Finite Group Databasebeta

← #13151280

Subgroups — #13151280

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×D9C211yesmaximal, characteristic, complemented
2C2×D9×#67C211yesmaximal, characteristic, complemented
3#11721839C211yesmaximal, characteristic, complemented
4C9×#939C211yesmaximal, characteristic, complemented
5#11721292C211yesmaximal, characteristic, complemented
6#11721290C211yesmaximal, characteristic, complemented
7#11721285C211yesmaximal, characteristic, complemented
8#11721277C211yesmaximal, characteristic, complemented
9#11721276C211yesmaximal, characteristic, complemented
10#11721269C211yesmaximal, characteristic, complemented
11C2×(C2×D9)⋊Dic3C211yesmaximal, characteristic, complemented
12#11721049C211yesmaximal, characteristic, complemented
13#11721031C211yesmaximal, characteristic, complemented
14#11720981C211yesmaximal, characteristic, complemented
15#11720938C211yesmaximal, characteristic, complemented
16#10595302—31nomaximal
17#10589707—31nomaximal
18C23×C3×D9C2211yescharacteristic
19C23×C3×D9C2211yescharacteristic, complemented
20C22×D3×D9C2211yescharacteristic, complemented
21C2×C3×D4×C9C2211yescharacteristic, complemented
22C2×#6233C2211yescharacteristic, complemented
23C2×#6233C2211yescharacteristic, complemented
24C22×C3⋊Dic9C2211yescharacteristic, complemented
25C2×C9×#67C2211yescharacteristic, complemented
26C2×C9×#67C2211yescharacteristic, complemented
27C2×C3×#611C2211yescharacteristic
28C2×C3×#611C2211yescharacteristic, complemented
29C22×C9×Dic3C2211yescharacteristic, complemented
30C3×D4×D9—24no—
31C2×C3×D36C2211yescharacteristic
32C2×C3×C4×D9C2211yescharacteristic, complemented
33D9×#67—24no—
34C2×#6194C2211yescharacteristic
35C2×#6194C2211yescharacteristic, complemented
36C2×#6192C2211yescharacteristic
37C2×#6192C2211yescharacteristic, complemented
38C2×Dic3×D9C2211yescharacteristic, complemented
39#88551C2211yescharacteristic, complemented
40#88536C2211yescharacteristic, complemented
41#88534C2211yescharacteristic, complemented
42C9×#217C2211yescharacteristic, complemented
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C9×Dic3⋊C4C2211yescharacteristic, complemented
45(C2×D3)⋊Dic9C2211yescharacteristic, complemented
46#88445C2211yescharacteristic, complemented
47(C2×D9)⋊Dic3C2211yescharacteristic, complemented
48(C2×D9)⋊Dic3C2211yescharacteristic, complemented
49(C2×D9)⋊Dic3C2211yescharacteristic, complemented
50(C2×D9)⋊Dic3C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic, complemented
52(C2×D9)⋊Dic3C2211yescharacteristic, complemented
