Finite Group Databasebeta

← #11897526

Subgroups — #11897526

Order 1152.

561 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589792C211yesmaximal, characteristic, complemented
2D4×Dic18C211yesmaximal, characteristic, complemented
3C9×#478C211yesmaximal, characteristic, complemented
4#10588743C211yesmaximal, characteristic, complemented
5#10588697C211yesmaximal, characteristic
6#10588570C211yesmaximal, characteristic, complemented
7#10588556C211yesmaximal, characteristic, complemented
8#10588550C211yesmaximal, characteristic, complemented
9#10588535C211yesmaximal, characteristic, complemented
10#10588526C211yesmaximal, characteristic, complemented
11#10588510C211yesmaximal, characteristic, complemented
12#10588465C211yesmaximal, characteristic
13#10588443C211yesmaximal, characteristic, complemented
14#10588441C211yesmaximal, characteristic, complemented
15#10588436C211yesmaximal, characteristic
16#81158—31nomaximal
17C22×Dic18—21no—
18C9×#125C2211yescharacteristic
19C4×D4×C9C2211yescharacteristic
20D4×Dic9C2211yescharacteristic
21D4×Dic9C2211yescharacteristic
22C2×#3673C2211yescharacteristic
23#63486—21no—
24#63459—21no—
25#63458—21no—
26#63458—21no—
27#63455C2211yescharacteristic
28#63455C2211yescharacteristic
29C4⋊C4×D9—21no—
30#63452C2211yescharacteristic
31#63450C2211yescharacteristic
32#63450C2211yescharacteristic
33#63450C2211yescharacteristic
34#63440—21no—
35#63440—21no—
36C4×D36C2211yescharacteristic
37#63431C2211yescharacteristic
38C4×Dic18C2211yescharacteristic
39C9×#107C2211yescharacteristic
40C9×#106C2211yescharacteristic
41C9×C4⋊C8C2211yescharacteristic
42C9×#102C2211yescharacteristic
43C9×#102C2211yescharacteristic
44#63392C2211yescharacteristic
45#63380C2211yescharacteristic
46#63380C2211yescharacteristic
47#63377C2211yescharacteristic
48#63377C2211yescharacteristic
49#63375C2211yescharacteristic
50Dic9⋊C8C2211yescharacteristic
51Dic9⋊C8C2211yescharacteristic
52C8×Dic9C2211yescharacteristic
53#63369C2211yescharacteristic
54#63367C2211yescharacteristic
55#63367C2211yescharacteristic
56#63367C2211yescharacteristic
57#63366C2211yescharacteristic
58#63366C2211yescharacteristic
59#63362C2211yescharacteristic
60#5690—31no—
61D4×Dic6—31no—
62C3×#478D311yescharacteristic
63#5064—31no—
64#5014—31no—
65#4890—31no—
66#4876—31no—
67#4870—31no—
68#4855—31no—
69#4842—31no—
70#4828—31no—
71#4785—31no—
72#4763—31no—
73#4761—31no—
74#4756—31no—
75C2×D4×C9C2311yescharacteristic
76C22×C4×C9—21no—
77C22×Dic9—21no—
78C22×Dic9—21no—
79C2×D36C2311yescharacteristic
80C2×C4×D9—21no—
81C2×C4×D9—21no—
82C2×C4×D9—21no—
83C2×Dic18—21no—
84C2×Dic18—21no—
85C2×Dic18—21no—
86C2×Dic18—21no—
87C2×Dic18—44no—
88C2×Dic18D411yescharacteristic
89C2×C8×C9C2311yescharacteristic
90C2×C8×C9C2311yescharacteristic
91C9×C4⋊C4—21no—
92C9×C4⋊C4—21no—
93C9×C4⋊C4C2311yescharacteristic
94C9×C4⋊C4C2311yescharacteristic
