Finite Group Databasebeta

← #13148395

Subgroups — #13148395

Order 1728.

1410 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88668C211yesmaximal, characteristic
2C22×(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
3C2×C4×D3×D9C211yesmaximal, characteristic, complemented
4C22⋊C4×C3⋊D9C211yesmaximal, characteristic, complemented
5C9×#67⋊C4C211yesmaximal, characteristic, complemented
6C3×#611⋊C4C211yesmaximal, characteristic, complemented
7#67×Dic9C211yesmaximal, characteristic, complemented
8Dic3×#611C211yesmaximal, characteristic, complemented
9#11721048C211yesmaximal, characteristic, complemented
10#11721030C211yesmaximal, characteristic, complemented
11#11721013C211yesmaximal, characteristic, complemented
12#11721002C211yesmaximal, characteristic, complemented
13#11720980C211yesmaximal, characteristic, complemented
14C4×(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
15#11720977C211yesmaximal, characteristic, complemented
16#10594255—31nomaximal
17C4×D4×D9—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×C4×C3⋊D9C2211yescharacteristic
21C2×C4×C3⋊D9C2211yescharacteristic
22C2×C9×#67C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C22×C9×Dic3C2211yescharacteristic, complemented
25C22×C3×Dic9C2211yescharacteristic, complemented
26C2×C4×D3×C9C2211yescharacteristic, complemented
27C2×C3×C4×D9C2211yescharacteristic, complemented
28#88668C418yescomplemented
29C2×#6195C2211yescharacteristic
30C2×D3×Dic9C2211yescharacteristic, complemented
31C2×#6192C2211yescharacteristic
32C2×(C3⋊D9)⋊C4—24no—
33C2×(C3⋊D9)⋊C4C2211yescharacteristic
34C2×(C3⋊D9)⋊C4C2211yescharacteristic
35C2×(C3⋊D9)⋊C4C2211yescharacteristic
36C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
37C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
38C2×Dic3×D9C2211yescharacteristic, complemented
39C4×D3×D9—24no—
40C3×C9×C22⋊C4C2211yescharacteristic, complemented
41#88551C2211yescharacteristic, complemented
42#88536C2211yescharacteristic, complemented
43#88536C2211yescharacteristic, complemented
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C9×Dic3⋊C4C2211yescharacteristic, complemented
47C4×C9×Dic3C2211yescharacteristic, complemented
48C3×Dic9⋊C4C2211yescharacteristic, complemented
49C3×C4×Dic9C2211yescharacteristic, complemented
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52Dic3⋊Dic9C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55Dic3×Dic9C2211yescharacteristic, complemented
56C2×#3811—31no—
57C22×#624—31no—
58C2×C4×D32—31no—
59C22⋊C4×C3⋊D3—31no—
60C3×#67⋊C4—31no—
61C3×#67⋊C4D311yescharacteristic
62Dic3×#67—31no—
63Dic3×#67—31no—
64#63921—31no—
65#63904—31no—
66#63904—31no—
67#63883—31no—
68C4×#624—31no—
69#63880—31no—
70#63880—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⋊C4D311yescharacteristic, complemented
82C22⋊C4×D9—31no—
83C22⋊C4×D9—31no—
84C22⋊C4×D9—61no—
85C4×D36—31no—
