Finite Group Databasebeta

← #11810277

Subgroups — #11810277

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×C4×D4×C9C211yesmaximal, characteristic, complemented
2C2×#63499C211yesmaximal, characteristic
3C2×#63491C211yesmaximal, characteristic, complemented
4C22×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
5#10588900C211yesmaximal, characteristic, complemented
6#10588893C211yesmaximal, characteristic, complemented
7#10588890C211yesmaximal, characteristic, complemented
8#10588673C211yesmaximal, characteristic, complemented
9#10588672C211yesmaximal, characteristic, complemented
10#10588639C211yesmaximal, characteristic, complemented
11#10588639C211yesmaximal, characteristic, complemented
12#10588635C211yesmaximal, characteristic, complemented
13#10588622C211yesmaximal, characteristic, complemented
14#10588620C211yesmaximal, characteristic, complemented
15#10588620C211yesmaximal, characteristic, complemented
16#82404—31nomaximal
17C24×D9C2211yescharacteristic
18C22×D4×C9C2211yescharacteristic
19C23×C4×C9C2211yescharacteristic
20C23×C4×C9C2211yescharacteristic, complemented
21C22×#611C2211yescharacteristic
22C22×#611C2211yescharacteristic
23C23×Dic9C2211yescharacteristic
24C4×D4×C9—24no—
25C2×C9×C4⋊C4C2211yescharacteristic, complemented
26C2×C9×C22⋊C4C2211yescharacteristic
27C2×C9×C22⋊C4C2211yescharacteristic, complemented
28C2×C42×C9C2211yescharacteristic, complemented
29C2×#3676C2211yescharacteristic
30C2×#3676C2211yescharacteristic
31C2×#3676C2211yescharacteristic, complemented
32C2×#3676C2211yescharacteristic, complemented
33#63499—24no—
34#63491—24no—
35C2×(C2×D9)⋊C4—24no—
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×(C2×D9)⋊C4C2211yescharacteristic
44C2×(C2×D9)⋊C4C2211yescharacteristic
45C2×(C2×D9)⋊C4C2211yescharacteristic
46C2×Dic9⋊C4C2211yescharacteristic, complemented
47C2×Dic9⋊C4C2211yescharacteristic, complemented
48C2×Dic9⋊C4C2211yescharacteristic, complemented
49C2×Dic9⋊C4C2211yescharacteristic, complemented
50C9⋊#95C2211yescharacteristic, complemented
51C9⋊#95C2211yescharacteristic, complemented
52C9⋊#95C2211yescharacteristic, complemented
53C9⋊#95C2211yescharacteristic, complemented
54C9⋊#95C2211yescharacteristic, complemented
55C9⋊#95C2211yescharacteristic, complemented
56C2×C3×C4×D4D311yescharacteristic
57C2×#937—31no—
58C2×#929—31no—
59C22×(C2×D3)⋊C4—31no—
60#5220—31no—
61#5213—31no—
62#5210—31no—
63#4993—31no—
64#4992—31no—
65#4959—31no—
66#4959—31no—
67#4955—31no—
68#4942—31no—
69#4940—31no—
70#4940—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—22no—
88C22×C4×C9—22no—
89C22×C4×C9—41no—
90C22×C4×C9—41no—
91C22×C4×C9C2311yescharacteristic
92C22×C4×C9C2311yescharacteristic
93C22×C4×C9C2311yescharacteristic
94C22×C4×C9C2311yescharacteristic
95C22×C4×C9C2311yescharacteristic
96C2×#611—22no—
97C2×#611—22no—
98C2×#611—22no—
99C2×#611—22no—
100C2×#611—41no—
101C2×#611—41no—
102C22×Dic9—22no—
103C22×Dic9—22no—
104C22×Dic9—41no—
105C22×Dic9C2311yescharacteristic
106C22×Dic9C2311yescharacteristic
107C22×Dic9C2311yescharacteristic
108C22×Dic9C2311yescharacteristic
109C22×Dic9C2311yescharacteristic
110C22×Dic9C2311yescharacteristic
111C9×C4⋊C4—22no—
112C9×C22⋊C4—22no—
113C9×C22⋊C4—22no—
114C42×C9—22no—
115#3676—22no—
116#3676—22no—
117#3676—22no—
118#3676—41no—
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—41no—
127(C2×D9)⋊C4—41no—
128(C2×D9)⋊C4D414yescomplemented
129Dic9⋊C4—22no—
130Dic9⋊C4—22no—
131Dic9⋊C4—41no—
132Dic9⋊C4—41no—
133#2418—91noSylow
134C24×D3—31no—
135C22×C3×D4C2×D311yescharacteristic
136C23×C3×C4C2×D311yescharacteristic
137C23×C3×C4C2×D311yescharacteristic
138C22×#67—31no—
139C22×#67—31no—
140C23×Dic3—31no—
141C3×C4×D4—24no—
142C2×C3×C4⋊C4C2×D311yescharacteristic
143C2×C3×C22⋊C4C2×D311yescharacteristic
144C2×C3×C22⋊C4C2×D311yescharacteristic
145C2×C3×C42C2×D311yescharacteristic
146C2×#217—31no—
147C2×#217—31no—
148C2×#217—31no—
149C2×#217—31no—
150#937—64no—
151#929—64no—
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×(C2×D3)⋊C4—31no—
161C2×(C2×D3)⋊C4—31no—
162C2×(C2×D3)⋊C4—64no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
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×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×C9—44no—
225C2×C4×C9C2×D412yes—
226C2×C4×C9C2×D412yes—
227#611—44no—
228#611—44no—
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—21no—
246C2×Dic9—44no—
247C2×Dic9C2×D412yes—
248C2×#123—91no—
249C2×#120—91no—
250C2×C4×D4D911yescharacteristic, complemented
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#6714yes—
277C22×C3×C4—22no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4—22no—
281C22×C3×C4—41no—
282C22×C3×C4—41no—
