Finite Group Databasebeta

← #11805737

Subgroups — #11805737

Order 1152.

882 conjugacy classes of subgroups.

The subgroup lattice has 603 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63455C211yesmaximal, characteristic
2C9×#387C211yesmaximal, characteristic, complemented
3#10588670C211yesmaximal, characteristic, complemented
4#10588667C211yesmaximal, characteristic, complemented
5#10588660C211yesmaximal, characteristic, complemented
6C4×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
7C4×(C2×D9)⋊C4C211yesmaximal, characteristic, complemented
8#10588350C211yesmaximal, characteristic, complemented
9#10588346C211yesmaximal, characteristic, complemented
10#10588345C211yesmaximal, characteristic
11#10588345C211yesmaximal, characteristic
12#10588344C211yesmaximal, characteristic, complemented
13D9×#95C211yesmaximal, characteristic, complemented
14#10588331C211yesmaximal, characteristic, complemented
15#10588328C211yesmaximal, characteristic, complemented
16#75306—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×C4×Dic9C2211yescharacteristic
37C2×C4×Dic9C2211yescharacteristic
38#63455C418yescomplemented
39C9×#95C2211yescharacteristic
40C9×#95C2211yescharacteristic
41C9×#95C2211yescharacteristic
42C9×#95C2211yescharacteristic
43C9⋊#95C2211yescharacteristic
44C9⋊#95C2211yescharacteristic
45C9⋊#95C2211yescharacteristic
46C9⋊#95C2211yescharacteristic
47C9⋊#95C2211yescharacteristic
48C9⋊#95C2211yescharacteristic
49C9⋊#95C2211yescharacteristic
50C9⋊#95C2211yescharacteristic
51C9⋊#95C2211yescharacteristic
52C9⋊#95C2211yescharacteristic
53C2×#893—31no—
54C3×#387D311yescharacteristic
55#4990—31no—
56#4987—31no—
57#4980—31no—
58C4×(C2×D3)⋊C4—31no—
59C4×(C2×D3)⋊C4—31no—
60#4670—31no—
61#4666—31no—
62#4665—31no—
63#4665—31no—
64#4664—31no—
65D3×#95—31no—
66#4651—31no—
67#4648—31no—
68C23×D9C2311yescharacteristic
69C23×D9C2311yescharacteristic
70C22×C4×C9C2311yescharacteristic
71C22×C4×C9C2311yescharacteristic
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C22×C4×C9C2311yescharacteristic
77C22×Dic9C2311yescharacteristic
78C22×Dic9C2311yescharacteristic
79C22×Dic9C2311yescharacteristic
80C22×Dic9C2311yescharacteristic
81C22×Dic9C2311yescharacteristic
82C22×Dic9C2311yescharacteristic
83C2×D36—22no—
84C2×D36—22no—
85C2×D36C2×C414yes—
86C2×C4×D9—22no—
87C2×C4×D9—22no—
88C2×C4×D9—22no—
89C2×C4×D9—22no—
90C2×C4×D9—41no—
91C2×C4×D9—41no—
92C2×C4×D9—41no—
93C2×C4×D9—41no—
94C2×C4×D9—41no—
95C2×C4×D9—41no—
96C2×C4×D9C2×C414yes—
97C2×C4×D9C2×C414yescomplemented
98C9×C4⋊C4—41no—
99C9×C4⋊C4C2×C414yescomplemented
100C42×C9—41no—
101(C2×D9)⋊C4—22no—
102(C2×D9)⋊C4—22no—
103(C2×D9)⋊C4—22no—
104(C2×D9)⋊C4—22no—
105(C2×D9)⋊C4—41no—
106(C2×D9)⋊C4—41no—
107(C2×D9)⋊C4C2×C414yes—
108(C2×D9)⋊C4C2×C414yescomplemented
109C4⋊Dic9—41no—
110C4×Dic9—22no—
111C4×Dic9—22no—
112C4×Dic9—41no—
113C4×Dic9C2×C414yescomplemented
114#2353—91noSylow
115C22×D12—31no—
116C22×C4×D3—31no—
117C22×C4×D3—31no—
118C22×C4×D3—31no—
119C22×C4×D3—31no—
120C2×C3×C4⋊C4C2×D311yescharacteristic
121C2×C3×C4⋊C4C2×D311yescharacteristic