86C42×D9—31no—
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9—22no—
89C22×C3⋊D9—22no—
90C22×C3⋊D9C2×C414yescomplemented
91C22×C3⋊D9C2311yescharacteristic
92C22×C3⋊D9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9C2×C414yescomplemented
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C4×C3⋊D9—22no—
103C4×C3⋊D9—22no—
104C9×#67C2×C414yescomplemented
105C3×#611C2×C414yescomplemented
106C2×C9×Dic3—22no—
107C2×C9×Dic3C2311yescharacteristic
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9—22no—
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C4×D3×C9—22no—
115C3×C4×D9—22no—
116#6195C2×C414yescomplemented
117D3×Dic9—22no—
118#6192C2×C414yescomplemented
119(C3⋊D9)⋊C4—22no—
120(C3⋊D9)⋊C4—22no—
121(C3⋊D9)⋊C4—22no—
122(C3⋊D9)⋊C4C2×C414yescomplemented
123(C3⋊D9)⋊C4D414yescomplemented
124Dic3×D9—22no—
125C4×D3×D4—91no—
126C4×D3×D4—91no—
127C23×C3⋊D3—31no—
128C22×D32—31no—
129C2×C4×C3⋊D3—31no—
130C2×C4×C3⋊D3—31no—
131C2×C3×#67—31no—
132C2×C3×#67C2×D311yescharacteristic
133C22×C3×Dic3—31no—
134C22×C3×Dic3C2×D311yescharacteristic
135C2×C3×C4×D3—31no—
136C2×C3×C4×D3C2×D311yescharacteristic
137#3811—38no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#624—31no—
141C2×#624—31no—
142C2×#624—31no—
143C2×#624—31no—
144C2×#624—31no—
145C2×#624—64no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148C4×D32—64no—
149C23×D9—31no—
150C23×D9—31no—
151C23×D9—61no—
152C32×C22⋊C4C2×D311yescharacteristic
153#3757—31no—
154#3752—31no—
155#3752—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4C2×D311yescharacteristic
158C3×Dic3⋊C4—31no—
159C3×Dic3⋊C4C2×D311yescharacteristic
160C3×C4×Dic3—31no—
161C3×C4×Dic3C2×D311yescharacteristic
162Dic3⋊Dic3—31no—
163Dic3⋊Dic3—31no—
164(C2×D3)⋊Dic3—31no—
165(C2×D3)⋊Dic3—31no—
166Dic32—31no—
167Dic32—31no—
168C2×D4×C9—31no—
169C22×C4×C9—31no—
170C22×C4×C9—31no—
171C2×#611—31no—
172C2×#611C2×D311yescharacteristic
173C22×Dic9—31no—
174C22×Dic9C2×D311yescharacteristic, complemented
175D4×D9—38no—
176C2×D36—31no—
177C2×C4×D9—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×D9—61no—
189C2×C4×D9C2×D311yescharacteristic, complemented
190C9×C4⋊C4—31no—
191C9×C22⋊C4—21no—
192C9×C22⋊C4—31no—
193C9×C22⋊C4C2×D311yescharacteristic, complemented
194C42×C9—31no—
195#3676—31no—
196#3676—31no—
197#3676—61no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—61no—
202(C2×D9)⋊C4—61no—
203(C2×D9)⋊C4C2×D311yescharacteristic, complemented
204C4⋊Dic9—31no—
205Dic9⋊C4—31no—
206Dic9⋊C4C2×D311yescharacteristic, complemented
207C4×Dic9—31no—
208C4×Dic9—31no—
209C4×Dic9C2×D311yescharacteristic, complemented
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⋊D9—28no—
217C2×C3⋊D9C22×C412yes—
218C2×C3⋊D9C22×C412yescomplemented
219C2×C3⋊D9C2×D412yes—
220C2×C3⋊D9#4112yes—
221C2×D3×C9—21no—
222C2×D3×C9—21no—
223C2×D3×C9C22×C412yescomplemented
224C2×C3×D9—21no—
225C2×C3×D9—21no—
