Finite Group Databasebeta

← C3×#10589693 #13152756

Subgroups — C3×#10589693 #13152756

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#611C211yesmaximal, characteristic, complemented
2C2×C3×#3699C211yesmaximal, characteristic, complemented
3C3×C9×#120C211yesmaximal, characteristic, complemented
4C2×C3×#3676C211yesmaximal, characteristic, complemented
5C3×#63501C211yesmaximal, characteristic, complemented
6C3×#63501C211yesmaximal, characteristic, complemented
7C3×#63500C211yesmaximal, characteristic, complemented
8C3×#63499C211yesmaximal, characteristic, complemented
9C3×D4×Dic9C211yesmaximal, characteristic, complemented
10C3×#63448C211yesmaximal, characteristic, complemented
11C3×#63447C211yesmaximal, characteristic, complemented
12C3×#63445C211yesmaximal, characteristic, complemented
13C3×#611⋊C4C211yesmaximal, characteristic, complemented
14C3×C22⋊C4×D9C211yesmaximal, characteristic, complemented
15C3×#63440C211yesmaximal, characteristic, complemented
16C3×#5591—31nomaximal
17#10589693C311yesmaximal, characteristic, direct product factor
18C24×C3×C9C2211yescharacteristic
19C23×C3×D9C2211yescharacteristic
20C2×C3×D4×C9C2211yescharacteristic
21C2×C3×D4×C9C2211yescharacteristic, complemented
22C2×C3×D4×C9C2211yescharacteristic, complemented
23C2×C3×#611—24no—
24C2×C3×#611C2211yescharacteristic
25C2×C3×#611C2211yescharacteristic
26C2×C3×#611C2211yescharacteristic
27C2×C3×#611C2211yescharacteristic
28C2×C3×#611C2211yescharacteristic, complemented
29C2×C3×#611C2211yescharacteristic, complemented
30C22×C3×Dic9C2211yescharacteristic
31C22×C3×Dic9C2211yescharacteristic, complemented
32C22×C3×Dic9C2211yescharacteristic, complemented
33C22×C3×Dic9C2211yescharacteristic, complemented
34C3×#3699—24no—
35C2×C3×C4×D9C2211yescharacteristic, complemented
36C2×C3×C4×D9C2211yescharacteristic, complemented
37C2×C3×Dic18C2211yescharacteristic, complemented
38C3×C9×C22⋊C4C2211yescharacteristic
39C3×C9×C22⋊C4C2211yescharacteristic, complemented
40C3×C9×C22⋊C4C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic
42C3×#3676C2211yescharacteristic
43C3×#3676C2211yescharacteristic, complemented
44C3×#3676C2211yescharacteristic, complemented
45C3×#3676C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
48C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
49C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
50C3×C4⋊Dic9C2211yescharacteristic, complemented
51C3×C4⋊Dic9C2211yescharacteristic, complemented
52C3×Dic9⋊C4C2211yescharacteristic, complemented
53C3×Dic9⋊C4C2211yescharacteristic, complemented
54C3×C4×Dic9C2211yescharacteristic, complemented
55C22×C3×#67—31no—
56C2×C3×#237—31no—
57C32×#120D311yescharacteristic
58C2×C3×#217—31no—
59C3×#939—31no—
60C3×#939—31no—
61C3×#938—31no—
62C3×#937—31no—
63C3×D4×Dic3—31no—
64C3×#886—31no—
65C3×#885—31no—
66C3×#883—31no—
67C3×#67⋊C4—31no—
68C3×D3×C22⋊C4—31no—
69C3×#878—31no—
