Finite Group Databasebeta

← #11786908

Subgroups — #11786908

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×#64102C211yesmaximal, characteristic
2C2×C32×#106C211yesmaximal, characteristic, complemented
3C2×#63648C211yesmaximal, characteristic
4#10592671C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic
6#10589416C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#70584—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×C4×C3⋊D3—21no—
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C32×C4⋊C4C2211yescharacteristic
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C2×#3750—21no—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19#64102—22no—
20#64102—22no—
21C32×#106—22no—
22#63658—21no—
23#63648C414yescomplemented
24#63636—22no—
25C2×#893—34no—
26C2×C3×#106D314yescomplemented
27C2×#821—34no—
28#4972—34no—
29C2×#809—34no—
30#4550—34no—
31#4529—34no—
32C23×C3⋊D3—21no—
33C22×C32×C4—21no—
34C22×C32×C4—21no—
35C22×C32×C4C2311yescharacteristic
36C22×C3⋊Dic3—21no—
37C22×C3⋊Dic3D411yescharacteristic
38C22×C3⋊Dic3D411yescharacteristic
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×C8C2×C412yescomplemented
51C32×C4⋊C4—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4D412yes—
55#3752—24no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)C2×C412yescomplemented
58#3750—42no—
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64#1864—91noSylow
65C22×D12—34no—
66C22×C4×D3—64no—
67C22×C3×C8C2×D314yes—
68C2×C3×C4⋊C4C2×D314yes—
69C2×C3×C4⋊C4C2×D314yes—
70C2×(C2×D3)⋊C4—64no—
71C2×C4⋊Dic3—34no—
72C2×Dic3⋊C4—64no—
73C2×C4×Dic3—34no—
74C22×C3⋊C8—34no—
75#893—68no—
76#893—68no—
77C3×#106—28no—
78C3⋊#95—64no—
79#821—316no—
80#809—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—22no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4—41no—
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—21no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—22no—
104C2×C3⋊Dic3—21no—
105C2×C3⋊Dic3—21no—
106C2×C3⋊Dic3—21no—
107C2×C3⋊Dic3—41no—
108C2×C3⋊Dic3—41no—
109C2×C3⋊Dic3SD1612yes—
110C4⋊(C3⋊D3)—22no—
111C4⋊(C3⋊D3)—22no—
112C4⋊(C3⋊D3)—22no—
113C4⋊(C3⋊D3)C4⋊C414yescomplemented
114C4×C3⋊D3—48no—
115C32×C8—22no—
116C3⋊(C3⋊C8)—41no—
117C2×C4×D4—91no—
118C2×#106C3⋊D311yescharacteristic, complemented
119C2×#102—91no—
120C2×#102—91no—
121#389—91no—
122#340—91no—
123#336—91no—
124C23×D3—64no—
125C22×C3×C4—24no—
126C22×C3×C4—24no—
127C22×C3×C4C22×D314yes—
128C22×Dic3—34no—
129C22×Dic3—34no—
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×C8C4×D318yescomplemented
143C3×C4⋊C4—24no—
144C3×C4⋊C4—24no—
145C3×C4⋊C4—24no—
146C3×C4⋊C4#6718yes—
147(C2×D3)⋊C4—616no—
148C4⋊Dic3—38no—
149C4⋊Dic3—64no—
150Dic3⋊C4—128no—
151C4×Dic3—64no—
152C4×Dic3—64no—
153C2×C3⋊C8—64no—
154C2×C3⋊C8—64no—
155C2×C3⋊C8—64no—
156C22×C32C4×D411yescharacteristic
157C22×C32#12011yescharacteristic
158C22×C32C22⋊Q811yescharacteristic
159C22×C32C2×SD1611yescharacteristic
160C22×C32#13511yescharacteristic
161C22×C32AGL(1,ℤ/8)11yescharacteristic
162C22×C32AGL(1,ℤ/8)11yescharacteristic
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—42no—
171C32×C4—81no—
172C32×C4C2×C4⋊C411yescharacteristic
173C32×C4C4×D411yescharacteristic
174C32×C4C22⋊Q811yescharacteristic
175C32×C4#12311yescharacteristic
176C3⋊Dic3—22no—
177C3⋊Dic3—42no—
178C3⋊Dic3—41no—
179C22×D4—91no—
180C23×C4—181no—
181C22×C8—91no—
182C22×C8C2×C3⋊D311yescharacteristic
183C4×D4—182no—
184C4×D4—182no—
185C2×C4⋊C4—91no—
186C2×C4⋊C4—181no—
187C2×C4⋊C4C2×C3⋊D311yescharacteristic
188C2×C4⋊C4C2×C3⋊D311yescharacteristic
189C2×C22⋊C4—181no—
190C2×C42—91no—
191#106—22no—
192#102—94no—
193#102—182no—
194#95—181no—
195C23×C3D3×D414yes—
196C22×D3—68no—
197C22×D3—68no—
198C22×D3—68no—
199C22×D3—124no—
200C22×D3—124no—
201C22×D3—124no—
202C22×D3—124no—
203C2×C3×C4—28no—
204C2×C3×C4—44no—
205C2×C3×C4—44no—
206C2×C3×C4—44no—
