Finite Group Databasebeta

← #11787565

Subgroups — #11787565

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×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C22×#3755C211yesmaximal, characteristic
3C2×C32×#103C211yesmaximal, characteristic, complemented
4C2×#63648C211yesmaximal, characteristic
5#10592687C211yesmaximal, characteristic
6#10589416C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#70240—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13Q8×C3⋊Dic3—22no—
14Q8×C3⋊Dic3—22no—
15C2×#3755—22no—
16C2×#3755—22no—
17C2×#3755C414yescomplemented
18C2×#3752—21no—
19C2×#3752—21no—
20C2×C4⋊(C3⋊Dic3)—21no—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C4×C3⋊Dic3—21no—
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C32×#103—22no—
26#63648—22no—
27C2×Q8×Dic3—34no—
28C22×#215—34no—
29C2×C3×#103D314yescomplemented
30C2×#821—34no—
31#4988—34no—
32#4550—34no—
33#4529—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×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3⋊Dic3D411yescharacteristic
46C22×C3⋊Dic3D411yescharacteristic
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—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58#3755—28no—
59#3752—42no—
60#3752—42no—
61C4⋊(C3⋊Dic3)—24no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)D412yes—
64C4×C3⋊Dic3—24no—
65C4×C3⋊Dic3—21no—
66C4×C3⋊Dic3—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—
73C22×C3×C8C2×D314yes—
74C2×C3×C4⋊C4C2×D314yes—
75Q8×Dic3—68no—
76Q8×Dic3—68no—
77C2×#215—316no—
78C2×#215—68no—
79C2×#215—68no—
80C2×(C2×D3)⋊C4—64no—
81C2×(C2×D3)⋊C4—64no—
82C2×C4⋊Dic3—34no—
83C2×C4⋊Dic3—64no—
84C2×C4×Dic3—34no—
85C2×C4×Dic3—64no—
86C22×C3⋊C8—34no—
87C3×#103—28no—
88#821—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—22no—
103C2×C32×C4—22no—
104C2×C32×C4—41no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—22no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3—41no—
121C2×C3⋊Dic3SD1612yescomplemented
122C4⋊(C3⋊D3)—22no—
123C4⋊(C3⋊D3)—22no—
124C4⋊(C3⋊D3)—41no—
125C4⋊(C3⋊D3)—41no—
126C32×C8—41no—
127C3⋊(C3⋊C8)—22no—
128C22×SD16—91no—
129C2×C4×Q8—91no—
130C2×#103C3⋊D311yescharacteristic, complemented
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×C4C22×D314yes—
145C22×Dic3—34no—
146C22×Dic3—34no—
147C22×Dic3—64no—
148C2×D12—38no—
149C2×D12—64no—
150C2×D12—64no—
151C2×D12—64no—
152C2×D12—64no—
153C2×D12—64no—
154C2×C3×C8—24no—
155C2×C3×C8—24no—
156C2×C3×C8—24no—
157C3×C4⋊C4—24no—
158C3×C4⋊C4—24no—
159#215—632no—
160(C2×D3)⋊C4—128no—
161(C2×D3)⋊C4—128no—
162C4⋊Dic3—38no—
163C4⋊Dic3—616no—
164C4⋊Dic3—64no—
165C4×Dic3—616no—
166C4×Dic3—64no—
167C4×Dic3—64no—
168C2×C3⋊C8—38no—
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—81no—
187C32×C4C2×C22⋊C411yescharacteristic
188C32×C4C4×D411yescharacteristic
189C32×C4#12111yescharacteristic
190C32×C4#12311yescharacteristic
191C3⋊Dic3—22no—
192C3⋊Dic3—41no—
193C3⋊Dic3—42no—
194C22×Q8C2×C3⋊D311yescharacteristic
195C22×D4—91no—
196C2×SD16—94no—
197C2×SD16—182no—
198C2×SD16—182no—
199C22×C8—91no—
200C22×C8C2×C3⋊D311yescharacteristic
201C4×Q8—182no—
202C4×Q8—182no—
203C2×C4⋊C4—91no—
204C2×C4⋊C4—181no—
205C2×C4⋊C4C2×C3⋊D311yescharacteristic
206C2×C22⋊C4—181no—
207C2×C22⋊C4—181no—
208C2×C42—91no—
209C2×C42—181no—
210#103—22no—
211#102—182no—
212C23×C3D3×D414yes—
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—28no—
227C2×C3×C4—44no—
228C2×C3×C4—44no—
229C2×C3×C4—44no—
