Finite Group Databasebeta

← #11786513

Subgroups — #11786513

Order 1152.

733 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63849C211yesmaximal, characteristic
2C2×#63647C211yesmaximal, characteristic
3C2×C3×#818C211yesmaximal, characteristic, complemented
4#10591325C211yesmaximal, characteristic
5C2×#63574C211yesmaximal, characteristic, complemented
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70633—31nomaximal
9#68877—31nomaximal
10C22×C4×C3⋊D3C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×#3722—21no—
18C2×#3722—21no—
19C2×Dic32—21no—
20#63849—22no—
21#63849—22no—
22#63647C414yescomplemented
23C3×#818—22no—
24#63579—21no—
25#63574—22no—
26C2×#892—31no—
27C2×#892—31no—
28C2×C3×#107—31no—
29C2×(C2×D3)⋊C8—31no—
30C2×(C2×D3)⋊C8—31no—
31C2×(C2×D3)⋊C8—61no—
32C2×#818D311yescharacteristic, complemented
33#4987—31no—
34#4987—31no—
35C2×#808—31no—
36C2×#808—31no—
37C3×#340—31no—
38#4551D311yescharacteristic, complemented
39#4529—31no—
40#4529—31no—
41C23×C3⋊D3D411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—21no—
46C2×C4×C3⋊D3—21no—
47C2×C4×C3⋊D3—21no—
48C2×C4×C3⋊D3C2×C412yes—
49C2×C4×C3⋊D3Q812yes—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C22×C3×Dic3—21no—
53C22×C3×Dic3—21no—
54C2×C32×C8—21no—
55C2×C32×C8—21no—
56C2×C32×C8C2×C412yes—
57C2×C3⋊(C3⋊C8)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)C2×C412yes—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3D412yes—
67C3×C4⋊Dic3D412yes—
68#3722—24no—
69#3722—42no—
70Dic32—24no—
71#1854—91noSylow
72C22×C4×D3—31no—
73C22×C4×D3—31no—
74C22×C4×D3—61no—
75C22×C3×C8—21no—
76C22×C3×C8C2×D311yescharacteristic
77C22×C3×C8C2×D311yescharacteristic
78C2×C3×C4⋊C4—31no—
79C2×C3×C4⋊C4—31no—
80C2×C3×C4⋊C4—31no—
81C2×C3×C4⋊C4—31no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×(C2×D3)⋊C4—61no—
85C2×(C2×D3)⋊C4—61no—
86C2×C4⋊Dic3C2×D311yescharacteristic
87C2×C4⋊Dic3C2×D311yescharacteristic
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4×Dic3—61no—
91C2×C4×Dic3—61no—
92C22×C3⋊C8—31no—
93C22×C3⋊C8—31no—
94C22×C3⋊C8—61no—
95#892—62no—
96#892—62no—
97#892—62no—
98#892—62no—
99C3×#107—62no—
100C3⋊#95—61no—
101C3⋊#95—61no—
102(C2×D3)⋊C8—34no—
103(C2×D3)⋊C8—34no—
104(C2×D3)⋊C8—64no—
105#818—22no—
106#808—62no—
107#808—62no—
108C23×C32C2×D411yescharacteristic
109C22×C3⋊D3—21no—
110C22×C3⋊D3—21no—
111C22×C3⋊D3—21no—
112C22×C3⋊D3—21no—
113C22×C3⋊D3—21no—
114C22×C3⋊D3—21no—
115C22×C3⋊D3C4⋊C412yes—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×Q811yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3C4⋊C412yes—
125C4×C3⋊D3—22no—
126C4×C3⋊D3—22no—
127C4×C3⋊D3—22no—
128C4×C3⋊D3—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3—41no—
141C32×C8—22no—
142C3⋊(C3⋊C8)—22no—
143C2×#117—91no—
144C2×#107—31no—
145C2×#106—91no—
146C2×C22⋊C8—91no—
147#380—91no—
148#340—31no—
149#340—91no—
150C23×D3—31no—
151C23×D3—31no—
152C23×D3—61no—
153C22×C3×C4—21no—
154C22×C3×C4—61no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C22×Dic3—21no—
161C22×Dic3—21no—
162C22×Dic3—21no—
163C22×Dic3—21no—
164C22×Dic3—31no—
165C22×Dic3—31no—
166C22×Dic3—61no—
167C2×C4×D3—32no—
168C2×C4×D3—32no—
169C2×C4×D3—32no—
170C2×C4×D3—32no—
171C2×C4×D3—62no—
172C2×C4×D3—62no—
173C2×C4×D3—61no—
174C2×C4×D3—61no—
175C2×C4×D3—61no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×C4×D3—61no—
179C2×C4×D3—61no—
180C2×C4×D3—61no—
181C2×C4×D3—121no—
182C2×C4×D3—121no—
183C2×C4×D3—121no—
184C2×C4×D3—121no—
185C2×C3×C8—21no—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—22no—
190C2×C3×C8—41no—
191C2×C3×C8—41no—
192C2×C3×C8C4×D312yes—
193C2×C3×C8C4×D312yes—
194C3×C4⋊C4—32no—
195C3×C4⋊C4—32no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202(C2×D3)⋊C4—64no—
