Finite Group Databasebeta

← #13150555

Subgroups — #13150555

Order 1728.

1096 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#611C211yesmaximal, characteristic, complemented
2C2×#88658C211yesmaximal, characteristic, complemented
3#11721819C211yesmaximal, characteristic, complemented
4C2×C9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C3×C4×#611C211yesmaximal, characteristic, complemented
6#11721287C211yesmaximal, characteristic, complemented
7#11721251C211yesmaximal, characteristic, complemented
8#11721051C211yesmaximal, characteristic, complemented
9D9×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#11721039C211yesmaximal, characteristic, complemented
11#11721033C211yesmaximal, characteristic, complemented
12#11721023C211yesmaximal, characteristic, complemented
13#11721013C211yesmaximal, characteristic, complemented
14#11720989C211yesmaximal, characteristic, complemented
15#11720956C211yesmaximal, characteristic, complemented
16#10595073—31nomaximal
17#10589592—31nomaximal
18C23×D3×C9C2211yescharacteristic
19C22×D3×D9C2211yescharacteristic
20C22×C3×C4×C9C2211yescharacteristic, complemented
21C2×#6233C2211yescharacteristic
22C2×#6233C2211yescharacteristic, complemented
23C2×C4⋊(C3⋊D9)C2211yescharacteristic, complemented
24C2×C3×#611C2211yescharacteristic
25C22×C9×Dic3C2211yescharacteristic, complemented
26C2×C3×C4×D9C2211yescharacteristic, complemented
27D3×#611—24no—
28C2×#6195C2211yescharacteristic
29C2×#6195C2211yescharacteristic
30C2×#6195C2211yescharacteristic, complemented
31C2×#6194C2211yescharacteristic
32C2×D3×Dic9C2211yescharacteristic
33C2×#6192C2211yescharacteristic, complemented
34C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
35#88658—24no—
36C2×Dic3×D9C2211yescharacteristic, complemented
37C2×#6189C2211yescharacteristic, complemented
38#88536C2211yescharacteristic, complemented
39#88536C2211yescharacteristic, complemented
40C4⋊(C3⋊Dic9)C2211yescharacteristic, complemented
41C3×#3676C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C9×(C2×D3)⋊C4C2211yescharacteristic
44C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C3×Dic9⋊C4C2211yescharacteristic, complemented
48C3×C4×Dic9C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51#88445C2211yescharacteristic, complemented
52#88445C2211yescharacteristic, complemented
53Dic9⋊Dic3C2211yescharacteristic, complemented
54Dic9⋊Dic3C2211yescharacteristic, complemented
55C2×D3×#67—31no—
56C2×#3804—31no—
57#64139—31no—
58C3×C4×#67—31no—
59C2×C3×(C2×D3)⋊C4D311yescharacteristic
60#63977—31no—
61#63966—31no—
62#63923—31no—
63D3×(C2×D3)⋊C4—31no—
64#63910—31no—
65#63906—31no—
66#63893—31no—
67#63891—31no—
68#63880—31no—
69#63852—31no—
70C22×#611—31no—
71C2×#3697—31no—
72C2×C9×C22⋊C4—31no—
73#63515—31no—
74#63492—31no—
