Finite Group Databasebeta

← #11803635

Subgroups — #11803635

Order 1152.

1044 conjugacy classes of subgroups.

The subgroup lattice has 681 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×C9C211yesmaximal, characteristic, complemented
2C2×#63501C211yesmaximal, characteristic
3C2×C4×#611C211yesmaximal, characteristic, complemented
4#10588900C211yesmaximal, characteristic, complemented
5#10588893C211yesmaximal, characteristic, complemented
6#10588890C211yesmaximal, characteristic, complemented
7C2×C9⋊#95C211yesmaximal, characteristic, complemented
8#10588669C211yesmaximal, characteristic, complemented
9#10588658C211yesmaximal, characteristic, complemented
10#10588638C211yesmaximal, characteristic, complemented
11#10588636C211yesmaximal, characteristic, complemented
12#10588624C211yesmaximal, characteristic, complemented
13#10588622C211yesmaximal, characteristic, complemented
14#10588620C211yesmaximal, characteristic, complemented
15#10588613C211yesmaximal, characteristic, complemented
16#82327—31nomaximal
17C22×D4×C9C2211yescharacteristic
18C23×C4×C9C2211yescharacteristic
19C23×C4×C9C2211yescharacteristic
20C22×#611C2211yescharacteristic
21C22×#611C2211yescharacteristic
22C23×Dic9C2211yescharacteristic
23C23×Dic9C2211yescharacteristic
24C22×C4×D9C2211yescharacteristic
25C4×D4×C9—24no—
26C2×C9×C4⋊C4C2211yescharacteristic
27C2×C9×C22⋊C4C2211yescharacteristic
28C2×C9×C22⋊C4C2211yescharacteristic
29C2×C42×C9C2211yescharacteristic
30C2×#3676C2211yescharacteristic
31C2×#3676C2211yescharacteristic
32C2×#3676C2211yescharacteristic
33C2×#3676C2211yescharacteristic
34#63501C418yescomplemented
35C4×#611—24no—
36C2×(C2×D9)⋊C4C2211yescharacteristic
37C2×(C2×D9)⋊C4C2211yescharacteristic
38C2×(C2×D9)⋊C4C2211yescharacteristic
39C2×(C2×D9)⋊C4C2211yescharacteristic
40C2×Dic9⋊C4C2211yescharacteristic
41C2×Dic9⋊C4C2211yescharacteristic
42C2×Dic9⋊C4C2211yescharacteristic
43C2×Dic9⋊C4C2211yescharacteristic
44C2×C4×Dic9C2211yescharacteristic
45C9⋊#95C2211yescharacteristic
46C9⋊#95C2211yescharacteristic
47C9⋊#95C2211yescharacteristic
48C9⋊#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C9⋊#95C2211yescharacteristic
54C9⋊#95C2211yescharacteristic
55C2×C3×C4×D4D311yescharacteristic
56C2×#939—31no—
57C2×C4×#67—31no—
58#5220—31no—
59#5213—31no—
60#5210—31no—
61C2×C3⋊#95—31no—
62#4989—31no—
63#4978—31no—
64#4958—31no—
65#4956—31no—
66#4944—31no—
67#4942—31no—
68#4940—31no—
69#4933—31no—
70C24×C9C2311yescharacteristic
71C24×C9C2311yescharacteristic
72C23×D9C2311yescharacteristic
73C2×D4×C9—22no—
74C2×D4×C9—22no—
75C2×D4×C9C2×C414yescomplemented
76C22×C4×C9—22no—
77C22×C4×C9—41no—
78C22×C4×C9—41no—
79C22×C4×C9—41no—
80C22×C4×C9—41no—
81C22×C4×C9D414yescomplemented
82C22×C4×C9C2311yescharacteristic
83C22×C4×C9C2311yescharacteristic
84C22×C4×C9C2311yescharacteristic
85C22×C4×C9C2311yescharacteristic
86C22×C4×C9C2311yescharacteristic
87C2×#611—22no—
88C2×#611—22no—
89C2×#611—41no—
90C2×#611—41no—
91C2×#611C2×C414yescomplemented
92C2×#611C2×C414yescomplemented
93C22×Dic9—22no—
94C22×Dic9—41no—
95C22×Dic9—41no—
96C22×Dic9—41no—
97C22×Dic9—41no—
98C22×Dic9C2×C414yescomplemented
99C22×Dic9C2311yescharacteristic
100C22×Dic9C2311yescharacteristic
101C22×Dic9C2311yescharacteristic
102C22×Dic9C2311yescharacteristic
103C22×Dic9C2311yescharacteristic
104C22×Dic9C2311yescharacteristic
105C22×Dic9C2311yescharacteristic
106C2×C4×D9—22no—
