Finite Group Databasebeta

← #11808752

Subgroups — #11808752

Order 1152.

1893 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C2×C4×#626C214yesmaximal, complemented
4C3×#4932C211yesmaximal, characteristic, complemented
5#10591395C212yesmaximal, complemented
6#10591391C212yesmaximal, complemented
7#10591350C212yesmaximal, complemented
8#10591317C212yesmaximal, complemented
9#82347—31nomaximal
10#73418—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3C2212yes—
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2212yes—
15C22×#626C2214yes—
16C2×C32×C42C2211yescharacteristic
17C2×#3752C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C4×C4⋊(C3⋊D3)—24no—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2212yes—
23C3×C4×D12—24no—
24C2×Dic3⋊Dic3C2214yes—
25C2×#3722C2214yes—
26C2×(C2×D3)⋊Dic3C2214yes—
27C4×#626—216no—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30C2×C3×C4×D4—31no—
31C2×C4×#67—34no—
32C2×C4×D12—34no—
33C2×C4×D12—31no—
34C2×C4×D12—31no—
35C2×C4×D12—61no—
36C2×C4×D12D311yescharacteristic, complemented
37C3×#376—31no—
38#5223—32no—
39#4993—32no—
40#4960—32no—
41#4949—32no—
42#4932D311yescharacteristic, complemented
43#4677—32no—
44#4677—32no—
45#4671—32no—
46#4671—32no—
47C23×C3⋊D3C2312yes—
48C23×C3×D3C2312yes—
49C22×C32×C4C2311yescharacteristic
50C22×C32×C4C2311yescharacteristic
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3C2312yes—
53C2×C4⋊(C3⋊D3)—24no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4×C3⋊D3—24no—
56C2×C4×C3⋊D3—28no—
57C22×C3×Dic3C2312yes—
58C22×C3×Dic3C2314yes—
59C2×C3×D12—24no—
60C2×C3×D12—22no—
61C2×C3×C4×D3—28no—
62C2×C3×C4×D3—24no—
63C2×#626—28no—
64C2×#626—28no—
65C2×#626—28no—
66C32×C42D414yescomplemented
67#3752—24no—
68C4⋊(C3⋊Dic3)—22no—
69C3×(C2×D3)⋊C4—24no—
70C3×C4⋊Dic3—22no—
71C3×C4×Dic3D418yescomplemented
72Dic3⋊Dic3—28no—
73#3722—28no—
74(C2×D3)⋊Dic3—28no—
75#2397—91noSylow
76C22×C3×D4—31no—
77C23×C3×C4—32no—
78C22×#67—34no—
79C22×D12—34no—
80C22×D12—31no—
81C22×D12—31no—
82C22×D12—61no—
83C22×D12C2×D311yescharacteristic
84C22×C4×D3—32no—
85C22×C4×D3—32no—
86C22×C4×D3—62no—
87C22×C4×D3C2×D312yes—
88C3×C4×D4—64no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C22⋊C4—32no—
91C2×C3×C42—21no—
92C2×C3×C42—32no—
93C2×C3×C42C2×D311yescharacteristic
94C2×C3×C42C2×D311yescharacteristic
95C2×#217—34no—
96C4×#67—616no—
97C2×(C2×D3)⋊C4—34no—
98C2×(C2×D3)⋊C4—32no—
99C2×(C2×D3)⋊C4—32no—
100C2×(C2×D3)⋊C4—34no—
101C2×(C2×D3)⋊C4—34no—
102C2×(C2×D3)⋊C4—62no—
103C2×(C2×D3)⋊C4C2×D312yes—
104C2×C4⋊Dic3—31no—
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—34no—
107C2×C4⋊Dic3—61no—
108C2×C4⋊Dic3C2×D311yescharacteristic
109C2×Dic3⋊C4—34no—
