Finite Group Databasebeta

← D9×#67⋊C4 #13148391

Subgroups — D9×#67⋊C4 #13148391

Order 1728.

1372 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D9×#67C211yesmaximal, characteristic
2C22×Dic3×D9C211yesmaximal, characteristic, complemented
3C2×C4×D3×D9C211yesmaximal, characteristic, complemented
4#11721727C211yesmaximal, characteristic, complemented
5C9×#67⋊C4C211yesmaximal, characteristic, complemented
6C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
7#67⋊Dic9C211yesmaximal, characteristic, complemented
8#11721240C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721028C211yesmaximal, characteristic, complemented
11#11720978C211yesmaximal, characteristic, complemented
12#11720977C211yesmaximal, characteristic, complemented
13#11720976C211yesmaximal, characteristic, complemented
14D9×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C4×Dic3×D9C211yesmaximal, characteristic, complemented
16D3×#67⋊C4—31nomaximal
17C4×D4×D9—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C22×C3⋊Dic9C2211yescharacteristic, complemented
22C2×C4×C3⋊D9C2211yescharacteristic, complemented
23C2×C9×#67C2211yescharacteristic
24C22×C9×Dic3C2211yescharacteristic, complemented
25C2×C4×D3×C9C2211yescharacteristic, complemented
26C2×C3×C4×D9C2211yescharacteristic
27C2×C3×C4×D9C2211yescharacteristic
28D9×#67C418yescomplemented
29C2×#6194C2211yescharacteristic
30C2×D3×Dic9C2211yescharacteristic, complemented
31C2×#6192C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
33C2×Dic3×D9—24no—
34C2×Dic3×D9C2211yescharacteristic
35C2×Dic3×D9C2211yescharacteristic
36C2×Dic3×D9C2211yescharacteristic
37C2×Dic3×D9C2211yescharacteristic, complemented
38C2×Dic3×D9C2211yescharacteristic, complemented
39C4×D3×D9—24no—
40C3×C9×C22⋊C4C2211yescharacteristic, complemented
41#88536C2211yescharacteristic, complemented
42#88534C2211yescharacteristic, complemented
43C4×C3⋊Dic9C2211yescharacteristic, complemented
44C3×#3676C2211yescharacteristic, complemented
45C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
48C9×Dic3⋊C4C2211yescharacteristic, complemented
49C4×C9×Dic3C2211yescharacteristic, complemented
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51#88445C2211yescharacteristic, complemented
52Dic3⋊Dic9C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55Dic3×Dic9C2211yescharacteristic, complemented
56C2×D3×#67—31no—
57C22×D3×Dic3—31no—
58C2×C4×D32—31no—
59#64090—31no—
60C3×#67⋊C4D311yescharacteristic
61C3×D3×C22⋊C4—31no—
62#67⋊Dic3—31no—
63#63952—31no—
64D3×(C2×D3)⋊C4—31no—
65#63902—31no—
66#63881—31no—
67#63880—31no—
68#63879—31no—
69D3×Dic3⋊C4—31no—
70C4×D3×Dic3—31no—
71C2×D4×D9—31no—
72C22×C4×D9—31no—
73C22×C4×D9—31no—
74C4×D4×C9—31no—
75D4×Dic9—31no—
76C4×#611—31no—
77C4×#611—31no—
78#63455—31no—
79C4⋊C4×D9—31no—
80#611⋊C4—31no—
81#611⋊C4—31no—
82#611⋊C4—61no—
83C22⋊C4×D9—31no—
84C22⋊C4×D9D311yescharacteristic, complemented
85C4×D36—31no—
86C42×D9—31no—
