Finite Group Databasebeta

← C2×#11722475 #13164705

Subgroups — C2×#11722475 #13164705

Order 1728.

2906 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×C4×C3⋊D9C211yesmaximal, characteristic, complemented
2C2×C9×#235C211yesmaximal, characteristic, complemented
3C2×C3×#3697C211yesmaximal, characteristic, complemented
4C2×#88668C212yesmaximal, complemented
5C2×#88663C212yesmaximal, complemented
6#11722475C2116yesmaximal, direct product factor
7C2×#88646C211yesmaximal, characteristic, complemented
8C2×C4×D3×D9C212yesmaximal, complemented
9C2×#88640C212yesmaximal, complemented
10C2×#88639C211yesmaximal, characteristic, complemented
11C2×(C3⋊D9)⋊Q8C211yesmaximal, characteristic, complemented
12C2×#88634C211yesmaximal, characteristic, complemented
13C2×#64306—31nomaximal
14C2×#41×D9—31nomaximal
15C23×C3⋊D9C2211yescharacteristic
16C22×D3×D9C2212yes—
17C22×C3×C4×C9C2211yescharacteristic, complemented
18C22×C3⋊Dic9C2211yescharacteristic, complemented
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C4×C3⋊D9C2218yescomplemented
22C2×C4×C3⋊D9C2211yescharacteristic, complemented
23C2×C4×C3⋊D9C2211yescharacteristic, complemented
24C2×C9×#67C2212yescomplemented
25C2×C3×#611C2212yescomplemented
26C9×#235C2218yescomplemented
27C2×C9×D12C2211yescharacteristic, complemented
28C2×C4×D3×C9C2212yescomplemented
29C3×#3697C2218yescomplemented
30C2×C3×D36C2211yescharacteristic, complemented
31C2×C3×C4×D9C2212yescomplemented
32C2×C9×Dic6C2211yescharacteristic, complemented
33C2×C3×Dic18C2211yescharacteristic, complemented
34#88668C22116yescomplemented
35C2×#6195C2212yescomplemented
36C2×#6194C2212yescomplemented
37#88663C22116yescomplemented
38C2×D3×Dic9C2212yescomplemented
39C2×#6192C2212yescomplemented
40C2×(C3⋊D9)⋊C4C2212yes—
41C2×Dic3×D9C2212yescomplemented
42C2×#6189C2212yescomplemented
43#88646C2218yescomplemented
44C4×D3×D9C22116yescomplemented
45#88640C22116yescomplemented
46#88639C2218yescomplemented
47(C3⋊D9)⋊Q8C2218yescomplemented
48#88634C2218yescomplemented
49C22×C4×C3⋊D3—31no—
50C2×C3×#235—31no—
51C2×C3×#235D311yescharacteristic
52C2×#3811—32no—
53C2×#3805—32no—
54#64306—316no—
55C2×#3802—31no—
56C2×C4×D32—32no—
57C2×#3798—32no—
58C2×#3797—31no—
59C2×#3796—31no—
60C2×#3796—31no—
61C2×C9×#41—31no—
62#41×D9—316no—
63C2×#3701—31no—
64C2×Q8×D9—31no—
65C2×#3699—32no—
66C2×#3699—31no—
67C2×D4×D9—32no—
68C2×D4×D9—31no—
69C2×#3697—32no—
70C2×#3697D311yescharacteristic, complemented
71C22×C4×D9—31no—
72C22×C4×D9—32no—
73C22×C4×D9—61no—
74C23×C3×C9C2311yescharacteristic
75C22×C3⋊D9—24no—
76C22×C3⋊D9C2311yescharacteristic
77C22×C3⋊D9C2314yes—
78C22×C3⋊D9C2311yescharacteristic
