Finite Group Databasebeta

← #11861117

Subgroups — #11861117

Order 1152.

977 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594786C211yesmaximal, characteristic
2C2×#63815C212yesmaximal, complemented
3#10592696C211yesmaximal, characteristic, complemented
4C3×#5005C212yesmaximal, complemented
5#10591143C211yesmaximal, characteristic, complemented
6#10590390C214yesmaximal, complemented
7#10590389C214yesmaximal, complemented
8#78989—32nomaximal
9C2×C3×#235C2212yes—
10C32×#117C2211yescharacteristic
11C2×#3748C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×#208C2212yes—
14#63827C414yescomplemented
15#63823C414yescomplemented
16#63822C2214yes—
17C2×#3711—22no—
18#63815—22no—
19#63815—22no—
20#63815C2214yescomplemented
21#63815C2214yescomplemented
22C2×D3×C3⋊C8—22no—
23#63630C2212yescomplemented
24C4×C3⋊(C3⋊C8)C2212yescomplemented
25C3×#805C2218yescomplemented
26#63578C2214yescomplemented
27#5822—32no—
28C2×#948—32no—
29C2×#907—32no—
30C3×#421—32no—
31#5124—32no—
32#5005D312yescomplemented
33#4997—32no—
34#4997—61no—
35#4824—38no—
36#4823—38no—
37C22×C32×C4C2311yescharacteristic
38C2×C3×#67—22no—
39C3×#235—22no—
40C3×#235—22no—
41C3×#235C2×C414yes—
42C3×#235C2314yes—
43C2×C3×D12C2×C412yes—
44C2×C3×C4×D3—22no—
45C2×C3×Dic6C2×C412yes—
46C32×C4⋊C4—21no—
47C32×C22⋊C4—21no—
48C32×C42C2312yes—
49#3748C2×C414yes—
50C2×C3⋊(C3⋊C8)D412yes—
51C2×C3⋊(C3⋊C8)D412yes—
52C2×C3⋊(C3⋊C8)C2312yes—
53C2×C3⋊(C3⋊C8)C2311yescharacteristic
54C2×C3⋊(C3⋊C8)C2311yescharacteristic
55C3×#208—22no—
56C3×#208C2314yes—
57C2×C3×C3⋊C8—22no—
58#3718C2×C414yes—
59#3715C2×C418yes—
60#3713C2×C414yes—
61#3711—24no—
62#3711—24no—
63D3×C3⋊C8—24no—
64D3×C3⋊C8—24no—
65#2955—91noSylow
66C2×C3×#41—32no—
67C2×#235C2×D312yes—
68C2×C3×M16—32no—
69C3×#117—21no—
70C3×#117C2×D312yes—
71#951—34no—
72#950—38no—
73#949—34no—
74#948—34no—
75#948—34no—
76#948—62no—
77#948—62no—
78#942—34no—
79#932—34no—
80C2×#208—32no—
81C2×#208—61no—
82C2×#208—62no—
83C2×#208C2×D312yes—
84C22×C3⋊C8—32no—
85C22×C3⋊C8—61no—
86C22×C3⋊C8—62no—
87#907—34no—
88#907—34no—
89#907—62no—
90#907—62no—
91C2×ΓL(1,𝔽25)—62no—
92C2×D3×C8—62no—
93C3×#104—38no—
94#822—38no—
95#805C2×D318yescomplemented
96#803—34no—
97#803—62no—
98C4×C3⋊C8—34no—
99C4×C3⋊C8—62no—
100C23×C32#4111yescharacteristic
101C22×C3×D3—22no—
102C2×C32×C4—22no—
103C2×C32×C4C22×C412yes—
104C2×C32×C4C2×D412yes—
105C2×C32×C4#4111yescharacteristic
106C2×C32×C4C2411yescharacteristic
107C3×#67—24no—
108C3×#67—24no—
109C2×C3×Dic3—22no—
110C3×D12—22no—
111C3×D12C22×C414yes—
112C3×C4×D3—24no—
113C3×C4×D3—24no—
114C3×Dic6—22no—
