Finite Group Databasebeta

← #11789906

Subgroups — #11789906

Order 1152.

641 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63642C211yesmaximal, characteristic, complemented
2C2×C3×#821C211yesmaximal, characteristic
3#10591357C211yesmaximal, characteristic, complemented
4#10591323C211yesmaximal, characteristic
5C2×#63562C211yesmaximal, characteristic
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70187—31nomaximal
9#68856—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×Dic3⋊Dic3—21no—
18C2×(C2×D3)⋊Dic3—21no—
19C2×(C2×D3)⋊Dic3—21no—
20#63642—22no—
21C3×#821C414yescomplemented
22#63579—21no—
23#63562—22no—
24C2×C3×#102—31no—
25#5221—31no—
26C2×#832—31no—
27C2×#821D311yescharacteristic
28C2×#815—31no—
29C2×#815—31no—
30C2×#815—61no—
31#4988—31no—
32#4984—31no—
33#4972—31no—
34C2×#809—31no—
35C3×#340—31no—
36#4551D311yescharacteristic, complemented
37#4529—31no—
38#4529—31no—
39C23×C3×D3—21no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3D411yescharacteristic
42C22×C3⋊Dic3D411yescharacteristic
43C22×C3×Dic3—21no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C2×C32×C8C2×C412yes—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)D412yes—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3C2×C412yes—
66Dic3⋊Dic3—42no—
67(C2×D3)⋊Dic3—42no—
68(C2×D3)⋊Dic3—42no—
69#1936—91noSylow
70C22×C3×D4—31no—
71C22×D12C2×D311yescharacteristic
72C22×C3×C8—21no—
73C22×C3×C8C2×D311yescharacteristic
74C22×C3×C8C2×D311yescharacteristic
75C2×C3×C4⋊C4—31no—
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—
82C2×C4⋊Dic3—61no—
83C2×C4⋊Dic3C2×D311yescharacteristic
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×C4⋊Dic3C2×D311yescharacteristic
86C2×Dic3⋊C4—61no—
87C2×C4×Dic3—31no—
88C2×C4×Dic3—31no—
89C2×C4×Dic3—61no—
90C22×C3⋊C8—31no—
91C22×C3⋊C8—31no—
92C22×C3⋊C8—61no—
93C3×#102—34no—
94#832—62no—
95C3⋊#95—61no—
96C3⋊#95—61no—
97#821Dic314yescomplemented
98#815—62no—
99#815—62no—
100#815—64no—
101#809—62no—
102C23×C32C2×D411yescharacteristic
103C22×C3×D3—22no—
104C22×C3×D3—41no—
105C22×C3×D3—41no—
106C22×C3×D3—41no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C22×C3×D3—41no—
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3×Dic3—22no—
123C2×C3×Dic3—41no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C3×D12—22no—
132C3×D12—22no—
133C3×D12—41no—
134C3×D12—41no—
135C32×C8—22no—
136C3⋊(C3⋊C8)—22no—
137C2×#102—31no—
138C2×#102—91no—
139C2×#97—91no—
140#390—91no—
141#389—91no—
142#340—31no—
143#340—91no—
144C24×C3—61no—
145C23×D3—21no—
146C2×C3×D4—32no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C2×C3×D4—61no—
152C22×C3×C4—21no—
153C22×C3×C4—61no—
154C22×C3×C4—61no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×Dic3—21no—
159C22×Dic3—21no—
160C22×Dic3—21no—
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—31no—
164C22×Dic3—31no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C2×D12—21no—
168C2×D12—21no—
169C2×D12—21no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12C2×Dic312yes—
173C2×C3×C8—22no—
174C2×C3×C8—22no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—22no—
180C2×C3×C8C4×D312yes—
181C2×C3×C8C2×Dic312yes—
182C3×C4⋊C4—32no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188#217—122no—
189#217—122no—
190(C2×D3)⋊C4—122no—
191(C2×D3)⋊C4—122no—
192C4⋊Dic3—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—122no—
198C4⋊Dic3C2×Dic312yes—
