Finite Group Databasebeta

← #11812963

Subgroups — #11812963

Order 1152.

915 conjugacy classes of subgroups.

The subgroup lattice has 663 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63492C211yesmaximal, characteristic
2C2×C4×#611C211yesmaximal, characteristic, complemented
3C2×C9×#95C211yesmaximal, characteristic, complemented
4#10588893C211yesmaximal, characteristic, complemented
5#10588893C211yesmaximal, characteristic, complemented
6#10588893C211yesmaximal, characteristic, complemented
7#10588890C211yesmaximal, characteristic, complemented
8#10588355C211yesmaximal, characteristic, complemented
9#10588355C211yesmaximal, characteristic, complemented
10#10588352C211yesmaximal, characteristic, complemented
11#10588349C211yesmaximal, characteristic, complemented
12#10588345C211yesmaximal, characteristic, complemented
13#10588344C211yesmaximal, characteristic, complemented
14#10588340C211yesmaximal, characteristic, complemented
15#10588335C211yesmaximal, characteristic, complemented
16#73377—31nomaximal
17C23×C4×C9C2211yescharacteristic
18C23×C4×C9C2211yescharacteristic
19C23×C4×C9C2211yescharacteristic
20C22×#611C2211yescharacteristic
21C22×#611C2211yescharacteristic
22C22×D36C2211yescharacteristic
23C22×C4×D9C2211yescharacteristic
24C2×#3676C2211yescharacteristic
25C2×#3676C2211yescharacteristic
26#63492—24no—
27C4×#611—24no—
28C2×(C2×D9)⋊C4C2211yescharacteristic
29C2×(C2×D9)⋊C4C2211yescharacteristic
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×C4⋊Dic9C2211yescharacteristic
38C2×Dic9⋊C4C2211yescharacteristic
39C2×Dic9⋊C4C2211yescharacteristic
40C2×Dic9⋊C4C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42C9×#95C2211yescharacteristic
43C9×#95C2211yescharacteristic
44C9×#95C2211yescharacteristic
45C9×#95C2211yescharacteristic
46C9⋊#95C2211yescharacteristic
47C9⋊#95C2211yescharacteristic
48C9⋊#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C9⋊#95C2211yescharacteristic
54C2×#930—31no—
55C2×C4×#67—31no—
56C2×C3×#95D311yescharacteristic
57#5213—31no—
58#5213—31no—
59#5213—31no—
60#5210—31no—
61#4675—31no—
62#4675—31no—
63#4672—31no—
64#4669—31no—
65#4665—31no—
66#4664—31no—
67#4660—31no—
68#4655—31no—
69C24×C9C2311yescharacteristic
70C23×D9C2311yescharacteristic
71C23×D9C2311yescharacteristic
72C22×C4×C9—22no—
73C22×C4×C9—22no—
74C22×C4×C9—22no—
75C22×C4×C9—22no—
76C22×C4×C9—22no—
77C22×C4×C9—41no—
78C22×C4×C9—41no—
79C22×C4×C9—41no—
80C22×C4×C9—41no—
81C22×C4×C9C2311yescharacteristic
82C22×C4×C9C2311yescharacteristic
83C22×C4×C9C2311yescharacteristic
84C22×C4×C9C2311yescharacteristic
85C22×C4×C9C2311yescharacteristic
86C22×C4×C9C2311yescharacteristic
87C2×#611—22no—
88C2×#611—22no—
89C2×#611—22no—
90C2×#611—22no—
91C2×#611—22no—
92C2×#611D414yes—
93C22×Dic9C2311yescharacteristic
94C22×Dic9C2311yescharacteristic
95C22×Dic9C2311yescharacteristic
96C22×Dic9C2311yescharacteristic
97C22×Dic9C2311yescharacteristic
98C22×Dic9C2311yescharacteristic
99C2×D36—22no—
100C2×D36—22no—
101C2×D36—41no—
102C2×C4×D9—22no—
103C2×C4×D9—22no—
104C2×C4×D9—41no—
105#3676—22no—
106#3676—22no—
107(C2×D9)⋊C4—22no—
108(C2×D9)⋊C4—22no—
109(C2×D9)⋊C4—22no—
110(C2×D9)⋊C4—22no—
111(C2×D9)⋊C4—41no—
112(C2×D9)⋊C4—41no—
113(C2×D9)⋊C4—41no—
114(C2×D9)⋊C4—41no—
115(C2×D9)⋊C4—41no—
116C4⋊Dic9—22no—
117Dic9⋊C4—22no—
118Dic9⋊C4—22no—
119Dic9⋊C4—41no—
120C4×Dic9—22no—
