Finite Group Databasebeta

← #13148394

Subgroups — #13148394

Order 1728.

1108 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#611C211yesmaximal, characteristic
2#11721727C211yesmaximal, characteristic, complemented
3D3×C9×C22⋊C4C211yesmaximal, characteristic, complemented
4C3×#611⋊C4C211yesmaximal, characteristic, complemented
5#611⋊Dic3C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
7#11721241C211yesmaximal, characteristic, complemented
8#11721048C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721030C211yesmaximal, characteristic, complemented
11C4×#6195C211yesmaximal, characteristic, complemented
12C4×#6194C211yesmaximal, characteristic, complemented
13#11721011C211yesmaximal, characteristic, complemented
14#11721010C211yesmaximal, characteristic, complemented
15#11720976C211yesmaximal, characteristic, complemented
16#10594254—31nomaximal
17#10589588—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C22×C3⋊Dic9C2211yescharacteristic, complemented
22C2×C4×C3⋊D9C2211yescharacteristic, complemented
23C2×C3×#611C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic, complemented
25C2×C4×D3×C9C2211yescharacteristic, complemented
26C2×C4×D3×C9C2211yescharacteristic, complemented
27C2×C3×C4×D9C2211yescharacteristic, complemented
28D3×#611C418yescomplemented
29C2×#6195C2211yescharacteristic
30C2×#6194C2211yescharacteristic
31C2×D3×Dic9C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
33C2×Dic3×D9C2211yescharacteristic, complemented
34C3×C9×C22⋊C4C2211yescharacteristic, complemented
35#88536C2211yescharacteristic, complemented
36#88534C2211yescharacteristic, complemented
37C4×C3⋊Dic9C2211yescharacteristic, complemented
38C9×#217C2211yescharacteristic, complemented
39C9×(C2×D3)⋊C4C2211yescharacteristic
40C9×(C2×D3)⋊C4C2211yescharacteristic
41C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
42C3×Dic9⋊C4C2211yescharacteristic, complemented
43C3×C4×Dic9C2211yescharacteristic, complemented
44(C2×D3)⋊Dic9C2211yescharacteristic
45(C2×D3)⋊Dic9C2211yescharacteristic
46(C2×D3)⋊Dic9C2211yescharacteristic, complemented
47(C2×D3)⋊Dic9C2211yescharacteristic, complemented
48#88445C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50#88442C2211yescharacteristic, complemented
51Dic9⋊Dic3C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53Dic3×Dic9C2211yescharacteristic, complemented
54C2×D3×#67—31no—
55#64090—31no—
56C3×#67⋊C4—31no—
57C3×D3×C22⋊C4D311yescharacteristic
58#67⋊Dic3—31no—
59C2×(C2×D3)⋊Dic3—31no—
60#63952—31no—
61#63921—31no—
62D3×(C2×D3)⋊C4—31no—
63#63904—31no—
64C4×#626—31no—
65C4×#625—31no—
66#63879—31no—
67#63878—31no—
68#63877—31no—
69C22×#611—31no—
70C2×C9×C22⋊C4—31no—
71C2×#3676—31no—
72C4×#611—31no—
73C4×#611—31no—
74C4×#611—31no—
75C4×#611—31no—
