Finite Group Databasebeta

← #13152000

Subgroups — #13152000

Order 1728.

876 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88551C211yesmaximal, characteristic, complemented
2C3×#63515C211yesmaximal, characteristic
3C2×C9×#217C211yesmaximal, characteristic, complemented
4#611⋊Dic3C211yesmaximal, characteristic, complemented
5Dic3×#611C211yesmaximal, characteristic, complemented
6#11721269C211yesmaximal, characteristic, complemented
7#11721267C211yesmaximal, characteristic, complemented
8#11721260C211yesmaximal, characteristic, complemented
9#11721259C211yesmaximal, characteristic, complemented
10#11721257C211yesmaximal, characteristic, complemented
11#11721249C211yesmaximal, characteristic, complemented
12#11721248C211yesmaximal, characteristic, complemented
13#11721247C211yesmaximal, characteristic, complemented
14#11721246C211yesmaximal, characteristic, complemented
15#11721244C211yesmaximal, characteristic, complemented
16#10595509—31nomaximal
17#10589597—31nomaximal
18C24×C3×C9C2211yescharacteristic
19C22×C3⋊Dic9C2211yescharacteristic
20C22×C3⋊Dic9C2211yescharacteristic
21C2×C3×#611C2211yescharacteristic
22C2×C3×#611C2211yescharacteristic
23C2×C3×#611C2211yescharacteristic
24C22×C9×Dic3C2211yescharacteristic
25C22×C9×Dic3C2211yescharacteristic
26C2×Dic3×D9C2211yescharacteristic, complemented
27C2×#6189C2211yescharacteristic, complemented
28#88551C2211yescharacteristic
29#88551C2211yescharacteristic
30#88551C2211yescharacteristic
31#88551C2211yescharacteristic
32C9×#217C2211yescharacteristic
33C9×#217C2211yescharacteristic
34C9×#217C2211yescharacteristic
35C9×#217C2211yescharacteristic
36C3×#3676C2211yescharacteristic
37C3×#3676C2211yescharacteristic
38C3×#3676C2211yescharacteristic
39(C2×D9)⋊Dic3C2211yescharacteristic, complemented
40(C2×D9)⋊Dic3C2211yescharacteristic, complemented
41(C2×D9)⋊Dic3C2211yescharacteristic, complemented
42Dic3⋊Dic9C2211yescharacteristic, complemented
43Dic3⋊Dic9C2211yescharacteristic, complemented
44Dic3⋊Dic9C2211yescharacteristic, complemented
45#88442C2211yescharacteristic, complemented
46#88442C2211yescharacteristic, complemented
47#88442C2211yescharacteristic, complemented
48Dic9⋊Dic3C2211yescharacteristic, complemented
49Dic9⋊Dic3C2211yescharacteristic, complemented
50Dic3×Dic9C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53C2×#3757—31no—
54C3×#953—31no—
55C2×C3×#217D311yescharacteristic
56#63982—31no—
57#67⋊Dic3—31no—
58Dic3×#67—31no—
59#63969—31no—
60#63964—31no—
61#63962—31no—
62#63961—31no—
63#63959—31no—
64#63957—31no—
65#63956—31no—
66#63956—31no—
67#63955—31no—
68C2×C9×C22⋊C4—31no—
69#63515D311yescharacteristic
70C2×#3676—31no—
71C2×#3676—61no—
72#63491—31no—
73C4×#611—31no—
74#63488—31no—
