Finite Group Databasebeta

← #11897529

Subgroups — #11897529

Order 1152.

561 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589829C211yesmaximal, characteristic, complemented
2#10589645C211yesmaximal, characteristic, complemented
3C9×#474C211yesmaximal, characteristic, complemented
4#10588760C211yesmaximal, characteristic, complemented
5C4×#3673C211yesmaximal, characteristic
6#10588571C212yesmaximal, complemented
7#10588556C212yesmaximal, complemented
8#10588526C211yesmaximal, characteristic, complemented
9#10588509C211yesmaximal, characteristic, complemented
10#10588465C212yesmaximal
11#10588441C212yesmaximal, complemented
12#80959—31nomaximal
13C2×Q8×D9—21no—
14C9×C4⋊Q8C2211yescharacteristic
15C4×D4×C9C2211yescharacteristic
16#63508—21no—
17D4×Dic9C2212yes—
18C2×#3673C2211yescharacteristic
19C2×C4⋊Dic9—21no—
20#63486—21no—
21#63458—22no—
22#63455C2212yes—
23#63452C2212yes—
24#63450C2212yes—
25#63440—22no—
26C4×D36C2211yescharacteristic
27#63431C2211yescharacteristic
28C4×Dic18C2211yescharacteristic
29C9×#107C2212yes—
30C9×C4⋊C8C2211yescharacteristic
31C9×#102C2212yes—
32#63392C2211yescharacteristic
33#63380C2212yes—
34#63377C2212yes—
35#63375C2212yes—
36Dic9⋊C8C2212yes—
37#63369C2211yescharacteristic
38#63367C2212yes—
39#63367C2212yes—
40#63366C2211yescharacteristic
41C4×C9⋊C8C2211yescharacteristic
42#5727—31no—
43#5543—31no—
44C3×#474D311yescharacteristic
45#5080—31no—
46C4×#213—31no—
47#4891—32no—
48#4876—32no—
49#4842—31no—
50#4831—31no—
51#4785—32no—
52#4761—32no—
53C2×Q8×C9—21no—
54C2×D4×C9C2311yescharacteristic
55C22×C4×C9—21no—
56C22×Dic9—22no—
57Q8×D9—44no—
58C2×D36C2311yescharacteristic
59C2×C4×D9—21no—
60C2×C4×D9—22no—
61C2×Dic18—22no—
62C2×Dic18—21no—
63C2×Dic18D411yescharacteristic
64C2×C8×C9C2312yes—
65C9×C4⋊C4—21no—
66C9×C4⋊C4C2311yescharacteristic
67C9×C4⋊C4C2312yes—
68C9×C22⋊C4—21no—
69C42×C9C2311yescharacteristic
70#3676—22no—
71#3673Q814yescomplemented
72(C2×D9)⋊C4—21no—
73(C2×D9)⋊C4—22no—
74C4⋊Dic9—21no—
75C4⋊Dic9—22no—
76C4⋊Dic9D411yescharacteristic
77C4⋊Dic9C2312yes—
78C4⋊Dic9C2311yescharacteristic
79Dic9⋊C4—22no—
80Dic9⋊C4—22no—
81Dic9⋊C4D412yes—
82C4×Dic9C2312yes—
83C2×C9⋊C8C2311yescharacteristic
84C2×C9⋊C8C2311yescharacteristic
85#3384—91noSylow
86C2×D3×Q8—61no—
87C3×C4⋊Q8C2×D311yescharacteristic
88C3×C4×D4C2×D311yescharacteristic
89#946—61no—
90D4×Dic3—32no—
91C2×#213—31no—
92C2×C4⋊Dic3—61no—
93#924—61no—
94#896—62no—
95#893—32no—
96#890—32no—
97#888—32no—
98#878—62no—
99C4×D12—31no—
100#869—31no—
101C4×Dic6—31no—
102C3×#107C2×D312yes—
103C3×C4⋊C8C2×D311yescharacteristic
104C3×#102C2×D312yes—
105#832—31no—
106#821—32no—
107#817—32no—
108#815—32no—
109Dic3⋊C8—32no—
110#809—31no—
111#808—32no—
112#808—32no—
113#807—31no—
114C4×C3⋊C8—31no—
115C23×C9—21no—