79C22×D3×C9C2312yes—
80C22×C3×D9C2312yes—
81C2×D3×D9—28no—
82C2×D3×D9C2318yes—
83C2×C3×C4×C9C2311yescharacteristic
84C2×C3×C4×C9C2311yescharacteristic
85C2×C3×C4×C9C2314yescomplemented
86C2×C3⋊Dic9C2311yescharacteristic
87C2×C3⋊Dic9C2311yescharacteristic
88C2×C3⋊Dic9C2314yescomplemented
89C4×C3⋊D9C2314yes—
90C4×C3⋊D9C2314yes—
91C4×C3⋊D9C2314yescomplemented
92C4×C3⋊D9C2314yescomplemented
93C9×#67C2318yescomplemented
94C3×#611C2318yescomplemented
95C2×C9×Dic3C2312yes—
96C2×C3×Dic9C2312yes—
97C9×D12C2314yescomplemented
98C4×D3×C9C2318yescomplemented
99C3×D36C2314yescomplemented
100C3×C4×D9C2318yescomplemented
101C9×Dic6C2314yescomplemented
102C3×Dic18C2314yescomplemented
103#6195C2318yescomplemented
104#6194C2318yescomplemented
105D3×Dic9C2318yescomplemented
106#6192C2318yescomplemented
107(C3⋊D9)⋊C4C2318yes—
108Dic3×D9C2318yescomplemented
109#6189C2318yescomplemented
110C2×D3×#41—91no—
111C2×D3×#41—91no—
112C23×C3⋊D3—31no—
113C22×D32—32no—
114C22×C32×C4C2×D311yescharacteristic
115C22×C3⋊Dic3—31no—
116C2×C4×C3⋊D3—31no—
117C2×C4×C3⋊D3—31no—
118C2×C4×C3⋊D3—31no—
119C2×C4×C3⋊D3—31no—
120C2×C4×C3⋊D3—38no—
121C2×C3×#67—32no—
122C2×C3×#67C2×D312yes—
123C3×#235—38no—
124C3×#235C2×D318yes—
125C2×C3×D12—31no—
126C2×C3×D12C2×D311yescharacteristic
127C2×C3×C4×D3—32no—
128C2×C3×C4×D3C2×D312yes—
129C2×C3×Dic6—31no—
130C2×C3×Dic6C2×D311yescharacteristic
131#3811—316no—
132C2×#627—32no—
133C2×#626—32no—
134C2×#626—32no—
135C2×#625—32no—
136C2×#624—32no—
137#3805—316no—
138C2×D3×Dic3—32no—
139C2×D3×Dic3—32no—
140#3802—38no—
141C4×D32—316no—
142#3798—316no—
143#3797—38no—
144#3796—38no—
145#3796—38no—
146C23×D9—31no—
147C23×D9—32no—
148C23×D9—61no—
149C9×#41—38no—
150C2×Q8×C9—31no—
151C2×D4×C9—32no—
152C2×D4×C9—31no—
153C22×C4×C9—21no—
154C22×C4×C9—32no—
155C22×C4×C9C2×D311yescharacteristic, complemented
156C2×#611—32no—
157C2×#611—32no—
158C2×#611C2×D312yescomplemented
159C22×Dic9—31no—
160C22×Dic9—32no—
161C22×Dic9—61no—
162#3701—38no—
163Q8×D9—38no—
164#3699—316no—
165#3699—38no—
166D4×D9—316no—
167D4×D9—38no—
168#3697—316no—
169#3697C2×D318yescomplemented
170C2×D36—32no—
171C2×D36C2×D311yescharacteristic, complemented
172C2×C4×D9—32no—
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9—31no—
176C2×C4×D9—31no—
177C2×C4×D9—38no—
178C2×C4×D9—32no—
179C2×C4×D9—316no—
180C2×C4×D9—61no—
181C2×C4×D9—61no—
182C2×C4×D9—68no—
183C2×C4×D9—61no—
184C2×C4×D9—61no—
185C2×C4×D9C2×D312yescomplemented
186C2×Dic18—32no—
187C2×Dic18C2×D311yescharacteristic, complemented
188C22×C3×C9—22no—
189C22×C3×C9C2412yes—
190C22×C3×C9C2411yescharacteristic
191C2×C3⋊D9—22no—
192C2×C3⋊D9—28no—
193C2×C3⋊D9#4114yescomplemented