76#611⋊C4—31no—
77#611⋊C4—31no—
78#611⋊C4—31no—
79#611⋊C4—61no—
80#611⋊C4D311yescharacteristic, complemented
81C22⋊C4×D9—31no—
82C22⋊C4×D9—31no—
83#63439—31no—
84#63439—31no—
85C23×C3×C9C2311yescharacteristic
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9—41no—
88C22×D3×C9—41no—
89C22×D3×C9C2×C414yescomplemented
90C22×D3×C9C2311yescharacteristic
91C22×D3×C9C2311yescharacteristic
92C22×C3×D9C2311yescharacteristic
93C2×D3×D9—41no—
94C2×D3×D9—41no—
95C2×D3×D9C2×C414yescomplemented
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3×C4×C9C2311yescharacteristic
98#6233C2×C414yescomplemented
99C2×C3⋊Dic9—41no—
100C2×C3⋊Dic9C2311yescharacteristic
101C2×C3⋊Dic9C2311yescharacteristic
102C2×C3⋊Dic9C2311yescharacteristic
103C4×C3⋊D9—41no—
104C3×#611C2×C414yescomplemented
105C2×C9×Dic3C2311yescharacteristic
106C2×C9×Dic3C2311yescharacteristic
107C2×C3×Dic9—41no—
108C2×C3×Dic9C2311yescharacteristic
109C2×C3×Dic9C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C4×D3×C9—41no—
112C4×D3×C9—41no—
113C3×C4×D9—41no—
114#6195C2×C414yescomplemented
115#6194C2×C414yescomplemented
116D3×Dic9C2×C414yescomplemented
117(C3⋊D9)⋊C4—41no—
118Dic3×D9—41no—
119#5545—91no—
120#5486—91no—
121C23×C3×D3C2×D311yescharacteristic
122C22×D32—31no—
123C2×#638—31no—
124C22×C3⋊Dic3—31no—
125C2×C4×C3⋊D3—31no—
126C2×C3×#67—31no—
127C22×C3×Dic3—31no—
128C2×C3×C4×D3—31no—
129C2×C3×C4×D3C2×D311yescharacteristic
130C2×C3×C4×D3C2×D311yescharacteristic
131D3×#67—38no—
132C2×#626—31no—
133C2×#625—31no—
134C2×#624—31no—
135C2×D3×Dic3—31no—
136C2×D3×Dic3—31no—
137C24×C9—31no—
138C23×D9—31no—
139C32×C22⋊C4C2×D311yescharacteristic
140#3752—31no—
141#3750—31no—
142C4×C3⋊Dic3—31no—
143C3×#217C2×D311yescharacteristic
144C3×(C2×D3)⋊C4—31no—
145C3×(C2×D3)⋊C4C2×D311yescharacteristic
146C3×(C2×D3)⋊C4C2×D311yescharacteristic
147C3×Dic3⋊C4—31no—
148C3×C4×Dic3—31no—
149#3724—31no—
150Dic3⋊Dic3—31no—
151#3722—31no—
152(C2×D3)⋊Dic3—31no—
153(C2×D3)⋊Dic3—31no—
154(C2×D3)⋊Dic3—31no—
155(C2×D3)⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157Dic32—31no—
158Dic32—31no—
159C22×C4×C9—31no—
160C22×C4×C9—31no—
161C2×#611—31no—
162C2×#611—31no—
163C2×#611—38no—
164C2×#611—31no—
165C2×#611—61no—
166C2×#611C2×D311yescharacteristic
167C22×Dic9—31no—
168C22×Dic9—31no—
169C22×Dic9—61no—
170C22×Dic9C2×D311yescharacteristic, complemented
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—61no—
175C2×C4×D9C2×D311yescharacteristic, complemented
176C9×C22⋊C4—21no—
177C9×C22⋊C4—31no—
178C9×C22⋊C4—31no—
179C9×C22⋊C4—31no—
180C9×C22⋊C4C2×D311yescharacteristic, complemented
181#3676—31no—
182#3676—31no—
183#3676—31no—
184#3676—31no—
185(C2×D9)⋊C4—31no—
186(C2×D9)⋊C4—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—61no—
189(C2×D9)⋊C4C2×D311yescharacteristic, complemented
