Finite Group Databasebeta

← #11794663

Subgroups — #11794663

Order 1152.

607 conjugacy classes of subgroups.

The subgroup lattice has 527 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#821C211yesmaximal, characteristic
2#10591359C211yesmaximal, characteristic, complemented
3#10591323C211yesmaximal, characteristic
4C2×#63562C211yesmaximal, characteristic
5#10589416C211yesmaximal, characteristic, complemented
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70165—31nomaximal
9#68902—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×#3724—21no—
18C2×#3724—21no—
19C2×(C2×D3)⋊Dic3—21no—
20C2×(C2×D3)⋊Dic3—21no—
21C3×#821—22no—
22#63562—22no—
23C2×C3×#102—31no—
24#5221—31no—
25C2×#832—31no—
26C2×#821D311yescharacteristic
27#4988—31no—
28#4975—31no—
29#4975—31no—
30C2×#809—31no—
31C3×#340—31no—
32#4551D311yescharacteristic, complemented
33#4550—31no—
34#4550—31no—
35#4550—61no—
36#4529—31no—
37#4529—31no—
38C23×C3×D3—21no—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3D411yescharacteristic
41C22×C3⋊Dic3D411yescharacteristic
42C22×C3×Dic3—21no—
43C22×C3×Dic3—21no—
44C22×C3×Dic3—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12D412yes—
51C2×C32×C8—21no—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C4×C3⋊Dic3—21no—
55C4×C3⋊Dic3—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65#3724—42no—
66#3724—42no—
67(C2×D3)⋊Dic3—42no—
68(C2×D3)⋊Dic3—42no—
69#2071—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⋊Dic3C2×D311yescharacteristic
83C2×C4⋊Dic3C2×D311yescharacteristic
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×Dic3⋊C4—61no—
86C2×Dic3⋊C4—61no—
87C2×Dic3⋊C4—61no—
88C2×Dic3⋊C4—61no—
89C2×C4×Dic3—31no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—61no—
92C22×C3⋊C8—31no—
93C22×C3⋊C8—31no—
94C22×C3⋊C8—61no—
95C3×#102—62no—
96#832—62no—
97#821—22no—
98#809—62no—
99C23×C32C2×D411yescharacteristic
100C22×C3×D3—22no—
101C22×C3×D3—41no—
102C22×C3×D3—41no—
103C22×C3×D3—41no—
104C22×C3×D3—41no—
105C22×C3×D3—41no—
106C22×C3×D3—41no—
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3D812yes—
118C2×C3⋊Dic3SD1612yes—
119C2×C3×Dic3—41no—
120C2×C3×Dic3—41no—
121C2×C3×Dic3—41no—
122C2×C3×Dic3—41no—
123C2×C3×Dic3—41no—
124C2×C3×Dic3—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C3×D12—22no—
129C3×D12—22no—
130C3×D12—41no—
131C3×D12—41no—
132C32×C8—41no—
133C3⋊(C3⋊C8)—41no—
134C2×#102—31no—
135C2×#102—91no—
136#390—91no—
137#384—91no—
138#340—31no—
139#340—91no—
140#336—91no—
141C24×C3—61no—
142C23×D3—21no—
143C2×C3×D4—32no—
144C2×C3×D4—61no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C22×C3×C4—21no—
150C22×C3×C4—61no—
151C22×C3×C4—61no—
152C22×C3×C4—61no—
153C22×C3×C4C22×D311yescharacteristic
154C22×C3×C4C22×D311yescharacteristic
155C22×Dic3—21no—
156C22×Dic3—21no—
157C22×Dic3—21no—
158C22×Dic3—31no—
159C22×Dic3—31no—
160C22×Dic3—31no—
161C22×Dic3—31no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C2×D12—21no—
165C2×D12—21no—
166C2×D12—21no—
167C2×D12—21no—
168C2×D12—21no—
169C2×D12#6712yes—
170C2×C3×C8—22no—
171C2×C3×C8—21no—
172C2×C3×C8—21no—
173C2×C3×C8—21no—
174C2×C3×C8—21no—
175C2×C3×C8—21no—
176C2×C3×C8—21no—
177C2×C3×C8—41no—
178C2×C3×C8—41no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185#217—122no—
186#217—122no—
187(C2×D3)⋊C4—122no—
188(C2×D3)⋊C4—122no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—21no—
192C4⋊Dic3—21no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195Dic3⋊C4—122no—