53Dic3⋊Dic9C2211yescharacteristic, complemented
54#88442C2211yescharacteristic, complemented
55C2×C3×D3×D4—31no—
56C2×D3×#67—31no—
57#64148—31no—
58C3×#939D311yescharacteristic
59#63983—31no—
60#63980—31no—
61#63978—31no—
62#63977—31no—
63#63976—31no—
64#63969—31no—
65C2×(C2×D3)⋊Dic3—31no—
66#63922—31no—
67#63905—31no—
68#63884—31no—
69#63850—31no—
70C2×D4×D9—31no—
71C2×D4×D9D311yescharacteristic, complemented
72C9×#121—31no—
73#63501—31no—
74#63501—31no—
75#63501—61no—
76#63499—31no—
77#63499—31no—
78#63492—31no—
79C2×(C2×D9)⋊C4—31no—
80#63456—31no—
81#63456—31no—
82#63445—31no—
83#63445—31no—
84#63444—31no—
85#63444—31no—
86C23×C3×C9C2311yescharacteristic
87C23×C3×C9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9C2311yescharacteristic
90C22×C3×D9—22no—
91C22×C3×D9—41no—
92C22×C3×D9—41no—
93C22×C3×D9—41no—
94C22×C3×D9—41no—
95C22×C3×D9D414yescomplemented
96C22×C3×D9C2311yescharacteristic
97C22×C3×D9C2311yescharacteristic
98C22×C3×D9C2311yescharacteristic
99C2×D3×D9—22no—
100C2×D3×D9—41no—
101C2×D3×D9—41no—
102C3×D4×C9—22no—
103C2×C3×C4×C9C2311yescharacteristic
104#6233—22no—
105#6233—41no—
106C2×C3⋊Dic9—41no—
107C2×C3⋊Dic9C2311yescharacteristic
108C2×C3⋊Dic9C2311yescharacteristic
109C2×C3⋊Dic9C2311yescharacteristic
110C9×#67—22no—
111C9×#67—41no—
112C3×#611—22no—
113C3×#611—22no—
114C2×C9×Dic3—41no—
115C2×C9×Dic3C2311yescharacteristic
116C2×C9×Dic3C2311yescharacteristic
117C2×C9×Dic3C2311yescharacteristic
118C2×C3×Dic9C2311yescharacteristic
119C3×D36—22no—
120C3×C4×D9—22no—
121#6194—22no—
122#6194—41no—
123#6192—22no—
124#6192—41no—
125Dic3×D9—22no—
126#5804—91no—
127#5605—91no—
128C23×C3×D3—31no—
129C23×C3×D3—31no—
130C22×D32—31no—
131C2×C32×D4C2×D311yescharacteristic
132C2×#638—31no—
133C2×#638—31no—
134C22×C3⋊Dic3—31no—
135C2×C3×#67—31no—
136C2×C3×#67—31no—
137C2×C3×#67C2×D311yescharacteristic
138C2×C3×#67C2×D311yescharacteristic
139C22×C3×Dic3C2×D311yescharacteristic
140C3×D3×D4—64no—
141C2×C3×D12—31no—
142C2×C3×C4×D3—31no—
143D3×#67—64no—
144C2×#626—31no—
145C2×#626—31no—
146C2×#625—31no—
147C2×#625—31no—
148C2×D3×Dic3—31no—
149C23×D9—31no—
150C23×D9C2×D311yescharacteristic
151C23×D9C2×D311yescharacteristic, complemented
152#3757—31no—
153#3752—31no—
154#3750—31no—
155C3×#217C2×D311yescharacteristic
156C3×(C2×D3)⋊C4C2×D311yescharacteristic
157C3×Dic3⋊C4C2×D311yescharacteristic
158#3724—31no—
159Dic3⋊Dic3—31no—
160#3722—31no—
161(C2×D3)⋊Dic3—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164(C2×D3)⋊Dic3—31no—
165(C2×D3)⋊Dic3—31no—
166(C2×D3)⋊Dic3—31no—
167(C2×D3)⋊Dic3—31no—
168C2×D4×C9—21no—
169C2×D4×C9—31no—
170C2×D4×C9—31no—
