Finite Group Databasebeta

← #11810286

Subgroups — #11810286

Order 1152.

1200 conjugacy classes of subgroups.

The subgroup lattice has 753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#123C211yesmaximal, characteristic, complemented
2C2×#63499C211yesmaximal, characteristic
3C2×C4×#611C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D9C211yesmaximal, characteristic, complemented
5#10588902C211yesmaximal, characteristic, complemented
6#10588893C211yesmaximal, characteristic, complemented
7#10588673C211yesmaximal, characteristic, complemented
8#10588670C211yesmaximal, characteristic, complemented
9#10588669C211yesmaximal, characteristic, complemented
10#10588667C211yesmaximal, characteristic, complemented
11#10588641C211yesmaximal, characteristic, complemented
12#10588636C211yesmaximal, characteristic, complemented
13#10588635C211yesmaximal, characteristic, complemented
14#10588632C211yesmaximal, characteristic, complemented
15#10588631C211yesmaximal, characteristic, complemented
16#82896—31nomaximal
17C24×D9C2211yescharacteristic
18C22×D4×C9C2211yescharacteristic
19C23×C4×C9C2211yescharacteristic, complemented
20C22×#611C2211yescharacteristic
21C22×#611C2211yescharacteristic
22C22×C4×D9C2211yescharacteristic
23C22×C4×D9C2211yescharacteristic
24C9×#123—24no—
25C2×C9×C4⋊C4C2211yescharacteristic, complemented
26C2×C9×C4⋊C4C2211yescharacteristic, complemented
27C2×C9×C22⋊C4C2211yescharacteristic
28C2×C9×C22⋊C4C2211yescharacteristic
29C2×C9×C22⋊C4C2211yescharacteristic, complemented
30C2×#3676C2211yescharacteristic
31C2×#3676C2211yescharacteristic
32C2×#3676C2211yescharacteristic
33C2×#3676C2211yescharacteristic, complemented
34C2×#3676C2211yescharacteristic, complemented
35#63499—24no—
36C4×#611—24no—
37C2×(C2×D9)⋊C4C2211yescharacteristic
38C2×(C2×D9)⋊C4C2211yescharacteristic
39C2×(C2×D9)⋊C4C2211yescharacteristic
40C2×(C2×D9)⋊C4C2211yescharacteristic
41C2×(C2×D9)⋊C4C2211yescharacteristic
42C2×(C2×D9)⋊C4C2211yescharacteristic
43C2×(C2×D9)⋊C4C2211yescharacteristic
44C2×(C2×D9)⋊C4C2211yescharacteristic
45C2×C4⋊Dic9C2211yescharacteristic, complemented
46C2×Dic9⋊C4C2211yescharacteristic, complemented
47C2×Dic9⋊C4C2211yescharacteristic, complemented
48C2×C4×Dic9C2211yescharacteristic, complemented
49C22⋊C4×D9—24no—
50C9⋊#95C2211yescharacteristic, complemented
51C9⋊#95C2211yescharacteristic, complemented
52C9⋊#95C2211yescharacteristic, complemented
53C9⋊#95C2211yescharacteristic, complemented
54C9⋊#95C2211yescharacteristic, complemented
55C9⋊#95C2211yescharacteristic, complemented
56C2×C3×#123D311yescharacteristic
57C2×#937—31no—
58C2×C4×#67—31no—
59C2×D3×C22⋊C4—31no—
60#5222—31no—
61#5213—31no—
62#4993—31no—
63#4990—31no—
64#4989—31no—
65#4987—31no—
66#4961—31no—
67#4956—31no—
68#4955—31no—
69#4952—31no—
70#4951—31no—
71C24×C9C2311yescharacteristic
72C24×C9C2311yescharacteristic
73C23×D9—22no—
74C23×D9—22no—
75C23×D9—22no—
76C23×D9—22no—
77C23×D9—22no—
78C23×D9—41no—
79C23×D9—41no—
80C23×D9C2311yescharacteristic
81C23×D9C2311yescharacteristic
82C2×D4×C9—22no—
83C2×D4×C9—22no—
84C2×D4×C9—41no—
85C22×C4×C9—22no—
86C22×C4×C9—22no—
87C22×C4×C9—41no—
88C22×C4×C9C2311yescharacteristic
89C22×C4×C9C2311yescharacteristic