194C2×C3⋊D9C2412yes—
195C2×C3⋊D9C2412yes—
196C2×D3×C9—24no—
197C2×D3×C9C2414yes—
198C2×C3×D9—24no—
199C2×C3×D9C2414yes—
200D3×D9—216no—
201C3×C4×C9C2412yes—
202C3×C4×C9C2412yes—
203C3⋊Dic9C2412yes—
204C3⋊Dic9C2412yes—
205C9×Dic3C2414yes—
206C3×Dic9C2414yes—
207C2×C3×#41—31no—
208C2×C3×#41—91no—
209D3×#41—916no—
210D3×#41—916no—
211C2×#239—91no—
212C2×#239—91no—
213C2×D3×Q8—91no—
214C2×D3×Q8—91no—
215C2×#237—91no—
216C2×#237—92no—
217C2×#237—92no—
218C2×#237—91no—
219C2×D3×D4—91no—
220C2×D3×D4—92no—
221C2×D3×D4—92no—
222C2×D3×D4—91no—
223C2×#235—31no—
224C2×#235—92no—
225C2×#235—92no—
226C2×#235D911yescharacteristic, complemented
227C22×C4×D3—92no—
228C22×C4×D3—91no—
229C22×C4×D3—91no—
230C22×C4×D3—92no—
231C22×C4×D3—181no—
232C23×C32C22×D311yescharacteristic
233C22×C3⋊D3—31no—
234C22×C3⋊D3—31no—
235C22×C3⋊D3—34no—
236C22×C3⋊D3—64no—
237C22×C3×D3—32no—
238C22×C3×D3C22×D312yes—
239C2×D32—38no—
240C2×D32—68no—
241C2×C32×C4C22×D311yescharacteristic
242C2×C32×C4C22×D311yescharacteristic
243C2×C32×C4C22×D314yes—
244C2×C3⋊Dic3—31no—
245C2×C3⋊Dic3—31no—
246C2×C3⋊Dic3—34no—
247C4×C3⋊D3—34no—
248C4×C3⋊D3—34no—
249C4×C3⋊D3—34no—
250C4×C3⋊D3—34no—
251C3×#67—38no—
252C3×#67C22×D318yes—
253C2×C3×Dic3—32no—
254C2×C3×Dic3C22×D312yes—
255C3×D12—34no—
256C3×D12C22×D314yes—
257C3×C4×D3—38no—
258C3×C4×D3C22×D318yes—
259C3×Dic6—34no—
260C3×Dic6C22×D314yes—
261#627—38no—
262#626—38no—
263#626—38no—
264#625—38no—
265#624—38no—
266D3×Dic3—38no—
267D3×Dic3—38no—
268C23×C9—21no—
269C23×C9—32no—
270C23×C9C22×D311yescharacteristic
271C22×D9—31no—
272C22×D9—31no—
273C22×D9—34no—
274C22×D9—38no—
275C22×D9—61no—
276C22×D9—61no—
277C22×D9—64no—
278C22×D9—68no—
279C22×D9—64no—
280C22×D9—68no—
281C22×D9C22×D312yes—
282Q8×C9—34no—
283D4×C9—38no—
284D4×C9—34no—
285C2×C4×C9—21no—
286C2×C4×C9—21no—
287C2×C4×C9—24no—
288C2×C4×C9—32no—
289C2×C4×C9—38no—
290C2×C4×C9C22×D311yescharacteristic
291C2×C4×C9C22×D311yescharacteristic
292C2×C4×C9C22×D314yescomplemented
293#611—38no—
294#611—38no—
295#611C22×D318yescomplemented
296C2×Dic9—31no—
297C2×Dic9—31no—
298C2×Dic9—34no—
299C2×Dic9—38no—
300C2×Dic9—61no—
301C2×Dic9—61no—
302C2×Dic9—64no—
303C2×Dic9C22×D312yes—
304D36—38no—
305D36C22×D314yescomplemented
306C4×D9—38no—
307C4×D9—34no—
308C4×D9—34no—
309C4×D9—34no—
310C4×D9—34no—
311C4×D9—38no—
312C4×D9—64no—
313C4×D9—64no—
314C4×D9—64no—
315C4×D9—64no—
316C4×D9C22×D318yescomplemented
317Dic18—38no—
318Dic18C22×D314yescomplemented
319C22×#41—271noSylow
320C2×C3×C9—22no—
321C2×C3×C9C2×#4112yescomplemented
322C2×C3×C9C2511yescharacteristic
323C3⋊D9—22no—
324C3⋊D9C2×#4114yescomplemented
325D3×C9—24no—
326C3×D9—24no—