95C9×C4⋊C4C2311yescharacteristic
96C9×C22⋊C4—21no—
97C42×C9C2311yescharacteristic
98#3676—21no—
99#3676—21no—
100#3673Q814yescomplemented
101(C2×D9)⋊C4—21no—
102(C2×D9)⋊C4—21no—
103(C2×D9)⋊C4—21no—
104C4⋊Dic9—21no—
105C4⋊Dic9—21no—
106C4⋊Dic9D411yescharacteristic
107C4⋊Dic9C2311yescharacteristic
108C4⋊Dic9C2311yescharacteristic
109C4⋊Dic9C2311yescharacteristic
110Dic9⋊C4—21no—
111Dic9⋊C4—21no—
112Dic9⋊C4—21no—
113Dic9⋊C4—21no—
114Dic9⋊C4D411yescharacteristic
115Dic9⋊C4D411yescharacteristic
116C4×Dic9C2311yescharacteristic
117C4×Dic9C2311yescharacteristic
118C2×C9⋊C8C2311yescharacteristic
119C2×C9⋊C8C2311yescharacteristic
120#3384—91noSylow
121C22×Dic6—61no—
122C3×#125C2×D311yescharacteristic
123C3×C4×D4C2×D311yescharacteristic
124D4×Dic3—31no—
125D4×Dic3—31no—
126C2×#213—31no—
127#924—61no—
128#897—61no—
129#896—61no—
130#896—61no—
131#893—31no—
132#893—31no—
133D3×C4⋊C4—61no—
134#890—31no—
135#888—31no—
136#888—31no—
137#888—31no—
138#878—61no—
139#878—61no—
140C4×D12—31no—
141#869—31no—
142C4×Dic6—31no—
143C3×#107C2×D311yescharacteristic
144C3×#106C2×D311yescharacteristic
145C3×C4⋊C8C2×D311yescharacteristic
146C3×#102C2×D311yescharacteristic
147C3×#102C2×D311yescharacteristic
148#832—31no—
149#821—31no—
150#821—31no—
151#817—31no—
152#817—31no—
153#815—31no—
154Dic3⋊C8—31no—
155Dic3⋊C8—31no—
156C8×Dic3—31no—
157#809—31no—
158#808—31no—
159#808—31no—
160#808—31no—
161#807—31no—
162#807—31no—
163#803—31no—
164C23×C9—21no—
165C22×D9—21no—
166D4×C9—21no—
167D4×C9C2×Q812yes—
168C2×C4×C9—21no—
169C2×C4×C9—21no—
170C2×C4×C9—21no—
171C2×C4×C9—42no—
172C2×C4×C9C2×D411yescharacteristic
173C2×C4×C9C2×D411yescharacteristic
174C2×C4×C9C2411yescharacteristic
175C2×Dic9—21no—
176C2×Dic9—21no—
177C2×Dic9—21no—
178C2×Dic9—42no—
179C2×Dic9—42no—
180C2×Dic9C2×D411yescharacteristic
181C2×Dic9C2×D411yescharacteristic
182C2×Dic9C2×D411yescharacteristic
183C2×Dic9C2×D411yescharacteristic
184D36—21no—
185D36C2×Q812yescomplemented
186C4×D9—42no—
187C4×D9—81no—
188C4×D9—81no—
189Dic18—22no—
190Dic18—42no—
191Dic18—42no—
192Dic18—42no—
193Dic18—81no—
194C8×C9—21no—
195C8×C9—21no—
196C9⋊C8—21no—
197C9⋊C8C2×Q812yescomplemented
198#554—91no—
199D4×Q8—91no—
200#501—91no—
201#501—91no—
202#498—91no—
203#478—91no—
204#478D911yescharacteristic, complemented
205#476—91no—
206#476—91no—
207#476—91no—
208#474—91no—
209#446—91no—
210#442—91no—
211#442—91no—
212C4×D8—91no—
213C2×C3×D4C22×D311yescharacteristic
214C22×C3×C4—21no—
215C22×Dic3—61no—
216C22×Dic3—61no—
217C2×D12—31no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×Dic6—31no—
222C2×Dic6—61no—
223C2×Dic6—61no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—124no—
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C3×C4⋊C4—21no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4C22×D311yescharacteristic
232C3×C4⋊C4C22×D311yescharacteristic
