Finite Group Databasebeta

← #11794658

Subgroups — #11794658

Order 1152.

641 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592674C211yesmaximal, characteristic, complemented
2C2×C3×#809C211yesmaximal, characteristic
3#10591323C211yesmaximal, characteristic
4C2×#63563C211yesmaximal, characteristic
5C3×#4529C211yesmaximal, characteristic, complemented
6#10589164C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#70165—31nomaximal
9#68902—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3750—21no—
14C2×#3750—21no—
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×(C2×D3)⋊Dic3—21no—
20C2×(C2×D3)⋊Dic3—21no—
21C3×#809—22no—
22#63563—22no—
23C2×C3×#102—31no—
24#5221—31no—
25C2×#832—31no—
26C2×#821—31no—
27#4988—31no—
28#4975—31no—
29#4975—31no—
30#4975—61no—
31C2×#809D311yescharacteristic
32C3×#340—31no—
33#4551—31no—
34#4550—31no—
35#4550—31no—
36#4529—31no—
37#4529D311yescharacteristic, complemented
38C23×C3×D3—21no—
39C22×C32×C4—21no—
40C22×C32×C4C2311yescharacteristic
41C22×C3⋊Dic3—21no—
42C22×C3⋊Dic3D411yescharacteristic
43C22×C3⋊Dic3D411yescharacteristic
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—
51C32×C4⋊C4—21no—
52C32×C4⋊C4—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55#3750—42no—
56#3750—42no—
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67(C2×D3)⋊Dic3—42no—
68(C2×D3)⋊Dic3—42no—
69#2071—91noSylow
70C22×C3×D4—31no—
71C22×D12C2×D311yescharacteristic
72C22×C3×C8—31no—
73C22×C3×C8—31no—
74C2×C3×C4⋊C4—21no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C4⋊C4C2×D311yescharacteristic
77C2×C3×C4⋊C4C2×D311yescharacteristic
78C2×#217—61no—
79C2×#217—61no—
80C2×(C2×D3)⋊C4—61no—
81C2×(C2×D3)⋊C4—61no—
82C2×C4⋊Dic3—31no—
83C2×C4⋊Dic3—31no—
84C2×C4⋊Dic3—61no—
85C2×C4⋊Dic3C2×D311yescharacteristic
86C2×Dic3⋊C4—61no—
87C2×Dic3⋊C4—61no—
88C2×Dic3⋊C4—61no—
89C2×Dic3⋊C4—61no—
90C2×Dic3⋊C4—62no—
91C2×Dic3⋊C4—62no—
92C2×C4×Dic3—31no—
93C2×C4×Dic3—31no—
94C2×C4×Dic3—61no—
95C22×C3⋊C8C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97C3×#102—62no—
98#832—62no—
99#821—62no—
100#809—22no—
101C23×C32C2×D411yescharacteristic
102C22×C3×D3—22no—
103C22×C3×D3—41no—
104C22×C3×D3—41no—
105C22×C3×D3—41no—
106C22×C3×D3—41no—
107C22×C3×D3—41no—
108C22×C3×D3—41no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4#4111yescharacteristic
114C2×C32×C4#4111yescharacteristic
115C2×C32×C4#4111yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3D812yes—
126C2×C3⋊Dic3SD1612yes—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—41no—
130C3×D12—22no—
131C3×D12—22no—
132C3×D12—41no—
133C3×D12—41no—
134C3×C3⋊C8—41no—
135C3×C3⋊C8—41no—
136C2×#102—31no—
137C2×#102—91no—
138#390—91no—
139#384—91no—
140#340—31no—
141#340—91no—
142#336—91no—
143C24×C3—61no—
144C23×D3—21no—
145C2×C3×D4—32no—
146C2×C3×D4—61no—
147C2×C3×D4—61no—
148C2×C3×D4—61no—
149C2×C3×D4—61no—
150C2×C3×D4—61no—
151C22×C3×C4—22no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—21no—
155C22×C3×C4—61no—
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C22×Dic3—21no—
159C22×Dic3—31no—
160C22×Dic3—31no—
161C22×Dic3—31no—
162C22×Dic3—31no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—62no—
166C22×Dic3—61no—
167C22×Dic3—61no—
168C2×D12—21no—
169C2×D12—21no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12#6712yes—
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C2×C3×C8—61no—
177C2×C3×C8—61no—
178C2×C3×C8—61no—
179C2×C3×C8—61no—
180C3×C4⋊C4—21no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—41no—
185C3×C4⋊C4—41no—
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—61no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4⋊Dic3—61no—
