Finite Group Databasebeta

← #11861118

Subgroups — #11861118

Order 1152.

1043 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596219C211yesmaximal, characteristic
2C2×#63817C212yesmaximal, complemented
3C3×#5125C211yesmaximal, characteristic, complemented
4C3×#5122C211yesmaximal, characteristic, complemented
5#10591113C212yesmaximal, complemented
6#10590918C214yesmaximal, complemented
7#10590917C214yesmaximal, complemented
8#79257—31nomaximal
9#78579—31nomaximal
10C2×#3828C2212yes—
11C2×C32×M16C2211yescharacteristic
12#64118C414yescomplemented
13#64117C414yescomplemented
14#64113C2214yes—
15C3×#926C2211yescharacteristic
16C2×C3×#208C2212yes—
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3712—22no—
19#63817—22no—
20#63817—22no—
21#63817C2214yescomplemented
22#63817C2214yescomplemented
23C2×#3710—22no—
24C3×#819C2214yescomplemented
25C3×#815C2212yescomplemented
26C3×C8×Dic3C2212yescomplemented
27#63570C2218yescomplemented
28#5748—31no—
29#5748—31no—
30#5748—61no—
31C2×#907—32no—
32C2×#901—32no—
33C3×#430—31no—
34C3×#405—31no—
35#5139—32no—
36#5125D311yescharacteristic, complemented
37#5122D311yescharacteristic, complemented
38#5005—32no—
39#4895—34no—
40#4894—34no—
41#4717—34no—
42#4700—34no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—22no—
45#3828—22no—
46#3828—22no—
47#3828C2×C414yes—
48#3828C2314yes—
49C2×C4⋊(C3⋊D3)C2×C412yes—
50C2×C4×C3⋊D3—22no—
51C2×#634C2×C412yes—
52C32×M16C2×C414yes—
53C2×C32×C8C2312yes—
54#3746C2×C414yes—
55#3745C2×C414yes—
56#3744C2×C418yes—
57C3×#217—21no—
58C3×C4⋊Dic3—21no—
59C3×C4×Dic3C2312yes—
60C3×#208—22no—
61C3×#208C2314yes—
62C2×C3×C3⋊C8—22no—
63C2×C3×C3⋊C8D412yes—
64C2×C3×C3⋊C8D412yes—
65C2×C3×C3⋊C8C2311yescharacteristic
66C2×C3×C3⋊C8C2311yescharacteristic
67#3712—24no—
68#3712—24no—
69#3710—24no—
70#3710—24no—
71#2955—91noSylow
72C2×#235—32no—
73C2×#235—32no—
74C2×#235—62no—
75C2×C3×M16—21no—
76C2×C3×M16—32no—
77C2×C3×M16C2×D311yescharacteristic
78C2×C3×M16C2×D311yescharacteristic
79C22×C3×C8—31no—
80C3×#117—31no—
81#926C2×D311yescharacteristic
82C2×#208C2×D312yes—
83C22×C3⋊C8C2×D311yescharacteristic
84#909—34no—
85#909—34no—
86#909—64no—
87#908—34no—
88#908—34no—
89#908—64no—
90#907—34no—
91#907—34no—
92#907—62no—
93#907—62no—
94#904—34no—
95#904—34no—
96#904—64no—
97#901—34no—
98#901—34no—
99#901—62no—
100#901—62no—
101C2×ΓL(1,𝔽25)—62no—
102C2×ΓL(1,𝔽25)—62no—
103C2×D3×C8—62no—
104C2×D3×C8—62no—
105C3×#108—34no—
106C3×#97—32no—
107C3×C4×C8—32no—
108#825—38no—
109#819C2×D314yescomplemented
110#815C2×D312yescomplemented
111C8×Dic3C2×D312yescomplemented
112#805—38no—
113C23×C32#4111yescharacteristic
114C22×C3⋊D3—22no—
115C2×C32×C4C22×C412yes—
116C2×C32×C4C2×D412yes—
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4C2411yescharacteristic
119#638—24no—
120#638—24no—
121C2×C3⋊Dic3—22no—
122C4⋊(C3⋊D3)—22no—
123C4⋊(C3⋊D3)C22×C414yes—
124C4×C3⋊D3—24no—
125C4×C3⋊D3—24no—
126#634—22no—
127#634C22×C414yes—
128C2×C3×Dic3—22no—
129C32×C8C22×C414yes—
130C3×C3⋊C8—24no—
131C3×C3⋊C8C2×D411yescharacteristic
132C3×C3⋊C8C2×D412yes—
