Finite Group Databasebeta

← #11824472

Subgroups — #11824472

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 513 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#63508C211yesmaximal, characteristic, complemented
3C2×#63506C211yesmaximal, characteristic, complemented
4C2×C4×#611C211yesmaximal, characteristic
5C2×#63486C211yesmaximal, characteristic, complemented
6C2×#63459C211yesmaximal, characteristic, complemented
7#10588673C212yesmaximal, complemented
8#10588655C212yesmaximal, complemented
9C4⋊C4×Dic9C211yesmaximal, characteristic, complemented
10#10588637C212yesmaximal
11#10588629C212yesmaximal, complemented
12#82780—31nomaximal
13C22×Q8×C9C2211yescharacteristic
14C23×C4×C9C2211yescharacteristic
15C22×#611C2211yescharacteristic
16C22×C4×D9C2211yescharacteristic
17C22×Dic18C2211yescharacteristic
18C9×C22⋊Q8—24no—
19C2×C9×C4⋊C4C2212yes—
20C2×C9×C4⋊C4C2211yescharacteristic
21C2×C9×C22⋊C4C2212yes—
22C2×#3676C2212yes—
23C2×#3676C2211yescharacteristic
24#63508—24no—
25#63506—24no—
26C4×#611—24no—
27C2×(C2×D9)⋊C4C2211yescharacteristic
28C2×(C2×D9)⋊C4C2212yes—
29C2×(C2×D9)⋊C4C2212yes—
30C2×C4⋊Dic9C2212yes—
31C2×C4⋊Dic9C2211yescharacteristic
32#63486—24no—
33C2×Dic9⋊C4C2212yes—
34C2×Dic9⋊C4C2212yes—
35C2×Dic9⋊C4C2211yescharacteristic
36C2×Dic9⋊C4C2212yes—
37C2×Dic9⋊C4C2212yes—
38C2×C4×Dic9C2212yes—
39C2×C4×Dic9C2211yescharacteristic
40#63459—24no—
41C9⋊#95C2212yes—
42C2×C3×C22⋊Q8D311yescharacteristic
43C2×#946—31no—
44C2×#944—31no—
45C2×C4×#67—31no—
46C2×#924—31no—
47C2×#897—31no—
48#4993—32no—
49#4975—32no—
50Dic3×C4⋊C4—31no—
51#4957—32no—
52#4949—32no—
53C24×C9C2311yescharacteristic
54C23×D9C2311yescharacteristic
55C2×Q8×C9—22no—
56C2×Q8×C9—22no—
57C2×Q8×C9—22no—
58C22×C4×C9—22no—
59C22×C4×C9—22no—
60C22×C4×C9—22no—
61C22×C4×C9C2312yes—
62C22×C4×C9C2311yescharacteristic
63C22×C4×C9C2312yes—
64C22×C4×C9C2311yescharacteristic
65C2×#611—22no—
66C2×#611—22no—
67C2×#611Q814yescomplemented
68C22×Dic9C2312yes—
69C22×Dic9C2311yescharacteristic
70C22×Dic9C2311yescharacteristic
71C22×Dic9C2312yes—
72C22×Dic9C2311yescharacteristic
73C2×C4×D9—22no—
74C2×C4×D9—22no—
75C2×C4×D9—22no—
76C2×Dic18—22no—
77C2×Dic18—22no—
78C2×Dic18—22no—
79C9×C4⋊C4—24no—
80C9×C4⋊C4D414yescomplemented
81C9×C22⋊C4—24no—
82#3676—22no—
83#3676—24no—
84(C2×D9)⋊C4—24no—
85(C2×D9)⋊C4—22no—
86(C2×D9)⋊C4—24no—
87C4⋊Dic9—24no—
88C4⋊Dic9D414yescomplemented
89Dic9⋊C4—22no—
90Dic9⋊C4—24no—
91Dic9⋊C4—24no—
92Dic9⋊C4—24no—
93Dic9⋊C4—24no—
94C4×Dic9—24no—
95C4×Dic9D414yes—
96#2542—91noSylow
97C22×C3×Q8C2×D311yescharacteristic
98C23×C3×C4C2×D311yescharacteristic
99C22×#67—31no—
100C22×C4×D3—31no—
101C22×Dic6—31no—
102C3×C22⋊Q8—24no—
103C2×C3×C4⋊C4C2×D312yes—
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×C3×C22⋊C4C2×D312yes—
106C2×#217—31no—
107C2×#217—32no—
108#946—64no—
