Finite Group Databasebeta

← #11786830

Subgroups — #11786830

Order 1152.

1086 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×#63648C211yesmaximal, characteristic
3C2×#63648C211yesmaximal, characteristic
4C2×#63645C211yesmaximal, characteristic, complemented
5#10592627C211yesmaximal, characteristic, complemented
6C32×#336C211yesmaximal, characteristic, complemented
7#10589417C211yesmaximal, characteristic, complemented
8#68670—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×C4×C3⋊D3—21no—
11C22×C32×C8C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C2×C32×C42C2211yescharacteristic
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750—21no—
19C4×C4⋊(C3⋊D3)—22no—
20C4×C4⋊(C3⋊D3)—22no—
21#63658—21no—
22#63648—22no—
23#63648C414yescomplemented
24#63645—22no—
25C2×C4×D12—34no—
26C2×#821—34no—
27C2×#821—34no—
28C2×#818—34no—
29#4928—34no—
30C3×#336D314yescomplemented
31#4551—34no—
32C23×C3⋊D3—21no—
33C22×C32×C4D411yescharacteristic
34C22×C32×C4D411yescharacteristic
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3—21no—
38C22×C3⋊Dic3—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)C2×C412yes—
43C2×C4⋊(C3⋊D3)D412yes—
44C2×C4⋊(C3⋊D3)Q812yes—
45C2×C4×C3⋊D3—24no—
46C2×C4×C3⋊D3—42no—
47C2×C4×C3⋊D3—42no—
48C2×C32×C8—21no—
49C2×C32×C8—21no—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C2×C32×C8C2×C412yescomplemented
54C32×C42—21no—
55C32×C42—21no—
56#3752—24no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)C2×C412yescomplemented
62C4⋊(C3⋊Dic3)D412yes—
63#3750—42no—
64#1862—91noSylow
65C22×D12—34no—
66C22×C4×D3—64no—
67C22×C3×C8C2×D314yes—
68C22×C3×C8C2×D314yes—
69C2×C3×C42C2×D314yes—
70C2×(C2×D3)⋊C4—64no—
71C2×C4⋊Dic3—34no—
72C2×C4⋊Dic3—34no—
73C2×C4⋊Dic3—34no—
74C2×Dic3⋊C4—64no—
75C4×D12—68no—
76C4×D12—68no—
77C3⋊#95—64no—
78#821—316no—
79#821—68no—
80#818—68no—
81C23×C32C2×D411yescharacteristic
82C22×C3⋊D3—22no—
83C22×C3⋊D3—22no—
84C22×C3⋊D3—22no—
85C22×C3⋊D3—41no—
86C22×C3⋊D3—41no—
87C22×C3⋊D3—41no—
88C22×C3⋊D3—41no—
89C2×C32×C4—21no—
90C2×C32×C4—21no—
91C2×C32×C4—21no—
92C2×C32×C4—21no—
93C2×C32×C4—21no—
94C2×C32×C4D812yes—
95C2×C32×C4C22×C411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4C2×Q811yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3—41no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3—41no—
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3—41no—
110C4⋊(C3⋊D3)—22no—
111C4⋊(C3⋊D3)—22no—
112C4⋊(C3⋊D3)—22no—
113C4⋊(C3⋊D3)C4⋊C414yescomplemented
114C4×C3⋊D3—48no—
115C32×C8—22no—
116C32×C8—41no—
117C2×C4×D4—91no—
118C2×#107—91no—
119C2×#102—91no—
120C2×#102—91no—
121#389—91no—
122#340—91no—
123#336C3⋊D311yescharacteristic, complemented
124C23×D3—64no—
125C22×C3×C4D1214yes—
126C22×C3×C4D1214yes—
127C22×C3×C4C22×D314yes—
128C22×Dic3—64no—
