Finite Group Databasebeta

← #11897533

Subgroups — #11897533

Order 1152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596201C211yesmaximal, characteristic, complemented
2#10596198C211yesmaximal, characteristic, complemented
3C32×#498C211yesmaximal, characteristic, complemented
4#10592786C211yesmaximal, characteristic, complemented
5#10592783C211yesmaximal, characteristic, complemented
6#10592570C212yesmaximal, complemented
7#10592569C212yesmaximal, complemented
8#10592568C212yesmaximal
9#10592555C212yesmaximal, complemented
10C4×#3745C211yesmaximal, characteristic
11#10592378C211yesmaximal, characteristic, complemented
12#81905—34nomaximal
13C2×Q8×C3⋊D3—21no—
14C32×C4⋊Q8C2211yescharacteristic
15C32×C4⋊Q8C2211yescharacteristic
16#64155—21no—
17#64155—22no—
18C2×#3745C2211yescharacteristic
19#64106—21no—
20#64105—22no—
21#64102C2212yes—
22#64102C2212yes—
23C4⋊C4×C3⋊D3—21no—
24#64099C2212yes—
25#64097C2212yes—
26C4×C4⋊(C3⋊D3)C2211yescharacteristic
27C4×C4⋊(C3⋊D3)C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C32×#106C2212yes—
30C32×#106C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2211yescharacteristic
33#63648C2211yescharacteristic
34#63645C2211yescharacteristic
35#63642C2212yes—
36#63641C2212yes—
37#63636C2212yes—
38#63636C2212yes—
39#63635C2212yes—
40#63634C2212yes—
41C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
42#5730—34no—
43#5727—34no—
44C3×#498D314yescomplemented
45#5087—34no—
46#5084—34no—
47#4871—38no—
48#4870—38no—
49#4869—38no—
50#4856—38no—
51C4×D24—34no—
52#4679—34no—
53C2×C32×Q8—21no—
54C2×C32×Q8—21no—
55Q8×C3⋊D3—44no—
56C2×C4⋊(C3⋊D3)C2311yescharacteristic
57C2×C4⋊(C3⋊D3)C2311yescharacteristic
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3—22no—
61C2×C4×C3⋊D3—22no—
62C2×#634—22no—
63C2×#634D411yescharacteristic
64C2×C32×C8C2311yescharacteristic
65C2×C32×C8C2311yescharacteristic
66C32×C4⋊C4—21no—
67C32×C4⋊C4—21no—
68C32×C4⋊C4C2312yes—
69C32×C4⋊C4C2312yes—
70C32×C42C2311yescharacteristic
71#3752—21no—
72#3752—21no—
73#3752—22no—
74#3752—22no—
75C4⋊(C3⋊Dic3)—22no—
76C4⋊(C3⋊Dic3)D411yescharacteristic
77C4⋊(C3⋊Dic3)C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—22no—
80#3750—22no—
81#3750D412yes—
82C4×C3⋊Dic3C2312yes—
83C2×C3⋊(C3⋊C8)C2312yes—
84#3745Q814yescomplemented
85#3384—91noSylow
86C2×D3×Q8—64no—
87C3×C4⋊Q8C2×D314yes—
88C3×C4⋊Q8C2×D314yes—
89#946—68no—
90#946—64no—
91C2×D24—34no—
92#897—64no—
93#896—68no—
94#893—38no—
95#893—38no—
96D3×C4⋊C4—64no—
97#890—38no—
98#888—38no—
99C4×D12—34no—
100C4×D12—34no—
101C4×Dic6—34no—
102C3×#106C2×D318yes—
103C3×#106C2×D318yes—
104C3×C4×C8C2×D314yes—
105#821—34no—
106#821—34no—
107#818—34no—
108#815—38no—
109Dic3⋊C8—38no—
110#809—38no—
111#809—38no—
112#808—38no—
113#807—38no—
