Finite Group Databasebeta

← #13148423

Subgroups — #13148423

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#611C211yesmaximal, characteristic, complemented
2C2×#88662C211yesmaximal, characteristic, complemented
3#11721727C211yesmaximal, characteristic, complemented
4C9×#882C211yesmaximal, characteristic, complemented
5C3×#63448C211yesmaximal, characteristic, complemented
6#11721290C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊Dic9C211yesmaximal, characteristic, complemented
8#11721050C211yesmaximal, characteristic, complemented
9#11721048C211yesmaximal, characteristic, complemented
10#11721045C211yesmaximal, characteristic, complemented
11#11721044C211yesmaximal, characteristic, complemented
12#11721026C211yesmaximal, characteristic, complemented
13#11721025C211yesmaximal, characteristic, complemented
14#11721016C211yesmaximal, characteristic, complemented
15#11720958C211yesmaximal, characteristic, complemented
16#10594294—31nomaximal
17#10589693—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C22×C3⋊Dic9C2211yescharacteristic, complemented
22C2×C4×C3⋊D9C2211yescharacteristic, complemented
23C2×C9×#67C2211yescharacteristic, complemented
24C2×C3×#611C2211yescharacteristic
25C22×C3×Dic9C2211yescharacteristic, complemented
26C2×C9×D12C2211yescharacteristic
27C2×C9×D12C2211yescharacteristic, complemented
28D3×#611—24no—
29C2×#6195C2211yescharacteristic
30C2×#6195C2211yescharacteristic, complemented
31C2×#6194C2211yescharacteristic
32C2×#6194C2211yescharacteristic, complemented
33#88662—24no—
34C2×D3×Dic9C2211yescharacteristic
35C2×D3×Dic9C2211yescharacteristic, complemented
36C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38C3×C9×C22⋊C4C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40#88534C2211yescharacteristic, complemented
41C4×C3⋊Dic9C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×C4⋊Dic9C2211yescharacteristic, complemented
47C3×C4⋊Dic9C2211yescharacteristic, complemented
48(C2×D3)⋊Dic9C2211yescharacteristic
49(C2×D3)⋊Dic9C2211yescharacteristic
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51(C2×D3)⋊Dic9C2211yescharacteristic, complemented
52(C2×D3)⋊Dic9C2211yescharacteristic, complemented
53(C2×D9)⋊Dic3C2211yescharacteristic, complemented
54#88442C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3804—31no—
57#64090—31no—
58C3×#886—31no—
59C3×#882D311yescharacteristic
60#63980—31no—
61C2×(C2×D3)⋊Dic3—31no—
62#63922—31no—
63#63921—31no—
64#63916—31no—
65#63915—31no—
66#63899—31no—
67#63898—31no—
68#63885—31no—
69#63854—31no—
70C22×#611—31no—
71C2×#3699—31no—
72C9×#120—31no—
73C2×#3676—31no—
74#63501—31no—
75#63501—31no—
76#63500—31no—
77#63499—31no—
78D4×Dic9—31no—
79#63448D311yescharacteristic, complemented
80#63447—31no—
81#63445—31no—
82#611⋊C4—31no—
83#611⋊C4—61no—
84C22⋊C4×D9—31no—
85#63440—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×D3×C9—22no—
89C22×D3×C9—22no—
90C22×D3×C9—41no—
91C22×D3×C9C2311yescharacteristic
92C22×D3×C9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×C3×C4×C9C2311yescharacteristic
99C2×C3×C4×C9C2311yescharacteristic
100#6233D414yescomplemented
