Finite Group Databasebeta

← #13152003

Subgroups — #13152003

Order 1728.

874 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721874C211yesmaximal, characteristic
2C2×C9×#217C211yesmaximal, characteristic, complemented
3C2×C3×#3676C211yesmaximal, characteristic, complemented
4#11721275C211yesmaximal, characteristic, complemented
5#11721255C211yesmaximal, characteristic, complemented
6#11721253C211yesmaximal, characteristic, complemented
7#11721251C211yesmaximal, characteristic, complemented
8#11721249C211yesmaximal, characteristic, complemented
9#11721247C211yesmaximal, characteristic, complemented
10#11721246C211yesmaximal, characteristic, complemented
11#11721245C211yesmaximal, characteristic, complemented
12#11721244C211yesmaximal, characteristic, complemented
13#11721242C211yesmaximal, characteristic, complemented
14#11721241C211yesmaximal, characteristic, complemented
15#11721240C211yesmaximal, characteristic, complemented
16#10595476—31nomaximal
17#10589597—31nomaximal
18C24×C3×C9C2211yescharacteristic
19C2×#6233C2211yescharacteristic
20C2×#6233C2211yescharacteristic
21C2×#6233C2211yescharacteristic
22C22×C9×Dic3C2211yescharacteristic
23C22×C9×Dic3C2211yescharacteristic
24C22×C3×Dic9C2211yescharacteristic
25C22×C3×Dic9C2211yescharacteristic
26C2×(C3⋊D9)⋊C4C2211yescharacteristic, complemented
27C2×#6189C2211yescharacteristic, complemented
28#88551C2211yescharacteristic
29#88551C2211yescharacteristic
30#88551C2211yescharacteristic
31C9×#217C2211yescharacteristic
32C9×#217C2211yescharacteristic
33C9×#217C2211yescharacteristic
34C9×#217C2211yescharacteristic
35C3×#3676C2211yescharacteristic
36C3×#3676C2211yescharacteristic
37C3×#3676C2211yescharacteristic
38C3×#3676C2211yescharacteristic
39#88445C2211yescharacteristic, complemented
40#88445C2211yescharacteristic, complemented
41#88445C2211yescharacteristic, complemented
42Dic3⋊Dic9C2211yescharacteristic, complemented
43Dic3⋊Dic9C2211yescharacteristic, complemented
44Dic3⋊Dic9C2211yescharacteristic, complemented
45#88442C2211yescharacteristic, complemented
46#88442C2211yescharacteristic, complemented
47Dic9⋊Dic3C2211yescharacteristic, complemented
48Dic9⋊Dic3C2211yescharacteristic, complemented
49Dic9⋊Dic3C2211yescharacteristic, complemented
50Dic3×Dic9C2211yescharacteristic, complemented
51Dic3×Dic9C2211yescharacteristic, complemented
52Dic3×Dic9C2211yescharacteristic, complemented
53#64162—31no—
54C2×C3×#217—31no—
55C2×C3×#217D311yescharacteristic
56#63975—31no—
57#63966—31no—
58#63966—31no—
59#63964—31no—
60#63964—31no—
61#63956—31no—
62#63956—31no—
63#63955—31no—
64#63955—31no—
65#63953—31no—
66#63952—31no—
67#63952—31no—
68C2×C9×C22⋊C4—31no—
69#63515—31no—
70#63515—61no—
71C2×#3676D311yescharacteristic, complemented
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
91#6233—22no—
92#6233—22no—
93#6233—41no—
94C2×C3⋊Dic9C2311yescharacteristic
95C2×C3⋊Dic9C2311yescharacteristic
96C2×C3⋊Dic9C2311yescharacteristic
97C2×C9×Dic3—22no—
98C2×C9×Dic3—41no—
99C2×C9×Dic3C2311yescharacteristic
100C2×C9×Dic3C2311yescharacteristic
