Finite Group Databasebeta

← #11786845

Subgroups — #11786845

Order 1152.

781 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×D12C211yesmaximal, characteristic
2C2×C3×#821C211yesmaximal, characteristic
3#10591212C211yesmaximal, characteristic, complemented
4C2×#63575C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic
6#10589417C211yesmaximal, characteristic, complemented
7C3×#4550C211yesmaximal, characteristic, complemented
8#70167—31nomaximal
9#68670—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×D3×Dic3—21no—
12C22×C32×C8C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×#3724—21no—
19C2×(C2×D3)⋊Dic3—21no—
20Dic3×D12—22no—
21Dic3×D12—22no—
22C3×#821—22no—
23#63579—21no—
24#63575—22no—
25#63563C414yescomplemented
26C2×D4×Dic3—31no—
27C2×C4×D12—31no—
28C2×C3×#102—31no—
29C2×#832—31no—
30C2×#821—31no—
31C2×#821D311yescharacteristic
32C2×#818—31no—
33#4972—31no—
34C2×#807—31no—
35#4928—31no—
36C3×#336—31no—
37#4551—31no—
38#4551—31no—
39#4551—61no—
40#4550D311yescharacteristic, complemented
41C23×C3×D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3D411yescharacteristic
47C22×C3×Dic3D411yescharacteristic
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C2×C3×D12D412yes—
53C2×C3×D12Q812yes—
54C2×D3×Dic3—24no—
55C2×D3×Dic3—42no—
56C2×D3×Dic3—42no—
57C2×C32×C8—21no—
58C2×C32×C8—21no—
59C2×C32×C8—21no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)C2×C412yescomplemented
63C4⋊(C3⋊Dic3)D412yes—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8C2×C412yescomplemented
71#3724—42no—
72(C2×D3)⋊Dic3—24no—
73#1862—91noSylow
74C22×C3×D4—31no—
75C23×Dic3—61no—
76C22×D12C2×D311yescharacteristic
77C22×C4×D3—61no—
78C22×C3×C8—21no—
79C22×C3×C8—31no—
80C22×C3×C8C2×D311yescharacteristic
81C22×C3×C8C2×D311yescharacteristic
82C2×C3×C4⋊C4—31no—
83C2×C3×C42—31no—
84C2×#217—61no—
85D4×Dic3—62no—
86D4×Dic3—62no—
87C2×(C2×D3)⋊C4—61no—
88C2×C4⋊Dic3—31no—
89C2×C4⋊Dic3—31no—
90C2×C4⋊Dic3—31no—
91C2×C4⋊Dic3—31no—
92C2×C4⋊Dic3—61no—
93C2×C4⋊Dic3—61no—
94C2×C4⋊Dic3C2×D311yescharacteristic
95C2×Dic3⋊C4—61no—
96C2×Dic3⋊C4—61no—
97C2×C4×Dic3C2×D311yescharacteristic
98C22×C3⋊C8C2×D311yescharacteristic
99C4×D12—62no—
100C4×D12—62no—
101C3×#102—62no—
102#832—34no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105#821—22no—
106#821—34no—
107#818—62no—
108#807—62no—
109C23×C32C2×D411yescharacteristic
110C22×C3×D3—22no—
111C22×C3×D3—22no—
112C22×C3×D3—22no—
113C22×C3×D3—41no—
114C22×C3×D3—41no—
115C22×C3×D3—41no—
116C22×C3×D3—41no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×Q811yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3⋊Dic3—41no—
128C2×C3⋊Dic3—41no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—21no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3D812yes—
138C3×D12—22no—
139C3×D12—22no—
140C3×D12—22no—
141C3×D12C4⋊C414yescomplemented
142D3×Dic3—48no—
143C32×C8—41no—
144C3×C3⋊C8—22no—
145C2×C4×D4—91no—
146C2×#107—91no—
147C2×#102—31no—
148C2×#102—91no—
149#389—91no—
150#340—91no—
151#336—31no—
152C24×C3—61no—
153C23×D3—21no—
154C2×C3×D4—32no—
155C2×C3×D4—32no—
156C2×C3×D4—32no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—31no—
162C22×C3×C4—31no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—64no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—121no—
173C22×Dic3—121no—
174C22×Dic3—122no—
175C22×Dic3—122no—
176C22×Dic3D1211yescharacteristic
177C22×Dic3D1211yescharacteristic
178C2×D12—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12Dic612yes—
182C2×D12C4×D312yes—
183C2×D12#6712yes—
184C2×C4×D3—64no—
185C2×C4×D3—122no—
186C2×C4×D3—122no—
187C2×C3×C8—22no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—32no—
195C2×C3×C8—41no—
196C2×C3×C8—41no—
197C2×C3×C8—61no—
198C2×C3×C8—61no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C42—61no—
