Finite Group Databasebeta

← #11810289

Subgroups — #11810289

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×#63499C211yesmaximal, characteristic
2C2×D4×Dic9C211yesmaximal, characteristic, complemented
3C22×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
4C2×#63448C211yesmaximal, characteristic, complemented
5C9×#386C211yesmaximal, characteristic, complemented
6#10588892C211yesmaximal, characteristic, complemented
7#10588641C211yesmaximal, characteristic, complemented
8#10588641C211yesmaximal, characteristic, complemented
9#10588638C211yesmaximal, characteristic, complemented
10#10588635C211yesmaximal, characteristic, complemented
11#10588630C211yesmaximal, characteristic, complemented
12#10588357C211yesmaximal, characteristic, complemented
13#10588354C211yesmaximal, characteristic, complemented
14#10588350C211yesmaximal, characteristic, complemented
15#10588350C211yesmaximal, characteristic, complemented
16#74891—31nomaximal
17C24×D9C2211yescharacteristic
18C22×D4×C9C2211yescharacteristic
19C23×C4×C9C2211yescharacteristic
20C22×#611C2211yescharacteristic
21C22×#611C2211yescharacteristic
22C23×Dic9C2211yescharacteristic
23C23×Dic9C2211yescharacteristic, complemented
24C2×C9×C22⋊C4C2211yescharacteristic
25C2×C9×C22⋊C4C2211yescharacteristic, complemented
26C2×C9×C22⋊C4C2211yescharacteristic, complemented
27C2×#3676C2211yescharacteristic
28C2×#3676C2211yescharacteristic
29C2×#3676C2211yescharacteristic, complemented
30#63499—24no—
31D4×Dic9—24no—
32C2×(C2×D9)⋊C4—24no—
33C2×(C2×D9)⋊C4C2211yescharacteristic
34C2×(C2×D9)⋊C4C2211yescharacteristic
35C2×(C2×D9)⋊C4C2211yescharacteristic
36C2×(C2×D9)⋊C4C2211yescharacteristic
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×C4⋊Dic9C2211yescharacteristic, complemented
44C2×C4⋊Dic9C2211yescharacteristic, complemented
45C2×C4⋊Dic9C2211yescharacteristic, complemented
46C2×C4⋊Dic9C2211yescharacteristic, complemented
47C2×C4⋊Dic9C2211yescharacteristic, complemented
48C2×C4×Dic9C2211yescharacteristic, complemented
49#63448—24no—
50C9×#95C2211yescharacteristic, complemented
51C9×#95C2211yescharacteristic, complemented
52C9⋊#95C2211yescharacteristic, complemented
53C9⋊#95C2211yescharacteristic, complemented
54C9⋊#95C2211yescharacteristic, complemented
55C9⋊#95C2211yescharacteristic, complemented
56C2×#937—31no—
57C2×D4×Dic3—31no—
58C22×(C2×D3)⋊C4—31no—
59C2×#886—31no—
60C3×#386D311yescharacteristic
61#5212—31no—
62#4961—31no—
63#4961—31no—
64#4958—31no—
65#4955—31no—
66#4950—31no—
67#4677—31no—
68#4674—31no—
69#4670—31no—
70#4670—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×C9D414yes—
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×#611—41no—
99C22×Dic9—22no—
100C22×Dic9—22no—
101C22×Dic9—22no—
102C22×Dic9—22no—
103C22×Dic9—41no—
104C22×Dic9—41no—
105C22×Dic9C2311yescharacteristic
106C22×Dic9C2311yescharacteristic
107C22×Dic9C2311yescharacteristic
108C22×Dic9C2311yescharacteristic
109C22×Dic9C2311yescharacteristic
110C22×Dic9C2311yescharacteristic
111C9×C22⋊C4—22no—
112C9×C22⋊C4—22no—
113C9×C22⋊C4—41no—
114#3676—22no—
115#3676—22no—
116#3676—22no—
117(C2×D9)⋊C4—22no—
118(C2×D9)⋊C4—22no—
119(C2×D9)⋊C4—22no—
120(C2×D9)⋊C4—22no—
121(C2×D9)⋊C4—22no—
122(C2×D9)⋊C4—22no—
123(C2×D9)⋊C4—22no—
124(C2×D9)⋊C4—41no—
125(C2×D9)⋊C4—41no—
126(C2×D9)⋊C4D414yescomplemented
127C4⋊Dic9—22no—
128C4⋊Dic9—22no—
129C4⋊Dic9—22no—
130C4⋊Dic9—41no—
131C4⋊Dic9—41no—
132C4×Dic9—22no—
133#2418—91noSylow
134C24×D3—31no—
135C22×C3×D4C2×D311yescharacteristic
136C23×C3×C4C2×D311yescharacteristic
137C22×#67—31no—
138C22×#67—31no—
139C23×Dic3—31no—
140C23×Dic3—31no—
141C2×C3×C22⋊C4C2×D311yescharacteristic
142C2×C3×C22⋊C4C2×D311yescharacteristic
143C2×C3×C22⋊C4C2×D311yescharacteristic
144C2×#217—31no—
145C2×#217—31no—
146C2×#217—31no—
147#937—64no—
148D4×Dic3—64no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