171C2×D4×C9C2×D311yescharacteristic, complemented
172C22×C4×C9—31no—
173C2×#611—31no—
174C2×#611—31no—
175C2×#611—31no—
176C2×#611—31no—
177C2×#611—61no—
178C2×#611—61no—
179C2×#611C2×D311yescharacteristic
180C2×#611C2×D311yescharacteristic, complemented
181C22×Dic9—31no—
182C22×Dic9—61no—
183D4×D9—24no—
184D4×D9—64no—
185C2×D36—31no—
186C2×D36—31no—
187C2×D36C2×D311yescharacteristic
188C2×C4×D9—31no—
189C2×C4×D9C2×D311yescharacteristic, complemented
190C9×C4⋊C4—31no—
191C9×C22⋊C4—31no—
192C9×C22⋊C4—31no—
193#3676—31no—
194#3676—31no—
195#3676—61no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—31no—
198(C2×D9)⋊C4—31no—
199(C2×D9)⋊C4—31no—
200(C2×D9)⋊C4—31no—
201(C2×D9)⋊C4—31no—
202(C2×D9)⋊C4—31no—
203(C2×D9)⋊C4—31no—
204(C2×D9)⋊C4—61no—
205C4⋊Dic9—31no—
206Dic9⋊C4—31no—
207Dic9⋊C4—31no—
208Dic9⋊C4—61no—
209C22×C3×C9—21no—
210C22×C3×C9—21no—
211C22×C3×C9—21no—
212C22×C3×C9—21no—
213C22×C3×C9—21no—
214C22×C3×C9C2×D412yes—
215C22×C3×C9C2411yescharacteristic
216C2×C3⋊D9—21no—
217C2×C3⋊D9—21no—
218C2×C3⋊D9—21no—
219C2×D3×C9—21no—
220C2×D3×C9—21no—
221C2×D3×C9—21no—
222C2×C3×D9—21no—
223C2×C3×D9—21no—
224C2×C3×D9—21no—
225C2×C3×D9—21no—
226C2×C3×D9—21no—
227C2×C3×D9—21no—
228C2×C3×D9—21no—
229C2×C3×D9—44no—
230C2×C3×D9—44no—
231C2×C3×D9C2×D412yes—
232C2×C3×D9C2×D412yes—
233D3×D9—44no—
234C3×C4×C9—21no—
235C3⋊Dic9—21no—
236C3⋊Dic9—21no—
237C3⋊Dic9—21no—
238C9×Dic3—21no—
239C9×Dic3—21no—
240C9×Dic3—21no—
241C3×Dic9—21no—
242C22×C3×D4—91no—
243C22×#67—91no—
244C2×D3×D4—31no—
245C2×D3×D4—91no—
246C3×#121—31no—
247#953—91no—
248#953—91no—
249C2×#217—91no—
250#939—91no—
251#939—91no—
252#939—91no—
253#939—91no—
254#939—91no—
255#939—181no—
256#939D911yescharacteristic, complemented
257#937—91no—
258#937—91no—
259#937—91no—
260#937—91no—
261#935—91no—
262#935—91no—
263#930—91no—
264#929—91no—
265#929—91no—
266C2×(C2×D3)⋊C4—91no—
267#894—91no—
268#894—91no—
269#883—91no—
270#883—91no—
271#882—91no—
272#882—91no—
273C23×C32C22×D311yescharacteristic
274C23×C32C22×D311yescharacteristic
275C22×C3⋊D3—31no—
276C22×C3×D3—31no—
277C22×C3×D3—31no—
278C22×C3×D3—34no—
279C22×C3×D3—31no—
280C22×C3×D3—62no—
281C22×C3×D3—121no—
282C22×C3×D3—121no—
283C22×C3×D3—121no—
284C22×C3×D3—121no—
285C22×C3×D3C22×D311yescharacteristic
286C2×D32—62no—
287C2×D32—121no—
288C2×D32—121no—
289C32×D4—22no—
290C2×C32×C4C22×D311yescharacteristic
291#638—62no—
292#638—121no—
293C2×C3⋊Dic3—31no—
294C2×C3⋊Dic3—31no—
295C2×C3⋊Dic3—31no—
296C2×C3⋊Dic3—121no—
297C3×#67—22no—
298C3×#67—41no—
299C3×#67—62no—
300C3×#67—62no—
301C2×C3×Dic3—31no—
