Finite Group Databasebeta

← #11898365

Subgroups — #11898365

Order 1152.

775 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593932C212yesmaximal, complemented
2C4×#3746C211yesmaximal, characteristic, complemented
3C3×#4696C211yesmaximal, characteristic
4C3×C8×Dic6C211yesmaximal, characteristic, complemented
5#10590896C211yesmaximal, characteristic, complemented
6#10590864C211yesmaximal, characteristic
7#10590859C212yesmaximal, complemented
8Dic3×Dic12C211yesmaximal, characteristic, complemented
9Dic3×D24C211yesmaximal, characteristic
10#10590752C212yesmaximal, complemented
11#10590378C212yesmaximal, complemented
12#81813—31nomaximal
13#79912—31nomaximal
14C2×#3746C2211yescharacteristic
15C4×#634C2212yes—
16C2×C3×Dic12C2211yescharacteristic
17C2×C3×D24C2211yescharacteristic
18C2×C3×#204C2212yes—
19C3×#875C2212yes—
20C3×C4×Dic6C2211yescharacteristic
21Dic3×D12C2212yes—
22#63887—22no—
23#63878—22no—
24#63866C2212yes—
25#63862—22no—
26#63860C2212yes—
27#63858—22no—
28Dic3×Dic6C2212yes—
29C2×#3719C2212yes—
30C2×#3716C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63645C2211yescharacteristic
33#63643C2212yes—
34C3×Dic3⋊C8C2211yescharacteristic
35C3×Dic3⋊C8C2211yescharacteristic
36C3×C8×Dic3C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39#63566C2212yes—
40#63563C2212yes—
41#5671—32no—
42#5584—32no—
43C3×#495—31no—
44C3×C8×Q8—31no—
45#5183—31no—
46Dic3×Q16—31no—
47#5166—32no—
48#5162—32no—
49#5155—31no—
50Dic3×D8—31no—
51#5054—32no—
52#4845—32no—
53#4845—32no—
54#4841—32no—
55#4699—31no—
56C4×Dic12—31no—
57C4×Dic12—31no—
58C4×Dic12—31no—
59C4×Dic12—61no—
60#4696—31no—
61#4696D311yescharacteristic
62C4×D24—31no—
63C8×Dic6D311yescharacteristic, complemented
64C2×#634C2312yes—
65C2×C3×D12C2312yes—
66C2×C3×Dic6D411yescharacteristic
67C2×C3×Dic6C2312yes—
68C2×D3×Dic3—22no—
69C2×C32×C8C2311yescharacteristic
70C2×C32×C8C2311yescharacteristic
71C32×C42C2311yescharacteristic
72C4⋊(C3⋊Dic3)C2312yes—
73#3750—22no—
74C4×C3⋊Dic3—22no—
75#3746—22no—
76C3×(C2×D3)⋊C4—22no—
77C3×(C2×D3)⋊C4—22no—
78C3×C4⋊Dic3D411yescharacteristic
79C3×Dic3⋊C4D411yescharacteristic
80C3×Dic3⋊C4D411yescharacteristic
81C3×C4×Dic3C2311yescharacteristic
82C3×C4×Dic3C2311yescharacteristic
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2311yescharacteristic
85C3×Dic12—22no—
86C3×D24—22no—
87C3×#204—42no—
88Dic3⋊Dic3—22no—
89Dic3⋊Dic3—22no—
90Dic3⋊Dic3—22no—
91(C2×D3)⋊Dic3—22no—
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94Dic32—22no—
95#3719—42no—
96#3716—42no—
97#3393—91noSylow
98C2×C3×Q16—31no—
99C2×C3×SD16—32no—
100C2×C3×D8—31no—
101C3×#124—32no—
102C3×C4×Q8—31no—
103#946—62no—
104Q8×Dic3—32no—
105#944—32no—
106C2×#216—32no—
107#936—32no—
