Finite Group Databasebeta

← #11805516

Subgroups — #11805516

Order 1152.

1621 conjugacy classes of subgroups.

The subgroup lattice has 466 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×#4936C211yesmaximal, characteristic, complemented
4C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#10591378C214yesmaximal, complemented
6#10591370C212yesmaximal, complemented
7#10591355C212yesmaximal, complemented
8#10591212C212yesmaximal, complemented
9#74228—31nomaximal
10#73770—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×#3724C2214yes—
22C2×#3722C2214yes—
23#63894—28no—
24C3×C3⋊#95C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×C3⋊#95C2212yes—
27C3×C3⋊#95C2212yes—
28#63579C2214yes—
29C2×#893—32no—
30C2×C4×D12—31no—
31C2×C4×D12—31no—
32C2×C4×D12—32no—
33C2×C4×D12—61no—
34C3×#382—31no—
35C3×C4×C4⋊C4—31no—
36#4989—34no—
37#4972—32no—
38#4936D311yescharacteristic, complemented
39C4×C4⋊Dic3D311yescharacteristic, complemented
40#4928—32no—
41#4668—34no—
42#4667—32no—
43#4667—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)D414yes—
53C2×C4⋊(C3⋊D3)Q814yes—
54C2×C4×C3⋊D3—44no—
55C2×C4×C3⋊D3C2×C418yescomplemented
56C22×C3×Dic3C2312yes—
57C22×C3×Dic3C2314yes—
58C22×C3×Dic3C2312yes—
59C2×#624—28no—
60C2×#624—28no—
61C2×#624—44no—
62C32×C42C2×C414yescomplemented
63#3752C2×C418yescomplemented
64C4⋊(C3⋊Dic3)C2×C414yescomplemented
65C3×C4⋊Dic3—24no—
66C3×C4⋊Dic3—24no—
67C3×C4×Dic3—24no—
68#3724—44no—
69#3722—28no—
70#2349—91noSylow
71C22×D12—31no—
72C22×D12—31no—
73C22×D12—61no—
74C22×C4×D3—32no—
75C22×C4×D3—32no—
76C22×C4×D3—34no—
77C22×C4×D3—34no—
78C22×C4×D3—62no—
79C2×C3×C4⋊C4—32no—
80C2×C3×C4⋊C4—32no—
81C2×C3×C42—21no—
82C2×C3×C42—32no—
83C2×C3×C42C2×D311yescharacteristic
84C2×C3×C42C2×D311yescharacteristic
85C2×(C2×D3)⋊C4—32no—
86C2×(C2×D3)⋊C4—32no—
87C2×(C2×D3)⋊C4—34no—
88C2×(C2×D3)⋊C4—34no—
89C2×(C2×D3)⋊C4—62no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—61no—
93C2×C4⋊Dic3C2×D312yes—
94C2×C4⋊Dic3C2×D312yes—
95C2×Dic3⋊C4—34no—
96C2×Dic3⋊C4—34no—
97C2×C4×Dic3C2×D312yes—
98#893—68no—
99C4×D12—38no—
100C4×D12—38no—
101C4×D12—68no—
102C4×D12—68no—
103C3×#95—31no—
104C3×#95—32no—
105C3×#95—31no—
106C3×#95—32no—
107C3⋊#95—34no—
108C3⋊#95—34no—
109C3⋊#95C2×D311yescharacteristic
110C3⋊#95C2×D312yes—
111C3⋊#95C2×D311yescharacteristic
112C3⋊#95C2×D312yes—
113C23×C32C2411yescharacteristic
114C22×C3⋊D3—24no—
115C22×C3⋊D3—24no—
116C22×C3⋊D3C22×C414yes—
117C22×C3⋊D3C2×D414yes—
118C22×C3⋊D3C2×Q814yes—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4C22×C412yes—
122C2×C32×C4C22×C412yes—
123C2×C32×C4C22×C412yes—
124C2×C32×C4C2×D412yes—
125C2×C32×C4C2×Q812yes—
126C2×C3⋊Dic3—24no—
127C2×C3⋊Dic3C22×C414yes—
128C4⋊(C3⋊D3)C4⋊C4116yescomplemented
129C4×C3⋊D3—48no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—24no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—24no—
138C2×C3×Dic3#4114yes—
139#624—416no—
140C2×C4×D4—92no—
141C2×C4×D4—91no—
142#389—92no—
143#385—94no—
144#382—31no—
145#380—92no—
146C4×C4⋊C4—31no—
147C2×#95—92no—
148C23×D3—32no—
149C23×D3—32no—
150C23×D3—62no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—32no—
155C22×C3×C4—34no—
156C22×C3×C4—32no—
157C22×C3×C4C22×D311yescharacteristic
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—32no—
