Finite Group Databasebeta

← #11789913

Subgroups — #11789913

Order 1152.

697 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592687C211yesmaximal, characteristic
2#10591357C211yesmaximal, characteristic, complemented
3C2×#63564C211yesmaximal, characteristic
4C2×#63564C211yesmaximal, characteristic
5C2×#63555C211yesmaximal, characteristic, complemented
6C3×#4529C211yesmaximal, characteristic, complemented
7C3×#4529C211yesmaximal, characteristic, complemented
8#68857—31nomaximal
9#68856—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×#3752—21no—
13C2×#3752—21no—
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×Dic3⋊Dic3—21no—
20#63579—21no—
21#63564—22no—
22#63564C414yescomplemented
23#63555—22no—
24C2×#821—31no—
25C2×#821—31no—
26C2×#815—31no—
27C2×#815—31no—
28#4988—31no—
29#4988—31no—
30#4988—61no—
31#4984—31no—
32#4972—31no—
33C2×#809—31no—
34C2×#809—31no—
35C3×#340—31no—
36C3×#340—31no—
37#4529D311yescharacteristic, complemented
38#4529D311yescharacteristic, complemented
39C23×C3⋊D3—21no—
40C22×C32×C4—21no—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3D411yescharacteristic
43C22×C3⋊Dic3D411yescharacteristic
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)C2×C412yes—
50C22×C3×Dic3—21no—
51C22×C3×Dic3—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4—21no—
54#3752—42no—
55#3752—42no—
56C4×C3⋊Dic3—21no—
57C4×C3⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3C2×C412yes—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8C2×C412yes—
67C2×C3×C3⋊C8D412yes—
68Dic3⋊Dic3—42no—
69#1936—91noSylow
70C22×D12—31no—
71C22×D12—31no—
72C22×D12—61no—
73C22×C3×C8—31no—
74C22×C3×C8—31no—
75C2×C3×C4⋊C4—21no—
76C2×C3×C4⋊C4—31no—
77C2×C3×C4⋊C4—31no—
78C2×C3×C4⋊C4C2×D311yescharacteristic
79C2×C3×C4⋊C4C2×D311yescharacteristic
80C2×(C2×D3)⋊C4—61no—
81C2×(C2×D3)⋊C4—61no—
82C2×(C2×D3)⋊C4—61no—
83C2×(C2×D3)⋊C4—61no—
84C2×(C2×D3)⋊C4—62no—
85C2×(C2×D3)⋊C4—62no—
86C2×C4⋊Dic3—61no—
87C2×C4⋊Dic3C2×D311yescharacteristic
88C2×C4⋊Dic3C2×D311yescharacteristic
89C2×Dic3⋊C4—61no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—61no—
93C22×C3⋊C8C2×D311yescharacteristic
94C22×C3⋊C8C2×D311yescharacteristic
95C3⋊#95—61no—
96C3⋊#95—61no—
97#821—34no—
98#821—62no—
99#815—62no—
100#815—62no—
101#809—34no—
102#809—62no—
103C23×C32C2×D411yescharacteristic
104C22×C3⋊D3—22no—
105C22×C3⋊D3—41no—
106C22×C3⋊D3—41no—
107C22×C3⋊D3—41no—
108C22×C3⋊D3—41no—
109C22×C3⋊D3—41no—
110C22×C3⋊D3—41no—
111C2×C32×C4—41no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120C2×C3⋊Dic3—21no—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C2×C3⋊Dic3—21no—
126C4⋊(C3⋊D3)—22no—
127C4⋊(C3⋊D3)—22no—
128C4⋊(C3⋊D3)—41no—
129C4⋊(C3⋊D3)—41no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C3×C3⋊C8—22no—
137C3×C3⋊C8—22no—
138C2×#102—91no—
139C2×#102—91no—
140C2×#97—91no—
141#390—91no—
142#389—91no—
143#340—31no—
144#340—31no—
145C23×D3—62no—
146C23×D3—61no—
147C23×D3—61no—
148C22×C3×C4—22no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—61no—
153C22×C3×C4—61no—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C22×Dic3—21no—
157C22×Dic3—21no—
158C22×Dic3—31no—
159C22×Dic3—31no—
160C22×Dic3—31no—
161C22×Dic3—31no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C2×D12—32no—
165C2×D12—32no—
166C2×D12—62no—
167C2×D12—61no—
168C2×D12—61no—
169C2×D12—61no—
170C2×D12—61no—
171C2×D12—61no—
172C2×D12—61no—
173C2×D12—61no—
174C2×D12—61no—
175C2×D12—62no—
176C2×D12—61no—
177C2×D12—61no—
178C2×D12—121no—
179C2×D12—121no—
180C2×D12—121no—
181C2×D12—121no—
182C2×C3×C8—32no—
183C2×C3×C8—32no—
184C2×C3×C8—61no—
185C2×C3×C8—61no—
186C2×C3×C8—61no—
187C2×C3×C8—61no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—21no—
190C3×C4⋊C4—21no—
191C3×C4⋊C4—21no—
192C3×C4⋊C4—32no—
