Finite Group Databasebeta

← C4×#88668 #13150526

Subgroups — C4×#88668 #13150526

Order 1728.

1514 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C3⋊D9C211yesmaximal, characteristic, complemented
2C2×#88668C211yesmaximal, characteristic
3C2×C4×D3×D9C211yesmaximal, characteristic, complemented
4C4×C9×#67C211yesmaximal, characteristic, complemented
5C3×C4×#611C211yesmaximal, characteristic, complemented
6#67⋊Dic9C211yesmaximal, characteristic, complemented
7#11721274C211yesmaximal, characteristic, complemented
8#611⋊Dic3C211yesmaximal, characteristic, complemented
9#11721048C211yesmaximal, characteristic, complemented
10C4×#6195C211yesmaximal, characteristic, complemented
11#11721014C211yesmaximal, characteristic, complemented
12C4×#6192C211yesmaximal, characteristic, complemented
13#11720980C211yesmaximal, characteristic, complemented
14C4×(C3⋊D9)⋊C4C211yesmaximal, characteristic, complemented
15#11720978C211yesmaximal, characteristic, complemented
16C4×#3811—31nomaximal
17C4×D4×D9—31nomaximal
18C23×C3⋊D9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C22×C3×C4×C9C2211yescharacteristic, complemented
21C22×C3⋊Dic9C2211yescharacteristic, complemented
22C2×C4×C3⋊D9—24no—
23C2×C4×C3⋊D9C2211yescharacteristic
24C2×C4×C3⋊D9C2211yescharacteristic
25C2×C4×C3⋊D9C2211yescharacteristic, complemented
26C2×C4×C3⋊D9C2211yescharacteristic, complemented
27C2×C9×#67C2211yescharacteristic
28C2×C3×#611C2211yescharacteristic
29C2×C4×D3×C9C2211yescharacteristic, complemented
30C2×C3×C4×D9C2211yescharacteristic, complemented
31#88668C418yesdirect product factor
32C2×#6195C2211yescharacteristic
33C2×D3×Dic9C2211yescharacteristic, complemented
34C2×#6192C2211yescharacteristic
35C2×(C3⋊D9)⋊C4C2211yescharacteristic
36C2×(C3⋊D9)⋊C4C2211yescharacteristic
37C2×(C3⋊D9)⋊C4C2211yescharacteristic
38C2×Dic3×D9C2211yescharacteristic, complemented
39C4×D3×D9—24no—
40C9×#217C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
44C9×Dic3⋊C4C2211yescharacteristic, complemented
45C4×C9×Dic3C2211yescharacteristic, complemented
46C3×Dic9⋊C4C2211yescharacteristic, complemented
47C3×C4×Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic, complemented
49#88445C2211yescharacteristic, complemented
50#88445C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52Dic3⋊Dic9C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55Dic3×Dic9C2211yescharacteristic, complemented
56C22×C4×C3⋊D3—31no—
57C2×#3811—31no—
58C2×C4×D32—31no—
59C3×C4×#67—31no—
60C3×C4×#67D311yescharacteristic
61#63974—31no—
62#67⋊Dic3—31no—
63#67⋊Dic3—31no—
64#63921—31no—
65C4×#626—31no—