226C2×C3×D9C22×C412yescomplemented
227D3×D9—28no—
228C3×C4×C9—21no—
229C3×C4×C9—21no—
230C3⋊Dic9—21no—
231C3⋊Dic9—21no—
232C9×Dic3—21no—
233C9×Dic3C22×C412yescomplemented
234C9×Dic3C2×D412yescomplemented
235C3×Dic9—21no—
236C3×Dic9C22×C412yescomplemented
237C3×Dic9C2×D412yescomplemented
238C2×D3×D4—91no—
239C2×D3×D4—91no—
240C22×C4×D3—91no—
241C22×C4×D3—91no—
242C22×C4×D3—91no—
243C22×C4×D3—91no—
244C3×C4×D4—31no—
245C3×C4×D4—91no—
246D4×Dic3—91no—
247D4×Dic3—91no—
248C4×#67—91no—
249C4×#67—91no—
250C4×#67—91no—
251C4×#67—91no—
252#893—91no—
253#893—91no—
254D3×C4⋊C4—91no—
255D3×C4⋊C4—91no—
256#67⋊C4—31no—
257#67⋊C4—91no—
258#67⋊C4—91no—
259#67⋊C4D911yescharacteristic, complemented
260D3×C22⋊C4—91no—
261D3×C22⋊C4—91no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4—91no—
264D3×C22⋊C4—181no—
265C4×D12—91no—
266C4×D12—91no—
267C42×D3—91no—
268C42×D3—91no—
269C23×C32C22×D311yescharacteristic
270C22×C3⋊D3—31no—
271C22×C3⋊D3—34no—
272C22×C3⋊D3—31no—
273C22×C3⋊D3—62no—
274C22×C3⋊D3—62no—
275C22×C3×D3—31no—
276C22×C3×D3C22×D311yescharacteristic
277C2×D32—34no—
278C2×D32—62no—
279C2×D32—62no—
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C4×C3⋊D3—62no—
285C4×C3⋊D3—62no—
286C3×#67—34no—
287C3×#67C4×D314yes—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—62no—
293C2×C3×Dic3C22×D311yescharacteristic
294C2×C3×Dic3C22×D311yescharacteristic
295C2×C3×Dic3C22×D311yescharacteristic
296C3×C4×D3—22no—
297C3×C4×D3—62no—
298#626—34no—
299#626—34no—
300#624—34no—
301#624—34no—
302#624—62no—
303#624—62no—
304#624—62no—
305D3×Dic3—62no—
306D3×Dic3—62no—
307C23×C9—21no—
308C23×C9—31no—
309C23×C9C22×D311yescharacteristic
310C22×D9—31no—
311C22×D9—34no—
312C22×D9—31no—
313C22×D9—34no—
314C22×D9—61no—
315C22×D9—61no—
316C22×D9—64no—
317C22×D9—62no—
318C22×D9—62no—
319C22×D9—62no—
320C22×D9—62no—
321C22×D9—122no—
322C22×D9—122no—
323C22×D9C22×D311yescharacteristic
324D4×C9—34no—
325C2×C4×C9—21no—
326C2×C4×C9—21no—
327C2×C4×C9—31no—
328C2×C4×C9—31no—
329C2×C4×C9—31no—
330C2×C4×C9—62no—
331C2×C4×C9—62no—
332C2×C4×C9C22×D311yescharacteristic
333C2×C4×C9C22×D311yescharacteristic
334#611—34no—
335#611C4×D314yescomplemented
336C2×Dic9—22no—
337C2×Dic9—31no—
338C2×Dic9—31no—
339C2×Dic9—61no—
340C2×Dic9—61no—
341C2×Dic9—62no—
342C2×Dic9C22×D311yescharacteristic
343C2×Dic9C22×D311yescharacteristic
344C2×Dic9C22×D311yescharacteristic
345D36—34no—
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—62no—
355C4×D9—122no—
356C4×D9—122no—
357C2×C4×D4—271noSylow
358C2×C3×C9—22no—
359C2×C3×C9C23×C411yescharacteristic
360C2×C3×C9C22×D411yescharacteristic
361C2×C3×C9C2×#4111yescharacteristic
362C3⋊D9—22no—
363C3⋊D9C4×D414yescomplemented
364D3×C9—22no—
365C3×D9—22no—
366C23×D3—91no—
367C23×D3—91no—
368C23×D3—91no—
369C23×D3—91no—
370C23×D3—181no—
371C2×C3×D4—31no—
372C2×C3×D4—91no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—91no—
376C22×C3×C4—91no—
