Finite Group Databasebeta

← #11793898

Subgroups — #11793898

Order 1152.

643 conjugacy classes of subgroups.

The subgroup lattice has 527 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#949C211yesmaximal, characteristic
2#10592933C211yesmaximal, characteristic, complemented
3C3×#5232C211yesmaximal, characteristic, complemented
4C2×#63578C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic, complemented
6C2×#63558C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#72093—31nomaximal
9#70307—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#949—22no—
15C3×#949—22no—
16C2×C3×#215—21no—
17C2×C3×#213—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63657—22no—
22C3×#835—21no—
23C3×#832—21no—
24#63578—22no—
25#63562—22no—
26#63558—22no—
27C2×C3×AGL(1,ℤ/8)—31no—
28C2×#949D311yescharacteristic
29C3×#417—31no—
30#5234—31no—
31#5234—31no—
32#5234—61no—
33#5232D311yescharacteristic, complemented
34C2×#833—31no—
35C2×#832—31no—
36C2×#823—31no—
37C2×#822—31no—
38C2×#822—31no—
39C2×#809—31no—
40#4554—31no—
41#4530—31no—
42C23×C3×D3—21no—
43C32×#41—21no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41—21no—
47C2×C32×Q8D411yescharacteristic
48C2×C32×D4—21no—
49C2×C32×D4D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3×Dic3—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12D412yes—
59#3748—21no—
60#3748—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)D412yes—
65C3×#215—24no—
66C3×#213—24no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C3×#208D412yes—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#2051—91noSylow
76C2×C3×#41—21no—
77C2×C3×#41C2×D311yescharacteristic
78C2×C3×#41C2×D311yescharacteristic
79C22×C3×D4—31no—
80C22×D12C2×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—
86C2×C3×M16—31no—
87C2×C3×C4⋊C4—31no—
88#949—22no—
89#949—22no—
90C2×#215—21no—
91C2×#213—21no—
92C2×C4⋊Dic3C2×D311yescharacteristic
93C2×#208—31no—
94C2×#208—31no—
95C2×#208—61no—
96C2×#208C2×D311yescharacteristic
97C2×#208C2×D311yescharacteristic
98C22×C3⋊C8—31no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—61no—
101C3×#103—61no—
102C3×#102—61no—
103#835—21no—
104#833—62no—
105#832—21no—
106#832—62no—
107#830—62no—
108#830—62no—
109#830—64no—
110#823—62no—
111#822—62no—
112#822—62no—
113#809—62no—
114C23×C32—21no—
115C23×C32#4111yescharacteristic
116C22×C3×D3—22no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—81no—
120C22×C3×D3—81no—
121C32×Q8—21no—
122C32×Q8—21no—
123C32×D4—21no—
124C32×D4—21no—
125C32×D4—41no—
126C32×D4—41no—
127C2×C32×C4—21no—
128C2×C32×C4—41no—
129C2×C32×C4—41no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C32×C4#4111yescharacteristic
136C2×C3×Dic3—41no—
137C2×C3×Dic3—81no—
138C3×D12—22no—
139C3×D12—22no—
140C3×D12—41no—
141C3×D12—41no—
142C3⋊(C3⋊C8)—22no—
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—41no—
146C2×AGL(1,ℤ/8)—31no—
147C2×#108—91no—
148#417—31no—
149C2×#102—91no—
150C2×#100—91no—
151#408—91no—
152#343—91no—
153C24×C3—61no—
154C23×D3—21no—
155C3×#41—21no—
156C3×#41—21no—
157C3×#41—21no—
158C3×#41—21no—
159C3×#41—21no—
160C3×#41—21no—
161C3×#41—21no—
162C3×#41—21no—
163C3×#41—41no—
164C3×#41—41no—
165C3×#41—41no—
166C3×#41—41no—
167C2×C3×Q8—21no—
168C2×C3×Q8#6711yescharacteristic
169C2×C3×Q8#6711yescharacteristic
170C2×C3×D4—22no—
171C2×C3×D4—21no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4—32no—
175C2×C3×D4—61no—
