Finite Group Databasebeta

← #11802681

Subgroups — #11802681

Order 1152.

1661 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic6C211yesmaximal, characteristic
2C2×C3×#872C211yesmaximal, characteristic
3C2×#63841C211yesmaximal, characteristic
4#10592628C211yesmaximal, characteristic, complemented
5C3×#4929C211yesmaximal, characteristic, complemented
6#10591362C214yesmaximal
7#10591235C214yesmaximal, complemented
8#10591220C211yesmaximal, characteristic, complemented
9#10591213C211yesmaximal, characteristic, complemented
10#82230—31nomaximal
11#76610—31nomaximal
12C22×#634C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#627C2212yes—
16C22×D3×Dic3C2212yes—
17C2×D3×Dic6—24no—
18C2×D3×Dic6—24no—
19C2×D3×Dic6C418yescomplemented
20C2×C32×C42C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C2×C3×(C2×D3)⋊C4C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C3×#872—24no—
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×Dic32C2212yes—
29#63841—24no—
30#63658C2214yes—
31C3×C3⋊#95C2214yes—
32#63579C2214yes—
33#63579C2214yes—
34C22×D3×Q8—31no—
35C23×Dic6—31no—
36C2×C3×#117—31no—
37C2×#926—31no—
38C2×#892—31no—
39C2×#872D311yescharacteristic
40C3×#391—31no—
41#5229—31no—
42#4973—31no—
43#4973—34no—
44#4943—34no—
45#4929—31no—
46#4929—31no—
47#4929—31no—
48#4929—31no—
49#4929—61no—
50#4929D311yescharacteristic, complemented
51#4664—34no—
52#4646—34no—
53C23×C3×D3C2311yescharacteristic
54C22×C32×C4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3C2312yes—
57C22×C3⋊Dic3C2312yes—
58C2×#634—22no—
59C2×#634—22no—
60C2×#634C2×C414yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2311yescharacteristic
65C2×C3×C4×D3C2×C414yes—
66C2×C3×C4×D3D414yes—
67C2×C3×C4×D3D414yes—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6C2×C414yes—
71C2×#627—24no—
72C2×#627—24no—
73C2×#627C2×C418yes—
74C2×D3×Dic3—24no—
75C2×D3×Dic3—24no—
76C2×D3×Dic3C2×C418yes—
77D3×Dic6—232no—
78C32×C42—22no—
79C4⋊(C3⋊Dic3)—22no—
80C3×(C2×D3)⋊C4—24no—
81C3×C4⋊Dic3—22no—
82C3×Dic3⋊C4—24no—
83C3×C4×Dic3—22no—
84(C2×D3)⋊Dic3—24no—
85Dic32—24no—
86#2310—91noSylow
87C22×C3×Q8—31no—
88C23×C3×C4—31no—
89C23×Dic3—32no—
90C2×D3×Q8—38no—
91C2×D3×Q8—64no—
92C2×D3×Q8—64no—
93C22×C4×D3—32no—
94C22×C4×D3C2×D311yescharacteristic
95C22×Dic6—31no—
96C22×Dic6—31no—
97C22×Dic6—32no—
98C22×Dic6—32no—
99C22×Dic6—38no—
100C22×Dic6—61no—
101C22×Dic6—64no—
102C22×Dic6—64no—
103C22×Dic6C2×D311yescharacteristic
104C3×#117—64no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C22⋊C4—32no—
108C2×C3×C42—21no—
109C2×C3×C42—31no—
110C2×C3×C42C2×D311yescharacteristic
111C2×C3×C42C2×D311yescharacteristic
112C2×#217—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4C2×D312yes—
115#926—64no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—61no—
119C2×C4⋊Dic3C2×D311yescharacteristic
120C2×Dic3⋊C4C2×D312yes—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—32no—
123C2×C4×Dic3C2×D311yescharacteristic
124#892—64no—
125#872—24no—
126C3×#95—34no—
127C3⋊#95—34no—
128C3⋊#95—34no—
129C3⋊#95—34no—
130C3⋊#95—34no—
131C3⋊#95—34no—
132C3⋊#95—34no—
133C3⋊#95—64no—
134C3⋊#95C2×D314yes—
135C23×C32C2411yescharacteristic
136C22×C3×D3—22no—
137C22×C3×D3—22no—
138C22×C3×D3C22×C412yes—
139C22×C3×D3C2×D412yes—
140C22×C3×D3C2×D412yes—
141C2×C32×C4—22no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4C22×C412yes—
145C2×C32×C4C2×D412yes—
146C2×C32×C4C2×D412yes—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—24no—
151C2×C3⋊Dic3C22×C414yes—
152#634—28no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—24no—
160C2×C3×Dic3C22×C414yes—
161C2×C3×Dic3C22×C412yes—
162C2×C3×Dic3C2×D412yes—
163C2×C3×Dic3C2×D412yes—
164C3×C4×D3C22⋊C4116yes—
165C3×Dic6—28no—
166#627—216no—
167D3×Dic3—216no—
168C23×Q8—91no—