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—64no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—31no—
165C2×C4×Dic3—31no—
166#886—64no—
167C3×#95C2×D311yescharacteristic
168C3×#95C2×D311yescharacteristic
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×C9C2×D412yes—
184C23×C9C2×D412yes—
185C23×C9#4112yes—
186C23×C9#4112yes—
187C23×C9C2411yescharacteristic
188C22×D9—28no—
189C22×D9—21no—
190C22×D9—21no—
191C22×D9—21no—
192C22×D9—21no—
193C22×D9—21no—
194C22×D9—21no—
195C22×D9—21no—
196C22×D9—21no—
197C22×D9—21no—
198C22×D9—21no—
199C22×D9—21no—
200C22×D9—21no—
201C22×D9—44no—
202C22×D9—44no—
203C22×D9—44no—
204C22×D9—44no—
205C22×D9—44no—
206C22×D9—44no—
207C22×D9C2×D412yes—
208C22×D9#4112yes—
209D4×C9—28no—
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—44no—
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×Dic9—44no—
246C2×Dic9—44no—
247C2×Dic9C2×D412yes—
248C2×#123—91no—
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#386D911yescharacteristic, complemented
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×D4D1214yes—
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—62no—
286C2×#67—62no—
287C2×#67—62no—
288C2×#67—62no—
289C2×#67—121no—
290C2×#67—121no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—62no—
298C22×Dic3—62no—
299C22×Dic3—62no—
300C22×Dic3—62no—
301C22×Dic3—121no—
302C22×Dic3—121no—
303C3×C22⋊C4—22no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—41no—
306#217—62no—
307#217—62no—
308#217—62no—
309(C2×D3)⋊C4—34no—
310(C2×D3)⋊C4—62no—
311(C2×D3)⋊C4—62no—
312(C2×D3)⋊C4—62no—
313(C2×D3)⋊C4—62no—
314(C2×D3)⋊C4—62no—
315(C2×D3)⋊C4—62no—
316(C2×D3)⋊C4—62no—
317(C2×D3)⋊C4—121no—
318(C2×D3)⋊C4—121no—
319C4⋊Dic3—62no—
320C4⋊Dic3—62no—
321C4⋊Dic3—62no—
322C4⋊Dic3—121no—
323C4⋊Dic3—121no—
324C4×Dic3—62no—
325C22×C9—22no—
326C22×C9—22no—
327C22×C9—22no—
328C22×C9—22no—
329C22×C9—22no—
330C22×C9—22no—
331C22×C9—22no—
332C22×C9—22no—
333C22×C9—22no—
334C22×C9—41no—
335C22×C9—41no—
336C22×C9—41no—
337C22×C9—41no—
338C22×C9#12314yescomplemented
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—416no—
353C2×D9—41no—
354C2×D9—41no—
355C2×D9—41no—
356C2×D9—41no—
357C2×D9—41no—
358C2×D9—41no—
359C2×D9—41no—
360C2×D9—41no—
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
379#123—184no—
380#120—184no—
381C4×D4—184no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C4⋊C4—91no—
386C2×C4⋊C4—91no—
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, complemented
403C2×C22⋊C4C2×D911yescharacteristic, complemented
404C2×C42—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95C2×D911yescharacteristic, complemented
410#95C2×D911yescharacteristic, complemented
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×C3C2×D1212yes—
422C23×C3C2×D1212yes—
423C23×C3#23712yes—
424C23×C3#23712yes—
425C23×C3C23×D311yescharacteristic
426C22×D3—32no—
427C22×D3—32no—
428C22×D3—68no—
429C22×D3—61no—
430C22×D3—61no—
431C22×D3—61no—
432C22×D3—61no—
433C22×D3—61no—
434C22×D3—61no—
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—28no—
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×D1212yes—
463C2×C3×C4D3×D412yes—
464#67—124no—
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—
484C2×Dic3—124no—
485C2×Dic3—124no—
486C2×C9—24no—
487C2×C9—42no—
488C2×C9C2×#12311yescharacteristic
489C2×C9#52511yescharacteristic
490C2×C9#53811yescharacteristic
491C2×C9D4211yescharacteristic
492C2×C9#54611yescharacteristic
493C2×C9#54611yescharacteristic
494C2×C9#55111yescharacteristic
495D9—42no—
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—182no—
511C2×D4—182no—
512C2×D4—182no—
513C2×D4—182no—
514C2×D4—361no—
515C2×D4—361no—
516C2×D4D3614yes—
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—182no—
538C4⋊C4—182no—
539C4⋊C4—182no—
540C4⋊C4—361no—
541C4⋊C4—361no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—41no—
545C22⋊C4—94no—
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—182no—
