Finite Group Databasebeta

← #11868819

Subgroups — #11868819

Order 1152.

987 conjugacy classes of subgroups.

The subgroup lattice has 571 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C2×C3×#869C211yesmaximal, characteristic, complemented
3C3×#4924C211yesmaximal, characteristic, complemented
4#10591130C212yesmaximal, complemented
5#10591106C212yesmaximal
6#10590313C212yesmaximal, complemented
7#10590307C212yesmaximal, complemented
8#10590300C212yesmaximal, complemented
9#10590284C212yesmaximal, complemented
10#83212—31nomaximal
11#79060—31nomaximal
12C2×#3828C2211yescharacteristic
13C22×C3×Dic6—21no—
14C2×C32×C42C2211yescharacteristic
15C4×#638—21no—
16C4×#638—21no—
17#64135C2211yescharacteristic
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20#64081—21no—
21C42×C3⋊D3—21no—
22C4×#634C2211yescharacteristic
23C4×#634C2211yescharacteristic
24C2×C3×C4⋊Dic3—21no—
25C2×C3×C4⋊Dic3C2212yes—
26C2×C3×#208C2212yes—
27C3×#869—21no—
28C3×#869—21no—
29C3×#869C2212yes—
30C3×#869C2212yes—
31C3×C4⋊(C3⋊C8)C2212yes—
32C3×C4⋊(C3⋊C8)C2212yes—
33#63575C2214yes—
34#63573C2214yes—
35#63567C2214yes—
36#63564C2214yes—
37C2×C3×C4⋊Q8—31no—
38C4×#235—31no—
39C4×#235—31no—
40C4×#235—61no—
41C2×#869D311yescharacteristic, complemented
42C3×#423—31no—
43#5133—32no—
44#5121—32no—
45#5094—32no—
46#5091—32no—
47#5087—32no—
48#5084—32no—
49#4966—32no—
50#4964—32no—
51#4924D311yescharacteristic, complemented
52#4851—32no—
53#4850—32no—
54#4846—32no—
55#4842—32no—
56C22×C32×C4D411yescharacteristic
57C22×C32×C4D411yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C2×#638—21no—
60#3828—22no—
61#3828Q814yescomplemented
62C2×C4⋊(C3⋊D3)C2311yescharacteristic
63C2×C4×C3⋊D3—21no—
64C2×C4×C3⋊D3—21no—
65C2×C4×C3⋊D3—21no—
66C2×#634C2311yescharacteristic
67C22×C3×Dic3—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—44no—
71C32×C42D411yescharacteristic
72C32×C42D411yescharacteristic
73C32×C42C2311yescharacteristic
74C32×C42C2311yescharacteristic
75#3757—21no—
76#3752—21no—
77#3752—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80#3750—21no—
81#3750—21no—
82C4×C3⋊Dic3—21no—
83C4×C3⋊Dic3—21no—
84C4×C3⋊Dic3—21no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3—22no—
88C3×C4⋊Dic3C2314yes—
89C3×#208—24no—
90C2×C3×C3⋊C8C2314yes—
91#3079—91noSylow
92C22×C3×Q8—61no—
93C2×#235—31no—
94C2×#235—31no—
95C2×#235—61no—
96C22×Dic6—21no—
97C2×C3×M16—32no—
98C3×C4⋊Q8—32no—
99C3×C4⋊Q8—32no—
100C3×C4⋊Q8—61no—
101C3×C4⋊Q8—61no—
102C2×C3×C4⋊C4—32no—
103C2×C3×C4⋊C4—61no—
104C2×C3×C42—21no—
105C2×C3×C42C2×D311yescharacteristic
106C2×C3×C42C2×D311yescharacteristic
107C4×#67—62no—
108C4×#67—62no—
109C4×#67—61no—
110C4×#67—61no—
111C4×#67—61no—
112C4×#67—61no—
113#926—31no—
114#926—31no—
115#926—61no—
116C2×C4⋊Dic3—21no—
117C2×C4⋊Dic3C2×D312yes—
118C2×#208C2×D312yes—
119C4×D12—31no—
120C4×D12—31no—
121C4×D12—31no—
122C4×D12—31no—
123C4×D12—61no—
124C4×D12—61no—
125#872—62no—
