Finite Group Databasebeta

← #11794042

Subgroups — #11794042

Order 1152.

972 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic
2C32×#391C211yesmaximal, characteristic, complemented
3C2×#63662C211yesmaximal, characteristic, complemented
4C2×#63636C211yesmaximal, characteristic
5#10592638C211yesmaximal, characteristic
6C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#69680—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3755—22no—
14C2×#3755—22no—
15C2×#3755—22no—
16C2×#3752—21no—
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C32×#95—21no—
22C32×#95—21no—
23#63662—22no—
24#63636—22no—
25C4⋊(C3⋊(C3⋊C8))—22no—
26C22×#215—34no—
27C3×#391D314yescomplemented
28C2×#835—34no—
29C2×#809—34no—
30#4939—34no—
31C2×C4⋊(C3⋊C8)—34no—
32#4529—34no—
33C23×C3⋊D3—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8—21no—
39C2×C32×Q8D412yes—
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4D411yescharacteristic
43C22×C32×C4D411yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)D412yes—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C42—21no—
55C32×C42—21no—
56#3755—28no—
57#3752—42no—
58#3752—42no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)D412yes—
67#2055—91noSylow
68C22×C3×Q8C2×D314yes—
69C22×D12—34no—
70C2×C3×C4⋊C4C2×D314yes—
71C2×C3×C42C2×D314yes—
72C2×#215—68no—
73C2×#215—68no—
74C2×#215—68no—
75C2×(C2×D3)⋊C4—64no—
76C2×(C2×D3)⋊C4—64no—
77C2×C4⋊Dic3—34no—
78C22×C3⋊C8—34no—
79C22×C3⋊C8—34no—
80C3×#95—24no—
81C3×#95—24no—
82#835—68no—
83#809—68no—
84C4⋊(C3⋊C8)—68no—
85C23×C32C2×D411yescharacteristic
86C22×C3⋊D3—22no—
87C22×C3⋊D3—41no—
88C22×C3⋊D3—41no—
89C22×C3⋊D3—41no—
90C22×C3⋊D3—41no—
91C22×C3⋊D3—41no—
92C22×C3⋊D3—41no—
93C32×Q8—22no—
94C32×Q8—22no—
95C32×Q8—41no—
96C32×Q8—41no—
97C2×C32×C4—21no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—22no—
101C2×C32×C4—21no—
102C2×C32×C4—21no—
103C2×C32×C4—41no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4SD1612yescomplemented
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C3⋊Dic3—41no—
116C2×C3⋊Dic3—41no—
117C2×C3⋊Dic3—41no—
118C4⋊(C3⋊D3)—22no—
119C4⋊(C3⋊D3)—22no—
120C4⋊(C3⋊D3)—41no—
121C4⋊(C3⋊D3)—41no—
122C3⋊(C3⋊C8)—22no—
123C3⋊(C3⋊C8)—41no—
124C22×SD16—91no—
125C2×C4⋊C8—91no—
126C2×#103—91no—
127C2×#102—91no—
128#391C3⋊D311yescharacteristic, complemented
129#390—91no—
130#340—91no—
131C23×D3—64no—
132C2×C3×Q8—24no—
133C2×C3×Q8—24no—
134C2×C3×Q8—24no—
135C2×C3×Q8—24no—
136C2×C3×Q8—24no—
137C2×C3×Q8D1218yes—
138C22×C3×C4—24no—
139C22×C3×C4—24no—
140C22×C3×C4#6714yes—
141C22×C3×C4#6714yes—
142C22×C3×C4C22×D314yes—
143C22×Dic3—64no—
144C2×D12—38no—
145C2×D12—64no—
146C2×D12—64no—
147C2×D12—64no—
148C2×D12—64no—
149C2×D12—64no—
150C3×C4⋊C4—24no—
151C3×C4⋊C4—24no—
152C3×C42—24no—
153C3×C42—24no—
154#215—632no—
155(C2×D3)⋊C4—128no—
156(C2×D3)⋊C4—128no—
157C4⋊Dic3—64no—
158C4⋊Dic3—64no—
159C2×C3⋊C8—38no—
160C2×C3⋊C8—64no—
161C2×C3⋊C8—64no—
162C2×C3⋊C8—64no—
163C2×C3⋊C8—64no—
164C2×C3⋊C8—64no—
165C22×C32#12111yescharacteristic
166C22×C32#12111yescharacteristic
167C22×C32#12111yescharacteristic
168C22×C32C2×SD1611yescharacteristic
169C22×C32#13511yescharacteristic
170C22×C32AGL(1,ℤ/8)11yescharacteristic
171C22×C32#13711yescharacteristic
172C2×C3⋊D3—42no—
173C2×C3⋊D3—42no—
174C2×C3⋊D3—42no—
175C2×C3⋊D3—81no—
176C2×C3⋊D3—81no—
177C2×C3⋊D3—81no—
178C2×C3⋊D3—81no—
179C32×C4—22no—
180C32×C4—42no—
181C32×C4—41no—
182C32×C4—81no—
183C32×C4#12011yescharacteristic
184C32×C4#12311yescharacteristic
185C32×C4#12311yescharacteristic
186C32×C4#12411yescharacteristic
187C3⋊Dic3—81no—
188C22×Q8C2×C3⋊D311yescharacteristic
189C22×D4—91no—
190C2×SD16—182no—
191C2×SD16—182no—
192C2×SD16—182no—
193C22×C8—91no—
194C22×C8—91no—
195C2×C4⋊C4—91no—
196C2×C4⋊C4C2×C3⋊D311yescharacteristic
197C2×C22⋊C4—181no—
198C2×C22⋊C4—181no—
199C2×C42C2×C3⋊D311yescharacteristic
200C4⋊C8—182no—
201#103—182no—
202#102—182no—
203#95—21no—
204#95—21no—
205C23×C3C2×#6714yes—
206C22×D3—68no—
207C22×D3—124no—
208C22×D3—124no—
209C22×D3—124no—
210C22×D3—124no—
211C22×D3—124no—
212C22×D3—124no—
213C3×Q8—28no—
214C3×Q8—28no—