122C2×C3×C42C2×D311yescharacteristic
123C2×(C2×D3)⋊C4—31no—
124C2×(C2×D3)⋊C4—31no—
125C2×(C2×D3)⋊C4—31no—
126C2×(C2×D3)⋊C4—31no—
127C2×(C2×D3)⋊C4—31no—
128C2×(C2×D3)⋊C4—31no—
129C2×(C2×D3)⋊C4—31no—
130C2×(C2×D3)⋊C4—31no—
131C2×C4⋊Dic3—31no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—31no—
135C2×C4×Dic3—31no—
136#893—38no—
137C3×#95C2×D311yescharacteristic
138C3×#95C2×D311yescharacteristic
139C3×#95C2×D311yescharacteristic
140C3×#95C2×D311yescharacteristic
141C3⋊#95—31no—
142C3⋊#95—31no—
143C3⋊#95—31no—
144C3⋊#95—31no—
145C3⋊#95—31no—
146C3⋊#95—31no—
147C3⋊#95—31no—
148C3⋊#95—31no—
149C3⋊#95—31no—
150C3⋊#95—31no—
151C23×C9C2411yescharacteristic
152C22×D9—21no—
153C22×D9—21no—
154C22×D9—21no—
155C22×D9—21no—
156C22×D9—21no—
157C22×D9—21no—
158C22×D9—21no—
159C22×D9—21no—
160C22×D9—21no—
161C22×D9—21no—
162C22×D9C22×C412yes—
163C22×D9C22×C412yes—
164C22×D9#4112yes—
165C22×D9#4112yes—
166C2×C4×C9—21no—
167C2×C4×C9—21no—
168C2×C4×C9—21no—
169C2×C4×C9—21no—
170C2×C4×C9—21no—
171C2×C4×C9—21no—
172C2×C4×C9—21no—
173C2×C4×C9—21no—
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×C9C22×C412yes—
184C2×C4×C9C22×C412yes—
185C2×C4×C9C22×C412yes—
186C2×C4×C9#4112yes—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9—21no—
190C2×Dic9—21no—
191C2×Dic9—21no—
192C2×Dic9—21no—
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×Dic9C22×C412yes—
203C2×Dic9C22×C412yes—
204C2×Dic9#4112yes—
205D36—28no—
206C4×D9—44no—
207C4×D9—44no—
208C4×D9—44no—
209C4×D9—44no—
210C2×C4×D4—91no—
211#388—91no—
212#388—91no—
213#387—91no—
214#387D911yescharacteristic, complemented
215#386—91no—
216#386—91no—
217#383—91no—
218#381—91no—
219#380—91no—
220C4×C22⋊C4—91no—
221C4×C22⋊C4—91no—
222C4×C22⋊C4—91no—
223#376—91no—
224C2×#95—91no—
225C23×D3—31no—
226C23×D3—31no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C22×Dic3—31no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C2×D12—34no—
241C2×D12—62no—
242C2×D12—62no—
243C2×C4×D3—34no—
244C2×C4×D3—34no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×C4×D3—62no—
248C2×C4×D3—62no—
249C2×C4×D3—121no—
250C2×C4×D3—121no—
251C2×C4×D3—121no—
252C2×C4×D3—121no—
253C2×C4×D3—121no—
254C2×C4×D3—121no—
255C3×C4⋊C4—41no—
256C3×C4⋊C4C4×D314yes—
257C3×C42—41no—
258(C2×D3)⋊C4—34no—
259(C2×D3)⋊C4—34no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—62no—
263(C2×D3)⋊C4—62no—
264(C2×D3)⋊C4—121no—
265(C2×D3)⋊C4—121no—
266C4⋊Dic3—121no—
267C4×Dic3—34no—
268C4×Dic3—62no—
269C4×Dic3—62no—
270C4×Dic3—121no—
271C22×C9C23×C411yescharacteristic
272C22×C9C2×#4111yescharacteristic
273C22×C9C2×#4111yescharacteristic
274C22×C9C2×#4111yescharacteristic
275C22×C9C2×#4111yescharacteristic
276C22×C9H(5,𝔽2)11yescharacteristic
277C22×C9H(5,𝔽2)11yescharacteristic
278C2×D9—22no—
279C2×D9—22no—
280C2×D9—22no—
281C2×D9—22no—
282C2×D9—22no—
283C2×D9—22no—
284C2×D9—22no—
285C2×D9—22no—
286C2×D9—22no—
287C2×D9—41no—
288C2×D9—41no—
289C2×D9—41no—
290C2×D9—41no—
291C2×D9#11714yes—
292C4×C9—22no—
293C4×C9—22no—
294C4×C9—22no—
295C4×C9—22no—
296C4×C9—41no—
297C4×C9—41no—
298C4×C9—41no—
