Finite Group Databasebeta

← #11793904

Subgroups — #11793904

Order 1152.

617 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63823C211yesmaximal, characteristic
2C2×#63649C211yesmaximal, characteristic, complemented
3C3×#5133C211yesmaximal, characteristic, complemented
4C2×C3×#823C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic, complemented
6#10591071C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70307—31nomaximal
9#70092—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3715—21no—
18#63823—22no—
19#63823—22no—
20C2×#3713—21no—
21#63649—22no—
22C3×#823—22no—
23C3×#821—21no—
24C3×#816—21no—
25#63562—22no—
26(C2×D3)⋊(C3⋊C8)—22no—
27C2×#949—31no—
28C2×#932—31no—
29C3×#417—31no—
30C2×C3×#100—31no—
31#5234—31no—
32C2×#832—31no—
33#5133D311yescharacteristic, complemented
34C2×#823D311yescharacteristic, complemented
35#5129—31no—
36C2×#822—31no—
37C2×#822—31no—
38C2×#822—61no—
39C2×#809—31no—
40#4554—31no—
41#4530—31no—
42C23×C3×D3—21no—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67—21no—
45C22×C3×Dic3—21no—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12D411yescharacteristic
56C2×C3×D12D412yes—
57C2×C3×C4×D3—21no—
58C2×C3×Dic6D411yescharacteristic
59C32×M16—21no—
60C32×M16—21no—
61C2×C32×C8—21no—
62#3748—21no—
63#3748D412yes—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)D412yes—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8—21no—
73#3715—24no—
74#3713—24no—
75#2051—91noSylow
76C2×C3×#41—31no—
77C22×C3×D4—31no—
78C2×#235C2×D311yescharacteristic
79C22×D12C2×D311yescharacteristic
80C2×C3×M16—21no—
81C2×C3×M16—31no—
82C2×C3×M16C2×D311yescharacteristic
83C2×C3×M16C2×D311yescharacteristic
84C2×C3×C4⋊C4—31no—
85#949—62no—
86#949—62no—
87C2×#215—61no—
88C2×#214—61no—
89#932—62no—
90#932—62no—
91C2×#213—61no—
92C2×#213—61no—
93C2×C4⋊Dic3C2×D311yescharacteristic
94C2×#208—31no—
95C2×#208—31no—
96C2×#208—61no—
97C2×#208C2×D311yescharacteristic
98C22×C3⋊C8—31no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—61no—
101C3×#103—61no—
102C3×#102—61no—
103C3×#100—62no—
104#832—62no—
105#830—62no—
106#823—22no—
107#822—62no—
108#822—62no—
109#822—64no—
110#821—21no—
111(C2×D3)⋊C8—62no—
112#816—21no—
113#809—62no—
114C23×C32#4111yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3—22no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—81no—
120C22×C3×D3—81no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C3×#67—41no—
128C3×#67—41no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—81no—
132C3×D12—21no—
133C3×D12—22no—
134C3×D12—22no—
135C3×D12—21no—
136C3×D12—41no—
137C3×D12—41no—
138C3×C4×D3—41no—
139C3×C4×D3—41no—
140C3×Dic6—21no—
141C3×Dic6—21no—
142C32×C8—41no—
143C3⋊(C3⋊C8)—22no—
144C3⋊(C3⋊C8)—22no—
145C3×C3⋊C8—41no—
146C2×AGL(1,ℤ/8)—91no—
147C2×#108—91no—
148#417—31no—
149C2×#102—91no—
150C2×#100—31no—
151#408—91no—
152#343—91no—
153C24×C3—61no—
154C23×D3—21no—
155C3×#41—61no—
156C3×#41—61no—
157C3×#41—61no—
158C3×#41—61no—
159C2×C3×Q8—31no—
160C2×C3×D4—32no—
161C2×C3×D4—31no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C2×C3×D4—61no—
168C22×C3×C4—21no—
169C22×C3×C4—61no—
170C22×C3×C4—61no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C2×#67—21no—
174C22×Dic3—21no—
175#235—21no—
