Finite Group Databasebeta

← #11775212

Subgroups — #11775212

Order 1152.

905 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C3×C4×#217C211yesmaximal, characteristic, complemented
3C3×#5207C211yesmaximal, characteristic, complemented
4#10589151C214yesmaximal, complemented
5#69977—31nomaximal
6#69444—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×#638—21no—
9C22×C4⋊(C3⋊D3)C411yescharacteristic, complemented
10#64139—21no—
11#64139—21no—
12#64139C412yescomplemented
13#64139C2212yes—
14C2×#3752—21no—
15C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
16C2×C3×#217—21no—
17C2×C3×C4×Dic3—21no—
18C2×C3×#208—21no—
19C3×C3⋊#95C2212yescomplemented
20C3×#830—21no—
21C3×#830C2212yescomplemented
22C2×#930—31no—
23C2×#930—31no—
24C2×#930—61no—
25C3×#407—31no—
26C3×C4×C22⋊C4—31no—
27C4×#217D311yescharacteristic, complemented
28#5207D311yescharacteristic, complemented
29#4470—34no—
30#4451—34no—
31C24×C32D411yescharacteristic
32C23×C3⋊D3—21no—
33C22×C32×C4—42no—
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4C2×C411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4D411yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C2×#638—22no—
41C2×#638—22no—
42C2×#638—44no—
43C22×C3⋊Dic3—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—42no—
46C2×C4⋊(C3⋊D3)C2×C412yes—
47C22×C3×Dic3—22no—
48#3752—22no—
49#3752—22no—
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)C2×C412yes—
52C3×#217—24no—
53C3×C4×Dic3—42no—
54C3×#208—42no—
55C2×C3×C3⋊C8—22no—
56#1507—91noSylow
57C23×C3×C4—21no—
58C23×C3×C4C2×D311yescharacteristic
59C23×C3×C4C2×D311yescharacteristic
60C22×#67—62no—
61C22×#67—61no—
62C22×#67—61no—
63C22×D12—31no—
64C22×D12—31no—
65C22×D12—61no—
66C2×C3×M16—61no—
67C2×C3×C22⋊C4—61no—
68C2×C3×C42—61no—
69C2×#217—21no—
70#930—32no—
71#930—32no—
72#930—32no—
73#930—32no—
74#930—62no—
75#930—62no—
76#930—62no—
77#930—62no—
78#930—61no—
79#930—61no—
80#930—61no—
81#930—61no—
82C2×(C2×D3)⋊C4—62no—
83C2×(C2×D3)⋊C4—61no—
84C2×(C2×D3)⋊C4—61no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—31no—
87C2×C4⋊Dic3—61no—
88C2×C4×Dic3—21no—
89C2×#208—21no—
90C3×C22⋊C8—32no—
91C3×C22⋊C8—61no—
92C3×#95—32no—
93C3⋊#95C2×D312yescomplemented
94#830—21no—
95#830C2×D312yescomplemented
96C23×C32—22no—
97C23×C32—22no—
98C23×C32—41no—
99C23×C32C22⋊C411yescharacteristic
100C23×C32C22⋊C411yescharacteristic
101C23×C32C2×D411yescharacteristic
102C22×C3⋊D3—22no—
103C22×C3⋊D3—42no—
104C22×C3⋊D3—42no—
105C22×C3⋊D3—42no—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—22no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4C22⋊C411yescharacteristic
113C2×C32×C4C22⋊C411yescharacteristic
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116#638—44no—
117#638—44no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—42no—
120C4⋊(C3⋊D3)—42no—
121C4⋊(C3⋊D3)—42no—
122C2×C3×Dic3—24no—
123C2×C3×Dic3—42no—
124C2×C3×Dic3—42no—
125C3×C3⋊C8—42no—
126C2×#121—91no—
127#407—31no—
128C4×C22⋊C4—31no—
129#327—94no—
130C24×C3—21no—
131C24×C3D1211yescharacteristic
132C24×C3#6711yescharacteristic
133C23×D3—62no—
134C23×D3—61no—
135C23×D3—61no—
136C22×C3×C4—21no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—21no—
141C22×C3×C4—21no—
142C22×C3×C4—42no—
143C22×C3×C4—42no—
144C22×C3×C4—44no—
145C22×C3×C4—62no—
146C22×C3×C4C4×D311yescharacteristic
147C22×C3×C4C4×D311yescharacteristic
148C22×C3×C4C4×D311yescharacteristic
149C22×C3×C4C4×D311yescharacteristic
150C22×C3×C4D1211yescharacteristic
151C22×C3×C4D1211yescharacteristic
152C22×C3×C4D1211yescharacteristic