101C2×C9×Dic3C2311yescharacteristic
102C2×C9×Dic3C2311yescharacteristic
103C2×C3×Dic9—22no—
104C2×C3×Dic9—41no—
105C2×C3×Dic9C2311yescharacteristic
106C2×C3×Dic9C2311yescharacteristic
107C2×C3×Dic9C2311yescharacteristic
108C2×C3×Dic9C2311yescharacteristic
109(C3⋊D9)⋊C4—41no—
110#6189—41no—
111#5495—91no—
112#5495—91no—
113C24×C32C2×D311yescharacteristic
114C2×#638—31no—
115C2×#638—31no—
116C2×#638—31no—
117C22×C3×Dic3—31no—
118C22×C3×Dic3—31no—
119C22×C3×Dic3C2×D311yescharacteristic
120C22×C3×Dic3C2×D311yescharacteristic
121C2×#627—31no—
122C2×#624—31no—
123C24×C9—21no—
124C24×C9C2×D311yescharacteristic
125#3757—31no—
126#3757—31no—
127#3757—31no—
128C3×#217—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—
138Dic3⋊Dic3—31no—
139Dic3⋊Dic3—31no—
140Dic3⋊Dic3—31no—
141Dic3⋊Dic3—31no—
142Dic3⋊Dic3—31no—
143Dic3⋊Dic3—31no—
144#3722—31no—
145#3722—31no—
146#3722—31no—
147Dic32—31no—
148Dic32—31no—
149Dic32—31no—
150C22×C4×C9—31no—
151C22×C4×C9—31no—
152C2×#611—31no—
153C2×#611—31no—
154C2×#611—31no—
155C2×#611—61no—
156C2×#611—61no—
157C2×#611—61no—
158C22×Dic9C2×D311yescharacteristic
159C22×Dic9C2×D311yescharacteristic
160C2×C4×D9—31no—
161C2×Dic18—31no—
162C9×C22⋊C4—31no—
163C9×C22⋊C4—31no—
164C9×C22⋊C4—31no—
165C9×C22⋊C4—31no—
166#3676—31no—
167#3676—31no—
168#3676—31no—
169#3676—61no—
170#3676—61no—
171#3676—61no—
172#3676C2×D311yescharacteristic
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—
207C9×Dic3—21no—
208C9×Dic3—21no—
209C9×Dic3—21no—
210C9×Dic3—21no—
211C3×Dic9—21no—
212C3×Dic9—21no—
213C3×Dic9—21no—
214C3×Dic9—21no—
215C2×C3×C22⋊C4—31no—
216C2×C3×C22⋊C4—91no—
217#953—91no—
218#953—91no—
219#953—181no—
220C2×#217—31no—
221C2×#217D911yescharacteristic, complemented
222#929—91no—
223#929—91no—
224C4×#67—91no—
225C4×#67—91no—
226#926—91no—
227#926—91no—
228#924—91no—
229#924—91no—
230#886—91no—
231#886—91no—
232#885—91no—
233#885—91no—
234#883—91no—
235#883—91no—
236#67⋊C4—91no—
237#67⋊C4—91no—
238#879—91no—
239#879—91no—
240#879—91no—
241#879—91no—
242#878—91no—
243#878—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—
253#638—62no—
254#638—62no—
255#638—121no—
256C2×C3⋊Dic3—31no—
257C2×C3⋊Dic3—31no—
258C2×C3⋊Dic3—31no—
259C2×C3×Dic3—22no—
260C2×C3×Dic3—31no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—31no—
264C2×C3×Dic3—41no—
265C2×C3×Dic3—62no—
266C2×C3×Dic3—121no—
267C2×C3×Dic3C22×D311yescharacteristic
268C2×C3×Dic3C22×D311yescharacteristic
269C2×C3×Dic3C22×D311yescharacteristic
270C2×C3×Dic3C22×D311yescharacteristic
271#627—121no—
272#624—121no—
273C23×C9—22no—
274C23×C9—22no—
275C23×C9—21no—
276C23×C9—21no—
277C23×C9—21no—
278C23×C9—42no—
279C23×C9—42no—
280C23×C9—41no—
281C23×C9—42no—
282C23×C9C22×D311yescharacteristic
283C23×C9C22×D311yescharacteristic
284C23×C9C22×D311yescharacteristic
285C22×D9—31no—
286C22×D9—61no—
287C2×C4×C9—31no—
288C2×C4×C9—31no—
289C2×C4×C9—31no—
290C2×C4×C9—31no—
291C2×C4×C9—62no—
292C2×C4×C9—121no—
293#611—62no—
294#611—62no—
295#611—122no—
296#611—122no—
297#611—121no—
298#611—122no—
299C2×Dic9—22no—
