Finite Group Databasebeta

← #11806918

Subgroups — #11806918

Order 1152.

948 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63449C211yesmaximal, characteristic, complemented
2C2×#63447C211yesmaximal, characteristic
3C2×#611⋊C4C211yesmaximal, characteristic
4C9×#388C211yesmaximal, characteristic, complemented
5#10588669C211yesmaximal, characteristic, complemented
6#10588637C211yesmaximal, characteristic
7#10588626C211yesmaximal, characteristic, complemented
8#10588624C211yesmaximal, characteristic, complemented
9C22⋊C4×Dic9C211yesmaximal, characteristic, complemented
10C4×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
11C4×Dic9⋊C4C211yesmaximal, characteristic, complemented
12#10588349C211yesmaximal, characteristic, complemented
13#10588349C211yesmaximal, characteristic, complemented
14#10588329C211yesmaximal, characteristic, complemented
15#10588326C211yesmaximal, characteristic, complemented
16#75481—31nomaximal
17C22×#611C2211yescharacteristic
18C23×Dic9C2211yescharacteristic
19C22×C4×D9C2211yescharacteristic
20C22×Dic18C2211yescharacteristic
21C2×C9×C4⋊C4C2211yescharacteristic
22C2×C9×C22⋊C4C2211yescharacteristic
23C2×C9×C22⋊C4C2211yescharacteristic
24C2×C9×C22⋊C4C2211yescharacteristic
25C2×C42×C9C2211yescharacteristic
26C2×#3676C2211yescharacteristic
27C2×#3676C2211yescharacteristic
28C2×(C2×D9)⋊C4C2211yescharacteristic
29C2×(C2×D9)⋊C4C2211yescharacteristic
30C2×(C2×D9)⋊C4C2211yescharacteristic
31C2×(C2×D9)⋊C4C2211yescharacteristic
32C2×(C2×D9)⋊C4C2211yescharacteristic
33C2×Dic9⋊C4C2211yescharacteristic
34C2×Dic9⋊C4C2211yescharacteristic
35C2×Dic9⋊C4C2211yescharacteristic
36C2×Dic9⋊C4C2211yescharacteristic
37C2×Dic9⋊C4C2211yescharacteristic
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42C2×C4×Dic9C2211yescharacteristic
43C2×C4×Dic9C2211yescharacteristic
44#63449—24no—
45#63447C418yescomplemented
46#611⋊C4—24no—
47C9×#95C2211yescharacteristic
48C9×#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C9⋊#95C2211yescharacteristic
54C9⋊#95C2211yescharacteristic
55C2×#887—31no—
56C2×#885—31no—
57C2×#67⋊C4—31no—
58C3×#388D311yescharacteristic
59#4989—31no—
60#4957—31no—
61#4946—31no—
62#4944—31no—
63Dic3×C22⋊C4—31no—
64C4×(C2×D3)⋊C4—31no—
65C4×Dic3⋊C4—31no—
66#4669—31no—
67#4669—31no—
68#4649—31no—
69#4646—31no—
70C24×C9C2311yescharacteristic
71C23×D9C2311yescharacteristic
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C2×#611—22no—
79C2×#611—22no—
80C2×#611C2×C414yes—
81C22×Dic9—22no—
82C22×Dic9—22no—
83C22×Dic9—41no—
84C22×Dic9C2311yescharacteristic
85C22×Dic9C2311yescharacteristic
86C22×Dic9C2311yescharacteristic
87C22×Dic9C2311yescharacteristic
88C22×Dic9C2311yescharacteristic
89C22×Dic9C2311yescharacteristic
90C22×Dic9C2311yescharacteristic
91C2×C4×D9—22no—
92C2×C4×D9—22no—
93C2×C4×D9—41no—
94C2×Dic18—22no—
95C2×Dic18—22no—
96C2×Dic18C2×C414yescomplemented
97C9×C4⋊C4—22no—
98C9×C22⋊C4—22no—
99C9×C22⋊C4—41no—
100C9×C22⋊C4C2×C414yescomplemented
101C42×C9—41no—
102#3676—22no—
103#3676C2×C414yescomplemented
104(C2×D9)⋊C4—22no—
105(C2×D9)⋊C4—22no—
106(C2×D9)⋊C4—41no—
107(C2×D9)⋊C4C2×C414yescomplemented
108(C2×D9)⋊C4C2×C414yescomplemented
109Dic9⋊C4—22no—
110Dic9⋊C4—22no—
111Dic9⋊C4—22no—
112Dic9⋊C4—22no—
113Dic9⋊C4D414yes—
114C4×Dic9—22no—
