Finite Group Databasebeta

← #11860839

Subgroups — #11860839

Order 1152.

966 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×Dic12C211yesmaximal, characteristic
2#10594357C212yesmaximal
3#10592552C211yesmaximal, characteristic, complemented
4C3×#4860C211yesmaximal, characteristic
5C3×#4853C211yesmaximal, characteristic, complemented
6#10590819C211yesmaximal, characteristic, complemented
7#10590810C211yesmaximal, characteristic, complemented
8#10590693C211yesmaximal, characteristic
9#10590600C212yesmaximal
10#10590482C212yesmaximal, complemented
11#10590481C212yesmaximal, complemented
12#79831—31nomaximal
13#79169—31nomaximal
14C2×D3×Dic6C2212yes—
15C2×#3746C2211yescharacteristic
16#64096C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C3×#892C2212yes—
20C3×#887C2212yes—
21C4×#627—22no—
22#63878—22no—
23#63877—22no—
24#63855C2211yescharacteristic
25#63844C2212yes—
26#63843C2212yes—
27#63837—22no—
28C2×#3719C2212yes—
29C2×#3711C2211yescharacteristic
30D3×Dic12C418yescomplemented
31C32×#106C2211yescharacteristic
32#63642C2211yescharacteristic
33#63637C2212yes—
34C3×#817C2211yescharacteristic
35C3×#815C2211yescharacteristic
36C3×#810C2212yes—
37C3×#807C2212yes—
38#63567C2212yes—
39#63565C2212yes—
40#63553C2211yescharacteristic
41Dic3×C3⋊C8C2211yescharacteristic
42C2×D3×Q16—31no—
43C22×Dic12—31no—
44#5572—32no—
45#5516—32no—
46C3×#441—31no—
47C3×#427—31no—
48#5184—31no—
49#5101—31no—
50C4×#216—32no—
51#5004—32no—
52#4873—32no—
53#4873—32no—
54#4860D311yescharacteristic
55#4853—31no—
56#4853—31no—
57#4853—31no—
58#4853—31no—
59#4853—61no—
60#4853D311yescharacteristic, complemented
61#4802—32no—
62#4790—32no—
63#4716—31no—
64#4708—31no—
65C2×#634C2312yes—
66C2×C3×C4×D3C2311yescharacteristic
67C2×C3×Dic6C2312yes—
68C2×#627—22no—
69C2×D3×Dic3—22no—
70D3×Dic6—24no—
71D3×Dic6C2×C418yes—
72C2×C32×C8C2311yescharacteristic
73C32×C4⋊C4C2312yes—
74#3750—22no—
75C4×C3⋊Dic3—22no—
76C4×C3⋊Dic3C2311yescharacteristic
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78#3746C2×C414yes—
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3C2312yes—
81C3×Dic3⋊C4—22no—
82C3×C4×Dic3—22no—
83C3×C4×Dic3—22no—
84C3×C4×Dic3C2311yescharacteristic
85C2×C3×C3⋊C8C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C3×Dic12C2×C414yes—
88C3×D3×C8C2×C414yes—
89#3724—22no—
90Dic3⋊Dic3—22no—
91Dic3⋊Dic3D412yes—
92(C2×D3)⋊Dic3D412yes—
93Dic32—22no—
94Dic32—22no—
95#3719C2×C418yes—
96#3711—22no—
97#2950—91noSylow
98C2×D3×Q8—32no—
99C22×Dic6—32no—
100C2×C3×Q16—31no—
101C22×C3×C8—31no—
102C3×C4×Q8—32no—
103C3×#117—32no—
104Q8×Dic3—32no—
105C2×#216—32no—
106#926—31no—
107C2×#208—31no—
108D3×Q16—38no—
109C2×Dic12—32no—
110C2×Dic12—31no—
111C2×Dic12—31no—
112C2×Dic12—38no—
113C2×Dic12—61no—
114C2×Dic12C2×D311yescharacteristic
115C2×ΓL(1,𝔽25)—31no—
116C2×D3×C8C2×D311yescharacteristic
117#892—62no—
118#892C2×D312yes—
119#887—32no—
120#887—32no—
121#887—32no—
122#887—32no—
123#887—62no—
124#887—62no—
125#887C2×D312yes—
126#877—62no—
127#877—62no—
128#872—31no—
129#872—62no—
130C4×Dic6—32no—
131C4×Dic6—62no—
132C4×Dic6—62no—
133C4×Dic6—62no—
134C3×#107—32no—
135C3×#106—21no—
136C3×#106—31no—
137C3×#106C2×D311yescharacteristic
138C3×#106C2×D311yescharacteristic
139C3×#103—32no—
140C3×#97—31no—
141#835—32no—
142#817C2×D311yescharacteristic
143#816—32no—
144#815—31no—
