Finite Group Databasebeta

← #11791133

Subgroups — #11791133

Order 1152.

510 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×SD16C211yesmaximal, characteristic
2#10588909C211yesmaximal, characteristic, complemented
3C2×#63395C211yesmaximal, characteristic, complemented
4#10588901C211yesmaximal, characteristic
5C2×#63392C211yesmaximal, characteristic
6C2×#63378C211yesmaximal, characteristic, complemented
7C2×#63375C211yesmaximal, characteristic, complemented
8#72050—31nomaximal
9C22×Q8×C9C2211yescharacteristic
10C22×D4×C9C2211yescharacteristic
11C2×C9×SD16—22no—
12C2×C9×SD16—22no—
13C2×C9×SD16C414yescomplemented
14C22×C8×C9C2211yescharacteristic
15C2×#3676—22no—
16C2×C4⋊Dic9C2211yescharacteristic
17C2×C4⋊Dic9C2211yescharacteristic
18C2×C4×Dic9C2211yescharacteristic
19C22×C9⋊C8C2211yescharacteristic
20#63395—22no—
21#63392—22no—
22C9⋊#95—22no—
23#63378—22no—
24#63375—22no—
25C22×C3×SD16D311yescharacteristic
26#5229—31no—
27C2×#835—31no—
28#5221—31no—
29C2×#832—31no—
30C2×#818—31no—
31C2×#815—31no—
32C24×C9—21no—
33C2×Q8×C9—21no—
34C2×Q8×C9—21no—
35C2×Q8×C9—21no—
36C2×Q8×C9—21no—
37C2×Q8×C9—21no—
38C2×Q8×C9C2×C412yes—
39C2×D4×C9—21no—
40C2×D4×C9—21no—
41C2×D4×C9—21no—
42C2×D4×C9—21no—
43C2×D4×C9—21no—
44C2×D4×C9C2×C412yes—
45C22×C4×C9—21no—
46C22×C4×C9C2311yescharacteristic
47C22×Dic9—21no—
48C22×Dic9—21no—
49C22×Dic9D412yes—
50C9×SD16—28no—
51C2×C8×C9C2×C412yes—
52C2×C8×C9D412yes—
53C2×C8×C9D412yes—
54#3676—44no—
55C4⋊Dic9—21no—
56C4⋊Dic9—21no—
57C4⋊Dic9—21no—
58C4⋊Dic9—21no—
59C4×Dic9—21no—
60C4×Dic9—21no—
61C2×C9⋊C8—21no—
62C2×C9⋊C8—21no—
63C2×C9⋊C8D412yes—
64#1973—91noSylow
65C22×C3×Q8C2×D311yescharacteristic
66C22×C3×D4C2×D311yescharacteristic
67C2×C3×SD16—22no—
68C2×C3×SD16—22no—
69C2×C3×SD16Dic314yes—
70C22×C3×C8C2×D311yescharacteristic
71C2×#217—62no—
72C2×C4⋊Dic3—31no—
73C2×C4⋊Dic3—31no—
74C2×C4×Dic3—31no—
75C22×C3⋊C8—31no—
76#835—62no—
77#832—62no—
78C3⋊#95—62no—
79#818—62no—
80#815—62no—
81C23×C9—22no—
82C23×C9—41no—
83C23×C9—41no—
84C23×C9—42no—
85C23×C9—42no—
86C23×C9C2×D411yescharacteristic
87Q8×C9—22no—
88Q8×C9—22no—
89Q8×C9—41no—
90Q8×C9—41no—
91D4×C9—22no—
92D4×C9—22no—
93D4×C9—41no—
94D4×C9—41no—
95C2×C4×C9—22no—
96C2×C4×C9—41no—
97C2×C4×C9—41no—
98C2×C4×C9C22×C411yescharacteristic
99C2×C4×C9C2×D411yescharacteristic
100C2×C4×C9C2×D411yescharacteristic
101C2×C4×C9C2×D411yescharacteristic
102C2×C4×C9#4111yescharacteristic
103C2×C4×C9#4111yescharacteristic
104C2×Dic9—22no—
105C2×Dic9—22no—
106C2×Dic9—22no—
107C2×Dic9—41no—
108C2×Dic9—41no—
109C2×Dic9—42no—
110C2×Dic9—42no—
111C8×C9C22⋊C414yescomplemented
112C9⋊C8—22no—
