Finite Group Databasebeta

← #11794650

Subgroups — #11794650

Order 1152.

411 conjugacy classes of subgroups.

The subgroup lattice has 357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63380C211yesmaximal, characteristic
2#10588668C211yesmaximal, characteristic
3#10588655C211yesmaximal, characteristic, complemented
4C2×#63369C211yesmaximal, characteristic
5C9×#340C211yesmaximal, characteristic, complemented
6#10588228C211yesmaximal, characteristic, complemented
7#10588206C211yesmaximal, characteristic, complemented
8#68902—31nomaximal
9C22×D36C2211yescharacteristic
10C22×C8×C9C2211yescharacteristic
11C2×C9×C4⋊C4C2211yescharacteristic
12C2×C9×C4⋊C4C2211yescharacteristic
13C2×(C2×D9)⋊C4—21no—
14C2×(C2×D9)⋊C4—21no—
15C2×C4⋊Dic9C2211yescharacteristic
16C2×Dic9⋊C4—21no—
17C2×Dic9⋊C4—21no—
18C2×C4×Dic9C2211yescharacteristic
19C22×C9⋊C8C2211yescharacteristic
20#63380—22no—
21#63369—22no—
22C2×#821—31no—
23#4988—31no—
24#4975—31no—
25C2×#809—31no—
26C3×#340D311yescharacteristic
27#4550—31no—
28#4529—31no—
29C23×D9—21no—
30C22×C4×C9—21no—
31C22×C4×C9—21no—
32C22×C4×C9C2311yescharacteristic
33C22×Dic9—21no—
34C22×Dic9D411yescharacteristic
35C22×Dic9D411yescharacteristic
36C2×D36—21no—
37C2×D36—21no—
38C2×D36—21no—
39C2×D36—21no—
40C2×D36—21no—
41C2×D36D412yes—
42C2×C8×C9—21no—
43C2×C8×C9—21no—
44C2×C8×C9—21no—
45C9×C4⋊C4—21no—
46C9×C4⋊C4—21no—
47C9×C4⋊C4—21no—
48C9×C4⋊C4—21no—
49(C2×D9)⋊C4—42no—
50(C2×D9)⋊C4—42no—
51C4⋊Dic9—21no—
52C4⋊Dic9—21no—
53Dic9⋊C4—42no—
54Dic9⋊C4—42no—
55C4×Dic9—21no—
56C4×Dic9—21no—
57C2×C9⋊C8—21no—
58C2×C9⋊C8—21no—
59C2×C9⋊C8—21no—
60#2071—91noSylow
61C22×D12—31no—
62C22×C3×C8C2×D311yescharacteristic
63C2×C3×C4⋊C4C2×D311yescharacteristic
64C2×C3×C4⋊C4C2×D311yescharacteristic
65C2×(C2×D3)⋊C4—61no—
66C2×(C2×D3)⋊C4—61no—
67C2×C4⋊Dic3—31no—
68C2×Dic3⋊C4—61no—
69C2×Dic3⋊C4—61no—
70C2×C4×Dic3—31no—
71C22×C3⋊C8—31no—
72#821—62no—
73#809—62no—
74C23×C9C2×D411yescharacteristic
75C22×D9—22no—
76C22×D9—41no—
77C22×D9—41no—
78C22×D9—41no—
79C22×D9—41no—
80C22×D9—41no—
81C22×D9—41no—
82C2×C4×C9—41no—
83C2×C4×C9—41no—
84C2×C4×C9—41no—
85C2×C4×C9—41no—
86C2×C4×C9—41no—
87C2×C4×C9—41no—
88C2×C4×C9C2×D411yescharacteristic
89C2×C4×C9#4111yescharacteristic
90C2×C4×C9#4111yescharacteristic
91C2×C4×C9#4111yescharacteristic
92C2×C4×C9#4111yescharacteristic
93C2×C4×C9#4111yescharacteristic
94C2×Dic9—21no—
95C2×Dic9—21no—
96C2×Dic9—21no—
97C2×Dic9—21no—
98C2×Dic9—41no—
99C2×Dic9—41no—
100C2×Dic9—41no—
101C2×Dic9D812yes—
102C2×Dic9SD1612yes—
103D36—22no—
104D36—22no—
105D36—41no—
106D36—41no—
107C8×C9—41no—
108C9⋊C8—41no—
109C2×#102—91no—
110C2×#102—91no—
111#390—91no—
112#384—91no—
113#340—91no—
114#340D911yescharacteristic, complemented
115#336—91no—
116C23×D3—61no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4C22×D311yescharacteristic
