Finite Group Databasebeta

← #11874449

Subgroups — #11874449

Order 1152.

1283 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595948C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C2×#63829C214yesmaximal, complemented
4C2×C3×#803C211yesmaximal, characteristic, complemented
5#10590374C212yesmaximal, complemented
6#10590372C212yesmaximal, complemented
7#10590371C212yesmaximal, complemented
8#10590351C212yesmaximal, complemented
9#83286—31nomaximal
10#78499—31nomaximal
11C2×#3828C2212yes—
12C2×C3×#235C2212yes—
13C2×C32×C42C2211yescharacteristic
14#64139—22no—
15#64084C2212yes—
16#64083C2211yescharacteristic
17C4×C4⋊(C3⋊D3)—22no—
18#64078C2211yescharacteristic
19C3×#930—22no—
20C22×C3×C3⋊C8C2212yes—
21C3×#875C2212yes—
22C3×#874C2211yescharacteristic
23C3×C4×D12—22no—
24C3×#869C2211yescharacteristic
25C2×#3719C2214yes—
26C2×#3717C2214yes—
27#63829—216no—
28C2×#3716C2214yes—
29C2×#3714C2214yes—
30C3×#803C2212yes—
31C3×#803C2212yes—
32C3×#532—31no—
33C2×#950—34no—
34C2×#904—34no—
35#5477—31no—
36#5477—31no—
37#5477—61no—
38#5477D311yescharacteristic, complemented
39C2×C3×#97—31no—
40#5086—32no—
41#5074—32no—
42#5060—32no—
43#5058—32no—
44C2×#803D311yescharacteristic, complemented
45#4715—32no—
46#4715—32no—
47#4712—32no—
48#4712—32no—
49C22×C32×C4D412yes—
50C22×C32×C4C2311yescharacteristic
51C2×#638—22no—
52#3828—28no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C2×C4×C3⋊D3—22no—
56C2×#634C2312yes—
57C2×C3×#67—22no—
58C3×#235—28no—
59C2×C3×D12—22no—
60C2×C3×D12C2312yes—
61C2×C3×C4×D3—22no—
62C2×C3×Dic6C2312yes—
63C32×C42D412yes—
64C32×C42C2311yescharacteristic
65C32×C42C2311yescharacteristic
66#3752—24no—
67C4⋊(C3⋊Dic3)—22no—
68C3×(C2×D3)⋊C4—24no—
69C3×C4⋊Dic3—22no—
70C2×C3×C3⋊C8D418yescomplemented
71C2×C3×C3⋊C8C2314yes—
72#3719—28no—
73#3717—28no—
74#3716—28no—
75#3714—28no—
76#3150—91noSylow
77C2×C3×#41—32no—
78C2×#235—32no—
79C2×#235—32no—
80C2×#235—62no—
81C2×#235C2×D312yes—
82C22×C3×C8—32no—
83C3×C4⋊Q8—31no—
84C3×#127—31no—
85C3×#124—32no—
86C3×#121—62no—
87C3×C4×D4—62no—
88C2×C3×C42—21no—
89C2×C3×C42C2×D311yescharacteristic
90C2×C3×C42C2×D311yescharacteristic
91#950—616no—
92C2×#216—34no—
93C2×#215—34no—
94C2×#214—34no—
95C2×#213—34no—
96#930—22no—
97#930—64no—
98#930—62no—
99#930—62no—
100C22×C3⋊C8C2×D312yes—
101C2×Dic12—34no—
102#904—616no—
103C2×D24—34no—
104C2×#204—34no—
105C2×#204—34no—
106#875—32no—
107#875—32no—
108#875—62no—
109#875C2×D312yes—
110#874—31no—
111#874—31no—
112#874—61no—
113#874C2×D311yescharacteristic
114C4×D12—22no—
115C4×D12—64no—
116C4×D12—62no—
117C4×D12—62no—
118#869—31no—
119#869—31no—
120#869—61no—
121#869C2×D311yescharacteristic
122C3×#97—32no—
123C3×#97—32no—
124#803C2×D312yes—
125#803C2×D312yes—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—22no—
128C22×C3×D3—22no—
129C2×C32×C4—42no—
130C2×C32×C4C2×D414yes—
131C2×C32×C4C2×D412yes—
132C2×C32×C4C2×D412yes—
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4C2411yescharacteristic
135#638—44no—
136C2×C3⋊Dic3—22no—
137C4⋊(C3⋊D3)—24no—
138C4⋊(C3⋊D3)—44no—
139C4×C3⋊D3—44no—
140#634—24no—