190Dic9⋊C4—31no—
191Dic9⋊C4—31no—
192Dic9⋊C4—31no—
193Dic9⋊C4—61no—
194Dic9⋊C4C2×D311yescharacteristic, complemented
195C4×Dic9—31no—
196C4×Dic9—31no—
197C4×Dic9—31no—
198C4×Dic9—61no—
199C4×Dic9C2×D311yescharacteristic, complemented
200C22×C3×C9—21no—
201C22×C3×C9—21no—
202C22×C3×C9C22×C412yes—
203C22×C3×C9C2411yescharacteristic
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9C22×C412yes—
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×D3×C9—21no—
211C2×D3×C9—44no—
212C2×D3×C9C22×C412yes—
213C2×D3×C9C22×C412yes—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216C2×C3×D9C22×C412yes—
217D3×D9—44no—
218C3×C4×C9—21no—
219C3×C4×C9—21no—
220C3⋊Dic9—21no—
221C3⋊Dic9—21no—
222C3⋊Dic9C22×C412yes—
223C9×Dic3—21no—
224C9×Dic3—21no—
225C3×Dic9—21no—
226C3×Dic9—21no—
227C3×Dic9C22×C412yes—
228C22×#67—91no—
229C2×D3×D4—91no—
230C3×C4×D4—91no—
231C2×C3×C22⋊C4—31no—
232C2×#217—91no—
233D4×Dic3—91no—
234C4×#67—91no—
235C4×#67—91no—
236C4×#67—91no—
237C4×#67—91no—
238C4×#67—91no—
239C4×#67—91no—
240C2×(C2×D3)⋊C4—91no—
241C2×(C2×D3)⋊C4—91no—
242#893—91no—
243#892—91no—
244#67⋊C4—31no—
245#67⋊C4—91no—
246#67⋊C4—91no—
247#67⋊C4—91no—
248#67⋊C4—91no—
249#67⋊C4—91no—
250#67⋊C4—181no—
251D3×C22⋊C4—91no—
252D3×C22⋊C4—91no—
253D3×C22⋊C4—91no—
254D3×C22⋊C4D911yescharacteristic, complemented
255#877—91no—
256#877—91no—
257C4×D12—91no—
258#872—91no—
259C23×C32C22×D311yescharacteristic
260C22×C3⋊D3—31no—
261C22×C3×D3—31no—
262C22×C3×D3—41no—
263C22×C3×D3—41no—
264C22×C3×D3C4×D314yes—
265C22×C3×D3C22×D311yescharacteristic
266C22×C3×D3C22×D311yescharacteristic
267C2×D32—34no—
268C2×D32—121no—
269C2×D32—121no—
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272#638—34no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C2×C3⋊Dic3—31no—
276C2×C3⋊Dic3—121no—
277C4×C3⋊D3—121no—
278C3×#67—34no—
279C2×C3×Dic3—31no—
280C2×C3×Dic3—31no—
281C2×C3×Dic3—31no—
282C2×C3×Dic3—121no—
283C2×C3×Dic3C22×D311yescharacteristic
284C2×C3×Dic3C22×D311yescharacteristic
285C3×C4×D3—41no—
286C3×C4×D3—41no—
287C3×C4×D3—121no—
288#626—34no—
289#625—34no—
290#624—121no—
291D3×Dic3—34no—
292D3×Dic3—121no—
293C23×C9—21no—
294C23×C9—31no—
295C23×C9—31no—
296C23×C9—34no—
297C23×C9—121no—
298C23×C9—121no—
299C23×C9C22×D311yescharacteristic
300C22×D9—31no—
301C22×D9—34no—
302C22×D9—61no—
303C22×D9—121no—
304C22×D9—121no—
305C22×D9C22×D311yescharacteristic
306C2×C4×C9—21no—
307C2×C4×C9—21no—
308C2×C4×C9—31no—
309C2×C4×C9—31no—
310C2×C4×C9—121no—
311C2×C4×C9—121no—
312C2×C4×C9C22×D311yescharacteristic
313C2×C4×C9C22×D311yescharacteristic
314#611—34no—
315#611—34no—
316#611—34no—
317#611—64no—
318#611C4×D314yescomplemented
319C2×Dic9—31no—
320C2×Dic9—34no—
321C2×Dic9—31no—
322C2×Dic9—31no—
323C2×Dic9—41no—
324C2×Dic9—61no—
