Finite Group Databasebeta

← #11808213

Subgroups — #11808213

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×C4×#638C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊(C3⋊D3)C212yesmaximal, complemented
4C32×C4×C22⋊C4C211yesmaximal, characteristic, complemented
5#10592660C212yesmaximal, complemented
6#10592659C212yesmaximal, complemented
7C4×#3752C212yesmaximal, complemented
8#10592372C211yesmaximal, characteristic, complemented
9#10592371C211yesmaximal, characteristic, complemented
10#10592370C211yesmaximal, characteristic, complemented
11#10592355C211yesmaximal, characteristic, complemented
12#73580—34nomaximal
13C23×C32×C4C2211yescharacteristic
14C22×#638C2212yes—
15C22×#638C2211yescharacteristic
16C2×#3828—24no—
17C2×#3828—28no—
18C22×C4⋊(C3⋊D3)C2212yes—
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C4×C3⋊D3C2212yes—
22C22×#634C2211yescharacteristic
23C2×C32×C22⋊C4C2212yes—
24C2×C32×C42C2212yes—
25C2×#3757C2211yescharacteristic
26C4×#638—24no—
27C2×#3752C2212yes—
28C2×#3752C2212yes—
29C2×#3752C2211yescharacteristic
30C2×#3752C2212yes—
31C2×#3752C2212yes—
32C2×C4⋊(C3⋊Dic3)C2212yes—
33C2×#3750C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic
35C4×C4⋊(C3⋊D3)—28no—
36C32×#95C2211yescharacteristic
37C32×#95C2211yescharacteristic
38#63658C2212yes—
39#63658C2212yes—
40C22×#235—34no—
41C2×C4×#67—34no—
42C2×C4×D12—38no—
43C3×C4×C22⋊C4D314yescomplemented
44#4961—38no—
45#4960—38no—
46C4×(C2×D3)⋊C4—38no—
47#4673—34no—
48#4672—34no—
49#4671—34no—
50#4656—34no—
51C24×C32C2311yescharacteristic
52C23×C3⋊D3C2312yes—
53C23×C3⋊D3C2311yescharacteristic
54C22×C32×C4—24no—
55C22×C32×C4D414yescomplemented
56C22×C32×C4C2312yes—
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×#638—24no—
61C2×#638—22no—
62C2×#638—24no—
63C2×#638—22no—
64C2×#638—24no—
65C2×#638—22no—
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2311yescharacteristic
70#3828—232no—
71C2×C4⋊(C3⋊D3)—24no—
72C2×C4⋊(C3⋊D3)—24no—
73C2×C4⋊(C3⋊D3)—24no—
74C2×C4⋊(C3⋊D3)—22no—
75C2×C4⋊(C3⋊D3)—24no—
76C2×C4×C3⋊D3—24no—
77C2×C4×C3⋊D3—24no—
78C2×C4×C3⋊D3—24no—
79C2×C4×C3⋊D3—22no—
80C2×C4×C3⋊D3D418yescomplemented
81C2×#634—22no—
82C2×#634—24no—
83C32×C22⋊C4—24no—
84C32×C42—24no—
85#3757—22no—
86#3752—24no—
87#3752—22no—
88#3752—24no—
89#3752—24no—
90#3752—24no—
91C4⋊(C3⋊Dic3)—24no—
92#3750—22no—
93C4×C3⋊Dic3—22no—
94#2388—91noSylow
95C23×C3×C4C2×D314yes—
96C22×#67—38no—
97C22×#67—34no—
98C2×#235—632no—
99C2×#235—616no—
100C22×D12—34no—
101C22×D12—38no—
102C22×C4×D3—38no—
103C22×C4×D3—34no—
104C22×Dic6—34no—
105C2×C3×C22⋊C4C2×D318yes—
106C2×C3×C42C2×D318yes—
107C2×#217—34no—
108C4×#67—616no—
109C2×(C2×D3)⋊C4—34no—
110C2×(C2×D3)⋊C4—38no—
111C2×(C2×D3)⋊C4—38no—
112C2×(C2×D3)⋊C4—38no—
113C2×(C2×D3)⋊C4—38no—