107C2×C4×D9—41no—
108C2×C4×D9—41no—
109C9×C4⋊C4—22no—
110C9×C22⋊C4—22no—
111C9×C22⋊C4—22no—
112C42×C9—22no—
113#3676—22no—
114#3676—41no—
115#3676—41no—
116#3676C2×C414yescomplemented
117(C2×D9)⋊C4—22no—
118(C2×D9)⋊C4—41no—
119(C2×D9)⋊C4—41no—
120(C2×D9)⋊C4C2×C414yescomplemented
121Dic9⋊C4—22no—
122Dic9⋊C4—41no—
123Dic9⋊C4—41no—
124Dic9⋊C4C2×C414yescomplemented
125C4×Dic9—22no—
126#2325—91noSylow
127C22×C3×D4C2×D311yescharacteristic
128C23×C3×C4C2×D311yescharacteristic
129C23×C3×C4C2×D311yescharacteristic
130C22×#67—31no—
131C22×#67—31no—
132C23×Dic3—31no—
133C23×Dic3—31no—
134C22×C4×D3—31no—
135C3×C4×D4—24no—
136C2×C3×C4⋊C4C2×D311yescharacteristic
137C2×C3×C22⋊C4C2×D311yescharacteristic
138C2×C3×C22⋊C4C2×D311yescharacteristic
139C2×C3×C42C2×D311yescharacteristic
140C2×#217—31no—
141C2×#217—31no—
142C2×#217—31no—
143C2×#217—31no—
144#939—38no—
145C4×#67—64no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—31no—
154C2×C4×Dic3—31no—
155C3⋊#95—31no—
156C3⋊#95—31no—
157C3⋊#95—31no—
158C3⋊#95—31no—
159C3⋊#95—31no—
160C3⋊#95—31no—
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×C9—21no—
172C23×C9—21no—
173C23×C9—21no—
174C23×C9—21no—
175C23×C9C22×C412yes—
176C23×C9C22×C412yes—
177C23×C9C2×D412yes—
178C23×C9#4112yes—
179C23×C9C2411yescharacteristic
180C22×D9—21no—
181C22×D9—21no—
182C22×D9—21no—
183C22×D9—21no—
184C22×D9—21no—
185C22×D9—21no—
186C22×D9C22×C412yes—
187D4×C9—28no—
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—44no—
201C2×C4×C9—44no—
202C2×C4×C9C22×C412yes—
203C2×C4×C9C2×D412yes—
204C2×C4×C9C2×D412yes—
205#611—28no—
206#611—44no—
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×Dic9—21no—
222C2×Dic9—21no—
223C2×Dic9—21no—
224C2×Dic9—21no—
225C2×Dic9—44no—
226C2×Dic9—44no—
227C2×Dic9C22×C412yes—
228C2×Dic9C22×C412yes—
229C2×Dic9C22×C412yes—
230C4×D9—44no—
231C2×#121—91no—
232C2×C4×D4—91no—
233C2×C4×D4D911yescharacteristic, complemented
234#388—91no—
235#388—91no—
236#387—91no—
237#387—91no—
238#386—91no—
239#386—91no—
240#386—91no—
241#386—91no—
242#385—91no—
243#385—91no—
244#380—91no—
245C2×#95—91no—
246C24×C3C22×D311yescharacteristic
247C24×C3C22×D311yescharacteristic
248C23×D3—31no—
249C2×C3×D4—22no—
250C2×C3×D4—22no—
251C2×C3×D4C4×D314yes—
252C22×C3×C4—22no—
253C22×C3×C4—41no—
254C22×C3×C4—41no—
255C22×C3×C4—41no—
256C22×C3×C4—41no—
257C22×C3×C4#6714yes—
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D311yescharacteristic
260C22×C3×C4C22×D311yescharacteristic
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C22×D311yescharacteristic
263C2×#67—34no—
264C2×#67—34no—
265C2×#67—62no—
266C2×#67—62no—
267C2×#67—121no—
268C2×#67—121no—
269C22×Dic3—31no—
270C22×Dic3—31no—
271C22×Dic3—31no—
272C22×Dic3—34no—
273C22×Dic3—31no—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—62no—
278C22×Dic3—121no—
279C22×Dic3—121no—
280C22×Dic3—121no—
281C22×Dic3—121no—
282C2×C4×D3—62no—
283C2×C4×D3—121no—
284C2×C4×D3—121no—
285C3×C4⋊C4—22no—
286C3×C22⋊C4—22no—
287C3×C22⋊C4—22no—
288C3×C42—22no—
289#217—34no—
290#217—62no—
291#217—121no—
292#217—121no—
293(C2×D3)⋊C4—34no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—121no—
296(C2×D3)⋊C4—121no—
297Dic3⋊C4—34no—
298Dic3⋊C4—62no—
299Dic3⋊C4—121no—
300Dic3⋊C4—121no—
301C4×Dic3—62no—
302C22×C9—22no—
303C22×C9—22no—
304C22×C9—22no—
305C22×C9—22no—
306C22×C9—22no—
307C22×C9—22no—
308C22×C9—22no—
309C22×C9—22no—
310C22×C9—22no—