198C4⋊Dic3—121no—
199C4⋊Dic3—121no—
200Dic3⋊C4—122no—
201Dic3⋊C4—122no—
202Dic3⋊C4—124no—
203Dic3⋊C4—124no—
204Dic3⋊C4—122no—
205Dic3⋊C4—122no—
206C4×Dic3—62no—
207C4×Dic3—62no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—21no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—21no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C22×C32#12111yescharacteristic
219C22×C32#12311yescharacteristic
220C22×C32#12411yescharacteristic
221C22×C32C2×D811yescharacteristic
222C22×C32C2×SD1611yescharacteristic
223C22×C32AGL(1,ℤ/8)11yescharacteristic
224C22×C32#13711yescharacteristic
225C2×C3×D3—42no—
226C2×C3×D3—42no—
227C2×C3×D3—42no—
228C2×C3×D3—81no—
229C2×C3×D3—81no—
230C2×C3×D3—81no—
231C2×C3×D3—81no—
232C32×C4—81no—
233C32×C4#12311yescharacteristic
234C32×C4#12311yescharacteristic
235C32×C4#12611yescharacteristic
236C32×C4#12611yescharacteristic
237C3⋊Dic3—22no—
238C3⋊Dic3—22no—
239C3⋊Dic3—81no—
240C3×Dic3—81no—
241C22×D4—31no—
242C22×C8—31no—
243C22×C8—31no—
244C2×C4⋊C4—31no—
245C2×C4⋊C4—91no—
246C2×C4⋊C4—181no—
247C2×C4⋊C4—181no—
248C2×C4⋊C4D3211yescharacteristic
249C2×C22⋊C4—181no—
250C2×C22⋊C4—181no—
251C2×C42—91no—
252#102—62no—
253#102—182no—
254C23×C3—21no—
255C23×C3—62no—
256C23×C3—121no—
257C23×C3—121no—
258C23×C3—121no—
259C23×C3—121no—
260C23×C3—121no—
261C23×C3—121no—
262C23×C3D3×D411yescharacteristic
263C23×C3D3×D411yescharacteristic
264C22×D3—22no—
265C22×D3—41no—
266C22×D3—41no—
267C22×D3—41no—
268C22×D3—41no—
269C22×D3—41no—
270C22×D3—41no—
271C3×D4—62no—
272C3×D4—62no—
273C3×D4—121no—
274C3×D4—121no—
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—42no—
282C2×C3×C4—42no—
283C2×C3×C4—42no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—121no—
291C2×C3×C4—121no—
292C2×C3×C4—121no—
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4#23511yescharacteristic
295C2×C3×C4#23511yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4#23511yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23711yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4#23711yescharacteristic
302C2×C3×C4#23711yescharacteristic
303C2×C3×C4#23911yescharacteristic
304C2×C3×C4C2×#6711yescharacteristic
305C2×Dic3—32no—
306C2×Dic3—32no—
307C2×Dic3—32no—
308C2×Dic3—32no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—62no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—61no—
319C2×Dic3—61no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—61no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—61no—
326C2×Dic3—122no—
327C2×Dic3—122no—
328C2×Dic3—122no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335D12—22no—
336D12—22no—
337D12—41no—
338D12—41no—
339C3×C8—121no—
340C3×C8—121no—
341C3⋊C8—41no—
342C3⋊C8—41no—
343C2×C32#39711yescharacteristic
344C2×C32#45911yescharacteristic
345C2×C32#46111yescharacteristic
346C2×C32#48011yescharacteristic
347C2×C32#48111yescharacteristic
348C2×C32#48611yescharacteristic
349C2×C32#48911yescharacteristic
350C3×D3—82no—
351C24—61no—
352C2×D4—32no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4—61no—
356C2×D4—61no—
357C2×D4—61no—
358C22×C4—21no—
359C22×C4—61no—
360C22×C4—91no—
361C22×C4—91no—
362C22×C4—181no—
363C22×C4C2×D3211yescharacteristic
364C2×C8—61no—
365C2×C8—61no—
366C2×C8—61no—
367C2×C8—61no—
368C2×C8—61no—
369C2×C8—61no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—181no—
375C4⋊C4—181no—
376C4⋊C4—362no—
377C4⋊C4—362no—
378C22⋊C4—362no—
379C22⋊C4—362no—
380C42—181no—
381C42—181no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—122no—
390C22×C3—122no—
391C22×C3—122no—
392C22×C3—241no—
393C22×C3—241no—
394C22×C3—241no—
395C22×C3—241no—
396C22×C3#88311yescharacteristic