70C22×#611C2×C311yescharacteristic, complemented
71C2×#3699C2×C311yescharacteristic, complemented
72C9×#120—21no—
73C9×#120C2×C311yescharacteristic, complemented
74C2×#3676C2×C311yescharacteristic, complemented
75#63501C2×C311yescharacteristic, complemented
76#63501C2×C311yescharacteristic, complemented
77#63500C2×C311yescharacteristic, complemented
78#63499C2×C311yescharacteristic, complemented
79D4×Dic9C2×C311yescharacteristic, complemented
80#63448C2×C311yescharacteristic, complemented
81#63447C2×C311yescharacteristic, complemented
82#63445C2×C311yescharacteristic, complemented
83#611⋊C4C2×C311yescharacteristic, complemented
84C22⋊C4×D9C2×C311yescharacteristic, complemented
85#63440C2×C311yescharacteristic, complemented
86C23×C3×C9—22no—
87C23×C3×C9—22no—
88C23×C3×C9—41no—
89C23×C3×C9C2311yescharacteristic
90C23×C3×C9C2311yescharacteristic
91C23×C3×C9C2311yescharacteristic
92C23×C3×C9C2311yescharacteristic
93C22×C3×D9—22no—
94C22×C3×D9—22no—
95C22×C3×D9—41no—
96C22×C3×D9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98C3×D4×C9—22no—
99C3×D4×C9—22no—
100C3×D4×C9—41no—
101C2×C3×C4×C9C2311yescharacteristic
102C2×C3×C4×C9C2311yescharacteristic
103C2×C3×C4×C9C2311yescharacteristic
104C3×#611—22no—
105C3×#611—22no—
106C3×#611—22no—
107C3×#611—22no—
108C3×#611—41no—
109C3×#611D414yescomplemented
110C2×C3×Dic9—22no—
111C2×C3×Dic9—22no—
112C2×C3×Dic9—22no—
113C2×C3×Dic9—41no—
114C2×C3×Dic9C2311yescharacteristic
115C2×C3×Dic9C2311yescharacteristic
116C2×C3×Dic9C2311yescharacteristic
117C2×C3×Dic9C2311yescharacteristic
118C2×C3×Dic9C2311yescharacteristic
119C2×C3×Dic9C2311yescharacteristic
120C3×C4×D9—22no—
121C3×C4×D9—41no—
122C3×Dic18—22no—
123C3×#546—91no—
124#5591—31no—
125C24×C32C2×D311yescharacteristic
126C23×C3×D3—31no—
127C2×C32×D4C2×D311yescharacteristic
128C2×C32×D4C2×D311yescharacteristic
129C2×C32×D4C2×D311yescharacteristic
130C2×C3×#67—31no—
131C2×C3×#67—31no—
132C2×C3×#67—31no—
133C2×C3×#67—31no—
134C2×C3×#67—31no—
135C2×C3×#67—31no—
136C2×C3×#67—64no—
137C22×C3×Dic3—31no—
138C22×C3×Dic3—31no—
139C22×C3×Dic3—31no—
140C22×C3×Dic3—31no—
141C3×#237—64no—
142C2×C3×C4×D3—31no—
143C2×C3×C4×D3—31no—
144C2×C3×Dic6—31no—
145C24×C9—21no—
146C24×C9C22×C311yescharacteristic
147C23×D9C22×C311yescharacteristic
148C32×C22⋊C4C2×D311yescharacteristic
149C32×C22⋊C4C2×D311yescharacteristic
150C32×C22⋊C4C2×D311yescharacteristic
151C3×#217—31no—
152C3×#217—31no—
153C3×#217—31no—
154C3×#217—31no—
155C3×#217—31no—
156C3×(C2×D3)⋊C4—31no—
157C3×(C2×D3)⋊C4—31no—
158C3×(C2×D3)⋊C4—31no—
159C3×(C2×D3)⋊C4—31no—
160C3×C4⋊Dic3—31no—
161C3×C4⋊Dic3—31no—
162C3×Dic3⋊C4—31no—
163C3×Dic3⋊C4—31no—
164C3×C4×Dic3—31no—
165C2×D4×C9—21no—
166C2×D4×C9—21no—
167C2×D4×C9—21no—
168C2×D4×C9C22×C311yescharacteristic
169C2×D4×C9C22×C311yescharacteristic, complemented
170C2×D4×C9C22×C311yescharacteristic, complemented
171C2×#611—24no—
172C2×#611C22×C311yescharacteristic