176C2×C3×D4—61no—
177C2×C3×D4—61no—
178C2×C3×D4—61no—
179C2×C3×D4—61no—
180C2×C3×D4#6711yescharacteristic
181C2×C3×D4#6711yescharacteristic
182C22×C3×C4—22no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—61no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12—21no—
195C2×D12#6712yes—
196C3×SD16—64no—
197C3×D8—64no—
198C3×M16—32no—
199C3×M16—61no—
200C3×M16—61no—
201C3×M16—61no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C3×C4⋊C4—61no—
205C3×C4⋊C4—61no—
206#215—24no—
207#213—24no—
208C4⋊Dic3—21no—
209C4⋊Dic3—21no—
210#208—21no—
211#208—21no—
212#208—21no—
213#208—61no—
214#208—61no—
215#208—61no—
216#208—61no—
217#208—121no—
218#208—121no—
219#208#6712yes—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—32no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—62no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—61no—
232C2×C3⋊C8—121no—
233C2×C3⋊C8—121no—
234C22×C32—21no—
235C22×C32—21no—
236C22×C32—41no—
237C22×C32—41no—
238C22×C32—41no—
239C22×C32#12111yescharacteristic
240C22×C32#12311yescharacteristic
241C22×C32#12411yescharacteristic
242C2×C3×D3—42no—
243C2×C3×D3—82no—
244C2×C3×D3—81no—
245C2×C3×D3—81no—
246C2×C3×D3—82no—
247C32×C4—41no—
248C32×C4#12011yescharacteristic
249C32×C4#12111yescharacteristic
250C32×C4#12111yescharacteristic
251C32×C4#12311yescharacteristic
252C3×Dic3—81no—
253C2×#41D3211yescharacteristic
254C22×D4—31no—
255AGL(1,ℤ/8)—62no—
256AGL(1,ℤ/8)—62no—
257C2×SD16—61no—
258C2×D8—61no—
259C2×M16—31no—
260C2×M16—31no—
261C2×M16—91no—
262C22×C8—91no—
263C2×C4⋊C4—31no—
264#108—182no—
265#103—61no—
266#102—61no—
267#102—182no—
268#100—182no—
269C22⋊C8—182no—
270C23×C3—22no—
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—21no—
274C23×C3—62no—
275C23×C3—121no—
276C23×C3—121no—
277C23×C3—241no—
278C23×C3—241no—
279C23×C3#23711yescharacteristic
280C23×C3#23711yescharacteristic
281C22×D3—22no—
282C22×D3—41no—
283C22×D3—41no—
284C22×D3—81no—
285C22×D3—81no—
286C3×Q8—21no—
287C3×Q8—21no—
288C3×Q8—21no—
289C3×Q8—21no—
290C3×Q8—41no—
291C3×Q8—41no—
292C3×D4—21no—
293C3×D4—21no—
294C3×D4—21no—
295C3×D4—21no—
296C3×D4—41no—
297C3×D4—41no—
298C3×D4—42no—
299C3×D4—42no—
300C3×D4—41no—
301C3×D4—41no—
302C3×D4—41no—
303C3×D4—41no—
304C3×D4—62no—
305C3×D4—62no—
306C3×D4—121no—
307C3×D4—121no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—42no—
318C2×C3×C4—42no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—41no—
322C2×C3×C4—41no—
323C2×C3×C4—121no—
324C2×C3×C4—241no—
325C2×C3×C4#23511yescharacteristic
326C2×C3×C4#23511yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4#23711yescharacteristic
332C2×C3×C4#23711yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334C2×C3×C4C2×#6711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337C2×Dic3—41no—
338C2×Dic3—81no—
339D12—22no—
340D12—22no—
341D12—41no—
342D12—41no—
343C3×C8—62no—
344C3×C8—121no—
345C3⋊C8—22no—
346C3⋊C8—41no—
347C3⋊C8—62no—
348C3⋊C8—62no—
349C3⋊C8—122no—
350C3⋊C8—122no—
351C3⋊C8—121no—
352C3⋊C8—121no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32—81no—
356C2×C32#39411yescharacteristic
357C2×C32#47111yescharacteristic
358C2×C32#47211yescharacteristic
359C3×D3—82no—
360C24—61no—
361#41—21no—
362#41—21no—
363#41—21no—
364#41—21no—
365C2×Q8#62511yescharacteristic
366C2×D4—21no—
367C2×D4—32no—
368C2×D4—61no—
369C2×D4—61no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4#62511yescharacteristic