193C3×C4⋊C4—41no—
194C3×C4⋊C4—41no—
195C3×C4⋊C4—61no—
196C3×C4⋊C4—61no—
197C3×C4⋊C4—61no—
198(C2×D3)⋊C4—124no—
199(C2×D3)⋊C4—124no—
200(C2×D3)⋊C4—122no—
201(C2×D3)⋊C4—122no—
202(C2×D3)⋊C4—122no—
203(C2×D3)⋊C4—122no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—122no—
208C4⋊Dic3C4×D312yes—
209Dic3⋊C4—122no—
210C4×Dic3—61no—
211C4×Dic3—61no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—121no—
215C4×Dic3—121no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8C4×D312yes—
221C2×C3⋊C8D1212yes—
222C22×C32C4×D411yescharacteristic
223C22×C32#12111yescharacteristic
224C22×C32#12411yescharacteristic
225C22×C32AGL(1,ℤ/8)11yescharacteristic
226C22×C32AGL(1,ℤ/8)11yescharacteristic
227C22×C32AGL(1,ℤ/8)11yescharacteristic
228C22×C32#13711yescharacteristic
229C2×C3⋊D3—42no—
230C2×C3⋊D3—42no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—81no—
233C2×C3⋊D3—81no—
234C2×C3⋊D3—81no—
235C2×C3⋊D3—81no—
236C32×C4—81no—
237C32×C4#11711yescharacteristic
238C32×C4C4×D411yescharacteristic
239C32×C4#12311yescharacteristic
240C32×C4#12611yescharacteristic
241C3⋊Dic3—41no—
242C3⋊Dic3—41no—
243C3×Dic3—42no—
244C3×Dic3—81no—
245C22×D4—91no—
246C22×C8—31no—
247C22×C8—31no—
248C2×C4⋊C4—31no—
249C2×C4⋊C4—31no—
250C2×C4⋊C4—181no—
251C2×C4⋊C4D3211yescharacteristic
252C2×C22⋊C4—181no—
253C2×C22⋊C4—181no—
254C2×C42—91no—
255#102—94no—
256#102—182no—
257#97—182no—
258#95—181no—
259C23×C3—21no—
260C23×C3D3×D411yescharacteristic
261C23×C3D3×D411yescharacteristic
262C22×D3—64no—
263C22×D3—62no—
264C22×D3—62no—
265C22×D3—122no—
266C22×D3—122no—
267C22×D3—122no—
268C22×D3—122no—
269C22×D3—122no—
270C22×D3—122no—
271C22×D3—121no—
272C22×D3—121no—
273C22×D3—121no—
274C22×D3—121no—
275C22×D3—121no—
276C22×D3—121no—
277C22×D3—121no—
278C22×D3—121no—
279C22×D3—121no—
280C22×D3—121no—
281C22×D3—121no—
282C22×D3—121no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—42no—
290C2×C3×C4—42no—
291C2×C3×C4—42no—
292C2×C3×C4—41no—
293C2×C3×C4—41no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—62no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4C2×C4×D311yescharacteristic
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4C2×D1211yescharacteristic
307C2×C3×C4#23511yescharacteristic
308C2×C3×C4#23511yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4#23711yescharacteristic
313C2×C3×C4#23711yescharacteristic
314C2×C3×C4#23911yescharacteristic
315C2×C3×C4#23911yescharacteristic
316C2×Dic3—22no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—61no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—61no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—121no—
337C2×Dic3—121no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340D12—62no—
341D12—62no—
342D12—62no—
343D12—62no—
344D12—122no—
345D12—122no—
346D12—122no—
347D12—122no—
348D12—121no—
349D12—121no—
350D12—121no—
351D12—121no—
352C3×C8—62no—
353C3×C8—62no—
354C3⋊C8—22no—
355C3⋊C8—22no—
356C2×C32#38811yescharacteristic
357C2×C32#44011yescharacteristic
358C2×C32#44211yescharacteristic
359C2×C32#46811yescharacteristic
360C2×C32#46911yescharacteristic
361C2×C32#48911yescharacteristic
362C2×C32#49011yescharacteristic
363C3⋊D3—82no—
364C24—181no—
365C2×D4—92no—
366C2×D4—181no—
367C2×D4—181no—
368C2×D4—181no—
369C2×D4—181no—
370C2×D4—181no—
371C22×C4—21no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4—91no—
375C22×C4—91no—
376C22×C4C2×D3211yescharacteristic
377C2×C8—32no—
378C2×C8—32no—
379C2×C8—61no—
380C2×C8—61no—
381C2×C8—61no—
382C2×C8—61no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—32no—
386C4⋊C4—61no—
387C4⋊C4—61no—
388C4⋊C4—61no—
389C4⋊C4—362no—
390C22⋊C4—362no—
391C22⋊C4—362no—
392C42—181no—
393C42—181no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3#67⋊C411yescharacteristic
402C22×C3#88411yescharacteristic