173C2×#611C22×C311yescharacteristic
174C2×#611C22×C311yescharacteristic
175C2×#611C22×C311yescharacteristic
176C2×#611C22×C311yescharacteristic, complemented
177C2×#611C22×C311yescharacteristic, complemented
178C22×Dic9C22×C311yescharacteristic
179C22×Dic9C22×C311yescharacteristic, complemented
180C22×Dic9C22×C311yescharacteristic, complemented
181C22×Dic9C22×C311yescharacteristic, complemented
182#3699—24no—
183C2×C4×D9C22×C311yescharacteristic, complemented
184C2×C4×D9C22×C311yescharacteristic, complemented
185C2×Dic18C22×C311yescharacteristic, complemented
186C9×C22⋊C4—21no—
187C9×C22⋊C4—21no—
188C9×C22⋊C4—21no—
189C9×C22⋊C4C22×C311yescharacteristic
190C9×C22⋊C4C22×C311yescharacteristic, complemented
191C9×C22⋊C4C22×C311yescharacteristic, complemented
192#3676C22×C311yescharacteristic
193#3676C22×C311yescharacteristic
194#3676C22×C311yescharacteristic, complemented
195#3676C22×C311yescharacteristic, complemented
196#3676C22×C311yescharacteristic, complemented
197(C2×D9)⋊C4C22×C311yescharacteristic, complemented
198(C2×D9)⋊C4C22×C311yescharacteristic, complemented
199(C2×D9)⋊C4C22×C311yescharacteristic, complemented
200(C2×D9)⋊C4C22×C311yescharacteristic, complemented
201C4⋊Dic9C22×C311yescharacteristic, complemented
202C4⋊Dic9C22×C311yescharacteristic, complemented
203Dic9⋊C4C22×C311yescharacteristic, complemented
204Dic9⋊C4C22×C311yescharacteristic, complemented
205C4×Dic9C22×C311yescharacteristic, complemented
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9—21no—
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9—21no—
213C22×C3×C9—21no—
214C22×C3×C9—21no—
215C22×C3×C9—21no—
216C22×C3×C9—44no—
217C22×C3×C9C2×D412yes—
218C22×C3×C9#4112yescomplemented
219C22×C3×C9C2411yescharacteristic
220C2×C3×D9—21no—
221C2×C3×D9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9—44no—
226C2×C3×D9C2×D412yes—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3×C4×C9—21no—
230C3×Dic9—21no—
231C3×Dic9—21no—
232C3×Dic9—21no—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C2×C3×#41—91no—
237C22×C3×D4—91no—
238C22×#67—31no—
239C2×#237—31no—
240C3×#124—91no—
241C3×#123—91no—
242C3×#123—91no—
243C3×C22⋊Q8—91no—
244C3×#121—91no—
245C3×#121—91no—
246C3×#121—91no—
247C3×#120—21no—
248C3×#120—91no—
249C3×#120D911yescharacteristic, complemented
250C3×#120C3×D311yescharacteristic
251C3×C4×D4—91no—
252C3×C4×D4—91no—
253C2×C3×C22⋊C4—91no—
254C2×C3×C22⋊C4—91no—
255C2×#217—31no—
256#939—31no—
257#939—31no—
258#938—31no—
259#937—31no—
260D4×Dic3—31no—
261#886—31no—
262#885—31no—
263#883—31no—
264#67⋊C4—31no—
265D3×C22⋊C4—31no—
266#878—31no—
267C23×C32—22no—
268C23×C32—22no—
269C23×C32—41no—
270C23×C32C22×D311yescharacteristic
271C23×C32C22×D311yescharacteristic
272C23×C32C22×D311yescharacteristic
273C23×C32C22×D311yescharacteristic
274C22×C3×D3—31no—
275C22×C3×D3—31no—
276C22×C3×D3—62no—
277C22×C3×D3—62no—
278C22×C3×D3—121no—
279C32×D4—22no—
280C32×D4—22no—
