Finite Group Databasebeta

← #11793907

Subgroups — #11793907

Order 1152.

613 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic
2C2×C3×#822C211yesmaximal, characteristic, complemented
3#10591088C211yesmaximal, characteristic, complemented
4C2×#63563C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6#10591070C211yesmaximal, characteristic, complemented
7#10589420C211yesmaximal, characteristic, complemented
8#72093—31nomaximal
9#70714—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C3×#908—22no—
18C3×#908—22no—
19C2×C3×D24—21no—
20C2×C3×#204—21no—
21C3×#822—22no—
22#63566—21no—
23#63563—21no—
24#63563—22no—
25#63558—22no—
26(C2×D3)⋊(C3⋊C8)—22no—
27C2×C3×AGL(1,ℤ/8)—31no—
28C2×#908D311yescharacteristic
29C2×C3×#108—31no—
30#5234—31no—
31#5232—31no—
32C2×#833—31no—
33C2×#832—31no—
34#5133—31no—
35C2×#823—31no—
36C2×#822D311yescharacteristic, complemented
37C2×#821—31no—
38#5110—31no—
39#4554—31no—
40#4554—31no—
41#4554—61no—
42C23×C3×D3—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C2×C3×#67—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×M16D412yes—
61C2×C32×C8—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64#3748—21no—
65#3748—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×#208—21no—
68C3×#208—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73C3×D24—24no—
74C3×#204—24no—
75#2051—91noSylow
76C2×C3×#41—31no—
77C22×C3×D4—31no—
78C2×#235C2×D311yescharacteristic
79C22×D12C2×D311yescharacteristic
80C3×AGL(1,ℤ/8)—62no—
81C3×AGL(1,ℤ/8)—62no—
82C2×C3×SD16—61no—
83C2×C3×D8—61no—
84C2×C3×M16—21no—
85C2×C3×M16—31no—
86C2×C3×M16C2×D311yescharacteristic
87C2×C3×M16C2×D311yescharacteristic
88C22×C3×C8—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—61no—
92C2×#208—31no—
93C2×#208—31no—
94C2×#208—61no—
95C2×#208C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97#908—22no—
98#908—22no—
99C2×D24—21no—
100C2×#204—21no—
101C3×#108—62no—
102#835—61no—
103#833—62no—
104#832—61no—
105#832—62no—
106#830—62no—
107#823—62no—
108#822—22no—
109#821—62no—
110#821—61no—
111(C2×D3)⋊C8—62no—
112#816—61no—
113C23×C32#4111yescharacteristic
114C22×C3×D3—21no—
115C22×C3×D3—22no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C22×C3×D3—81no—
119C22×C3×D3—81no—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—81no—
128C3×#67—41no—
129C3×#67—41no—
130C2×C3×Dic3—21no—
131C3×D12—22no—
132C3×D12—21no—
133C3×D12—22no—
134C3×D12—21no—
135C3×D12—41no—
136C3×D12—41no—
137C3×C4×D3—41no—
138C3×C4×D3—41no—
139C3×Dic6—21no—
140C3×Dic6—21no—
141C32×C8—22no—
142C3⋊(C3⋊C8)—41no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—41no—
145C2×AGL(1,ℤ/8)—31no—
146C2×#108—31no—
147#417—91no—
148C2×#102—91no—
149C2×#100—91no—
150#408—91no—
151#343—91no—
152C24×C3—61no—
153C23×D3—21no—
154C3×#41—61no—
155C3×#41—61no—
156C3×#41—61no—
157C3×#41—61no—
158C2×C3×Q8—31no—
159C2×C3×D4—31no—
160C2×C3×D4—32no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C2×C3×D4—61no—
166C2×C3×D4—61no—
167C22×C3×C4—21no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C2×#67—21no—