66C4×#626—31no—
67#63883—31no—
68C4×#624—31no—
69#63881—31no—
70#63881—31no—
71C2×D4×D9—31no—
72C22×C4×D9—31no—
73C22×C4×D9—31no—
74C22×C4×D9—61no—
75C4×D4×C9—31no—
76D4×Dic9—31no—
77C4×#611—31no—
78C4×#611D311yescharacteristic, complemented
79#63455—31no—
80C4⋊C4×D9—31no—
81#611⋊C4—31no—
82#611⋊C4—31no—
83C22⋊C4×D9—31no—
84C22⋊C4×D9—31no—
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×C9—22no—
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3×C4×C9C2311yescharacteristic
101C2×C3⋊Dic9—22no—
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C4×C3⋊D9—22no—
105C4×C3⋊D9—22no—
106C4×C3⋊D9—22no—
107C4×C3⋊D9D414yescomplemented
108C9×#67C2×C414yescomplemented
109C3×#611C2×C414yescomplemented
110C2×C9×Dic3C2311yescharacteristic
111C2×C9×Dic3C2311yescharacteristic
112C2×C9×Dic3C2311yescharacteristic
113C2×C3×Dic9C2311yescharacteristic
114C2×C3×Dic9C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C4×D3×C9—22no—
117C3×C4×D9—22no—
118#6195C2×C414yescomplemented
119D3×Dic9—22no—
120#6192C2×C414yescomplemented
121(C3⋊D9)⋊C4—22no—
122(C3⋊D9)⋊C4—22no—
123(C3⋊D9)⋊C4C2×C414yescomplemented
124Dic3×D9—22no—
125C4×D3×D4—91no—
126C4×D3×D4—91no—
127C23×C3⋊D3—31no—
128C22×D32—31no—
129C22×C32×C4C2×D311yescharacteristic
130C22×C3⋊Dic3—31no—
131C2×C4×C3⋊D3—31no—
132C2×C4×C3⋊D3—31no—
133C2×C4×C3⋊D3—31no—
134C2×C4×C3⋊D3—31no—
135C2×C4×C3⋊D3—64no—
136C2×C3×#67—31no—
137C2×C3×#67C2×D311yescharacteristic
138C2×C3×C4×D3—31no—
139C2×C3×C4×D3C2×D311yescharacteristic
140#3811—38no—
141C2×#626—31no—
142C2×#626—31no—
143C2×#624—31no—
144C2×#624—31no—
145C2×#624—31no—
146C2×D3×Dic3—31no—
147C2×D3×Dic3—31no—
148C4×D32—64no—
149C23×D9—31no—
150C23×D9—31no—
151C23×D9—61no—
152C3×#217—31no—
153C3×#217C2×D311yescharacteristic
154C3×(C2×D3)⋊C4—31no—
155C3×(C2×D3)⋊C4C2×D311yescharacteristic
156C3×Dic3⋊C4—31no—
157C3×Dic3⋊C4C2×D311yescharacteristic
158C3×C4×Dic3—31no—
159C3×C4×Dic3C2×D311yescharacteristic
160Dic3⋊Dic3—31no—
161Dic3⋊Dic3—31no—
162#3722—31no—
163#3722—31no—
164(C2×D3)⋊Dic3—31no—
165(C2×D3)⋊Dic3—31no—
166Dic32—31no—
167Dic32—31no—
168C2×D4×C9—31no—
169C22×C4×C9—21no—
170C22×C4×C9—31no—
171C22×C4×C9C2×D311yescharacteristic, complemented
172C2×#611—31no—
173C2×#611C2×D311yescharacteristic
174C22×Dic9—31no—
175C22×Dic9—31no—
176C22×Dic9—61no—
177D4×D9—38no—
178C2×D36—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—31no—
186C2×C4×D9—31no—
187C2×C4×D9—64no—
188C2×C4×D9—64no—
189C2×C4×D9—61no—
190C2×C4×D9—61no—
191C2×C4×D9—61no—
192C2×C4×D9—61no—
193C2×C4×D9—68no—
194C2×C4×D9C2×D311yescharacteristic, complemented
195C9×C4⋊C4—31no—