196Dic3⋊C4—122no—
197Dic3⋊C4—122no—
198Dic3⋊C4—122no—
199C4×Dic3—61no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C4×Dic3—121no—
204C4×Dic3—121no—
205C2×C3⋊C8—62no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—121no—
213C2×C3⋊C8—121no—
214C22×C32#12111yescharacteristic
215C22×C32#12311yescharacteristic
216C22×C32#12411yescharacteristic
217C22×C32C2×D811yescharacteristic
218C22×C32C2×SD1611yescharacteristic
219C22×C32AGL(1,ℤ/8)11yescharacteristic
220C22×C32#13711yescharacteristic
221C2×C3×D3—42no—
222C2×C3×D3—42no—
223C2×C3×D3—42no—
224C2×C3×D3—81no—
225C2×C3×D3—81no—
226C2×C3×D3—81no—
227C2×C3×D3—81no—
228C32×C4#12311yescharacteristic
229C32×C4#12311yescharacteristic
230C32×C4#12611yescharacteristic
231C32×C4#12611yescharacteristic
232C3⋊Dic3—22no—
233C3⋊Dic3—22no—
234C3×Dic3—81no—
235C3×Dic3—81no—
236C3×Dic3—81no—
237C22×D4—31no—
238C22×C8—91no—
239C22×C8D3211yescharacteristic
240C2×C4⋊C4—31no—
241C2×C4⋊C4—31no—
242C2×C4⋊C4—31no—
243C2×C4⋊C4—181no—
244C2×C4⋊C4—181no—
245C2×C22⋊C4—181no—
246C2×C22⋊C4—181no—
247C2×C42—91no—
248#102—62no—
249#102—182no—
250C23×C3—21no—
251C23×C3—62no—
252C23×C3—121no—
253C23×C3—121no—
254C23×C3—121no—
255C23×C3—121no—
256C23×C3—121no—
257C23×C3—121no—
258C23×C3D3×D411yescharacteristic
259C23×C3D3×D411yescharacteristic
260C22×D3—22no—
261C22×D3—41no—
262C22×D3—41no—
263C22×D3—41no—
264C22×D3—41no—
265C22×D3—41no—
266C22×D3—41no—
267C3×D4—62no—
268C3×D4—62no—
269C3×D4—121no—
270C3×D4—121no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—121no—
278C2×C3×C4—121no—
279C2×C3×C4—121no—
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#23511yescharacteristic
287C2×C3×C4#23511yescharacteristic
288C2×C3×C4#23511yescharacteristic
289C2×C3×C4#23511yescharacteristic
290C2×C3×C4#23511yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
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—32no—
299C2×Dic3—32no—
300C2×Dic3—32no—
301C2×Dic3—32no—
302C2×Dic3—41no—
303C2×Dic3—41no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—41no—
308C2×Dic3—41no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—62no—
312C2×Dic3—62no—
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—121no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—121no—
325D12—22no—
326D12—22no—
327D12—41no—
328D12—41no—
329C3×C8—42no—
330C3×C8—41no—
331C3×C8—41no—
332C3⋊C8—122no—
333C3⋊C8—121no—
334C3⋊C8—121no—
335C2×C32#39711yescharacteristic
336C2×C32#45911yescharacteristic
337C2×C32#46111yescharacteristic
338C2×C32#48011yescharacteristic
339C2×C32#48111yescharacteristic
340C2×C32#48611yescharacteristic
341C2×C32#48911yescharacteristic
342C3×D3—82no—
343C24—61no—
344C2×D4—32no—
345C2×D4—61no—
346C2×D4—61no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C22×C4—61no—
351C22×C4—61no—
352C22×C4—61no—
353C22×C4—91no—
354C22×C4—91no—
355C22×C4C2×D3211yescharacteristic
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—181no—
360C2×C8—181no—
361C2×C8—181no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—362no—
369C4⋊C4—362no—
370C22⋊C4—362no—
371C22⋊C4—362no—
372C42—181no—
373C42—181no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—122no—
382C22×C3—122no—
383C22×C3—122no—
384C22×C3—241no—
385C22×C3—241no—
386C22×C3—241no—
387C22×C3—241no—
388C22×C3#88311yescharacteristic
389C22×C3#88411yescharacteristic
390C22×C3#88511yescharacteristic
391C22×C3#88511yescharacteristic
392C22×C3#89411yescharacteristic
