Finite Group Databasebeta

← #11810313

Subgroups — #11810313

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
1C22×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
2C2×#63456C211yesmaximal, characteristic, complemented
3C2×#63444C211yesmaximal, characteristic
4C2×#611⋊C4C211yesmaximal, characteristic, complemented
5C9×#380C211yesmaximal, characteristic, complemented
6#10588893C211yesmaximal, characteristic, complemented
7#10588673C211yesmaximal, characteristic, complemented
8#10588671C211yesmaximal, characteristic, complemented
9#10588670C211yesmaximal, characteristic, complemented
10#10588635C211yesmaximal, characteristic, complemented
11#10588626C211yesmaximal, characteristic, complemented
12#10588355C211yesmaximal, characteristic, complemented
13#10588352C211yesmaximal, characteristic, complemented
14#10588349C211yesmaximal, characteristic, complemented
15#10588345C211yesmaximal, characteristic, complemented
16#74021—31nomaximal
17C24×D9C2211yescharacteristic
18C23×C4×C9C2211yescharacteristic
19C22×#611C2211yescharacteristic
20C23×Dic9C2211yescharacteristic
21C22×D36C2211yescharacteristic
22C22×D36C2211yescharacteristic
23C22×C4×D9C2211yescharacteristic, complemented
24C2×C9×C4⋊C4C2211yescharacteristic, complemented
25C2×C9×C4⋊C4C2211yescharacteristic, complemented
26C2×C9×C22⋊C4C2211yescharacteristic
27C2×C9×C22⋊C4C2211yescharacteristic
28C2×#3676C2211yescharacteristic
29C2×(C2×D9)⋊C4—24no—
30C2×(C2×D9)⋊C4C2211yescharacteristic
31C2×(C2×D9)⋊C4C2211yescharacteristic
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×Dic9⋊C4C2211yescharacteristic, complemented
44C2×Dic9⋊C4C2211yescharacteristic, complemented
45C2×Dic9⋊C4C2211yescharacteristic, complemented
46C2×C4×Dic9C2211yescharacteristic, complemented
47#63456—24no—
48#63444—24no—
49#611⋊C4—24no—
50C9×#95C2211yescharacteristic, complemented
51C9×#95C2211yescharacteristic, complemented
52C9⋊#95C2211yescharacteristic, complemented
53C9⋊#95C2211yescharacteristic, complemented
54C9⋊#95C2211yescharacteristic, complemented
55C9⋊#95C2211yescharacteristic, complemented
56C22×(C2×D3)⋊C4—31no—
57C2×#894—31no—
58C2×#882—31no—
59C2×#67⋊C4—31no—
60C3×#380D311yescharacteristic
61#5213—31no—
62#4993—31no—
63#4991—31no—
64#4990—31no—
65#4955—31no—
66#4946—31no—
67#4675—31no—
68#4672—31no—
69#4669—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×C9—22no—
83C22×C4×C9—22no—
84C22×C4×C9—41no—
85C22×C4×C9C2311yescharacteristic
86C22×C4×C9C2311yescharacteristic
87C22×C4×C9C2311yescharacteristic
88C22×C4×C9C2311yescharacteristic
89C22×C4×C9C2311yescharacteristic
90C22×C4×C9C2311yescharacteristic
91C2×#611—22no—
92C2×#611—22no—
93C2×#611D414yes—
94C22×Dic9—22no—
95C22×Dic9—22no—
96C22×Dic9—41no—
97C22×Dic9C2311yescharacteristic
98C22×Dic9C2311yescharacteristic
99C22×Dic9C2311yescharacteristic
100C22×Dic9C2311yescharacteristic
101C22×Dic9C2311yescharacteristic
102C2×D36—22no—
103C2×D36—22no—
104C2×D36—22no—
105C2×D36—22no—
106C2×D36—41no—
107C2×D36—41no—
108C2×C4×D9—22no—
109C2×C4×D9—22no—
110C2×C4×D9—41no—
111C9×C4⋊C4—22no—
112C9×C4⋊C4—41no—
113C9×C22⋊C4—22no—
114C9×C22⋊C4—22no—
115#3676—22no—
116(C2×D9)⋊C4—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—22no—
125(C2×D9)⋊C4—41no—
126(C2×D9)⋊C4—41no—
127(C2×D9)⋊C4—41no—
128(C2×D9)⋊C4D414yescomplemented
129Dic9⋊C4—22no—
130Dic9⋊C4—22no—
131Dic9⋊C4—41no—
132C4×Dic9—22no—
133#2418—91noSylow
134C24×D3—31no—
135C23×C3×C4C2×D311yescharacteristic
136C22×#67—31no—
137C23×Dic3—31no—
138C22×D12—31no—
139C22×D12—31no—
140C22×C4×D3—31no—
141C2×C3×C4⋊C4C2×D311yescharacteristic
142C2×C3×C4⋊C4C2×D311yescharacteristic
143C2×C3×C22⋊C4C2×D311yescharacteristic
144C2×C3×C22⋊C4C2×D311yescharacteristic
145C2×#217—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—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—64no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×C4×Dic3—31no—
164#894—64no—
165#882—64no—