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9—22no—
91C22×C3×D9—22no—
92C22×C3×D9C2×C414yescomplemented
93C22×C3×D9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9C2×C414yescomplemented
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100#6233C2×C414yescomplemented
101C2×C3⋊Dic9—22no—
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C4×C3⋊D9—22no—
106C9×#67C2×C414yescomplemented
107C2×C9×Dic3—22no—
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C9×Dic3C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C4×D3×C9—22no—
114C3×C4×D9—22no—
115C3×C4×D9—22no—
116#6194C2×C414yescomplemented
117D3×Dic9—22no—
118#6192C2×C414yescomplemented
119(C3⋊D9)⋊C4—22no—
120Dic3×D9—22no—
121Dic3×D9—22no—
122Dic3×D9—22no—
123Dic3×D9C2×C414yescomplemented
124Dic3×D9D414yescomplemented
125C4×D3×D4—91no—
126C2×#67⋊C4—91no—
127C23×C3×D3—31no—
128C22×D32—31no—
129C2×#638—31no—
130C22×C3⋊Dic3—31no—
131C2×C4×C3⋊D3—31no—
132C2×C3×#67C2×D311yescharacteristic
133C22×C3×Dic3C2×D311yescharacteristic
134C2×C3×C4×D3—31no—
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3C2×D311yescharacteristic
137D3×#67—38no—
138C2×#626—31no—
139C2×#625—31no—
140C2×#624—31no—
141C2×D3×Dic3—31no—
142C2×D3×Dic3—31no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C2×D3×Dic3—31no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—64no—
148C4×D32—64no—
149C23×D9—31no—
150C23×D9C2×D311yescharacteristic
151C32×C22⋊C4C2×D311yescharacteristic
152#3752—31no—
153#3750—31no—
154C4×C3⋊Dic3—31no—
155C3×#217—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4C2×D311yescharacteristic
159C3×Dic3⋊C4C2×D311yescharacteristic
160C3×C4×Dic3C2×D311yescharacteristic
161#3724—31no—
162Dic3⋊Dic3—31no—
163#3722—31no—
164(C2×D3)⋊Dic3—31no—
165Dic32—31no—
166Dic32—31no—
167C2×D4×C9—31no—
168C22×C4×C9—31no—
169C22×C4×C9—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—61no—
173C22×Dic9—31no—
174C22×Dic9—31no—
175C22×Dic9—61no—
176D4×D9—38no—
177C2×D36—31no—
178C2×C4×D9—31no—
179C2×C4×D9—31no—
180C2×C4×D9—31no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—31no—
184C2×C4×D9—31no—
185C2×C4×D9—64no—
186C2×C4×D9—64no—
187C2×C4×D9—61no—
188C2×C4×D9C2×D311yescharacteristic
189C2×C4×D9C2×D311yescharacteristic
190C9×C4⋊C4—31no—
191C9×C22⋊C4—21no—
192C9×C22⋊C4—31no—
193C9×C22⋊C4C2×D311yescharacteristic, complemented
194C42×C9—31no—
195#3676—31no—
196#3676C2×D311yescharacteristic, complemented
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—61no—
200(C2×D9)⋊C4C2×D311yescharacteristic, complemented
201(C2×D9)⋊C4C2×D311yescharacteristic, complemented
202C4⋊Dic9—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4—31no—
205Dic9⋊C4—61no—
206C4×Dic9—31no—
207C4×Dic9—31no—
208C4×Dic9—31no—
209C4×Dic9—61no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9C22×C412yescomplemented
213C22×C3×C9C2411yescharacteristic
214C2×C3⋊D9—21no—
215C2×C3⋊D9—21no—
216C2×C3⋊D9C22×C412yescomplemented