121#2444—91noSylow
122C23×C3×C4C2×D311yescharacteristic
123C23×C3×C4C2×D311yescharacteristic
124C23×C3×C4C2×D311yescharacteristic
125C22×#67—31no—
126C22×#67—31no—
127C22×D12—31no—
128C22×C4×D3—31no—
129C2×#217—31no—
130C2×#217—31no—
131#930—64no—
132C4×#67—64no—
133C2×(C2×D3)⋊C4—31no—
134C2×(C2×D3)⋊C4—31no—
135C2×(C2×D3)⋊C4—31no—
136C2×(C2×D3)⋊C4—31no—
137C2×(C2×D3)⋊C4—31no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—31no—
142C2×C4⋊Dic3—31no—
143C2×Dic3⋊C4—31no—
144C2×Dic3⋊C4—31no—
145C2×Dic3⋊C4—31no—
146C2×C4×Dic3—31no—
147C3×#95C2×D311yescharacteristic
148C3×#95C2×D311yescharacteristic
149C3×#95C2×D311yescharacteristic
150C3×#95C2×D311yescharacteristic
151C3⋊#95—31no—
152C3⋊#95—31no—
153C3⋊#95—31no—
154C3⋊#95—31no—
155C3⋊#95—31no—
156C3⋊#95—31no—
157C3⋊#95—31no—
158C3⋊#95—31no—
159C23×C9—21no—
160C23×C9—21no—
161C23×C9—21no—
162C23×C9—21no—
163C23×C9C2×D412yes—
164C23×C9#4112yes—
165C23×C9#4112yes—
166C23×C9C2411yescharacteristic
167C22×D9—21no—
168C22×D9—21no—
169C22×D9—21no—
170C22×D9—21no—
171C22×D9—21no—
172C22×D9—21no—
173C22×D9—21no—
174C22×D9—21no—
175C22×D9—21no—
176C22×D9—21no—
177C22×D9—21no—
178C22×D9—21no—
179C22×D9—21no—
180C22×D9C2×D412yes—
181C2×C4×C9—21no—
182C2×C4×C9—21no—
183C2×C4×C9—21no—
184C2×C4×C9—21no—
185C2×C4×C9—21no—
186C2×C4×C9—21no—
187C2×C4×C9—21no—
188C2×C4×C9—21no—
189C2×C4×C9—21no—
190C2×C4×C9—21no—
191C2×C4×C9—21no—
192C2×C4×C9—21no—
193C2×C4×C9—21no—
194C2×C4×C9—21no—
195C2×C4×C9—21no—
196C2×C4×C9—21no—
197C2×C4×C9—44no—
198C2×C4×C9—44no—
199C2×C4×C9—44no—
200C2×C4×C9#4112yes—
201C2×C4×C9#4112yes—
202#611—28no—
203#611—44no—
204C2×Dic9—21no—
205C2×Dic9—21no—
206C2×Dic9—21no—
207C2×Dic9—21no—
208C2×Dic9—21no—
209C2×Dic9—21no—
210C2×Dic9—21no—
211C2×Dic9—21no—
212C2×Dic9—21no—
213C2×Dic9—21no—
214C2×Dic9—21no—
215C2×Dic9—21no—
216C2×Dic9—21no—
217C2×Dic9—21no—
218C2×Dic9—21no—
219C2×Dic9—21no—
220C2×Dic9—21no—
221C2×Dic9C2×D412yes—
222D36—44no—
223C4×D9—44no—
224C2×#121—91no—
225C2×C4×D4—91no—
226#400—91no—
227#397—91no—
228#397—91no—
229#394—91no—
230#388—91no—
231#387—91no—
232#386—91no—
233#386—91no—
234#386—91no—
235#386—91no—
236#385—91no—
237#381—91no—
238C2×#95D911yescharacteristic, complemented
239C24×C3C22×D311yescharacteristic
240C23×D3—31no—
241C23×D3—31no—
242C22×C3×C4—22no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—41no—
248C22×C3×C4—41no—
249C22×C3×C4—41no—
250C22×C3×C4—41no—
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C22×C3×C4C22×D311yescharacteristic
257C2×#67—34no—
258C2×#67—62no—
259C2×#67—62no—
260C2×#67—62no—
261C2×#67—62no—
262C2×#67—62no—
263C22×Dic3—31no—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C22×Dic3—31no—
269C2×D12—62no—
270C2×D12—62no—
271C2×D12—121no—
272C2×C4×D3—62no—
273C2×C4×D3—62no—
274C2×C4×D3—121no—
275#217—62no—
276#217—62no—
277(C2×D3)⋊C4—62no—
278(C2×D3)⋊C4—62no—
279(C2×D3)⋊C4—62no—
280(C2×D3)⋊C4—62no—
281(C2×D3)⋊C4—121no—
282(C2×D3)⋊C4—121no—
283(C2×D3)⋊C4—121no—
284(C2×D3)⋊C4—121no—
285(C2×D3)⋊C4—121no—
286C4⋊Dic3—62no—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289Dic3⋊C4—121no—
290C4×Dic3—62no—
291C22×C9—22no—
292C22×C9—22no—
293C22×C9—22no—
294C22×C9—22no—
295C22×C9—22no—
296C22×C9—22no—
297C22×C9#12314yes—
298C22×C9C22×D411yescharacteristic
299C22×C9C2×#4111yescharacteristic
300C22×C9C2×#4111yescharacteristic
301C22×C9C2×#4111yescharacteristic