281C32×D4—41no—
282C2×C32×C4C22×D311yescharacteristic
283C2×C32×C4C22×D311yescharacteristic
284C2×C32×C4C22×D311yescharacteristic
285C3×#67—34no—
286C3×#67—62no—
287C3×#67—62no—
288C3×#67—62no—
289C3×#67—62no—
290C3×#67—121no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—31no—
293C2×C3×Dic3—31no—
294C2×C3×Dic3—31no—
295C2×C3×Dic3—31no—
296C2×C3×Dic3—31no—
297C2×C3×Dic3—62no—
298C2×C3×Dic3—62no—
299C2×C3×Dic3—62no—
300C2×C3×Dic3—121no—
301C3×C4×D3—62no—
302C3×C4×D3—121no—
303C3×Dic6—62no—
304C23×C9—22no—
305C23×C9—22no—
306C23×C9—21no—
307C23×C9—21no—
308C23×C9—21no—
309C23×C9—21no—
310C23×C9—42no—
311C23×C9—42no—
312C23×C9—41no—
313C23×C9—42no—
314C23×C9C23×C311yescharacteristic
315C23×C9C23×C311yescharacteristic
316C23×C9C23×C311yescharacteristic
317C23×C9C23×C311yescharacteristic
318C22×D9—22no—
319C22×D9—22no—
320C22×D9—41no—
321C22×D9C23×C311yescharacteristic
322C22×D9C23×C311yescharacteristic
323D4×C9—22no—
324D4×C9—22no—
325D4×C9—42no—
326D4×C9—42no—
327D4×C9—41no—
328D4×C9—42no—
329C2×C4×C9—21no—
330C2×C4×C9—21no—
331C2×C4×C9—21no—
332C2×C4×C9C23×C311yescharacteristic
333C2×C4×C9C23×C311yescharacteristic
334C2×C4×C9C23×C311yescharacteristic
335#611—22no—
336#611—22no—
337#611—22no—
338#611—22no—
339#611—41no—
340#611C3×D414yescomplemented
341C2×Dic9—22no—
342C2×Dic9—22no—
343C2×Dic9—22no—
344C2×Dic9—41no—
345C2×Dic9C23×C311yescharacteristic
346C2×Dic9C23×C311yescharacteristic
347C2×Dic9C23×C311yescharacteristic
348C2×Dic9C23×C311yescharacteristic
349C2×Dic9C23×C311yescharacteristic
350C2×Dic9C23×C311yescharacteristic
351C4×D9—22no—
352C4×D9—41no—
353Dic18—22no—
354#546—91noSylow
355C2×C3×C9—22no—
356C2×C3×C9—22no—
357C2×C3×C9—41no—
358C2×C3×C9—41no—
359C2×C3×C9C22×D411yescharacteristic
360C2×C3×C9C2×#4111yescharacteristic
361C2×C3×C9H(5,𝔽2)11yescharacteristic
362C3×D9—22no—
363C3×D9—41no—
364C24×C3—21no—
365C24×C3—91no—
366C24×C3C2×D911yescharacteristic
367C24×C3C2×C3×D311yescharacteristic
368C23×D3—31no—
369C3×#41—184no—
370C2×C3×Q8—91no—
371C2×C3×D4—21no—
372C2×C3×D4—21no—
373C2×C3×D4—21no—
374C2×C3×D4—91no—
375C2×C3×D4—91no—
376C2×C3×D4—91no—
377C2×C3×D4—91no—
378C2×C3×D4—91no—
379C2×C3×D4—91no—
380C2×C3×D4—184no—
381C2×C3×D4C2×D911yescharacteristic
382C2×C3×D4C2×D911yescharacteristic, complemented
383C2×C3×D4C2×D911yescharacteristic, complemented
384C2×C3×D4C2×C3×D311yescharacteristic
385C2×C3×D4C2×C3×D311yescharacteristic
386C2×C3×D4C2×C3×D311yescharacteristic
387C22×C3×C4—91no—
388C22×C3×C4—91no—
389C22×C3×C4—91no—
390C22×C3×C4—91no—
391C22×C3×C4—91no—
392C22×C3×C4—91no—
393C2×#67—31no—
394C2×#67—31no—
395C2×#67—31no—
396C2×#67—31no—
397C2×#67—31no—
398C2×#67—31no—
399C2×#67—64no—
400C22×Dic3—31no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—31no—
404#237—64no—
405C2×C4×D3—31no—
406C2×C4×D3—31no—
407C2×Dic6—31no—
408C3×C4⋊C4—91no—
409C3×C4⋊C4—91no—
410C3×C4⋊C4—91no—
411C3×C4⋊C4—91no—
412C3×C22⋊C4—21no—