115C3×Dic6C22×C414yes—
116C3⋊(C3⋊C8)C22×C414yes—
117C3⋊(C3⋊C8)C2×D411yescharacteristic
118C3⋊(C3⋊C8)C2×D412yes—
119C3⋊(C3⋊C8)C2×D411yescharacteristic
120C3×C3⋊C8—24no—
121#575—91no—
122C2×#131—92no—
123#444—94no—
124#443—94no—
125#430—91no—
126#421—32no—
127#405—91no—
128C3×#41—34no—
129C3×#41—34no—
130C3×#41—62no—
131C3×#41—62no—
132C2×C3×Q8—32no—
133C2×C3×D4—32no—
134C2×C3×D4—62no—
135C22×C3×C4—21no—
136C22×C3×C4—62no—
137C22×C3×C4C22×D312yes—
138C2×#67—22no—
139#235—22no—
140#235—22no—
141#235C4×D314yes—
142#235C22×D314yes—
143C2×D12C4×D312yes—
144C2×C4×D3—22no—
145C2×Dic6C4×D312yes—
146C3×M16—34no—
147C3×M16—62no—
148C2×C3×C8—62no—
149C3×C4⋊C4—22no—
150C3×C4⋊C4—22no—
151C3×C22⋊C4—22no—
152C3×C22⋊C4—22no—
153C3×C42—22no—
154C3×C42C22×D314yes—
155#216—38no—
156#215—38no—
157#214—38no—
158#213—38no—
159#208—22no—
160#208—34no—
161#208—34no—
162#208—64no—
163#208—64no—
164#208—64no—
165#208C22×D314yes—
166C2×C3⋊C8—22no—
167C2×C3⋊C8—32no—
168C2×C3⋊C8—32no—
169C2×C3⋊C8—32no—
170C2×C3⋊C8—32no—
171C2×C3⋊C8—32no—
172C2×C3⋊C8—34no—
173C2×C3⋊C8—32no—
174C2×C3⋊C8—61no—
175C2×C3⋊C8—62no—
176C2×C3⋊C8—61no—
177C2×C3⋊C8—62no—
178C2×C3⋊C8—62no—
179C2×C3⋊C8—64no—
180C2×C3⋊C8—64no—
181ΓL(1,𝔽25)—64no—
182ΓL(1,𝔽25)—64no—
183D3×C8—64no—
184D3×C8—64no—
185C22×C32—41no—
186C22×C32C4×D412yes—
187C22×C32C2×#4111yescharacteristic
188C2×C3×D3—24no—
189C2×C3×D3—44no—
190C32×C4—42no—
191C32×C4C4×D412yes—
192C32×C4C23×C411yescharacteristic
193C32×C4C22×D411yescharacteristic
194C3×Dic3—24no—
195C2×#41—32no—
196#137—94no—
197AGL(1,ℤ/8)—94no—
198#135—94no—
199#131—94no—
200#131—94no—
201#131—182no—
202#131—182no—
203C2×M16—32no—
204C2×M16—91no—
205C2×M16—182no—
206C22×C8—91no—
207C22×C8—182no—
208#117D3211yescharacteristic
209#108—94no—
210#104—38no—
211#97—92no—
212C4×C8—92no—
213C23×C3—21no—
214C23×C3—62no—
215C23×C3#23712yes—
216C22×D3—22no—
217C3×Q8—34no—
218C3×Q8—62no—
219C3×D4—34no—
220C3×D4—64no—
221C3×D4—64no—
222C3×D4—62no—
223C2×C3×C4—24no—
224C2×C3×C4—24no—
225C2×C3×C4—21no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—21no—
229C2×C3×C4—62no—
230C2×C3×C4—64no—
231C2×C3×C4—64no—
232C2×C3×C4C2×C4×D312yes—
233C2×C3×C4C2×C4×D312yes—
234C2×C3×C4D3×D412yes—
235C2×C3×C4D3×D412yes—
236C2×C3×C4#23712yes—
237C2×C3×C4C23×D312yes—
238#67—24no—
239#67—24no—
240C2×Dic3—22no—
241D12—22no—
242D12C2×C4×D314yes—
243C4×D3—24no—
244C4×D3—24no—
245Dic6—22no—
246Dic6C2×C4×D314yes—
247C3×C8—64no—
248C3⋊C8—24no—
249C3⋊C8—38no—
250C3⋊C8—32no—
251C3⋊C8—32no—
252C3⋊C8—32no—
253C3⋊C8—32no—
254C3⋊C8—64no—
255C3⋊C8—61no—
256C3⋊C8—62no—
257C3⋊C8—61no—
258C2×C32—21no—