196C9×C22⋊C4—31no—
197C9×C22⋊C4—31no—
198C42×C9—31no—
199#3676—31no—
200#3676C2×D311yescharacteristic, complemented
201(C2×D9)⋊C4—31no—
202(C2×D9)⋊C4—31no—
203(C2×D9)⋊C4—31no—
204(C2×D9)⋊C4C2×D311yescharacteristic, complemented
205C4⋊Dic9—31no—
206Dic9⋊C4—31no—
207Dic9⋊C4C2×D311yescharacteristic, complemented
208C4×Dic9—31no—
209C4×Dic9—31no—
210C4×Dic9C2×D311yescharacteristic, complemented
211C22×C3×C9—21no—
212C22×C3×C9—21no—
213C22×C3×C9C22×C412yescomplemented
214C22×C3×C9C2411yescharacteristic
215C2×C3⋊D9—21no—
216C2×C3⋊D9—21no—
217C2×C3⋊D9—28no—
218C2×C3⋊D9C22×C412yes—
219C2×C3⋊D9C22×C412yescomplemented
220C2×C3⋊D9C2×D412yes—
221C2×C3⋊D9#4112yes—
222C2×D3×C9—21no—
223C2×D3×C9—21no—
224C2×D3×C9C22×C412yescomplemented
225C2×C3×D9—21no—
226C2×C3×D9—21no—
227C2×C3×D9C22×C412yescomplemented
228D3×D9—28no—
229C3×C4×C9—21no—
230C3×C4×C9C2×D412yescomplemented
231C3⋊Dic9—21no—
232C3⋊Dic9C2×D412yescomplemented
233C9×Dic3—21no—
234C9×Dic3—21no—
235C9×Dic3C22×C412yescomplemented
236C3×Dic9—21no—
237C3×Dic9—21no—
238C3×Dic9C22×C412yescomplemented
239C2×D3×D4—91no—
240C2×D3×D4—91no—
241C22×C4×D3—91no—
242C22×C4×D3—91no—
243C22×C4×D3—91no—
244C22×C4×D3—91no—
245C22×C4×D3—181no—
246C3×C4×D4—31no—
247C3×C4×D4—91no—
248D4×Dic3—91no—
249D4×Dic3—91no—
250C4×#67—31no—
251C4×#67—91no—
252C4×#67—91no—
253C4×#67D911yescharacteristic, complemented
254#893—91no—
255#893—91no—
256D3×C4⋊C4—91no—
257D3×C4⋊C4—91no—
258#67⋊C4—91no—
259#67⋊C4—91no—
260#67⋊C4—91no—
261#67⋊C4—91no—
262D3×C22⋊C4—91no—
263D3×C22⋊C4—91no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4—91no—
266C4×D12—91no—
267C4×D12—91no—
268C42×D3—91no—
269C42×D3—91no—
270C23×C32C22×D311yescharacteristic
271C22×C3⋊D3—31no—
272C22×C3⋊D3—34no—
273C22×C3⋊D3—31no—
274C22×C3⋊D3—62no—
275C22×C3⋊D3—62no—
276C22×C3×D3—31no—
277C22×C3×D3C22×D311yescharacteristic
278C2×D32—34no—
279C2×D32—62no—
280C2×D32—62no—
281C2×C32×C4—22no—
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C2×C3⋊Dic3—62no—
287C4×C3⋊D3—34no—
288C4×C3⋊D3—62no—
289C4×C3⋊D3—62no—
290C4×C3⋊D3—62no—
291C3×#67—34no—
292C3×#67C4×D314yes—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3C22×D311yescharacteristic
297C2×C3×Dic3C22×D311yescharacteristic
298C2×C3×Dic3C22×D311yescharacteristic
299C3×C4×D3—22no—
300C3×C4×D3—62no—
301#626—34no—
302#626—34no—
303#624—34no—
304#624—62no—
305#624—62no—
306D3×Dic3—62no—
307D3×Dic3—62no—
308C23×C9—21no—
309C23×C9—31no—
310C23×C9C22×D311yescharacteristic
311C22×D9—31no—
312C22×D9—34no—
313C22×D9—31no—
314C22×D9—34no—
315C22×D9—61no—
316C22×D9—61no—
317C22×D9—64no—