145#815—31no—
146#815—61no—
147#815C2×D311yescharacteristic
148C8×Dic3—31no—
149C8×Dic3—31no—
150C8×Dic3—31no—
151#810—32no—
152#810—32no—
153#810—32no—
154#810—32no—
155#810—62no—
156#810C2×D312yes—
157#807C2×D312yes—
158C4×C3⋊C8—31no—
159C22×C3×D3C2×D411yescharacteristic
160C2×C32×C4—22no—
161C2×C32×C4C2411yescharacteristic
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3C2×D412yes—
164#634—22no—
165#634C22×C414yes—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3C2×D412yes—
169C2×C3×Dic3C2×D411yescharacteristic
170C3×C4×D3C22×C412yes—
171C3×C4×D3#4112yes—
172C3×Dic6—22no—
173C3×Dic6C22×C414yes—
174#627—28no—
175D3×Dic3—28no—
176C32×C8C22×C412yes—
177C3⋊(C3⋊C8)—21no—
178C3×C3⋊C8—21no—
179C3×C3⋊C8C22×C412yes—
180C22×Q16—91no—
181#519—92no—
182#441—31no—
183#441—91no—
184#441—91no—
185#441—91no—
186C4×Q16—92no—
187C4×Q16—92no—
188#427—31no—
189#419—92no—
190#405—91no—
191C2×C3×Q8—32no—
192C22×C3×C4—31no—
193C22×Dic3—62no—
194D3×Q8—38no—
195D3×Q8—64no—
196C2×C4×D3—62no—
197C2×C4×D3C22×D311yescharacteristic
198C2×Dic6—32no—
199C2×Dic6—32no—
200C2×Dic6—38no—
201C2×Dic6—62no—
202C2×Dic6—64no—
203C2×Dic6—62no—
204C2×Dic6—62no—
205C2×Dic6C22×D312yes—
206C3×Q16—34no—
207C2×C3×C8—21no—
208C2×C3×C8—31no—
209C2×C3×C8—34no—
210C2×C3×C8—31no—
211C2×C3×C8C22×D311yescharacteristic
212C2×C3×C8C22×D311yescharacteristic
213C3×C4⋊C4—22no—
214C3×C4⋊C4—32no—
215C3×C4⋊C4—62no—
216C3×C4⋊C4C22×D312yes—
217C3×C4⋊C4C22×D312yes—
218C3×C22⋊C4—62no—
219C3×C42—31no—
220C3×C42—62no—
221C3×C42—62no—
222#217—32no—
223#216—38no—
224(C2×D3)⋊C4—22no—
225(C2×D3)⋊C4—32no—
226C4⋊Dic3—32no—
227C4⋊Dic3—62no—
228C4⋊Dic3C22×D312yes—
229Dic3⋊C4—22no—
230Dic3⋊C4—32no—
231Dic3⋊C4—62no—
232Dic3⋊C4—62no—
233Dic3⋊C4—62no—
234Dic3⋊C4—62no—
235Dic3⋊C4—62no—
236Dic3⋊C4—122no—
237C4×Dic3—22no—
238C4×Dic3—22no—
239C4×Dic3—31no—
240C4×Dic3—31no—
241C4×Dic3—61no—
242C4×Dic3—62no—
243C4×Dic3—62no—
244C4×Dic3—62no—
245C4×Dic3—62no—
246C4×Dic3—62no—
247C4×Dic3—62no—
248C4×Dic3—122no—
249C4×Dic3C22×D311yescharacteristic
250#208—62no—
251C2×C3⋊C8—31no—
252C2×C3⋊C8—31no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8C22×D311yescharacteristic
255C2×C3⋊C8C22×D311yescharacteristic
256Dic12—38no—
257Dic12—34no—
258Dic12—34no—
259Dic12—64no—
260Dic12C4×D314yes—
261ΓL(1,𝔽25)—62no—
262D3×C8C4×D314yes—
263C22×C32C22×D411yescharacteristic
264C2×C3×D3—22no—
265C2×C3×D3C4×D412yes—
266C32×C4—42no—
267C32×C4C23×C411yescharacteristic
268C32×C4C2×#4111yescharacteristic
269C3⋊Dic3—24no—
270C3⋊Dic3—22no—
271C3×Dic3—24no—
272C3×Dic3—22no—
273C3×Dic3—42no—
274C3×Dic3C4×D412yes—
275C22×Q8—92no—
276C2×Q16—31no—
277C2×Q16—98no—
278C2×Q16—92no—
279C2×Q16—91no—
280C2×M16—91no—
281C22×C8—31no—
282C4×Q8—32no—
283C4×Q8—92no—
284C4×Q8—92no—
285C4×Q8—92no—
286C4×Q8—182no—
287C4×Q8—182no—
288#117—32no—
289#117—91no—
290#117—182no—
291#117—182no—
292#107—32no—
293#106—31no—
294#106D3211yescharacteristic
295#103—32no—
296#103—92no—
297#103—92no—
298#103—92no—
299#97—31no—
300#97—91no—
301C4×C8—91no—
302C4×C8—91no—
303C23×C3—31no—
304C22×D3D3×D411yescharacteristic
305C3×Q8—34no—
306C3×Q8—62no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—31no—
311C2×C3×C4—32no—
312C2×C3×C4—32no—
313C2×C3×C4—32no—
314C2×C3×C4—42no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319C2×Dic3—22no—
320C2×Dic3—22no—
