Finite Group Databasebeta

← #11800921

Subgroups — #11800921

Order 1152.

1773 conjugacy classes of subgroups.

The subgroup lattice has 461 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
2C2×#63894C212yesmaximal
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4C3×#4932C211yesmaximal, characteristic, complemented
5#10591370C212yesmaximal, complemented
6Dic3×C4⋊Dic3C212yesmaximal, complemented
7#10591260C212yesmaximal, complemented
8#10591233C214yesmaximal, complemented
9#73751—31nomaximal
10#73412—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3C2212yes—
13C22×#624C2214yes—
14C2×C32×C42C2211yescharacteristic
15C2×#3752C2212yes—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C418yescomplemented
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×C3×C4×Dic3C2212yes—
21C2×#3722C2214yes—
22C2×Dic32C2214yes—
23#63894C4116yescomplemented
24C3×C3⋊#95C2212yes—
25C3×C3⋊#95C2211yescharacteristic
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2211yescharacteristic
28#63579C2214yes—
29C2×#893—32no—
30C2×C4×D12—31no—
31C2×C4×D12—31no—
32C2×C4×D12—32no—
33C2×C4×D12—61no—
34C3×C4×C4⋊C4—31no—
35C3×#376—31no—
36Dic3×C4⋊C4—32no—
37C4×(C2×D3)⋊C4—34no—
38C4×C4⋊Dic3—32no—
39C4×C4⋊Dic3D311yescharacteristic, complemented
40#4932D311yescharacteristic, complemented
41#4666—34no—
42#4666—32no—
43#4666—32no—
44D3×#95—32no—
45D3×#95—32no—
46C23×C3⋊D3C2312yes—
47C22×C32×C4C2311yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C32×C4C2311yescharacteristic
50C22×C3⋊Dic3C2312yes—
51C2×C4⋊(C3⋊D3)C2×C414yes—
52C2×C4⋊(C3⋊D3)C2×C418yes—
53C2×C4×C3⋊D3—44no—
54C2×C4×C3⋊D3C2×C418yescomplemented
55C22×C3×Dic3C2314yes—
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2312yes—
58C2×#624—44no—
59C2×#624—44no—
60C2×#624C2×C4116yescomplemented
61C32×C42C2×C414yescomplemented
62#3752C2×C418yescomplemented
63C4⋊(C3⋊Dic3)C2×C414yescomplemented
64C3×C4⋊Dic3C2×C418yescomplemented
65C3×C4×Dic3—42no—
66C3×C4×Dic3C2×C418yescomplemented
67#3722C2×C4116yescomplemented
68Dic32—44no—
69#2275—91noSylow
70C22×D12—31no—
71C22×D12—31no—
72C22×D12—61no—
73C22×C4×D3—32no—
74C22×C4×D3—32no—
75C22×C4×D3—34no—
76C22×C4×D3—34no—
77C22×C4×D3—62no—
78C2×C3×C4⋊C4—32no—
79C2×C3×C42—21no—
80C2×C3×C42—32no—
81C2×C3×C42—32no—
82C2×C3×C42C2×D311yescharacteristic
83C2×C3×C42C2×D311yescharacteristic
84C2×(C2×D3)⋊C4—32no—
85C2×(C2×D3)⋊C4—32no—
86C2×(C2×D3)⋊C4—34no—
87C2×(C2×D3)⋊C4—34no—
88C2×(C2×D3)⋊C4—62no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3C2×D312yes—
93C2×C4×Dic3—34no—
94C2×C4×Dic3—34no—
95C2×C4×Dic3C2×D312yes—
96C2×C4×Dic3C2×D312yes—
97#893—316no—
98C4×D12—38no—
99C4×D12—38no—
100C4×D12—316no—
