Finite Group Databasebeta

← #11794070

Subgroups — #11794070

Order 1152.

705 conjugacy classes of subgroups.

The subgroup lattice has 569 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3715C211yesmaximal, characteristic
2C3×#4988C211yesmaximal, characteristic
3C2×C3×#810C211yesmaximal, characteristic, complemented
4#10591220C211yesmaximal, characteristic, complemented
5C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic
7#10589395C211yesmaximal, characteristic, complemented
8#70280—31nomaximal
9#69651—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×(C2×D3)⋊C4—21no—
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×#3715—22no—
20C2×#3715—22no—
21C2×#3715—22no—
22C3×#810—22no—
23#63579—21no—
24#63579—21no—
25Dic3⋊(C3⋊C8)—22no—
26#63563—22no—
27C22×#215—31no—
28C22×#214—31no—
29C2×C3×#103—31no—
30C3×#390—31no—
31#5229—31no—
32C2×#832—31no—
33C2×#821—31no—
34C2×Dic3⋊C8—31no—
35#4988D311yescharacteristic
36C2×#810D311yescharacteristic, complemented
37#4929—31no—
38C2×C4⋊(C3⋊C8)—31no—
39#4529—31no—
40#4529—31no—
41#4529—61no—
42C23×C3×D3—21no—
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D411yescharacteristic
48C22×C3×Dic3D411yescharacteristic
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12D412yes—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6D412yes—
61C32×C4⋊C4—21no—
62C32×C4⋊C4—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4⋊(C3⋊Dic3)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)D412yes—
68C3×(C2×D3)⋊C4—42no—
69C3×(C2×D3)⋊C4—42no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#3715—28no—
76#2055—91noSylow
77C22×C3×Q8—31no—
78C22×C3×D4—31no—
79C22×D12C2×D311yescharacteristic
80C22×Dic6C2×D311yescharacteristic
81C22×C3×C8—31no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4C2×D311yescharacteristic
84C2×C3×C4⋊C4C2×D311yescharacteristic
85C2×C3×C22⋊C4—61no—
86C2×C3×C22⋊C4—61no—
87C2×C3×C42—31no—
88C2×#215—62no—
89C2×#215—62no—
90C2×#215—62no—
91C2×#214—62no—
92C2×#214—62no—
93C2×#214—62no—
94C2×(C2×D3)⋊C4—21no—
95C2×(C2×D3)⋊C4—21no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—61no—
99C2×C4×Dic3C2×D311yescharacteristic
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—61no—
103C22×C3⋊C8C2×D311yescharacteristic
104C3×#103—62no—
105#832—62no—
106C3⋊#95—61no—
107C3⋊#95—61no—
108C3⋊#95—61no—
109C3⋊#95—61no—
110#821—62no—
111Dic3⋊C8—62no—
112#810—22no—
113C4⋊(C3⋊C8)—62no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—22no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—41no—
122C2×C32×C4—41no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3⋊Dic3—41no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—22no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3SD1612yescomplemented
143C3×D12—22no—
144C3×D12—22no—
145C3×D12—41no—
146C3×D12—41no—
147C3×Dic6—22no—
148C3×Dic6—22no—
149C3×Dic6—41no—
150C3×Dic6—41no—
151C3⋊(C3⋊C8)—22no—
152C3×C3⋊C8—41no—
153C22×SD16—91no—
154C2×C4⋊C8—91no—
155C2×#103—31no—
156C2×#102—91no—
157#391—91no—
158#390—31no—
159#340—91no—
160C24×C3—61no—
161C23×D3—21no—
162C2×C3×Q8—32no—
163C2×C3×Q8—61no—
164C2×C3×Q8—61no—
165C2×C3×Q8—61no—
166C2×C3×Q8—61no—
167C2×C3×Q8—61no—
168C2×C3×D4—32no—
169C2×C3×D4—61no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C22×C3×C4—21no—
175C22×C3×C4—21no—
176C22×C3×C4—21no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—41no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C22×Dic3—21no—
184C22×Dic3—61no—
185C22×Dic3—61no—
186C22×Dic3—121no—
187C22×Dic3#6711yescharacteristic
188C22×Dic3#6711yescharacteristic
189C2×D12—21no—
190C2×D12—21no—
191C2×D12—21no—
192C2×D12—21no—
193C2×D12—21no—
194C2×D12D1212yes—
195C2×Dic6—21no—
196C2×Dic6—21no—
197C2×Dic6—21no—
198C2×Dic6—21no—
199C2×Dic6—21no—
200C2×Dic6#6712yes—
201C2×C3×C8—61no—
202C2×C3×C8—61no—
203C2×C3×C8—61no—
