Finite Group Databasebeta

← #11873261

Subgroups — #11873261

Order 1152.

537 conjugacy classes of subgroups.

The subgroup lattice has 489 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589914C211yesmaximal, characteristic
2#10589727C211yesmaximal, characteristic
3C9×#451C211yesmaximal, characteristic
4#10588907C211yesmaximal, characteristic
5#10588864C211yesmaximal, characteristic, complemented
6#10588862C211yesmaximal, characteristic, complemented
7#10588862C211yesmaximal, characteristic, complemented
8Q16×Dic9C211yesmaximal, characteristic, complemented
9#10588725C211yesmaximal, characteristic
10#10588479C211yesmaximal, characteristic, complemented
11#10588476C211yesmaximal, characteristic, complemented
12#10588470C211yesmaximal, characteristic, complemented
13#10588469C211yesmaximal, characteristic, complemented
14#10588403C211yesmaximal, characteristic
15#10588400C211yesmaximal, characteristic
16#80177—31nomaximal
17C22×Q8×C9C2211yescharacteristic
18C2×C9×Q16C2211yescharacteristic
19C2×C9×Q16C2211yescharacteristic
20C9×C22⋊Q8C2211yescharacteristic
21Q8×Dic9—21no—
22Q8×Dic9—21no—
23Q8×Dic9C2211yescharacteristic
24Q8×Dic9C2211yescharacteristic
25Q8×Dic9C2211yescharacteristic
26Q8×Dic9C2211yescharacteristic
27Q8×Dic9C2211yescharacteristic
28#63506C2211yescharacteristic
29C2×#3674C2211yescharacteristic
30C2×#3674C2211yescharacteristic
31#63488—21no—
32#63488—21no—
33#63488C2211yescharacteristic
34#63488C2211yescharacteristic
35#63486C2211yescharacteristic
36#63452—21no—
37#63452C2211yescharacteristic
38#63451—21no—
39#63449C2211yescharacteristic
40#63441—21no—
41#63441—21no—
42C9×#103C2211yescharacteristic
43C9×#103C2211yescharacteristic
44C9×C22⋊C8C2211yescharacteristic
45#63395C2211yescharacteristic
46#63395C2211yescharacteristic
47#63395C2211yescharacteristic
48#63395C2211yescharacteristic
49#63389C2211yescharacteristic
50#63378C2211yescharacteristic
51#63377C2211yescharacteristic
52#63376C2211yescharacteristic
53#63376C2211yescharacteristic
54#63375C2211yescharacteristic
55Dic9⋊C8C2211yescharacteristic
56Dic9⋊C8C2211yescharacteristic
57C8×Dic9C2211yescharacteristic
58#63367C2211yescharacteristic
59#63366C2211yescharacteristic
60#5812—31no—
61#5625—31no—
62C3×#451D311yescharacteristic
63#5228—31no—
64#5184—31no—
65#5182—31no—
66#5182—31no—
67Dic3×Q16—31no—
68#5045—31no—
69#4799—31no—
70#4796—31no—
71#4790—31no—
72#4789—31no—
73#4723—31no—
74#4720—31no—
75C2×Q8×C9—22no—
76C2×Q8×C9—22no—
77C2×Q8×C9—21no—
78C2×Q8×C9C2311yescharacteristic
79C2×Q8×C9C2311yescharacteristic
80C2×Q8×C9C2311yescharacteristic
81C22×C4×C9—21no—
82C22×C4×C9C2311yescharacteristic
83C2×Dic18C2311yescharacteristic
84C9×Q16—22no—
85C9×Q16—22no—
86C2×C8×C9C2311yescharacteristic
87C2×C8×C9C2311yescharacteristic
88C9×C4⋊C4—21no—
89C9×C4⋊C4C2311yescharacteristic
90C9×C22⋊C4—21no—
91#3676—21no—
92#3676—21no—
93#3676D411yescharacteristic
94#3676D411yescharacteristic
95#3674—22no—
96#3674—22no—
97C4⋊Dic9—21no—
98C4⋊Dic9—21no—
99C4⋊Dic9—21no—
100C4⋊Dic9—21no—
101C4⋊Dic9—21no—
102C4⋊Dic9—21no—
103C4⋊Dic9D411yescharacteristic
104C4⋊Dic9D411yescharacteristic
105C4⋊Dic9C2311yescharacteristic
106C4⋊Dic9C2311yescharacteristic
107C4⋊Dic9C2311yescharacteristic
108Dic9⋊C4—21no—
109Dic9⋊C4—21no—
110Dic9⋊C4—21no—
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113C4×Dic9—21no—
114C4×Dic9—21no—
115C4×Dic9—21no—
116C4×Dic9—21no—
117C4×Dic9—21no—
118C4×Dic9—21no—
119C4×Dic9—21no—
120C4×Dic9C2311yescharacteristic
121C4×Dic9C2311yescharacteristic
122C2×C9⋊C8C2311yescharacteristic
123C2×C9⋊C8C2311yescharacteristic
