Finite Group Databasebeta

← #11792436

Subgroups — #11792436

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
1C2×#64149C211yesmaximal, characteristic, complemented
2C22×#3753C211yesmaximal, characteristic, complemented
3C22×#3745C211yesmaximal, characteristic, complemented
4C2×C32×#102C211yesmaximal, characteristic, complemented
5#10592687C211yesmaximal, characteristic, complemented
6C2×#63636C211yesmaximal, characteristic, complemented
7#10589416C211yesmaximal, characteristic, complemented
8#70209—34nomaximal
9C22×C32×D4C2211yescharacteristic
10C22×#638—22no—
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C4⋊C4C2211yescharacteristic
15#64149—22no—
16#64149—22no—
17C2×#3753—22no—
18C2×#3753—22no—
19C2×#3753—22no—
20C2×#3752—22no—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×#3745—22no—
24C2×#3745—22no—
25C2×#3745—22no—
26C32×#102—22no—
27#63636—22no—
28C2×#940—34no—
29C22×#213—34no—
30C22×D24—34no—
31C2×C3×#102D314yescomplemented
32#4988—34no—
33C2×#809—34no—
34#4550—34no—
35C24×C32—21no—
36C23×C3⋊D3—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×D4D412yes—
44C22×C32×C4—21no—
45C22×C32×C4C2311yescharacteristic
46C2×#638—28no—
47C2×#638—44no—
48C2×#638—44no—
49C22×C3⋊Dic3D412yes—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)D412yes—
61C2×C4⋊(C3⋊D3)D412yescomplemented
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64C2×C32×C8D412yescomplemented
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67#3753—28no—
68#3752—44no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C2×C3⋊(C3⋊C8)—21no—
73C2×C3⋊(C3⋊C8)D412yescomplemented
74#3745—28no—
75#2011—91noSylow
76C22×C3×D4C2×D314yes—
77C22×#67—68no—
78C22×D12—34no—
79C22×D12—34no—
80C22×C3×C8C2×D314yes—
81C2×C3×C4⋊C4C2×D314yes—
82#940—68no—
83#940—68no—
84C2×#213—68no—
85C2×#213—68no—
86C2×#213—68no—
87C2×(C2×D3)⋊C4—68no—
88C2×C4×Dic3—34no—
89C22×C3⋊C8—34no—
90C2×D24—68no—
91C2×D24—68no—
92C2×D24—68no—
93C3×#102—28no—
94#809—68no—
95C23×C32—22no—
96C23×C32—41no—
97C23×C32—41no—
98C23×C32—42no—
99C23×C32—42no—
100C23×C32C2×D411yescharacteristic
101C22×C3⋊D3—22no—
102C22×C3⋊D3—22no—
103C22×C3⋊D3—41no—
104C22×C3⋊D3—41no—
105C22×C3⋊D3—41no—
106C22×C3⋊D3—41no—
107C22×C3⋊D3—42no—
108C22×C3⋊D3—42no—
109C22×C3⋊D3—42no—
110C22×C3⋊D3—42no—
111C32×D4—22no—
112C32×D4—22no—
113C32×D4—41no—
114C32×D4—41no—
115C2×C32×C4—41no—
116C2×C32×C4—42no—
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123#638—416no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3D814yescomplemented
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)—22no—
131C4⋊(C3⋊D3)—41no—
132C4⋊(C3⋊D3)—41no—
133C4⋊(C3⋊D3)—41no—
134C4⋊(C3⋊D3)—41no—
135C32×C8—22no—
136C3⋊(C3⋊C8)—22no—
137C22×D8—91no—
138C22×D8—91no—
139C2×#127—91no—
140C2×#102—91no—
141C2×#102C3⋊D311yescharacteristic, complemented
142#390—91no—
143#336—91no—
144C24×C3—24no—
145C23×D3—64no—
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×D4D1218yes—