101C2×C3⋊Dic9—41no—
102C2×C3⋊Dic9C2311yescharacteristic
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C4×C3⋊D9—41no—
106C9×#67—22no—
107C3×#611—22no—
108C2×C9×Dic3C2311yescharacteristic
109C2×C3×Dic9—22no—
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C9×D12—22no—
114C9×D12—41no—
115#6195—22no—
116#6195—22no—
117#6194—22no—
118#6194—41no—
119D3×Dic9—22no—
120D3×Dic9—22no—
121(C3⋊D9)⋊C4—22no—
122#6189—22no—
123#5654—91no—
124#5591—91no—
125C23×C3×D3C2×D311yescharacteristic
126C22×D32—31no—
127C2×#638—31no—
128C22×C3⋊Dic3—31no—
129C2×C4×C3⋊D3—31no—
130C2×C3×#67—31no—
131C2×C3×#67C2×D311yescharacteristic
132C22×C3×Dic3—31no—
133C2×C3×D12C2×D311yescharacteristic
134C2×C3×D12C2×D311yescharacteristic
135D3×#67—64no—
136C2×#627—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#625—31no—
140C2×#625—31no—
141C2×#624—31no—
142#3804—64no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C24×C9—31no—
146C23×D9—31no—
147C32×C22⋊C4C2×D311yescharacteristic
148#3752—31no—
149#3750—31no—
150C4×C3⋊Dic3—31no—
151C3×(C2×D3)⋊C4—31no—
152C3×(C2×D3)⋊C4—31no—
153C3×(C2×D3)⋊C4C2×D311yescharacteristic
154C3×(C2×D3)⋊C4C2×D311yescharacteristic
155C3×C4⋊Dic3—31no—
156C3×C4⋊Dic3—31no—
157#3724—31no—
158(C2×D3)⋊Dic3—31no—
159(C2×D3)⋊Dic3—31no—
160(C2×D3)⋊Dic3—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164C2×D4×C9—31no—
165C2×D4×C9—31no—
166C2×D4×C9—31no—
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—64no—
173C2×#611—61no—
174C2×#611C2×D311yescharacteristic
175C22×Dic9—31no—
176C22×Dic9—31no—
177C22×Dic9—31no—
178C22×Dic9—61no—
179C22×Dic9C2×D311yescharacteristic, complemented
180#3699—64no—
181C2×C4×D9—31no—
182C2×C4×D9—31no—
183C2×C4×D9—61no—
184C2×Dic18—31no—
185C9×C22⋊C4—21no—
186C9×C22⋊C4—31no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4C2×D311yescharacteristic, complemented
189#3676—31no—
190#3676—31no—
191#3676—31no—
192#3676—31no—
193#3676—31no—
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—61no—
197(C2×D9)⋊C4C2×D311yescharacteristic, complemented
198(C2×D9)⋊C4C2×D311yescharacteristic, complemented
199C4⋊Dic9C2×D311yescharacteristic, complemented
200C4⋊Dic9C2×D311yescharacteristic, complemented
201Dic9⋊C4—31no—
202Dic9⋊C4—31no—
203Dic9⋊C4—61no—
204C4×Dic9—31no—
205C4×Dic9—61no—
206C22×C3×C9—21no—
207C22×C3×C9—21no—
208C22×C3×C9C2×D412yes—
209C22×C3×C9C2411yescharacteristic
210C2×C3⋊D9—21no—
211C2×C3⋊D9—21no—
212C2×C3⋊D9C2×D412yes—
213C2×D3×C9—21no—
214C2×D3×C9—21no—
215C2×D3×C9—21no—
216C2×D3×C9—21no—
217C2×D3×C9—21no—
218C2×D3×C9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9—44no—
222C2×D3×C9#4112yescomplemented
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9—21no—
226D3×D9—44no—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C3⋊Dic9C2×D412yes—
232C9×Dic3—21no—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9—21no—
236C22×#67—91no—
237C2×#237—91no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C3×#123—91no—
241C3×#120—31no—
242C2×#217—91no—
243#939—91no—
244#939—91no—
245#939—91no—
246#938—91no—
247#937—91no—
248D4×Dic3—91no—
249C2×(C2×D3)⋊C4—91no—
250#896—91no—
251#895—91no—
252#894—91no—