199Dic3⋊C4—122no—
200C4×Dic3—62no—
201C4×Dic3—62no—
202C4×Dic3—61no—
203C4×Dic3—61no—
204C4×Dic3—61no—
205C4×Dic3—61no—
206C2×C3⋊C8—32no—
207C2×C3⋊C8—32no—
208C2×C3⋊C8—62no—
209C2×C3⋊C8—62no—
210C2×C3⋊C8—62no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C22×C32C4×D411yescharacteristic
216C22×C32#12111yescharacteristic
217C22×C32#12411yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C22×C32AGL(1,ℤ/8)11yescharacteristic
220C22×C32AGL(1,ℤ/8)11yescharacteristic
221C22×C32#13711yescharacteristic
222C2×C3×D3—42no—
223C2×C3×D3—42no—
224C2×C3×D3—42no—
225C2×C3×D3—81no—
226C2×C3×D3—81no—
227C2×C3×D3—81no—
228C2×C3×D3—81no—
229C32×C4#11711yescharacteristic
230C32×C4C4×D411yescharacteristic
231C32×C4#12311yescharacteristic
232C32×C4#12611yescharacteristic
233C3⋊Dic3—41no—
234C3⋊Dic3—41no—
235C3×Dic3—42no—
236C3×Dic3—81no—
237C3×Dic3—81no—
238C22×D4—31no—
239C22×C8—91no—
240C22×C8D3211yescharacteristic
241C2×C4⋊C4—31no—
242C2×C4⋊C4—31no—
243C2×C4⋊C4—31no—
244C2×C4⋊C4—181no—
245C2×C22⋊C4—181no—
246C2×C22⋊C4—181no—
247C2×C42—91no—
248#102—34no—
249#102—182no—
250#97—182no—
251#95—181no—
252C23×C3—21no—
253C23×C3—62no—
254C23×C3—121no—
255C23×C3—121no—
256C23×C3—121no—
257C23×C3—121no—
258C23×C3—121no—
259C23×C3—121no—
260C23×C3D3×D411yescharacteristic
261C23×C3D3×D411yescharacteristic
262C22×D3—22no—
263C22×D3—41no—
264C22×D3—41no—
265C22×D3—41no—
266C22×D3—41no—
267C22×D3—41no—
268C22×D3—41no—
269C3×D4—62no—
270C3×D4—62no—
271C3×D4—121no—
272C3×D4—121no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—62no—
280C2×C3×C4—121no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4#23511yescharacteristic
290C2×C3×C4#23511yescharacteristic
291C2×C3×C4#23511yescharacteristic
292C2×C3×C4#23511yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4#23711yescharacteristic
296C2×C3×C4#23711yescharacteristic
297C2×C3×C4#23711yescharacteristic
298C2×C3×C4#23911yescharacteristic
299C2×C3×C4C22×Dic311yescharacteristic
300C2×Dic3—22no—
301C2×Dic3—41no—
302C2×Dic3—41no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327D12—22no—
328D12—22no—
329D12—41no—
330D12—41no—
331C3×C8—24no—
332C3×C8—22no—
333C3×C8—22no—
334C3⋊C8—64no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C2×C32#38811yescharacteristic
338C2×C32#44011yescharacteristic
339C2×C32#44211yescharacteristic
340C2×C32#46811yescharacteristic
341C2×C32#46911yescharacteristic
342C2×C32#48911yescharacteristic
343C2×C32#49011yescharacteristic
344C3×D3—82no—
345C24—61no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C22×C4—61no—
353C22×C4—61no—
354C22×C4—61no—
355C22×C4—91no—
356C22×C4—91no—
357C22×C4C2×D3211yescharacteristic
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—92no—
361C2×C8—181no—
362C2×C8—181no—
363C2×C8D3×Dic312yes—
364C4⋊C4—32no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—61no—
370C4⋊C4—362no—
371C22⋊C4—362no—
372C22⋊C4—362no—
373C42—181no—
374C42—181no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—122no—
383C22×C3—122no—
384C22×C3—122no—
385C22×C3—241no—
386C22×C3—241no—
387C22×C3—241no—
388C22×C3—241no—
389C22×C3#88411yescharacteristic
390C22×C3#88411yescharacteristic
391C22×C3#88511yescharacteristic
392C22×C3#88511yescharacteristic
393C22×C3#89311yescharacteristic
394C22×C3#91111yescharacteristic
395C22×C3#91111yescharacteristic
396C22×C3#91111yescharacteristic
397C22×C3#91411yescharacteristic
