Finite Group Databasebeta

← #11808210

Subgroups — #11808210

Order 1152.

2832 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic, complemented
2C2×C32×C4×D4C211yesmaximal, characteristic, complemented
3C2×C4×#638C212yesmaximal, complemented
4#10592922C212yesmaximal, complemented
5C4×#3757C211yesmaximal, characteristic, complemented
6#10592690C211yesmaximal, characteristic, complemented
7#10592678C211yesmaximal, characteristic, complemented
8#10592659C211yesmaximal, characteristic, complemented
9#10592658C212yesmaximal, complemented
10#10592646C211yesmaximal, characteristic, complemented
11C4×#3752C212yesmaximal, complemented
12#82400—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C23×C32×C4C2211yescharacteristic
15C23×C32×C4C2211yescharacteristic
16C22×#638C2212yes—
17C22×#638C2212yes—
18C2×#3828—24no—
19C2×#3828—28no—
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2212yes—
22C22×#634C2211yescharacteristic
23C32×C4×D4—24no—
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×C32×C22⋊C4C2211yescharacteristic
27C2×C32×C42C2211yescharacteristic
28C2×#3757C2212yes—
29C2×#3757C2212yes—
30C4×#638—28no—
31C2×#3752C2212yes—
32C2×#3752C2212yes—
33C2×#3752C2212yes—
34C2×#3750C2212yes—
35C2×C4×C3⋊Dic3C2212yes—
36#63658C2212yes—
37#63658C2212yes—
38#63658C2211yescharacteristic
39#63658C2211yescharacteristic
40C22×#235—34no—
41C2×C3×C4×D4D314yescomplemented
42C2×C4×#67—38no—
43#5223—38no—
44C4×#217—34no—
45#4991—34no—
46#4979—34no—
47#4960—34no—
48#4959—38no—
49#4947—34no—
50C4×(C2×D3)⋊C4—38no—
51C24×C32C2311yescharacteristic
52C24×C32C2311yescharacteristic
53C23×C3⋊D3C2312yes—
54C2×C32×D4—22no—
55C2×C32×D4—22no—
56C2×C32×D4—22no—
57C22×C32×C4—24no—
58C22×C32×C4—24no—
59C22×C32×C4—22no—
60C22×C32×C4D414yescomplemented
61C22×C32×C4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C2×#638—24no—
67C2×#638—24no—
68C2×#638—24no—
69C2×#638—24no—
70C2×#638—24no—
71C2×#638—24no—
72C22×C3⋊Dic3C2312yes—
73C22×C3⋊Dic3C2312yes—
74C22×C3⋊Dic3C2312yes—
75#3828—232no—
76C2×C4⋊(C3⋊D3)—24no—
77C2×C4⋊(C3⋊D3)—22no—
78C2×C4×C3⋊D3—24no—
79C2×C4×C3⋊D3—24no—
80C2×C4×C3⋊D3D418yescomplemented
81C2×#634—22no—
82C2×#634—24no—
83C32×C4⋊C4—22no—
84C32×C22⋊C4—22no—
85C32×C22⋊C4—22no—
86C32×C42—22no—
87#3757—24no—
88#3757—24no—
89#3752—24no—
90#3752—24no—
91#3752—24no—
92#3750—24no—
93C4×C3⋊Dic3—24no—
94#2388—91noSylow
95C22×C3×D4C2×D314yes—
96C23×C3×C4C2×D314yes—
97C23×C3×C4C2×D314yes—
98C22×#67—38no—
99C22×#67—38no—
100C2×#235—632no—
101C2×#235—616no—
102C22×D12—34no—
103C22×C4×D3—38no—
104C22×Dic6—34no—
105C3×C4×D4—216no—
106C2×C3×C4⋊C4C2×D314yes—
107C2×C3×C22⋊C4C2×D314yes—
108C2×C3×C22⋊C4C2×D314yes—
109C2×C3×C42C2×D314yes—
110C2×#217—38no—
111C2×#217—38no—
112C4×#67—632no—
113C2×(C2×D3)⋊C4—38no—
114C2×(C2×D3)⋊C4—38no—