299Dic9—22no—
300Dic9—22no—
301Dic9—22no—
302Dic9—41no—
303Dic9—41no—
304Dic9—41no—
305C22×D4—91no—
306C23×C4—91no—
307C23×C4—91no—
308C23×C4—91no—
309C23×C4—91no—
310C4×D4—98no—
311C2×C4⋊C4—91no—
312C2×C4⋊C4C2×D911yescharacteristic
313C2×C4⋊C4C2×D911yescharacteristic
314C2×C22⋊C4—91no—
315C2×C22⋊C4—91no—
316C2×C22⋊C4—91no—
317C2×C22⋊C4—91no—
318C2×C22⋊C4—91no—
319C2×C22⋊C4—91no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—91no—
322C2×C42—91no—
323C2×C42—91no—
324C2×C42—91no—
325C2×C42—91no—
326C2×C42C2×D911yescharacteristic
327#95—91no—
328#95—91no—
329#95—91no—
330#95—91no—
331#95—91no—
332#95—91no—
333#95—91no—
334#95—91no—
335#95—91no—
336#95—91no—
337#95C2×D911yescharacteristic
338#95C2×D911yescharacteristic
339#95C2×D911yescharacteristic
340#95C2×D911yescharacteristic
341C23×C3C23×D311yescharacteristic
342C22×D3—32no—
343C22×D3—32no—
344C22×D3—32no—
345C22×D3—32no—
346C22×D3—61no—
347C22×D3—61no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—61no—
353C22×D3—61no—
354C22×D3—61no—
355C22×D3—61no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4C2×C4×D312yes—
374C2×C3×C4C2×C4×D312yes—
375C2×C3×C4C2×C4×D312yes—
376C2×C3×C4#23912yes—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—61no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—61no—
394C2×Dic3—61no—
395D12—68no—
396C4×D3—124no—
397C4×D3—124no—
398C4×D3—124no—
399C4×D3—124no—
400C2×C9C2×#11711yescharacteristic
401C2×C9C4×#4111yescharacteristic
402C2×C9#51811yescharacteristic
403C2×C9#55111yescharacteristic
404C2×C9#55111yescharacteristic
405C2×C9#55311yescharacteristic
406C2×C9#55311yescharacteristic
407D9—24no—
408D9—42no—
409C24—91no—
410C24—91no—
411C2×D4—94no—
412C2×D4—182no—
413C2×D4—182no—
414C22×C4—91no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—94no—
418C22×C4—94no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4—91no—
422C22×C4—182no—
423C22×C4—182no—
424C22×C4—182no—
425C22×C4—182no—
426C22×C4—361no—
427C22×C4—361no—
428C22×C4—361no—
429C22×C4—361no—
430C22×C4—361no—
431C22×C4—361no—
432C22×C4C22×D911yescharacteristic
433C22×C4C22×D911yescharacteristic
434C22×C4C22×D911yescharacteristic
435C22×C4C22×D911yescharacteristic
436C22×C4C22×D911yescharacteristic
437C22×C4C22×D911yescharacteristic
438C22×C4C22×D911yescharacteristic
439C4⋊C4—41no—
440C4⋊C4—361no—
441C4⋊C4C4×D914yescomplemented
442C22⋊C4—94no—
443C22⋊C4—94no—
444C22⋊C4—182no—
445C22⋊C4—182no—
446C22⋊C4—182no—
447C22⋊C4—182no—
448C22⋊C4—361no—
449C22⋊C4—361no—
450C42—41no—
451C42—94no—
452C42—182no—
453C42—182no—
454C42—361no—
455C22×C3C22×C4×D311yescharacteristic
456C22×C3#100411yescharacteristic
457C22×C3C2×#23911yescharacteristic
458C22×C3D3×#4111yescharacteristic
459C22×C3D3×#4111yescharacteristic
460C22×C3D3×#4111yescharacteristic
461C22×C3#100911yescharacteristic
462C2×D3—34no—
463C2×D3—62no—
464C2×D3—62no—
465C2×D3—62no—
466C2×D3—62no—
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—62no—
470C2×D3—62no—
471C2×D3—62no—
472C2×D3—121no—
473C2×D3—121no—
474C2×D3—121no—
475C2×D3—121no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—22no—