75#63492—61no—
76#63491—31no—
77C4×#611D311yescharacteristic, complemented
78#63447—31no—
79#63446—31no—
80#63446—31no—
81#63445—31no—
82#63444—31no—
83#611⋊C4—31no—
84C22⋊C4×D9—31no—
85#63440—31no—
86C23×C3×C9C2311yescharacteristic
87C22×C3⋊D9C2311yescharacteristic
88C22×C3⋊D9C2311yescharacteristic
89C22×D3×C9—22no—
90C22×D3×C9—22no—
91C22×D3×C9—41no—
92C22×D3×C9C2311yescharacteristic
93C22×D3×C9C2311yescharacteristic
94C22×C3×D9C2311yescharacteristic
95C2×D3×D9—22no—
96C2×D3×D9—22no—
97C2×D3×D9—41no—
98C2×C3×C4×C9—41no—
99C2×C3×C4×C9C2311yescharacteristic
100C2×C3×C4×C9C2311yescharacteristic
101#6233—22no—
102#6233—22no—
103C2×C3⋊Dic9C2311yescharacteristic
104C2×C3⋊Dic9C2311yescharacteristic
105C4⋊(C3⋊D9)—41no—
106C3×#611D414yescomplemented
107C2×C9×Dic3—22no—
108C2×C9×Dic3C2311yescharacteristic
109C2×C9×Dic3C2311yescharacteristic
110C2×C3×Dic9C2311yescharacteristic
111C2×C3×Dic9C2311yescharacteristic
112C2×C3×Dic9C2311yescharacteristic
113C3×C4×D9—41no—
114#6195—22no—
115#6195—22no—
116#6195—41no—
117#6194—22no—
118D3×Dic9—22no—
119#6192—22no—
120(C3⋊D9)⋊C4—22no—
121Dic3×D9—22no—
122#6189—22no—
123#5554—91no—
124#5490—91no—
125C23×C3×D3C2×D311yescharacteristic
126C22×D32—31no—
127C22×C32×C4C2×D311yescharacteristic
128C2×#638—31no—
129C2×#638—31no—
130C2×C4⋊(C3⋊D3)—31no—
131C2×C3×#67—31no—
132C22×C3×Dic3C2×D311yescharacteristic
133C2×C3×C4×D3—31no—
134D3×#67—64no—
135C2×#627—31no—
136C2×#626—31no—
137C2×#626—31no—
138C2×#626—31no—
139C2×#626—31no—
140C2×#625—31no—
141C2×#624—31no—
142#3804—64no—
143C2×D3×Dic3—31no—
144C2×D3×Dic3—31no—
145C24×C9—31no—
146C23×D9—31no—
147#3752—31no—
148#3752—31no—
149C4⋊(C3⋊Dic3)—31no—
150C3×#217—31no—
151C3×(C2×D3)⋊C4—31no—
152C3×(C2×D3)⋊C4C2×D311yescharacteristic
153C3×(C2×D3)⋊C4C2×D311yescharacteristic
154C3×(C2×D3)⋊C4C2×D311yescharacteristic
155C3×(C2×D3)⋊C4C2×D311yescharacteristic
156C3×Dic3⋊C4—31no—
157C3×C4×Dic3—31no—
158Dic3⋊Dic3—31no—
159Dic3⋊Dic3—31no—
160#3722—31no—
161#3722—31no—
162(C2×D3)⋊Dic3—31no—
163(C2×D3)⋊Dic3—31no—
164C22×C4×C9—21no—
165C22×C4×C9—31no—
166C22×C4×C9C2×D311yescharacteristic, complemented
167C2×#611—31no—
168C2×#611—31no—
169C2×#611—31no—
170C2×#611—31no—
171C2×#611—31no—
172C2×#611—31no—
173C2×#611—64no—
174C2×#611—61no—
175C2×#611—61no—
176C2×#611C2×D311yescharacteristic
177C22×Dic9—31no—
178#3697—64no—
179C2×D36—31no—
180C2×D36—31no—
181C2×D36—61no—
182C2×C4×D9—31no—
183C2×C4×D9—31no—
184C2×C4×D9C2×D311yescharacteristic, complemented
185C2×Dic18—31no—
186C9×C22⋊C4—31no—
187C9×C22⋊C4—31no—
188C9×C22⋊C4—31no—
189C9×C22⋊C4—31no—
190#3676—31no—
191#3676—31no—
192#3676C2×D311yescharacteristic, complemented
193(C2×D9)⋊C4—31no—
194(C2×D9)⋊C4—31no—
195(C2×D9)⋊C4—31no—
196(C2×D9)⋊C4—31no—
197(C2×D9)⋊C4—61no—
198(C2×D9)⋊C4—61no—