204C3×C4⋊C4—22no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—21no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—41no—
210C3×C22⋊C4—122no—
211C3×C22⋊C4—122no—
212C3×C42—61no—
213C3×C42—61no—
214#215—68no—
215#214—68no—
216(C2×D3)⋊C4—42no—
217(C2×D3)⋊C4—42no—
218C4⋊Dic3—62no—
219C4⋊Dic3—61no—
220C4⋊Dic3—61no—
221C4⋊Dic3—61no—
222C4⋊Dic3—61no—
223C4⋊Dic3—121no—
224C4×Dic3—21no—
225C4×Dic3—21no—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—21no—
229C2×C3⋊C8—32no—
230C2×C3⋊C8—32no—
231C2×C3⋊C8—62no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—61no—
235C2×C3⋊C8—61no—
236C2×C3⋊C8—121no—
237C2×C3⋊C8—121no—
238C22×C32#12111yescharacteristic
239C22×C32#12111yescharacteristic
240C22×C32#12111yescharacteristic
241C22×C32C2×SD1611yescharacteristic
242C22×C32#13511yescharacteristic
243C22×C32AGL(1,ℤ/8)11yescharacteristic
244C22×C32#13711yescharacteristic
245C2×C3×D3—42no—
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C2×C3×D3—81no—
249C2×C3×D3—81no—
250C2×C3×D3—81no—
251C2×C3×D3—81no—
252C32×C4—81no—
253C32×C4#12011yescharacteristic
254C32×C4#12311yescharacteristic
255C32×C4#12311yescharacteristic
256C32×C4#12411yescharacteristic
257C3⋊Dic3—81no—
258C3×Dic3—22no—
259C3×Dic3—42no—
260C3×Dic3—41no—
261C22×Q8—31no—
262C22×D4—31no—
263C2×SD16—182no—
264C2×SD16—182no—
265C2×SD16—182no—
266C22×C8—31no—
267C22×C8—91no—
268C2×C4⋊C4—91no—
269C2×C4⋊C4D3211yescharacteristic
270C2×C22⋊C4—61no—
271C2×C22⋊C4—61no—
272C2×C42—31no—
273C4⋊C8—182no—
274#103—62no—
275#102—182no—
276#95—181no—
277#95—181no—
278C23×C3—21no—
279C23×C3—62no—
280C23×C3—121no—
281C23×C3—121no—
282C23×C3—121no—
283C23×C3—121no—
284C23×C3—121no—
285C23×C3—121no—
286C23×C3D3×D411yescharacteristic
287C23×C3C2×#6711yescharacteristic
288C22×D3—22no—
289C22×D3—41no—
290C22×D3—41no—
291C22×D3—41no—
292C22×D3—41no—
293C22×D3—41no—
294C22×D3—41no—
295C3×Q8—62no—
296C3×Q8—62no—
297C3×Q8—121no—
298C3×Q8—121no—
299C3×D4—62no—
300C3×D4—62no—
301C3×D4—121no—
302C3×D4—121no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—32no—
310C2×C3×C4—42no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—61no—
318C2×C3×C4—61no—
319C2×C3×C4—61no—
320C2×C3×C4—61no—
321C2×C3×C4—61no—
322C2×C3×C4—62no—
323C2×C3×C4—81no—
324C2×C3×C4—81no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4C2×D1211yescharacteristic
328C2×C3×C4#23511yescharacteristic
329C2×C3×C4#23511yescharacteristic
330C2×C3×C4#23511yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4#23711yescharacteristic
336C2×C3×C4#23711yescharacteristic
337C2×C3×C4#23711yescharacteristic
338C2×C3×C4C2×#6711yescharacteristic
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—22no—
344C2×Dic3—21no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—122no—
348C2×Dic3—121no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—241no—
355C2×Dic3—241no—
356C2×Dic3#21412yescomplemented
357D12—22no—
358D12—22no—
359D12—41no—
360D12—41no—
361Dic6—22no—
362Dic6—22no—
363Dic6—41no—
364Dic6—41no—
365C3×C8—121no—
366C3⋊C8—41no—
367C3⋊C8—62no—
368C3⋊C8—62no—
369C3⋊C8—122no—
370C2×C32#39411yescharacteristic
371C2×C32#46011yescharacteristic
372C2×C32#46111yescharacteristic
373C2×C32#46311yescharacteristic
374C2×C32#46411yescharacteristic
375C2×C32#46511yescharacteristic
376C2×C32#46811yescharacteristic
377C3×D3—82no—
378C24—61no—
379C2×Q8—32no—
380C2×Q8—61no—
381C2×Q8—61no—
382C2×Q8—61no—
383C2×Q8—61no—
384C2×Q8—61no—
385C2×D4—32no—
386C2×D4—61no—
387C2×D4—61no—
388C2×D4—61no—
389C2×D4—61no—
390C2×D4—61no—
391C22×C4—21no—
392C22×C4—31no—
393C22×C4—31no—
394C22×C4—61no—
395C22×C4—181no—
396C22×C4C2×D3211yescharacteristic
397SD16—188no—
398C2×C8—61no—
399C2×C8—61no—
400C2×C8—61no—
401C2×C8—92no—
402C2×C8—181no—
403C2×C8—181no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—181no—
407C4⋊C4—181no—
408C22⋊C4—122no—
409C22⋊C4—122no—
410C42—61no—