124#3127—91noSylow
125C22×C3×Q8C2×D311yescharacteristic
126C2×C3×Q16C2×D311yescharacteristic
127C2×C3×Q16C2×D311yescharacteristic
128C3×C22⋊Q8C2×D311yescharacteristic
129Q8×Dic3—31no—
130Q8×Dic3—31no—
131Q8×Dic3—31no—
132Q8×Dic3—31no—
133Q8×Dic3—31no—
134Q8×Dic3—61no—
135Q8×Dic3—61no—
136#944—31no—
137C2×#216—31no—
138C2×#216—31no—
139#926—31no—
140#926—31no—
141#926—61no—
142#926—61no—
143#924—31no—
144#890—31no—
145#890—61no—
146#889—61no—
147#887—31no—
148#879—61no—
149#879—61no—
150C3×#103C2×D311yescharacteristic
151C3×#103C2×D311yescharacteristic
152C3×C22⋊C8C2×D311yescharacteristic
153#835—31no—
154#835—31no—
155#835—31no—
156#835—31no—
157#830—31no—
158#818—31no—
159#817—31no—
160#816—31no—
161#816—31no—
162#815—31no—
163Dic3⋊C8—31no—
164Dic3⋊C8—31no—
165C8×Dic3—31no—
166#808—31no—
167#807—31no—
168C23×C9C2×D411yescharacteristic
169Q8×C9—24no—
170Q8×C9—21no—
171Q8×C9—21no—
172Q8×C9—21no—
173Q8×C9—21no—
174Q8×C9#4112yes—
175Q8×C9#4112yes—
176C2×C4×C9—24no—
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×C9C2×D411yescharacteristic
184C2×C4×C9C2411yescharacteristic
185C2×Dic9—21no—
186C2×Dic9—21no—
187C2×Dic9—21no—
188C2×Dic9—21no—
189C2×Dic9C2×D411yescharacteristic
190C2×Dic9C2×D411yescharacteristic
191C2×Dic9C2×D411yescharacteristic
192C2×Dic9C2×D411yescharacteristic
193Dic18—21no—
194Dic18—21no—
195C8×C9—21no—
196C8×C9—21no—
197C9⋊C8—21no—
198C9⋊C8—21no—
199#541—91no—
200#519—91no—
201#485—91no—
202#485—91no—
203#479—91no—
204#479—91no—
205#462—91no—
206#462—91no—
207#451—91no—
208#451D911yescharacteristic
209#441—91no—
210#441—91no—
211C4×Q16—91no—
212C4×Q16—91no—
213#433—91no—
214C2×C3×Q8—22no—
215C2×C3×Q8—22no—
216C2×C3×Q8—21no—
217C2×C3×Q8C22×D311yescharacteristic
218C2×C3×Q8C22×D311yescharacteristic
219C2×C3×Q8C22×D311yescharacteristic
220C22×C3×C4—21no—
221C22×C3×C4C22×D311yescharacteristic
222C2×Dic6—31no—
223C3×Q16—22no—
224C3×Q16—22no—
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C3×C4⋊C4—21no—
228C3×C4⋊C4C22×D311yescharacteristic
229C3×C22⋊C4—21no—
230#217—31no—
231#217—31no—
232#217—61no—
233#217—61no—
234#216—62no—
235#216—62no—
236C4⋊Dic3—31no—
237C4⋊Dic3—31no—
238C4⋊Dic3—31no—
239C4⋊Dic3—31no—
240C4⋊Dic3—31no—
241C4⋊Dic3—61no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—61no—
247Dic3⋊C4—61no—
248Dic3⋊C4—61no—
249Dic3⋊C4—61no—
250Dic3⋊C4—61no—
251Dic3⋊C4—61no—
252C4×Dic3—31no—
253C4×Dic3—31no—
254C4×Dic3—61no—
255C4×Dic3—61no—
256C4×Dic3—61no—
257C4×Dic3—61no—
258C4×Dic3—61no—
259C4×Dic3—61no—
260C4×Dic3—61no—
261C2×C3⋊C8—31no—
262C2×C3⋊C8—31no—
263C22×C9—21no—
264C22×C9—21no—
265C22×C9—21no—
266C22×C9C22×D411yescharacteristic
267C4×C9—22no—
268C4×C9—22no—
269C4×C9—21no—
270C4×C9—41no—
271C4×C9—41no—
272C4×C9C2×#4111yescharacteristic
273C4×C9C2×#4111yescharacteristic
274Dic9—21no—
275Dic9—21no—
276Dic9—21no—
277Dic9—21no—
278Dic9—41no—
279Dic9—41no—
280Dic9—41no—
281Dic9—41no—
282C22×Q8C2×D911yescharacteristic
283C2×Q16—91no—
284C2×Q16—91no—
285C2×Q16C2×D911yescharacteristic
286C2×Q16C2×D911yescharacteristic
287C4⋊Q8—91no—
288#126—181no—
289#126—181no—
290#125—91no—
291#125—181no—
292#125—181no—
293C22⋊Q8—91no—
294C22⋊Q8C2×D911yescharacteristic
295C4×Q8—91no—
296C4×Q8—91no—
297C4×Q8—91no—
298C4×Q8—91no—
299C4×Q8—91no—
300C4×Q8—91no—
301C4×Q8—181no—
302C4×Q8—181no—
303#117—91no—
304#117—91no—
305#117—181no—
306#117—181no—
307#107—91no—
308#107—91no—
309#106—91no—
310#106—91no—
311C4⋊C8—91no—
312C4⋊C8—91no—
313#103—91no—
314#103—91no—
315#103—91no—
316#103—91no—
317#103—91no—
318#103—91no—
319#103C2×D911yescharacteristic
