Finite Group Databasebeta

← #13150277

Subgroups — #13150277

Order 1728.

806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88534C211yesmaximal, characteristic, complemented
2C4×C9×#67C211yesmaximal, characteristic, complemented
3C3×#63492C211yesmaximal, characteristic, complemented
4#11721290C211yesmaximal, characteristic, complemented
5#11721290C211yesmaximal, characteristic, complemented
6#611⋊Dic3C211yesmaximal, characteristic, complemented
7#611⋊Dic3C211yesmaximal, characteristic, complemented
8#11721032C211yesmaximal, characteristic, complemented
9#11720982C211yesmaximal, characteristic, complemented
10#11720981C211yesmaximal, characteristic, complemented
11#11720976C211yesmaximal, characteristic, complemented
12#11720974C211yesmaximal, characteristic, complemented
13#11720962C211yesmaximal, characteristic, complemented
14#11720947C211yesmaximal, characteristic, complemented
15#11720919C211yesmaximal, characteristic, complemented
16#10594962—31nomaximal
17#10589642—31nomaximal
18C22×C3×C4×C9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×C9×#67C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C2×C4×D3×C9C2211yescharacteristic
25C2×C3×D36C2211yescharacteristic
26C2×#6194C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×Dic3×D9C2211yescharacteristic
29C2×Dic3×D9C2211yescharacteristic
30#88534C2211yescharacteristic
31#88534C2211yescharacteristic
32#88534C2211yescharacteristic
33#88534C2211yescharacteristic
34C9×#217C2211yescharacteristic
35C9×(C2×D3)⋊C4C2211yescharacteristic
36C3×(C2×D9)⋊C4C2211yescharacteristic
37C3×(C2×D9)⋊C4C2211yescharacteristic
38C9×Dic3⋊C4C2211yescharacteristic
39C4×C9×Dic3C2211yescharacteristic
40C3×C4⋊Dic9C2211yescharacteristic
41(C2×D3)⋊Dic9C2211yescharacteristic
42(C2×D3)⋊Dic9C2211yescharacteristic
43(C2×D9)⋊Dic3C2211yescharacteristic
44(C2×D9)⋊Dic3C2211yescharacteristic
45(C2×D9)⋊Dic3C2211yescharacteristic
46(C2×D9)⋊Dic3C2211yescharacteristic
47#88442C2211yescharacteristic
48#88442C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic9⋊Dic3C2211yescharacteristic
51Dic3×Dic9C2211yescharacteristic
52Dic3×Dic9C2211yescharacteristic
53C2×#3750—31no—
54C3×#930—31no—
55C3×C4×#67D311yescharacteristic
56#63980—31no—
57#63980—31no—
58#67⋊Dic3—31no—
59#67⋊Dic3—31no—
60#63905—31no—
61#63885—31no—
62#63884—31no—
63#63879—31no—
64#63877—31no—
65#63859—31no—
66#63858—31no—
67#63847—31no—
68C4×D4×C9—31no—
69#63501—31no—
70#63501—31no—
71#63492D311yescharacteristic, complemented
72#63491—31no—
73C4×#611—31no—
74C2×Dic9⋊C4—31no—
75C2×Dic9⋊C4—61no—
76#63456—31no—
77#63451—31no—
78#63446—31no—
79#611⋊C4—31no—
80#611⋊C4—31no—
81#63441—31no—
82#63438—31no—
83#63434—31no—
84C23×C3×C9C2311yescharacteristic
85C22×D3×C9C2311yescharacteristic
86C22×C3×D9C2311yescharacteristic
87C22×C3×D9C2311yescharacteristic
88C2×C3×C4×C9—41no—
89C2×C3×C4×C9C2311yescharacteristic
90C2×C3×C4×C9C2311yescharacteristic
91C2×C3⋊Dic9—22no—
92C2×C3⋊Dic9—41no—
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C9×#67—22no—
98C3×#611—22no—
99C3×#611—22no—
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C4×D3×C9—41no—
106C3×D36—41no—
107#6194—22no—