109#944—64no—
110C4×#67—64no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—32no—
116#924—64no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×Dic3⋊C4—31no—
121C2×Dic3⋊C4—32no—
122C2×C4×Dic3—31no—
123C2×C4×Dic3—32no—
124#897—64no—
125C3⋊#95—32no—
126C23×C9—21no—
127C23×C9—21no—
128C23×C9—21no—
129C23×C9—21no—
130C23×C9—21no—
131C23×C9—21no—
132C23×C9C2×Q812yes—
133C23×C9C2411yescharacteristic
134C22×D9—21no—
135C22×D9—21no—
136C22×D9—21no—
137C22×D9—21no—
138C22×D9—21no—
139C22×D9—21no—
140C22×D9C2×Q812yes—
141Q8×C9—44no—
142C2×C4×C9—22no—
143C2×C4×C9—22no—
144C2×C4×C9—21no—
145C2×C4×C9—22no—
146C2×C4×C9—21no—
147C2×C4×C9—22no—
148C2×C4×C9—22no—
149C2×C4×C9—21no—
150C2×C4×C9—44no—
151C2×C4×C9C2×D412yes—
152C2×C4×C9C2×D412yes—
153C2×C4×C9C2×D414yes—
154C2×C4×C9C2×D412yes—
155#611—28no—
156C2×Dic9—22no—
157C2×Dic9—21no—
158C2×Dic9—22no—
159C2×Dic9—21no—
160C2×Dic9—22no—
161C2×Dic9—21no—
162C2×Dic9—22no—
163C2×Dic9—21no—
164C2×Dic9—21no—
165C2×Dic9—22no—
166C2×Dic9C2×D412yes—
167C2×Dic9C2×D414yes—
168C2×Dic9C2×D412yes—
169C2×Dic9C2×Q812yes—
170C2×Dic9#4112yes—
171C4×D9—44no—
172Dic18—44no—
173C2×C4⋊Q8—91no—
174C2×C22⋊Q8—91no—
175C2×C22⋊Q8—91no—
176C2×C22⋊Q8—91no—
177C2×C22⋊Q8D911yescharacteristic, complemented
178C2×C4×D4—91no—
179#399—92no—
180#399—92no—
181#390—92no—
182#384—92no—
183C4×C4⋊C4—91no—
184C24×C3C22×D311yescharacteristic
185C23×D3—31no—
186C2×C3×Q8—22no—
187C2×C3×Q8—22no—
188C2×C3×Q8—22no—
189C22×C3×C4—22no—
190C22×C3×C4—22no—
191C22×C3×C4—22no—
192C22×C3×C4C22×D312yes—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D312yes—
195C22×C3×C4C22×D311yescharacteristic
196C2×#67—34no—
197C2×#67—62no—
198C2×#67—62no—
199C22×Dic3—31no—
200C22×Dic3—31no—
201C22×Dic3—32no—
202C22×Dic3—31no—
203C22×Dic3—32no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×Dic6—62no—
208C2×Dic6—62no—
209C2×Dic6—62no—
210C3×C4⋊C4—24no—
211C3×C4⋊C4#6714yes—
212C3×C22⋊C4—24no—
213#217—64no—
214#217—62no—
215(C2×D3)⋊C4—62no—
216(C2×D3)⋊C4—64no—
217(C2×D3)⋊C4—64no—
218C4⋊Dic3—34no—
219C4⋊Dic3—64no—
220Dic3⋊C4—64no—
221Dic3⋊C4—62no—
222Dic3⋊C4—64no—
223Dic3⋊C4—64no—
224Dic3⋊C4—64no—
225C4×Dic3—34no—
226C4×Dic3—64no—
227C22×C9—22no—
228C22×C9—22no—
229C22×C9—22no—
230C22×C9—41no—
231C22×C9—41no—
232C22×C9—41no—
233C22×C9—41no—
234C22×C9C22×D411yescharacteristic
235C22×C9C22×D411yescharacteristic
236C22×C9C22×D411yescharacteristic
237C22×C9C22×Q811yescharacteristic
238C22×C9C2×#4111yescharacteristic
239C22×C92−1+411yescharacteristic
240C22×C92−1+411yescharacteristic
241C2×D9—22no—
242C2×D9—22no—
243C2×D9—22no—
244C2×D9—41no—
245C2×D9—41no—
246C2×D9—41no—
247C2×D9—41no—
248C4×C9—24no—
249C4×C9—41no—
250C4×C9—42no—
251C4×C9#12714yes—
252Dic9—22no—
253Dic9—24no—
254Dic9—42no—
255Dic9—41no—
256Dic9C22⋊Q814yescomplemented
257C22×Q8—91no—