300C2×Dic9—31no—
301C2×Dic9—31no—
302C2×Dic9—31no—
303C2×Dic9—41no—
304C2×Dic9—61no—
305C2×Dic9—61no—
306C2×Dic9—61no—
307C2×Dic9C22×D311yescharacteristic
308C2×Dic9C22×D311yescharacteristic
309C2×Dic9C22×D311yescharacteristic
310C2×Dic9C22×D311yescharacteristic
311C4×D9—121no—
312Dic18—121no—
313#551—271noSylow
314C2×C3×C9—22no—
315C2×C3×C9—22no—
316C2×C3×C9—41no—
317C2×C3×C9C2×#4111yescharacteristic
318C2×C3×C9C2×#4111yescharacteristic
319C2×C3×C9H(5,𝔽2)11yescharacteristic
320C3⋊D9—41no—
321C24×C3—21no—
322C24×C3C2×D911yescharacteristic
323C24×C3D3211yescharacteristic
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—91no—
327C22×C3×C4—91no—
328C2×#67—91no—
329C2×#67—91no—
330C2×#67—91no—
331C2×#67—91no—
332C2×#67—91no—
333C2×#67—91no—
334C2×#67—181no—
335C2×#67—181no—
336C2×#67—181no—
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3C2×D911yescharacteristic
340C22×Dic3C2×D911yescharacteristic
341C2×C4×D3—91no—
342C2×C4×D3—91no—
343C2×Dic6—91no—
344C2×Dic6—91no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—91no—
350C3×C22⋊C4—91no—
351C3×C22⋊C4—91no—
352C3×C22⋊C4—91no—
353#217—31no—
354#217—31no—
355#217—31no—
356#217—31no—
357#217—91no—
358#217—91no—
359#217—91no—
360#217—91no—
361#217—91no—
362#217—91no—
363#217—181no—
364#217—181no—
365#217—181no—
366#217C2×D911yescharacteristic
367#217C2×D911yescharacteristic
368#217C2×D911yescharacteristic
369#217C2×D911yescharacteristic
370(C2×D3)⋊C4—91no—
371(C2×D3)⋊C4—91no—
372(C2×D3)⋊C4—91no—
373(C2×D3)⋊C4—91no—
374(C2×D3)⋊C4—91no—
375(C2×D3)⋊C4—91no—
376C4⋊Dic3—91no—
377C4⋊Dic3—91no—
378C4⋊Dic3—91no—
379C4⋊Dic3—91no—
380C4⋊Dic3—91no—
381C4⋊Dic3—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—
391Dic3⋊C4—91no—
392C4×Dic3—91no—
393C4×Dic3—91no—
394C4×Dic3—91no—
395C4×Dic3—91no—
396C4×Dic3—91no—
397C4×Dic3—91no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32—21no—
401C22×C32—21no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—44no—
406C22×C32#23512yes—
407C22×C32#23712yes—
408C22×C32C23×D311yescharacteristic
409C2×C3⋊D3—61no—
410C2×C3⋊D3—61no—
411C2×C3⋊D3—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—
422C3×Dic3—61no—
423C22×C9—21no—
424C22×C9—21no—
425C22×C9—21no—
426C22×C9—21no—
427C22×C9—22no—
428C22×C9—21no—
429C22×C9—21no—
430C22×C9—21no—
431C22×C9—21no—
432C22×C9—22no—
433C22×C9—22no—
434C22×C9—41no—
435C22×C9—41no—
436C22×C9—41no—
437C22×C9—41no—
438C22×C9—41no—
439C22×C9—41no—
440C22×C9—44no—
441C22×C9—48no—
442C22×C9#23512yes—
443C22×C9#23712yes—
444C22×C9C23×D311yescharacteristic
445C2×D9—61no—
446C2×D9—61no—
447C2×D9—61no—
448C2×D9—121no—
449C2×D9—121no—
450C2×D9—121no—
451C4×C9—61no—
452C4×C9—61no—
453C4×C9—61no—
454C4×C9—61no—
455Dic9—21no—
456Dic9—21no—
457Dic9—21no—
458Dic9—21no—
459Dic9—61no—
460Dic9—61no—
461Dic9—61no—
462Dic9—121no—
463Dic9—121no—
464Dic9—121no—
465#126—271no—
466#126—271no—
467#124—271no—
468#123—271no—
469#123—271no—
470#123—271no—
471C22⋊Q8—271no—
472C22⋊Q8—271no—
473#120—271no—
474C4×D4—271no—
475C4×D4—271no—
476#117—271no—
477#117—271no—
478C2×C22⋊C4—31no—