318C22×D9—62no—
319C22×D9—62no—
320C22×D9—62no—
321C22×D9—62no—
322C22×D9—64no—
323C22×D9—64no—
324C22×D9C22×D311yescharacteristic
325D4×C9—34no—
326C2×C4×C9—24no—
327C2×C4×C9—22no—
328C2×C4×C9—21no—
329C2×C4×C9—21no—
330C2×C4×C9—31no—
331C2×C4×C9—31no—
332C2×C4×C9—31no—
333C2×C4×C9—62no—
334C2×C4×C9C22×D311yescharacteristic
335C2×C4×C9C22×D311yescharacteristic
336#611—34no—
337#611C4×D314yescomplemented
338C2×Dic9—31no—
339C2×Dic9—31no—
340C2×Dic9—61no—
341C2×Dic9—61no—
342C2×Dic9—62no—
343C2×Dic9—62no—
344C2×Dic9—64no—
345C2×Dic9C22×D311yescharacteristic
346C2×Dic9C22×D311yescharacteristic
347C2×Dic9C22×D311yescharacteristic
348D36—34no—
349C4×D9—22no—
350C4×D9—34no—
351C4×D9—34no—
352C4×D9—64no—
353C4×D9—62no—
354C4×D9—62no—
355C4×D9—62no—
356C4×D9—62no—
357C4×D9—62no—
358C4×D9—64no—
359C4×D9—64no—
360C4×D9—64no—
361C4×D9—62no—
362C2×C4×D4—271noSylow
363C2×C3×C9—22no—
364C2×C3×C9C23×C411yescharacteristic
365C2×C3×C9C22×D411yescharacteristic
366C2×C3×C9C2×#4111yescharacteristic
367C3⋊D9—22no—
368C3⋊D9C4×D414yescomplemented
369D3×C9—22no—
370C3×D9—22no—
371C23×D3—91no—
372C23×D3—91no—
373C23×D3—91no—
374C23×D3—91no—
375C23×D3—181no—
376C2×C3×D4—31no—
377C2×C3×D4—91no—
378C22×C3×C4—21no—
379C22×C3×C4—31no—
380C22×C3×C4—91no—
381C22×C3×C4C2×D911yescharacteristic, complemented
382C22×C3×C4D3211yescharacteristic
383C2×#67—31no—
384C2×#67—91no—
385C2×#67—91no—
386C2×#67C2×D911yescharacteristic
387C22×Dic3—91no—
388C22×Dic3—91no—
389C22×Dic3—91no—
390C22×Dic3—91no—
391C22×Dic3—181no—
392D3×D4—98no—
393D3×D4—98no—
394C2×D12—91no—
395C2×D12—91no—
396C2×C4×D3—31no—
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—91no—
407C2×C4×D3—91no—
408C2×C4×D3—91no—
409C2×C4×D3—91no—
410C2×C4×D3—91no—
411C2×C4×D3—91no—
412C2×C4×D3—91no—
413C2×C4×D3—181no—
414C2×C4×D3—181no—
415C2×C4×D3—181no—
416C2×C4×D3—181no—
417C2×C4×D3—184no—
418C2×C4×D3—184no—
419C2×C4×D3—184no—
420C2×C4×D3—184no—
421C2×C4×D3—188no—
422C2×C4×D3C2×D911yescharacteristic, complemented
423C3×C4⋊C4—31no—
424C3×C4⋊C4—91no—
425C3×C22⋊C4—31no—
426C3×C22⋊C4—31no—
427C3×C22⋊C4—91no—
428C3×C22⋊C4—91no—
429C3×C42—31no—
430C3×C42—91no—
431#217—31no—
432#217—91no—
433#217—91no—
434#217C2×D911yescharacteristic, complemented
435(C2×D3)⋊C4—31no—
436(C2×D3)⋊C4—91no—
437(C2×D3)⋊C4—91no—
438(C2×D3)⋊C4—91no—
439(C2×D3)⋊C4—91no—
440(C2×D3)⋊C4—91no—
441(C2×D3)⋊C4—91no—
442(C2×D3)⋊C4C2×D911yescharacteristic, complemented
443C4⋊Dic3—91no—
444C4⋊Dic3—91no—
445Dic3⋊C4—31no—
446Dic3⋊C4—91no—
447Dic3⋊C4—91no—
448Dic3⋊C4C2×D911yescharacteristic, complemented
449C4×Dic3—31no—
450C4×Dic3—91no—