377C2×#67—31no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67C2×D911yescharacteristic
381C22×Dic3—31no—
382C22×Dic3—91no—
383C22×Dic3—91no—
384C22×Dic3C2×D911yescharacteristic, complemented
385D3×D4—98no—
386D3×D4—98no—
387C2×D12—91no—
388C2×D12—91no—
389C2×C4×D3—31no—
390C2×C4×D3—91no—
391C2×C4×D3—91no—
392C2×C4×D3—91no—
393C2×C4×D3—91no—
394C2×C4×D3—91no—
395C2×C4×D3—91no—
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—181no—
408C2×C4×D3—184no—
409C2×C4×D3—184no—
410C2×C4×D3—184no—
411C2×C4×D3—184no—
412C2×C4×D3C2×D911yescharacteristic, complemented
413C3×C4⋊C4—31no—
414C3×C4⋊C4—91no—
415C3×C22⋊C4—21no—
416C3×C22⋊C4—31no—
417C3×C22⋊C4—91no—
418C3×C22⋊C4C2×D911yescharacteristic, complemented
419C3×C22⋊C4D3211yescharacteristic
420C3×C42—31no—
421C3×C42—91no—
422#217—91no—
423#217—91no—
424#217—91no—
425#217—91no—
426#217—181no—
427(C2×D3)⋊C4—31no—
428(C2×D3)⋊C4—91no—
429(C2×D3)⋊C4—91no—
430(C2×D3)⋊C4—91no—
431(C2×D3)⋊C4—91no—
432(C2×D3)⋊C4—91no—
433(C2×D3)⋊C4—91no—
434(C2×D3)⋊C4—181no—
435(C2×D3)⋊C4—181no—
436(C2×D3)⋊C4C2×D911yescharacteristic, complemented
437C4⋊Dic3—91no—
438C4⋊Dic3—91no—
439Dic3⋊C4—31no—
440Dic3⋊C4—91no—
441Dic3⋊C4—91no—
442Dic3⋊C4C2×D911yescharacteristic, complemented
443C4×Dic3—31no—
444C4×Dic3—91no—
445C4×Dic3—91no—
446C4×Dic3—91no—
447C4×Dic3—91no—
448C4×Dic3C2×D911yescharacteristic, complemented
449C22×C32—21no—
450C22×C32—21no—
451C22×C32C2×C4×D312yes—
452C22×C32C23×D311yescharacteristic
453C2×C3⋊D3—32no—
454C2×C3⋊D3—32no—
455C2×C3⋊D3—32no—
456C2×C3⋊D3—32no—
457C2×C3⋊D3—68no—
458C2×C3⋊D3—61no—
459C2×C3⋊D3—61no—
460C2×C3×D3—21no—
461C2×C3×D3—21no—
462C2×C3×D3—32no—
463C2×C3×D3—61no—
464C2×C3×D3—61no—
465C2×C3×D3C2×C4×D312yes—
466D32—68no—
467C32×C4—21no—
468C32×C4—21no—
469C3⋊Dic3—61no—
470C3⋊Dic3—61no—
471C3×Dic3—21no—
472C3×Dic3—32no—
473C3×Dic3—32no—
474C3×Dic3—61no—
475C3×Dic3C2×C4×D312yes—
476C3×Dic3D3×D412yes—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—21no—
480C22×C9—22no—
481C22×C9—32no—
482C22×C9—41no—
483C22×C9—41no—
484C22×C9—61no—
485C22×C9—61no—
486C22×C9C2×C4×D312yescomplemented
487C22×C9C23×D311yescharacteristic
488C2×D9—21no—
489C2×D9—21no—
490C2×D9—32no—
491C2×D9—32no—
492C2×D9—32no—
493C2×D9—32no—
494C2×D9—62no—
495C2×D9—62no—
496C2×D9—62no—
497C2×D9—62no—
498C2×D9—68no—
499C2×D9—68no—
500C2×D9—61no—
501C2×D9—61no—
502C2×D9—128no—
503C2×D9—121no—
504C2×D9—121no—
505C2×D9C2×C4×D312yescomplemented
506C4×C9—21no—
507C4×C9—21no—
508C4×C9—32no—
509C4×C9—32no—
510C4×C9—41no—
511C4×C9—41no—
512C4×C9—61no—
513Dic9—21no—
514Dic9—61no—
515Dic9—61no—
516Dic9—121no—
517Dic9—121no—
518Dic9C2×C4×D312yescomplemented
519Dic9D3×D412yescomplemented
520C22×D4—271no—
521C23×C4—271no—
522C23×C4—271no—
523C4×D4—31no—
524C4×D4—91no—
525C4×D4—271no—
526C4×D4—271no—
527C4×D4—271no—
528C4×D4—271no—
529C4×D4—271no—
530C4×D4—271no—
531C2×C4⋊C4—271no—