302C2×C3×Dic3—41no—
303C2×C3×Dic3C22×D311yescharacteristic
304C2×C3×Dic3C22×D311yescharacteristic
305C2×C3×Dic3C22×D311yescharacteristic
306C3×D12—62no—
307C3×C4×D3—62no—
308#626—62no—
309#626—121no—
310#625—62no—
311#625—121no—
312D3×Dic3—62no—
313C23×C9—21no—
314C23×C9—21no—
315C23×C9—31no—
316C23×C9C22×D311yescharacteristic
317C23×C9C22×D311yescharacteristic
318C22×D9—22no—
319C22×D9—31no—
320C22×D9—41no—
321C22×D9—41no—
322C22×D9—41no—
323C22×D9—41no—
324C22×D9—61no—
325C22×D9—62no—
326C22×D9—121no—
327C22×D9—121no—
328C22×D9#6714yescomplemented
329C22×D9C22×D311yescharacteristic
330C22×D9C22×D311yescharacteristic
331C22×D9C22×D311yescharacteristic
332D4×C9—22no—
333D4×C9—42no—
334D4×C9—62no—
335D4×C9—121no—
336C2×C4×C9—21no—
337C2×C4×C9—31no—
338C2×C4×C9—31no—
339C2×C4×C9—31no—
340C2×C4×C9—121no—
341C2×C4×C9C22×D311yescharacteristic
342#611—22no—
343#611—22no—
344#611—62no—
345#611—62no—
346#611—122no—
347#611—121no—
348#611—121no—
349#611—122no—
350C2×Dic9—31no—
351C2×Dic9—31no—
352C2×Dic9—31no—
353C2×Dic9—61no—
354C2×Dic9—61no—
355C2×Dic9—61no—
356C2×Dic9—121no—
357C2×Dic9—122no—
358C2×Dic9C22×D311yescharacteristic
359D36—22no—
360D36—62no—
361D36—121no—
362C4×D9—22no—
363C4×D9—62no—
364#534—271noSylow
365C2×C3×C9—22no—
366C2×C3×C9—41no—
367C2×C3×C9C22×D411yescharacteristic
368C2×C3×C9H(5,𝔽2)11yescharacteristic
369C2×C3×C9H(5,𝔽2)11yescharacteristic
370C3⋊D9—41no—
371D3×C9—41no—
372C3×D9—22no—
373C3×D9—22no—
374C3×D9—41no—
375C24×C3—91no—
376C24×C3—91no—
377C23×D3—31no—
378C23×D3—31no—
379C23×D3—91no—
380C23×D3—91no—
381C2×C3×D4—21no—
382C2×C3×D4—31no—
383C2×C3×D4—31no—
384C2×C3×D4—91no—
385C2×C3×D4—91no—
386C2×C3×D4—91no—
387C2×C3×D4—184no—
388C2×C3×D4C2×D911yescharacteristic, complemented
389C2×C3×D4D3211yescharacteristic
390C22×C3×C4—31no—
391C22×C3×C4—91no—
392C2×#67—31no—
393C2×#67—31no—
394C2×#67—91no—
395C2×#67—91no—
396C2×#67—91no—
397C2×#67—91no—
398C2×#67—91no—
399C2×#67—91no—
400C2×#67—91no—
401C2×#67—91no—
402C2×#67—91no—
403C2×#67—91no—
404C2×#67—181no—
405C2×#67—181no—
406C2×#67—184no—
407C2×#67C2×D911yescharacteristic, complemented
408C2×#67C2×D911yescharacteristic, complemented
409C22×Dic3—91no—
410C22×Dic3—91no—
411C22×Dic3—91no—
412C22×Dic3—181no—
413C22×Dic3C2×D911yescharacteristic, complemented
414D3×D4—64no—
415D3×D4—184no—
416C2×D12—31no—
417C2×D12—91no—
418C2×D12—91no—
419C2×C4×D3—31no—
420C2×C4×D3—91no—
421C3×C4⋊C4—31no—
422C3×C22⋊C4—31no—
423C3×C22⋊C4—31no—
424#217—91no—
425#217—91no—
426#217—91no—
427#217—91no—
428#217—91no—
429#217—91no—
430#217—91no—
431#217—91no—
432#217—91no—
433#217—181no—
