Finite Group Databasebeta

← #11887605

Subgroups — #11887605

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#10596201C211yesmaximal, characteristic
2#10596198C211yesmaximal, characteristic
3C32×#487C211yesmaximal, characteristic, complemented
4#10592790C211yesmaximal, characteristic, complemented
5#10592789C211yesmaximal, characteristic, complemented
6#10592512C212yesmaximal, complemented
7#10592510C212yesmaximal, complemented
8#10592508C212yesmaximal, complemented
9C3⋊D3×#103C212yesmaximal, complemented
10C4×#3746C211yesmaximal, characteristic, complemented
11C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic
12#81613—34nomaximal
13C2×Q8×C3⋊D3C2212yes—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16#64155—22no—
17#64155C2212yes—
18C2×#3756C2212yes—
19C2×#3746C2211yescharacteristic
20C2×C8×C3⋊D3C2212yes—
21#64106C2212yes—
22#64105—22no—
23#64102—21no—
24#64102—21no—
25C4⋊C4×C3⋊D3C2212yes—
26#64099—21no—
27#64097—21no—
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C32×#103C2212yes—
32C32×#103C2212yes—
33C32×C4×C8C2211yescharacteristic
34#63662C2212yes—
35#63647C2212yes—
36#63645C2211yescharacteristic
37#63643C2211yescharacteristic
38#63643C2211yescharacteristic
39#63637C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5730—34no—
43#5727—34no—
44C3×#487D314yescomplemented
45#5091—34no—
46#5090—34no—
47#4813—38no—
48#4811—38no—
49#4809—38no—
50D3×#103—38no—
51C4×Dic12—34no—
52C8×D12—34no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2312yes—
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×#634C2311yescharacteristic
63C2×#634C2311yescharacteristic
64C2×C32×C8C2311yescharacteristic
65C2×C32×C8C2311yescharacteristic
66C32×C4⋊C4—21no—
67C32×C4⋊C4—21no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4C2312yes—
70C32×C42C2311yescharacteristic
71#3756—42no—
72#3752—22no—
73#3752—22no—
74#3752D412yes—
75C4⋊(C3⋊Dic3)—22no—
76C4⋊(C3⋊Dic3)D411yescharacteristic
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—21no—
80#3750—21no—
81#3750—22no—
82#3750—22no—
83C4×C3⋊Dic3—21no—
84C4×C3⋊Dic3—21no—
85C2×C3⋊(C3⋊C8)C2312yes—
86#3746—22no—
87C8×C3⋊D3—42no—
88#3299—91noSylow
89C2×D3×Q8—38no—
90C3×C4⋊Q8C2×D314yes—
91C3×C4⋊Q8C2×D314yes—
92#946—38no—
93#946—68no—
94C2×#216—38no—
95C2×Dic12—34no—
96C2×D3×C8—38no—
97#897—38no—
98#896—68no—
99#893—64no—
100#893—64no—
101D3×C4⋊C4—38no—
102#890—64no—
103#888—64no—
104C4×D12—34no—
105C4×Dic6—34no—
106C4×Dic6—34no—
107C3×#103C2×D318yes—
108C3×#103C2×D318yes—
109C3×C4×C8C2×D314yes—
110#835—38no—
111(C2×D3)⋊C8—38no—
112#818—34no—
113#816—34no—
114#816—34no—
