Finite Group Databasebeta

← #11786521

Subgroups — #11786521

Order 1152.

689 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63841C211yesmaximal, characteristic
2C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
3C2×C3×#817C211yesmaximal, characteristic, complemented
4#10591313C211yesmaximal, characteristic
5C2×#63575C211yesmaximal, characteristic, complemented
6#10589417C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#70580—31nomaximal
9#69929—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×(C2×D3)⋊Dic3—21no—
18C2×(C2×D3)⋊Dic3—21no—
19C2×Dic32—21no—
20#63841—22no—
21#63841—22no—
22C3×(C2×D3)⋊C8C414yescomplemented
23C3×#817—22no—
24#63579—21no—
25#63575—22no—
26C2×#926—31no—
27C2×#892—31no—
28C2×C3×#106—31no—
29C2×C3×C22⋊C8—31no—
30#5212—31no—
31C2×(C2×D3)⋊C8D311yescharacteristic
32C2×#818—31no—
33C2×#817D311yescharacteristic, complemented
34#4987—31no—
35C2×#807—31no—
36#4551—31no—
37#4551—31no—
38#4551—31no—
39#4551—61no—
40#4529—31no—
41C23×C3×D3D411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3C2×C412yes—
53C2×C3×C4×D3Q812yes—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C2×C32×C8C2×C412yes—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)—21no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)D412yes—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3D412yes—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8C2×C412yes—
68(C2×D3)⋊Dic3—24no—
69(C2×D3)⋊Dic3—42no—
70Dic32—24no—
71#1854—91noSylow
72C23×C3×C4—31no—
73C22×C4×D3C2×D311yescharacteristic
74C22×C3×C8—21no—
75C22×C3×C8—31no—
76C22×C3×C8C2×D311yescharacteristic
77C22×C3×C8C2×D311yescharacteristic
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4—31no—
80C2×#217—61no—
81C2×#217—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84#926—62no—
85#926—62no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—61no—
91C2×C4⋊Dic3—61no—
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×C4⋊Dic3C2×D311yescharacteristic
94C2×C4×Dic3—61no—
95C2×C4×Dic3—61no—
96C22×C3⋊C8C2×D311yescharacteristic
97#892—62no—
98#892—62no—
99C3×#106—62no—
100C3×C22⋊C8—34no—
101C3⋊#95—61no—
102C3⋊#95—61no—
103(C2×D3)⋊C8Dic314yescomplemented
104#818—62no—
105#817—22no—
106#807—62no—
107C23×C32C2×D411yescharacteristic
108C22×C3×D3—21no—
109C22×C3×D3—21no—
110C22×C3×D3—21no—
111C22×C3×D3—21no—
112C22×C3×D3—21no—
113C22×C3×D3—21no—
114C22×C3×D3C4⋊C412yes—
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×Q811yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C3⋊Dic3—22no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3C4⋊C412yes—
136C3×C4×D3—22no—
137C3×C4×D3—22no—
138C3×C4×D3—22no—
139C3×C4×D3—22no—
140C32×C8—22no—
141C3×C3⋊C8—22no—
142C2×#117—91no—
143C2×#107—91no—
144C2×#106—31no—
145C2×C22⋊C8—31no—
146#380—91no—
147#340—91no—
148#340—91no—
149C24×C3—31no—
150C23×D3D1211yescharacteristic
151C22×C3×C4—21no—
152C22×C3×C4—31no—
153C22×C3×C4—32no—
154C22×C3×C4—32no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—21no—
164C22×Dic3—21no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—121no—
170C22×Dic3—121no—
171C22×Dic3D1211yescharacteristic
172C2×C4×D3—21no—
173C2×C4×D3—21no—
174C2×C4×D3—21no—
175C2×C4×D3—21no—
176C2×C4×D3Dic612yes—
177C2×C4×D3C2×Dic312yes—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—21no—
181C2×C3×C8—21no—
182C2×C3×C8—22no—
183C2×C3×C8—32no—
184C2×C3×C8—41no—
185C2×C3×C8—41no—
186C2×C3×C8—61no—
187C2×C3×C8—61no—
188C2×C3×C8C4×D312yes—
189C2×C3×C8C2×Dic312yes—
190C3×C4⋊C4—32no—
191C3×C4⋊C4—61no—
192C3×C4⋊C4—61no—
193C3×C4⋊C4—61no—
194#217—64no—
195#217—122no—
196(C2×D3)⋊C4—64no—