327C23×D3—92no—
328C23×D3—91no—
329C23×D3—91no—
330C23×D3—92no—
331C23×D3—181no—
332C3×#41—38no—
333C3×#41—98no—
334C2×C3×Q8—31no—
335C2×C3×Q8—91no—
336C2×C3×D4—32no—
337C2×C3×D4—31no—
338C2×C3×D4—92no—
339C2×C3×D4—91no—
340C22×C3×C4—21no—
341C22×C3×C4—32no—
342C22×C3×C4—92no—
343C22×C3×C4C2×D911yescharacteristic, complemented
344C22×C3×C4D3211yescharacteristic
345C2×#67—32no—
346C2×#67—92no—
347C2×#67—92no—
348C2×#67—92no—
349C2×#67—92no—
350C2×#67C2×D912yescomplemented
351C22×Dic3—92no—
352C22×Dic3—91no—
353C22×Dic3—91no—
354C22×Dic3—92no—
355C22×Dic3—181no—
356#239—98no—
357#239—98no—
358D3×Q8—98no—
359D3×Q8—98no—
360#237—98no—
361#237—916no—
362#237—916no—
363#237—98no—
364D3×D4—98no—
365D3×D4—916no—
366D3×D4—916no—
367D3×D4—98no—
368#235—38no—
369#235—916no—
370#235—916no—
371#235C2×D918yescomplemented
372C2×D12—31no—
373C2×D12—92no—
374C2×D12—92no—
375C2×D12C2×D911yescharacteristic, complemented
376C2×C4×D3—32no—
377C2×C4×D3—916no—
378C2×C4×D3—92no—
379C2×C4×D3—92no—
380C2×C4×D3—92no—
381C2×C4×D3—91no—
382C2×C4×D3—91no—
383C2×C4×D3—91no—
384C2×C4×D3—91no—
385C2×C4×D3—98no—
386C2×C4×D3—91no—
387C2×C4×D3—91no—
388C2×C4×D3—91no—
389C2×C4×D3—91no—
390C2×C4×D3—98no—
391C2×C4×D3—92no—
392C2×C4×D3—916no—
393C2×C4×D3—181no—
394C2×C4×D3—181no—
395C2×C4×D3—181no—
396C2×C4×D3—181no—
397C2×C4×D3—188no—
398C2×C4×D3C2×D912yescomplemented
399C2×Dic6—31no—
400C2×Dic6—92no—
401C2×Dic6—92no—
402C2×Dic6C2×D911yescharacteristic, complemented
403C22×C32—22no—
404C22×C32C23×D312yes—
405C22×C32C23×D311yescharacteristic
406C2×C3⋊D3—34no—
407C2×C3⋊D3—32no—
408C2×C3⋊D3—32no—
409C2×C3⋊D3—68no—
410C2×C3⋊D3—62no—
411C2×C3×D3—24no—
412C2×C3×D3—34no—
413C2×C3×D3—64no—
414C2×C3×D3C23×D314yes—
415D32—616no—
416C32×C4C23×D312yes—
417C32×C4C23×D312yes—
418C3⋊Dic3—32no—
419C3⋊Dic3—32no—
420C3×Dic3—34no—
421C3×Dic3C23×D314yes—
422C22×C9—24no—
423C22×C9—22no—
424C22×C9—22no—
425C22×C9—21no—
426C22×C9—34no—
427C22×C9—64no—
428C22×C9C23×D312yes—
429C22×C9C23×D311yescharacteristic
430C2×D9—24no—
431C2×D9—34no—
432C2×D9—32no—
433C2×D9—32no—
434C2×D9—64no—
435C2×D9—62no—
436C2×D9—62no—
437C2×D9—616no—
438C2×D9—68no—
439C2×D9—616no—
440C2×D9—64no—
441C2×D9—62no—
442C2×D9C23×D314yes—
443C4×C9—22no—
444C4×C9—22no—
445C4×C9—34no—
446C4×C9C23×D312yes—
447C4×C9C23×D312yes—
448Dic9—32no—
449Dic9—32no—
450Dic9—62no—
451Dic9—62no—
452Dic9C23×D314yes—
453C2×#41—31no—
454C2×#41—91no—
455C2×#41—272no—
456C2×#41—272no—
457C2×#41—271no—
458C2×#41—271no—
459C2×#41—2716no—
460C22×Q8—271no—
461C22×D4—272no—
462C22×D4—271no—
463C23×C4—272no—
464C23×C4—271no—
465C3×C9C22×#4111yescharacteristic, complemented, Sylow
466C23×C3—21no—
