Finite Group Databasebeta

← #11803359

Subgroups — #11803359

Order 1152.

948 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63456C211yesmaximal, characteristic
2C2×C4⋊C4×D9C211yesmaximal, characteristic, complemented
3C2×C4×D36C211yesmaximal, characteristic
4C9×#387C211yesmaximal, characteristic, complemented
5#10588669C211yesmaximal, characteristic, complemented
6#10588664C211yesmaximal, characteristic, complemented
7#10588613C211yesmaximal, characteristic, complemented
8#10588350C211yesmaximal, characteristic, complemented
9#10588349C211yesmaximal, characteristic, complemented
10#10588348C211yesmaximal, characteristic, complemented
11#10588348C211yesmaximal, characteristic, complemented
12#10588346C211yesmaximal, characteristic, complemented
13#10588345C211yesmaximal, characteristic
14#10588344C211yesmaximal, characteristic, complemented
15#10588327C211yesmaximal, characteristic, complemented
16#75297—31nomaximal
17C22×D36C2211yescharacteristic
18C22×C4×D9C2211yescharacteristic
19C22×C4×D9C2211yescharacteristic
20C22×C4×D9C2211yescharacteristic
21C22×C4×D9C2211yescharacteristic
22C2×C9×C4⋊C4C2211yescharacteristic
23C2×C9×C4⋊C4C2211yescharacteristic
24C2×C42×C9C2211yescharacteristic
25C2×(C2×D9)⋊C4C2211yescharacteristic
26C2×(C2×D9)⋊C4C2211yescharacteristic
27C2×(C2×D9)⋊C4C2211yescharacteristic
28C2×(C2×D9)⋊C4C2211yescharacteristic
29C2×(C2×D9)⋊C4C2211yescharacteristic
30C2×(C2×D9)⋊C4C2211yescharacteristic
31C2×(C2×D9)⋊C4C2211yescharacteristic
32C2×(C2×D9)⋊C4C2211yescharacteristic
33C2×C4⋊Dic9C2211yescharacteristic
34C2×C4⋊Dic9C2211yescharacteristic
35C2×C4⋊Dic9C2211yescharacteristic
36C2×Dic9⋊C4C2211yescharacteristic
37C2×Dic9⋊C4C2211yescharacteristic
38C2×Dic9⋊C4C2211yescharacteristic
39C2×Dic9⋊C4C2211yescharacteristic
40C2×C4×Dic9C2211yescharacteristic
41C2×C4×Dic9C2211yescharacteristic
42#63456C418yescomplemented
43C4⋊C4×D9—24no—
44C4×D36—24no—
45C9×#95C2211yescharacteristic
46C9×#95C2211yescharacteristic
47C9×#95C2211yescharacteristic
48C9×#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C9⋊#95C2211yescharacteristic
54C9⋊#95C2211yescharacteristic
55C2×#894—31no—
56C2×D3×C4⋊C4—31no—
57C2×C4×D12—31no—
58C3×#387D311yescharacteristic
59#4989—31no—
60#4984—31no—
61#4933—31no—
62#4670—31no—
63#4669—31no—
64#4668—31no—
65#4668—31no—
66#4666—31no—
67#4665—31no—
68#4664—31no—
69#4647—31no—
70C23×D9C2311yescharacteristic
71C23×D9C2311yescharacteristic
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×C4×C9C2311yescharacteristic
78C22×C4×C9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82C22×Dic9C2311yescharacteristic
83C22×Dic9C2311yescharacteristic
84C22×Dic9C2311yescharacteristic
85C2×D36—22no—
86C2×D36—22no—
87C2×D36C2×C414yes—
88C2×C4×D9—22no—
89C2×C4×D9—22no—
90C2×C4×D9—22no—
91C2×C4×D9—22no—
92C2×C4×D9—41no—
93C2×C4×D9—41no—
94C2×C4×D9—41no—
95C2×C4×D9—41no—
96C2×C4×D9—41no—
97C2×C4×D9—41no—
98C2×C4×D9C2×C414yescomplemented
99C2×C4×D9D414yes—
100C9×C4⋊C4—22no—
101C9×C4⋊C4C2×C414yescomplemented
102C42×C9—22no—
103(C2×D9)⋊C4—22no—
104(C2×D9)⋊C4—22no—
105(C2×D9)⋊C4—22no—
106(C2×D9)⋊C4—41no—
107(C2×D9)⋊C4—41no—
108(C2×D9)⋊C4C2×C414yescomplemented
109(C2×D9)⋊C4C2×C414yescomplemented
