Finite Group Databasebeta

← #11807716

Subgroups — #11807716

Order 1152.

864 conjugacy classes of subgroups.

The subgroup lattice has 657 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63446C211yesmaximal, characteristic
2C9×#385C211yesmaximal, characteristic, complemented
3#10588893C211yesmaximal, characteristic, complemented
4#10588893C211yesmaximal, characteristic, complemented
5#10588670C211yesmaximal, characteristic, complemented
6#10588668C211yesmaximal, characteristic, complemented
7#10588667C211yesmaximal, characteristic, complemented
8#10588658C211yesmaximal, characteristic, complemented
9#10588637C211yesmaximal, characteristic, complemented
10#10588636C211yesmaximal, characteristic, complemented
11#10588631C211yesmaximal, characteristic, complemented
12#10588348C211yesmaximal, characteristic, complemented
13#10588345C211yesmaximal, characteristic, complemented
14#10588344C211yesmaximal, characteristic, complemented
15#10588332C211yesmaximal, characteristic, complemented
16#74401—31nomaximal
17C23×C4×C9C2211yescharacteristic
18C22×#611C2211yescharacteristic
19C22×#611C2211yescharacteristic
20C22×D36C2211yescharacteristic
21C22×C4×D9C2211yescharacteristic
22C22×C4×D9C2211yescharacteristic
23C2×C9×C4⋊C4C2211yescharacteristic
24C2×C9×C4⋊C4C2211yescharacteristic
25C2×C9×C22⋊C4C2211yescharacteristic
26C2×C9×C22⋊C4C2211yescharacteristic
27C2×#3676C2211yescharacteristic
28C2×#3676C2211yescharacteristic
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×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42#63446C418yescomplemented
43C9×#95C2211yescharacteristic
44C9×#95C2211yescharacteristic
45C9⋊#95C2211yescharacteristic
46C9⋊#95C2211yescharacteristic
47C9⋊#95C2211yescharacteristic
48C9⋊#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C2×#884—31no—
54C3×#385D311yescharacteristic
55#5213—31no—
56#5213—31no—
57#4990—31no—
58#4988—31no—
59#4987—31no—
60#4978—31no—
61#4957—31no—
62#4956—31no—
63#4951—31no—
64#4668—31no—
65#4665—31no—
66#4664—31no—
67#4652—31no—
68C24×C9C2311yescharacteristic
69C23×D9C2311yescharacteristic
70C23×D9C2311yescharacteristic
71C22×C4×C9—41no—
72C22×C4×C9—41no—
73C22×C4×C9—41no—
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C22×C4×C9C2311yescharacteristic
79C22×C4×C9C2311yescharacteristic
80C2×#611—41no—
81C2×#611—41no—
82C2×#611—41no—
83C2×#611—41no—
84C2×#611C2×C414yes—
85C2×#611C2×C414yescomplemented
86C22×Dic9C2311yescharacteristic
87C22×Dic9C2311yescharacteristic
88C22×Dic9C2311yescharacteristic
89C22×Dic9C2311yescharacteristic
90C22×Dic9C2311yescharacteristic
91C22×Dic9C2311yescharacteristic
92C2×D36—41no—
93C2×D36—41no—
94C2×D36C2×C414yescomplemented
95C2×C4×D9—41no—
96C2×C4×D9—41no—
97C2×C4×D9—41no—
98C2×C4×D9—41no—
99C2×C4×D9—41no—
100C2×C4×D9C2×C414yescomplemented
101C9×C4⋊C4—41no—
102C9×C4⋊C4—41no—
103C9×C22⋊C4—41no—
104C9×C22⋊C4C2×C414yescomplemented
105#3676—41no—
106#3676—41no—
107(C2×D9)⋊C4—41no—
108(C2×D9)⋊C4—41no—
109(C2×D9)⋊C4—41no—
110(C2×D9)⋊C4—41no—
111(C2×D9)⋊C4—41no—
112(C2×D9)⋊C4—41no—
113(C2×D9)⋊C4—41no—
114(C2×D9)⋊C4C2×C414yescomplemented
115C4⋊Dic9—41no—
116Dic9⋊C4—41no—
