Finite Group Databasebeta

← #11803550

Subgroups — #11803550

Order 1152.

1002 conjugacy classes of subgroups.

The subgroup lattice has 675 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#611C211yesmaximal, characteristic, complemented
2C2×#63454C211yesmaximal, characteristic, complemented
3C2×#63446C211yesmaximal, characteristic
4C9×#385C211yesmaximal, characteristic, complemented
5#10588893C211yesmaximal, characteristic, complemented
6#10588669C211yesmaximal, characteristic, complemented
7#10588668C211yesmaximal, characteristic, complemented
8#10588656C211yesmaximal, characteristic, complemented
9#10588637C211yesmaximal, characteristic, complemented
10#10588637C211yesmaximal, characteristic, complemented
11#10588631C211yesmaximal, characteristic, complemented
12#10588350C211yesmaximal, characteristic, complemented
13#10588347C211yesmaximal, characteristic, complemented
14#10588345C211yesmaximal, characteristic, complemented
15#10588329C211yesmaximal, characteristic, complemented
16#74385—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
29C4×#611—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×C4⋊Dic9C2211yescharacteristic
39C2×Dic9⋊C4C2211yescharacteristic
40C2×Dic9⋊C4C2211yescharacteristic
41C2×Dic9⋊C4C2211yescharacteristic
42C2×Dic9⋊C4C2211yescharacteristic
43C2×C4×Dic9C2211yescharacteristic
44C2×C4×Dic9C2211yescharacteristic
45C2×C4×Dic9C2211yescharacteristic
46C2×C4×Dic9C2211yescharacteristic
47#63454—24no—
48#63446C418yescomplemented
49C9×#95C2211yescharacteristic
50C9×#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C9⋊#95C2211yescharacteristic
54C9⋊#95C2211yescharacteristic
55C2×C4×#67—31no—
56C2×#892—31no—
57C2×#884—31no—
58C3×#385D311yescharacteristic
59#5213—31no—
60#4989—31no—
61#4988—31no—
62#4976—31no—
63#4957—31no—
64#4957—31no—
65#4951—31no—
66#4670—31no—
67#4667—31no—
68#4665—31no—
69#4649—31no—
70C24×C9C2311yescharacteristic
71C23×D9C2311yescharacteristic
72C23×D9C2311yescharacteristic
73C22×C4×C9—22no—
74C22×C4×C9—41no—
75C22×C4×C9—41no—
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C22×C4×C9C2311yescharacteristic
79C22×C4×C9C2311yescharacteristic
80C22×C4×C9C2311yescharacteristic
81C22×C4×C9C2311yescharacteristic
82C2×#611—22no—
83C2×#611—22no—
84C2×#611—41no—
85C2×#611—41no—
86C2×#611C2×C414yes—
87C2×#611C2×C414yescomplemented
88C22×Dic9C2311yescharacteristic
89C22×Dic9C2311yescharacteristic
90C22×Dic9C2311yescharacteristic
91C22×Dic9C2311yescharacteristic
92C22×Dic9C2311yescharacteristic
93C22×Dic9C2311yescharacteristic
94C2×D36—41no—
95C2×D36—41no—
96C2×D36C2×C414yescomplemented
97C2×C4×D9—22no—
98C2×C4×D9—22no—
99C2×C4×D9—22no—
100C2×C4×D9—41no—
101C2×C4×D9—41no—
102C2×C4×D9C2×C414yescomplemented