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9C22×C412yescomplemented
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—28no—
223C2×C3×D9C22×C412yes—
224C2×C3×D9C22×C412yescomplemented
225C2×C3×D9C2×D412yes—
226C2×C3×D9#4112yes—
227D3×D9—28no—
228C3×C4×C9—21no—
229C3×C4×C9—21no—
230C3⋊Dic9—21no—
231C3⋊Dic9C22×C412yescomplemented
232C3⋊Dic9C2×D412yescomplemented
233C9×Dic3—21no—
234C9×Dic3C22×C412yescomplemented
235C9×Dic3C2×D412yescomplemented
236C3×Dic9—21no—
237C3×Dic9—21no—
238C22×#67—91no—
239C23×Dic3—91no—
240C2×D3×D4—91no—
241C22×C4×D3—91no—
242C22×C4×D3—91no—
243C22×C4×D3—91no—
244C3×C4×D4—31no—
245C2×C3×C22⋊C4—91no—
246D4×Dic3—91no—
247C4×#67—91no—
248C4×#67—91no—
249C2×(C2×D3)⋊C4—91no—
250C2×Dic3⋊C4—91no—
251C2×C4×Dic3—91no—
252#893—91no—
253D3×C4⋊C4—91no—
254#67⋊C4—91no—
255#67⋊C4—91no—
256#67⋊C4—91no—
257#67⋊C4—91no—
258#67⋊C4—91no—
259#67⋊C4—91no—
260#67⋊C4—91no—
261#67⋊C4—91no—
262#67⋊C4—91no—
263#67⋊C4—181no—
264#67⋊C4D911yescharacteristic, direct product factor
265D3×C22⋊C4—31no—
266D3×C22⋊C4—91no—
267C4×D12—91no—
268C42×D3—91no—
269C23×C32C22×D311yescharacteristic
270C22×C3⋊D3—31no—
271C22×C3×D3—31no—
272C22×C3×D3—34no—
273C22×C3×D3—31no—
274C22×C3×D3—62no—
275C22×C3×D3—62no—
276C22×C3×D3C22×D311yescharacteristic
277C2×D32—34no—
278C2×D32—62no—
279C2×D32—62no—
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282#638—34no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—62no—
287C4×C3⋊D3—62no—
288C3×#67C4×D314yes—
289C2×C3×Dic3—22no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D311yescharacteristic
295C3×C4×D3—22no—
296C3×C4×D3—62no—
297C3×C4×D3—62no—
298#626—34no—
299#625—34no—
300#624—62no—
301D3×Dic3—34no—
302D3×Dic3—34no—
303D3×Dic3—62no—
304D3×Dic3—62no—
305D3×Dic3—62no—
306D3×Dic3—62no—
307C23×C9—21no—
308C23×C9—31no—
309C23×C9C22×D311yescharacteristic
310C22×D9—22no—
311C22×D9—22no—
312C22×D9—31no—
313C22×D9—34no—
314C22×D9—61no—
315C22×D9—62no—
316C22×D9—62no—
317C22×D9C4×D314yescomplemented
318C22×D9C22×D311yescharacteristic
319C22×D9C22×D311yescharacteristic
320D4×C9—34no—
321C2×C4×C9—21no—
322C2×C4×C9—21no—
323C2×C4×C9—31no—
324C2×C4×C9—31no—
325C2×C4×C9—31no—
326C2×C4×C9—62no—
327C2×C4×C9—62no—
328C2×C4×C9C22×D311yescharacteristic
329C2×C4×C9C22×D311yescharacteristic
330#611—34no—
331#611—34no—
332#611—64no—
333C2×Dic9—31no—
334C2×Dic9—31no—
335C2×Dic9—31no—
336C2×Dic9—61no—
337C2×Dic9—61no—
338C2×Dic9—61no—
339C2×Dic9—62no—
340C2×Dic9—62no—
341C2×Dic9—122no—
342C2×Dic9C22×D311yescharacteristic
343C2×Dic9C22×D311yescharacteristic
344D36—34no—
345C4×D9—22no—
346C4×D9—22no—
347C4×D9—34no—
348C4×D9—34no—
349C4×D9—62no—
350C4×D9—62no—
351C4×D9—62no—
352C4×D9—62no—
353C4×D9—62no—
354C4×D9—122no—
355C2×C4×D4—271noSylow
356C2×C3×C9—22no—
357C2×C3×C9C23×C411yescharacteristic
358C2×C3×C9C22×D411yescharacteristic
359C2×C3×C9C2×#4111yescharacteristic
360C3⋊D9—22no—
361D3×C9—22no—
362C3×D9—22no—
363C3×D9C4×D414yescomplemented
364C24×C3—91no—