302C22×C9C2×#4111yescharacteristic
303C22×C9H(5,𝔽2)11yescharacteristic
304C22×C9H(5,𝔽2)11yescharacteristic
305C2×D9—22no—
306C2×D9—22no—
307C2×D9—22no—
308C2×D9—41no—
309C2×D9—41no—
310C2×D9—41no—
311C2×D9—41no—
312C2×D9—41no—
313C2×D9—41no—
314C2×D9—41no—
315C2×D9—41no—
316C2×D9—41no—
317C2×D9—41no—
318C2×D9—41no—
319C4×C9—22no—
320C4×C9—22no—
321C4×C9—41no—
322C4×C9—41no—
323C4×C9—41no—
324C4×C9—41no—
325Dic9—22no—
326Dic9—41no—
327Dic9—41no—
328Dic9—41no—
329Dic9—41no—
330Dic9—41no—
331C22×D4—91no—
332C22×D4—91no—
333C22×D4—91no—
334C23×C4—91no—
335C23×C4C2×D911yescharacteristic
336C23×C4C2×D911yescharacteristic
337C23×C4C2×D911yescharacteristic
338#121—184no—
339C4×D4—184no—
340C2×C4⋊C4—91no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—91no—
343C2×C4⋊C4—91no—
344C2×C22⋊C4—91no—
345C2×C22⋊C4—91no—
346C2×C22⋊C4—91no—
347C2×C22⋊C4—91no—
348C2×C22⋊C4—91no—
349C2×C22⋊C4—91no—
350C2×C22⋊C4—91no—
351C2×C22⋊C4—91no—
352C2×C22⋊C4—91no—
353C2×C22⋊C4—91no—
354C2×C22⋊C4—91no—
355C2×C42—91no—
356#95—91no—
357#95—91no—
358#95—91no—
359#95—91no—
360#95—91no—
361#95—91no—
362#95—91no—
363#95—91no—
364#95C2×D911yescharacteristic
365#95C2×D911yescharacteristic
366#95C2×D911yescharacteristic
367#95C2×D911yescharacteristic
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3#23512yes—
373C23×C3D3×D412yes—
374C23×C3#23912yes—
375C23×C3C23×D311yescharacteristic
376C22×D3—32no—
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—61no—
380C22×D3—61no—
381C22×D3—61no—
382C22×D3—61no—
383C22×D3—61no—
384C22×D3—61no—
385C22×D3—61no—
386C22×D3—61no—
387C22×D3—61no—
388C22×D3—61no—
389C22×D3—61no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—44no—
407C2×C3×C4—44no—
408C2×C3×C4—44no—
409C2×C3×C4#23512yes—
410C2×C3×C4#23512yes—
411#67—68no—
412#67—124no—
413C2×Dic3—32no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423C2×Dic3—61no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—61no—
431D12—124no—
432C4×D3—124no—
433C2×C9—24no—
434C2×C9C2×#12311yescharacteristic
435C2×C9#52911yescharacteristic
436C2×C9#53811yescharacteristic
437C2×C9#54611yescharacteristic
438C2×C9#54611yescharacteristic
439C2×C9#55311yescharacteristic
440C2×C9#55311yescharacteristic
441D9—42no—
442D9—81no—
443C24—91no—
444C24—91no—
445C24C22×D911yescharacteristic
446C2×D4—94no—
447C2×D4—182no—
448C2×D4—182no—
449C2×D4—182no—
450C2×D4—182no—
451C2×D4—182no—
452C2×D4—182no—
453C2×D4—182no—
454C2×D4—361no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—91no—
465C22×C4—91no—
466C22×C4—91no—
467C22×C4—91no—
468C22×C4—91no—
469C22×C4—91no—
470C22×C4—182no—
471C22×C4—182no—
472C22×C4—361no—
473C22×C4C22×D911yescharacteristic
474C22×C4C22×D911yescharacteristic
475C22×C4C22×D911yescharacteristic
476C22×C4C22×D911yescharacteristic
477C22×C4C22×D911yescharacteristic
478C22×C4C22×D911yescharacteristic
479C4⋊C4—182no—
480C4⋊C4—182no—
481C4⋊C4—182no—
482C4⋊C4—361no—
483C22⋊C4—182no—
484C22⋊C4—182no—
485C22⋊C4—182no—
486C22⋊C4—182no—
487C22⋊C4—182no—
488C22⋊C4—182no—
489C22⋊C4—361no—
490C22⋊C4—361no—
491C22⋊C4—361no—
492C22⋊C4—361no—
493C22⋊C4—361no—
494C42—182no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3#89414yes—
502C22×C3C2×#23511yescharacteristic
503C22×C3C2×#23511yescharacteristic
504C22×C3C2×#23511yescharacteristic
505C22×C3C2×D3×D411yescharacteristic
506C22×C3#100411yescharacteristic
