Finite Group Databasebeta

← #11775610

Subgroups — #11775610

Order 1152.

693 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#924C211yesmaximal, characteristic
2#10592911C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4#10589152C214yesmaximal, complemented
5#71690—31nomaximal
6#69946—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×C3×Dic6C411yescharacteristic, complemented
9C2×#3757—21no—
10C2×C4⋊(C3⋊Dic3)—21no—
11C2×C3×#217—21no—
12C2×C3×C4⋊Dic3C411yescharacteristic, complemented
13C3×#924—21no—
14C3×#924—21no—
15C3×#924C412yescomplemented
16C3×#924C2212yes—
17C2×C3×Dic3⋊C4—21no—
18C22×C3×C3⋊C8—21no—
19#63658C2212yes—
20C3×#830—21no—
21C3×#830C2212yes—
22C2×C3×C22⋊Q8—31no—
23C2×#924D311yescharacteristic
24C2×C3×C22⋊C8—31no—
25#5212—31no—
26#5212—31no—
27#5212—61no—
28C2×#830D311yescharacteristic
29#4538—34no—
30#4467—34no—
31C24×C32D411yescharacteristic
32C22×C32×C4—42no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—22no—
40C22×C3×Dic3—21no—
41C22×C3×Dic3—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—42no—
44C2×C3×Dic6C2×C412yes—
45#3757—42no—
46C4⋊(C3⋊Dic3)—42no—
47C3×#217—22no—
48C3×#217—22no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3C2×C412yes—
51C3×Dic3⋊C4—22no—
52C3×Dic3⋊C4—22no—
53C2×C3×C3⋊C8—22no—
54C2×C3×C3⋊C8—42no—
55#1520—91noSylow
56C22×C3×Q8—31no—
57C23×C3×C4—21no—
58C23×C3×C4C2×D311yescharacteristic
59C23×C3×C4C2×D311yescharacteristic
60C22×Dic6Dic311yescharacteristic, complemented
61C22×C3×C8—61no—
62C3×C22⋊Q8—32no—
63C3×C22⋊Q8—32no—
64C3×C22⋊Q8—61no—
65C3×C22⋊Q8—61no—
66C2×C3×C4⋊C4—31no—
67C2×C3×C4⋊C4—61no—
68C2×C3×C22⋊C4—61no—
69C2×#217—21no—
70C2×#217—62no—
71C2×#217—61no—
72C2×#217—61no—
73C2×C4⋊Dic3—62no—
74C2×C4⋊Dic3—61no—
75C2×C4⋊Dic3—61no—
76C2×C4⋊Dic3Dic311yescharacteristic, complemented
77#924—21no—
78#924—21no—
79#924Dic312yescomplemented
80#924C2×D312yes—
81C2×Dic3⋊C4—21no—
82C22×C3⋊C8—21no—
83C3×C22⋊C8—32no—
84C3×C22⋊C8—61no—
85C3⋊#95—32no—
86C3⋊#95—32no—
87C3⋊#95—62no—
88#830—21no—
89#830C2×D312yes—
90C23×C32—41no—
91C23×C32—41no—
92C23×C32C22⋊C411yescharacteristic
93C23×C32C22⋊C411yescharacteristic
94C23×C32SD1612yes—
95C23×C32Q1612yes—
96C23×C32C2×D411yescharacteristic
97C2×C32×C4—22no—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4C22⋊C411yescharacteristic
104C2×C32×C4C22⋊C411yescharacteristic
105C2×C32×C4C22×C411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—42no—
108C2×C3⋊Dic3—42no—
109C2×C3⋊Dic3—42no—
110C2×C3×Dic3—22no—
111C2×C3×Dic3—22no—
112C2×C3×Dic3—42no—
113C2×C3×Dic3—42no—
114C3×Dic6—42no—
115C3×Dic6—42no—
116C3×C3⋊C8—42no—
117C2×C22⋊Q8—31no—
118C2×C22⋊C8—31no—
119#380—91no—
120#328—94no—
121C24×C3—21no—
122C24×C3D1211yescharacteristic
123C24×C3#6711yescharacteristic
124C2×C3×Q8—32no—
125C2×C3×Q8—61no—
126C2×C3×Q8—122no—
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—42no—
134C22×C3×C4—42no—
135C22×C3×C4—44no—
136C22×C3×C4—61no—
137C22×C3×C4—61no—
138C22×C3×C4C4×D311yescharacteristic
139C22×C3×C4C4×D311yescharacteristic
140C22×C3×C4D1211yescharacteristic
141C22×C3×C4C2×Dic311yescharacteristic
142C22×C3×C4C2×Dic311yescharacteristic
143C22×C3×C4#6711yescharacteristic
144C22×C3×C4#6711yescharacteristic
145C22×C3×C4#6711yescharacteristic
146C22×C3×C4#6711yescharacteristic
147C22×C3×C4#6711yescharacteristic
