Finite Group Databasebeta

← #11868418

Subgroups — #11868418

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594374C211yesmaximal, characteristic
2#10594363C211yesmaximal, characteristic
3C3⋊D3×#106C211yesmaximal, characteristic
4C3×#4854C212yesmaximal, complemented
5#10590803C212yesmaximal, complemented
6#10590672C211yesmaximal, characteristic
7#10590658C211yesmaximal, characteristic
8#10590601C211yesmaximal, characteristic
9#10590575C211yesmaximal, characteristic
10#10590556C212yesmaximal, complemented
11#10590486C212yesmaximal, complemented
12D3×#475—32nomaximal
13C2×#3797—21no—
14C2×#3797C2211yescharacteristic
15C2×C8×C3⋊D3C2211yescharacteristic
16C4⋊C4×C3⋊D3C2211yescharacteristic
17C4⋊C4×C3⋊D3C2211yescharacteristic
18C3×#888C2212yes—
19C3×#887C2212yes—
20#63918C2212yes—
21#63900C2211yescharacteristic
22#63883—21no—
23#63883—21no—
24C4×#624—21no—
25C4×#624C2211yescharacteristic
26Dic3×Dic6C2212yes—
27#63839—22no—
28#63837—22no—
29C2×#3710C2211yescharacteristic
30C32×#106C2211yescharacteristic
31#63644C2211yescharacteristic
32#63635C2211yescharacteristic
33#63635C2211yescharacteristic
34C3×#816C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×#810C2212yes—
37C3×#808C2212yes—
38#63573C2212yes—
39Dic3⋊(C3⋊C8)C2212yes—
40#63566C2212yes—
41#63565C2212yes—
42D3×C4⋊Q8—32no—
43C4×D3×Q8—32no—
44C3×#475—32no—
45#5094—32no—
46#5020—32no—
47D3×#106—32no—
48D3×#106—32no—
49D3×#106—61no—
50#4854—32no—
51#4854D312yescomplemented
52#4851—32no—
53D3×C4⋊C8—32no—
54D3×#103—32no—
55D3×#103—32no—
56#4791—32no—
57#4791—32no—
58C2×C4×C3⋊D3—21no—
59C2×C4×C3⋊D3—21no—
60C2×C4×C3⋊D3C2311yescharacteristic
61C2×C3×Dic6—22no—
62C2×C3×Dic6C2312yes—
63C2×#627—21no—
64C2×#627—22no—
65C2×#624—21no—
66C2×#624—21no—
67C2×#624D411yescharacteristic
68C2×#624D411yescharacteristic
69#3797—22no—
70#3797—44no—
71#3797Q814yescomplemented
72C2×C32×C8C2311yescharacteristic
73C32×C4⋊C4C2311yescharacteristic
74C32×C4⋊C4C2311yescharacteristic
75C4⋊(C3⋊Dic3)C2311yescharacteristic
76C4⋊(C3⋊Dic3)C2311yescharacteristic
77#3750—21no—
78#3750—21no—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C8×C3⋊D3—22no—
81C3×C4⋊Dic3C2312yes—
82C3×Dic3⋊C4—22no—
83C3×Dic3⋊C4—22no—
84C3×C4×Dic3—22no—
85C3×C4×Dic3C2312yes—
86C2×C3×C3⋊C8C2312yes—
87#3724—21no—
88Dic3⋊Dic3—22no—
89Dic3⋊Dic3—22no—
90Dic32—22no—
91Dic32D412yes—
92#3710—22no—
93C2×#475—91noSylow
94C2×D3×Q8—32no—
95C2×D3×Q8—62no—
96C3×C4⋊Q8—32no—
97C3×C4×Q8—32no—
98Q8×Dic3—32no—
99#944—62no—
100C2×D3×C8—32no—
101C2×D3×C8—32no—
102C2×D3×C8—61no—
103D3×C4⋊C4—32no—
104D3×C4⋊C4—32no—
105D3×C4⋊C4—32no—
106D3×C4⋊C4—61no—
107D3×C4⋊C4—61no—
108D3×C4⋊C4—62no—
109D3×C4⋊C4—62no—
110#888—32no—
111#888—62no—
112#888C2×D312yes—
113#887—62no—
114#887C2×D312yes—
115C42×D3—32no—
116C42×D3—62no—
117#869—32no—
118C4×Dic6—32no—
119C4×Dic6—62no—
120C3×#106—21no—
121C3×#106—32no—
122C3×#106C2×D312yes—
123C3×C4⋊C8—32no—
124C3×#103—32no—
125C3×#103—32no—
126#835—32no—
127#835—32no—
128#817—32no—
129#817—32no—
130#817—61no—
131#816—32no—
132#816C2×D312yes—
133Dic3⋊C8—32no—
134Dic3⋊C8C2×D312yes—
135#810—32no—
136#810C2×D312yes—
137#808—32no—
138#808—32no—
139#808—32no—
140#808—61no—
141#808—61no—
142#808C2×D312yes—