532C2×C22⋊C4—271no—
533C2×C22⋊C4—271no—
534C2×C42—271no—
535C3×C9C2×C4×D411yescharacteristic, complemented, Sylow
536C23×C3—21no—
537C23×C3—31no—
538C23×C3—91no—
539C23×C3C22×D911yescharacteristic
540C23×C3C2×D3211yescharacteristic
541C22×D3—31no—
542C22×D3—94no—
543C22×D3—91no—
544C22×D3—91no—
545C22×D3—91no—
546C22×D3—94no—
547C22×D3—91no—
548C22×D3—94no—
549C22×D3—94no—
550C22×D3—181no—
551C22×D3—181no—
552C22×D3—184no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—182no—
556C22×D3—182no—
557C22×D3—182no—
558C22×D3—182no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—362no—
562C22×D3—362no—
563C22×D3C22×D911yescharacteristic
564C3×D4—34no—
565C3×D4—94no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—31no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—62no—
572C2×C3×C4—62no—
573C2×C3×C4—91no—
574C2×C3×C4—91no—
575C2×C3×C4—91no—
576C2×C3×C4—182no—
577C2×C3×C4—182no—
578C2×C3×C4C22×D911yescharacteristic
579C2×C3×C4C22×D911yescharacteristic
580C2×C3×C4C2×D3211yescharacteristic
581C2×C3×C4C2×D3211yescharacteristic
582#67—34no—
583#67—94no—
584#67—94no—
585#67C4×D914yescomplemented
586C2×Dic3—22no—
587C2×Dic3—31no—
588C2×Dic3—31no—
589C2×Dic3—31no—
590C2×Dic3—62no—
591C2×Dic3—91no—
592C2×Dic3—91no—
593C2×Dic3—91no—
594C2×Dic3—91no—
595C2×Dic3—181no—
596C2×Dic3—181no—
597C2×Dic3—182no—
598C2×Dic3—182no—
599C2×Dic3C22×D911yescharacteristic
600C2×Dic3C22×D911yescharacteristic
601C2×Dic3C22×D911yescharacteristic
602D12—94no—
603D12—94no—
604C4×D3—22no—
605C4×D3—62no—
606C4×D3—94no—
607C4×D3—94no—
608C4×D3—94no—
609C4×D3—94no—
610C4×D3—182no—
611C4×D3—182no—
612C4×D3—182no—
613C4×D3—182no—
614C4×D3—182no—
615C4×D3—182no—
616C4×D3—182no—
617C4×D3—182no—
618C4×D3—182no—
619C4×D3—182no—
620C4×D3—182no—
621C4×D3—182no—
622C4×D3—362no—
623C4×D3—362no—
624C2×C32—22no—
625C2×C32C22×C4×D311yescharacteristic
626C2×C32C2×D3×D411yescharacteristic
627C2×C32D3×#4111yescharacteristic
628C3⋊D3—34no—
629C3⋊D3—62no—
630C3×D3—22no—
631C3×D3—62no—
632C2×C9—22no—
633C2×C9—21no—
634C2×C9—21no—
635C2×C9—21no—
636C2×C9—42no—
637C2×C9—62no—
638C2×C9C22×C4×D311yescharacteristic
639C2×C9C2×D3×D411yescharacteristic
640C2×C9D3×#4111yescharacteristic
641D9—22no—
642D9—34no—
643D9—64no—
644D9—62no—
645D9—122no—
646C24—271no—
647C24—271no—
648C2×D4—31no—
649C2×D4—91no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—278no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—91no—
656C22×C4—91no—
657C22×C4—271no—
658C22×C4—271no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4—271no—
662C22×C4—271no—
663C22×C4—271no—
664C22×C4—271no—
665C22×C4—271no—
666C22×C4—544no—
667C22×C4—544no—
668C4⋊C4—31no—
669C4⋊C4—91no—
670C4⋊C4—271no—
671C4⋊C4—271no—
672C22⋊C4—31no—
673C22⋊C4—91no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C22⋊C4—271no—
679C22⋊C4D3×D911yescharacteristic, complemented
680C42—31no—
681C42—91no—
682C42—271no—