374C22×C4—21no—
375C22×C4—61no—
376C22×C4C2×D3211yescharacteristic
377SD16—64no—
378D8—64no—
379M16—32no—
380M16—61no—
381M16—61no—
382M16—61no—
383M16—181no—
384M16—181no—
385C2×C8—61no—
386C2×C8—61no—
387C2×C8—92no—
388C2×C8—181no—
389C2×C8—181no—
390C2×C8—181no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—42no—
403C22×C3—42no—
404C22×C3—42no—
405C22×C3—41no—
406C22×C3—41no—
407C22×C3—41no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3—41no—
411C22×C3—122no—
412C22×C3—242no—
413C22×C3—242no—
414C22×C3—241no—
415C22×C3—241no—
416C22×C3#88311yescharacteristic
417C22×C3#88511yescharacteristic
418C22×C3#93511yescharacteristic
419C22×C3#93611yescharacteristic
420C22×C3#93911yescharacteristic
421C22×C3#93911yescharacteristic
422C2×D3—42no—
423C2×D3—82no—
424C2×D3—81no—
425C2×D3—81no—
426C2×D3—82no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—42no—
432C3×C4—41no—
433C3×C4—41no—
434C3×C4—241no—
435C3×C4#88411yescharacteristic
436C3×C4#88411yescharacteristic
437C3×C4#92911yescharacteristic
438C3×C4#93511yescharacteristic
439C3×C4#93711yescharacteristic
440C3×C4#93811yescharacteristic
441C3×C4#93911yescharacteristic
442C3×C4#95311yescharacteristic
443Dic3—81no—
444C32#205111yescharacteristic, complemented, Sylow
445C23—21no—
446C23—62no—
447C23—121no—
448C23—121no—
449C23—241no—
450C23—241no—
451C23#380511yescharacteristic
452Q8—21no—
453Q8—21no—
454D4—21no—
455D4—21no—
456D4—41no—
457D4—41no—
458D4—62no—
459D4—62no—
460D4—121no—
461D4—121no—
462C2×C4—21no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—121no—
466C2×C4—241no—
467C2×C4#380411yescharacteristic
468C2×C4#380411yescharacteristic
469C2×C4C2×#62511yescharacteristic
470C2×C4D3×#6711yescharacteristic
471C2×C4D3×#6711yescharacteristic
472C2×C4#381111yescharacteristic
473C8—62no—
474C8—121no—
475C8—182no—
476C8—361no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—41no—
485C2×C3—41no—
486C2×C3—82no—
487C2×C3—81no—
488C2×C3—81no—
489C2×C3—242no—
490C2×C3#495911yescharacteristic
491C2×C3#519911yescharacteristic
492C2×C3#519911yescharacteristic
493C2×C3#520011yescharacteristic
494C2×C3#520311yescharacteristic
495C2×C3#522211yescharacteristic
496D3—82no—
497C22—21no—
498C22—21no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—122no—
503C22—242no—
504C22—242no—
505C22—241no—
506C22—241no—
507C22#6395911yescharacteristic
508C22#6396911yescharacteristic
509C22#6398011yescharacteristic
510C4—41no—
511C4—241no—
512C4#6395811yescharacteristic
513C4#6396111yescharacteristic
514C4#6397111yescharacteristic
515C4#6397611yescharacteristic
516C3—21no—
517C3#7030711yescharacteristic, complemented
518C3#7209311yescharacteristic, complemented
519C2—21no—
520C2—21no—
521C2—81no—
522C2—242no—
523C2#1059167811yescharacteristic
524C2#1059168111yescharacteristic
525C2#1059170811yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC22×C32#121
prime radicalC2×C3×#949C2
hypercenterC2×#41D32
hypocenterC32#2051
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10592933C2semidirect
3. C3×#5232C2semidirect
4. C2×#63578C2semidirect
5. C2×#63562C2semidirect
6. C2×#63558C2semidirect
7. #10589167C2semidirect
33. #5232D3semidirect
444. C32#2051semidirect
517. C3#70307semidirect
518. C3#72093semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9492
#105929332
C3×#52322
C2×#635782
C2×#635622
C2×#635582
#105891672
#720933
#703073