393C22×C3D3×D811yescharacteristic
394C22×C3D3×D811yescharacteristic
395C22×C3#91111yescharacteristic
396C22×C3D3×SD1611yescharacteristic
397C22×C3D3×SD1611yescharacteristic
398C22×C3#91411yescharacteristic
399C22×C3#91511yescharacteristic
400C22×C3#91811yescharacteristic
401C22×C3#93911yescharacteristic
402C2×D3—42no—
403C2×D3—42no—
404C2×D3—42no—
405C2×D3—81no—
406C2×D3—81no—
407C2×D3—81no—
408C2×D3—81no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—241no—
414C3×C4—241no—
415C3×C4—241no—
416C3×C4#87611yescharacteristic
417C3×C4#87911yescharacteristic
418C3×C4#87911yescharacteristic
419C3×C4#88311yescharacteristic
420C3×C4#89411yescharacteristic
421C3×C4#89811yescharacteristic
422C3×C4#92911yescharacteristic
423C3×C4#93511yescharacteristic
424Dic3—62no—
425Dic3—62no—
426Dic3—62no—
427Dic3—62no—
428Dic3—81no—
429Dic3—81no—
430Dic3—81no—
431Dic3—122no—
432Dic3—122no—
433C32#207111yescharacteristic, complemented, Sylow
434C23—62no—
435C23—121no—
436C23—121no—
437C23—121no—
438C23—121no—
439C23—121no—
440C23—121no—
441C23#380211yescharacteristic
442D4—62no—
443D4—62no—
444D4—121no—
445D4—121no—
446C2×C4—92no—
447C2×C4—92no—
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—121no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4—181no—
460C2×C4—181no—
461C2×C4#379511yescharacteristic
462C2×C4#379811yescharacteristic
463C2×C4#379911yescharacteristic
464C2×C4#380411yescharacteristic
465C2×C4#380511yescharacteristic
466C2×C4D3×#6711yescharacteristic
467C8—41no—
468C8—361no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—21no—
473C2×C3—21no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—242no—
477C2×C3#467511yescharacteristic
478C2×C3#476011yescharacteristic
479C2×C3#476011yescharacteristic
480C2×C3#476511yescharacteristic
481C2×C3#477411yescharacteristic
482C2×C3#477711yescharacteristic
483C2×C3#478611yescharacteristic
484C2×C3#479411yescharacteristic
485C2×C3#481811yescharacteristic
486C2×C3#486311yescharacteristic
487C2×C3#488211yescharacteristic
488C2×C3#495211yescharacteristic
489C2×C3#515011yescharacteristic
490C2×C3#516211yescharacteristic
491D3—82no—
492C22—122no—
493C22—122no—
494C22—122no—
495C22—241no—
496C22—241no—
497C22—241no—
498C22—241no—
499C22#6379611yescharacteristic
500C22#6379711yescharacteristic
501C22#6379811yescharacteristic
502C22#6381111yescharacteristic
503C22#6385411yescharacteristic
504C22#6388511yescharacteristic
505C22#6391511yescharacteristic
506C4—182no—
507C4—182no—
508C4—241no—
509C4—241no—
510C4—241no—
511C4#6385011yescharacteristic
512C4#6385911yescharacteristic
513C4#6386111yescharacteristic
514C4#6396911yescharacteristic
515C3—21no—
516C3#6890211yescharacteristic, complemented
517C3#7016511yescharacteristic, complemented
518C2—242no—
519C2#1059064911yescharacteristic
520C2#1059065011yescharacteristic
521C2#1059074811yescharacteristic
522C2#1059074911yescharacteristic
523C2#1059086611yescharacteristic
524C2#1059088511yescharacteristic
525C2#1059129911yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32#2071
LCSG ▷ C22×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
2. #10591359C2semidirect
5. #10589416C2semidirect
6. C3×#4551C2semidirect
7. #10589163C2semidirect
32. #4551D3semidirect
433. C32#2071semidirect
516. C3#68902semidirect
517. C3#70165semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8212
#105913592
#105913232
C2×#635622
#105894162
C3×#45512
#105891632
#701653
#689023