Finite Group Databasebeta

← #11810304

Subgroups — #11810304

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×#63456C211yesmaximal, characteristic, complemented
2C2×#63455C211yesmaximal, characteristic, complemented
3C2×#63444C211yesmaximal, characteristic
4C2×C22⋊C4×D9C211yesmaximal, characteristic, complemented
5C9×#399C211yesmaximal, characteristic, complemented
6#10588672C211yesmaximal, characteristic, complemented
7#10588671C211yesmaximal, characteristic, complemented
8#10588669C211yesmaximal, characteristic, complemented
9#10588667C211yesmaximal, characteristic, complemented
10#10588641C211yesmaximal, characteristic, complemented
11#10588636C211yesmaximal, characteristic, complemented
12#10588635C211yesmaximal, characteristic, complemented
13#10588624C211yesmaximal, characteristic, complemented
14#10588350C211yesmaximal, characteristic, complemented
15#10588345C211yesmaximal, characteristic, complemented
16#78101—31nomaximal
17C24×D9C2211yescharacteristic
18C22×#611C2211yescharacteristic
19C22×D36C2211yescharacteristic
20C22×D36C2211yescharacteristic
21C22×C4×D9C2211yescharacteristic
22C22×C4×D9C2211yescharacteristic
23C22×C4×D9C2211yescharacteristic, complemented
24C2×C9×C4⋊C4C2211yescharacteristic, complemented
25C2×C9×C4⋊C4C2211yescharacteristic, complemented
26C2×C9×C4⋊C4C2211yescharacteristic, complemented
27C2×C9×C22⋊C4C2211yescharacteristic
28C2×C9×C22⋊C4C2211yescharacteristic
29C2×C9×C22⋊C4C2211yescharacteristic
30C2×#3676C2211yescharacteristic
31C2×#3676C2211yescharacteristic
32C2×(C2×D9)⋊C4C2211yescharacteristic
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, complemented
41C2×(C2×D9)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D9)⋊C4C2211yescharacteristic, complemented
43C2×C4⋊Dic9C2211yescharacteristic, complemented
44C2×Dic9⋊C4C2211yescharacteristic, complemented
45C2×C4×Dic9C2211yescharacteristic, complemented
46#63456—24no—
47#63455—24no—
48#63444—24no—
49C22⋊C4×D9—24no—
50C9×#95C2211yescharacteristic, complemented
51C9⋊#95C2211yescharacteristic, complemented
52C9⋊#95C2211yescharacteristic, complemented
53C9⋊#95C2211yescharacteristic, complemented
54C9⋊#95C2211yescharacteristic, complemented
55C9⋊#95C2211yescharacteristic, complemented
56C2×#894—31no—
57C2×#893—31no—
58C2×#882—31no—
59C2×D3×C22⋊C4—31no—
60C3×#399D311yescharacteristic
61#4992—31no—
62#4991—31no—
63#4989—31no—
64#4987—31no—
65#4961—31no—
66#4956—31no—
67#4955—31no—
68#4944—31no—
69#4670—31no—
70#4665—31no—
71C24×C9C2311yescharacteristic
72C23×D9—22no—
73C23×D9—22no—
74C23×D9—22no—
75C23×D9—22no—
76C23×D9—22no—
77C23×D9—41no—
78C23×D9—41no—
79C23×D9C2311yescharacteristic
80C23×D9C2311yescharacteristic
81C23×D9C2311yescharacteristic
82C22×C4×C9C2311yescharacteristic
83C22×C4×C9C2311yescharacteristic
84C22×C4×C9C2311yescharacteristic
85C22×C4×C9C2311yescharacteristic
86C22×C4×C9C2311yescharacteristic
87C22×C4×C9C2311yescharacteristic
88C2×#611—22no—
89C2×#611—22no—
90C2×#611—41no—
91C22×Dic9C2311yescharacteristic
92C22×Dic9C2311yescharacteristic
93C22×Dic9C2311yescharacteristic
94C22×Dic9C2311yescharacteristic
95C22×Dic9C2311yescharacteristic
96C2×D36—22no—
97C2×D36—22no—
98C2×D36—22no—
99C2×D36—22no—
100C2×D36—41no—
101C2×D36D414yes—
102C2×C4×D9—22no—