110(C2×D9)⋊C4C2×C414yescomplemented
111C4⋊Dic9—22no—
112C4⋊Dic9—22no—
113C4⋊Dic9—41no—
114Dic9⋊C4—22no—
115Dic9⋊C4—22no—
116Dic9⋊C4—41no—
117Dic9⋊C4C2×C414yescomplemented
118C4×Dic9—41no—
119C4×Dic9—41no—
120#2322—91noSylow
121C22×D12—31no—
122C22×C4×D3—31no—
123C22×C4×D3—31no—
124C22×C4×D3—31no—
125C22×C4×D3—31no—
126C2×C3×C4⋊C4C2×D311yescharacteristic
127C2×C3×C4⋊C4C2×D311yescharacteristic
128C2×C3×C42C2×D311yescharacteristic
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4—31no—
131C2×(C2×D3)⋊C4—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×C4⋊Dic3—31no—
138C2×C4⋊Dic3—31no—
139C2×C4⋊Dic3—31no—
140C2×Dic3⋊C4—31no—
141C2×Dic3⋊C4—31no—
142C2×Dic3⋊C4—31no—
143C2×Dic3⋊C4—31no—
144C2×C4×Dic3—31no—
145C2×C4×Dic3—31no—
146#894—38no—
147D3×C4⋊C4—64no—
148C4×D12—64no—
149C3×#95C2×D311yescharacteristic
150C3×#95C2×D311yescharacteristic
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×C9C2411yescharacteristic
160C22×D9—21no—
161C22×D9—21no—
162C22×D9—21no—
163C22×D9—21no—
164C22×D9—21no—
165C22×D9—21no—
166C22×D9—21no—
167C22×D9—21no—
168C22×D9—21no—
169C22×D9—21no—
170C22×D9C22×C412yes—
171C22×D9C22×C412yes—
172C22×D9C2×D412yes—
173C22×D9#4112yes—
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×C9—21no—
190C2×C4×C9—21no—
191C2×C4×C9C22×C412yes—
192C2×C4×C9C22×C412yes—
193C2×C4×C9C22×C412yes—
194C2×C4×C9C2×D412yes—
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—21no—
207C2×Dic9—21no—
208C2×Dic9—21no—
209C2×Dic9—21no—
210C2×Dic9C22×C412yes—
211C2×Dic9C22×C412yes—
212C2×Dic9C2×D412yes—
213D36—28no—
214C4×D9—28no—
215C4×D9—44no—
216C4×D9—44no—
217C4×D9—44no—
218C2×#123—91no—
219C2×C4×D4—91no—
220C22×C4⋊C4—91no—
221#389—91no—
222#389—91no—
223#388—91no—
224#388—91no—
225#387—91no—
226#387D911yescharacteristic, complemented
227#386—91no—
228#385—91no—
229#385—91no—
230#385—91no—
231#381—91no—
232C4×C22⋊C4—91no—
233C23×D3—31no—
234C23×D3—31no—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C22×D311yescharacteristic
242C22×Dic3—31no—
243C22×Dic3—31no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—31no—
247C22×Dic3—31no—
248C2×D12—34no—
249C2×D12—62no—
250C2×D12—62no—
251C2×C4×D3—34no—
252C2×C4×D3—34no—
253C2×C4×D3—62no—
254C2×C4×D3—62no—
255C2×C4×D3—62no—
256C2×C4×D3—62no—
257C2×C4×D3—121no—
258C2×C4×D3—121no—
259C2×C4×D3—121no—
260C2×C4×D3—121no—
261C2×C4×D3—121no—
262C2×C4×D3—121no—
263C3×C4⋊C4—22no—
264C3×C4⋊C4C4×D314yes—
265C3×C42—22no—
266(C2×D3)⋊C4—34no—
267(C2×D3)⋊C4—34no—
268(C2×D3)⋊C4—34no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—62no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—121no—
273(C2×D3)⋊C4—121no—
274C4⋊Dic3—62no—
275C4⋊Dic3—62no—
276C4⋊Dic3—121no—
277Dic3⋊C4—34no—
278Dic3⋊C4—62no—
279Dic3⋊C4—62no—
280Dic3⋊C4—121no—
281C4×Dic3—121no—
282C4×Dic3—121no—
283C22×C9C23×C411yescharacteristic
284C22×C9C22×D411yescharacteristic
285C22×C9C2×#4111yescharacteristic
286C22×C9H(5,𝔽2)11yescharacteristic
287C22×C9H(5,𝔽2)11yescharacteristic
288C22×C92−1+411yescharacteristic
289C22×C92−1+411yescharacteristic
290C2×D9—22no—
291C2×D9—22no—
292C2×D9—22no—
293C2×D9—22no—
294C2×D9—22no—
295C2×D9—22no—
296C2×D9—22no—
297C2×D9—22no—