413C3×C22⋊C4—21no—
414C3×C22⋊C4—21no—
415C3×C22⋊C4—91no—
416C3×C22⋊C4—91no—
417C3×C22⋊C4—91no—
418C3×C22⋊C4—91no—
419C3×C22⋊C4—91no—
420C3×C22⋊C4—91no—
421C3×C22⋊C4—91no—
422C3×C22⋊C4—91no—
423C3×C22⋊C4—91no—
424C3×C22⋊C4C2×D911yescharacteristic
425C3×C22⋊C4C2×D911yescharacteristic, complemented
426C3×C22⋊C4C2×D911yescharacteristic, complemented
427C3×C22⋊C4C2×C3×D311yescharacteristic
428C3×C22⋊C4C2×C3×D311yescharacteristic
429C3×C22⋊C4C2×C3×D311yescharacteristic
430C3×C42—91no—
431#217—31no—
432#217—31no—
433#217—31no—
434#217—31no—
435#217—31no—
436(C2×D3)⋊C4—31no—
437(C2×D3)⋊C4—31no—
438(C2×D3)⋊C4—31no—
439(C2×D3)⋊C4—31no—
440C4⋊Dic3—31no—
441C4⋊Dic3—31no—
442Dic3⋊C4—31no—
443Dic3⋊C4—31no—
444C4×Dic3—31no—
445C22×C32—21no—
446C22×C32—21no—
447C22×C32—21no—
448C22×C32—21no—
449C22×C32—21no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—21no—
454C22×C32—21no—
455C22×C32—44no—
456C22×C32D3×D412yes—
457C22×C32#23712yes—
458C22×C32C23×D311yescharacteristic
459C2×C3×D3—32no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3—61no—
463C2×C3×D3—61no—
464C2×C3×D3—61no—
465C2×C3×D3—124no—
466C32×C4—21no—
467C32×C4—21no—
468C32×C4—21no—
469C3×Dic3—32no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C3×Dic3—61no—
474C3×Dic3—61no—
475C22×C9—21no—
476C22×C9—21no—
477C22×C9—21no—
478C22×C9—21no—
479C22×C9—22no—
480C22×C9—21no—
481C22×C9—21no—
482C22×C9—21no—
483C22×C9—21no—
484C22×C9—21no—
485C22×C9—21no—
486C22×C9—21no—
487C22×C9—22no—
488C22×C9—22no—
489C22×C9—41no—
490C22×C9—41no—
491C22×C9—41no—
492C22×C9—41no—
493C22×C9—41no—
494C22×C9—41no—
495C22×C9—41no—
496C22×C9—41no—
497C22×C9—41no—
498C22×C9—44no—
499C22×C9—48no—
500C22×C9C2×C3×D412yes—
501C22×C9C3×#4112yescomplemented
502C22×C9C24×C311yescharacteristic
503C2×D9—21no—
504C2×D9—21no—
505C2×D9—21no—
506C2×D9—21no—
507C2×D9—21no—
508C2×D9—44no—
509C2×D9C2×C3×D412yes—
510C4×C9—21no—
511C4×C9—21no—
512C4×C9—21no—
513C4×C9—41no—
514C4×C9—41no—
515C4×C9—41no—
516Dic9—21no—
517Dic9—21no—
518Dic9—21no—
519Dic9—21no—
520Dic9—21no—
521Dic9C2×C3×D412yes—
522C2×#41—91no—
523C22×D4—91no—
524#124—91no—
525#123—91no—
526#123—91no—
527C22⋊Q8—91no—
528#121—91no—
529#121—91no—
530#121—91no—
531#120—91no—
532#120C3×D911yescharacteristic, complemented
533C4×D4—91no—
534C4×D4—91no—
535C2×C22⋊C4—91no—
536C2×C22⋊C4—91no—
537C3×C9#54611yescharacteristic, complemented, Sylow
538C23×C3—22no—
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—21no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3—21no—
546C23×C3—42no—
547C23×C3—42no—
548C23×C3—41no—
549C23×C3—41no—
550C23×C3—42no—
551C23×C3—91no—
552C23×C3—91no—
553C23×C3—182no—
554C23×C3—182no—
555C23×C3—361no—
556C23×C3C22×D911yescharacteristic
557C23×C3C22×D911yescharacteristic
558C23×C3C22×D911yescharacteristic
559C23×C3C22×D911yescharacteristic
560C23×C3C22×C3×D311yescharacteristic
561C23×C3C22×C3×D311yescharacteristic