101C4×D12—68no—
102C3×#95—31no—
103C3×#95—32no—
104C3×#95—32no—
105C3×#95—31no—
106C3⋊#95—34no—
107C3⋊#95—34no—
108C3⋊#95C2×D311yescharacteristic
109C3⋊#95C2×D312yes—
110C3⋊#95C2×D311yescharacteristic
111C3⋊#95C2×D312yes—
112C23×C32C2411yescharacteristic
113C22×C3⋊D3—22no—
114C22×C3⋊D3—24no—
115C22×C3⋊D3—22no—
116C22×C3⋊D3C22×C418yes—
117C22×C3⋊D3C22×C414yes—
118C2×C32×C4—22no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4C22×C412yes—
122C2×C32×C4C22×C412yes—
123C2×C32×C4C22×C414yes—
124C2×C32×C4C22×C412yes—
125C2×C3⋊Dic3—24no—
126C2×C3⋊Dic3C22×C414yes—
127C4⋊(C3⋊D3)C42116yescomplemented
128C4×C3⋊D3—48no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—24no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3C22×C414yes—
136C2×C3×Dic3C22×C418yes—
137C2×C3×Dic3C22×C414yes—
138#624—416no—
139C2×C4×D4—92no—
140C2×C4×D4—91no—
141C4×C4⋊C4—31no—
142C4×C4⋊C4—92no—
143C4×C22⋊C4—92no—
144C4×C22⋊C4—94no—
145#376—31no—
146C2×#95—92no—
147C23×D3—32no—
148C23×D3—32no—
149C23×D3—62no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—32no—
154C22×C3×C4—34no—
155C22×C3×C4—32no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×Dic3—32no—
163C22×Dic3—32no—
164C22×Dic3—62no—
165C22×Dic3C22×D312yes—
166C22×Dic3C22×D314yes—
167C22×Dic3C22×D312yes—
168C2×D12—38no—
169C2×D12—34no—
170C2×D12—34no—
171C2×D12—38no—
172C2×D12—64no—
173C2×D12—68no—
174C2×C4×D3—38no—
175C2×C4×D3—38no—
176C2×C4×D3—316no—
177C2×C4×D3—316no—
178C2×C4×D3—68no—
179C2×C4×D3—124no—
180C2×C4×D3—124no—
181C2×C4×D3—124no—
182C2×C4×D3—124no—
183C2×C4×D3—124no—
184C2×C4×D3—124no—
185C2×C4×D3—128no—
186C3×C4⋊C4—38no—
187C3×C42—24no—
188C3×C42—38no—
189C3×C42—122no—
190C3×C42C4×D314yescomplemented
191C3×C42C4×D314yescomplemented
192(C2×D3)⋊C4—38no—
193(C2×D3)⋊C4—38no—
194(C2×D3)⋊C4—316no—
195(C2×D3)⋊C4—316no—
196(C2×D3)⋊C4—68no—
197C4⋊Dic3—34no—
198C4⋊Dic3—34no—
199C4⋊Dic3—64no—
200C4⋊Dic3C4×D318yescomplemented
201C4×Dic3—42no—
202C4×Dic3—124no—
203C4×Dic3—124no—
204C4×Dic3C4×D318yescomplemented
205C22×C32C23×C412yes—
206C22×C32C23×C411yescharacteristic
207C22×C32H(5,𝔽2)11yescharacteristic
208C22×C32H(5,𝔽2)12yes—
209C22×C322−1+411yescharacteristic
210C2×C3⋊D3—28no—
211C2×C3⋊D3—24no—
212C2×C3⋊D3—24no—
213C2×C3⋊D3—28no—
214C2×C3⋊D3C2×C4218yes—
215C32×C4—22no—
216C32×C4—22no—
217C32×C4C2×C4214yes—
218C3⋊Dic3—24no—
219C3×Dic3—24no—
220C3×Dic3—28no—
221C3×Dic3—24no—
222C22×D4—91no—
223C23×C4—94no—
224C23×C4—92no—
225C4×D4—916no—
226C4×D4—98no—
227C2×C4⋊C4—32no—
228C2×C4⋊C4—91no—
229C2×C22⋊C4—94no—
230C2×C22⋊C4—92no—
231C2×C42—32no—
232C2×C42—32no—
233C2×C42—94no—
234C2×C42D3211yescharacteristic
235#95—31no—
236#95—32no—
