Finite Group Databasebeta

← #11785237

Subgroups — #11785237

Order 1152.

1068 conjugacy classes of subgroups.

The subgroup lattice has 369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic
2C2×#63648C211yesmaximal, characteristic
3C2×#63641C211yesmaximal, characteristic, complemented
4#10592676C211yesmaximal, characteristic, complemented
5C2×#63636C211yesmaximal, characteristic
6C32×#340C211yesmaximal, characteristic, complemented
7#10589395C211yesmaximal, characteristic, complemented
8#68893—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×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18#64102—22no—
19#64102C414yescomplemented
20#63658—21no—
21#63658—21no—
22#63648—22no—
23#63641—22no—
24#63636—22no—
25C2×#893—34no—
26C2×#821—34no—
27C2×Dic3⋊C8—34no—
28#4977—34no—
29C2×#809—34no—
30C3×#340D314yescomplemented
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×C8—21no—
51C32×C4⋊C4—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4C2×C412yes—
55#3752—24no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4×C3⋊Dic3C2×C412yes—
59C4×C3⋊Dic3D412yes—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63#1804—91noSylow
64C22×D12—34no—
65C22×C4×D3—64no—
66C22×C3×C8C2×D314yes—
67C2×C3×C4⋊C4C2×D314yes—
68C2×C3×C4⋊C4C2×D314yes—
69C2×(C2×D3)⋊C4—64no—
70C2×C4⋊Dic3—34no—
71C2×C4×Dic3—34no—
72C22×C3⋊C8—34no—
73#893—316no—
74#893—68no—
75C3⋊#95—64no—
76C3⋊#95—64no—
77#821—68no—
78Dic3⋊C8—68no—
79#809—68no—
80C23×C32C2×D411yescharacteristic
81C22×C3⋊D3—22no—
82C22×C3⋊D3—22no—
83C22×C3⋊D3—22no—
84C22×C3⋊D3—41no—
85C22×C3⋊D3—41no—
86C22×C3⋊D3—41no—
87C22×C3⋊D3—41no—
88C2×C32×C4—22no—
89C2×C32×C4—41no—
90C2×C32×C4—41no—
91C2×C32×C4—41no—
92C2×C32×C4—41no—
93C2×C32×C4—41no—
94C2×C32×C4C22×C411yescharacteristic
95C2×C32×C4C2×D411yescharacteristic
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×Q811yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C32×C4#4111yescharacteristic
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C2×C3⋊Dic3—21no—
104C2×C3⋊Dic3—41no—
105C2×C3⋊Dic3—41no—
106C2×C3⋊Dic3—41no—
107C2×C3⋊Dic3C22⋊C412yes—
108C2×C3⋊Dic3C22⋊C412yes—
109C4⋊(C3⋊D3)—22no—
110C4⋊(C3⋊D3)—22no—
111C4⋊(C3⋊D3)—22no—
112C4⋊(C3⋊D3)C4⋊C414yes—
113C4×C3⋊D3—48no—
114C32×C8—41no—
115C3⋊(C3⋊C8)—41no—
116C2×C4×D4—91no—
117C2×C4⋊C8—91no—
118C2×#102—91no—
119C2×#102—91no—
120#382—91no—
121#340—91no—
122#340C3⋊D311yescharacteristic, complemented
123C23×D3—64no—
124C22×C3×C4—24no—
125C22×C3×C4—24no—
126C22×C3×C4C22×D314yes—
127C22×Dic3—34no—
128C22×Dic3—34no—
129C22×Dic3—64no—
130C2×D12—38no—
131C2×D12—38no—
132C2×D12—38no—
133C2×D12—64no—
134C2×D12—64no—
135C2×D12—64no—
136C2×C4×D3—616no—
137C2×C4×D3—128no—
138C2×C4×D3—128no—
139C2×C3×C8—24no—
140C2×C3×C8—24no—
141C2×C3×C8—24no—
142C3×C4⋊C4—24no—
143C3×C4⋊C4—24no—
144C3×C4⋊C4—24no—
145C3×C4⋊C4C4×D318yes—
146(C2×D3)⋊C4—616no—
147C4⋊Dic3—64no—
148C4⋊Dic3—64no—
149C4×Dic3—38no—
150C4×Dic3—38no—
151C2×C3⋊C8—64no—
152C2×C3⋊C8—64no—
153C2×C3⋊C8—64no—
154C22×C32C2×C22⋊C411yescharacteristic
155C22×C32#12111yescharacteristic
156C22×C32C22⋊Q811yescharacteristic
157C22×C32#13511yescharacteristic
158C22×C32#13511yescharacteristic
159C22×C32AGL(1,ℤ/8)11yescharacteristic
160C22×C32AGL(1,ℤ/8)11yescharacteristic
161C2×C3⋊D3—24no—
162C2×C3⋊D3—42no—
163C2×C3⋊D3—42no—
164C2×C3⋊D3—42no—
165C2×C3⋊D3—42no—
166C2×C3⋊D3—42no—
167C2×C3⋊D3—42no—
168C32×C4—42no—
169C32×C4—81no—
170C32×C4C2×C4⋊C411yescharacteristic
171C32×C4#11711yescharacteristic
172C32×C4#12111yescharacteristic
173C32×C4C22⋊Q811yescharacteristic
174C3⋊Dic3—22no—
175C3⋊Dic3—22no—
176C3⋊Dic3—81no—
177C22×D4—91no—
178C23×C4—181no—
179C22×C8—91no—
180C22×C8C2×C3⋊D311yescharacteristic
181C4×D4—94no—
182C4×D4—182no—
183C2×C4⋊C4—91no—
184C2×C4⋊C4C2×C3⋊D311yescharacteristic
185C2×C4⋊C4C2×C3⋊D311yescharacteristic
186C2×C22⋊C4—181no—
187C2×C42—91no—
188C4⋊C8—182no—
189#102—182no—
190#102—182no—
191#95—181no—