397C22×C3#88411yescharacteristic
398C22×C3#88511yescharacteristic
399C22×C3#88511yescharacteristic
400C22×C3#89411yescharacteristic
401C22×C3D3×D811yescharacteristic
402C22×C3D3×D811yescharacteristic
403C22×C3#91111yescharacteristic
404C22×C3D3×SD1611yescharacteristic
405C22×C3D3×SD1611yescharacteristic
406C22×C3#91411yescharacteristic
407C22×C3#91511yescharacteristic
408C22×C3#91811yescharacteristic
409C22×C3#93911yescharacteristic
410C2×D3—42no—
411C2×D3—42no—
412C2×D3—42no—
413C2×D3—81no—
414C2×D3—81no—
415C2×D3—81no—
416C2×D3—81no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—82no—
422C3×C4—81no—
423C3×C4—81no—
424C3×C4—241no—
425C3×C4#87611yescharacteristic
426C3×C4#87911yescharacteristic
427C3×C4#87911yescharacteristic
428C3×C4#88311yescharacteristic
429C3×C4#89411yescharacteristic
430C3×C4#89811yescharacteristic
431C3×C4#92911yescharacteristic
432C3×C4#93511yescharacteristic
433Dic3—64no—
434Dic3—64no—
435Dic3—62no—
436Dic3—62no—
437Dic3—62no—
438Dic3—62no—
439Dic3—81no—
440Dic3—242no—
441Dic3—241no—
442Dic3—241no—
443C32#207111yescharacteristic, complemented, Sylow
444C23—62no—
445C23—121no—
446C23—121no—
447C23—121no—
448C23—121no—
449C23—121no—
450C23—121no—
451C23#381111yescharacteristic
452D4—62no—
453D4—62no—
454D4—121no—
455D4—121no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—92no—
460C2×C4—92no—
461C2×C4—121no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—181no—
465C2×C4—181no—
466C2×C4—181no—
467C2×C4—181no—
468C2×C4—361no—
469C2×C4—361no—
470C2×C4—361no—
471C2×C4#379511yescharacteristic
472C2×C4#379511yescharacteristic
473C2×C4#379611yescharacteristic
474C2×C4#379811yescharacteristic
475C2×C4#380411yescharacteristic
476C2×C4D3×#6711yescharacteristic
477C8—121no—
478C8—121no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—242no—
487C2×C3#467511yescharacteristic
488C2×C3#476011yescharacteristic
489C2×C3#476011yescharacteristic
490C2×C3#476511yescharacteristic
491C2×C3#477411yescharacteristic
492C2×C3#477711yescharacteristic
493C2×C3#478611yescharacteristic
494C2×C3#479411yescharacteristic
495C2×C3#481811yescharacteristic
496C2×C3#486311yescharacteristic
497C2×C3#488211yescharacteristic
498C2×C3#495211yescharacteristic
499C2×C3#515011yescharacteristic
500C2×C3#516211yescharacteristic
501D3—82no—
502C22—122no—
503C22—122no—
504C22—122no—
505C22—241no—
506C22—241no—
507C22—241no—
508C22—241no—
509C22#6385311yescharacteristic
510C22#6391311yescharacteristic
511C22#6392611yescharacteristic
512C22#6393711yescharacteristic
513C22#6394011yescharacteristic
514C22#6395111yescharacteristic
515C22#6397111yescharacteristic
516C4—81no—
517C4—182no—
518C4—182no—
519C4—241no—
520C4—721no—
521C4#6385811yescharacteristic
522C4#6385911yescharacteristic
523C4#6388411yescharacteristic
524C4#6390511yescharacteristic
525C3—21no—
526C3#6890211yescharacteristic, complemented
527C3#7016511yescharacteristic, complemented
528C2—242no—
529C2#1059051011yescharacteristic
530C2#1059051111yescharacteristic
531C2#1059054111yescharacteristic
532C2#1059055211yescharacteristic
533C2#1059129811yescharacteristic
534C2#1059143311yescharacteristic
535C2#1059156911yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2071
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #10592674C2semidirect
5. C3×#4529C2semidirect
6. #10589164C2semidirect
7. #10589156C2semidirect
37. #4529D3semidirect
443. C32#2071semidirect
526. C3#68902semidirect
527. C3#70165semidirect

Maximal subgroups

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

subgroupindex
#105926742
C2×C3×#8092
#105913232
C2×#635632
C3×#45292
#105891642
#105891562
#701653
#689023