199(C2×D9)⋊C4C2×D311yescharacteristic, complemented
200C4⋊Dic9—31no—
201C4⋊Dic9—61no—
202Dic9⋊C4—31no—
203Dic9⋊C4—31no—
204Dic9⋊C4C2×D311yescharacteristic, complemented
205C4×Dic9C2×D311yescharacteristic, complemented
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⋊D9—21no—
213C2×C3⋊D9—21no—
214C2×C3⋊D9—21no—
215C2×C3⋊D9—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×D9C2×D412yes—
226D3×D9—44no—
227C3×C4×C9—21no—
228C3×C4×C9—21no—
229C3⋊Dic9—21no—
230C3⋊Dic9—21no—
231C9×Dic3—21no—
232C9×Dic3—21no—
233C3×Dic9—21no—
234C3×Dic9—21no—
235C3×Dic9C2×D412yes—
236C22×#67—91no—
237C2×#237—91no—
238C2×D3×D4—91no—
239C2×#235—91no—
240C3×C4×D4—91no—
241C2×C3×C22⋊C4—31no—
242#953—91no—
243#930—91no—
244#930—91no—
245#930—91no—
246#930—181no—
247#929—91no—
248C4×#67—31no—
249C2×(C2×D3)⋊C4—91no—
250C2×(C2×D3)⋊C4D911yescharacteristic, complemented
251#897—91no—
252#895—91no—
253#886—91no—
254#886—91no—
255#885—91no—
256#884—91no—
257#884—91no—
258#883—91no—
259#882—91no—
260#882—91no—
261#882—91no—
262#67⋊C4—91no—
263D3×C22⋊C4—91no—
264#878—91no—
265#875—91no—
266C4×D12—91no—
267C23×C32C22×D311yescharacteristic
268C22×C3⋊D3—31no—
269C22×C3⋊D3—31no—
270C22×C3×D3—22no—
271C22×C3×D3—22no—
272C22×C3×D3—31no—
273C22×C3×D3—41no—
274C22×C3×D3C22×D311yescharacteristic
275C22×C3×D3C22×D311yescharacteristic
276C2×D32—62no—
277C2×D32—62no—
278C2×D32—121no—
279C2×C32×C4—41no—
280C2×C32×C4C22×D311yescharacteristic
281C2×C32×C4C22×D311yescharacteristic
282#638—62no—
283#638—62no—
284C2×C3⋊Dic3—31no—
285C2×C3⋊Dic3—31no—
286C4⋊(C3⋊D3)—121no—
287C3×#67—34no—
288C2×C3×Dic3—22no—
289C2×C3×Dic3—31no—
290C2×C3×Dic3—31no—
291C2×C3×Dic3—31no—
292C2×C3×Dic3C22×D311yescharacteristic
293C2×C3×Dic3C22×D311yescharacteristic
294C3×C4×D3—121no—
295#627—62no—
296#626—62no—
297#626—62no—
298#626—62no—
299#626—121no—
300#625—62no—
301#624—62no—
302D3×Dic3—62no—
303D3×Dic3—62no—
304C23×C9—21no—
305C23×C9—31no—
306C23×C9—31no—
307C23×C9—62no—
308C23×C9—62no—
309C23×C9—121no—
310C23×C9C22×D311yescharacteristic
311C22×D9—31no—
312C22×D9—31no—
313C22×D9—61no—
314C22×D9—61no—
315C22×D9—62no—
316C22×D9—62no—
317C22×D9—121no—
318C22×D9C22×D311yescharacteristic
319C2×C4×C9—21no—
320C2×C4×C9—21no—
321C2×C4×C9—31no—
322C2×C4×C9—31no—
323C2×C4×C9—41no—
324C2×C4×C9—42no—
325C2×C4×C9—62no—
326C2×C4×C9C22×D311yescharacteristic
327C2×C4×C9C22×D311yescharacteristic
328#611—62no—
329#611—62no—
330#611—62no—
331#611—62no—
332#611—62no—
333#611—122no—
334#611—122no—
335#611—121no—
336#611D1214yescomplemented
337C2×Dic9—31no—
338C2×Dic9—31no—
339C2×Dic9—61no—
340C2×Dic9—61no—
341C2×Dic9—62no—
342C2×Dic9C22×D311yescharacteristic
343C2×Dic9C22×D311yescharacteristic
344C2×Dic9C22×D311yescharacteristic
345D36—62no—
346D36—121no—
347D36—122no—
348C4×D9—41no—
349C4×D9—62no—
350C4×D9—62no—