115C4×Dic9—22no—
116C4×Dic9—22no—
117C4×Dic9—22no—
118C4×Dic9—41no—
119C4×Dic9C2×C414yescomplemented
120#2367—91noSylow
121C22×#67—31no—
122C23×Dic3—31no—
123C22×C4×D3—31no—
124C22×Dic6—31no—
125C2×C3×C4⋊C4C2×D311yescharacteristic
126C2×C3×C22⋊C4C2×D311yescharacteristic
127C2×C3×C22⋊C4C2×D311yescharacteristic
128C2×C3×C22⋊C4C2×D311yescharacteristic
129C2×C3×C42C2×D311yescharacteristic
130C2×#217—31no—
131C2×#217—31no—
132C2×(C2×D3)⋊C4—31no—
133C2×(C2×D3)⋊C4—31no—
134C2×(C2×D3)⋊C4—31no—
135C2×(C2×D3)⋊C4—31no—
136C2×(C2×D3)⋊C4—31no—
137C2×Dic3⋊C4—31no—
138C2×Dic3⋊C4—31no—
139C2×Dic3⋊C4—31no—
140C2×Dic3⋊C4—31no—
141C2×Dic3⋊C4—31no—
142C2×C4×Dic3—31no—
143C2×C4×Dic3—31no—
144C2×C4×Dic3—31no—
145C2×C4×Dic3—31no—
146C2×C4×Dic3—31no—
147C2×C4×Dic3—31no—
148#887—64no—
149#885—38no—
150#67⋊C4—64no—
151C3×#95C2×D311yescharacteristic
152C3×#95C2×D311yescharacteristic
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×C9—21no—
164C23×C9—21no—
165C23×C9C22×C412yes—
166C23×C9C2411yescharacteristic
167C22×D9—21no—
168C22×D9—21no—
169C22×D9—21no—
170C22×D9—21no—
171C22×D9—21no—
172C22×D9—21no—
173C22×D9C22×C412yes—
174C2×C4×C9—21no—
175C2×C4×C9—21no—
176C2×C4×C9—21no—
177C2×C4×C9—21no—
178C2×C4×C9—21no—
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×C9C22×C412yes—
190C2×C4×C9C22×C412yes—
191C2×C4×C9C2×D412yes—
192#611—28no—
193C2×Dic9—21no—
194C2×Dic9—21no—
195C2×Dic9—21no—
196C2×Dic9—21no—
197C2×Dic9—21no—
198C2×Dic9—21no—
199C2×Dic9—21no—
200C2×Dic9—21no—
201C2×Dic9—21no—
202C2×Dic9—21no—
203C2×Dic9—21no—
204C2×Dic9—21no—
205C2×Dic9—21no—
206C2×Dic9—44no—
207C2×Dic9C22×C412yes—
208C2×Dic9C22×C412yes—
209C2×Dic9C22×C412yes—
210C2×Dic9C2×D412yes—
211C2×Dic9C2×D412yes—
212C2×Dic9#4112yes—
213C2×Dic9#4112yes—
214C2×Dic9#4112yes—
215C4×D9—44no—
216Dic18—28no—
217C2×#124—91no—
218C2×C4×Q8—91no—
219C2×C4×D4—91no—
220#391—91no—
221#390—91no—
222#388—91no—
223#388—91no—
224#388—91no—
225#388D911yescharacteristic, complemented
226#385—91no—
227#385—91no—
228C4×C4⋊C4—91no—
229C4×C4⋊C4—91no—
230C4×C22⋊C4—91no—
231C4×C22⋊C4—91no—
232C24×C3C22×D311yescharacteristic
233C23×D3—31no—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C2×#67—34no—
241C2×#67—62no—
242C2×#67—62no—
243C22×Dic3—31no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C22×Dic3—31no—
249C22×Dic3—31no—
250C22×Dic3—62no—
251C22×Dic3—62no—
252C22×Dic3—121no—
253C2×C4×D3—62no—
254C2×C4×D3—62no—
255C2×C4×D3—121no—
256C2×Dic6—34no—
257C2×Dic6—62no—
258C2×Dic6—62no—
259C3×C4⋊C4—22no—
260C3×C22⋊C4—22no—
261C3×C22⋊C4—41no—
262C3×C22⋊C4C4×D314yes—
263C3×C42—41no—
264#217—34no—
265#217—62no—
266(C2×D3)⋊C4—34no—
267(C2×D3)⋊C4—34no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—121no—
271Dic3⋊C4—34no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276C4×Dic3—34no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C4×Dic3—62no—
280C4×Dic3—62no—
281C4×Dic3—121no—
282C22×C9—22no—
283C22×C9—22no—
284C22×C9—22no—
285C22×C9—41no—
286C22×C9—41no—
287C22×C9—41no—
288C22×C9—41no—
289C22×C9C23×C411yescharacteristic
290C22×C9C22×D411yescharacteristic
291C22×C9C2×#4111yescharacteristic
292C22×C9C2×#4111yescharacteristic
293C22×C9C2×#4111yescharacteristic
294C22×C9H(5,𝔽2)11yescharacteristic
295C22×C92−1+411yescharacteristic