153C22×C3×C4—24no—
154C22×C3×C4C22×D314yes—
155C2×#67—632no—
156C2×#67—1216no—
157C2×#67—1216no—
158C22×Dic3—38no—
159C2×D12—38no—
160C2×D12—38no—
161C2×D12—64no—
162C2×D12—64no—
163C2×D12—64no—
164C2×D12—64no—
165C2×D12—64no—
166C2×D12—64no—
167C2×D12—64no—
168C2×D12—64no—
169C2×D12—64no—
170C2×D12—64no—
171C2×C3×C8—24no—
172C2×C3×C8—24no—
173C2×C3×C8#6718yescomplemented
174C3×C4⋊C4—24no—
175C3×C4⋊C4—24no—
176#213—632no—
177(C2×D3)⋊C4—1216no—
178C4×Dic3—64no—
179C4×Dic3—64no—
180C2×C3⋊C8—38no—
181C2×C3⋊C8—64no—
182C2×C3⋊C8—64no—
183D24—632no—
184C22×C32—42no—
185C22×C32—44no—
186C22×C32—82no—
187C22×C32—81no—
188C22×C32—81no—
189C22×C32#12011yescharacteristic
190C22×C32#12111yescharacteristic
191C22×C32#12711yescharacteristic
192C22×C32C2×D812yes—
193C22×C32AGL(1,ℤ/8)12yes—
194C2×C3⋊D3—42no—
195C2×C3⋊D3—42no—
196C2×C3⋊D3—44no—
197C2×C3⋊D3—44no—
198C2×C3⋊D3—82no—
199C2×C3⋊D3—82no—
200C2×C3⋊D3—81no—
201C2×C3⋊D3—81no—
202C2×C3⋊D3—81no—
203C2×C3⋊D3—81no—
204C32×C4—81no—
205C32×C4#12011yescharacteristic
206C32×C4#12011yescharacteristic
207C32×C4#12111yescharacteristic
208C32×C4#12111yescharacteristic
209C3⋊Dic3—24no—
210C22×D4—91no—
211C22×D4—91no—
212C22×D4—182no—
213C22×D4C2×C3⋊D311yescharacteristic
214C2×D8—182no—
215C2×D8—182no—
216C2×D8—182no—
217C2×D8—182no—
218C2×D8—182no—
219C2×D8—182no—
220C22×C8—91no—
221C22×C8C2×C3⋊D311yescharacteristic
222#127—182no—
223#127—182no—
224C2×C4⋊C4C2×C3⋊D311yescharacteristic
225C2×C22⋊C4—182no—
226C2×C42—91no—
227#102—22no—
228#102—182no—
229C23×C3—28no—
230C23×C3—44no—
231C23×C3—48no—
232C23×C3—48no—
233C23×C3—44no—
234C23×C3D3×D414yes—
235C22×D3—68no—
236C22×D3—68no—
237C22×D3—124no—
238C22×D3—124no—
239C22×D3—128no—
240C22×D3—128no—
241C22×D3—128no—
242C22×D3—128no—
243C22×D3—124no—
244C22×D3—124no—
245C3×D4—28no—
246C3×D4—28no—
247C3×D4—44no—
248C3×D4—44no—
249C2×C3×C4—48no—
250C2×C3×C4—44no—
251C2×C3×C4C2×D1214yes—
252C2×C3×C4#23514yes—
253C2×C3×C4D3×D414yes—
254C2×C3×C4D3×D414yes—
255C2×C3×C4D3×D414yes—
256C2×C3×C4C2×#6714yes—
257#67—1264no—
258C2×Dic3—316no—
259C2×Dic3—68no—
260C2×Dic3—68no—
261D12—68no—
262D12—68no—
263D12—68no—
264D12—68no—
265D12—124no—
266D12—124no—
267D12—124no—
268D12—124no—
269C3×C8—28no—
270C3⋊C8—68no—
271C2×C32—82no—
272C2×C32#39211yescharacteristic
273C2×C32#44712yes—
274C2×C32#45912yes—
275C2×C32#49311yescharacteristic
276C2×C32#49611yescharacteristic
277C3⋊D3—82no—
278C3⋊D3—82no—
279C24—21no—
280C24—181no—
281C24—181no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—92no—
288C2×D4—92no—
289C2×D4—188no—
290C2×D4—181no—
291C2×D4—181no—
292C2×D4—181no—
293C2×D4—181no—
294C2×D4—181no—
295C2×D4—181no—
296C2×D4—181no—
297C2×D4—181no—
298C2×D4—181no—
299C2×D4—181no—
300C2×D4—364no—
301C2×D4—364no—
302C2×D4C4⋊(C3⋊D3)12yes—
303C22×C4—21no—
304C22×C4—92no—
305C22×C4C22×C3⋊D311yescharacteristic
306D8—188no—
307D8—188no—
308C2×C8—21no—
309C2×C8—21no—
310C2×C8—92no—
311C2×C8—181no—
