Finite Group Databasebeta

← #11787429

Subgroups — #11787429

Order 1152.

1206 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2C2×#64102C211yesmaximal, characteristic
3#10592672C211yesmaximal, characteristic, complemented
4C2×#63637C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic
6C32×#340C211yesmaximal, characteristic, complemented
7#10589416C211yesmaximal, characteristic, complemented
8#68896—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×C4×C3⋊D3—21no—
11C22×#634C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×#3752—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×#3744—22no—
19C2×#3744—22no—
20C2×#3744C414yescomplemented
21#64102—22no—
22#64102—22no—
23#63658—21no—
24#63658—21no—
25#63637—22no—
26#63636—22no—
27C22×#204—34no—
28C2×#893—34no—
29#4973—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)C2×C412yes—
45C2×C4⋊(C3⋊D3)D412yes—
46C2×C4⋊(C3⋊D3)D412yes—
47C2×C4×C3⋊D3—24no—
48C2×C4×C3⋊D3—42no—
49C2×C4×C3⋊D3—42no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634C2×C412yescomplemented
56C2×C32×C8—21no—
57C2×C32×C8—21no—
58C2×C32×C8C2×C412yescomplemented
59C32×C4⋊C4—21no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4—21no—
62C32×C4⋊C4D412yes—
63#3752—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#1877—91noSylow
71C22×D12—34no—
72C22×C4×D3—64no—
73C22×Dic6—34no—
74C22×C3×C8C2×D314yes—
75C2×C3×C4⋊C4C2×D314yes—
76C2×C3×C4⋊C4C2×D314yes—
77C2×(C2×D3)⋊C4—64no—
78C2×C4×Dic3—34no—
79C22×C3⋊C8—34no—
80C2×#204—316no—
81C2×#204—68no—
82C2×#204—68no—
83#893—68no—
84#893—68no—
85C3⋊#95—64no—
86C3⋊#95—64no—
87#810—68no—
88#809—68no—
89C23×C32C2×D411yescharacteristic
90C22×C3⋊D3—22no—
91C22×C3⋊D3—22no—
92C22×C3⋊D3—22no—
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—21no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—22no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—41no—
116C2×C3⋊Dic3—41no—
117C2×C3⋊Dic3SD1612yescomplemented
118C4⋊(C3⋊D3)—22no—
119C4⋊(C3⋊D3)—22no—
120C4⋊(C3⋊D3)—22no—
121C4⋊(C3⋊D3)C22⋊C414yes—
122C4×C3⋊D3—48no—
123#634—22no—
124#634—22no—
125#634—41no—
126#634—41no—
127C32×C8—22no—
128C3⋊(C3⋊C8)—41no—
129C22×SD16—91no—
130C2×C4×D4—91no—
131C2×#103—91no—
132C2×#102—91no—
133#391—91no—
134#340C3⋊D311yescharacteristic, complemented
135#336—91no—
136C23×D3—64no—
137C22×C3×C4—24no—
138C22×C3×C4—24no—
139C22×C3×C4C22×D314yes—
140C22×Dic3—34no—
141C22×Dic3—34no—
142C22×Dic3—64no—
143C2×D12—38no—
144C2×D12—38no—
145C2×D12—38no—
146C2×D12—64no—
147C2×D12—64no—
148C2×D12—64no—
149C2×C4×D3—616no—
150C2×C4×D3—128no—
151C2×C4×D3—128no—
152C2×Dic6—38no—
153C2×Dic6—64no—
154C2×Dic6—64no—
155C2×Dic6—64no—
156C2×Dic6—64no—
157C2×Dic6—64no—
158C2×C3×C8—24no—
159C2×C3×C8—24no—
160C2×C3×C8C4×D318yescomplemented
