Finite Group Databasebeta

← #11787574

Subgroups — #11787574

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
1C22×#3744C211yesmaximal, characteristic
2C2×#64096C211yesmaximal, characteristic, complemented
3#10592687C211yesmaximal, characteristic
4C2×#63637C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic
6C32×#340C211yesmaximal, characteristic, complemented
7#10589416C211yesmaximal, characteristic, complemented
8#68909—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×#3752—21no—
16C2×#3750—21no—
17C2×C4×C3⋊Dic3—21no—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C22×C3⋊(C3⋊C8)C2211yescharacteristic
20C2×#3744—22no—
21C2×#3744—22no—
22C2×#3744C414yescomplemented
23#64096—22no—
24#64096—22no—
25#63637—22no—
26#63636—22no—
27C22×#204—34no—
28C2×#887—34no—
29#4988—34no—
30C2×#810—34no—
31C2×#809—34no—
32C3×#340D314yescomplemented
33#4550—34no—
34C23×C3⋊D3—21no—
35C22×C32×C4—21no—
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)C2×C412yes—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634C2×C412yes—
51C2×#634D412yes—
52C2×#634D412yes—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C2×C32×C8C2×C412yes—
56C32×C4⋊C4—21no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4—21no—
59C32×C4⋊C4D412yes—
60#3752—42no—
61#3752—42no—
62#3750—24no—
63C4×C3⋊Dic3—24no—
64C4×C3⋊Dic3—21no—
65C4×C3⋊Dic3—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)—21no—
69#3744—28no—
70#1880—91noSylow
71C22×D12—34no—
72C22×Dic6—34no—
73C22×C3×C8C2×D314yes—
74C2×C3×C4⋊C4C2×D314yes—
75C2×C3×C4⋊C4C2×D314yes—
76C2×(C2×D3)⋊C4—64no—
77C2×(C2×D3)⋊C4—64no—
78C2×Dic3⋊C4—64no—
79C2×C4×Dic3—34no—
80C2×C4×Dic3—64no—
81C22×C3⋊C8—34no—
82C2×#204—316no—
83C2×#204—68no—
84C2×#204—68no—
85#887—68no—
86#887—68no—
87#810—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—
97C2×C32×C4—22no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4C22×C411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3SD1612yescomplemented
118C4⋊(C3⋊D3)—22no—
119C4⋊(C3⋊D3)—22no—
120C4⋊(C3⋊D3)—41no—
121C4⋊(C3⋊D3)—41no—
122#634—22no—
123#634—22no—
124#634—22no—
125#634C22⋊C414yescomplemented
126C32×C8—22no—
127C3⋊(C3⋊C8)—41no—
128C22×SD16—91no—
129C2×C4×Q8—91no—
130C2×#103—91no—
131C2×#102—91no—
132#390—91no—
133#340C3⋊D311yescharacteristic, complemented
134#336—91no—
135C23×D3—64no—
136C22×C3×C4—24no—
137C22×C3×C4—24no—
138C22×C3×C4C22×D314yes—
139C22×Dic3—34no—
140C22×Dic3—34no—
141C22×Dic3—64no—
142C2×D12—38no—
143C2×D12—64no—
144C2×D12—64no—
145C2×D12—64no—
146C2×D12—64no—
147C2×D12—64no—
148C2×Dic6—38no—
149C2×Dic6—38no—
150C2×Dic6—38no—
151C2×Dic6—64no—
152C2×Dic6—64no—
153C2×Dic6—64no—
154C2×C3×C8—24no—
155C2×C3×C8—24no—
156C2×C3×C8C4×D318yes—
157C3×C4⋊C4—24no—
158C3×C4⋊C4—24no—
159C3×C4⋊C4—24no—
160C3×C4⋊C4D1218yes—
161(C2×D3)⋊C4—128no—
162(C2×D3)⋊C4—128no—
163Dic3⋊C4—616no—
164C4×Dic3—616no—
165C4×Dic3—64no—
166C4×Dic3—64no—
167C2×C3⋊C8—64no—
168C2×C3⋊C8—64no—
169C2×C3⋊C8—64no—
170#204—632no—
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—42no—
186C32×C4—81no—
187C32×C4C2×C22⋊C411yescharacteristic
188C32×C4C4×D411yescharacteristic
189C32×C4#12111yescharacteristic
190C32×C4#12311yescharacteristic
191C3⋊Dic3—24no—
192C3⋊Dic3—22no—
193C3⋊Dic3—41no—
194C22×Q8—91no—
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—181no—
204C2×C4⋊C4C2×C3⋊D311yescharacteristic
205C2×C4⋊C4C2×C3⋊D311yescharacteristic
206C2×C22⋊C4—181no—
207C2×C22⋊C4—181no—
208C2×C42—91no—
209C2×C42—181no—
210#103—182no—
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—
220C2×C3×C4—28no—
221C2×C3×C4—44no—
222C2×C3×C4—44no—
223C2×C3×C4—44no—
224C2×C3×C4—44no—