451C4×Dic3—91no—
452C4×Dic3—91no—
453C4×Dic3—91no—
454C4×Dic3C2×D911yescharacteristic, complemented
455C22×C32—21no—
456C22×C32—21no—
457C22×C32C2×C4×D312yes—
458C22×C32C23×D311yescharacteristic
459C2×C3⋊D3—32no—
460C2×C3⋊D3—32no—
461C2×C3⋊D3—32no—
462C2×C3⋊D3—32no—
463C2×C3⋊D3—68no—
464C2×C3⋊D3—61no—
465C2×C3⋊D3—61no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—32no—
469C2×C3×D3—61no—
470C2×C3×D3—61no—
471C2×C3×D3C2×C4×D312yes—
472D32—68no—
473C32×C4—21no—
474C32×C4D3×D412yes—
475C3⋊Dic3—32no—
476C3⋊Dic3—61no—
477C3×Dic3—21no—
478C3×Dic3—21no—
479C3×Dic3—32no—
480C3×Dic3—61no—
481C3×Dic3—61no—
482C3×Dic3C2×C4×D312yes—
483C22×C9—22no—
484C22×C9—22no—
485C22×C9—21no—
486C22×C9—21no—
487C22×C9—21no—
488C22×C9—22no—
489C22×C9—32no—
490C22×C9—61no—
491C22×C9—61no—
492C22×C9C2×C4×D312yescomplemented
493C22×C9C23×D311yescharacteristic
494C2×D9—21no—
495C2×D9—21no—
496C2×D9—32no—
497C2×D9—32no—
498C2×D9—32no—
499C2×D9—32no—
500C2×D9—62no—
501C2×D9—62no—
502C2×D9—62no—
503C2×D9—62no—
504C2×D9—68no—
505C2×D9—68no—
506C2×D9—62no—
507C2×D9—616no—
508C2×D9—62no—
509C2×D9—61no—
510C2×D9—61no—
511C2×D9C2×C4×D312yescomplemented
512C4×C9—22no—
513C4×C9—21no—
514C4×C9—22no—
515C4×C9—32no—
516C4×C9—61no—
517C4×C9—61no—
518C4×C9D3×D412yescomplemented
519Dic9—21no—
520Dic9—21no—
521Dic9—32no—
522Dic9—62no—
523Dic9—62no—
524Dic9—61no—
525Dic9C2×C4×D312yescomplemented
526C22×D4—271no—
527C23×C4—271no—
528C23×C4—271no—
529C4×D4—31no—
530C4×D4—91no—
531C4×D4—271no—
532C4×D4—271no—
533C4×D4—271no—
534C4×D4—271no—
535C4×D4—271no—
536C4×D4—271no—
537C2×C4⋊C4—271no—
538C2×C22⋊C4—271no—
539C2×C22⋊C4—271no—
540C2×C42—271no—
541C3×C9C2×C4×D411yescharacteristic, complemented, Sylow
542C23×C3—21no—
543C23×C3—31no—
544C23×C3—91no—
545C23×C3C22×D911yescharacteristic
546C23×C3C2×D3211yescharacteristic
547C22×D3—31no—
548C22×D3—94no—
549C22×D3—91no—
550C22×D3—91no—
551C22×D3—91no—
552C22×D3—94no—
553C22×D3—91no—
554C22×D3—94no—
555C22×D3—94no—
556C22×D3—181no—
557C22×D3—181no—
558C22×D3—184no—
559C22×D3—182no—
560C22×D3—182no—
561C22×D3—182no—
562C22×D3—182no—
563C22×D3—182no—
564C22×D3—182no—
565C22×D3—182no—
566C22×D3—182no—
567C22×D3—184no—
568C22×D3—184no—
569C22×D3C22×D911yescharacteristic
570C3×D4—34no—
571C3×D4—94no—
572C2×C3×C4—24no—
573C2×C3×C4—22no—
574C2×C3×C4—22no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—31no—
580C2×C3×C4—62no—
581C2×C3×C4—91no—
582C2×C3×C4—91no—
583C2×C3×C4—91no—
584C2×C3×C4—182no—
585C2×C3×C4C22×D911yescharacteristic
586C2×C3×C4C22×D911yescharacteristic
587C2×C3×C4C2×D3211yescharacteristic