172C22×Dic3—62no—
173C22×Dic3—61no—
174C22×Dic3—61no—
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×SD16—64no—
189C3×D8—64no—
190C3×M16—21no—
191C3×M16—21no—
192C3×M16—22no—
193C3×M16—41no—
194C3×M16—61no—
195C3×M16—61no—
196C3×M16#6712yes—
197C3×M16#6712yes—
198C2×C3×C8—21no—
199C2×C3×C8—21no—
200C2×C3×C8—32no—
201C2×C3×C8—41no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C2×C3×C8—61no—
205C4⋊Dic3—61no—
206C4⋊Dic3—61no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—121no—
210C4⋊Dic3—121no—
211#208—21no—
212#208—21no—
213#208—62no—
214#208—61no—
215#208—61no—
216#208—61no—
217#208—61no—
218#208—121no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—121no—
225C2×C3⋊C8D1212yes—
226D24—24no—
227#204—24no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32#12111yescharacteristic
231C22×C32#12311yescharacteristic
232C22×C32#12411yescharacteristic
233C2×C3×D3—41no—
234C2×C3×D3—42no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C2×C3×D3—82no—
238C2×C3×D3—81no—
239C2×C3×D3—81no—
240C2×C3×D3—82no—
241C32×C4#12011yescharacteristic
242C32×C4#12111yescharacteristic
243C32×C4#12111yescharacteristic
244C32×C4#12311yescharacteristic
245C3⋊Dic3—81no—
246C3×Dic3—41no—
247C2×#41—31no—
248C22×D4—31no—
249AGL(1,ℤ/8)—62no—
250AGL(1,ℤ/8)—62no—
251C2×SD16—61no—
252C2×D8—61no—
253C2×M16—31no—
254C2×M16—91no—
255C2×M16D3211yescharacteristic
256C22×C8—31no—
257C2×C4⋊C4—91no—
258#108—62no—
259#103—181no—
260#102—182no—
261#102—181no—
262#100—182no—
263C22⋊C8—182no—
264C23×C3—21no—
265C23×C3—61no—
266C23×C3—62no—
267C23×C3—121no—
268C23×C3—121no—
269C23×C3—241no—
270C23×C3—241no—
271C23×C3#23711yescharacteristic
272C23×C3#23911yescharacteristic
273C22×D3—21no—
274C22×D3—22no—
275C22×D3—41no—
276C22×D3—41no—
277C22×D3—81no—
278C22×D3—81no—
279C3×Q8—61no—
280C3×Q8—61no—
281C3×D4—61no—
282C3×D4—62no—
283C3×D4—61no—
284C3×D4—62no—
285C3×D4—121no—
286C3×D4—121no—
287C3×D4—121no—
288C3×D4—121no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—61no—
296C2×C3×C4—121no—
297C2×C3×C4—121no—
298C2×C3×C4C2×D1211yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4D3×D411yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4#23711yescharacteristic
304C2×C3×C4#23711yescharacteristic
305C2×C3×C4#23911yescharacteristic
306C2×C3×C4C2×#6711yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308C2×C3×C4C2×#6711yescharacteristic
309C2×C3×C4C2×#6711yescharacteristic
310#67—41no—
311#67—41no—
312C2×Dic3—21no—
313C2×Dic3—122no—
314C2×Dic3—121no—
315C2×Dic3—121no—
316C2×Dic3—241no—
317C2×Dic3—241no—
318C2×Dic3—242no—
319D12—21no—
320D12—22no—
321D12—22no—
322D12—21no—
323D12—41no—
324D12—41no—
325C4×D3—41no—
326C4×D3—41no—
327Dic6—21no—
328Dic6—21no—
329C3×C8—22no—
330C3×C8—22no—
331C3×C8—42no—
332C3×C8—62no—
333C3×C8—121no—
334C3⋊C8—22no—
335C3⋊C8—41no—
336C3⋊C8—122no—
337C3⋊C8—121no—
338C3⋊C8—121no—
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—181no—
362C22×C4C2×D3211yescharacteristic
363SD16—64no—
364D8—64no—
365M16—21no—
366M16—61no—