164C22×Dic3—32no—
165C22×Dic3—62no—
166C22×Dic3C22×D314yes—
167C22×Dic3C22×D312yes—
168C22×Dic3C22×D312yes—
169C2×D12—34no—
170C2×D12—34no—
171C2×D12—34no—
172C2×D12—34no—
173C2×D12—34no—
174C2×D12—34no—
175C2×D12—64no—
176C2×D12—64no—
177C2×D12—64no—
178C2×C4×D3—38no—
179C2×C4×D3—38no—
180C2×C4×D3—68no—
181C2×C4×D3—68no—
182C2×C4×D3—68no—
183C2×C4×D3—68no—
184C2×C4×D3—68no—
185C2×C4×D3—124no—
186C2×C4×D3—124no—
187C2×C4×D3—124no—
188C2×C4×D3—124no—
189C2×C4×D3—128no—
190C3×C4⋊C4—64no—
191C3×C4⋊C4—64no—
192C3×C42—24no—
193C3×C42—64no—
194C3×C42C4×D314yescomplemented
195C3×C42C4×D314yescomplemented
196(C2×D3)⋊C4—38no—
197(C2×D3)⋊C4—38no—
198(C2×D3)⋊C4—68no—
199(C2×D3)⋊C4—68no—
200(C2×D3)⋊C4—68no—
201C4⋊Dic3—24no—
202C4⋊Dic3—24no—
203C4⋊Dic3—34no—
204C4⋊Dic3—34no—
205C4⋊Dic3—64no—
206Dic3⋊C4—124no—
207Dic3⋊C4—124no—
208C4×Dic3—24no—
209C22×C32C23×C411yescharacteristic
210C22×C32C22×D411yescharacteristic
211C22×C32C22×Q811yescharacteristic
212C22×C32C2×#4112yes—
213C22×C32H(5,𝔽2)12yes—
214C2×C3⋊D3—24no—
215C2×C3⋊D3—24no—
216C2×C3⋊D3—28no—
217C2×C3⋊D3—28no—
218C2×C3⋊D3C2×C4⋊C418yes—
219C32×C4—22no—
220C32×C4—22no—
221C32×C4C2×C4⋊C414yes—
222C3⋊Dic3—24no—
223C3×Dic3—24no—
224C3×Dic3—44no—
225C3×Dic3—42no—
226C22×D4—91no—
227C23×C4—94no—
228C23×C4—92no—
229C4×D4—98no—
230C4×D4—188no—
231C2×C4⋊C4—32no—
232C2×C4⋊C4—32no—
233C2×C4⋊C4—91no—
234C2×C4⋊C4—94no—
235C2×C22⋊C4—92no—
236C2×C22⋊C4—94no—
237C2×C42—32no—
238C2×C42D3211yescharacteristic
239#95—31no—
240#95—32no—
241#95—31no—
242#95—32no—
243#95—94no—
244C23×C3—21no—
245C23×C3C23×D311yescharacteristic
246C23×C3C23×D311yescharacteristic
247C22×D3—34no—
248C22×D3—34no—
249C22×D3—34no—
250C22×D3—34no—
251C22×D3—34no—
252C22×D3—34no—
253C22×D3—64no—
254C22×D3—64no—
255C22×D3—64no—
256C22×D3—64no—
257C22×D3—64no—
258C22×D3—64no—
259C22×D3—64no—
260C22×D3—124no—
261C22×D3—124no—
262C2×C3×C4—24no—
263C2×C3×C4—22no—
264C2×C3×C4—22no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—34no—
273C2×C3×C4—42no—
274C2×C3×C4—62no—
275C2×C3×C4—62no—
276C2×C3×C4—64no—
277C2×C3×C4—62no—
278C2×C3×C4—64no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4—64no—
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×C3×C4D3×D412yes—
289C2×C3×C4D3×D412yes—
290C2×C3×C4D3×Q812yes—
291C2×C3×C4D3×Q812yes—
292C2×Dic3—22no—
293C2×Dic3—22no—
294C2×Dic3—22no—
295C2×Dic3—22no—
296C2×Dic3—24no—
297C2×Dic3—24no—
298C2×Dic3—22no—
299C2×Dic3—24no—
300C2×Dic3—34no—
301C2×Dic3—34no—
302C2×Dic3—64no—
303C2×Dic3—64no—
304C2×Dic3—64no—
305C2×Dic3—124no—
306C2×Dic3#23514yes—
307D12—316no—
308D12—316no—
309D12—616no—
310C4×D3—1216no—
311C4×D3—1216no—
312C4×D3—128no—
313C4×D3—128no—
314C4×D3—1216no—
315C2×C32C22×C4⋊C411yescharacteristic
316C2×C32C4×#4111yescharacteristic
317C2×C32#51811yescharacteristic
318C2×C32#54612yes—
319C2×C32#55412yes—
320C3⋊D3—28no—
321C24—92no—
322C2×D4—94no—
323C2×D4—94no—
324C2×D4—94no—
325C22×C4—32no—
326C22×C4—34no—
327C22×C4—32no—
328C22×C4—92no—
329C22×C4—98no—
330C22×C4—188no—
331C22×C4—188no—
332C22×C4—364no—
333C22×C4—364no—
334C22×C4C2×D3211yescharacteristic
335C22×C4C2×D3211yescharacteristic
336C22×C4C2×D3211yescharacteristic
337C4⋊C4—64no—
338C4⋊C4—64no—
339C4⋊C4—94no—
340C4⋊C4—364no—