258C22×Q8C2×D911yescharacteristic
259C22×D4—91no—
260C23×C4—91no—
261C23×C4C2×D911yescharacteristic
262C4⋊Q8—184no—
263C22⋊Q8—24no—
264C22⋊Q8—184no—
265C22⋊Q8—184no—
266C22⋊Q8—184no—
267C4×D4—184no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4—91no—
270C2×C4⋊C4—92no—
271C2×C4⋊C4—92no—
272C2×C4⋊C4—92no—
273C2×C4⋊C4—92no—
274C2×C4⋊C4—92no—
275C2×C4⋊C4C2×D912yes—
276C2×C4⋊C4C2×D911yescharacteristic
277C2×C22⋊C4—91no—
278C2×C22⋊C4—92no—
279C2×C22⋊C4—91no—
280C2×C22⋊C4—92no—
281C2×C22⋊C4—92no—
282C2×C22⋊C4C2×D912yes—
283C2×C42—91no—
284C2×C42—92no—
285#95—92no—
286C23×C3—21no—
287C23×C3—21no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—21no—
292C23×C3D3×Q812yes—
293C23×C3C23×D311yescharacteristic
294C22×D3—32no—
295C22×D3—61no—
296C22×D3—61no—
297C22×D3—61no—
298C22×D3—61no—
299C22×D3—61no—
300C22×D3—61no—
301C3×Q8—44no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—44no—
311C2×C3×C4D3×D412yes—
312C2×C3×C4D3×D412yes—
313C2×C3×C4C2×#6714yes—
314C2×C3×C4C2×#6712yes—
315#67—68no—
316C2×Dic3—32no—
317C2×Dic3—32no—
318C2×Dic3—32no—
319C2×Dic3—32no—
320C2×Dic3—34no—
321C2×Dic3—61no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—61no—
325C2×Dic3—62no—
326C2×Dic3—61no—
327C2×Dic3—62no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—62no—
331C4×D3—124no—
332Dic6—124no—
333C2×C9—42no—
334C2×C9C2×C22⋊Q811yescharacteristic
335C2×C9C2×#12711yescharacteristic
336C2×C9#53611yescharacteristic
337C2×C9#54711yescharacteristic
338C2×C9#54711yescharacteristic
339C2×C9D4×Q811yescharacteristic
340C2×C9D4×Q811yescharacteristic
341D9—42no—
342C24—91no—
343C24C22×D911yescharacteristic
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—182no—
348C2×Q8—182no—
349C2×Q8—182no—
350C2×D4—94no—
351C2×D4—182no—
352C2×D4—182no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—91no—
357C22×C4—91no—
358C22×C4—92no—
359C22×C4—92no—
360C22×C4—91no—
361C22×C4—182no—
362C22×C4—182no—
363C22×C4—182no—
364C22×C4C22×D912yes—
365C22×C4C22×D911yescharacteristic
366C22×C4C22×D912yes—
367C22×C4C22×D911yescharacteristic
368C4⋊C4—24no—
369C4⋊C4—94no—
370C4⋊C4—182no—
371C4⋊C4—184no—
372C4⋊C4—184no—
373C4⋊C4—184no—
374C4⋊C4—184no—
375C4⋊C4—184no—
376C4⋊C4#61114yescomplemented
377C22⋊C4—24no—
378C22⋊C4—182no—
379C22⋊C4—184no—
380C22⋊C4—182no—
381C22⋊C4—184no—
382C22⋊C4—184no—
383C42—94no—
384C42—184no—
385C22×C3—22no—
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—41no—
389C22×C3—41no—
390C22×C3—41no—
391C22×C3—41no—
392C22×C3C2×D3×D411yescharacteristic
393C22×C3C2×D3×D411yescharacteristic
394C22×C3C2×D3×Q811yescharacteristic
395C22×C3#100711yescharacteristic
396C22×C3D3×#4111yescharacteristic
397C22×C3#101011yescharacteristic
398C22×C3C22×#6711yescharacteristic
399C2×D3—62no—
400C2×D3—62no—
401C2×D3—62no—
402C2×D3—121no—
403C2×D3—121no—
404C2×D3—121no—