298C2×D9—22no—
299C2×D9—41no—
300C2×D9—41no—
301C2×D9—41no—
302C2×D9—41no—
303C2×D9C4×D414yes—
304C4×C9—22no—
305C4×C9—22no—
306C4×C9—22no—
307C4×C9—22no—
308C4×C9—41no—
309C4×C9—41no—
310C4×C9—41no—
311Dic9—22no—
312Dic9—22no—
313Dic9—22no—
314Dic9—41no—
315Dic9—41no—
316Dic9—41no—
317C22×D4—91no—
318C23×C4—91no—
319C23×C4—91no—
320C23×C4—91no—
321C23×C4—91no—
322#123—98no—
323C4×D4—184no—
324C2×C4⋊C4—91no—
325C2×C4⋊C4—91no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4—91no—
328C2×C4⋊C4—91no—
329C2×C4⋊C4—91no—
330C2×C4⋊C4—91no—
331C2×C4⋊C4—184no—
332C2×C4⋊C4C2×D911yescharacteristic
333C2×C4⋊C4C2×D911yescharacteristic
334C2×C22⋊C4—91no—
335C2×C22⋊C4—91no—
336C2×C22⋊C4—91no—
337C2×C22⋊C4—91no—
338C2×C22⋊C4—91no—
339C2×C22⋊C4—91no—
340C2×C22⋊C4—91no—
341C2×C22⋊C4—91no—
342C2×C42—91no—
343C2×C42—91no—
344C2×C42C2×D911yescharacteristic
345#95—91no—
346#95—91no—
347#95—91no—
348#95—91no—
349#95—91no—
350#95—91no—
351#95C2×D911yescharacteristic
352#95C2×D911yescharacteristic
353#95C2×D911yescharacteristic
354#95C2×D911yescharacteristic
355C23×C3C23×D311yescharacteristic
356C22×D3—32no—
357C22×D3—32no—
358C22×D3—32no—
359C22×D3—32no—
360C22×D3—61no—
361C22×D3—61no—
362C22×D3—61no—
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—61no—
366C22×D3—61no—
367C22×D3—61no—
368C22×D3—61no—
369C22×D3—61no—
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×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4C2×C4×D312yes—
388C2×C3×C4C2×C4×D312yes—
389C2×C3×C4C2×C4×D312yes—
390C2×C3×C4D3×D412yes—
391C2×Dic3—32no—
392C2×Dic3—32no—
393C2×Dic3—32no—
394C2×Dic3—61no—
395C2×Dic3—61no—
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—
409D12—68no—
410C4×D3—68no—
411C4×D3—124no—
412C4×D3—124no—
413C4×D3—124no—
414C2×C9C2×C4×D411yescharacteristic
415C2×C9#52011yescharacteristic
416C2×C9#52011yescharacteristic
417C2×C9#53411yescharacteristic
418C2×C9#53611yescharacteristic
419C2×C9#53911yescharacteristic
420C2×C9#53911yescharacteristic
421D9—24no—
422D9—42no—
423C24—91no—
424C24—91no—
425C2×D4—94no—
426C2×D4—182no—
427C2×D4—182no—
428C22×C4—91no—
429C22×C4—91no—
430C22×C4—91no—
431C22×C4—94no—
432C22×C4—94no—
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×C4—361no—
443C22×C4—361no—
444C22×C4—361no—
445C22×C4—361no—
446C22×C4C22×D911yescharacteristic
447C22×C4C22×D911yescharacteristic
448C22×C4C22×D911yescharacteristic
449C22×C4C22×D911yescharacteristic
450C22×C4C22×D911yescharacteristic
451C22×C4C22×D911yescharacteristic
452C22×C4C22×D911yescharacteristic
453C4⋊C4—22no—
454C4⋊C4—94no—
455C4⋊C4—182no—
456C4⋊C4—182no—
457C4⋊C4—182no—
458C4⋊C4—182no—
459C4⋊C4—361no—
460C4⋊C4—361no—
461C4⋊C4C4×D914yescomplemented
462C22⋊C4—94no—
463C22⋊C4—94no—
464C22⋊C4—94no—
465C22⋊C4—182no—
466C22⋊C4—182no—
467C22⋊C4—182no—
468C22⋊C4—361no—
469C22⋊C4—361no—
470C42—22no—
471C42—361no—
472C42—361no—
473C22×C3C22×C4×D311yescharacteristic
474C22×C3C2×D3×D411yescharacteristic
475C22×C3#100711yescharacteristic
476C22×C3D3×#4111yescharacteristic
477C22×C3#100911yescharacteristic
478C22×C3#100911yescharacteristic
479C22×C3#101011yescharacteristic
480C2×D3—34no—
481C2×D3—62no—
482C2×D3—62no—
483C2×D3—62no—
484C2×D3—62no—
