Finite Group Databasebeta

← #11807871

Subgroups — #11807871

Order 1152.

780 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63447C211yesmaximal, characteristic
2C9×#388C211yesmaximal, characteristic, complemented
3#10588670C211yesmaximal, characteristic, complemented
4#10588657C211yesmaximal, characteristic, complemented
5#10588638C211yesmaximal, characteristic
6#10588636C211yesmaximal, characteristic
7#10588630C211yesmaximal, characteristic, complemented
8#10588626C211yesmaximal, characteristic, complemented
9#10588624C211yesmaximal, characteristic, complemented
10#10588620C211yesmaximal, characteristic, complemented
11#10588609C211yesmaximal, characteristic, complemented
12#10588348C211yesmaximal, characteristic, complemented
13#10588348C211yesmaximal, characteristic, complemented
14#10588330C211yesmaximal, characteristic, complemented
15#10588326C211yesmaximal, characteristic, complemented
16#75493—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×C4⋊Dic9C2211yescharacteristic
34C2×C4⋊Dic9C2211yescharacteristic
35C2×Dic9⋊C4C2211yescharacteristic
36C2×Dic9⋊C4C2211yescharacteristic
37C2×Dic9⋊C4C2211yescharacteristic
38C2×C4×Dic9C2211yescharacteristic
39C2×C4×Dic9C2211yescharacteristic
40#63447C418yescomplemented
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×#885—31no—
54C3×#388D311yescharacteristic
55#4990—31no—
56#4977—31no—
57#4958—31no—
58#4956—31no—
59#4950—31no—
60#4946—31no—
61#4944—31no—
62#4940—31no—
63#4929—31no—
64#4668—31no—
65#4668—31no—
66#4650—31no—
67#4646—31no—
68C24×C9C2311yescharacteristic
69C23×D9C2311yescharacteristic
70C22×C4×C9C2311yescharacteristic
71C22×C4×C9C2311yescharacteristic
72C22×C4×C9C2311yescharacteristic
73C22×C4×C9C2311yescharacteristic
74C22×C4×C9C2311yescharacteristic
75C22×C4×C9C2311yescharacteristic
76C2×#611—41no—
77C2×#611—41no—
78C2×#611C2×C414yes—
79C22×Dic9—41no—
80C22×Dic9—41no—
81C22×Dic9—41no—
82C22×Dic9C2311yescharacteristic
83C22×Dic9C2311yescharacteristic
84C22×Dic9C2311yescharacteristic
85C22×Dic9C2311yescharacteristic
86C22×Dic9C2311yescharacteristic
87C22×Dic9C2311yescharacteristic
88C22×Dic9C2311yescharacteristic
89C2×C4×D9—41no—
90C2×C4×D9—41no—
91C2×C4×D9—41no—
92C2×Dic18—41no—
93C2×Dic18—41no—
94C2×Dic18C2×C414yescomplemented
95C9×C4⋊C4—41no—
96C9×C22⋊C4—41no—
97C9×C22⋊C4—41no—
98C9×C22⋊C4C2×C414yescomplemented
99C42×C9—41no—
100#3676—41no—
101#3676C2×C414yescomplemented
102(C2×D9)⋊C4—41no—
103(C2×D9)⋊C4—41no—
104(C2×D9)⋊C4—41no—
105(C2×D9)⋊C4C2×C414yescomplemented
106(C2×D9)⋊C4C2×C414yescomplemented
107C4⋊Dic9—41no—
108C4⋊Dic9—41no—
109Dic9⋊C4—41no—
110Dic9⋊C4—41no—
111Dic9⋊C4—41no—
112C4×Dic9—41no—
113C4×Dic9C2×C414yescomplemented
114#2379—91noSylow
115C22×#67—31no—
116C23×Dic3—31no—
117C22×C4×D3—31no—
118C22×Dic6—31no—
119C2×C3×C4⋊C4C2×D311yescharacteristic
120C2×C3×C22⋊C4C2×D311yescharacteristic
121C2×C3×C22⋊C4C2×D311yescharacteristic
122C2×C3×C22⋊C4C2×D311yescharacteristic
123C2×C3×C42C2×D311yescharacteristic
124C2×#217—31no—
125C2×#217—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×Dic3⋊C4—31no—
134C2×Dic3⋊C4—31no—
135C2×Dic3⋊C4—31no—
136C2×C4×Dic3—31no—
137C2×C4×Dic3—31no—
138#885—38no—
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×C9—21no—
152C23×C9—21no—
153C23×C9—21no—
154C23×C9—21no—
155C23×C9—21no—
156C23×C9—21no—
157C23×C9C22×C412yes—
158C23×C9C2411yescharacteristic
159C22×D9—21no—
160C22×D9—21no—
161C22×D9—21no—
162C22×D9—21no—
163C22×D9—21no—
164C22×D9—21no—
165C22×D9C22×C412yes—
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×C9C22×C412yes—
183C2×C4×C9C22×C412yes—
184#611—44no—
185C2×Dic9—21no—
186C2×Dic9—21no—
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×Dic9—21no—