120C22×Dic3—31no—
121C22×Dic3—31no—
122C22×Dic3—61no—
123C2×D12—32no—
124C2×D12—61no—
125C2×D12—61no—
126C2×D12—61no—
127C2×D12—61no—
128C2×D12—61no—
129C2×C3×C8—21no—
130C2×C3×C8—21no—
131C2×C3×C8—21no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—21no—
135C3×C4⋊C4—21no—
136(C2×D3)⋊C4—122no—
137(C2×D3)⋊C4—122no—
138C4⋊Dic3—61no—
139C4⋊Dic3—61no—
140Dic3⋊C4—122no—
141Dic3⋊C4—122no—
142C4×Dic3—61no—
143C4×Dic3—61no—
144C2×C3⋊C8—61no—
145C2×C3⋊C8—61no—
146C2×C3⋊C8—61no—
147C22×C9#12111yescharacteristic
148C22×C9#12311yescharacteristic
149C22×C9#12411yescharacteristic
150C22×C9C2×D811yescharacteristic
151C22×C9C2×SD1611yescharacteristic
152C22×C9AGL(1,ℤ/8)11yescharacteristic
153C22×C9#13711yescharacteristic
154C2×D9—42no—
155C2×D9—42no—
156C2×D9—42no—
157C2×D9—81no—
158C2×D9—81no—
159C2×D9—81no—
160C2×D9—81no—
161C4×C9—81no—
162C4×C9—81no—
163C4×C9#12311yescharacteristic
164C4×C9#12311yescharacteristic
165C4×C9#12611yescharacteristic
166C4×C9#12611yescharacteristic
167Dic9—22no—
168Dic9—22no—
169Dic9—81no—
170C22×D4—91no—
171C22×C8—91no—
172C22×C8C2×D911yescharacteristic
173C2×C4⋊C4—91no—
174C2×C4⋊C4—181no—
175C2×C4⋊C4—181no—
176C2×C4⋊C4C2×D911yescharacteristic
177C2×C4⋊C4C2×D911yescharacteristic
178C2×C22⋊C4—181no—
179C2×C22⋊C4—181no—
180C2×C42—91no—
181#102—182no—
182#102—182no—
183C23×C3D3×D411yescharacteristic
184C22×D3—62no—
185C22×D3—121no—
186C22×D3—121no—
187C22×D3—121no—
188C22×D3—121no—
189C22×D3—121no—
190C22×D3—121no—
191C2×C3×C4—41no—
192C2×C3×C4—41no—
193C2×C3×C4—41no—
194C2×C3×C4—41no—
195C2×C3×C4—41no—
196C2×C3×C4—41no—
197C2×C3×C4#23511yescharacteristic
198C2×C3×C4#23511yescharacteristic
199C2×C3×C4#23511yescharacteristic
200C2×C3×C4D3×D411yescharacteristic
201C2×C3×C4#23711yescharacteristic
202C2×C3×C4#23911yescharacteristic
203C2×Dic3—32no—
204C2×Dic3—32no—
205C2×Dic3—61no—
206C2×Dic3—61no—
207C2×Dic3—61no—
208C2×Dic3—61no—
209C2×Dic3—121no—
210C2×Dic3—121no—
211C2×Dic3—121no—
212D12—62no—
213D12—62no—
214D12—121no—
215D12—121no—
216C3×C8—41no—
217C3⋊C8—121no—
218C2×C9#39711yescharacteristic
219C2×C9#45911yescharacteristic
220C2×C9#46111yescharacteristic
221C2×C9#48011yescharacteristic
222C2×C9#48111yescharacteristic
223C2×C9#48611yescharacteristic
224C2×C9#48911yescharacteristic
225D9—82no—
226C24—181no—
227C2×D4—92no—
228C2×D4—181no—
229C2×D4—181no—
230C2×D4—181no—
231C2×D4—181no—
232C2×D4—181no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—91no—
236C22×C4—91no—
237C22×C4—181no—
238C22×C4C22×D911yescharacteristic
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—181no—
243C2×C8—181no—
244C2×C8—181no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C4⋊C4—362no—
252C4⋊C4—362no—
253C22⋊C4—362no—
254C22⋊C4—362no—
255C42—181no—
256C42—181no—