117Dic9⋊C4C2×C414yescomplemented
118C4×Dic9—41no—
119C4×Dic9—41no—
120#2377—91noSylow
121C23×C3×C4C2×D311yescharacteristic
122C22×#67—31no—
123C22×#67—31no—
124C22×D12—31no—
125C22×C4×D3—31no—
126C22×C4×D3—31no—
127C2×C3×C4⋊C4C2×D311yescharacteristic
128C2×C3×C4⋊C4C2×D311yescharacteristic
129C2×C3×C22⋊C4C2×D311yescharacteristic
130C2×C3×C22⋊C4C2×D311yescharacteristic
131C2×#217—31no—
132C2×#217—31no—
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×C4⋊Dic3—31no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4—31no—
144C2×C4×Dic3—31no—
145C2×C4×Dic3—31no—
146#884—38no—
147C3×#95C2×D311yescharacteristic
148C3×#95C2×D311yescharacteristic
149C3⋊#95—31no—
150C3⋊#95—31no—
151C3⋊#95—31no—
152C3⋊#95—31no—
153C3⋊#95—31no—
154C3⋊#95—31no—
155C3⋊#95—31no—
156C3⋊#95—31no—
157C23×C9—21no—
158C23×C9—21no—
159C23×C9—21no—
160C23×C9—21no—
161C23×C9—21no—
162C23×C9—21no—
163C23×C9C22×C412yes—
164C23×C9C2411yescharacteristic
165C22×D9—21no—
166C22×D9—21no—
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×D9C22×C412yes—
178C22×D9C22×C412yes—
179C2×C4×C9—21no—
180C2×C4×C9—21no—
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—44no—
196C2×C4×C9C22×C412yes—
197C2×C4×C9C22×C412yes—
198#611—44no—
199#611—44no—
200C2×Dic9—21no—
201C2×Dic9—21no—
202C2×Dic9—21no—
203C2×Dic9—21no—
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×Dic9C22×C412yes—
217C2×Dic9C22×C412yes—
218D36—44no—
219C4×D9—44no—
220C4×D9—44no—
221C2×#121—91no—
222#390—91no—
223#390—91no—
224#388—91no—
225#388—91no—
226#387—91no—
227#387—91no—
228#386—91no—
229#386—91no—
230#386—91no—
231#386—91no—
232#385—91no—
233#385D911yescharacteristic, complemented
234#381—91no—
235#380—91no—
236C24×C3C22×D311yescharacteristic
237C23×D3—31no—
238C23×D3—31no—
239C22×C3×C4—41no—
240C22×C3×C4—41no—
241C22×C3×C4—41no—
242C22×C3×C4C22×D311yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C2×#67—34no—
249C2×#67—34no—
250C2×#67—121no—
251C2×#67—121no—
252C2×#67—121no—
253C2×#67—121no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C2×D12—34no—
261C2×D12—121no—
262C2×D12—121no—
263C2×C4×D3—34no—
264C2×C4×D3—121no—
265C2×C4×D3—121no—
266C2×C4×D3—121no—
267C2×C4×D3—121no—
268C2×C4×D3—121no—
269C3×C4⋊C4—41no—
270C3×C4⋊C4—41no—
271C3×C22⋊C4—41no—
272C3×C22⋊C4C4×D314yes—
273#217—121no—
274#217—121no—
275(C2×D3)⋊C4—34no—
276(C2×D3)⋊C4—121no—
277(C2×D3)⋊C4—121no—
278(C2×D3)⋊C4—121no—
279(C2×D3)⋊C4—121no—
280(C2×D3)⋊C4—121no—
281(C2×D3)⋊C4—121no—
282(C2×D3)⋊C4—121no—
283C4⋊Dic3—121no—
284Dic3⋊C4—34no—
285Dic3⋊C4—121no—
286C4×Dic3—121no—
287C4×Dic3—121no—
288C22×C9—22no—
289C22×C9—22no—
290C22×C9—22no—
291C22×C9—41no—
292C22×C9—41no—
293C22×C9—41no—
294C22×C9—41no—
295C22×C9C23×C411yescharacteristic
296C22×C9H(5,𝔽2)11yescharacteristic
297C22×C9H(5,𝔽2)11yescharacteristic
298C22×C9H(5,𝔽2)11yescharacteristic
299C22×C9H(5,𝔽2)11yescharacteristic
300C22×C9H(5,𝔽2)11yescharacteristic
301C22×C92−1+411yescharacteristic
302C2×D9—22no—
303C2×D9—22no—
304C2×D9—22no—
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—
316C4×C9—22no—
317C4×C9—22no—
318C4×C9—41no—
319C4×C9—41no—
320C4×C9—41no—
321C4×C9—41no—
322Dic9—22no—