75#63486—31no—
76#63448—31no—
77#63447—31no—
78#63445—31no—
79#611⋊C4—31no—
80#63441—31no—
81#63441—31no—
82#63440—31no—
83#63439—31no—
84C23×C3×C9—22no—
85C23×C3×C9—22no—
86C23×C3×C9—41no—
87C23×C3×C9C2311yescharacteristic
88C23×C3×C9C2311yescharacteristic
89C23×C3×C9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×C3⋊Dic9—22no—
92C2×C3⋊Dic9—41no—
93C2×C3⋊Dic9C2311yescharacteristic
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C3×#611—22no—
98C3×#611—22no—
99C3×#611—41no—
100C2×C9×Dic3—22no—
101C2×C9×Dic3—41no—
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C9×Dic3C2311yescharacteristic
105C2×C9×Dic3C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109Dic3×D9—41no—
110#6189—41no—
111#5587—91no—
112#5495—91no—
113C24×C32C2×D311yescharacteristic
114C22×C3⋊Dic3—31no—
115C22×C3⋊Dic3—31no—
116C2×C3×#67—31no—
117C2×C3×#67—31no—
118C2×C3×#67—31no—
119C22×C3×Dic3C2×D311yescharacteristic
120C22×C3×Dic3C2×D311yescharacteristic
121C2×#627—31no—
122C2×D3×Dic3—31no—
123C24×C9—21no—
124C24×C9C2×D311yescharacteristic
125#3757—31no—
126#3757—31no—
127#3757—31no—
128#3757—31no—
129C3×#217—31no—
130C3×#217—31no—
131C3×#217—31no—
132C3×#217C2×D311yescharacteristic
133C3×#217C2×D311yescharacteristic
134C3×#217C2×D311yescharacteristic
135C3×#217C2×D311yescharacteristic
136#3724—31no—
137#3724—31no—
138#3724—31no—
139Dic3⋊Dic3—31no—
140Dic3⋊Dic3—31no—
141Dic3⋊Dic3—31no—
142Dic3⋊Dic3—31no—
143Dic3⋊Dic3—31no—
144(C2×D3)⋊Dic3—31no—
145(C2×D3)⋊Dic3—31no—
146(C2×D3)⋊Dic3—31no—
147Dic32—31no—
148Dic32—31no—
149Dic32—31no—
150C22×C4×C9—31no—
151C22×C4×C9—31no—
152C2×#611C2×D311yescharacteristic
153C2×#611C2×D311yescharacteristic
154C2×#611C2×D311yescharacteristic
155C22×Dic9—31no—
156C22×Dic9—31no—
157C22×Dic9—61no—
158C22×Dic9—61no—
159C2×C4×D9—31no—
160C2×Dic18—31no—
161C9×C22⋊C4—31no—
162C9×C22⋊C4—31no—
163C9×C22⋊C4—31no—
164C9×C22⋊C4—31no—
165#3676—31no—
166#3676—31no—
167#3676—31no—
168#3676—31no—
169#3676—61no—
170#3676—61no—
171#3676—61no—
172#3676—61no—
173#3676C2×D311yescharacteristic
174#3676C2×D311yescharacteristic
175#3676C2×D311yescharacteristic
176(C2×D9)⋊C4—31no—
177(C2×D9)⋊C4—31no—
178(C2×D9)⋊C4—31no—
179C4⋊Dic9—31no—
180C4⋊Dic9—31no—
181C4⋊Dic9—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—31no—
184Dic9⋊C4—31no—
185Dic9⋊C4—31no—
186Dic9⋊C4—31no—
187C4×Dic9—31no—
188C4×Dic9—31no—
189C4×Dic9—31no—
190C22×C3×C9—21no—
191C22×C3×C9—21no—
192C22×C3×C9—21no—
193C22×C3×C9—21no—
194C22×C3×C9—21no—
195C22×C3×C9—21no—
196C22×C3×C9—21no—
197C22×C3×C9—44no—
198C22×C3×C9#4112yes—
199C22×C3×C9#4112yes—
200C22×C3×C9C2411yescharacteristic
201C2×C3×D9—21no—
202C2×C3×D9—21no—
203C2×C3×D9—21no—
204C3⋊Dic9—21no—
205C3⋊Dic9—21no—
206C3⋊Dic9—21no—