113C22×SD16D911yescharacteristic
114C2×#107—91no—
115C2×#103—91no—
116C2×#102—91no—
117C2×#97—91no—
118#391—91no—
119#390—91no—
120C24×C3—21no—
121C2×C3×Q8—21no—
122C2×C3×Q8—21no—
123C2×C3×Q8—21no—
124C2×C3×Q8—21no—
125C2×C3×Q8—21no—
126C2×C3×Q8C2×Dic312yes—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4C2×Dic312yes—
133C22×C3×C4—21no—
134C22×C3×C4C22×D311yescharacteristic
135C22×Dic3—32no—
136C22×Dic3—61no—
137C22×Dic3—61no—
138C3×SD16—28no—
139C2×C3×C8C2×Dic312yes—
140C2×C3×C8#6712yes—
141C2×C3×C8#6712yes—
142#217—124no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—61no—
146C4⋊Dic3—61no—
147C4×Dic3—61no—
148C4×Dic3—61no—
149C2×C3⋊C8—32no—
150C2×C3⋊C8—61no—
151C2×C3⋊C8—61no—
152C22×C9—42no—
153C22×C9—44no—
154C22×C9—82no—
155C22×C9—81no—
156C22×C9—81no—
157C22×C9C4×D411yescharacteristic
158C22×C9#12111yescharacteristic
159C22×C9#12711yescharacteristic
160C22×C9AGL(1,ℤ/8)12yes—
161C22×C9#13712yes—
162C4×C9—42no—
163C4×C9C2×C22⋊C411yescharacteristic
164C4×C9C4×D411yescharacteristic
165C4×C9#12111yescharacteristic
166C4×C9#12411yescharacteristic
167Dic9—42no—
168Dic9—81no—
169Dic9—81no—
170C22×Q8C2×D911yescharacteristic
171C22×D4C2×D911yescharacteristic
172C2×SD16—22no—
173C2×SD16—22no—
174C2×SD16Dic914yescomplemented
175C22×C8—91no—
176C22×C8C2×D911yescharacteristic
177C2×C4⋊C4—91no—
178C2×C4⋊C4—91no—
179C2×C22⋊C4—182no—
180C2×C42—91no—
181#107—182no—
182#103—182no—
183#102—182no—
184#97—182no—
185#95—182no—
186C23×C3—22no—
187C23×C3—42no—
188C23×C3—42no—
189C23×C3—41no—
190C23×C3—41no—
191C23×C3D3×D411yescharacteristic
192C3×Q8—22no—
193C3×Q8—22no—
194C3×Q8—41no—
195C3×Q8—41no—
196C3×D4—22no—
197C3×D4—22no—
198C3×D4—41no—
199C3×D4—41no—
200C2×C3×C4—22no—
201C2×C3×C4—41no—
202C2×C3×C4—41no—
203C2×C3×C4D3×D411yescharacteristic
204C2×C3×C4#23711yescharacteristic
205C2×C3×C4#23711yescharacteristic
206C2×C3×C4C22×Dic311yescharacteristic
207C2×C3×C4C2×#6711yescharacteristic
208C2×C3×C4C2×#6711yescharacteristic
209C2×Dic3—62no—
210C2×Dic3—62no—
211C2×Dic3—62no—
212C2×Dic3—122no—
213C2×Dic3—122no—
214C2×Dic3—121no—
215C2×Dic3—121no—
216C3×C8#21714yes—
217C3⋊C8—62no—
218C2×C9—82no—
219C2×C9#39011yescharacteristic
220C2×C9#44012yes—
221C2×C9#46812yes—
222C2×C9#49611yescharacteristic
223C2×C9#49711yescharacteristic
224C24—21no—
225C2×Q8—21no—
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8C2×Dic912yes—
231C2×D4—21no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4C2×Dic912yes—
237C22×C4—21no—
238C22×C4—92no—
239C22×C4—181no—
240C22×C4—181no—
241C22×C4C22×D911yescharacteristic
242SD16—28no—
243C2×C8—92no—
244C2×C8—181no—
245C2×C8—181no—
246C2×C8C2×Dic912yes—