148C22×C3×C4C22×D311yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C22×Dic3—21no—
151C22×Dic3—21no—
152C22×Dic3—64no—
153C22×Dic3—62no—
154C22×Dic3—62no—
155C2×Dic6—21no—
156C2×Dic6—42no—
157C2×Dic6C2×Dic312yes—
158C2×C3×C8—62no—
159C2×C3×C8—122no—
160C3×C4⋊C4—32no—
161C3×C4⋊C4—62no—
162C3×C4⋊C4—61no—
163C3×C4⋊C4—62no—
164C3×C22⋊C4—62no—
165C3×C22⋊C4—62no—
166#217—22no—
167#217—22no—
168#217—124no—
169#217—122no—
170#217—122no—
171C4⋊Dic3—21no—
172C4⋊Dic3—124no—
173C4⋊Dic3—122no—
174C4⋊Dic3—122no—
175C4⋊Dic3C2×Dic312yes—
176Dic3⋊C4—22no—
177Dic3⋊C4—22no—
178C2×C3⋊C8—22no—
179C2×C3⋊C8—42no—
180C22×C32—21no—
181C22×C32—21no—
182C22×C32—21no—
183C22×C32—21no—
184C22×C32—21no—
185C22×C32—21no—
186C22×C32—42no—
187C22×C32—42no—
188C22×C32#10312yes—
189C22×C32#10312yes—
190C22×C32C2×C22⋊C411yescharacteristic
191C22×C32C2×SD1611yescharacteristic
192C22×C32C2×Q1611yescharacteristic
193C32×C4—21no—
194C32×C4—21no—
195C32×C4—21no—
196C32×C4#9912yes—
197C3⋊Dic3—82no—
198C3×Dic3—42no—
199C3×Dic3—42no—
200C22×Q8—31no—
201C23×C4D3211yescharacteristic
202C22×C8—61no—
203C22⋊Q8—32no—
204C22⋊Q8—32no—
205C22⋊Q8—61no—
206C22⋊Q8—61no—
207C2×C4⋊C4—31no—
208C2×C4⋊C4—61no—
209C2×C4⋊C4—181no—
210C2×C22⋊C4—61no—
211C2×C22⋊C4—181no—
212C22⋊C8—32no—
213C22⋊C8—61no—
214#95—92no—
215C23×C3—22no—
216C23×C3—22no—
217C23×C3—21no—
218C23×C3—21no—
219C23×C3—21no—
220C23×C3—41no—
221C23×C3—41no—
222C23×C3—41no—
223C23×C3—41no—
224C23×C3—42no—
225C23×C3—42no—
226C23×C3#20412yes—
227C23×C3Dic1212yes—
228C23×C3(C2×D3)⋊C411yescharacteristic
229C23×C3(C2×D3)⋊C411yescharacteristic
230C23×C3#21512yes—
231C23×C3#21612yes—
232C23×C3#21711yescharacteristic
233C23×C3#21711yescharacteristic
234C23×C3C2×D1211yescharacteristic
235C23×C3C2×#6711yescharacteristic
236C3×Q8—122no—
237C3×Q8—122no—
238C2×C3×C4—24no—
239C2×C3×C4—22no—
240C2×C3×C4—22no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—22no—
244C2×C3×C4—22no—
245C2×C3×C4—21no—
246C2×C3×C4—21no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—42no—
250C2×C3×C4—42no—
251C2×C3×C4—41no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—41no—
257C2×C3×C4—42no—
258C2×C3×C4—42no—
259C2×C3×C4—42no—
260C2×C3×C4—62no—
261C2×C3×C4—62no—
262C2×C3×C4—122no—
263C2×C3×C4—122no—
264C2×C3×C4(C2×D3)⋊C411yescharacteristic
265C2×C3×C4(C2×D3)⋊C411yescharacteristic
266C2×C3×C4#21711yescharacteristic
267C2×C3×C4#21711yescharacteristic
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4C22×Dic311yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271C2×C3×C4C2×#6711yescharacteristic
272C2×Dic3—22no—
273C2×Dic3—22no—
274C2×Dic3—42no—
275C2×Dic3—42no—
276C2×Dic3—124no—
277C2×Dic3—122no—
278C2×Dic3—122no—
279C2×Dic3—124no—
280C2×Dic3—124no—
281C2×Dic3—122no—
282C2×Dic3—122no—
283C2×Dic3—122no—
284C2×Dic3—122no—
285Dic6—42no—
286Dic6—42no—
287C3×C8—122no—
288C3⋊C8—42no—
289C2×C32—21no—
290C2×C32—21no—
291C2×C32—22no—
292C2×C32—22no—
293C2×C32C2×#9911yescharacteristic
294C2×C32C2×#10311yescharacteristic
295C2×C32#42111yescharacteristic
296C24#62611yescharacteristic
297C2×Q8—32no—
298C2×Q8—61no—
299C2×Q8—122no—
300C22×C4—42no—
301C22×C4—61no—
302C22×C4—61no—
303C22×C4—182no—
304C22×C4D3×Dic311yescharacteristic
305C22×C4D3×Dic311yescharacteristic
306C22×C4#62511yescharacteristic
