Finite Group Databasebeta

← #11895829

Subgroups — #11895829

Order 1152.

1116 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#10596055C211yesmaximal, characteristic, complemented
2Q8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
3C32×#446C211yesmaximal, characteristic, complemented
4#10592549C212yesmaximal, complemented
5#10592545C211yesmaximal, characteristic, complemented
6#10592543C212yesmaximal
7#10592540C211yesmaximal, characteristic, complemented
8#10592413C212yesmaximal, complemented
9#10592409C212yesmaximal, complemented
10C4×#3745C211yesmaximal, characteristic
11#10592380C211yesmaximal, characteristic, complemented
12#79970—34nomaximal
13C2×Q8×C3⋊D3—21no—
14C32×C4×Q8C2211yescharacteristic
15#64155—21no—
16C2×#3745C2211yescharacteristic
17C2×#3744C2212yes—
18#64107—22no—
19#64106—21no—
20#64106—22no—
21#64101—21no—
22#64084C2212yes—
23C4×C4⋊(C3⋊D3)C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2212yes—
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26#64078C2211yescharacteristic
27#64078C2211yescharacteristic
28#64078C2212yes—
29C4×#634C2212yes—
30C32×C4⋊C8C2211yescharacteristic
31C32×C4⋊C8C2212yes—
32C32×#97C2212yes—
33C32×C4×C8C2211yescharacteristic
34#63648C2212yes—
35#63648C2211yescharacteristic
36#63648C2211yescharacteristic
37#63645C2212yes—
38#63645C2211yescharacteristic
39#63643C2212yes—
40#63643C2212yes—
41#63643C2212yes—
42#5584—34no—
43Q8×D12—34no—
44C3×#446D314yescomplemented
45#4850—38no—
46#4846—34no—
47#4844—38no—
48#4841—34no—
49#4714—38no—
50#4710—38no—
51C4×D24—34no—
52#4681—34no—
53C2×C32×Q8D411yescharacteristic
54Q8×C3⋊D3—44no—
55C2×C4⋊(C3⋊D3)C2311yescharacteristic
56C2×C4⋊(C3⋊D3)C2311yescharacteristic
57C2×C4×C3⋊D3—21no—
58C2×C4×C3⋊D3—22no—
59C2×C4×C3⋊D3—21no—
60C2×#634—22no—
61C2×#634—21no—
62C2×#634C2312yes—
63C2×C32×C8C2312yes—
64C2×C32×C8C2311yescharacteristic
65C2×C32×C8C2311yescharacteristic
66C32×C4⋊C4D411yescharacteristic
67C32×C4⋊C4D412yes—
68C32×C42C2312yes—
69C32×C42C2311yescharacteristic
70#3752—22no—
71#3752—21no—
72#3752—21no—
73#3752—22no—
74#3752—22no—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)—22no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2312yes—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—22no—
83C4×C3⋊Dic3—22no—
84#3745—22no—
85#3744—24no—
86#3367—91noSylow
87C2×D3×Q8—64no—
88C3×C4×Q8C2×D314yes—
89#946—64no—
90C2×D24—34no—
91C2×#204—38no—
92#898—68no—
93#897—64no—
94#897—68no—
95#892—64no—
96#875—38no—
97C4×D12—34no—
98C4×D12—34no—
99C4×D12—38no—
100#869—34no—
101#869—38no—
102#869—34no—
103C4×Dic6—38no—
104C3×C4⋊C8C2×D314yes—
105C3×C4⋊C8C2×D318yes—
106C3×#97C2×D318yes—
107C3×C4×C8C2×D314yes—
108#821—34no—
109#821—34no—
110#821—38no—
111#818—34no—
112#818—38no—
113#816—38no—
114#816—38no—
115#816—38no—
116C22×C3⋊D3—21no—
117C22×C3⋊D3—21no—
