Finite Group Databasebeta

← #11895823

Subgroups — #11895823

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
1C32×D4×Q8C211yesmaximal, characteristic, complemented
2#10596055C211yesmaximal, characteristic, complemented
3#10592792C211yesmaximal, characteristic, complemented
4#10592790C212yesmaximal, complemented
5#10592788C212yesmaximal, complemented
6#10592786C211yesmaximal, characteristic, complemented
7#10592723C211yesmaximal, characteristic, complemented
8#10592718C211yesmaximal, characteristic, complemented
9#10592717C212yesmaximal, complemented
10#10592715C212yesmaximal
11C4×#3753C211yesmaximal, characteristic
12#83563—34nomaximal
13C22×C32×Q8—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4⋊Q8C2212yes—
16C32×C22⋊Q8—21no—
17C32×C22⋊Q8—22no—
18C32×C4×Q8C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C32×C4×D4C2212yes—
21#64155—21no—
22C2×#3754C2212yes—
23C2×#3753C2211yescharacteristic
24#64107—22no—
25#64101—21no—
26#64084C2212yes—
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28#64078C2211yescharacteristic
29C4×#634C2212yes—
30#63659C2211yescharacteristic
31#63637C2212yes—
32#63637C2212yes—
33#63637C2212yes—
34#63636C2212yes—
35#63636C2211yescharacteristic
36#63634C2212yes—
37#63634C2211yescharacteristic
38C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
39C4⋊(C3⋊(C3⋊C8))C2212yes—
40#63630C2212yes—
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42C3×D4×Q8D314yescomplemented
43#5584—34no—
44#5093—34no—
45#5091—38no—
46#5089—38no—
47#5087—34no—
48#5024—34no—
49#5019—34no—
50#5018—38no—
51#5016—38no—
52C4×#213—34no—
53C2×C32×Q8—22no—
54C2×C32×Q8—21no—
55C2×C32×Q8—44no—
56C2×C32×Q8D411yescharacteristic
57C2×C32×D4C2311yescharacteristic
58C22×C32×C4—22no—
59C22×C32×C4—21no—
60C2×C4⋊(C3⋊D3)C2311yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×#634C2312yes—
63C32×C4⋊C4—22no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4D411yescharacteristic
66C32×C4⋊C4D412yes—
67C32×C4⋊C4C2312yes—
68C32×C4⋊C4C2311yescharacteristic
69C32×C22⋊C4—22no—
70C32×C22⋊C4—21no—
71C32×C42C2312yes—
72C32×C42C2311yescharacteristic
73#3754—24no—
74#3753—22no—
75#3752—21no—
76#3752—22no—
77#3752—22no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81#3750—22no—
82C4×C3⋊Dic3—22no—
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2312yes—
86#3367—91noSylow
87C22×C3×Q8—24no—
88C3×C4⋊Q8C2×D314yes—
89C3×C4⋊Q8C2×D318yes—
90C3×C22⋊Q8—24no—
91C3×C22⋊Q8—28no—
92C3×C4×Q8C2×D314yes—
93C3×C4×D4C2×D314yes—
94C3×C4×D4C2×D318yes—
95#946—64no—
96C2×#214—38no—
97C2×#213—34no—
98#898—68no—
99#892—64no—
100#875—38no—
101C4×D12—34no—
102#869—34no—
103C4×Dic6—38no—
104#832—34no—
105#810—38no—
106#810—38no—
107#810—38no—
108#809—34no—
109#809—38no—
110#807—34no—
111#807—38no—
112C4⋊(C3⋊C8)—38no—
113C4⋊(C3⋊C8)—34no—