207C3⋊Dic9—21no—
208C9×Dic3—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C9×Dic3—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C3×#120—91no—
216C2×C3×C22⋊C4—31no—
217#953—31no—
218C2×#217—91no—
219C2×#217—91no—
220C2×#217—181no—
221C2×#217D911yescharacteristic, complemented
222#936—91no—
223#935—91no—
224#935—91no—
225#935—91no—
226D4×Dic3—91no—
227D4×Dic3—91no—
228#929—91no—
229C4×#67—91no—
230#926—91no—
231#924—91no—
232#886—91no—
233#885—91no—
234#883—91no—
235#67⋊C4—91no—
236#879—91no—
237#879—91no—
238#879—91no—
239#879—91no—
240#878—91no—
241#878—91no—
242#878—91no—
243#877—91no—
244#877—91no—
245#877—91no—
246C23×C32—22no—
247C23×C32—22no—
248C23×C32—41no—
249C23×C32C22×D311yescharacteristic
250C23×C32C22×D311yescharacteristic
251C23×C32C22×D311yescharacteristic
252C22×C3×D3—31no—
253C2×C3⋊Dic3—31no—
254C2×C3⋊Dic3—31no—
255C2×C3⋊Dic3—31no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—62no—
258C2×C3⋊Dic3—121no—
259C3×#67—62no—
260C3×#67—62no—
261C3×#67—121no—
262C2×C3×Dic3—22no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—31no—
265C2×C3×Dic3—31no—
266C2×C3×Dic3—41no—
267C2×C3×Dic3C22×D311yescharacteristic
268C2×C3×Dic3C22×D311yescharacteristic
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271#627—121no—
272D3×Dic3—121no—
273C23×C9—24no—
274C23×C9—22no—
275C23×C9—22no—
276C23×C9—21no—
277C23×C9—21no—
278C23×C9—21no—
279C23×C9—42no—
280C23×C9—41no—
281C23×C9—42no—
282C23×C9C22×D311yescharacteristic
283C23×C9C22×D311yescharacteristic
284C23×C9C22×D311yescharacteristic
285C22×D9C22×D311yescharacteristic
286C2×C4×C9—31no—
287C2×C4×C9—31no—
288C2×C4×C9—31no—
289C2×C4×C9—31no—
290C2×C4×C9—62no—
291C2×C4×C9—121no—
292#611—22no—
293#611—22no—
294#611—41no—
295C2×Dic9—31no—
296C2×Dic9—31no—
297C2×Dic9—31no—
298C2×Dic9—31no—
299C2×Dic9—61no—
300C2×Dic9—61no—
301C2×Dic9—61no—
302C2×Dic9—61no—
303C2×Dic9—62no—
304C2×Dic9—122no—
305C2×Dic9—121no—
306C2×Dic9—122no—
307C2×Dic9C22×D311yescharacteristic
308C2×Dic9C22×D311yescharacteristic
309C2×Dic9C22×D311yescharacteristic
310C4×D9—121no—
311Dic18—121no—
312#551—271noSylow
313C2×C3×C9—22no—
314C2×C3×C9—22no—
315C2×C3×C9—41no—
316C2×C3×C9C2×#4111yescharacteristic
317C2×C3×C9C2×#4111yescharacteristic
318C2×C3×C9H(5,𝔽2)11yescharacteristic
319C3×D9—41no—
320C24×C3—21no—
321C24×C3C2×D911yescharacteristic
322C24×C3D3211yescharacteristic
323C2×C3×D4—91no—
324C2×C3×D4—91no—
325C2×C3×D4—91no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C2×#67—31no—
329C2×#67—31no—
330C2×#67—31no—
331C22×Dic3—91no—
332C22×Dic3—91no—
333C22×Dic3—91no—
334C22×Dic3—91no—
335C22×Dic3—91no—
336C22×Dic3—181no—
337C22×Dic3—181no—
338C22×Dic3C2×D911yescharacteristic
339C22×Dic3C2×D911yescharacteristic
