Finite Group Databasebeta

← #11788654

Subgroups — #11788654

Order 1152.

468 conjugacy classes of subgroups.

The subgroup lattice has 351 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63511C211yesmaximal, characteristic
2C2×#63510C211yesmaximal, characteristic
3C9×#417C211yesmaximal, characteristic
4C2×#63382C211yesmaximal, characteristic, complemented
5C2×#63368C211yesmaximal, characteristic, complemented
6#10588231C211yesmaximal, characteristic, complemented
7#10588207C211yesmaximal, characteristic, complemented
8#70304—31nomaximal
9C2×C9×#41C2211yescharacteristic
10C22×Dic18C2211yescharacteristic
11C2×C9×M16C2211yescharacteristic
12C2×C9×C4⋊C4C2211yescharacteristic
13#63511—22no—
14#63511C414yescomplemented
15#63510—22no—
16#63510—22no—
17C2×#3674—21no—
18C2×#3672—21no—
19C2×#3667—21no—
20C2×#3667C2211yescharacteristic
21C2×#3667C2211yescharacteristic
22C22×C9⋊C8—21no—
23C22×C9⋊C8C2211yescharacteristic
24C9×#103—21no—
25C9×#102—21no—
26#63382—22no—
27#63368—21no—
28#63368—21no—
29C2×#951—31no—
30C2×#948—31no—
31C3×#417D311yescharacteristic
32C2×#824—31no—
33C2×#810—31no—
34#4558—31no—
35#4530—31no—
36C9×#41—21no—
37C9×#41—21no—
38C9×#41C2×C412yes—
39C9×#41D412yes—
40C2×Q8×C9D411yescharacteristic
41C2×D4×C9—21no—
42C2×D4×C9D411yescharacteristic
43C22×C4×C9—21no—
44C22×C4×C9—21no—
45C22×C4×C9C2311yescharacteristic
46C22×Dic9—21no—
47C2×Dic18—21no—
48C2×Dic18—21no—
49C2×Dic18—21no—
50C2×Dic18—21no—
51C2×Dic18—21no—
52C2×Dic18C2×C412yes—
53C9×M16—21no—
54C9×M16—21no—
55C2×C8×C9—21no—
56C9×C4⋊C4—21no—
57C9×C4⋊C4—21no—
58#3674—24no—
59#3672—24no—
60#3667—24no—
61#3667—21no—
62#3667—21no—
63#3667C2×C412yes—
64#3667D412yes—
65C2×C9⋊C8—24no—
66C2×C9⋊C8—21no—
67C2×C9⋊C8—21no—
68C2×C9⋊C8—21no—
69C2×C9⋊C8—21no—
70C2×C9⋊C8D411yescharacteristic
71C2×C9⋊C8D411yescharacteristic
72#1908—91noSylow
73C2×C3×#41C2×D311yescharacteristic
74C22×Dic6—31no—
75C2×C3×M16C2×D311yescharacteristic
76C2×C3×C4⋊C4C2×D311yescharacteristic
77#951—34no—
78#951—62no—
79#948—62no—
80#948—62no—
81C2×#216—61no—
82C2×#214—61no—
83C2×#208—31no—
84C2×#208—31no—
85C2×#208—61no—
86C22×C3⋊C8—31no—
87C22×C3⋊C8—61no—
88C3×#103—21no—
89C3×#102—21no—
90#824—62no—
91#810—61no—
92#810—61no—
93C23×C9—21no—
94C23×C9#4111yescharacteristic
95Q8×C9—21no—
96Q8×C9C22⋊C412yes—
97D4×C9—22no—
98D4×C9—22no—
99D4×C9—21no—
100D4×C9C22⋊C412yes—
101C2×C4×C9—21no—
102C2×C4×C9—22no—
103C2×C4×C9—22no—
104C2×C4×C9—41no—
105C2×C4×C9—81no—
106C2×C4×C9C22×C411yescharacteristic
107C2×C4×C9C2×D411yescharacteristic
108C2×C4×C9C2×D411yescharacteristic
109C2×C4×C9C2×D411yescharacteristic
110C2×C4×C9C2×D411yescharacteristic
111C2×C4×C9#4111yescharacteristic
