Finite Group Databasebeta

← #11792427

Subgroups — #11792427

Order 1152.

1530 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×D8C211yesmaximal, characteristic, complemented
2C2×#64149C211yesmaximal, characteristic, complemented
3C22×#3753C211yesmaximal, characteristic, complemented
4#10592920C211yesmaximal, characteristic, complemented
5C2×#63659C211yesmaximal, characteristic, complemented
6C2×#63648C211yesmaximal, characteristic, complemented
7#10589416C211yesmaximal, characteristic, complemented
8#72044—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×C32×D4C2211yescharacteristic
11C22×#638—22no—
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C2×C32×D8—22no—
14C2×C32×D8—22no—
15C2×C32×D8—22no—
16C22×C32×C8C2211yescharacteristic
17C2×#3757—22no—
18#64149—22no—
19#64149—22no—
20C2×#3753—22no—
21C2×#3753—22no—
22C2×#3753—22no—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26#63659—22no—
27#63648—22no—
28C22×C3×D8D314yescomplemented
29C2×#940—34no—
30C22×#213—34no—
31#5221—34no—
32C2×#832—34no—
33C2×#821—34no—
34#4550—34no—
35C24×C32—21no—
36C24×C32—21no—
37C23×C3⋊D3—21no—
38C2×C32×D4—21no—
39C2×C32×D4—21no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4D412yes—
49C2×C32×D4D412yescomplemented
50C22×C32×C4C2311yescharacteristic
51C2×#638—28no—
52C2×#638—44no—
53C2×#638—44no—
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3D412yes—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)D412yes—
62C32×D8—28no—
63C2×C32×C8—21no—
64C2×C32×C8—21no—
65C2×C32×C8D412yescomplemented
66#3757—44no—
67#3753—28no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—21no—
70C4×C3⋊Dic3—21no—
71C4×C3⋊Dic3—21no—
72C2×C3⋊(C3⋊C8)—21no—
73C2×C3⋊(C3⋊C8)—21no—
74C2×C3⋊(C3⋊C8)D412yescomplemented
75#2011—91noSylow
76C22×C3×D4C2×D314yes—
77C22×C3×D4C2×D314yes—
78C22×#67—68no—
79C22×D12—34no—
80C2×C3×D8—28no—
81C2×C3×D8—28no—
82C2×C3×D8—28no—
83C22×C3×C8C2×D314yes—
84C2×#217—68no—
85#940—68no—
86#940—68no—
87C2×#213—68no—
88C2×#213—68no—
89C2×#213—68no—
90C2×C4⋊Dic3—34no—
91C2×C4×Dic3—34no—
92C22×C3⋊C8—34no—
93#832—68no—
94#821—68no—
95C23×C32—22no—
96C23×C32—22no—
97C23×C32—41no—
98C23×C32—41no—
99C23×C32—41no—
100C23×C32—41no—
101C23×C32—42no—
102C23×C32—42no—
103C23×C32—42no—
104C23×C32—42no—
105C23×C32C2×D411yescharacteristic
106C22×C3⋊D3—22no—
107C22×C3⋊D3—41no—
108C22×C3⋊D3—41no—
109C22×C3⋊D3—42no—
110C22×C3⋊D3—42no—
111C32×D4—22no—
112C32×D4—22no—
113C32×D4—22no—
114C32×D4—22no—
115C32×D4—41no—
116C32×D4—41no—
117C32×D4—41no—
118C32×D4—41no—
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4#4111yescharacteristic
125#638—416no—
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—41no—
129C2×C3⋊Dic3—42no—
130C2×C3⋊Dic3D814yescomplemented
131C4⋊(C3⋊D3)—22no—
132C4⋊(C3⋊D3)—22no—
133C4⋊(C3⋊D3)—41no—
134C4⋊(C3⋊D3)—41no—
135C32×C8—22no—
136C3⋊(C3⋊C8)—22no—
137C22×D8—91no—
138C22×D8C3⋊D311yescharacteristic, complemented
139C2×#127—91no—
140C2×#102—91no—
141C2×#102—91no—
142#390—91no—
143#336—91no—
144C24×C3—24no—
145C24×C3—24no—