141C3×#67—44no—
142C2×C3×Dic3—22no—
143C3×D12—24no—
144C3×D12—44no—
145C3×C4×D3—44no—
146C3×Dic6—24no—
147C3×C3⋊C8C2×D418yes—
148C2×#135—94no—
149#532—31no—
150#532—91no—
151#497—92no—
152#497—92no—
153#496—92no—
154#496—92no—
155C2×#97—31no—
156C3×#41—68no—
157C2×C3×Q8—32no—
158C2×C3×D4—32no—
159C2×C3×D4—62no—
160C2×C3×D4—62no—
161C22×C3×C4—22no—
162C22×C3×C4—21no—
163C22×C3×C4—62no—
164C22×C3×C4D1212yes—
165C22×C3×C4#6712yes—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—22no—
169C2×#67—64no—
170C2×#67—62no—
171C2×#67—62no—
172#235—28no—
173#235—68no—
174#235—68no—
175#235—128no—
176C2×D12—22no—
177C2×D12—32no—
178C2×D12—32no—
179C2×D12—62no—
180C2×D12—64no—
181C2×D12—62no—
182C2×D12—62no—
183C2×D12C22×D312yes—
184C2×C4×D3—22no—
185C2×C4×D3—64no—
186C2×C4×D3—62no—
187C2×C4×D3—62no—
188C2×Dic6—32no—
189C2×Dic6—32no—
190C2×Dic6—62no—
191C2×Dic6C22×D312yes—
192C2×C3×C8—38no—
193C2×C3×C8—34no—
194C3×C4⋊C4—62no—
195C3×C22⋊C4—64no—
196C3×C42—22no—
197C3×C42—21no—
198C3×C42—21no—
199C3×C42D1212yes—
200C3×C42#6712yes—
201C3×C42C22×D311yescharacteristic
202C3×C42C22×D311yescharacteristic
203C3×C42C22×D311yescharacteristic
204C3×C42C22×D311yescharacteristic
205#216—68no—
206#215—68no—
207#214—68no—
208#213—68no—
209(C2×D3)⋊C4—24no—
210(C2×D3)⋊C4—68no—
211(C2×D3)⋊C4—64no—
212(C2×D3)⋊C4—64no—
213C4⋊Dic3—22no—
214C4⋊Dic3—64no—
215C4⋊Dic3—62no—
216C4⋊Dic3—62no—
217C2×C3⋊C8D1218yescomplemented
218C2×C3⋊C8C22×D314yes—
219Dic12—68no—
220D24—68no—
221#204—68no—
222#204—68no—
223C22×C32—22no—
224C22×C32#12712yes—
225C22×C32C22×D411yescharacteristic
226C2×C3⋊D3—42no—
227C2×C3⋊D3—44no—
228C2×C3×D3—42no—
229C2×C3×D3—44no—
230C32×C4—22no—
231C32×C4—22no—
232C32×C4#12712yes—
233C32×C4C22×D412yes—
234C3⋊Dic3—42no—
235C3×Dic3—42no—
236C2×#41—32no—
237C2×#41—92no—
238#135—1816no—
239C2×Q16—94no—
240C2×SD16—94no—
241C2×SD16—94no—
242C2×D8—94no—
243C22×C8—32no—
244C4⋊Q8—31no—
245C4⋊Q8—91no—
246#127—31no—
247#127—91no—
248#124—32no—
249#124—92no—
250#121—62no—
251#121—182no—
252C4×D4—62no—
253C4×D4—182no—
254C2×C42D3211yescharacteristic
255#97—32no—
256#97—32no—
257C23×C3—21no—
258C23×C3—62no—
259C23×C3C2×D1211yescharacteristic
260C23×C3C2×#6711yescharacteristic
261C22×D3—22no—
262C22×D3—64no—
263C22×D3—62no—
264C22×D3—62no—
265C3×Q8—64no—
266C3×D4—64no—
267C3×D4—124no—
268C3×D4—124no—
269C2×C3×C4—21no—
270C2×C3×C4—24no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—42no—
275C2×C3×C4—42no—
276C2×C3×C4—44no—
277C2×C3×C4—62no—
278C2×C3×C4—124no—
279C2×C3×C4C2×D1214yes—
280C2×C3×C4C2×D1212yes—
281C2×C3×C4C2×D1212yes—
282C2×C3×C4C2×D1211yescharacteristic
283C2×C3×C4D3×D414yes—
284C2×C3×C4C2×#6712yes—
285C2×C3×C4C2×#6712yes—
286C2×C3×C4C2×#6711yescharacteristic
287C2×C3×C4C23×D311yescharacteristic
288C2×C3×C4C23×D311yescharacteristic
289#67—44no—
290#67—128no—
291#67—124no—
292#67—124no—
293C2×Dic3—22no—
294C2×Dic3—64no—
295C2×Dic3—62no—
296C2×Dic3—62no—
297D12—24no—
298D12—44no—
299D12—64no—
300D12—64no—
301D12—124no—
302D12—128no—
303D12—124no—
304D12—124no—
305C4×D3—44no—
306C4×D3—128no—
307C4×D3—124no—