114#803—38no—
115C4×C3⋊C8—34no—
116C23×C32—21no—
117C22×C3⋊D3—21no—
118C32×Q8—22no—
119C32×Q8—44no—
120C32×Q8—42no—
121C32×D4—21no—
122C32×D4#4112yes—
123C2×C32×C4—22no—
124C2×C32×C4—21no—
125C2×C32×C4—44no—
126C2×C32×C4—42no—
127C2×C32×C4C2×D412yes—
128C2×C32×C4C2×D412yes—
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2411yescharacteristic
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—22no—
134C4⋊(C3⋊D3)—21no—
135C4⋊(C3⋊D3)—21no—
136C4×C3⋊D3—42no—
137#634—22no—
138#634—22no—
139C3⋊(C3⋊C8)—21no—
140C3⋊(C3⋊C8)—22no—
141C3⋊(C3⋊C8)—21no—
142#556—91no—
143D4×Q8C3⋊D311yescharacteristic, complemented
144#489—92no—
145#487—91no—
146#477—92no—
147#474—91no—
148#463—92no—
149#461—91no—
150#446—91no—
151#440—92no—
152C4×D8—91no—
153C2×C3×Q8—28no—
154C2×C3×Q8—24no—
155C2×C3×Q8—416no—
156C2×C3×Q8#6714yes—
157C2×C3×D4C22×D314yes—
158C22×C3×C4—28no—
159C22×C3×C4—24no—
160C2×D12—34no—
161C2×C4×D3—64no—
162C2×Dic6—38no—
163C3×C4⋊C4—28no—
164C3×C4⋊C4—24no—
165C3×C4⋊C4#6714yes—
166C3×C4⋊C4#6718yes—
167C3×C4⋊C4C22×D314yes—
168C3×C4⋊C4C22×D318yes—
169C3×C22⋊C4—28no—
170C3×C22⋊C4—24no—
171C3×C42C22×D314yes—
172C3×C42C22×D318yes—
173#214—616no—
174#213—68no—
175(C2×D3)⋊C4—64no—
176(C2×D3)⋊C4—68no—
177(C2×D3)⋊C4—68no—
178C4⋊Dic3—34no—
179C4⋊Dic3—64no—
180C4⋊Dic3—64no—
181Dic3⋊C4—68no—
182C4×Dic3—68no—
183C2×C3⋊C8—34no—
184C2×C3⋊C8—34no—
185C2×C3⋊C8—38no—
186C22×C32—22no—
187C22×C32—41no—
188C22×C32—41no—
189C22×C32C22×D411yescharacteristic
190C2×C3⋊D3—41no—
191C2×C3⋊D3—41no—
192C2×C3⋊D3—41no—
193C32×C4—22no—
194C32×C4—22no—
195C32×C4—21no—
196C32×C4—42no—
197C32×C4—41no—
198C32×C4AGL(1,ℤ/8)12yes—
199C32×C4C2×#4111yescharacteristic
200C32×C42−1+411yescharacteristic
201C3⋊Dic3—42no—
202C3⋊Dic3—41no—
203C22×Q8—21no—
204C2×SD16—92no—
205C2×D8—91no—
206C4⋊Q8—91no—
207C4⋊Q8C2×C3⋊D311yescharacteristic
208C4⋊Q8C2×C3⋊D312yes—
209#126—182no—
210#124—92no—
211C22⋊Q8—21no—
212C22⋊Q8—22no—
213C22⋊Q8—181no—
214C4×Q8—92no—
215C4×Q8C2×C3⋊D311yescharacteristic
216C4×D4—91no—
217C4×D4C2×C3⋊D311yescharacteristic
218C4×D4C2×C3⋊D312yes—
219#117—181no—
220#107—91no—
221#107—92no—
222C4⋊C8—91no—
223C4⋊C8—92no—
224#103—92no—
225#103—92no—
226#103—92no—
227#102—91no—
228#102—91no—
229#102—92no—
230#97—92no—
231C4×C8—91no—
232C23×C3—24no—
233C22×D3—64no—
234C3×Q8—28no—
235C3×Q8—416no—
236C3×Q8—48no—
237C3×D4—24no—
238C3×D4#23918yes—
239C2×C3×C4—28no—
240C2×C3×C4—24no—
241C2×C3×C4—416no—
242C2×C3×C4—48no—
243C2×C3×C4C2×#6718yes—
244C2×C3×C4C2×#6718yes—
245C2×C3×C4C2×#6714yes—
246C2×C3×C4C2×#6714yes—
247C2×C3×C4C23×D314yes—
248C2×Dic3—64no—
249C2×Dic3—68no—
250D12—64no—
251D12—64no—
252C4×D3—128no—
253Dic6—68no—
254Dic6—68no—
255C3⋊C8—64no—
256C3⋊C8—68no—
257C3⋊C8—64no—
258C2×C32—42no—
259C2×C32#54811yescharacteristic