133C3×C3⋊C8C2×D411yescharacteristic
134#575—91no—
135C2×#131—92no—
136#444—94no—
137#443—94no—
138#430—31no—
139#421—92no—
140#405—31no—
141C22×C3×C4—21no—
142C22×C3×C4C22×D311yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C2×#67—62no—
145C2×#67—62no—
146C2×#67—122no—
147#235—34no—
148#235—34no—
149#235—34no—
150#235—34no—
151#235—64no—
152#235—64no—
153#235—62no—
154#235—62no—
155#235—62no—
156#235—62no—
157#235—122no—
158#235—122no—
159C2×D12—32no—
160C2×D12—32no—
161C2×D12—62no—
162C2×C4×D3—62no—
163C2×C4×D3—62no—
164C2×C4×D3—122no—
165C2×Dic6—32no—
166C2×Dic6—32no—
167C2×Dic6—62no—
168C3×M16—24no—
169C3×M16—34no—
170C3×M16—62no—
171C3×M16C4×D314yes—
172C3×M16C4×D314yes—
173C2×C3×C8—22no—
174C2×C3×C8—32no—
175C2×C3×C8—32no—
176C2×C3×C8—31no—
177C2×C3×C8—31no—
178C2×C3×C8—62no—
179C2×C3×C8C22×D312yes—
180C2×C3×C8C22×D312yes—
181C3×C4⋊C4—61no—
182C3×C22⋊C4—61no—
183C3×C42—32no—
184#217—21no—
185C4⋊Dic3—21no—
186C4×Dic3C22×D312yes—
187#208—22no—
188#208C22×D314yes—
189C2×C3⋊C8—22no—
190C2×C3⋊C8D1212yes—
191C2×C3⋊C8D1212yes—
192C2×C3⋊C8C22×D311yescharacteristic
193C2×C3⋊C8C22×D311yescharacteristic
194Dic12—34no—
195Dic12—34no—
196Dic12—64no—
197D24—34no—
198D24—34no—
199D24—64no—
200#204—38no—
201#204—38no—
202#204—68no—
203ΓL(1,𝔽25)—64no—
204ΓL(1,𝔽25)—64no—
205ΓL(1,𝔽25)—64no—
206ΓL(1,𝔽25)—64no—
207D3×C8—64no—
208D3×C8—64no—
209D3×C8—64no—
210D3×C8—64no—
211C22×C32—41no—
212C22×C32C4×D412yes—
213C22×C32C2×#4111yescharacteristic
214C2×C3⋊D3—24no—
215C2×C3⋊D3—44no—
216C32×C4C4×D412yes—
217C32×C4C23×C411yescharacteristic
218C32×C4C22×D411yescharacteristic
219C3⋊Dic3—24no—
220C3×Dic3—42no—
221C2×#41—92no—
222#137—94no—
223AGL(1,ℤ/8)—94no—
224#135—94no—
225#131—94no—
226#131—94no—
227#131—182no—
228#131—182no—
229C2×M16—32no—
230C2×M16—182no—
231C2×M16D3211yescharacteristic
232C22×C8—31no—
233C22×C8—182no—
234#117—31no—
235#108—34no—
236#104—98no—
237#97—32no—
238C4×C8—32no—
239C23×C3—21no—
240C23×C3#23511yescharacteristic
241C23×C3#23911yescharacteristic
242C22×D3—62no—
243C22×D3—62no—
244C22×D3—122no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4—62no—
250C2×C3×C4C2×C4×D312yes—
251C2×C3×C4C2×C4×D312yes—
252C2×C3×C4C2×D1212yes—
253C2×C3×C4#23511yescharacteristic
254C2×C3×C4D3×D412yes—
255C2×C3×C4#23911yescharacteristic
256C2×C3×C4C23×D311yescharacteristic
257C2×C3×C4C23×D311yescharacteristic
258#67—64no—
259#67—64no—
260#67—64no—
261#67—64no—
262#67—124no—
263#67—124no—
264C2×Dic3—22no—
265C2×Dic3—62no—
266C2×Dic3—62no—
267C2×Dic3—122no—
268D12—34no—
269D12—34no—
270D12—64no—
271D12—62no—
272D12—62no—
273D12—122no—
274C4×D3—64no—
275C4×D3—64no—
276C4×D3—64no—
277C4×D3—64no—
278C4×D3—124no—
279C4×D3—124no—
280Dic6—34no—
281Dic6—34no—
282Dic6—64no—
283Dic6—62no—
284Dic6—62no—
285Dic6—122no—
286C3×C8—24no—
287C3×C8—31no—
288C3×C8—32no—
289C3×C8—31no—
290C3×C8—64no—
291C3×C8C2×C4×D314yes—
292C3×C8C2×C4×D314yes—
293C3⋊C8—24no—
294C3⋊C8C2×D1211yescharacteristic
295C3⋊C8C2×D1212yes—
296C3⋊C8C2×D1211yescharacteristic
297C2×C32—21no—
298C2×C32—22no—
