Finite Group Databasebeta

← #11787570

Subgroups — #11787570

Order 1152.

561 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×C9C211yesmaximal, characteristic, complemented
2C22×#3675C211yesmaximal, characteristic
3C2×#63395C211yesmaximal, characteristic, complemented
4C2×#63369C211yesmaximal, characteristic
5#10588619C211yesmaximal, characteristic
6#10588206C211yesmaximal, characteristic, complemented
7#10588200C211yesmaximal, characteristic, complemented
8#71633—31nomaximal
9C22×Q8×C9C2211yescharacteristic
10C22×D36C2211yescharacteristic
11C4×Q8×C9—22no—
12C4×Q8×C9—22no—
13C2×C9×C4⋊C4—21no—
14C2×C9×C4⋊C4C2211yescharacteristic
15C2×C42×C9—21no—
16C2×C42×C9C2211yescharacteristic
17C2×#3675—22no—
18C2×#3675—22no—
19C2×#3675C414yescomplemented
20C2×(C2×D9)⋊C4—21no—
21C2×(C2×D9)⋊C4—21no—
22C2×C4⋊Dic9C2211yescharacteristic
23C22×C9⋊C8C2211yescharacteristic
24C22×C9⋊C8C2211yescharacteristic
25#63395—22no—
26#63369—22no—
27C2×C3×C4×Q8D311yescharacteristic
28C22×#215—31no—
29C2×#835—31no—
30C2×#809—31no—
31#4939—31no—
32#4529—31no—
33#4524—31no—
34C23×D9—21no—
35C2×Q8×C9—21no—
36C2×Q8×C9—21no—
37C2×Q8×C9—21no—
38C2×Q8×C9C2×C412yes—
39C2×Q8×C9D412yes—
40C2×Q8×C9D412yes—
41C22×C4×C9—21no—
42C22×C4×C9—21no—
43C22×C4×C9D411yescharacteristic
44C22×C4×C9D411yescharacteristic
45C22×C4×C9C2311yescharacteristic
46C22×Dic9—21no—
47C2×D36—21no—
48C2×D36—21no—
49C2×D36—21no—
50C2×D36—21no—
51C2×D36—21no—
52C2×D36C2×C412yes—
53C9×C4⋊C4—24no—
54C9×C4⋊C4—21no—
55C9×C4⋊C4D412yes—
56C42×C9—24no—
57C42×C9—21no—
58C42×C9—21no—
59#3675—28no—
60(C2×D9)⋊C4—42no—
61(C2×D9)⋊C4—42no—
62C4⋊Dic9—21no—
63C4⋊Dic9—21no—
64C2×C9⋊C8—21no—
65C2×C9⋊C8—21no—
66C2×C9⋊C8—21no—
67C2×C9⋊C8—21no—
68C2×C9⋊C8—21no—
69C2×C9⋊C8C2×C412yes—
70#1880—91noSylow
71C22×C3×Q8C2×D311yescharacteristic
72C22×D12—31no—
73C3×C4×Q8—22no—
74C3×C4×Q8—22no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C42—21no—
78C2×C3×C42C2×D311yescharacteristic
79C2×#215—34no—
80C2×#215—62no—
81C2×#215—62no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×C4⋊Dic3—31no—
85C22×C3⋊C8—31no—
86C22×C3⋊C8—31no—
87#835—62no—
88#809—62no—
89C23×C9C2×D411yescharacteristic
90C22×D9—22no—
91C22×D9—41no—
92C22×D9—41no—
93C22×D9—41no—
94C22×D9—41no—
95C22×D9—41no—
96C22×D9—41no—
97Q8×C9—22no—
98Q8×C9—22no—
99Q8×C9—22no—
100Q8×C9C22⋊C414yescomplemented
101C2×C4×C9—22no—
102C2×C4×C9—21no—
103C2×C4×C9—22no—
104C2×C4×C9—22no—
105C2×C4×C9—21no—
106C2×C4×C9—21no—
107C2×C4×C9—22no—
108C2×C4×C9—21no—
109C2×C4×C9—21no—
110C2×C4×C9—41no—
111C2×C4×C9—41no—
112C2×C4×C9SD1612yescomplemented
113C2×C4×C9C22×C411yescharacteristic
114C2×C4×C9C2×D411yescharacteristic
115C2×C4×C9C2×D411yescharacteristic
116C2×C4×C9C2×D411yescharacteristic
117C2×C4×C9#4111yescharacteristic
118C2×C4×C9#4111yescharacteristic
119C2×Dic9—41no—
120C2×Dic9—41no—
121C2×Dic9—41no—
122D36—22no—
123D36—22no—
124D36—41no—
125D36—41no—
126C9⋊C8—22no—
127C9⋊C8—41no—
128C22×SD16—91no—
129C2×C4×Q8D911yescharacteristic, complemented
130C2×#103—91no—
131C2×#102—91no—
132#390—91no—
133#340—91no—
134#336—91no—
135C23×D3—61no—
136C2×C3×Q8—21no—
137C2×C3×Q8—21no—