434#217C2×D911yescharacteristic, complemented
435(C2×D3)⋊C4—91no—
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)⋊C4—91no—
443(C2×D3)⋊C4—91no—
444(C2×D3)⋊C4—91no—
445(C2×D3)⋊C4—91no—
446(C2×D3)⋊C4—181no—
447(C2×D3)⋊C4C2×D911yescharacteristic, complemented
448C4⋊Dic3—91no—
449Dic3⋊C4—91no—
450Dic3⋊C4—91no—
451Dic3⋊C4—91no—
452Dic3⋊C4—91no—
453Dic3⋊C4—91no—
454Dic3⋊C4—181no—
455Dic3⋊C4C2×D911yescharacteristic, complemented
456C22×C32—21no—
457C22×C32—21no—
458C22×C32—21no—
459C22×C32—21no—
460C22×C32—21no—
461C22×C32D3×D412yes—
462C22×C32C23×D311yescharacteristic
463C2×C3⋊D3—61no—
464C2×C3⋊D3—61no—
465C2×C3⋊D3—61no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—32no—
470C2×C3×D3—32no—
471C2×C3×D3—61no—
472C2×C3×D3—61no—
473C2×C3×D3—61no—
474C2×C3×D3—61no—
475C2×C3×D3—61no—
476C2×C3×D3—61no—
477C2×C3×D3—61no—
478C2×C3×D3—124no—
479C2×C3×D3—124no—
480D32—124no—
481C32×C4—21no—
482C3⋊Dic3—61no—
483C3⋊Dic3—61no—
484C3⋊Dic3—61no—
485C3×Dic3—21no—
486C3×Dic3—21no—
487C3×Dic3—21no—
488C3×Dic3—61no—
489C22×C9—21no—
490C22×C9—21no—
491C22×C9—21no—
492C22×C9—21no—
493C22×C9—21no—
494C22×C9—21no—
495C22×C9—22no—
496C22×C9—41no—
497C22×C9—41no—
498C22×C9—41no—
499C22×C9—41no—
500C22×C9—41no—
501C22×C9—61no—
502C22×C9—61no—
503C22×C9—61no—
504C22×C9C2×#6712yes—
505C22×C9C23×D311yescharacteristic
506C2×D9—21no—
507C2×D9—21no—
508C2×D9—21no—
509C2×D9—21no—
510C2×D9—21no—
511C2×D9—21no—
512C2×D9—21no—
513C2×D9—44no—
514C2×D9—44no—
515C2×D9—61no—
516C2×D9—61no—
517C2×D9—61no—
518C2×D9—121no—
519C2×D9—121no—
520C2×D9—121no—
521C2×D9—124no—
522C2×D9C2×#6712yes—
523C2×D9C2×#6712yes—
524C4×C9—21no—
525C4×C9—41no—
526C4×C9—61no—
527C4×C9—61no—
528C4×C9—61no—
529Dic9—21no—
530Dic9—62no—
531Dic9—61no—
532Dic9—61no—
533Dic9—61no—
534Dic9—121no—
535Dic9—121no—
536C22×D4—91no—
537C22×D4—271no—
538#123—271no—
539#123—271no—
540#123—271no—
541#123—271no—
542#121—31no—
543#121—271no—
544#121—271no—
545#121—271no—
546#120—271no—
547#120—271no—
548#120—271no—
549#120—271no—
550C2×C22⋊C4—271no—
551C3×C9#53411yescharacteristic, complemented, Sylow
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—31no—
555C23×C3—91no—
556C23×C3—91no—
557C23×C3—94no—
558C23×C3—91no—
559C23×C3—182no—
560C23×C3—361no—
561C23×C3—361no—
562C23×C3—361no—
563C23×C3—361no—
564C23×C3C22×D911yescharacteristic
565C23×C3C22×D911yescharacteristic
566C23×C3C2×D3211yescharacteristic
567C23×C3C2×D3211yescharacteristic
568C22×D3—31no—
569C22×D3—31no—
570C22×D3—34no—
571C22×D3—31no—
572C22×D3—62no—
573C22×D3—91no—
574C22×D3—91no—
575C22×D3—121no—
576C22×D3—121no—
