Finite Group Databasebeta

← #11793912

Subgroups — #11793912

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×#63825C211yesmaximal, characteristic
2C2×#63650C211yesmaximal, characteristic, complemented
3C3×#5129C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5C2×#63564C211yesmaximal, characteristic, complemented
6#10591087C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#70003—31nomaximal
9#68986—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3717—21no—
18#63825—22no—
19#63825—22no—
20C2×#3714—21no—
21#63650—22no—
22C3×(C2×D3)⋊C8—22no—
23#63577—22no—
24#63565—21no—
25#63564—22no—
26#63562—21no—
27C2×#949—31no—
28C2×#908—31no—
29C3×#408—31no—
30#5232—31no—
31C2×#823—31no—
32C2×#823—31no—
33C2×#823—61no—
34#5129D311yescharacteristic, complemented
35C2×#822—31no—
36C2×#821—31no—
37C2×#819—31no—
38#4966—31no—
39C2×#809—31no—
40C3×#343—31no—
41#4554D311yescharacteristic, complemented
42C23×C3⋊D3—21no—
43C22×C32×C4C2311yescharacteristic
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)D412yes—
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
59C32×M16—21no—
60C32×M16—21no—
61C2×C32×C8—21no—
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×#208—21no—
68C3×#208D412yes—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8D412yes—
73#3717—24no—
74#3714—24no—
75#2051—91noSylow
76C2×C3×#41—31no—
77C2×#235C2×D311yescharacteristic
78C22×D12—31no—
79C22×D12—31no—
80C22×D12—61no—
81C2×C3×M16—21no—
82C2×C3×M16—31no—
83C2×C3×M16C2×D311yescharacteristic
84C2×C3×M16C2×D311yescharacteristic
85C22×C3×C8—31no—
86C2×C3×C4⋊C4—31no—
87#949—62no—
88#949—62no—
89C2×#215—61no—
90C2×#213—61no—
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×#208—31no—
93C2×#208—31no—
94C2×#208—61no—
95C2×#208C2×D311yescharacteristic
96C22×C3⋊C8C2×D311yescharacteristic
97#908—62no—
98#908—62no—
99C2×D24—61no—
100C2×#204—61no—
101C3×C22⋊C8—62no—
102#835—61no—
103#832—61no—
104#823—62no—
105#823—62no—
106#823—64no—
107#822—62no—
108#821—62no—
109(C2×D3)⋊C8—22no—
110#819—62no—
111#810—61no—
112#809—61no—
113#809—62no—
114C23×C32#4111yescharacteristic
115C22×C3⋊D3—22no—
116C22×C3⋊D3—41no—
117C22×C3⋊D3—41no—
118C22×C3⋊D3—81no—
119C22×C3⋊D3—81no—
120C22×C3×D3—21no—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—22no—
129C4⋊(C3⋊D3)—41no—
130C4⋊(C3⋊D3)—41no—
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—
142C32×C8—41no—
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—22no—
145C3×C3⋊C8—22no—
146C2×AGL(1,ℤ/8)—91no—
147C2×#108—91no—
148#417—91no—
149C2×#102—91no—
150C2×#100—91no—
151#408—31no—
152#343—31no—
153C23×D3—62no—
154C23×D3—61no—
155C23×D3—61no—
156C3×#41—61no—
157C3×#41—61no—
158C3×#41—61no—
159C3×#41—61no—
160C2×C3×Q8—31no—
161C2×C3×D4—31no—
162C2×C3×D4—61no—
163C22×C3×C4—21no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C2×#67—21no—
169C22×Dic3—21no—
170#235—21no—
171#235—21no—
172#235—21no—
173#235—21no—
174C2×D12—32no—
175C2×D12—32no—
176C2×D12—62no—
177C2×D12—61no—
178C2×D12—61no—
179C2×D12—61no—
180C2×D12—61no—
181C2×D12—61no—
182C2×D12—61no—
183C2×D12—61no—
184C2×D12—61no—
185C2×D12—62no—
186C2×D12—61no—
187C2×D12—61no—
188C2×D12—121no—
189C2×D12—121no—
190C2×D12—121no—