176#235—21no—
177#235—21no—
178#235—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12#6711yescharacteristic
185C2×D12#6712yes—
186C2×C4×D3—21no—
187C2×Dic6#6711yescharacteristic
188C3×M16—22no—
189C3×M16—21no—
190C3×M16—21no—
191C3×M16—21no—
192C3×M16—21no—
193C3×M16—41no—
194C3×M16—61no—
195C3×M16—61no—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—41no—
199C2×C3×C8—61no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202#215—64no—
203#214—64no—
204#213—64no—
205#213—64no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208#208—21no—
209#208—21no—
210#208—32no—
211#208—32no—
212#208—62no—
213#208—61no—
214#208—61no—
215#208—121no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—32no—
218C2×C3⋊C8—32no—
219C2×C3⋊C8—62no—
220C2×C3⋊C8—62no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—121no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32#12111yescharacteristic
232C22×C32#12311yescharacteristic
233C22×C32#12411yescharacteristic
234C2×C3×D3—41no—
235C2×C3×D3—42no—
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C2×C3×D3—82no—
239C2×C3×D3—81no—
240C2×C3×D3—81no—
241C2×C3×D3—82no—
242C32×C4#12011yescharacteristic
243C32×C4#12111yescharacteristic
244C32×C4#12111yescharacteristic
245C32×C4#12311yescharacteristic
246C3×Dic3—41no—
247C3×Dic3—81no—
248C2×#41—31no—
249C22×D4—31no—
250AGL(1,ℤ/8)—182no—
251AGL(1,ℤ/8)—182no—
252C2×SD16—181no—
253C2×D8—181no—
254C2×M16—31no—
255C2×M16—91no—
256C2×M16D3211yescharacteristic
257C22×C8—91no—
258C2×C4⋊C4—31no—
259#108—182no—
260#103—61no—
261#102—61no—
262#102—182no—
263#100—62no—
264C22⋊C8—182no—
265C23×C3—21no—
266C23×C3—61no—
267C23×C3—62no—
268C23×C3—121no—
269C23×C3—121no—
270C23×C3—241no—
271C23×C3—241no—
272C23×C3#23511yescharacteristic
273C23×C3#23711yescharacteristic
274C22×D3—21no—
275C22×D3—22no—
276C22×D3—41no—
277C22×D3—41no—
278C22×D3—81no—
279C22×D3—81no—
280C3×Q8—61no—
281C3×Q8—61no—
282C3×D4—61no—
283C3×D4—62no—
284C3×D4—61no—
285C3×D4—62no—
286C3×D4—121no—
287C3×D4—121no—
288C3×D4—121no—
289C3×D4—121no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—61no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—241no—
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4#23511yescharacteristic
303C2×C3×C4#23511yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4#23711yescharacteristic
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313#67—41no—
314#67—41no—
315C2×Dic3—21no—
316C2×Dic3—41no—
317C2×Dic3—81no—
318D12—21no—
319D12—21no—
320D12—22no—
321D12—22no—
322D12—41no—
323D12—41no—
324C4×D3—41no—
325C4×D3—41no—
326Dic6—21no—
327Dic6—21no—
328C3×C8—42no—
329C3×C8—41no—
330C3×C8—41no—
331C3×C8—121no—
332C3⋊C8—41no—
333C3⋊C8—64no—
334C3⋊C8—62no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C3⋊C8—62no—
338C3⋊C8—122no—
339C2×C32—21no—
340C2×C32—21no—
341C2×C32#39411yescharacteristic
342C2×C32#47111yescharacteristic
343C2×C32#47211yescharacteristic
344C3×D3—81no—
345C3×D3—82no—
346C24—61no—
347#41—61no—
348#41—61no—
349#41—61no—
350#41—61no—
351C2×Q8—31no—
352C2×D4—32no—
353C2×D4—31no—
354C2×D4—61no—
355C2×D4—61no—
356C2×D4—61no—
357C2×D4—61no—
358C2×D4—61no—
359C2×D4—61no—
360C22×C4—61no—
361C22×C4—61no—
362C22×C4C2×D3211yescharacteristic
363SD16—184no—
