Finite Group Databasebeta

← #11898265

Subgroups — #11898265

Order 1152.

971 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#10593906C212yesmaximal, complemented
2C8×#634C211yesmaximal, characteristic, complemented
3C3×#4695C211yesmaximal, characteristic, complemented
4C3×C4×D24C211yesmaximal, characteristic, complemented
5#10590886C212yesmaximal, complemented
6#10590777C212yesmaximal, complemented
7#10590749C214yesmaximal, complemented
8#10590347C212yesmaximal, complemented
9#81778—31nomaximal
10#79578—31nomaximal
11C2×#3795—22no—
12C4×#634C2211yescharacteristic
13C2×C3×D24C2211yescharacteristic
14C2×C3×D24C2212yes—
15C2×C3×D24C2212yes—
16C3×#874C2212yes—
17C3×C4×D12C2212yes—
18#63914C2214yes—
19#63908—22no—
20#63898C2214yes—
21#63885—24no—
22C2×#3713C2214yes—
23C32×C4×C8C2211yescharacteristic
24#63641C2212yes—
25C8×C3⋊Dic3C2212yes—
26C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
27C3×#821C2212yes—
28C3×#818C2211yescharacteristic
29#63562C2214yes—
30#5718—32no—
31#5553—32no—
32C3×#493—31no—
33C3×C4×D8—31no—
34#5151—32no—
35#5151—32no—
36#5150—34no—
37Dic3×D8—32no—
38#5072—32no—
39#5015—32no—
40#4872—32no—
41#4786—34no—
42#4695D311yescharacteristic, complemented
43C4×D24D311yescharacteristic, complemented
44C8×Dic6—31no—
45C8×Dic6—31no—
46C8×Dic6—61no—
47C2×#634D411yescharacteristic
48C2×C3×D12—22no—
49C2×C3×D12—22no—
50C2×C3×D12C2314yes—
51C2×C3×D12C2312yes—
52C2×C3×C4×D3—22no—
53C2×#625—24no—
54C2×#625—24no—
55C2×D3×Dic3—24no—
56#3795—48no—
57C2×C32×C8C2311yescharacteristic
58C2×C32×C8C2311yescharacteristic
59C32×C42C2311yescharacteristic
60C4⋊(C3⋊Dic3)D411yescharacteristic
61#3750D412yes—
62C4×C3⋊Dic3C2312yes—
63C2×C3⋊(C3⋊C8)C2312yes—
64C3×(C2×D3)⋊C4—22no—
65C3×C4⋊Dic3C2312yes—
66C3×D24—22no—
67C3×D24—24no—
68C3×D24—42no—
69(C2×D3)⋊Dic3—24no—
70#3713—44no—
71#3391—91noSylow
72C2×#237—62no—
73C2×#235—62no—
74C2×C3×D8—32no—
75C2×C3×D8—31no—
76C2×C3×D8—32no—
77C3×#127—32no—
78C3×C4×D4—32no—
79#940—34no—
80#940—34no—
81#939—64no—
82#938—62no—
83D4×Dic3—34no—
84C2×#213—34no—
85C2×#213—34no—
86#930—62no—
87C2×D24C2×D312yes—
88C2×D24C2×D311yescharacteristic
89C2×D24C2×D312yes—
90#893—34no—
91#884—64no—
92#874C2×D312yes—
93C4×D12C2×D312yes—
94C4×Dic6—31no—
95C4×Dic6—31no—
96C4×Dic6—61no—
97C3×#107—31no—
98C3×#102—32no—
99C3×C4×C8—21no—
100C3×C4×C8C2×D311yescharacteristic
101C3×C4×C8C2×D311yescharacteristic
102#832—34no—
103#821C2×D312yes—
104#818C2×D311yescharacteristic
105Dic3⋊C8—32no—
106Dic3⋊C8—32no—
107Dic3⋊C8—62no—
108C8×Dic3—32no—
109C8×Dic3—32no—
110C8×Dic3—62no—
111#809—34no—
112C4⋊(C3⋊C8)—31no—
113C4⋊(C3⋊C8)—31no—
114C4⋊(C3⋊C8)—61no—
115C22×C3×D3—24no—
116C22×C3×D3—22no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2411yescharacteristic
120C2×C3⋊Dic3C2×D412yes—
121C2×C3⋊Dic3C2×D412yes—
122#634D814yescomplemented
123C2×C3×Dic3—22no—
124C3×D12—22no—
125C3×D12—24no—
126C3×D12—22no—
127C3×D12—24no—
128C3×D12—44no—
129C3×D12—82no—
130C3×C4×D3—44no—
131#625—48no—