325C2×Dic9—61no—
326C2×Dic9—61no—
327C2×Dic9—121no—
328C2×Dic9—122no—
329C2×Dic9C22×D311yescharacteristic
330C2×Dic9C22×D311yescharacteristic
331C2×Dic9C22×D311yescharacteristic
332C4×D9—41no—
333C4×D9—121no—
334C4×D9—121no—
335C4×D9—122no—
336C4×D9—121no—
337#518—271noSylow
338C2×C3×C9—22no—
339C2×C3×C9C23×C411yescharacteristic
340C2×C3×C9H(5,𝔽2)11yescharacteristic
341C2×C3×C9H(5,𝔽2)11yescharacteristic
342C3⋊D9—22no—
343D3×C9—22no—
344D3×C9—22no—
345C3×D9—22no—
346C24×C3—31no—
347C23×D3—91no—
348C23×D3—91no—
349C23×D3C2×D911yescharacteristic
350C2×C3×D4—91no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—91no—
354C22×C3×C4—91no—
355C2×#67—31no—
356C2×#67—91no—
357C2×#67—98no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C2×#67—181no—
363C22×Dic3—31no—
364C22×Dic3—91no—
365C22×Dic3—91no—
366C22×Dic3—91no—
367C22×Dic3—91no—
368C22×Dic3—181no—
369D3×D4—98no—
370C2×D12—91no—
371C2×C4×D3—31no—
372C2×C4×D3—91no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—181no—
379C2×C4×D3C2×D911yescharacteristic, complemented
380C2×C4×D3C2×D911yescharacteristic, complemented
381C3×C4⋊C4—91no—
382C3×C22⋊C4—21no—
383C3×C22⋊C4—31no—
384C3×C22⋊C4—31no—
385C3×C22⋊C4—31no—
386C3×C22⋊C4—91no—
387C3×C22⋊C4C2×D911yescharacteristic, complemented
388C3×C22⋊C4D3211yescharacteristic
389C3×C42—91no—
390#217—91no—
391#217—91no—
392#217—91no—
393#217—91no—
394#217—91no—
395#217C2×D911yescharacteristic, complemented
396(C2×D3)⋊C4—31no—
397(C2×D3)⋊C4—91no—
398(C2×D3)⋊C4—91no—
399(C2×D3)⋊C4—91no—
400(C2×D3)⋊C4—91no—
401(C2×D3)⋊C4—91no—
402(C2×D3)⋊C4—91no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—181no—
407(C2×D3)⋊C4C2×D911yescharacteristic
408(C2×D3)⋊C4C2×D911yescharacteristic
409C4⋊Dic3—91no—
410Dic3⋊C4—31no—
411Dic3⋊C4—91no—
412Dic3⋊C4—91no—
413Dic3⋊C4—91no—
414Dic3⋊C4—91no—
415Dic3⋊C4—91no—
416Dic3⋊C4—181no—
417C4×Dic3—31no—
418C4×Dic3—91no—
419C4×Dic3—91no—
420C4×Dic3—91no—
421C4×Dic3—91no—
422C4×Dic3—91no—
423C4×Dic3—91no—
424C4×Dic3—181no—
425C22×C32—21no—
426C22×C32—21no—
427C22×C32C2×C4×D312yes—
428C22×C32C23×D311yescharacteristic
429C2×C3⋊D3—32no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—61no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—32no—
437C2×C3×D3—44no—
438C2×C3×D3—61no—
439C2×C3×D3—61no—
440C2×C3×D3C2×C4×D312yes—
441C2×C3×D3C2×C4×D312yes—
442D32—124no—
443C32×C4—21no—
444C32×C4—21no—
445C3⋊Dic3—32no—
446C3⋊Dic3—61no—
447C3⋊Dic3—61no—
448C3×Dic3—21no—
449C3×Dic3—21no—
450C3×Dic3—32no—
451C3×Dic3—61no—
452C3×Dic3—61no—
453C22×C9—21no—
454C22×C9—21no—
455C22×C9—21no—
456C22×C9—22no—
457C22×C9—32no—
458C22×C9—32no—
459C22×C9—41no—
460C22×C9—41no—
461C22×C9—61no—
462C22×C9—61no—
463C22×C9—61no—
464C22×C9—61no—
465C22×C9—124no—
466C22×C9C2×C4×D312yes—