103C2×C4×D9—22no—
104C2×C4×D9—22no—
105C2×C4×D9—22no—
106C2×C4×D9—22no—
107C2×C4×D9—22no—
108C2×C4×D9—41no—
109C2×C4×D9—41no—
110C2×C4×D9—41no—
111C9×C4⋊C4—22no—
112C9×C4⋊C4—22no—
113C9×C4⋊C4—41no—
114C9×C22⋊C4—22no—
115C9×C22⋊C4—22no—
116C9×C22⋊C4—41no—
117#3676—22no—
118#3676—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—22no—
125(C2×D9)⋊C4—22no—
126(C2×D9)⋊C4—22no—
127(C2×D9)⋊C4—41no—
128(C2×D9)⋊C4—41no—
129(C2×D9)⋊C4D414yescomplemented
130C4⋊Dic9—41no—
131Dic9⋊C4—22no—
132C4×Dic9—22no—
133#2418—91noSylow
134C24×D3—31no—
135C22×#67—31no—
136C22×D12—31no—
137C22×D12—31no—
138C22×C4×D3—31no—
139C22×C4×D3—31no—
140C22×C4×D3—31no—
141C2×C3×C4⋊C4C2×D311yescharacteristic
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×(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—31no—
160C2×C4⋊Dic3—31no—
161C2×Dic3⋊C4—31no—
162C2×C4×Dic3—31no—
163#894—64no—
164#893—64no—
165#882—64no—
166D3×C22⋊C4—64no—
167C3×#95C2×D311yescharacteristic
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#4112yes—
180C23×C9C2411yescharacteristic
181C22×D9—21no—
182C22×D9—21no—
183C22×D9—21no—
184C22×D9—21no—
185C22×D9—28no—
186C22×D9—21no—
187C22×D9—21no—
188C22×D9—21no—
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—44no—
199C22×D9—44no—
200C22×D9—44no—
201C22×D9—44no—
202C22×D9—44no—
203C22×D9—44no—
204C22×D9C2×D412yes—
205C22×D9C2×D412yes—
206C22×D9C2×D412yes—
207C22×D9#4112yes—
208C22×D9#4112yes—
209C2×C4×C9—21no—
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—21no—
224C2×C4×C9—21no—
225C2×C4×C9C2×D412yes—
226C2×C4×C9C2×D412yes—
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×Dic9C2×D412yes—
243D36—28no—
244D36—44no—
245C4×D9—44no—
246C4×D9—44no—
247C4×D9—44no—
248C2×#123—91no—
249C2×#120—91no—
250C2×C4×D4—91no—
251C22×C22⋊C4—91no—
252#399D911yescharacteristic, complemented
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
264C23×D3—31no—
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—
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C22×D311yescharacteristic
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C2×#67—62no—
281C2×#67—62no—
282C2×#67—121no—
283C22×Dic3—31no—
284C22×Dic3—31no—
285C22×Dic3—31no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C2×D12—34no—
289C2×D12—62no—
290C2×D12—62no—
291C2×D12—62no—
292C2×D12—62no—
293C2×D12—121no—
294C2×C4×D3—62no—
295C2×C4×D3—62no—
296C2×C4×D3—62no—
297C2×C4×D3—62no—
298C2×C4×D3—62no—
299C2×C4×D3—62no—
300C2×C4×D3—121no—
301C2×C4×D3—121no—
302C2×C4×D3—121no—
303C3×C4⋊C4—22no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—41no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4—22no—
308C3×C22⋊C4—41no—
309#217—62no—
310#217—62no—
311(C2×D3)⋊C4—34no—
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—62no—
318(C2×D3)⋊C4—62no—
319(C2×D3)⋊C4—62no—
320(C2×D3)⋊C4—121no—
321(C2×D3)⋊C4—121no—
322C4⋊Dic3—121no—
323Dic3⋊C4—62no—
324C4×Dic3—62no—
325C22×C9—22no—
326C22×C9—22no—
327C22×C9—22no—
328C22×C9—41no—
329C22×C9—41no—
330C22×C9—41no—
331C22×C9—41no—
332C22×C9C22×D411yescharacteristic
333C22×C9C22×D411yescharacteristic
334C22×C9C2×#4111yescharacteristic
335C22×C9C2×#4111yescharacteristic
336C22×C9C2×#4111yescharacteristic
337C22×C9H(5,𝔽2)11yescharacteristic