116C22×D9—21no—
117Q8×C9—42no—
118D4×C9—21no—
119D4×C9C2×Q812yescomplemented
120C2×C4×C9—21no—
121C2×C4×C9—22no—
122C2×C4×C9—42no—
123C2×C4×C9C2×D411yescharacteristic
124C2×C4×C9C2×D411yescharacteristic
125C2×C4×C9C2411yescharacteristic
126C2×Dic9—21no—
127C2×Dic9—22no—
128C2×Dic9—82no—
129C2×Dic9C2×D412yes—
130C2×Dic9C2×D412yes—
131D36—21no—
132D36C2×Q812yes—
133C4×D9—44no—
134C4×D9—42no—
135Dic18—22no—
136Dic18—44no—
137Dic18—81no—
138C8×C9—22no—
139C9⋊C8—21no—
140C9⋊C8C2×Q812yescomplemented
141#554—91no—
142D4×Q8—91no—
143#501—92no—
144#498—91no—
145#478—92no—
146#476—91no—
147#476—92no—
148#474D911yescharacteristic, complemented
149#446—91no—
150#442—92no—
151C4×D8—91no—
152C2×C3×Q8—21no—
153C2×C3×D4C22×D311yescharacteristic
154C22×C3×C4—21no—
155C22×Dic3—62no—
156D3×Q8—124no—
157C2×D12—31no—
158C2×C4×D3—62no—
159C2×C4×D3—61no—
160C2×Dic6—31no—
161C2×Dic6—62no—
162C2×Dic6—61no—
163C2×C3×C8C22×D312yes—
164C3×C4⋊C4—21no—
165C3×C4⋊C4C22×D311yescharacteristic
166C3×C4⋊C4C22×D312yes—
167C3×C22⋊C4—21no—
168C3×C42C22×D311yescharacteristic
169#217—62no—
170#213—34no—
171(C2×D3)⋊C4—62no—
172(C2×D3)⋊C4—61no—
173C4⋊Dic3—31no—
174C4⋊Dic3—31no—
175C4⋊Dic3—32no—
176C4⋊Dic3—62no—
177C4⋊Dic3—61no—
178Dic3⋊C4—32no—
179Dic3⋊C4—62no—
180Dic3⋊C4—62no—
181C4×Dic3—32no—
182C2×C3⋊C8—31no—
183C2×C3⋊C8—31no—
184C22×C9—22no—
185C22×C9—41no—
186C22×C9—41no—
187C22×C9C22×D411yescharacteristic
188C2×D9—22no—
189C2×D9—41no—
190C2×D9—41no—
191C4×C9—21no—
192C4×C9—42no—
193C4×C9—41no—
194C4×C9AGL(1,ℤ/8)12yes—
195C4×C9C22×Q811yescharacteristic
196C4×C92−1+411yescharacteristic
197Dic9—22no—
198Dic9—22no—
199Dic9—41no—
200Dic9—42no—
201C22×Q8—181no—
202C2×D8—91no—
203C4⋊Q8—92no—
204C4⋊Q8—91no—
205C4⋊Q8C2×D911yescharacteristic
206#125—92no—
207C22⋊Q8—182no—
208C22⋊Q8—182no—
209C22⋊Q8—181no—
210C22⋊Q8—181no—
211C4×Q8—91no—
212C4×D4—92no—
213C4×D4—92no—
214C4×D4—91no—
215C4×D4C2×D911yescharacteristic
216C2×C4⋊C4—181no—
217#107—91no—
218#107C2×D912yes—
219#106—92no—
220#106—92no—
221#106—92no—
222C4⋊C8—92no—
223C4⋊C8C2×D911yescharacteristic
224#102—91no—
225#102—92no—
226#102—91no—
227#102C2×D912yes—
228#97—92no—
229C4×C8—91no—
230C23×C3—21no—
231C22×D3—61no—
232C3×Q8—42no—
233C3×D4—21no—
234C3×D4D3×Q812yes—
235C2×C3×C4—21no—
236C2×C3×C4—22no—
237C2×C3×C4—42no—
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4C23×D311yescharacteristic
241C2×Dic3—32no—
242C2×Dic3—32no—
243C2×Dic3—61no—
244C2×Dic3—62no—
245C2×Dic3—242no—
246D12—32no—
247D12—61no—
248C4×D3—124no—
249C4×D3—122no—
250Dic6—62no—
251Dic6—124no—
252Dic6—241no—
253C3×C8—22no—
254C3⋊C8—32no—
255C3⋊C8—61no—
256C2×C9—42no—
257C2×C9D4×Q811yescharacteristic
258C2×C9C2×AGL(1,ℤ/8)11yescharacteristic
259C2×C9#57711yescharacteristic
260D9—42no—
261C2×Q8—21no—
262C2×Q8—91no—
