Finite Group Databasebeta

← #11780092

Subgroups — #11780092

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#10589828C211yesmaximal, characteristic
2#10588758C211yesmaximal, characteristic, complemented
3#10588530C211yesmaximal, characteristic, complemented
4#10588525C211yesmaximal, characteristic, complemented
5C9×#332C211yesmaximal, characteristic, complemented
6#10588162C211yesmaximal, characteristic, complemented
7#10588162C211yesmaximal, characteristic, complemented
8#68436—31nomaximal
9C2×#3701—21no—
10C9×C4⋊Q8C2211yescharacteristic
11#63508—21no—
12C2×#3664—21no—
13#63457—21no—
14#63456—22no—
15C4⋊C4×D9—21no—
16C4×D36C2211yescharacteristic
17C4×D36C2211yescharacteristic
18#63431C2211yescharacteristic
19C9×C4⋊C8C2211yescharacteristic
20C9×C4⋊C8C2211yescharacteristic
21#63380—21no—
22#63378—21no—
23#63376—21no—
24#63366—22no—
25C4×C9⋊C8C2211yescharacteristic
26#5726—31no—
27#5078—31no—
28#4846—31no—
29#4841—31no—
30C3×#332D311yescharacteristic
31#4483—31no—
32#4483—31no—
33C2×Q8×C9—21no—
34#3701—42no—
35#3701—42no—
36C2×D36—22no—
37C2×D36D411yescharacteristic
38C2×D36D411yescharacteristic
39C2×C4×D9—22no—
40C2×C4×D9—21no—
41C2×C4×D9—21no—
42C2×Dic18—21no—
43C2×C8×C9—21no—
44C2×C8×C9—21no—
45C9×C4⋊C4—21no—
46C9×C4⋊C4D412yes—
47C42×C9C2311yescharacteristic
48(C2×D9)⋊C4—22no—
49(C2×D9)⋊C4—21no—
50(C2×D9)⋊C4—21no—
51C4⋊Dic9—21no—
52C4⋊Dic9—21no—
53C4⋊Dic9D411yescharacteristic
54C4⋊Dic9D411yescharacteristic
55Dic9⋊C4—22no—
56C2×C9⋊C8—21no—
57#3664—42no—
58#1647—91noSylow
59C2×#239—61no—
60C3×C4⋊Q8C2×D311yescharacteristic
61#946—61no—
62C2×#204—61no—
63#895—61no—
64#894—62no—
65D3×C4⋊C4—61no—
66C4×D12—31no—
67C4×D12—31no—
68#869—31no—
69C3×C4⋊C8C2×D311yescharacteristic
70C3×C4⋊C8C2×D311yescharacteristic
71#821—61no—
72#818—61no—
73#816—61no—
74#807—62no—
75C4×C3⋊C8—31no—
76C22×D9—21no—
77C22×D9—21no—
78Q8×C9—41no—
79Q8×C9—41no—
80C2×C4×C9—22no—
81C2×C4×C9C2×D411yescharacteristic
82C2×C4×C9C2×D411yescharacteristic
83C2×C4×C9C2×D411yescharacteristic
84C2×Dic9—21no—
85C2×Dic9—21no—
86C2×Dic9—41no—
87D36—21no—
88D36—21no—
89D36—21no—
90D36—44no—
91D36D812yes—
92C4×D9—44no—
93C4×D9—41no—
94C4×D9—41no—
95C4×D9—41no—
96C4×D9—41no—
97Dic18—41no—
98Dic18—41no—
99C8×C9—41no—
100C8×C9—41no—
101C9⋊C8—22no—
102#547—91no—
103#500—91no—
104#474—91no—
105#461—91no—
106#332D911yescharacteristic, complemented
107D4⋊C8—91no—
108D4⋊C8—91no—
109C2×C3×Q8—21no—
110#239—122no—
111#239—122no—
112C2×D12—31no—
113C2×D12—31no—
114C2×D12—62no—
115C2×C4×D3—62no—
116C2×C4×D3—61no—
117C2×C4×D3—61no—
118C2×Dic6—61no—
119C2×C3×C8—21no—
120C2×C3×C8—21no—
121C3×C4⋊C4—21no—
122C3×C4⋊C4D1212yes—
123C3×C42C22×D311yescharacteristic
124(C2×D3)⋊C4—62no—
125(C2×D3)⋊C4—61no—
126(C2×D3)⋊C4—61no—
127C4⋊Dic3—31no—
128C4⋊Dic3—31no—
129C4⋊Dic3—61no—
130C4⋊Dic3—61no—
131Dic3⋊C4—62no—
132C2×C3⋊C8—61no—
133#204—122no—
134C22×C9#12011yescharacteristic
135C2×D9—22no—
136C2×D9—41no—
137C2×D9—41no—
138C2×D9—41no—
139C2×D9—41no—
140C2×D9—41no—
141C4×C9—21no—
142C4×C9—42no—
143C4×C9C2×D811yescharacteristic
144C4×C9#13511yescharacteristic
145C4×C9AGL(1,ℤ/8)11yescharacteristic
146C4×C9#13711yescharacteristic
147Dic9—41no—
148Dic9—41no—
149Dic9—81no—
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×D4—91no—