108#6194—41no—
109Dic3×D9—22no—
110Dic3×D9—41no—
111#5601—91no—
112#5540—91no—
113C22×C32×C4C2×D311yescharacteristic
114C22×C3⋊Dic3—31no—
115C22×C3⋊Dic3—31no—
116C2×C3×#67—31no—
117C2×C3×#67—31no—
118C2×C3×#67C2×D311yescharacteristic
119C2×C3×D12—31no—
120C2×C3×C4×D3C2×D311yescharacteristic
121C2×#625—31no—
122C2×#625—31no—
123C2×D3×Dic3—31no—
124C2×D3×Dic3—31no—
125#3750—31no—
126#3750—31no—
127#3750—31no—
128#3750—31no—
129C3×#217C2×D311yescharacteristic
130C3×(C2×D3)⋊C4—31no—
131C3×(C2×D3)⋊C4—31no—
132C3×(C2×D3)⋊C4C2×D311yescharacteristic
133C3×C4⋊Dic3—31no—
134C3×Dic3⋊C4C2×D311yescharacteristic
135C3×C4×Dic3C2×D311yescharacteristic
136#3724—31no—
137#3724—31no—
138Dic3⋊Dic3—31no—
139Dic3⋊Dic3—31no—
140(C2×D3)⋊Dic3—31no—
141(C2×D3)⋊Dic3—31no—
142(C2×D3)⋊Dic3—31no—
143(C2×D3)⋊Dic3—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146Dic32—31no—
147Dic32—31no—
148C2×D4×C9—31no—
149C22×C4×C9—21no—
150C22×C4×C9—31no—
151C22×C4×C9C2×D311yescharacteristic
152C2×#611—31no—
153C2×#611—31no—
154C2×#611C2×D311yescharacteristic
155C2×#611C2×D311yescharacteristic
156C22×Dic9—31no—
157C22×Dic9—31no—
158C22×Dic9—61no—
159C22×Dic9—61no—
160C2×D36C2×D311yescharacteristic
161C2×C4×D9—31no—
162C2×C4×D9—31no—
163C9×C4⋊C4—31no—
164C9×C22⋊C4—31no—
165C9×C22⋊C4—31no—
166C42×C9—31no—
167#3676—31no—
168#3676—31no—
169(C2×D9)⋊C4—31no—
170(C2×D9)⋊C4—31no—
171(C2×D9)⋊C4—31no—
172(C2×D9)⋊C4—31no—
173(C2×D9)⋊C4C2×D311yescharacteristic
174(C2×D9)⋊C4C2×D311yescharacteristic
175C4⋊Dic9C2×D311yescharacteristic
176Dic9⋊C4—31no—
177Dic9⋊C4—31no—
178Dic9⋊C4—31no—
179Dic9⋊C4—31no—
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4—61no—
185Dic9⋊C4—61no—
186Dic9⋊C4—61no—
187Dic9⋊C4—61no—
188C4×Dic9—31no—
189C4×Dic9—31no—
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9#4112yes—
193C22×C3×C9C2411yescharacteristic
194C2×D3×C9—21no—
195C2×D3×C9—21no—
196C2×D3×C9—21no—
197C2×C3×D9—21no—
198C2×C3×D9—21no—
199C2×C3×D9—21no—
200C2×C3×D9—21no—
201C2×C3×D9—21no—
202C2×C3×D9—21no—
203C3×C4×C9—21no—
204C3×C4×C9—21no—
205C3⋊Dic9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C3⋊Dic9#4112yes—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C9×Dic3—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×#121—91no—
215C3×C4×D4—31no—
216#939—91no—
217#939—91no—
218#939—91no—
219#939—91no—
220#939—91no—
221#935—91no—
222D4×Dic3—91no—
223D4×Dic3—91no—
224#930—31no—
225#929—91no—
226C4×#67—91no—
227C4×#67D911yescharacteristic, complemented
228C2×Dic3⋊C4—91no—
229C2×Dic3⋊C4—91no—
230C2×Dic3⋊C4—181no—
231#898—91no—
232#894—91no—
233#889—91no—
234#889—91no—
235#884—91no—
236#883—91no—
237#67⋊C4—91no—
238#67⋊C4—91no—
239#67⋊C4—91no—
240#879—91no—
241#879—91no—
242#877—91no—
243#876—91no—
244#872—91no—
245C23×C32C22×D311yescharacteristic
246C22×C3×D3—31no—
247C22×C3×D3—31no—
248C22×C3×D3C22×D311yescharacteristic
249C2×C32×C4—41no—
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C3⋊Dic3—31no—
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—62no—
257C2×C3⋊Dic3—121no—
258C3×#67—22no—
259C3×#67—62no—
260C3×#67—62no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3C22×D311yescharacteristic
