Finite Group Databasebeta

← #11878898

Subgroups — #11878898

Order 1152.

827 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593909C211yesmaximal, characteristic
2#10593866C211yesmaximal, characteristic
3#10592384C211yesmaximal, characteristic
4C3×#4699C211yesmaximal, characteristic, complemented
5C3×#4681C211yesmaximal, characteristic, complemented
6#10590950C214yesmaximal
7#10590798C214yesmaximal, complemented
8#10590387C211yesmaximal, characteristic, complemented
9#10590290C211yesmaximal, characteristic, complemented
10#81802—31nomaximal
11#81604—31nomaximal
12C2×#3797C2212yes—
13C42×C3⋊D3C2211yescharacteristic
14C2×C3×Dic12C2214yes—
15C3×#869C2211yescharacteristic
16C3×#869C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×#869C2211yescharacteristic
19#63919—21no—
20#63919—21no—
21#63900—21no—
22#63900—21no—
23#63873C2212yes—
24#63872—21no—
25#63871—21no—
26#63871C2212yes—
27#63849—21no—
28#63843—21no—
29#63843C2212yes—
30C2×#3718C2214yes—
31C32×C4×C8C2211yescharacteristic
32#63647C2212yes—
33#63641C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#816C2214yes—
36#63565C2214yes—
37#5728—31no—
38#5728—31no—
39D3×C4⋊Q8—31no—
40D3×C4⋊Q8—31no—
41C3×#494—31no—
42C3×#487—31no—
43#5186—34no—
44#5182—34no—
45#5093—31no—
46#5092—31no—
47#5092—31no—
48#5079—31no—
49#4809—34no—
50#4795—34no—
51#4699D311yescharacteristic, complemented
52#4685—31no—
53#4685—31no—
54#4685—61no—
55#4681D311yescharacteristic, complemented
56C2×C4×C3⋊D3D411yescharacteristic
57C2×C4×C3⋊D3D411yescharacteristic
58C2×C4×C3⋊D3C2311yescharacteristic
59C2×C3×Dic6—21no—
60C2×C3×Dic6C2312yes—
61C2×C3×Dic6C2312yes—
62C2×C3×Dic6C2312yes—
63C2×#627—22no—
64C2×#624—22no—
65#3797—44no—
66C2×C32×C8C2312yes—
67C32×C42C2311yescharacteristic
68C4×C3⋊Dic3D411yescharacteristic
69C4×C3⋊Dic3D411yescharacteristic
70C4×C3⋊Dic3C2311yescharacteristic
71C2×C3⋊(C3⋊C8)C2312yes—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3—21no—
79C3×C4⋊Dic3C2312yes—
80C3×Dic12—44no—
81#3724—22no—
82#3724—22no—
83Dic3⋊Dic3—22no—
84Dic3⋊Dic3—22no—
85#3722—22no—
86Dic32—22no—
87#3718—44no—
88#3209—91noSylow
89C2×D3×Q8—32no—
90C2×D3×Q8—32no—
91C2×C3×Q16—34no—
92C3×C4⋊Q8—31no—
93C3×C4⋊Q8—31no—
94C3×C4⋊Q8—31no—
95C3×C4⋊Q8—31no—
96#946—32no—
97#946—61no—
98Q8×Dic3—32no—
99Q8×Dic3—61no—
100#944—32no—
101#944—32no—
102C2×#216—34no—
103C2×#216—34no—
104C2×Dic12C2×D314yes—
105#897—32no—
106#897—61no—
107#892—61no—
108#892—61no—
109D3×C4⋊C4—61no—
110D3×C4⋊C4—61no—
111D3×C4⋊C4—61no—
112D3×C4⋊C4—61no—
113#890—61no—
114#890—61no—
115#888—61no—
116#888—61no—
117#888—61no—
118#888—61no—
119#887—32no—
120#887—61no—
121C42×D3—31no—
122C42×D3—31no—
123C42×D3—61no—
124#869C2×D311yescharacteristic
125#869C2×D311yescharacteristic
126#869C2×D311yescharacteristic
127#869C2×D311yescharacteristic
128C3×#103—34no—
129C3×C4×C8—21no—
130C3×C4×C8C2×D311yescharacteristic
131C3×C4×C8C2×D311yescharacteristic
132#835—34no—
133(C2×D3)⋊C8—32no—
134(C2×D3)⋊C8—32no—
135(C2×D3)⋊C8—62no—
136#816C2×D314yes—
137Dic3⋊C8—32no—
138Dic3⋊C8—32no—
139Dic3⋊C8—62no—
140#810—34no—
141C4×C3⋊C8—31no—
142C4×C3⋊C8—31no—
143C4×C3⋊C8—61no—