103C9×C4⋊C4—22no—
104C9×C4⋊C4—41no—
105C9×C22⋊C4—41no—
106C9×C22⋊C4C2×C414yescomplemented
107#3676—22no—
108#3676—41no—
109(C2×D9)⋊C4—22no—
110(C2×D9)⋊C4—22no—
111(C2×D9)⋊C4—22no—
112(C2×D9)⋊C4—41no—
113(C2×D9)⋊C4—41no—
114(C2×D9)⋊C4—41no—
115(C2×D9)⋊C4—41no—
116(C2×D9)⋊C4C2×C414yescomplemented
117C4⋊Dic9—22no—
118Dic9⋊C4—22no—
119Dic9⋊C4—22no—
120Dic9⋊C4—41no—
121Dic9⋊C4C2×C414yescomplemented
122C4×Dic9—22no—
123C4×Dic9—41no—
124C4×Dic9—41no—
125C4×Dic9D414yescomplemented
126#2324—91noSylow
127C23×C3×C4C2×D311yescharacteristic
128C22×#67—31no—
129C22×#67—31no—
130C22×D12—31no—
131C22×C4×D3—31no—
132C22×C4×D3—31no—
133C2×C3×C4⋊C4C2×D311yescharacteristic
134C2×C3×C4⋊C4C2×D311yescharacteristic
135C2×C3×C22⋊C4C2×D311yescharacteristic
136C2×C3×C22⋊C4C2×D311yescharacteristic
137C2×#217—31no—
138C2×#217—31no—
139C4×#67—64no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—31no—
144C2×(C2×D3)⋊C4—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×C4⋊Dic3—31no—
149C2×Dic3⋊C4—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—31no—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—31no—
157#892—64no—
158#884—38no—
159C3×#95C2×D311yescharacteristic
160C3×#95C2×D311yescharacteristic
161C3⋊#95—31no—
162C3⋊#95—31no—
163C3⋊#95—31no—
164C3⋊#95—31no—
165C23×C9—21no—
166C23×C9—21no—
167C23×C9—21no—
168C23×C9—21no—
169C23×C9—21no—
170C23×C9—21no—
171C23×C9C22×C412yes—
172C23×C9C2411yescharacteristic
173C22×D9—21no—
174C22×D9—21no—
175C22×D9—21no—
176C22×D9—21no—
177C22×D9—21no—
178C22×D9—21no—
179C22×D9—21no—
180C22×D9—21no—
181C22×D9—21no—
182C22×D9—21no—
183C22×D9—21no—
184C22×D9—21no—
185C22×D9C22×C412yes—
186C22×D9C22×C412yes—
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—21no—
198C2×C4×C9—21no—
199C2×C4×C9—21no—
200C2×C4×C9—21no—
201C2×C4×C9—21no—
202C2×C4×C9—44no—
203C2×C4×C9C22×C412yes—
204C2×C4×C9C22×C412yes—
205C2×C4×C9C2×D412yes—
206#611—28no—
207#611—44no—
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×Dic9C22×C412yes—
222C2×Dic9C22×C412yes—
223C2×Dic9C2×D412yes—
224C2×Dic9C2×D412yes—
225C2×Dic9#4112yes—
226D36—44no—
227C4×D9—28no—
228C4×D9—44no—
229C2×#121—91no—
230C2×C4×D4—91no—
231C2×#117—91no—
232#390—91no—
233#390—91no—
234#390—91no—
235#389—91no—
236#388—91no—
237#388—91no—
238#386—91no—
239#386—91no—
240#385—91no—
241#385D911yescharacteristic, complemented
242#380—91no—
243C4×C4⋊C4—91no—
244C24×C3C22×D311yescharacteristic
245C23×D3—31no—
246C23×D3—31no—
247C22×C3×C4—22no—
248C22×C3×C4—41no—
249C22×C3×C4—41no—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C2×#67—34no—
257C2×#67—34no—
258C2×#67—62no—
259C2×#67—62no—
260C2×#67—121no—
261C2×#67—121no—
262C22×Dic3—31no—
263C22×Dic3—31no—
264C22×Dic3—31no—