577C22×D3—121no—
578C22×D3—121no—
579C22×D3—181no—
580C22×D3—182no—
581C22×D3—182no—
582C22×D3—361no—
583C22×D3—361no—
584C22×D3—361no—
585C22×D3—361no—
586C22×D3C22×D911yescharacteristic
587C3×D4—22no—
588C3×D4—22no—
589C3×D4—42no—
590C3×D4—62no—
591C3×D4—121no—
592C3×D4—182no—
593C3×D4—182no—
594C3×D4—182no—
595C2×C3×C4—21no—
596C2×C3×C4—31no—
597C2×C3×C4—31no—
598C2×C3×C4—31no—
599C2×C3×C4—91no—
600C2×C3×C4—121no—
601C2×C3×C4—182no—
602C2×C3×C4C22×D911yescharacteristic
603C2×C3×C4C2×D3211yescharacteristic
604#67—22no—
605#67—41no—
606#67—62no—
607#67—62no—
608#67—182no—
609#67—182no—
610#67—182no—
611#67—182no—
612#67—182no—
613#67—362no—
614#67—361no—
615#67—361no—
616#67—361no—
617#67—361no—
618#67—361no—
619#67—362no—
620C2×Dic3—31no—
621C2×Dic3—41no—
622C2×Dic3—91no—
623C2×Dic3—91no—
624C2×Dic3—91no—
625C2×Dic3—91no—
626C2×Dic3—91no—
627C2×Dic3—91no—
628C2×Dic3—181no—
629C2×Dic3—181no—
630C2×Dic3—181no—
631C2×Dic3—182no—
632C2×Dic3—361no—
633C2×Dic3—361no—
634C2×Dic3—362no—
635C2×Dic3C22×D911yescharacteristic
636C2×Dic3C22×D911yescharacteristic
637C2×Dic3C22×D911yescharacteristic
638D12—62no—
639D12—182no—
640D12—361no—
641C4×D3—62no—
642C4×D3—182no—
643C2×C32—22no—
644C2×C32—41no—
645C2×C32C2×D3×D411yescharacteristic
646C2×C32#100411yescharacteristic
647C2×C32#100911yescharacteristic
648C3⋊D3—121no—
649C3×D3—41no—
650C3×D3—62no—
651C3×D3—62no—
652C3×D3—121no—
653C2×C9—22no—
654C2×C9—21no—
655C2×C9—21no—
656C2×C9—21no—
657C2×C9—42no—
658C2×C9—41no—
659C2×C9—81no—
660C2×C9—121no—
661C2×C9#100411yescharacteristic
662C2×C9#100411yescharacteristic
663C2×C9C22×#6711yescharacteristic
664D9—22no—
665D9—22no—
666D9—41no—
667D9—121no—
668D9—241no—
669C24—91no—
670C24—91no—
671C24—271no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—91no—
675C2×D4—91no—
676C2×D4—91no—
677C2×D4—184no—
678C2×D4—271no—
679C2×D4—271no—
680C2×D4—271no—
681C2×D4—271no—
682C2×D4—271no—
683C2×D4—271no—
684C2×D4—544no—
685C2×D4D3×D911yescharacteristic, complemented
686C22×C4—31no—
687C22×C4—91no—
688C22×C4—271no—
689C22×C4—271no—
690C4⋊C4—31no—
691C4⋊C4—271no—
692C4⋊C4—271no—
693C4⋊C4—271no—
694C22⋊C4—31no—
695C22⋊C4—31no—
696C22⋊C4—271no—
697C22⋊C4—271no—
698C22⋊C4—271no—
699C22⋊C4—271no—
700C22⋊C4—271no—
701C22⋊C4—271no—
702C22⋊C4—271no—
703C22⋊C4—271no—
704C22⋊C4—271no—
705C22⋊C4—271no—
706C22×C3—21no—
707C22×C3—21no—
708C22×C3—21no—
709C22×C3—21no—
710C22×C3—21no—
711C22×C3—21no—
712C22×C3—21no—
713C22×C3—21no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—22no—
718C22×C3—41no—
719C22×C3—41no—
720C22×C3—41no—
721C22×C3—41no—