320#103C2×D911yescharacteristic
321C22⋊C8—91no—
322C22⋊C8C2×D911yescharacteristic
323#97—91no—
324C4×C8—91no—
325C23×C3D3×D411yescharacteristic
326C3×Q8—24no—
327C3×Q8—21no—
328C3×Q8—21no—
329C3×Q8—21no—
330C3×Q8—21no—
331C3×Q8#23712yes—
332C3×Q8#23712yes—
333C2×C3×C4—24no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×Dic3—31no—
343C2×Dic3—31no—
344C2×Dic3—31no—
345C2×Dic3—31no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350Dic6—61no—
351Dic6—61no—
352C3×C8—21no—
353C3×C8—21no—
354C3⋊C8—61no—
355C3⋊C8—61no—
356C2×C9—41no—
357C2×C9#52511yescharacteristic
358C2×C9#57811yescharacteristic
359C2×C9#57811yescharacteristic
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—21no—
363C2×Q8—91no—
364C2×Q8C22×D911yescharacteristic
365C2×Q8C22×D911yescharacteristic
366C2×Q8C22×D911yescharacteristic
367C22×C4—21no—
368C22×C4C22×D911yescharacteristic
369Q16—22no—
370Q16—22no—
371Q16—182no—
372Q16—182no—
373C2×C8—91no—
374C2×C8—91no—
375C2×C8C22×D911yescharacteristic
376C2×C8C22×D911yescharacteristic
377C4⋊C4—21no—
378C4⋊C4—91no—
379C4⋊C4—91no—
380C4⋊C4—91no—
381C4⋊C4—91no—
382C4⋊C4—91no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—181no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4—181no—
394C4⋊C4C22×D911yescharacteristic
395C22⋊C4—21no—
396C22⋊C4—91no—
397C22⋊C4—91no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C42—91no—
401C42—91no—
402C42—181no—
403C42—181no—
404C42—181no—
405C42—181no—
406C42—181no—
407C42—181no—
408C42—181no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3C2×D3×D411yescharacteristic
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—21no—
416C3×C4—41no—
417C3×C4—41no—
418C3×C4C2×#23711yescharacteristic
419C3×C4C2×#23711yescharacteristic
420Dic3—61no—
421Dic3—61no—
422Dic3—61no—
423Dic3—61no—
424Dic3—121no—
425Dic3—121no—
426Dic3—121no—
427Dic3—121no—
428C9#312711yescharacteristic, complemented, Sylow
429C23D4×D911yescharacteristic
430Q8—24no—
431Q8—21no—
432Q8—21no—
433Q8—21no—
434Q8—21no—
435Q8—181no—
436Q8—181no—
437Q8#369912yes—
438Q8#369912yes—
439C2×C4—24no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—91no—
447C2×C4—91no—
448C2×C4—91no—
449C2×C4—91no—
450C2×C4—181no—
451C2×C4—181no—
452C2×C4—181no—
453C2×C4—181no—
454C2×C4D4×D911yescharacteristic
455C2×C4C23×D911yescharacteristic
456C8—21no—
457C8—21no—
458C8—181no—
459C8—181no—
460C2×C3—41no—
461C2×C3#558611yescharacteristic
462C2×C3#576611yescharacteristic
463C2×C3#577911yescharacteristic
464C22—21no—
465C22—21no—
466C22—21no—
467C22C2×D4×D911yescharacteristic
468C4—22no—
469C4—22no—
470C4—21no—
471C4—41no—
472C4—41no—
473C4—181no—
474C4—181no—
475C4—181no—
476C4—181no—
477C4—361no—
478C4—361no—
479C4—361no—
480C4—361no—
481C4C2×#369911yescharacteristic
482C4C2×#369911yescharacteristic
483C3#8017711yescharacteristic
484C2—41no—
485C2#1058968811yescharacteristic
486C2#1058986811yescharacteristic
487C2#1058988111yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#451C2
socleC22×C3C2×D3×D4
prime radicalC23×C3D3×D4
hypercenter#451D9
hypocenterC9#3127
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
5. #10588864C2semidirect
6. #10588862C2semidirect
7. #10588862C2semidirect
8. Q16×Dic9C2semidirect
10. #10588479C2semidirect
11. #10588476C2semidirect
12. #10588470C2semidirect
13. #10588469C2semidirect
428. C9#3127semidirect

Maximal subgroups

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

subgroupindex
#105899142
#105897272
C9×#4512
#105889072
#105888642
#105888622
Q16×Dic92
#105887252
#105884792
#105884762
#105884702
#105884692
#105884032
#105884002
#801773