes—
677C2×C3—24no—
678C2×C3—24no—
679C2×C3—24no—
680C2×C3—21no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—44no—
684C2×C3—44no—
685C2×C3—44no—
686C2×C3—84no—
687C2×C3—122no—
688C2×C3#559814yesdirect product factor
689C2×C3C3×#54814yescomplemented
690C2×C3C22×D3×D411yescharacteristic
691C2×C3C22×#23711yescharacteristic
692C2×C3C2×#101011yescharacteristic
693C2×C3C23×C3×D411yescharacteristic
694C2×C3C22×C3×#4111yescharacteristic
695C2×C3C2×C3×2−1+411yescharacteristic
696D3—42no—
697C22—28no—
698C22—22no—
699C22—22no—
700C22—24no—
701C22—24no—
702C22—24no—
703C22—48no—
704C22—62no—
705C22—62no—
706C22—62no—
707C22—124no—
708C22C2×C3×D3×D412yes—
709C22C2×C3×#23712yes—
710C22C2×C3×#23714yescomplemented
711C22C3×#101012yes—
712C22C24×C3×D311yescharacteristic
713C4—22no—
714C4—24no—
715C4—38no—
716C4—62no—
717C4—64no—
718C4—62no—
719C4—62no—
720C4C2×C3×D3×D414yes—
721C3—21no—
722C3C2×#559811yescharacteristic, direct product factor
723C3C2×C3×#54811yescharacteristic, complemented
724C2—24no—
725C2—44no—
726C2—122no—
727C2C3×#559814yesdirect product factor
728C2C22×C3×D3×D411yescharacteristic
729C2C22×C3×#23711yescharacteristic
730C2C2×C3×#101011yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×#121C2
socleC23×C32C24
hypercenterC2×C3×#121D3
hypocenterC3C2×C3×#548
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C23×C3×Dic6C2semidirect
3. C2×C32×#121C2semidirect
4. C2×C3×#939C2semidirect
5. C2×C3×#936C2semidirect
6. C2×C3×D4×Dic3C2semidirect
7. C2×C3×C4×#67C2semidirect
8. C3×#5598C2direct (N × H)
9. C2×C3×#897C2semidirect
10. C2×C3×#887C2semidirect
11. C2×C3×#885C2semidirect
12. C2×C3×#878C2semidirect
14. C2×#5598C3direct (N × H)
23. C2×C3×#237C22semidirect
29. C22×C3×Dic6C22semidirect
30. C32×#121C22semidirect
36. C3×#939C22semidirect
37. C3×#936C22semidirect
38. C3×D4×Dic3C22semidirect
39. C3×C4×#67C22semidirect
47. C3×#897C22semidirect
48. C3×#887C22semidirect
49. C3×#885C22semidirect
50. C3×#878C22semidirect
53. C22×#237C2×C3semidirect
54. C23×Dic6C2×C3semidirect
62. C2×C3×#121D3semidirect
63. C2×C3×#121C2×C3semidirect
67. C2×#939C2×C3semidirect
68. C2×#936C2×C3semidirect
69. C2×D4×Dic3C2×C3semidirect
70. C2×C4×#67C2×C3semidirect
71. #5598C2×C3direct (N × H)
72. C2×#897C2×C3semidirect
73. C2×#887C2×C3semidirect
74. C2×#885C2×C3semidirect
75. C2×#878C2×C3semidirect
107. C2×C3×Dic6D4semidirect
150. C2×#237C22×C3semidirect
156. C22×Dic6C22×C3semidirect
163. C3×#121C2×D3semidirect
164. C3×#121C22×C3semidirect
187. #939C22×C3semidirect
188. #936C22×C3semidirect
189. D4×Dic3C22×C3semidirect
190. C4×#67C22×C3semidirect
198. #897C22×C3semidirect
199. #887C22×C3semidirect
200. #885C22×C3semidirect
201. #878C22×C3semidirect
207. C23×C32#41semidirect
241. C3×Dic6C2×D4semidirect
250. C2×#121C3×D3semidirect
331. C2×Dic6C3×D4semidirect
370. C22×C32C2×#41semidirect
405. #121C2×C3×D3semidirect
444. C23×C3#237semidirect
445. C23×C3C3×#41semidirect
518. Dic6C2×C3×D4semidirect
521. C2×C32#548semidirect
605. C22×C3C2×#237semidirect
609. C22×C3C2×C3×#41semidirect
636. C32C2×#548semidirect
646. C23C3×#237semidirect
688. C2×C3#5598direct (N × H)
689. C2×C3C3×#548semidirect
710. C22C2×C3×#237semidirect
722. C3C2×#5598direct (N × H)
723. C3C2×C3×#548semidirect
727. C2C3×#5598direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C23×C3×Dic62
C2×C32×#1212
C2×C3×#9392
C2×C3×#9362
C2×C3×D4×Dic32
C2×C3×C4×#672
C3×#55982
C2×C3×#8972
C2×C3×#8872
C2×C3×#8852
C2×C3×#8782
C2×C3×#5483
C2×#55983