722C22×C3—41no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—92no—
727C22×C3—92no—
728C22×C3—181no—
729C22×C3—181no—
730C22×C3—181no—
731C22×C3—181no—
732C22×C3—181no—
733C22×C3—181no—
734C22×C3—181no—
735C22×C3—364no—
736C22×C3—364no—
737C22×C3D4×D912yes—
738C22×C3C23×D911yescharacteristic
739C22×C3D3×#6712yes—
740C22×C3C22×D3211yescharacteristic
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—32no—
745C2×D3—32no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—61no—
749C2×D3—61no—
750C2×D3—61no—
751C2×D3—61no—
752C2×D3—61no—
753C2×D3—124no—
754C2×D3—124no—
755C2×D3—181no—
756C2×D3—181no—
757C2×D3—181no—
758C2×D3—181no—
759C2×D3—181no—
760C2×D3—181no—
761C2×D3—361no—
762C2×D3—361no—
763C2×D3—361no—
764C2×D3—364no—
765C2×D3—364no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—41no—
769C3×C4—61no—
770C3×C4—61no—
771C3×C4—61no—
772C3×C4—181no—
773Dic3—21no—
774Dic3—21no—
775Dic3—21no—
776Dic3—61no—
777Dic3—182no—
778Dic3—181no—
779Dic3—181no—
780Dic3—181no—
781Dic3—181no—
782Dic3—181no—
783Dic3—181no—
784Dic3—361no—
785Dic3—361no—
786C32#560511yescharacteristic
787C9—21no—
788C9#580411yescharacteristic, complemented
789C23—31no—
790C23—91no—
791C23—91no—
792C23—94no—
793C23—91no—
794C23—182no—
795C23—271no—
796C23—361no—
797C23—361no—
798C23—361no—
799C23—361no—
800C23—542no—
801C23—1081no—
802C23—1081no—
803C23C2×D3×D911yescharacteristic
804C23C2×D3×D911yescharacteristic
805D4—22no—
806D4—62no—
807D4—121no—
808D4—182no—
809D4—182no—
810D4—182no—
811D4—542no—
812D4—542no—
813D4—542no—
814D4—1081no—
815D4—1081no—
816D4—1081no—
817C2×C4—31no—
818C2×C4—31no—
819C2×C4—31no—
820C2×C4—91no—
821C2×C4—121no—
822C2×C4—182no—
823C2×C4—271no—
824C2×C4—271no—
825C2×C4—271no—
826C2×C4—542no—
827C2×C4—1081no—
828C2×C4C2×D3×D911yescharacteristic
829C2×C3—22no—
830C2×C3—22no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—42no—
835C2×C3—41no—
836C2×C3—41no—
837C2×C3—81no—
838C2×C3—121no—
839C2×C3—182no—
840C2×C3—182no—
841C2×C3—361no—
842C2×C3C2×D4×D911yescharacteristic
843C2×C3#6371011yescharacteristic
844C2×C3#6371511yescharacteristic
845C2×C3#6431311yescharacteristic
846C2×C3#6431411yescharacteristic
847C2×C3C2×D3×#6711yescharacteristic
848D3—41no—
849D3—62no—
850D3—62no—
851D3—121no—
852D3—361no—
853D3—361no—
854D3—721no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—61no—
861C22—61no—
862C22—61no—
863C22—92no—
864C22—92no—
865C22—181no—
866C22—181no—
867C22—181no—
868C22—181no—
869C22—181no—
870C22—181no—
871C22—181no—
872C22—364no—
873C22—364no—
874C22—541no—
875C22—541no—
876C22—541no—
877C22—1084no—
