Finite Group Databasebeta

← #11898264

Subgroups — #11898264

Order 1152.

987 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593900C212yesmaximal, complemented
2C4×#3745C211yesmaximal, characteristic, complemented
3C3×#4695C211yesmaximal, characteristic, complemented
4C3×C8×Dic6C211yesmaximal, characteristic, complemented
5#10590880C212yesmaximal, complemented
6Dic3×D24C212yesmaximal, complemented
7#10590753C214yesmaximal, complemented
8#10590355C212yesmaximal, complemented
9#81778—31nomaximal
10#79910—31nomaximal
11C2×#3796—22no—
12C2×#3745C2211yescharacteristic
13C4×C4⋊(C3⋊D3)C2212yes—
14C2×C3×D24C2212yes—
15C2×C3×D24C2212yes—
16C3×#874C2212yes—
17C3×C4×Dic6C2211yescharacteristic
18#63916—22no—
19#63911C2214yes—
20Dic3×D12C2214yes—
21#63886—24no—
22C2×#3714C2214yes—
23C32×C4×C8C2211yescharacteristic
24#63648C2212yes—
25#63645C2211yescharacteristic
26C3×Dic3⋊C8C2212yes—
27C3×C8×Dic3C2212yes—
28C3×C4⋊(C3⋊C8)C2211yescharacteristic
29#63563C2214yes—
30#5718—32no—
31#5577—32no—
32C3×#493—31no—
33C3×C8×Q8—31no—
34#5151—32no—
35#5150—34no—
36Dic3×D8—32no—
37#5072—32no—
38#4843—34no—
39#4843—32no—
40#4695—32no—
41#4695D311yescharacteristic, complemented
42C4×D24—32no—
43C4×D24—31no—
44C4×D24—31no—
45C4×D24—61no—
46C8×Dic6D311yescharacteristic, complemented
47C2×C4⋊(C3⋊D3)C2312yes—
48C2×C4×C3⋊D3—22no—
49C2×C3×D12—22no—
50C2×C3×D12—22no—
51C2×C3×D12C2314yes—
52C2×C3×Dic6D411yescharacteristic
53C2×#626—24no—
54C2×#626—24no—
55C2×D3×Dic3—24no—
56#3796—48no—
57C2×C32×C8C2311yescharacteristic
58C2×C32×C8C2311yescharacteristic
59C32×C42C2311yescharacteristic
60#3752—22no—
61C4⋊(C3⋊Dic3)C2312yes—
62#3745—22no—
63C3×C4⋊Dic3D411yescharacteristic
64C3×Dic3⋊C4D412yes—
65C3×C4×Dic3C2312yes—
66C2×C3×C3⋊C8C2312yes—
67C3×D24—24no—
68C3×D24—42no—
69(C2×D3)⋊Dic3—24no—
70#3714—44no—
71#3391—91noSylow
72C2×#239—62no—
73C2×#237—62no—
74C2×C3×D8—32no—
75C2×C3×D8—32no—
76C3×#127—32no—
77C3×C4×Q8—31no—
78#940—34no—
79#939—64no—
80#938—62no—
81D4×Dic3—34no—
82C2×#213—34no—
83C2×D24—31no—
84C2×D24—31no—
85C2×D24—34no—
86C2×D24—61no—
87C2×D24C2×D312yes—
88C2×D24C2×D312yes—
89#895—64no—
90#895—62no—
91#874—34no—
92#874C2×D312yes—
93C4×D12—34no—
94C4×D12—32no—
95C4×D12—32no—
96C4×D12—62no—
97C4×Dic6C2×D311yescharacteristic
98C3×C4⋊C8—32no—
99C3×C4⋊C8—31no—
100C3×C4×C8—21no—
101C3×C4×C8—32no—
102C3×C4×C8C2×D311yescharacteristic
103C3×C4×C8C2×D311yescharacteristic
104#832—34no—
105#821—34no—
106#821—32no—
107#821—32no—
108#821—62no—
109#818—31no—
110#818—31no—
111#818—61no—
112Dic3⋊C8C2×D312yes—
113C8×Dic3C2×D312yes—
114C4⋊(C3⋊C8)C2×D311yescharacteristic
115C22×C3⋊D3—22no—
116C22×C3×D3—24no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2411yescharacteristic
120C2×C3⋊Dic3—22no—
121C4⋊(C3⋊D3)—22no—
122C4⋊(C3⋊D3)—22no—
123C4×C3⋊D3—44no—
124C2×C3×Dic3C2×D412yes—
125C2×C3×Dic3C2×D412yes—
126C3×D12—24no—
127C3×D12—24no—
128C3×D12—44no—
129C3×D12—82no—
130C3×Dic6D814yescomplemented
131#626—48no—
132#626—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—92no—