265C22×Dic3—31no—
266C22×Dic3—31no—
267C22×Dic3—31no—
268C2×D12—34no—
269C2×D12—121no—
270C2×D12—121no—
271C2×C4×D3—34no—
272C2×C4×D3—62no—
273C2×C4×D3—62no—
274C2×C4×D3—62no—
275C2×C4×D3—121no—
276C2×C4×D3—121no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—41no—
279C3×C22⋊C4—41no—
280C3×C22⋊C4C4×D314yes—
281#217—62no—
282#217—121no—
283(C2×D3)⋊C4—34no—
284(C2×D3)⋊C4—62no—
285(C2×D3)⋊C4—62no—
286(C2×D3)⋊C4—62no—
287(C2×D3)⋊C4—121no—
288(C2×D3)⋊C4—121no—
289(C2×D3)⋊C4—121no—
290(C2×D3)⋊C4—121no—
291C4⋊Dic3—62no—
292Dic3⋊C4—34no—
293Dic3⋊C4—62no—
294Dic3⋊C4—62no—
295Dic3⋊C4—121no—
296C4×Dic3—34no—
297C4×Dic3—62no—
298C4×Dic3—121no—
299C4×Dic3—121no—
300C22×C9—22no—
301C22×C9—22no—
302C22×C9—22no—
303C22×C9—41no—
304C22×C9—41no—
305C22×C9—41no—
306C22×C9—41no—
307C22×C9C23×C411yescharacteristic
308C22×C9C22×D411yescharacteristic
309C22×C9C2×#4111yescharacteristic
310C22×C9H(5,𝔽2)11yescharacteristic
311C22×C9H(5,𝔽2)11yescharacteristic
312C22×C9H(5,𝔽2)11yescharacteristic
313C22×C92−1+411yescharacteristic
314C2×D9—22no—
315C2×D9—22no—
316C2×D9—22no—
317C2×D9—22no—
318C2×D9—22no—
319C2×D9—22no—
320C2×D9—41no—
321C2×D9—41no—
322C2×D9—41no—
323C2×D9—41no—
324C2×D9—41no—
325C2×D9—41no—
326C2×D9—41no—
327C2×D9—41no—
328C4×C9—22no—
329C4×C9—22no—
330C4×C9—22no—
331C4×C9—41no—
332C4×C9—41no—
333C4×C9—41no—
334Dic9—22no—
335Dic9—22no—
336Dic9—41no—
337Dic9—41no—
338Dic9—41no—
339Dic9C4×D414yes—
340C22×D4—91no—
341C22×D4—91no—
342C22×D4—91no—
343C23×C4—91no—
344C23×C4—91no—
345C23×C4C2×D911yescharacteristic
346#121—98no—
347C4×D4—184no—
348#117—184no—
349C2×C4⋊C4—91no—
350C2×C4⋊C4—91no—
351C2×C4⋊C4—91no—
352C2×C4⋊C4—91no—
353C2×C4⋊C4—91no—
354C2×C4⋊C4C2×D911yescharacteristic
355C2×C4⋊C4C2×D911yescharacteristic
356C2×C22⋊C4—91no—
357C2×C22⋊C4—91no—
358C2×C22⋊C4—91no—
359C2×C22⋊C4—91no—
360C2×C22⋊C4—91no—
361C2×C22⋊C4—91no—
362C2×C22⋊C4—91no—
363C2×C22⋊C4—91no—
364C2×C22⋊C4—91no—
365C2×C22⋊C4—91no—
366C2×C22⋊C4C2×D911yescharacteristic
367C2×C22⋊C4C2×D911yescharacteristic
368C2×C42—91no—
369C2×C42—91no—
370C2×C42—91no—
371C2×C42—91no—
372#95—91no—
373#95—91no—
374#95—91no—
375#95—91no—
376#95C2×D911yescharacteristic
377#95C2×D911yescharacteristic
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3C2×C4×D312yes—
385C23×C3C23×D311yescharacteristic
386C22×D3—32no—
387C22×D3—32no—
388C22×D3—61no—
389C22×D3—61no—
390C22×D3—61no—
391C22×D3—61no—
392C22×D3—61no—
393C22×D3—61no—
394C22×D3—61no—
395C22×D3—61no—
396C22×D3—61no—
397C22×D3—61no—
398C22×D3—61no—
399C22×D3—61no—
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—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—44no—
416C2×C3×C4C2×C4×D312yes—
417C2×C3×C4C2×C4×D312yes—