307C22×C4#62511yescharacteristic
308C22×C4#62611yescharacteristic
309C22×C4C2×D3211yescharacteristic
310C2×C8—62no—
311C2×C8—122no—
312C4⋊C4—32no—
313C4⋊C4—61no—
314C4⋊C4—62no—
315C4⋊C4—62no—
316C4⋊C4—362no—
317C22⋊C4—62no—
318C22⋊C4—62no—
319C22⋊C4—362no—
320C22×C3—22no—
321C22×C3—22no—
322C22×C3—21no—
323C22×C3—21no—
324C22×C3—21no—
325C22×C3—21no—
326C22×C3—21no—
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—41no—
340C22×C3—41no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—42no—
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—42no—
347C22×C3—44no—
348C22×C3—44no—
349C22×C3#81612yes—
350C22×C3#81612yes—
351C22×C3#83512yes—
352C22×C3#83512yes—
353C22×C3C2×#20411yescharacteristic
354C22×C3C2×Dic1211yescharacteristic
355C22×C3C2×(C2×D3)⋊C411yescharacteristic
356C22×C3C2×#21511yescharacteristic
357C22×C3C2×#21611yescharacteristic
358C22×C3C2×#21711yescharacteristic
359C3×C4—22no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—21no—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—22no—
367C3×C4—41no—
368C3×C4—41no—
369C3×C4—122no—
370C3×C4—122no—
371C3×C4#80612yes—
372C3×C4#83412yes—
373Dic3—42no—
374Dic3—42no—
375Dic3—244no—
376Dic3—242no—
377Dic3—242no—
378C32#152011yescharacteristic, complemented, Sylow
379C23—41no—
380C23—41no—
381C23#371712yes—
382C23#371912yes—
383C23(C2×D3)⋊Dic311yescharacteristic
384C23(C2×D3)⋊Dic311yescharacteristic
385C23C2×#62611yescharacteristic
386Q8—122no—
387Q8—122no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—62no—
395C2×C4—62no—
396C2×C4—122no—
397C2×C4—122no—
398C2×C4—362no—
399C2×C4—362no—
400C2×C4—362no—
401C2×C4(C2×D3)⋊Dic311yescharacteristic
402C2×C4(C2×D3)⋊Dic311yescharacteristic
403C2×C4C2×D3×Dic311yescharacteristic
404C2×C4C2×#62511yescharacteristic
405C8—122no—
406C2×C3—22no—
407C2×C3—22no—
408C2×C3—21no—
409C2×C3—22no—
410C2×C3—22no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—22no—
414C2×C3—22no—
415C2×C3—21no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—42no—
420C2×C3—42no—
421C2×C3C2×#80611yescharacteristic
422C2×C3C2×#81611yescharacteristic
423C2×C3#513911yescharacteristic
424C2×C3C2×#83411yescharacteristic
425C2×C3C2×#83511yescharacteristic
426C2×C3#523611yescharacteristic
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—42no—
434C22—42no—
435C22#6356612yes—
436C22#6356612yes—
437C22C2×#371711yescharacteristic
438C22C2×#371911yescharacteristic
439C22C2×(C2×D3)⋊Dic311yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—122no—
444C4—122no—
445C4—722no—
446C4#6358012yes—
447C3—21no—
448C3#6994611yescharacteristic, complemented
449C3#7169011yescharacteristic, complemented
450C2—21no—
451C2—22no—
452C2—22no—
453C2—21no—
454C2C2×#6356611yescharacteristic
455C2#1059111011yescharacteristic
456C2C2×#6358011yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C32D4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1520
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #10589152C2semidirect
8. C22×C3×Dic6C4semidirect
12. C2×C3×C4⋊Dic3C4semidirect
15. C3×#924C4semidirect
60. C22×Dic6Dic3semidirect
76. C2×C4⋊Dic3Dic3semidirect
79. #924Dic3semidirect
378. C32#1520semidirect
448. C3#69946semidirect
449. C3#71690semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9242
#105929112
C2×C3×#8302
#105891522
#716903
#699463