Finite Group Databasebeta

← #11785351

Subgroups — #11785351

Order 1152.

729 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×C3⋊C8C211yesmaximal, characteristic
2C3×#4987C211yesmaximal, characteristic
3C2×C3×#808C211yesmaximal, characteristic, complemented
4#10591313C211yesmaximal, characteristic
5C2×#63573C211yesmaximal, characteristic, complemented
6#10589395C211yesmaximal, characteristic, complemented
7#10589163C211yesmaximal, characteristic, complemented
8#70577—31nomaximal
9#69511—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×(C2×D3)⋊C4—21no—
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C2×(C2×D3)⋊Dic3—21no—
19C2×D3×C3⋊C8—22no—
20C2×D3×C3⋊C8—22no—
21C2×D3×C3⋊C8C414yescomplemented
22C3×C3⋊#95—21no—
23C3×#808—22no—
24#63579—21no—
25#63573—22no—
26C23×C3⋊C8—31no—
27C22×D3×C8—31no—
28C2×C3×#106—31no—
29C3×#380—31no—
30#5212—31no—
31C2×#817—31no—
32#4987—31no—
33#4987D311yescharacteristic
34C2×#808—31no—
35C2×#808D311yescharacteristic, complemented
36#4529—31no—
37#4529—31no—
38#4529—31no—
39#4529—31no—
40#4529—61no—
41C23×C3×D3D411yescharacteristic
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D411yescharacteristic
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3C2×C412yes—
53C2×C3×C4×D3Q812yes—
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)C2×C412yes—
61C3×(C2×D3)⋊C4—42no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C2×C3×C3⋊C8C2×C412yes—
67C2×C3×C3⋊C8D412yes—
68C2×C3×C3⋊C8D412yes—
69(C2×D3)⋊Dic3—42no—
70D3×C3⋊C8—28no—
71#1807—91noSylow
72C23×C3×C4—31no—
73C22×C4×D3C2×D311yescharacteristic
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×C3×C22⋊C4—61no—
81C2×#217—61no—
82C2×(C2×D3)⋊C4—21no—
83C2×(C2×D3)⋊C4—61no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—61no—
87C2×C4⋊Dic3C2×D311yescharacteristic
88C2×C4⋊Dic3C2×D311yescharacteristic
89C22×C3⋊C8—31no—
90C22×C3⋊C8—31no—
91C22×C3⋊C8—34no—
92C22×C3⋊C8—61no—
93C22×C3⋊C8—62no—
94C22×C3⋊C8—62no—
95C22×C3⋊C8C2×D311yescharacteristic
96C2×D3×C8—34no—
97C2×D3×C8—62no—
98C2×D3×C8—62no—
99C3×#106—62no—
100C3×#95—61no—
101C3⋊#95—21no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104#817—62no—
105#808—22no—
106#808—62no—
107C23×C32C2×D411yescharacteristic
108C22×C3×D3—21no—
109C22×C3×D3—21no—
110C22×C3×D3—21no—
111C22×C3×D3—21no—
112C22×C3×D3C4⋊C412yes—
113C22×C3×D3SD1612yes—
114C22×C3×D3SD1612yes—
115C2×C32×C4—41no—
116C2×C32×C4—41no—
117C2×C32×C4—41no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×Q811yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—41no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3C4⋊C412yes—
136C3×C4×D3—22no—
137C3×C4×D3—22no—
138C3×C4×D3—22no—
139C3×C4×D3—22no—
140C3⋊(C3⋊C8)—22no—
141C3×C3⋊C8C22⋊C414yescomplemented
142C23×C8—91no—
143C2×#106—31no—
144C2×#106—91no—
145#380—31no—
146#380—91no—
147#340—91no—
148#340—91no—
149C24×C3—31no—
150C23×D3#6711yescharacteristic
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—21no—
154C22×C3×C4—31no—
155C22×C3×C4—32no—
156C22×C3×C4—32no—
157C22×C3×C4—41no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—21no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—121no—
171C22×Dic3#6711yescharacteristic
172C2×C4×D3—21no—
173C2×C4×D3—21no—
174C2×C4×D3—21no—
175C2×C4×D3—21no—
176C2×C4×D3Dic612yes—
177C2×C4×D3C4×D312yes—
178C2×C3×C8—32no—
179C2×C3×C8—32no—
180C2×C3×C8—32no—
181C3×C4⋊C4—22no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—41no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4—61no—
191C3×C22⋊C4—122no—
192#217—122no—
193(C2×D3)⋊C4—42no—
194(C2×D3)⋊C4—122no—
195C4⋊Dic3—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—62no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3—61no—
203C4⋊Dic3—61no—
204C4⋊Dic3—121no—
205C2×C3⋊C8—32no—