479C2×C22⋊C4—91no—
480C3×C9#55111yescharacteristic, complemented, Sylow
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—21no—
486C23×C3—21no—
487C23×C3—21no—
488C23×C3—42no—
489C23×C3—42no—
490C23×C3—41no—
491C23×C3—41no—
492C23×C3—42no—
493C23×C3C22×D911yescharacteristic
494C23×C3C22×D911yescharacteristic
495C23×C3C22×D911yescharacteristic
496C23×C3C2×D3211yescharacteristic
497C23×C3C2×D3211yescharacteristic
498C23×C3C2×D3211yescharacteristic
499C22×D3—91no—
500C22×D3—91no—
501C22×D3—181no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—62no—
507C2×C3×C4—91no—
508C2×C3×C4—91no—
509C2×C3×C4—91no—
510C2×C3×C4—91no—
511C2×C3×C4—121no—
512C2×C3×C4—182no—
513C2×C3×C4—361no—
514#67—182no—
515#67—182no—
516#67—182no—
517#67—182no—
518#67—362no—
519#67—362no—
520#67—361no—
521#67—361no—
522#67—362no—
523C2×Dic3—22no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—41no—
529C2×Dic3—62no—
530C2×Dic3—91no—
531C2×Dic3—91no—
532C2×Dic3—91no—
533C2×Dic3—91no—
534C2×Dic3—91no—
535C2×Dic3—91no—
536C2×Dic3—121no—
537C2×Dic3—181no—
538C2×Dic3—181no—
539C2×Dic3—181no—
540C2×Dic3C22×D911yescharacteristic
541C2×Dic3C22×D911yescharacteristic
542C2×Dic3C22×D911yescharacteristic
543C2×Dic3C22×D911yescharacteristic
544C4×D3—361no—
545C4×D3—361no—
546Dic6—361no—
547Dic6—361no—
548C2×C32—22no—
549C2×C32—22no—
550C2×C32—41no—
551C2×C32C2×#23511yescharacteristic
552C2×C32C2×#23711yescharacteristic
553C2×C32#100411yescharacteristic
554C3⋊D3—121no—
555C2×C9—22no—
556C2×C9—22no—
557C2×C9—21no—
558C2×C9—21no—
559C2×C9—21no—
560C2×C9—42no—
561C2×C9—42no—
562C2×C9—42no—
563C2×C9—41no—
564C2×C9C2×#23511yescharacteristic
565C2×C9C2×#23711yescharacteristic
566C2×C9#100411yescharacteristic
567D9—121no—
568D9—241no—
569C24D3×D911yescharacteristic
570C2×Q8—271no—
571C2×D4—271no—
572C2×D4—271no—
573C2×D4—271no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—271no—
579C4⋊C4—271no—
580C4⋊C4—271no—
581C4⋊C4—271no—
582C4⋊C4—271no—
583C4⋊C4—271no—
584C4⋊C4—271no—
585C4⋊C4—271no—
586C4⋊C4—271no—
587C22⋊C4—31no—
588C22⋊C4—31no—
589C22⋊C4—31no—
590C22⋊C4—31no—
591C22⋊C4—91no—
592C22⋊C4—91no—
593C22⋊C4—91no—
594C22⋊C4—91no—
595C22⋊C4—271no—
596C22⋊C4—271no—
597C22⋊C4—271no—
598C22⋊C4—271no—
599C22⋊C4—271no—
600C22⋊C4—271no—
601C42—271no—
602C42—271no—
603C42—271no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—22no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—22no—
621C22×C3—22no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—44no—
629C22×C3—44no—
630C22×C3—48no—
631C22×C3#369712yes—
632C22×C3#369912yes—
633C22×C3C23×D911yescharacteristic
634C22×C3#380412yes—
635C22×C3#380412yes—
636C22×C3C22×D3211yescharacteristic
637C2×D3—181no—
638C2×D3—181no—
639C2×D3—181no—
640C2×D3—181no—
641C2×D3—181no—
642C2×D3—181no—
643C2×D3—361no—
644C2×D3—361no—
645C2×D3—361no—
646C3×C4—61no—
647C3×C4—61no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—181no—
651C3×C4—181no—
652C3×C4—181no—
653C3×C4—181no—
654Dic3—21no—
655Dic3—21no—
656Dic3—21no—
657Dic3—21no—
658Dic3—61no—
659Dic3—61no—