264C2×C3×Dic3C22×D311yescharacteristic
265C2×C3×Dic3C22×D311yescharacteristic
266C3×D12—121no—
267C3×C4×D3—41no—
268#625—62no—
269#625—121no—
270D3×Dic3—62no—
271D3×Dic3—121no—
272C23×C9—21no—
273C23×C9—31no—
274C23×C9C22×D311yescharacteristic
275C22×D9C22×D311yescharacteristic
276C22×D9C22×D311yescharacteristic
277D4×C9—62no—
278C2×C4×C9—21no—
279C2×C4×C9—21no—
280C2×C4×C9—31no—
281C2×C4×C9—31no—
282C2×C4×C9—31no—
283C2×C4×C9—41no—
284C2×C4×C9—42no—
285C2×C4×C9—121no—
286C2×C4×C9C22×D311yescharacteristic
287C2×C4×C9C22×D311yescharacteristic
288#611—22no—
289#611—22no—
290#611—62no—
291#611—121no—
292C2×Dic9—31no—
293C2×Dic9—31no—
294C2×Dic9—31no—
295C2×Dic9—31no—
296C2×Dic9—61no—
297C2×Dic9—61no—
298C2×Dic9—61no—
299C2×Dic9—61no—
300C2×Dic9—62no—
301C2×Dic9—64no—
302C2×Dic9—121no—
303C2×Dic9—122no—
304C2×Dic9C22×D311yescharacteristic
305C2×Dic9C22×D311yescharacteristic
306D36—41no—
307C4×D9—62no—
308C4×D9—121no—
309#553—271noSylow
310C2×C3×C9—22no—
311C2×C3×C9C2×#4111yescharacteristic
312C2×C3×C9C2×#4111yescharacteristic
313C2×C3×C9H(5,𝔽2)11yescharacteristic
314D3×C9—41no—
315C3×D9—41no—
316C3×D9—41no—
317C2×C3×D4—31no—
318C2×C3×D4—91no—
319C2×C3×D4—91no—
320C2×C3×D4—91no—
321C22×C3×C4—21no—
322C22×C3×C4—31no—
323C22×C3×C4C2×D911yescharacteristic
324C22×C3×C4D3211yescharacteristic
325C2×#67—31no—
326C2×#67—31no—
327C2×#67—91no—
328C2×#67—91no—
329C2×#67—91no—
330C2×#67—91no—
331C2×#67C2×D911yescharacteristic
332C22×Dic3—91no—
333C22×Dic3—91no—
334C22×Dic3—91no—
335C22×Dic3—91no—
336C22×Dic3—91no—
337C22×Dic3—91no—
338C22×Dic3—181no—
339C22×Dic3—181no—
340C2×D12—31no—
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×C4×D3C2×D911yescharacteristic
344C3×C4⋊C4—31no—
345C3×C4⋊C4—91no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—91no—
349C3×C22⋊C4—91no—
350C3×C42—31no—
351#217—91no—
352#217—91no—
353#217—91no—
354#217—91no—
355#217—91no—
356#217—91no—
357#217C2×D911yescharacteristic
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—91no—
361(C2×D3)⋊C4—91no—
362(C2×D3)⋊C4—91no—
363(C2×D3)⋊C4—91no—
364(C2×D3)⋊C4—91no—
365(C2×D3)⋊C4—91no—
366(C2×D3)⋊C4C2×D911yescharacteristic
367C4⋊Dic3—31no—
368C4⋊Dic3—91no—
369C4⋊Dic3—91no—
370Dic3⋊C4—91no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4—91no—
374Dic3⋊C4—91no—
375Dic3⋊C4—91no—
376Dic3⋊C4—91no—
377Dic3⋊C4—91no—
378Dic3⋊C4—91no—
379Dic3⋊C4—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—181no—
385Dic3⋊C4—181no—
386Dic3⋊C4—181no—
387Dic3⋊C4—181no—
388Dic3⋊C4C2×D911yescharacteristic
389C4×Dic3—91no—
390C4×Dic3—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3C2×D911yescharacteristic
394C22×C32—21no—
395C22×C32—21no—
396C22×C32#23512yes—
397C22×C32C23×D311yescharacteristic
398C2×C3×D3—21no—
399C2×C3×D3—21no—
400C2×C3×D3—21no—
401C2×C3×D3—61no—
402C2×C3×D3—61no—
403C2×C3×D3—61no—
404C2×C3×D3—61no—
405C2×C3×D3—61no—
406C2×C3×D3—61no—
407C32×C4—21no—
408C32×C4—21no—
409C3⋊Dic3—32no—
410C3⋊Dic3—61no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—61no—
417C3×Dic3—61no—
418C22×C9—22no—
419C22×C9—22no—
420C22×C9—21no—
421C22×C9—21no—
422C22×C9—21no—
423C22×C9—22no—
