Finite Group Databasebeta

← #11895917

Subgroups — #11895917

Order 1152.

573 conjugacy classes of subgroups.

The subgroup lattice has 375 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589672C211yesmaximal, characteristic, complemented
2#10589655C211yesmaximal, characteristic
3C4×C9×SD16C211yesmaximal, characteristic, complemented
4#10588843C212yesmaximal, complemented
5#10588710C211yesmaximal, characteristic, complemented
6#10588690C211yesmaximal, characteristic, complemented
7#10588551C212yesmaximal, complemented
8#10588497C212yesmaximal, complemented
9#10588444C212yesmaximal, complemented
10#10588376C211yesmaximal, characteristic, complemented
11#10588359C211yesmaximal, characteristic, complemented
12#79625—31nomaximal
13C2×#3697—21no—
14C2×C9×SD16C2211yescharacteristic
15C4×Q8×C9C2211yescharacteristic
16C4×D4×C9C2211yescharacteristic
17Q8×Dic9C2212yes—
18C2×#3675C2212yes—
19#63502C2212yes—
20#63492—21no—
21#63455C2212yes—
22#63452—22no—
23#63452C2212yes—
24#63446—22no—
25#63436C2211yescharacteristic
26#63431—21no—
27#63431C2211yescharacteristic
28C4×Dic18—21no—
29C4×Dic18C2211yescharacteristic
30C9×#106C2211yescharacteristic
31C9×#103C2211yescharacteristic
32C9×#102C2211yescharacteristic
33C4×C8×C9C2211yescharacteristic
34#63392C2212yes—
35#63380C2212yes—
36#63380C2212yes—
37#63375C2212yes—
38Dic9⋊C8C2212yes—
39#63369C2212yes—
40#63366C2212yes—
41C4⋊(C9⋊C8)C2211yescharacteristic
42#5570—31no—
43#5553—31no—
44C3×C4×SD16D311yescharacteristic
45#5163—32no—
46#5027—31no—
47#5007—31no—
48#4871—32no—
49#4817—32no—
50#4764—32no—
51#4694—31no—
52#4679—31no—
53C2×Q8×C9C2311yescharacteristic
54C2×D4×C9C2311yescharacteristic
55C22×C4×C9—21no—
56C2×#611—22no—
57C2×#611—22no—
58#3697—44no—
59C2×D36—21no—
60C2×D36—21no—
61C2×D36C2312yes—
62C2×C4×D9—22no—
63C2×Dic18—21no—
64C2×Dic18D411yescharacteristic
65C9×SD16—22no—
66C2×C8×C9C2311yescharacteristic
67C2×C8×C9C2311yescharacteristic
68C9×C4⋊C4—21no—
69C9×C4⋊C4C2311yescharacteristic
70C9×C4⋊C4C2311yescharacteristic
71C9×C22⋊C4—21no—
72C42×C9—21no—
73C42×C9C2311yescharacteristic
74#3675—24no—
75(C2×D9)⋊C4—22no—
76C4⋊Dic9—21no—
77C4⋊Dic9—22no—
78C4⋊Dic9—22no—
79C4⋊Dic9D411yescharacteristic
80C4⋊Dic9C2312yes—
81Dic9⋊C4—22no—
82Dic9⋊C4D412yes—
83C4×Dic9—22no—
84C4×Dic9C2312yes—
85C2×C9⋊C8C2312yes—
86#3368—91noSylow
87C2×#235—61no—
88C2×C3×SD16C2×D311yescharacteristic
89C3×C4×Q8C2×D311yescharacteristic
90C3×C4×D4C2×D311yescharacteristic
91Q8×Dic3—32no—
92C2×#215—32no—
93#940—32no—
94#930—61no—
95#893—32no—
96#890—32no—
97#890—62no—
98#884—62no—
99#874—31no—
100#869—31no—
101#869—61no—
102C4×Dic6—31no—
103C4×Dic6—61no—
104C3×#106C2×D311yescharacteristic
105C3×#103C2×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#807—32no—
115C4⋊(C3⋊C8)—31no—
116C23×C9—21no—
117C22×D9—22no—
118Q8×C9—21no—
119Q8×C9#4112yescomplemented
