Finite Group Databasebeta

← #11808191

Subgroups — #11808191

Order 1152.

2025 conjugacy classes of subgroups.

The subgroup lattice has 463 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3797C211yesmaximal, characteristic
2C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
3C2×#63883C212yesmaximal
4C3×#4979C212yesmaximal, complemented
5#10591397C212yesmaximal, complemented
6#10591370C212yesmaximal
7#10591370C211yesmaximal, characteristic
8#10591346C212yesmaximal, complemented
9#10591195C212yesmaximal, complemented
10D3×#395—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×Dic6C2212yes—
15C22×#627C2212yes—
16C22×#624C2212yes—
17C22×#624C2212yes—
18C2×#3797—24no—
19C2×#3797—28no—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C4⋊C4×C3⋊D3—24no—
25C2×C3×Dic3⋊C4C2214yes—
26C2×Dic3⋊Dic3C2214yes—
27#63883—28no—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2214yes—
30#63579C2214yes—
31#63579C2212yes—
32C22×D3×Q8—32no—
33C2×D3×C4⋊C4—32no—
34C2×D3×C4⋊C4—34no—
35C2×D3×C4⋊C4—61no—
36C3×#395—32no—
37#5230—32no—
38#4979—34no—
39#4979D312yescomplemented
40D3×#95—32no—
41D3×#95—34no—
42#4656—32no—
43#4656—34no—
44C23×C3⋊D3C2311yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3C2311yescharacteristic
49C22×C3⋊Dic3C2311yescharacteristic
50C22×C3⋊Dic3C2311yescharacteristic
51C2×C4×C3⋊D3—22no—
52C2×C4×C3⋊D3—24no—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3—24no—
56C2×C4×C3⋊D3D414yes—
57C2×C4×C3⋊D3Q814yescomplemented
58C22×C3×Dic3C2314yes—
59C22×C3×Dic3C2314yes—
60C2×C3×Dic6—24no—
61C2×C3×Dic6—28no—
62C2×#627—24no—
63C2×#627—28no—
64C2×#624—24no—
65C2×#624—24no—
66C2×#624—24no—
67C2×#624—24no—
68C2×#624D418yes—
69C2×#624Q818yescomplemented
70#3797—232no—
71C32×C4⋊C4—22no—
72C4⋊(C3⋊Dic3)—22no—
73#3750—22no—
74#3750—22no—
75C3×Dic3⋊C4—28no—
76Dic3⋊Dic3—28no—
77C2×#395—91noSylow
78C22×C3×Q8—32no—
79C2×D3×Q8—68no—
80C2×D3×Q8—616no—
81C22×C4×D3—32no—
82C22×C4×D3—32no—
83C22×C4×D3—34no—
84C22×C4×D3—34no—
85C22×C4×D3—32no—
86C22×C4×D3—61no—
87C22×C4×D3—61no—
88C22×C4×D3—61no—
89C22×Dic6—34no—
90C22×Dic6C2×D312yes—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4—34no—
93C2×C3×C4⋊C4C2×D312yes—
94C2×C4⋊Dic3—32no—
95C2×C4⋊Dic3—34no—
96C2×C4⋊Dic3—61no—
97C2×Dic3⋊C4—32no—
98C2×Dic3⋊C4—32no—
99C2×Dic3⋊C4—34no—
100C2×Dic3⋊C4—61no—
101C2×Dic3⋊C4—61no—
102C2×Dic3⋊C4C2×D314yes—
103D3×C4⋊C4—616no—
104D3×C4⋊C4—68no—
105D3×C4⋊C4—68no—
106C3×#95—32no—
107C3×#95—34no—
108C3⋊#95—34no—
109C3⋊#95—34no—
110C3⋊#95—34no—
111C3⋊#95C2×D314yes—
112C3⋊#95C2×D312yes—
113C23×C32C2411yescharacteristic
114C22×C3⋊D3C2×D414yes—
115C22×C3⋊D3C2×D412yes—
116C22×C3⋊D3C2×Q814yes—
117C22×C3⋊D3C2×Q812yes—
118C22×C3⋊D3#4112yes—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4—21no—
122C2×C32×C4—22no—
123C2×C32×C4—22no—
124C2×C32×C4C2×D412yes—
125C2×C32×C4C2×Q812yescomplemented
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—22no—
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3C2×D412yes—
132C2×C3⋊Dic3C2×Q812yescomplemented
133C4×C3⋊D3—28no—
134C4×C3⋊D3—28no—
135C4×C3⋊D3—44no—
136C2×C3×Dic3—24no—
137C2×C3×Dic3—24no—
138C2×C3×Dic3—24no—
139C2×C3×Dic3—24no—
140C2×C3×Dic3C2×D418yes—
141C2×C3×Dic3C2×Q818yescomplemented
142C3×Dic6—216no—
143#627—216no—
144#624—216no—
145#624—216no—