403C22×C3#88511yescharacteristic
404C22×C3#88511yescharacteristic
405C22×C3#89311yescharacteristic
406C22×C3#89511yescharacteristic
407C22×C3#91111yescharacteristic
408C22×C3#91111yescharacteristic
409C22×C3#91411yescharacteristic
410C22×C3#91411yescharacteristic
411C22×C3#91411yescharacteristic
412C22×C3#91411yescharacteristic
413C22×C3#91811yescharacteristic
414C22×C3#91811yescharacteristic
415C2×D3—124no—
416C2×D3—124no—
417C2×D3—124no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—122no—
423C2×D3—122no—
424C2×D3—242no—
425C2×D3—242no—
426C2×D3—242no—
427C2×D3—242no—
428C2×D3—241no—
429C2×D3—241no—
430C2×D3—241no—
431C2×D3—241no—
432C2×D3—241no—
433C2×D3—241no—
434C2×D3—241no—
435C2×D3—241no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—82no—
441C3×C4—81no—
442C3×C4—81no—
443C3×C4—122no—
444C3×C4—241no—
445C3×C4#87211yescharacteristic
446C3×C4C4×D1211yescharacteristic
447C3×C4#67⋊C411yescharacteristic
448C3×C4#88611yescharacteristic
449C3×C4#89211yescharacteristic
450C3×C4#89411yescharacteristic
451C3×C4#89811yescharacteristic
452C3×C4#89811yescharacteristic
453Dic3—42no—
454Dic3—81no—
455Dic3—122no—
456Dic3—122no—
457Dic3—121no—
458Dic3—121no—
459Dic3—121no—
460Dic3—121no—
461C32#193611yescharacteristic, complemented, Sylow
462C23—182no—
463C23—361no—
464C23—361no—
465C23—361no—
466C23—361no—
467C23—361no—
468C23—361no—
469C23#381111yescharacteristic
470D4—182no—
471D4—182no—
472D4—361no—
473D4—361no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—62no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4#379611yescharacteristic
490C2×C4#379911yescharacteristic
491C2×C4C4×D3211yescharacteristic
492C2×C4D3×D1211yescharacteristic
493C2×C4#380411yescharacteristic
494C2×C4#380411yescharacteristic
495C8—62no—
496C8—62no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3#466911yescharacteristic
505C2×C3#467011yescharacteristic
506C2×C3#476411yescharacteristic
507C2×C3#476411yescharacteristic
508C2×C3#478211yescharacteristic
509C2×C3#478511yescharacteristic
510C2×C3#479411yescharacteristic
511C2×C3#479411yescharacteristic
512C2×C3#481211yescharacteristic
513C2×C3#481711yescharacteristic
514C2×C3#486511yescharacteristic
515C2×C3#486911yescharacteristic
516C2×C3#488611yescharacteristic
517C2×C3#488911yescharacteristic
518D3—244no—
519D3—242no—
520D3—242no—
521C22—362no—
522C22—362no—
523C22—362no—
524C22—721no—
525C22—721no—
526C22—721no—
527C22—721no—
528C22#6388111yescharacteristic
529C22#6391011yescharacteristic
530C22#6393711yescharacteristic
531C22#6393711yescharacteristic
532C22#6394111yescharacteristic
533C22#6394511yescharacteristic
534C22#6395311yescharacteristic
535C4—81no—
536C4—122no—
537C4—241no—
538C4—361no—
539C4—361no—
540C4#6383611yescharacteristic
541C4#6384811yescharacteristic
542C4#6388011yescharacteristic
543C4#6389011yescharacteristic
544C3—21no—
545C3#6885611yescharacteristic, complemented
546C3#6885711yescharacteristic, complemented
547C2—722no—
548C2#1059046211yescharacteristic
549C2#1059048411yescharacteristic
550C2#1059050811yescharacteristic
551C2#1059052211yescharacteristic
552C2#1059125911yescharacteristic
553C2#1059148011yescharacteristic
554C2#1059163211yescharacteristic
subgroupG/H
centerC23#3811
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1936
LCSG ▷ C2×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
2. #10591357C2semidirect
5. C2×#63555C2semidirect
6. C3×#4529C2semidirect
7. C3×#4529C2semidirect
22. #63564C4semidirect
37. #4529D3semidirect
38. #4529D3semidirect
461. C32#1936semidirect
545. C3#68856semidirect
546. C3#68857semidirect

Maximal subgroups

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

subgroupindex
#105926872
#105913572
C2×#635642
C2×#635552
C3×#45292
#688573
#688563