120D4×C9—21no—
121D4×C9—21no—
122C2×C4×C9—21no—
123C2×C4×C9—21no—
124C2×C4×C9—21no—
125C2×C4×C9—42no—
126C2×C4×C9C2×D411yescharacteristic
127C2×C4×C9C2×D411yescharacteristic
128C2×C4×C9C2411yescharacteristic
129#611—44no—
130#611—82no—
131C2×Dic9—22no—
132C2×Dic9C2×D412yes—
133C2×Dic9C2×D412yes—
134D36—22no—
135D36—22no—
136D36—42no—
137D36—81no—
138C4×D9—44no—
139Dic18—22no—
140Dic18—42no—
141C8×C9—21no—
142C8×C9—21no—
143C9⋊C8—22no—
144#557—91no—
145#550—91no—
146#490—92no—
147#486—91no—
148#478—92no—
149#474—91no—
150#460—92no—
151#460—91no—
152#446—91no—
153#440—92no—
154C4×SD16D911yescharacteristic, complemented
155C2×C3×Q8C22×D311yescharacteristic
156C2×C3×D4C22×D311yescharacteristic
157C22×C3×C4—21no—
158C2×#67—62no—
159C2×#67—62no—
160#235—124no—
161C2×D12—32no—
162C2×D12—61no—
163C2×D12—61no—
164C2×C4×D3—62no—
165C2×Dic6—31no—
166C2×Dic6—61no—
167C3×SD16—22no—
168C2×C3×C8C22×D311yescharacteristic
169C2×C3×C8C22×D311yescharacteristic
170C3×C4⋊C4—21no—
171C3×C4⋊C4C22×D311yescharacteristic
172C3×C4⋊C4C22×D311yescharacteristic
173C3×C22⋊C4—21no—
174C3×C42—21no—
175C3×C42C22×D311yescharacteristic
176#215—64no—
177(C2×D3)⋊C4—62no—
178C4⋊Dic3—31no—
179C4⋊Dic3—32no—
180C4⋊Dic3—62no—
181C4⋊Dic3—62no—
182C4⋊Dic3—61no—
183Dic3⋊C4—32no—
184Dic3⋊C4—62no—
185C4×Dic3—32no—
186C4×Dic3—62no—
187C2×C3⋊C8—32no—
188C22×C9—41no—
189C22×C9—41no—
190C22×C9—41no—
191C22×C9C22×D411yescharacteristic
192C2×D9—42no—
193C2×D9—42no—
194C2×D9—42no—
195C4×C9—22no—
196C4×C9—21no—
197C4×C9—41no—
198C4×C9—41no—
199C4×C9AGL(1,ℤ/8)12yes—
200C4×C9C2×#4111yescharacteristic
201C4×C92−1+411yescharacteristic
202Dic9—22no—
203Dic9—22no—
204Dic9—42no—
205C2×#41—181no—
206C2×SD16—92no—
207C2×SD16C2×D911yescharacteristic
208C4⋊Q8—91no—
209C4⋊Q8—181no—
210#127—92no—
211#127—91no—
212#125—92no—
213#125—182no—
214#121—182no—
215#121—181no—
216C4×Q8—91no—
217C4×Q8—92no—
218C4×Q8—181no—
219C4×Q8C2×D911yescharacteristic
220C4×D4—92no—
221C4×D4C2×D911yescharacteristic
222#107—92no—
223#106C2×D911yescharacteristic
224C4⋊C8—92no—
225C4⋊C8—91no—
226#103C2×D911yescharacteristic
227#102—92no—
228#102—92no—
229#102—92no—
230#102—92no—
231#102C2×D911yescharacteristic
232#97—92no—
233C4×C8C2×D911yescharacteristic
234C23×C3—21no—
235C22×D3—62no—
236C3×Q8—21no—
237C3×Q8#23512yes—
238C3×D4—21no—
239C3×D4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—42no—
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4C23×D311yescharacteristic
247#67—124no—
248#67—242no—
249C2×Dic3—32no—
250C2×Dic3—32no—
251C2×Dic3—62no—
252D12—62no—
253D12—62no—
254D12—122no—
255D12—241no—
256C4×D3—124no—
257Dic6—62no—
258Dic6—122no—
259C3×C8—21no—
260C3×C8—21no—
261C3⋊C8—62no—
262C2×C9—81no—
263C2×C9#54811yescharacteristic
264C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
265C2×C9#57711yescharacteristic
266D9—82no—
