Finite Group Databasebeta

← #11860363

Subgroups — #11860363

Order 1152.

726 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63471C211yesmaximal, characteristic
2#10589624C211yesmaximal, characteristic
3C2×#63449C211yesmaximal, characteristic, complemented
4C9×#428C211yesmaximal, characteristic, complemented
5M16×Dic9C211yesmaximal, characteristic, complemented
6#10588681C211yesmaximal, characteristic, complemented
7#10588649C211yesmaximal, characteristic
8#10588569C212yesmaximal, complemented
9#10588553C212yesmaximal, complemented
10#10588533C212yesmaximal, complemented
11#10588532C212yesmaximal, complemented
12#79200—31nomaximal
13C2×#3697C2211yescharacteristic
14C22×Dic18C2211yescharacteristic
15C2×C9×M16C2211yescharacteristic
16C9×#117C2211yescharacteristic
17C2×C9×C4⋊C4C2211yescharacteristic
18C2×Dic9⋊C4—21no—
19C2×C4×Dic9—21no—
20C2×C4×Dic9C2211yescharacteristic
21C2×#3667C2211yescharacteristic
22#63471C418yescomplemented
23C2×#3664C2212yes—
24C2×Dic36C2212yes—
25#63455C2211yescharacteristic
26#63455C2211yescharacteristic
27#63449—21no—
28#63449—21no—
29#63449C2212yes—
30#63449C2211yescharacteristic
31#63449C2212yes—
32#63449C2211yescharacteristic
33#611⋊C4—21no—
34#611⋊C4—21no—
35#63434—21no—
36C42×D9—21no—
37C9×#107C2212yes—
38C9×#106C2212yes—
39#63375C2212yes—
40C8×Dic9C2212yes—
41#63369C2212yes—
42#63368C2212yes—
43#63368C2212yes—
44#63368C2212yes—
45C2×#909—31no—
46#5522—31no—
47C2×#887—31no—
48C3×#428D311yescharacteristic
49Dic3×M16—31no—
50#5004—31no—
51#4966—31no—
52#4889—32no—
53#4873—32no—
54#4853—32no—
55#4852—32no—
56C22×C4×C9—21no—
57C22×C4×C9C2311yescharacteristic
58C2×#611—21no—
59C22×Dic9—21no—
60C22×Dic9D411yescharacteristic
61C22×Dic9D411yescharacteristic
62#3697—22no—
63#3697C2×C414yes—
64C2×D36C2311yescharacteristic
65C2×C4×D9—21no—
66C2×C4×D9—21no—
67C2×C4×D9—21no—
68C2×Dic18—21no—
69C2×Dic18—22no—
70C2×Dic18C2×C414yescomplemented
71C2×Dic18C2312yes—
72C2×Dic18C2311yescharacteristic
73C9×M16C2×C414yescomplemented
74C2×C8×C9C2312yes—
75C9×C4⋊C4—21no—
76C9×C4⋊C4C2312yes—
77C9×C4⋊C4C2311yescharacteristic
78C9×C4⋊C4C2311yescharacteristic
79C9×C22⋊C4—21no—
80C42×C9—21no—
81(C2×D9)⋊C4—21no—
82(C2×D9)⋊C4—21no—
83Dic9⋊C4—21no—
84Dic9⋊C4—21no—
85Dic9⋊C4—22no—
86Dic9⋊C4—22no—
87C4×Dic9—21no—
88C4×Dic9—21no—
89C4×Dic9—22no—
90C4×Dic9—22no—
91C4×Dic9D411yescharacteristic
92C4×Dic9D411yescharacteristic
93C4×Dic9C2311yescharacteristic
94C4×Dic9C2311yescharacteristic
95#3667—22no—
96C2×C9⋊C8C2312yes—
97#3664C2×C418yescomplemented
98Dic36C2×C418yescomplemented
99C4×#137—91noSylow
100C2×#235—31no—
101C22×Dic6—31no—
102C2×C3×M16C2×D311yescharacteristic
103C3×#117C2×D311yescharacteristic
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×Dic3⋊C4—61no—
106C2×C4×Dic3—31no—
107C2×C4×Dic3—61no—
108C2×#208—31no—
109#909—38no—
110C2×Dic12—32no—
111C2×#204—32no—
112#893—31no—
113#893—31no—
114#887—31no—
115#887—32no—
116#887—32no—
117#887—31no—
118#887—61no—
119#887—61no—
120#67⋊C4—61no—
121#67⋊C4—61no—
122#872—61no—
123C42×D3—61no—
124C3×#107C2×D312yes—
125C3×#106C2×D312yes—
126#815—32no—
127C8×Dic3—32no—
128#810—32no—
129#810—32no—
130#810—32no—
131#809—32no—
132C23×C9C2×D411yescharacteristic
133C22×D9—21no—
134C2×C4×C9—22no—
135C2×C4×C9—21no—
