Finite Group Databasebeta

← #11780098

Subgroups — #11780098

Order 1152.

360 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589653C211yesmaximal, characteristic
2#10588690C211yesmaximal, characteristic, complemented
3#10588525C211yesmaximal, characteristic, complemented
4#10588362C211yesmaximal, characteristic, complemented
5C9×D4⋊C8C211yesmaximal, characteristic, complemented
6#10588159C211yesmaximal, characteristic, complemented
7#10588136C211yesmaximal, characteristic, complemented
8#68184—31nomaximal
9C2×#3697—21no—
10C4×D4×C9C2211yescharacteristic
11#63500—21no—
12#63486—21no—
13C2×#3664—21no—
14C4⋊C4×D9—21no—
15#63445—22no—
16C4×D36C2211yescharacteristic
17#63431C2211yescharacteristic
18#63431C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20C4×C8×C9C2211yescharacteristic
21#63392—21no—
22#63378—22no—
23#63376—21no—
24#63366—21no—
25C4⋊(C9⋊C8)C2211yescharacteristic
26#5551—31no—
27#5007—31no—
28#4841—31no—
29#4682—31no—
30C3×D4⋊C8D311yescharacteristic
31#4482—31no—
32#4459—31no—
33C2×D4×C9D411yescharacteristic
34C22×C4×C9—21no—
35C2×#611—22no—
36#3697—42no—
37#3697—42no—
38C2×D36D411yescharacteristic
39C2×C4×D9—22no—
40C2×C4×D9—21no—
41C2×Dic18—21no—
42C2×Dic18—21no—
43C2×C8×C9—21no—
44C2×C8×C9—21no—
45C9×C4⋊C4D411yescharacteristic
46C9×C22⋊C4—21no—
47C42×C9C2311yescharacteristic
48#3676—22no—
49(C2×D9)⋊C4—21no—
50C4⋊Dic9—21no—
51C4⋊Dic9—21no—
52C4⋊Dic9—21no—
53C4⋊Dic9D411yescharacteristic
54C4⋊Dic9D412yes—
55Dic9⋊C4—22no—
56C2×C9⋊C8—21no—
57#3664—42no—
58#1647—91noSylow
59C2×#235—61no—
60C3×C4×D4C2×D311yescharacteristic
61#938—61no—
62#924—61no—
63C2×#204—61no—
64D3×C4⋊C4—61no—
65#883—62no—
66C4×D12—31no—
67#869—31no—
68#869—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4×C8C2×D311yescharacteristic
71#832—61no—
72#818—62no—
73#816—61no—
74#807—61no—
75C4⋊(C3⋊C8)—31no—
76C23×C9—21no—
77C22×D9—21no—
78D4×C9—21no—
79D4×C9—21no—
80C2×C4×C9—21no—
81C2×C4×C9—41no—
82C2×C4×C9—41no—
83C2×C4×C9C2×D411yescharacteristic
84C2×C4×C9C2×D411yescharacteristic
85C2×C4×C9C2×D411yescharacteristic
86#611—44no—
87C2×Dic9—21no—
88C2×Dic9—22no—
89C2×Dic9—41no—
90D36—21no—
91D36D812yes—
92C4×D9—44no—
93C4×D9—41no—
94C4×D9—41no—
95Dic18—41no—
96Dic18—41no—
97Dic18—41no—
98Dic18—41no—
99C8×C9—22no—
100C8×C9—41no—
101C9⋊C8—41no—
102#547—91no—
103#500—91no—
104#474—91no—
105#461—91no—
106#332—91no—
107D4⋊C8—91no—
108D4⋊C8D911yescharacteristic, complemented
109C2×C3×D4D1211yescharacteristic
110C22×C3×C4—21no—
111C2×#67—62no—
112#235—122no—
113#235—122no—
114C2×D12—31no—
115C2×C4×D3—62no—
116C2×C4×D3—61no—
117C2×Dic6—61no—
118C2×Dic6—61no—
119C2×C3×C8—21no—
120C2×C3×C8—21no—
121C3×C4⋊C4D1211yescharacteristic
122C3×C22⋊C4—21no—
123C3×C42C22×D311yescharacteristic
124#217—62no—
125(C2×D3)⋊C4—61no—
126C4⋊Dic3—31no—
127C4⋊Dic3—32no—
128C4⋊Dic3—61no—
129C4⋊Dic3—61no—
130C4⋊Dic3—61no—
131Dic3⋊C4—62no—
132C2×C3⋊C8—61no—
133#204—122no—
134C22×C9—41no—
135C22×C9—41no—
136C22×C9—41no—
137C22×C9#12011yescharacteristic
138C2×D9—22no—
139C2×D9—41no—
140C2×D9—41no—
141C4×C9—21no—
142C4×C9—41no—
143C4×C9C2×D811yescharacteristic
144C4×C9#13511yescharacteristic
145C4×C9AGL(1,ℤ/8)11yescharacteristic
146C4×C9#13711yescharacteristic
147Dic9—42no—
148Dic9—41no—
149Dic9—81no—
150C2×#41—181no—
151C2×SD16—181no—
152C4⋊Q8—91no—