267#41—364no—
268C2×Q8—91no—
269C2×Q8—181no—
270C2×Q8C22×D911yescharacteristic
271C2×D4—92no—
272C2×D4—182no—
273C2×D4—182no—
274C2×D4—181no—
275C2×D4—181no—
276C2×D4C22×D911yescharacteristic
277C22×C4—21no—
278C22×C4—182no—
279SD16—22no—
280SD16—184no—
281C2×C8—92no—
282C2×C8C22×D911yescharacteristic
283C2×C8C22×D911yescharacteristic
284C4⋊C4—21no—
285C4⋊C4—91no—
286C4⋊C4—92no—
287C4⋊C4—92no—
288C4⋊C4—182no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—181no—
292C4⋊C4C22×D911yescharacteristic
293C4⋊C4C22×D911yescharacteristic
294C22⋊C4—21no—
295C22⋊C4—182no—
296C42—21no—
297C42—92no—
298C42—182no—
299C42C22×D911yescharacteristic
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3C2×D3×D411yescharacteristic
304C2×D3—122no—
305C2×D3—122no—
306C2×D3—122no—
307C3×C4—21no—
308C3×C4—22no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4#91412yes—
312C3×C4C2×#23511yescharacteristic
313C3×C4#101011yescharacteristic
314Dic3—62no—
315Dic3—62no—
316Dic3—122no—
317C9#336811yescharacteristic, complemented, Sylow
318C23—21no—
319C23—182no—
320Q8—21no—
321Q8—182no—
322Q8—362no—
323Q8#369712yescomplemented
324D4—21no—
325D4—21no—
326D4—182no—
327D4—182no—
328D4—364no—
329D4—362no—
330D4—721no—
331D4—722no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—42no—
336C2×C4—92no—
337C2×C4—92no—
338C2×C4—182no—
339C2×C4—364no—
340C2×C4D4×D911yescharacteristic
341C2×C4D4×D911yescharacteristic
342C2×C4C23×D911yescharacteristic
343C8—21no—
344C8—21no—
345C8—182no—
346C2×C3—81no—
347C2×C3#555211yescharacteristic
348C2×C3C2×#91411yescharacteristic
349C2×C3#577011yescharacteristic
350D3—242no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—362no—
355C22—362no—
356C22—362no—
357C22C2×D4×D911yescharacteristic
358C4—21no—
359C4—22no—
360C4—41no—
361C4—41no—
362C4—182no—
363C4—182no—
364C4—362no—
365C4#6347612yes—
366C4C2×#369711yescharacteristic
367C4#6371611yescharacteristic
368C3#7962511yescharacteristic
369C2—81no—
370C2—722no—
371C2#1058965411yescharacteristic
372C2C2×#6347611yescharacteristic
373C2#1058987211yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC4×C9×SD16C2
socleC22×C3C2×D3×D4
prime radical#10589655C2
hypercenterC4×SD16D9
hypocenterC9#3368
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #10589672C2semidirect
3. C4×C9×SD16C2semidirect
4. #10588843C2semidirect
5. #10588710C2semidirect
6. #10588690C2semidirect
7. #10588551C2semidirect
8. #10588497C2semidirect
9. #10588444C2semidirect
10. #10588376C2semidirect
11. #10588359C2semidirect
119. Q8×C9#41semidirect
154. C4×SD16D9semidirect
317. C9#3368semidirect
323. Q8#3697semidirect

Maximal subgroups

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

subgroupindex
#105896722
#105896552
C4×C9×SD162
#105888432
#105887102
#105886902
#105885512
#105884972
#105884442
#105883762
#105883592
#796253