126#872—61no—
127#872—61no—
128C42×D3—62no—
129C42×D3—61no—
130C42×D3—61no—
131#869—21no—
132#869—21no—
133#869C2×D312yes—
134#869C2×D312yes—
135C4×Dic6—31no—
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6—61no—
141C3×C4⋊C8—32no—
142C3×C4⋊C8—32no—
143#821—34no—
144#818—34no—
145#817—34no—
146#816—34no—
147#810—34no—
148#809—34no—
149#808—34no—
150#807—34no—
151C4⋊(C3⋊C8)C2×D312yes—
152C4⋊(C3⋊C8)C2×D312yes—
153C23×C32C2×D411yescharacteristic
154C22×C3⋊D3—21no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×Q812yes—
163C2×C32×C4#4112yes—
164C2×C32×C4C2411yescharacteristic
165#638—24no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—21no—
168C2×C3⋊Dic3—21no—
169C4⋊(C3⋊D3)—21no—
170C4⋊(C3⋊D3)C2×Q812yescomplemented
171C4×C3⋊D3—24no—
172C4×C3⋊D3—42no—
173C4×C3⋊D3—42no—
174#634—21no—
175#634C2×Q812yescomplemented
176C2×C3×Dic3—24no—
177C2×C3×Dic3—44no—
178C3×Dic6—44no—
179C3×Dic6—44no—
180C3×C3⋊C8—24no—
181C2×C4⋊Q8—31no—
182C4×#41—91no—
183#477—92no—
184#476—92no—
185#475—92no—
186#474—92no—
187#428—92no—
188#423—31no—
189#417—92no—
190C2×C3×Q8—62no—
191C2×C3×Q8—62no—
192C2×C3×Q8—124no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—62no—
197C22×C3×C4D1211yescharacteristic
198C22×C3×C4D1211yescharacteristic
199C22×C3×C4#6711yescharacteristic
200C22×C3×C4#6711yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C2×#67—62no—
204C2×#67—61no—
205C2×#67—61no—
206C22×Dic3—22no—
207#235—34no—
208#235—34no—
209#235—64no—
210#235—64no—
211#235—62no—
212#235—62no—
213C2×D12—31no—
214C2×D12—31no—
215C2×D12—61no—
216C2×C4×D3—62no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—62no—
220C2×C4×D3—62no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×Dic6—22no—
226C2×Dic6—22no—
227C2×Dic6—31no—
228C2×Dic6—31no—
229C2×Dic6—44no—
230C2×Dic6—61no—
231C3×M16—64no—
232C2×C3×C8—34no—
233C3×C4⋊C4—34no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C42—21no—
238C3×C42—21no—
239C3×C42—21no—
240C3×C42—21no—
241C3×C42D1211yescharacteristic
242C3×C42D1211yescharacteristic
243C3×C42#6711yescharacteristic
244C3×C42#6711yescharacteristic
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D311yescharacteristic
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D311yescharacteristic
249#217—62no—
250#217—61no—
251#217—61no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—61no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—61no—
258C4⋊Dic3—22no—
259C4⋊Dic3—22no—
260C4⋊Dic3—22no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—31no—
265C4⋊Dic3—61no—
266C4⋊Dic3—61no—
267C4⋊Dic3C22×D314yes—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—61no—
271Dic3⋊C4—61no—
272Dic3⋊C4—61no—
273Dic3⋊C4—61no—
274C4×Dic3—62no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—61no—
278C4×Dic3—61no—
279C4×Dic3—61no—
280C4×Dic3—61no—
281C4×Dic3—61no—
282C4×Dic3—61no—
283#208—24no—
284C2×C3⋊C8C22×D314yes—
285C22×C32—21no—
286C22×C32—21no—
