Finite Group Databasebeta

← #11793900

Subgroups — #11793900

Order 1152.

657 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#932C211yesmaximal, characteristic
2C2×#63660C211yesmaximal, characteristic, complemented
3C2×C3×#832C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5#10591087C211yesmaximal, characteristic, complemented
6#10591070C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#72093—31nomaximal
9#70196—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#214—21no—
15C3×#932—22no—
16C3×#932—22no—
17C2×C3×#213—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21#63660—22no—
22C3×#832—22no—
23#63577—22no—
24#63565—21no—
25#63562—21no—
26(C2×D3)⋊(C3⋊C8)—22no—
27C2×C3×AGL(1,ℤ/8)—31no—
28C2×#932D311yescharacteristic
29C2×C3×#102—31no—
30#5234—31no—
31#5232—31no—
32C2×#833—31no—
33C2×#833—31no—
34C2×#833—61no—
35C2×#832D311yescharacteristic, complemented
36C2×#822—31no—
37#5110—31no—
38C2×#819—31no—
39#4966—31no—
40#4554—31no—
41#4530—31no—
42C24×C32—21no—
43C2×C32×D4—21no—
44C2×C32×D4—21no—
45C2×C32×D4—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4D412yes—
49C22×C32×C4C2311yescharacteristic
50C2×C3×#67—21no—
51C22×C3×Dic3—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12D411yescharacteristic
57C2×C3×C4×D3—21no—
58C2×C3×Dic6D411yescharacteristic
59#3748—21no—
60#3748—21no—
61#3748—21no—
62#3748—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×#214—24no—
66C3×#213—24no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×#208—21no—
70C3×#208D412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8D412yes—
75#2051—91noSylow
76C2×C3×#41—31no—
77C22×C3×D4—21no—
78C22×C3×D4C2×D311yescharacteristic
79C22×C3×D4C2×D311yescharacteristic
80C2×#235C2×D311yescharacteristic
81C3×AGL(1,ℤ/8)—62no—
82C3×AGL(1,ℤ/8)—62no—
83C2×C3×SD16—61no—
84C2×C3×D8—61no—
85C2×C3×M16—31no—
86C22×C3×C8—31no—
87C2×C3×C4⋊C4—31no—
88C2×#214—21no—
89#932—22no—
90#932—22no—
91C2×#213—21no—
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×#208—31no—
94C2×#208—31no—
95C2×#208—31no—
96C2×#208—31no—
97C2×#208—61no—
98C2×#208—61no—
99C2×#208C2×D311yescharacteristic
100C22×C3⋊C8C2×D311yescharacteristic
101C3×#102—62no—
102#835—61no—
103#833—64no—
104#833—62no—
105#833—62no—
106#832—22no—
107#832—61no—
108#830—62no—
109#822—62no—
110(C2×D3)⋊C8—62no—
111#819—62no—
112#810—61no—
113#809—61no—
114C23×C32—22no—
115C23×C32—41no—
116C23×C32—41no—
117C23×C32—81no—
118C23×C32—81no—
119C23×C32#4111yescharacteristic
120C22×C3×D3—21no—
121C32×D4—22no—
122C32×D4—22no—
123C32×D4—41no—
124C32×D4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C3×#67—41no—
132C3×#67—41no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—81no—
136C3×D12—21no—
137C3×D12—21no—
138C3×C4×D3—41no—
139C3×C4×D3—41no—
140C3×Dic6—21no—
141C3×Dic6—21no—
142C3⋊(C3⋊C8)—41no—
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—22no—
146C2×AGL(1,ℤ/8)—31no—
147C2×#108—91no—
148#417—91no—
149C2×#102—31no—
150C2×#100—91no—
151#408—91no—
152#343—91no—
153C24×C3—22no—
154C24×C3—21no—
155C24×C3—21no—
156C3×#41—61no—
157C3×#41—61no—
158C3×#41—61no—
159C3×#41—61no—
160C2×C3×Q8—31no—
161C2×C3×D4—22no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4—21no—
165C2×C3×D4—21no—
166C2×C3×D4—21no—
167C2×C3×D4—21no—
168C2×C3×D4—21no—
169C2×C3×D4—21no—
170C2×C3×D4—21no—
171C2×C3×D4—21no—
172C2×C3×D4—22no—
173C2×C3×D4—31no—
174C2×C3×D4—41no—
175C2×C3×D4—41no—
176C2×C3×D4—41no—
177C2×C3×D4—41no—