115C2×(C2×D3)⋊C4—38no—
116C2×Dic3⋊C4—38no—
117C2×C4×Dic3—38no—
118C3⋊#95—38no—
119C3⋊#95—38no—
120C3⋊#95—34no—
121C3⋊#95—34no—
122C23×C32—22no—
123C23×C32—21no—
124C23×C32—22no—
125C23×C32—22no—
126C23×C32—22no—
127C23×C32—21no—
128C23×C32—21no—
129C23×C32—21no—
130C23×C32C2×D412yes—
131C23×C32#4112yescomplemented
132C23×C32C2411yescharacteristic
133C22×C3⋊D3—22no—
134C22×C3⋊D3—22no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3C2×D414yes—
140C32×D4—28no—
141C2×C32×C4—21no—
142C2×C32×C4—22no—
143C2×C32×C4—21no—
144C2×C32×C4—28no—
145C2×C32×C4—22no—
146C2×C32×C4—21no—
147C2×C32×C4—21no—
148C2×C32×C4—22no—
149C2×C32×C4—44no—
150C2×C32×C4C2×D414yes—
151C2×C32×C4C2×D412yes—
152C2×C32×C4C2×D412yes—
153C2×C32×C4#4112yescomplemented
154#638—216no—
155#638—216no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3C2×D414yes—
164C2×C3⋊Dic3#4114yescomplemented
165C4⋊(C3⋊D3)—28no—
166C4×C3⋊D3—216no—
167#634—28no—
168C22×#41—91no—
169C2×C4×D4—92no—
170C2×C4×D4C3⋊D311yescharacteristic, complemented
171#395—91no—
172#394—91no—
173#394—92no—
174#393—91no—
175#392—92no—
176#392—91no—
177C4×C22⋊C4—91no—
178C4×C22⋊C4—92no—
179C24×C3C22×D314yes—
180C24×C3C22×D314yes—
181C23×D3—38no—
182C2×C3×D4—28no—
183C2×C3×D4—28no—
184C2×C3×D4—28no—
185C22×C3×C4—216no—
186C22×C3×C4—216no—
187C22×C3×C4—28no—
188C22×C3×C4#67116yescomplemented
189C22×C3×C4C22×D314yes—
190C22×C3×C4C22×D314yes—
191C22×C3×C4C22×D314yes—
192C22×C3×C4C22×D314yes—
193C22×C3×C4C22×D314yes—
194C2×#67—616no—
195C2×#67—616no—
196C2×#67—616no—
197C2×#67—616no—
198C2×#67—616no—
199C2×#67—616no—
200C22×Dic3—38no—
201C22×Dic3—38no—
202C22×Dic3—38no—
203#235—6128no—
204C2×D12—616no—
205C2×D12—68no—
206C2×C4×D3—332no—
207C2×C4×D3—616no—
208C2×C4×D3—616no—
209C2×Dic6—616no—
210C2×Dic6—68no—
211C3×C4⋊C4—28no—
212C3×C22⋊C4—28no—
213C3×C22⋊C4—28no—
214C3×C42—28no—
215#217—616no—
216#217—616no—
217(C2×D3)⋊C4—616no—
218(C2×D3)⋊C4—616no—
219(C2×D3)⋊C4—616no—
220Dic3⋊C4—616no—
221C4×Dic3—616no—
222C22×C32—22no—
223C22×C32—24no—
224C22×C32—22no—
225C22×C32—22no—
226C22×C32—22no—
227C22×C32—41no—
228C22×C32—42no—
229C22×C32—42no—
230C22×C32—42no—
231C22×C32—41no—
232C22×C32C22×D412yes—
233C22×C32C22×D411yescharacteristic
234C22×C32C2×#4111yescharacteristic
235C22×C32C2×#4111yescharacteristic
236C22×C32C2×#4112yes—
237C2×C3⋊D3—24no—
238C2×C3⋊D3—24no—
239C2×C3⋊D3—24no—
240C2×C3⋊D3—42no—
241C2×C3⋊D3—42no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—42no—
244C32×C4—22no—
245C32×C4—22no—
246C32×C4—41no—
247C32×C4—41no—
248C32×C4#12014yes—
249C3⋊Dic3—24no—
250C3⋊Dic3—24no—
251C3⋊Dic3—42no—
252C2×#41—188no—
253C2×#41—184no—
254C22×Q8—91no—
255C22×D4—92no—
256C22×D4—92no—
257C22×D4—91no—
258C22×D4C2×C3⋊D311yescharacteristic
259C23×C4—92no—