110C2×C4×Dic3C2×D312yes—
111C4×D12—24no—
112C4×D12—68no—
113C4×D12—616no—
114C4×D12—64no—
115C4×D12—64no—
116C3×#95—32no—
117C3×#95—32no—
118C3⋊#95C2×D312yes—
119C3⋊#95C2×D312yes—
120C23×C32C2411yescharacteristic
121C22×C3⋊D3—22no—
122C22×C3⋊D3—22no—
123C22×C3⋊D3—24no—
124C22×C3⋊D3—24no—
125C22×C3⋊D3#4114yes—
126C22×C3×D3—24no—
127C22×C3×D3—22no—
128C22×C3×D3—24no—
129C22×C3×D3—22no—
130C22×C3×D3#4114yes—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4C2×D414yes—
134C2×C32×C4C2×D412yes—
135C2×C32×C4C2×D412yes—
136C2×C32×C4C2×D412yes—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—24no—
139C4⋊(C3⋊D3)—28no—
140C4×C3⋊D3—48no—
141C2×C3×Dic3—24no—
142C2×C3×Dic3—24no—
143C2×C3×Dic3—24no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3C2×D418yes—
146C3×D12—28no—
147C3×C4×D3—48no—
148#626—232no—
149C2×C4×D4—31no—
150C2×C4×D4—94no—
151C2×C4×D4—91no—
152#399—92no—
153#399—92no—
154#392—92no—
155#392—92no—
156#376—31no—
157C24×C3—32no—
158C23×D3—32no—
159C23×D3—32no—
160C23×D3—62no—
161C23×D3C22×D312yes—
162C2×C3×D4—64no—
163C2×C3×D4—62no—
164C22×C3×C4—21no—
165C22×C3×C4—21no—
166C22×C3×C4—21no—
167C22×C3×C4—34no—
168C22×C3×C4—32no—
169C22×C3×C4—68no—
170C22×C3×C4—64no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C22×C3×C4C22×D311yescharacteristic
177C2×#67—68no—
178C2×#67—68no—
179C2×#67—68no—
180C22×Dic3—32no—
181C22×Dic3—32no—
182C22×Dic3—62no—
183C22×Dic3C22×D312yes—
184C22×Dic3C22×D314yes—
185C2×D12—24no—
186C2×D12—22no—
187C2×D12—64no—
188C2×D12—64no—
189C2×D12—64no—
190C2×D12—68no—
191C2×D12—68no—
192C2×D12—68no—
193C2×D12—68no—
194C2×D12—62no—
195C2×D12—62no—
196C2×C4×D3—28no—
197C2×C4×D3—24no—
198C2×C4×D3—68no—
199C2×C4×D3—64no—
200C2×C4×D3—68no—
201C2×C4×D3—68no—
202C2×C4×D3—64no—
203C2×C4×D3—128no—
204C3×C4⋊C4—62no—
205C3×C22⋊C4—64no—
206C3×C42—24no—
207C3×C42—38no—
208C3×C42D1214yescomplemented
209C3×C42#6714yescomplemented
210#217—68no—
211(C2×D3)⋊C4—24no—
212(C2×D3)⋊C4—68no—
213(C2×D3)⋊C4—68no—
214(C2×D3)⋊C4—68no—
215(C2×D3)⋊C4—64no—
216(C2×D3)⋊C4—64no—
217(C2×D3)⋊C4—68no—
218C4⋊Dic3—22no—
219C4⋊Dic3—68no—
220C4⋊Dic3—64no—
221C4⋊Dic3—62no—
222C4⋊Dic3—62no—
223Dic3⋊C4—68no—
224C4×Dic3D1218yescomplemented
225C22×C32C22×D412yes—
226C22×C32C22×D411yescharacteristic
227C22×C32C2×#4112yes—
228C22×C32C2×#4112yes—
229C2×C3⋊D3—24no—
230C2×C3⋊D3—28no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—44no—
233C2×C3⋊D3—42no—
234C2×C3×D3—28no—
235C2×C3×D3—24no—
236C2×C3×D3—44no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C32×C4—22no—
240C32×C4—22no—
241C32×C4#12714yes—
242C3⋊Dic3—42no—
243C3×Dic3—28no—
244C3×Dic3—42no—
245C22×D4—31no—
246C22×D4—94no—
247C22×D4—91no—
248C23×C4—32no—
249C23×C4—92no—