225C2×C3×C4—44no—
226C2×C3×C4C2×C4×D314yes—
227C2×C3×C4C2×D1214yes—
228C2×C3×C4#23514yes—
229C2×C3×C4D3×D414yes—
230C2×C3×C4D3×D414yes—
231C2×C3×C4#23914yes—
232C2×Dic3—38no—
233C2×Dic3—64no—
234C2×Dic3—68no—
235C2×Dic3—68no—
236C2×Dic3—68no—
237C2×Dic3—64no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240C2×Dic3—64no—
241D12—68no—
242D12—68no—
243D12—124no—
244D12—124no—
245Dic6—316no—
246Dic6—68no—
247Dic6—68no—
248Dic6—68no—
249C3×C8—28no—
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—92no—
261C2×Q8—92no—
262C2×Q8—92no—
263C2×Q8—181no—
264C2×Q8—181no—
265C2×Q8—181no—
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—181no—
282C2×C8—181no—
283C2×C8—181no—
284C2×C8C4×C3⋊D312yes—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—21no—
288C4⋊C4—184no—
289C4⋊C4C4⋊(C3⋊D3)12yes—
290C22⋊C4—362no—
291C22⋊C4—362no—
292C42—184no—
293C42—181no—
294C42—181no—
295C22×C3#88214yes—
296C22×C3#88414yes—
297C22×C3#89314yes—
298C22×C3#91114yes—
299C22×C3D3×SD1614yes—
300C22×C3#91614yes—
301C22×C3#91814yes—
302C2×D3—128no—
303C2×D3—128no—
304C2×D3—128no—
305C2×D3—244no—
306C2×D3—244no—
307C2×D3—244no—
308C2×D3—244no—
309C3×C4—48no—
310C3×C4—84no—
311C3×C4C4×D1214yes—
312C3×C4D3×C22⋊C414yes—
313C3×C4#89414yes—
314C3×C4#89514yes—
315Dic3—616no—
316Dic3—68no—
317Dic3—124no—
318C32#188011yescharacteristic, complemented, Sylow
319C23—182no—
320C23—361no—
321C23—361no—
322C23—361no—
323C23—361no—
324C23—361no—
325C23—361no—
326C23D4×C3⋊D311yescharacteristic
327Q8—94no—
328Q8—182no—
329Q8—182no—
330Q8—182no—
331D4—182no—
332D4—182no—
333D4—361no—
334D4—361no—
335C2×C4—22no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—92no—
342C2×C4—181no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4—182no—
346C2×C4—181no—
347C2×C4—181no—
348C2×C4—181no—
349C2×C4—181no—
350C2×C4C2×C4×C3⋊D311yescharacteristic
351C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
352C2×C4#382811yescharacteristic
353C2×C4D4×C3⋊D311yescharacteristic
354C2×C4D4×C3⋊D311yescharacteristic
355C2×C4#383211yescharacteristic
356C8—22no—
357C8—361no—
358C2×C3#466514yes—
359C2×C3#476214yes—
360C2×C3#478114yes—
361C2×C3#479814yes—
362C2×C3#480614yes—
363C2×C3#485214yes—
364C2×C3#488914yes—
365D3—248no—
366C22—362no—
367C22—362no—
368C22—362no—
369C22—721no—
370C22—721no—
371C22—721no—
372C22—721no—
373C22#6409111yescharacteristic
374C22#6409311yescharacteristic
375C22#6410211yescharacteristic
376C22#6412011yescharacteristic
377C22SD16×C3⋊D311yescharacteristic
378C22#6412511yescharacteristic
379C22#6412711yescharacteristic
380C4—42no—
381C4—81no—
382C4—184no—
383C4—182no—
384C4—361no—
385C4C4×C4⋊(C3⋊D3)11yescharacteristic
386C4C22⋊C4×C3⋊D311yescharacteristic
387C4#6410311yescharacteristic
388C4#6410411yescharacteristic
389C3#6890914yescomplemented
390C2—722no—
391C2#1059236411yescharacteristic
392C2#1059246111yescharacteristic
393C2#1059248011yescharacteristic
394C2#1059249711yescharacteristic
395C2#1059250511yescharacteristic
396C2#1059255111yescharacteristic
397C2#1059258811yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#340C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenter#340C3⋊D3
hypocenterC32#1880
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#64096C2semidirect
4. C2×#63637C2semidirect
6. C32×#340C2semidirect
7. #10589416C2semidirect
22. C2×#3744C4semidirect
32. C3×#340D3semidirect
117. C2×C3⋊Dic3SD16semidirect
125. #634C22⋊C4semidirect
133. #340C3⋊D3semidirect
318. C32#1880semidirect
389. C3#68909semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
C2×#640962
#105926872
C2×#636372
C2×#636362
C32×#3402
#105894162
#689093