141#459—94no—
142C8×Q8—31no—
143C4×D8—92no—
144C4×D8—91no—
145C2×C3×Q8—31no—
146C2×C3×D4—34no—
147C2×C3×D4—62no—
148C2×C3×D4—62no—
149C2×#67—64no—
150C2×#67—64no—
151C22×Dic3—64no—
152#239—128no—
153#237—128no—
154C2×D12—22no—
155C2×D12—22no—
156C2×D12—32no—
157C2×D12—32no—
158C2×D12—62no—
159C2×D12—64no—
160C2×D12—64no—
161C2×D12C22×D314yes—
162C2×C4×D3—64no—
163C2×C4×D3—62no—
164C2×C4×D3—62no—
165C2×C4×D3—122no—
166C2×Dic6D1211yescharacteristic
167C3×D8—64no—
168C3×D8—122no—
169C2×C3×C8—21no—
170C2×C3×C8—21no—
171C2×C3×C8—32no—
172C2×C3×C8C22×D311yescharacteristic
173C2×C3×C8C22×D311yescharacteristic
174C2×C3×C8C22×D311yescharacteristic
175C2×C3×C8C22×D311yescharacteristic
176C3×C4⋊C4—32no—
177C3×C4⋊C4—31no—
178C3×C42—21no—
179C3×C42—32no—
180C3×C42C22×D311yescharacteristic
181C3×C42C22×D311yescharacteristic
182#217—64no—
183#213—124no—
184(C2×D3)⋊C4—64no—
185(C2×D3)⋊C4—62no—
186(C2×D3)⋊C4—62no—
187(C2×D3)⋊C4—122no—
188C4⋊Dic3—32no—
189C4⋊Dic3—32no—
190C4⋊Dic3—62no—
191C4⋊Dic3D1211yescharacteristic
192Dic3⋊C4D1212yes—
193C4×Dic3C22×D312yes—
194C2×C3⋊C8C22×D312yes—
195D24—24no—
196D24—42no—
197D24—64no—
198D24—62no—
199D24—62no—
200D24—124no—
201C22×C32C22×D411yescharacteristic
202C2×C3⋊D3—42no—
203C2×C3⋊D3—42no—
204C2×C3⋊D3—42no—
205C2×C3×D3—44no—
206C2×C3×D3—44no—
207C2×C3×D3—44no—
208C32×C4—21no—
209C32×C4C2×D812yes—
210C32×C4C2×#4111yescharacteristic
211C32×C4H(5,𝔽2)11yescharacteristic
212C3⋊Dic3—42no—
213C3×Dic3—22no—
214C3×Dic3C2×D814yes—
215C2×#41—182no—
216C2×D8—32no—
217C2×D8—32no—
218C2×D8—94no—
219C2×D8—91no—
220#127—32no—
221#127—94no—
222#121—182no—
223#121—184no—
224C4×Q8—31no—
225C4×D4—94no—
226C4×D4—92no—
227#107—91no—
228C4⋊C8—32no—
229C4⋊C8—31no—
230#102—94no—
231#102—92no—
232C4×C8—32no—
233C4×C8D3211yescharacteristic
234C23×C3—64no—
235C22×D3—24no—
236C22×D3—62no—
237C22×D3—62no—
238C22×D3—122no—
239C3×Q8—34no—
240C3×D4—64no—
241C3×D4—64no—
242C3×D4—124no—
243C3×D4—242no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—32no—
248C2×C3×C4—32no—
249C2×C3×C4C2×D1211yescharacteristic
250C2×C3×C4C2×D1211yescharacteristic
251C2×C3×C4D3×D411yescharacteristic
252C2×C3×C4D3×D411yescharacteristic
253C2×C3×C4C23×D311yescharacteristic
254C2×C3×C4C23×D311yescharacteristic
255#67—128no—
256#67—244no—
257C2×Dic3—62no—
258C2×Dic3—62no—
259C2×Dic3—122no—
260C2×Dic3—128no—
261C2×Dic3C2×D1212yes—
262C2×Dic3C2×D1212yes—
263D12—24no—
264D12—24no—
265D12—44no—
266D12—64no—
267D12—62no—
268D12—62no—
269D12—62no—
270D12—62no—
271D12—82no—
272D12—122no—
273D12—128no—
274D12—244no—
275C4×D3—128no—
276C4×D3—124no—
277C4×D3—124no—
278C4×D3—244no—
279Dic6D2414yescomplemented
280C3×C8—21no—
281C3×C8—21no—
282C3×C8—22no—
283C3×C8—41no—
284C3×C8—62no—
285C3×C8#23712yescomplemented
286C3×C8#23912yescomplemented
287C3⋊C8—22no—
288C2×C32#55011yescharacteristic
289C2×C32C22×D811yescharacteristic
290C2×C32#57611yescharacteristic
291C3⋊D3—82no—
292C3×D3—84no—
293#41—368no—
294C2×Q8—31no—
295C2×D4—34no—
296C2×D4—62no—
297C2×D4—62no—
298C2×D4—92no—
299C2×D4—184no—