136C2×C4×C9—21no—
137C2×C4×C9—42no—
138C2×C4×C9C22×C412yes—
139C2×C4×C9C2×D411yescharacteristic
140C2×C4×C9#4112yes—
141C2×C4×C9C2411yescharacteristic
142#611—24no—
143C2×Dic9—24no—
144C2×Dic9—22no—
145C2×Dic9—21no—
146C2×Dic9—22no—
147C2×Dic9—41no—
148C2×Dic9C2×D411yescharacteristic
149C2×Dic9C2×D411yescharacteristic
150C2×Dic9C2×D411yescharacteristic
151C2×Dic9C2×D411yescharacteristic
152D36—21no—
153D36C22×C412yes—
154C4×D9—24no—
155C4×D9—42no—
156C4×D9—42no—
157Dic18—24no—
158Dic18—22no—
159Dic18—21no—
160Dic18C22×C412yes—
161Dic18C22×C414yes—
162C8×C9C22×C414yes—
163C9⋊C8—22no—
164C2×#137—91no—
165C4×#41—91no—
166C2×C4×Q8—91no—
167#441—92no—
168#440—92no—
169C4×Q16—92no—
170C4×SD16—92no—
171#428D911yescharacteristic, complemented
172#419—91no—
173#417—91no—
174C4×M16—91no—
175C22×C3×C4—21no—
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—61no—
178C22×Dic3—31no—
179C22×Dic3—31no—
180C22×Dic3—61no—
181#235—34no—
182#235—62no—
183C2×D12—31no—
184C2×C4×D3—61no—
185C2×C4×D3—61no—
186C2×C4×D3—61no—
187C2×Dic6—34no—
188C2×Dic6—32no—
189C2×Dic6—31no—
190C2×Dic6—61no—
191C2×Dic6—62no—
192C3×M16C4×D314yes—
193C2×C3×C8C22×D312yes—
194C3×C4⋊C4—21no—
195C3×C4⋊C4C22×D312yes—
196C3×C4⋊C4C22×D311yescharacteristic
197C3×C4⋊C4C22×D311yescharacteristic
198C3×C22⋊C4—21no—
199C3×C42—21no—
200(C2×D3)⋊C4—61no—
201(C2×D3)⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—62no—
205Dic3⋊C4—62no—
206C4×Dic3—31no—
207C4×Dic3—31no—
208C4×Dic3—31no—
209C4×Dic3—31no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—62no—
213C4×Dic3—62no—
214#208—62no—
215C2×C3⋊C8—32no—
216Dic12—38no—
217#204—38no—
218C22×C9—21no—
219C22×C9—21no—
220C22×C9C4×D412yes—
221C22×C9C22×D411yescharacteristic
222C2×D9—22no—
223C2×D9—41no—
224C2×D9—41no—
225C4×C9—41no—
226C4×C9—41no—
227C4×C9—42no—
228C4×C9C4×D412yes—
229C4×C9C23×C411yescharacteristic
230C4×C9C2×#4111yescharacteristic
231Dic9—24no—
232Dic9—22no—
233Dic9—21no—
234Dic9—21no—
235Dic9—21no—
236Dic9#13712yescomplemented
237C2×#41—91no—
238C22×Q8—91no—
239#137—98no—
240C2×Q16—92no—
241C2×SD16—92no—
242C2×M16—91no—
243C2×M16C2×D911yescharacteristic
244C4×Q8—92no—
245C4×Q8—92no—
246C4×Q8—91no—
247C4×Q8—91no—
248C4×Q8—181no—
249C4×Q8—181no—
250C4×D4—91no—
251C4×D4—91no—
252C4×D4—181no—
253C4×D4—181no—
254#117—181no—
255#117C2×D911yescharacteristic
256C2×C4⋊C4—181no—
257C2×C4⋊C4C2×D911yescharacteristic
258C2×C42—91no—
259C2×C42—181no—
260C2×C42—181no—
261#107C2×D912yes—
262#106C2×D912yes—
263#103—92no—
264#103—92no—
265#103—92no—
266#102—92no—
267#97—92no—
268C4×C8—92no—
269C23×C3D3×D411yescharacteristic
270C22×D3—61no—
271C2×C3×C4—22no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—42no—
275C2×C3×C4C2×C4×D312yes—
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4#23912yes—
278C2×C3×C4C23×D311yescharacteristic
279#67—64no—
280C2×Dic3—31no—
281C2×Dic3—31no—
282C2×Dic3—31no—
283C2×Dic3—31no—
284C2×Dic3—62no—
285C2×Dic3—64no—
286C2×Dic3—62no—
287C2×Dic3—61no—
288C2×Dic3—121no—
289D12—32no—
290D12—61no—
291C4×D3—64no—
292C4×D3—122no—
293C4×D3—122no—
294Dic6—34no—
295Dic6—32no—
296Dic6—64no—
297Dic6—62no—
298Dic6—61no—
299C3×C8C2×C4×D314yes—
300C3⋊C8—62no—
301C2×C9—22no—
302C2×C9C2×C4×D411yescharacteristic
303C2×C9C2×#13711yescharacteristic