114C2×C4⋊Dic3—38no—
115C2×Dic3⋊C4—34no—
116C2×C4×Dic3—34no—
117C4×D12—632no—
118C3×#95C2×D314yes—
119C3×#95C2×D314yes—
120C3⋊#95—38no—
121C3⋊#95—38no—
122C23×C32—22no—
123C23×C32—22no—
124C23×C32—21no—
125C23×C32—21no—
126C23×C32C2×D412yes—
127C23×C32C2411yescharacteristic
128C22×C3⋊D3—22no—
129C22×C3⋊D3—21no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—22no—
132C22×C3⋊D3—22no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3—22no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—21no—
138C22×C3⋊D3C2×D414yes—
139C22×C3⋊D3#4112yescomplemented
140C2×C32×C4—22no—
141C2×C32×C4—22no—
142C2×C32×C4—22no—
143C2×C32×C4—28no—
144C2×C32×C4—22no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2×D414yes—
150C2×C32×C4#4114yescomplemented
151#638—216no—
152#638—28no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—21no—
159C2×C3⋊Dic3—22no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3C2×D414yes—
162C2×C3⋊Dic3#4112yescomplemented
163C4⋊(C3⋊D3)—216no—
164C4⋊(C3⋊D3)—28no—
165C4×C3⋊D3—216no—
166C4×C3⋊D3—44no—
167#634—28no—
168C22×#41—91no—
169C2×C4×D4—91no—
170C2×C4×D4—92no—
171#395—91no—
172#394—92no—
173#394—91no—
174#393—91no—
175#392—92no—
176#392—91no—
177C4×C22⋊C4—92no—
178C4×C22⋊C4C3⋊D311yescharacteristic, complemented
179C24×C3C22×D314yes—
180C23×D3—38no—
181C23×D3—34no—
182C22×C3×C4—216no—
183C22×C3×C4D12116yescomplemented
184C22×C3×C4C22×D318yes—
185C22×C3×C4C22×D314yes—
186C22×C3×C4C22×D318yes—
187C22×C3×C4C22×D314yes—
188C2×#67—616no—
189C2×#67—68no—
190C2×#67—616no—
191C2×#67—68no—
192C2×#67—68no—
193C2×#67—616no—
194C22×Dic3—34no—
195C22×Dic3—38no—
196C22×Dic3—34no—
197C22×Dic3—34no—
198#235—6128no—
199C2×D12—616no—
200C2×D12—616no—
201C2×D12—616no—
202C2×D12—68no—
203C2×D12—616no—
204C2×C4×D3—332no—
205C2×C4×D3—616no—
206C2×C4×D3—616no—
207C2×C4×D3—68no—
208C2×C4×D3—616no—
209C2×Dic6—616no—
210C2×Dic6—68no—
211C3×C22⋊C4—216no—
212C3×C42—216no—
213#217—68no—
214(C2×D3)⋊C4—616no—
215(C2×D3)⋊C4—616no—
216(C2×D3)⋊C4—616no—
217(C2×D3)⋊C4—68no—
218(C2×D3)⋊C4—616no—
219C4⋊Dic3—616no—
220Dic3⋊C4—68no—
221C4×Dic3—68no—
222C22×C32—22no—
223C22×C32—22no—
224C22×C32—22no—
225C22×C32—42no—
226C22×C32—42no—
227C22×C32C22×D411yescharacteristic
228C22×C32C22×D412yes—
229C22×C32C2×#4112yes—
230C22×C32C2×#4111yescharacteristic
231C22×C32C2×#4111yescharacteristic
232C2×C3⋊D3—24no—
233C2×C3⋊D3—24no—
234C2×C3⋊D3—24no—
235C2×C3⋊D3—22no—
236C2×C3⋊D3—24no—
237C2×C3⋊D3—41no—
238C2×C3⋊D3—42no—
239C2×C3⋊D3—42no—
240C2×C3⋊D3—41no—
241C2×C3⋊D3—42no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—42no—
244C32×C4—22no—
245C32×C4—24no—
246C32×C4—42no—
247C32×C4#12014yes—
248C3⋊Dic3—24no—
249C3⋊Dic3—22no—
250C3⋊Dic3—41no—
251C3⋊Dic3—41no—
252C2×#41—188no—
253C2×#41—184no—
254C22×Q8—91no—