367M16—61no—
368M16—181no—
369M16—181no—
370M16#62512yes—
371C2×C8—21no—
372C2×C8—32no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—61no—
376C2×C8—181no—
377C4⋊C4—181no—
378C4⋊C4—181no—
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—121no—
390C22×C3—121no—
391C22×C3—122no—
392C22×C3—242no—
393C22×C3—242no—
394C22×C3—241no—
395C22×C3—241no—
396C22×C3#89411yescharacteristic
397C22×C3#89511yescharacteristic
398C22×C3#93511yescharacteristic
399C22×C3#93611yescharacteristic
400C22×C3#93911yescharacteristic
401C22×C3#94711yescharacteristic
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#89411yescharacteristic
416C3×C4#89511yescharacteristic
417C3×C4#93011yescharacteristic
418C3×C4#93511yescharacteristic
419C3×C4#93711yescharacteristic
420C3×C4#93811yescharacteristic
421C3×C4#93911yescharacteristic
422C3×C4#95311yescharacteristic
423Dic3—41no—
424Dic3—242no—
425Dic3—241no—
426Dic3—241no—
427C32#205111yescharacteristic, complemented, Sylow
428C23—61no—
429C23—62no—
430C23—121no—
431C23—121no—
432C23—241no—
433C23—241no—
434C23#379611yescharacteristic
435Q8—61no—
436Q8—61no—
437D4—61no—
438D4—62no—
439D4—61no—
440D4—62no—
441D4—121no—
442D4—121no—
443D4—121no—
444D4—121no—
445C2×C4—61no—
446C2×C4—121no—
447C2×C4—121no—
448C2×C4—361no—
449C2×C4—721no—
450C2×C4#379511yescharacteristic
451C2×C4#379611yescharacteristic
452C2×C4D3×D1211yescharacteristic
453C2×C4C2×#62511yescharacteristic
454C2×C4D3×#6711yescharacteristic
455C2×C4D3×#6711yescharacteristic
456C8—22no—
457C8—62no—
458C8—121no—
459C8—361no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—41no—
468C2×C3—41no—
469C2×C3—241no—
470C2×C3—242no—
471C2×C3#489711yescharacteristic
472C2×C3#489811yescharacteristic
473C2×C3#499111yescharacteristic
474C2×C3#519911yescharacteristic
475C2×C3#520011yescharacteristic
476C2×C3#522211yescharacteristic
477D3—81no—
478D3—82no—
479C22—21no—
480C22—21no—
481C22—121no—
482C22—121no—
483C22—121no—
484C22—122no—
485C22—242no—
486C22—242no—
487C22—241no—
488C22—241no—
489C22#6386311yescharacteristic
490C22#6388411yescharacteristic
491C22#6388611yescharacteristic
492C4—121no—
493C4—721no—
494C4#6388411yescharacteristic
495C4#6388611yescharacteristic
496C4#6390811yescharacteristic
497C4#6397611yescharacteristic
498C3—21no—
499C3#7071411yescharacteristic, complemented
500C3#7209311yescharacteristic, complemented
501C2—21no—
502C2—21no—
503C2—241no—
504C2—242no—
505C2#1059098411yescharacteristic
506C2#1059098611yescharacteristic
507C2#1059130011yescharacteristic
subgroupG/H
centerC22#63886
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×C3×#908C2
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×C3×#822C2semidirect
3. #10591088C2semidirect
4. C2×#63563C2semidirect
5. C2×#63558C2semidirect
6. #10591070C2semidirect
7. #10589420C2semidirect
36. C2×#822D3semidirect
427. C32#2051semidirect
499. C3#70714semidirect
500. C3#72093semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C2×C3×#8222
#105910882
C2×#635632
C2×#635582
#105910702
#105894202
#720933
#707143