Finite Group Databasebeta

← #11785184

Subgroups — #11785184

Order 1152.

813 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63898C211yesmaximal, characteristic
2C2×#63641C211yesmaximal, characteristic, complemented
3C2×C3×#821C211yesmaximal, characteristic
4#10591359C211yesmaximal, characteristic, complemented
5C2×#63562C211yesmaximal, characteristic
6C3×#4551C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70153—31nomaximal
9#68892—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×D3×Dic3—21no—
12C22×C32×C8C2211yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×#3724—21no—
19C2×#3724—21no—
20C2×(C2×D3)⋊Dic3—21no—
21#63898—22no—
22#63898C414yescomplemented
23#63641—22no—
24C3×#821—22no—
25#63562—22no—
26C2×D4×Dic3—31no—
27C2×#893—31no—
28C2×C3×#102—31no—
29C2×#832—31no—
30C2×#821D311yescharacteristic
31C2×Dic3⋊C8—31no—
32C2×Dic3⋊C8—31no—
33C2×Dic3⋊C8—61no—
34#4975—31no—
35#4975—31no—
36C2×#809—31no—
37C3×#340—31no—
38#4551D311yescharacteristic, complemented
39#4529—31no—
40#4529—31no—
41C23×C3×D3—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3D411yescharacteristic
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3—21no—
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⋊Dic3C2×C412yes—
61C4×C3⋊Dic3D412yes—
62C2×C3⋊(C3⋊C8)—21no—
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3C2×C412yes—
71#3724—42no—
72#3724—42no—
73(C2×D3)⋊Dic3—24no—
74#1802—91noSylow
75C22×C3×D4—31no—
76C23×Dic3—61no—
77C22×D12C2×D311yescharacteristic
78C22×C4×D3—61no—
79C22×C3×C8—21no—
80C22×C3×C8C2×D311yescharacteristic
81C22×C3×C8C2×D311yescharacteristic
82C2×C3×C4⋊C4—31no—
83C2×C3×C4⋊C4—31no—
84C2×C3×C4⋊C4—31no—
85C2×#217—61no—
86D4×Dic3—34no—
87D4×Dic3—62no—
88C2×(C2×D3)⋊C4—61no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×Dic3⋊C4—61no—
93C2×Dic3⋊C4—61no—
94C2×Dic3⋊C4—61no—
95C2×Dic3⋊C4—61no—
96C2×C4×Dic3—31no—
97C2×C4×Dic3—31no—
98C2×C4×Dic3—61no—
99C22×C3⋊C8—31no—
100C22×C3⋊C8—31no—
101C22×C3⋊C8—61no—
102#893—34no—
103#893—62no—
104C3×#102—62no—
105#832—62no—
106#821—22no—
107Dic3⋊C8—62no—
108Dic3⋊C8—62no—
109Dic3⋊C8—64no—
110#809—62no—
111C23×C32C2×D411yescharacteristic
112C22×C3×D3—22no—
113C22×C3×D3—22no—
114C22×C3×D3—22no—
115C22×C3×D3—41no—
116C22×C3×D3—41no—
117C22×C3×D3—41no—
118C22×C3×D3—41no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×Q811yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C3⋊Dic3—21no—
126C2×C3⋊Dic3—21no—
127C2×C3⋊Dic3C22⋊C412yes—
128C2×C3⋊Dic3C22⋊C412yes—
129C2×C3⋊Dic3D812yes—
130C2×C3⋊Dic3SD1612yes—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3—41no—
137C2×C3×Dic3—41no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C3×D12—22no—
141C3×D12—22no—
142C3×D12—22no—
143C3×D12C4⋊C414yescomplemented
144D3×Dic3—48no—
145C32×C8—41no—
146C3⋊(C3⋊C8)—41no—
147C2×C4×D4—91no—
148C2×C4⋊C8—91no—
149C2×#102—31no—
150C2×#102—91no—
151#384—91no—
152#340—31no—
153#340—91no—
154C24×C3—61no—
155C23×D3—21no—
156C2×C3×D4—32no—
157C2×C3×D4—32no—
158C2×C3×D4—32no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C22×C3×C4—21no—
163C22×C3×C4—61no—
164C22×C3×C4—61no—
165C22×C3×C4—61no—
166C22×C3×C4C22×D311yescharacteristic
167C22×C3×C4C22×D311yescharacteristic
168C22×Dic3—21no—
169C22×Dic3—21no—
170C22×Dic3—21no—
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3—64no—
178C22×Dic3—122no—
179C22×Dic3—122no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12Dic612yes—
184C2×D12C4×D312yes—
185C2×D12#6712yes—
186C2×C4×D3—64no—
187C2×C4×D3—122no—
188C2×C4×D3—122no—
189C2×C3×C8—22no—
190C2×C3×C8—21no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—21no—
196C2×C3×C8—41no—
197C2×C3×C8—41no—
198C3×C4⋊C4—32no—
199C3×C4⋊C4—61no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C3×C4⋊C4—61no—