351Dic18—62no—
352#546—271noSylow
353C2×C3×C9—22no—
354C2×C3×C9C22×D411yescharacteristic
355C2×C3×C9C2×#4111yescharacteristic
356C2×C3×C9H(5,𝔽2)11yescharacteristic
357C3⋊D9—41no—
358C3⋊D9—41no—
359D3×C9—22no—
360D3×C9—41no—
361C3×D9—22no—
362C24×C3—31no—
363C23×D3—91no—
364C23×D3—91no—
365C23×D3C2×D911yescharacteristic
366C2×C3×D4—91no—
367C22×C3×C4—21no—
368C22×C3×C4—31no—
369C22×C3×C4—91no—
370C22×C3×C4C2×D911yescharacteristic, complemented
371C22×C3×C4D3211yescharacteristic
372C2×#67—31no—
373C2×#67—91no—
374C2×#67—91no—
375C2×#67—91no—
376C2×#67—91no—
377C2×#67—91no—
378C2×#67—91no—
379C2×#67—91no—
380C2×#67—91no—
381C2×#67—91no—
382C2×#67—91no—
383C2×#67—181no—
384C2×#67—181no—
385C2×#67—184no—
386C22×Dic3—91no—
387C22×Dic3—91no—
388C22×Dic3C2×D911yescharacteristic, complemented
389#237—184no—
390D3×D4—184no—
391#235—184no—
392C2×D12—91no—
393C2×D12—91no—
394C2×D12—91no—
395C2×D12—91no—
396C2×D12—91no—
397C2×D12—91no—
398C2×D12—181no—
399C2×C4×D3—31no—
400C2×C4×D3—91no—
401C2×C4×D3—91no—
402C2×C4×D3—91no—
403C2×C4×D3—91no—
404C2×Dic6—91no—
405C2×Dic6—91no—
406C3×C4⋊C4—91no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—31no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—31no—
411C3×C22⋊C4—91no—
412C3×C22⋊C4—91no—
413C3×C42—91no—
414#217—31no—
415#217—91no—
416#217—91no—
417(C2×D3)⋊C4—31no—
418(C2×D3)⋊C4—91no—
419(C2×D3)⋊C4—91no—
420(C2×D3)⋊C4—91no—
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—181no—
429(C2×D3)⋊C4—181no—
430(C2×D3)⋊C4C2×D911yescharacteristic
431(C2×D3)⋊C4C2×D911yescharacteristic
432(C2×D3)⋊C4C2×D911yescharacteristic, complemented
433(C2×D3)⋊C4C2×D911yescharacteristic, complemented
434C4⋊Dic3—91no—
435C4⋊Dic3—91no—
436C4⋊Dic3—91no—
437C4⋊Dic3—91no—
438C4⋊Dic3—181no—
439Dic3⋊C4—31no—
440Dic3⋊C4—91no—
441Dic3⋊C4—91no—
442C4×Dic3—31no—
443C22×C32—21no—
444C22×C32—21no—
445C22×C32D3×D412yes—
446C22×C32C23×D311yescharacteristic
447C2×C3⋊D3—61no—
448C2×C3⋊D3—61no—
449C2×C3⋊D3—61no—
450C2×C3⋊D3—61no—
451C2×C3⋊D3—61no—
452C2×C3⋊D3—61no—
453C2×C3×D3—21no—
454C2×C3×D3—21no—
455C2×C3×D3—21no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
458C2×C3×D3—32no—
459C2×C3×D3—44no—
460C2×C3×D3—61no—
461C2×C3×D3—61no—
462C2×C3×D3#23512yes—
463D32—124no—
464C32×C4—21no—
465C32×C4—21no—
466C3⋊Dic3—61no—
467C3⋊Dic3—61no—
468C3×Dic3—21no—
469C3×Dic3—21no—
470C3×Dic3—32no—
471C3×Dic3—61no—
472C3×Dic3—61no—
473C22×C9—21no—
474C22×C9—21no—
475C22×C9—21no—
476C22×C9—22no—
477C22×C9—32no—
478C22×C9—41no—
479C22×C9—41no—
480C22×C9—61no—
481C22×C9—61no—
482C22×C9—61no—
483C22×C9—61no—
484C22×C9—61no—
485C22×C9—124no—
486C22×C9C2×D1212yes—
487C22×C9C23×D311yescharacteristic
488C2×D9—21no—
489C2×D9—21no—
490C2×D9—61no—
491C2×D9—61no—
492C2×D9—61no—
493C2×D9—61no—
494C2×D9—61no—
495C2×D9—61no—
