Finite Group Databasebeta

← #11780086

Subgroups — #11780086

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
2C9×#474C211yesmaximal, characteristic, complemented
3#10588768C211yesmaximal, characteristic, complemented
4#10588758C211yesmaximal, characteristic, complemented
5D4⋊(C9⋊C8)C211yesmaximal, characteristic, complemented
6#10588162C211yesmaximal, characteristic, complemented
7#10588161C211yesmaximal, characteristic, complemented
8#71110—31nomaximal
9C2×#3697—21no—
10C9×C4⋊Q8C2211yescharacteristic
11C4×D4×C9C2211yescharacteristic
12C2×#3675—21no—
13#63500—21no—
14#63486—21no—
15C4⋊C4×D9—21no—
16#63445—22no—
17C4×D36C2211yescharacteristic
18#63431C2211yescharacteristic
19C9×#107—21no—
20C9×C4⋊C8C2211yescharacteristic
21C9×#102—21no—
22#63395—21no—
23#63366—22no—
24C4⋊(C9⋊C8)C2211yescharacteristic
25C4×C9⋊C8C2211yescharacteristic
26#5551—31no—
27C3×#474D311yescharacteristic
28#5083—31no—
29#5078—31no—
30D4⋊(C3⋊C8)—31no—
31#4486—31no—
32#4483—31no—
33C2×Q8×C9—21no—
34C2×D4×C9D411yescharacteristic
35C22×C4×C9—21no—
36C2×#611—22no—
37#3697—42no—
38#3697—42no—
39C2×D36D411yescharacteristic
40C2×C4×D9—22no—
41C2×C4×D9—21no—
42C2×Dic18—21no—
43C2×C8×C9—21no—
44C9×C4⋊C4—21no—
45C9×C4⋊C4—21no—
46C9×C4⋊C4D411yescharacteristic
47C9×C22⋊C4—21no—
48C42×C9C2311yescharacteristic
49#3676—22no—
50#3675—42no—
51(C2×D9)⋊C4—21no—
52C4⋊Dic9—21no—
53C4⋊Dic9D412yes—
54C4⋊Dic9D411yescharacteristic
55Dic9⋊C4—22no—
56C2×C9⋊C8—21no—
57C2×C9⋊C8—21no—
58#1647—91noSylow
59C2×#235—61no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4×D4C2×D311yescharacteristic
62C2×#215—61no—
63#938—61no—
64#924—61no—
65D3×C4⋊C4—61no—
66#883—62no—
67C4×D12—31no—
68#869—31no—
69C3×#107—21no—
70C3×C4⋊C8C2×D311yescharacteristic
71C3×#102—21no—
72#835—61no—
73#807—62no—
74C4⋊(C3⋊C8)—31no—
75C4×C3⋊C8—31no—
76C23×C9—21no—
77C22×D9—21no—
78Q8×C9—41no—
79Q8×C9—41no—
80D4×C9—21no—
81D4×C9—21no—
82C2×C4×C9—21no—
83C2×C4×C9—41no—
84C2×C4×C9—41no—
85C2×C4×C9—41no—
86C2×C4×C9C2×D411yescharacteristic
87C2×C4×C9C2×D411yescharacteristic
88C2×C4×C9C2×D411yescharacteristic
89#611—44no—
90C2×Dic9—21no—
91C2×Dic9—22no—
92D36—21no—
93D36D812yes—
94C4×D9—44no—
95C4×D9—41no—
96C4×D9—41no—
97Dic18—41no—
98Dic18—41no—
99C8×C9—41no—
100C9⋊C8—22no—
101C9⋊C8—41no—
102#547—91no—
103#500—91no—
104#474D911yescharacteristic, complemented
105#461—91no—
106#332—91no—
107D4⋊C8—91no—
108D4⋊C8—91no—
109C2×C3×Q8—21no—
110C2×C3×D4#6711yescharacteristic
111C22×C3×C4—21no—
112C2×#67—62no—
113#235—122no—
114#235—122no—
115C2×D12—31no—
116C2×C4×D3—62no—
117C2×C4×D3—61no—
118C2×Dic6—61no—
119C2×C3×C8—21no—
120C3×C4⋊C4—21no—
121C3×C4⋊C4—21no—
122C3×C4⋊C4#6711yescharacteristic
123C3×C22⋊C4—21no—
124C3×C42C22×D311yescharacteristic
125#217—62no—
126#215—122no—
127(C2×D3)⋊C4—61no—
128C4⋊Dic3—32no—
129C4⋊Dic3—31no—
130C4⋊Dic3—61no—
131Dic3⋊C4—62no—
132C2×C3⋊C8—61no—
133C2×C3⋊C8—61no—
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×C9—81no—
144C4×C9C2×D811yescharacteristic
145C4×C9#13511yescharacteristic
146C4×C9AGL(1,ℤ/8)11yescharacteristic
147C4×C9#13711yescharacteristic
148Dic9—42no—
149Dic9—41no—
150C2×#41—181no—
151C2×SD16—181no—