112C2×Dic9—22no—
113C2×Dic9—41no—
114C2×Dic9—41no—
115Dic18—22no—
116Dic18—22no—
117Dic18—41no—
118Dic18—41no—
119C8×C9—41no—
120C9⋊C8—22no—
121C9⋊C8—21no—
122C9⋊C8—22no—
123C9⋊C8—21no—
124C2×#137—91no—
125C2×#131—91no—
126#417D911yescharacteristic
127C2×#103—91no—
128C2×#101—91no—
129#343—91no—
130#341—91no—
131C3×#41—21no—
132C3×#41—21no—
133C3×#41C4×D312yes—
134C3×#41D1212yes—
135C2×C3×Q8#6711yescharacteristic
136C2×C3×D4—21no—
137C2×C3×D4#6711yescharacteristic
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4C22×D311yescharacteristic
141C22×Dic3—61no—
142C2×Dic6—32no—
143C2×Dic6—61no—
144C2×Dic6—61no—
145C2×Dic6—61no—
146C2×Dic6—61no—
147C2×Dic6—61no—
148C3×M16—21no—
149C3×M16—21no—
150C2×C3×C8—21no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153#216—64no—
154#214—64no—
155#208—32no—
156#208—32no—
157#208—64no—
158#208—61no—
159#208—61no—
160C2×C3⋊C8—31no—
161C2×C3⋊C8—31no—
162C2×C3⋊C8—64no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—61no—
166C2×C3⋊C8—61no—
167C22×C9—21no—
168C22×C9—21no—
169C22×C9—22no—
170C22×C9—41no—
171C22×C9—41no—
172C22×C9C4×D411yescharacteristic
173C22×C9#12111yescharacteristic
174C22×C9#12311yescharacteristic
175C4×C9—22no—
176C4×C9—81no—
177C4×C9C2×C22⋊C411yescharacteristic
178C4×C9C4×D411yescharacteristic
179C4×C9#12011yescharacteristic
180C4×C9#12111yescharacteristic
181Dic9—42no—
182C2×#41C2×D911yescharacteristic
183C22×Q8—91no—
184#137—94no—
185#137—182no—
186C2×Q16—181no—
187C2×SD16—181no—
188#131—182no—
189#131—182no—
190C2×M16—91no—
191C2×M16—91no—
192C2×M16—181no—
193C2×M16C2×D911yescharacteristic
194C22×C8—91no—
195C22×C8—181no—
196C2×C4⋊C4C2×D911yescharacteristic
197#103—21no—
198#103—181no—
199#103—181no—
200#102—21no—
201#101—182no—
202C23×C3—21no—
203C23×C3#23711yescharacteristic
204C3×Q8—21no—
205C3×Q8(C2×D3)⋊C412yes—
206C3×D4—22no—
207C3×D4—22no—
208C3×D4—21no—
209C3×D4(C2×D3)⋊C412yes—
210C2×C3×C4—21no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—41no—
214C2×C3×C4—81no—
215C2×C3×C4C2×C4×D311yescharacteristic
216C2×C3×C4C2×D1211yescharacteristic
217C2×C3×C4D3×D411yescharacteristic
218C2×C3×C4D3×D411yescharacteristic
219C2×C3×C4#23711yescharacteristic
220C2×C3×C4C2×#6711yescharacteristic
221C2×Dic3—62no—
222C2×Dic3—121no—
223C2×Dic3—121no—
224Dic6—62no—
225Dic6—62no—
226Dic6—121no—
227Dic6—121no—
228C3×C8—41no—
229C3⋊C8—61no—
230C3⋊C8—61no—
231C3⋊C8—62no—
232C3⋊C8—62no—
233C2×C9—21no—
234C2×C9—21no—
235C2×C9—42no—
236C2×C9#38611yescharacteristic
237C2×C9#47111yescharacteristic
238C2×C9#47311yescharacteristic
239#41—21no—
240#41—21no—
241#41C4×D912yes—
242#41D3612yes—
243C2×Q8—92no—
244C2×Q8—181no—
245C2×Q8—181no—
246C2×Q8—181no—