365C23×D3—31no—
366C23×D3—91no—
367C23×D3—91no—
368C2×C3×D4—31no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—91no—
372C22×C3×C4—91no—
373C2×#67—91no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—98no—
378C2×#67—91no—
379C2×#67—181no—
380C2×#67C2×D911yescharacteristic
381C22×Dic3—91no—
382C22×Dic3—91no—
383C22×Dic3—91no—
384C22×Dic3—91no—
385C22×Dic3—91no—
386C22×Dic3—91no—
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—181no—
390C22×Dic3—184no—
391C22×Dic3C2×D911yescharacteristic, complemented
392D3×D4—98no—
393C2×D12—91no—
394C2×C4×D3—31no—
395C2×C4×D3—31no—
396C2×C4×D3—91no—
397C2×C4×D3—91no—
398C2×C4×D3—91no—
399C2×C4×D3—91no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×C4×D3—91no—
405C2×C4×D3—91no—
406C2×C4×D3—181no—
407C2×C4×D3—184no—
408C2×C4×D3—184no—
409C2×C4×D3—184no—
410C2×C4×D3C2×D911yescharacteristic, complemented
411C3×C4⋊C4—31no—
412C3×C22⋊C4—21no—
413C3×C22⋊C4—31no—
414C3×C22⋊C4—91no—
415C3×C22⋊C4—91no—
416C3×C22⋊C4—91no—
417C3×C22⋊C4C2×D911yescharacteristic, complemented
418C3×C22⋊C4D3211yescharacteristic
419C3×C42—31no—
420#217—31no—
421#217—91no—
422(C2×D3)⋊C4—31no—
423(C2×D3)⋊C4—31no—
424(C2×D3)⋊C4—91no—
425(C2×D3)⋊C4—91no—
426(C2×D3)⋊C4—91no—
427(C2×D3)⋊C4—91no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—181no—
430(C2×D3)⋊C4C2×D911yescharacteristic, complemented
431C4⋊Dic3—91no—
432Dic3⋊C4—91no—
433Dic3⋊C4—91no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—181no—
438Dic3⋊C4C2×D911yescharacteristic, complemented
439C4×Dic3—91no—
440C4×Dic3—91no—
441C4×Dic3—91no—
442C4×Dic3—91no—
443C4×Dic3—91no—
444C4×Dic3—91no—
445C4×Dic3—181no—
446C4×Dic3C2×D911yescharacteristic, complemented
447C22×C32—21no—
448C22×C32—21no—
449C22×C32C2×C4×D312yes—
450C22×C32C23×D311yescharacteristic
451C2×C3⋊D3—32no—
452C2×C3⋊D3—61no—
453C2×C3⋊D3—61no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—32no—
457C2×C3×D3—32no—
458C2×C3×D3—32no—
459C2×C3×D3—32no—
460C2×C3×D3—68no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3C2×C4×D312yes—
464D32—68no—
465C32×C4—21no—
466C32×C4—21no—
467C3⋊Dic3—32no—
468C3⋊Dic3—32no—
469C3⋊Dic3—61no—
470C3×Dic3—21no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C3×Dic3C2×C4×D312yes—
474C3×Dic3D3×D412yes—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—22no—
479C22×C9—32no—
480C22×C9—41no—
481C22×C9—41no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9C2×C4×D312yescomplemented
485C22×C9C23×D311yescharacteristic
486C2×D9—21no—
487C2×D9—21no—
488C2×D9—28no—
489C2×D9—32no—
490C2×D9—62no—
491C2×D9—61no—
492C2×D9—61no—
493C2×D9—68no—
494C2×D9—121no—
495C2×D9—121no—
496C2×D9C2×C4×D312yes—
497C2×D9C2×C4×D312yescomplemented
498C2×D9D3×D412yes—
499C2×D9#23712yes—
500C4×C9—21no—
501C4×C9—21no—
502C4×C9—32no—
503C4×C9—32no—
504C4×C9—41no—
505C4×C9—41no—
506C4×C9—61no—
507Dic9—21no—
508Dic9—21no—
509Dic9—32no—
510Dic9—32no—
511Dic9—62no—
512Dic9—62no—
513Dic9—61no—
514Dic9—121no—