90C22×C4×C9C2311yescharacteristic
91C22×C4×C9C2311yescharacteristic
92C22×C4×C9C2311yescharacteristic
93C2×#611—22no—
94C2×#611—22no—
95C2×#611—22no—
96C2×#611—22no—
97C2×#611—41no—
98C2×#611D414yes—
99C22×Dic9C2311yescharacteristic
100C22×Dic9C2311yescharacteristic
101C22×Dic9C2311yescharacteristic
102C22×Dic9C2311yescharacteristic
103C22×Dic9C2311yescharacteristic
104C22×Dic9C2311yescharacteristic
105C2×C4×D9—22no—
106C2×C4×D9—22no—
107C2×C4×D9—22no—
108C2×C4×D9—22no—
109C2×C4×D9—41no—
110C2×C4×D9—41no—
111C9×C4⋊C4—22no—
112C9×C4⋊C4—22no—
113C9×C22⋊C4—22no—
114C9×C22⋊C4—22no—
115C9×C22⋊C4D414yescomplemented
116#3676—22no—
117#3676—22no—
118#3676—22no—
119#3676—41no—
120#3676—41no—
121(C2×D9)⋊C4—22no—
122(C2×D9)⋊C4—22no—
123(C2×D9)⋊C4—22no—
124(C2×D9)⋊C4—22no—
125(C2×D9)⋊C4—22no—
126(C2×D9)⋊C4—22no—
127(C2×D9)⋊C4—22no—
128(C2×D9)⋊C4—41no—
129C4⋊Dic9—41no—
130Dic9⋊C4—22no—
131Dic9⋊C4—41no—
132C4×Dic9—22no—
133#2418—91noSylow
134C24×D3—31no—
135C22×C3×D4C2×D311yescharacteristic
136C23×C3×C4C2×D311yescharacteristic
137C22×#67—31no—
138C22×#67—31no—
139C22×C4×D3—31no—
140C22×C4×D3—31no—
141C3×#123—24no—
142C2×C3×C4⋊C4C2×D311yescharacteristic
143C2×C3×C4⋊C4C2×D311yescharacteristic
144C2×C3×C22⋊C4C2×D311yescharacteristic
145C2×C3×C22⋊C4C2×D311yescharacteristic
146C2×C3×C22⋊C4C2×D311yescharacteristic
147C2×#217—31no—
148C2×#217—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152#937—64no—
153C4×#67—64no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—31no—
160C2×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×C4⋊Dic3—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×C4×Dic3—31no—
166D3×C22⋊C4—64no—
167C3⋊#95—31no—
168C3⋊#95—31no—
169C3⋊#95—31no—
170C3⋊#95—31no—
171C3⋊#95—31no—
172C3⋊#95—31no—
173C23×C9—21no—
174C23×C9—21no—
175C23×C9—21no—
176C23×C9—21no—
177C23×C9—21no—
178C23×C9—21no—
179C23×C9—21no—
180C23×C9—21no—
181C23×C9—21no—
182C23×C9—21no—
183C23×C9—21no—
184C23×C9—21no—
185C23×C9C2×D412yes—
186C23×C9C2×D412yes—
187C23×C9C2411yescharacteristic
188C22×D9—21no—
189C22×D9—21no—
190C22×D9—21no—
191C22×D9—21no—
192C22×D9—28no—
193C22×D9—21no—
194C22×D9—21no—
195C22×D9—21no—
196C22×D9—21no—
197C22×D9—21no—
198C22×D9—21no—
199C22×D9—44no—
200C22×D9—44no—
201C22×D9—44no—
202C22×D9—44no—
203C22×D9—44no—
204C22×D9—44no—
205C22×D9C2×D412yes—
206C22×D9#4112yes—
207C22×D9#4112yes—
208C22×D9#4112yes—
209D4×C9—44no—
210C2×C4×C9—21no—
211C2×C4×C9—21no—
212C2×C4×C9—21no—
213C2×C4×C9—21no—
214C2×C4×C9—21no—
215C2×C4×C9—21no—
216C2×C4×C9—21no—
217C2×C4×C9—21no—
218C2×C4×C9—21no—
219C2×C4×C9—21no—
220C2×C4×C9—21no—
221C2×C4×C9—21no—
222C2×C4×C9—21no—
223C2×C4×C9—44no—
224C2×C4×C9C2×D412yes—
225C2×C4×C9C2×D412yes—
226#611—28no—
227#611—44no—
228C2×Dic9—21no—
229C2×Dic9—21no—
230C2×Dic9—21no—
231C2×Dic9—21no—
232C2×Dic9—21no—
233C2×Dic9—21no—
234C2×Dic9—21no—
235C2×Dic9—21no—
236C2×Dic9—21no—
237C2×Dic9—21no—
238C2×Dic9—21no—
239C2×Dic9—21no—
240C2×Dic9—21no—
241C2×Dic9—21no—
242C2×Dic9—21no—
243C2×Dic9—21no—
244C2×Dic9—21no—
245C2×Dic9C2×D412yes—
246C4×D9—44no—
247C4×D9—44no—
248C2×#123D911yescharacteristic, complemented
249C2×#120—91no—
250C2×C4×D4—91no—
251C22×C22⋊C4—91no—
252#399—91no—
253#397—91no—
254#394—91no—