308C4×D3—124no—
309Dic6—24no—
310Dic6—64no—
311Dic6—64no—
312Dic6—124no—
313C3×C8—38no—
314C3⋊C8C2×D1218yes—
315C2×C32—22no—
316C2×C32C2×#12711yescharacteristic
317C2×C32#57512yes—
318C3⋊D3—82no—
319C3×D3—82no—
320#41—68no—
321#41—188no—
322C2×Q8—32no—
323C2×Q8—92no—
324C2×D4—32no—
325C2×D4—62no—
326C2×D4—62no—
327C2×D4—92no—
328C2×D4—182no—
329C2×D4—182no—
330C22×C4—62no—
331C22×C4—182no—
332C22×C4#62612yes—
333C22×C4C2×D3211yescharacteristic
334Q16—188no—
335SD16—188no—
336SD16—188no—
337D8—188no—
338C2×C8—34no—
339C2×C8—38no—
340C4⋊C4—62no—
341C4⋊C4—182no—
342C22⋊C4—64no—
343C22⋊C4—184no—
344C42#62612yes—
345C42C2×D3211yescharacteristic
346C42C2×D3211yescharacteristic
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—21no—
350C22×C3—22no—
351C22×C3—42no—
352C22×C3—122no—
353C22×C3—124no—
354C22×C3#87412yes—
355C22×C3#94012yes—
356C22×C3C22×D1211yescharacteristic
357C22×C3C22×#6711yescharacteristic
358C2×D3—42no—
359C2×D3—44no—
360C2×D3—124no—
361C2×D3—128no—
362C2×D3—122no—
363C2×D3—124no—
364C2×D3—122no—
365C2×D3—124no—
366C3×C4—24no—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—22no—
371C3×C4—22no—
372C3×C4—22no—
373C3×C4—42no—
374C3×C4—122no—
375C3×C4#87412yes—
376C3×C4#94012yes—
377C3×C4C22×D1212yes—
378C3×C4C2×D3×D412yes—
379Dic3—42no—
380Dic3—124no—
381Dic3—122no—
382Dic3—122no—
383C32#315011yescharacteristic, complemented, Sylow
384C23—62no—
385C23—182no—
386C23C2×#62611yescharacteristic
387Q8—64no—
388Q8—184no—
389D4—64no—
390D4—124no—
391D4—124no—
392D4—184no—
393D4—364no—
394D4—364no—
395C2×C4—42no—
396C2×C4—62no—
397C2×C4—124no—
398C2×C4—182no—
399C2×C4—364no—
400C2×C4D3×D1214yes—
401C2×C4C2×#62612yes—
402C2×C4C2×#62612yes—
403C2×C4C2×#62611yescharacteristic
404C2×C4C22×D3211yescharacteristic
405C8—38no—
406C2×C3—22no—
407C2×C3—22no—
408C2×C3—21no—
409C2×C3—22no—
410C2×C3—42no—
411C2×C3—242no—
412C2×C3C2×#87411yescharacteristic
413C2×C3#574812yes—
414C2×C3C2×#94011yescharacteristic
415C2×C3#582212yes—
416D3—82no—
417D3—244no—
418D3—242no—
419D3—242no—
420C22—22no—
421C22—122no—
422C22—124no—
423C22—362no—
424C22—364no—
425C22#6391112yes—
426C22C22×#62611yescharacteristic
427C4—22no—
428C4—22no—
429C4—122no—
430C4—362no—
431C4#6391112yes—
432C4C2×D3×D1212yes—
433C3—21no—
434C3#7849911yescharacteristic, complemented
435C3#8328611yescharacteristic, complemented
436C2—22no—
437C2—242no—
438C2—722no—
439C2#1059479512yes—
440C2C2×#6391111yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
hypercenterC2×C42D32
hypocenterC32#3150
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595948C2semidirect
2. C3×#5477C2semidirect
3. C2×#63829C2semidirect
4. C2×C3×#803C2semidirect
5. #10590374C2semidirect
6. #10590372C2semidirect
7. #10590371C2semidirect
8. #10590351C2semidirect
38. #5477D3semidirect
44. C2×#803D3semidirect
70. C2×C3×C3⋊C8D4semidirect
217. C2×C3⋊C8D12semidirect
383. C32#3150semidirect
434. C3#78499semidirect
435. C3#83286semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×#54772
C2×#638292
C2×C3×#8032
#105903742
#105903722
#105903712
#105903512
#832863
#784993