683C42—271no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—22no—
690C22×C3—32no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—61no—
694C22×C3—61no—
695C22×C3—92no—
696C22×C3—181no—
697C22×C3—181no—
698C22×C3C2×C4×D912yescomplemented
699C22×C3C23×D911yescharacteristic
700C22×C3C4×D3212yes—
701C22×C3C22×D3211yescharacteristic
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—32no—
705C2×D3—61no—
706C2×D3—61no—
707C2×D3—92no—
708C2×D3—92no—
709C2×D3—92no—
710C2×D3—92no—
711C2×D3—92no—
712C2×D3—92no—
713C2×D3—92no—
714C2×D3—92no—
715C2×D3—182no—
716C2×D3—182no—
717C2×D3—182no—
718C2×D3—182no—
719C2×D3—188no—
720C2×D3—188no—
721C2×D3—188no—
722C2×D3—188no—
723C2×D3—181no—
724C2×D3—181no—
725C2×D3—181no—
726C2×D3—181no—
727C2×D3—368no—
728C2×D3—361no—
729C2×D3—361no—
730C2×D3C2×C4×D912yescomplemented
731C3×C4—21no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—32no—
736C3×C4—32no—
737C3×C4—41no—
738C3×C4—41no—
739C3×C4—61no—
740C3×C4—92no—
741C3×C4—92no—
742C3×C4—181no—
743Dic3—21no—
744Dic3—32no—
745Dic3—32no—
746Dic3—61no—
747Dic3—181no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—361no—
752Dic3—361no—
753Dic3C2×C4×D912yescomplemented
754Dic3D4×D912yescomplemented
755C32C4×D3×D411yescharacteristic
756C9—21no—
757C9C4×D3×D411yescharacteristic, complemented
758C23—31no—
759C23—91no—
760C23—274no—
761C23—271no—
762C23—271no—
763C23—274no—
764C23—542no—
765C23—542no—
766C23—542no—
767C23—542no—
768C23C2×D3×D911yescharacteristic
769D4—34no—
770D4—94no—
771D4—274no—
772D4—274no—
773C2×C4—31no—
774C2×C4—31no—
775C2×C4—31no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—91no—
779C2×C4—91no—
780C2×C4—91no—
781C2×C4—182no—
782C2×C4—182no—
783C2×C4—274no—
784C2×C4—274no—
785C2×C4—271no—
786C2×C4—271no—
787C2×C4—542no—
788C2×C4—542no—
789C2×C4—542no—
790C2×C4—542no—
791C2×C4—542no—
792C2×C4—542no—
793C2×C4—542no—
794C2×C4C2×D3×D911yescharacteristic
795C2×C4C2×D3×D911yescharacteristic
796C2×C3—22no—
797C2×C3—22no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—42no—
802C2×C3—62no—
803C2×C3—182no—
804C2×C3C22×C4×D911yescharacteristic
805C2×C3C2×D4×D911yescharacteristic
806C2×C3#41×D911yescharacteristic
807C2×C3C2×C4×D3211yescharacteristic
808C2×C3D32×D411yescharacteristic
809C2×C3#6431211yescharacteristic
810D3—22no—
811D3—62no—
812D3—94no—
813D3—94no—
814D3—184no—
815D3—182no—
816D3—182no—
817D3—362no—
818C22—21no—
819C22—21no—
820C22—32no—
821C22—61no—
822C22—61no—
823C22—92no—
824C22—181no—
825C22—181no—
826C22—272no—
827C22—272no—
828C22—272no—
829C22—272no—
830C22—548no—
831C22—548no—
832C22—541no—
833C22—541no—
834C22C4×D3×D912yescomplemented
835C22C22×D3×D911yescharacteristic
836C4—21no—
837C4—21no—
838C4—32no—
839C4—32no—
840C4—61no—
841C4—92no—
842C4—92no—
843C4—181no—
844C4—541no—
845C4—541no—
846C3—21no—
847C3C4×D4×D911yescharacteristic, complemented
848C3#1059425511yescharacteristic
