Finite Group Databasebeta

← #11887614

Subgroups — #11887614

Order 1152.

1164 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
1#10596050C211yesmaximal, characteristic
2Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic
3C32×C4×Q16C211yesmaximal, characteristic, complemented
4#10592885C212yesmaximal, complemented
5#10592730C211yesmaximal, characteristic, complemented
6#10592720C211yesmaximal, characteristic, complemented
7#10592583C212yesmaximal, complemented
8#10592512C212yesmaximal, complemented
9C3⋊D3×#103C212yesmaximal, complemented
10C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic
11#10592380C211yesmaximal, characteristic, complemented
12#79735—34nomaximal
13C2×Q8×C3⋊D3C2212yes—
14C2×C32×Q16C2211yescharacteristic
15C32×C4×Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17#64155C2212yes—
18C2×#3756C2212yes—
19C2×C8×C3⋊D3C2212yes—
20#64106—22no—
21#64106C2212yes—
22#64105—22no—
23C4⋊C4×C3⋊D3C2212yes—
24C4×C4⋊(C3⋊D3)—21no—
25C4×C4⋊(C3⋊D3)—21no—
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27#64079—21no—
28#64078—21no—
29#64078C2211yescharacteristic
30#64078C2211yescharacteristic
31C32×#107C2211yescharacteristic
32C32×#103C2211yescharacteristic
33C32×#103C2211yescharacteristic
34C32×C4×C8C2211yescharacteristic
35#63662C2212yes—
36#63647C2212yes—
37#63643C2212yes—
38#63643C2212yes—
39#63637C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5579—34no—
43Q8×D12—34no—
44C3×C4×Q16D314yescomplemented
45#5186—38no—
46#5031—34no—
47#5021—34no—
48#4884—38no—
49#4813—38no—
50D3×#103—38no—
51C8×D12—34no—
52#4681—34no—
53C2×C32×Q8C2311yescharacteristic
54C2×C32×Q8C2311yescharacteristic
55Q8×C3⋊D3—24no—
56Q8×C3⋊D3—42no—
57C2×C4⋊(C3⋊D3)D411yescharacteristic
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3C2312yes—
61C2×#634—22no—
62C2×#634—21no—
63C2×#634C2312yes—
64C32×Q16—22no—
65C2×C32×C8C2311yescharacteristic
66C2×C32×C8C2311yescharacteristic
67C32×C4⋊C4—21no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4C2311yescharacteristic
70C32×C4⋊C4C2311yescharacteristic
71C32×C42—21no—
72C32×C42—21no—
73C32×C42C2311yescharacteristic
74#3756—42no—
75#3752—22no—
76#3752—22no—
77#3752D412yes—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)—22no—
82C4⋊(C3⋊Dic3)D411yescharacteristic
83C4⋊(C3⋊Dic3)C2312yes—
84#3750—22no—
85#3750—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C8×C3⋊D3—42no—
88#3299—91noSylow
89C2×D3×Q8—38no—
90C2×C3×Q16C2×D314yes—
91C3×C4×Q8C2×D314yes—
92C3×C4×Q8C2×D314yes—
93#946—38no—
94C2×#216—38no—
95C2×D3×C8—38no—
96#897—38no—
97#897—68no—
98#896—68no—
99D3×C4⋊C4—38no—
100C4×D12—34no—
101C4×D12—64no—
102C4×D12—64no—
103#870—64no—
104#869—34no—
105#869—34no—
106#869—64no—
107C3×#107C2×D314yes—
108C3×#103C2×D314yes—
109C3×#103C2×D314yes—
110C3×C4×C8C2×D314yes—
111#835—38no—
112(C2×D3)⋊C8—38no—
