Finite Group Databasebeta

← #11895715

Subgroups — #11895715

Order 1152.

594 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589655C211yesmaximal, characteristic, complemented
2#10589645C211yesmaximal, characteristic, complemented
3C4×C9×D8C211yesmaximal, characteristic, complemented
4#10588830C212yesmaximal, complemented
5#10588698C211yesmaximal, characteristic, complemented
6#10588691C211yesmaximal, characteristic, complemented
7#10588571C212yesmaximal, complemented
8#10588465C212yesmaximal, complemented
9#10588444C212yesmaximal, complemented
10#10588376C211yesmaximal, characteristic, complemented
11#10588359C211yesmaximal, characteristic, complemented
12#79570—31nomaximal
13C2×#3697—21no—
14C2×C9×D8C2211yescharacteristic
15C4×D4×C9C2211yescharacteristic
16C4×D4×C9C2211yescharacteristic
17#63502C2212yes—
18D4×Dic9C2212yes—
19C2×#3673C2212yes—
20#63492—21no—
21C2×C4⋊Dic9—21no—
22#63486—21no—
23#63455C2212yes—
24#63452C2212yes—
25#63446—22no—
26#63440—22no—
27#63436C2211yescharacteristic
28#63431C2211yescharacteristic
29C4×Dic18C2211yescharacteristic
30C9×#107C2211yescharacteristic
31C9×#102C2211yescharacteristic
32C9×#102C2211yescharacteristic
33C4×C8×C9C2211yescharacteristic
34#63392C2212yes—
35#63380C2212yes—
36#63380C2212yes—
37#63375C2212yes—
38Dic9⋊C8C2212yes—
39#63369C2212yes—
40#63367C2212yes—
41C4⋊(C9⋊C8)C2211yescharacteristic
42#5553—31no—
43#5543—31no—
44C3×C4×D8D311yescharacteristic
45#5150—32no—
46#5015—31no—
47#5008—31no—
48#4891—32no—
49#4785—32no—
50#4764—32no—
51#4694—31no—
52#4679—31no—
53C2×D4×C9C2311yescharacteristic
54C2×D4×C9C2311yescharacteristic
55C22×C4×C9—21no—
56C22×C4×C9—21no—
57C2×#611—22no—
58C2×#611—22no—
59C22×Dic9—22no—
60#3697—44no—
61C2×D36—21no—
62C2×D36—21no—
63C2×D36C2312yes—
64C2×C4×D9—22no—
65C2×Dic18—21no—
66C2×Dic18D411yescharacteristic
67C9×D8—22no—
68C2×C8×C9C2311yescharacteristic
69C2×C8×C9C2311yescharacteristic
70C9×C4⋊C4C2311yescharacteristic
71C9×C4⋊C4C2311yescharacteristic
72C9×C22⋊C4—21no—
73C9×C22⋊C4—21no—
74C42×C9C2311yescharacteristic
75#3676—22no—
76#3673—24no—
77(C2×D9)⋊C4—22no—
78C4⋊Dic9—21no—
79C4⋊Dic9—22no—
80C4⋊Dic9D411yescharacteristic
81C4⋊Dic9C2312yes—
82Dic9⋊C4—22no—
83Dic9⋊C4D412yes—
84C4×Dic9C2312yes—
85C2×C9⋊C8C2312yes—
86#3366—91noSylow
87C2×#235—61no—
88C2×C3×D8C2×D311yescharacteristic
89C3×C4×D4C2×D311yescharacteristic
90C3×C4×D4C2×D311yescharacteristic
91#940—32no—
92D4×Dic3—32no—
93C2×#213—32no—
94#930—61no—
95C2×C4⋊Dic3—61no—
96#924—61no—
97#893—32no—
98#890—32no—
99#884—62no—
100#878—62no—
101#874—31no—
102#869—31no—
103C4×Dic6—31no—
104C3×#107C2×D311yescharacteristic
105C3×#102C2×D311yescharacteristic
106C3×#102C2×D311yescharacteristic
107C3×C4×C8C2×D311yescharacteristic
108#832—32no—
109#821—32no—
110#821—32no—
111#815—32no—
112Dic3⋊C8—32no—
113#809—32no—
114#808—32no—
115C4⋊(C3⋊C8)—31no—
116C23×C9—21no—
117C23×C9—21no—
118C22×D9—22no—
119D4×C9—21no—
120D4×C9—21no—