143C4⋊(C3⋊C8)—32no—
144C22×C3⋊D3C2×D411yescharacteristic
145C2×C32×C4—21no—
146C2×C32×C4—21no—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—21no—
150C2×C3⋊Dic3C2×D411yescharacteristic
151C4×C3⋊D3—42no—
152C4×C3⋊D3—42no—
153C4×C3⋊D3C2×Q812yes—
154C4×C3⋊D3#4112yes—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3C2×D412yes—
158C2×C3×Dic3C2×D412yes—
159C3×Dic6—22no—
160C3×Dic6—44no—
161C3×Dic6C2×Q814yescomplemented
162#627—24no—
163#627—44no—
164#624—24no—
165#624—22no—
166#624—42no—
167#624SD1614yes—
168C32×C8—21no—
169C3⋊(C3⋊C8)—21no—
170C3×C3⋊C8—22no—
171C2×C4⋊Q8—91no—
172C2×C4×Q8—91no—
173#475—32no—
174#475—92no—
175#475—92no—
176#475—92no—
177C2×#106—91no—
178C2×#106—91no—
179C2×C4⋊C8—91no—
180C2×#103—91no—
181C2×#103—91no—
182C2×C3×Q8—32no—
183C2×C3×Q8—62no—
184D3×Q8—38no—
185D3×Q8—64no—
186D3×Q8—128no—
187C2×C4×D3—32no—
188C2×C4×D3—32no—
189C2×C4×D3—32no—
190C2×C4×D3—61no—
191C2×C4×D3—62no—
192C2×C4×D3—62no—
193C2×C4×D3—62no—
194C2×C4×D3—62no—
195C2×C4×D3—121no—
196C2×C4×D3—121no—
197C2×Dic6—22no—
198C2×Dic6—62no—
199C2×Dic6—62no—
200C2×Dic6—62no—
201C2×Dic6C22×D312yes—
202C2×C3×C8—21no—
203C2×C3×C8—32no—
204C2×C3×C8C22×D312yes—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—62no—
209C3×C4⋊C4—62no—
210C3×C4⋊C4C22×D312yes—
211C3×C4⋊C4C22×D312yes—
212C3×C42—32no—
213C3×C42—62no—
214C4⋊Dic3—32no—
215C4⋊Dic3—32no—
216C4⋊Dic3—61no—
217C4⋊Dic3—61no—
218C4⋊Dic3—62no—
219C4⋊Dic3—62no—
220C4⋊Dic3C22×D312yes—
221Dic3⋊C4—22no—
222Dic3⋊C4—22no—
223Dic3⋊C4—62no—
224Dic3⋊C4—62no—
225Dic3⋊C4—62no—
226Dic3⋊C4—62no—
227Dic3⋊C4—62no—
228Dic3⋊C4—121no—
229Dic3⋊C4—121no—
230C4×Dic3—22no—
231C4×Dic3—32no—
232C4×Dic3—32no—
233C4×Dic3—62no—
234C4×Dic3—62no—
235C4×Dic3C22×D312yes—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8C22×D312yes—
239D3×C8—64no—
240D3×C8—64no—
241D3×C8—64no—
242C22×C32C22×D411yescharacteristic
243C2×C3⋊D3C22⋊Q812yes—
244C2×C3⋊D3C2×SD1612yes—
245C2×C3⋊D3#13712yes—
246C32×C4—41no—
247C32×C4—41no—
248C32×C4C22×Q811yescharacteristic
249C32×C4C2×#4111yescharacteristic
250C3⋊Dic3—41no—
251C3⋊Dic3—41no—
252C3⋊Dic3C22⋊Q812yes—
253C3×Dic3—24no—
254C3×Dic3—22no—
255C3×Dic3—42no—
256C3×Dic3C2×SD1614yes—
257C22×Q8—91no—
258C22×Q8—181no—
259C22×C8—91no—
260C22×C8—91no—
261C4⋊Q8—32no—
262C4⋊Q8—92no—
263C4⋊Q8—182no—
264C4×Q8—32no—
265C4×Q8—92no—
266C4×Q8—182no—
267C2×C4⋊C4—91no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4—91no—
270C2×C4⋊C4—181no—
271C2×C4⋊C4—181no—
272C2×C42—91no—
273C2×C42—181no—
274#106—32no—
275#106—92no—
276#106—91no—
277#106—91no—
278#106—91no—
279#106D3211yescharacteristic
280C4⋊C8—32no—
281C4⋊C8—92no—
282#103—32no—
283#103—32no—
284#103—92no—
285#103—92no—
286C22×D3—32no—
287C22×D3—61no—
288C3×Q8—34no—
289C3×Q8—62no—
290C3×Q8—124no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—32no—
295C2×C3×C4—32no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4C23×D312yes—
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—32no—
304C2×Dic3—61no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—121no—
308C2×Dic3—121no—
309C2×Dic3D3×D412yes—
310C2×Dic3D3×D412yes—
311C4×D3—34no—
312C4×D3—34no—
313C4×D3—38no—
314C4×D3—62no—
315C4×D3—62no—