237#95—32no—
238#95—31no—
239#95—94no—
240C23×C3—21no—
241C23×C3C23×D311yescharacteristic
242C23×C3C23×D311yescharacteristic
243C22×D3—38no—
244C22×D3—38no—
245C22×D3—34no—
246C22×D3—34no—
247C22×D3—64no—
248C22×D3—68no—
249C22×D3—62no—
250C22×D3—62no—
251C22×D3—62no—
252C22×D3—64no—
253C22×D3—64no—
254C22×D3—62no—
255C22×D3—124no—
256C22×D3—122no—
257C22×D3—122no—
258C2×C3×C4—24no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—22no—
263C2×C3×C4—22no—
264C2×C3×C4—21no—
265C2×C3×C4—24no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—34no—
270C2×C3×C4—38no—
271C2×C3×C4—34no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—62no—
277C2×C3×C4—64no—
278C2×C3×C4—64no—
279C2×C3×C4—62no—
280C2×C3×C4C2×C4×D314yes—
281C2×C3×C4C2×C4×D314yes—
282C2×C3×C4C2×C4×D312yes—
283C2×C3×C4C2×C4×D312yes—
284C2×C3×C4C2×C4×D312yes—
285C2×C3×C4C2×C4×D312yes—
286C2×C3×C4C2×C4×D312yes—
287C2×C3×C4C2×C4×D312yes—
288C2×Dic3—24no—
289C2×Dic3—22no—
290C2×Dic3—24no—
291C2×Dic3—22no—
292C2×Dic3—22no—
293C2×Dic3—22no—
294C2×Dic3—34no—
295C2×Dic3—34no—
296C2×Dic3—64no—
297C2×Dic3—64no—
298C2×Dic3—64no—
299C2×Dic3—124no—
300C2×Dic3C2×C4×D314yes—
301C2×Dic3C2×C4×D314yes—
302C2×Dic3C2×C4×D318yes—
303D12—316no—
304D12—316no—
305D12—616no—
306C4×D3—1216no—
307C4×D3—1216no—
308C4×D3—128no—
309C4×D3—128no—
310C4×D3—1216no—
311C2×C32C22×C4211yescharacteristic
312C2×C32#51811yescharacteristic
313C2×C32#51812yes—
314C2×C32#52011yescharacteristic
315C2×C32#52012yes—
316C3⋊D3—28no—
317C24—92no—
318C2×D4—98no—
319C2×D4—94no—
320C22×C4—32no—
321C22×C4—32no—
322C22×C4—34no—
323C22×C4—916no—
324C22×C4—92no—
325C22×C4—98no—
326C22×C4—364no—
327C22×C4—364no—
328C22×C4—364no—
329C22×C4C2×D3211yescharacteristic
330C22×C4C2×D3211yescharacteristic
331C22×C4C2×D3211yescharacteristic
332C4⋊C4—38no—
333C4⋊C4—94no—
334C22⋊C4—916no—
335C22⋊C4—98no—
336C42—38no—
337C42—122no—
338C42—364no—
339C42#62414yescomplemented
340C22×C3—21no—
341C22×C3—22no—
342C22×C3—21no—
343C22×C3—22no—
344C22×C3—21no—
345C22×C3C22×C4×D312yes—
346C22×C3C22×C4×D312yes—
347C22×C3C22×C4×D311yescharacteristic
348C22×C3C22×C4×D311yescharacteristic
349C22×C3#100411yescharacteristic
350C22×C3#100711yescharacteristic
351C22×C3#100911yescharacteristic
352C22×C3#100912yes—
353C22×C3#100912yes—
354C22×C3#101011yescharacteristic
355C2×D3—38no—
356C2×D3—38no—
357C2×D3—68no—
358C2×D3—64no—
359C2×D3—64no—
360C2×D3—64no—
361C2×D3—68no—
362C2×D3—68no—
363C2×D3—64no—
364C2×D3—68no—
365C2×D3—68no—
366C2×D3—124no—
367C2×D3—128no—
368C2×D3—124no—
369C2×D3—128no—
370C3×C4—24no—
371C3×C4—22no—
372C3×C4—22no—
373C3×C4—22no—
374C3×C4—22no—
375C3×C4—24no—
376C3×C4—42no—