129C22×Dic3—64no—
130C22×Dic3—64no—
131C2×D12—38no—
132C2×D12—38no—
133C2×D12—38no—
134C2×D12—64no—
135C2×D12—64no—
136C2×D12—64no—
137C2×C4×D3—616no—
138C2×C4×D3—128no—
139C2×C4×D3—128no—
140C2×C3×C8—24no—
141C2×C3×C8—24no—
142C2×C3×C8—24no—
143C2×C3×C8—24no—
144C2×C3×C8—24no—
145C2×C3×C8C4×D318yescomplemented
146C3×C42—24no—
147C3×C42—24no—
148(C2×D3)⋊C4—616no—
149C4⋊Dic3—38no—
150C4⋊Dic3—38no—
151C4⋊Dic3—64no—
152C4⋊Dic3—64no—
153C4⋊Dic3—64no—
154C4⋊Dic3—64no—
155Dic3⋊C4—128no—
156C22×C32C4×D411yescharacteristic
157C22×C32#12011yescharacteristic
158C22×C32C22⋊Q811yescharacteristic
159C22×C32C2×D811yescharacteristic
160C22×C32#13511yescharacteristic
161C22×C32AGL(1,ℤ/8)11yescharacteristic
162C22×C32#13711yescharacteristic
163C2×C3⋊D3—24no—
164C2×C3⋊D3—42no—
165C2×C3⋊D3—42no—
166C2×C3⋊D3—42no—
167C2×C3⋊D3—42no—
168C2×C3⋊D3—42no—
169C2×C3⋊D3—42no—
170C32×C4—22no—
171C32×C4—41no—
172C32×C4C2×C4⋊C411yescharacteristic
173C32×C4C4×D411yescharacteristic
174C32×C4C22⋊Q811yescharacteristic
175C32×C4#12311yescharacteristic
176C3⋊Dic3—42no—
177C3⋊Dic3—42no—
178C3⋊Dic3—81no—
179C22×D4—91no—
180C23×C4—181no—
181C22×C8C2×C3⋊D311yescharacteristic
182C22×C8C2×C3⋊D311yescharacteristic
183C4×D4—182no—
184C4×D4—182no—
185C2×C4⋊C4—91no—
186C2×C4⋊C4—91no—
187C2×C4⋊C4—91no—
188C2×C4⋊C4—181no—
189C2×C22⋊C4—181no—
190C2×C42C2×C3⋊D311yescharacteristic
191#107—182no—
192#102—94no—
193#102—182no—
194#95—181no—
195C23×C3C2×D1214yes—
196C22×D3—68no—
197C22×D3—68no—
198C22×D3—68no—
199C22×D3—124no—
200C22×D3—124no—
201C22×D3—124no—
202C22×D3—124no—
203C2×C3×C4—24no—
204C2×C3×C4—24no—
205C2×C3×C4—24no—
206C2×C3×C4—24no—
207C2×C3×C4—24no—
208C2×C3×C4D2418yes—
209C2×C3×C4C2×C4×D314yes—
210C2×C3×C4#23514yes—
211C2×C3×C4D3×D414yes—
212C2×C3×C4D3×D414yes—
213C2×C3×C4#23714yes—
214C2×C3×C4D3×Q814yes—
215C2×Dic3—68no—
216C2×Dic3—68no—
217C2×Dic3—124no—
218C2×Dic3—124no—
219C2×Dic3—124no—
220C2×Dic3—124no—
221C2×Dic3—124no—
222C2×Dic3—124no—
223C2×Dic3—124no—
224D12—316no—
225D12—68no—
226D12—68no—
227D12—68no—
228C4×D3—1232no—
229C3×C8—28no—
230C3×C8—44no—
231C2×C32#38511yescharacteristic
232C2×C32C4×D811yescharacteristic
233C2×C32#44011yescharacteristic
234C2×C32#44711yescharacteristic
235C2×C32#45211yescharacteristic
236C2×C32#47411yescharacteristic
237C2×C32#47811yescharacteristic
238C3⋊D3—44no—
239C24—181no—
240C2×D4—92no—
241C2×D4—92no—
242C2×D4—92no—
243C2×D4—181no—
244C2×D4—181no—
245C2×D4—181no—
246C22×C4—184no—
247C22×C4—181no—
248C22×C4—181no—
249C22×C4—181no—
250C22×C4—362no—
251C22×C4—362no—
252C22×C4C4⋊(C3⋊D3)11yescharacteristic
253C22×C4C4⋊(C3⋊D3)11yescharacteristic
254C22×C4C22×C3⋊D311yescharacteristic
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8C4×C3⋊D312yescomplemented
261C4⋊C4—92no—
262C4⋊C4—92no—
263C4⋊C4—181no—