146C23×Q8—91no—
147C22×C4⋊C4—92no—
148C22×C4⋊C4—91no—
149#395—32no—
150#395—92no—
151#395—92no—
152#395—92no—
153C2×#95—92no—
154C2×#95—91no—
155C23×D3—32no—
156C23×D3—61no—
157C2×C3×Q8—68no—
158C2×C3×Q8—64no—
159C22×C3×C4—21no—
160C22×C3×C4—21no—
161C22×C3×C4—21no—
162C22×C3×C4—34no—
163C22×C3×C4—34no—
164C22×C3×C4C22×D312yes—
165C22×C3×C4C22×D312yes—
166C22×C3×C4C22×D312yes—
167C22×Dic3—32no—
168C22×Dic3—32no—
169C22×Dic3—32no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173C22×Dic3C22×D314yes—
174C22×Dic3C22×D314yes—
175D3×Q8—664no—
176C2×C4×D3—38no—
177C2×C4×D3—38no—
178C2×C4×D3—316no—
179C2×C4×D3—316no—
180C2×C4×D3—64no—
181C2×C4×D3—64no—
182C2×C4×D3—68no—
183C2×C4×D3—68no—
184C2×C4×D3—68no—
185C2×C4×D3—68no—
186C2×C4×D3—64no—
187C2×C4×D3—68no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×C4×D3—64no—
191C2×C4×D3—64no—
192C2×C4×D3—68no—
193C2×C4×D3—64no—
194C2×C4×D3—124no—
195C2×C4×D3—124no—
196C2×Dic6—24no—
197C2×Dic6—28no—
198C2×Dic6—68no—
199C2×Dic6—68no—
200C2×Dic6—68no—
201C3×C4⋊C4—24no—
202C3×C4⋊C4—24no—
203C3×C4⋊C4—68no—
204C4⋊Dic3—64no—
205C4⋊Dic3—64no—
206C4⋊Dic3—68no—
207Dic3⋊C4—28no—
208Dic3⋊C4—68no—
209Dic3⋊C4—64no—
210Dic3⋊C4—64no—
211Dic3⋊C4—64no—
212Dic3⋊C4—64no—
213C22×C32C22×D412yes—
214C22×C32C22×D411yescharacteristic
215C22×C32C22×Q812yes—
216C22×C32C22×Q811yescharacteristic
217C22×C32C2×#4111yescharacteristic
218C2×C3⋊D3#12014yes—
219C2×C3⋊D3C22⋊Q818yes—
220C2×C3⋊D3C22⋊Q814yes—
221C2×C3⋊D3C4⋊Q818yes—
222C2×C3⋊D3C4⋊Q814yes—
223C32×C4—22no—
224C32×C4—22no—
225C32×C4—41no—
226C3⋊Dic3—22no—
227C3⋊Dic3—22no—
228C3⋊Dic3—41no—
229C3×Dic3—28no—
230C3×Dic3—28no—
231C22×Q8—32no—
232C22×Q8—92no—
233C22×Q8—188no—
234C22×Q8—184no—
235C23×C4—92no—
236C23×C4—92no—
237C23×C4—91no—
238C23×C4—91no—
239C23×C4—91no—
240C2×C4⋊C4—34no—
241C2×C4⋊C4—94no—
242C2×C4⋊C4—91no—
243C2×C4⋊C4—91no—
244C2×C4⋊C4—91no—
245C2×C4⋊C4—184no—
246C2×C4⋊C4—188no—
247C2×C4⋊C4D3211yescharacteristic
248#95—32no—
249#95—34no—
250#95—92no—
251#95—94no—
252C23×C3—21no—
253C23×C3C23×D312yes—
254C22×D3—38no—
255C22×D3—34no—
256C22×D3—34no—
257C22×D3—38no—
258C22×D3—34no—
259C22×D3—62no—
260C22×D3—64no—
261C22×D3—62no—
262C22×D3—64no—
263C22×D3—62no—
264C3×Q8—616no—
265C2×C3×C4—22no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—24no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—24no—
272C2×C3×C4—22no—
273C2×C3×C4—22no—
274C2×C3×C4—22no—
275C2×C3×C4—38no—
276C2×C3×C4—38no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—64no—
280C2×C3×C4—64no—
281C2×C3×C4—64no—
282C2×C3×C4—64no—
283C2×C3×C4D3×D414yes—
284C2×C3×C4D3×Q814yescomplemented
285C2×Dic3—24no—
286C2×Dic3—24no—
287C2×Dic3—24no—
288C2×Dic3—24no—
289C2×Dic3—34no—
290C2×Dic3—34no—
291C2×Dic3—62no—
292C2×Dic3—62no—
293C2×Dic3—62no—
294C2×Dic3—62no—
295C2×Dic3—62no—
296C2×Dic3—64no—
297C2×Dic3—62no—
298C2×Dic3—62no—
299C2×Dic3—64no—
300C2×Dic3—62no—
301C2×Dic3—122no—
302C2×Dic3—122no—
303C2×Dic3D3×D418yes—
304C2×Dic3D3×Q818yescomplemented
305C4×D3—632no—
306C4×D3—632no—
307C4×D3—616no—
308C4×D3—616no—
309C4×D3—616no—
310C4×D3—128no—
311C4×D3—128no—
312C4×D3—128no—
313Dic6—216no—
314Dic6—632no—
315C2×C32C2×#12011yescharacteristic
316C2×C32C2×C22⋊Q812yes—
317C2×C32C2×C22⋊Q811yescharacteristic
318C2×C32C2×C4⋊Q811yescharacteristic