146C23×D3—64no—
147C2×C3×D4—24no—
148C2×C3×D4—24no—
149C2×C3×D4—24no—
150C2×C3×D4—24no—
151C2×C3×D4—24no—
152C2×C3×D4—24no—
153C2×C3×D4—24no—
154C2×C3×D4—24no—
155C2×C3×D4—24no—
156C2×C3×D4—24no—
157C2×C3×D4#6718yes—
158C2×C3×D4#6718yescomplemented
159C22×C3×C4C22×D314yes—
160C2×#67—632no—
161C2×#67—1216no—
162C2×#67—1216no—
163C22×Dic3—38no—
164C22×Dic3—64no—
165C2×D12—38no—
166C2×D12—64no—
167C2×D12—64no—
168C2×D12—64no—
169C2×D12—64no—
170C2×D12—64no—
171C3×D8—232no—
172C2×C3×C8—24no—
173C2×C3×C8—24no—
174C2×C3×C8#6718yescomplemented
175#217—1216no—
176#213—632no—
177C4⋊Dic3—64no—
178C4⋊Dic3—64no—
179C4×Dic3—64no—
180C4×Dic3—64no—
181C2×C3⋊C8—38no—
182C2×C3⋊C8—64no—
183C2×C3⋊C8—64no—
184C22×C32—42no—
185C22×C32—42no—
186C22×C32—44no—
187C22×C32—44no—
188C22×C32—82no—
189C22×C32—82no—
190C22×C32—81no—
191C22×C32—81no—
192C22×C32—81no—
193C22×C32—81no—
194C22×C32#12011yescharacteristic
195C22×C32#12111yescharacteristic
196C22×C32#12711yescharacteristic
197C22×C32C2×D812yes—
198C22×C32AGL(1,ℤ/8)12yes—
199C2×C3⋊D3—42no—
200C2×C3⋊D3—44no—
201C2×C3⋊D3—82no—
202C2×C3⋊D3—81no—
203C2×C3⋊D3—81no—
204C32×C4#12011yescharacteristic
205C32×C4#12011yescharacteristic
206C32×C4#12111yescharacteristic
207C32×C4#12111yescharacteristic
208C3⋊Dic3—24no—
209C3⋊Dic3—81no—
210C22×D4—91no—
211C22×D4—182no—
212C22×D4C2×C3⋊D311yescharacteristic
213C22×D4C2×C3⋊D311yescharacteristic
214C2×D8—22no—
215C2×D8—22no—
216C2×D8—22no—
217C2×D8—182no—
218C2×D8—182no—
219C2×D8—182no—
220C22×C8—91no—
221C22×C8C2×C3⋊D311yescharacteristic
222#127—182no—
223#127—182no—
224C2×C4⋊C4—91no—
225C2×C22⋊C4—182no—
226C2×C42—91no—
227#102—182no—
228#102—182no—
229C23×C3—28no—
230C23×C3—28no—
231C23×C3—48no—
232C23×C3—48no—
233C23×C3—48no—
234C23×C3—48no—
235C23×C3—44no—
236C23×C3—44no—
237C23×C3—44no—
238C23×C3—44no—
239C23×C3D3×D414yes—
240C22×D3—68no—
241C22×D3—128no—
242C22×D3—128no—
243C22×D3—124no—
244C22×D3—124no—
245C3×D4—28no—
246C3×D4—28no—
247C3×D4—28no—
248C3×D4—28no—
249C3×D4—44no—
250C3×D4—44no—
251C3×D4—44no—
252C3×D4—44no—
253C2×C3×C4D3×D414yes—
254C2×C3×C4D3×D414yes—
255C2×C3×C4#23714yes—
256C2×C3×C4C2×#6714yes—
257C2×C3×C4C2×#6714yes—
258C2×C3×C4C2×#6714yes—
259#67—1264no—
260C2×Dic3—316no—
261C2×Dic3—68no—
262C2×Dic3—68no—
263C2×Dic3—128no—
264C2×Dic3—124no—
265D12—68no—
266D12—68no—
267D12—124no—
268D12—124no—
269C3×C8—28no—
270C3⋊C8—68no—
271C2×C32—82no—
272C2×C32—82no—
273C2×C32#39211yescharacteristic
274C2×C32#44712yes—
275C2×C32#45912yes—
276C2×C32#49311yescharacteristic
277C2×C32#49611yescharacteristic
278C3⋊D3—82no—
279C24—21no—
280C24—21no—
281C24—181no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—92no—
293C2×D4—188no—
294C2×D4—181no—
295C2×D4—181no—
296C2×D4—181no—
297C2×D4—181no—
298C2×D4—181no—
299C2×D4—364no—
300C2×D4—364no—
301C2×D4#63812yes—
302C2×D4#63812yescomplemented
303C22×C4—92no—
304C22×C4—181no—
305C22×C4C22×C3⋊D311yescharacteristic
306D8—28no—
307D8—188no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—92no—
311C2×C8—181no—