588C2×C3×C4C2×D3211yescharacteristic
589#67—34no—
590#67—94no—
591#67—94no—
592#67C4×D914yescomplemented
593C2×Dic3—31no—
594C2×Dic3—31no—
595C2×Dic3—31no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—91no—
599C2×Dic3—91no—
600C2×Dic3—181no—
601C2×Dic3—181no—
602C2×Dic3—182no—
603C2×Dic3—182no—
604C2×Dic3—182no—
605C2×Dic3—182no—
606C2×Dic3—184no—
607C2×Dic3C22×D911yescharacteristic
608C2×Dic3C22×D911yescharacteristic
609C2×Dic3C22×D911yescharacteristic
610D12—94no—
611D12—94no—
612C4×D3—22no—
613C4×D3—62no—
614C4×D3—94no—
615C4×D3—94no—
616C4×D3—94no—
617C4×D3—94no—
618C4×D3—184no—
619C4×D3—182no—
620C4×D3—182no—
621C4×D3—182no—
622C4×D3—182no—
623C4×D3—182no—
624C4×D3—182no—
625C4×D3—182no—
626C4×D3—182no—
627C4×D3—182no—
628C4×D3—182no—
629C4×D3—184no—
630C4×D3—184no—
631C4×D3—184no—
632C4×D3—182no—
633C4×D3—182no—
634C2×C32—22no—
635C2×C32C22×C4×D311yescharacteristic
636C2×C32C2×D3×D411yescharacteristic
637C2×C32D3×#4111yescharacteristic
638C3⋊D3—34no—
639C3⋊D3—62no—
640C3×D3—22no—
641C3×D3—62no—
642C2×C9—24no—
643C2×C9—22no—
644C2×C9—21no—
645C2×C9—21no—
646C2×C9—21no—
647C2×C9—62no—
648C2×C9C22×C4×D311yescharacteristic
649C2×C9C2×D3×D411yescharacteristic
650C2×C9D3×#4111yescharacteristic
651D9—22no—
652D9—34no—
653D9—64no—
654D9—64no—
655D9—62no—
656C24—271no—
657C24—271no—
658C2×D4—31no—
659C2×D4—91no—
660C2×D4—271no—
661C2×D4—271no—
662C2×D4—278no—
663C22×C4—31no—
664C22×C4—91no—
665C22×C4—271no—
666C22×C4—271no—
667C22×C4—271no—
668C22×C4—271no—
669C22×C4—271no—
670C22×C4—271no—
671C22×C4—271no—
672C22×C4—271no—
673C22×C4—271no—
674C22×C4—271no—
675C22×C4—544no—
676C22×C4—544no—
677C22×C4D3×D911yescharacteristic, complemented
678C4⋊C4—31no—
679C4⋊C4—91no—
680C4⋊C4—271no—
681C4⋊C4—271no—
682C22⋊C4—31no—
683C22⋊C4—31no—
684C22⋊C4—91no—
685C22⋊C4—91no—
686C22⋊C4—271no—
687C22⋊C4—271no—
688C22⋊C4—271no—
689C22⋊C4—271no—
690C42—31no—
691C42—91no—
692C42—271no—
693C42—271no—
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—22no—
702C22×C3—32no—
703C22×C3—61no—
704C22×C3—61no—
705C22×C3—92no—
706C22×C3—181no—
707C22×C3—181no—
708C22×C3C2×C4×D912yescomplemented
709C22×C3C23×D911yescharacteristic
710C22×C3C4×D3212yes—
711C22×C3C22×D3211yescharacteristic
712C2×D3—21no—
713C2×D3—21no—
714C2×D3—32no—
715C2×D3—61no—
716C2×D3—61no—
717C2×D3—92no—
718C2×D3—92no—
719C2×D3—92no—
720C2×D3—92no—
721C2×D3—92no—
722C2×D3—92no—
723C2×D3—92no—
724C2×D3—92no—
725C2×D3—182no—
726C2×D3—182no—
727C2×D3—182no—
728C2×D3—182no—
729C2×D3—188no—
730C2×D3—188no—
731C2×D3—188no—
732C2×D3—188no—
733C2×D3—182no—
734C2×D3—1816no—
735C2×D3—182no—