108D4×Dic3—32no—
109C2×#214—32no—
110C2×Dic12—31no—
111C2×Dic12—31no—
112C2×Dic12—32no—
113C2×Dic12—61no—
114C2×Dic12C2×D311yescharacteristic
115C2×D24C2×D311yescharacteristic
116C2×#204—32no—
117C2×#204C2×D312yes—
118#898—62no—
119#898—62no—
120#892—62no—
121#879—62no—
122#879—62no—
123#878—62no—
124#877—62no—
125#875—32no—
126#875C2×D312yes—
127C4×D12—32no—
128#869—32no—
129C4×Dic6—32no—
130C4×Dic6—32no—
131C4×Dic6—32no—
132C4×Dic6—62no—
133C4×Dic6C2×D311yescharacteristic
134C3×C4⋊C8—31no—
135C3×C4⋊C8—31no—
136C3×C4⋊C8—31no—
137C3×C4×C8—21no—
138C3×C4×C8—31no—
139C3×C4×C8—31no—
140C3×C4×C8C2×D311yescharacteristic
141C3×C4×C8C2×D311yescharacteristic
142#835—32no—
143#832—32no—
144#821—32no—
145#818—31no—
146#818—31no—
147#818—61no—
148#816—32no—
149#816—32no—
150#816—32no—
151#816—62no—
152Dic3⋊C8C2×D311yescharacteristic
153Dic3⋊C8C2×D311yescharacteristic
154C8×Dic3C2×D311yescharacteristic
155C8×Dic3C2×D311yescharacteristic
156C4⋊(C3⋊C8)C2×D311yescharacteristic
157C22×C3×D3—22no—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2411yescharacteristic
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163#634—22no—
164#634—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3C2×D411yescharacteristic
167C2×C3×Dic3C2×D411yescharacteristic
168C2×C3×Dic3C2×D411yescharacteristic
169C2×C3×Dic3C2×D411yescharacteristic
170C3×D12—22no—
171C3×D12—22no—
172C3×Dic6—22no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175D3×Dic3—44no—
176C32×C8—21no—
177C32×C8#4112yes—
178C3×C3⋊C8—21no—
179C3×C3⋊C8—21no—
180#556—92no—
181#495—31no—
182#495—91no—
183#494—91no—
184#464—92no—
185#464—92no—
186#461—92no—
187C8×Q8—31no—
188C4×Q16—91no—
189C4×Q16—91no—
190C4×D8—91no—
191C2×C3×Q8—31no—
192C2×C3×Q8—32no—
193C2×C3×D4—32no—
194C22×Dic3—62no—
195C2×D12C22×D312yes—
196C2×C4×D3—62no—
197C2×Dic6—32no—
198C2×Dic6—32no—
199C2×Dic6—62no—
200C2×Dic6D1211yescharacteristic
201C2×Dic6C22×D312yes—
202C3×Q16—62no—
203C3×SD16—122no—
204C3×D8—62no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—31no—
208C2×C3×C8—31no—
209C2×C3×C8C22×D311yescharacteristic
210C2×C3×C8C22×D311yescharacteristic
211C2×C3×C8C22×D311yescharacteristic
212C2×C3×C8C22×D311yescharacteristic
213C3×C4⋊C4—31no—
214C3×C4⋊C4—31no—
215C3×C4⋊C4—31no—
216C3×C22⋊C4—62no—
217C3×C22⋊C4—62no—
218C3×C42—21no—
219C3×C42—31no—
220C3×C42—31no—
221C3×C42C22×D311yescharacteristic
222C3×C42C22×D311yescharacteristic
223#217—62no—
224#217—62no—
225#217—62no—
226#216—122no—
227#214—122no—
228(C2×D3)⋊C4—22no—
229(C2×D3)⋊C4—22no—
230(C2×D3)⋊C4—62no—
231(C2×D3)⋊C4—62no—
232(C2×D3)⋊C4—62no—
233C4⋊Dic3—32no—
234C4⋊Dic3—32no—
235C4⋊Dic3—62no—
236C4⋊Dic3—62no—
237C4⋊Dic3—62no—
238C4⋊Dic3—62no—