496C2×D9—121no—
497C2×D9—121no—
498C2×D9—121no—
499C2×D9—121no—
500C2×D9—121no—
501C2×D9—121no—
502C2×D9—124no—
503C2×D9C2×D1212yes—
504C4×C9—22no—
505C4×C9—21no—
506C4×C9—21no—
507C4×C9—41no—
508C4×C9—61no—
509C4×C9—61no—
510Dic9—21no—
511Dic9—21no—
512Dic9—61no—
513Dic9—61no—
514Dic9—121no—
515Dic9—121no—
516Dic9C2×D1212yes—
517C2×#41—271no—
518C22×D4—271no—
519#124—271no—
520#123—271no—
521#123—271no—
522C22⋊Q8—271no—
523#121—271no—
524#121—271no—
525#121—271no—
526#120—271no—
527#120—271no—
528C4×D4—91no—
529C4×D4—271no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—271no—
532C3×C9#54611yescharacteristic, complemented, Sylow
533C23×C3—21no—
534C23×C3—31no—
535C23×C3—31no—
536C23×C3—62no—
537C23×C3—62no—
538C23×C3—91no—
539C23×C3—121no—
540C23×C3C22×D911yescharacteristic
541C23×C3C2×D3211yescharacteristic
542C22×D3—22no—
543C22×D3—22no—
544C22×D3—31no—
545C22×D3—41no—
546C22×D3—91no—
547C22×D3—91no—
548C22×D3—91no—
549C22×D3—91no—
550C22×D3—181no—
551C22×D3—181no—
552C22×D3—182no—
553C22×D3—182no—
554C22×D3—182no—
555C22×D3—182no—
556C22×D3—361no—
557C22×D3—361no—
558C22×D3C22×D911yescharacteristic
559C22×D3C22×D911yescharacteristic
560C3×D4—94no—
561C2×C3×C4—21no—
562C2×C3×C4—21no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—41no—
566C2×C3×C4—41no—
567C2×C3×C4—42no—
568C2×C3×C4—62no—
569C2×C3×C4—91no—
570C2×C3×C4—91no—
571C2×C3×C4—91no—
572C2×C3×C4—361no—
573C2×C3×C4C22×D911yescharacteristic
574C2×C3×C4C22×D911yescharacteristic
575C2×C3×C4C2×D3211yescharacteristic
576C2×C3×C4C2×D3211yescharacteristic
577#67—34no—
578#67—182no—
579#67—182no—
580#67—182no—
581#67—182no—
582#67—182no—
583#67—182no—
584#67—182no—
585#67—182no—
586#67—182no—
587#67—362no—
588#67—362no—
589#67—361no—
590C2×Dic3—22no—
591C2×Dic3—31no—
592C2×Dic3—31no—
593C2×Dic3—31no—
594C2×Dic3—91no—
595C2×Dic3—91no—
596C2×Dic3—91no—
597C2×Dic3—91no—
598C2×Dic3—181no—
599C2×Dic3—181no—
600C2×Dic3—182no—
601C2×Dic3—182no—
602C2×Dic3C22×D911yescharacteristic
603C2×Dic3C22×D911yescharacteristic
604D12—182no—
605D12—182no—
606D12—182no—
607D12—361no—
608D12—361no—
609D12—362no—
610D12—361no—
611C4×D3—121no—
612C4×D3—182no—
613C4×D3—182no—
614C4×D3—182no—
615C4×D3—182no—
616Dic6—182no—
617Dic6—182no—
618C2×C32—22no—
619C2×C32C2×#23511yescharacteristic
620C2×C32C2×D3×D411yescharacteristic
621C2×C32#100411yescharacteristic
622C3⋊D3—121no—
623C3⋊D3—121no—
624C3×D3—22no—
625C3×D3—41no—
626C3×D3—62no—
627C2×C9—22no—
628C2×C9—21no—
629C2×C9—21no—
630C2×C9—21no—
631C2×C9—42no—
632C2×C9—62no—
633C2×C9—121no—
634C2×C9C22×D1211yescharacteristic
635C2×C9#100411yescharacteristic
636C2×C9D3×#4111yescharacteristic
637D9—22no—
638D9—121no—
639D9—121no—
640D9—241no—
641D9—241no—
642C24—31no—
643C24—271no—
644#41—544no—
645C2×Q8—271no—
646C2×D4—91no—