253#893—91no—
254#886—31no—
255#885—91no—
256#885—91no—
257#884—91no—
258#883—91no—
259#882—91no—
260#882D911yescharacteristic, complemented
261#67⋊C4—91no—
262#67⋊C4—91no—
263#67⋊C4—181no—
264D3×C22⋊C4—91no—
265D3×C22⋊C4—91no—
266#878—91no—
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3×D3—22no—
270C22×C3×D3—22no—
271C22×C3×D3—31no—
272C22×C3×D3—41no—
273C22×C3×D3C22×D311yescharacteristic
274C22×C3×D3C22×D311yescharacteristic
275C22×C3×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C2×C32×C4C22×D311yescharacteristic
280C2×C32×C4C22×D311yescharacteristic
281#638—34no—
282C2×C3⋊Dic3—31no—
283C2×C3⋊Dic3—31no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—121no—
286C4×C3⋊D3—121no—
287C3×#67—22no—
288C3×#67—62no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3—62no—
293C2×C3×Dic3C22×D311yescharacteristic
294C3×D12—22no—
295C3×D12—41no—
296#627—62no—
297#626—62no—
298#626—62no—
299#625—62no—
300#625—121no—
301#624—62no—
302D3×Dic3—62no—
303D3×Dic3—62no—
304C23×C9—21no—
305C23×C9—31no—
306C23×C9—31no—
307C23×C9—31no—
308C23×C9—62no—
309C23×C9—62no—
310C23×C9—121no—
311C23×C9C22×D311yescharacteristic
312C22×D9—31no—
313C22×D9—61no—
314C22×D9—62no—
315C22×D9—62no—
316C22×D9—121no—
317C22×D9C22×D311yescharacteristic
318D4×C9—62no—
319D4×C9—62no—
320D4×C9—121no—
321C2×C4×C9—21no—
322C2×C4×C9—21no—
323C2×C4×C9—31no—
324C2×C4×C9C22×D311yescharacteristic
325C2×C4×C9C22×D311yescharacteristic
326#611—22no—
327#611—34no—
328#611—64no—
329#611—62no—
330#611—62no—
331#611—62no—
332#611—121no—
333C2×Dic9—22no—
334C2×Dic9—31no—
335C2×Dic9—31no—
336C2×Dic9—31no—
337C2×Dic9—61no—
338C2×Dic9—61no—
339C2×Dic9—61no—
340C2×Dic9—62no—
341C2×Dic9—62no—
342C2×Dic9—121no—
343C2×Dic9—122no—
344C2×Dic9C22×D311yescharacteristic
345C2×Dic9C22×D311yescharacteristic
346C2×Dic9C22×D311yescharacteristic
347C4×D9—62no—
348C4×D9—121no—
349C4×D9—122no—
350Dic18—62no—
351#546—271noSylow
352C2×C3×C9—22no—
353C2×C3×C9C22×D411yescharacteristic
354C2×C3×C9C2×#4111yescharacteristic
355C2×C3×C9H(5,𝔽2)11yescharacteristic
356C3⋊D9—22no—
357D3×C9—22no—
358D3×C9—41no—
359D3×C9—41no—
360C3×D9—41no—
361C24×C3—31no—
362C23×D3—91no—
363C23×D3—91no—
364C23×D3C2×D911yescharacteristic
365C2×C3×D4—31no—
366C2×C3×D4—31no—
367C2×C3×D4—31no—
368C2×C3×D4—91no—
369C22×C3×C4—91no—
370C2×#67—31no—
371C2×#67—91no—
372C2×#67—91no—
373C2×#67—91no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—181no—
380C2×#67—184no—
381C2×#67C2×D911yescharacteristic, complemented
382C22×Dic3—31no—
383C22×Dic3—91no—
384C22×Dic3—91no—
385C22×Dic3—91no—
386C22×Dic3—91no—
387C22×Dic3—181no—
388#237—184no—
389D3×D4—184no—
390#235—184no—
391C2×D12—91no—
392C2×D12—91no—
393C2×D12C2×D911yescharacteristic
394C2×D12C2×D911yescharacteristic, complemented
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—181no—
402C2×Dic6—91no—
403C2×Dic6—91no—
404C3×C4⋊C4—91no—
405C3×C4⋊C4—91no—
406C3×C22⋊C4—21no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—91no—
411C3×C22⋊C4C2×D911yescharacteristic, complemented
412C3×C22⋊C4D3211yescharacteristic
413#217—91no—
414#217—91no—
415#217—91no—
416#217—91no—