197(C2×D3)⋊C4—122no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—21no—
201C4⋊Dic3—32no—
202C4⋊Dic3—32no—
203C4⋊Dic3—62no—
204C4⋊Dic3—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—62no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—121no—
212C4⋊Dic3—121no—
213C4⋊Dic3#6712yes—
214C4×Dic3—64no—
215C4×Dic3—64no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8C2×Dic312yes—
219C22×C32C2×C4⋊C411yescharacteristic
220C22×C32#12011yescharacteristic
221C22×C32#12311yescharacteristic
222C22×C32#13511yescharacteristic
223C22×C32#13511yescharacteristic
224C22×C32AGL(1,ℤ/8)11yescharacteristic
225C22×C32#13711yescharacteristic
226C2×C3×D3—22no—
227C2×C3×D3—22no—
228C2×C3×D3—22no—
229C2×C3×D3—41no—
230C2×C3×D3—41no—
231C2×C3×D3—41no—
232C2×C3×D3—41no—
233C32×C4C4×D411yescharacteristic
234C32×C4C4×D411yescharacteristic
235C32×C4C22⋊Q811yescharacteristic
236C32×C4C22⋊Q811yescharacteristic
237C3⋊Dic3—42no—
238C3⋊Dic3—81no—
239C3×Dic3—22no—
240C3×Dic3—42no—
241C3×Dic3—81no—
242C23×C4—31no—
243C22×C8—31no—
244C22×C8D3211yescharacteristic
245#117—182no—
246#117—182no—
247C2×C4⋊C4—31no—
248C2×C4⋊C4—31no—
249C2×C4⋊C4—91no—
250C2×C4⋊C4—91no—
251C2×C22⋊C4—181no—
252C2×C22⋊C4—181no—
253C2×C42—181no—
254#107—182no—
255#106—62no—
256C22⋊C8—34no—
257#95—181no—
258C23×C3—21no—
259C23×C3—32no—
260C23×C3—61no—
261C23×C3—61no—
262C23×C3—61no—
263C23×C3—61no—
264C23×C3—61no—
265C23×C3—61no—
266C23×C3C2×D1211yescharacteristic
267C23×C3D3×D411yescharacteristic
268C22×D3—21no—
269C22×D3—21no—
270C22×D3—21no—
271C22×D3—21no—
272C22×D3—21no—
273C22×D3—21no—
274C22×D3C4⋊Dic312yes—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—32no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—62no—
285C2×C3×C4—62no—
286C2×C3×C4—62no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—121no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4C2×Dic611yescharacteristic
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4#23711yescharacteristic
302C2×C3×C4D3×Q811yescharacteristic
303C2×C3×C4#23911yescharacteristic
304C2×C3×C4C22×Dic311yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306C2×Dic3—21no—
307C2×Dic3—21no—
308C2×Dic3—22no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—122no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—121no—
321C2×Dic3—122no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—241no—
329C2×Dic3—241no—
330C2×Dic3—241no—
331C2×Dic3—241no—
332C2×Dic3C4⋊Dic312yes—
333C4×D3—22no—
334C4×D3—22no—
335C4×D3—22no—
336C4×D3—22no—
337C3×C8—22no—
338C3×C8—22no—
339C3×C8—42no—
340C3×C8—62no—
341C3⋊C8—22no—
342C2×C32#38511yescharacteristic
343C2×C32#42711yescharacteristic
344C2×C32#42811yescharacteristic
345C2×C32#44911yescharacteristic
346C2×C32#45211yescharacteristic
347C2×C32#48211yescharacteristic
348C2×C32#48511yescharacteristic
349C3×D3—42no—
350C24—31no—
351C22×C4—31no—
352C22×C4—32no—
353C22×C4—32no—
354C22×C4—61no—
355C22×C4—61no—
356C22×C4—61no—
357C22×C4—61no—
358C22×C4—61no—
359C22×C4—61no—
360C22×C4—181no—
361C22×C4—181no—
362C22×C4C2×D3211yescharacteristic
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—32no—
366C2×C8—61no—
367C2×C8—61no—
368C2×C8D3×Dic312yes—
369C4⋊C4—32no—
370C4⋊C4—61no—
371C4⋊C4—61no—
372C4⋊C4—61no—
373C4⋊C4—92no—
374C4⋊C4—181no—
375C4⋊C4—181no—
376C4⋊C4—181no—
377C22⋊C4—184no—
378C22⋊C4—362no—
379C42—184no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—62no—
388C22×C3—62no—
389C22×C3—62no—
390C22×C3—121no—
391C22×C3—121no—
392C22×C3—121no—
393C22×C3—121no—
394C22×C3#88211yescharacteristic
395C22×C3#88611yescharacteristic
396C22×C3D3×C4⋊C411yescharacteristic