287C22×C32C22⋊Q812yes—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—22no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—41no—
292C32×C4—21no—
293C32×C4—21no—
294C32×C4C22⋊Q812yes—
295C32×C4AGL(1,ℤ/8)12yes—
296C32×C4#13712yes—
297C32×C4C22×Q811yescharacteristic
298C32×C4C2×#4111yescharacteristic
299C3⋊Dic3—22no—
300C3⋊Dic3—41no—
301C3⋊Dic3—41no—
302C3×Dic3—44no—
303C2×#41—91no—
304C22×Q8—61no—
305C2×M16—32no—
306C4⋊Q8—32no—
307C4⋊Q8—32no—
308C4⋊Q8—61no—
309C4⋊Q8—61no—
310C4×Q8—91no—
311C4×Q8—91no—
312C4×D4—91no—
313C4×D4—91no—
314C4×D4—181no—
315C4×D4—181no—
316#117—91no—
317#117—181no—
318C2×C4⋊C4—32no—
319C2×C4⋊C4—61no—
320C2×C42—181no—
321C2×C42D3211yescharacteristic
322#107—94no—
323#106—94no—
324C4⋊C8—32no—
325C4⋊C8—32no—
326#103—94no—
327#102—94no—
328C23×C3—21no—
329C23×C3C2×D1211yescharacteristic
330C23×C3C2×#6711yescharacteristic
331C22×D3—62no—
332C22×D3—61no—
333C22×D3—61no—
334C3×Q8—124no—
335C3×Q8—124no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—42no—
349C2×C3×C4—42no—
350C2×C3×C4—64no—
351C2×C3×C4—124no—
352C2×C3×C4C2×D1211yescharacteristic
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4C2×D1211yescharacteristic
357C2×C3×C4#23712yes—
358C2×C3×C4D3×Q812yes—
359C2×C3×C4D3×Q812yes—
360C2×C3×C4#23912yes—
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C2×#6711yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368#67—68no—
369#67—64no—
370#67—64no—
371C2×Dic3—24no—
372C2×Dic3—44no—
373C2×Dic3—62no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—61no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—61no—
382D12—32no—
383D12—32no—
384D12—62no—
385D12—62no—
386D12—61no—
387D12—61no—
388C4×D3—68no—
389C4×D3—64no—
390C4×D3—64no—
391C4×D3—124no—
392C4×D3—124no—
393C4×D3—122no—
394C4×D3—122no—
395C4×D3—122no—
396C4×D3—122no—
397Dic6—32no—
398Dic6—32no—
399Dic6—44no—
400Dic6—44no—
401Dic6—62no—
402Dic6—62no—
403Dic6—61no—
404Dic6—61no—
405C3×C8—64no—
406C3⋊C8—24no—
407C2×C32—22no—
408C2×C32C2×C22⋊Q811yescharacteristic
409C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
410C2×C32C2×#13711yescharacteristic
411C3⋊D3—42no—
412#41—94no—
413#41—182no—
414C2×Q8—62no—
415C2×Q8—62no—
416C2×Q8—91no—
417C2×Q8—124no—
418C2×D4—91no—
419C2×D4—181no—
420C22×C4—62no—
421C22×C4—181no—
422C22×C4—181no—
423C22×C4—181no—
424C22×C4#62611yescharacteristic
425C22×C4#62611yescharacteristic
426C22×C4C2×D3211yescharacteristic
427M16—64no—
428C2×C8—34no—
429C4⋊C4—34no—
430C4⋊C4—62no—
431C4⋊C4—62no—
432C4⋊C4—62no—
433C4⋊C4—91no—
434C4⋊C4—91no—
435C4⋊C4—181no—
436C4⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C22⋊C4—181no—
440C42—181no—
441C42—181no—
442C42—181no—
443C42#62611yescharacteristic
444C42#62611yescharacteristic
445C42C2×D3211yescharacteristic
446C42C2×D3211yescharacteristic
447C22×C3—21no—
448C22×C3—21no—
449C22×C3—21no—
450C22×C3—21no—
451C22×C3—21no—
452C22×C3—22no—
453C22×C3—41no—
454C22×C3—41no—
