Finite Group Databasebeta

← #11793905

Subgroups — #11793905

Order 1152.

713 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64117C211yesmaximal, characteristic
2C2×C3×#822C211yesmaximal, characteristic, complemented
3#10591106C211yesmaximal, characteristic, complemented
4C2×#63564C211yesmaximal, characteristic, complemented
5C2×#63559C211yesmaximal, characteristic, complemented
6#10591073C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#70714—31nomaximal
9#68986—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64117—22no—
14#64117—22no—
15C2×#3745—21no—
16C2×#3744—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#822—22no—
22#63567—21no—
23#63564—21no—
24#63564—22no—
25#63559—22no—
26#63557—22no—
27C2×#908—31no—
28C2×#908—31no—
29C2×#908—61no—
30C2×C3×#108—31no—
31#5133—31no—
32C2×#823—31no—
33C2×#823—31no—
34#5129—31no—
35C2×#822D311yescharacteristic, complemented
36C2×#821—31no—
37#5110—31no—
38#4966—31no—
39C2×#809—31no—
40C3×#343—31no—
41#4554D311yescharacteristic, complemented
42C23×C3⋊D3—21no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—21no—
45#3828—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—21no—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)D412yes—
55C2×C4⋊(C3⋊D3)D411yescharacteristic
56C2×C4×C3⋊D3—21no—
57C2×#634D411yescharacteristic
58C22×C3×Dic3—21no—
59C32×M16—21no—
60C32×M16D412yes—
61C2×C32×C8—21no—
62#3745—24no—
63#3744—24no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×#208—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C2×C3×C3⋊C8—21no—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8D412yes—
75#2051—91noSylow
76C2×#235—31no—
77C2×#235—31no—
78C2×#235—61no—
79C22×D12—31no—
80C22×D12—31no—
81C22×D12—61no—
82C2×C3×M16—21no—
83C2×C3×M16—31no—
84C2×C3×M16—31no—
85C2×C3×M16C2×D311yescharacteristic
86C2×C3×M16C2×D311yescharacteristic
87C22×C3×C8—31no—
88C2×C3×C4⋊C4—31no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×#208C2×D311yescharacteristic
91C2×#208C2×D311yescharacteristic
92C22×C3⋊C8C2×D311yescharacteristic
93#908—62no—
94#908—62no—
95#908—64no—
96#908—64no—
97#908—62no—
98#908—62no—
99C2×D24—61no—
100C2×D24—61no—
101C2×D24—62no—
102C2×#204—61no—
103C2×#204—61no—
104C2×#204—62no—
105C3×#108—62no—
106#823—62no—
107#823—62no—
108#822—22no—
109#821—62no—
110#821—61no—
111(C2×D3)⋊C8—62no—
112(C2×D3)⋊C8—62no—
113#816—61no—
114#810—61no—
115#809—61no—
116#809—62no—
117C23×C32#4111yescharacteristic
118C22×C3⋊D3—21no—
119C22×C3⋊D3—22no—
120C22×C3⋊D3—41no—
121C22×C3⋊D3—41no—
122C22×C3⋊D3—81no—
123C22×C3⋊D3—81no—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130#638—41no—
131#638—41no—
132C2×C3⋊Dic3—21no—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—21no—
135C4⋊(C3⋊D3)—22no—
136C4⋊(C3⋊D3)—21no—
137C4⋊(C3⋊D3)—41no—
138C4⋊(C3⋊D3)—41no—
139C4×C3⋊D3—41no—
140C4×C3⋊D3—41no—
141#634—21no—
142#634—21no—
143C2×C3×Dic3—41no—
144C2×C3×Dic3—81no—
145C32×C8—22no—
146C3×C3⋊C8—22no—
147C3×C3⋊C8—41no—
148C3×C3⋊C8—41no—
149C2×AGL(1,ℤ/8)—91no—
150C2×#108—31no—
151#417—91no—
152C2×#102—91no—
153C2×#100—91no—
154#408—91no—
155#343—31no—
156C23×D3—61no—
157C23×D3—61no—
158C23×D3—121no—
159C22×C3×C4—21no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C2×#67—61no—
164C2×#67—61no—
165C2×#67—121no—
166C22×Dic3—21no—
167#235—62no—
168#235—62no—
169#235—61no—
170#235—61no—
171#235—61no—
172#235—61no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—61no—
177#235—121no—
178#235—121no—
179C2×D12—31no—
180C2×D12—31no—