250C4×D4—64no—
251C4×D4—1816no—
252C4×D4—184no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—94no—
255C2×C4⋊C4—91no—
256C2×C22⋊C4—32no—
257C2×C22⋊C4—94no—
258C2×C22⋊C4—94no—
259C2×C22⋊C4—92no—
260C2×C42—32no—
261C2×C42D3211yescharacteristic
262#95—32no—
263#95—32no—
264C23×C3—21no—
265C23×C3—34no—
266C23×C3—64no—
267C23×C3—62no—
268C23×C3—64no—
269C23×C3—62no—
270C23×C3C23×D311yescharacteristic
271C23×C3C23×D311yescharacteristic
272C22×D3—22no—
273C22×D3—24no—
274C22×D3—24no—
275C22×D3—22no—
276C22×D3—34no—
277C22×D3—34no—
278C22×D3—64no—
279C22×D3—64no—
280C22×D3—64no—
281C22×D3—62no—
282C22×D3—64no—
283C22×D3—64no—
284C22×D3—64no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—64no—
288C22×D3—62no—
289C22×D3—124no—
290C22×D3—124no—
291C22×D3#23514yes—
292C3×D4—68no—
293C2×C3×C4—24no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—24no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—38no—
303C2×C3×C4—42no—
304C2×C3×C4—64no—
305C2×C3×C4—64no—
306C2×C3×C4—64no—
307C2×C3×C4—62no—
308C2×C3×C4—128no—
309C2×C3×C4C2×D1214yes—
310C2×C3×C4C2×D1212yes—
311C2×C3×C4C2×D1212yes—
312C2×C3×C4C2×D1212yes—
313C2×C3×C4D3×D414yes—
314C2×C3×C4C2×#6712yes—
315C2×C3×C4C2×#6712yes—
316C2×C3×C4C2×#6712yes—
317#67—632no—
318C2×Dic3—24no—
319C2×Dic3—24no—
320C2×Dic3—24no—
321C2×Dic3—22no—
322C2×Dic3—64no—
323C2×Dic3—64no—
324C2×Dic3—62no—
325C2×Dic3—64no—
326C2×Dic3—62no—
327C2×Dic3—124no—
328C2×Dic3C2×D1218yes—
329D12—28no—
330D12—616no—
331D12—68no—
332D12—68no—
333D12—632no—
334C4×D3—48no—
335C4×D3—1216no—
336C4×D3—128no—
337C4×D3—128no—
338C2×C32#52511yescharacteristic
339C2×C32#52514yes—
340C2×C32#52511yescharacteristic
341C2×C32C2×#12711yescharacteristic
342C3⋊D3—44no—
343C3×D3—44no—
344C24—32no—
345C24—92no—
346C2×D4—64no—
347C2×D4—62no—
348C2×D4—184no—
349C2×D4—188no—
350C2×D4—188no—
351C2×D4—188no—
352C2×D4—182no—
353C22×C4—34no—
354C22×C4—32no—
355C22×C4—68no—
356C22×C4—64no—
357C22×C4—92no—
358C22×C4—188no—
359C22×C4—184no—
360C22×C4C2×D3211yescharacteristic
361C22×C4C2×D3211yescharacteristic
362C22×C4C2×D3211yescharacteristic
363C4⋊C4—62no—
364C4⋊C4—188no—
365C4⋊C4—182no—
366C22⋊C4—64no—
367C22⋊C4—188no—
368C22⋊C4—188no—
369C22⋊C4—184no—
370C42—38no—
371C42#62614yescomplemented
372C22×C3—22no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—68no—
377C22×C3—64no—
378C22×C3—122no—
379C22×C3—124no—
380C22×C3—122no—
381C22×C3C22×D1212yes—
382C22×C3C22×D1211yescharacteristic
383C22×C3C2×#23512yes—
384C22×C3C2×D3×D412yes—
385C22×C3D3×#4112yes—
386C22×C3D3×#4112yes—
387C22×C3D3×#4112yes—
388C22×C3C22×#6711yescharacteristic
389C2×D3—24no—
390C2×D3—28no—
391C2×D3—44no—
392C2×D3—42no—
393C2×D3—42no—
394C2×D3—68no—