263C2×Q8—182no—
264C2×Q8—181no—
265C2×Q8—364no—
266C2×D4—91no—
267C2×D4C22×D911yescharacteristic
268C22×C4—21no—
269C22×C4—182no—
270C22×C4—182no—
271C22×C4—181no—
272D8—94no—
273C2×C8—91no—
274C2×C8—91no—
275C2×C8C22×D912yes—
276C4⋊C4—21no—
277C4⋊C4—91no—
278C4⋊C4—92no—
279C4⋊C4—92no—
280C4⋊C4—91no—
281C4⋊C4—182no—
282C4⋊C4—182no—
283C4⋊C4—182no—
284C4⋊C4—181no—
285C4⋊C4C22×D911yescharacteristic
286C4⋊C4C22×D912yes—
287C22⋊C4—21no—
288C22⋊C4—182no—
289C22⋊C4—182no—
290C22⋊C4—181no—
291C42—92no—
292C42C22×D911yescharacteristic
293C22×C3—22no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3C2×D3×D411yescharacteristic
297C2×D3—62no—
298C2×D3—121no—
299C2×D3—121no—
300C3×C4—21no—
301C3×C4—42no—
302C3×C4—41no—
303C3×C4#91112yes—
304C3×C4C2×D3×Q811yescharacteristic
305C3×C4#101011yescharacteristic
306Dic3—62no—
307Dic3—62no—
308Dic3—121no—
309Dic3—122no—
310C9#338411yescharacteristic, complemented, Sylow
311C23—21no—
312C23—181no—
313Q8—42no—
314Q8—182no—
315Q8—364no—
316Q8—721no—
317D4—21no—
318D4—92no—
319D4—181no—
320D4Q8×D912yescomplemented
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—42no—
324C2×C4—92no—
325C2×C4—92no—
326C2×C4—182no—
327C2×C4—181no—
328C2×C4—364no—
329C2×C4—362no—
330C2×C4—722no—
331C2×C4D4×D911yescharacteristic
332C2×C4D4×D911yescharacteristic
333C2×C4C23×D911yescharacteristic
334C8—22no—
335C8—92no—
336C8—181no—
337C2×C3—42no—
338C2×C3#563211yescharacteristic
339C2×C3C2×#91111yescharacteristic
340C2×C3#577811yescharacteristic
341D3—122no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—182no—
346C22—361no—
347C22—361no—
348C22C2×D4×D911yescharacteristic
349C4—21no—
350C4—41no—
351C4—42no—
352C4—182no—
353C4—182no—
354C4—361no—
355C4—362no—
356C4#6347312yes—
357C4C2×Q8×D911yescharacteristic
358C4#6371611yescharacteristic
359C3#8095911yescharacteristic
360C2—42no—
361C2—362no—
362C2#1058973411yescharacteristic
363C2C2×#6347311yescharacteristic
364C2#1058988011yescharacteristic
subgroupG/H
centerC22C2×D4×D9
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#474C2
socleC22×C3C2×D3×D4
prime radicalC2×#3673C22
hypercenter#474D9
hypocenterC9#3384
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10589829C2semidirect
2. #10589645C2semidirect
3. C9×#474C2semidirect
4. #10588760C2semidirect
6. #10588571C2semidirect
7. #10588556C2semidirect
8. #10588526C2semidirect
9. #10588509C2semidirect
11. #10588441C2semidirect
71. #3673Q8semidirect
119. D4×C9C2×Q8semidirect
140. C9⋊C8C2×Q8semidirect
148. #474D9semidirect
310. C9#3384semidirect
320. D4Q8×D9semidirect

Maximal subgroups

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

subgroupindex
#105898292
#105896452
C9×#4742
#105887602
C4×#36732
#105885712
#105885562
#105885262
#105885092
#105884652
#105884412
#809593