202C3×C42—61no—
203#217—64no—
204(C2×D3)⋊C4—64no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—32no—
208C4⋊Dic3—32no—
209C4⋊Dic3—32no—
210C4⋊Dic3—32no—
211C4⋊Dic3—62no—
212C4⋊Dic3—62no—
213C4⋊Dic3—61no—
214C4⋊Dic3—61no—
215C4⋊Dic3—61no—
216C4⋊Dic3—61no—
217C4⋊Dic3—121no—
218C4⋊Dic3—121no—
219Dic3⋊C4—122no—
220Dic3⋊C4—122no—
221C4×Dic3—21no—
222C4×Dic3—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—21no—
225C2×C3⋊C8C4×D312yescomplemented
226C22×C32C4×D411yescharacteristic
227C22×C32#12011yescharacteristic
228C22×C32C22⋊Q811yescharacteristic
229C22×C32C2×D811yescharacteristic
230C22×C32#13511yescharacteristic
231C22×C32AGL(1,ℤ/8)11yescharacteristic
232C22×C32#13711yescharacteristic
233C2×C3×D3—24no—
234C2×C3×D3—42no—
235C2×C3×D3—42no—
236C2×C3×D3—42no—
237C2×C3×D3—42no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240C32×C4C2×C4⋊C411yescharacteristic
241C32×C4C4×D411yescharacteristic
242C32×C4C22⋊Q811yescharacteristic
243C32×C4#12311yescharacteristic
244C3⋊Dic3—42no—
245C3⋊Dic3—42no—
246C3×Dic3—22no—
247C3×Dic3—41no—
248C3×Dic3—81no—
249C22×D4—31no—
250C23×C4—181no—
251C22×C8—31no—
252C22×C8D3211yescharacteristic
253C4×D4—182no—
254C4×D4—182no—
255C2×C4⋊C4—31no—
256C2×C4⋊C4—91no—
257C2×C4⋊C4—91no—
258C2×C4⋊C4—181no—
259C2×C22⋊C4—181no—
260C2×C42—31no—
261#107—182no—
262#102—62no—
263#102—94no—
264#95—181no—
265C23×C3—21no—
266C23×C3—62no—
267C23×C3—62no—
268C23×C3—62no—
269C23×C3—121no—
270C23×C3—121no—
271C23×C3—121no—
272C23×C3—121no—
273C23×C3C2×D1211yescharacteristic
274C23×C3D3×D411yescharacteristic
275C22×D3—22no—
276C22×D3—22no—
277C22×D3—22no—
278C22×D3—41no—
279C22×D3—41no—
280C22×D3—41no—
281C22×D3—41no—
282C3×D4—34no—
283C3×D4—62no—
284C3×D4—62no—
285C3×D4—62no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—32no—
293C2×C3×C4—61no—
294C2×C3×C4—61no—
295C2×C3×C4—61no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4C2×Dic611yescharacteristic
302C2×C3×C4C2×C4×D311yescharacteristic
303C2×C3×C4C2×C4×D311yescharacteristic
304C2×C3×C4#23511yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4#23711yescharacteristic
309C2×C3×C4#23711yescharacteristic
310C2×C3×C4#23711yescharacteristic
311C2×C3×C4D3×Q811yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×Dic3—21no—
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—21no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—62no—
325C2×Dic3—122no—
326C2×Dic3—122no—
327C2×Dic3—128no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—121no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—241no—
337C2×Dic3—241no—
338C2×Dic3—241no—
339C2×Dic3—241no—
340C2×Dic3D2412yes—
341D12—22no—
342D12—22no—
343D12—22no—
344D12Dic3⋊C414yescomplemented
345C4×D3—128no—
346C3×C8—42no—
347C3×C8—41no—
348C3×C8—41no—
349C3×C8—62no—
350C3⋊C8—22no—
351C2×C32#38511yescharacteristic
352C2×C32C4×D811yescharacteristic
353C2×C32#44011yescharacteristic
354C2×C32#44711yescharacteristic
355C2×C32#45211yescharacteristic
356C2×C32#47411yescharacteristic
357C2×C32#47811yescharacteristic
358C3×D3—44no—
359C24—61no—
360C2×D4—32no—
361C2×D4—32no—
362C2×D4—32no—
363C2×D4—61no—
364C2×D4—61no—
365C2×D4—61no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—61no—
369C22×C4—184no—
370C22×C4—181no—
371C22×C4—181no—
372C22×C4—362no—
373C22×C4—362no—
374C22×C4C2×D3211yescharacteristic
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—32no—
379C2×C8—61no—
380C2×C8—61no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C4⋊C4—92no—
384C4⋊C4—92no—
385C4⋊C4—181no—
386C4⋊C4—181no—
387C4⋊C4—362no—
388C22⋊C4—184no—
389C42—61no—
390C42—61no—
391C22×C3—21no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—64no—
399C22×C3—122no—
400C22×C3—122no—
401C22×C3—122no—
402C22×C3—122no—
403C22×C3—122no—
404C22×C3—122no—
405C22×C3C4×D1211yescharacteristic