311C22×C9—41no—
312C22×C9—41no—
313C22×C9—41no—
314C22×C9—41no—
315C22×C9C4×D414yes—
316C22×C9C23×C411yescharacteristic
317C22×C9C22×D411yescharacteristic
318C22×C9C2×#4111yescharacteristic
319C22×C9H(5,𝔽2)11yescharacteristic
320C22×C9H(5,𝔽2)11yescharacteristic
321C22×C9H(5,𝔽2)11yescharacteristic
322C22×C92−1+411yescharacteristic
323C2×D9—22no—
324C2×D9—22no—
325C2×D9—22no—
326C2×D9—41no—
327C2×D9—41no—
328C2×D9—41no—
329C2×D9—41no—
330C4×C9—22no—
331C4×C9—22no—
332C4×C9—22no—
333C4×C9—41no—
334C4×C9—41no—
335Dic9—22no—
336Dic9—22no—
337Dic9—22no—
338Dic9—41no—
339Dic9—41no—
340Dic9—41no—
341Dic9—41no—
342C22×D4—91no—
343C22×D4—91no—
344C22×D4C2×D911yescharacteristic
345C23×C4—91no—
346C23×C4—91no—
347C23×C4—91no—
348C23×C4C2×D911yescharacteristic
349C23×C4C2×D911yescharacteristic
350#121—98no—
351C4×D4—24no—
352C4×D4—184no—
353C2×C4⋊C4—91no—
354C2×C4⋊C4—91no—
355C2×C4⋊C4—91no—
356C2×C4⋊C4—91no—
357C2×C4⋊C4C2×D911yescharacteristic
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×C42C2×D911yescharacteristic
370#95—91no—
371#95—91no—
372#95—91no—
373#95—91no—
374#95—91no—
375#95—91no—
376#95—91no—
377#95—91no—
378#95—91no—
379#95—91no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3C2×C4×D312yes—
391C23×C3C2×C4×D312yes—
392C23×C3#23512yes—
393C23×C3C2×#6712yes—
394C23×C3C23×D311yescharacteristic
395C22×D3—32no—
396C22×D3—61no—
397C22×D3—61no—
398C22×D3—61no—
399C22×D3—61no—
400C22×D3—61no—
401C22×D3—61no—
402C3×D4—28no—
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×C4—44no—
417C2×C3×C4C2×C4×D312yes—
418C2×C3×C4C2×#6712yes—
419C2×C3×C4C2×#6712yes—
420#67—68no—
421#67—124no—
422C2×Dic3—32no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—61no—
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—
439C2×Dic3—61no—
440C2×Dic3—61no—
441C2×Dic3—61no—
442C2×Dic3—61no—
443C2×Dic3—124no—
444C2×Dic3—124no—
445C4×D3—124no—
446C2×C9—24no—
447C2×C9—42no—
448C2×C9C2×C4×D411yescharacteristic
449C2×C9#51811yescharacteristic
450C2×C9#52011yescharacteristic
451C2×C9#53411yescharacteristic
452C2×C9#53711yescharacteristic
453C2×C9#53811yescharacteristic
454C2×C9#53911yescharacteristic
455D9—42no—
456C24—91no—
457C24C22×D911yescharacteristic
458C24C22×D911yescharacteristic
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—94no—
462C2×D4—94no—
463C2×D4—182no—
464C2×D4—182no—
465C2×D4—361no—
466C2×D4—361no—
467C2×D4C4×D914yescomplemented
468C22×C4—22no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—91no—
474C22×C4—91no—
475C22×C4—91no—
476C22×C4—94no—
477C22×C4—91no—
478C22×C4—91no—
479C22×C4—91no—
480C22×C4—91no—
481C22×C4—182no—
482C22×C4—182no—
483C22×C4—361no—
484C22×C4—361no—
485C22×C4—361no—
486C22×C4—361no—
487C22×C4—361no—
488C22×C4—361no—
489C22×C4#61114yescomplemented
490C22×C4C22×D911yescharacteristic
491C22×C4C22×D911yescharacteristic
492C22×C4C22×D911yescharacteristic
493C22×C4C22×D911yescharacteristic
494C22×C4C22×D911yescharacteristic
495C4⋊C4—22no—
496C4⋊C4—94no—
497C4⋊C4—182no—
498C4⋊C4—361no—
499C4⋊C4—361no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—94no—
503C22⋊C4—94no—
504C22⋊C4—182no—
505C22⋊C4—182no—
506C22⋊C4—361no—
507C22⋊C4—361no—
508C22⋊C4—361no—
509C22⋊C4—361no—
510C42—22no—
511C42—182no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3C4×#6714yes—
526C22×C3C22×C4×D311yescharacteristic
527C22×C3C2×#23511yescharacteristic
528C22×C3#100411yescharacteristic