161C3×C4⋊C4—24no—
162C3×C4⋊C4—24no—
163C3×C4⋊C4—24no—
164C3×C4⋊C4D1218yes—
165(C2×D3)⋊C4—616no—
166C4×Dic3—64no—
167C4×Dic3—64no—
168C2×C3⋊C8—64no—
169C2×C3⋊C8—64no—
170C2×C3⋊C8—64no—
171#204—632no—
172C22×C32C4×D411yescharacteristic
173C22×C32#12011yescharacteristic
174C22×C32#12111yescharacteristic
175C22×C32C2×SD1611yescharacteristic
176C22×C32#13511yescharacteristic
177C22×C32AGL(1,ℤ/8)11yescharacteristic
178C22×C32#13711yescharacteristic
179C2×C3⋊D3—24no—
180C2×C3⋊D3—42no—
181C2×C3⋊D3—42no—
182C2×C3⋊D3—42no—
183C2×C3⋊D3—42no—
184C2×C3⋊D3—42no—
185C2×C3⋊D3—42no—
186C32×C4—42no—
187C32×C4—81no—
188C32×C4C2×C22⋊C411yescharacteristic
189C32×C4C4×D411yescharacteristic
190C32×C4#12111yescharacteristic
191C32×C4#12311yescharacteristic
192C3⋊Dic3—22no—
193C3⋊Dic3—42no—
194C3⋊Dic3—41no—
195C22×Q8—91no—
196C22×D4—91no—
197C23×C4—181no—
198C2×SD16—94no—
199C2×SD16—182no—
200C2×SD16—182no—
201C22×C8—91no—
202C22×C8C2×C3⋊D311yescharacteristic
203C4×D4—182no—
204C4×D4—182no—
205C2×C4⋊C4C2×C3⋊D311yescharacteristic
206C2×C4⋊C4C2×C3⋊D311yescharacteristic
207C2×C22⋊C4—181no—
208C2×C42—91no—
209#103—182no—
210#102—182no—
211#95—181no—
212#95—181no—
213C23×C3D3×D414yes—
214C22×D3—68no—
215C22×D3—68no—
216C22×D3—68no—
217C22×D3—124no—
218C22×D3—124no—
219C22×D3—124no—
220C22×D3—124no—
221C2×C3×C4—28no—
222C2×C3×C4—44no—
223C2×C3×C4—44no—
224C2×C3×C4—44no—
225C2×C3×C4—44no—
226C2×C3×C4—44no—
227C2×C3×C4C2×C4×D314yes—
228C2×C3×C4C2×D1214yes—
229C2×C3×C4#23514yes—
230C2×C3×C4D3×D414yes—
231C2×C3×C4D3×D414yes—
232C2×C3×C4#23914yes—
233C2×Dic3—38no—
234C2×Dic3—64no—
235C2×Dic3—64no—
236C2×Dic3—64no—
237C2×Dic3—68no—
238C2×Dic3—64no—
239C2×Dic3—64no—
240C2×Dic3—124no—
241C2×Dic3—124no—
242D12—316no—
243D12—68no—
244D12—68no—
245D12—68no—
246C4×D3—1232no—
247Dic6—68no—
248Dic6—68no—
249Dic6—124no—
250Dic6—124no—
251C3×C8—28no—
252C3⋊C8—124no—
253C2×C32#38611yescharacteristic
254C2×C32C4×SD1611yescharacteristic
255C2×C32#44011yescharacteristic
256C2×C32#45011yescharacteristic
257C2×C32#45211yescharacteristic
258C2×C32#46111yescharacteristic
259C2×C32#46311yescharacteristic
260C3⋊D3—44no—
261C24—181no—
262C2×Q8—92no—
263C2×Q8—181no—
264C2×Q8—181no—
265C2×Q8—181no—
266C2×Q8—181no—
267C2×Q8—181no—
268C2×D4—92no—
269C2×D4—92no—
270C2×D4—92no—
271C2×D4—181no—
272C2×D4—181no—
273C2×D4—181no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—91no—
277C22×C4—91no—
278C22×C4—184no—
279C22×C4—181no—
280C22×C4—362no—
281C22×C4—362no—
282C22×C4C22×C3⋊D311yescharacteristic
283SD16—188no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—181no—
287C2×C8—181no—
288C2×C8—181no—
289C2×C8C4×C3⋊D312yescomplemented
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4C4⋊(C3⋊D3)12yes—
294C22⋊C4—184no—