736C2×D3—181no—
737C2×D3—181no—
738C2×D3—181no—
739C2×D3—181no—
740C2×D3C2×C4×D912yescomplemented
741C3×C4—22no—
742C3×C4—21no—
743C3×C4—21no—
744C3×C4—22no—
745C3×C4—32no—
746C3×C4—61no—
747C3×C4—61no—
748C3×C4—92no—
749C3×C4—181no—
750C3×C4—181no—
751C3×C4D4×D912yescomplemented
752C3×C4#381112yes—
753Dic3—21no—
754Dic3—21no—
755Dic3—32no—
756Dic3—61no—
757Dic3—61no—
758Dic3—92no—
759Dic3—92no—
760Dic3—182no—
761Dic3—182no—
762Dic3—181no—
763Dic3—181no—
764Dic3C2×C4×D912yescomplemented
765C32C4×D3×D411yescharacteristic
766C9—21no—
767C9C4×D3×D411yescharacteristic, complemented
768C23—31no—
769C23—91no—
770C23—274no—
771C23—271no—
772C23—271no—
773C23—274no—
774C23—542no—
775C23—542no—
776C23—542no—
777C23—542no—
778C23C2×D3×D911yescharacteristic
779D4—34no—
780D4—94no—
781D4—274no—
782D4—274no—
783C2×C4—22no—
784C2×C4—31no—
785C2×C4—31no—
786C2×C4—31no—
787C2×C4—62no—
788C2×C4—91no—
789C2×C4—91no—
790C2×C4—91no—
791C2×C4—182no—
792C2×C4—274no—
793C2×C4—271no—
794C2×C4—274no—
795C2×C4—271no—
796C2×C4—542no—
797C2×C4—542no—
798C2×C4—542no—
799C2×C4—542no—
800C2×C4—542no—
801C2×C4—542no—
802C2×C4—542no—
803C2×C4—542no—
804C2×C4C2×D3×D911yescharacteristic
805C2×C4C2×D3×D911yescharacteristic
806C2×C3—24no—
807C2×C3—22no—
808C2×C3—22no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—62no—
813C2×C3—182no—
814C2×C3C22×C4×D911yescharacteristic
815C2×C3C2×D4×D911yescharacteristic
816C2×C3#41×D911yescharacteristic
817C2×C3C2×C4×D3211yescharacteristic
818C2×C3#6430611yescharacteristic
819C2×C3C2×#381111yescharacteristic
820D3—22no—
821D3—62no—
822D3—94no—
823D3—94no—
824D3—184no—
825D3—184no—
826D3—182no—
827D3—182no—
828C22—21no—
829C22—21no—
830C22—32no—
831C22—61no—
832C22—61no—
833C22—92no—
834C22—181no—
835C22—181no—
836C22—272no—
837C22—272no—
838C22—272no—
839C22—272no—
840C22—548no—
841C22—548no—
842C22—541no—
843C22—541no—
844C22C4×D3×D912yescomplemented
845C22C22×D3×D911yescharacteristic
846C4—21no—
847C4—32no—
848C4—61no—
849C4—61no—
850C4—92no—
851C4—181no—
852C4—181no—
853C4—272no—
854C4—541no—
855C4#8866812yesdirect product factor
856C3—21no—
857C3C4×D4×D911yescharacteristic, complemented
858C3C4×#381111yescharacteristic
859C2—22no—
860C2—62no—
861C2—182no—
862C2—274no—
863C2—542no—
864C2C2×C4×D3×D911yescharacteristic
865C2#1172247511yescharacteristic
866C2C2×#8866811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
socleC22×C32C23×D3
prime radicalC2×#88668C2
cosocleC22×C3×C9C24
hypercenterC22×C4D3×D9
hypocenterC3×C9C2×C4×D4
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
3. C2×C4×D3×D9C2semidirect