132#625—84no—
133D3×Dic3—48no—
134C32×C8—21no—
135C32×C8#4112yescomplemented
136C3⋊(C3⋊C8)—22no—
137#550—92no—
138#493—31no—
139#493—92no—
140#459—94no—
141#459—92no—
142C8×Q8—91no—
143C4×D8—31no—
144C4×D8—92no—
145C2×C3×D4—34no—
146C2×C3×D4—32no—
147C2×C3×D4—62no—
148C2×C3×D4—62no—
149C22×C3×C4—62no—
150C2×#67—64no—
151C2×#67—64no—
152C2×#67—64no—
153C2×#67—64no—
154C22×Dic3—64no—
155#237—128no—
156#235—128no—
157C2×D12—22no—
158C2×D12—22no—
159C2×D12C22×D314yes—
160C2×D12C22×D312yes—
161C2×C4×D3—22no—
162C2×C4×D3—64no—
163C2×Dic6—31no—
164C2×Dic6—31no—
165C2×Dic6—61no—
166C3×D8—64no—
167C3×D8—62no—
168C3×D8—122no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8C22×D311yescharacteristic
172C2×C3×C8C22×D311yescharacteristic
173C2×C3×C8C22×D311yescharacteristic
174C2×C3×C8C22×D311yescharacteristic
175C3×C4⋊C4—32no—
176C3×C22⋊C4—62no—
177C3×C42—21no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180#217—64no—
181#213—124no—
182#213—124no—
183(C2×D3)⋊C4—22no—
184(C2×D3)⋊C4—64no—
185C4⋊Dic3—31no—
186C4⋊Dic3—31no—
187C4⋊Dic3—61no—
188C4⋊Dic3C22×D312yes—
189Dic3⋊C4—32no—
190Dic3⋊C4—32no—
191Dic3⋊C4—62no—
192C4×Dic3—32no—
193C4×Dic3—32no—
194C4×Dic3—62no—
195C2×C3⋊C8—32no—
196C2×C3⋊C8—32no—
197C2×C3⋊C8—62no—
198D24—22no—
199D24—24no—
200D24—42no—
201C22×C32C22×D411yescharacteristic
202C2×C3×D3—44no—
203C2×C3×D3—42no—
204C2×C3×D3—44no—
205C2×C3×D3—42no—
206C2×C3×D3—42no—
207C2×C3×D3—44no—
208C32×C4—21no—
209C32×C4C2×D812yes—
210C32×C4C2×#4111yescharacteristic
211C32×C4H(5,𝔽2)11yescharacteristic
212C3⋊Dic3—22no—
213C3⋊Dic3C2×D814yes—
214C3×Dic3—42no—
215C2×#41—182no—
216C2×D8—31no—
217C2×D8—32no—
218C2×D8—32no—
219C2×D8—94no—
220#127—32no—
221#127—94no—
222#121—184no—
223#121—182no—
224C4×Q8—91no—
225C4×D4—32no—
226C4×D4—94no—
227#107—31no—
228C4⋊C8—92no—
229C4⋊C8—91no—
230#102—32no—
231#102—94no—
232C4×C8—92no—
233C4×C8D3211yescharacteristic
234C23×C3—64no—
235C23×C3—62no—
236C22×D3—22no—
237C22×D3—24no—
238C3×D4—64no—
239C3×D4—62no—
240C3×D4—62no—
241C3×D4—64no—
242C3×D4—124no—
243C3×D4—242no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—62no—
248C2×C3×C4—124no—
249C2×C3×C4D3×D411yescharacteristic
250C2×C3×C4D3×D411yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4C23×D311yescharacteristic
254C2×C3×C4C23×D311yescharacteristic
255#67—128no—
256#67—128no—
257#67—244no—
258#67—244no—
259C2×Dic3—22no—
260C2×Dic3—32no—
261C2×Dic3—32no—
262C2×Dic3—32no—
263C2×Dic3—32no—
264C2×Dic3—62no—
265C2×Dic3—62no—
266C2×Dic3—128no—
267D12—22no—
268D12—24no—
269D12—24no—
270D12—22no—
271D12—44no—
272D12—82no—
273C4×D3—44no—
274C4×D3—128no—
275Dic6—34no—
276Dic6—34no—
277Dic6—64no—
278C3×C8—21no—
279C3×C8—21no—
280C3×C8—22no—
281C3×C8—41no—
282C3×C8#23512yescomplemented
283C3×C8#23712yescomplemented
284C3⋊C8—62no—
285C3⋊C8—62no—
286C3⋊C8—122no—
287C2×C32#55011yescharacteristic
288C2×C32C22×D811yescharacteristic
289C2×C32#57611yescharacteristic
290C3×D3—84no—
291C3×D3—82no—
292#41—368no—
293C2×Q8—91no—