191C2×D12—121no—
192C2×D12D1211yescharacteristic
193C2×C4×D3—21no—
194C2×Dic6D1211yescharacteristic
195C3×M16—22no—
196C3×M16—21no—
197C3×M16—21no—
198C3×M16—21no—
199C3×M16—21no—
200C3×M16—32no—
201C3×M16—41no—
202C3×M16—61no—
203C2×C3×C8—21no—
204C2×C3×C8—21no—
205C2×C3×C8—32no—
206C2×C3×C8—41no—
207C2×C3×C8—61no—
208C2×C3×C8—61no—
209C2×C3×C8—61no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4—61no—
212#215—64no—
213#213—64no—
214C4⋊Dic3—21no—
215C4⋊Dic3—21no—
216#208—21no—
217#208—62no—
218#208—61no—
219#208—61no—
220#208—61no—
221#208—61no—
222#208—121no—
223#208D1212yes—
224C2×C3⋊C8—21no—
225C2×C3⋊C8—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—121no—
230C2×C3⋊C8#6712yes—
231D24—64no—
232#204—64no—
233C22×C32—21no—
234C22×C32—21no—
235C22×C32#12111yescharacteristic
236C22×C32#12311yescharacteristic
237C22×C32#12411yescharacteristic
238C2×C3⋊D3—42no—
239C2×C3⋊D3—82no—
240C2×C3⋊D3—81no—
241C2×C3⋊D3—81no—
242C2×C3⋊D3—82no—
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×D4—91no—
254AGL(1,ℤ/8)—182no—
255AGL(1,ℤ/8)—182no—
256C2×SD16—181no—
257C2×D8—181no—
258C2×M16—31no—
259C2×M16—91no—
260C2×M16D3211yescharacteristic
261C22×C8—31no—
262C2×C4⋊C4—31no—
263#108—182no—
264#103—181no—
265#102—182no—
266#102—181no—
267#100—182no—
268C22⋊C8—62no—
269C23×C3—21no—
270C23×C3—61no—
271C23×C3#23511yescharacteristic
272C23×C3#23511yescharacteristic
273C22×D3—21no—
274C22×D3—64no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—122no—
278C22×D3—122no—
279C22×D3—121no—
280C22×D3—121no—
281C22×D3—121no—
282C22×D3—121no—
283C22×D3—241no—
284C22×D3—241no—
285C22×D3—241no—
286C22×D3—241no—
287C22×D3—242no—
288C22×D3—242no—
289C3×Q8—61no—
290C3×Q8—61no—
291C3×D4—61no—
292C3×D4—61no—
293C3×D4—121no—
294C3×D4—121no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—61no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4—241no—
306C2×C3×C4C2×D1211yescharacteristic
307C2×C3×C4C2×D1211yescharacteristic
308C2×C3×C4#23511yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4#23711yescharacteristic
315C2×C3×C4#23711yescharacteristic
316C2×C3×C4#23911yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318#67—41no—
319#67—41no—
320C2×Dic3—21no—
321C2×Dic3—41no—
322C2×Dic3—81no—
323D12—21no—
324D12—21no—
325D12—62no—
326D12—62no—
327D12—62no—
328D12—62no—
329D12—122no—
330D12—122no—
331D12—122no—
332D12—122no—
333D12—121no—
334D12—121no—
335D12—121no—
336D12—121no—
337C4×D3—41no—
338C4×D3—41no—
339Dic6—21no—
340Dic6—21no—
341C3×C8—42no—
342C3×C8—41no—
343C3×C8—41no—
344C3×C8—62no—
345C3×C8—62no—
346C3⋊C8—22no—
347C3⋊C8—22no—
348C3⋊C8—122no—
349C3⋊C8—121no—
350C3⋊C8—121no—
351C2×C32—21no—
352C2×C32—21no—
353C2×C32#39411yescharacteristic
354C2×C32#47111yescharacteristic
355C2×C32#47211yescharacteristic
356C3⋊D3—82no—
357C3×D3—81no—
358C24—181no—
359#41—61no—
360#41—61no—
361#41—61no—
362#41—61no—
363C2×Q8—31no—
364C2×D4—31no—
365C2×D4—61no—
366C2×D4—92no—
367C2×D4—181no—
368C2×D4—181no—
369C2×D4—181no—
370C2×D4—181no—
371C2×D4—181no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4C2×D3211yescharacteristic
375SD16—184no—
376D8—184no—
377M16—21no—
378M16—21no—
379M16—32no—