203C2×Dic9—44no—
204C2×Dic9C22×C412yes—
205C2×Dic9C22×C412yes—
206C2×Dic9C22×C412yes—
207C4×D9—44no—
208Dic18—44no—
209C2×#124—91no—
210#391—91no—
211#391—91no—
212#388—91no—
213#388—91no—
214#388—91no—
215#388D911yescharacteristic, complemented
216#386—91no—
217#386—91no—
218#385—91no—
219#385—91no—
220#385—91no—
221#385—91no—
222#382—91no—
223#382—91no—
224C24×C3C22×D311yescharacteristic
225C23×D3—31no—
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—34no—
233C2×#67—121no—
234C2×#67—121no—
235C22×Dic3—31no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—121no—
243C22×Dic3—121no—
244C22×Dic3—121no—
245C2×C4×D3—121no—
246C2×C4×D3—121no—
247C2×C4×D3—121no—
248C2×Dic6—34no—
249C2×Dic6—121no—
250C2×Dic6—121no—
251C3×C4⋊C4—41no—
252C3×C22⋊C4—41no—
253C3×C22⋊C4—41no—
254C3×C22⋊C4C4×D314yes—
255C3×C42—41no—
256#217—34no—
257#217—121no—
258(C2×D3)⋊C4—34no—
259(C2×D3)⋊C4—34no—
260(C2×D3)⋊C4—121no—
261(C2×D3)⋊C4—121no—
262(C2×D3)⋊C4—121no—
263C4⋊Dic3—121no—
264C4⋊Dic3—121no—
265Dic3⋊C4—121no—
266Dic3⋊C4—121no—
267Dic3⋊C4—121no—
268C4×Dic3—34no—
269C4×Dic3—121no—
270C22×C9—22no—
271C22×C9—22no—
272C22×C9—22no—
273C22×C9—41no—
274C22×C9—41no—
275C22×C9—41no—
276C22×C9—41no—
277C22×C9C23×C411yescharacteristic
278C22×C9H(5,𝔽2)11yescharacteristic
279C22×C9H(5,𝔽2)11yescharacteristic
280C22×C9H(5,𝔽2)11yescharacteristic
281C22×C9H(5,𝔽2)11yescharacteristic
282C22×C92−1+411yescharacteristic
283C22×C92−1+411yescharacteristic
284C2×D9—22no—
285C2×D9—22no—
286C2×D9—22no—
287C2×D9—41no—
288C2×D9—41no—
289C2×D9—41no—
290C2×D9—41no—
291C4×C9—22no—
292C4×C9—22no—
293C4×C9—41no—
294C4×C9—41no—
295C4×C9—41no—
296C4×C9—41no—
297Dic9—22no—
298Dic9—22no—
299Dic9—22no—
300Dic9—41no—
301Dic9—41no—
302Dic9—41no—
303Dic9—41no—
304C22×Q8—91no—
305C22×D4—91no—
306C23×C4—91no—
307C23×C4—91no—
308#124—98no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4—91no—
312C2×C4⋊C4—91no—
313C2×C4⋊C4—91no—
314C2×C4⋊C4C2×D911yescharacteristic
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×C22⋊C4C2×D911yescharacteristic
323C2×C22⋊C4C2×D911yescharacteristic
324C2×C22⋊C4C2×D911yescharacteristic
325C2×C42—91no—
326C2×C42—91no—
327C2×C42C2×D911yescharacteristic
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#95—91no—
338#95C2×D911yescharacteristic
339#95C2×D911yescharacteristic
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3C2×C4×D312yes—
347C23×C3C23×D311yescharacteristic
348C22×D3—32no—
349C22×D3—61no—
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—61no—
353C22×D3—61no—
354C22×D3—61no—
355C2×C3×C4—21no—
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×C4C2×C4×D312yes—
372C2×C3×C4C2×C4×D312yes—
373#67—124no—
374C2×Dic3—32no—
375C2×Dic3—32no—
376C2×Dic3—32no—
377C2×Dic3—61no—
378C2×Dic3—61no—
379C2×Dic3—61no—
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—
395C2×Dic3—124no—
396C4×D3—124no—
397Dic6—124no—
398C2×C9—42no—
399C2×C9#51811yescharacteristic
400C2×C9#52011yescharacteristic
401C2×C9#52011yescharacteristic
402C2×C9H(3,𝔽4)11yescharacteristic
403C2×C9#56211yescharacteristic
404C2×C9#56211yescharacteristic
405C2×C9#56311yescharacteristic
406D9—42no—
407C24—91no—
408C24C22×D911yescharacteristic
409C2×Q8—94no—
410C2×Q8—361no—
411C2×Q8—361no—
412C2×D4—94no—
413C2×D4—361no—
414C2×D4—361no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—91no—
420C22×C4—91no—
421C22×C4—91no—
422C22×C4—361no—
423C22×C4—361no—
424C22×C4—361no—
425C22×C4—361no—
426C22×C4—361no—
427C22×C4—361no—
428C22×C4C22×D911yescharacteristic
429C22×C4C22×D911yescharacteristic
430C22×C4C22×D911yescharacteristic
431C22×C4C22×D911yescharacteristic
432C22×C4C22×D911yescharacteristic