113#816—38no—
114#816—38no—
115#810—38no—
116#807—38no—
117C4⋊(C3⋊C8)—34no—
118C22×C3⋊D3C2×D412yes—
119C32×Q8—21no—
120C32×Q8—21no—
121C32×Q8—21no—
122C32×Q8#4112yes—
123C2×C32×C4—21no—
124C2×C32×C4—21no—
125C2×C32×C4—21no—
126C2×C32×C4—21no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2411yescharacteristic
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—22no—
132C2×C3⋊Dic3C2×D412yes—
133C4⋊(C3⋊D3)Q1614yescomplemented
134C4×C3⋊D3—22no—
135C4×C3⋊D3—22no—
136C4×C3⋊D3—44no—
137C4×C3⋊D3—82no—
138#634—22no—
139#634—22no—
140#634—44no—
141#634—81no—
142C32×C8—21no—
143C32×C8—21no—
144C3⋊(C3⋊C8)—22no—
145#554—91no—
146D4×Q8—91no—
147#487—91no—
148#484—92no—
149#477—91no—
150#467—92no—
151#462—91no—
152#451—92no—
153C4×Q16C3⋊D311yescharacteristic, complemented
154C8×D4—91no—
155C2×#103—92no—
156C2×C3×Q8C22×D314yes—
157C2×C3×Q8C22×D314yes—
158D3×Q8—616no—
159D3×Q8—128no—
160C2×D12—34no—
161C2×C4×D3—38no—
162C2×C4×D3—68no—
163C2×C4×D3—68no—
164C2×Dic6—38no—
165C2×Dic6—68no—
166C2×Dic6—64no—
167C3×Q16—28no—
168C2×C3×C8C22×D314yes—
169C2×C3×C8C22×D314yes—
170C3×C4⋊C4—24no—
171C3×C4⋊C4—24no—
172C3×C4⋊C4C22×D314yes—
173C3×C4⋊C4C22×D314yes—
174C3×C42—24no—
175C3×C42—24no—
176C3×C42C22×D314yes—
177#216—128no—
178(C2×D3)⋊C4—38no—
179(C2×D3)⋊C4—68no—
180(C2×D3)⋊C4—68no—
181C4⋊Dic3—34no—
182C4⋊Dic3—38no—
183C4⋊Dic3—68no—
184C4⋊Dic3—64no—
185C4⋊Dic3—64no—
186C4⋊Dic3—64no—
187Dic3⋊C4—68no—
188Dic3⋊C4—68no—
189C2×C3⋊C8—38no—
190D3×C8—128no—
191C22×C32C22×D411yescharacteristic
192C2×C3⋊D3—22no—
193C2×C3⋊D3—22no—
194C2×C3⋊D3C2×Q1614yes—
195C32×C4—22no—
196C32×C4—21no—
197C32×C4—41no—
198C32×C4—41no—
199C32×C4—41no—
200C32×C4C2×Q1612yes—
201C32×C4C2×#4111yescharacteristic
202C32×C4H(5,𝔽2)11yescharacteristic
203C3⋊Dic3—22no—
204C3⋊Dic3—42no—
205C3⋊Dic3—42no—
206C22×Q8—92no—
207C2×Q16—92no—
208C2×Q16C2×C3⋊D311yescharacteristic
209C22×C8—92no—
210C4⋊Q8—91no—
211C4⋊Q8—91no—
212C4⋊Q8—181no—
213#125—181no—
214C22⋊Q8—92no—
215C22⋊Q8—92no—
216C22⋊Q8—182no—
217C22⋊Q8—182no—
218C4×Q8C2×C3⋊D311yescharacteristic
219C4×Q8C2×C3⋊D311yescharacteristic
220C4×D4—91no—
221C4×D4—181no—
222C4×D4—181no—
223C2×C4⋊C4—92no—
224#107—92no—
225#107C2×C3⋊D311yescharacteristic
226C4⋊C8—91no—
227#103—92no—
228#103—92no—
229#103—92no—
230#103—92no—
231#103C2×C3⋊D311yescharacteristic
232#103C2×C3⋊D311yescharacteristic
233C22⋊C8—92no—
234C4×C8C2×C3⋊D311yescharacteristic
235C22×D3—38no—
236C3×Q8—24no—
237C3×Q8—24no—
238C3×Q8—24no—
239C3×Q8#23518yes—
240C2×C3×C4—24no—
241C2×C3×C4—24no—
242C2×C3×C4—24no—
243C2×C3×C4—24no—
244C2×C3×C4D3×D414yes—
245C2×C3×C4D3×D414yes—
246C2×C3×C4C23×D314yes—
247C2×Dic3—38no—
248C2×Dic3—68no—
249C2×Dic3—68no—
250D12—316no—
251C4×D3—68no—
252C4×D3—68no—
253C4×D3—1216no—
254C4×D3—248no—
255Dic6—68no—
256Dic6—68no—
257Dic6—1216no—
258Dic6—244no—
259C3×C8—24no—
260C3×C8—24no—