507C22×C3#100411yescharacteristic
508C22×C3C2×#23911yescharacteristic
509C2×D3—62no—
510C2×D3—62no—
511C2×D3—62no—
512C2×D3—121no—
513C2×D3—121no—
514C2×D3—121no—
515C2×D3—121no—
516C2×D3—121no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C2×D3—121no—
522C2×D3—121no—
523C3×C4—22no—
524C3×C4—22no—
525C3×C4—41no—
526C3×C4—41no—
527C3×C4—41no—
528C3×C4—41no—
529Dic3—62no—
530Dic3—121no—
531Dic3—121no—
532Dic3—121no—
533Dic3—121no—
534Dic3—121no—
535C9#244411yescharacteristic, complemented, Sylow
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—92no—
541C23—181no—
542C23—181no—
543C23—181no—
544C23—181no—
545C23—181no—
546C23—181no—
547C23—181no—
548C23—181no—
549C23—181no—
550C23—181no—
551C23—181no—
552C23—181no—
553C23—181no—
554C23#369712yes—
555C23D4×D912yes—
556C23#370112yes—
557C23C23×D911yescharacteristic
558D4—188no—
559D4—364no—
560D4—364no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—92no—
581C2×C4—181no—
582C2×C4—181no—
583C2×C4—181no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—181no—
587C2×C4—181no—
588C2×C4—181no—
589C2×C4—181no—
590C2×C4—181no—
591C2×C4—181no—
592C2×C4—181no—
593C2×C4—181no—
594C2×C4—181no—
595C2×C4—181no—
596C2×C4—181no—
597C2×C4—181no—
598C2×C4—364no—
599C2×C4#369712yes—
600C2×C4#369712yes—
601C2×C3—24no—
602C2×C3#547911yescharacteristic
603C2×C3#549011yescharacteristic
604C2×C3#549011yescharacteristic
605C2×C3#549411yescharacteristic
606C2×C3C2×#89411yescharacteristic
607C2×C3#551411yescharacteristic
608C2×C3#551411yescharacteristic
609D3—122no—
610D3—241no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—182no—
618C22—182no—
619C22—182no—
620C22—361no—
621C22—361no—
622C22—361no—
623C22—361no—
624C22—361no—
625C22—361no—
626C22—361no—
627C22—361no—
628C22—361no—
629C22—361no—
630C22—361no—
631C22#6345614yes—
632C22C2×#369711yescharacteristic
633C22C2×#369711yescharacteristic
634C22C2×#369711yescharacteristic
635C22C2×D4×D911yescharacteristic
636C22#6371011yescharacteristic
637C22#6371011yescharacteristic
638C22C2×#370111yescharacteristic
639C4—22no—
640C4—22no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—41no—
645C4—182no—
646C4—361no—
647C4—361no—
648C4—361no—
649C4—361no—
650C4—361no—
651C3#7337711yescharacteristic
652C2—24no—
653C2—362no—
654C2—721no—
655C2#1058958111yescharacteristic
656C2#1058959211yescharacteristic
657C2#1058959211yescharacteristic
658C2#1058959611yescharacteristic
659C2C2×#6345611yescharacteristic
660C2#1058961611yescharacteristic
661C2#1058961611yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC2×C9×#95C2
prime radicalC2×#63492C2
hypercenterC2×#95D9
hypocenterC9#2444
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
2. C2×C4×#611C2semidirect
3. C2×C9×#95C2semidirect
4. #10588893C2semidirect
5. #10588893C2semidirect
6. #10588893C2semidirect
7. #10588890C2semidirect
8. #10588355C2semidirect
9. #10588355C2semidirect
10. #10588352C2semidirect
11. #10588349C2semidirect
12. #10588345C2semidirect
13. #10588344C2semidirect
14. #10588340C2semidirect
15. #10588335C2semidirect
238. C2×#95D9semidirect
535. C9#2444semidirect

Maximal subgroups

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

subgroupindex
C2×#634922
C2×C4×#6112
C2×C9×#952
#105888932
#105888902
#105883552
#105883522
#105883492
#105883452
#105883442
#105883402
#105883352
#733773