878C22D9×#6712yes—
879C22C22×D3×D911yescharacteristic
880C4—21no—
881C4—61no—
882C4—61no—
883C4—61no—
884C4—181no—
885C4—541no—
886C4—541no—
887C4—541no—
888C3—21no—
889C3#1058970711yescharacteristic, complemented
890C3#1059530211yescharacteristic
891C2—22no—
892C2—41no—
893C2—121no—
894C2—182no—
895C2—182no—
896C2—361no—
897C2—1081no—
898C2#1172249911yescharacteristic
899C2#1172250111yescharacteristic
900C2C2×D9×#6711yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC2×C3×D4×C9C22
socleC22×C32C23×D3
hypercenterC2×D4D3×D9
hypocenterC3×C9#534
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×D9C2semidirect
2. C2×D9×#67C2semidirect
3. #11721839C2semidirect
4. C9×#939C2semidirect
5. #11721292C2semidirect
6. #11721290C2semidirect
7. #11721285C2semidirect
8. #11721277C2semidirect
9. #11721276C2semidirect
10. #11721269C2semidirect
11. C2×(C2×D9)⋊Dic3C2semidirect
12. #11721049C2semidirect
13. #11721031C2semidirect
14. #11720981C2semidirect
15. #11720938C2semidirect
19. C23×C3×D9C22semidirect
20. C22×D3×D9C22semidirect
21. C2×C3×D4×C9C22semidirect
22. C2×#6233C22semidirect
23. C2×#6233C22semidirect
24. C22×C3⋊Dic9C22semidirect
25. C2×C9×#67C22semidirect
26. C2×C9×#67C22semidirect
28. C2×C3×#611C22semidirect
29. C22×C9×Dic3C22semidirect
32. C2×C3×C4×D9C22semidirect
35. C2×#6194C22semidirect
37. C2×#6192C22semidirect
38. C2×Dic3×D9C22semidirect
39. #88551C22semidirect
40. #88536C22semidirect
41. #88534C22semidirect
42. C9×#217C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
44. C9×Dic3⋊C4C22semidirect
45. (C2×D3)⋊Dic9C22semidirect
46. #88445C22semidirect
47. (C2×D9)⋊Dic3C22semidirect
48. (C2×D9)⋊Dic3C22semidirect
49. (C2×D9)⋊Dic3C22semidirect
50. (C2×D9)⋊Dic3C22semidirect
51. (C2×D9)⋊Dic3C22semidirect
52. (C2×D9)⋊Dic3C22semidirect
53. Dic3⋊Dic9C22semidirect
54. #88442C22semidirect
71. C2×D4×D9D3semidirect
95. C22×C3×D9D4semidirect
151. C23×D9C2×D3semidirect
171. C2×D4×C9C2×D3semidirect
180. C2×#611C2×D3semidirect
189. C2×C4×D9C2×D3semidirect
256. #939D9semidirect
328. C22×D9#67semidirect
388. C2×C3×D4C2×D9semidirect
407. C2×#67C2×D9semidirect
408. C2×#67C2×D9semidirect
413. C22×Dic3C2×D9semidirect
434. #217C2×D9semidirect
447. (C2×D3)⋊C4C2×D9semidirect
455. Dic3⋊C4C2×D9semidirect
551. C3×C9#534semidirect
685. C2×D4D3×D9semidirect
788. C9#5804semidirect
889. C3#10589707semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×D92
C2×D9×#672
#117218392
C9×#9392
#117212922
#117212902
#117212852
#117212772
#117212762
#117212692
C2×(C2×D9)⋊Dic32
#117210492
#117210312
#117209812
#117209382
#105953023
#105897073