849C2—22no—
850C2—62no—
851C2—182no—
852C2—274no—
853C2—542no—
854C2C2×C4×D3×D911yescharacteristic
855C2D3×D4×D911yescharacteristic
856C2#1172249811yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×#88668C2
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×(C3⋊D9)⋊C4C2semidirect
3. C2×C4×D3×D9C2semidirect
4. C22⋊C4×C3⋊D9C2semidirect
5. C9×#67⋊C4C2semidirect
6. C3×#611⋊C4C2semidirect
7. #67×Dic9C2semidirect
8. Dic3×#611C2semidirect
9. #11721048C2semidirect
10. #11721030C2semidirect
11. #11721013C2semidirect
12. #11721002C2semidirect
13. #11720980C2semidirect
14. C4×(C3⋊D9)⋊C4C2semidirect
15. #11720977C2semidirect
24. C22×C9×Dic3C22semidirect
25. C22×C3×Dic9C22semidirect
26. C2×C4×D3×C9C22semidirect
27. C2×C3×C4×D9C22semidirect
28. #88668C4semidirect
30. C2×D3×Dic9C22semidirect
36. C2×(C3⋊D9)⋊C4C22semidirect
37. C2×(C3⋊D9)⋊C4C22semidirect
38. C2×Dic3×D9C22semidirect
40. C3×C9×C22⋊C4C22semidirect
41. #88551C22semidirect
42. #88536C22semidirect
43. #88536C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C9×Dic3⋊C4C22semidirect
47. C4×C9×Dic3C22semidirect
48. C3×Dic9⋊C4C22semidirect
49. C3×C4×Dic9C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. Dic3⋊Dic9C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
55. Dic3×Dic9C22semidirect
81. #611⋊C4D3semidirect
90. C22×C3⋊D9C2×C4semidirect
97. C2×D3×D9C2×C4semidirect
104. C9×#67C2×C4semidirect
105. C3×#611C2×C4semidirect
116. #6195C2×C4semidirect
118. #6192C2×C4semidirect
122. (C3⋊D9)⋊C4C2×C4semidirect
123. (C3⋊D9)⋊C4D4semidirect
174. C22×Dic9C2×D3semidirect
189. C2×C4×D9C2×D3semidirect
193. C9×C22⋊C4C2×D3semidirect
203. (C2×D9)⋊C4C2×D3semidirect
206. Dic9⋊C4C2×D3semidirect
209. C4×Dic9C2×D3semidirect
212. C22×C3×C9C22×C4semidirect
218. C2×C3⋊D9C22×C4semidirect
223. C2×D3×C9C22×C4semidirect
226. C2×C3×D9C22×C4semidirect
233. C9×Dic3C22×C4semidirect
234. C9×Dic3C2×D4semidirect
236. C3×Dic9C22×C4semidirect
237. C3×Dic9C2×D4semidirect
259. #67⋊C4D9semidirect
335. #611C4×D3semidirect
363. C3⋊D9C4×D4semidirect
384. C22×Dic3C2×D9semidirect
412. C2×C4×D3C2×D9semidirect
418. C3×C22⋊C4C2×D9semidirect
436. (C2×D3)⋊C4C2×D9semidirect
442. Dic3⋊C4C2×D9semidirect
448. C4×Dic3C2×D9semidirect
486. C22×C9C2×C4×D3semidirect
505. C2×D9C2×C4×D3semidirect
518. Dic9C2×C4×D3semidirect
519. Dic9D3×D4semidirect
535. C3×C9C2×C4×D4semidirect
585. #67C4×D9semidirect
679. C22⋊C4D3×D9semidirect
698. C22×C3C2×C4×D9semidirect
730. C2×D3C2×C4×D9semidirect
753. Dic3C2×C4×D9semidirect
754. Dic3D4×D9semidirect
757. C9C4×D3×D4semidirect
834. C22C4×D3×D9semidirect
847. C3C4×D4×D9semidirect

Maximal subgroups

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

subgroupindex
C2×#886682
C22×(C3⋊D9)⋊C42
C2×C4×D3×D92
C22⋊C4×C3⋊D92
C9×#67⋊C42
C3×#611⋊C42
#67×Dic92
Dic3×#6112
#117210482
#117210302
#117210132
#117210022
#117209802
C4×(C3⋊D9)⋊C42
#117209772
#105942553
C4×D4×D93