Finite Group Databasebeta

← #11784695

Subgroups — #11784695

Order 1152.

2544 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×C3⋊D3C211yesmaximal, characteristic
2C2×C32×#102C211yesmaximal, characteristic, complemented
3C2×#63659C211yesmaximal, characteristic, complemented
4C2×#63648C211yesmaximal, characteristic, complemented
5C2×#63647C211yesmaximal, characteristic, complemented
6#10592686C211yesmaximal, characteristic, complemented
7C2×#63636C211yesmaximal, characteristic, complemented
8#70198—34nomaximal
9C24×C3⋊D3—21no—
10C22×C32×D4C2211yescharacteristic
11C22×#638—21no—
12C2×D4×C3⋊D3—22no—
13C2×D4×C3⋊D3—22no—
14C2×D4×C3⋊D3—22no—
15C2×D4×C3⋊D3—22no—
16C2×D4×C3⋊D3—22no—
17C2×D4×C3⋊D3C414yescomplemented
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic, complemented
21C2×C32×C4⋊C4C2211yescharacteristic, complemented
22C2×#3752—21no—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
24C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
25C32×#102—22no—
26#63659—22no—
27#63658—21no—
28#63648—22no—
29#63647—22no—
30#63636—22no—
31C22×D3×D4—34no—
32C2×C3×#102D314yescomplemented
33C2×#832—34no—
34C2×#821—34no—
35C2×(C2×D3)⋊C8—34no—
36#4987—34no—
37C2×#809—34no—
38C24×C32—21no—
39C23×C3⋊D3—24no—
40C23×C3⋊D3—24no—
41C23×C3⋊D3—21no—
42C23×C3⋊D3—24no—
43C23×C3⋊D3—42no—
44C23×C3⋊D3—42no—
45C23×C3⋊D3—42no—
46C23×C3⋊D3—42no—
47C23×C3⋊D3D411yescharacteristic
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4C2×C412yes—
52C2×C32×D4D412yes—
53C2×C32×D4D412yes—
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C2×#638—24no—
57C2×#638—24no—
58C2×#638—24no—
59C22×C3⋊Dic3—21no—
60C22×C3⋊Dic3D411yescharacteristic
61D4×C3⋊D3—28no—
62D4×C3⋊D3—28no—
63D4×C3⋊D3—28no—
64D4×C3⋊D3—28no—
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2×C412yes—
69C2×C4⋊(C3⋊D3)D412yes—
70C2×C4⋊(C3⋊D3)D412yes—
71C2×C4×C3⋊D3—21no—
72C2×C4×C3⋊D3—21no—
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—21no—
75C2×C4×C3⋊D3C2×C412yes—
76C2×C4×C3⋊D3D412yes—
77C2×C32×C8—21no—
78C2×C32×C8—21no—
79C2×C32×C8—21no—
80C32×C4⋊C4—21no—
81C32×C4⋊C4—21no—
82#3752—42no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)—21no—
85C2×C3⋊(C3⋊C8)—21no—
86C2×C3⋊(C3⋊C8)—21no—
87C2×C3⋊(C3⋊C8)—21no—
88#1786—91noSylow
89C24×D3—64no—
90C22×C3×D4C2×D314yes—
91C22×#67—64no—
92C2×D3×D4—316no—
93C2×D3×D4—68no—
94C2×D3×D4—68no—
95C2×D3×D4—68no—
96C2×D3×D4—68no—
97C2×D3×D4—68no—
98C22×D12—34no—
99C22×C4×D3—34no—
100C22×C3×C8C2×D314yescomplemented
101C2×C3×C4⋊C4C2×D314yescomplemented
102C2×(C2×D3)⋊C4—64no—
103C2×C4⋊Dic3—34no—
104C22×C3⋊C8—34no—
105C3×#102—28no—
106#832—68no—
107C3⋊#95—64no—
108#821—68no—
109(C2×D3)⋊C8—68no—
110#809—68no—
111C23×C32—22no—
112C23×C32—22no—
113C23×C32—22no—
114C23×C32—41no—
115C23×C32—41no—
116C23×C32—41no—
117C23×C32—41no—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—21no—
120C22×C3⋊D3—21no—
121C22×C3⋊D3—21no—
122C22×C3⋊D3—21no—
123C22×C3⋊D3—216no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3—48no—
128C22×C3⋊D3—48no—
129C22×C3⋊D3—48no—
130C22×C3⋊D3—48no—
131C22×C3⋊D3—48no—