4. C4×C9×#67C2semidirect
5. C3×C4×#611C2semidirect
6. #67⋊Dic9C2semidirect
7. #11721274C2semidirect
8. #611⋊Dic3C2semidirect
9. #11721048C2semidirect
10. C4×#6195C2semidirect
11. #11721014C2semidirect
12. C4×#6192C2semidirect
13. #11720980C2semidirect
14. C4×(C3⋊D9)⋊C4C2semidirect
15. #11720978C2semidirect
20. C22×C3×C4×C9C22semidirect
21. C22×C3⋊Dic9C22semidirect
25. C2×C4×C3⋊D9C22semidirect
26. C2×C4×C3⋊D9C22semidirect
29. C2×C4×D3×C9C22semidirect
30. C2×C3×C4×D9C22semidirect
31. #88668C4direct (N × H)
33. C2×D3×Dic9C22semidirect
38. C2×Dic3×D9C22semidirect
40. C9×#217C22semidirect
41. C3×#3676C22semidirect
42. C9×(C2×D3)⋊C4C22semidirect
43. C3×(C2×D9)⋊C4C22semidirect
44. C9×Dic3⋊C4C22semidirect
45. C4×C9×Dic3C22semidirect
46. C3×Dic9⋊C4C22semidirect
47. C3×C4×Dic9C22semidirect
48. (C2×D3)⋊Dic9C22semidirect
49. #88445C22semidirect
50. #88445C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. Dic3⋊Dic9C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic3×Dic9C22semidirect
55. Dic3×Dic9C22semidirect
78. C4×#611D3semidirect
90. C22×C3⋊D9C2×C4semidirect
97. C2×D3×D9C2×C4semidirect
107. C4×C3⋊D9D4semidirect
108. C9×#67C2×C4semidirect
109. C3×#611C2×C4semidirect
118. #6195C2×C4semidirect
120. #6192C2×C4semidirect
123. (C3⋊D9)⋊C4C2×C4semidirect
171. C22×C4×C9C2×D3semidirect
194. C2×C4×D9C2×D3semidirect
200. #3676C2×D3semidirect
204. (C2×D9)⋊C4C2×D3semidirect
207. Dic9⋊C4C2×D3semidirect
210. C4×Dic9C2×D3semidirect
213. C22×C3×C9C22×C4semidirect
219. C2×C3⋊D9C22×C4semidirect
224. C2×D3×C9C22×C4semidirect
227. C2×C3×D9C22×C4semidirect
230. C3×C4×C9C2×D4semidirect
232. C3⋊Dic9C2×D4semidirect
235. C9×Dic3C22×C4semidirect
238. C3×Dic9C22×C4semidirect
253. C4×#67D9semidirect
337. #611C4×D3semidirect
368. C3⋊D9C4×D4semidirect
381. C22×C3×C4C2×D9semidirect
422. C2×C4×D3C2×D9semidirect
434. #217C2×D9semidirect
442. (C2×D3)⋊C4C2×D9semidirect
448. Dic3⋊C4C2×D9semidirect
454. C4×Dic3C2×D9semidirect
492. C22×C9C2×C4×D3semidirect
511. C2×D9C2×C4×D3semidirect
518. C4×C9D3×D4semidirect
525. Dic9C2×C4×D3semidirect
541. C3×C9C2×C4×D4semidirect
592. #67C4×D9semidirect
677. C22×C4D3×D9semidirect
708. C22×C3C2×C4×D9semidirect
740. C2×D3C2×C4×D9semidirect
751. C3×C4D4×D9semidirect
764. Dic3C2×C4×D9semidirect
767. C9C4×D3×D4semidirect
844. C22C4×D3×D9semidirect
855. C4#88668direct (N × H)
857. C3C4×D4×D9semidirect

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×#886682
C2×C4×D3×D92
C4×C9×#672
C3×C4×#6112
#67⋊Dic92
#117212742
#611⋊Dic32
#117210482
C4×#61952
#117210142
C4×#61922
#117209802
C4×(C3⋊D9)⋊C42
#117209782
C4×#38113
C4×D4×D93