304C2×C9#57511yescharacteristic
305D9—42no—
306#41—94no—
307#41—182no—
308C2×Q8—94no—
309C2×Q8—92no—
310C2×Q8—91no—
311C2×Q8—181no—
312C2×Q8—182no—
313C2×D4—91no—
314C2×D4—181no—
315C22×C4—21no—
316C22×C4—91no—
317C22×C4—91no—
318C22×C4—181no—
319C22×C4—181no—
320C22×C4—181no—
321C22×C4—181no—
322C22×C4C22×D911yescharacteristic
323Q16—98no—
324SD16—98no—
325M16—182no—
326M16C4×D914yescomplemented
327C2×C8—92no—
328C2×C8C22×D912yes—
329C4⋊C4—21no—
330C4⋊C4—182no—
331C4⋊C4—182no—
332C4⋊C4—181no—
333C4⋊C4—181no—
334C4⋊C4C22×D912yes—
335C4⋊C4C22×D911yescharacteristic
336C4⋊C4C22×D911yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—181no—
339C22⋊C4—181no—
340C42—21no—
341C42—91no—
342C42—91no—
343C42—91no—
344C42—91no—
345C42—181no—
346C42—181no—
347C42—182no—
348C42—182no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3#89312yes—
352C22×C3C2×D3×D411yescharacteristic
353C2×D3—62no—
354C2×D3—121no—
355C2×D3—121no—
356C3×C4—41no—
357C3×C4—42no—
358C3×C4—41no—
359C3×C4#89312yes—
360C3×C4C22×C4×D311yescharacteristic
361C3×C4C2×#23911yescharacteristic
362Dic3—32no—
363Dic3—64no—
364Dic3—62no—
365Dic3—61no—
366Dic3—61no—
367Dic3—61no—
368C9C4×#13711yescharacteristic, complemented, Sylow
369C23—181no—
370C23D4×D911yescharacteristic
371Q8—94no—
372Q8—92no—
373Q8—184no—
374Q8—182no—
375Q8—181no—
376D4—92no—
377D4—184no—
378D4—181no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—42no—
383C2×C4—91no—
384C2×C4—91no—
385C2×C4—91no—
386C2×C4—91no—
387C2×C4—182no—
388C2×C4—181no—
389C2×C4—182no—
390C2×C4—184no—
391C2×C4—184no—
392C2×C4—362no—
393C2×C4—362no—
394C2×C4—361no—
395C2×C4C2×C4×D912yes—
396C2×C4D4×D911yescharacteristic
397C2×C4#370112yes—
398C2×C4C23×D911yescharacteristic
399C8—182no—
400C8C2×C4×D914yes—
401C2×C3—22no—
402C2×C3C2×#89311yescharacteristic
403C2×C3#577311yescharacteristic
404C2×C3D3×#13711yescharacteristic
405D3—122no—
406C22—21no—
407C22—21no—
408C22—182no—
409C22—361no—
410C22—361no—
411C22#6345512yes—
412C22C2×D4×D911yescharacteristic
413C4—42no—
414C4—41no—
415C4—41no—
416C4—92no—
417C4—182no—
418C4—184no—
419C4—181no—
420C4—181no—
421C4—181no—
422C4#6345512yes—
423C4C22×C4×D911yescharacteristic
424C4C2×#370111yescharacteristic
425C3#7920011yescharacteristic
426C2—22no—
427C2—362no—
428C2C2×#6345511yescharacteristic
429C2#1058987511yescharacteristic
430C2D9×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutatorC4×C9C23×C4
FrattiniC2×C3×C4C23×D3
FittingC9×#428C2
socleC22×C3C2×D3×D4
prime radicalC2×#3697C22
cosocleC2×C4×C9C24
hypercenter#428D9
hypocenterC9C4×#137
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
3. C2×#63449C2semidirect
4. C9×#428C2semidirect
5. M16×Dic9C2semidirect
6. #10588681C2semidirect
8. #10588569C2semidirect
9. #10588553C2semidirect
10. #10588533C2semidirect
11. #10588532C2semidirect
22. #63471C4semidirect
70. C2×Dic18C2×C4semidirect
73. C9×M16C2×C4semidirect
97. #3664C2×C4semidirect
98. Dic36C2×C4semidirect
171. #428D9semidirect
236. Dic9#137semidirect
326. M16C4×D9semidirect
368. C9C4×#137semidirect

Maximal subgroups

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

subgroupindex
C2×#634712
#105896242
C2×#634492
C9×#4282
M16×Dic92
#105886812
#105886492
#105885692
#105885532
#105885332
#105885322
#792003