340C2×C4×D3—91no—
341C2×Dic6—91no—
342C2×Dic6—91no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—91no—
348C3×C22⋊C4—91no—
349C3×C22⋊C4—91no—
350#217—31no—
351#217—31no—
352#217—31no—
353#217—91no—
354#217—91no—
355#217—91no—
356#217—91no—
357#217—91no—
358#217—91no—
359#217—91no—
360#217—91no—
361#217—91no—
362#217—91no—
363#217—91no—
364#217—181no—
365#217—181no—
366#217—181no—
367#217—181no—
368#217C2×D911yescharacteristic
369#217C2×D911yescharacteristic
370#217C2×D911yescharacteristic
371#217C2×D911yescharacteristic
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375C4⋊Dic3—91no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—91no—
380Dic3⋊C4—91no—
381Dic3⋊C4—91no—
382Dic3⋊C4—91no—
383Dic3⋊C4—91no—
384Dic3⋊C4—91no—
385Dic3⋊C4—91no—
386Dic3⋊C4—91no—
387Dic3⋊C4—91no—
388Dic3⋊C4—91no—
389Dic3⋊C4—91no—
390Dic3⋊C4—91no—
391C4×Dic3—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—44no—
405C22×C32#23512yes—
406C22×C32#23712yes—
407C22×C32C23×D311yescharacteristic
408C2×C3×D3—61no—
409C2×C3×D3—61no—
410C2×C3×D3—61no—
411C3⋊Dic3—61no—
412C3⋊Dic3—61no—
413C3⋊Dic3—61no—
414C3⋊Dic3—61no—
415C3×Dic3—21no—
416C3×Dic3—21no—
417C3×Dic3—21no—
418C3×Dic3—21no—
419C3×Dic3—61no—
420C3×Dic3—61no—
421C3×Dic3—61no—
422C22×C9—22no—
423C22×C9—22no—
424C22×C9—21no—
425C22×C9—21no—
426C22×C9—21no—
427C22×C9—21no—
428C22×C9—22no—
429C22×C9—21no—
430C22×C9—21no—
431C22×C9—21no—
432C22×C9—21no—
433C22×C9—22no—
434C22×C9—22no—
435C22×C9—41no—
436C22×C9—41no—
437C22×C9—41no—
438C22×C9—41no—
439C22×C9—44no—
440C22×C9—48no—
441C22×C9#23712yes—
442C22×C9#23712yes—
443C22×C9C23×D311yescharacteristic
444C2×D9—21no—
445C2×D9—21no—
446C2×D9—21no—
447C4×C9—61no—
448C4×C9—61no—
449C4×C9—61no—
450C4×C9—61no—
451Dic9—21no—
452Dic9—21no—
453Dic9—21no—
454Dic9—61no—
455Dic9—61no—
456Dic9—61no—
457Dic9—61no—
458Dic9—121no—
459Dic9—121no—
460Dic9—121no—
461Dic9—121no—
462#126—271no—
463#126—271no—
464#124—271no—
465#123—271no—
466#123—271no—
467#123—271no—
468C22⋊Q8—271no—
469C22⋊Q8—271no—
470#120—91no—
471C4×D4—271no—
472C4×D4—271no—
473#117—271no—
474#117—271no—
475C2×C22⋊C4—31no—
476C2×C22⋊C4—271no—
477C3×C9#55111yescharacteristic, complemented, Sylow
478C23×C3—24no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—21no—
486C23×C3—42no—
487C23×C3—41no—
488C23×C3—41no—
489C23×C3—42no—
490C23×C3—91no—
491C23×C3C22×D911yescharacteristic
492C23×C3C22×D911yescharacteristic
493C23×C3C22×D911yescharacteristic
494C23×C3C2×D3211yescharacteristic
495C23×C3C2×D3211yescharacteristic
496C23×C3C2×D3211yescharacteristic
497C22×D3—31no—
498C3×D4—182no—
499C3×D4—182no—
500C3×D4—361no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—62no—
506C2×C3×C4—91no—
507C2×C3×C4—91no—