380M16—61no—
381M16—181no—
382M16—181no—
383C2×C8—21no—
384C2×C8—32no—
385C2×C8—61no—
386C2×C8—61no—
387C2×C8—61no—
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—121no—
401C22×C3—121no—
402C22×C3—121no—
403C22×C3#87511yescharacteristic
404C22×C3#88311yescharacteristic
405C22×C3#88411yescharacteristic
406C22×C3#88511yescharacteristic
407C22×C3#89411yescharacteristic
408C22×C3#93011yescharacteristic
409C2×D3—41no—
410C2×D3—41no—
411C2×D3—41no—
412C2×D3—124no—
413C2×D3—122no—
414C2×D3—122no—
415C2×D3—242no—
416C2×D3—242no—
417C2×D3—242no—
418C2×D3—242no—
419C2×D3—244no—
420C2×D3—241no—
421C2×D3—241no—
422C2×D3—241no—
423C2×D3—241no—
424C2×D3—242no—
425C2×D3—242no—
426C2×D3—244no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—121no—
432C3×C4—241no—
433C3×C4#88211yescharacteristic
434C3×C4#88211yescharacteristic
435C3×C4#88411yescharacteristic
436C3×C4#88611yescharacteristic
437C3×C4#89411yescharacteristic
438C3×C4#89511yescharacteristic
439C3×C4#93811yescharacteristic
440C3×C4#93911yescharacteristic
441Dic3—41no—
442Dic3—81no—
443C32#205111yescharacteristic, complemented, Sylow
444C23—61no—
445C23—182no—
446C23—361no—
447C23—361no—
448C23—721no—
449C23—721no—
450C23#379811yescharacteristic
451Q8—61no—
452Q8—61no—
453D4—61no—
454D4—61no—
455D4—121no—
456D4—121no—
457D4—182no—
458D4—182no—
459D4—361no—
460D4—361no—
461C2×C4—61no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—121no—
465C2×C4—241no—
466C2×C4#379611yescharacteristic
467C2×C4D3×D1211yescharacteristic
468C2×C4D3×D1211yescharacteristic
469C2×C4#380411yescharacteristic
470C2×C4D3×#6711yescharacteristic
471C2×C4#381111yescharacteristic
472C8—41no—
473C8—62no—
474C8—62no—
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—241no—
486C2×C3#467211yescharacteristic
487C2×C3#474911yescharacteristic
488C2×C3#475411yescharacteristic
489C2×C3#496111yescharacteristic
490C2×C3#514111yescharacteristic
491C2×C3#514211yescharacteristic
492D3—81no—
493D3—244no—
494D3—242no—
495D3—242no—
496C22—21no—
497C22—21no—
498C22—121no—
499C22—121no—
500C22—121no—
501C22—362no—
502C22—722no—
503C22—722no—
504C22—721no—
505C22—721no—
506C22#6385211yescharacteristic
507C22#6385311yescharacteristic
508C22#6390611yescharacteristic
509C4—121no—
510C4—241no—
511C4#6388611yescharacteristic
512C4#6389011yescharacteristic
513C4#6392311yescharacteristic
514C4#6395811yescharacteristic
515C3—21no—
516C3#6898611yescharacteristic, complemented
517C3#7000311yescharacteristic, complemented
518C2—21no—
519C2—21no—
520C2—241no—
521C2—722no—
522C2#1059099711yescharacteristic
523C2#1059099811yescharacteristic
524C2#1059131211yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#63825C2
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×#63650C2semidirect
3. C3×#5129C2semidirect
4. C2×#63577C2semidirect
5. C2×#63564C2semidirect
6. #10591087C2semidirect
7. C3×#4554C2semidirect
34. #5129D3semidirect
41. #4554D3semidirect
443. C32#2051semidirect
516. C3#68986semidirect
517. C3#70003semidirect

Maximal subgroups

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

subgroupindex
C2×#638252
C2×#636502
C3×#51292
C2×#635772
C2×#635642
#105910872
C3×#45542
#700033
#689863