299C2×C32C2×C4×D411yescharacteristic
300C3⋊D3—44no—
301#41—94no—
302#41—94no—
303#41—182no—
304#41—182no—
305C2×Q8—92no—
306C2×D4—92no—
307C2×D4—182no—
308C22×C4—182no—
309C22×C4C2×D3211yescharacteristic
310Q16—94no—
311SD16—98no—
312D8—94no—
313M16—34no—
314M16—62no—
315M16—184no—
316M16—184no—
317M16#62414yes—
318C2×C8—31no—
319C2×C8—31no—
320C2×C8—32no—
321C2×C8—32no—
322C2×C8—62no—
323C2×C8—184no—
324C2×C8—184no—
325C2×C8C2×D3212yes—
326C4⋊C4—61no—
327C22⋊C4—61no—
328C42—32no—
329C22×C3—21no—
330C22×C3—22no—
331C22×C3—41no—
332C22×C3—41no—
333C22×C3—81no—
334C22×C3C4×D1212yes—
335C22×C3#89312yes—
336C22×C3C2×#23511yescharacteristic
337C22×C3C2×#23911yescharacteristic
338C2×D3—64no—
339C2×D3—64no—
340C2×D3—124no—
341C2×D3—124no—
342C2×D3—124no—
343C2×D3—244no—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—22no—
347C3×C4—122no—
348C3×C4C4×D1212yes—
349C3×C4#89312yes—
350C3×C4C22×C4×D311yescharacteristic
351C3×C4C22×C4×D311yescharacteristic
352C3×C4C22×D1211yescharacteristic
353C3×C4C2×D3×D411yescharacteristic
354Dic3—42no—
355Dic3—64no—
356Dic3—64no—
357Dic3—124no—
358C32#295511yescharacteristic, complemented, Sylow
359C23—182no—
360C23#379911yescharacteristic
361Q8—94no—
362Q8—182no—
363D4—94no—
364D4—184no—
365D4—184no—
366D4—182no—
367C2×C4—62no—
368C2×C4—182no—
369C2×C4—184no—
370C2×C4—184no—
371C2×C4#379911yescharacteristic
372C2×C4D3×D1212yes—
373C2×C4C2×#62412yes—
374C2×C4C22×D3211yescharacteristic
375C8—31no—
376C8—32no—
377C8—31no—
378C8—64no—
379C8C2×#62414yes—
380C2×C3—21no—
381C2×C3—22no—
382C2×C3—21no—
383C2×C3—22no—
384C2×C3—21no—
385C2×C3—42no—
386C2×C3—41no—
387C2×C3C2×C4×D1211yescharacteristic
388C2×C3C2×#89311yescharacteristic
389D3—124no—
390D3—124no—
391D3—244no—
392C22—41no—
393C22—184no—
394C22—364no—
395C22#6389412yes—
396C22C2×#379911yescharacteristic
397C4—122no—
398C4—184no—
399C4#6389412yes—
400C4C2×D3×D1211yescharacteristic
401C4C22×#62411yescharacteristic
402C3—21no—
403C3#7857911yescharacteristic, complemented
404C3#7925711yescharacteristic, complemented
405C2—21no—
406C2—22no—
407C2—364no—
408C2C2×#6389411yescharacteristic
subgroupG/H
centerC4C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C2×C4×D4
prime radical#10596219C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2955
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63817C2semidirect
3. C3×#5125C2semidirect
4. C3×#5122C2semidirect
5. #10591113C2semidirect
6. #10590918C2semidirect
7. #10590917C2semidirect
12. #64118C4semidirect
13. #64117C4semidirect
21. #63817C22semidirect
22. #63817C22semidirect
24. C3×#819C22semidirect
25. C3×#815C22semidirect
26. C3×C8×Dic3C22semidirect
27. #63570C22semidirect
36. #5125D3semidirect
37. #5122D3semidirect
109. #819C2×D3semidirect
110. #815C2×D3semidirect
111. C8×Dic3C2×D3semidirect
358. C32#2955semidirect
403. C3#78579semidirect
404. C3#79257semidirect

Maximal subgroups

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

subgroupindex
#105962192
C2×#638172
C3×#51252
C3×#51222
#105911132
#105909182
#105909172
#792573
#785793