153C22×C3×C4#6711yescharacteristic
154C22×C3×C4#6711yescharacteristic
155C22×C3×C4#6711yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C22×C3×C4C22×D311yescharacteristic
158C2×#67—64no—
159C2×#67—64no—
160C2×#67—62no—
161C2×#67—62no—
162C2×#67—62no—
163C2×#67—62no—
164C2×#67—128no—
165C2×#67—124no—
166C2×#67—124no—
167C22×Dic3—22no—
168C22×Dic3—62no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C2×D12—32no—
172C2×D12—32no—
173C2×D12—62no—
174C2×D12—62no—
175C2×D12—61no—
176C2×D12—61no—
177C2×D12—124no—
178C2×D12—122no—
179C2×D12—122no—
180C3×M16—122no—
181C2×C3×C8—62no—
182C3×C22⋊C4—64no—
183C3×C42—122no—
184#217—24no—
185(C2×D3)⋊C4—64no—
186(C2×D3)⋊C4—64no—
187(C2×D3)⋊C4—62no—
188(C2×D3)⋊C4—62no—
189(C2×D3)⋊C4—62no—
190(C2×D3)⋊C4—62no—
191C4⋊Dic3—32no—
192C4⋊Dic3—32no—
193C4⋊Dic3—62no—
194C4⋊Dic3—62no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4×Dic3—42no—
198#208—42no—
199C2×C3⋊C8—22no—
200C22×C32—21no—
201C22×C32—21no—
202C22×C32—21no—
203C22×C32—21no—
204C22×C32—21no—
205C22×C32—21no—
206C22×C32—21no—
207C22×C32—44no—
208C22×C32#10412yes—
209C22×C32C2×C22⋊C411yescharacteristic
210C22×C32AGL(1,ℤ/8)12yes—
211C2×C3⋊D3—42no—
212C2×C3⋊D3—42no—
213C2×C3⋊D3—42no—
214C2×C3⋊D3—84no—
215C32×C4—21no—
216C32×C4—21no—
217C32×C4—21no—
218C32×C4#9912yes—
219C3⋊Dic3—42no—
220C3×Dic3—44no—
221C22×D4—91no—
222C22×D4—181no—
223C23×C4D3211yescharacteristic
224C2×M16—61no—
225#121—92no—
226#121—92no—
227#121—181no—
228#121—181no—
229C2×C4⋊C4—91no—
230C2×C22⋊C4—61no—
231C2×C22⋊C4—181no—
232C2×C42—61no—
233C22⋊C8—32no—
234C22⋊C8—61no—
235#95—32no—
236C23×C3—24no—
237C23×C3—22no—
238C23×C3—22no—
239C23×C3—22no—
240C23×C3—22no—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—21no—
244C23×C3—42no—
245C23×C3—41no—
246C23×C3—41no—
247C23×C3—42no—
248C23×C3(C2×D3)⋊C411yescharacteristic
249C23×C3(C2×D3)⋊C411yescharacteristic
250C23×C3(C2×D3)⋊C411yescharacteristic
251C23×C3(C2×D3)⋊C411yescharacteristic
252C23×C3C2×D1211yescharacteristic
253C23×C3C2×#6711yescharacteristic
254C22×D3—64no—
255C22×D3—62no—
256C22×D3—62no—
257C22×D3—124no—
258C22×D3—122no—
259C22×D3—122no—
260C22×D3—124no—
261C22×D3—122no—
262C22×D3—122no—
263C22×D3—124no—
264C22×D3—122no—
265C22×D3—122no—
266C2×C3×C4—24no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—22no—
272C2×C3×C4—22no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—41no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—41no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—42no—
286C2×C3×C4—42no—
287C2×C3×C4—42no—
288C2×C3×C4—64no—
289C2×C3×C4—122no—
290C2×C3×C4—122no—
291C2×C3×C4(C2×D3)⋊C411yescharacteristic
292C2×C3×C4(C2×D3)⋊C411yescharacteristic
293C2×C3×C4(C2×D3)⋊C411yescharacteristic
294C2×C3×C4(C2×D3)⋊C411yescharacteristic
295C2×C3×C4C2×C4×D311yescharacteristic
296C2×C3×C4C2×C4×D311yescharacteristic
297C2×C3×C4C2×D1211yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299#67—128no—
300#67—124no—
301#67—124no—
302#67—128no—
303#67—124no—
304#67—124no—
305C2×Dic3—24no—
306C2×Dic3—42no—
307C2×Dic3—42no—
308C2×Dic3—64no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—124no—
312C2×Dic3—122no—
313C2×Dic3—122no—
314D12—122no—
315D12—122no—
316D12—124no—
317D12—124no—
318D12—122no—
319D12—122no—
320C3×C8—122no—
321C3⋊C8—42no—
322C2×C32—22no—
323C2×C32—22no—
324C2×C32—41no—
325C2×C32C2×#9911yescharacteristic
326C2×C32#41811yescharacteristic
327C2×C32C2×#10411yescharacteristic
328C3⋊D3—82no—
329C24—181no—
330C24#62611yescharacteristic
331C2×D4—92no—