114C4⋊(C3⋊C8)—34no—
115C22×C3⋊D3—21no—
116C22×C3⋊D3—21no—
117C32×Q8—42no—
118C32×Q8—81no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2411yescharacteristic
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3C2×D412yes—
127C2×C3⋊Dic3C2×D412yes—
128C4⋊(C3⋊D3)—21no—
129C4⋊(C3⋊D3)—21no—
130C4⋊(C3⋊D3)C2×Q812yes—
131C4⋊(C3⋊D3)C2×Q812yescomplemented
132C4×C3⋊D3—44no—
133C4×C3⋊D3—42no—
134C4×C3⋊D3—42no—
135C4×C3⋊D3—82no—
136#634—22no—
137#634—44no—
138C32×C8—21no—
139C32×C8C2×Q812yescomplemented
140C3⋊(C3⋊C8)—22no—
141#554—91no—
142D4×Q8—91no—
143#501—92no—
144#498C3⋊D311yescharacteristic, complemented
145#478—92no—
146#476—91no—
147#476—92no—
148#474—91no—
149#446—91no—
150#442—92no—
151C4×D8—91no—
152C2×C3×Q8—24no—
153C2×C3×Q8—24no—
154D3×Q8—1216no—
155C2×D12—34no—
156C2×D12—34no—
157C2×C4×D3—68no—
158C2×C4×D3—64no—
159C2×C4×D3—64no—
160C2×C4×D3—68no—
161C2×Dic6—34no—
162C2×Dic6—68no—
163C2×C3×C8C22×D314yes—
164C2×C3×C8C22×D314yes—
165C3×C4⋊C4—24no—
166C3×C4⋊C4—24no—
167C3×C4⋊C4C22×D318yes—
168C3×C4⋊C4C22×D318yes—
169C3×C42C22×D314yes—
170(C2×D3)⋊C4—68no—
171(C2×D3)⋊C4—68no—
172(C2×D3)⋊C4—64no—
173(C2×D3)⋊C4—64no—
174C4⋊Dic3—34no—
175C4⋊Dic3—34no—
176C4⋊Dic3—34no—
177C4⋊Dic3—68no—
178Dic3⋊C4—38no—
179Dic3⋊C4—68no—
180Dic3⋊C4—68no—
181C4×Dic3—38no—
182C2×C3⋊C8—38no—
183D24—316no—
184C22×C32C22×D411yescharacteristic
185C2×C3⋊D3—22no—
186C2×C3⋊D3—22no—
187C2×C3⋊D3—41no—
188C2×C3⋊D3—41no—
189C2×C3⋊D3—41no—
190C2×C3⋊D3—41no—
191C32×C4—21no—
192C32×C4—42no—
193C32×C4—42no—
194C32×C4AGL(1,ℤ/8)12yes—
195C32×C4C22×Q811yescharacteristic
196C32×C42−1+411yescharacteristic
197C3⋊Dic3—22no—
198C3⋊Dic3—22no—
199C3⋊Dic3—41no—
200C3⋊Dic3—41no—
201C22×Q8—181no—
202C2×D8—91no—
203C4⋊Q8—92no—
204C4⋊Q8C2×C3⋊D311yescharacteristic
205C4⋊Q8C2×C3⋊D311yescharacteristic
206#125—92no—
207C22⋊Q8—182no—
208C22⋊Q8—181no—
209C22⋊Q8—181no—
210C22⋊Q8—182no—
211C4×Q8—91no—
212C4×D4—92no—
213C4×D4—92no—
214C4×D4—91no—
215C4×D4—91no—
216C2×C4⋊C4—181no—
217#107—91no—
218#107—92no—
219#106—92no—
220#106C2×C3⋊D312yes—
221#106C2×C3⋊D312yes—
222C4⋊C8—92no—
223C4⋊C8—91no—
224#102—91no—
225#102—91no—
226#102—92no—
227#102—92no—
228#97—92no—
229C4×C8C2×C3⋊D311yescharacteristic
230C22×D3—64no—
231C22×D3—64no—
232C3×Q8—48no—
233C3×Q8—84no—
234C2×C3×C4—28no—
235C2×C3×C4—28no—
236C2×C3×C4D3×D414yes—
237C2×C3×C4D3×D414yes—
238C2×C3×C4C23×D314yes—
239C2×Dic3—38no—
240C2×Dic3—38no—
241C2×Dic3—64no—
242C2×Dic3—64no—
243D12—38no—
244D12—38no—
245D12—64no—
246D12—64no—
247C4×D3—1216no—
248C4×D3—128no—
249C4×D3—128no—
250C4×D3—248no—
251Dic6—68no—
252Dic6—1216no—
253C3×C8—24no—
254C3×C8D3×Q818yescomplemented
255C3⋊C8—68no—
256C2×C32D4×Q811yescharacteristic
257C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
258C2×C32#57711yescharacteristic