405C2×D3—121no—
406C3×C4—24no—
407C3×C4—41no—
408C3×C4—42no—
409C3×C4#94014yes—
410Dic3—34no—
411Dic3—62no—
412Dic3—64no—
413Dic3—122no—
414Dic3—121no—
415C9#254211yescharacteristic, complemented, Sylow
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—92no—
423C23—181no—
424C23—181no—
425C23—181no—
426C23—181no—
427C23—181no—
428C23—181no—
429C23Q8×D912yes—
430C23C23×D911yescharacteristic
431Q8—44no—
432Q8—364no—
433D4—188no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—21no—
442C2×C4—44no—
443C2×C4—92no—
444C2×C4—92no—
445C2×C4—92no—
446C2×C4—92no—
447C2×C4—94no—
448C2×C4—181no—
449C2×C4—182no—
450C2×C4—182no—
451C2×C4—181no—
452C2×C4—181no—
453C2×C4—182no—
454C2×C4—181no—
455C2×C4—182no—
456C2×C4—182no—
457C2×C4—181no—
458C2×C4—364no—
459C2×C4D4×D912yes—
460C2×C4D4×D912yes—
461C2×C4C2×#61114yes—
462C2×C4C2×#61112yes—
463C2×C3—42no—
464C2×C3D3×C22⋊Q811yescharacteristic
465C2×C3#562811yescharacteristic
466C2×C3#563111yescharacteristic
467C2×C3#563211yescharacteristic
468C2×C3C2×#94011yescharacteristic
469C2×C3Q8×#6711yescharacteristic
470C2×C3#582411yescharacteristic
471D3—122no—
472C22—22no—
473C22—22no—
474C22—22no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—182no—
480C22—182no—
481C22—182no—
482C22—361no—
483C22—361no—
484C22—361no—
485C22—361no—
486C22C2×D4×D911yescharacteristic
487C22C2×D4×D911yescharacteristic
488C22C2×Q8×D911yescharacteristic
489C22#6371311yescharacteristic
490C22#41×D911yescharacteristic
491C22#6371611yescharacteristic
492C22C22×#61111yescharacteristic
493C4—24no—
494C4—41no—
495C4—42no—
496C4—94no—
497C4—182no—
498C4—184no—
499C4—361no—
500C4—362no—
501C4#6350214yes—
502C3#8278011yescharacteristic
503C2—42no—
504C2—362no—
505C2D9×C22⋊Q811yescharacteristic
506C2#1058973011yescharacteristic
507C2#1058973311yescharacteristic
508C2#1058973411yescharacteristic
509C2C2×#6350211yescharacteristic
510C2Q8×#61111yescharacteristic
511C2#1058992611yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC23×C9C24
Frattini, socleC23×C3C23×D3
FittingC2×C9×C22⋊Q8C2
prime radicalC22×#611C22
hypercenterC2×C22⋊Q8D9
hypocenterC9#2542
LCSG ▷ C23×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C9×C22⋊Q8C2semidirect
2. C2×#63508C2semidirect
3. C2×#63506C2semidirect
5. C2×#63486C2semidirect
6. C2×#63459C2semidirect
7. #10588673C2semidirect
8. #10588655C2semidirect
9. C4⋊C4×Dic9C2semidirect
11. #10588629C2semidirect
67. C2×#611Q8semidirect
80. C9×C4⋊C4D4semidirect
88. C4⋊Dic9D4semidirect
177. C2×C22⋊Q8D9semidirect
256. Dic9C22⋊Q8semidirect
376. C4⋊C4#611semidirect
415. C9#2542semidirect

Maximal subgroups

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

subgroupindex
C2×C9×C22⋊Q82
C2×#635082
C2×#635062
C2×C4×#6112
C2×#634862
C2×#634592
#105886732
#105886552
C4⋊C4×Dic92
#105886372
#105886292
#827803