424C22×C9—61no—
425C22×C9—61no—
426C22×C9—61no—
427C22×C9#23712yes—
428C22×C9C23×D311yescharacteristic
429C2×D9—21no—
430C2×D9—21no—
431C2×D9—21no—
432C2×D9—21no—
433C2×D9—21no—
434C2×D9—21no—
435C4×C9—21no—
436C4×C9—21no—
437C4×C9—41no—
438C4×C9—41no—
439C4×C9—61no—
440C4×C9—61no—
441C4×C9—61no—
442Dic9—21no—
443Dic9—21no—
444Dic9—32no—
445Dic9—62no—
446Dic9—62no—
447Dic9—61no—
448Dic9—61no—
449Dic9—61no—
450Dic9—121no—
451Dic9—121no—
452#126—271no—
453#126—271no—
454#125—271no—
455#123—271no—
456#123—271no—
457#121—91no—
458#121—271no—
459#121—271no—
460#121—271no—
461C4×D4—31no—
462C4×D4—271no—
463C4×D4—271no—
464C4×D4—271no—
465#117—271no—
466C2×C4⋊C4—271no—
467C3×C9#55311yescharacteristic, complemented, Sylow
468C23×C3—21no—
469C23×C3—31no—
470C23×C3—91no—
471C23×C3—91no—
472C23×C3C22×D911yescharacteristic
473C23×C3C2×D3211yescharacteristic
474C22×D3—31no—
475C22×D3—31no—
476C22×D3C22×D911yescharacteristic
477C3×D4—62no—
478C3×D4—182no—
479C3×D4—182no—
480C3×D4—361no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—31no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—42no—
489C2×C3×C4—91no—
490C2×C3×C4—91no—
491C2×C3×C4—121no—
492C2×C3×C4C22×D911yescharacteristic
493C2×C3×C4C22×D911yescharacteristic
494C2×C3×C4C2×D3211yescharacteristic
495C2×C3×C4C2×D3211yescharacteristic
496#67—22no—
497#67—62no—
498#67—62no—
499#67—182no—
500#67—182no—
501#67—361no—
502#67—361no—
503C2×Dic3—31no—
504C2×Dic3—31no—
505C2×Dic3—91no—
506C2×Dic3—91no—
507C2×Dic3—91no—
508C2×Dic3—91no—
509C2×Dic3—91no—
510C2×Dic3—91no—
511C2×Dic3—91no—
512C2×Dic3—91no—
513C2×Dic3—181no—
514C2×Dic3—181no—
515C2×Dic3—181no—
516C2×Dic3—181no—
517C2×Dic3—182no—
518C2×Dic3—182no—
519C2×Dic3—182no—
520C2×Dic3—184no—
521C2×Dic3—361no—
522C2×Dic3—361no—
523C2×Dic3—361no—
524C2×Dic3—362no—
525C2×Dic3C22×D911yescharacteristic
526C2×Dic3C22×D911yescharacteristic
527C2×Dic3C22×D911yescharacteristic
528D12—121no—
529C4×D3—41no—
530C4×D3—182no—
531C4×D3—361no—
532C2×C32—22no—
533C2×C32C2×#23511yescharacteristic
534C2×C32#100411yescharacteristic
535C2×C32D3×#4111yescharacteristic
536C3×D3—41no—
537C3×D3—121no—
538C3×D3—121no—
539C2×C9—24no—
540C2×C9—22no—
541C2×C9—21no—
542C2×C9—21no—
543C2×C9—21no—
544C2×C9—121no—
545C2×C9C2×#23711yescharacteristic
546C2×C9#100411yescharacteristic
547C2×C9D3×#4111yescharacteristic
548D9—41no—
549D9—41no—
550C2×D4—31no—
551C2×D4—91no—
552C2×D4—91no—
553C2×D4—91no—
554C2×D4—271no—
555C2×D4—271no—
556C22×C4—31no—
557C22×C4—271no—
558C22×C4—271no—
559C22×C4—271no—
560C22×C4—271no—
561C22×C4D3×D911yescharacteristic
562C4⋊C4—31no—
563C4⋊C4—91no—
564C4⋊C4—271no—
565C4⋊C4—271no—
566C4⋊C4—271no—
567C4⋊C4—271no—
568C4⋊C4—271no—
569C4⋊C4—271no—
570C4⋊C4—271no—
571C4⋊C4—271no—
572C22⋊C4—31no—
573C22⋊C4—31no—
574C22⋊C4—91no—
575C22⋊C4—91no—
576C22⋊C4—271no—
577C22⋊C4—271no—
578C22⋊C4—271no—
579C22⋊C4—271no—
580C22⋊C4—271no—
581C22⋊C4—271no—
582C42—31no—
583C42—271no—
584C42—271no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—21no—
588C22×C3—21no—
589C22×C3—21no—
590C22×C3—21no—
591C22×C3—22no—
592C22×C3—21no—
593C22×C3—61no—
594C22×C3—61no—
595C22×C3—61no—
596C22×C3—181no—