364D8—184no—
365M16—21no—
366M16—21no—
367M16—61no—
368M16—61no—
369M16—92no—
370M16—181no—
371C2×C8—21no—
372C2×C8—61no—
373C2×C8—92no—
374C2×C8—181no—
375C2×C8—181no—
376C2×C8—181no—
377C4⋊C4—61no—
378C4⋊C4—61no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3—121no—
389C22×C3—122no—
390C22×C3—121no—
391C22×C3—121no—
392C22×C3—242no—
393C22×C3—242no—
394C22×C3—241no—
395C22×C3—241no—
396C22×C3#88311yescharacteristic
397C22×C3#88411yescharacteristic
398C22×C3#88511yescharacteristic
399C22×C3#88511yescharacteristic
400C22×C3#92911yescharacteristic
401C22×C3#93911yescharacteristic
402C2×D3—41no—
403C2×D3—41no—
404C2×D3—41no—
405C2×D3—42no—
406C2×D3—82no—
407C2×D3—81no—
408C2×D3—81no—
409C2×D3—82no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—121no—
415C3×C4—241no—
416C3×C4#88311yescharacteristic
417C3×C4#88411yescharacteristic
418C3×C4#88411yescharacteristic
419C3×C4#88411yescharacteristic
420C3×C4#92911yescharacteristic
421C3×C4#93711yescharacteristic
422C3×C4#93711yescharacteristic
423C3×C4#93911yescharacteristic
424Dic3—41no—
425Dic3—81no—
426C32#205111yescharacteristic, complemented, Sylow
427C23—61no—
428C23—62no—
429C23—121no—
430C23—121no—
431C23—241no—
432C23—241no—
433C23#379511yescharacteristic
434Q8—61no—
435Q8—61no—
436D4—62no—
437D4—61no—
438D4—61no—
439D4—62no—
440D4—121no—
441D4—121no—
442D4—121no—
443D4—121no—
444C2×C4—61no—
445C2×C4—121no—
446C2×C4—121no—
447C2×C4—121no—
448C2×C4—241no—
449C2×C4#379511yescharacteristic
450C2×C4#379811yescharacteristic
451C2×C4#380211yescharacteristic
452C2×C4D3×#6711yescharacteristic
453C2×C4D3×#6711yescharacteristic
454C2×C4#381111yescharacteristic
455C8—41no—
456C8—121no—
457C8—182no—
458C8—182no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—242no—
469C2×C3—241no—
470C2×C3#474811yescharacteristic
471C2×C3#474911yescharacteristic
472C2×C3#495911yescharacteristic
473C2×C3#495911yescharacteristic
474C2×C3#519911yescharacteristic
475C2×C3#520311yescharacteristic
476D3—81no—
477D3—82no—
478C22—21no—
479C22—21no—
480C22—121no—
481C22—121no—
482C22—121no—
483C22—122no—
484C22—242no—
485C22—242no—
486C22—241no—
487C22—241no—
488C22#6388511yescharacteristic
489C22#6390511yescharacteristic
490C22#6391311yescharacteristic
491C4—121no—
492C4—241no—
493C4#6388511yescharacteristic
494C4#6390511yescharacteristic
495C4#6391211yescharacteristic
496C4#6398311yescharacteristic
497C3—21no—
498C3#7009211yescharacteristic, complemented
499C3#7030711yescharacteristic, complemented
500C2—21no—
501C2—21no—
502C2—241no—
503C2—242no—
504C2#1059097911yescharacteristic
505C2#1059098211yescharacteristic
506C2#1059138811yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#63823C2
hypercenterC2×M16D32
hypocenterC32#2051
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63649C2semidirect
3. C3×#5133C2semidirect
4. C2×C3×#823C2semidirect
5. C2×#63562C2semidirect
6. #10591071C2semidirect
7. #10589167C2semidirect
33. #5133D3semidirect
34. C2×#823D3semidirect
426. C32#2051semidirect
498. C3#70092semidirect
499. C3#70307semidirect

Maximal subgroups

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

subgroupindex
C2×#638232
C2×#636492
C3×#51332
C2×C3×#8232
C2×#635622
#105910712
#105891672
#703073
#700923