207C2×C3×C4—44no—
208C2×C3×C4—44no—
209C2×C3×C4C2×C4×D314yes—
210C2×C3×C4#23514yes—
211C2×C3×C4D3×D414yes—
212C2×C3×C4D3×Q814yes—
213C2×C3×C4#23914yes—
214C2×C3×C4C2×#6714yes—
215C2×Dic3—38no—
216C2×Dic3—64no—
217C2×Dic3—64no—
218C2×Dic3—68no—
219C2×Dic3—64no—
220C2×Dic3—64no—
221C2×Dic3—64no—
222C2×Dic3—124no—
223C2×Dic3—124no—
224D12—316no—
225D12—68no—
226D12—68no—
227D12—68no—
228C4×D3—1232no—
229C3×C8—28no—
230C3⋊C8—124no—
231C2×C32#38511yescharacteristic
232C2×C32C4×SD1611yescharacteristic
233C2×C32#44211yescharacteristic
234C2×C32#44911yescharacteristic
235C2×C32#45011yescharacteristic
236C2×C32#47611yescharacteristic
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—21no—
247C22×C4—21no—
248C22×C4—91no—
249C22×C4—91no—
250C22×C4—184no—
251C22×C4—181no—
252C22×C4—362no—
253C22×C4—362no—
254C22×C4C22×C3⋊D311yescharacteristic
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—181no—
258C2×C8—181no—
259C2×C8—181no—
260C2×C8C4×C3⋊D312yescomplemented
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—92no—
265C4⋊C4—181no—
266C4⋊C4—362no—
267C4⋊C4#63812yes—
268C22⋊C4—184no—
269C42—181no—
270C42—181no—
271C22×C3#89314yes—
272C22×C3#89614yes—
273C22×C3D3×SD1614yes—
274C22×C3#91414yes—
275C22×C3#91414yes—
276C22×C3#91614yes—
277C22×C3#93714yes—
278C2×D3—616no—
279C2×D3—128no—
280C2×D3—128no—
281C2×D3—128no—
282C2×D3—128no—
283C2×D3—128no—
284C2×D3—128no—
285C3×C4—48no—
286C3×C4—84no—
287C3×C4D3×C4⋊C414yes—
288C3×C4#89414yes—
289C3×C4C4×#6714yes—
290C3×C4#94614yes—
291Dic3—68no—
292Dic3—128no—
293Dic3—124no—
294C32#186411yescharacteristic, complemented, Sylow
295C23—182no—
296C23—182no—
297C23—182no—
298C23—361no—
299C23—361no—
300C23—361no—
301C23—361no—
302C23D4×C3⋊D311yescharacteristic
303D4—94no—
304D4—182no—
305D4—182no—
306D4—182no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—92no—
314C2×C4—181no—
315C2×C4—181no—
316C2×C4—182no—
317C2×C4—181no—
318C2×C4—181no—
319C2×C4—181no—
320C2×C4—368no—
321C2×C4—361no—
322C2×C4—361no—
323C2×C4C2×C4×C3⋊D311yescharacteristic
324C2×C4#382811yescharacteristic
325C2×C4D4×C3⋊D311yescharacteristic
326C2×C4Q8×C3⋊D311yescharacteristic
327C2×C4#383211yescharacteristic
328C2×C4C2×#63811yescharacteristic
329C8—22no—
330C8—361no—
331C2×C3#485214yes—
332C2×C3#486914yes—
333C2×C3#487014yes—
334C2×C3#487114yes—
335C2×C3#498914yes—
336C2×C3#516914yes—
337C2×C3#517214yes—
338D3—1216no—
339C22—184no—
340C22—362no—
341C22—362no—
342C22—362no—
343C22—362no—
344C22—362no—
345C22—362no—
346C22#6410211yescharacteristic
347C22#6410511yescharacteristic
348C22SD16×C3⋊D311yescharacteristic
349C22#6412311yescharacteristic
350C22#6412311yescharacteristic
351C22#6412511yescharacteristic
352C22#6414611yescharacteristic
353C4—42no—
354C4—81no—
355C4—182no—
356C4—362no—
357C4—361no—
358C4C4⋊C4×C3⋊D311yescharacteristic
359C4#6410311yescharacteristic
360C4C4×#63811yescharacteristic
361C4#6415511yescharacteristic
362C3#7058414yescomplemented
363C2—364no—
364C2#1059255111yescharacteristic
365C2#1059256811yescharacteristic
366C2#1059256911yescharacteristic
367C2#1059257011yescharacteristic
368C2#1059268811yescharacteristic
369C2#1059286811yescharacteristic
370C2#1059287111yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#106C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×#106C3⋊D3
hypocenterC32#1864
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×C32×#106C2semidirect
4. #10592671C2semidirect
6. #10589416C2semidirect
7. #10589395C2semidirect
23. #63648C4semidirect
26. C2×C3×#106D3semidirect
50. C2×C32×C8C2×C4semidirect
57. C4⋊(C3⋊Dic3)C2×C4semidirect
113. C4⋊(C3⋊D3)C4⋊C4semidirect
118. C2×#106C3⋊D3semidirect
142. C2×C3×C8C4×D3semidirect
260. C2×C8C4×C3⋊D3semidirect
294. C32#1864semidirect
362. C3#70584semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×C32×#1062
C2×#636482
#105926712
C2×#636362
#105894162
#105893952
#705843