417#217—91no—
418#217—91no—
419(C2×D3)⋊C4—31no—
420(C2×D3)⋊C4—31no—
421(C2×D3)⋊C4—91no—
422(C2×D3)⋊C4—91no—
423(C2×D3)⋊C4—91no—
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
431(C2×D3)⋊C4C2×D911yescharacteristic, complemented
432C4⋊Dic3—31no—
433C4⋊Dic3—31no—
434Dic3⋊C4—91no—
435Dic3⋊C4—91no—
436Dic3⋊C4—91no—
437Dic3⋊C4—91no—
438Dic3⋊C4—181no—
439C4×Dic3—91no—
440C4×Dic3—91no—
441C4×Dic3—181no—
442C22×C32—21no—
443C22×C32—21no—
444C22×C32D3×D412yes—
445C22×C32C23×D311yescharacteristic
446C2×C3⋊D3—32no—
447C2×C3⋊D3—61no—
448C2×C3⋊D3—61no—
449C2×C3×D3—21no—
450C2×C3×D3—21no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—44no—
458C2×C3×D3—61no—
459C2×C3×D3—61no—
460C2×C3×D3—61no—
461C2×C3×D3#23712yes—
462D32—124no—
463C32×C4—21no—
464C32×C4—21no—
465C3⋊Dic3—32no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3×Dic3—21no—
469C3×Dic3—61no—
470C3×Dic3—61no—
471C3×Dic3—61no—
472C22×C9—21no—
473C22×C9—21no—
474C22×C9—21no—
475C22×C9—22no—
476C22×C9—32no—
477C22×C9—41no—
478C22×C9—41no—
479C22×C9—61no—
480C22×C9—61no—
481C22×C9—61no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9—61no—
485C22×C9—61no—
486C22×C9—61no—
487C22×C9—124no—
488C22×C9D3×D412yes—
489C22×C9C23×D311yescharacteristic
490C2×D9—21no—
491C2×D9—21no—
492C2×D9—21no—
493C2×D9—32no—
494C2×D9—62no—
495C2×D9—61no—
496C2×D9—61no—
497C2×D9—121no—
498C2×D9—121no—
499C2×D9—124no—
500C4×C9—21no—
501C4×C9—21no—
502C4×C9—41no—
503C4×C9—41no—
504C4×C9—61no—
505Dic9—21no—
506Dic9—21no—
507Dic9—21no—
508Dic9—32no—
509Dic9—62no—
510Dic9—62no—
511Dic9—61no—
512Dic9—61no—
513Dic9—121no—
514C2×#41—271no—
515C22×D4—271no—
516#124—271no—
517#123—91no—
518#123—271no—
519C22⋊Q8—271no—
520#121—271no—
521#121—271no—
522#121—271no—
523#120—31no—
524#120—271no—
525C4×D4—271no—
526C4×D4—271no—
527C2×C22⋊C4—271no—
528C2×C22⋊C4—271no—
529C3×C9#54611yescharacteristic, complemented, Sylow
530C23×C3—21no—
531C23×C3—31no—
532C23×C3—31no—
533C23×C3—31no—
534C23×C3—62no—
535C23×C3—62no—
536C23×C3—91no—
537C23×C3—121no—
538C23×C3C22×D911yescharacteristic
539C23×C3C2×D3211yescharacteristic
540C22×D3—22no—
541C22×D3—22no—
542C22×D3—31no—
543C22×D3—41no—
544C22×D3—91no—
545C22×D3—91no—
546C22×D3—181no—
547C22×D3—182no—
548C22×D3—182no—
549C22×D3—182no—
550C22×D3—182no—
551C22×D3—361no—
552C22×D3—361no—
553C22×D3C22×D911yescharacteristic
554C22×D3C22×D911yescharacteristic
555C22×D3C22×D911yescharacteristic
556C3×D4—62no—
557C3×D4—62no—
558C3×D4—121no—
559C3×D4—182no—
560C2×C3×C4—21no—
561C2×C3×C4—21no—
562C2×C3×C4—31no—
563C2×C3×C4—91no—
564C2×C3×C4—91no—
565C2×C3×C4—91no—
566C2×C3×C4—182no—
567C2×C3×C4C22×D911yescharacteristic
568C2×C3×C4C22×D911yescharacteristic
569C2×C3×C4C2×D3211yescharacteristic
570C2×C3×C4C2×D3211yescharacteristic
571#67—22no—
572#67—62no—
573#67—94no—
574#67—94no—
575#67—184no—
576#67—182no—
577#67—182no—
578#67—182no—
579#67—182no—
580#67—361no—
581#67—361no—
582C2×Dic3—31no—
583C2×Dic3—31no—
584C2×Dic3—31no—
585C2×Dic3—62no—
586C2×Dic3—91no—
587C2×Dic3—91no—
588C2×Dic3—91no—
589C2×Dic3—91no—
590C2×Dic3—91no—
591C2×Dic3—91no—
592C2×Dic3—181no—
593C2×Dic3—181no—
594C2×Dic3—181no—