132C22×C3⋊D3—41no—
133C22×C3⋊D3—41no—
134C22×C3⋊D3—41no—
135C22×C3⋊D3—41no—
136C22×C3⋊D3—48no—
137C22×C3⋊D3C22⋊C412yes—
138C22×C3⋊D3D812yes—
139C22×C3⋊D3SD1612yes—
140C32×D4—22no—
141C32×D4—22no—
142C32×D4—22no—
143C32×D4C22⋊C414yescomplemented
144C2×C32×C4—41no—
145C2×C32×C4—41no—
146C2×C32×C4—41no—
147C2×C32×C4C22×C411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153#638—216no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3—21no—
156C2×C3⋊Dic3—41no—
157C2×C3⋊Dic3—41no—
158C2×C3⋊Dic3—41no—
159C2×C3⋊Dic3C22⋊C412yes—
160C4⋊(C3⋊D3)—22no—
161C4⋊(C3⋊D3)—22no—
162C4⋊(C3⋊D3)—22no—
163C4⋊(C3⋊D3)C22⋊C414yescomplemented
164C4×C3⋊D3—22no—
165C4×C3⋊D3—22no—
166C4×C3⋊D3—22no—
167C4×C3⋊D3—22no—
168C32×C8—41no—
169C3⋊(C3⋊C8)—41no—
170C23×D4—91no—
171C2×#102—91no—
172C2×#102—91no—
173C2×#102—91no—
174C2×#102C3⋊D311yescharacteristic, complemented
175C2×C22⋊C8—91no—
176#380—91no—
177C24×C3—24no—
178C23×D3—34no—
179C23×D3—616no—
180C23×D3—616no—
181C23×D3—616no—
182C23×D3—64no—
183C23×D3—128no—
184C23×D3—128no—
185C23×D3—128no—
186C23×D3—128no—
187C2×C3×D4—24no—
188C2×C3×D4—24no—
189C2×C3×D4—24no—
190C2×C3×D4C4×D318yes—
191C2×C3×D4D1218yes—
192C2×C3×D4#6718yes—
193C22×C3×C4—24no—
194C22×C3×C4C22×D314yes—
195C2×#67—616no—
196C2×#67—616no—
197C2×#67—616no—
198C22×Dic3—34no—
199C22×Dic3—64no—
200D3×D4—632no—
201D3×D4—632no—
202D3×D4—632no—
203D3×D4—632no—
204C2×D12—38no—
205C2×D12—38no—
206C2×D12—38no—
207C2×D12—64no—
208C2×D12—64no—
209C2×D12—64no—
210C2×C4×D3—38no—
211C2×C4×D3—38no—
212C2×C4×D3—64no—
213C2×C4×D3—64no—
214C2×C4×D3—64no—
215C2×C4×D3—64no—
216C2×C3×C8—24no—
217C2×C3×C8—24no—
218C2×C3×C8—24no—
219C3×C4⋊C4—24no—
220C3×C4⋊C4—24no—
221(C2×D3)⋊C4—128no—
222C4⋊Dic3—64no—
223C4⋊Dic3—64no—
224C2×C3⋊C8—64no—
225C2×C3⋊C8—64no—
226C2×C3⋊C8—64no—
227C22×C32—24no—
228C22×C32—42no—
229C22×C32—42no—
230C22×C32—42no—
231C22×C32—42no—
232C22×C32—42no—
233C22×C32—42no—
234C22×C32C2×C22⋊C411yescharacteristic
235C22×C32#12011yescharacteristic
236C22×C32#12011yescharacteristic
237C22×C32C2×D811yescharacteristic
238C22×C32C2×SD1611yescharacteristic
239C22×C32AGL(1,ℤ/8)11yescharacteristic
240C22×C32AGL(1,ℤ/8)11yescharacteristic
241C2×C3⋊D3—22no—
242C2×C3⋊D3—22no—
243C2×C3⋊D3—22no—
244C2×C3⋊D3—22no—
245C2×C3⋊D3—22no—
246C2×C3⋊D3—22no—
247C2×C3⋊D3—24no—
248C2×C3⋊D3—432no—
249C2×C3⋊D3—42no—
250C2×C3⋊D3—42no—
251C2×C3⋊D3—42no—
252C2×C3⋊D3—42no—
253C2×C3⋊D3—42no—
254C2×C3⋊D3—42no—
255C2×C3⋊D3#10214yescomplemented
256C32×C4—81no—
257C32×C4C2×C22⋊C411yescharacteristic
258C32×C4C2×C22⋊C411yescharacteristic
259C32×C4#12011yescharacteristic
260C32×C4#12011yescharacteristic
261C3⋊Dic3—22no—
262C3⋊Dic3—81no—
263C25—181no—
264C22×D4—94no—
265C22×D4—91no—
266C22×D4—182no—
267C22×D4—181no—
268C22×D4—182no—
269C22×D4—182no—
270C22×D4—182no—
271C22×D4—182no—
272C22×D4C2×C3⋊D311yescharacteristic
273C23×C4—91no—
274C22×C8—91no—
275C22×C8C2×C3⋊D311yescharacteristic, complemented
276C2×C4⋊C4—91no—
277C2×C4⋊C4C2×C3⋊D311yescharacteristic, complemented
278C2×C22⋊C4—181no—
279#102—22no—
280#102—182no—
281#102—182no—