647C2×D4—271no—
648C2×D4—271no—
649C2×D4—271no—
650C2×D4—271no—
651C2×D4—271no—
652C2×D4—271no—
653C2×D4—271no—
654C2×D4—271no—
655C2×D4—544no—
656C22×C4—31no—
657C22×C4—91no—
658C22×C4—271no—
659C22×C4—271no—
660C22×C4—271no—
661C22×C4D3×D911yescharacteristic, complemented
662C4⋊C4—91no—
663C4⋊C4—271no—
664C4⋊C4—271no—
665C4⋊C4—271no—
666C22⋊C4—31no—
667C22⋊C4—31no—
668C22⋊C4—31no—
669C22⋊C4—31no—
670C22⋊C4—91no—
671C22⋊C4—91no—
672C22⋊C4—271no—
673C22⋊C4—271no—
674C22⋊C4—271no—
675C22⋊C4—271no—
676C22⋊C4—271no—
677C22⋊C4—271no—
678C42—91no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—22no—
685C22×C3—32no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—61no—
689C22×C3—61no—
690C22×C3—61no—
691C22×C3—61no—
692C22×C3—61no—
693C22×C3—92no—
694C22×C3—124no—
695C22×C3—181no—
696C22×C3—181no—
697C22×C3D4×D912yes—
698C22×C3C23×D911yescharacteristic
699C22×C3D3×D1212yes—
700C22×C3C22×D3211yescharacteristic
701C2×D3—21no—
702C2×D3—21no—
703C2×D3—21no—
704C2×D3—21no—
705C2×D3—21no—
706C2×D3—32no—
707C2×D3—44no—
708C2×D3—61no—
709C2×D3—61no—
710C2×D3—181no—
711C2×D3—181no—
712C2×D3—181no—
713C2×D3—181no—
714C2×D3—181no—
715C2×D3—181no—
716C2×D3—181no—
717C2×D3—181no—
718C2×D3—181no—
719C2×D3—181no—
720C2×D3—181no—
721C2×D3—181no—
722C2×D3—361no—
723C2×D3—361no—
724C2×D3—361no—
725C2×D3—361no—
726C2×D3—361no—
727C2×D3—361no—
728C2×D3—364no—
729C2×D3—364no—
730C2×D3#369712yescomplemented
731C3×C4—22no—
732C3×C4—21no—
733C3×C4—21no—
734C3×C4—21no—
735C3×C4—21no—
736C3×C4—41no—
737C3×C4—61no—
738C3×C4—61no—
739C3×C4—92no—
740C3×C4—181no—
741C3×C4—181no—
742Dic3—21no—
743Dic3—21no—
744Dic3—32no—
745Dic3—61no—
746Dic3—61no—
747Dic3—181no—
748Dic3—181no—
749Dic3—181no—
750Dic3—181no—
751Dic3—361no—
752Dic3—361no—
753C32#549011yescharacteristic
754C9—21no—
755C9#555411yescharacteristic, complemented
756C23—31no—
757C23—31no—
758C23—62no—
759C23—62no—
760C23—91no—
761C23—121no—
762C23—271no—
763C23—271no—
764C23—542no—
765C23—542no—
766C23—1081no—
767C23C2×D3×D911yescharacteristic
768Q8—542no—
769D4—94no—
770D4—542no—
771D4—542no—
772D4—542no—
773D4—542no—
774D4—542no—
775D4—542no—
776D4—1081no—
777D4—1081no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—41no—
781C2×C4—62no—
782C2×C4—91no—
783C2×C4—91no—
784C2×C4—91no—
785C2×C4—271no—
786C2×C4—271no—
787C2×C4—361no—
788C2×C4—542no—
789C2×C4—542no—
790C2×C4—542no—
791C2×C4C2×D3×D911yescharacteristic
792C2×C4C2×D3×D911yescharacteristic
793C2×C3—22no—
794C2×C3—22no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—42no—
799C2×C3—62no—
800C2×C3—121no—
801C2×C3—182no—
802C2×C3C2×#369711yescharacteristic
803C2×C3C2×D4×D911yescharacteristic
804C2×C3#6371011yescharacteristic
805C2×C3C2×D3×D1211yescharacteristic
806C2×C3D3×#23511yescharacteristic