660Dic3—61no—
661Dic3—61no—
662Dic3—181no—
663Dic3—181no—
664Dic3—181no—
665Dic3—181no—
666Dic3—181no—
667Dic3—181no—
668Dic3—361no—
669Dic3—361no—
670Dic3—361no—
671C32#549511yescharacteristic
672C9—21no—
673C9#549511yescharacteristic, complemented
674C23—22no—
675C23—22no—
676C23—41no—
677C23—271no—
678C23C2×D3×D911yescharacteristic
679C23C2×D3×D911yescharacteristic
680C23C2×D3×D911yescharacteristic
681Q8—1081no—
682D4—542no—
683D4—542no—
684D4—1081no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—31no—
688C2×C4—31no—
689C2×C4—62no—
690C2×C4—91no—
691C2×C4—91no—
692C2×C4—91no—
693C2×C4—91no—
694C2×C4—121no—
695C2×C4—182no—
696C2×C4—271no—
697C2×C4—271no—
698C2×C4—271no—
699C2×C4—361no—
700C2×C4—1081no—
701C2×C3—22no—
702C2×C3—22no—
703C2×C3—22no—
704C2×C3—22no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—42no—
709C2×C3—42no—
710C2×C3—42no—
711C2×C3—41no—
712C2×C3—41no—
713C2×C3C2×#369711yescharacteristic
714C2×C3C2×#369911yescharacteristic
715C2×C3#6371011yescharacteristic
716C2×C3C2×#380411yescharacteristic
717C2×C3C2×#380411yescharacteristic
718C2×C3#6433011yescharacteristic
719D3—361no—
720D3—361no—
721D3—721no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—44no—
730C22—541no—
731C22—541no—
732C22—541no—
733C22#8865812yes—
734C22#8866212yes—
735C22C22×D3×D911yescharacteristic
736C4—61no—
737C4—61no—
738C4—61no—
739C4—61no—
740C4—181no—
741C4—181no—
742C4—181no—
743C4—181no—
744C4—541no—
745C4—541no—
746C4—541no—
747C3—21no—
748C3#1058959711yescharacteristic, complemented
749C3#1059547611yescharacteristic
750C2—22no—
751C2—22no—
752C2—41no—
753C2—1081no—
754C2C2×#8865811yescharacteristic
755C2C2×#8866211yescharacteristic
756C2#1172253511yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC24×C3×C9C22
socleC22×C32C23×D3
prime radical#11721874C2
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
2. C2×C9×#217C2semidirect
3. C2×C3×#3676C2semidirect
4. #11721275C2semidirect
5. #11721255C2semidirect
6. #11721253C2semidirect
7. #11721251C2semidirect
8. #11721249C2semidirect
9. #11721247C2semidirect
10. #11721246C2semidirect
11. #11721245C2semidirect
12. #11721244C2semidirect
13. #11721242C2semidirect
14. #11721241C2semidirect
15. #11721240C2semidirect
26. C2×(C3⋊D9)⋊C4C22semidirect
27. C2×#6189C22semidirect
39. #88445C22semidirect
40. #88445C22semidirect
41. #88445C22semidirect
42. Dic3⋊Dic9C22semidirect
43. Dic3⋊Dic9C22semidirect
44. Dic3⋊Dic9C22semidirect
45. #88442C22semidirect
46. #88442C22semidirect
47. Dic9⋊Dic3C22semidirect
48. Dic9⋊Dic3C22semidirect
49. Dic9⋊Dic3C22semidirect
50. Dic3×Dic9C22semidirect
51. Dic3×Dic9C22semidirect
52. Dic3×Dic9C22semidirect
71. C2×#3676D3semidirect
221. C2×#217D9semidirect
480. C3×C9#551semidirect
673. C9#5495semidirect
748. C3#10589597semidirect

Maximal subgroups

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

subgroupindex
#117218742
C2×C9×#2172
C2×C3×#36762
#117212752
#117212552
#117212532
#117212512
#117212492
#117212472
#117212462
#117212452
#117212442
#117212422
#117212412
#117212402
#105954763
#105895973