233C3×C4⋊C4C22×D311yescharacteristic
234C3×C22⋊C4—21no—
235C3×C42C22×D311yescharacteristic
236#217—61no—
237#217—61no—
238#213—34no—
239(C2×D3)⋊C4—61no—
240(C2×D3)⋊C4—61no—
241(C2×D3)⋊C4—61no—
242C4⋊Dic3—31no—
243C4⋊Dic3—31no—
244C4⋊Dic3—31no—
245C4⋊Dic3—31no—
246C4⋊Dic3—61no—
247C4⋊Dic3—61no—
248Dic3⋊C4—31no—
249Dic3⋊C4—31no—
250Dic3⋊C4—61no—
251Dic3⋊C4—61no—
252Dic3⋊C4—61no—
253Dic3⋊C4—61no—
254C4×Dic3—31no—
255C4×Dic3—31no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—31no—
258C22×C9—22no—
259C22×C9—41no—
260C22×C9—41no—
261C22×C9C22×D411yescharacteristic
262C2×D9—22no—
263C2×D9—41no—
264C2×D9—41no—
265C4×C9—21no—
266C4×C9—21no—
267C4×C9—41no—
268C4×C9—41no—
269C4×C9—41no—
270C4×C9C22×Q811yescharacteristic
271C4×C92−1+411yescharacteristic
272Dic9—21no—
273Dic9—21no—
274Dic9—21no—
275Dic9—41no—
276Dic9—41no—
277Dic9—41no—
278Dic9AGL(1,ℤ/8)12yes—
279C22×Q8—181no—
280C2×D8—91no—
281C4⋊Q8—91no—
282C4⋊Q8—91no—
283C4⋊Q8—91no—
284C4⋊Q8—91no—
285#125—91no—
286#125C2×D911yescharacteristic
287C22⋊Q8—181no—
288C22⋊Q8—181no—
289C22⋊Q8—181no—
290C22⋊Q8—181no—
291C22⋊Q8—181no—
292C22⋊Q8—181no—
293C4×Q8—91no—
294C4×D4—91no—
295C4×D4—91no—
296C4×D4—91no—
297C4×D4—91no—
298C4×D4—91no—
299C4×D4C2×D911yescharacteristic
300C2×C4⋊C4—181no—
301#107—91no—
302#107—91no—
303#107C2×D911yescharacteristic
304#106—91no—
305#106—91no—
306#106—91no—
307#106—91no—
308#106—91no—
309#106C2×D911yescharacteristic
310C4⋊C8—91no—
311C4⋊C8—91no—
312C4⋊C8C2×D911yescharacteristic
313#102—91no—
314#102—91no—
315#102—91no—
316#102—91no—
317#102C2×D911yescharacteristic
318#102C2×D911yescharacteristic
319#97—91no—
320#97—91no—
321C4×C8—91no—
322C23×C3—21no—
323C22×D3—61no—
324C3×D4—21no—
325C3×D4D3×Q812yes—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—42no—
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4C23×D311yescharacteristic
333C2×Dic3—31no—
334C2×Dic3—31no—
335C2×Dic3—31no—
336C2×Dic3—31no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—122no—
341C2×Dic3—122no—
342D12—32no—
343D12—61no—
344C4×D3—122no—
345C4×D3—241no—
346C4×D3—241no—
347Dic6—62no—
348Dic6—122no—
349Dic6—122no—
350Dic6—122no—
351Dic6—241no—
352C3×C8—21no—
353C3×C8—21no—
354C3⋊C8—32no—
355C3⋊C8—61no—
356C2×C9—42no—
357C2×C9D4×Q811yescharacteristic
358C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
359C2×C9#57711yescharacteristic
360D9—42no—
361C2×Q8—91no—
362C2×Q8—181no—
363C2×Q8—181no—
364C2×Q8—181no—
365C2×Q8—181no—
366C2×Q8—364no—
367C2×D4—91no—
368C2×D4C22×D911yescharacteristic
369C22×C4—21no—
370C22×C4—181no—
371C22×C4—181no—
372C22×C4—181no—
373C22×C4—181no—
374C22×C4—181no—
375D8—94no—
376C2×C8—91no—
377C2×C8—91no—
378C2×C8C22×D911yescharacteristic
379C2×C8C22×D911yescharacteristic
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—91no—
383C4⋊C4—91no—
384C4⋊C4—91no—
385C4⋊C4—91no—
386C4⋊C4—91no—
387C4⋊C4—91no—