159C2×C4⋊C4—181no—
160#107—181no—
161#107—182no—
162C4⋊C8C2×D911yescharacteristic
163C4⋊C8C2×D911yescharacteristic
164#103—181no—
165#102—181no—
166C4×C8—91no—
167C22×D3—61no—
168C22×D3—61no—
169C3×Q8—41no—
170C3×Q8—41no—
171C2×C3×C4—22no—
172C2×C3×C4C2×D1211yescharacteristic
173C2×C3×C4D3×D411yescharacteristic
174C2×C3×C4D3×D411yescharacteristic
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—121no—
178D12—32no—
179D12—61no—
180D12—61no—
181D12—61no—
182D12—124no—
183C4×D3—124no—
184C4×D3—121no—
185C4×D3—121no—
186C4×D3—121no—
187C4×D3—121no—
188Dic6—121no—
189Dic6—121no—
190C3×C8—41no—
191C3×C8—41no—
192C3⋊C8—62no—
193C2×C9#44711yescharacteristic
194C2×C9#45211yescharacteristic
195C2×C9#45611yescharacteristic
196D9—42no—
197D9—81no—
198#41—362no—
199#41—362no—
200C2×Q8—21no—
201C2×Q8—181no—
202C2×D4—91no—
203C2×D4—91no—
204C2×D4—182no—
205C22×C4—182no—
206C22×C4—181no—
207C22×C4—181no—
208SD16—362no—
209C2×C8—21no—
210C2×C8—21no—
211C2×C8—181no—
212C4⋊C4—21no—
213C4⋊C4—91no—
214C4⋊C4—91no—
215C4⋊C4—182no—
216C4⋊C4—181no—
217C4⋊C4—181no—
218C4⋊C4D3612yes—
219C22⋊C4—182no—
220C22⋊C4—181no—
221C22⋊C4—181no—
222C42C22×D911yescharacteristic
223C22×C3#88211yescharacteristic
224C2×D3—62no—
225C2×D3—121no—
226C2×D3—121no—
227C2×D3—121no—
228C2×D3—121no—
229C2×D3—121no—
230C3×C4—21no—
231C3×C4—42no—
232C3×C4D3×D811yescharacteristic
233C3×C4#91411yescharacteristic
234C3×C4#91611yescharacteristic
235C3×C4#91811yescharacteristic
236Dic3—121no—
237Dic3—121no—
238Dic3—241no—
239C9#164711yescharacteristic, complemented, Sylow
240C23—181no—
241C23—181no—
242Q8—41no—
243Q8—41no—
244Q8—361no—
245Q8—361no—
246D4—92no—
247D4—181no—
248D4—181no—
249D4—181no—
250D4—364no—
251C2×C4—22no—
252C2×C4—181no—
253C2×C4—181no—
254C2×C4—364no—
255C2×C4—361no—
256C2×C4—361no—
257C2×C4—361no—
258C2×C4—361no—
259C2×C4—361no—
260C2×C4C2×D3611yescharacteristic
261C2×C4D4×D911yescharacteristic
262C2×C4D4×D911yescharacteristic
263C8—41no—
264C8—41no—
265C8—182no—
266C2×C3#475211yescharacteristic
267C2×C3#477311yescharacteristic
268C2×C3#480811yescharacteristic
269D3—122no—
270D3—241no—
271C22—182no—
272C22—361no—
273C22—361no—
274C22—361no—
275C22—361no—
276C22—361no—
277C22#6344411yescharacteristic
278C4—21no—
279C4—42no—
280C4—361no—
281C4—361no—
282C4—721no—
283C4D8×D911yescharacteristic
284C4#6347611yescharacteristic
285C4#6347811yescharacteristic
286C4#6348011yescharacteristic
287C3#6843611yescharacteristic
288C2—362no—
289C2—721no—
290C2#1058843211yescharacteristic
291C2#1058845311yescharacteristic
292C2#1058848811yescharacteristic
subgroupG/H
centerC22#63444
commutator, cosocleC42×C9C23
FrattiniC3×C42C22×D3
FittingC9×#332C2
socleC22×C3#882
prime radical#10589828C2
hypercenter#332D9
hypocenterC9#1647
LCSG ▷ C42×C9 ▷ C22×C9 ▷ C9
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #10588758C2semidirect
3. #10588530C2semidirect
4. #10588525C2semidirect
5. C9×#332C2semidirect
6. #10588162C2semidirect
7. #10588162C2semidirect
106. #332D9semidirect
239. C9#1647semidirect

Maximal subgroups

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

subgroupindex
#105898282
#105887582
#105885302
#105885252
C9×#3322
#105881622
#684363