206C2×C3⋊C8—32no—
207C2×C3⋊C8—62no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—68no—
213C2×C3⋊C8—121no—
214C2×C3⋊C8—121no—
215C2×C3⋊C8C4×D312yes—
216C2×C3⋊C8D1212yes—
217C2×C3⋊C8#6712yes—
218D3×C8—68no—
219C22×C32C2×C4⋊C411yescharacteristic
220C22×C32#12111yescharacteristic
221C22×C32#12111yescharacteristic
222C22×C32C2×SD1611yescharacteristic
223C22×C32C2×SD1611yescharacteristic
224C22×C32#13511yescharacteristic
225C22×C32#13511yescharacteristic
226C2×C3×D3—22no—
227C2×C3×D3—22no—
228C2×C3×D3—22no—
229C2×C3×D3—22no—
230C2×C3×D3—22no—
231C2×C3×D3—22no—
232C2×C3×D3#10614yescomplemented
233C32×C4—81no—
234C32×C4C2×C22⋊C411yescharacteristic
235C32×C4#11711yescharacteristic
236C32×C4C22⋊Q811yescharacteristic
237C32×C4C22⋊Q811yescharacteristic
238C3⋊Dic3—81no—
239C3×Dic3—22no—
240C3×Dic3—81no—
241C3×Dic3—81no—
242C23×C4—31no—
243C22×C8—31no—
244C22×C8—94no—
245C22×C8—91no—
246C22×C8—182no—
247C22×C8—182no—
248C2×C4⋊C4—31no—
249C2×C4⋊C4—31no—
250C2×C4⋊C4—91no—
251C2×C4⋊C4D3211yescharacteristic
252C2×C22⋊C4—61no—
253C2×C22⋊C4—181no—
254#106—62no—
255#106—182no—
256#95—61no—
257#95—181no—
258C23×C3—21no—
259C23×C3—32no—
260C23×C3—32no—
261C23×C3—32no—
262C23×C3—61no—
263C23×C3—61no—
264C23×C3—61no—
265C23×C3—61no—
266C23×C3D3×D411yescharacteristic
267C23×C3C2×#6711yescharacteristic
268C22×D3—21no—
269C22×D3—21no—
270C22×D3—21no—
271C22×D3—21no—
272C22×D3Dic3⋊C412yes—
273C22×D3#21412yes—
274C22×D3#21512yes—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—32no—
282C2×C3×C4—42no—
283C2×C3×C4—41no—
284C2×C3×C4—41no—
285C2×C3×C4—41no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—41no—
289C2×C3×C4—61no—
290C2×C3×C4—61no—
291C2×C3×C4—62no—
292C2×C3×C4—62no—
293C2×C3×C4—62no—
294C2×C3×C4—62no—
295C2×C3×C4—81no—
296C2×C3×C4—81no—
297C2×C3×C4—121no—
298C2×C3×C4—121no—
299C2×C3×C4—121no—
300C2×C3×C4—121no—
301C2×C3×C4—121no—
302C2×C3×C4—121no—
303C2×C3×C4C2×Dic611yescharacteristic
304C2×C3×C4C2×C4×D311yescharacteristic
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4C2×D1211yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4#23711yescharacteristic
310C2×C3×C4#23711yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4D3×Q811yescharacteristic
313C2×C3×C4#23911yescharacteristic
314C2×C3×C4C2×#6711yescharacteristic
315C2×Dic3—21no—
316C2×Dic3—21no—
317C2×Dic3—41no—
318C2×Dic3—41no—
319C2×Dic3—41no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—41no—
323C2×Dic3—122no—
324C2×Dic3—121no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328C2×Dic3—121no—
329C2×Dic3—121no—
330C2×Dic3—241no—
331C2×Dic3—241no—
332C2×Dic3Dic3⋊C412yes—
333C4×D3—22no—
334C4×D3—22no—
335C4×D3—22no—
336C4×D3—22no—
337C3×C8—34no—
338C3⋊C8—62no—
339C3⋊C8—62no—
340C3⋊C8—122no—
341C3⋊C8(C2×D3)⋊C414yescomplemented
342C2×C32#38011yescharacteristic
343C2×C32C2×#10611yescharacteristic
344C2×C32#42711yescharacteristic
345C2×C32#46511yescharacteristic
346C2×C32#46511yescharacteristic
347C2×C32#46511yescharacteristic
348C2×C32#46511yescharacteristic
349C3×D3—24no—
350C24—31no—
351C22×C4—21no—
352C22×C4—31no—
353C22×C4—32no—
354C22×C4—32no—
355C22×C4—61no—
356C22×C4—61no—
357C22×C4—61no—
358C22×C4—61no—
359C22×C4—61no—
360C22×C4—61no—
361C22×C4—181no—
362C22×C4C2×D3211yescharacteristic
363C2×C8—32no—
364C2×C8—32no—
365C2×C8—32no—
366C2×C8—92no—
367C2×C8—188no—
368C2×C8—181no—
369C2×C8—181no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—61no—
373C4⋊C4—61no—
374C4⋊C4—61no—
375C4⋊C4—61no—
376C4⋊C4—181no—
377C4⋊C4—181no—
378C22⋊C4—122no—
379C22⋊C4—362no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—34no—
388C22×C3—62no—
389C22×C3—62no—
390C22×C3—62no—
391C22×C3—62no—
392C22×C3—62no—
393C22×C3—62no—
394C22×C3D3×C4⋊C411yescharacteristic
395C22×C3#89511yescharacteristic