178C2×C3×D4—61no—
179C2×C3×D4D1212yes—
180C2×C3×D4#6712yes—
181C22×C3×C4—21no—
182C22×C3×C4—61no—
183C22×C3×C4—61no—
184C22×C3×C4C22×D311yescharacteristic
185C22×C3×C4C22×D311yescharacteristic
186C2×#67—21no—
187C22×Dic3—21no—
188#235—21no—
189#235—21no—
190#235—21no—
191#235—21no—
192C2×D12#6711yescharacteristic
193C2×C4×D3—21no—
194C2×Dic6#6711yescharacteristic
195C3×SD16—64no—
196C3×D8—64no—
197C3×M16—32no—
198C3×M16—61no—
199C2×C3×C8—32no—
200C2×C3×C8—61no—
201C2×C3×C8—61no—
202C2×C3×C8—61no—
203C3×C4⋊C4—61no—
204C3×C4⋊C4—61no—
205#214—24no—
206#213—24no—
207C4⋊Dic3—21no—
208C4⋊Dic3—21no—
209#208—21no—
210#208—62no—
211#208—62no—
212#208—61no—
213#208—61no—
214#208—61no—
215#208—61no—
216#208—61no—
217#208—61no—
218#208—61no—
219#208—61no—
220#208—121no—
221#208—121no—
222#208#6712yes—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—121no—
231C2×C3⋊C8—121no—
232C2×C3⋊C8#6712yes—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32—42no—
236C22×C32—82no—
237C22×C32—82no—
238C22×C32—81no—
239C22×C32—81no—
240C22×C32#12111yescharacteristic
241C22×C32#12311yescharacteristic
242C22×C32#12411yescharacteristic
243C2×C3×D3—41no—
244C2×C3×D3—41no—
245C2×C3×D3—41no—
246C32×C4#12011yescharacteristic
247C32×C4#12111yescharacteristic
248C32×C4#12111yescharacteristic
249C32×C4#12311yescharacteristic
250C3×Dic3—41no—
251C3×Dic3—81no—
252C2×#41—31no—
253C22×D4D3211yescharacteristic
254AGL(1,ℤ/8)—62no—
255AGL(1,ℤ/8)—62no—
256C2×SD16—61no—
257C2×D8—61no—
258C2×M16—31no—
259C2×M16—91no—
260C2×M16—91no—
261C22×C8—31no—
262C2×C4⋊C4—31no—
263#108—182no—
264#103—181no—
265#102—62no—
266#102—181no—
267#100—182no—
268C22⋊C8—182no—
269C23×C3—24no—
270C23×C3—22no—
271C23×C3—22no—
272C23×C3—21no—
273C23×C3—42no—
274C23×C3—42no—
275C23×C3—41no—
276C23×C3—41no—
277C23×C3—41no—
278C23×C3—41no—
279C23×C3—61no—
280C23×C3—81no—
281C23×C3—81no—
282C23×C3—81no—
283C23×C3—81no—
284C23×C3—82no—
285C23×C3—82no—
286C23×C3#23711yescharacteristic
287C23×C3#23711yescharacteristic
288C22×D3—21no—
289C3×Q8—61no—
290C3×Q8—61no—
291C3×D4—22no—
292C3×D4—22no—
293C3×D4—22no—
294C3×D4—22no—
295C3×D4—42no—
296C3×D4—42no—
297C3×D4—42no—
298C3×D4—42no—
299C3×D4—41no—
300C3×D4—41no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—61no—
304C3×D4—61no—
305C3×D4—121no—
306C3×D4—121no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—61no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4—121no—
317C2×C3×C4—241no—
318C2×C3×C4C2×D1211yescharacteristic
319C2×C3×C4#23511yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4#23711yescharacteristic
324C2×C3×C4#23711yescharacteristic
325C2×C3×C4#23711yescharacteristic
326C2×C3×C4C2×#6711yescharacteristic
327C2×C3×C4C2×#6711yescharacteristic
328C2×C3×C4C2×#6711yescharacteristic
329C2×C3×C4C2×#6711yescharacteristic
330#67—41no—
331#67—41no—
332C2×Dic3—21no—
333C2×Dic3—41no—
334C2×Dic3—81no—
335D12—21no—
336D12—21no—
337C4×D3—41no—
338C4×D3—41no—
339Dic6—21no—
340Dic6—21no—
341C3×C8—62no—
342C3×C8—62no—
343C3⋊C8—22no—
344C3⋊C8—22no—
345C3⋊C8—122no—
346C3⋊C8—122no—
347C3⋊C8—121no—
348C3⋊C8—121no—
349C3⋊C8—121no—
350C3⋊C8—121no—
351C2×C32—21no—
352C2×C32—21no—
353C2×C32—82no—
354C2×C32#39411yescharacteristic
355C2×C32#47111yescharacteristic
356C2×C32#47211yescharacteristic
357C3×D3—81no—
358C24—21no—
359#41—61no—
360#41—61no—
361#41—61no—
362#41—61no—
363C2×Q8—31no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—31no—
370C2×D4—61no—