152C4⋊Q8—91no—
153C4⋊Q8C2×D911yescharacteristic
154#123—182no—
155C22⋊Q8—181no—
156#121—181no—
157C4×D4—91no—
158C4×D4C2×D911yescharacteristic
159C2×C4⋊C4—181no—
160#107—21no—
161#107—182no—
162C4⋊C8—91no—
163C4⋊C8C2×D911yescharacteristic
164#103—181no—
165#102—21no—
166C4×C8—91no—
167C23×C3—21no—
168C22×D3—61no—
169C3×Q8—41no—
170C3×Q8—41no—
171C3×D4—21no—
172C3×D4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—41no—
175C2×C3×C4—41no—
176C2×C3×C4—41no—
177C2×C3×C4D3×D411yescharacteristic
178C2×C3×C4D3×D411yescharacteristic
179C2×C3×C4C2×#6711yescharacteristic
180#67—124no—
181C2×Dic3—61no—
182C2×Dic3—62no—
183D12—32no—
184D12—61no—
185C4×D3—124no—
186C4×D3—121no—
187C4×D3—121no—
188Dic6—121no—
189Dic6—121no—
190C3×C8—41no—
191C3⋊C8—62no—
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—21no—
201C2×Q8—181no—
202C2×D4—91no—
203C2×D4—182no—
204C2×D4#61111yescharacteristic
205C22×C4—21no—
206C22×C4—182no—
207C22×C4—181no—
208SD16—362no—
209C2×C8—21no—
210C2×C8—181no—
211C2×C8—181no—
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—91no—
215C4⋊C4—92no—
216C4⋊C4—182no—
217C4⋊C4—181no—
218C4⋊C4#61111yescharacteristic
219C22⋊C4—21no—
220C22⋊C4—182no—
221C22⋊C4—181no—
222C42C22×D911yescharacteristic
223C22×C3—41no—
224C22×C3—41no—
225C22×C3—41no—
226C22×C3#93711yescharacteristic
227C2×D3—62no—
228C2×D3—121no—
229C2×D3—121no—
230C3×C4—21no—
231C3×C4—41no—
232C3×C4—81no—
233C3×C4D3×D811yescharacteristic
234C3×C4#91111yescharacteristic
235C3×C4#94211yescharacteristic
236C3×C4#95011yescharacteristic
237Dic3—122no—
238Dic3—121no—
239C9#164711yescharacteristic, complemented, Sylow
240C23—21no—
241C23—181no—
242Q8—41no—
243Q8—41no—
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—41no—
255C2×C4—181no—
256C2×C4—182no—
257C2×C4—364no—
258C2×C4—361no—
259C2×C4—361no—
260C2×C4D4×D911yescharacteristic
261C2×C4D4×D911yescharacteristic
262C2×C4C2×#61111yescharacteristic
263C8—41no—
264C8—182no—
265C8—361no—
266C2×C3—81no—
267C2×C3#504711yescharacteristic
268C2×C3#515611yescharacteristic
269C2×C3#520511yescharacteristic
270D3—122no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—182no—
275C22—361no—
276C22—361no—
277C22#6349911yescharacteristic
278C4—21no—
279C4—41no—
280C4—81no—
281C4—361no—
282C4—362no—
283C4D8×D911yescharacteristic
284C4#6347311yescharacteristic
285C4#6350511yescharacteristic
286C4#6351311yescharacteristic
287C3#7111011yescharacteristic
288C2—81no—
289C2—362no—
290C2#1058873011yescharacteristic
291C2#1058883611yescharacteristic
292C2#1058888511yescharacteristic
subgroupG/H
centerC22#63499
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#474C2
socleC22×C3#937
prime radical#10589653C2
hypercenter#474D9
hypocenterC9#1647
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. C9×#474C2semidirect
3. #10588768C2semidirect
4. #10588758C2semidirect
5. D4⋊(C9⋊C8)C2semidirect
6. #10588162C2semidirect
7. #10588161C2semidirect
104. #474D9semidirect
239. C9#1647semidirect

Maximal subgroups

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

subgroupindex
#105896532
C9×#4742
#105887682
#105887582
D4⋊(C9⋊C8)2
#105881622
#105881612
#711103