406C22×C3#87811yescharacteristic
407C22×C3#67⋊C411yescharacteristic
408C22×C3#88211yescharacteristic
409C22×C3#89711yescharacteristic
410C22×C3C2×D2411yescharacteristic
411C22×C3#90411yescharacteristic
412C22×C3#90811yescharacteristic
413C22×C3#90911yescharacteristic
414C22×C3D3×D811yescharacteristic
415C22×C3#91111yescharacteristic
416C22×C3#91511yescharacteristic
417C22×C3#91611yescharacteristic
418C22×C3#93711yescharacteristic
419C2×D3—24no—
420C2×D3—42no—
421C2×D3—42no—
422C2×D3—42no—
423C2×D3—42no—
424C2×D3—42no—
425C2×D3—42no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—62no—
431C3×C4—121no—
432C3×C4—241no—
433C3×C4#87811yescharacteristic
434C3×C4#67⋊C411yescharacteristic
435C3×C4#67⋊C411yescharacteristic
436C3×C4#88311yescharacteristic
437C3×C4D3×C4⋊C411yescharacteristic
438C3×C4#89611yescharacteristic
439C3×C4C2×Dic3⋊C411yescharacteristic
440C3×C4#93511yescharacteristic
441Dic3—22no—
442Dic3—41no—
443Dic3—81no—
444Dic3—122no—
445Dic3—122no—
446Dic3—122no—
447Dic3—122no—
448Dic3—242no—
449Dic3—242no—
450C32#186211yescharacteristic, complemented, Sylow
451C23—62no—
452C23—62no—
453C23—62no—
454C23—121no—
455C23—121no—
456C23—121no—
457C23—121no—
458C23D3×D1211yescharacteristic
459D4—34no—
460D4—62no—
461D4—62no—
462D4—62no—
463C2×C4—32no—
464C2×C4—61no—
465C2×C4—61no—
466C2×C4—61no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4—121no—
472C2×C4—182no—
473C2×C4—182no—
474C2×C4—368no—
475C2×C4—361no—
476C2×C4—361no—
477C2×C4—361no—
478C2×C4—361no—
479C2×C4D3×Dic611yescharacteristic
480C2×C4C4×D3211yescharacteristic
481C2×C4#380211yescharacteristic
482C2×C4#380411yescharacteristic
483C2×C4#380511yescharacteristic
484C2×C4D3×#6711yescharacteristic
485C8—41no—
486C8—62no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—124no—
495C2×C3#466811yescharacteristic
496C2×C3C4×D2411yescharacteristic
497C2×C3#471011yescharacteristic
498C2×C3#473211yescharacteristic
499C2×C3#473311yescharacteristic
500C2×C3#475611yescharacteristic
501C2×C3#475711yescharacteristic
502C2×C3#475911yescharacteristic
503C2×C3#476311yescharacteristic
504C2×C3#484611yescharacteristic
505C2×C3#484711yescharacteristic
506C2×C3#494611yescharacteristic
507C2×C3#515611yescharacteristic
508C2×C3#517311yescharacteristic
509D3—44no—
510C22—64no—
511C22—122no—
512C22—122no—
513C22—122no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22D3×D2411yescharacteristic
518C22#6379511yescharacteristic
519C22#6380011yescharacteristic
520C22#6380611yescharacteristic
521C22#6388011yescharacteristic
522C22#6389311yescharacteristic
523C22#6392211yescharacteristic
524C4—62no—
525C4—121no—
526C4—241no—
527C4—362no—
528C4—362no—
529C4D3×Dic3⋊C411yescharacteristic
530C4#6389911yescharacteristic
531C4#6390211yescharacteristic
532C4#6396911yescharacteristic
533C3—21no—
534C3#6867011yescharacteristic, complemented
535C3#7016711yescharacteristic, complemented
536C2—124no—
537C2#1059074511yescharacteristic
538C2#1059074711yescharacteristic
539C2#1059076211yescharacteristic
540C2#1059077211yescharacteristic
541C2#1059094411yescharacteristic
542C2#1059096011yescharacteristic
543C2#1059137311yescharacteristic
subgroupG/H
centerC23D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1862
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. #10591212C2semidirect
4. C2×#63575C2semidirect
6. #10589417C2semidirect
7. C3×#4550C2semidirect
25. #63563C4semidirect
40. #4550D3semidirect
62. C4⋊(C3⋊Dic3)C2×C4semidirect
70. C2×C3×C3⋊C8C2×C4semidirect
141. C3×D12C4⋊C4semidirect
225. C2×C3⋊C8C4×D3semidirect
344. D12Dic3⋊C4semidirect
450. C32#1862semidirect
534. C3#68670semidirect
535. C3#70167semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×D122
C2×C3×#8212
#105912122
C2×#635752
C2×#635632
#105894172
C3×#45502
#701673
#686703