323Dic9—22no—
324Dic9—41no—
325Dic9—41no—
326Dic9—41no—
327Dic9—41no—
328C22×D4—91no—
329C22×D4—91no—
330C22×D4—91no—
331C23×C4—91no—
332C23×C4—91no—
333C23×C4C2×D911yescharacteristic
334#121—98no—
335C2×C4⋊C4—91no—
336C2×C4⋊C4—91no—
337C2×C4⋊C4—91no—
338C2×C4⋊C4C2×D911yescharacteristic
339C2×C4⋊C4C2×D911yescharacteristic
340C2×C22⋊C4—91no—
341C2×C22⋊C4—91no—
342C2×C22⋊C4—91no—
343C2×C22⋊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⋊C4C2×D911yescharacteristic
351C2×C22⋊C4C2×D911yescharacteristic
352C2×C42—91no—
353C2×C42—91no—
354#95—91no—
355#95—91no—
356#95—91no—
357#95—91no—
358#95—91no—
359#95—91no—
360#95—91no—
361#95—91no—
362#95C2×D911yescharacteristic
363#95C2×D911yescharacteristic
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3C2×C4×D312yes—
371C23×C3C23×D311yescharacteristic
372C22×D3—32no—
373C22×D3—32no—
374C22×D3—61no—
375C22×D3—61no—
376C22×D3—61no—
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—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
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—44no—
403C2×C3×C4C2×C4×D312yes—
404C2×C3×C4C2×C4×D312yes—
405#67—124no—
406#67—124no—
407C2×Dic3—32no—
408C2×Dic3—32no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—61no—
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—
425D12—124no—
426C4×D3—124no—
427C4×D3—124no—
428C2×C9—42no—
429C2×C9#51811yescharacteristic
430C2×C9#51811yescharacteristic
431C2×C9#52011yescharacteristic
432C2×C9#56011yescharacteristic
433C2×C9#56011yescharacteristic
434C2×C9#56211yescharacteristic
435C2×C9#56211yescharacteristic
436D9—42no—
437D9—42no—
438C24—91no—
439C24—91no—
440C24C22×D911yescharacteristic
441C2×D4—94no—
442C2×D4—94no—
443C2×D4—94no—
444C2×D4—361no—
445C2×D4—361no—
446C2×D4—361no—
447C2×D4—361no—
448C2×D4—361no—
449C2×D4—361no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—91no—
454C22×C4—91no—
455C22×C4—94no—
456C22×C4—91no—
457C22×C4—91no—
458C22×C4—91no—
459C22×C4—91no—
460C22×C4—361no—
461C22×C4—361no—
462C22×C4—361no—
463C22×C4—361no—
464C22×C4—361no—
465C22×C4C22×D911yescharacteristic
466C22×C4C22×D911yescharacteristic
467C22×C4C22×D911yescharacteristic
468C22×C4C22×D911yescharacteristic
469C22×C4C22×D911yescharacteristic
470C22×C4C22×D911yescharacteristic
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—94no—
474C4⋊C4—361no—
475C4⋊C4—361no—
476C22⋊C4—41no—
477C22⋊C4—94no—
478C22⋊C4—361no—
479C22⋊C4—361no—
480C22⋊C4—361no—
481C22⋊C4—361no—
482C22⋊C4—361no—
483C22⋊C4—361no—
484C22⋊C4—361no—
485C22⋊C4—361no—
486C22⋊C4—361no—
487C22⋊C4C4×D914yescomplemented
488C42—361no—
489C42—361no—
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3C22×C4×D311yescharacteristic
498C22×C3#100411yescharacteristic
499C22×C3#100411yescharacteristic
500C22×C3#100411yescharacteristic
501C22×C3#100711yescharacteristic
502C22×C3#100911yescharacteristic
503C22×C3#100911yescharacteristic
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—62no—
510C2×D3—121no—
511C2×D3—121no—
512C2×D3—121no—
513C2×D3—121no—
514C2×D3—121no—
515C2×D3—121no—
516C2×D3—121no—
517C2×D3—121no—
518C3×C4—22no—
519C3×C4—22no—
520C3×C4—41no—
521C3×C4—41no—
