Finite Group Databasebeta

← #11787423

Subgroups — #11787423

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×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
3C2×#63648C211yesmaximal, characteristic
4C2×#63643C211yesmaximal, characteristic, complemented
5#10592628C211yesmaximal, characteristic, complemented
6C32×#336C211yesmaximal, characteristic, complemented
7#10589417C211yesmaximal, characteristic, complemented
8#68672—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×C4×C3⋊D3—21no—
11C22×#634C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×#3752—21no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3744—22no—
19C2×#3744—22no—
20C2×#3744C414yescomplemented
21C4×C4⋊(C3⋊D3)—22no—
22C4×C4⋊(C3⋊D3)—22no—
23#63658—21no—
24#63658—21no—
25#63648—22no—
26#63643—22no—
27C22×#204—34no—
28C2×C4×D12—34no—
29C2×#821—34no—
30C2×#816—34no—
31#4929—34no—
32C3×#336D314yescomplemented
33#4551—34no—
34C23×C3⋊D3—21no—
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3—21no—
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×C8—21no—
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8C2×C412yescomplemented
62C32×C42—21no—
63C32×C42—21no—
64#3752—24no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)D412yes—
69#3744—28no—
70#1877—91noSylow
71C22×D12—34no—
72C22×C4×D3—64no—
73C22×Dic6—34no—
74C22×C3×C8C2×D314yes—
75C22×C3×C8C2×D314yes—
76C2×C3×C42C2×D314yes—
77C2×(C2×D3)⋊C4—64no—
78C2×C4⋊Dic3—34no—
79C2×C4⋊Dic3—34no—
80C2×#204—316no—
81C2×#204—68no—
82C2×#204—68no—
83C4×D12—68no—
84C4×D12—68no—
85C3⋊#95—64no—
86C3⋊#95—64no—
87#821—68no—
88#816—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—21no—
98C2×C32×C4—21no—
99C2×C32×C4—21no—
100C2×C32×C4—21no—
101C2×C32×C4—21no—
102C2×C32×C4SD1612yescomplemented
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—22no—
111C2×C3⋊Dic3—41no—
112C2×C3⋊Dic3—41no—
113C2×C3⋊Dic3—41no—
114C2×C3⋊Dic3—41no—
115C2×C3⋊Dic3—41no—
116C2×C3⋊Dic3—41no—
117C2×C3⋊Dic3—41no—
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—
128C32×C8—41no—
129C22×SD16—91no—
130C2×C4×D4—91no—
131C2×#103—91no—
132C2×#102—91no—
133#391—91no—
134#340—91no—
135#336C3⋊D311yescharacteristic, complemented
136C23×D3—64no—
137C22×C3×C4D1214yes—
138C22×C3×C4D1214yes—
139C22×C3×C4C22×D314yes—
140C22×Dic3—64no—
141C22×Dic3—64no—
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×C8—24no—
161C2×C3×C8—24no—
162C2×C3×C8—24no—
163C2×C3×C8C4×D318yescomplemented
164C3×C42—24no—
165C3×C42—24no—
166(C2×D3)⋊C4—616no—
167C4⋊Dic3—38no—
168C4⋊Dic3—64no—
169C4⋊Dic3—64no—
170C4⋊Dic3—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—22no—
187C32×C4—41no—
188C32×C4C2×C22⋊C411yescharacteristic
189C32×C4C4×D411yescharacteristic
190C32×C4#12111yescharacteristic
191C32×C4#12311yescharacteristic
192C3⋊Dic3—42no—
193C3⋊Dic3—42no—
194C3⋊Dic3—81no—
195C22×Q8—91no—
196C22×D4—91no—
197C23×C4—181no—
198C2×SD16—94no—
199C2×SD16—182no—
200C2×SD16—182no—
201C22×C8C2×C3⋊D311yescharacteristic
202C22×C8C2×C3⋊D311yescharacteristic
203C4×D4—182no—
204C4×D4—182no—
205C2×C4⋊C4—91no—
206C2×C4⋊C4—91no—
207C2×C22⋊C4—181no—
208C2×C42C2×C3⋊D311yescharacteristic
209#103—182no—
210#102—182no—
211#95—181no—
212#95—181no—
213C23×C3C2×D1214yes—
214C22×D3—68no—
215C22×D3—68no—
216C22×D3—68no—
217C22×D3—124no—
218C22×D3—124no—
219C22×D3—124no—
220C22×D3—124no—
221C2×C3×C4—24no—
222C2×C3×C4—24no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—24no—
226C2×C3×C4#20418yescomplemented
227C2×C3×C4C2×C4×D314yes—
228C2×C3×C4#23514yes—
229C2×C3×C4D3×D414yes—
230C2×C3×C4D3×D414yes—
231C2×C3×C4D3×D414yes—
232C2×C3×C4#23914yes—