257C22×C3#88411yescharacteristic
258C22×C3#88511yescharacteristic
259C22×C3#89411yescharacteristic
260C22×C3D3×D811yescharacteristic
261C22×C3D3×SD1611yescharacteristic
262C22×C3#91411yescharacteristic
263C22×C3#91811yescharacteristic
264C2×D3—122no—
265C2×D3—122no—
266C2×D3—122no—
267C2×D3—241no—
268C2×D3—241no—
269C2×D3—241no—
270C2×D3—241no—
271C3×C4—81no—
272C3×C4—81no—
273C3×C4#87611yescharacteristic
274C3×C4#88311yescharacteristic
275C3×C4#89411yescharacteristic
276C3×C4#89811yescharacteristic
277Dic3—62no—
278Dic3—62no—
279Dic3—241no—
280C9#207111yescharacteristic, complemented, Sylow
281C23—182no—
282C23—361no—
283C23—361no—
284C23—361no—
285C23—361no—
286C23—361no—
287C23—361no—
288C23D4×D911yescharacteristic
289D4—182no—
290D4—182no—
291D4—361no—
292D4—361no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—92no—
300C2×C4—92no—
301C2×C4—181no—
302C2×C4—181no—
303C2×C4—181no—
304C2×C4—181no—
305C2×C4—361no—
306C2×C4—361no—
307C2×C4—361no—
308C2×C4#369711yescharacteristic
309C2×C4#369711yescharacteristic
310C2×C4#369711yescharacteristic
311C2×C4D4×D911yescharacteristic
312C2×C4#369911yescharacteristic
313C2×C4#370111yescharacteristic
314C8—41no—
315C8—361no—
316C2×C3#467511yescharacteristic
317C2×C3#476011yescharacteristic
318C2×C3#478611yescharacteristic
319C2×C3#479411yescharacteristic
320C2×C3#481811yescharacteristic
321C2×C3#486311yescharacteristic
322C2×C3#488211yescharacteristic
323D3—242no—
324C22—362no—
325C22—362no—
326C22—362no—
327C22—721no—
328C22—721no—
329C22—721no—
330C22—721no—
331C22#6344611yescharacteristic
332C22#6344711yescharacteristic
333C22#6345611yescharacteristic
334C22D8×D911yescharacteristic
335C22SD16×D911yescharacteristic
336C22#6347611yescharacteristic
337C22#6348011yescharacteristic
338C4—81no—
339C4—81no—
340C4—182no—
341C4—182no—
342C4—721no—
343C4#6343811yescharacteristic
344C4#6344511yescharacteristic
345C4#6345611yescharacteristic
346C4#6346011yescharacteristic
347C3#6890211yescharacteristic
348C2—722no—
349C2#1058835511yescharacteristic
350C2#1058844011yescharacteristic
351C2#1058846611yescharacteristic
352C2#1058847411yescharacteristic
353C2#1058849811yescharacteristic
354C2#1058854311yescharacteristic
355C2#1058856211yescharacteristic
subgroupG/H
centerC23D4×D9
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC9×#340C2
socleC23×C3D3×D4
prime radicalC22×D36C22
hypercenter#340D9
hypocenterC9#2071
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
3. #10588655C2semidirect
5. C9×#340C2semidirect
6. #10588228C2semidirect
7. #10588206C2semidirect
114. #340D9semidirect
280. C9#2071semidirect

Maximal subgroups

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

subgroupindex
C2×#633802
#105886682
#105886552
C2×#633692
C9×#3402
#105882282
#105882062
#689023