418C2×C3×C4D3×D412yes—
419#67—68no—
420#67—124no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—32no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—61no—
431C2×Dic3—61no—
432C2×Dic3—61no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—61no—
436C2×Dic3—61no—
437C2×Dic3—61no—
438C2×Dic3—61no—
439D12—124no—
440C4×D3—68no—
441C4×D3—124no—
442C2×C9—42no—
443C2×C9C2×C4×D411yescharacteristic
444C2×C9#51811yescharacteristic
445C2×C9#52011yescharacteristic
446C2×C9#53511yescharacteristic
447C2×C9#53711yescharacteristic
448C2×C9#54011yescharacteristic
449C2×C9#54211yescharacteristic
450D9—42no—
451D9—42no—
452C24—91no—
453C24—91no—
454C24C22×D911yescharacteristic
455C2×D4—94no—
456C2×D4—94no—
457C2×D4—94no—
458C2×D4—182no—
459C2×D4—182no—
460C2×D4—361no—
461C2×D4—361no—
462C2×D4—361no—
463C2×D4—361no—
464C22×C4—22no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—91no—
468C22×C4—91no—
469C22×C4—91no—
470C22×C4—94no—
471C22×C4—91no—
472C22×C4—91no—
473C22×C4—91no—
474C22×C4—182no—
475C22×C4—182no—
476C22×C4—182no—
477C22×C4—361no—
478C22×C4—361no—
479C22×C4C22×D911yescharacteristic
480C22×C4C22×D911yescharacteristic
481C22×C4C22×D911yescharacteristic
482C22×C4C22×D911yescharacteristic
483C22×C4C22×D911yescharacteristic
484C22×C4C22×D911yescharacteristic
485C4⋊C4—22no—
486C4⋊C4—41no—
487C4⋊C4—94no—
488C4⋊C4—182no—
489C4⋊C4—182no—
490C4⋊C4—182no—
491C4⋊C4—361no—
492C22⋊C4—41no—
493C22⋊C4—94no—
494C22⋊C4—182no—
495C22⋊C4—182no—
496C22⋊C4—182no—
497C22⋊C4—182no—
498C22⋊C4—361no—
499C22⋊C4—361no—
500C22⋊C4—361no—
501C22⋊C4—361no—
502C22⋊C4—361no—
503C22⋊C4C4×D914yescomplemented
504C42—94no—
505C42—182no—
506C42—361no—
507C42—361no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3C22×C4×D311yescharacteristic
516C22×C3C2×D3×D411yescharacteristic
517C22×C3#100411yescharacteristic
518C22×C3#100411yescharacteristic
519C22×C3#100711yescharacteristic
520C22×C3D3×#4111yescharacteristic
521C22×C3#100911yescharacteristic
522C2×D3—62no—
523C2×D3—62no—
524C2×D3—62no—
525C2×D3—62no—
526C2×D3—62no—
527C2×D3—62no—
528C2×D3—121no—
529C2×D3—121no—
530C2×D3—121no—
531C2×D3—121no—
532C2×D3—121no—
533C2×D3—121no—
534C2×D3—121no—
535C2×D3—121no—
536C3×C4—22no—
537C3×C4—22no—
538C3×C4—22no—
539C3×C4—41no—
540C3×C4—41no—
541C3×C4—41no—
542Dic3—34no—
543Dic3—62no—
544Dic3—62no—
545Dic3—121no—
546Dic3—121no—
547Dic3—121no—
548C9#232411yescharacteristic, complemented, Sylow
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—92no—
556C23—92no—
557C23—181no—
558C23—181no—
559C23—181no—
560C23—181no—
561C23—181no—
562C23—181no—
563C23—181no—
564C23—181no—
565C23—181no—
566C23—181no—
567C23—181no—
568C23—181no—
569C23C2×C4×D912yes—
570C23C23×D911yescharacteristic