121D4×C9—21no—
122D4×C9#4112yescomplemented
123C2×C4×C9—21no—
124C2×C4×C9—21no—
125C2×C4×C9—42no—
126C2×C4×C9—42no—
127C2×C4×C9C2×D411yescharacteristic
128C2×C4×C9C2×D411yescharacteristic
129C2×C4×C9C2411yescharacteristic
130#611—44no—
131#611—82no—
132C2×Dic9—22no—
133C2×Dic9—82no—
134C2×Dic9C2×D412yes—
135C2×Dic9C2×D412yes—
136D36—22no—
137D36—22no—
138D36—42no—
139D36—81no—
140C4×D9—44no—
141Dic18—22no—
142Dic18—81no—
143C8×C9—21no—
144C8×C9—21no—
145C9⋊C8—22no—
146#554—91no—
147#550—91no—
148#490—92no—
149#486—91no—
150#478—92no—
151#476—91no—
152#459—92no—
153#459—91no—
154#446—91no—
155#442—92no—
156C4×D8D911yescharacteristic, complemented
157C2×C3×D4C22×D311yescharacteristic
158C2×C3×D4C22×D311yescharacteristic
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C2×#67—62no—
162C2×#67—62no—
163C22×Dic3—62no—
164#235—124no—
165C2×D12—32no—
166C2×D12—61no—
167C2×D12—61no—
168C2×C4×D3—62no—
169C2×Dic6—31no—
170C2×Dic6—61no—
171C3×D8—22no—
172C2×C3×C8C22×D311yescharacteristic
173C2×C3×C8C22×D311yescharacteristic
174C3×C4⋊C4C22×D311yescharacteristic
175C3×C4⋊C4C22×D311yescharacteristic
176C3×C22⋊C4—21no—
177C3×C22⋊C4—21no—
178C3×C42C22×D311yescharacteristic
179#217—62no—
180#213—64no—
181(C2×D3)⋊C4—62no—
182C4⋊Dic3—31no—
183C4⋊Dic3—32no—
184C4⋊Dic3—62no—
185C4⋊Dic3—61no—
186Dic3⋊C4—32no—
187Dic3⋊C4—62no—
188C4×Dic3—32no—
189C2×C3⋊C8—32no—
190C22×C9—22no—
191C22×C9—41no—
192C22×C9—41no—
193C22×C9—41no—
194C22×C9—41no—
195C22×C9—41no—
196C22×C9C22×D411yescharacteristic
197C2×D9—42no—
198C2×D9—42no—
199C2×D9—42no—
200C4×C9—21no—
201C4×C9—41no—
202C4×C9—41no—
203C4×C9AGL(1,ℤ/8)12yes—
204C4×C9C2×#4111yescharacteristic
205C4×C92−1+411yescharacteristic
206Dic9—22no—
207Dic9—22no—
208Dic9—42no—
209C2×#41—181no—
210C2×D8—92no—
211C2×D8C2×D911yescharacteristic
212C4⋊Q8—91no—
213#127—92no—
214#127—91no—
215#125—92no—
216C22⋊Q8—182no—
217C22⋊Q8—181no—
218#121—182no—
219#121—181no—
220C4×Q8—91no—
221C4×D4—92no—
222C4×D4—92no—
223C4×D4C2×D911yescharacteristic
224C4×D4C2×D911yescharacteristic
225C2×C4⋊C4—181no—
226#107C2×D911yescharacteristic
227#106—92no—
228C4⋊C8—92no—
229C4⋊C8—91no—
230#102—92no—
231#102—92no—
232#102—92no—
233#102—92no—
234#102C2×D911yescharacteristic
235#102C2×D911yescharacteristic
236#97—92no—
237C4×C8C2×D911yescharacteristic
238C23×C3—21no—
239C23×C3—21no—
240C22×D3—62no—
241C3×D4—21no—
242C3×D4—21no—
243C3×D4—21no—
244C3×D4#23512yes—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—42no—
248C2×C3×C4—42no—
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4C23×D311yescharacteristic
252#67—124no—
253#67—242no—
254C2×Dic3—32no—
255C2×Dic3—32no—
256C2×Dic3—62no—
257C2×Dic3—242no—
258D12—62no—
259D12—62no—
260D12—122no—
261D12—241no—
262C4×D3—124no—
263Dic6—62no—
264Dic6—241no—
265C3×C8—21no—
266C3×C8—21no—
267C3⋊C8—62no—
268C2×C9—42no—
269C2×C9—81no—
270C2×C9#54811yescharacteristic
271C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
