Finite Group Databasebeta

← #11787571

Subgroups — #11787571

Order 1152.

1122 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×C32×C4×Q8C211yesmaximal, characteristic, complemented
2C22×#3755C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic, complemented
4C2×#63636C211yesmaximal, characteristic
5#10592638C211yesmaximal, characteristic
6#10589395C211yesmaximal, characteristic, complemented
7#10589390C211yesmaximal, characteristic, complemented
8#71633—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C32×C4×Q8—22no—
12C32×C4×Q8—22no—
13C2×C32×C4⋊C4—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C32×C42—21no—
16C2×C32×C42C2211yescharacteristic
17C2×#3755—22no—
18C2×#3755—22no—
19C2×#3755C414yescomplemented
20C2×#3752—21no—
21C2×#3752—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#63662—22no—
26#63636—22no—
27C2×C3×C4×Q8D314yescomplemented
28C22×#215—34no—
29C2×#835—34no—
30C2×#809—34no—
31#4939—34no—
32#4529—34no—
33#4524—34no—
34C23×C3⋊D3—21no—
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8C2×C412yes—
39C2×C32×Q8D412yes—
40C2×C32×Q8D412yes—
41C22×C32×C4—21no—
42C22×C32×C4—21no—
43C22×C32×C4D411yescharacteristic
44C22×C32×C4D411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—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)—21no—
52C2×C4⋊(C3⋊D3)C2×C412yes—
53C32×C4⋊C4—24no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4D412yes—
56C32×C42—24no—
57C32×C42—21no—
58C32×C42—21no—
59#3755—28no—
60#3752—42no—
61#3752—42no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69C2×C3⋊(C3⋊C8)C2×C412yes—
70#1880—91noSylow
71C22×C3×Q8C2×D314yes—
72C22×D12—34no—
73C3×C4×Q8—28no—
74C3×C4×Q8—28no—
75C2×C3×C4⋊C4—24no—
76C2×C3×C4⋊C4C2×D314yes—
77C2×C3×C42—24no—
78C2×C3×C42C2×D314yes—
79C2×#215—316no—
80C2×#215—68no—
81C2×#215—68no—
82C2×(C2×D3)⋊C4—64no—
83C2×(C2×D3)⋊C4—64no—
84C2×C4⋊Dic3—34no—
85C22×C3⋊C8—34no—
86C22×C3⋊C8—34no—
87#835—68no—
88#809—68no—
89C23×C32C2×D411yescharacteristic
90C22×C3⋊D3—22no—
91C22×C3⋊D3—41no—
92C22×C3⋊D3—41no—
93C22×C3⋊D3—41no—
94C22×C3⋊D3—41no—
95C22×C3⋊D3—41no—
96C22×C3⋊D3—41no—
97C32×Q8—22no—
98C32×Q8—22no—
99C32×Q8—22no—
100C32×Q8C22⋊C414yescomplemented
101C2×C32×C4—22no—
102C2×C32×C4—21no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4—21no—
106C2×C32×C4—21no—
107C2×C32×C4—22no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4SD1612yescomplemented
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3—41no—
122C4⋊(C3⋊D3)—22no—
123C4⋊(C3⋊D3)—22no—
124C4⋊(C3⋊D3)—41no—
125C4⋊(C3⋊D3)—41no—
126C3⋊(C3⋊C8)—22no—
127C3⋊(C3⋊C8)—41no—
128C22×SD16—91no—
129C2×C4×Q8C3⋊D311yescharacteristic, complemented
130C2×#103—91no—
131C2×#102—91no—
132#390—91no—
133#340—91no—
134#336—91no—
135C23×D3—64no—
136C2×C3×Q8—24no—
137C2×C3×Q8—24no—
138C2×C3×Q8—24no—