247C2×C8#61112yes—
248C2×C8#61112yes—
249C4⋊C4—181no—
250C4⋊C4—181no—
251C4⋊C4—181no—
252C4⋊C4—181no—
253C22⋊C4—364no—
254C42—181no—
255C42—181no—
256C22×C3—44no—
257C22×C3—42no—
258C22×C3—81no—
259C22×C3—82no—
260C22×C3—81no—
261C22×C3#91412yes—
262C22×C3#91512yes—
263C22×C3D4×Dic311yescharacteristic
264C22×C3#93811yescharacteristic
265C22×C3#94011yescharacteristic
266C3×C4—42no—
267C3×C4D4×Dic311yescharacteristic
268C3×C4#93611yescharacteristic
269C3×C4#93811yescharacteristic
270C3×C4C2×#21711yescharacteristic
271Dic3—122no—
272Dic3—241no—
273Dic3—241no—
274C9#197311yescharacteristic, complemented, Sylow
275C23—22no—
276C23—41no—
277C23—41no—
278C23—42no—
279C23—42no—
280C23D4×D911yescharacteristic
281Q8—22no—
282Q8—22no—
283Q8—41no—
284Q8—41no—
285D4—22no—
286D4—22no—
287D4—41no—
288D4—41no—
289C2×C4—22no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—182no—
293C2×C4—182no—
294C2×C4—182no—
295C2×C4—361no—
296C2×C4—361no—
297C2×C4—362no—
298C2×C4—362no—
299C2×C4D4×D911yescharacteristic
300C2×C4#369911yescharacteristic
301C2×C4#369911yescharacteristic
302C2×C4C22×Dic911yescharacteristic
303C2×C4C2×#61111yescharacteristic
304C2×C4C2×#61111yescharacteristic
305C8—182no—
306C8#367614yescomplemented
307C2×C3—82no—
308C2×C3#516412yes—
309C2×C3#516711yescharacteristic
310C2×C3#517412yes—
311C2×C3#517611yescharacteristic
312C2×C3#522111yescharacteristic
313C22—44no—
314C22—42no—
315C22—81no—
316C22—82no—
317C22—81no—
318C22#6347612yes—
319C22#6347712yes—
320C22D4×Dic911yescharacteristic
321C22#6350011yescharacteristic
322C22#6350211yescharacteristic
323C4—42no—
324C4—362no—
325C4—721no—
326C4—721no—
327C4D4×Dic911yescharacteristic
328C4#6349811yescharacteristic
329C4#6350011yescharacteristic
330C4C2×#367611yescharacteristic
331C3#7205011yescharacteristic
332C2—82no—
333C2#1058884412yes—
334C2#1058884711yescharacteristic
335C2#1058885412yes—
336C2#1058885611yescharacteristic
337C2#1058890111yescharacteristic
subgroupG/H
centerC23D4×D9
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC22×C9×SD16C2
socleC23×C3D3×D4
prime radicalC22×C3×D4C2×D3
cosocleC22×C4×C9C23
hypercenterC22×SD16D9
hypocenterC9#1973
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
2. #10588909C2semidirect
3. C2×#63395C2semidirect
6. C2×#63378C2semidirect
7. C2×#63375C2semidirect
13. C2×C9×SD16C4semidirect
111. C8×C9C22⋊C4semidirect
174. C2×SD16Dic9semidirect
274. C9#1973semidirect
306. C8#3676semidirect

Maximal subgroups

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

subgroupindex
C22×C9×SD162
#105889092
C2×#633952
#105889012
C2×#633922
C2×#633782
C2×#633752
#720503