296C2×D9—22no—
297C2×D9—22no—
298C2×D9—22no—
299C2×D9—41no—
300C2×D9—41no—
301C2×D9—41no—
302C2×D9—41no—
303C4×C9—22no—
304C4×C9—22no—
305C4×C9—22no—
306C4×C9—41no—
307C4×C9—41no—
308C4×C9—41no—
309Dic9—22no—
310Dic9—22no—
311Dic9—22no—
312Dic9—22no—
313Dic9—22no—
314Dic9—41no—
315Dic9C4×D414yes—
316C22×Q8—91no—
317C22×D4—91no—
318C23×C4—91no—
319C23×C4—91no—
320#124—98no—
321C4×Q8—184no—
322C4×D4—184no—
323C2×C4⋊C4—91no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4C2×D911yescharacteristic
329C2×C22⋊C4—91no—
330C2×C22⋊C4—91no—
331C2×C22⋊C4—91no—
332C2×C22⋊C4—91no—
333C2×C22⋊C4—91no—
334C2×C22⋊C4—91no—
335C2×C22⋊C4—91no—
336C2×C22⋊C4C2×D911yescharacteristic
337C2×C22⋊C4C2×D911yescharacteristic
338C2×C22⋊C4C2×D911yescharacteristic
339C2×C42—91no—
340C2×C42—91no—
341C2×C42—91no—
342C2×C42—91no—
343C2×C42—91no—
344C2×C42—91no—
345C2×C42C2×D911yescharacteristic
346#95—91no—
347#95—91no—
348#95—91no—
349#95—91no—
350#95—91no—
351#95—91no—
352#95C2×D911yescharacteristic
353#95C2×D911yescharacteristic
354C23×C3—21no—
355C23×C3—21no—
356C23×C3—21no—
357C23×C3—21no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3C2×C4×D312yes—
361C23×C3C23×D311yescharacteristic
362C22×D3—32no—
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—61no—
366C22×D3—61no—
367C22×D3—61no—
368C22×D3—61no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4C2×C4×D312yes—
385C2×C3×C4C2×C4×D312yes—
386C2×C3×C4D3×D412yes—
387#67—68no—
388C2×Dic3—32no—
389C2×Dic3—32no—
390C2×Dic3—32no—
391C2×Dic3—32no—
392C2×Dic3—32no—
393C2×Dic3—32no—
394C2×Dic3—32no—
395C2×Dic3—32no—
396C2×Dic3—61no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—61no—
400C2×Dic3—61no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—124no—
410C4×D3—124no—
411Dic6—68no—
412C2×C9—42no—
413C2×C9C2×C4×D411yescharacteristic
414C2×C9C4×#4111yescharacteristic
415C2×C9#52011yescharacteristic
416C2×C9#54611yescharacteristic
417C2×C9#54811yescharacteristic
418C2×C9#55611yescharacteristic
419C2×C9#55911yescharacteristic
420D9—42no—
421C24—91no—
422C24C22×D911yescharacteristic
423C2×Q8—94no—
424C2×Q8—182no—
425C2×Q8—182no—
426C2×D4—94no—
427C2×D4—182no—
428C2×D4—182no—
429C22×C4—91no—
430C22×C4—91no—
431C22×C4—91no—
432C22×C4—91no—
433C22×C4—91no—
434C22×C4—91no—
435C22×C4—91no—
436C22×C4—182no—
437C22×C4—182no—
438C22×C4—182no—
439C22×C4—182no—
440C22×C4—361no—
441C22×C4—361no—
442C22×C4C22×D911yescharacteristic
443C22×C4C22×D911yescharacteristic
444C22×C4C22×D911yescharacteristic
445C22×C4C22×D911yescharacteristic
446C22×C4C22×D911yescharacteristic
447C22×C4C22×D911yescharacteristic
448C4⋊C4—22no—
449C4⋊C4—94no—
450C4⋊C4—182no—
451C4⋊C4—182no—
452C4⋊C4—182no—
453C4⋊C4—182no—
454C22⋊C4—22no—
455C22⋊C4—41no—
456C22⋊C4—94no—
457C22⋊C4—94no—
458C22⋊C4—94no—
459C22⋊C4—182no—
460C22⋊C4—182no—
461C22⋊C4—182no—
462C22⋊C4—361no—
463C22⋊C4C4×D914yescomplemented
464C42—41no—
465C42—94no—
466C42—182no—
467C42—182no—
468C42—182no—
469C42—182no—
470C42—361no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—41no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—41no—
478C22×C3C22×C4×D311yescharacteristic
479C22×C3C2×D3×D411yescharacteristic
480C22×C3#100411yescharacteristic
481C22×C3D3×#4111yescharacteristic