139C2×C3×Q8C4×D318yes—
140C2×C3×Q8D1218yes—
141C2×C3×Q8#6718yes—
142C22×C3×C4—24no—
143C22×C3×C4—24no—
144C22×C3×C4#6714yes—
145C22×C3×C4#6714yes—
146C22×C3×C4C22×D314yes—
147C22×Dic3—64no—
148C2×D12—38no—
149C2×D12—64no—
150C2×D12—64no—
151C2×D12—64no—
152C2×D12—64no—
153C2×D12—64no—
154C3×C4⋊C4—216no—
155C3×C4⋊C4—24no—
156C3×C4⋊C4#6718yes—
157C3×C42—216no—
158C3×C42—24no—
159C3×C42—24no—
160#215—632no—
161(C2×D3)⋊C4—128no—
162(C2×D3)⋊C4—128no—
163C4⋊Dic3—64no—
164C4⋊Dic3—64no—
165C2×C3⋊C8—38no—
166C2×C3⋊C8—64no—
167C2×C3⋊C8—64no—
168C2×C3⋊C8—64no—
169C2×C3⋊C8—64no—
170C2×C3⋊C8—64no—
171C22×C32C4×D411yescharacteristic
172C22×C32#12011yescharacteristic
173C22×C32#12111yescharacteristic
174C22×C32C2×SD1611yescharacteristic
175C22×C32#13511yescharacteristic
176C22×C32AGL(1,ℤ/8)11yescharacteristic
177C22×C32#13711yescharacteristic
178C2×C3⋊D3—42no—
179C2×C3⋊D3—42no—
180C2×C3⋊D3—42no—
181C2×C3⋊D3—81no—
182C2×C3⋊D3—81no—
183C2×C3⋊D3—81no—
184C2×C3⋊D3—81no—
185C32×C4—24no—
186C32×C4—22no—
187C32×C4—41no—
188C32×C4—42no—
189C32×C4C2×C22⋊C411yescharacteristic
190C32×C4C4×D411yescharacteristic
191C32×C4#12111yescharacteristic
192C32×C4#12311yescharacteristic
193C3⋊Dic3—81no—
194C22×Q8C2×C3⋊D311yescharacteristic
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×C3⋊D311yescharacteristic
206C2×C22⋊C4—181no—
207C2×C22⋊C4—181no—
208C2×C42—21no—
209C2×C42C2×C3⋊D311yescharacteristic
210#103—182no—
211#102—182no—
212C23×C3C2×#6714yes—
213C22×D3—68no—
214C22×D3—124no—
215C22×D3—124no—
216C22×D3—124no—
217C22×D3—124no—
218C22×D3—124no—
219C22×D3—124no—
220C3×Q8—28no—
221C3×Q8—28no—
222C3×Q8—28no—
223C3×Q8(C2×D3)⋊C4116yescomplemented
224C2×C3×C4—28no—
225C2×C3×C4—28no—
226C2×C3×C4—24no—
227C2×C3×C4—24no—
228C2×C3×C4—28no—
229C2×C3×C4—24no—
230C2×C3×C4—24no—
231C2×C3×C4—24no—
232C2×C3×C4—28no—
233C2×C3×C4—44no—
234C2×C3×C4—44no—
235C2×C3×C4#21518yescomplemented
236C2×C3×C4C2×C4×D314yes—
237C2×C3×C4C2×D1214yes—
238C2×C3×C4#23514yes—
239C2×C3×C4#23514yes—
240C2×C3×C4C2×#6714yes—
241C2×C3×C4C2×#6714yes—
242C2×Dic3—124no—
243C2×Dic3—124no—
244C2×Dic3—124no—
245D12—68no—
246D12—68no—
247D12—124no—
248D12—124no—
249C3⋊C8—68no—
250C3⋊C8—124no—
251C2×C32#38611yescharacteristic
252C2×C32C4×SD1611yescharacteristic
253C2×C32#44011yescharacteristic
254C2×C32#44811yescharacteristic
255C2×C32#44911yescharacteristic
256C2×C32#46011yescharacteristic
257C2×C32#46411yescharacteristic
258C3⋊D3—82no—
259C24—181no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8C4×C3⋊D312yes—
264C2×Q8C4⋊(C3⋊D3)12yes—
265C2×Q8#63812yes—
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#63811yescharacteristic
276C22×C4#63811yescharacteristic
277C22×C4C22×C3⋊D311yescharacteristic
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#63812yes—