203(C2×D3)⋊C4—64no—
204(C2×D3)⋊C4—122no—
205(C2×D3)⋊C4—122no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211C4⋊Dic3—21no—
212C4⋊Dic3D1212yes—
213C4⋊Dic3#6712yes—
214C4×Dic3—64no—
215C4×Dic3—64no—
216C2×C3⋊C8—32no—
217C2×C3⋊C8—32no—
218C2×C3⋊C8—62no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—121no—
224C2×C3⋊C8—121no—
225C22×C32C2×C4⋊C411yescharacteristic
226C22×C32#12011yescharacteristic
227C22×C32#12311yescharacteristic
228C22×C32#13511yescharacteristic
229C22×C32#13511yescharacteristic
230C22×C32AGL(1,ℤ/8)11yescharacteristic
231C22×C32#13711yescharacteristic
232C2×C3⋊D3—22no—
233C2×C3⋊D3—22no—
234C2×C3⋊D3—22no—
235C2×C3⋊D3—41no—
236C2×C3⋊D3—41no—
237C2×C3⋊D3—41no—
238C2×C3⋊D3—41no—
239C32×C4C4×D411yescharacteristic
240C32×C4C4×D411yescharacteristic
241C32×C4C22⋊Q811yescharacteristic
242C32×C4C22⋊Q811yescharacteristic
243C3⋊Dic3—22no—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C3×Dic3—81no—
247C3×Dic3—81no—
248C23×C4—91no—
249C22×C8—91no—
250C22×C8D3211yescharacteristic
251#117—182no—
252#117—182no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—31no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—31no—
257C2×C22⋊C4—181no—
258C2×C22⋊C4—181no—
259C2×C42—181no—
260#107—62no—
261#106—182no—
262C22⋊C8—94no—
263#95—181no—
264C23×C3—21no—
265C23×C3D3×D411yescharacteristic
266C23×C3D3×D411yescharacteristic
267C22×D3—32no—
268C22×D3—32no—
269C22×D3—62no—
270C22×D3—62no—
271C22×D3—62no—
272C22×D3—61no—
273C22×D3—61no—
274C22×D3—61no—
275C22×D3—61no—
276C22×D3—61no—
277C22×D3—61no—
278C22×D3—61no—
279C22×D3—61no—
280C22×D3—61no—
281C22×D3—61no—
282C22×D3—61no—
283C22×D3—61no—
284C22×D3—121no—
285C22×D3—121no—
286C22×D3—121no—
287C22×D3—121no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—121no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4—121no—
306C2×C3×C4C2×C4×D311yescharacteristic
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4C2×D1211yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4#23511yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4#23711yescharacteristic
314C2×C3×C4D3×Q811yescharacteristic
315C2×C3×C4D3×Q811yescharacteristic
316C2×C3×C4#23911yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—32no—
321C2×Dic3—32no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—41no—
325C2×Dic3—41no—
326C2×Dic3—41no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—62no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—61no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C4×D3—62no—
340C4×D3—62no—
341C4×D3—62no—
342C4×D3—62no—
343C4×D3—62no—
344C4×D3—62no—
345C4×D3—62no—
346C4×D3—62no—
347C4×D3—122no—
348C4×D3—122no—
349C4×D3—122no—
350C4×D3—122no—
351C3×C8—22no—
352C3×C8—22no—
353C3×C8—42no—
354C3⋊C8—62no—
355C3⋊C8—62no—
356C3⋊C8—122no—
357C2×C32#38511yescharacteristic
358C2×C32#42711yescharacteristic
359C2×C32#42811yescharacteristic
360C2×C32#44911yescharacteristic
361C2×C32#45211yescharacteristic
362C2×C32#48211yescharacteristic
363C2×C32#48511yescharacteristic
364C3⋊D3—42no—
365C24—91no—
366C22×C4—61no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—91no—
371C22×C4—92no—
372C22×C4—92no—
373C22×C4—181no—
374C22×C4—181no—
375C22×C4—181no—
376C22×C4—181no—
377C22×C4C2×D3211yescharacteristic
378C2×C8—21no—
379C2×C8—21no—
380C2×C8—92no—
381C2×C8—181no—
382C2×C8—181no—
383C2×C8#62412yes—
384C4⋊C4—32no—
385C4⋊C4—32no—
386C4⋊C4—61no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—61no—
392C22⋊C4—184no—
393C22⋊C4—362no—
394C42—184no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3#88211yescharacteristic
403C22×C3#88311yescharacteristic
404C22×C3D3×C4⋊C411yescharacteristic
405C22×C3D3×C4⋊C411yescharacteristic