118C32×Q8—22no—
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2×D412yes—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2411yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—22no—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)—21no—
130C4⋊(C3⋊D3)—21no—
131C4⋊(C3⋊D3)#4112yes—
132C4×C3⋊D3—44no—
133C4×C3⋊D3—42no—
134C4×C3⋊D3—42no—
135#634—22no—
136#634—22no—
137#634—44no—
138#634—42no—
139C32×C8—22no—
140C32×C8—21no—
141C32×C8—21no—
142#556—91no—
143D4×Q8—91no—
144#489—92no—
145#487—91no—
146#477—92no—
147#474—91no—
148#463—92no—
149#461—91no—
150#446C3⋊D311yescharacteristic, complemented
151#440—92no—
152C4×D8—91no—
153C2×C3×Q8D1214yes—
154D3×Q8—1216no—
155C2×D12—34no—
156C2×D12—34no—
157C2×C4×D3—64no—
158C2×C4×D3—68no—
159C2×C4×D3—64no—
160C2×Dic6—38no—
161C2×Dic6—68no—
162C2×Dic6—64no—
163C2×C3×C8C22×D314yes—
164C2×C3×C8C22×D314yes—
165C2×C3×C8C22×D318yes—
166C3×C4⋊C4D1214yes—
167C3×C4⋊C4D1218yes—
168C3×C42C22×D314yes—
169C3×C42C22×D318yes—
170(C2×D3)⋊C4—68no—
171(C2×D3)⋊C4—64no—
172(C2×D3)⋊C4—64no—
173(C2×D3)⋊C4—68no—
174(C2×D3)⋊C4—68no—
175C4⋊Dic3—38no—
176C4⋊Dic3—34no—
177C4⋊Dic3—34no—
178C4⋊Dic3—64no—
179C4⋊Dic3—68no—
180C4⋊Dic3—64no—
181C4⋊Dic3—64no—
182Dic3⋊C4—68no—
183C4×Dic3—68no—
184D24—68no—
185#204—616no—
186C22×C32C22×D411yescharacteristic
187C2×C3⋊D3—22no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3—41no—
190C2×C3⋊D3—41no—
191C2×C3⋊D3—41no—
192C2×C3⋊D3—41no—
193C32×C4—22no—
194C32×C4—22no—
195C32×C4—21no—
196C32×C4AGL(1,ℤ/8)12yes—
197C32×C4C2×#4111yescharacteristic
198C32×C42−1+411yescharacteristic
199C3⋊Dic3—42no—
200C3⋊Dic3—41no—
201C3⋊Dic3—42no—
202C3⋊Dic3—41no—
203C22×Q8—181no—
204C2×SD16—92no—
205C2×D8—91no—
206C4⋊Q8—91no—
207C4⋊Q8—92no—
208C4⋊Q8—91no—
209#126—182no—
210#124—92no—
211C22⋊Q8—181no—
212C22⋊Q8—181no—
213C22⋊Q8—182no—
214C4×Q8—92no—
215C4×Q8C2×C3⋊D311yescharacteristic
216C4×D4—91no—
217C4×D4—92no—
218C4×D4—91no—
219#117—181no—
220#107—91no—
221#107—92no—
222C4⋊C8C2×C3⋊D311yescharacteristic
223C4⋊C8C2×C3⋊D312yes—
224#103—92no—
225#103—92no—
226#103—92no—
227#102—91no—
228#102—91no—
229#102—92no—
230#97C2×C3⋊D312yes—
231C4×C8C2×C3⋊D311yescharacteristic
232C22×D3—64no—
233C22×D3—64no—
234C3×Q8—28no—
235C2×C3×C4C2×D1218yes—
236C2×C3×C4C2×D1218yes—
237C2×C3×C4C2×D1214yes—
238C2×C3×C4C2×D1214yes—
239C2×C3×C4C23×D314yes—
240C2×Dic3—64no—
241C2×Dic3—68no—
242C2×Dic3—64no—
243C2×Dic3—68no—
244D12—38no—
245D12—64no—
246D12—64no—
247D12—64no—
248C4×D3—1216no—
249C4×D3—128no—
250C4×D3—128no—
251Dic6—68no—
252Dic6—68no—
253Dic6—1216no—
254Dic6—128no—
255C3×C8—24no—
256C3×C8—28no—
257C3×C8—24no—
258C2×C32#54811yescharacteristic
259C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
260C2×C32#57811yescharacteristic
261C3⋊D3—42no—
262C3⋊D3—81no—
263C2×Q8—92no—
264C2×Q8—182no—
265C2×Q8—181no—