562C23×C3C22×C3×D311yescharacteristic
563C23×C3C22×C3×D311yescharacteristic
564C22×D3—31no—
565C22×D3—31no—
566C22×D3—62no—
567C22×D3—62no—
568C22×D3—121no—
569C3×Q8—182no—
570C3×D4—22no—
571C3×D4—22no—
572C3×D4—22no—
573C3×D4—22no—
574C3×D4—42no—
575C3×D4—42no—
576C3×D4—41no—
577C3×D4—41no—
578C3×D4—42no—
579C3×D4—94no—
580C3×D4—182no—
581C3×D4—182no—
582C3×D4—182no—
583C3×D4—182no—
584C3×D4—361no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—91no—
589C2×C3×C4—91no—
590C2×C3×C4—91no—
591C2×C3×C4—91no—
592C2×C3×C4—91no—
593C2×C3×C4—91no—
594C2×C3×C4—182no—
595C2×C3×C4—182no—
596C2×C3×C4—182no—
597C2×C3×C4—182no—
598C2×C3×C4—361no—
599C2×C3×C4—361no—
600C2×C3×C4C22×D911yescharacteristic
601C2×C3×C4C22×D911yescharacteristic
602C2×C3×C4C22×D911yescharacteristic
603C2×C3×C4C22×C3×D311yescharacteristic
604C2×C3×C4C22×C3×D311yescharacteristic
605C2×C3×C4C22×C3×D311yescharacteristic
606#67—34no—
607#67—62no—
608#67—62no—
609#67—62no—
610#67—62no—
611#67—121no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—62no—
619C2×Dic3—62no—
620C2×Dic3—62no—
621C2×Dic3—121no—
622C4×D3—62no—
623C4×D3—121no—
624Dic6—62no—
625C2×C32—22no—
626C2×C32—22no—
627C2×C32—41no—
628C2×C32—41no—
629C2×C32C2×D3×D411yescharacteristic
630C2×C32C2×#23711yescharacteristic
631C2×C32#100411yescharacteristic
632C3×D3—62no—
633C3×D3—121no—
634C2×C9—22no—
635C2×C9—22no—
636C2×C9—21no—
637C2×C9—21no—
638C2×C9—21no—
639C2×C9—42no—
640C2×C9—42no—
641C2×C9—42no—
642C2×C9—41no—
643C2×C9—41no—
644C2×C9—81no—
645C2×C9C22×C3×D411yescharacteristic
646C2×C9C2×C3×#4111yescharacteristic
647C2×C9C3×H(5,𝔽2)11yescharacteristic
648D9—22no—
649D9—41no—
650C24—91no—
651C24C2×C3×D911yescharacteristic
652#41—184no—
653C2×Q8—91no—
654C2×D4—91no—
655C2×D4—91no—
656C2×D4—91no—
657C2×D4—91no—
658C2×D4—91no—
659C2×D4—91no—
660C2×D4—184no—
661C2×D4C2×C3×D911yescharacteristic
662C2×D4C2×C3×D911yescharacteristic, complemented
663C2×D4C2×C3×D911yescharacteristic, complemented
664C22×C4—91no—
665C22×C4—91no—
666C22×C4—91no—
667C22×C4—91no—
668C22×C4—91no—
669C22×C4—91no—
670C4⋊C4—91no—
671C4⋊C4—91no—
672C4⋊C4—91no—
673C4⋊C4—91no—
674C22⋊C4—91no—
675C22⋊C4—91no—
676C22⋊C4—91no—
677C22⋊C4—91no—
678C22⋊C4—91no—
679C22⋊C4—91no—
680C22⋊C4—91no—
681C22⋊C4—91no—
682C22⋊C4—91no—
683C22⋊C4C2×C3×D911yescharacteristic
684C22⋊C4C2×C3×D911yescharacteristic, complemented
685C22⋊C4C2×C3×D911yescharacteristic, complemented
686C42—91no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—21no—
694C22×C3—21no—
695C22×C3—22no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—22no—
710C22×C3—22no—
711C22×C3—41no—
712C22×C3—41no—
713C22×C3—41no—
714C22×C3—41no—
715C22×C3—41no—
716C22×C3—41no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—44no—
721C22×C3—44no—
722C22×C3—48no—
723C22×C3—92no—
724C22×C3—181no—
725C22×C3—181no—
726C22×C3—181no—
727C22×C3—181no—
728C22×C3—181no—
729C22×C3—364no—
730C22×C3D4×D912yes—