259C2×C32—22no—
260C2×C32C2×C4×D411yescharacteristic
261C3×D3—44no—
262#41—34no—
263#41—34no—
264#41—62no—
265#41—62no—
266C2×Q8—32no—
267C2×D4—32no—
268C2×D4—62no—
269C22×C4—62no—
270C22×C4C2×D3211yescharacteristic
271Q16—94no—
272SD16—98no—
273D8—94no—
274M16—34no—
275M16—62no—
276M16—94no—
277M16—184no—
278M16—184no—
279C2×C8—62no—
280C2×C8—91no—
281C2×C8—92no—
282C2×C8—91no—
283C2×C8—92no—
284C2×C8—92no—
285C2×C8—184no—
286C2×C8—184no—
287C4⋊C4—21no—
288C22⋊C4—21no—
289C42C2×D3212yes—
290C22×C3—21no—
291C22×C3—22no—
292C22×C3—42no—
293C22×C3—42no—
294C22×C3—64no—
295C22×C3—124no—
296C22×C3#67⋊C412yes—
297C22×C3#67⋊C412yes—
298C22×C3C2×#23712yes—
299C2×D3—24no—
300C2×D3—44no—
301C3×C4—21no—
302C3×C4—21no—
303C3×C4—22no—
304C3×C4—44no—
305C3×C4—44no—
306C3×C4—64no—
307C3×C4#67⋊C412yes—
308C3×C4#67⋊C412yes—
309C3×C4C22×C4×D312yes—
310C3×C4C2×D3×D412yes—
311Dic3—24no—
312C32#295511yescharacteristic, complemented, Sylow
313C23—62no—
314C23#380511yescharacteristic
315Q8—34no—
316Q8—62no—
317D4—34no—
318D4—64no—
319D4—64no—
320D4—62no—
321C2×C4—22no—
322C2×C4—62no—
323C2×C4—64no—
324C2×C4—64no—
325C2×C4C4×D3212yes—
326C2×C4#380212yes—
327C2×C4#380511yescharacteristic
328C2×C4C22×D3211yescharacteristic
329C8—64no—
330C8—94no—
331C8—91no—
332C8—92no—
333C8—91no—
334C2×C3—22no—
335C2×C3—22no—
336C2×C3—22no—
337C2×C3—22no—
338C2×C3—21no—
339C2×C3—42no—
340C2×C3—124no—
341C2×C3C2×#67⋊C412yes—
342D3—44no—
343C22—41no—
344C22—64no—
345C22—124no—
346C22#6390212yes—
347C22C2×#380511yescharacteristic
348C4—42no—
349C4—64no—
350C4#6390212yes—
351C4C2×C4×D3211yescharacteristic
352C4C2×#380211yescharacteristic
353C3—21no—
354C3#7898912yescomplemented
355C2—21no—
356C2—22no—
357C2—124no—
358C2C2×#6390211yescharacteristic
subgroupG/H
centerC4C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC2×C32C2×C4×D4
prime radical#10594786C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2955
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#63815C2semidirect
3. #10592696C2semidirect
4. C3×#5005C2semidirect
5. #10591143C2semidirect
6. #10590390C2semidirect
7. #10590389C2semidirect
14. #63827C4semidirect
15. #63823C4semidirect
20. #63815C22semidirect
21. #63815C22semidirect
23. #63630C22semidirect
24. C4×C3⋊(C3⋊C8)C22semidirect
25. C3×#805C22semidirect
26. #63578C22semidirect
32. #5005D3semidirect
95. #805C2×D3semidirect
312. C32#2955semidirect
354. C3#78989semidirect

Maximal subgroups

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

subgroupindex
#105947862
C2×#638152
#105926962
C3×#50052
#105911432
#105903902
#105903892
#789893