522C3×C4—41no—
523C3×C4—41no—
524Dic3—62no—
525Dic3—62no—
526Dic3—121no—
527Dic3—121no—
528Dic3—121no—
529Dic3—121no—
530C9#237711yescharacteristic, complemented, Sylow
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—92no—
538C23—92no—
539C23—181no—
540C23—181no—
541C23—181no—
542C23—181no—
543C23—181no—
544C23—181no—
545C23—181no—
546C23—181no—
547C23—181no—
548C23—181no—
549C23—181no—
550C23—181no—
551C23C2×C4×D912yes—
552C23C23×D911yescharacteristic
553D4—364no—
554D4—364no—
555D4—364no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
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—44no—
573C2×C4—92no—
574C2×C4—92no—
575C2×C4—181no—
576C2×C4—181no—
577C2×C4—181no—
578C2×C4—181no—
579C2×C4—181no—
580C2×C4—181no—
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—364no—
592C2×C4—364no—
593C2×C4C2×C4×D912yes—
594C2×C4C2×C4×D912yes—
595C2×C3—42no—
596C2×C3#550411yescharacteristic
597C2×C3#554511yescharacteristic
598C2×C3#554511yescharacteristic
599C2×C3#559511yescharacteristic
600C2×C3#564711yescharacteristic
601C2×C3#564711yescharacteristic
602C2×C3#566611yescharacteristic
603D3—122no—
604D3—122no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—182no—
613C22—182no—
614C22—182no—
615C22—182no—
616C22—182no—
617C22—182no—
618C22—361no—
619C22—361no—
620C22—361no—
621C22—361no—
622C22—361no—
623C22—361no—
624C22—361no—
625C22—361no—
626C22C22×C4×D911yescharacteristic
627C22#6371011yescharacteristic
628C22#6371011yescharacteristic
629C22#6371011yescharacteristic
630C22#6371311yescharacteristic
631C22#6371511yescharacteristic
632C22#6371511yescharacteristic
633C4—22no—
634C4—22no—
635C4—41no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—182no—
640C4—182no—
641C4—361no—
642C4—361no—
643C4—361no—
644C4—361no—
645C3#7440111yescharacteristic
646C2—42no—
647C2—362no—
648C2—362no—
649C2#1058960611yescharacteristic
650C2#1058964711yescharacteristic
651C2#1058964711yescharacteristic
652C2#1058969711yescharacteristic
653C2#1058974911yescharacteristic
654C2#1058974911yescharacteristic
655C2#1058976811yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#385C2
prime radicalC2×#63446C2
cosocleC23×C9C24
hypercenter#385D9
hypocenterC9#2377
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C9×#385C2semidirect
3. #10588893C2semidirect
4. #10588893C2semidirect
5. #10588670C2semidirect
6. #10588668C2semidirect
7. #10588667C2semidirect
8. #10588658C2semidirect
9. #10588637C2semidirect
10. #10588636C2semidirect
11. #10588631C2semidirect
12. #10588348C2semidirect
13. #10588345C2semidirect
14. #10588344C2semidirect
15. #10588332C2semidirect
42. #63446C4semidirect
85. C2×#611C2×C4semidirect
94. C2×D36C2×C4semidirect
100. C2×C4×D9C2×C4semidirect
104. C9×C22⋊C4C2×C4semidirect
114. (C2×D9)⋊C4C2×C4semidirect
117. Dic9⋊C4C2×C4semidirect
233. #385D9semidirect
487. C22⋊C4C4×D9semidirect
530. C9#2377semidirect

Maximal subgroups

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

subgroupindex
C2×#634462
C9×#3852
#105888932
#105886702
#105886682
#105886672
#105886582
#105886372
#105886362
#105886312
#105883482
#105883452
#105883442
#105883322
#744013