731C22×C3#369912yescomplemented
732C22×C3C23×D911yescharacteristic
733C22×C3C3×D3×D412yes—
734C22×C3C3×#23712yes—
735C22×C3C23×C3×D311yescharacteristic
736C2×D3—32no—
737C2×D3—61no—
738C2×D3—61no—
739C2×D3—61no—
740C2×D3—61no—
741C2×D3—61no—
742C2×D3—124no—
743C3×C4—21no—
744C3×C4—21no—
745C3×C4—21no—
746C3×C4—21no—
747C3×C4—21no—
748C3×C4—21no—
749C3×C4—41no—
750C3×C4—41no—
751C3×C4—41no—
752C3×C4—92no—
753C3×C4—181no—
754C3×C4—181no—
755C3×C4—181no—
756C3×C4—181no—
757C3×C4—181no—
758Dic3—32no—
759Dic3—61no—
760Dic3—61no—
761Dic3—61no—
762Dic3—61no—
763Dic3—61no—
764C32#559111yescharacteristic
765C9—21no—
766C9C3×#54611yescharacteristic, complemented
767C23—22no—
768C23—22no—
769C23—41no—
770C23—91no—
771C23—91no—
772C23—182no—
773C23—182no—
774C23—361no—
775C23C22×C3×D911yescharacteristic
776C23C22×C3×D911yescharacteristic
777C23C22×C3×D911yescharacteristic
778C23C22×C3×D911yescharacteristic
779Q8—182no—
780D4—22no—
781D4—22no—
782D4—41no—
783D4—94no—
784D4—182no—
785D4—182no—
786D4—182no—
787D4—182no—
788D4—361no—
789C2×C4—91no—
790C2×C4—91no—
791C2×C4—91no—
792C2×C4—91no—
793C2×C4—91no—
794C2×C4—91no—
795C2×C4—182no—
796C2×C4—182no—
797C2×C4—182no—
798C2×C4—182no—
799C2×C4—361no—
800C2×C4—361no—
801C2×C4C22×C3×D911yescharacteristic
802C2×C4C22×C3×D911yescharacteristic
803C2×C4C22×C3×D911yescharacteristic
804C2×C3—22no—
805C2×C3—22no—
806C2×C3—22no—
807C2×C3—22no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—42no—
812C2×C3—42no—
813C2×C3—42no—
814C2×C3—41no—
815C2×C3—41no—
816C2×C3—41no—
817C2×C3—41no—
818C2×C3—81no—
819C2×C3—182no—
820C2×C3—361no—
821C2×C3C2×D4×D911yescharacteristic
822C2×C3C2×#369911yescharacteristic
823C2×C3#6371011yescharacteristic
824C2×C3C2×C3×D3×D411yescharacteristic
825C2×C3C2×C3×#23711yescharacteristic
826C2×C3C3×#100411yescharacteristic
827D3—62no—
828D3—121no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—44no—
840C22—92no—
841C22—181no—
842C22—181no—
843C22—181no—
844C22—181no—
845C22—181no—
846C22—364no—
847C22C3×D4×D912yes—
848C22C3×#369912yescomplemented
849C22C23×C3×D911yescharacteristic
850C4—21no—
851C4—21no—
852C4—21no—
853C4—92no—
854C4—181no—
855C4—181no—
856C4—181no—
857C4—181no—
858C4—181no—
859C3—21no—
860C3#1058969311yescharacteristic, direct product factor
861C3C3×#559111yescharacteristic
862C2—22no—
863C2—22no—
864C2—41no—
865C2—41no—
866C2—182no—
867C2—361no—
868C2C2×C3×D4×D911yescharacteristic
869C2C2×C3×#369911yescharacteristic
870C2C3×#6371011yescharacteristic
subgroupG/H
centerC22×C3C23×D9
commutator, cosocleC22×C9C24×C3
FrattiniC22×C3C23×C3×D3
FittingC3×C9×#120C2
socleC22×C32C23×D3
hypercenterC3×#120D9
hypocenterC9C3×#546
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C22×C3 ◁ C3×#120

Complements

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

NH ≅ G/Ntype
1. C22×C3×#611C2semidirect
2. C2×C3×#3699C2semidirect
3. C3×C9×#120C2semidirect
4. C2×C3×#3676C2semidirect