255#394—91no—
256#388—91no—
257#388—91no—
258#386—91no—
259#386—91no—
260#385—91no—
261#380—91no—
262#379—91no—
263C24×C3C22×D311yescharacteristic
264C24×C3C22×D311yescharacteristic
265C23×D3—31no—
266C23×D3—31no—
267C23×D3—62no—
268C23×D3—62no—
269C23×D3—62no—
270C23×D3—62no—
271C23×D3—62no—
272C23×D3—121no—
273C23×D3—121no—
274C2×C3×D4—22no—
275C2×C3×D4—22no—
276C2×C3×D4—41no—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—41no—
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C2×#67—34no—
286C2×#67—62no—
287C2×#67—62no—
288C2×#67—62no—
289C2×#67—62no—
290C2×#67—121no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C2×C4×D3—62no—
298C2×C4×D3—62no—
299C2×C4×D3—62no—
300C2×C4×D3—62no—
301C2×C4×D3—121no—
302C2×C4×D3—121no—
303C3×C4⋊C4—22no—
304C3×C4⋊C4—22no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4#6714yes—
308#217—62no—
309#217—62no—
310#217—62no—
311#217—121no—
312#217—121no—
313(C2×D3)⋊C4—62no—
314(C2×D3)⋊C4—62no—
315(C2×D3)⋊C4—62no—
316(C2×D3)⋊C4—62no—
317(C2×D3)⋊C4—62no—
318(C2×D3)⋊C4—62no—
319(C2×D3)⋊C4—62no—
320(C2×D3)⋊C4—121no—
321C4⋊Dic3—121no—
322Dic3⋊C4—62no—
323Dic3⋊C4—121no—
324C4×Dic3—62no—
325C22×C9—22no—
326C22×C9—22no—
327C22×C9—22no—
328C22×C9—22no—
329C22×C9—22no—
330C22×C9—22no—
331C22×C9—41no—
332C22×C9—41no—
333C22×C9—41no—
334C22×C9—41no—
335C22×C9—41no—
336C22×C9—41no—
337C22×C9—41no—
338C22×C9—41no—
339C22×C9C22×D411yescharacteristic
340C22×C9C22×D411yescharacteristic
341C22×C9C2×#4111yescharacteristic
342C22×C9C2×#4111yescharacteristic
343C22×C9C2×#4111yescharacteristic
344C22×C9H(5,𝔽2)11yescharacteristic
345C22×C9H(5,𝔽2)11yescharacteristic
346C2×D9—22no—
347C2×D9—22no—
348C2×D9—22no—
349C2×D9—22no—
350C2×D9—22no—
351C2×D9—22no—
352C2×D9—22no—
353C2×D9—22no—
354C2×D9—22no—
355C2×D9—416no—
356C2×D9—41no—
357C2×D9—41no—
358C2×D9—41no—
359C2×D9—41no—
360C2×D9#12314yescomplemented
361C4×C9—22no—
362C4×C9—22no—
363C4×C9—41no—
364C4×C9—41no—
365C4×C9—41no—
366Dic9—22no—
367Dic9—41no—
368Dic9—41no—
369Dic9—41no—
370Dic9—41no—
371Dic9—41no—
372C25—91no—
373C22×D4—91no—
374C22×D4—91no—
375C22×D4C2×D911yescharacteristic
376C23×C4—91no—
377C23×C4—91no—
378C23×C4C2×D911yescharacteristic, complemented
379#123—24no—
380#120—184no—
381C4×D4—184no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C4⋊C4C2×D911yescharacteristic, complemented
386C2×C4⋊C4C2×D911yescharacteristic, complemented
387C2×C22⋊C4—91no—
388C2×C22⋊C4—91no—
389C2×C22⋊C4—91no—
390C2×C22⋊C4—91no—
391C2×C22⋊C4—91no—
392C2×C22⋊C4—91no—
393C2×C22⋊C4—91no—
394C2×C22⋊C4—91no—
395C2×C22⋊C4—91no—
396C2×C22⋊C4—91no—
397C2×C22⋊C4—91no—
398C2×C22⋊C4—91no—
399C2×C22⋊C4—91no—
400C2×C22⋊C4—184no—
401C2×C22⋊C4C2×D911yescharacteristic
402C2×C22⋊C4C2×D911yescharacteristic
403C2×C22⋊C4C2×D911yescharacteristic, complemented
404C2×C42—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95—91no—
410#95—91no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—21no—
423C23×C3D3×D412yes—
424C23×C3C2×#6712yes—
425C23×C3C23×D311yescharacteristic
426C22×D3—32no—
427C22×D3—32no—
428C22×D3—32no—
429C22×D3—32no—
430C22×D3—61no—
431C22×D3—61no—
432C22×D3—61no—
433C22×D3—61no—
434C22×D3—68no—
435C22×D3—61no—
436C22×D3—61no—
437C22×D3—61no—