138C2×C3×Q8—21no—
139C2×C3×Q8C4×D312yes—
140C2×C3×Q8D1212yes—
141C2×C3×Q8#6712yes—
142C22×C3×C4—21no—
143C22×C3×C4—21no—
144C22×C3×C4#6711yescharacteristic
145C22×C3×C4#6711yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C22×Dic3—61no—
148C2×D12—32no—
149C2×D12—61no—
150C2×D12—61no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C3×C4⋊C4—24no—
155C3×C4⋊C4—21no—
156C3×C4⋊C4#6712yes—
157C3×C42—24no—
158C3×C42—21no—
159C3×C42—21no—
160#215—68no—
161(C2×D3)⋊C4—122no—
162(C2×D3)⋊C4—122no—
163C4⋊Dic3—61no—
164C4⋊Dic3—61no—
165C2×C3⋊C8—32no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8—61no—
168C2×C3⋊C8—61no—
169C2×C3⋊C8—61no—
170C2×C3⋊C8—61no—
171C22×C9C4×D411yescharacteristic
172C22×C9#12011yescharacteristic
173C22×C9#12111yescharacteristic
174C22×C9C2×SD1611yescharacteristic
175C22×C9#13511yescharacteristic
176C22×C9AGL(1,ℤ/8)11yescharacteristic
177C22×C9#13711yescharacteristic
178C2×D9—42no—
179C2×D9—42no—
180C2×D9—42no—
181C2×D9—81no—
182C2×D9—81no—
183C2×D9—81no—
184C2×D9—81no—
185C4×C9—24no—
186C4×C9—22no—
187C4×C9—41no—
188C4×C9—42no—
189C4×C9C2×C22⋊C411yescharacteristic
190C4×C9C4×D411yescharacteristic
191C4×C9#12111yescharacteristic
192C4×C9#12311yescharacteristic
193Dic9—81no—
194C22×Q8C2×D911yescharacteristic
195C22×D4—91no—
196C2×SD16—94no—
197C2×SD16—182no—
198C2×SD16—182no—
199C22×C8—91no—
200C22×C8—91no—
201C4×Q8—22no—
202C4×Q8—22no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—91no—
205C2×C4⋊C4C2×D911yescharacteristic
206C2×C22⋊C4—181no—
207C2×C22⋊C4—181no—
208C2×C42—21no—
209C2×C42C2×D911yescharacteristic
210#103—182no—
211#102—182no—
212C23×C3C2×#6711yescharacteristic
213C22×D3—62no—
214C22×D3—121no—
215C22×D3—121no—
216C22×D3—121no—
217C22×D3—121no—
218C22×D3—121no—
219C22×D3—121no—
220C3×Q8—22no—
221C3×Q8—22no—
222C3×Q8—22no—
223C3×Q8(C2×D3)⋊C414yes—
224C2×C3×C4—22no—
225C2×C3×C4—22no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—22no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—22no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4#21512yes—
236C2×C3×C4C2×C4×D311yescharacteristic
237C2×C3×C4C2×D1211yescharacteristic
238C2×C3×C4#23511yescharacteristic
239C2×C3×C4#23511yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241C2×C3×C4C2×#6711yescharacteristic
242C2×Dic3—121no—
243C2×Dic3—121no—
244C2×Dic3—121no—
245D12—62no—
246D12—62no—
247D12—121no—
248D12—121no—
249C3⋊C8—62no—
250C3⋊C8—121no—
251C2×C9#38611yescharacteristic
252C2×C9C4×SD1611yescharacteristic
253C2×C9#44011yescharacteristic
254C2×C9#44811yescharacteristic
255C2×C9#44911yescharacteristic
256C2×C9#46011yescharacteristic
257C2×C9#46411yescharacteristic
258D9—82no—
259C24—181no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8C4×D912yes—
264C2×Q8D3612yes—
265C2×Q8#61112yes—
266C2×D4—92no—
267C2×D4—181no—
268C2×D4—181no—
269C2×D4—181no—
270C2×D4—181no—
271C2×D4—181no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—181no—
275C22×C4#61111yescharacteristic
276C22×C4#61111yescharacteristic
277C22×C4C22×D911yescharacteristic
278SD16—188no—
279C2×C8—92no—
280C2×C8—181no—
281C2×C8—181no—
282C2×C8—181no—
283C2×C8—181no—