153C4⋊Q8—91no—
154#123—182no—
155C22⋊Q8—181no—
156#121—181no—
157C4×D4—91no—
158C4×D4C2×D911yescharacteristic
159C2×C4⋊C4—181no—
160#107—182no—
161#107—181no—
162C4⋊C8—91no—
163C4⋊C8C2×D911yescharacteristic
164#103—181no—
165#102—181no—
166C4×C8C2×D911yescharacteristic
167C23×C3—21no—
168C22×D3—61no—
169C3×D4—21no—
170C3×D4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—41no—
173C2×C3×C4—41no—
174C2×C3×C4C2×D1211yescharacteristic
175C2×C3×C4D3×D411yescharacteristic
176C2×C3×C4D3×D411yescharacteristic
177#67—124no—
178C2×Dic3—61no—
179C2×Dic3—62no—
180C2×Dic3—121no—
181D12—32no—
182D12—61no—
183C4×D3—124no—
184C4×D3—121no—
185C4×D3—121no—
186Dic6—121no—
187Dic6—121no—
188Dic6—121no—
189Dic6—121no—
190C3×C8—22no—
191C3×C8—41no—
192C3⋊C8—121no—
193C2×C9—81no—
194C2×C9#44711yescharacteristic
195C2×C9#45211yescharacteristic
196C2×C9#45611yescharacteristic
197D9—42no—
198#41—362no—
199#41—362no—
200C2×Q8—181no—
201C2×Q8—181no—
202C2×D4—91no—
203C2×D4—182no—
204C2×D4D3611yescharacteristic
205C22×C4—21no—
206C22×C4—182no—
207C22×C4—181no—
208SD16—362no—
209C2×C8—21no—
210C2×C8—21no—
211C2×C8—181no—
212C4⋊C4—91no—
213C4⋊C4—92no—
214C4⋊C4—182no—
215C4⋊C4—181no—
216C4⋊C4—181no—
217C4⋊C4—181no—
218C4⋊C4D3611yescharacteristic
219C22⋊C4—21no—
220C22⋊C4—182no—
221C22⋊C4—181no—
222C42C22×D911yescharacteristic
223C22×C3—41no—
224C22×C3—41no—
225C22×C3—41no—
226C22×C3#88211yescharacteristic
227C2×D3—62no—
228C2×D3—121no—
229C2×D3—121no—
230C3×C4—21no—
231C3×C4—41no—
232C3×C4#90411yescharacteristic
233C3×C4#90911yescharacteristic
234C3×C4D3×D811yescharacteristic
235C3×C4#91411yescharacteristic
236Dic3—121no—
237Dic3—122no—
238Dic3—241no—
239C9#164711yescharacteristic, complemented, Sylow
240C23—21no—
241C23—181no—
242Q8—361no—
243Q8—361no—
244Q8—361no—
245Q8—361no—
246D4—21no—
247D4—21no—
248D4—92no—
249D4—181no—
250D4—364no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—181no—
255C2×C4—182no—
256C2×C4—364no—
257C2×C4—361no—
258C2×C4—361no—
259C2×C4—361no—
260C2×C4C2×D3611yescharacteristic
261C2×C4D4×D911yescharacteristic
262C2×C4D4×D911yescharacteristic
263C8—22no—
264C8—41no—
265C8—361no—
266C2×C3—81no—
267C2×C3#473311yescharacteristic
268C2×C3#477311yescharacteristic
269C2×C3#482611yescharacteristic
270D3—122no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—182no—
275C22—361no—
276C22—361no—
277C22#6344411yescharacteristic
278C4—21no—
279C4—41no—
280C4—362no—
281C4—361no—
282C4—721no—
283C4#6346711yescharacteristic
284C4#6347111yescharacteristic
285C4D8×D911yescharacteristic
286C4#6347611yescharacteristic
287C3#6818411yescharacteristic
288C2—81no—
289C2—362no—
290C2#1058841511yescharacteristic
291C2#1058845311yescharacteristic
292C2#1058850611yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×D4⋊C8C2
socleC22×C3#882
prime radical#10589653C2
hypercenterD4⋊C8D9
hypocenterC9#1647
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10588690C2semidirect
3. #10588525C2semidirect
4. #10588362C2semidirect
5. C9×D4⋊C8C2semidirect
6. #10588159C2semidirect
7. #10588136C2semidirect
108. D4⋊C8D9semidirect
239. C9#1647semidirect

Maximal subgroups

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

subgroupindex
#105896532
#105886902
#105885252
#105883622
C9×D4⋊C82
#105881592
#105881362
#681843