264C4⋊C4—181no—
265C4⋊C4—181no—
266C4⋊C4—181no—
267C4⋊C4—362no—
268C22⋊C4—184no—
269C42—21no—
270C42—21no—
271C22×C3C4×D1214yes—
272C22×C3#88214yes—
273C22×C3#89714yes—
274C22×C3C2×D2414yes—
275C22×C3#90414yes—
276C22×C3#90814yes—
277C22×C3#90914yes—
278C2×D3—616no—
279C2×D3—128no—
280C2×D3—128no—
281C2×D3—128no—
282C2×D3—128no—
283C2×D3—128no—
284C2×D3—128no—
285C3×C4—28no—
286C3×C4—44no—
287C3×C4#67⋊C414yes—
288C3×C4#88314yes—
289C3×C4D3×C4⋊C414yes—
290C3×C4#89614yes—
291Dic3—128no—
292Dic3—128no—
293Dic3—244no—
294C32#186211yescharacteristic, complemented, Sylow
295C23—182no—
296C23—182no—
297C23—182no—
298C23—361no—
299C23—361no—
300C23—361no—
301C23—361no—
302C23C2×C4⋊(C3⋊D3)11yescharacteristic
303D4—94no—
304D4—182no—
305D4—182no—
306D4—182no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—182no—
313C2×C4—182no—
314C2×C4—368no—
315C2×C4—361no—
316C2×C4—361no—
317C2×C4—361no—
318C2×C4—361no—
319C2×C4—361no—
320C2×C4—361no—
321C2×C4—361no—
322C2×C4#374512yes—
323C2×C4C2×C4×C3⋊D311yescharacteristic
324C2×C4#382811yescharacteristic
325C2×C4D4×C3⋊D311yescharacteristic
326C2×C4D4×C3⋊D311yescharacteristic
327C2×C4#383011yescharacteristic
328C2×C4Q8×C3⋊D311yescharacteristic
329C8—22no—
330C8—41no—
331C2×C3#466814yes—
332C2×C3C4×D2414yes—
333C2×C3#471014yes—
334C2×C3#473214yes—
335C2×C3#473314yes—
336C2×C3#484614yes—
337C2×C3#484714yes—
338D3—1216no—
339C22—184no—
340C22—362no—
341C22—362no—
342C22—362no—
343C22—362no—
344C22—362no—
345C22—362no—
346C22C4×C4⋊(C3⋊D3)11yescharacteristic
347C22#6409111yescharacteristic
348C22#6410611yescharacteristic
349C22C2×#374511yescharacteristic
350C22#6411311yescharacteristic
351C22#6411711yescharacteristic
352C22#6411811yescharacteristic
353C4—22no—
354C4—41no—
355C4—362no—
356C4—362no—
357C4—721no—
358C4#6409011yescharacteristic
359C4#6409211yescharacteristic
360C4C4⋊C4×C3⋊D311yescharacteristic
361C4#6410511yescharacteristic
362C3#6867014yescomplemented
363C2—364no—
364C2#1059236711yescharacteristic
365C2C4×#374511yescharacteristic
366C2#1059240911yescharacteristic
367C2#1059243111yescharacteristic
368C2#1059243211yescharacteristic
369C2#1059254511yescharacteristic
370C2#1059254611yescharacteristic
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#1862
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×#63645C2semidirect
5. #10592627C2semidirect
6. C32×#336C2semidirect
7. #10589417C2semidirect
23. #63648C4semidirect
30. C3×#336D3semidirect
53. C2×C32×C8C2×C4semidirect
61. C4⋊(C3⋊Dic3)C2×C4semidirect
113. C4⋊(C3⋊D3)C4⋊C4semidirect
123. #336C3⋊D3semidirect
145. C2×C3×C8C4×D3semidirect
260. C2×C8C4×C3⋊D3semidirect
294. C32#1862semidirect
362. C3#68670semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×#636482
C2×#636452
#105926272
C32×#3362
#105894172
#686703