272C2×C9#57611yescharacteristic
273D9—82no—
274#41—364no—
275C2×Q8—91no—
276C2×Q8—181no—
277C2×D4—92no—
278C2×D4—182no—
279C2×D4—182no—
280C2×D4—181no—
281C2×D4—181no—
282C2×D4C22×D911yescharacteristic
283C2×D4C22×D911yescharacteristic
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—182no—
287C22×C4—182no—
288D8—22no—
289D8—184no—
290C2×C8—92no—
291C2×C8C22×D911yescharacteristic
292C2×C8C22×D911yescharacteristic
293C4⋊C4—91no—
294C4⋊C4—92no—
295C4⋊C4—92no—
296C4⋊C4—182no—
297C4⋊C4—182no—
298C4⋊C4—181no—
299C4⋊C4C22×D911yescharacteristic
300C4⋊C4C22×D911yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—182no—
304C22⋊C4—182no—
305C42—92no—
306C42C22×D911yescharacteristic
307C22×C3—22no—
308C22×C3—41no—
309C22×C3—41no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3C2×D3×D411yescharacteristic
314C2×D3—122no—
315C2×D3—122no—
316C2×D3—122no—
317C3×C4—21no—
318C3×C4—41no—
319C3×C4—41no—
320C3×C4#91112yes—
321C3×C4C2×#23511yescharacteristic
322C3×C4#101011yescharacteristic
323Dic3—62no—
324Dic3—62no—
325Dic3—122no—
326C9#336611yescharacteristic, complemented, Sylow
327C23—21no—
328C23—21no—
329C23—182no—
330Q8—182no—
331Q8—721no—
332D4—21no—
333D4—21no—
334D4—21no—
335D4—182no—
336D4—182no—
337D4—364no—
338D4—362no—
339D4—721no—
340D4—722no—
341D4#369712yescomplemented
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—92no—
347C2×C4—92no—
348C2×C4—182no—
349C2×C4—364no—
350C2×C4—722no—
351C2×C4D4×D911yescharacteristic
352C2×C4D4×D911yescharacteristic
353C2×C4C23×D911yescharacteristic
354C8—21no—
355C8—21no—
356C8—182no—
357C2×C3—42no—
358C2×C3—81no—
359C2×C3#555211yescharacteristic
360C2×C3C2×#91111yescharacteristic
361C2×C3#576911yescharacteristic
362D3—242no—
363C22—22no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—362no—
370C22—362no—
371C22—362no—
372C22C2×D4×D911yescharacteristic
373C4—21no—
374C4—41no—
375C4—41no—
376C4—182no—
377C4—182no—
378C4—362no—
379C4#6347312yes—
380C4C2×#369711yescharacteristic
381C4#6371611yescharacteristic
382C3#7957011yescharacteristic
383C2—42no—
384C2—81no—
385C2—722no—
386C2#1058965411yescharacteristic
387C2C2×#6347311yescharacteristic
388C2#1058987111yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC4×C9×D8C2
socleC22×C3C2×D3×D4
hypercenterC4×D8D9
hypocenterC9#3366
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10589655C2semidirect
2. #10589645C2semidirect
3. C4×C9×D8C2semidirect
4. #10588830C2semidirect
5. #10588698C2semidirect
6. #10588691C2semidirect
7. #10588571C2semidirect
8. #10588465C2semidirect
9. #10588444C2semidirect
10. #10588376C2semidirect
11. #10588359C2semidirect
122. D4×C9#41semidirect
156. C4×D8D9semidirect
326. C9#3366semidirect
341. D4#3697semidirect

Maximal subgroups

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

subgroupindex
#105896552
#105896452
C4×C9×D82
#105888302
#105886982
#105886912
#105885712
#105884652
#105884442
#105883762
#105883592
#795703