282#102—182no—
283C22⋊C8—182no—
284#95—181no—
285C23×C3—28no—
286C23×C3—28no—
287C23×C3—28no—
288C23×C3—44no—
289C23×C3—44no—
290C23×C3—44no—
291C23×C3—44no—
292C23×C3D3×D414yes—
293C22×D3—38no—
294C22×D3—38no—
295C22×D3—38no—
296C22×D3—64no—
297C22×D3—64no—
298C22×D3—64no—
299C22×D3—64no—
300C22×D3—664no—
301C22×D3—68no—
302C22×D3—68no—
303C22×D3—68no—
304C22×D3—1232no—
305C22×D3—1232no—
306C22×D3—1232no—
307C22×D3—1232no—
308C22×D3—1232no—
309C22×D3—1232no—
310C22×D3—124no—
311C22×D3—124no—
312C22×D3—124no—
313C22×D3—124no—
314C3×D4—28no—
315C3×D4—28no—
316C3×D4—28no—
317C3×D4(C2×D3)⋊C4116yescomplemented
318C2×C3×C4—44no—
319C2×C3×C4—44no—
320C2×C3×C4—44no—
321C2×C3×C4C2×C4×D314yes—
322C2×C3×C4C2×D1214yes—
323C2×C3×C4D3×D414yes—
324C2×C3×C4D3×D414yes—
325C2×C3×C4D3×D414yes—
326C2×C3×C4C2×#6714yes—
327#67—664no—
328C2×Dic3—38no—
329C2×Dic3—64no—
330C2×Dic3—64no—
331C2×Dic3—124no—
332C2×Dic3—124no—
333C2×Dic3—124no—
334D12—316no—
335D12—68no—
336D12—68no—
337D12—68no—
338C4×D3—68no—
339C4×D3—68no—
340C4×D3—68no—
341C4×D3—68no—
342C3×C8—44no—
343C3⋊C8—124no—
344C2×C32—44no—
345C2×C32#37911yescharacteristic
346C2×C32C2×#10211yescharacteristic
347C2×C32#41811yescharacteristic
348C2×C32#44711yescharacteristic
349C2×C32#44711yescharacteristic
350C2×C32#45011yescharacteristic
351C2×C32#45011yescharacteristic
352C3⋊D3—24no—
353C3⋊D3—44no—
354C24—21no—
355C24—91no—
356C24—184no—
357C24—184no—
358C24—184no—
359C24—181no—
360C24—362no—
361C24—362no—
362C24—362no—
363C24—362no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—92no—
368C2×D4—92no—
369C2×D4—92no—
370C2×D4—184no—
371C2×D4—188no—
372C2×D4—188no—
373C2×D4—188no—
374C2×D4—184no—
375C2×D4—184no—
376C2×D4—188no—
377C2×D4—181no—
378C2×D4—181no—
379C2×D4—181no—
380C2×D4C4×C3⋊D312yes—
381C2×D4C4⋊(C3⋊D3)12yes—
382C2×D4#63812yes—
383C22×C4—21no—
384C22×C4—91no—
385C22×C4—92no—
386C22×C4—92no—
387C22×C4—181no—
388C22×C4—181no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4—181no—
392C22×C4C22×C3⋊D311yescharacteristic
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—181no—
397C2×C8—181no—
398C2×C8—181no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—181no—
402C4⋊C4—181no—
403C22⋊C4—362no—
404C22×C3—216no—
405C22×C3—48no—
406C22×C3—48no—
407C22×C3—48no—
408C22×C3—48no—
409C22×C3—48no—
410C22×C3—48no—
411C22×C3D3×C22⋊C414yes—
412C22×C3#88214yes—
413C22×C3D3×D814yes—
414C22×C3#91114yes—
415C22×C3D3×SD1614yes—
416C22×C3#91414yes—
417C22×C3#93714yes—
418C2×D3—316no—
419C2×D3—68no—
420C2×D3—68no—
421C2×D3—68no—
422C2×D3—68no—
423C2×D3—68no—
424C2×D3—68no—
425C2×D3—616no—
426C2×D3—12128no—
427C2×D3—128no—
428C2×D3—128no—
429C2×D3—128no—
430C2×D3—128no—
431C2×D3—128no—
432C2×D3—128no—
433C3×C4—84no—
434C3×C4D3×C22⋊C414yes—
435C3×C4#88214yes—
436C3×C4C2×(C2×D3)⋊C414yes—
437C3×C4#93714yes—
438Dic3—68no—
439Dic3—244no—
440C32#178611yescharacteristic, complemented, Sylow
441C23—22no—
442C23—22no—
443C23—22no—
444C23—41no—
445C23—41no—
446C23—41no—
447C23—41no—
448C23—92no—
449C23—92no—
450C23—92no—
451C23—1816no—
452C23—181no—