406C22×C3#89411yescharacteristic
407C22×C3#91111yescharacteristic
408C22×C3#91211yescharacteristic
409C22×C3#91211yescharacteristic
410C22×C3#91411yescharacteristic
411C22×C3#91511yescharacteristic
412C22×C3#91811yescharacteristic
413C22×C3#91911yescharacteristic
414C22×C3#91911yescharacteristic
415C22×C3#93711yescharacteristic
416C2×D3—64no—
417C2×D3—62no—
418C2×D3—62no—
419C2×D3—62no—
420C2×D3—62no—
421C2×D3—62no—
422C2×D3—62no—
423C2×D3—122no—
424C2×D3—122no—
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—122no—
428C2×D3—122no—
429C2×D3—121no—
430C2×D3—121no—
431C2×D3—121no—
432C2×D3—121no—
433C2×D3—121no—
434C2×D3—121no—
435C2×D3—121no—
436C2×D3—121no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—122no—
442C3×C4—122no—
443C3×C4—241no—
444C3×C4—241no—
445C3×C4C4×D1211yescharacteristic
446C3×C4#67⋊C411yescharacteristic
447C3×C4#89311yescharacteristic
448C3×C4#89611yescharacteristic
449C3×C4#89611yescharacteristic
450C3×C4#89711yescharacteristic
451C3×C4C4×#6711yescharacteristic
452C3×C4#94611yescharacteristic
453Dic3—42no—
454Dic3—42no—
455Dic3—62no—
456Dic3—62no—
457Dic3—81no—
458Dic3—81no—
459Dic3—122no—
460C32#185411yescharacteristic, complemented, Sylow
461C23—92no—
462C23—181no—
463C23—181no—
464C23—181no—
465C23—181no—
466C23—181no—
467C23—181no—
468C23#380211yescharacteristic
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—92no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4—181no—
483C2×C4—181no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—182no—
487C2×C4—182no—
488C2×C4#379711yescharacteristic
489C2×C4#379911yescharacteristic
490C2×C4D3×D1211yescharacteristic
491C2×C4#380411yescharacteristic
492C2×C4C2×#62411yescharacteristic
493C2×C4D3×#6711yescharacteristic
494C8—22no—
495C8—182no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3#466811yescharacteristic
504C2×C3#478311yescharacteristic
505C2×C3#478411yescharacteristic
506C2×C3#481011yescharacteristic
507C2×C3#481411yescharacteristic
508C2×C3#486111yescharacteristic
509C2×C3#488011yescharacteristic
510C2×C3#488011yescharacteristic
511C2×C3#488111yescharacteristic
512C2×C3#488511yescharacteristic
513C2×C3#488811yescharacteristic
514C2×C3#498911yescharacteristic
515C2×C3#515811yescharacteristic
516C2×C3#518711yescharacteristic
517D3—124no—
518D3—122no—
519D3—122no—
520C22—182no—
521C22—182no—
522C22—182no—
523C22—361no—
524C22—361no—
525C22—361no—
526C22—361no—
527C22#6379811yescharacteristic
528C22#6381011yescharacteristic
529C22#6381011yescharacteristic
530C22#6381111yescharacteristic
531C22#6385411yescharacteristic
532C22#6390011yescharacteristic
533C22#6392211yescharacteristic
534C4—122no—
535C4—122no—
536C4—182no—
537C4—241no—
538C4—241no—
539C4#6388811yescharacteristic
540C4#6389411yescharacteristic
541C4#6389511yescharacteristic
542C4#6395211yescharacteristic
543C3—21no—
544C3#6887711yescharacteristic, complemented
545C3#7063311yescharacteristic, complemented
546C2—362no—
547C2#1059065111yescharacteristic
548C2#1059068811yescharacteristic
549C2#1059071411yescharacteristic
550C2#1059071511yescharacteristic
551C2#1059096311yescharacteristic
552C2#1059096511yescharacteristic
553C2#1059137811yescharacteristic
subgroupG/H
centerC23#3802
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×#818C2semidirect
5. C2×#63574C2semidirect
6. C3×#4551C2semidirect
7. #10589163C2semidirect
22. #63647C4semidirect
32. C2×#818D3semidirect
38. #4551D3semidirect
460. C32#1854semidirect
544. C3#68877semidirect
545. C3#70633semidirect

Maximal subgroups

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

subgroupindex
C2×#638492
C2×#636472
C2×C3×#8182
#105913252
C2×#635742
C3×#45512
#105891632
#706333
#688773