230C2×C3×C4C2×C4×D314yes—
231C2×C3×C4C2×D1214yes—
232C2×C3×C4D3×D414yes—
233C2×C3×C4#23714yes—
234C2×C3×C4#23714yes—
235C2×C3×C4C2×#6714yes—
236C2×Dic3—38no—
237C2×Dic3—64no—
238C2×Dic3—64no—
239C2×Dic3—68no—
240C2×Dic3—64no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243C2×Dic3—124no—
244C2×Dic3—124no—
245D12—68no—
246D12—68no—
247D12—124no—
248D12—124no—
249C3×C8—44no—
250C3⋊C8—68no—
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—91no—
275C22×C4—91no—
276C22×C4—181no—
277C22×C4C22×C3⋊D311yescharacteristic
278SD16—188no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—92no—
283C2×C8—181no—
284C2×C8—181no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—92no—
288C4⋊C4—184no—
289C4⋊C4—181no—
290C22⋊C4—362no—
291C22⋊C4—362no—
292C42—184no—
293C42—181no—
294C42—181no—
295C22×C3#67⋊C414yes—
296C22×C3#88214yes—
297C22×C3D3×SD1614yes—
298C22×C3#91414yes—
299C22×C3#91814yes—
300C22×C3#91914yes—
301C22×C3#93914yes—
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—84no—
311C3×C4#67⋊C414yes—
312C3×C4#88614yes—
313C3×C4C2×(C2×D3)⋊C414yes—
314C3×C4#93914yes—
315Dic3—68no—
316Dic3—124no—
317Dic3—128no—
318C32#188011yescharacteristic, complemented, Sylow
319C23—182no—
320C23—361no—
321C23—361no—
322C23—361no—
323C23—361no—
324C23—361no—
325C23—361no—
326C23D4×C3⋊D311yescharacteristic
327Q8—22no—
328Q8—22no—
329Q8—22no—
330Q8#375214yescomplemented
331D4—182no—
332D4—182no—
333D4—361no—
334D4—361no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—92no—
342C2×C4—181no—
343C2×C4—181no—
344C2×C4—182no—
345C2×C4—181no—
346C2×C4—181no—
347C2×C4—181no—
348C2×C4—361no—
349C2×C4—361no—
350C2×C4C2×C4×C3⋊D311yescharacteristic
351C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
352C2×C4D4×C3⋊D311yescharacteristic
353C2×C4#383011yescharacteristic
354C2×C4#383011yescharacteristic
355C2×C4C2×#63811yescharacteristic
356C8—41no—
357C8—182no—
358C2×C3#478814yes—
359C2×C3#480614yes—
360C2×C3#481014yes—
361C2×C3#481714yes—
362C2×C3#495814yes—
363C2×C3#516314yes—
364C2×C3#518514yes—
365D3—248no—
366C22—362no—
367C22—362no—
368C22—362no—
369C22—721no—
370C22—721no—
371C22—721no—
372C22—721no—
373C22#6409011yescharacteristic
374C22#6409111yescharacteristic
375C22SD16×C3⋊D311yescharacteristic
376C22#6412311yescharacteristic
377C22#6412711yescharacteristic
378C22#6412811yescharacteristic
379C22#6414811yescharacteristic
380C4—24no—
381C4—81no—
382C4—182no—
383C4—361no—
384C4—362no—
385C4#6409011yescharacteristic
386C4#6409511yescharacteristic
387C4C2×#375211yescharacteristic
388C4#6414811yescharacteristic
389C3#7024014yescomplemented
390C2—722no—
391C2#1059248711yescharacteristic
392C2#1059250511yescharacteristic
393C2#1059250911yescharacteristic
394C2#1059251611yescharacteristic
395C2#1059265711yescharacteristic
396C2#1059286211yescharacteristic
397C2#1059288411yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×#103C3⋊D3
hypocenterC32#1880
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊Dic3C2semidirect
3. C2×C32×#103C2semidirect
6. #10589416C2semidirect
7. #10589395C2semidirect
17. C2×#3755C4semidirect
29. C2×C3×#103D3semidirect
100. C32×Q8C22⋊C4semidirect
121. C2×C3⋊Dic3SD16semidirect
130. C2×#103C3⋊D3semidirect
223. C3×Q8(C2×D3)⋊C4semidirect
318. C32#1880semidirect
330. Q8#3752semidirect
389. C3#70240semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C22×#37552
C2×C32×#1032
C2×#636482
#105926872
#105894162
#105893952
#702403