482C22×C3D3×#4111yescharacteristic
483C22×C3D3×#4111yescharacteristic
484C22×C3#101011yescharacteristic
485C2×D3—62no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—121no—
489C2×D3—121no—
490C2×D3—121no—
491C2×D3—121no—
492C3×C4—22no—
493C3×C4—22no—
494C3×C4—22no—
495C3×C4—41no—
496C3×C4—41no—
497C3×C4—41no—
498Dic3—34no—
499Dic3—62no—
500Dic3—62no—
501Dic3—62no—
502Dic3—62no—
503Dic3—62no—
504Dic3—121no—
505C9#236711yescharacteristic, complemented, Sylow
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—92no—
513C23—181no—
514C23—181no—
515C23—181no—
516C23—181no—
517C23—181no—
518C23—181no—
519C23C2×C4×D912yes—
520C23C23×D911yescharacteristic
521Q8—188no—
522D4—188no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—92no—
539C2×C4—92no—
540C2×C4—92no—
541C2×C4—92no—
542C2×C4—92no—
543C2×C4—92no—
544C2×C4—92no—
545C2×C4—92no—
546C2×C4—181no—
547C2×C4—181no—
548C2×C4—181no—
549C2×C4—181no—
550C2×C4—181no—
551C2×C4—181no—
552C2×C4—181no—
553C2×C4—181no—
554C2×C4—181no—
555C2×C4—181no—
556C2×C4—181no—
557C2×C4—181no—
558C2×C4—181no—
559C2×C4—364no—
560C2×C4—364no—
561C2×C4C2×C4×D912yes—
562C2×C4C2×C4×D912yes—
563C2×C4D4×D912yes—
564C2×C3—42no—
565C2×C3#552211yescharacteristic
566C2×C3C4×D3×D411yescharacteristic
567C2×C3#554611yescharacteristic
568C2×C3#561011yescharacteristic
569C2×C3#566411yescharacteristic
570C2×C3#567711yescharacteristic
571C2×C3#570211yescharacteristic
572D3—122no—
573C22—22no—
574C22—22no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—182no—
581C22—182no—
582C22—182no—
583C22—361no—
584C22—361no—
585C22—361no—
586C22—361no—
587C22C22×C4×D911yescharacteristic
588C22C2×D4×D911yescharacteristic
589C22#6371011yescharacteristic
590C22#41×D911yescharacteristic
591C22#41×D911yescharacteristic
592C22#41×D911yescharacteristic
593C22#6371611yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—94no—
601C4—182no—
602C4—182no—
603C4—182no—
604C4—182no—
605C4—182no—
606C4—361no—
607C3#7548111yescharacteristic
608C2—42no—
609C2—362no—
610C2#1058962411yescharacteristic
611C2C4×D4×D911yescharacteristic
612C2#1058964811yescharacteristic
613C2#1058971211yescharacteristic
614C2#1058976611yescharacteristic
615C2#1058977911yescharacteristic
616C2#1058980411yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#388C2
prime radicalC22×#611C22
cosocleC23×C9C24
hypercenter#388D9
hypocenterC9#2367
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#63449C2semidirect
4. C9×#388C2semidirect
5. #10588669C2semidirect
7. #10588626C2semidirect
8. #10588624C2semidirect
9. C22⋊C4×Dic9C2semidirect
10. C4×(C2×D9)⋊C4C2semidirect
11. C4×Dic9⋊C4C2semidirect
12. #10588349C2semidirect
13. #10588349C2semidirect
14. #10588329C2semidirect
15. #10588326C2semidirect
45. #63447C4semidirect
96. C2×Dic18C2×C4semidirect
100. C9×C22⋊C4C2×C4semidirect
103. #3676C2×C4semidirect
107. (C2×D9)⋊C4C2×C4semidirect
108. (C2×D9)⋊C4C2×C4semidirect
119. C4×Dic9C2×C4semidirect
225. #388D9semidirect
463. C22⋊C4C4×D9semidirect
505. C9#2367semidirect

Maximal subgroups

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

subgroupindex
C2×#634492
C2×#634472
C2×#611⋊C42
C9×#3882
#105886692
#105886372
#105886262
#105886242
C22⋊C4×Dic92
C4×(C2×D9)⋊C42
C4×Dic9⋊C42
#105883492
#105883292
#105883262
#754813