215C3×Q8—44no—
216C3×Q8—44no—
217C2×C3×C4—24no—
218C2×C3×C4—24no—
219C2×C3×C4—28no—
220C2×C3×C4—24no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—44no—
224C2×C3×C4—44no—
225C2×C3×C4—44no—
226C2×C3×C4—44no—
227C2×C3×C4—44no—
228C2×C3×C4#21518yescomplemented
229C2×C3×C4C2×D1214yes—
230C2×C3×C4#23514yes—
231C2×C3×C4D3×D414yes—
232C2×C3×C4D3×D414yes—
233C2×C3×C4#23714yes—
234C2×C3×C4#23714yes—
235C2×Dic3—124no—
236C2×Dic3—124no—
237C2×Dic3—124no—
238D12—68no—
239D12—68no—
240D12—124no—
241D12—124no—
242C3⋊C8—68no—
243C3⋊C8—124no—
244C2×C32#39411yescharacteristic
245C2×C32#46011yescharacteristic
246C2×C32#46111yescharacteristic
247C2×C32#46311yescharacteristic
248C2×C32#46411yescharacteristic
249C2×C32#46511yescharacteristic
250C2×C32#46811yescharacteristic
251C3⋊D3—82no—
252C24—181no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8C4⋊(C3⋊D3)12yes—
259C2×D4—92no—
260C2×D4—181no—
261C2×D4—181no—
262C2×D4—181no—
263C2×D4—181no—
264C2×D4—181no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—181no—
268C22×C4#63811yescharacteristic
269C22×C4#63811yescharacteristic
270C22×C4C22×C3⋊D311yescharacteristic
271SD16—188no—
272C2×C8—92no—
273C2×C8—181no—
274C2×C8—181no—
275C2×C8—181no—
276C2×C8—181no—
277C2×C8—181no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—181no—
281C4⋊C4—181no—
282C22⋊C4—362no—
283C22⋊C4—362no—
284C42—21no—
285C42—21no—
286C22×C3#93014yes—
287C22×C3#93814yes—
288C22×C3#93914yes—
289C22×C3C2×#21514yes—
290C22×C3#94214yes—
291C22×C3#94914yes—
292C22×C3#95014yes—
293C2×D3—128no—
294C2×D3—128no—
295C2×D3—128no—
296C2×D3—244no—
297C2×D3—244no—
298C2×D3—244no—
299C2×D3—244no—
300C3×C4—28no—
301C3×C4—48no—
302C3×C4—44no—
303C3×C4—84no—
304C3×C4#88214yes—
305C3×C4#88314yes—
306C3×C4#88514yes—
307C3×C4#88614yes—
308Dic3—244no—
309C32#205511yescharacteristic, complemented, Sylow
310C23—182no—
311C23—361no—
312C23—361no—
313C23—361no—
314C23—361no—
315C23—361no—
316C23—361no—
317C23C2×#63811yescharacteristic
318Q8—22no—
319Q8—22no—
320Q8—41no—
321Q8—41no—
322D4—182no—
323D4—182no—
324D4—361no—
325D4—361no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—361no—
338C2×C4—361no—
339C2×C4—361no—
340C2×C4#375512yescomplemented
341C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
342C2×C4#382811yescharacteristic
343C2×C4D4×C3⋊D311yescharacteristic
344C2×C4D4×C3⋊D311yescharacteristic
345C2×C4#383011yescharacteristic
346C2×C4#383011yescharacteristic
347C8—182no—
348C8—361no—
349C2×C3#496114yes—
350C2×C3#502714yes—
351C2×C3#502814yes—
352C2×C3#504814yes—
353C2×C3#504914yes—
354C2×C3#505714yes—
355C2×C3#508314yes—
356D3—248no—
357C22—362no—
358C22—362no—
359C22—362no—
360C22—721no—
361C22—721no—
362C22—721no—
363C22—721no—
364C22#6413911yescharacteristic
365C22#6414711yescharacteristic
366C22#6414811yescharacteristic
367C22C2×#375511yescharacteristic
368C22#6415111yescharacteristic
369C22#6415811yescharacteristic
370C22#6415911yescharacteristic
371C4—22no—
372C4—42no—
373C4—41no—
374C4—81no—
375C4—721no—
376C4#6409111yescharacteristic
377C4#6409211yescharacteristic
378C4#6409411yescharacteristic
379C4#6409511yescharacteristic
380C3#6968014yescomplemented
381C2—722no—
382C2#1059266011yescharacteristic
383C2#1059272611yescharacteristic
384C2#1059272711yescharacteristic
385C2#1059274711yescharacteristic
386C2#1059274811yescharacteristic
387C2#1059275611yescharacteristic
388C2#1059278211yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#391C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#391C3⋊D3
hypocenterC32#2055
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C32×#391C2semidirect
3. C2×#63662C2semidirect
6. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
7. #10589395C2semidirect
27. C3×#391D3semidirect
108. C2×C32×C4SD16semidirect
128. #391C3⋊D3semidirect
228. C2×C3×C4#215semidirect
309. C32#2055semidirect
340. C2×C4#3755semidirect
380. C3#69680semidirect

Maximal subgroups

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

subgroupindex
C22×#37552
C32×#3912
C2×#636622
C2×#636362
#105926382
C2×C4⋊(C3⋊(C3⋊C8))2
#105893952
#696803