467C22×C9C23×D311yescharacteristic
468C2×D9—21no—
469C2×D9—21no—
470C2×D9—32no—
471C2×D9—62no—
472C2×D9—61no—
473C2×D9—61no—
474C2×D9—121no—
475C2×D9—121no—
476C2×D9—124no—
477C2×D9C2×C4×D312yes—
478C4×C9—21no—
479C4×C9—21no—
480C4×C9—41no—
481C4×C9—41no—
482C4×C9—61no—
483C4×C9—61no—
484Dic9—21no—
485Dic9—21no—
486Dic9—32no—
487Dic9—62no—
488Dic9—62no—
489Dic9—61no—
490Dic9—61no—
491Dic9—121no—
492Dic9C2×C4×D312yes—
493C22×D4—271no—
494C4×D4—91no—
495C4×D4—271no—
496C4×D4—271no—
497C4×D4—271no—
498C4×D4—271no—
499C4×D4—271no—
500C4×D4—271no—
501C4×D4—271no—
502#117—271no—
503#117—271no—
504C2×C22⋊C4—31no—
505C2×C22⋊C4—271no—
506C2×C22⋊C4—271no—
507C2×C22⋊C4—271no—
508C3×C9#51811yescharacteristic, complemented, Sylow
509C23×C3—21no—
510C23×C3—31no—
511C23×C3—31no—
512C23×C3—34no—
513C23×C3—91no—
514C23×C3—121no—
515C23×C3—121no—
516C23×C3C22×D911yescharacteristic
517C23×C3C2×D3211yescharacteristic
518C22×D3—31no—
519C22×D3—41no—
520C22×D3—41no—
521C22×D3—94no—
522C22×D3—91no—
523C22×D3—91no—
524C22×D3—94no—
525C22×D3—181no—
526C22×D3—361no—
527C22×D3—361no—
528C22×D3—361no—
529C22×D3—361no—
530C22×D3C4×D914yescomplemented
531C22×D3C22×D911yescharacteristic
532C22×D3C22×D911yescharacteristic
533C3×D4—94no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—91no—
539C2×C3×C4—91no—
540C2×C3×C4—91no—
541C2×C3×C4—121no—
542C2×C3×C4—121no—
543C2×C3×C4—361no—
544C2×C3×C4—361no—
545C2×C3×C4C22×D911yescharacteristic
546C2×C3×C4C22×D911yescharacteristic
547C2×C3×C4C2×D3211yescharacteristic
548C2×C3×C4C2×D3211yescharacteristic
549#67—34no—
550#67—94no—
551#67—94no—
552#67—94no—
553#67—94no—
554#67—94no—
555#67—184no—
556C2×Dic3—31no—
557C2×Dic3—31no—
558C2×Dic3—31no—
559C2×Dic3—94no—
560C2×Dic3—91no—
561C2×Dic3—91no—
562C2×Dic3—91no—
563C2×Dic3—91no—
564C2×Dic3—91no—
565C2×Dic3—91no—
566C2×Dic3—121no—
567C2×Dic3—181no—
568C2×Dic3—181no—
569C2×Dic3—181no—
570C2×Dic3—361no—
571C2×Dic3—361no—
572C2×Dic3—361no—
573C2×Dic3—362no—
574C2×Dic3C22×D911yescharacteristic
575C2×Dic3C22×D911yescharacteristic
576D12—94no—
577C4×D3—41no—
578C4×D3—41no—
579C4×D3—94no—
580C4×D3—121no—
581C4×D3—361no—
582C4×D3—361no—
583C4×D3—361no—
584C4×D3—361no—
585C4×D3—362no—
586C4×D3—361no—
587C2×C32—22no—
588C2×C32C22×C4×D311yescharacteristic
589C2×C32#100411yescharacteristic
590C2×C32#100411yescharacteristic
591C3⋊D3—62no—
592C3×D3—22no—
593C3×D3—22no—
594C3×D3—62no—
595C2×C9—22no—
596C2×C9—21no—
597C2×C9—21no—
598C2×C9—21no—
599C2×C9—42no—
600C2×C9—62no—
601C2×C9—62no—
602C2×C9C22×C4×D311yescharacteristic
603C2×C9#100411yescharacteristic
604C2×C9#100911yescharacteristic
605D9—22no—
606D9—62no—
607D9—122no—
608C24—31no—
609C24—271no—
610C2×D4—91no—
611C2×D4—271no—
612C2×D4—278no—
613C2×D4—271no—
614C2×D4—271no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—271no—