319C2×C32C2×C4⋊Q812yes—
320C3⋊D3#39518yescomplemented
321C24—91no—
322C2×Q8—68no—
323C2×Q8—64no—
324C2×Q8—188no—
325C2×Q8—184no—
326C2×Q8—1832no—
327C22×C4—34no—
328C22×C4—34no—
329C22×C4—98no—
330C22×C4—98no—
331C22×C4—91no—
332C22×C4—91no—
333C22×C4—94no—
334C22×C4—94no—
335C22×C4—91no—
336C22×C4—182no—
337C22×C4—184no—
338C22×C4—182no—
339C22×C4—182no—
340C22×C4—184no—
341C22×C4—184no—
342C22×C4—184no—
343C22×C4—184no—
344C22×C4—184no—
345C22×C4C2×D3211yescharacteristic
346C22×C4C2×D3211yescharacteristic
347C22×C4C2×D3211yescharacteristic
348C4⋊C4—22no—
349C4⋊C4—68no—
350C4⋊C4—182no—
351C4⋊C4—182no—
352C4⋊C4—188no—
353C4⋊C4—182no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—22no—
357C22×C3—22no—
358C22×C3—21no—
359C22×C3C2×D3×D414yes—
360C22×C3C2×D3×D412yes—
361C22×C3C2×D3×Q812yes—
362C22×C3C2×D3×Q814yes—
363C22×C3D3×#4112yes—
364C2×D3—38no—
365C2×D3—316no—
366C2×D3—38no—
367C2×D3—316no—
368C2×D3—38no—
369C2×D3—64no—
370C2×D3—64no—
371C2×D3—68no—
372C2×D3—64no—
373C2×D3—68no—
374C3×C4—24no—
375C3×C4—24no—
376C3×C4—24no—
377C3×C4—42no—
378C3×C4—42no—
379C3×C4—42no—
380C3×C4—68no—
381C3×C4—68no—
382Dic3—28no—
383Dic3—28no—
384Dic3—64no—
385Dic3—64no—
386Dic3—64no—
387Dic3—122no—
388Dic3—122no—
389Dic3—122no—
390C32C2×#39511yescharacteristic, complemented, Sylow
391C23—92no—
392C23—92no—
393C23—94no—
394C23—94no—
395C23—92no—
396C23C22×D3211yescharacteristic
397Q8—616no—
398Q8—1816no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—38no—
405C2×C4—38no—
406C2×C4—64no—
407C2×C4—64no—
408C2×C4—64no—
409C2×C4—64no—
410C2×C4—92no—
411C2×C4—92no—
412C2×C4—188no—
413C2×C4—188no—
414C2×C4—1816no—
415C2×C4—1816no—
416C2×C4—181no—
417C2×C4—182no—
418C2×C4—181no—
419C2×C4—182no—
420C2×C4—181no—
421C2×C4—364no—
422C2×C4#379712yescomplemented
423C2×C4#381112yes—
424C2×C3—21no—
425C2×C3—22no—
426C2×C3—22no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3D3×#12012yes—
430C2×C3D3×C22⋊Q814yes—
431C2×C3D3×C22⋊Q812yes—
432C2×C3D3×C4⋊Q812yes—
433C2×C3D3×C4⋊Q814yes—
434D3—316no—
435D3—68no—
436C22—94no—
437C22—98no—
438C22—98no—
439C22—94no—
440C22—94no—
441C22C2×#379711yescharacteristic
442C22#6430611yescharacteristic
443C22D32×D412yes—
444C22D32×Q812yes—
445C22C2×#381111yescharacteristic
446C4—22no—
447C4—22no—
448C4—41no—
449C4—68no—
450C4—68no—
451C4—182no—
452C4—182no—
453C4—361no—
454C3—21no—
455C3D3×#39512yescomplemented
456C2—98no—
457C2#1059437412yes—
458C2#1059462412yes—
459C2#1059492511yescharacteristic
460C2#1059527811yescharacteristic
461C2#1059536511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#395
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4979C2semidirect
5. #10591397C2semidirect
8. #10591346C2semidirect
9. #10591195C2semidirect
39. #4979D3semidirect
57. C2×C4×C3⋊D3Q8semidirect
69. C2×#624Q8semidirect
125. C2×C32×C4C2×Q8semidirect
132. C2×C3⋊Dic3C2×Q8semidirect
141. C2×C3×Dic3C2×Q8semidirect
284. C2×C3×C4D3×Q8semidirect
304. C2×Dic3D3×Q8semidirect
320. C3⋊D3#395semidirect
390. C32C2×#395semidirect
422. C2×C4#3797semidirect
455. C3D3×#395semidirect

Maximal subgroups

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

subgroupindex
C22×#37972
C2×C4⋊C4×C3⋊D32
C2×#638832
C3×#49792
#105913972
#105913702
#105913462
#105911952
D3×#3953