508C2×C3×C4—91no—
509C2×C3×C4—121no—
510#67—62no—
511#67—62no—
512#67—121no—
513C2×Dic3—22no—
514C2×Dic3—31no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—41no—
518C2×Dic3—91no—
519C2×Dic3—91no—
520C2×Dic3—91no—
521C2×Dic3—91no—
522C2×Dic3—91no—
523C2×Dic3—91no—
524C2×Dic3—91no—
525C2×Dic3—91no—
526C2×Dic3—181no—
527C2×Dic3—181no—
528C2×Dic3—181no—
529C2×Dic3—181no—
530C2×Dic3—182no—
531C2×Dic3—182no—
532C2×Dic3—362no—
533C2×Dic3—361no—
534C2×Dic3—361no—
535C2×Dic3—361no—
536C2×Dic3—362no—
537C2×Dic3C22×D911yescharacteristic
538C2×Dic3C22×D911yescharacteristic
539C2×Dic3C22×D911yescharacteristic
540C2×Dic3C22×D911yescharacteristic
541C4×D3—361no—
542Dic6—361no—
543Dic6—361no—
544C2×C32—22no—
545C2×C32—22no—
546C2×C32—41no—
547C2×C32C2×#23511yescharacteristic
548C2×C32C2×#23711yescharacteristic
549C2×C32#100411yescharacteristic
550C3×D3—121no—
551C2×C9—24no—
552C2×C9—22no—
553C2×C9—22no—
554C2×C9—21no—
555C2×C9—21no—
556C2×C9—21no—
557C2×C9—42no—
558C2×C9—42no—
559C2×C9—41no—
560C2×C9C2×#23711yescharacteristic
561C2×C9C2×#23711yescharacteristic
562C2×C9#100411yescharacteristic
563D9—41no—
564C24D3×D911yescharacteristic
565C2×Q8—271no—
566C2×D4—91no—
567C2×D4—91no—
568C2×D4—91no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—271no—
572C22×C4—271no—
573C22×C4—271no—
574C4⋊C4—271no—
575C4⋊C4—271no—
576C4⋊C4—271no—
577C4⋊C4—271no—
578C4⋊C4—271no—
579C4⋊C4—271no—
580C4⋊C4—271no—
581C4⋊C4—271no—
582C22⋊C4—31no—
583C22⋊C4—31no—
584C22⋊C4—31no—
585C22⋊C4—31no—
586C22⋊C4—91no—
587C22⋊C4—91no—
588C22⋊C4—91no—
589C22⋊C4—271no—
590C22⋊C4—271no—
591C22⋊C4—271no—
592C22⋊C4—271no—
593C22⋊C4—271no—
594C22⋊C4—271no—
595C22⋊C4—271no—
596C42—271no—
597C42—271no—
598C42—271no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—22no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—22no—
618C22×C3—22no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—44no—
624C22×C3—44no—
625C22×C3—48no—
626C22×C3—181no—
627C22×C3—181no—
628C22×C3—181no—
629C22×C3#369712yes—
630C22×C3#369912yes—
631C22×C3C23×D911yescharacteristic
632C22×C3#380412yes—
633C22×C3#380512yes—
634C22×C3C22×D3211yescharacteristic
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C3×C4—61no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—181no—
643C3×C4—181no—
644C3×C4—181no—
645Dic3—21no—
646Dic3—21no—
647Dic3—21no—
648Dic3—21no—
649Dic3—61no—
650Dic3—61no—
651Dic3—61no—
652Dic3—181no—
653Dic3—181no—
654Dic3—181no—
655Dic3—181no—
656Dic3—181no—
657Dic3—181no—
658Dic3—181no—
659Dic3—181no—
660Dic3—361no—
661Dic3—361no—
662Dic3—361no—
663Dic3—361no—
664C32#549511yescharacteristic
665C9—21no—
666C9#558711yescharacteristic, complemented
667C23—22no—
668C23—22no—
669C23—41no—