515C22×D4—271no—
516C23×C4—271no—
517C23×C4—271no—
518C4×D4—31no—
519C4×D4—271no—
520C4×D4—271no—
521C4×D4—271no—
522C4×D4—271no—
523C4×D4—271no—
524C4×D4—271no—
525C4×D4—271no—
526C2×C4⋊C4—271no—
527C2×C22⋊C4—91no—
528C2×C22⋊C4—271no—
529C2×C42—271no—
530C3×C9C2×C4×D411yescharacteristic, complemented, Sylow
531C23×C3—21no—
532C23×C3—31no—
533C23×C3—91no—
534C23×C3—94no—
535C23×C3—91no—
536C23×C3—182no—
537C23×C3—182no—
538C23×C3C22×D911yescharacteristic
539C23×C3C2×D3211yescharacteristic
540C22×D3—31no—
541C22×D3—31no—
542C22×D3—34no—
543C22×D3—62no—
544C22×D3—62no—
545C22×D3—94no—
546C22×D3—91no—
547C22×D3—91no—
548C22×D3—94no—
549C22×D3—181no—
550C22×D3—182no—
551C22×D3—182no—
552C22×D3—182no—
553C22×D3—182no—
554C22×D3C22×D911yescharacteristic
555C3×D4—34no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—31no—
559C2×C3×C4—31no—
560C2×C3×C4—31no—
561C2×C3×C4—62no—
562C2×C3×C4—62no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—182no—
566C2×C3×C4—182no—
567C2×C3×C4C22×D911yescharacteristic
568C2×C3×C4C22×D911yescharacteristic
569C2×C3×C4C2×D3211yescharacteristic
570C2×C3×C4C2×D3211yescharacteristic
571#67—94no—
572#67—94no—
573#67—94no—
574#67—94no—
575#67—94no—
576#67—184no—
577#67C4×D914yescomplemented
578C2×Dic3—22no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—91no—
582C2×Dic3—91no—
583C2×Dic3—91no—
584C2×Dic3—91no—
585C2×Dic3—94no—
586C2×Dic3—94no—
587C2×Dic3—91no—
588C2×Dic3—91no—
589C2×Dic3—181no—
590C2×Dic3—181no—
591C2×Dic3—181no—
592C2×Dic3—182no—
593C2×Dic3—182no—
594C2×Dic3—182no—
595C2×Dic3—182no—
596C2×Dic3—182no—
597C2×Dic3—182no—
598C2×Dic3—362no—
599C2×Dic3C22×D911yescharacteristic
600C2×Dic3C22×D911yescharacteristic
601C2×Dic3C22×D911yescharacteristic
602D12—94no—
603C4×D3—22no—
604C4×D3—62no—
605C4×D3—62no—
606C4×D3—94no—
607C4×D3—94no—
608C4×D3—182no—
609C4×D3—182no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—182no—
613C4×D3—182no—
614C4×D3—182no—
615C4×D3—182no—
616C4×D3—362no—
617C2×C32—22no—
618C2×C32C22×C4×D311yescharacteristic
619C2×C32C2×D3×D411yescharacteristic
620C2×C32D3×#4111yescharacteristic
621C3⋊D3—62no—
622C3×D3—22no—
623C3×D3—34no—
624C3×D3—62no—
625C2×C9—22no—
626C2×C9—21no—
627C2×C9—21no—
628C2×C9—21no—
629C2×C9—42no—
630C2×C9—62no—
631C2×C9C22×C4×D311yescharacteristic
632C2×C9C2×D3×D411yescharacteristic
633C2×C9C2×#23711yescharacteristic
634D9—22no—
635D9—62no—
636D9—122no—
637D9#67⋊C414yesdirect product factor
638C24—91no—
639C24—271no—
640C2×D4—31no—
641C2×D4—271no—
642C2×D4—278no—
643C2×D4—271no—
644C2×D4—271no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—91no—
648C22×C4—91no—
649C22×C4—271no—
650C22×C4—271no—
651C22×C4—271no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C22×C4—271no—
656C22×C4—271no—
657C22×C4—271no—
658C22×C4—544no—
659C22×C4—544no—
660C4⋊C4—31no—
661C4⋊C4—271no—
662C4⋊C4—271no—
663C4⋊C4—271no—
664C22⋊C4—31no—
665C22⋊C4—91no—
666C22⋊C4—91no—
667C22⋊C4—91no—