332C2×D4—182no—
333C2×D4—182no—
334C2×D4—181no—
335C2×D4—362no—
336C2×D4—364no—
337C22×C4—42no—
338C22×C4—62no—
339C22×C4—181no—
340C22×C4#62411yescharacteristic
341C22×C4#62411yescharacteristic
342C22×C4#62611yescharacteristic
343C22×C4#62611yescharacteristic
344C22×C4#62611yescharacteristic
345C22×C4C2×D3211yescharacteristic
346M16—122no—
347C2×C8—62no—
348C4⋊C4—92no—
349C4⋊C4—181no—
350C22⋊C4—64no—
351C22⋊C4—182no—
352C22⋊C4—182no—
353C42—122no—
354C22×C3—22no—
355C22×C3—22no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—22no—
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—22no—
372C22×C3—22no—
373C22×C3—21no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—44no—
379C22×C3—44no—
380C22×C3—48no—
381C22×C3#80512yes—
382C22×C3#82512yes—
383C22×C3#90812yes—
384C22×C3C2×(C2×D3)⋊C411yescharacteristic
385C22×C3C2×(C2×D3)⋊C411yescharacteristic
386C22×C3#94912yes—
387C2×D3—124no—
388C2×D3—124no—
389C2×D3—124no—
390C2×D3—122no—
391C2×D3—122no—
392C2×D3—122no—
393C2×D3—122no—
394C2×D3—122no—
395C2×D3—122no—
396C2×D3—248no—
397C2×D3—244no—
398C2×D3—244no—
399C3×C4—22no—
400C3×C4—21no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—22no—
407C3×C4—41no—
408C3×C4—41no—
409C3×C4—124no—
410C3×C4#80612yes—
411C3×C4#80612yes—
412Dic3—44no—
413Dic3—124no—
414Dic3—122no—
415Dic3—122no—
416C32#150711yescharacteristic, complemented, Sylow
417C23—22no—
418C23—22no—
419C23—41no—
420C23—182no—
421C23—362no—
422C23—362no—
423C23—362no—
424C23#372211yescharacteristic
425C23#372211yescharacteristic
426C23C2×#62611yescharacteristic
427D4—362no—
428D4—364no—
429D4—364no—
430D4—362no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—64no—
438C2×C4—122no—
439C2×C4—122no—
440C2×C4—182no—
441C2×C4—362no—
442C2×C4#372211yescharacteristic
443C2×C4#372211yescharacteristic
444C2×C4C2×#62411yescharacteristic
445C2×C4C2×#62611yescharacteristic
446C8—122no—
447C2×C3—24no—
448C2×C3—22no—
449C2×C3—22no—
450C2×C3—22no—
451C2×C3—22no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—42no—
456C2×C3—42no—
457C2×C3—41no—
458C2×C3—41no—
459C2×C3C2×#80511yescharacteristic
460C2×C3C2×#80611yescharacteristic
461C2×C3C2×#80611yescharacteristic
462C2×C3#500111yescharacteristic
463C2×C3#513111yescharacteristic
464C2×C3C2×#82511yescharacteristic
465D3—244no—
466D3—242no—
467D3—242no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—44no—
476C22—362no—
477C22—362no—
478C22—362no—
479C22—724no—
480C22#6357012yes—
481C22#6382512yes—
482C22C2×#372211yescharacteristic
483C4—21no—
484C4—21no—
485C4—21no—
486C4—124no—
487C4—362no—
488C4#6358112yes—
489C3—21no—
490C3#6944411yescharacteristic, complemented
491C3#6997711yescharacteristic, complemented
492C2—22no—
493C2—22no—
494C2—41no—
495C2—722no—
496C2#1059109611yescharacteristic
497C2C2×#6357011yescharacteristic
498C2C2×#6358111yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#64139C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1507
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×#217C2semidirect
3. C3×#5207C2semidirect
4. #10589151C2semidirect
9. C22×C4⋊(C3⋊D3)C4semidirect
12. #64139C4semidirect
15. C2×C4⋊(C3⋊Dic3)C4semidirect
19. C3×C3⋊#95C22semidirect
21. C3×#830C22semidirect
27. C4×#217D3semidirect
28. #5207D3semidirect
93. C3⋊#95C2×D3semidirect
95. #830C2×D3semidirect
416. C32#1507semidirect
490. C3#69444semidirect
491. C3#69977semidirect

Maximal subgroups

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

subgroupindex
C2×#641392
C3×C4×#2172
C3×#52072
#105891512
#699773
#694443