670C23—91no—
671C23C2×D3×D911yescharacteristic
672C23C2×D3×D911yescharacteristic
673C23C2×D3×D911yescharacteristic
674Q8—1081no—
675D4—182no—
676D4—182no—
677D4—361no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—62no—
683C2×C4—91no—
684C2×C4—91no—
685C2×C4—91no—
686C2×C4—121no—
687C2×C4—271no—
688C2×C4—271no—
689C2×C4—271no—
690C2×C4—271no—
691C2×C4—542no—
692C2×C4—1081no—
693C2×C4—1081no—
694C2×C3—24no—
695C2×C3—22no—
696C2×C3—22no—
697C2×C3—22no—
698C2×C3—22no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—42no—
703C2×C3—42no—
704C2×C3—41no—
705C2×C3—41no—
706C2×C3—361no—
707C2×C3C2×#369711yescharacteristic
708C2×C3C2×#369911yescharacteristic
709C2×C3#6371011yescharacteristic
710C2×C3C2×#380411yescharacteristic
711C2×C3C2×#380511yescharacteristic
712C2×C3#6433011yescharacteristic
713D3—121no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—44no—
722C22—181no—
723C22—181no—
724C22—181no—
725C22#8865812yes—
726C22#8866312yes—
727C22C22×D3×D911yescharacteristic
728C4—61no—
729C4—61no—
730C4—61no—
731C4—61no—
732C4—181no—
733C4—181no—
734C4—181no—
735C4—541no—
736C4—541no—
737C4—541no—
738C4—541no—
739C3—21no—
740C3#1058959711yescharacteristic, complemented
741C3#1059550911yescharacteristic
742C2—22no—
743C2—22no—
744C2—41no—
745C2—361no—
746C2C2×#8865811yescharacteristic
747C2C2×#8866311yescharacteristic
748C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC24×C3×C9C22
socleC22×C32C23×D3
prime radicalC3×#63515C2
hypercenterC24D3×D9
hypocenterC3×C9#551
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C2×#88551C2semidirect
3. C2×C9×#217C2semidirect
4. #611⋊Dic3C2semidirect
5. Dic3×#611C2semidirect
6. #11721269C2semidirect
7. #11721267C2semidirect
8. #11721260C2semidirect
9. #11721259C2semidirect
10. #11721257C2semidirect
11. #11721249C2semidirect
12. #11721248C2semidirect
13. #11721247C2semidirect
14. #11721246C2semidirect
15. #11721244C2semidirect
26. C2×Dic3×D9C22semidirect
27. C2×#6189C22semidirect
39. (C2×D9)⋊Dic3C22semidirect
40. (C2×D9)⋊Dic3C22semidirect
41. (C2×D9)⋊Dic3C22semidirect
42. Dic3⋊Dic9C22semidirect
43. Dic3⋊Dic9C22semidirect
44. Dic3⋊Dic9C22semidirect
45. #88442C22semidirect
46. #88442C22semidirect
47. #88442C22semidirect
48. Dic9⋊Dic3C22semidirect
49. Dic9⋊Dic3C22semidirect
50. Dic3×Dic9C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
221. C2×#217D9semidirect
477. C3×C9#551semidirect
666. C9#5587semidirect
740. C3#10589597semidirect

Maximal subgroups

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

subgroupindex
C2×#885512
C3×#635152
C2×C9×#2172
#611⋊Dic32
Dic3×#6112
#117212692
#117212672
#117212602
#117212592
#117212572
#117212492
#117212482
#117212472
#117212462
#117212442
#105955093
#105895973