300C2×D4—184no—
301C22×C4—184no—
302C22×C4—182no—
303D8—64no—
304D8—122no—
305D8—182no—
306D8—364no—
307C2×C8—32no—
308C2×C8C2×D3211yescharacteristic
309C2×C8C2×D3211yescharacteristic
310C4⋊C4—32no—
311C4⋊C4—31no—
312C4⋊C4—92no—
313C22⋊C4—184no—
314C22⋊C4—182no—
315C42—32no—
316C42C2×D3211yescharacteristic
317C22×C3—21no—
318C22×C3—124no—
319C22×C3—124no—
320C22×C3—124no—
321C22×C3C22×D1211yescharacteristic
322C22×C3C2×D3×D411yescharacteristic
323C2×D3—44no—
324C2×D3—44no—
325C2×D3—44no—
326C2×D3—124no—
327C2×D3—122no—
328C2×D3—122no—
329C2×D3—122no—
330C2×D3—122no—
331C2×D3—122no—
332C2×D3—122no—
333C2×D3—242no—
334C2×D3—242no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—22no—
339C3×C4—21no—
340C3×C4—34no—
341C3×C4—41no—
342C3×C4—62no—
343C3×C4C2×D2412yes—
344C3×C4D3×D812yes—
345C3×C4C2×#23711yescharacteristic
346C3×C4#100411yescharacteristic
347C3×C4C2×#23911yescharacteristic
348C3×C4#100911yescharacteristic
349Dic3—22no—
350Dic3—122no—
351Dic3—122no—
352Dic3—242no—
353Dic3C2×D2414yes—
354C32#339111yescharacteristic, complemented, Sylow
355C23—64no—
356C23—182no—
357Q8—34no—
358D4—64no—
359D4—64no—
360D4—124no—
361D4—182no—
362D4—182no—
363D4—242no—
364D4—368no—
365D4—724no—
366C2×C4—32no—
367C2×C4—32no—
368C2×C4—182no—
369C2×C4—368no—
370C2×C4—364no—
371C2×C4D3×D1211yescharacteristic
372C2×C4D3×D1211yescharacteristic
373C2×C4C22×D3211yescharacteristic
374C8—21no—
375C8—62no—
376C8#379612yescomplemented
377C2×C3—21no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—244no—
381C2×C3#557711yescharacteristic
382C2×C3#571811yescharacteristic
383C2×C3C22×D2411yescharacteristic
384C2×C3#575211yescharacteristic
385C2×C3C2×D3×D811yescharacteristic
386C2×C3#575711yescharacteristic
387D3—84no—
388D3—244no—
389D3—242no—
390D3—242no—
391C22—124no—
392C22—124no—
393C22—124no—
394C22—362no—
395C22—362no—
396C22—362no—
397C22C2×D3×D1211yescharacteristic
398C4—21no—
399C4—34no—
400C4—62no—
401C4—362no—
402C4D3×D2412yes—
403C4C2×#379611yescharacteristic
404C4#6430711yescharacteristic
405C3—21no—
406C3#7991011yescharacteristic, complemented
407C3#8177811yescharacteristic, complemented
408C2—244no—
409C2—722no—
410C2#1059390011yescharacteristic
411C2C2×D3×D2411yescharacteristic
412C2#1059467811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
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. #10593900C2semidirect
2. C4×#3745C2semidirect
3. C3×#4695C2semidirect
4. C3×C8×Dic6C2semidirect
5. #10590880C2semidirect
6. Dic3×D24C2semidirect
7. #10590753C2semidirect
8. #10590355C2semidirect
41. #4695D3semidirect
46. C8×Dic6D3semidirect
130. C3×Dic6D8semidirect
135. C32×C8#41semidirect
279. Dic6D24semidirect
285. C3×C8#237semidirect
286. C3×C8#239semidirect
354. C32#3391semidirect
376. C8#3796semidirect
406. C3#79910semidirect
407. C3#81778semidirect

Maximal subgroups

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

subgroupindex
#105939002
C4×#37452
C3×#46952
C3×C8×Dic62
#105908802
Dic3×D242
#105907532
#105903552
#817783
#799103