371C2×D4#62612yes—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4C2×D3211yescharacteristic
375SD16—64no—
376D8—64no—
377M16—32no—
378M16—61no—
379M16—181no—
380M16—181no—
381M16—181no—
382M16—181no—
383C2×C8—32no—
384C2×C8—61no—
385C2×C8—61no—
386C2×C8—61no—
387C2×C8—181no—
388C2×C8—181no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—41no—
399C22×C3—41no—
400C22×C3—44no—
401C22×C3—42no—
402C22×C3—42no—
403C22×C3—82no—
404C22×C3—82no—
405C22×C3—82no—
406C22×C3—82no—
407C22×C3—82no—
408C22×C3—82no—
409C22×C3—84no—
410C22×C3—84no—
411C22×C3—81no—
412C22×C3—81no—
413C22×C3—81no—
414C22×C3—81no—
415C22×C3—121no—
416C22×C3—121no—
417C22×C3—121no—
418C22×C3#88511yescharacteristic
419C22×C3#88611yescharacteristic
420C22×C3#93511yescharacteristic
421C22×C3#93611yescharacteristic
422C22×C3#93811yescharacteristic
423C22×C3#93911yescharacteristic
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—41no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—121no—
432C3×C4—241no—
433C3×C4#88211yescharacteristic
434C3×C4#88311yescharacteristic
435C3×C4#93011yescharacteristic
436C3×C4#93511yescharacteristic
437C3×C4#93811yescharacteristic
438C3×C4#93911yescharacteristic
439C3×C4#93911yescharacteristic
440C3×C4#95311yescharacteristic
441Dic3—41no—
442Dic3—81no—
443C32#205111yescharacteristic, complemented, Sylow
444C23—22no—
445C23—41no—
446C23—41no—
447C23—61no—
448C23—81no—
449C23—81no—
450C23#380511yescharacteristic
451Q8—61no—
452Q8—61no—
453D4—22no—
454D4—22no—
455D4—41no—
456D4—41no—
457D4—61no—
458D4—61no—
459D4—121no—
460D4—121no—
461C2×C4—61no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—241no—
466C2×C4#380411yescharacteristic
467C2×C4#380511yescharacteristic
468C2×C4C2×#62611yescharacteristic
469C2×C4D3×#6711yescharacteristic
470C2×C4D3×#6711yescharacteristic
471C2×C4D3×#6711yescharacteristic
472C8—62no—
473C8—62no—
474C8—361no—
475C8—361no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—41no—
484C2×C3—41no—
485C2×C3—84no—
486C2×C3—82no—
487C2×C3—82no—
488C2×C3—241no—
489C2×C3#496111yescharacteristic
490C2×C3#516011yescharacteristic
491C2×C3#517711yescharacteristic
492C2×C3#519911yescharacteristic
493C2×C3#520011yescharacteristic
494C2×C3#522211yescharacteristic
495D3—81no—
496C22—21no—
497C22—21no—
498C22—42no—
499C22—82no—
500C22—82no—
501C22—81no—
502C22—81no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22#6395911yescharacteristic
507C22#6396211yescharacteristic
508C22#6397011yescharacteristic
509C4—121no—
510C4—241no—
511C4#6396911yescharacteristic
512C4#6397011yescharacteristic
513C4#6397711yescharacteristic
514C4#6397811yescharacteristic
515C3—21no—
516C3#7019611yescharacteristic, complemented
517C3#7209311yescharacteristic, complemented
518C2—21no—
519C2—21no—
520C2—82no—
521C2—241no—
522C2#1059150511yescharacteristic
523C2#1059150611yescharacteristic
524C2#1059170911yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#121
prime radicalC2×C3×#932C2
hypercenterC22×D4D32
hypocenterC32#2051
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63660C2semidirect
3. C2×C3×#832C2semidirect
4. C2×#63577C2semidirect
5. #10591087C2semidirect
6. #10591070C2semidirect
7. #10589167C2semidirect
35. C2×#832D3semidirect
443. C32#2051semidirect
516. C3#70196semidirect
517. C3#72093semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9322
C2×#636602
C2×C3×#8322
C2×#635772
#105910872
#105910702
#105891672
#720933
#701963