620C22×C4—271no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—271no—
624C4⋊C4—91no—
625C4⋊C4—271no—
626C4⋊C4—271no—
627C4⋊C4—271no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—31no—
631C22⋊C4—91no—
632C22⋊C4—271no—
633C22⋊C4—271no—
634C22⋊C4—271no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4D3×D911yescharacteristic, complemented
640C42—91no—
641C42—271no—
642C42—271no—
643C42—271no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—22no—
650C22×C3—32no—
651C22×C3—32no—
652C22×C3—41no—
653C22×C3—41no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3—61no—
658C22×C3—92no—
659C22×C3—124no—
660C22×C3—181no—
661C22×C3—181no—
662C22×C3C2×C4×D912yes—
663C22×C3C23×D911yescharacteristic
664C22×C3C4×D3212yes—
665C22×C3C22×D3211yescharacteristic
666C2×D3—21no—
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—32no—
671C2×D3—44no—
672C2×D3—61no—
673C2×D3—61no—
674C2×D3—92no—
675C2×D3—92no—
676C2×D3—182no—
677C2×D3—181no—
678C2×D3—181no—
679C2×D3—181no—
680C2×D3—181no—
681C2×D3—361no—
682C2×D3—361no—
683C2×D3—364no—
684C2×D3—364no—
685C2×D3C2×C4×D912yes—
686C2×D3C2×C4×D912yes—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—41no—
692C3×C4—41no—
693C3×C4—61no—
694C3×C4—61no—
695C3×C4—92no—
696C3×C4—181no—
697C3×C4—181no—
698Dic3—21no—
699Dic3—21no—
700Dic3—32no—
701Dic3—61no—
702Dic3—61no—
703Dic3—92no—
704Dic3—92no—
705Dic3—182no—
706Dic3—182no—
707Dic3—181no—
708Dic3—181no—
709Dic3—181no—
710Dic3—181no—
711Dic3—361no—
712C32#548611yescharacteristic
713C9—21no—
714C9#554511yescharacteristic, complemented
715C23—31no—
716C23—31no—
717C23—34no—
718C23—91no—
719C23—121no—
720C23—121no—
721C23—274no—
722C23—271no—
723C23—1081no—
724C23—1081no—
725C23C2×D3×D911yescharacteristic
726D4—94no—
727D4—274no—
728D4—274no—
729D4—274no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—91no—
733C2×C4—91no—
734C2×C4—91no—
735C2×C4—121no—
736C2×C4—121no—
737C2×C4—274no—
738C2×C4—271no—
739C2×C4—271no—
740C2×C4—271no—
741C2×C4—361no—
742C2×C4—361no—
743C2×C4—1081no—
744C2×C4—1081no—
745C2×C4—1081no—
746C2×C4—1081no—
747C2×C4C2×D3×D911yescharacteristic
748C2×C4C2×D3×D911yescharacteristic
749C2×C3—22no—
750C2×C3—22no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—62no—
756C2×C3—62no—
757C2×C3—182no—
758C2×C3C22×C4×D911yescharacteristic
759C2×C3#6371011yescharacteristic
760C2×C3#6371011yescharacteristic
761C2×C3C2×C4×D3211yescharacteristic
762C2×C3#6431311yescharacteristic
763C2×C3#6431411yescharacteristic
764D3—22no—
765D3—22no—
766D3—62no—
767D3—182no—
768D3—182no—
769D3—362no—
770C22—21no—
771C22—21no—
772C22—32no—
773C22—32no—
774C22—61no—
775C22—61no—
776C22—61no—
777C22—61no—
778C22—92no—
779C22—124no—
780C22—181no—
781C22—181no—
782C22—272no—