144C22×C3⋊D3C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
149C2×C3⋊Dic3C2×D411yescharacteristic
150C2×C3⋊Dic3C2×D411yescharacteristic
151C4×C3⋊D3—22no—
152C4×C3⋊D3—22no—
153C4×C3⋊D3Q1614yescomplemented
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C3×Dic6—24no—
159C3×Dic6—24no—
160C3×Dic6—24no—
161C3×Dic6—42no—
162#627—44no—
163#624—44no—
164C32×C8—22no—
165C3⋊(C3⋊C8)—22no—
166#533—91no—
167C2×C4⋊Q8—91no—
168#494—31no—
169#494—91no—
170#487—31no—
171#487—91no—
172#462—94no—
173#451—94no—
174#431—91no—
175C2×C3×Q8—32no—
176C2×C3×Q8—32no—
177C2×C3×Q8—32no—
178C2×C3×Q8—61no—
179D3×Q8—124no—
180D3×Q8—124no—
181C2×C4×D3—31no—
182C2×C4×D3—31no—
183C2×C4×D3—31no—
184C2×C4×D3—31no—
185C2×C4×D3—31no—
186C2×C4×D3—31no—
187C2×C4×D3—61no—
188C2×C4×D3—61no—
189C2×C4×D3—61no—
190C2×C4×D3—62no—
191C2×C4×D3—62no—
192C2×Dic6—21no—
193C2×Dic6—62no—
194C2×Dic6—62no—
195C2×Dic6C22×D312yes—
196C2×Dic6C22×D312yes—
197C2×Dic6C22×D312yes—
198C3×Q16—124no—
199C2×C3×C8—22no—
200C2×C3×C8C22×D312yes—
201C2×C3×C8C22×D312yes—
202C3×C4⋊C4—32no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C42—21no—
211C3×C42C22×D311yescharacteristic
212C3×C42C22×D311yescharacteristic
213#216—124no—
214#216—124no—
215(C2×D3)⋊C4—62no—
216(C2×D3)⋊C4—62no—
217C4⋊Dic3—21no—
218C4⋊Dic3—21no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224C4⋊Dic3—62no—
225C4⋊Dic3—62no—
226C4⋊Dic3C22×D312yes—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229Dic3⋊C4—62no—
230Dic3⋊C4—62no—
231Dic3⋊C4—62no—
232Dic3⋊C4—62no—
233C4×Dic3—31no—
234C4×Dic3—31no—
235C4×Dic3—31no—
236C4×Dic3—31no—
237C4×Dic3—31no—
238C4×Dic3—31no—
239C4×Dic3—61no—
240C4×Dic3—61no—
241C4×Dic3—61no—
242C4×Dic3—62no—
243C4×Dic3—62no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—62no—
247Dic12—44no—
248C22×C32C22×D411yescharacteristic
249C2×C3⋊D3—21no—
250C2×C3⋊D3—21no—
251C2×C3⋊D3C2×Q1612yes—
252C32×C4C2×Q1612yes—
253C32×C4#13712yes—
254C32×C4H(5,𝔽2)12yes—
255C3⋊Dic3—21no—
256C3⋊Dic3—21no—
257C3⋊Dic3C2×Q1612yes—
258C3×Dic3—42no—
259C3×Dic3—42no—
260C3×Dic3—42no—
261C3×Dic3—42no—
262C22×Q8—92no—
263C2×Q16—34no—
264C2×Q16—94no—
265C4⋊Q8—31no—
266C4⋊Q8—31no—
267C4⋊Q8—31no—
268C4⋊Q8—31no—
269C4⋊Q8—92no—
270C4⋊Q8—181no—
271C4⋊Q8—181no—
272#125—181no—
273C22⋊Q8—92no—
274C22⋊Q8—181no—
275C4×Q8—92no—
276C4×Q8—181no—
277#117—181no—
278C2×C4⋊C4—181no—
279C2×C4⋊C4—181no—
280C2×C42—91no—
281C4⋊C8—92no—
282#103—34no—
283#103—94no—
284C22⋊C8—92no—
285C4×C8—91no—
286C4×C8D3211yescharacteristic
287C22×D3—31no—
288C22×D3—31no—
289C22×D3—61no—
290C3×Q8—64no—
291C3×Q8—64no—
292C3×Q8—64no—
293C3×Q8—122no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4—62no—
300C2×C3×C4—62no—
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4C23×D311yescharacteristic
306C2×C3×C4C23×D311yescharacteristic
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—31no—
312C2×Dic3—31no—
313C2×Dic3—31no—
314C2×Dic3—31no—
315C2×Dic3—31no—
316C2×Dic3—31no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C4×D3—34no—
321C4×D3—34no—
322C4×D3—64no—
323C4×D3—62no—
324C4×D3—62no—
325C4×D3—62no—
326C4×D3—62no—
327C4×D3—122no—
328C4×D3—122no—
329C4×D3—124no—