266C2×Q8—364no—
267C2×Q8C4⋊(C3⋊D3)11yescharacteristic
268C2×D4—91no—
269C2×D4—91no—
270C22×C4—181no—
271C22×C4—182no—
272C22×C4—181no—
273SD16—184no—
274D8—182no—
275C2×C8C22×C3⋊D311yescharacteristic
276C2×C8C22×C3⋊D311yescharacteristic
277C2×C8C22×C3⋊D312yes—
278C4⋊C4—91no—
279C4⋊C4—92no—
280C4⋊C4—91no—
281C4⋊C4—181no—
282C4⋊C4—182no—
283C4⋊C4—182no—
284C4⋊C4—181no—
285C4⋊C4—181no—
286C4⋊C4C4⋊(C3⋊D3)11yescharacteristic
287C4⋊C4C4⋊(C3⋊D3)12yes—
288C22⋊C4—182no—
289C22⋊C4—182no—
290C22⋊C4—181no—
291C22⋊C4—181no—
292C22⋊C4—182no—
293C42—182no—
294C42C22×C3⋊D311yescharacteristic
295C42C22×C3⋊D312yes—
296C22×C3C22×D1214yes—
297C2×D3—68no—
298C2×D3—124no—
299C2×D3—124no—
300C2×D3—124no—
301C2×D3—124no—
302C2×D3—124no—
303C3×C4—28no—
304C3×C4—28no—
305C3×C4—24no—
306C3×C4#90818yes—
307C3×C4#100714yes—
308C3×C4D3×#4114yes—
309Dic3—124no—
310Dic3—128no—
311Dic3—124no—
312Dic3—128no—
313C32#336711yescharacteristic, complemented, Sylow
314C23—181no—
315C23—181no—
316Q8—22no—
317Q8—182no—
318Q8—182no—
319Q8—364no—
320Q8—362no—
321D4—92no—
322D4—181no—
323D4—181no—
324D4—181no—
325C2×C4—181no—
326C2×C4—182no—
327C2×C4—182no—
328C2×C4—181no—
329C2×C4—364no—
330C2×C4—362no—
331C2×C4—362no—
332C2×C4C2×C4⋊(C3⋊D3)12yes—
333C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
334C2×C4C2×C4⋊(C3⋊D3)12yes—
335C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
336C2×C4C23×C3⋊D311yescharacteristic
337C8—21no—
338C8—21no—
339C8—22no—
340C2×C3#557614yes—
341C2×C3C2×#90814yes—
342C2×C3#575314yes—
343D3—128no—
344D3—244no—
345C22—182no—
346C22—361no—
347C22—361no—
348C22—361no—
349C22—361no—
350C22—361no—
351C22C22×C4⋊(C3⋊D3)11yescharacteristic
352C4—22no—
353C4—22no—
354C4—21no—
355C4—362no—
356C4—361no—
357C4—361no—
358C4—362no—
359C4#6411712yes—
360C4#6436411yescharacteristic
361C4#41×C3⋊D311yescharacteristic
362C3#7997014yescomplemented
363C2—362no—
364C2—721no—
365C2#1059604711yescharacteristic
366C2C2×#6411711yescharacteristic
367C2#1059622411yescharacteristic
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#446C2
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenter#446C3⋊D3
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #446

Complements

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

NH ≅ G/Ntype
1. #10596055C2semidirect
2. Q8×C4⋊(C3⋊D3)C2semidirect
3. C32×#446C2semidirect
4. #10592549C2semidirect
5. #10592545C2semidirect
7. #10592540C2semidirect
8. #10592413C2semidirect
9. #10592409C2semidirect
11. #10592380C2semidirect
44. C3×#446D3semidirect
150. #446C3⋊D3semidirect
313. C32#3367semidirect
362. C3#79970semidirect

Maximal subgroups

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

subgroupindex
#105960552
Q8×C4⋊(C3⋊D3)2
C32×#4462
#105925492
#105925452
#105925432
#105925402
#105924132
#105924092
C4×#37452
#105923802
#799703