485C2×D3—62no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—62no—
489C2×D3—62no—
490C2×D3—121no—
491C2×D3—121no—
492C2×D3—121no—
493C2×D3—121no—
494C3×C4—22no—
495C3×C4—22no—
496C3×C4—22no—
497C3×C4—22no—
498C3×C4—41no—
499C3×C4—41no—
500C3×C4—41no—
501Dic3—62no—
502Dic3—62no—
503Dic3—62no—
504Dic3—121no—
505Dic3—121no—
506Dic3—121no—
507C9#232211yescharacteristic, complemented, Sylow
508C23—92no—
509C23—92no—
510C23—92no—
511C23—92no—
512C23—181no—
513C23—181no—
514C23—181no—
515C23—181no—
516C23—181no—
517C23—181no—
518C23—181no—
519C23—181no—
520C23—181no—
521C23—181no—
522C23C23×D911yescharacteristic
523D4—188no—
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—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—92no—
542C2×C4—92no—
543C2×C4—92no—
544C2×C4—188no—
545C2×C4—181no—
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—181no—
560C2×C4—364no—
561C2×C4—364no—
562C2×C4—364no—
563C2×C4C2×C4×D912yes—
564C2×C4C2×C4×D912yes—
565C2×C4C2×C4×D912yes—
566C2×C4D4×D912yes—
567C2×C3#552311yescharacteristic
568C2×C3C4×D3×D411yescharacteristic
569C2×C3#557411yescharacteristic
570C2×C3#562811yescharacteristic
571C2×C3#565311yescharacteristic
572C2×C3#569211yescharacteristic
573C2×C3#570711yescharacteristic
574D3—64no—
575D3—122no—
576C22—94no—
577C22—182no—
578C22—182no—
579C22—182no—
580C22—182no—
581C22—182no—
582C22—182no—
583C22—182no—
584C22—182no—
585C22—182no—
586C22—361no—
587C22—361no—
588C22—361no—
589C22—361no—
590C22C22×C4×D911yescharacteristic
591C22C2×D4×D911yescharacteristic
592C22#6371311yescharacteristic
593C22#41×D911yescharacteristic
594C22#6371511yescharacteristic
595C22#6371511yescharacteristic
596C22#6371611yescharacteristic
597C4—22no—
598C4—22no—
599C4—22no—
600C4—22no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—182no—
605C4—182no—
606C4—182no—
607C4—361no—
608C4—361no—
609C4—361no—
610C3#7529711yescharacteristic
611C2—184no—
612C2—362no—
613C2#1058962511yescharacteristic
614C2C4×D4×D911yescharacteristic
615C2#1058967611yescharacteristic
616C2#1058973011yescharacteristic
617C2#1058975511yescharacteristic
618C2#1058979411yescharacteristic
619C2#1058980911yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#387C2
prime radicalC22×D36C22
cosocleC23×C9C24
hypercenter#387D9
hypocenterC9#2322
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D9C2semidirect
4. C9×#387C2semidirect
5. #10588669C2semidirect
6. #10588664C2semidirect
7. #10588613C2semidirect
8. #10588350C2semidirect
9. #10588349C2semidirect
10. #10588348C2semidirect
11. #10588348C2semidirect
12. #10588346C2semidirect
14. #10588344C2semidirect
15. #10588327C2semidirect
42. #63456C4semidirect
98. C2×C4×D9C2×C4semidirect
101. C9×C4⋊C4C2×C4semidirect
108. (C2×D9)⋊C4C2×C4semidirect
109. (C2×D9)⋊C4C2×C4semidirect
110. (C2×D9)⋊C4C2×C4semidirect
117. Dic9⋊C4C2×C4semidirect
226. #387D9semidirect
461. C4⋊C4C4×D9semidirect
507. C9#2322semidirect

Maximal subgroups

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

subgroupindex
C2×#634562
C2×C4⋊C4×D92
C2×C4×D362
C9×#3872
#105886692
#105886642
#105886132
#105883502
#105883492
#105883482
#105883462
#105883452
#105883442
#105883272
#752973