290C22⋊C4—362no—
291C22⋊C4—362no—
292C42—24no—
293C42—21no—
294C42—21no—
295C22×C3C4×#6714yes—
296C22×C3#93014yes—
297C22×C3C2×#21514yes—
298C22×C3#94214yes—
299C22×C3#94914yes—
300C22×C3#95014yes—
301C22×C3#95314yes—
302C2×D3—128no—
303C2×D3—128no—
304C2×D3—128no—
305C2×D3—244no—
306C2×D3—244no—
307C2×D3—244no—
308C2×D3—244no—
309C3×C4—216no—
310C3×C4—28no—
311C3×C4—44no—
312C3×C4—48no—
313C3×C4C2×(C2×D3)⋊C414yes—
314C3×C4C4×#6714yes—
315C3×C4#92914yes—
316C3×C4#93014yes—
317Dic3—244no—
318C32#188011yescharacteristic, complemented, Sylow
319C23—182no—
320C23—361no—
321C23—361no—
322C23—361no—
323C23—361no—
324C23—361no—
325C23—361no—
326C23C2×#63811yescharacteristic
327Q8—22no—
328Q8—22no—
329Q8—22no—
330Q8#375214yescomplemented
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#375512yescomplemented
350C2×C4C2×C4×C3⋊D311yescharacteristic
351C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
352C2×C4#382811yescharacteristic
353C2×C4#382811yescharacteristic
354C2×C4C2×#63811yescharacteristic
355C2×C4C2×#63811yescharacteristic
356C8—182no—
357C8—361no—
358C2×C3C4×#21514yes—
359C2×C3#502614yes—
360C2×C3#502714yes—
361C2×C3#502814yes—
362C2×C3#521314yes—
363C2×C3#522714yes—
364C2×C3#523814yes—
365D3—248no—
366C22—362no—
367C22—362no—
368C22—362no—
369C22—721no—
370C22—721no—
371C22—721no—
372C22—721no—
373C22C4×#63811yescharacteristic
374C22#6413911yescharacteristic
375C22C2×#375511yescharacteristic
376C22#6415111yescharacteristic
377C22#6415811yescharacteristic
378C22#6415911yescharacteristic
379C22#6416211yescharacteristic
380C4—24no—
381C4—22no—
382C4—41no—
383C4—42no—
384C4—721no—
385C4C2×#375211yescharacteristic
386C4C4×#63811yescharacteristic
387C4#6413811yescharacteristic
388C4#6413911yescharacteristic
389C3#7163314yescomplemented
390C2—722no—
391C2C4×#375511yescharacteristic
392C2#1059272511yescharacteristic
393C2#1059272611yescharacteristic
394C2#1059272711yescharacteristic
395C2#1059291211yescharacteristic
396C2#1059292611yescharacteristic
397C2#1059293711yescharacteristic
subgroupG/H
centerC23C2×#638
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×C4×Q8C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×C4×Q8C3⋊D3
hypocenterC32#1880
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×Q8C2semidirect
3. C2×#63662C2semidirect
6. #10589395C2semidirect
7. #10589390C2semidirect
19. C2×#3755C4semidirect
27. C2×C3×C4×Q8D3semidirect
100. C32×Q8C22⋊C4semidirect
112. C2×C32×C4SD16semidirect
129. C2×C4×Q8C3⋊D3semidirect
223. C3×Q8(C2×D3)⋊C4semidirect
235. C2×C3×C4#215semidirect
318. C32#1880semidirect
330. Q8#3752semidirect
349. C2×C4#3755semidirect
389. C3#71633semidirect

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C22×#37552
C2×#636622
C2×#636362
#105926382
#105893952
#105893902
#716333