453C23—181no—
454C23—181no—
455C23—181no—
456C23—182no—
457C23—182no—
458C23—182no—
459C23—368no—
460C23—368no—
461C23—368no—
462C23—368no—
463C23—368no—
464C23—368no—
465C23—361no—
466C23—361no—
467C23—361no—
468C23—361no—
469C23D4×C3⋊D311yescharacteristic
470D4—22no—
471D4—22no—
472D4—22no—
473D4—94no—
474D4—1816no—
475D4—182no—
476D4—182no—
477D4—182no—
478D4#375214yescomplemented
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—92no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—182no—
486C2×C4—182no—
487C2×C4—182no—
488C2×C4—182no—
489C2×C4—361no—
490C2×C4—361no—
491C2×C4—361no—
492C2×C4C2×C4×C3⋊D311yescharacteristic
493C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
494C2×C4D4×C3⋊D311yescharacteristic
495C2×C4D4×C3⋊D311yescharacteristic
496C2×C4D4×C3⋊D311yescharacteristic
497C2×C4C2×#63811yescharacteristic
498C8—41no—
499C8—361no—
500C2×C3—416no—
501C2×C3D3×#10214yes—
502C2×C3#477014yes—
503C2×C3#477314yes—
504C2×C3#477614yes—
505C2×C3#495514yes—
506C2×C3#515614yes—
507C2×C3#516914yes—
508D3—616no—
509D3—1216no—
510C22—24no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—94no—
518C22—182no—
519C22—182no—
520C22—182no—
521C22—182no—
522C22—182no—
523C22—182no—
524C22—184no—
525C22—3632no—
526C22—362no—
527C22—362no—
528C22—362no—
529C22—362no—
530C22—362no—
531C22—362no—
532C22C22⋊C4×C3⋊D311yescharacteristic
533C22#6409111yescharacteristic
534C22D8×C3⋊D311yescharacteristic
535C22#6412011yescharacteristic
536C22SD16×C3⋊D311yescharacteristic
537C22#6412311yescharacteristic
538C22#6414611yescharacteristic
539C4—81no—
540C4—182no—
541C4—721no—
542C4C22⋊C4×C3⋊D311yescharacteristic
543C4#6409111yescharacteristic
544C4C2×#375211yescharacteristic
545C4#6414611yescharacteristic
546C3#7019814yescomplemented
547C2—44no—
548C2—184no—
549C2—364no—
550C2C3⋊D3×#10211yescharacteristic
551C2#1059246911yescharacteristic
552C2#1059247211yescharacteristic
553C2#1059247511yescharacteristic
554C2#1059265411yescharacteristic
555C2#1059285511yescharacteristic
556C2#1059286811yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#102C2
socleC23×C32C2×D4
prime radicalC22×D4×C3⋊D3C2
cosocleC22×C32×C4C23
hypercenterC2×#102C3⋊D3
hypocenterC32#1786
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×C32×#102C2semidirect
3. C2×#63659C2semidirect
4. C2×#63648C2semidirect
5. C2×#63647C2semidirect
6. #10592686C2semidirect
7. C2×#63636C2semidirect
17. C2×D4×C3⋊D3C4semidirect
20. C22×C32×C8C22semidirect
21. C2×C32×C4⋊C4C22semidirect
23. C2×C4⋊(C3⋊Dic3)C22semidirect
24. C22×C3⋊(C3⋊C8)C22semidirect
32. C2×C3×#102D3semidirect
100. C22×C3×C8C2×D3semidirect
101. C2×C3×C4⋊C4C2×D3semidirect
143. C32×D4C22⋊C4semidirect
163. C4⋊(C3⋊D3)C22⋊C4semidirect
174. C2×#102C3⋊D3semidirect
255. C2×C3⋊D3#102semidirect
275. C22×C8C2×C3⋊D3semidirect
277. C2×C4⋊C4C2×C3⋊D3semidirect
317. C3×D4(C2×D3)⋊C4semidirect
440. C32#1786semidirect
478. D4#3752semidirect
546. C3#70198semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C2×C32×#1022
C2×#636592
C2×#636482
C2×#636472
#105926862
C2×#636362
#701983