115#810—38no—
116#807—38no—
117C4⋊(C3⋊C8)—34no—
118C22×C3⋊D3C2×D412yes—
119C32×Q8—22no—
120C32×Q8—22no—
121C32×Q8—81no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2411yescharacteristic
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3C2×D412yes—
132C4⋊(C3⋊D3)Q1614yescomplemented
133C4×C3⋊D3—22no—
134C4×C3⋊D3—22no—
135C4×C3⋊D3—44no—
136C4×C3⋊D3—82no—
137#634—21no—
138#634—21no—
139#634—21no—
140#634—44no—
141#634#4112yes—
142C32×C8—21no—
143C32×C8—21no—
144C3⋊(C3⋊C8)—22no—
145#554—91no—
146D4×Q8—91no—
147#487C3⋊D311yescharacteristic, complemented
148#484—92no—
149#477—91no—
150#467—92no—
151#462—91no—
152#451—92no—
153C4×Q16—91no—
154C8×D4—91no—
155C2×#103—92no—
156C2×C3×Q8—24no—
157C2×C3×Q8C22×D318yes—
158D3×Q8—616no—
159D3×Q8—128no—
160C2×D12—34no—
161C2×C4×D3—38no—
162C2×C4×D3—68no—
163C2×C4×D3—68no—
164C2×Dic6—34no—
165C2×Dic6—34no—
166C2×Dic6—68no—
167C2×C3×C8C22×D314yes—
168C2×C3×C8C22×D314yes—
169C3×C4⋊C4—24no—
170C3×C4⋊C4—24no—
171C3×C4⋊C4—24no—
172C3×C4⋊C4C22×D318yes—
173C3×C42C22×D314yes—
174#216—128no—
175(C2×D3)⋊C4—38no—
176(C2×D3)⋊C4—68no—
177(C2×D3)⋊C4—68no—
178C4⋊Dic3—34no—
179C4⋊Dic3—34no—
180C4⋊Dic3—34no—
181C4⋊Dic3—68no—
182Dic3⋊C4—68no—
183Dic3⋊C4—68no—
184Dic3⋊C4—64no—
185Dic3⋊C4—64no—
186C4×Dic3—64no—
187C4×Dic3—64no—
188C2×C3⋊C8—38no—
189Dic12—68no—
190D3×C8—128no—
191C22×C32C22×D411yescharacteristic
192C2×C3⋊D3—22no—
193C2×C3⋊D3—22no—
194C2×C3⋊D3C2×Q1614yes—
195C32×C4—21no—
196C32×C4—42no—
197C32×C4—42no—
198C32×C4C2×Q1612yes—
199C32×C4C2×#4111yescharacteristic
200C32×C4H(5,𝔽2)11yescharacteristic
201C3⋊Dic3—22no—
202C3⋊Dic3—22no—
203C3⋊Dic3—41no—
204C3⋊Dic3—41no—
205C3⋊Dic3—41no—
206C22×Q8—92no—
207C2×Q16—92no—
208C2×Q16—91no—
209C22×C8—92no—
210C4⋊Q8—181no—
211C4⋊Q8C2×C3⋊D311yescharacteristic
212C4⋊Q8C2×C3⋊D311yescharacteristic
213#125—181no—
214C22⋊Q8—92no—
215C22⋊Q8—92no—
216C22⋊Q8—182no—
217C22⋊Q8—182no—
218C4×Q8—91no—
219C4×Q8—91no—
220C4×D4—91no—
221C4×D4—181no—
222C4×D4—181no—
223C2×C4⋊C4—92no—
224#107—91no—
225#107—92no—
226C4⋊C8—91no—
227#103—92no—
228#103—91no—
229#103—91no—
230#103—92no—
231#103C2×C3⋊D312yes—
232#103C2×C3⋊D312yes—
233C22⋊C8—92no—
234C4×C8C2×C3⋊D311yescharacteristic
235C22×D3—38no—
236C3×Q8—28no—
237C3×Q8—28no—
238C3×Q8—84no—
239C2×C3×C4—28no—
240C2×C3×C4—28no—
241C2×C3×C4D3×D414yes—
242C2×C3×C4D3×D414yes—
243C2×C3×C4C23×D314yes—
244C2×Dic3—38no—
245C2×Dic3—64no—
246C2×Dic3—64no—
247C2×Dic3—64no—
248C2×Dic3—64no—
249D12—316no—
250C4×D3—68no—
251C4×D3—68no—
252C4×D3—1216no—
253C4×D3—248no—
254Dic6—38no—
255Dic6—64no—
256Dic6—64no—
257Dic6—64no—
258Dic6—1216no—
259C3×C8—24no—