571D4—188no—
572D4—364no—
573D4—364no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—44no—
590C2×C4—92no—
591C2×C4—92no—
592C2×C4—92no—
593C2×C4—92no—
594C2×C4—92no—
595C2×C4—188no—
596C2×C4—181no—
597C2×C4—181no—
598C2×C4—181no—
599C2×C4—181no—
600C2×C4—181no—
601C2×C4—181no—
602C2×C4—181no—
603C2×C4—181no—
604C2×C4—181no—
605C2×C4—181no—
606C2×C4—181no—
607C2×C4—181no—
608C2×C4—181no—
609C2×C4—364no—
610C2×C4C2×C4×D912yes—
611C2×C4C2×C4×D912yes—
612C2×C4D4×D912yes—
613C2×C3—42no—
614C2×C3#550411yescharacteristic
615C2×C3C4×D3×D411yescharacteristic
616C2×C3#554511yescharacteristic
617C2×C3#559211yescharacteristic
618C2×C3#562911yescharacteristic
619C2×C3#564011yescharacteristic
620C2×C3#566311yescharacteristic
621D3—122no—
622D3—122no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—182no—
631C22—182no—
632C22—182no—
633C22—182no—
634C22—182no—
635C22—182no—
636C22—361no—
637C22—361no—
638C22—361no—
639C22—361no—
640C22—361no—
641C22—361no—
642C22—361no—
643C22—361no—
644C22C22×C4×D911yescharacteristic
645C22C2×D4×D911yescharacteristic
646C22#6371011yescharacteristic
647C22#6371011yescharacteristic
648C22#6371311yescharacteristic
649C22#41×D911yescharacteristic
650C22#6371511yescharacteristic
651C4—22no—
652C4—22no—
653C4—22no—
654C4—41no—
655C4—41no—
656C4—41no—
657C4—94no—
658C4—182no—
659C4—182no—
660C4—361no—
661C4—361no—
662C4—361no—
663C3#7438511yescharacteristic
664C2—42no—
665C2—362no—
666C2—362no—
667C2#1058960611yescharacteristic
668C2C4×D4×D911yescharacteristic
669C2#1058964711yescharacteristic
670C2#1058969411yescharacteristic
671C2#1058973111yescharacteristic
672C2#1058974211yescharacteristic
673C2#1058976511yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#385C2
prime radicalC2×#63446C2
cosocleC23×C9C24
hypercenter#385D9
hypocenterC9#2324
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×C4×#611C2semidirect
2. C2×#63454C2semidirect
4. C9×#385C2semidirect
5. #10588893C2semidirect
6. #10588669C2semidirect
7. #10588668C2semidirect
8. #10588656C2semidirect
9. #10588637C2semidirect
10. #10588637C2semidirect
11. #10588631C2semidirect
12. #10588350C2semidirect
13. #10588347C2semidirect
14. #10588345C2semidirect
15. #10588329C2semidirect
48. #63446C4semidirect
87. C2×#611C2×C4semidirect
96. C2×D36C2×C4semidirect
102. C2×C4×D9C2×C4semidirect
106. C9×C22⋊C4C2×C4semidirect
116. (C2×D9)⋊C4C2×C4semidirect
121. Dic9⋊C4C2×C4semidirect
125. C4×Dic9D4semidirect
241. #385D9semidirect
503. C22⋊C4C4×D9semidirect
548. C9#2324semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6112
C2×#634542
C2×#634462
C9×#3852
#105888932
#105886692
#105886682
#105886562
#105886372
#105886312
#105883502
#105883472
#105883452
#105883292
#743853