166#67⋊C4—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×C9C2×D412yes—
178C23×C9#4112yes—
179C23×C9#4112yes—
180C23×C9C2411yescharacteristic
181C22×D9—28no—
182C22×D9—21no—
183C22×D9—21no—
184C22×D9—21no—
185C22×D9—21no—
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—21no—
199C22×D9—21no—
200C22×D9—44no—
201C22×D9—44no—
202C22×D9—44no—
203C22×D9—44no—
204C22×D9—44no—
205C22×D9—44no—
206C22×D9C2×D412yes—
207C22×D9C2×D412yes—
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×C9—21no—
226C2×C4×C9—44no—
227C2×C4×C9C2×D412yes—
228#611—28no—
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—44no—
243C2×Dic9C2×D412yes—
244C2×Dic9C2×D412yes—
245D36—44no—
246D36—44no—
247C4×D9—44no—
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#386—91no—
260#385—91no—
261#380D911yescharacteristic, complemented
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×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—41no—
277C22×C3×C4C22×D311yescharacteristic
278C22×C3×C4C22×D311yescharacteristic
279C22×C3×C4C22×D311yescharacteristic
280C22×C3×C4C22×D311yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C2×#67—34no—
284C2×#67—62no—
285C2×#67—62no—
286C22×Dic3—31no—
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—62no—
292C22×Dic3—62no—
293C22×Dic3—121no—
294C2×D12—62no—
295C2×D12—62no—
296C2×D12—62no—
297C2×D12—62no—
298C2×D12—121no—
299C2×D12—121no—
300C2×C4×D3—62no—
301C2×C4×D3—62no—
302C2×C4×D3—121no—
303C3×C4⋊C4—22no—
304C3×C4⋊C4—41no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—22no—
307#217—62no—
308(C2×D3)⋊C4—34no—
309(C2×D3)⋊C4—62no—
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—62no—
318(C2×D3)⋊C4—121no—
319(C2×D3)⋊C4—121no—
320(C2×D3)⋊C4—121no—
321Dic3⋊C4—62no—
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#12314yescomplemented
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—416no—
349C2×D9—41no—
350C2×D9—41no—
351C2×D9—41no—
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—41no—
361C4×C9—22no—
362C4×C9—41no—
363C4×C9—41no—
364C4×C9—41no—
365C4×C9—41no—
366C4×C9—41no—
367Dic9—22no—
368Dic9—22no—
369Dic9—41no—
370Dic9—41no—
371Dic9—41no—
372C25—91no—
373C22×D4—91no—
374C22×D4—91no—
375C22×D4—91no—
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⋊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—91no—
401C2×C22⋊C4—184no—
402C2×C22⋊C4C2×D911yescharacteristic
403C2×C22⋊C4C2×D911yescharacteristic
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#23512yes—
416C23×C3D3×D412yes—
417C23×C3#23912yes—
418C23×C3C23×D311yescharacteristic
419C22×D3—32no—
420C22×D3—32no—
421C22×D3—32no—
422C22×D3—68no—
423C22×D3—61no—
424C22×D3—61no—
425C22×D3—61no—
426C22×D3—61no—
427C22×D3—61no—
428C22×D3—61no—
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×C4—21no—
464C2×C3×C4—44no—
465C2×C3×C4D3×D412yes—
466#67—68no—
467C2×Dic3—32no—
468C2×Dic3—32no—
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—124no—
483D12—124no—
484D12—124no—
485C4×D3—124no—
486C2×C9—24no—
487C2×C9C2×#12311yescharacteristic
488C2×C9#52511yescharacteristic
489C2×C9#53811yescharacteristic
490C2×C9D4211yescharacteristic
491C2×C9#54611yescharacteristic
492C2×C9#54611yescharacteristic
493C2×C9#55111yescharacteristic
494D9—42no—
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—22no—
518C22×C4—22no—
519C22×C4—41no—
520C22×C4—91no—
521C22×C4—91no—
522C22×C4—91no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—182no—
526C22×C4—182no—
527C22×C4—182no—
528C22×C4—182no—
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—41no—
539C4⋊C4—182no—
540C4⋊C4—182no—
541C4⋊C4—361no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—94no—
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—182no—
555C22⋊C4—361no—
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#89414yes—
566C22×C3C2×#23511yescharacteristic
567C22×C3C2×D3×D411yescharacteristic
568C22×C3C2×D3×D411yescharacteristic