338C22×C9H(5,𝔽2)11yescharacteristic
339C2×D9—22no—
340C2×D9—22no—
341C2×D9—22no—
342C2×D9—22no—
343C2×D9—22no—
344C2×D9—22no—
345C2×D9—22no—
346C2×D9—22no—
347C2×D9—22no—
348C2×D9—22no—
349C2×D9—22no—
350C2×D9—22no—
351C2×D9—416no—
352C2×D9—41no—
353C2×D9—41no—
354C2×D9—41no—
355C2×D9—41no—
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—
366C4×C9—41no—
367Dic9—22no—
368Dic9—41no—
369Dic9—41no—
370Dic9—41no—
371Dic9—41no—
372C25—91no—
373C22×D4—91no—
374C22×D4—91no—
375C22×D4—91no—
376C23×C4—91no—
377C23×C4—91no—
378C23×C4—91no—
379#123—184no—
380#120—184no—
381C4×D4—184no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4C2×D911yescharacteristic, complemented
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
404C2×C42—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95—91no—
410#95C2×D911yescharacteristic, complemented
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3#23912yes—
418C23×C3C23×D311yescharacteristic
419C22×D3—32no—
420C22×D3—32no—
421C22×D3—32no—
422C22×D3—32no—
423C22×D3—32no—
424C22×D3—61no—
425C22×D3—61no—
426C22×D3—61no—
427C22×D3—61no—
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—
447C2×C3×C4—21no—
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—21no—
462C2×C3×C4—21no—
463C2×C3×C4D3×D412yes—
464C2×C3×C4D3×D412yes—
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—
481D12—68no—
482D12—124no—
483C4×D3—124no—
484C4×D3—124no—
485C4×D3—124no—
486C2×C9—42no—
487C2×C9C2×#12311yescharacteristic
488C2×C9#52511yescharacteristic
489C2×C9#53811yescharacteristic
490C2×C9D4211yescharacteristic
491C2×C9#54611yescharacteristic
492C2×C9#54611yescharacteristic
493C2×C9#55111yescharacteristic
494D9—24no—
495D9—42no—
496D9—42no—
497C24—91no—
498C24—91no—
499C24—91no—
500C24—182no—
501C24—182no—
502C24—182no—
503C24—182no—
504C24—182no—
505C24—361no—
506C24—361no—
507C24C22×D911yescharacteristic
508C2×D4—94no—
509C2×D4—182no—
510C2×D4—182no—
511C2×D4—182no—
512C2×D4—182no—
513C2×D4—182no—
514C2×D4—182no—
515C2×D4—361no—
516C2×D4—361no—
517C22×C4—91no—
518C22×C4—91no—
519C22×C4—91no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—182no—
523C22×C4—182no—
524C22×C4—182no—
525C22×C4—182no—
526C22×C4—182no—
527C22×C4—182no—
528C22×C4—361no—
529C22×C4—361no—
530C22×C4—361no—
531C22×C4C22×D911yescharacteristic
532C22×C4C22×D911yescharacteristic
533C22×C4C22×D911yescharacteristic
534C22×C4C22×D911yescharacteristic
535C22×C4C22×D911yescharacteristic
536C22×C4C22×D911yescharacteristic
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—41no—
540C4⋊C4—182no—
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—41no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3C2×D3×D411yescharacteristic
567C22×C3C2×D3×D411yescharacteristic
568C22×C3#100411yescharacteristic
569C22×C3C2×#23911yescharacteristic
570C22×C3D3×#4111yescharacteristic
571C22×C3D3×#4111yescharacteristic
572C22×C3#100911yescharacteristic
573C2×D3—34no—
574C2×D3—62no—
575C2×D3—62no—
576C2×D3—62no—
577C2×D3—62no—
578C2×D3—62no—
579C2×D3—62no—
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—
600C3×C4—41no—
601Dic3—62no—
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—92no—
614C23—92no—
615C23—92no—
616C23—92no—
617C23—92no—
618C23—188no—
619C23—181no—