396C22×C3D3×SD1611yescharacteristic
397C22×C3D3×SD1611yescharacteristic
398C22×C3#91611yescharacteristic
399C22×C3#91611yescharacteristic
400C22×C3C2×Dic3⋊C411yescharacteristic
401C22×C3C2×#21411yescharacteristic
402C22×C3#93811yescharacteristic
403C22×C3#93911yescharacteristic
404C22×C3#93911yescharacteristic
405C22×C3C2×#21511yescharacteristic
406C22×C3#95011yescharacteristic
407C22×C3#95011yescharacteristic
408C2×D3—22no—
409C2×D3—22no—
410C2×D3—22no—
411C2×D3—22no—
412C2×D3—22no—
413C2×D3—22no—
414C2×D3#80814yescomplemented
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—62no—
420C3×C4—82no—
421C3×C4—81no—
422C3×C4—81no—
423C3×C4—241no—
424C3×C4—241no—
425C3×C4#87711yescharacteristic
426C3×C4#87811yescharacteristic
427C3×C4#87811yescharacteristic
428C3×C4D3×C22⋊C411yescharacteristic
429C3×C4#89211yescharacteristic
430C3×C4#89711yescharacteristic
431C3×C4C2×(C2×D3)⋊C411yescharacteristic
432C3×C4#94611yescharacteristic
433Dic3—22no—
434Dic3—81no—
435Dic3—81no—
436Dic3—242no—
437Dic3—241no—
438Dic3—241no—
439C32#180711yescharacteristic, complemented, Sylow
440C23—32no—
441C23—32no—
442C23—32no—
443C23—61no—
444C23—61no—
445C23—61no—
446C23—61no—
447C23D3×#6711yescharacteristic
448C2×C4—32no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—62no—
455C2×C4—62no—
456C2×C4—62no—
457C2×C4—62no—
458C2×C4—121no—
459C2×C4—121no—
460C2×C4—121no—
461C2×C4—121no—
462C2×C4—121no—
463C2×C4—121no—
464C2×C4—361no—
465C2×C4—361no—
466C2×C4—361no—
467C2×C4D3×Dic611yescharacteristic
468C2×C4#379611yescharacteristic
469C2×C4C4×D3211yescharacteristic
470C2×C4D3×D1211yescharacteristic
471C2×C4#380511yescharacteristic
472C2×C4D3×#6711yescharacteristic
473C8—34no—
474C8—182no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—64no—
483C2×C3D3×#10611yescharacteristic
484C2×C3#486011yescharacteristic
485C2×C3#486411yescharacteristic
486C2×C3#486411yescharacteristic
487C2×C3#494211yescharacteristic
488C2×C3C2×#80811yescharacteristic
489C2×C3#498711yescharacteristic
490C2×C3#499811yescharacteristic
491C2×C3#504111yescharacteristic
492C2×C3#504111yescharacteristic
493C2×C3#504811yescharacteristic
494C2×C3#504811yescharacteristic
495C2×C3#517111yescharacteristic
496C2×C3#517111yescharacteristic
497D3—24no—
498C22—34no—
499C22—62no—
500C22—62no—
501C22—62no—
502C22—62no—
503C22—62no—
504C22—62no—
505C22D3×Dic3⋊C411yescharacteristic
506C22#6388611yescharacteristic
507C22D3×#21411yescharacteristic
508C22#6393511yescharacteristic
509C22D3×#21511yescharacteristic
510C22#6394711yescharacteristic
511C22#6397011yescharacteristic
512C4—62no—
513C4—81no—
514C4—241no—
515C4—241no—
516C4—721no—
517C4#6387811yescharacteristic
518C4#6388711yescharacteristic
519C4#6389311yescharacteristic
520C4D3×(C2×D3)⋊C411yescharacteristic
521C3—21no—
522C3#6951111yescharacteristic, complemented
523C3#7057711yescharacteristic, complemented
524C2—64no—
525C2D3×#80811yescharacteristic
526C2#1059057211yescharacteristic
527C2#1059057711yescharacteristic
528C2#1059057811yescharacteristic
529C2#1059136611yescharacteristic
530C2#1059149911yescharacteristic
531C2#1059163411yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1807
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
3. C2×C3×#808C2semidirect
5. C2×#63573C2semidirect
6. #10589395C2semidirect
7. #10589163C2semidirect
21. C2×D3×C3⋊C8C4semidirect
35. C2×#808D3semidirect
141. C3×C3⋊C8C22⋊C4semidirect
232. C2×C3×D3#106semidirect
341. C3⋊C8(C2×D3)⋊C4semidirect
414. C2×D3#808semidirect
439. C32#1807semidirect
522. C3#69511semidirect
523. C3#70577semidirect

Maximal subgroups

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

subgroupindex
C22×D3×C3⋊C82
C3×#49872
C2×C3×#8082
#105913132
C2×#635732
#105893952
#105891632
#705773
#695113