312C2×C8—181no—
313C2×C8#63812yescomplemented
314C4⋊C4—21no—
315C4⋊C4—21no—
316C22⋊C4—364no—
317C42—181no—
318C42—181no—
319C22×C3—48no—
320C22×C3—416no—
321C22×C3—84no—
322C22×C3—84no—
323C22×C3—88no—
324C22×C3#88214yes—
325C22×C3#88414yes—
326C22×C3D3×D818yes—
327C22×C3#91418yes—
328C22×C3#94014yes—
329C2×D3—128no—
330C2×D3—128no—
331C2×D3—1216no—
332C2×D3—1216no—
333C2×D3—244no—
334C2×D3—244no—
335C2×D3—244no—
336C2×D3—244no—
337C2×D3—248no—
338C2×D3—248no—
339C3×C4—84no—
340C3×C4#88214yes—
341C3×C4#88414yes—
342C3×C4#93014yes—
343C3×C4#93714yes—
344Dic3—616no—
345C32#201111yescharacteristic, complemented, Sylow
346C23—22no—
347C23—41no—
348C23—42no—
349C23—42no—
350C23—41no—
351C23—182no—
352C23—182no—
353C23—361no—
354C23—361no—
355C23—362no—
356C23—362no—
357C23—362no—
358C23—362no—
359C23—361no—
360C23—361no—
361C23D4×C3⋊D311yescharacteristic
362D4—22no—
363D4—22no—
364D4—41no—
365D4—41no—
366D4—182no—
367D4—182no—
368D4—182no—
369D4—182no—
370D4—3616no—
371D4—361no—
372D4—361no—
373D4—361no—
374D4—361no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—94no—
378C2×C4—182no—
379C2×C4—182no—
380C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
381C2×C4#382811yescharacteristic
382C2×C4D4×C3⋊D311yescharacteristic
383C2×C4D4×C3⋊D311yescharacteristic
384C2×C4D4×C3⋊D311yescharacteristic
385C2×C4C2×#63811yescharacteristic
386C8—22no—
387C8—182no—
388C2×C3—88no—
389C2×C3#477318yes—
390C2×C3#478618yes—
391C2×C3#496014yes—
392C2×C3#515114yes—
393C2×C3#517614yes—
394D3—248no—
395D3—248no—
396C22—42no—
397C22—44no—
398C22—81no—
399C22—81no—
400C22—82no—
401C22—362no—
402C22—362no—
403C22—364no—
404C22—364no—
405C22—721no—
406C22—721no—
407C22—721no—
408C22—721no—
409C22—722no—
410C22—722no—
411C22#6409111yescharacteristic
412C22#6409311yescharacteristic
413C22D8×C3⋊D312yes—
414C22#6412312yes—
415C22#6414911yescharacteristic
416C4—81no—
417C4—184no—
418C4#6409111yescharacteristic
419C4#6409311yescharacteristic
420C4#6413911yescharacteristic
421C4#6414611yescharacteristic
422C3#7020914yescomplemented
423C2—82no—
424C2—722no—
425C2—722no—
426C2#1059247212yes—
427C2#1059248512yes—
428C2#1059265911yescharacteristic
429C2#1059285011yescharacteristic
430C2#1059287511yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
hypercenterC2×#102C3⋊D3
hypocenterC32#2011
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#64149C2semidirect
2. C22×#3753C2semidirect
3. C22×#3745C2semidirect
4. C2×C32×#102C2semidirect
5. #10592687C2semidirect
6. C2×#63636C2semidirect
7. #10589416C2semidirect
31. C2×C3×#102D3semidirect
61. C2×C4⋊(C3⋊D3)D4semidirect
64. C2×C32×C8D4semidirect
73. C2×C3⋊(C3⋊C8)D4semidirect
126. C2×C3⋊Dic3D8semidirect
141. C2×#102C3⋊D3semidirect
173. C2×C3×C8#67semidirect
313. C2×C8#638semidirect
345. C32#2011semidirect
422. C3#70209semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C22×#37532
C22×#37452
C2×C32×#1022
#105926872
C2×#636362
#105894162
#702093