438C22×D3—61no—
439C22×D3—61no—
440C22×D3—61no—
441C22×D3—124no—
442C22×D3—124no—
443C22×D3—124no—
444C22×D3—124no—
445C22×D3—124no—
446C22×D3—124no—
447C3×D4—44no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—44no—
462C2×C3×C4C2×#6712yes—
463C2×C3×C4C2×#6712yes—
464#67—68no—
465#67—124no—
466C2×Dic3—32no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—61no—
470C2×Dic3—61no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3—61no—
475C2×Dic3—61no—
476C2×Dic3—61no—
477C2×Dic3—61no—
478C2×Dic3—61no—
479C2×Dic3—61no—
480C2×Dic3—61no—
481C2×Dic3—61no—
482C2×Dic3—61no—
483C2×Dic3—61no—
484C4×D3—124no—
485C4×D3—124no—
486C2×C9—42no—
487C2×C9—42no—
488C2×C9C2×#12311yescharacteristic
489C2×C9#52511yescharacteristic
490C2×C9#53811yescharacteristic
491C2×C9D4211yescharacteristic
492C2×C9#54611yescharacteristic
493C2×C9#54611yescharacteristic
494C2×C9#55111yescharacteristic
495D9—24no—
496D9—42no—
497C24—91no—
498C24—91no—
499C24—182no—
500C24—182no—
501C24—182no—
502C24—182no—
503C24—182no—
504C24—361no—
505C24—361no—
506C24C22×D911yescharacteristic
507C24C22×D911yescharacteristic
508C2×D4—22no—
509C2×D4—22no—
510C2×D4—41no—
511C2×D4—94no—
512C2×D4—182no—
513C2×D4—182no—
514C2×D4—182no—
515C2×D4—182no—
516C2×D4—361no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—41no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—91no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—91no—
526C22×C4—182no—
527C22×C4—182no—
528C22×C4—182no—
529C22×C4—182no—
530C22×C4—361no—
531C22×C4—361no—
532C22×C4C22×D911yescharacteristic
533C22×C4C22×D911yescharacteristic
534C22×C4C22×D911yescharacteristic
535C22×C4C22×D911yescharacteristic
536C22×C4C22×D911yescharacteristic
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—182no—
540C4⋊C4—361no—
541C4⋊C4—361no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—182no—
545C22⋊C4—182no—
546C22⋊C4—182no—
547C22⋊C4—182no—
548C22⋊C4—182no—
549C22⋊C4—182no—
550C22⋊C4—182no—
551C22⋊C4—182no—
552C22⋊C4—182no—
553C22⋊C4—182no—
554C22⋊C4—361no—
555C22⋊C4—361no—
556C22⋊C4—361no—
557C22⋊C4#61114yescomplemented
558C42—182no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3C2×D3×D411yescharacteristic
574C22×C3#100411yescharacteristic
575C22×C3D3×#4111yescharacteristic
576C22×C3D3×#4111yescharacteristic
577C22×C3D3×#4111yescharacteristic
578C22×C3#100911yescharacteristic
579C22×C3C22×#6711yescharacteristic
580C2×D3—34no—
581C2×D3—62no—
582C2×D3—62no—
583C2×D3—62no—
584C2×D3—62no—
585C2×D3—62no—
586C2×D3—62no—
587C2×D3—62no—
588C2×D3—62no—
589C2×D3—62no—
590C2×D3—1216no—
591C2×D3—121no—
592C2×D3—121no—
593C2×D3—121no—
594C2×D3—121no—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600Dic3—62no—
601Dic3—121no—
602Dic3—121no—
603Dic3—121no—
604Dic3—121no—
605Dic3—121no—
606C9#241811yescharacteristic, complemented, Sylow
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—92no—
620C23—92no—
621C23—92no—
622C23—92no—
623C23—188no—
624C23—181no—
625C23—181no—
626C23—181no—
627C23—181no—
628C23—181no—
629C23—181no—
630C23—181no—
631C23—181no—
632C23—181no—
633C23—181no—
634C23—364no—
635C23—364no—
636C23—364no—
637C23—364no—
638C23—364no—
639C23—364no—
640C23D4×D912yes—
641C23C2×#61112yes—