597C22×C3—181no—
598C22×C3—181no—
599C22×C3—181no—
600C22×C3—181no—
601C22×C3—181no—
602C22×C3#369712yes—
603C22×C3C23×D911yescharacteristic
604C22×C3#379512yes—
605C22×C3C22×D3211yescharacteristic
606C2×D3—21no—
607C2×D3—21no—
608C2×D3—21no—
609C2×D3—61no—
610C2×D3—61no—
611C2×D3—61no—
612C2×D3—61no—
613C2×D3—61no—
614C2×D3—61no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—21no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—61no—
622C3×C4—61no—
623C3×C4—61no—
624C3×C4—181no—
625C3×C4—181no—
626Dic3—21no—
627Dic3—21no—
628Dic3—21no—
629Dic3—61no—
630Dic3—61no—
631Dic3—92no—
632Dic3—92no—
633Dic3—182no—
634Dic3—182no—
635Dic3—181no—
636Dic3—181no—
637Dic3—181no—
638Dic3—181no—
639Dic3—181no—
640Dic3—181no—
641Dic3—361no—
642Dic3—361no—
643C32#554011yescharacteristic
644C9—21no—
645C9#560111yescharacteristic, complemented
646C23—31no—
647C23—91no—
648C23—91no—
649C23C2×D3×D911yescharacteristic
650D4—62no—
651D4—182no—
652D4—182no—
653D4—361no—
654D4—542no—
655D4—1081no—
656C2×C4—31no—
657C2×C4—31no—
658C2×C4—31no—
659C2×C4—41no—
660C2×C4—91no—
661C2×C4—91no—
662C2×C4—121no—
663C2×C4—271no—
664C2×C4—271no—
665C2×C4—271no—
666C2×C4—271no—
667C2×C4—542no—
668C2×C4—542no—
669C2×C4—1081no—
670C2×C4—1081no—
671C2×C4C2×D3×D911yescharacteristic
672C2×C4C2×D3×D911yescharacteristic
673C2×C3—24no—
674C2×C3—22no—
675C2×C3—22no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—121no—
680C2×C3—361no—
681C2×C3—361no—
682C2×C3C2×#369711yescharacteristic
683C2×C3#6371011yescharacteristic
684C2×C3#41×D911yescharacteristic
685C2×C3C2×#379511yescharacteristic
686C2×C3#6430611yescharacteristic
687C2×C3#6433011yescharacteristic
688D3—41no—
689D3—121no—
690D3—121no—
691C22—21no—
692C22—21no—
693C22—61no—
694C22—61no—
695C22—61no—
696C22—181no—
697C22—181no—
698C22—181no—
699C22—181no—
700C22—181no—
701C22—181no—
702C22#8864112yes—
703C22C22×D3×D911yescharacteristic
704C4—21no—
705C4—21no—
706C4—61no—
707C4—61no—
708C4—61no—
709C4—181no—
710C4—181no—
711C4—272no—
712C4—541no—
713C4—541no—
714C4—541no—
715C3—21no—
716C3#1058964211yescharacteristic, complemented
717C3#1059496211yescharacteristic
718C2—22no—
719C2—121no—
720C2—361no—
721C2—361no—
722C2C2×#8864111yescharacteristic
723C2#1172247511yescharacteristic
724C2#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#553
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×#88534C2semidirect
2. C4×C9×#67C2semidirect
3. C3×#63492C2semidirect
4. #11721290C2semidirect
5. #11721290C2semidirect
6. #611⋊Dic3C2semidirect
7. #611⋊Dic3C2semidirect
8. #11721032C2semidirect
9. #11720982C2semidirect
10. #11720981C2semidirect
11. #11720976C2semidirect
12. #11720974C2semidirect
13. #11720962C2semidirect
14. #11720947C2semidirect
15. #11720919C2semidirect
71. #63492D3semidirect
227. C4×#67D9semidirect
467. C3×C9#553semidirect
645. C9#5601semidirect
716. C3#10589642semidirect

Maximal subgroups

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

subgroupindex
C2×#885342
C4×C9×#672
C3×#634922
#117212902
#611⋊Dic32
#117210322
#117209822
#117209812
#117209762
#117209742
#117209622
#117209472
#117209192
#105949623
#105896423