312C2×C8—181no—
313C2×C8#63812yescomplemented
314C4⋊C4—181no—
315C4⋊C4—181no—
316C22⋊C4—364no—
317C42—181no—
318C42—181no—
319C22×C3—416no—
320C22×C3—416no—
321C22×C3—48no—
322C22×C3—48no—
323C22×C3—88no—
324C22×C3—84no—
325C22×C3—84no—
326C22×C3—84no—
327C22×C3—84no—
328C22×C3—88no—
329C22×C3D3×D818yes—
330C22×C3#91118yes—
331C22×C3#93714yes—
332C22×C3#93914yes—
333C22×C3#94014yes—
334C2×D3—1216no—
335C2×D3—128no—
336C2×D3—248no—
337C2×D3—244no—
338C2×D3—244no—
339C3×C4#93714yes—
340C3×C4#93814yes—
341C3×C4#93914yes—
342C3×C4#95314yes—
343Dic3—616no—
344Dic3—244no—
345C32#201111yescharacteristic, complemented, Sylow
346C23—22no—
347C23—22no—
348C23—42no—
349C23—42no—
350C23—42no—
351C23—42no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—182no—
357C23—362no—
358C23—362no—
359C23—361no—
360C23—361no—
361C23D4×C3⋊D311yescharacteristic
362D4—22no—
363D4—22no—
364D4—22no—
365D4—22no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—41no—
370D4—182no—
371D4—182no—
372D4—3616no—
373D4—361no—
374D4—361no—
375C2×C4—94no—
376C2×C4—182no—
377C2×C4—182no—
378C2×C4—362no—
379C2×C4—361no—
380C2×C4D4×C3⋊D311yescharacteristic
381C2×C4D4×C3⋊D311yescharacteristic
382C2×C4#383011yescharacteristic
383C2×C4C2×#63811yescharacteristic
384C2×C4C2×#63811yescharacteristic
385C2×C4C2×#63811yescharacteristic
386C8—22no—
387C8—182no—
388C2×C3—88no—
389C2×C3—88no—
390C2×C3#515018yes—
391C2×C3#515114yes—
392C2×C3#515414yes—
393C2×C3#515618yes—
394C2×C3#522314yes—
395D3—248no—
396C22—44no—
397C22—44no—
398C22—42no—
399C22—42no—
400C22—82no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—82no—
406C22—364no—
407C22—362no—
408C22—722no—
409C22—721no—
410C22—721no—
411C22D8×C3⋊D312yes—
412C22#6412012yes—
413C22#6414611yescharacteristic
414C22#6414811yescharacteristic
415C22#6414911yescharacteristic
416C4—184no—
417C4—721no—
418C4#6414611yescharacteristic
419C4#6414711yescharacteristic
420C4#6414811yescharacteristic
421C4#6416211yescharacteristic
422C3#7204414yescomplemented
423C2—82no—
424C2—82no—
425C2—722no—
426C2#1059284912yes—
427C2#1059285011yescharacteristic
428C2#1059285311yescharacteristic
429C2#1059285512yes—
430C2#1059292211yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC22×C32×D8C2
socleC23×C32C2×D4
hypercenterC22×D8C3⋊D3
hypocenterC32#2011
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×C32×D8C2semidirect
2. C2×#64149C2semidirect
3. C22×#3753C2semidirect
4. #10592920C2semidirect
5. C2×#63659C2semidirect
6. C2×#63648C2semidirect
7. #10589416C2semidirect
28. C22×C3×D8D3semidirect
49. C2×C32×D4D4semidirect
65. C2×C32×C8D4semidirect
74. C2×C3⋊(C3⋊C8)D4semidirect
130. C2×C3⋊Dic3D8semidirect
138. C22×D8C3⋊D3semidirect
158. C2×C3×D4#67semidirect
174. C2×C3×C8#67semidirect
302. C2×D4#638semidirect
313. C2×C8#638semidirect
345. C32#2011semidirect
422. C3#72044semidirect

Maximal subgroups

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

subgroupindex
C22×C32×D82
C2×#641492
C22×#37532
#105929202
C2×#636592
C2×#636482
#105894162
#720443