388C4⋊C4—181no—
389C4⋊C4—181no—
390C4⋊C4—181no—
391C4⋊C4—181no—
392C4⋊C4—181no—
393C4⋊C4—181no—
394C4⋊C4C22×D911yescharacteristic
395C4⋊C4C22×D911yescharacteristic
396C4⋊C4C22×D911yescharacteristic
397C22⋊C4—21no—
398C22⋊C4—181no—
399C22⋊C4—181no—
400C22⋊C4—181no—
401C22⋊C4—181no—
402C22⋊C4—181no—
403C42—91no—
404C42—91no—
405C42C22×D911yescharacteristic
406C22×C3—22no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3C2×D3×D411yescharacteristic
410C2×D3—62no—
411C2×D3—121no—
412C2×D3—121no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—41no—
416C3×C4—41no—
417C3×C4—41no—
418C3×C4C2×D3×Q811yescharacteristic
419C3×C4#101011yescharacteristic
420Dic3—32no—
421Dic3—61no—
422Dic3—61no—
423Dic3—61no—
424Dic3—121no—
425Dic3—121no—
426Dic3—121no—
427C9#338411yescharacteristic, complemented, Sylow
428C23—21no—
429C23—181no—
430Q8—182no—
431Q8—362no—
432Q8—362no—
433Q8—362no—
434Q8—721no—
435D4—21no—
436D4—92no—
437D4—181no—
438D4Q8×D912yes—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—42no—
443C2×C4—91no—
444C2×C4—91no—
445C2×C4—91no—
446C2×C4—91no—
447C2×C4—181no—
448C2×C4—181no—
449C2×C4—181no—
450C2×C4—362no—
451C2×C4—362no—
452C2×C4—362no—
453C2×C4—721no—
454C2×C4—721no—
455C2×C4D4×D911yescharacteristic
456C2×C4D4×D911yescharacteristic
457C2×C4C23×D911yescharacteristic
458C8—21no—
459C8—21no—
460C8—92no—
461C8—181no—
462C2×C3—42no—
463C2×C3#563211yescharacteristic
464C2×C3#577011yescharacteristic
465C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
466D3—122no—
467C22—22no—
468C22—41no—
469C22—41no—
470C22—182no—
471C22—361no—
472C22—361no—
473C22C2×D4×D911yescharacteristic
474C4—21no—
475C4—21no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—92no—
480C4—181no—
481C4—181no—
482C4—181no—
483C4—361no—
484C4—361no—
485C4—361no—
486C4C2×Q8×D911yescharacteristic
487C4#6371611yescharacteristic
488C3#8115811yescharacteristic
489C2—42no—
490C2—362no—
491C2#1058973411yescharacteristic
492C2#1058987211yescharacteristic
493C2D9×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#478C2
socleC22×C3C2×D3×D4
prime radicalC2×#3673C22
hypercenter#478D9
hypocenterC9#3384
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10589792C2semidirect
2. D4×Dic18C2semidirect
3. C9×#478C2semidirect
4. #10588743C2semidirect
6. #10588570C2semidirect
7. #10588556C2semidirect
8. #10588550C2semidirect
9. #10588535C2semidirect
10. #10588526C2semidirect
11. #10588510C2semidirect
13. #10588443C2semidirect
14. #10588441C2semidirect
100. #3673Q8semidirect
185. D36C2×Q8semidirect
197. C9⋊C8C2×Q8semidirect
204. #478D9semidirect
427. C9#3384semidirect

Maximal subgroups

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

subgroupindex
#105897922
D4×Dic182
C9×#4782
#105887432
#105886972
#105885702
#105885562
#105885502
#105885352
#105885262
#105885102
#105884652
#105884432
#105884412
#105884362
#811583