294C2×D4—32no—
295C2×D4—34no—
296C2×D4—62no—
297C2×D4—62no—
298C2×D4—184no—
299C2×D4—184no—
300C22×C4—62no—
301C22×C4—184no—
302D8—62no—
303D8—64no—
304D8—122no—
305D8—364no—
306C2×C8—92no—
307C2×C8C2×D3211yescharacteristic
308C2×C8C2×D3211yescharacteristic
309C4⋊C4—32no—
310C4⋊C4—92no—
311C4⋊C4—91no—
312C22⋊C4—62no—
313C22⋊C4—184no—
314C42—92no—
315C42C2×D3211yescharacteristic
316C22×C3—21no—
317C22×C3—122no—
318C22×C3—124no—
319C22×C3—122no—
320C22×C3—122no—
321C22×C3—124no—
322C22×C3—124no—
323C22×C3C2×D3×D411yescharacteristic
324C22×C3C2×D3×D411yescharacteristic
325C2×D3—44no—
326C2×D3—42no—
327C2×D3—44no—
328C2×D3—44no—
329C2×D3—42no—
330C2×D3—42no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—22no—
336C3×C4—41no—
337C3×C4—122no—
338C3×C4D3×D812yes—
339C3×C4D3×D812yes—
340C3×C4C2×#23511yescharacteristic
341C3×C4C2×#23711yescharacteristic
342C3×C4#100411yescharacteristic
343C3×C4#100911yescharacteristic
344Dic3—34no—
345Dic3—34no—
346Dic3—42no—
347Dic3—64no—
348Dic3—62no—
349Dic3—62no—
350Dic3—122no—
351C32#339111yescharacteristic, complemented, Sylow
352C23—62no—
353C23—64no—
354Q8—94no—
355D4—62no—
356D4—64no—
357D4—64no—
358D4—62no—
359D4—124no—
360D4—242no—
361D4—368no—
362D4—724no—
363C2×C4—62no—
364C2×C4—92no—
365C2×C4—92no—
366C2×C4—124no—
367C2×C4—368no—
368C2×C4#380211yescharacteristic
369C2×C4#380211yescharacteristic
370C2×C4C22×D3211yescharacteristic
371C8—21no—
372C8—182no—
373C8#379512yescomplemented
374C2×C3—21no—
375C2×C3—21no—
376C2×C3—21no—
377C2×C3—242no—
378C2×C3—244no—
379C2×C3#555311yescharacteristic
380C2×C3#571811yescharacteristic
381C2×C3C2×D3×D811yescharacteristic
382C2×C3C2×D3×D811yescharacteristic
383C2×C3#575711yescharacteristic
384C2×C3#576911yescharacteristic
385D3—84no—
386D3—82no—
387C22—124no—
388C22—122no—
389C22—122no—
390C22—124no—
391C22—124no—
392C22—122no—
393C22C2×#380211yescharacteristic
394C4—21no—
395C4—94no—
396C4—122no—
397C4—182no—
398C4#6379712yes—
399C4C2×#379511yescharacteristic
400C4#6430711yescharacteristic
401C3—21no—
402C3#7957811yescharacteristic, complemented
403C3#8177811yescharacteristic, complemented
404C2—242no—
405C2—244no—
406C2#1059390611yescharacteristic
407C2C2×#6379711yescharacteristic
408C2#1059468711yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3391
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10593906C2semidirect
2. C8×#634C2semidirect
3. C3×#4695C2semidirect
4. C3×C4×D24C2semidirect
5. #10590886C2semidirect
6. #10590777C2semidirect
7. #10590749C2semidirect
8. #10590347C2semidirect
42. #4695D3semidirect
43. C4×D24D3semidirect
122. #634D8semidirect
135. C32×C8#41semidirect
282. C3×C8#235semidirect
283. C3×C8#237semidirect
351. C32#3391semidirect
373. C8#3795semidirect
402. C3#79578semidirect
403. C3#81778semidirect

Maximal subgroups

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

subgroupindex
#105939062
C8×#6342
C3×#46952
C3×C4×D242
#105908862
#105907772
#105907492
#105903472
#817783
#795783