261C3⋊C8—68no—
262C2×C32#54611yescharacteristic
263C2×C32C22×Q1611yescharacteristic
264C2×C32#57711yescharacteristic
265C3⋊D3—24no—
266C2×Q8—92no—
267C2×Q8—182no—
268C2×Q8—181no—
269C2×Q8—184no—
270C2×Q8—362no—
271C2×Q8C22×C3⋊D311yescharacteristic
272C2×Q8C22×C3⋊D311yescharacteristic
273C2×D4—91no—
274C22×C4—92no—
275C22×C4—182no—
276C22×C4—182no—
277Q16—22no—
278Q16—362no—
279C2×C8—92no—
280C2×C8—362no—
281C2×C8C22×C3⋊D311yescharacteristic
282C2×C8C22×C3⋊D311yescharacteristic
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—91no—
286C4⋊C4—92no—
287C4⋊C4—182no—
288C4⋊C4—182no—
289C4⋊C4—182no—
290C4⋊C4—181no—
291C4⋊C4—181no—
292C4⋊C4—181no—
293C4⋊C4C22×C3⋊D311yescharacteristic
294C4⋊C4C22×C3⋊D311yescharacteristic
295C22⋊C4—92no—
296C22⋊C4—182no—
297C22⋊C4—182no—
298C42—21no—
299C42—21no—
300C42C22×C3⋊D311yescharacteristic
301C22×C3C2×D3×D414yes—
302C2×D3—316no—
303C2×D3—68no—
304C2×D3—68no—
305C3×C4—24no—
306C3×C4—28no—
307C3×C4—44no—
308C3×C4—44no—
309C3×C4—44no—
310C3×C4D3×Q1618yes—
311C3×C4C2×#23514yes—
312C3×C4#100914yes—
313Dic3—68no—
314Dic3—128no—
315Dic3—128no—
316C32#329911yescharacteristic, complemented, Sylow
317C23—92no—
318Q8—21no—
319Q8—21no—
320Q8—21no—
321Q8—182no—
322Q8—182no—
323Q8—364no—
324Q8—721no—
325Q8#382812yes—
326D4—94no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—92no—
332C2×C4—182no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—364no—
337C2×C4—722no—
338C2×C4D4×C3⋊D311yescharacteristic
339C2×C4D4×C3⋊D311yescharacteristic
340C2×C4C23×C3⋊D311yescharacteristic
341C8—21no—
342C8—21no—
343C8—182no—
344C2×C3#555014yes—
345C2×C3C2×D3×Q1614yes—
346C2×C3#577014yes—
347D3—616no—
348C22—94no—
349C22—182no—
350C22—182no—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—21no—
353C4—22no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—182no—
358C4—362no—
359C4—362no—
360C4Q16×C3⋊D312yes—
361C4C2×#382811yescharacteristic
362C4#6436611yescharacteristic
363C3#7973514yescomplemented
364C2—184no—
365C2#1059602111yescharacteristic
366C2C2×Q16×C3⋊D311yescharacteristic
367C2#1059624111yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×Q16C2
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenterC4×Q16C3⋊D3
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C32×C4×Q16C2semidirect
4. #10592885C2semidirect
5. #10592730C2semidirect
6. #10592720C2semidirect
7. #10592583C2semidirect
8. #10592512C2semidirect
9. C3⋊D3×#103C2semidirect
11. #10592380C2semidirect
44. C3×C4×Q16D3semidirect
133. C4⋊(C3⋊D3)Q16semidirect
153. C4×Q16C3⋊D3semidirect
316. C32#3299semidirect
363. C3#79735semidirect

Maximal subgroups

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

subgroupindex
#105960502
Q8×C4⋊(C3⋊D3)2
C32×C4×Q162
#105928852
#105927302
#105927202
#105925832
#105925122
C3⋊D3×#1032
C8×C4⋊(C3⋊D3)2
#105923802
#797353