411C42—61no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—122no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3—241no—
423C22×C3—241no—
424C22×C3—241no—
425C22×C3—241no—
426C22×C3#88411yescharacteristic
427C22×C3#88411yescharacteristic
428C22×C3D3×SD1611yescharacteristic
429C22×C3#91411yescharacteristic
430C22×C3#91811yescharacteristic
431C22×C3#91911yescharacteristic
432C22×C3#93011yescharacteristic
433C22×C3#93211yescharacteristic
434C22×C3C2×#21411yescharacteristic
435C22×C3#93811yescharacteristic
436C22×C3#93911yescharacteristic
437C22×C3#93911yescharacteristic
438C22×C3#95011yescharacteristic
439C22×C3#95111yescharacteristic
440C2×D3—42no—
441C2×D3—42no—
442C2×D3—42no—
443C2×D3—81no—
444C2×D3—81no—
445C2×D3—81no—
446C2×D3—81no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—62no—
452C3×C4—82no—
453C3×C4—81no—
454C3×C4—81no—
455C3×C4—122no—
456C3×C4—121no—
457C3×C4#88211yescharacteristic
458C3×C4#88311yescharacteristic
459C3×C4#88311yescharacteristic
460C3×C4#88511yescharacteristic
461C3×C4#88511yescharacteristic
462C3×C4#88611yescharacteristic
463C3×C4#92911yescharacteristic
464C3×C4#93711yescharacteristic
465Dic3—22no—
466Dic3—42no—
467Dic3—41no—
468Dic3—242no—
469Dic3—241no—
470Dic3—241no—
471C32#205511yescharacteristic, complemented, Sylow
472C23—62no—
473C23—121no—
474C23—121no—
475C23—121no—
476C23—121no—
477C23—121no—
478C23—121no—
479C23D3×#6711yescharacteristic
480Q8—62no—
481Q8—62no—
482Q8—121no—
483Q8—121no—
484D4—62no—
485D4—62no—
486D4—121no—
487D4—121no—
488C2×C4—32no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—61no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—62no—
498C2×C4—121no—
499C2×C4—121no—
500C2×C4—361no—
501C2×C4—361no—
502C2×C4—361no—
503C2×C4#379511yescharacteristic
504C2×C4#379811yescharacteristic
505C2×C4D3×D1211yescharacteristic
506C2×C4#380211yescharacteristic
507C2×C4#380511yescharacteristic
508C2×C4D3×#6711yescharacteristic
509C8—121no—
510C8—182no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—242no—
519C2×C3#480711yescharacteristic
520C2×C3#481211yescharacteristic
521C2×C3#481811yescharacteristic
522C2×C3#481911yescharacteristic
523C2×C3#495911yescharacteristic
524C2×C3#496111yescharacteristic
525C2×C3#501611yescharacteristic
526C2×C3#501911yescharacteristic
527C2×C3#504111yescharacteristic
528C2×C3#504211yescharacteristic
529C2×C3#505411yescharacteristic
530C2×C3#507511yescharacteristic
531C2×C3#516311yescharacteristic
532C2×C3#518511yescharacteristic
533D3—82no—
534C22—122no—
535C22—122no—
536C22—122no—
537C22—241no—
538C22—241no—
539C22—241no—
540C22—241no—
541C22#6388511yescharacteristic
542C22#6390611yescharacteristic
543C22D3×#21411yescharacteristic
544C22#6393411yescharacteristic
545C22#6394311yescharacteristic
546C22#6394911yescharacteristic
547C22#6397011yescharacteristic
548C4—62no—
549C4—81no—
550C4—121no—
551C4—122no—
552C4—721no—
553C4#6389111yescharacteristic
554C4#6390511yescharacteristic
555C4#6391511yescharacteristic
556C4#6392211yescharacteristic
557C3—21no—
558C3#6965111yescharacteristic, complemented
559C3#7028011yescharacteristic, complemented
560C2—242no—
561C2#1059051411yescharacteristic
562C2#1059051511yescharacteristic
563C2#1059053411yescharacteristic
564C2#1059055911yescharacteristic
565C2#1059139011yescharacteristic
566C2#1059143811yescharacteristic
567C2#1059157811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2055
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C3×#810C2semidirect
4. #10591220C2semidirect
5. C2×Dic3⋊(C3⋊C8)C2semidirect
7. #10589395C2semidirect
36. C2×#810D3semidirect
142. C2×C3×Dic3SD16semidirect
356. C2×Dic3#214semidirect
471. C32#2055semidirect
558. C3#69651semidirect
559. C3#70280semidirect

Maximal subgroups

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

subgroupindex
C22×#37152
C3×#49882
C2×C3×#8102
#105912202
C2×Dic3⋊(C3⋊C8)2
C2×#635632
#105893952
#702803
#696513