467C23×C3—32no—
468C23×C3—92no—
469C23×C3C22×D911yescharacteristic
470C23×C3C2×D3211yescharacteristic
471C22×D3—32no—
472C22×D3—98no—
473C22×D3—91no—
474C22×D3—91no—
475C22×D3—91no—
476C22×D3—94no—
477C22×D3—91no—
478C22×D3—94no—
479C22×D3—98no—
480C22×D3—181no—
481C22×D3—181no—
482C22×D3—184no—
483C22×D3—188no—
484C22×D3—188no—
485C22×D3—184no—
486C22×D3—184no—
487C22×D3—188no—
488C22×D3C22×D912yes—
489C3×Q8—34no—
490C3×Q8—94no—
491C3×D4—38no—
492C3×D4—34no—
493C3×D4—98no—
494C3×D4—94no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—24no—
498C2×C3×C4—32no—
499C2×C3×C4—38no—
500C2×C3×C4—92no—
501C2×C3×C4—98no—
502C2×C3×C4C22×D911yescharacteristic
503C2×C3×C4C22×D911yescharacteristic
504C2×C3×C4C22×D914yescomplemented
505C2×C3×C4C2×D3211yescharacteristic
506C2×C3×C4C2×D3211yescharacteristic
507C2×C3×C4C2×D3214yes—
508#67—38no—
509#67—98no—
510#67—98no—
511#67—98no—
512#67—98no—
513#67C22×D918yescomplemented
514C2×Dic3—32no—
515C2×Dic3—98no—
516C2×Dic3—91no—
517C2×Dic3—91no—
518C2×Dic3—94no—
519C2×Dic3—91no—
520C2×Dic3—91no—
521C2×Dic3—94no—
522C2×Dic3—98no—
523C2×Dic3—181no—
524C2×Dic3—181no—
525C2×Dic3—184no—
526C2×Dic3C22×D912yes—
527D12—34no—
528D12—98no—
529D12—98no—
530D12C22×D914yescomplemented
531C4×D3—38no—
532C4×D3—98no—
533C4×D3—98no—
534C4×D3—98no—
535C4×D3—94no—
536C4×D3—94no—
537C4×D3—94no—
538C4×D3—94no—
539C4×D3—94no—
540C4×D3—94no—
541C4×D3—94no—
542C4×D3—94no—
543C4×D3—98no—
544C4×D3—184no—
545C4×D3—184no—
546C4×D3—184no—
547C4×D3—184no—
548C4×D3C22×D918yescomplemented
549Dic6—34no—
550Dic6—98no—
551Dic6—98no—
552Dic6C22×D914yescomplemented
553C2×C32—22no—
554C2×C32D3×#4112yes—
555C2×C32C24×D311yescharacteristic
556C3⋊D3—34no—
557C3⋊D3—62no—
558C3×D3—24no—
559C3×D3—64no—
560C2×C9—24no—
561C2×C9—22no—
562C2×C9—22no—
563C2×C9—21no—
564C2×C9—64no—
565C2×C9D3×#4112yescomplemented
566C2×C9C24×D311yescharacteristic
567D9—24no—
568D9—34no—
569D9—64no—
570D9—64no—
571D9—62no—
572C24—272no—
573C24—271no—
574#41—38no—
575#41—98no—
576#41—2716no—
577#41—2716no—
578#41—278no—
579#41—278no—
580C2×Q8—31no—
581C2×Q8—91no—
582C2×Q8—272no—
583C2×Q8—278no—
584C2×D4—32no—
585C2×D4—31no—
586C2×D4—92no—
587C2×D4—91no—
588C2×D4—272no—
589C2×D4—272no—
590C2×D4—2716no—
591C2×D4—278no—
592C2×D4—272no—
593C22×C4—32no—
594C22×C4—92no—
595C22×C4—272no—
596C22×C4—2716no—
597C22×C4—272no—
598C22×C4—272no—
599C22×C4—271no—
600C22×C4—271no—
601C22×C4—271no—
602C22×C4—271no—
603C22×C4—271no—
604C22×C4—278no—
605C22×C4D3×D911yescharacteristic, complemented
606C22×C3—24no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—21no—
611C22×C3—34no—
612C22×C3—64no—
613C22×C3—94no—
