Finite Group Databasebeta

← #11785828

Subgroups — #11785828

Order 1152.

657 conjugacy classes of subgroups.

The subgroup lattice has 525 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
3#10591313C211yesmaximal, characteristic
4#10589417C211yesmaximal, characteristic, complemented
5C3×#4551C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589164C211yesmaximal, characteristic, complemented
8#69926—31nomaximal
9#68873—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#63841C414yescomplemented
22C3×(C2×D3)⋊C8—22no—
23#63579—21no—
24C2×#926—31no—
25C2×#892—31no—
26C2×C3×C22⋊C8—31no—
27#5212—31no—
28C2×(C2×D3)⋊C8D311yescharacteristic
29#4987—31no—
30C3×#340—31no—
31#4551—31no—
32#4551—31no—
33#4551—31no—
34#4551—31no—
35#4551—61no—
36#4551D311yescharacteristic, complemented
37#4529—31no—
38#4529—31no—
39C23×C3×D3D411yescharacteristic
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3—21no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3D411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3C2×C412yes—
51C2×C3×C4×D3D412yes—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C4⋊(C3⋊Dic3)—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4⋊(C3⋊Dic3)C2×C412yes—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3C2×C412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66(C2×D3)⋊Dic3—24no—
67(C2×D3)⋊Dic3—42no—
68Dic32—24no—
69#1825—91noSylow
70C23×C3×C4—31no—
71C22×C4×D3C2×D311yescharacteristic
72C22×C3×C8—21no—
73C22×C3×C8—31no—
74C22×C3×C8C2×D311yescharacteristic
75C22×C3×C8C2×D311yescharacteristic
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4—31no—
78C2×#217—61no—
79C2×#217—61no—
80C2×(C2×D3)⋊C4—61no—
81C2×(C2×D3)⋊C4—61no—
82#926—34no—
83#926—62no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—31no—
88C2×C4⋊Dic3—61no—
89C2×C4⋊Dic3—61no—
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×C4×Dic3—61no—
93C2×C4×Dic3—61no—
94C22×C3⋊C8C2×D311yescharacteristic
95#892—34no—
96#892—62no—
97C3×C22⋊C8—62no—
98C3⋊#95—61no—
99C3⋊#95—61no—
100(C2×D3)⋊C8—22no—
101C23×C32C2×D411yescharacteristic
102C22×C3×D3—21no—
103C22×C3×D3—21no—
104C22×C3×D3—21no—
105C22×C3×D3—21no—
106C22×C3×D3—21no—
107C22×C3×D3—21no—
108C22×C3×D3C22⋊C412yes—
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—41no—
117C2×C3⋊Dic3—41no—
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3—41no—
121C2×C3×Dic3—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3—22no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3C22⋊C412yes—
130C3×C4×D3—22no—
131C3×C4×D3—22no—
132C3×C4×D3—22no—
133C3×C4×D3—22no—
134C32×C8—41no—
135C3×C3⋊C8—41no—
136C2×#117—91no—
137C2×C22⋊C8—31no—
138#380—91no—
139#340—31no—
140#340—91no—
141#340—91no—
142#340—91no—
143C24×C3—31no—
144C23×D3D1211yescharacteristic
145C22×C3×C4—21no—
146C22×C3×C4—31no—
147C22×C3×C4—32no—
148C22×C3×C4—32no—
149C22×C3×C4—61no—
150C22×C3×C4—61no—
151C22×C3×C4—61no—
152C22×C3×C4—61no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×Dic3—21no—
158C22×Dic3—21no—
159C22×Dic3—61no—
160C22×Dic3—61no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—121no—
164C22×Dic3—121no—
165C22×Dic3D1211yescharacteristic
166C2×C4×D3—21no—
167C2×C4×D3—21no—
168C2×C4×D3—21no—
169C2×C4×D3—21no—
170C2×C4×D3C4×D312yes—
171C2×C4×D3#6712yes—
172C2×C3×C8—22no—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—41no—
180C2×C3×C8—41no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C3×C4⋊C4—32no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188#217—64no—
189#217—122no—
190(C2×D3)⋊C4—64no—
191(C2×D3)⋊C4—122no—
192C4⋊Dic3—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—32no—