595C2×Dic3—182no—
596C2×Dic3—182no—
597C2×Dic3—361no—
598C2×Dic3—361no—
599C2×Dic3—362no—
600C2×Dic3C22×D911yescharacteristic
601D12—22no—
602D12—41no—
603D12—182no—
604D12—182no—
605C4×D3—182no—
606C4×D3—182no—
607C4×D3—182no—
608C4×D3—182no—
609C4×D3—361no—
610C4×D3—361no—
611C4×D3—362no—
612Dic6—182no—
613Dic6—182no—
614C2×C32—22no—
615C2×C32C2×D3×D411yescharacteristic
616C2×C32C2×#23711yescharacteristic
617C2×C32#100411yescharacteristic
618C3⋊D3—62no—
619C3×D3—22no—
620C3×D3—41no—
621C3×D3—41no—
622C3×D3—121no—
623C2×C9—22no—
624C2×C9—21no—
625C2×C9—21no—
626C2×C9—21no—
627C2×C9—42no—
628C2×C9—62no—
629C2×C9—121no—
630C2×C9—121no—
631C2×C9C2×D3×D411yescharacteristic
632C2×C9D3×#4111yescharacteristic
633C2×C9#100911yescharacteristic
634D9—41no—
635D9—62no—
636D9—122no—
637C24—31no—
638C24—271no—
639#41—544no—
640C2×Q8—271no—
641C2×D4—31no—
642C2×D4—31no—
643C2×D4—31no—
644C2×D4—91no—
645C2×D4—271no—
646C2×D4—271no—
647C2×D4—271no—
648C2×D4—271no—
649C2×D4—271no—
650C2×D4—544no—
651C22×C4—91no—
652C22×C4—271no—
653C22×C4—271no—
654C22×C4—271no—
655C22×C4—271no—
656C22×C4—271no—
657C4⋊C4—91no—
658C4⋊C4—91no—
659C4⋊C4—271no—
660C4⋊C4—271no—
661C22⋊C4—31no—
662C22⋊C4—31no—
663C22⋊C4—91no—
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⋊C4D3×D911yescharacteristic, complemented
673C42—271no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—22no—
680C22×C3—32no—
681C22×C3—41no—
682C22×C3—41no—
683C22×C3—61no—
684C22×C3—61no—
685C22×C3—61no—
686C22×C3—61no—
687C22×C3—61no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—61no—
691C22×C3—124no—
692C22×C3—181no—
693C22×C3—181no—
694C22×C3—181no—
695C22×C3D4×D912yes—
696C22×C3C23×D911yescharacteristic
697C22×C3#380212yes—
698C22×C3C22×D3211yescharacteristic
699C2×D3—21no—
700C2×D3—21no—
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—21no—
707C2×D3—44no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—61no—
711C2×D3—92no—
712C2×D3—92no—
713C2×D3—182no—
714C2×D3—181no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—361no—
719C2×D3—361no—
720C2×D3—364no—
721C2×D3—364no—
722C2×D3#369912yescomplemented
723C3×C4—21no—
724C3×C4—21no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—41no—
728C3×C4—41no—
729C3×C4—61no—
730C3×C4—181no—
731C3×C4—181no—
732C3×C4—181no—
733Dic3—21no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—92no—
738Dic3—92no—
739Dic3—182no—
740Dic3—182no—
741Dic3—181no—
742Dic3—181no—
743Dic3—181no—
744Dic3—181no—
745Dic3—361no—
746C32#559111yescharacteristic
747C9—21no—
748C9#565411yescharacteristic, complemented
749C23—31no—
750C23—31no—
751C23—31no—
752C23—62no—
753C23—62no—
754C23—91no—
755C23—121no—
756C23—271no—
757C23—542no—
758C23—542no—
759C23—1081no—
760C23C2×D3×D911yescharacteristic
761Q8—542no—
762D4—62no—
763D4—62no—
764D4—121no—
765D4—182no—
766D4—274no—
767D4—542no—
768D4—542no—
769D4—542no—
770D4—1081no—
771C2×C4—31no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—91no—
775C2×C4—182no—
776C2×C4—271no—
777C2×C4—271no—
778C2×C4—271no—
779C2×C4—542no—
780C2×C4—542no—
781C2×C4—542no—
782C2×C4—1081no—
783C2×C4—1081no—
784C2×C4C2×D3×D911yescharacteristic