316C4×D3—64no—
317C4×D3—68no—
318C4×D3—124no—
319C4×D3—124no—
320C4×D3—124no—
321C4×D3—242no—
322C4×D3—242no—
323Dic6—22no—
324Dic6—44no—
325Dic6—68no—
326Dic6—124no—
327Dic6—124no—
328Dic6D3×Q814yescomplemented
329C3×C8—22no—
330C3×C8—22no—
331C3×C8—62no—
332C3⋊C8—22no—
333C3⋊C8—62no—
334C3⋊C8—62no—
335C2×C32C2×C22⋊Q811yescharacteristic
336C2×C32C22×SD1611yescharacteristic
337C2×C32C2×#13711yescharacteristic
338C3⋊D3#47514yescomplemented
339C2×Q8—32no—
340C2×Q8—62no—
341C2×Q8—94no—
342C2×Q8—182no—
343C2×Q8—181no—
344C2×Q8—182no—
345C2×Q8—364no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—181no—
350C22×C4—181no—
351C22×C4—181no—
352C22×C4—181no—
353C2×C8—32no—
354C2×C8—91no—
355C2×C8—182no—
356C2×C8—182no—
357C2×C8C2×D3211yescharacteristic
358C4⋊C4—32no—
359C4⋊C4—62no—
360C4⋊C4—62no—
361C4⋊C4—91no—
362C4⋊C4—91no—
363C4⋊C4—181no—
364C4⋊C4—181no—
365C4⋊C4—182no—
366C4⋊C4—182no—
367C4⋊C4—181no—
368C4⋊C4C2×D3211yescharacteristic
369C4⋊C4C2×D3211yescharacteristic
370C42—32no—
371C42—62no—
372C42—92no—
373C42—182no—
374C22×C3—21no—
375C22×C3C2×D3×D412yes—
376C2×D3—34no—
377C2×D3—34no—
378C2×D3—34no—
379C2×D3—62no—
380C2×D3—62no—
381C2×D3—62no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—34no—
385C3×C4—42no—
386C3×C4—42no—
387C3×C4—62no—
388C3×C4—64no—
389C3×C4—81no—
390C3×C4—81no—
391C3×C4—122no—
392C3×C4C2×D3×Q812yes—
393C3×C4D3×#4112yes—
394Dic3—22no—
395Dic3—24no—
396Dic3—34no—
397Dic3—42no—
398Dic3—62no—
399Dic3—122no—
400Dic3—122no—
401Dic3—241no—
402Dic3—241no—
403Dic3D3×SD1614yes—
404C32C2×#47511yescharacteristic, complemented, Sylow
405C23—91no—
406Q8—34no—
407Q8—62no—
408Q8—124no—
409Q8—184no—
410Q8—364no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—32no—
414C2×C4—32no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—94no—
418C2×C4—91no—
419C2×C4—92no—
420C2×C4—92no—
421C2×C4—182no—
422C2×C4—184no—
423C2×C4—181no—
424C2×C4—181no—
425C2×C4—362no—
426C2×C4—362no—
427C2×C4—362no—
428C2×C4C22×D3211yescharacteristic
429C8—21no—
430C8—62no—
431C8—181no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3D3×C22⋊Q812yes—
436C2×C3C2×D3×SD1612yes—
437C2×C3D3×#13712yes—
438D3—38no—
439D3—64no—
440C22—92no—
441C22—92no—
442C22—92no—
443C22D32×D411yescharacteristic
444C4—34no—
445C4—41no—
446C4—41no—
447C4—64no—
448C4—62no—
449C4—92no—
450C4—122no—
451C4—361no—
452C4—361no—
453C4#6430611yescharacteristic
454C4D32×Q811yescharacteristic
455C3—21no—
456C3D3×#47512yescomplemented
457C2—94no—
458C2#1059462411yescharacteristic
459C2D32×SD1611yescharacteristic
460C2#1059474211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#106D32
hypocenterC32C2×#475
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
4. C3×#4854C2semidirect
5. #10590803C2semidirect
10. #10590556C2semidirect
11. #10590486C2semidirect
51. #4854D3semidirect
71. #3797Q8semidirect
161. C3×Dic6C2×Q8semidirect
328. Dic6D3×Q8semidirect
338. C3⋊D3#475semidirect
404. C32C2×#475semidirect
456. C3D3×#475semidirect

Maximal subgroups

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

subgroupindex
#105943742
#105943632
C3⋊D3×#1062
C3×#48542
#105908032
#105906722
#105906582
#105906012
#105905752
#105905562
#105904862
D3×#4753