341C22⋊C4—98no—
342C22⋊C4—188no—
343C42—64no—
344C42#62414yescomplemented
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—21no—
350C22×C3C22×C4×D311yescharacteristic
351C22×C3C22×C4×D311yescharacteristic
352C22×C3C2×#23512yes—
353C22×C3C2×D3×D411yescharacteristic
354C22×C3C2×D3×D411yescharacteristic
355C22×C3C2×D3×Q811yescharacteristic
356C22×C3C2×D3×Q811yescharacteristic
357C22×C3D3×#4112yes—
358C22×C3#100912yes—
359C22×C3#100912yes—
360C2×D3—38no—
361C2×D3—38no—
362C2×D3—68no—
363C2×D3—68no—
364C2×D3—68no—
365C2×D3—64no—
366C2×D3—64no—
367C2×D3—64no—
368C2×D3—64no—
369C2×D3—68no—
370C2×D3—68no—
371C2×D3—124no—
372C2×D3—124no—
373C2×D3—128no—
374C2×D3—128no—
375C3×C4—24no—
376C3×C4—22no—
377C3×C4—22no—
378C3×C4—22no—
379C3×C4—22no—
380C3×C4—24no—
381C3×C4—42no—
382C3×C4—64no—
383C3×C4—122no—
384C3×C4—124no—
385C3×C4D3×C4⋊C414yes—
386C3×C4D3×C4⋊C414yes—
387Dic3—24no—
388Dic3—44no—
389Dic3—42no—
390Dic3—64no—
391Dic3—64no—
392Dic3—124no—
393C32#234911yescharacteristic, complemented, Sylow
394C23—94no—
395C23—94no—
396C23—94no—
397C23—184no—
398C23—184no—
399C23C22×D3211yescharacteristic
400D4—916no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—34no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—64no—
408C2×C4—62no—
409C2×C4—64no—
410C2×C4—62no—
411C2×C4—64no—
412C2×C4—94no—
413C2×C4—184no—
414C2×C4—368no—
415C2×C4—3616no—
416C2×C4#379712yes—
417C2×C4#380212yes—
418C2×C4C2×#62412yes—
419C2×C4C2×#62412yes—
420C2×C4C2×#62412yes—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—22no—
424C2×C3—21no—
425C2×C3—22no—
426C2×C3C4×#23511yescharacteristic
427C2×C3C2×D3×C4⋊C411yescharacteristic
428C2×C3C2×D3×C4⋊C411yescharacteristic
429C2×C3#552111yescharacteristic
430C2×C3#552111yescharacteristic
431C2×C3#552211yescharacteristic
432C2×C3#555012yes—
433C2×C3#557912yes—
434C2×C3#567612yes—
435C2×C3#569012yes—
436D3—68no—
437D3—68no—
438D3—128no—
439C22—98no—
440C22—184no—
441C22—188no—
442C22—184no—
443C22—188no—
444C22C2×#379711yescharacteristic
445C22C2×#380211yescharacteristic
446C22D3×#23512yes—
447C22#6430812yes—
448C22C22×#62411yescharacteristic
449C4—22no—
450C4—22no—
451C4—64no—
452C4—124no—
453C4—122no—
454C4—184no—
455C4#6390014yes—
456C3—21no—
457C3#7377011yescharacteristic, complemented
458C3#7422811yescharacteristic, complemented
459C2—188no—
460C2#1059393812yes—
461C2#1059400712yes—
462C2C2×#6390011yescharacteristic
463C2#1059495411yescharacteristic
464C2#1059499611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C42D32
hypocenterC32#2349
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×#4936C2semidirect
4. C3×C4×C4⋊Dic3C2semidirect
5. #10591378C2semidirect
6. #10591370C2semidirect
7. #10591355C2semidirect
8. #10591212C2semidirect
17. C4×C4⋊(C3⋊D3)C4semidirect
38. #4936D3semidirect
39. C4×C4⋊Dic3D3semidirect
55. C2×C4×C3⋊D3C2×C4semidirect
62. C32×C42C2×C4semidirect
63. #3752C2×C4semidirect
64. C4⋊(C3⋊Dic3)C2×C4semidirect
128. C4⋊(C3⋊D3)C4⋊C4semidirect
194. C3×C42C4×D3semidirect
195. C3×C42C4×D3semidirect
344. C42#624semidirect
393. C32#2349semidirect
457. C3#73770semidirect
458. C3#74228semidirect

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×#49362
C3×C4×C4⋊Dic32
#105913782
#105913702
#105913552
#105912122
#742283
#737703