239C4⋊Dic3D1211yescharacteristic
240Dic3⋊C4—62no—
241Dic3⋊C4—62no—
242Dic3⋊C4—62no—
243Dic3⋊C4—62no—
244Dic3⋊C4—62no—
245Dic3⋊C4—122no—
246Dic3⋊C4D1211yescharacteristic
247Dic3⋊C4D1211yescharacteristic
248C4×Dic3—62no—
249C4×Dic3—62no—
250C4×Dic3—62no—
251C4×Dic3—62no—
252C4×Dic3—122no—
253C4×Dic3C22×D311yescharacteristic
254C4×Dic3C22×D311yescharacteristic
255C2×C3⋊C8C22×D311yescharacteristic
256C2×C3⋊C8C22×D311yescharacteristic
257Dic12—22no—
258Dic12—64no—
259Dic12—62no—
260Dic12—62no—
261Dic12—122no—
262D24—22no—
263#204—42no—
264#204—122no—
265C22×C32C22×D411yescharacteristic
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—42no—
269C32×C4—21no—
270C32×C4—21no—
271C32×C4C2×#4111yescharacteristic
272C32×C4H(5,𝔽2)11yescharacteristic
273C3⋊Dic3—42no—
274C3⋊Dic3—42no—
275C3×Dic3—21no—
276C3×Dic3—21no—
277C3×Dic3—21no—
278C3×Dic3—42no—
279C3×Dic3#13512yes—
280C2×Q16—31no—
281C2×Q16—92no—
282C2×Q16—91no—
283C2×SD16—32no—
284C2×SD16—92no—
285C2×D8—31no—
286C4⋊Q8—92no—
287#126—182no—
288#126—182no—
289#124—32no—
290#124—92no—
291C22⋊Q8—182no—
292C4×Q8—31no—
293C4×Q8—92no—
294C4×Q8—92no—
295C4×D4—92no—
296#117—182no—
297#107—91no—
298C4⋊C8—31no—
299C4⋊C8—31no—
300C4⋊C8—31no—
301#103—92no—
302#103—92no—
303#102—92no—
304C4×C8—31no—
305C4×C8—31no—
306C4×C8D3211yescharacteristic
307C23×C3—62no—
308C22×D3—22no—
309C3×Q8—62no—
310C3×Q8—62no—
311C3×Q8—62no—
312C3×D4—62no—
313C3×D4—62no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—31no—
318C2×C3×C4—31no—
319C2×C3×C4—31no—
320C2×C3×C4—31no—
321C2×C3×C4—62no—
322C2×C3×C4C2×D1211yescharacteristic
323C2×C3×C4C2×D1211yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328C2×Dic3—22no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—122no—
334C2×Dic3—122no—
335C2×Dic3—124no—
336C2×Dic3C2×D1211yescharacteristic
337C2×Dic3C2×D1211yescharacteristic
338C2×Dic3C2×D1211yescharacteristic
339C2×Dic3C2×D1211yescharacteristic
340D12—22no—
341D12—22no—
342C4×D3—124no—
343Dic6—22no—
344Dic6—22no—
345Dic6—22no—
346Dic6—64no—
347Dic6—62no—
348Dic6—62no—
349Dic6—62no—
350Dic6—62no—
351Dic6—122no—
352C3×C8—21no—
353C3×C8—21no—
354C3×C8—22no—
355C3×C8—41no—
356C3×C8—61no—
357C3×C8—61no—
358C3×C8#23712yes—
359C3×C8#23912yes—
360C3⋊C8—21no—
361C3⋊C8—21no—
362C2×C32#55011yescharacteristic
363C2×C32C2×#13511yescharacteristic
364C2×C32#57811yescharacteristic
365C3×D3—82no—
366C2×Q8—31no—
367C2×Q8—32no—
368C2×Q8—92no—
369C2×D4—32no—
370C22×C4—182no—
371Q16—62no—
372Q16—182no—
373Q16—362no—
374SD16—122no—
375SD16—362no—
376D8—62no—
377C2×C8—31no—
378C2×C8—31no—
379C2×C8C2×D3211yescharacteristic
380C2×C8C2×D3211yescharacteristic
381C4⋊C4—31no—
382C4⋊C4—31no—
383C4⋊C4—31no—
384C4⋊C4—92no—
385C4⋊C4—182no—