196C4⋊Dic3—32no—
197C4⋊Dic3—62no—
198C4⋊Dic3—61no—
199C4⋊Dic3—61no—
200C4⋊Dic3—62no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—61no—
205C4⋊Dic3—121no—
206C4⋊Dic3—121no—
207C4⋊Dic3C4×D312yes—
208C4×Dic3—64no—
209C4×Dic3—64no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C22×C32C2×C22⋊C411yescharacteristic
214C22×C32#12311yescharacteristic
215C22×C32#12311yescharacteristic
216C22×C32#13511yescharacteristic
217C22×C32#13511yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C22×C32#13711yescharacteristic
220C2×C3×D3—22no—
221C2×C3×D3—22no—
222C2×C3×D3—22no—
223C2×C3×D3—41no—
224C2×C3×D3—41no—
225C2×C3×D3—41no—
226C2×C3×D3—41no—
227C32×C4#11711yescharacteristic
228C32×C4#11711yescharacteristic
229C32×C4#12311yescharacteristic
230C32×C4#12311yescharacteristic
231C3⋊Dic3—42no—
232C3⋊Dic3—81no—
233C3×Dic3—22no—
234C3×Dic3—42no—
235C3×Dic3—81no—
236C23×C4—31no—
237C22×C8—31no—
238C22×C8D3211yescharacteristic
239#117—94no—
240#117—182no—
241C2×C4⋊C4—31no—
242C2×C4⋊C4—31no—
243C2×C4⋊C4—91no—
244C2×C4⋊C4—91no—
245C2×C22⋊C4—181no—
246C2×C22⋊C4—181no—
247C2×C42—181no—
248C22⋊C8—62no—
249#95—181no—
250C23×C3—21no—
251C23×C3—32no—
252C23×C3—61no—
253C23×C3—61no—
254C23×C3—61no—
255C23×C3—61no—
256C23×C3—61no—
257C23×C3—61no—
258C23×C3C2×D1211yescharacteristic
259C23×C3D3×D411yescharacteristic
260C22×D3—21no—
261C22×D3—21no—
262C22×D3—21no—
263C22×D3—21no—
264C22×D3—21no—
265C22×D3—21no—
266C22×D3(C2×D3)⋊C412yes—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—32no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4—62no—
277C2×C3×C4—62no—
278C2×C3×C4—62no—
279C2×C3×C4—62no—
280C2×C3×C4—62no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4C2×C4×D311yescharacteristic
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4#23511yescharacteristic
289C2×C3×C4#23511yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4#23711yescharacteristic
292C2×C3×C4#23711yescharacteristic
293C2×C3×C4#23711yescharacteristic
294C2×C3×C4#23711yescharacteristic
295C2×C3×C4#23711yescharacteristic
296C2×C3×C4#23911yescharacteristic
297C2×C3×C4C2×#6711yescharacteristic
298C2×Dic3—21no—
299C2×Dic3—21no—
300C2×Dic3—22no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—122no—
309C2×Dic3—121no—
310C2×Dic3—121no—
311C2×Dic3—121no—
312C2×Dic3—121no—
313C2×Dic3—122no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—121no—
317C2×Dic3—121no—
318C2×Dic3—121no—
319C2×Dic3—121no—
320C2×Dic3—241no—
321C2×Dic3—241no—
322C2×Dic3—241no—
323C2×Dic3—241no—
324C2×Dic3(C2×D3)⋊C412yes—
325C4×D3—22no—
326C4×D3—22no—
327C4×D3—22no—
328C4×D3—22no—
329C3×C8—42no—
330C3×C8—41no—
331C3×C8—41no—
332C3×C8—121no—
333C3⋊C8—41no—
334C2×C32#38111yescharacteristic
335C2×C32#41611yescharacteristic
336C2×C32#41711yescharacteristic
337C2×C32#48211yescharacteristic
338C2×C32#48211yescharacteristic
339C2×C32#48511yescharacteristic
340C2×C32#48511yescharacteristic
341C3×D3—42no—
342C24—31no—
343C22×C4—31no—
344C22×C4—32no—
345C22×C4—32no—
346C22×C4—61no—
347C22×C4—61no—
348C22×C4—61no—
349C22×C4—61no—
350C22×C4—61no—
351C22×C4—61no—
352C22×C4—181no—
353C22×C4—181no—
354C22×C4C2×D3211yescharacteristic
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—61no—
359C2×C8—61no—
360C2×C8—61no—
361C4⋊C4—32no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—92no—
366C4⋊C4—181no—
367C4⋊C4—181no—
368C4⋊C4—181no—
369C22⋊C4—184no—
370C22⋊C4—362no—
371C42—184no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—62no—
380C22×C3—62no—
381C22×C3—62no—
382C22×C3—121no—
383C22×C3—121no—
384C22×C3—121no—
385C22×C3—121no—