783C22—541no—
784C22—541no—
785C22—1084no—
786C22C4×D3×D912yes—
787C22C22×D3×D911yescharacteristic
788C4—21no—
789C4—21no—
790C4—61no—
791C4—61no—
792C4—92no—
793C4—181no—
794C4—181no—
795C4—272no—
796C4—541no—
797C4—541no—
798C3—21no—
799C3#1058958811yescharacteristic, complemented
800C3#1059425411yescharacteristic
801C2—22no—
802C2—62no—
803C2—62no—
804C2—182no—
805C2—542no—
806C2C2×C4×D3×D911yescharacteristic
807C2#1172249911yescharacteristic
808C2#1172250011yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutatorC2×C3×C9C23×C4
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radicalC2×D3×#611C2
cosocleC22×C3×C9C24
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#518
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. #11721727C2semidirect
3. D3×C9×C22⋊C4C2semidirect
4. C3×#611⋊C4C2semidirect
5. #611⋊Dic3C2semidirect
6. C2×(C2×D3)⋊Dic9C2semidirect
7. #11721241C2semidirect
8. #11721048C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721030C2semidirect
11. C4×#6195C2semidirect
12. C4×#6194C2semidirect
13. #11721011C2semidirect
14. #11721010C2semidirect
15. #11720976C2semidirect
21. C22×C3⋊Dic9C22semidirect
22. C2×C4×C3⋊D9C22semidirect
24. C22×C3×Dic9C22semidirect
25. C2×C4×D3×C9C22semidirect
26. C2×C4×D3×C9C22semidirect
27. C2×C3×C4×D9C22semidirect
28. D3×#611C4semidirect
32. C2×(C3⋊D9)⋊C4C22semidirect
33. C2×Dic3×D9C22semidirect
34. C3×C9×C22⋊C4C22semidirect
35. #88536C22semidirect
36. #88534C22semidirect
37. C4×C3⋊Dic9C22semidirect
38. C9×#217C22semidirect
41. C3×(C2×D9)⋊C4C22semidirect
42. C3×Dic9⋊C4C22semidirect
43. C3×C4×Dic9C22semidirect
46. (C2×D3)⋊Dic9C22semidirect
47. (C2×D3)⋊Dic9C22semidirect
48. #88445C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. #88442C22semidirect
51. Dic9⋊Dic3C22semidirect
52. Dic3×Dic9C22semidirect
53. Dic3×Dic9C22semidirect
80. #611⋊C4D3semidirect
89. C22×D3×C9C2×C4semidirect
95. C2×D3×D9C2×C4semidirect
98. #6233C2×C4semidirect
104. C3×#611C2×C4semidirect
114. #6195C2×C4semidirect
115. #6194C2×C4semidirect
116. D3×Dic9C2×C4semidirect
170. C22×Dic9C2×D3semidirect
175. C2×C4×D9C2×D3semidirect
180. C9×C22⋊C4C2×D3semidirect
189. (C2×D9)⋊C4C2×D3semidirect
194. Dic9⋊C4C2×D3semidirect
199. C4×Dic9C2×D3semidirect
254. D3×C22⋊C4D9semidirect
318. #611C4×D3semidirect
379. C2×C4×D3C2×D9semidirect
380. C2×C4×D3C2×D9semidirect
387. C3×C22⋊C4C2×D9semidirect
395. #217C2×D9semidirect
508. C3×C9#518semidirect
530. C22×D3C4×D9semidirect
639. C22⋊C4D3×D9semidirect
714. C9#5545semidirect
799. C3#10589588semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
#117217272
D3×C9×C22⋊C42
C3×#611⋊C42
#611⋊Dic32
C2×(C2×D3)⋊Dic92
#117212412
#117210482
D9×(C2×D3)⋊C42
#117210302
C4×#61952
C4×#61942
#117210112
#117210102
#117209762
#105942543
#105895883