479C3×C4—22no—
480C3×C4—41no—
481C3×C4—41no—
482C3×C4—41no—
483Dic3—62no—
484Dic3—62no—
485Dic3—62no—
486Dic3—121no—
487Dic3—121no—
488Dic3—121no—
489C9#235311yescharacteristic, complemented, Sylow
490C23—92no—
491C23—92no—
492C23—92no—
493C23—92no—
494C23—181no—
495C23—181no—
496C23—181no—
497C23—181no—
498C23—181no—
499C23—181no—
500C23—181no—
501C23—181no—
502C23—181no—
503C23—181no—
504C23C23×D911yescharacteristic
505D4—188no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—92no—
524C2×C4—92no—
525C2×C4—92no—
526C2×C4—181no—
527C2×C4—181no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—181no—
531C2×C4—181no—
532C2×C4—181no—
533C2×C4—181no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4—181no—
537C2×C4—181no—
538C2×C4—181no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—364no—
542C2×C4—364no—
543C2×C4—364no—
544C2×C4—364no—
545C2×C4C2×C4×D912yes—
546C2×C4C2×C4×D912yes—
547C2×C4C2×C4×D912yes—
548C2×C4#370112yes—
549C2×C3D3×#11711yescharacteristic
550C2×C3#554511yescharacteristic
551C2×C3C4×#23911yescharacteristic
552C2×C3#563711yescharacteristic
553C2×C3#566111yescharacteristic
554C2×C3#569511yescharacteristic
555C2×C3#570511yescharacteristic
556D3—64no—
557D3—122no—
558C22—94no—
559C22—182no—
560C22—182no—
561C22—182no—
562C22—182no—
563C22—182no—
564C22—182no—
565C22—182no—
566C22—182no—
567C22—182no—
568C22—361no—
569C22—361no—
570C22—361no—
571C22—361no—
572C22C22×C4×D911yescharacteristic
573C22#6371011yescharacteristic
574C22C2×#370111yescharacteristic
575C22#41×D911yescharacteristic
576C22#41×D911yescharacteristic
577C22#41×D911yescharacteristic
578C22#6371511yescharacteristic
579C4—22no—
580C4—22no—
581C4—22no—
582C4—22no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—182no—
587C4—182no—
588C4—182no—
589C4—361no—
590C4—361no—
591C4—361no—
592C3#7530611yescharacteristic
593C2—184no—
594C2—362no—
595C2D9×#11711yescharacteristic
596C2#1058964711yescharacteristic
597C2C4×#370111yescharacteristic
598C2#1058973911yescharacteristic
599C2#1058976311yescharacteristic
600C2#1058979711yescharacteristic
601C2#1058980711yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#387C2
prime radicalC22×D36C22
cosocleC23×C9C24
hypercenter#387D9
hypocenterC9#2353
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C9×#387C2semidirect
3. #10588670C2semidirect
4. #10588667C2semidirect
5. #10588660C2semidirect
6. C4×(C2×D9)⋊C4C2semidirect
7. C4×(C2×D9)⋊C4C2semidirect
8. #10588350C2semidirect
9. #10588346C2semidirect
12. #10588344C2semidirect
13. D9×#95C2semidirect
14. #10588331C2semidirect
15. #10588328C2semidirect
38. #63455C4semidirect
97. C2×C4×D9C2×C4semidirect
99. C9×C4⋊C4C2×C4semidirect
108. (C2×D9)⋊C4C2×C4semidirect
113. C4×Dic9C2×C4semidirect
214. #387D9semidirect
441. C4⋊C4C4×D9semidirect
489. C9#2353semidirect

Maximal subgroups

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

subgroupindex
C2×#634552
C9×#3872
#105886702
#105886672
#105886602
C4×(C2×D9)⋊C42
#105883502
#105883462
#105883452
#105883442
D9×#952
#105883312
#105883282
#753063