569C22×C3#100411yescharacteristic
570C22×C3C2×#23911yescharacteristic
571C22×C3D3×#4111yescharacteristic
572C22×C3#100911yescharacteristic
573C2×D3—62no—
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—1216no—
583C2×D3—121no—
584C2×D3—121no—
585C2×D3—121no—
586C2×D3—121no—
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—41no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—41no—
601Dic3—62no—
602Dic3—62no—
603Dic3—121no—
604Dic3—121no—
605Dic3—121no—
606C9#241811yescharacteristic, complemented, Sylow
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—92no—
612C23—92no—
613C23—92no—
614C23—188no—
615C23—181no—
616C23—181no—
617C23—181no—
618C23—181no—
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—364no—
634C23—364no—
635C23—364no—
636C23—364no—
637C23—364no—
638C23—364no—
639C23#369712yes—
640C23D4×D912yes—
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—21no—
663C2×C4—44no—
664C2×C4—92no—
665C2×C4—92no—
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—181no—
679C2×C4—364no—
680C2×C4—364no—
681C2×C4D4×D912yes—
682C2×C3—24no—
683C2×C3#549011yescharacteristic
684C2×C3C2×#89411yescharacteristic
685C2×C3#552711yescharacteristic
686C2×C3#560911yescharacteristic
687C2×C3#561011yescharacteristic
688C2×C3#562711yescharacteristic
689C2×C3#564411yescharacteristic
690D3—122no—
691D3—122no—
692D3—122no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—182no—
700C22—182no—
701C22—182no—
702C22—182no—
703C22—182no—
704C22—182no—
705C22—182no—
706C22—182no—
707C22—182no—
708C22—3616no—
709C22—361no—
710C22—361no—
711C22—361no—
712C22—361no—
713C22—361no—
714C22—361no—
715C22—361no—
716C22—361no—
717C22—361no—
718C22—361no—
719C22—361no—
720C22—361no—
721C22#6345614yescomplemented
722C22C2×#369711yescharacteristic
723C22C2×D4×D911yescharacteristic
724C22C2×D4×D911yescharacteristic
725C22#6371011yescharacteristic
726C22C2×#370111yescharacteristic
727C22#41×D911yescharacteristic
728C22#6371511yescharacteristic
729C4—22no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—182no—
736C4—182no—
737C4—361no—
738C4—361no—
739C4—361no—
740C3#7402111yescharacteristic
741C2—24no—
742C2—362no—
743C2—362no—
744C2—362no—
745C2#1058959211yescharacteristic
746C2C2×#6345611yescharacteristic
747C2#1058962911yescharacteristic
748C2#1058971111yescharacteristic
749C2#1058971211yescharacteristic
750C2#1058972911yescharacteristic
751C2#1058974611yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC9×#380C2
prime radicalC2×#63444C2
hypercenter#380D9
hypocenterC9#2418
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C22×(C2×D9)⋊C4C2semidirect
2. C2×#63456C2semidirect
4. C2×#611⋊C4C2semidirect
5. C9×#380C2semidirect
6. #10588893C2semidirect
7. #10588673C2semidirect
8. #10588671C2semidirect
9. #10588670C2semidirect
10. #10588635C2semidirect
11. #10588626C2semidirect
12. #10588355C2semidirect
13. #10588352C2semidirect
14. #10588349C2semidirect
15. #10588345C2semidirect
23. C22×C4×D9C22semidirect
24. C2×C9×C4⋊C4C22semidirect
25. C2×C9×C4⋊C4C22semidirect
40. C2×(C2×D9)⋊C4C22semidirect
41. C2×(C2×D9)⋊C4C22semidirect
42. C2×(C2×D9)⋊C4C22semidirect
43. C2×Dic9⋊C4C22semidirect
44. C2×Dic9⋊C4C22semidirect
45. C2×Dic9⋊C4C22semidirect
46. C2×C4×Dic9C22semidirect
50. C9×#95C22semidirect
51. C9×#95C22semidirect
52. C9⋊#95C22semidirect
53. C9⋊#95C22semidirect
54. C9⋊#95C22semidirect
55. C9⋊#95C22semidirect
128. (C2×D9)⋊C4D4semidirect
261. #380D9semidirect
331. C22×C9#123semidirect
385. C2×C4⋊C4C2×D9semidirect
386. C2×C4⋊C4C2×D9semidirect
409. #95C2×D9semidirect
410. #95C2×D9semidirect
606. C9#2418semidirect
721. C22#63456semidirect

Maximal subgroups

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

subgroupindex
C22×(C2×D9)⋊C42
C2×#634562
C2×#634442
C2×#611⋊C42
C9×#3802
#105888932
#105886732
#105886712
#105886702
#105886352
#105886262
#105883552
#105883522
#105883492
#105883452
#740213