321C2×Dic3—32no—
322C2×Dic3—32no—
323C2×Dic3—62no—
324C2×Dic3—68no—
325C2×Dic3—62no—
326C2×Dic3—62no—
327C2×Dic3—122no—
328C2×Dic3D3×D412yes—
329C2×Dic3D3×D411yescharacteristic
330C4×D3—68no—
331C4×D3C2×C4×D312yes—
332C4×D3#23912yes—
333Dic6—22no—
334Dic6—34no—
335Dic6—34no—
336Dic6—64no—
337Dic6—68no—
338Dic6—62no—
339Dic6—62no—
340Dic6—68no—
341Dic6—122no—
342Dic6C2×C4×D314yes—
343C3×C8—22no—
344C3×C8—32no—
345C3×C8—61no—
346C3×C8C2×C4×D312yes—
347C3×C8C2×C4×D312yes—
348C3⋊C8—21no—
349C3⋊C8—61no—
350C3⋊C8—61no—
351C3⋊C8—121no—
352C3⋊C8C2×C4×D312yes—
353C2×C32C2×C4×D411yescharacteristic
354C2×C32#57812yes—
355C3×D3—22no—
356C2×Q8—32no—
357C2×Q8—98no—
358C2×Q8—92no—
359C2×Q8—182no—
360C2×Q8—184no—
361C22×C4—31no—
362C22×C4—182no—
363Q16—34no—
364Q16—98no—
365Q16—94no—
366M16—182no—
367C2×C8—31no—
368C2×C8—34no—
369C2×C8—31no—
370C2×C8—91no—
371C2×C8C2×D3211yescharacteristic
372C4⋊C4—32no—
373C4⋊C4—62no—
374C4⋊C4—92no—
375C4⋊C4—182no—
376C4⋊C4—182no—
377C4⋊C4—182no—
378C4⋊C4C2×D3212yes—
379C22⋊C4—62no—
380C22⋊C4—92no—
381C42—31no—
382C42—62no—
383C42—62no—
384C42—91no—
385C42—182no—
386C42—182no—
387C42—182no—
388C22×C3—21no—
389C22×C3—32no—
390C22×C3—62no—
391C22×C3C2×D3×D411yescharacteristic
392C22×C3C2×D3×D411yescharacteristic
393C2×D3—22no—
394C2×D3#89312yes—
395C3×C4—21no—
396C3×C4—21no—
397C3×C4—32no—
398C3×C4—42no—
399C3×C4—42no—
400C3×C4—64no—
401C3×C4—62no—
402C3×C4—82no—
403C3×C4—122no—
404C3×C4C22×C4×D311yescharacteristic
405C3×C4C22×C4×D311yescharacteristic
406C3×C4C2×#23911yescharacteristic
407C3×C4D3×#4111yescharacteristic
408Dic3—22no—
409Dic3—24no—
410Dic3—42no—
411Dic3—64no—
412Dic3—62no—
413Dic3—62no—
414Dic3—64no—
415Dic3—124no—
416Dic3—122no—
417Dic3#89312yes—
418C32#295011yescharacteristic, complemented, Sylow
419C23—31no—
420Q8—34no—
421Q8—62no—
422Q8—94no—
423Q8—188no—
424Q8—182no—
425C2×C4—22no—
426C2×C4—31no—
427C2×C4—32no—
428C2×C4—32no—
429C2×C4—32no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—92no—
433C2×C4—188no—
434C2×C4—182no—
435C2×C4C22×D3211yescharacteristic
436C8—32no—
437C8—61no—
438C8—181no—
439C8C4×D3212yes—
440C2×C3—21no—
441C2×C3—22no—
442C2×C3—62no—
443C2×C3C2×#89311yescharacteristic
444C2×C3C4×D3×D411yescharacteristic
445C2×C3#577112yes—
446C2×C3#577912yes—
447D3—22no—
448C22—32no—
449C22—62no—
450C22D32×D411yescharacteristic
451C4—32no—
452C4—42no—
453C4—64no—
454C4—62no—
455C4—122no—
456C4—184no—
457C4—182no—
458C4C2×C4×D3211yescharacteristic
459C4D3×#23911yescharacteristic
460C3—21no—
461C3#7916911yescharacteristic, complemented
462C3#7983111yescharacteristic, complemented
463C2—62no—
464C2D3×#89311yescharacteristic
465C2#1059475612yes—
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×C3×D3C2×D4
cosocleC2×C32×C4C24
hypercenter#106D32
hypocenterC32#2950
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #10592552C2semidirect
5. C3×#4853C2semidirect
6. #10590819C2semidirect
7. #10590810C2semidirect
10. #10590482C2semidirect
11. #10590481C2semidirect
30. D3×Dic12C4semidirect
60. #4853D3semidirect
418. C32#2950semidirect
461. C3#79169semidirect
462. C3#79831semidirect

Maximal subgroups

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

subgroupindex
C2×D3×Dic122
#105943572
#105925522
C3×#48602
C3×#48532
#105908192
#105908102
#105906932
#105906002
#105904822
#105904812
#798313
#791693