203C3×C4⋊C4—61no—
204#217—64no—
205(C2×D3)⋊C4—64no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3—21no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211C4⋊Dic3C4×D312yes—
212Dic3⋊C4—122no—
213Dic3⋊C4—122no—
214Dic3⋊C4—122no—
215Dic3⋊C4—122no—
216C4×Dic3—32no—
217C4×Dic3—32no—
218C4×Dic3—32no—
219C4×Dic3—32no—
220C4×Dic3—62no—
221C4×Dic3—62no—
222C2×C3⋊C8—62no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—61no—
229C2×C3⋊C8—121no—
230C2×C3⋊C8—121no—
231C22×C32C2×C22⋊C411yescharacteristic
232C22×C32#12111yescharacteristic
233C22×C32C22⋊Q811yescharacteristic
234C22×C32C2×D811yescharacteristic
235C22×C32C2×SD1611yescharacteristic
236C22×C32AGL(1,ℤ/8)11yescharacteristic
237C22×C32#13711yescharacteristic
238C2×C3×D3—24no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3—42no—
242C2×C3×D3—42no—
243C2×C3×D3—42no—
244C2×C3×D3—42no—
245C32×C4C2×C4⋊C411yescharacteristic
246C32×C4#11711yescharacteristic
247C32×C4#12111yescharacteristic
248C32×C4C22⋊Q811yescharacteristic
249C3⋊Dic3—22no—
250C3⋊Dic3#10214yescomplemented
251C3×Dic3—42no—
252C3×Dic3—81no—
253C3×Dic3—81no—
254C22×D4—31no—
255C23×C4—181no—
256C22×C8—91no—
257C22×C8D3211yescharacteristic
258C4×D4—94no—
259C4×D4—182no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4—31no—
263C2×C4⋊C4—181no—
264C2×C4⋊C4—181no—
265C2×C22⋊C4—181no—
266C2×C42—91no—
267C4⋊C8—182no—
268#102—62no—
269#102—182no—
270C23×C3—21no—
271C23×C3—62no—
272C23×C3—62no—
273C23×C3—62no—
274C23×C3—121no—
275C23×C3—121no—
276C23×C3—121no—
277C23×C3—121no—
278C23×C3D3×D411yescharacteristic
279C23×C3D3×D411yescharacteristic
280C22×D3—22no—
281C22×D3—22no—
282C22×D3—22no—
283C22×D3—41no—
284C22×D3—41no—
285C22×D3—41no—
286C22×D3—41no—
287C3×D4—34no—
288C3×D4—62no—
289C3×D4—62no—
290C3×D4—62no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—62no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4—121no—
306C2×C3×C4C2×Dic611yescharacteristic
307C2×C3×C4C2×C4×D311yescharacteristic
308C2×C3×C4C2×C4×D311yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4#23511yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4#23711yescharacteristic
315C2×C3×C4#23711yescharacteristic
316C2×C3×C4D3×Q811yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318C2×Dic3—22no—
319C2×Dic3—32no—
320C2×Dic3—32no—
321C2×Dic3—32no—
322C2×Dic3—32no—
323C2×Dic3—32no—
324C2×Dic3—32no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3—41no—
333C2×Dic3—41no—
334C2×Dic3—41no—
335C2×Dic3—62no—
336C2×Dic3—62no—
337C2×Dic3—62no—
338C2×Dic3—62no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—128no—
346D12—22no—
347D12—22no—
348D12—22no—
349D12Dic3⋊C414yescomplemented
350C4×D3—128no—
351C3×C8—42no—
352C3×C8—41no—
353C3×C8—41no—
354C3⋊C8—122no—
355C3⋊C8—121no—
356C3⋊C8—121no—
357C2×C32#38011yescharacteristic
358C2×C32C2×#10211yescharacteristic
359C2×C32#41711yescharacteristic
360C2×C32#45911yescharacteristic
361C2×C32#46111yescharacteristic
362C2×C32#47411yescharacteristic
363C2×C32#47611yescharacteristic
364C3×D3—44no—
365C24—61no—
366C2×D4—32no—
367C2×D4—32no—
368C2×D4—32no—
369C2×D4—61no—
370C2×D4—61no—
371C2×D4—61no—
372C22×C4—61no—
373C22×C4—61no—
374C22×C4—61no—
375C22×C4—91no—
376C22×C4—91no—
377C22×C4—184no—
378C22×C4—362no—
379C22×C4—362no—
380C22×C4C2×D3211yescharacteristic
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—181no—
385C2×C8—181no—
386C2×C8—181no—
387C4⋊C4—32no—
388C4⋊C4—61no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C4⋊C4—362no—
394C4⋊C4—362no—
395C22⋊C4—184no—
396C42—92no—
397C42—92no—
398C22×C3—21no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—64no—
406C22×C3—122no—
407C22×C3—122no—
408C22×C3—122no—
409C22×C3—122no—
410C22×C3—122no—
411C22×C3—122no—
412C22×C3#87811yescharacteristic