377C3×C4—68no—
378C3×C4—64no—
379C3×C4—64no—
380C3×C4C42×D314yes—
381C3×C4C42×D314yes—
382Dic3—24no—
383Dic3—24no—
384Dic3—28no—
385Dic3—64no—
386Dic3—64no—
387Dic3—124no—
388C32#227511yescharacteristic, complemented, Sylow
389C23—98no—
390C23—94no—
391C23—182no—
392C23—182no—
393C23—184no—
394C23C22×D3211yescharacteristic
395D4—916no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—22no—
399C2×C4—34no—
400C2×C4—34no—
401C2×C4—38no—
402C2×C4—62no—
403C2×C4—64no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—64no—
407C2×C4—62no—
408C2×C4—94no—
409C2×C4—184no—
410C2×C4—368no—
411C2×C4—3616no—
412C2×C4C4×D3214yes—
413C2×C4C2×#62412yes—
414C2×C4C2×#62412yes—
415C2×C4C2×#62412yes—
416C2×C3—21no—
417C2×C3—22no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—22no—
421C2×C3C2×C42×D311yescharacteristic
422C2×C3C2×C42×D311yescharacteristic
423C2×C3#550411yescharacteristic
424C2×C3#552111yescharacteristic
425C2×C3#552111yescharacteristic
426C2×C3#552112yes—
427C2×C3#552312yes—
428C2×C3#552311yescharacteristic
429C2×C3#554512yes—
430C2×C3#557412yes—
431D3—68no—
432D3—68no—
433D3—128no—
434C22—98no—
435C22—188no—
436C22—184no—
437C22—184no—
438C22—188no—
439C22#6429711yescharacteristic
440C22C2×C4×D3212yes—
441C22#6430711yescharacteristic
442C22#6430812yes—
443C22C22×#62411yescharacteristic
444C4—22no—
445C4—22no—
446C4—64no—
447C4—64no—
448C4—68no—
449C4—184no—
450C4C4×#62414yes—
451C3—21no—
452C3#7341211yescharacteristic, complemented
453C3#7375111yescharacteristic, complemented
454C2—188no—
455C2#1059389012yes—
456C2#1059399412yes—
457C2C2×C4×#62411yescharacteristic
458C2#1059499011yescharacteristic
459C2#1059499611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#2275
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×C4×C4⋊Dic3C2semidirect
4. C3×#4932C2semidirect
5. #10591370C2semidirect
6. Dic3×C4⋊Dic3C2semidirect
7. #10591260C2semidirect
8. #10591233C2semidirect
17. C4×C4⋊(C3⋊D3)C4semidirect
23. #63894C4semidirect
39. C4×C4⋊Dic3D3semidirect
40. #4932D3semidirect
54. C2×C4×C3⋊D3C2×C4semidirect
60. C2×#624C2×C4semidirect
61. C32×C42C2×C4semidirect
62. #3752C2×C4semidirect
63. C4⋊(C3⋊Dic3)C2×C4semidirect
64. C3×C4⋊Dic3C2×C4semidirect
66. C3×C4×Dic3C2×C4semidirect
67. #3722C2×C4semidirect
127. C4⋊(C3⋊D3)C42semidirect
190. C3×C42C4×D3semidirect
191. C3×C42C4×D3semidirect
200. C4⋊Dic3C4×D3semidirect
204. C4×Dic3C4×D3semidirect
339. C42#624semidirect
388. C32#2275semidirect
452. C3#73412semidirect
453. C3#73751semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×#638942
C3×C4×C4⋊Dic32
C3×#49322
#105913702
Dic3×C4⋊Dic32
#105912602
#105912332
#737513
#734123