395C2×D3—64no—
396C2×D3—68no—
397C2×D3—68no—
398C2×D3—64no—
399C2×D3—128no—
400C2×D3—124no—
401C2×D3—128no—
402C2×D3—124no—
403C2×D3—122no—
404C2×D3—124no—
405C2×D3—122no—
406C2×D3—122no—
407C2×D3—124no—
408C2×D3—122no—
409C3×C4—24no—
410C3×C4—22no—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—24no—
415C3×C4—42no—
416C3×C4—68no—
417C3×C4—122no—
418C3×C4#87414yes—
419C3×C4#94014yes—
420Dic3—28no—
421Dic3—42no—
422Dic3—124no—
423Dic3—122no—
424Dic3—122no—
425C32#239711yescharacteristic, complemented, Sylow
426C23—34no—
427C23—64no—
428C23—62no—
429C23—64no—
430C23—62no—
431C23—94no—
432C23—184no—
433C23—184no—
434C23—182no—
435C23—182no—
436C23C22×D3211yescharacteristic
437D4—68no—
438D4—188no—
439D4—1832no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—38no—
443C2×C4—64no—
444C2×C4—64no—
445C2×C4—64no—
446C2×C4—62no—
447C2×C4—128no—
448C2×C4—184no—
449C2×C4—182no—
450C2×C4—368no—
451C2×C4D3×D1214yes—
452C2×C4C2×#62612yes—
453C2×C4C2×#62612yes—
454C2×C4C2×#62612yes—
455C2×C3—21no—
456C2×C3—24no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—124no—
460C2×C3C2×#87411yescharacteristic
461C2×C3#552414yes—
462C2×C3#552411yescharacteristic
463C2×C3#552411yescharacteristic
464C2×C3#554714yes—
465C2×C3#579111yescharacteristic
466C2×C3C2×#94011yescharacteristic
467C2×C3#582811yescharacteristic
468D3—44no—
469D3—128no—
470D3—124no—
471D3—124no—
472C22—68no—
473C22—64no—
474C22—122no—
475C22—124no—
476C22—122no—
477C22—188no—
478C22—184no—
479C22—362no—
480C22—364no—
481C22—362no—
482C22C2×D3×D1212yes—
483C22D3×#23512yes—
484C22#6430612yes—
485C22C22×#62611yescharacteristic
486C4—22no—
487C4—22no—
488C4—68no—
489C4—122no—
490C4—362no—
491C4#6391114yes—
492C3—21no—
493C3#7341811yescharacteristic, complemented
494C3#8234711yescharacteristic, complemented
495C2—124no—
496C2—364no—
497C2#1059399714yes—
498C2C2×#6391111yescharacteristic
499C2#1059502311yescharacteristic
500C2#1059503411yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#2397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C4⋊(C3⋊D3)C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C2×C4×#626C2semidirect
4. C3×#4932C2semidirect
5. #10591395C2semidirect
6. #10591391C2semidirect
7. #10591350C2semidirect
8. #10591317C2semidirect
36. C2×C4×D12D3semidirect
42. #4932D3semidirect
66. C32×C42D4semidirect
71. C3×C4×Dic3D4semidirect
208. C3×C42D12semidirect
209. C3×C42#67semidirect
224. C4×Dic3D12semidirect
371. C42#626semidirect
425. C32#2397semidirect
493. C3#73418semidirect
494. C3#82347semidirect

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×C3×C4×D122
C2×C4×#6262
C3×#49322
#105913952
#105913912
#105913502
#105913172
#823473
#734183