455C22×C3#89712yes—
456C22×C3#94612yes—
457C22×C3C22×D1211yescharacteristic
458C22×C3C22×#6711yescharacteristic
459C2×D3—64no—
460C2×D3—62no—
461C2×D3—62no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—121no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—21no—
473C3×C4—21no—
474C3×C4—22no—
475C3×C4—22no—
476C3×C4—22no—
477C3×C4—41no—
478C3×C4—41no—
479C3×C4—124no—
480C3×C4#89712yes—
481C3×C4#90812yes—
482C3×C4#90912yes—
483C3×C4#93212yes—
484C3×C4#94212yes—
485C3×C4#94612yes—
486C3×C4C2×#23711yescharacteristic
487C3×C4C2×D3×Q811yescharacteristic
488C3×C4C2×D3×Q811yescharacteristic
489C3×C4C2×#23911yescharacteristic
490Dic3—44no—
491Dic3—64no—
492Dic3—62no—
493Dic3—62no—
494Dic3—122no—
495Dic3—122no—
496Dic3—121no—
497Dic3—121no—
498Dic3—121no—
499Dic3—121no—
500C32#307911yescharacteristic, complemented, Sylow
501C23—181no—
502C23C2×#62611yescharacteristic
503Q8—92no—
504Q8—124no—
505Q8—124no—
506Q8—181no—
507D4—92no—
508D4—184no—
509D4—181no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—64no—
513C2×C4—124no—
514C2×C4—181no—
515C2×C4—184no—
516C2×C4—181no—
517C2×C4—181no—
518C2×C4—362no—
519C2×C4—362no—
520C2×C4#379612yes—
521C2×C4#379712yes—
522C2×C4C2×#62611yescharacteristic
523C2×C4C2×#62611yescharacteristic
524C2×C4C2×#62611yescharacteristic
525C2×C4C2×#62611yescharacteristic
526C2×C4C2×#62611yescharacteristic
527C2×C4C22×D3211yescharacteristic
528C8—64no—
529C2×C3—22no—
530C2×C3—22no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—42no—
535C2×C3C2×#89711yescharacteristic
536C2×C3C2×#90811yescharacteristic
537C2×C3C2×#90911yescharacteristic
538C2×C3C2×#93211yescharacteristic
539C2×C3C2×#94211yescharacteristic
540C2×C3C2×#94611yescharacteristic
541D3—124no—
542D3—122no—
543D3—122no—
544C22—21no—
545C22—21no—
546C22—182no—
547C22—361no—
548C22—361no—
549C22#6387112yes—
550C22C22×#62611yescharacteristic
551C4—21no—
552C4—21no—
553C4—124no—
554C4—182no—
555C4—361no—
556C4—361no—
557C4#6383012yes—
558C4#6383312yes—
559C4#6387112yes—
560C4C2×#379611yescharacteristic
561C4C2×#379711yescharacteristic
562C3—21no—
563C3#7906011yescharacteristic, complemented
564C3#8321211yescharacteristic, complemented
565C2—22no—
566C2—362no—
567C2C2×#6383011yescharacteristic
568C2C2×#6383311yescharacteristic
569C2C2×#6387111yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
hypercenterC2×C42D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#869C2semidirect
3. C3×#4924C2semidirect
4. #10591130C2semidirect
6. #10590313C2semidirect
7. #10590307C2semidirect
8. #10590300C2semidirect
9. #10590284C2semidirect
41. C2×#869D3semidirect
51. #4924D3semidirect
61. #3828Q8semidirect
170. C4⋊(C3⋊D3)C2×Q8semidirect
175. #634C2×Q8semidirect
500. C32#3079semidirect
563. C3#79060semidirect
564. C3#83212semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C2×C3×#8692
C3×#49242
#105911302
#105911062
#105903132
#105903072
#105903002
#105902842
#832123
#790603