5. C3×#63501C2semidirect
6. C3×#63501C2semidirect
7. C3×#63500C2semidirect
8. C3×#63499C2semidirect
9. C3×D4×Dic9C2semidirect
10. C3×#63448C2semidirect
11. C3×#63447C2semidirect
12. C3×#63445C2semidirect
13. C3×#611⋊C4C2semidirect
14. C3×C22⋊C4×D9C2semidirect
15. C3×#63440C2semidirect
17. #10589693C3direct (N × H)
21. C2×C3×D4×C9C22semidirect
22. C2×C3×D4×C9C22semidirect
28. C2×C3×#611C22semidirect
29. C2×C3×#611C22semidirect
31. C22×C3×Dic9C22semidirect
32. C22×C3×Dic9C22semidirect
33. C22×C3×Dic9C22semidirect
35. C2×C3×C4×D9C22semidirect
36. C2×C3×C4×D9C22semidirect
37. C2×C3×Dic18C22semidirect
39. C3×C9×C22⋊C4C22semidirect
40. C3×C9×C22⋊C4C22semidirect
43. C3×#3676C22semidirect
44. C3×#3676C22semidirect
45. C3×#3676C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C3×(C2×D9)⋊C4C22semidirect
48. C3×(C2×D9)⋊C4C22semidirect
49. C3×(C2×D9)⋊C4C22semidirect
50. C3×C4⋊Dic9C22semidirect
51. C3×C4⋊Dic9C22semidirect
52. C3×Dic9⋊C4C22semidirect
53. C3×Dic9⋊C4C22semidirect
54. C3×C4×Dic9C22semidirect
70. C22×#611C2×C3semidirect
71. C2×#3699C2×C3semidirect
73. C9×#120C2×C3semidirect
74. C2×#3676C2×C3semidirect
75. #63501C2×C3semidirect
76. #63501C2×C3semidirect
77. #63500C2×C3semidirect
78. #63499C2×C3semidirect
79. D4×Dic9C2×C3semidirect
80. #63448C2×C3semidirect
81. #63447C2×C3semidirect
82. #63445C2×C3semidirect
83. #611⋊C4C2×C3semidirect
84. C22⋊C4×D9C2×C3semidirect
85. #63440C2×C3semidirect
109. C3×#611D4semidirect
169. C2×D4×C9C22×C3semidirect
170. C2×D4×C9C22×C3semidirect
176. C2×#611C22×C3semidirect
177. C2×#611C22×C3semidirect
179. C22×Dic9C22×C3semidirect
180. C22×Dic9C22×C3semidirect
181. C22×Dic9C22×C3semidirect
183. C2×C4×D9C22×C3semidirect
184. C2×C4×D9C22×C3semidirect
185. C2×Dic18C22×C3semidirect
190. C9×C22⋊C4C22×C3semidirect
191. C9×C22⋊C4C22×C3semidirect
194. #3676C22×C3semidirect
195. #3676C22×C3semidirect
196. #3676C22×C3semidirect
197. (C2×D9)⋊C4C22×C3semidirect
198. (C2×D9)⋊C4C22×C3semidirect
199. (C2×D9)⋊C4C22×C3semidirect
200. (C2×D9)⋊C4C22×C3semidirect
201. C4⋊Dic9C22×C3semidirect
202. C4⋊Dic9C22×C3semidirect
203. Dic9⋊C4C22×C3semidirect
204. Dic9⋊C4C22×C3semidirect
205. C4×Dic9C22×C3semidirect
218. C22×C3×C9#41semidirect
249. C3×#120D9semidirect
340. #611C3×D4semidirect
382. C2×C3×D4C2×D9semidirect
383. C2×C3×D4C2×D9semidirect
425. C3×C22⋊C4C2×D9semidirect
426. C3×C22⋊C4C2×D9semidirect
501. C22×C9C3×#41semidirect
532. #120C3×D9semidirect
537. C3×C9#546semidirect
662. C2×D4C2×C3×D9semidirect
663. C2×D4C2×C3×D9semidirect
684. C22⋊C4C2×C3×D9semidirect
685. C22⋊C4C2×C3×D9semidirect
731. C22×C3#3699semidirect
766. C9C3×#546semidirect
848. C22C3×#3699semidirect
860. C3#10589693direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6112
C2×C3×#36992
C3×C9×#1202
C2×C3×#36762
C3×#635012
C3×#635002
C3×#634992
C3×D4×Dic92
C3×#634482
C3×#634472
C3×#634452
C3×#611⋊C42
C3×C22⋊C4×D92
C3×#634402
C3×#55913
#105896933