192#95—181no—
193C23×C3D3×D414yes—
194C22×D3—68no—
195C22×D3—68no—
196C22×D3—68no—
197C22×D3—124no—
198C22×D3—124no—
199C22×D3—124no—
200C22×D3—124no—
201C2×C3×C4—28no—
202C2×C3×C4—44no—
203C2×C3×C4—44no—
204C2×C3×C4—44no—
205C2×C3×C4—44no—
206C2×C3×C4—44no—
207C2×C3×C4C2×C4×D314yes—
208C2×C3×C4#23514yes—
209C2×C3×C4#23514yes—
210C2×C3×C4D3×D414yes—
211C2×C3×C4D3×D414yes—
212C2×C3×C4D3×Q814yes—
213C2×Dic3—38no—
214C2×Dic3—38no—
215C2×Dic3—64no—
216C2×Dic3—64no—
217C2×Dic3—64no—
218C2×Dic3—64no—
219C2×Dic3—124no—
220C2×Dic3—124no—
221C2×Dic3—124no—
222D12—316no—
223D12—68no—
224D12—68no—
225D12—68no—
226C4×D3—1232no—
227C3×C8—44no—
228C3⋊C8—124no—
229C2×C32#38011yescharacteristic
230C2×C32#41611yescharacteristic
231C2×C32#41811yescharacteristic
232C2×C32#46311yescharacteristic
233C2×C32#46311yescharacteristic
234C2×C32#47811yescharacteristic
235C2×C32#47811yescharacteristic
236C3⋊D3—44no—
237C24—181no—
238C2×D4—92no—
239C2×D4—92no—
240C2×D4—92no—
241C2×D4—181no—
242C2×D4—181no—
243C2×D4—181no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—184no—
249C22×C4—181no—
250C22×C4—362no—
251C22×C4—362no—
252C22×C4C22×C3⋊D311yescharacteristic
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—181no—
257C2×C8—181no—
258C2×C8—181no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—181no—
263C4⋊C4—181no—
264C4⋊C4C4×C3⋊D312yes—
265C22⋊C4—184no—
266C42—92no—
267C42—92no—
268C22×C3D3×C22⋊C414yes—
269C22×C3#88414yes—
270C22×C3#89614yes—
271C22×C3#91114yes—
272C22×C3#91414yes—
273C22×C3#91614yes—
274C22×C3#91914yes—
275C2×D3—616no—
276C2×D3—128no—
277C2×D3—128no—
278C2×D3—128no—
279C2×D3—128no—
280C2×D3—128no—
281C2×D3—128no—
282C3×C4—48no—
283C3×C4—84no—
284C3×C4#87214yes—
285C3×C4#88414yes—
286C3×C4D3×C4⋊C414yes—
287C3×C4#89614yes—
288Dic3—68no—
289Dic3—68no—
290Dic3—244no—
291C32#180411yescharacteristic, complemented, Sylow
292C23—182no—
293C23—182no—
294C23—182no—
295C23—361no—
296C23—361no—
297C23—361no—
298C23—361no—
299C23D4×C3⋊D311yescharacteristic
300D4—94no—
301D4—182no—
302D4—182no—
303D4—182no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—92no—
311C2×C4—92no—
312C2×C4—181no—
313C2×C4—181no—
314C2×C4—181no—
315C2×C4—181no—
316C2×C4—368no—
317C2×C4—361no—
318C2×C4—361no—
319C2×C4—361no—
320C2×C4C2×C4×C3⋊D311yescharacteristic
321C2×C4#382811yescharacteristic
322C2×C4#382811yescharacteristic
323C2×C4D4×C3⋊D311yescharacteristic
324C2×C4D4×C3⋊D311yescharacteristic
325C2×C4Q8×C3⋊D311yescharacteristic
326C8—41no—
327C8—361no—
328C2×C3#466714yes—
329C2×C3#477014yes—
330C2×C3#478714yes—
331C2×C3#480414yes—
332C2×C3#481914yes—
333C2×C3#487114yes—
334C2×C3#489114yes—
335D3—1216no—
336C22—184no—
337C22—362no—
338C22—362no—
339C22—362no—
340C22—362no—
341C22—362no—
342C22—362no—
343C22C22⋊C4×C3⋊D311yescharacteristic
344C22#6409311yescharacteristic
345C22#6410511yescharacteristic
346C22#6412011yescharacteristic
347C22#6412311yescharacteristic
348C22#6412511yescharacteristic
349C22#6412811yescharacteristic
350C4—42no—
351C4—81no—
352C4—182no—
353C4—182no—
354C4—721no—
355C4#6408111yescharacteristic
356C4#6409311yescharacteristic
357C4C4⋊C4×C3⋊D311yescharacteristic
358C4#6410511yescharacteristic
359C3#6889314yescomplemented
360C2—364no—
361C2#1059236611yescharacteristic
362C2#1059246911yescharacteristic
363C2#1059248611yescharacteristic
364C2#1059250311yescharacteristic
365C2#1059251811yescharacteristic
366C2#1059257011yescharacteristic
367C2#1059259011yescharacteristic
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#1804
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. C2×#63641C2semidirect
4. #10592676C2semidirect
6. C32×#340C2semidirect
7. #10589395C2semidirect
19. #64102C4semidirect
30. C3×#340D3semidirect
122. #340C3⋊D3semidirect
291. C32#1804semidirect
359. C3#68893semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#636482
C2×#636412
#105926762
C2×#636362
C32×#3402
#105893952
#688933