255C22×D4—91no—
256C22×D4—92no—
257C22×D4—92no—
258C22×D4—91no—
259C23×C4—92no—
260C23×C4—91no—
261C23×C4C2×C3⋊D311yescharacteristic
262C4×D4—188no—
263C4×D4—184no—
264C2×C4⋊C4—91no—
265C2×C4⋊C4—92no—
266C2×C22⋊C4—91no—
267C2×C22⋊C4—92no—
268C2×C22⋊C4—91no—
269C2×C22⋊C4—92no—
270C2×C22⋊C4—92no—
271C2×C22⋊C4—92no—
272C2×C22⋊C4C2×C3⋊D312yes—
273C2×C42—91no—
274C2×C42C2×C3⋊D312yes—
275#95—92no—
276#95—92no—
277#95C2×C3⋊D311yescharacteristic
278#95C2×C3⋊D311yescharacteristic
279C23×C3—28no—
280C23×C3—28no—
281C23×C3—24no—
282C23×C3—24no—
283C23×C3C2×D1218yes—
284C23×C3C23×D314yes—
285C22×D3—316no—
286C22×D3—38no—
287C22×D3—64no—
288C22×D3—68no—
289C22×D3—68no—
290C22×D3—68no—
291C22×D3—68no—
292C22×D3—68no—
293C22×D3—68no—
294C22×D3—68no—
295C22×D3—68no—
296C22×D3—64no—
297C2×C3×C4—28no—
298C2×C3×C4—28no—
299C2×C3×C4—28no—
300C2×C3×C4—232no—
301C2×C3×C4—28no—
302C2×C3×C4—28no—
303C2×C3×C4—28no—
304C2×C3×C4C2×D1218yes—
305C2×C3×C4C2×D1218yes—
306C2×C3×C4#235116yescomplemented
307C2×C3×C4D3×D4116yes—
308#67—664no—
309#67—632no—
310C2×Dic3—316no—
311C2×Dic3—38no—
312C2×Dic3—64no—
313C2×Dic3—68no—
314C2×Dic3—68no—
315C2×Dic3—64no—
316C2×Dic3—64no—
317C2×Dic3—64no—
318C2×Dic3—68no—
319C2×Dic3—68no—
320D12—664no—
321D12—632no—
322C4×D3—664no—
323C4×D3—1216no—
324Dic6—632no—
325C2×C32—42no—
326C2×C32C2×#12011yescharacteristic
327C2×C32#52511yescharacteristic
328C2×C32#52512yes—
329C2×C32#53211yescharacteristic
330C2×C32#53212yes—
331C3⋊D3—44no—
332C3⋊D3—42no—
333C24—92no—
334C24—91no—
335C24C22×C3⋊D311yescharacteristic
336#41—1832no—
337C2×Q8—184no—
338C2×Q8—182no—
339C2×D4—184no—
340C2×D4—184no—
341C2×D4—184no—
342C2×D4—184no—
343C2×D4—182no—
344C2×D4—184no—
345C2×D4—182no—
346C2×D4—182no—
347C2×D4—184no—
348C2×D4—182no—
349C2×D4—184no—
350C22×C4—24no—
351C22×C4—91no—
352C22×C4—92no—
353C22×C4—98no—
354C22×C4—91no—
355C22×C4—91no—
356C22×C4—184no—
357C22×C4—184no—
358C22×C4—182no—
359C22×C4—184no—
360C22×C4C4⋊(C3⋊D3)14yescomplemented
361C22×C4C22×C3⋊D312yes—
362C22×C4C22×C3⋊D311yescharacteristic
363C22×C4C22×C3⋊D312yes—
364C22×C4C22×C3⋊D311yescharacteristic
365C4⋊C4—184no—
366C4⋊C4—182no—
367C22⋊C4—24no—
368C22⋊C4—184no—
369C22⋊C4—184no—
370C22⋊C4—184no—
371C22⋊C4—182no—
372C22⋊C4—182no—
373C22⋊C4—184no—
374C42—24no—
375C42—182no—
376C22×C3—28no—
377C22×C3—28no—
378C22×C3—28no—
379C22×C3—48no—
380C22×C3—48no—
381C22×C3C22×D1214yes—
382C22×C3C2×#23518yes—
383C22×C3C2×D3×D418yes—
384C22×C3D3×#4114yes—
385C22×C3D3×#4114yes—
386C2×D3—616no—
387C2×D3—68no—
388C2×D3—616no—
389C2×D3—616no—
390C2×D3—616no—
391C2×D3—124no—
392C2×D3—128no—
393C2×D3—124no—
394C2×D3—128no—
395C2×D3—128no—
396C2×D3—128no—
397C2×D3—128no—
398C3×C4—28no—
399C3×C4—216no—
400C3×C4—48no—
401C3×C4#882116yes—
402Dic3—616no—