614C22×C3—184no—
615C22×C3C23×D912yes—
616C22×C3C23×D911yescharacteristic
617C22×C3C22×D3212yes—
618C22×C3C22×D3211yescharacteristic
619C2×D3—24no—
620C2×D3—34no—
621C2×D3—64no—
622C2×D3—94no—
623C2×D3—92no—
624C2×D3—92no—
625C2×D3—94no—
626C2×D3—92no—
627C2×D3—92no—
628C2×D3—182no—
629C2×D3—182no—
630C2×D3—184no—
631C2×D3—1816no—
632C2×D3—1816no—
633C2×D3—188no—
634C2×D3—188no—
635C2×D3—1816no—
636C2×D3—184no—
637C2×D3—182no—
638C2×D3—182no—
639C2×D3C23×D914yes—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—34no—
643C3×C4—94no—
644C3×C4C23×D912yes—
645C3×C4C23×D912yes—
646C3×C4C22×D3212yes—
647C3×C4C22×D3212yes—
648Dic3—34no—
649Dic3—92no—
650Dic3—92no—
651Dic3—92no—
652Dic3—92no—
653Dic3—182no—
654Dic3—182no—
655Dic3C23×D914yes—
656C32C2×D3×#4111yescharacteristic
657C9—21no—
658C9C2×D3×#4111yescharacteristic, complemented
659C23—32no—
660C23—92no—
661C23—278no—
662C23—271no—
663C23—274no—
664C23—271no—
665C23—544no—
666C23—548no—
667C23C2×D3×D911yescharacteristic
668Q8—34no—
669Q8—94no—
670Q8—278no—
671D4—38no—
672D4—34no—
673D4—98no—
674D4—94no—
675D4—278no—
676D4—278no—
677D4—278no—
678C2×C4—32no—
679C2×C4—38no—
680C2×C4—92no—
681C2×C4—98no—
682C2×C4—278no—
683C2×C4—278no—
684C2×C4—278no—
685C2×C4—271no—
686C2×C4—271no—
687C2×C4—274no—
688C2×C4—274no—
689C2×C4—274no—
690C2×C4—274no—
691C2×C4—274no—
692C2×C4C2×D3×D911yescharacteristic
693C2×C4C2×D3×D911yescharacteristic
694C2×C4C2×D3×D914yescomplemented
695C2×C3—24no—
696C2×C3—22no—
697C2×C3—22no—
698C2×C3—21no—
699C2×C3—22no—
700C2×C3—64no—
701C2×C3—184no—
702C2×C3#41×D912yescomplemented
703C2×C3C24×D911yescharacteristic
704C2×C3#6430612yes—
705C2×C3C23×D3211yescharacteristic
706D3—24no—
707D3—64no—
708D3—94no—
709D3—94no—
710D3—184no—
711D3—184no—
712D3—182no—
713D3—182no—
714C22—22no—
715C22—34no—
716C22—64no—
717C22—94no—
718C22—184no—
719C22—272no—
720C22—274no—
721C22—272no—
722C22—548no—
723C22—5416no—
724C22—542no—
725C22C22×D3×D912yes—
726C22C22×D3×D911yescharacteristic
727C4—34no—
728C4—94no—
729C4—272no—
730C4—272no—
731C4C22×D3×D912yes—
732C4C22×D3×D912yes—
733C3—21no—
734C3C2×#41×D911yescharacteristic, complemented
735C3C2×#6430611yescharacteristic
736C2—22no—
737C2—64no—
738C2—184no—
739C2—274no—
740C2—542no—
741C2#1172247512yesdirect product factor
742C2C23×D3×D911yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutator, cosocleC2×C3×C9C25
FrattiniC2×C3C23×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
hypercenterC22×C4D3×D9
hypocenterC3×C9C22×#41
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C3⋊D9C2semidirect
2. C2×C9×#235C2semidirect
3. C2×C3×#3697C2semidirect
4. C2×#88668C2semidirect