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C2×#67—62no—
289C2×#67—62no—
290C2×#67—62no—
291C2×#67—62no—
292C2×#67—121no—
293C2×#67—121no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—62no—
301C22×Dic3—62no—
302C22×Dic3—121no—
303C3×C4⋊C4—22no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—22no—
306C3×C42—22no—
307#217—62no—
308#217—62no—
309#217—62no—
310#217—121no—
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—121no—
320(C2×D3)⋊C4—121no—
321Dic3⋊C4—62no—
322Dic3⋊C4—62no—
323Dic3⋊C4—121no—
324Dic3⋊C4—121no—
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×C4C2×D911yescharacteristic
378C23×C4C2×D911yescharacteristic, complemented
379#123—184no—
380#120—184no—
381C4×D4—24no—
382C2×C4⋊C4—91no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C4⋊C4—91no—
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, complemented
404C2×C42C2×D911yescharacteristic, complemented
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#23512yes—
422C23×C3#23512yes—
423C23×C3C2×#6712yes—
424C23×C3C2×#6712yes—
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×C4—44no—
463C2×C3×C4D3×D412yes—
464C2×C3×C4C2×#6712yes—
465#67—124no—
466#67—124no—
467C2×Dic3—32no—
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—61no—
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×D4#61114yes—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—91no—
524C22×C4—91no—
525C22×C4—91no—
526C22×C4—91no—
527C22×C4—91no—
528C22×C4—91no—
529C22×C4—182no—
530C22×C4—182no—
531C22×C4—361no—
532C22×C4C22×D911yescharacteristic
533C22×C4C22×D911yescharacteristic
534C22×C4C22×D911yescharacteristic
535C22×C4C22×D911yescharacteristic
536C22×C4C22×D911yescharacteristic
537C4⋊C4—22no—
538C4⋊C4—182no—
539C4⋊C4—182no—
540C4⋊C4—361no—
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—22no—
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#92914yes—
573C22×C3C2×#23511yescharacteristic
574C22×C3C2×#23511yescharacteristic
575C22×C3C2×D3×D411yescharacteristic
576C22×C3#100411yescharacteristic
577C22×C3D3×#4111yescharacteristic
578C22×C3#100911yescharacteristic
579C22×C3C22×#6711yescharacteristic
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—
638C23#369712yes—
639C23#369712yes—
640C23C2×#61112yes—
641C23C2×#61112yes—
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—44no—
661C2×C4—92no—
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—181no—
679C2×C4—364no—
680C2×C4D4×D912yes—
681C2×C4C2×#61112yes—
682C2×C3—24no—
683C2×C3—42no—
684C2×C3#554711yescharacteristic
685C2×C3#555011yescharacteristic
686C2×C3#555611yescharacteristic
687C2×C3#556011yescharacteristic
688C2×C3C2×#92911yescharacteristic
689C2×C3D4×#6711yescharacteristic
690C2×C3#582911yescharacteristic
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#6349114yescomplemented
722C22C2×#369711yescharacteristic
723C22C2×#369711yescharacteristic
724C22C2×D4×D911yescharacteristic
725C22#6371011yescharacteristic
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#8240411yescharacteristic
741C2—24no—
742C2—42no—
743C2—362no—
744C2—362no—
745C2#1058964911yescharacteristic
746C2#1058965211yescharacteristic
747C2#1058965811yescharacteristic
748C2#1058966211yescharacteristic
749C2C2×#6349111yescharacteristic
750C2D4×#61111yescharacteristic
751C2#1058993111yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC2×C4×D4×C9C2
prime radicalC2×#63499C2
hypercenterC2×C4×D4D9
hypocenterC9#2418
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C4×D4×C9C2semidirect
3. C2×#63491C2semidirect
4. C22×(C2×D9)⋊C4C2semidirect
5. #10588900C2semidirect
6. #10588893C2semidirect
7. #10588890C2semidirect
8. #10588673C2semidirect
9. #10588672C2semidirect
10. #10588639C2semidirect
11. #10588639C2semidirect
12. #10588635C2semidirect
13. #10588622C2semidirect
14. #10588620C2semidirect
15. #10588620C2semidirect
20. C23×C4×C9C22semidirect
25. C2×C9×C4⋊C4C22semidirect
27. C2×C9×C22⋊C4C22semidirect
28. C2×C42×C9C22semidirect
31. C2×#3676C22semidirect
32. C2×#3676C22semidirect
46. C2×Dic9⋊C4C22semidirect
47. C2×Dic9⋊C4C22semidirect
48. C2×Dic9⋊C4C22semidirect
49. C2×Dic9⋊C4C22semidirect
50. C9⋊#95C22semidirect
51. C9⋊#95C22semidirect
52. C9⋊#95C22semidirect
53. C9⋊#95C22semidirect
54. C9⋊#95C22semidirect
55. C9⋊#95C22semidirect
128. (C2×D9)⋊C4D4semidirect
250. C2×C4×D4D9semidirect
338. C22×C9#123semidirect
378. C23×C4C2×D9semidirect
386. C2×C4⋊C4C2×D9semidirect
403. C2×C22⋊C4C2×D9semidirect
404. C2×C42C2×D9semidirect
606. C9#2418semidirect
721. C22#63491semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C92
C2×#634992
C2×#634912
C22×(C2×D9)⋊C42
#105889002
#105888932
#105888902
#105886732
#105886722
#105886392
#105886352
#105886222
#105886202
#824043