403Dic3—68no—
404Dic3—124no—
405Dic3—124no—
406C32#238811yescharacteristic, complemented, Sylow
407C23—22no—
408C23—22no—
409C23—21no—
410C23—21no—
411C23—94no—
412C23—92no—
413C23—181no—
414C23—182no—
415C23—182no—
416C23—182no—
417C23—182no—
418C23—182no—
419C23—182no—
420C23—182no—
421C23—181no—
422C23—182no—
423C23C2×C4⋊(C3⋊D3)12yes—
424C23C23×C3⋊D311yescharacteristic
425Q8—188no—
426D4—188no—
427D4—1816no—
428D4—1816no—
429D4—188no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—28no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—94no—
438C2×C4—92no—
439C2×C4—181no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4—181no—
443C2×C4—1816no—
444C2×C4—181no—
445C2×C4—181no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—364no—
449C2×C4C2×C4⋊(C3⋊D3)12yes—
450C2×C4C2×C4⋊(C3⋊D3)12yes—
451C2×C4#382814yescomplemented
452C2×C4D4×C3⋊D314yes—
453C2×C3—48no—
454C2×C3#547714yes—
455C2×C3C2×#88214yes—
456C2×C3#552414yes—
457C2×C3#554718yes—
458C2×C3#554818yes—
459D3—1216no—
460D3—128no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—42no—
465C22—42no—
466C22—184no—
467C22—182no—
468C22—184no—
469C22—184no—
470C22—184no—
471C22—361no—
472C22—362no—
473C22—361no—
474C22—362no—
475C22—362no—
476C22—362no—
477C22—362no—
478C22C22×C4⋊(C3⋊D3)11yescharacteristic
479C22C2×#382812yes—
480C22C2×D4×C3⋊D312yes—
481C22#41×C3⋊D311yescharacteristic
482C22#41×C3⋊D311yescharacteristic
483C4—22no—
484C4—24no—
485C4—42no—
486C4—184no—
487C4—182no—
488C4—361no—
489C4—361no—
490C4#6409114yes—
491C3#7358014yescomplemented
492C2—42no—
493C2—364no—
494C2—362no—
495C2#1059594811yescharacteristic
496C2C2×#6409111yescharacteristic
497C2#1059599511yescharacteristic
498C2#1059601812yes—
499C2#1059601912yes—
subgroupG/H
centerC22×C4C22×C3⋊D3
commutator, socle, cosocleC23×C32C24
FrattiniC23C23×C3⋊D3
FittingC32×C4×C22⋊C4C2
hypercenterC4×C22⋊C4C3⋊D3
hypocenterC32#2388
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C2×C4×#638C2semidirect
3. C2×C4×C4⋊(C3⋊D3)C2semidirect
4. C32×C4×C22⋊C4C2semidirect
5. #10592660C2semidirect
6. #10592659C2semidirect
7. C4×#3752C2semidirect
8. #10592372C2semidirect
9. #10592371C2semidirect
10. #10592370C2semidirect
11. #10592355C2semidirect
43. C3×C4×C22⋊C4D3semidirect
55. C22×C32×C4D4semidirect
80. C2×C4×C3⋊D3D4semidirect
139. C22×C3⋊D3#41semidirect
150. C2×C32×C4#41semidirect
162. C2×C3⋊Dic3#41semidirect
178. C4×C22⋊C4C3⋊D3semidirect
183. C22×C3×C4D12semidirect
306. C2×C3×C4#235semidirect
360. C22×C4C4⋊(C3⋊D3)semidirect
406. C32#2388semidirect
451. C2×C4#3828semidirect
491. C3#73580semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C4×#6382
C2×C4×C4⋊(C3⋊D3)2
C32×C4×C22⋊C42
#105926602
#105926592
C4×#37522
#105923722
#105923712
#105923702
#105923552
#735803