181C2×D12—32no—
182C2×D12—32no—
183C2×D12—61no—
184C2×D12—62no—
185C2×D12—62no—
186C2×D12—62no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—61no—
196C2×D12—61no—
197C2×D12—121no—
198C2×D12—121no—
199C2×D12—121no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—121no—
203C2×Dic6—31no—
204C2×Dic6—31no—
205C2×Dic6—61no—
206C3×M16—22no—
207C3×M16—21no—
208C3×M16—21no—
209C3×M16—22no—
210C3×M16—61no—
211C3×M16—61no—
212C3×M16—61no—
213C3×M16—61no—
214C3×M16D1212yes—
215C3×M16#6712yes—
216C2×C3×C8—22no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—32no—
220C2×C3×C8—61no—
221C2×C3×C8—61no—
222C2×C3×C8—61no—
223C2×C3×C8—61no—
224C3×C4⋊C4—61no—
225C3×C4⋊C4—61no—
226C4⋊Dic3—21no—
227C4⋊Dic3—21no—
228#208—21no—
229#208—21no—
230#208—21no—
231#208—21no—
232C2×C3⋊C8—21no—
233C2×C3⋊C8—21no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8D1212yes—
237D24—68no—
238D24—64no—
239D24—64no—
240#204—68no—
241#204—64no—
242#204—64no—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32#12111yescharacteristic
246C22×C32#12311yescharacteristic
247C22×C32#12411yescharacteristic
248C2×C3⋊D3—41no—
249C2×C3⋊D3—42no—
250C2×C3⋊D3—41no—
251C2×C3⋊D3—41no—
252C2×C3⋊D3—82no—
253C2×C3⋊D3—81no—
254C2×C3⋊D3—81no—
255C2×C3⋊D3—82no—
256C32×C4#12011yescharacteristic
257C32×C4#12111yescharacteristic
258C32×C4#12111yescharacteristic
259C32×C4#12311yescharacteristic
260C3⋊Dic3—41no—
261C3×Dic3—81no—
262C2×#41—91no—
263C22×D4—91no—
264AGL(1,ℤ/8)—182no—
265AGL(1,ℤ/8)—182no—
266C2×SD16—181no—
267C2×D8—181no—
268C2×M16—31no—
269C2×M16—31no—
270C2×M16D3211yescharacteristic
271C22×C8—31no—
272C2×C4⋊C4—31no—
273#108—62no—
274#103—181no—
275#102—182no—
276#102—181no—
277#100—182no—
278C22⋊C8—182no—
279C23×C3—21no—
280C23×C3#23511yescharacteristic
281C23×C3#23911yescharacteristic
282C22×D3—61no—
283C22×D3—61no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—121no—
287C22×D3—122no—
288C22×D3—122no—
289C22×D3—122no—
290C22×D3—121no—
291C22×D3—121no—
292C22×D3—121no—
293C22×D3—121no—
294C22×D3—242no—
295C22×D3—242no—
296C22×D3—241no—
297C22×D3—241no—
298C22×D3—241no—
299C22×D3—241no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—121no—
307C2×C3×C4—241no—
308C2×C3×C4C2×D1211yescharacteristic
309C2×C3×C4C2×D1211yescharacteristic
310C2×C3×C4#23511yescharacteristic
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4#23911yescharacteristic
318C2×C3×C4#23911yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320#67—122no—
321#67—122no—
322#67—121no—
323#67—121no—
324#67—121no—
325#67—121no—
326C2×Dic3—41no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—81no—
330C2×Dic3—121no—
331D12—64no—
332D12—62no—
333D12—62no—
334D12—61no—
335D12—62no—
336D12—61no—
337D12—61no—
338D12—62no—
339D12—62no—
340D12—61no—
341D12—122no—
342D12—121no—
343D12—122no—
344D12—122no—
345D12—121no—
346D12—121no—
347D12—121no—
348D12—121no—
349C4×D3—122no—
350C4×D3—122no—
351C4×D3—121no—
352C4×D3—121no—
353C4×D3—121no—
354C4×D3—121no—
355Dic6—62no—
356Dic6—61no—
357Dic6—61no—
358Dic6—61no—
359Dic6—61no—
360Dic6—121no—
361C3×C8—24no—
362C3×C8—22no—
363C3×C8—22no—
364C3×C8—62no—
365C3×C8—121no—
366C3×C8—121no—
367C3⋊C8—22no—
368C3⋊C8—41no—
369C3⋊C8—41no—
370C2×C32—21no—
371C2×C32—21no—
372C2×C32#39411yescharacteristic
373C2×C32#47111yescharacteristic
374C2×C32#47211yescharacteristic
375C3⋊D3—81no—
376C3⋊D3—82no—
377C24—181no—
378#41—181no—
379#41—181no—
380#41—181no—
381#41—181no—
382C2×Q8—91no—
383C2×D4—92no—
384C2×D4—91no—
385C2×D4—181no—