260C3×C8—24no—
261C3⋊C8—68no—
262C2×C32#54611yescharacteristic
263C2×C32C22×Q1611yescharacteristic
264C2×C32#57711yescharacteristic
265C3⋊D3—24no—
266C2×Q8—21no—
267C2×Q8—91no—
268C2×Q8—91no—
269C2×Q8—182no—
270C2×Q8—184no—
271C2×Q8—362no—
272C2×Q8C22×C3⋊D312yes—
273C2×D4—91no—
274C22×C4—92no—
275C22×C4—182no—
276C22×C4—182no—
277Q16—182no—
278Q16—362no—
279C2×C8—92no—
280C2×C8—362no—
281C2×C8C22×C3⋊D311yescharacteristic
282C2×C8C22×C3⋊D311yescharacteristic
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—91no—
287C4⋊C4—91no—
288C4⋊C4—91no—
289C4⋊C4—182no—
290C4⋊C4—182no—
291C4⋊C4—182no—
292C4⋊C4—181no—
293C4⋊C4—181no—
294C4⋊C4C22×C3⋊D312yes—
295C22⋊C4—92no—
296C22⋊C4—182no—
297C22⋊C4—182no—
298C42—181no—
299C42—181no—
300C42C22×C3⋊D311yescharacteristic
301C22×C3C2×D3×D414yes—
302C2×D3—316no—
303C2×D3—68no—
304C2×D3—68no—
305C3×C4—24no—
306C3×C4—48no—
307C3×C4—48no—
308C3×C4D3×Q1618yes—
309C3×C4D3×#4114yes—
310C3×C4#100914yes—
311Dic3—68no—
312Dic3—68no—
313Dic3—124no—
314Dic3—124no—
315Dic3—124no—
316C32#329911yescharacteristic, complemented, Sylow
317C23—92no—
318Q8—22no—
319Q8—22no—
320Q8—81no—
321Q8—92no—
322Q8—181no—
323Q8—181no—
324Q8—181no—
325Q8—364no—
326D4—94no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—92no—
330C2×C4—181no—
331C2×C4—182no—
332C2×C4—182no—
333C2×C4—181no—
334C2×C4—181no—
335C2×C4—181no—
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#567614yes—
345C2×C3#576214yes—
346C2×C3C2×D3×Q1614yes—
347D3—616no—
348C22—94no—
349C22—182no—
350C22—182no—
351C22C2×D4×C3⋊D311yescharacteristic
352C4—21no—
353C4—42no—
354C4—42no—
355C4—182no—
356C4—182no—
357C4—361no—
358C4—361no—
359C4—361no—
360C4Q16×C3⋊D312yes—
361C4#41×C3⋊D311yescharacteristic
362C4#6436611yescharacteristic
363C3#8161314yescomplemented
364C2—184no—
365C2#1059614711yescharacteristic
366C2#1059623311yescharacteristic
367C2C2×Q16×C3⋊D311yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#487C2
socleC22×C32C22×D4
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#487C3⋊D3
hypocenterC32#3299
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. C32×#487C2semidirect
4. #10592790C2semidirect
5. #10592789C2semidirect
6. #10592512C2semidirect
7. #10592510C2semidirect
8. #10592508C2semidirect
9. C3⋊D3×#103C2semidirect
10. C4×#3746C2semidirect
44. C3×#487D3semidirect
132. C4⋊(C3⋊D3)Q16semidirect
147. #487C3⋊D3semidirect
316. C32#3299semidirect
363. C3#81613semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105961982
C32×#4872
#105927902
#105927892
#105925122
#105925102
#105925082
C3⋊D3×#1032
C4×#37462
C8×C4⋊(C3⋊D3)2
#816133