5. C2×#88663C2semidirect
6. #11722475C2direct (N × H)
7. C2×#88646C2semidirect
8. C2×C4×D3×D9C2semidirect
9. C2×#88640C2semidirect
10. C2×#88639C2semidirect
11. C2×(C3⋊D9)⋊Q8C2semidirect
12. C2×#88634C2semidirect
17. C22×C3×C4×C9C22semidirect
18. C22×C3⋊Dic9C22semidirect
21. C2×C4×C3⋊D9C22semidirect
22. C2×C4×C3⋊D9C22semidirect
23. C2×C4×C3⋊D9C22semidirect
24. C2×C9×#67C22semidirect
25. C2×C3×#611C22semidirect
26. C9×#235C22semidirect
27. C2×C9×D12C22semidirect
28. C2×C4×D3×C9C22semidirect
29. C3×#3697C22semidirect
30. C2×C3×D36C22semidirect
31. C2×C3×C4×D9C22semidirect
32. C2×C9×Dic6C22semidirect
33. C2×C3×Dic18C22semidirect
34. #88668C22semidirect
35. C2×#6195C22semidirect
36. C2×#6194C22semidirect
37. #88663C22semidirect
38. C2×D3×Dic9C22semidirect
39. C2×#6192C22semidirect
41. C2×Dic3×D9C22semidirect
42. C2×#6189C22semidirect
43. #88646C22semidirect
44. C4×D3×D9C22semidirect
45. #88640C22semidirect
46. #88639C22semidirect
47. (C3⋊D9)⋊Q8C22semidirect
48. #88634C22semidirect
70. C2×#3697D3semidirect
85. C2×C3×C4×C9C23semidirect
88. C2×C3⋊Dic9C23semidirect
91. C4×C3⋊D9C23semidirect
92. C4×C3⋊D9C23semidirect
93. C9×#67C23semidirect
94. C3×#611C23semidirect
97. C9×D12C23semidirect
98. C4×D3×C9C23semidirect
99. C3×D36C23semidirect
100. C3×C4×D9C23semidirect
101. C9×Dic6C23semidirect
102. C3×Dic18C23semidirect
103. #6195C23semidirect
104. #6194C23semidirect
105. D3×Dic9C23semidirect
106. #6192C23semidirect
108. Dic3×D9C23semidirect
109. #6189C23semidirect
155. C22×C4×C9C2×D3semidirect
158. C2×#611C2×D3semidirect
169. #3697C2×D3semidirect
171. C2×D36C2×D3semidirect
185. C2×C4×D9C2×D3semidirect
187. C2×Dic18C2×D3semidirect
193. C2×C3⋊D9#41semidirect
226. C2×#235D9semidirect
292. C2×C4×C9C22×D3semidirect
295. #611C22×D3semidirect
305. D36C22×D3semidirect
316. C4×D9C22×D3semidirect
318. Dic18C22×D3semidirect
321. C2×C3×C9C2×#41semidirect
324. C3⋊D9C2×#41semidirect
343. C22×C3×C4C2×D9semidirect
350. C2×#67C2×D9semidirect
371. #235C2×D9semidirect
375. C2×D12C2×D9semidirect
398. C2×C4×D3C2×D9semidirect
402. C2×Dic6C2×D9semidirect
465. C3×C9C22×#41semidirect
504. C2×C3×C4C22×D9semidirect
513. #67C22×D9semidirect
530. D12C22×D9semidirect
548. C4×D3C22×D9semidirect
552. Dic6C22×D9semidirect
565. C2×C9D3×#41semidirect
605. C22×C4D3×D9semidirect
658. C9C2×D3×#41semidirect
694. C2×C4C2×D3×D9semidirect
702. C2×C3#41×D9semidirect
734. C3C2×#41×D9semidirect
741. C2#11722475direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C3⋊D92
C2×C9×#2352
C2×C3×#36972
C2×#886682
C2×#886632
#117224752
C2×#886462
C2×C4×D3×D92
C2×#886402
C2×#886392
C2×(C3⋊D9)⋊Q82
C2×#886342
C2×#643063
C2×#41×D93