386C2×D4—181no—
387C2×D4—181no—
388C2×D4—181no—
389C2×D4—181no—
390C2×D4—181no—
391C22×C4—61no—
392C22×C4—181no—
393C22×C4C2×D3211yescharacteristic
394SD16—184no—
395D8—184no—
396M16—21no—
397M16—61no—
398M16—61no—
399M16—61no—
400M16—61no—
401M16#62612yes—
402C2×C8—21no—
403C2×C8—32no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—61no—
407C2×C8—61no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3#87511yescharacteristic
420C22×C3#88411yescharacteristic
421C22×C3#89411yescharacteristic
422C22×C3#89411yescharacteristic
423C22×C3#89511yescharacteristic
424C22×C3#94711yescharacteristic
425C2×D3—122no—
426C2×D3—124no—
427C2×D3—121no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—122no—
431C2×D3—121no—
432C2×D3—122no—
433C2×D3—121no—
434C2×D3—121no—
435C2×D3—241no—
436C2×D3—241no—
437C2×D3—242no—
438C2×D3—242no—
439C2×D3—242no—
440C2×D3—242no—
441C2×D3—244no—
442C2×D3—244no—
443C2×D3—241no—
444C2×D3—241no—
445C2×D3—241no—
446C2×D3—241no—
447C2×D3—242no—
448C2×D3—242no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—241no—
454C3×C4#88211yescharacteristic
455C3×C4#88411yescharacteristic
456C3×C4#89411yescharacteristic
457C3×C4#89411yescharacteristic
458C3×C4#89511yescharacteristic
459C3×C4#89511yescharacteristic
460C3×C4#93011yescharacteristic
461C3×C4#93711yescharacteristic
462Dic3—81no—
463Dic3—122no—
464Dic3—121no—
465Dic3—121no—
466C32#205111yescharacteristic, complemented, Sylow
467C23—181no—
468C23—182no—
469C23—361no—
470C23—361no—
471C23—721no—
472C23—721no—
473C23#379911yescharacteristic
474Q8—181no—
475Q8—181no—
476D4—181no—
477D4—182no—
478D4—181no—
479D4—182no—
480D4—361no—
481D4—361no—
482D4—361no—
483D4—361no—
484C2×C4—121no—
485C2×C4—181no—
486C2×C4—241no—
487C2×C4—361no—
488C2×C4—361no—
489C2×C4#379911yescharacteristic
490C2×C4#379911yescharacteristic
491C2×C4D3×D1211yescharacteristic
492C2×C4C2×#62611yescharacteristic
493C2×C4#381111yescharacteristic
494C2×C4#381111yescharacteristic
495C8—22no—
496C8—62no—
497C8—121no—
498C8—121no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—41no—
507C2×C3—41no—
508C2×C3#467211yescharacteristic
509C2×C3#474911yescharacteristic
510C2×C3#475411yescharacteristic
511C2×C3#489711yescharacteristic
512C2×C3#489811yescharacteristic
513C2×C3#499111yescharacteristic
514D3—244no—
515D3—242no—
516D3—241no—
517D3—242no—
518D3—241no—
519D3—242no—
520C22—21no—
521C22—21no—
522C22—361no—
523C22—361no—
524C22—361no—
525C22—362no—
526C22—722no—
527C22—722no—
528C22—721no—
529C22—721no—
530C22#6386411yescharacteristic
531C22#6389711yescharacteristic
532C22#6391011yescharacteristic
533C4—241no—
534C4—361no—
535C4#6389711yescharacteristic
536C4#6390911yescharacteristic
537C4#6391011yescharacteristic
538C4#6398111yescharacteristic
539C3—21no—
540C3#6898611yescharacteristic, complemented
541C3#7071411yescharacteristic, complemented
542C2—21no—
543C2—21no—
544C2—721no—
545C2—722no—
546C2#1059098711yescharacteristic
547C2#1059099011yescharacteristic
548C2#1059132111yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#64117C2
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. #10591106C2semidirect
4. C2×#63564C2semidirect
5. C2×#63559C2semidirect
6. #10591073C2semidirect
7. C3×#4554C2semidirect
35. C2×#822D3semidirect
41. #4554D3semidirect
466. C32#2051semidirect
540. C3#68986semidirect
541. C3#70714semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
C2×C3×#8222
#105911062
C2×#635642
C2×#635592
#105910732
C3×#45542
#707143
#689863