260C23×C4C2×C3⋊D311yescharacteristic
261C23×C4C2×C3⋊D311yescharacteristic
262C4×D4—24no—
263C4×D4—188no—
264C2×C4⋊C4—92no—
265C2×C4⋊C4C2×C3⋊D311yescharacteristic
266C2×C22⋊C4—92no—
267C2×C22⋊C4—92no—
268C2×C22⋊C4—92no—
269C2×C22⋊C4—92no—
270C2×C22⋊C4—92no—
271C2×C22⋊C4C2×C3⋊D311yescharacteristic
272C2×C22⋊C4C2×C3⋊D311yescharacteristic
273C2×C42—92no—
274C2×C42C2×C3⋊D311yescharacteristic
275#95—91no—
276#95—92no—
277#95—92no—
278#95—91no—
279C23×C3—24no—
280C23×C3—24no—
281C23×C3—24no—
282C23×C3—28no—
283C23×C3—28no—
284C23×C3—28no—
285C23×C3—28no—
286C23×C3—24no—
287C23×C3#23518yescomplemented
288C23×C3C2×#6718yes—
289C23×C3C23×D314yes—
290C22×D3—316no—
291C22×D3—68no—
292C22×D3—68no—
293C22×D3—68no—
294C22×D3—68no—
295C22×D3—68no—
296C22×D3—68no—
297C3×D4—232no—
298C2×C3×C4—24no—
299C2×C3×C4—28no—
300C2×C3×C4—24no—
301C2×C3×C4—232no—
302C2×C3×C4—28no—
303C2×C3×C4—28no—
304C2×C3×C4—24no—
305C2×C3×C4—24no—
306C2×C3×C4—416no—
307C2×C3×C4#23518yescomplemented
308C2×C3×C4D3×D4116yes—
309C2×C3×C4C2×#6718yes—
310C2×C3×C4C2×#6718yes—
311#67—664no—
312#67—664no—
313C2×Dic3—316no—
314C2×Dic3—316no—
315C2×Dic3—68no—
316C2×Dic3—68no—
317C2×Dic3—68no—
318C2×Dic3—68no—
319C2×Dic3—68no—
320C2×Dic3—68no—
321C2×Dic3—68no—
322D12—632no—
323C4×D3—664no—
324Dic6—632no—
325C2×C32—42no—
326C2×C32—42no—
327C2×C32C2×#12011yescharacteristic
328C2×C32#52511yescharacteristic
329C2×C32#52512yes—
330C2×C32#53212yes—
331C2×C32#53211yescharacteristic
332C3⋊D3—44no—
333C24—92no—
334C24C22×C3⋊D311yescharacteristic
335C24C22×C3⋊D311yescharacteristic
336#41—1832no—
337C2×Q8—184no—
338C2×Q8—182no—
339C2×D4—22no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—184no—
343C2×D4—184no—
344C2×D4—184no—
345C2×D4—184no—
346C2×D4—184no—
347C2×D4—184no—
348C2×D4—184no—
349C2×D4—182no—
350C22×C4—24no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—92no—
354C22×C4—92no—
355C22×C4—98no—
356C22×C4—92no—
357C22×C4—184no—
358C22×C4—184no—
359C22×C4#63814yescomplemented
360C22×C4C22×C3⋊D311yescharacteristic
361C22×C4C22×C3⋊D311yescharacteristic
362C22×C4C22×C3⋊D311yescharacteristic
363C22×C4C22×C3⋊D311yescharacteristic
364C22×C4C22×C3⋊D311yescharacteristic
365C4⋊C4—22no—
366C4⋊C4—184no—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—184no—
370C22⋊C4—184no—
371C22⋊C4—184no—
372C22⋊C4—184no—
373C22⋊C4—184no—
374C42—22no—
375C42—184no—
376C22×C3—28no—
377C22×C3—28no—
378C22×C3—28no—
379C22×C3—216no—
380C22×C3—28no—
381C22×C3—44no—
382C22×C3—48no—
383C22×C3—48no—
384C22×C3—48no—
385C22×C3—44no—
386C22×C3C2×#23514yes—
387C22×C3C2×#23514yes—
388C22×C3C2×D3×D418yes—
389C22×C3D3×#4118yes—
390C22×C3C22×#6714yes—
391C2×D3—616no—
392C2×D3—616no—
393C2×D3—616no—
394C2×D3—128no—
395C2×D3—128no—
396C2×D3—128no—
397C2×D3—128no—
398C3×C4—28no—
399C3×C4—28no—