807C2×C3#6433011yescharacteristic
808D3—22no—
809D3—41no—
810D3—62no—
811D3—361no—
812D3—361no—
813D3—361no—
814D3—361no—
815D3—721no—
816D3—721no—
817C22—21no—
818C22—21no—
819C22—32no—
820C22—61no—
821C22—61no—
822C22—61no—
823C22—61no—
824C22—61no—
825C22—92no—
826C22—124no—
827C22—181no—
828C22—181no—
829C22—541no—
830C22—541no—
831C22—541no—
832C22—541no—
833C22—541no—
834C22—541no—
835C22—1084no—
836C22D9×D1212yes—
837C22C22×D3×D911yescharacteristic
838C4—21no—
839C4—21no—
840C4—61no—
841C4—61no—
842C4—92no—
843C4—181no—
844C4—181no—
845C4—541no—
846C4—541no—
847C3—21no—
848C3#1058959211yescharacteristic, complemented
849C3#1059507311yescharacteristic
850C2—22no—
851C2—62no—
852C2—121no—
853C2—182no—
854C2—1081no—
855C2—1081no—
856C2C2×D9×D1211yescharacteristic
857C2D3×#369711yescharacteristic
858C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC22×C3×C4×C9C22
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×#88658C2semidirect
3. #11721819C2semidirect
4. C2×C9×(C2×D3)⋊C4C2semidirect
5. C3×C4×#611C2semidirect
6. #11721287C2semidirect
7. #11721251C2semidirect
8. #11721051C2semidirect
9. D9×(C2×D3)⋊C4C2semidirect
10. #11721039C2semidirect
11. #11721033C2semidirect
12. #11721023C2semidirect
13. #11721013C2semidirect
14. #11720989C2semidirect
15. #11720956C2semidirect
20. C22×C3×C4×C9C22semidirect
22. C2×#6233C22semidirect
23. C2×C4⋊(C3⋊D9)C22semidirect
25. C22×C9×Dic3C22semidirect
26. C2×C3×C4×D9C22semidirect
30. C2×#6195C22semidirect
33. C2×#6192C22semidirect
34. C2×(C3⋊D9)⋊C4C22semidirect
36. C2×Dic3×D9C22semidirect
37. C2×#6189C22semidirect
38. #88536C22semidirect
39. #88536C22semidirect
40. C4⋊(C3⋊Dic9)C22semidirect
41. C3×#3676C22semidirect
44. C9×(C2×D3)⋊C4C22semidirect
45. C9×(C2×D3)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C3×Dic9⋊C4C22semidirect
48. C3×C4×Dic9C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
51. #88445C22semidirect
52. #88445C22semidirect
53. Dic9⋊Dic3C22semidirect
54. Dic9⋊Dic3C22semidirect
77. C4×#611D3semidirect
106. C3×#611D4semidirect
166. C22×C4×C9C2×D3semidirect
184. C2×C4×D9C2×D3semidirect
192. #3676C2×D3semidirect
199. (C2×D9)⋊C4C2×D3semidirect
204. Dic9⋊C4C2×D3semidirect
205. C4×Dic9C2×D3semidirect
222. C2×D3×C9#41semidirect
250. C2×(C2×D3)⋊C4D9semidirect
336. #611D12semidirect
370. C22×C3×C4C2×D9semidirect
388. C22×Dic3C2×D9semidirect
432. (C2×D3)⋊C4C2×D9semidirect
433. (C2×D3)⋊C4C2×D9semidirect
532. C3×C9#546semidirect
661. C22×C4D3×D9semidirect
730. C2×D3#3697semidirect
755. C9#5554semidirect
848. C3#10589592semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6112
C2×#886582
#117218192
C2×C9×(C2×D3)⋊C42
C3×C4×#6112
#117212872
#117212512
#117210512
D9×(C2×D3)⋊C42
#117210392
#117210332
#117210232
#117210132
#117209892
#117209562
#105950733
#105895923