668C22⋊C4—271no—
669C22⋊C4—271no—
670C22⋊C4—271no—
671C22⋊C4D3×D911yescharacteristic, complemented
672C42—31no—
673C42—271no—
674C42—271no—
675C42—271no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—22no—
682C22×C3—32no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—92no—
688C22×C3—92no—
689C22×C3—92no—
690C22×C3—92no—
691C22×C3—188no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3C2×C4×D912yescomplemented
695C22×C3C23×D911yescharacteristic
696C22×C3C4×D3212yes—
697C22×C3C22×D3211yescharacteristic
698C2×D3—21no—
699C2×D3—21no—
700C2×D3—32no—
701C2×D3—32no—
702C2×D3—32no—
703C2×D3—32no—
704C2×D3—68no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—92no—
708C2×D3—92no—
709C2×D3—182no—
710C2×D3—188no—
711C2×D3—188no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—181no—
716C2×D3—361no—
717C2×D3—361no—
718C2×D3C2×C4×D912yescomplemented
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—32no—
724C3×C4—32no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—61no—
728C3×C4—181no—
729C3×C4—181no—
730Dic3—21no—
731Dic3—61no—
732Dic3—61no—
733Dic3—92no—
734Dic3—92no—
735Dic3—92no—
736Dic3—92no—
737Dic3—182no—
738Dic3—182no—
739Dic3—181no—
740Dic3—181no—
741Dic3—361no—
742Dic3C2×C4×D912yescomplemented
743Dic3D4×D912yescomplemented
744C32C4×D3×D411yescharacteristic
745C9—21no—
746C9C2×#67⋊C411yescharacteristic, complemented
747C23—31no—
748C23—91no—
749C23—91no—
750C23—94no—
751C23—182no—
752C23—182no—
753C23—274no—
754C23—271no—
755C23—542no—
756C23—542no—
757C23C2×D3×D911yescharacteristic
758D4—34no—
759D4—274no—
760D4—274no—
761D4—274no—
762C2×C4—31no—
763C2×C4—31no—
764C2×C4—31no—
765C2×C4—62no—
766C2×C4—62no—
767C2×C4—91no—
768C2×C4—91no—
769C2×C4—182no—
770C2×C4—182no—
771C2×C4—274no—
772C2×C4—274no—
773C2×C4—271no—
774C2×C4—271no—
775C2×C4—271no—
776C2×C4—542no—
777C2×C4—542no—
778C2×C4—542no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4—542no—
783C2×C4C2×D3×D911yescharacteristic
784C2×C4C2×D3×D911yescharacteristic
785C2×C3—22no—
786C2×C3—22no—
787C2×C3—21no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—42no—
791C2×C3—62no—
792C2×C3—94no—
793C2×C3—182no—
794C2×C3C22×C4×D911yescharacteristic
795C2×C3C2×D4×D911yescharacteristic
796C2×C3#41×D911yescharacteristic
797C2×C3C2×C4×D3211yescharacteristic
798C2×C3D32×D411yescharacteristic
799C2×C3D3×#23711yescharacteristic
800D3—22no—
801D3—34no—
802D3—62no—
803D3—182no—
804D3—182no—
805D3—362no—
806C22—21no—
807C22—21no—
808C22—32no—
809C22—61no—
810C22—61no—
811C22—92no—
812C22—92no—
813C22—92no—
814C22—92no—
815C22—188no—
816C22—181no—
817C22—181no—
818C22—272no—
819C22—548no—
820C22—541no—
821C22—541no—
822C22C4×D3×D912yescomplemented
823C22C22×D3×D911yescharacteristic
824C4—21no—
825C4—21no—
826C4—32no—
827C4—32no—
828C4—61no—
829C4—181no—
830C4—181no—
831C4—272no—
832C4—272no—
833C4—541no—
834C3—21no—
835C3C4×D4×D911yescharacteristic, complemented