433C22×C4C22×D911yescharacteristic
434C4⋊C4—41no—
435C4⋊C4—361no—
436C4⋊C4—361no—
437C4⋊C4—361no—
438C4⋊C4—361no—
439C4⋊C4—361no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—94no—
443C22⋊C4—94no—
444C22⋊C4—94no—
445C22⋊C4—361no—
446C22⋊C4—361no—
447C22⋊C4—361no—
448C22⋊C4—361no—
449C22⋊C4C4×D914yescomplemented
450C42—41no—
451C42—94no—
452C42—361no—
453C22×C3—22no—
454C22×C3—22no—
455C22×C3—22no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3C22×C4×D311yescharacteristic
461C22×C3#100411yescharacteristic
462C22×C3#100411yescharacteristic
463C22×C3#100911yescharacteristic
464C22×C3#100911yescharacteristic
465C22×C3#101011yescharacteristic
466C22×C3#101011yescharacteristic
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—62no—
470C2×D3—121no—
471C2×D3—121no—
472C2×D3—121no—
473C2×D3—121no—
474C3×C4—22no—
475C3×C4—22no—
476C3×C4—41no—
477C3×C4—41no—
478C3×C4—41no—
479C3×C4—41no—
480Dic3—62no—
481Dic3—62no—
482Dic3—62no—
483Dic3—121no—
484Dic3—121no—
485Dic3—121no—
486Dic3—121no—
487C9#237911yescharacteristic, complemented, Sylow
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—92no—
495C23—181no—
496C23—181no—
497C23—181no—
498C23—181no—
499C23—181no—
500C23—181no—
501C23C2×C4×D912yes—
502C23C23×D911yescharacteristic
503Q8—364no—
504D4—364no—
505C2×C4—21no—
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—92no—
522C2×C4—92no—
523C2×C4—92no—
524C2×C4—181no—
525C2×C4—181no—
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—181no—
542C2×C4—364no—
543C2×C4—364no—
544C2×C4C2×C4×D912yes—
545C2×C4C2×C4×D912yes—
546C2×C3—42no—
547C2×C3#552311yescharacteristic
548C2×C3#554511yescharacteristic
549C2×C3#554611yescharacteristic
550C2×C3#562111yescharacteristic
551C2×C3#566711yescharacteristic
552C2×C3#568311yescharacteristic
553C2×C3#571211yescharacteristic
554D3—122no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—182no—
563C22—182no—
564C22—182no—
565C22—361no—
566C22—361no—
567C22—361no—
568C22—361no—
569C22C22×C4×D911yescharacteristic
570C22#6371011yescharacteristic
571C22#6371011yescharacteristic
572C22#6371511yescharacteristic
573C22#6371511yescharacteristic
574C22#6371611yescharacteristic
575C22#6371611yescharacteristic
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—182no—
583C4—182no—
584C4—182no—
585C4—361no—
586C4—361no—
587C4—361no—
588C4—361no—
589C3#7549311yescharacteristic
590C2—42no—
591C2—362no—
592C2#1058962511yescharacteristic
593C2#1058964711yescharacteristic
594C2#1058964811yescharacteristic
595C2#1058972311yescharacteristic
596C2#1058976911yescharacteristic
597C2#1058978511yescharacteristic
598C2#1058981411yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC9×#388C2
prime radicalC22×#611C22
cosocleC23×C9C24
hypercenter#388D9
hypocenterC9#2379
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C9×#388C2semidirect
3. #10588670C2semidirect
4. #10588657C2semidirect
7. #10588630C2semidirect
8. #10588626C2semidirect
9. #10588624C2semidirect
10. #10588620C2semidirect
11. #10588609C2semidirect
12. #10588348C2semidirect
13. #10588348C2semidirect
14. #10588330C2semidirect
15. #10588326C2semidirect
40. #63447C4semidirect
94. C2×Dic18C2×C4semidirect
98. C9×C22⋊C4C2×C4semidirect
101. #3676C2×C4semidirect
105. (C2×D9)⋊C4C2×C4semidirect
106. (C2×D9)⋊C4C2×C4semidirect
113. C4×Dic9C2×C4semidirect
215. #388D9semidirect
449. C22⋊C4C4×D9semidirect
487. C9#2379semidirect

Maximal subgroups

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

subgroupindex
C2×#634472
C9×#3882
#105886702
#105886572
#105886382
#105886362
#105886302
#105886262
#105886242
#105886202
#105886092
#105883482
#105883302
#105883262
#754933