555C22⋊C4—182no—
556C22⋊C4—361no—
557C22⋊C4—361no—
558C42—182no—
559C22×C3—22no—
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—41no—
569C22×C3—41no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3#88614yes—
573C22×C3C22×D1211yescharacteristic
574C22×C3C2×D3×D411yescharacteristic
575C22×C3C2×#23711yescharacteristic
576C22×C3C2×#23711yescharacteristic
577C22×C3#100411yescharacteristic
578C22×C3D3×#4111yescharacteristic
579C22×C3#100911yescharacteristic
580C2×D3—62no—
581C2×D3—62no—
582C2×D3—62no—
583C2×D3—62no—
584C2×D3—62no—
585C2×D3—62no—
586C2×D3—1216no—
587C2×D3—121no—
588C2×D3—121no—
589C2×D3—121no—
590C2×D3—121no—
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—92no—
618C23—92no—
619C23—188no—
620C23—181no—
621C23—181no—
622C23—181no—
623C23—181no—
624C23—181no—
625C23—181no—
626C23—181no—
627C23—181no—
628C23—181no—
629C23—181no—
630C23—181no—
631C23—181no—
632C23—364no—
633C23—364no—
634C23—364no—
635C23—364no—
636C23—364no—
637C23—364no—
638C23C2×D3612yes—
639C23C2×D3612yes—
640C23#369912yes—
641C23#369912yes—
642C23C23×D911yescharacteristic
643D4—28no—
644D4—364no—
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×D3612yes—
681C2×C4D4×D912yes—
682C2×C3—24no—
683C2×C3—42no—
684C2×C3C2×#88611yescharacteristic
685C2×C3D4×D1211yescharacteristic
686C2×C3#555411yescharacteristic
687C2×C3#559111yescharacteristic
688C2×C3#560611yescharacteristic
689C2×C3#561711yescharacteristic
690C2×C3#565811yescharacteristic
691D3—122no—
692D3—122no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—182no—
707C22—182no—
708C22—182no—
709C22—182no—
710C22—182no—
711C22—182no—
712C22—3616no—
713C22—361no—
714C22—361no—
715C22—361no—
716C22—361no—
717C22—361no—
718C22—361no—
719C22—361no—
720C22—361no—
721C22#6344814yescomplemented
722C22C22×D3611yescharacteristic
723C22C2×D4×D911yescharacteristic
724C22C2×#369911yescharacteristic
725C22C2×#369911yescharacteristic
726C22#6371011yescharacteristic
727C22#41×D911yescharacteristic
728C22#6371511yescharacteristic
729C4—22no—
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—182no—
735C4—361no—
736C4—361no—
737C4—361no—
738C4—361no—
739C4—361no—
740C3#7489111yescharacteristic
741C2—24no—
742C2—42no—
743C2—362no—
744C2—362no—
745C2C2×#6344811yescharacteristic
746C2D4×D3611yescharacteristic
747C2#1058965611yescharacteristic
748C2#1058969311yescharacteristic
749C2#1058970811yescharacteristic
750C2#1058971911yescharacteristic
751C2#1058976011yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#386C2
prime radicalC2×#63499C2
hypercenter#386D9
hypocenterC9#2418
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic9C2semidirect
3. C22×(C2×D9)⋊C4C2semidirect
4. C2×#63448C2semidirect
5. C9×#386C2semidirect
6. #10588892C2semidirect
7. #10588641C2semidirect
8. #10588641C2semidirect
9. #10588638C2semidirect
10. #10588635C2semidirect
11. #10588630C2semidirect
12. #10588357C2semidirect
13. #10588354C2semidirect
14. #10588350C2semidirect
15. #10588350C2semidirect
23. C23×Dic9C22semidirect
25. C2×C9×C22⋊C4C22semidirect
26. C2×C9×C22⋊C4C22semidirect
29. C2×#3676C22semidirect
43. C2×C4⋊Dic9C22semidirect
44. C2×C4⋊Dic9C22semidirect
45. C2×C4⋊Dic9C22semidirect
46. C2×C4⋊Dic9C22semidirect
47. C2×C4⋊Dic9C22semidirect
48. C2×C4×Dic9C22semidirect
50. C9×#95C22semidirect
51. C9×#95C22semidirect
52. C9⋊#95C22semidirect
53. C9⋊#95C22semidirect
54. C9⋊#95C22semidirect
55. C9⋊#95C22semidirect
126. (C2×D9)⋊C4D4semidirect
259. #386D9semidirect
338. C22×C9#123semidirect
402. C2×C22⋊C4C2×D9semidirect
403. C2×C22⋊C4C2×D9semidirect
409. #95C2×D9semidirect
410. #95C2×D9semidirect
606. C9#2418semidirect
721. C22#63448semidirect

Maximal subgroups

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

subgroupindex
C2×#634992
C2×D4×Dic92
C22×(C2×D9)⋊C42
C2×#634482
C9×#3862
#105888922
#105886412
#105886382
#105886352
#105886302
#105883572
#105883542
#105883502
#748913