529C22×C3#100411yescharacteristic
530C22×C3#100911yescharacteristic
531C22×C3#101011yescharacteristic
532C22×C3C22×#6711yescharacteristic
533C2×D3—62no—
534C2×D3—62no—
535C2×D3—62no—
536C2×D3—121no—
537C2×D3—121no—
538C2×D3—121no—
539C2×D3—121no—
540C3×C4—22no—
541C3×C4—22no—
542C3×C4—22no—
543C3×C4—41no—
544C3×C4—41no—
545Dic3—62no—
546Dic3—62no—
547Dic3—62no—
548Dic3—121no—
549Dic3—121no—
550Dic3—121no—
551Dic3—121no—
552C9#232511yescharacteristic, complemented, Sylow
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—92no—
564C23—181no—
565C23—181no—
566C23—181no—
567C23—181no—
568C23—181no—
569C23—181no—
570C23C2×C4×D912yes—
571C23C2×C4×D912yes—
572C23#369712yes—
573C23C2×#61112yes—
574C23C23×D911yescharacteristic
575D4—28no—
576D4—188no—
577D4—364no—
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—21no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4—92no—
593C2×C4—92no—
594C2×C4—92no—
595C2×C4—181no—
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—181no—
610C2×C4—181no—
611C2×C4—181no—
612C2×C4—181no—
613C2×C4—364no—
614C2×C4—364no—
615C2×C4—364no—
616C2×C4C2×C4×D912yes—
617C2×C4C2×#61112yes—
618C2×C4C2×#61112yes—
619C2×C3—24no—
620C2×C3—42no—
621C2×C3#554511yescharacteristic
622C2×C3#554611yescharacteristic
623C2×C3#556011yescharacteristic
624C2×C3#556411yescharacteristic
625C2×C3C2×C4×#6711yescharacteristic
626C2×C3#580411yescharacteristic
627C2×C3#583311yescharacteristic
628D3—122no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—182no—
643C22—182no—
644C22—182no—
645C22—361no—
646C22—361no—
647C22—361no—
648C22—361no—
649C22C4×#61114yes—
650C22C22×C4×D911yescharacteristic
651C22C2×#369711yescharacteristic
652C22#6371011yescharacteristic
653C22#6371011yescharacteristic
654C22#6371511yescharacteristic
655C22#6371611yescharacteristic
656C22C22×#61111yescharacteristic
657C4—22no—
658C4—22no—
659C4—22no—
660C4—41no—
661C4—41no—
662C4—182no—
663C4—182no—
664C4—182no—
665C4—361no—
666C4—361no—
667C4—361no—
668C4—361no—
669C3#8232711yescharacteristic
670C2—24no—
671C2—42no—
672C2—362no—
673C2#1058964711yescharacteristic
674C2#1058964811yescharacteristic
675C2#1058966211yescharacteristic
676C2#1058966611yescharacteristic
677C2C2×C4×#61111yescharacteristic
678C2#1058990611yescharacteristic
679C2#1058993511yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC2×C4×D4×C9C2
prime radicalC2×#63501C2
cosocleC23×C9C24
hypercenterC2×C4×D4D9
hypocenterC9#2325
LCSG ▷ C22×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×C4×#611C2semidirect
4. #10588900C2semidirect
5. #10588893C2semidirect
6. #10588890C2semidirect
7. C2×C9⋊#95C2semidirect
8. #10588669C2semidirect
9. #10588658C2semidirect
10. #10588638C2semidirect
11. #10588636C2semidirect
12. #10588624C2semidirect
13. #10588622C2semidirect
14. #10588620C2semidirect
15. #10588613C2semidirect
34. #63501C4semidirect
75. C2×D4×C9C2×C4semidirect
81. C22×C4×C9D4semidirect
91. C2×#611C2×C4semidirect
92. C2×#611C2×C4semidirect
98. C22×Dic9C2×C4semidirect
116. #3676C2×C4semidirect
120. (C2×D9)⋊C4C2×C4semidirect
124. Dic9⋊C4C2×C4semidirect
233. C2×C4×D4D9semidirect
467. C2×D4C4×D9semidirect
489. C22×C4#611semidirect
552. C9#2325semidirect

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×#635012
C2×C4×#6112
#105889002
#105888932
#105888902
C2×C9⋊#952
#105886692
#105886582
#105886382
#105886362
#105886242
#105886222
#105886202
#105886132
#823273