785C2×C4C2×D3×D911yescharacteristic
786C2×C3—22no—
787C2×C3—22no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—42no—
792C2×C3—62no—
793C2×C3—121no—
794C2×C3—121no—
795C2×C3—361no—
796C2×C3C2×D4×D911yescharacteristic
797C2×C3C2×#369911yescharacteristic
798C2×C3#6371011yescharacteristic
799C2×C3C2×#380211yescharacteristic
800C2×C3D3×#23711yescharacteristic
801C2×C3#6431411yescharacteristic
802D3—22no—
803D3—41no—
804D3—41no—
805D3—121no—
806D3—182no—
807D3—182no—
808D3—362no—
809C22—21no—
810C22—21no—
811C22—32no—
812C22—61no—
813C22—61no—
814C22—61no—
815C22—61no—
816C22—61no—
817C22—61no—
818C22—61no—
819C22—61no—
820C22—124no—
821C22—181no—
822C22—181no—
823C22—181no—
824C22—272no—
825C22—541no—
826C22—541no—
827C22—1084no—
828C22#8864612yes—
829C22C22×D3×D911yescharacteristic
830C4—21no—
831C4—21no—
832C4—61no—
833C4—181no—
834C4—181no—
835C4—181no—
836C4—272no—
837C4—541no—
838C4—541no—
839C3—21no—
840C3#1058969311yescharacteristic, complemented
841C3#1059429411yescharacteristic
842C2—22no—
843C2—62no—
844C2—121no—
845C2—121no—
846C2—361no—
847C2—542no—
848C2C2×#8864611yescharacteristic
849C2D3×#369911yescharacteristic
850C2#1172250011yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#546
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×#611C2semidirect
2. C2×#88662C2semidirect
3. #11721727C2semidirect
4. C9×#882C2semidirect
5. C3×#63448C2semidirect
6. #11721290C2semidirect
7. C2×(C2×D3)⋊Dic9C2semidirect
8. #11721050C2semidirect
9. #11721048C2semidirect
10. #11721045C2semidirect
11. #11721044C2semidirect
12. #11721026C2semidirect
13. #11721025C2semidirect
14. #11721016C2semidirect
15. #11720958C2semidirect
21. C22×C3⋊Dic9C22semidirect
22. C2×C4×C3⋊D9C22semidirect
23. C2×C9×#67C22semidirect
25. C22×C3×Dic9C22semidirect
27. C2×C9×D12C22semidirect
30. C2×#6195C22semidirect
32. C2×#6194C22semidirect
35. C2×D3×Dic9C22semidirect
36. C2×(C3⋊D9)⋊C4C22semidirect
37. C2×#6189C22semidirect
38. C3×C9×C22⋊C4C22semidirect
39. #88536C22semidirect
40. #88534C22semidirect
41. C4×C3⋊Dic9C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C3×(C2×D9)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×C4⋊Dic9C22semidirect
47. C3×C4⋊Dic9C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
51. (C2×D3)⋊Dic9C22semidirect
52. (C2×D3)⋊Dic9C22semidirect
53. (C2×D9)⋊Dic3C22semidirect
54. #88442C22semidirect
79. #63448D3semidirect
100. #6233D4semidirect
179. C22×Dic9C2×D3semidirect
188. C9×C22⋊C4C2×D3semidirect
197. (C2×D9)⋊C4C2×D3semidirect
198. (C2×D9)⋊C4C2×D3semidirect
199. C4⋊Dic9C2×D3semidirect
200. C4⋊Dic9C2×D3semidirect
222. C2×D3×C9#41semidirect
260. #882D9semidirect
381. C2×#67C2×D9semidirect
394. C2×D12C2×D9semidirect
411. C3×C22⋊C4C2×D9semidirect
431. (C2×D3)⋊C4C2×D9semidirect
529. C3×C9#546semidirect
672. C22⋊C4D3×D9semidirect
722. C2×D3#3699semidirect
748. C9#5654semidirect
840. C3#10589693semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
C2×#886622
#117217272
C9×#8822
C3×#634482
#117212902
C2×(C2×D3)⋊Dic92
#117210502
#117210482
#117210452
#117210442
#117210262
#117210252
#117210162
#117209582
#105942943
#105896933