284C2×C8—181no—
285C4⋊C4—24no—
286C4⋊C4—21no—
287C4⋊C4—181no—
288C4⋊C4—181no—
289C4⋊C4#61112yes—
290C22⋊C4—362no—
291C22⋊C4—362no—
292C42—24no—
293C42—21no—
294C42—21no—
295C22×C3C4×#6711yescharacteristic
296C22×C3#93011yescharacteristic
297C22×C3C2×#21511yescharacteristic
298C22×C3#94211yescharacteristic
299C22×C3#94911yescharacteristic
300C22×C3#95011yescharacteristic
301C22×C3#95311yescharacteristic
302C2×D3—122no—
303C2×D3—122no—
304C2×D3—122no—
305C2×D3—241no—
306C2×D3—241no—
307C2×D3—241no—
308C2×D3—241no—
309C3×C4—24no—
310C3×C4—22no—
311C3×C4—41no—
312C3×C4—42no—
313C3×C4C2×(C2×D3)⋊C411yescharacteristic
314C3×C4C4×#6711yescharacteristic
315C3×C4#92911yescharacteristic
316C3×C4#93011yescharacteristic
317Dic3—241no—
318C9#188011yescharacteristic, complemented, Sylow
319C23—182no—
320C23—361no—
321C23—361no—
322C23—361no—
323C23—361no—
324C23—361no—
325C23—361no—
326C23C2×#61111yescharacteristic
327Q8—22no—
328Q8—22no—
329Q8—22no—
330Q8(C2×D9)⋊C414yescomplemented
331D4—182no—
332D4—182no—
333D4—361no—
334D4—361no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—361no—
347C2×C4—361no—
348C2×C4—361no—
349C2×C4#367512yescomplemented
350C2×C4C2×C4×D911yescharacteristic
351C2×C4C2×D3611yescharacteristic
352C2×C4#369711yescharacteristic
353C2×C4#369711yescharacteristic
354C2×C4C2×#61111yescharacteristic
355C2×C4C2×#61111yescharacteristic
356C8—182no—
357C8—361no—
358C2×C3C4×#21511yescharacteristic
359C2×C3#502611yescharacteristic
360C2×C3#502711yescharacteristic
361C2×C3#502811yescharacteristic
362C2×C3#521311yescharacteristic
363C2×C3#522711yescharacteristic
364C2×C3#523811yescharacteristic
365D3—242no—
366C22—362no—
367C22—362no—
368C22—362no—
369C22—721no—
370C22—721no—
371C22—721no—
372C22—721no—
373C22C4×#61111yescharacteristic
374C22#6349211yescharacteristic
375C22C2×#367511yescharacteristic
376C22#6350511yescharacteristic
377C22#6351211yescharacteristic
378C22#6351311yescharacteristic
379C22#6351511yescharacteristic
380C4—24no—
381C4—22no—
382C4—41no—
383C4—42no—
384C4—721no—
385C4C2×(C2×D9)⋊C411yescharacteristic
386C4C4×#61111yescharacteristic
387C4#6349111yescharacteristic
388C4#6349211yescharacteristic
389C3#7163311yescharacteristic
390C2—722no—
391C2C4×#367511yescharacteristic
392C2#1058870911yescharacteristic
393C2#1058871011yescharacteristic
394C2#1058871111yescharacteristic
395C2#1058889311yescharacteristic
396C2#1058890811yescharacteristic
397C2#1058891911yescharacteristic
subgroupG/H
centerC23C2×#611
commutatorC2×C4×C9C22×C4
FrattiniC22×C3×C4C22×D3
FittingC2×C4×Q8×C9C2
socleC23×C3C2×#67
prime radicalC22×D36C22
cosocleC22×C4×C9C23
hypercenterC2×C4×Q8D9
hypocenterC9#1880
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×C9C2semidirect
3. C2×#63395C2semidirect
6. #10588206C2semidirect
7. #10588200C2semidirect
19. C2×#3675C4semidirect
100. Q8×C9C22⋊C4semidirect
112. C2×C4×C9SD16semidirect
129. C2×C4×Q8D9semidirect
318. C9#1880semidirect
330. Q8(C2×D9)⋊C4semidirect
349. C2×C4#3675semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×C92
C22×#36752
C2×#633952
C2×#633692
#105886192
#105882062
#105882002
#716333