397C22×C3#89411yescharacteristic
398C22×C3#90411yescharacteristic
399C22×C3#90411yescharacteristic
400C22×C3#90811yescharacteristic
401C22×C3#90911yescharacteristic
402C22×C3#91411yescharacteristic
403C22×C3#91511yescharacteristic
404C22×C3#91611yescharacteristic
405C22×C3#91611yescharacteristic
406C22×C3C2×C4⋊Dic311yescharacteristic
407C22×C3#93711yescharacteristic
408C2×D3—22no—
409C2×D3—22no—
410C2×D3—22no—
411C2×D3—41no—
412C2×D3—41no—
413C2×D3—41no—
414C2×D3—41no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—62no—
420C3×C4—122no—
421C3×C4—241no—
422C3×C4#87811yescharacteristic
423C3×C4#87811yescharacteristic
424C3×C4#89311yescharacteristic
425C3×C4#89611yescharacteristic
426C3×C4C4×#6711yescharacteristic
427C3×C4D4×Dic311yescharacteristic
428C3×C4D4×Dic311yescharacteristic
429C3×C4#94611yescharacteristic
430Dic3—22no—
431Dic3—42no—
432Dic3—81no—
433Dic3—122no—
434Dic3—122no—
435Dic3—242no—
436Dic3—242no—
437Dic3—241no—
438Dic3—241no—
439C32#185411yescharacteristic, complemented, Sylow
440C23—32no—
441C23—61no—
442C23—61no—
443C23—61no—
444C23—61no—
445C23—61no—
446C23—61no—
447C23D3×D1211yescharacteristic
448C2×C4—32no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—62no—
452C2×C4—62no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—121no—
457C2×C4—121no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—182no—
462C2×C4—361no—
463C2×C4—361no—
464C2×C4—361no—
465C2×C4—361no—
466C2×C4—361no—
467C2×C4D3×Dic611yescharacteristic
468C2×C4#379611yescharacteristic
469C2×C4#380211yescharacteristic
470C2×C4C2×D3×Dic311yescharacteristic
471C2×C4#380411yescharacteristic
472C2×C4D3×#6711yescharacteristic
473C8—22no—
474C8—62no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—122no—
483C2×C3#472311yescharacteristic
484C2×C3#473311yescharacteristic
485C2×C3#473411yescharacteristic
486C2×C3#473711yescharacteristic
487C2×C3#486011yescharacteristic
488C2×C3#486111yescharacteristic
489C2×C3#486611yescharacteristic
490C2×C3#486811yescharacteristic
491C2×C3#495011yescharacteristic
492C2×C3#498911yescharacteristic
493C2×C3#510611yescharacteristic
494C2×C3#512111yescharacteristic
495C2×C3#517211yescharacteristic
496C2×C3#517311yescharacteristic
497D3—42no—
498C22—62no—
499C22—62no—
500C22—62no—
501C22—121no—
502C22—121no—
503C22—121no—
504C22—121no—
505C22#6379411yescharacteristic
506C22#6380011yescharacteristic
507C22#6380611yescharacteristic
508C22#6380611yescharacteristic
509C22D3×C4⋊Dic311yescharacteristic
510C22#6389011yescharacteristic
511C22#6392211yescharacteristic
512C4—62no—
513C4—122no—
514C4—241no—
515C4—362no—
516C4—721no—
517C4#6388711yescharacteristic
518C4#6389811yescharacteristic
519C4#6389911yescharacteristic
520C4Dic3×#6711yescharacteristic
521C3—21no—
522C3#6992911yescharacteristic, complemented
523C3#7058011yescharacteristic, complemented
524C2—122no—
525C2#1059068111yescharacteristic
526C2#1059070411yescharacteristic
527C2#1059070611yescharacteristic
528C2#1059070911yescharacteristic
529C2#1059082311yescharacteristic
530C2#1059096011yescharacteristic
531C2#1059137711yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1854
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C2×C3×#817C2semidirect
5. C2×#63575C2semidirect
6. #10589417C2semidirect
7. #10589164C2semidirect
22. C3×(C2×D3)⋊C8C4semidirect
33. C2×#817D3semidirect
103. (C2×D3)⋊C8Dic3semidirect
439. C32#1854semidirect
522. C3#69929semidirect
523. C3#70580semidirect

Maximal subgroups

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

subgroupindex
C2×#638412
C2×C3×(C2×D3)⋊C82
C2×C3×#8172
#105913132
C2×#635752
#105894172
#105891642
#705803
#699293