400C3×C4—44no—
401C3×C4—44no—
402C3×C4#937116yes—
403Dic3—616no—
404Dic3—616no—
405Dic3—128no—
406C32#238811yescharacteristic, complemented, Sylow
407C23—21no—
408C23—21no—
409C23—21no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—22no—
414C23—21no—
415C23—94no—
416C23—182no—
417C23—182no—
418C23—182no—
419C23—182no—
420C23—182no—
421C23—182no—
422C23#382812yescomplemented
423C23C2×#63812yes—
424C23C23×C3⋊D311yescharacteristic
425Q8—188no—
426D4—28no—
427D4—188no—
428D4—1816no—
429D4—1816no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—28no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—44no—
439C2×C4—94no—
440C2×C4—94no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4—182no—
444C2×C4—182no—
445C2×C4—1816no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—182no—
449C2×C4#382812yescomplemented
450C2×C4D4×C3⋊D314yes—
451C2×C4C2×#63812yes—
452C2×C4C2×#63812yes—
453C2×C3—48no—
454C2×C3—48no—
455C2×C3#554718yes—
456C2×C3#554818yes—
457C2×C3#579114yes—
458C2×C3C2×#93714yes—
459C2×C3#583214yes—
460D3—1216no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—24no—
465C22—22no—
466C22—41no—
467C22—42no—
468C22—42no—
469C22—42no—
470C22—41no—
471C22—184no—
472C22—184no—
473C22—184no—
474C22—362no—
475C22—362no—
476C22—362no—
477C22—362no—
478C22C2×#382811yescharacteristic
479C22C2×#382811yescharacteristic
480C22C2×D4×C3⋊D312yes—
481C22#41×C3⋊D312yes—
482C22C22×#63811yescharacteristic
483C4—22no—
484C4—22no—
485C4—41no—
486C4—41no—
487C4—184no—
488C4—184no—
489C4—362no—
490C4#6414614yes—
491C3#8240014yescomplemented
492C2—42no—
493C2—42no—
494C2—364no—
495C2#1059601812yes—
496C2#1059601912yes—
497C2#1059626211yescharacteristic
498C2C2×#6414611yescharacteristic
499C2#1059630311yescharacteristic
subgroupG/H
centerC22×C4C22×C3⋊D3
commutator, socle, cosocleC23×C32C24
FrattiniC23C23×C3⋊D3
FittingC2×C32×C4×D4C2
hypercenterC2×C4×D4C3⋊D3
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C2×C32×C4×D4C2semidirect
3. C2×C4×#638C2semidirect
4. #10592922C2semidirect
5. C4×#3757C2semidirect
6. #10592690C2semidirect
7. #10592678C2semidirect
8. #10592659C2semidirect
9. #10592658C2semidirect
10. #10592646C2semidirect
11. C4×#3752C2semidirect
41. C2×C3×C4×D4D3semidirect
60. C22×C32×C4D4semidirect
80. C2×C4×C3⋊D3D4semidirect
131. C23×C32#41semidirect
153. C2×C32×C4#41semidirect
164. C2×C3⋊Dic3#41semidirect
170. C2×C4×D4C3⋊D3semidirect
188. C22×C3×C4#67semidirect
287. C23×C3#235semidirect
307. C2×C3×C4#235semidirect
359. C22×C4#638semidirect
406. C32#2388semidirect
422. C23#3828semidirect
449. C2×C4#3828semidirect
491. C3#82400semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C32×C4×D42
C2×C4×#6382
#105929222
C4×#37572
#105926902
#105926782
#105926592
#105926582
#105926462
C4×#37522
#824003