386C22×C3D3×C22⋊C411yescharacteristic
387C22×C3#88311yescharacteristic
388C22×C3#88611yescharacteristic
389C22×C3#88611yescharacteristic
390C22×C3#89411yescharacteristic
391C22×C3#90411yescharacteristic
392C22×C3#90411yescharacteristic
393C22×C3#90811yescharacteristic
394C22×C3#90911yescharacteristic
395C22×C3#91211yescharacteristic
396C22×C3#91411yescharacteristic
397C22×C3#91611yescharacteristic
398C22×C3#91811yescharacteristic
399C22×C3C2×(C2×D3)⋊C411yescharacteristic
400C2×D3—22no—
401C2×D3—22no—
402C2×D3—22no—
403C2×D3—41no—
404C2×D3—41no—
405C2×D3—41no—
406C2×D3—41no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—62no—
412C3×C4—122no—
413C3×C4—241no—
414C3×C4#87211yescharacteristic
415C3×C4#87711yescharacteristic
416C3×C4#87711yescharacteristic
417C3×C4#88311yescharacteristic
418C3×C4#89211yescharacteristic
419C3×C4#89411yescharacteristic
420C3×C4#93511yescharacteristic
421C3×C4#93511yescharacteristic
422Dic3—22no—
423Dic3—42no—
424Dic3—81no—
425Dic3—122no—
426Dic3—122no—
427Dic3—242no—
428Dic3—242no—
429Dic3—241no—
430Dic3—241no—
431C32#182511yescharacteristic, complemented, Sylow
432C23—32no—
433C23—61no—
434C23—61no—
435C23—61no—
436C23—61no—
437C23—61no—
438C23—61no—
439C23D3×D1211yescharacteristic
440C2×C4—32no—
441C2×C4—61no—
442C2×C4—61no—
443C2×C4—62no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—121no—
449C2×C4—121no—
450C2×C4—121no—
451C2×C4—121no—
452C2×C4—121no—
453C2×C4—182no—
454C2×C4—361no—
455C2×C4—361no—
456C2×C4—361no—
457C2×C4—361no—
458C2×C4—361no—
459C2×C4#379511yescharacteristic
460C2×C4#379611yescharacteristic
461C2×C4C4×D3211yescharacteristic
462C2×C4#380411yescharacteristic
463C2×C4#380511yescharacteristic
464C2×C4D3×#6711yescharacteristic
465C8—41no—
466C8—121no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—122no—
475C2×C3#466411yescharacteristic
476C2×C3#472311yescharacteristic
477C2×C3#472311yescharacteristic
478C2×C3#473711yescharacteristic
479C2×C3#473711yescharacteristic
480C2×C3#477211yescharacteristic
481C2×C3#478411yescharacteristic
482C2×C3#480311yescharacteristic
483C2×C3#481511yescharacteristic
484C2×C3#486611yescharacteristic
485C2×C3#488811yescharacteristic
486C2×C3#494311yescharacteristic
487C2×C3#511311yescharacteristic
488C2×C3#513311yescharacteristic
489D3—42no—
490C22—62no—
491C22—62no—
492C22—62no—
493C22—121no—
494C22—121no—
495C22—121no—
496C22—121no—
497C22#6379411yescharacteristic
498C22#6380111yescharacteristic
499C22#6380611yescharacteristic
500C22#6380711yescharacteristic
501C22#6389011yescharacteristic
502C22#6389111yescharacteristic
503C22D3×(C2×D3)⋊C411yescharacteristic
504C4—62no—
505C4—122no—
506C4—241no—
507C4—362no—
508C4—721no—
509C4#6387711yescharacteristic
510C4#6387811yescharacteristic
511C4#6388411yescharacteristic
512C4#6396911yescharacteristic
513C3—21no—
514C3#6887311yescharacteristic, complemented
515C3#6992611yescharacteristic, complemented
516C2—122no—
517C2#1059067111yescharacteristic
518C2#1059070411yescharacteristic
519C2#1059070811yescharacteristic
520C2#1059071111yescharacteristic
521C2#1059083411yescharacteristic
522C2#1059095411yescharacteristic
523C2#1059136211yescharacteristic
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#1825
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
4. #10589417C2semidirect
5. C3×#4551C2semidirect
6. #10589164C2semidirect
7. #10589164C2semidirect
21. #63841C4semidirect
36. #4551D3semidirect
431. C32#1825semidirect
514. C3#68873semidirect
515. C3#69926semidirect

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
#105913132
#105894172
C3×#45512
#105891642
#699263
#688733