330C4×D3—124no—
331Dic6—24no—
332Dic6—24no—
333Dic6—24no—
334Dic6—42no—
335Dic6—124no—
336Dic6—124no—
337C3×C8—22no—
338C3×C8—22no—
339C3×C8—42no—
340C3⋊C8—62no—
341C3⋊C8—62no—
342C3⋊C8—122no—
343C2×C32#53511yescharacteristic
344C2×C32C22×Q1611yescharacteristic
345C2×C32C2×#13711yescharacteristic
346C3⋊D3—22no—
347C2×Q8—32no—
348C2×Q8—32no—
349C2×Q8—32no—
350C2×Q8—61no—
351C2×Q8—182no—
352C2×Q8—364no—
353C22×C4—91no—
354C22×C4—91no—
355C22×C4—91no—
356C22×C4—182no—
357Q16—124no—
358Q16—364no—
359C2×C8—92no—
360C2×C8C2×D3212yes—
361C4⋊C4—32no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—182no—
370C4⋊C4—182no—
371C4⋊C4—182no—
372C4⋊C4—182no—
373C22⋊C4—182no—
374C42—91no—
375C42—91no—
376C42—91no—
377C42—182no—
378C42C2×D3211yescharacteristic
379C22×C3—21no—
380C22×C3C2×D3×D411yescharacteristic
381C22×C3C2×D3×D411yescharacteristic
382C2×D3—32no—
383C2×D3—32no—
384C2×D3—62no—
385C2×D3—61no—
386C2×D3—61no—
387C2×D3—61no—
388C2×D3—61no—
389C2×D3—121no—
390C2×D3—121no—
391C3×C4—22no—
392C3×C4—22no—
393C3×C4—22no—
394C3×C4—122no—
395C3×C4—122no—
396C3×C4—122no—
397C3×C4—122no—
398C3×C4#91512yes—
399C3×C4D3×Q1612yes—
400C3×C4D3×Q1612yes—
401C3×C4#91812yes—
402C3×C4#100412yes—
403C3×C4#100912yes—
404Dic3—32no—
405Dic3—32no—
406Dic3—42no—
407Dic3—42no—
408Dic3—42no—
409Dic3—42no—
410Dic3—62no—
411Dic3—61no—
412Dic3—61no—
413Dic3—61no—
414Dic3—61no—
415Dic3—121no—
416Dic3—121no—
417C32#320911yescharacteristic, complemented, Sylow
418C23—91no—
419Q8—64no—
420Q8—64no—
421Q8—64no—
422Q8—122no—
423Q8—364no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—91no—
429C2×C4—94no—
430C2×C4—91no—
431C2×C4—91no—
432C2×C4—182no—
433C2×C4—182no—
434C2×C4—364no—
435C2×C4#380211yescharacteristic
436C2×C4#380211yescharacteristic
437C2×C4C22×D3211yescharacteristic
438C8—22no—
439C8—182no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3#567411yescharacteristic
444C2×C3#571511yescharacteristic
445C2×C3C2×#91511yescharacteristic
446C2×C3C2×D3×Q1611yescharacteristic
447C2×C3C2×D3×Q1611yescharacteristic
448C2×C3C2×#91811yescharacteristic
449D3—62no—
450D3—62no—
451D3—122no—
452C22—92no—
453C22—181no—
454C22—181no—
455C22C2×#380211yescharacteristic
456C4—92no—
457C4—122no—
458C4—122no—
459C4—122no—
460C4—122no—
461C4—181no—
462C4—181no—
463C4#6380212yes—
464C4#6381112yes—
465C4#6430712yes—
466C3—21no—
467C3#8160411yescharacteristic, complemented
468C3#8180211yescharacteristic, complemented
469C2—182no—
470C2#1059401011yescharacteristic
471C2C2×#6380211yescharacteristic
472C2C2×#6381111yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4×C8D32
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
4. C3×#4699C2semidirect
5. C3×#4681C2semidirect
7. #10590798C2semidirect
8. #10590387C2semidirect
9. #10590290C2semidirect
51. #4699D3semidirect
55. #4681D3semidirect
153. C4×C3⋊D3Q16semidirect
417. C32#3209semidirect
467. C3#81604semidirect
468. C3#81802semidirect

Maximal subgroups

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

subgroupindex
#105939092
#105938662
#105923842
C3×#46992
C3×#46812
#105909502
#105907982
#105903872
#105902902
#818023
#816043