398C22×C3#91411yescharacteristic
399C22×C3#91411yescharacteristic
400C22×C3#91511yescharacteristic
401C22×C3#91811yescharacteristic
402C22×C3D4×Dic311yescharacteristic
403C2×D3—42no—
404C2×D3—42no—
405C2×D3—42no—
406C2×D3—81no—
407C2×D3—81no—
408C2×D3—81no—
409C2×D3—81no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—122no—
415C3×C4—241no—
416C3×C4—241no—
417C3×C4#87211yescharacteristic
418C3×C4#87911yescharacteristic
419C3×C4#67⋊C411yescharacteristic
420C3×C4#88311yescharacteristic
421C3×C4#89411yescharacteristic
422C3×C4#89811yescharacteristic
423C3×C4#92611yescharacteristic
424C3×C4D4×Dic311yescharacteristic
425Dic3—42no—
426Dic3—81no—
427Dic3—81no—
428Dic3—122no—
429Dic3—122no—
430Dic3—121no—
431Dic3—121no—
432Dic3—121no—
433Dic3—121no—
434C32#193611yescharacteristic, complemented, Sylow
435C23—62no—
436C23—121no—
437C23—121no—
438C23—121no—
439C23—121no—
440C23—121no—
441C23—121no—
442C23#380211yescharacteristic
443D4—62no—
444D4—62no—
445D4—121no—
446D4—121no—
447C2×C4—62no—
448C2×C4—121no—
449C2×C4—121no—
450C2×C4—121no—
451C2×C4—121no—
452C2×C4—121no—
453C2×C4—121no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4—181no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4—181no—
462C2×C4#379611yescharacteristic
463C2×C4#379811yescharacteristic
464C2×C4#379811yescharacteristic
465C2×C4C2×D3×Dic311yescharacteristic
466C2×C4#380511yescharacteristic
467C2×C4#381111yescharacteristic
468C8—22no—
469C8—182no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—242no—
478C2×C3#466911yescharacteristic
479C2×C3#476411yescharacteristic
480C2×C3#476411yescharacteristic
481C2×C3#476511yescharacteristic
482C2×C3#478011yescharacteristic
483C2×C3#478211yescharacteristic
484C2×C3#478211yescharacteristic
485C2×C3#479411yescharacteristic
486C2×C3#481211yescharacteristic
487C2×C3#486911yescharacteristic
488C2×C3#488911yescharacteristic
489C2×C3#495111yescharacteristic
490C2×C3#515211yescharacteristic
491C2×C3#516411yescharacteristic
492D3—82no—
493C22—122no—
494C22—122no—
495C22—122no—
496C22—241no—
497C22—241no—
498C22—241no—
499C22—241no—
500C22#6379811yescharacteristic
501C22#6379811yescharacteristic
502C22#6379811yescharacteristic
503C22#6381111yescharacteristic
504C22#6389811yescharacteristic
505C22#6391211yescharacteristic
506C22#6391511yescharacteristic
507C4—122no—
508C4—241no—
509C4—241no—
510C4—361no—
511C4—361no—
512C4#6385311yescharacteristic
513C4#6385511yescharacteristic
514C4#6386211yescharacteristic
515C4#67⋊Dic311yescharacteristic
516C3—21no—
517C3#6885611yescharacteristic, complemented
518C3#7018711yescharacteristic, complemented
519C2—242no—
520C2#1059077911yescharacteristic
521C2#1059078111yescharacteristic
522C2#1059084011yescharacteristic
523C2#1059084211yescharacteristic
524C2#1059086611yescharacteristic
525C2#1059088811yescharacteristic
526C2#1059128611yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1936
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
1. C2×#63642C2semidirect
3. #10591357C2semidirect
6. C3×#4551C2semidirect
7. #10589163C2semidirect
21. C3×#821C4semidirect
36. #4551D3semidirect
97. #821Dic3semidirect
434. C32#1936semidirect
517. C3#68856semidirect
518. C3#70187semidirect

Maximal subgroups

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

subgroupindex
C2×#636422
C2×C3×#8212
#105913572
#105913232
C2×#635622
C3×#45512
#105891632
#701873
#688563