295C42—181no—
296C42—181no—
297C22×C3#88214yes—
298C22×C3#88414yes—
299C22×C3#89314yes—
300C22×C3#91114yes—
301C22×C3D3×SD1614yes—
302C22×C3#91614yes—
303C22×C3#91814yes—
304C2×D3—616no—
305C2×D3—128no—
306C2×D3—128no—
307C2×D3—128no—
308C2×D3—128no—
309C2×D3—128no—
310C2×D3—128no—
311C3×C4—48no—
312C3×C4—84no—
313C3×C4C4×D1214yes—
314C3×C4D3×C22⋊C414yes—
315C3×C4#89414yes—
316C3×C4#89514yes—
317Dic3—68no—
318Dic3—128no—
319Dic3—124no—
320C32#187711yescharacteristic, complemented, Sylow
321C23—182no—
322C23—182no—
323C23—182no—
324C23—361no—
325C23—361no—
326C23—361no—
327C23—361no—
328C23D4×C3⋊D311yescharacteristic
329Q8—182no—
330Q8—182no—
331Q8—361no—
332Q8—361no—
333D4—94no—
334D4—182no—
335D4—182no—
336D4—182no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—92no—
344C2×C4—181no—
345C2×C4—181no—
346C2×C4—181no—
347C2×C4—182no—
348C2×C4—181no—
349C2×C4—181no—
350C2×C4—368no—
351C2×C4—361no—
352C2×C4—361no—
353C2×C4C2×C4×C3⋊D311yescharacteristic
354C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
355C2×C4#382811yescharacteristic
356C2×C4D4×C3⋊D311yescharacteristic
357C2×C4D4×C3⋊D311yescharacteristic
358C2×C4#383211yescharacteristic
359C8—22no—
360C8—361no—
361C2×C3#466514yes—
362C2×C3#477614yes—
363C2×C3#478714yes—
364C2×C3#480814yes—
365C2×C3#481814yes—
366C2×C3#485214yes—
367C2×C3#488914yes—
368D3—1216no—
369C22—184no—
370C22—362no—
371C22—362no—
372C22—362no—
373C22—362no—
374C22—362no—
375C22—362no—
376C22#6409111yescharacteristic
377C22#6409311yescharacteristic
378C22#6410211yescharacteristic
379C22#6412011yescharacteristic
380C22SD16×C3⋊D311yescharacteristic
381C22#6412511yescharacteristic
382C22#6412711yescharacteristic
383C4—42no—
384C4—81no—
385C4—182no—
386C4—362no—
387C4—361no—
388C4C4×C4⋊(C3⋊D3)11yescharacteristic
389C4C22⋊C4×C3⋊D311yescharacteristic
390C4#6410311yescharacteristic
391C4#6410411yescharacteristic
392C3#6889614yescomplemented
393C2—364no—
394C2#1059236411yescharacteristic
395C2#1059247511yescharacteristic
396C2#1059248611yescharacteristic
397C2#1059250711yescharacteristic
398C2#1059251711yescharacteristic
399C2#1059255111yescharacteristic
400C2#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#1877
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
3. #10592672C2semidirect
4. C2×#63637C2semidirect
6. C32×#340C2semidirect
7. #10589416C2semidirect
20. C2×#3744C4semidirect
32. C3×#340D3semidirect
55. C2×#634C2×C4semidirect
58. C2×C32×C8C2×C4semidirect
117. C2×C3⋊Dic3SD16semidirect
134. #340C3⋊D3semidirect
160. C2×C3×C8C4×D3semidirect
289. C2×C8C4×C3⋊D3semidirect
320. C32#1877semidirect
392. C3#68896semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
C2×#641022
#105926722
C2×#636372
C2×#636362
C32×#3402
#105894162
#688963