233C2×Dic3—68no—
234C2×Dic3—68no—
235C2×Dic3—124no—
236C2×Dic3—124no—
237C2×Dic3—124no—
238C2×Dic3—124no—
239C2×Dic3—124no—
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—44no—
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—184no—
275C22×C4—181no—
276C22×C4—181no—
277C22×C4—181no—
278C22×C4—362no—
279C22×C4—362no—
280C22×C4C4⋊(C3⋊D3)11yescharacteristic
281C22×C4C4⋊(C3⋊D3)11yescharacteristic
282C22×C4C22×C3⋊D311yescharacteristic
283SD16—188no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8C4×C3⋊D312yescomplemented
290C4⋊C4—92no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C4⋊C4—181no—
294C22⋊C4—184no—
295C42—21no—
296C42—21no—
297C22×C3C4×D1214yes—
298C22×C3#88214yes—
299C22×C3#89514yes—
300C22×C3C2×#20414yes—
301C22×C3#90414yes—
302C22×C3#90814yes—
303C22×C3#90914yes—
304C2×D3—616no—
305C2×D3—128no—
306C2×D3—128no—
307C2×D3—128no—
308C2×D3—128no—
309C2×D3—128no—
310C2×D3—128no—
311C3×C4—28no—
312C3×C4—44no—
313C3×C4D3×C22⋊C414yes—
314C3×C4#88414yes—
315C3×C4#89314yes—
316C3×C4#89414yes—
317Dic3—128no—
318Dic3—128no—
319Dic3—244no—
320C32#187711yescharacteristic, complemented, Sylow
321C23—182no—
322C23—182no—
323C23—182no—
324C23—361no—
325C23—361no—
326C23—361no—
327C23—361no—
328C23C2×C4⋊(C3⋊D3)11yescharacteristic
329Q8—182no—
330Q8—182no—
331Q8—361no—
332Q8—361no—
333D4—94no—
334D4—182no—
335D4—182no—
336D4—182no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—182no—
343C2×C4—182no—
344C2×C4—368no—
345C2×C4—361no—
346C2×C4—361no—
347C2×C4—361no—
348C2×C4—361no—
349C2×C4—361no—
350C2×C4—361no—
351C2×C4—361no—
352C2×C4#374412yescomplemented
353C2×C4C2×C4×C3⋊D311yescharacteristic
354C2×C4#382811yescharacteristic
355C2×C4D4×C3⋊D311yescharacteristic
356C2×C4D4×C3⋊D311yescharacteristic
357C2×C4D4×C3⋊D311yescharacteristic
358C2×C4#383211yescharacteristic
359C8—22no—
360C8—41no—
361C2×C3#466514yes—
362C2×C3C4×#20414yes—
363C2×C3#471014yes—
364C2×C3#473114yes—
365C2×C3#473314yes—
366C2×C3#484114yes—
367C2×C3#484414yes—
368D3—1216no—
369C22—184no—
370C22—362no—
371C22—362no—
372C22—362no—
373C22—362no—
374C22—362no—
375C22—362no—
376C22C4×C4⋊(C3⋊D3)11yescharacteristic
377C22#6409111yescharacteristic
378C22#6410411yescharacteristic
379C22C2×#374411yescharacteristic
380C22#6411311yescharacteristic
381C22#6411711yescharacteristic
382C22#6411811yescharacteristic
383C4—22no—
384C4—41no—
385C4—362no—
386C4—362no—
387C4—721no—
388C4C22⋊C4×C3⋊D311yescharacteristic
389C4#6409311yescharacteristic
390C4#6410211yescharacteristic
391C4#6410311yescharacteristic
392C3#6867214yescomplemented
393C2—364no—
394C2#1059236411yescharacteristic
395C2C4×#374411yescharacteristic
396C2#1059240911yescharacteristic
397C2#1059243011yescharacteristic
398C2#1059243211yescharacteristic
399C2#1059254011yescharacteristic
400C2#1059254311yescharacteristic
subgroupG/H
centerC23C2×C4⋊(C3⋊D3)
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#336C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenter#336C3⋊D3
hypocenterC32#1877
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
4. C2×#63643C2semidirect
5. #10592628C2semidirect
6. C32×#336C2semidirect
7. #10589417C2semidirect
20. C2×#3744C4semidirect
32. C3×#336D3semidirect
55. C2×#634C2×C4semidirect
61. C2×C32×C8C2×C4semidirect
102. C2×C32×C4SD16semidirect
135. #336C3⋊D3semidirect
163. C2×C3×C8C4×D3semidirect
226. C2×C3×C4#204semidirect
289. C2×C8C4×C3⋊D3semidirect
320. C32#1877semidirect
352. C2×C4#3744semidirect
392. C3#68672semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
C2×C4×C4⋊(C3⋊D3)2
C2×#636482
C2×#636432
#105926282
C32×#3362
#105894172
#686723