413C22×C3D3×C22⋊C411yescharacteristic
414C22×C3D3×C22⋊C411yescharacteristic
415C22×C3#88411yescharacteristic
416C22×C3#89611yescharacteristic
417C22×C3D3×D811yescharacteristic
418C22×C3D3×D811yescharacteristic
419C22×C3#91111yescharacteristic
420C22×C3D3×SD1611yescharacteristic
421C22×C3D3×SD1611yescharacteristic
422C22×C3#91411yescharacteristic
423C22×C3#91511yescharacteristic
424C22×C3#91811yescharacteristic
425C22×C3#93911yescharacteristic
426C2×D3—24no—
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—42no—
430C2×D3—42no—
431C2×D3—42no—
432C2×D3—42no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—122no—
438C3×C4—241no—
439C3×C4—241no—
440C3×C4#87211yescharacteristic
441C3×C4#87711yescharacteristic
442C3×C4#87811yescharacteristic
443C3×C4#88411yescharacteristic
444C3×C4D3×C4⋊C411yescharacteristic
445C3×C4#89611yescharacteristic
446C3×C4C2×Dic3⋊C411yescharacteristic
447C3×C4#93911yescharacteristic
448Dic3—34no—
449Dic3—34no—
450Dic3—42no—
451Dic3—64no—
452Dic3—62no—
453Dic3—62no—
454Dic3—81no—
455Dic3—81no—
456Dic3—122no—
457C32#180211yescharacteristic, complemented, Sylow
458C23—62no—
459C23—62no—
460C23—62no—
461C23—121no—
462C23—121no—
463C23—121no—
464C23—121no—
465C23#380211yescharacteristic
466D4—34no—
467D4—62no—
468D4—62no—
469D4—62no—
470C2×C4—62no—
471C2×C4—92no—
472C2×C4—92no—
473C2×C4—92no—
474C2×C4—92no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—121no—
480C2×C4—121no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—368no—
486C2×C4D3×Dic611yescharacteristic
487C2×C4#379511yescharacteristic
488C2×C4C4×D3211yescharacteristic
489C2×C4#380411yescharacteristic
490C2×C4D3×#6711yescharacteristic
491C2×C4#381111yescharacteristic
492C8—41no—
493C8—361no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—124no—
502C2×C3#466711yescharacteristic
503C2×C3#475911yescharacteristic
504C2×C3#476111yescharacteristic
505C2×C3D3×#10211yescharacteristic
506C2×C3D3×#10211yescharacteristic
507C2×C3#477111yescharacteristic
508C2×C3#478611yescharacteristic
509C2×C3#480311yescharacteristic
510C2×C3#481811yescharacteristic
511C2×C3#487011yescharacteristic
512C2×C3#489011yescharacteristic
513C2×C3#494211yescharacteristic
514C2×C3#515011yescharacteristic
515C2×C3#516211yescharacteristic
516D3—44no—
517C22—64no—
518C22—122no—
519C22—122no—
520C22—122no—
521C22—122no—
522C22—122no—
523C22—122no—
524C22#6379611yescharacteristic
525C22#6379711yescharacteristic
526C22#6379811yescharacteristic
527C22#6381111yescharacteristic
528C22#6388511yescharacteristic
529C22#6389911yescharacteristic
530C22#6392111yescharacteristic
531C4—94no—
532C4—122no—
533C4—182no—
534C4—241no—
535C4—241no—
536C4D3×Dic3⋊C411yescharacteristic
537C4#6387711yescharacteristic
538C4#6389611yescharacteristic
539C4#6397111yescharacteristic
540C3—21no—
541C3#6889211yescharacteristic, complemented
542C3#7015311yescharacteristic, complemented
543C2—124no—
544C2#1059074811yescharacteristic
545C2#1059074911yescharacteristic
546C2#1059077611yescharacteristic
547C2#1059077811yescharacteristic
548C2#1059094011yescharacteristic
549C2#1059095711yescharacteristic
550C2#1059136911yescharacteristic
subgroupG/H
centerC23#3802
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1802
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
2. C2×#63641C2semidirect
4. #10591359C2semidirect
6. C3×#4551C2semidirect
7. #10589163C2semidirect
22. #63898C4semidirect
38. #4551D3semidirect
143. C3×D12C4⋊C4semidirect
250. C3⋊Dic3#102semidirect
349. D12Dic3⋊C4semidirect
457. C32#1802semidirect
541. C3#68892semidirect
542. C3#70153semidirect

Maximal subgroups

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

subgroupindex
C2×#638982
C2×#636412
C2×C3×#8212
#105913592
C2×#635622
C3×#45512
#105891632
#701533
#688923