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—181no—
633C23—181no—
634C23—181no—
635C23—364no—
636C23—364no—
637C23—364no—
638C23—364no—
639C23—364no—
640C23—364no—
641C23#370112yes—
642C23C23×D911yescharacteristic
643D4—188no—
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—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—92no—
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—364no—
678C2×C4—364no—
679C2×C4—364no—
680C2×C4D4×D912yes—
681C2×C4D4×D912yes—
682C2×C3—42no—
683C2×C3#562711yescharacteristic
684C2×C3#563011yescharacteristic
685C2×C3#563711yescharacteristic
686C2×C3D3×#12311yescharacteristic
687C2×C3#565411yescharacteristic
688C2×C3#565711yescharacteristic
689C2×C3#571711yescharacteristic
690D3—64no—
691D3—122no—
692D3—122no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—94no—
701C22—182no—
702C22—182no—
703C22—182no—
704C22—182no—
705C22—182no—
706C22—182no—
707C22—182no—
708C22—182no—
709C22—182no—
710C22—182no—
711C22—182no—
712C22—182no—
713C22—3616no—
714C22—361no—
715C22—361no—
716C22—361no—
717C22—361no—
718C22—361no—
719C22—361no—
720C22—361no—
721C22—361no—
722C22C2×D4×D911yescharacteristic
723C22C2×D4×D911yescharacteristic
724C22#6371011yescharacteristic
725C22C2×#370111yescharacteristic
726C22#41×D911yescharacteristic
727C22#41×D911yescharacteristic
728C22#6371511yescharacteristic
729C4—22no—
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—182no—
736C4—361no—
737C4—361no—
738C4—361no—
739C4—361no—
740C3#7810111yescharacteristic
741C2—42no—
742C2—184no—
743C2—362no—
744C2—362no—
745C2#1058972911yescharacteristic
746C2#1058973211yescharacteristic
747C2#1058973911yescharacteristic
748C2D9×#12311yescharacteristic
749C2#1058975611yescharacteristic
750C2#1058975911yescharacteristic
751C2#1058981911yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#399C2
prime radicalC2×#63444C2
hypercenter#399D9
hypocenterC9#2418
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#63456C2semidirect
2. C2×#63455C2semidirect
4. C2×C22⋊C4×D9C2semidirect
5. C9×#399C2semidirect
6. #10588672C2semidirect
7. #10588671C2semidirect
8. #10588669C2semidirect
9. #10588667C2semidirect
10. #10588641C2semidirect
11. #10588636C2semidirect
12. #10588635C2semidirect
13. #10588624C2semidirect
14. #10588350C2semidirect
15. #10588345C2semidirect
23. C22×C4×D9C22semidirect
24. C2×C9×C4⋊C4C22semidirect
25. C2×C9×C4⋊C4C22semidirect
26. C2×C9×C4⋊C4C22semidirect
40. C2×(C2×D9)⋊C4C22semidirect
41. C2×(C2×D9)⋊C4C22semidirect
42. C2×(C2×D9)⋊C4C22semidirect
43. C2×C4⋊Dic9C22semidirect
44. C2×Dic9⋊C4C22semidirect
45. C2×C4×Dic9C22semidirect
50. C9×#95C22semidirect
51. C9⋊#95C22semidirect
52. C9⋊#95C22semidirect
53. C9⋊#95C22semidirect
54. C9⋊#95C22semidirect
55. C9⋊#95C22semidirect
129. (C2×D9)⋊C4D4semidirect
252. #399D9semidirect
360. C2×D9#123semidirect
384. C2×C4⋊C4C2×D9semidirect
385. C2×C4⋊C4C2×D9semidirect
386. C2×C4⋊C4C2×D9semidirect
410. #95C2×D9semidirect
606. C9#2418semidirect

Maximal subgroups

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

subgroupindex
C2×#634562
C2×#634552
C2×#634442
C2×C22⋊C4×D92
C9×#3992
#105886722
#105886712
#105886692
#105886672
#105886412
#105886362
#105886352
#105886242
#105883502
#105883452
#781013