260C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
261C2×C32#57811yescharacteristic
262C3⋊D3—81no—
263C2×Q8—22no—
264C2×Q8—21no—
265C2×Q8—44no—
266C2×Q8—92no—
267C2×Q8#63811yescharacteristic
268C2×D4—91no—
269C2×D4C22×C3⋊D311yescharacteristic
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—181no—
273SD16—184no—
274D8—182no—
275C2×C8—91no—
276C2×C8—91no—
277C2×C8—92no—
278C4⋊C4—22no—
279C4⋊C4—21no—
280C4⋊C4—91no—
281C4⋊C4—181no—
282C4⋊C4—182no—
283C4⋊C4—181no—
284C4⋊C4#63811yescharacteristic
285C4⋊C4#63812yes—
286C4⋊C4C22×C3⋊D311yescharacteristic
287C4⋊C4C22×C3⋊D312yes—
288C22⋊C4—22no—
289C22⋊C4—21no—
290C22⋊C4—182no—
291C22⋊C4—181no—
292C22⋊C4—182no—
293C42—182no—
294C42C22×C3⋊D311yescharacteristic
295C42C22×C3⋊D312yes—
296C22×C3—28no—
297C22×C3—44no—
298C22×C3—44no—
299C22×C3C22×#6714yes—
300C2×D3—124no—
301C2×D3—124no—
302C2×D3—124no—
303C3×C4—28no—
304C3×C4—28no—
305C3×C4—24no—
306C3×C4—48no—
307C3×C4—44no—
308C3×C4#93218yes—
309C3×C4C2×#23914yes—
310C3×C4#100714yes—
311Dic3—124no—
312Dic3—128no—
313C32#336711yescharacteristic, complemented, Sylow
314C23—21no—
315C23—181no—
316Q8—22no—
317Q8—44no—
318Q8—42no—
319Q8—182no—
320Q8—182no—
321D4—21no—
322D4—181no—
323D4—181no—
324D4#383212yes—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—44no—
328C2×C4—42no—
329C2×C4—181no—
330C2×C4—182no—
331C2×C4—362no—
332C2×C4C2×#63812yes—
333C2×C4C2×#63811yescharacteristic
334C2×C4C2×#63812yes—
335C2×C4C2×#63811yescharacteristic
336C2×C4C23×C3⋊D311yescharacteristic
337C8—181no—
338C8—182no—
339C8—181no—
340C2×C3—48no—
341C2×C3C2×#93214yes—
342C2×C3#581714yes—
343C2×C3#583814yes—
344D3—244no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—361no—
349C22—361no—
350C22—361no—
351C22C22×#63811yescharacteristic
352C4—22no—
353C4—22no—
354C4—21no—
355C4—42no—
356C4—41no—
357C4—361no—
358C4—362no—
359C4#6414112yes—
360C4C2×#383211yescharacteristic
361C4#6436411yescharacteristic
362C3#8356314yescomplemented
363C2—42no—
364C2—721no—
365C2C2×#6414111yescharacteristic
366C2#1059628811yescharacteristic
367C2#1059630911yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×D4×Q8C2
socleC22×C32C22×D4
prime radicalC2×#3753C22
hypercenterD4×Q8C3⋊D3
hypocenterC32#3367
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. C32×D4×Q8C2semidirect
2. #10596055C2semidirect
3. #10592792C2semidirect
4. #10592790C2semidirect
5. #10592788C2semidirect
6. #10592786C2semidirect
7. #10592723C2semidirect
8. #10592718C2semidirect
9. #10592717C2semidirect
42. C3×D4×Q8D3semidirect
143. D4×Q8C3⋊D3semidirect
313. C32#3367semidirect
362. C3#83563semidirect

Maximal subgroups

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

subgroupindex
C32×D4×Q82
#105960552
#105927922
#105927902
#105927882
#105927862
#105927232
#105927182
#105927172
#105927152
C4×#37532
#835633