386C4⋊C4—182no—
387C4⋊C4—182no—
388C4⋊C4—182no—
389C22⋊C4—62no—
390C22⋊C4—62no—
391C22⋊C4—182no—
392C22⋊C4—182no—
393C22⋊C4—182no—
394C42—31no—
395C42—31no—
396C42—182no—
397C42—182no—
398C42C2×D3211yescharacteristic
399C22×C3—21no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3C22×D1211yescharacteristic
404C22×C3C2×D3×D411yescharacteristic
405C2×D3—42no—
406C2×D3—42no—
407C2×D3—42no—
408C3×C4—22no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—32no—
416C3×C4—41no—
417C3×C4—61no—
418C3×C4—61no—
419C3×C4—61no—
420C3×C4—122no—
421C3×C4C2×#23711yescharacteristic
422C3×C4#100411yescharacteristic
423C3×C4C2×#23911yescharacteristic
424C3×C4#100911yescharacteristic
425Dic3—21no—
426Dic3—21no—
427Dic3—21no—
428Dic3—42no—
429Dic3—124no—
430Dic3—122no—
431Dic3—122no—
432Dic3—122no—
433Dic3—122no—
434Dic3—242no—
435Dic3#90412yes—
436C32#339311yescharacteristic, complemented, Sylow
437C23—62no—
438Q8—62no—
439Q8—62no—
440Q8—62no—
441Q8—182no—
442Q8—182no—
443D4—62no—
444D4—62no—
445C2×C4—31no—
446C2×C4—31no—
447C2×C4—31no—
448C2×C4—31no—
449C2×C4—62no—
450C2×C4—182no—
451C2×C4—182no—
452C2×C4—364no—
453C2×C4D3×D1211yescharacteristic
454C2×C4D3×D1211yescharacteristic
455C2×C4C22×D3211yescharacteristic
456C8—21no—
457C8—61no—
458C8—61no—
459C8#379612yes—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—242no—
464C2×C3#557711yescharacteristic
465C2×C3#571811yescharacteristic
466C2×C3C2×#90411yescharacteristic
467C2×C3#575311yescharacteristic
468C2×C3D3×#13511yescharacteristic
469C2×C3#577111yescharacteristic
470D3—82no—
471C22—122no—
472C22—122no—
473C22—122no—
474C22C2×D3×D1211yescharacteristic
475C4—21no—
476C4—21no—
477C4—32no—
478C4—61no—
479C4—61no—
480C4—61no—
481C4—122no—
482C4—362no—
483C4—362no—
484C4C2×#379611yescharacteristic
485C4#6430711yescharacteristic
486C3—21no—
487C3#7991211yescharacteristic, complemented
488C3#8181311yescharacteristic, complemented
489C2—242no—
490C2#1059390011yescharacteristic
491C2D3×#90411yescharacteristic
492C2#1059469211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×D24C22
hypercenterC4×C8D32
hypocenterC32#3393
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
1. #10593932C2semidirect
2. C4×#3746C2semidirect
4. C3×C8×Dic6C2semidirect
5. #10590896C2semidirect
7. #10590859C2semidirect
8. Dic3×Dic12C2semidirect
10. #10590752C2semidirect
11. #10590378C2semidirect
63. C8×Dic6D3semidirect
436. C32#3393semidirect
487. C3#79912semidirect
488. C3#81813semidirect

Maximal subgroups

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

subgroupindex
#105939322
C4×#37462
C3×#46962
C3×C8×Dic62
#105908962
#105908642
#105908592
Dic3×Dic122
Dic3×D242
#105907522
#105903782
#818133
#799123