836C3D3×#67⋊C411yescharacteristic
837C2—22no—
838C2—62no—
839C2—94no—
840C2—182no—
841C2—542no—
842C2C2×C4×D3×D911yescharacteristic
843C2D3×D4×D911yescharacteristic
844C2D9×#23711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×D9×#67C2
cosocleC22×C3×C9C24
hypercenterC22⋊C4D3×D9
hypocenterC3×C9C2×C4×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Dic3×D9C2semidirect
3. C2×C4×D3×D9C2semidirect
4. #11721727C2semidirect
5. C9×#67⋊C4C2semidirect
6. C3×C22⋊C4×D9C2semidirect
7. #67⋊Dic9C2semidirect
8. #11721240C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721028C2semidirect
11. #11720978C2semidirect
12. #11720977C2semidirect
13. #11720976C2semidirect
14. D9×Dic3⋊C4C2semidirect
15. C4×Dic3×D9C2semidirect
21. C22×C3⋊Dic9C22semidirect
22. C2×C4×C3⋊D9C22semidirect
24. C22×C9×Dic3C22semidirect
25. C2×C4×D3×C9C22semidirect
28. D9×#67C4semidirect
30. C2×D3×Dic9C22semidirect
32. C2×(C3⋊D9)⋊C4C22semidirect
37. C2×Dic3×D9C22semidirect
38. C2×Dic3×D9C22semidirect
40. C3×C9×C22⋊C4C22semidirect
41. #88536C22semidirect
42. #88534C22semidirect
43. C4×C3⋊Dic9C22semidirect
44. C3×#3676C22semidirect
45. C9×(C2×D3)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C3×(C2×D9)⋊C4C22semidirect
48. C9×Dic3⋊C4C22semidirect
49. C4×C9×Dic3C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
51. #88445C22semidirect
52. Dic3⋊Dic9C22semidirect
53. #88442C22semidirect
54. Dic3×Dic9C22semidirect
55. Dic3×Dic9C22semidirect
84. C22⋊C4×D9D3semidirect
92. C22×C3×D9C2×C4semidirect
97. C2×D3×D9C2×C4semidirect
100. #6233C2×C4semidirect
106. C9×#67C2×C4semidirect
116. #6194C2×C4semidirect
118. #6192C2×C4semidirect
123. Dic3×D9C2×C4semidirect
124. Dic3×D9D4semidirect
193. C9×C22⋊C4C2×D3semidirect
196. #3676C2×D3semidirect
200. (C2×D9)⋊C4C2×D3semidirect
201. (C2×D9)⋊C4C2×D3semidirect
212. C22×C3×C9C22×C4semidirect
216. C2×C3⋊D9C22×C4semidirect
219. C2×D3×C9C22×C4semidirect
224. C2×C3×D9C22×C4semidirect
231. C3⋊Dic9C22×C4semidirect
232. C3⋊Dic9C2×D4semidirect
234. C9×Dic3C22×C4semidirect
235. C9×Dic3C2×D4semidirect
264. #67⋊C4D9direct (N × H)
317. C22×D9C4×D3semidirect
363. C3×D9C4×D4semidirect
391. C22×Dic3C2×D9semidirect
410. C2×C4×D3C2×D9semidirect
417. C3×C22⋊C4C2×D9semidirect
430. (C2×D3)⋊C4C2×D9semidirect
438. Dic3⋊C4C2×D9semidirect
446. C4×Dic3C2×D9semidirect
484. C22×C9C2×C4×D3semidirect
497. C2×D9C2×C4×D3semidirect
530. C3×C9C2×C4×D4semidirect
577. #67C4×D9semidirect
637. D9#67⋊C4direct (N × H)
671. C22⋊C4D3×D9semidirect
694. C22×C3C2×C4×D9semidirect
718. C2×D3C2×C4×D9semidirect
742. Dic3C2×C4×D9semidirect
743. Dic3D4×D9semidirect
746. C9C2×#67⋊C4semidirect
822. C22C4×D3×D9semidirect
835. C3C4×D4×D9semidirect

Maximal subgroups

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

subgroupindex
C2×D9×#672
C22×Dic3×D92
C2×C4×D3×D92
#117217272
C9×#67⋊C42
C3×C22⋊C4×D92
#67⋊Dic92
#117212402
D9×(C2×D3)⋊C42
#117210282
#117209782
#117209772
#117209762
D9×Dic3⋊C42
C4×Dic3×D92
D3×#67⋊C43
C4×D4×D93