259C3⋊D3—42no—
260C3⋊D3—42no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—91no—
264C2×Q8—182no—
265C2×Q8—364no—
266C2×D4—91no—
267C2×D4—91no—
268C22×C4—182no—
269C22×C4—182no—
270C22×C4—181no—
271C22×C4—181no—
272D8—94no—
273C2×C8—92no—
274C2×C8C22×C3⋊D311yescharacteristic
275C2×C8C22×C3⋊D311yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—91no—
279C4⋊C4—92no—
280C4⋊C4—91no—
281C4⋊C4—91no—
282C4⋊C4—182no—
283C4⋊C4—182no—
284C4⋊C4—182no—
285C4⋊C4C22×C3⋊D312yes—
286C4⋊C4C22×C3⋊D312yes—
287C22⋊C4—182no—
288C22⋊C4—182no—
289C22⋊C4—181no—
290C22⋊C4—181no—
291C42—92no—
292C42C22×C3⋊D311yescharacteristic
293C22×C3C2×D3×D414yes—
294C2×D3—68no—
295C2×D3—68no—
296C2×D3—124no—
297C2×D3—124no—
298C2×D3—124no—
299C2×D3—124no—
300C3×C4—24no—
301C3×C4—48no—
302C3×C4—48no—
303C3×C4#91418yes—
304C3×C4C2×D3×Q814yes—
305C3×C4#100714yes—
306Dic3—68no—
307Dic3—68no—
308Dic3—124no—
309Dic3—124no—
310C32#338411yescharacteristic, complemented, Sylow
311C23—181no—
312C23—181no—
313Q8—42no—
314Q8—81no—
315Q8—182no—
316Q8—364no—
317D4—92no—
318D4—92no—
319D4—181no—
320D4—181no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—92no—
324C2×C4—92no—
325C2×C4—181no—
326C2×C4—181no—
327C2×C4—364no—
328C2×C4—362no—
329C2×C4—362no—
330C2×C4—722no—
331C2×C4D4×C3⋊D311yescharacteristic
332C2×C4D4×C3⋊D311yescharacteristic
333C2×C4C23×C3⋊D311yescharacteristic
334C8—21no—
335C8—182no—
336C8Q8×C3⋊D312yescomplemented
337C2×C3#572714yes—
338C2×C3C2×#91414yes—
339C2×C3#576214yes—
340D3—128no—
341D3—128no—
342C22—182no—
343C22—182no—
344C22—361no—
345C22—361no—
346C22—361no—
347C22—361no—
348C22C2×D4×C3⋊D311yescharacteristic
349C4—21no—
350C4—42no—
351C4—42no—
352C4—182no—
353C4—182no—
354C4—361no—
355C4—361no—
356C4#6412312yes—
357C4C2×Q8×C3⋊D311yescharacteristic
358C4#6436411yescharacteristic
359C3#8190514yescomplemented
360C2—362no—
361C2—362no—
362C2#1059619811yescharacteristic
363C2C2×#6412311yescharacteristic
364C2#1059623311yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#498C2
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenter#498C3⋊D3
hypocenterC32#3384
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
2. #10596198C2semidirect
3. C32×#498C2semidirect
4. #10592786C2semidirect
5. #10592783C2semidirect
6. #10592570C2semidirect
7. #10592569C2semidirect
9. #10592555C2semidirect
11. #10592378C2semidirect
44. C3×#498D3semidirect
84. #3745Q8semidirect
131. C4⋊(C3⋊D3)C2×Q8semidirect
139. C32×C8C2×Q8semidirect
144. #498C3⋊D3semidirect
254. C3×C8D3×Q8semidirect
310. C32#3384semidirect
336. C8Q8×C3⋊D3semidirect
359. C3#81905semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105961982
C32×#4982
#105927862
#105927832
#105925702
#105925692
#105925682
#105925552
C4×#37452
#105923782
#819053