247C2×Q8—181no—
248C2×Q8—181no—
249C2×Q8#61111yescharacteristic
250C2×D4—21no—
251C2×D4#61111yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—181no—
255C22×C4C22×D911yescharacteristic
256Q16—184no—
257SD16—184no—
258M16—21no—
259M16—21no—
260M16—92no—
261M16—92no—
262M16—184no—
263M16—181no—
264M16—181no—
265C2×C8—21no—
266C2×C8—91no—
267C2×C8—91no—
268C2×C8—184no—
269C2×C8—181no—
270C2×C8—181no—
271C2×C8—181no—
272C2×C8—181no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—22no—
278C22×C3—41no—
279C22×C3—41no—
280C22×C3#67⋊C411yescharacteristic
281C22×C3#88611yescharacteristic
282C22×C3#93911yescharacteristic
283C3×C4—22no—
284C3×C4—81no—
285C3×C4#67⋊C411yescharacteristic
286C3×C4#88211yescharacteristic
287C3×C4C2×(C2×D3)⋊C411yescharacteristic
288C3×C4#93911yescharacteristic
289Dic3—122no—
290C9#190811yescharacteristic, complemented, Sylow
291C23—21no—
292C23#369911yescharacteristic
293Q8—21no—
294Q8—182no—
295Q8—182no—
296Q8—361no—
297Q8—361no—
298Q8(C2×D9)⋊C412yes—
299D4—22no—
300D4—22no—
301D4—21no—
302D4(C2×D9)⋊C412yes—
303C2×C4—21no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—182no—
309C2×C4—361no—
310C2×C4—361no—
311C2×C4C2×C4×D911yescharacteristic
312C2×C4C2×D3611yescharacteristic
313C2×C4D4×D911yescharacteristic
314C2×C4D4×D911yescharacteristic
315C2×C4#369911yescharacteristic
316C2×C4C2×#61111yescharacteristic
317C8—41no—
318C8—182no—
319C8—181no—
320C8—181no—
321C8—182no—
322C2×C3—21no—
323C2×C3—21no—
324C2×C3—42no—
325C2×C3#495811yescharacteristic
326C2×C3#520011yescharacteristic
327C2×C3#520411yescharacteristic
328C22—21no—
329C22—21no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22#611⋊C411yescharacteristic
334C22#6344811yescharacteristic
335C22#6350111yescharacteristic
336C4—22no—
337C4—81no—
338C4—362no—
339C4#611⋊C411yescharacteristic
340C4#6344411yescharacteristic
341C4C2×(C2×D9)⋊C411yescharacteristic
342C4#6350111yescharacteristic
343C3#7030411yescharacteristic
344C2—21no—
345C2—21no—
346C2—42no—
347C2#1058863811yescharacteristic
348C2#1058887811yescharacteristic
349C2#1058888211yescharacteristic
subgroupG/H
centerC22#63501
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC9×#417C2
socleC22×C3#939
prime radicalC2×C3×#41C2×D3
cosocleC22×C4×C9C23
hypercenter#417D9
hypocenterC9#1908
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
4. C2×#63382C2semidirect
5. C2×#63368C2semidirect
6. #10588231C2semidirect
7. #10588207C2semidirect
14. #63511C4semidirect
290. C9#1908semidirect

Maximal subgroups

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

subgroupindex
C2×#635112
C2×#635102
C9×#4172
C2×#633822
C2×#633682
#105882312
#105882072
#703043