642C23C23×D911yescharacteristic
643D4—44no—
644D4—188no—
645D4—364no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—44no—
660C2×C4—92no—
661C2×C4—181no—
662C2×C4—181no—
663C2×C4—181no—
664C2×C4—181no—
665C2×C4—181no—
666C2×C4—181no—
667C2×C4—181no—
668C2×C4—181no—
669C2×C4—181no—
670C2×C4—181no—
671C2×C4—181no—
672C2×C4—181no—
673C2×C4—181no—
674C2×C4—181no—
675C2×C4—181no—
676C2×C4—181no—
677C2×C4—181no—
678C2×C4—364no—
679C2×C4—364no—
680C2×C4C2×#61112yes—
681C2×C4C2×#61112yes—
682C2×C3—42no—
683C2×C3—42no—
684C2×C3D3×#12311yescharacteristic
685C2×C3#565411yescharacteristic
686C2×C3#565711yescharacteristic
687C2×C3#565911yescharacteristic
688C2×C3D4×#6711yescharacteristic
689C2×C3#582811yescharacteristic
690C2×C3#582911yescharacteristic
691D3—64no—
692D3—122no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—94no—
708C22—182no—
709C22—182no—
710C22—182no—
711C22—182no—
712C22—182no—
713C22—182no—
714C22—182no—
715C22—182no—
716C22—182no—
717C22—3616no—
718C22—361no—
719C22—361no—
720C22—361no—
721C22—361no—
722C22C2×D4×D911yescharacteristic
723C22#6371011yescharacteristic
724C22#41×D911yescharacteristic
725C22#41×D911yescharacteristic
726C22#41×D911yescharacteristic
727C22#6371511yescharacteristic
728C22C22×#61111yescharacteristic
729C4—22no—
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—182no—
735C4—361no—
736C4—361no—
737C4—361no—
738C4—361no—
739C4—361no—
740C3#8289611yescharacteristic
741C2—42no—
742C2—42no—
743C2—184no—
744C2—362no—
745C2D9×#12311yescharacteristic
746C2#1058975611yescharacteristic
747C2#1058975911yescharacteristic
748C2#1058976111yescharacteristic
749C2D4×#61111yescharacteristic
750C2#1058993011yescharacteristic
751C2#1058993111yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC2×C9×#123C2
prime radicalC2×#63499C2
hypercenterC2×#123D9
hypocenterC9#2418
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C9×#123C2semidirect
3. C2×C4×#611C2semidirect
4. C2×C22⋊C4×D9C2semidirect
5. #10588902C2semidirect
6. #10588893C2semidirect
7. #10588673C2semidirect
8. #10588670C2semidirect
9. #10588669C2semidirect
10. #10588667C2semidirect
11. #10588641C2semidirect
12. #10588636C2semidirect
13. #10588635C2semidirect
14. #10588632C2semidirect
15. #10588631C2semidirect
19. C23×C4×C9C22semidirect
25. C2×C9×C4⋊C4C22semidirect
26. C2×C9×C4⋊C4C22semidirect
29. C2×C9×C22⋊C4C22semidirect
33. C2×#3676C22semidirect
34. C2×#3676C22semidirect
45. C2×C4⋊Dic9C22semidirect
46. C2×Dic9⋊C4C22semidirect
47. C2×Dic9⋊C4C22semidirect
48. C2×C4×Dic9C22semidirect
50. C9⋊#95C22semidirect
51. C9⋊#95C22semidirect
52. C9⋊#95C22semidirect
53. C9⋊#95C22semidirect
54. C9⋊#95C22semidirect
55. C9⋊#95C22semidirect
115. C9×C22⋊C4D4semidirect
248. C2×#123D9semidirect
360. C2×D9#123semidirect
378. C23×C4C2×D9semidirect
385. C2×C4⋊C4C2×D9semidirect
386. C2×C4⋊C4C2×D9semidirect
403. C2×C22⋊C4C2×D9semidirect
557. C22⋊C4#611semidirect
606. C9#2418semidirect

Maximal subgroups

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

subgroupindex
C2×C9×#1232
C2×#634992
C2×C4×#6112
C2×C22⋊C4×D92
#105889022
#105888932
#105886732
#105886702
#105886692
#105886672
#105886412
#105886362
#105886352
#105886322
#105886312
#828963