169C2×#117—31no—
170C2×#117—91no—
171#391—31no—
172#391—94no—
173#391—91no—
174#391—91no—
175#391—91no—
176#381—94no—
177C24×C3—31no—
178C23×D3C22×D311yescharacteristic
179C2×C3×Q8—34no—
180C2×C3×Q8—62no—
181C2×C3×Q8—62no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—31no—
185C22×C3×C4—34no—
186C22×C3×C4—34no—
187C22×C3×C4—34no—
188C22×C3×C4—32no—
189C22×C3×C4—32no—
190C22×C3×C4—32no—
191C22×C3×C4C22×D312yes—
192C22×C3×C4C22×D312yes—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×Dic3—32no—
196C22×Dic3—32no—
197C22×Dic3—38no—
198C22×Dic3—32no—
199C22×Dic3—32no—
200C22×Dic3—62no—
201C22×Dic3—62no—
202C22×Dic3—64no—
203C22×Dic3—64no—
204C22×Dic3C22×D312yes—
205C22×Dic3C22×D312yes—
206C22×Dic3C22×D312yes—
207C22×Dic3C22×D311yescharacteristic
208D3×Q8—632no—
209C2×C4×D3—38no—
210C2×C4×D3—64no—
211C2×C4×D3—64no—
212C2×C4×D3C4×D314yes—
213C2×C4×D3D1214yes—
214C2×C4×D3#6714yes—
215C2×Dic6—22no—
216C2×Dic6—22no—
217C2×Dic6—34no—
218C2×Dic6—34no—
219C2×Dic6—38no—
220C2×Dic6—38no—
221C2×Dic6—64no—
222C2×Dic6—632no—
223C2×Dic6—64no—
224C2×Dic6—64no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C2×Dic6—62no—
229C2×Dic6—64no—
230C2×Dic6—64no—
231C2×Dic6—122no—
232C2×Dic6—122no—
233C2×Dic6C4×D314yes—
234C3×C4⋊C4—64no—
235C3×C4⋊C4—62no—
236C3×C22⋊C4—64no—
237C3×C42—22no—
238C3×C42—22no—
239C3×C42—42no—
240C3×C42—62no—
241#217—64no—
242(C2×D3)⋊C4—24no—
243(C2×D3)⋊C4—64no—
244C4⋊Dic3—22no—
245C4⋊Dic3—62no—
246C4⋊Dic3—62no—
247C4⋊Dic3—122no—
248Dic3⋊C4—24no—
249C4×Dic3—22no—
250C4×Dic3—64no—
251C4×Dic3—64no—
252C22×C32C23×C411yescharacteristic
253C22×C32C22×D411yescharacteristic
254C22×C32C22×D411yescharacteristic
255C22×C322−1+412yes—
256C22×C322−1+412yes—
257C2×C3×D3—24no—
258C2×C3×D3—22no—
259C2×C3×D3—22no—
260C2×C3×D3—24no—
261C2×C3×D3C2×C22⋊C414yes—
262C32×C4—42no—
263C32×C4C2×C22⋊C414yes—
264C3⋊Dic3—24no—
265C3⋊Dic3—42no—
266C3×Dic3—24no—
267C3×Dic3—42no—
268C3×Dic3—42no—
269C3×Dic3C2×C22⋊C414yes—
270C22×Q8—31no—
271C22×Q8—92no—
272C22×Q8—98no—
273C22×Q8—91no—
274C22×Q8—184no—
275C22×Q8—184no—
276C23×C4—31no—
277C23×C4—92no—
278#117—64no—
279#117—184no—
280C2×C4⋊C4—32no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—91no—
283C2×C22⋊C4—32no—
284C2×C22⋊C4—92no—
285C2×C42—31no—
286C2×C42—92no—
287C2×C42D3211yescharacteristic
288#95—34no—
289#95—94no—
290#95—94no—
291#95—94no—
292C23×C3—21no—
293C23×C3—32no—
294C23×C3—32no—
295C23×C3—32no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3C23×D311yescharacteristic
299C23×C3C23×D311yescharacteristic
300C22×D3—22no—
301C22×D3—22no—
302C22×D3C2×C4×D312yes—
303C22×D3C2×D1212yes—
304C22×D3C2×#6712yes—
305C3×Q8—68no—
306C2×C3×C4—24no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—22no—
311C2×C3×C4—22no—
312C2×C3×C4—22no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—32no—
317C2×C3×C4—32no—
318C2×C3×C4—32no—
319C2×C3×C4—316no—
320C2×C3×C4—34no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—64no—
329C2×C3×C4—62no—
330C2×C3×C4C2×C4×D312yes—
331C2×C3×C4C2×C4×D312yes—
332C2×C3×C4C2×D1212yes—
333C2×C3×C4D3×D412yes—
334C2×C3×C4D3×D412yes—
335C2×C3×C4C2×#6712yes—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—24no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—34no—
344C2×Dic3—34no—
345C2×Dic3—64no—
346C2×Dic3—616no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—62no—
353C2×Dic3—64no—
354C2×Dic3—64no—
355C2×Dic3—122no—
356C2×Dic3—122no—
357C2×Dic3—122no—
358C2×Dic3—124no—
359C2×Dic3C2×C4×D314yes—
360C2×Dic3C2×C4×D312yes—
361C2×Dic3C2×D1212yes—
362C2×Dic3C2×#6712yes—
363C4×D3—616no—
364C4×D3(C2×D3)⋊C4116yes—
365Dic6—28no—
366Dic6—616no—
367Dic6—68no—
368Dic6—68no—
369Dic6—616no—
370Dic6—128no—
371C2×C32C22×C22⋊C411yescharacteristic
372C2×C32#51912yes—
373C2×C32#53611yescharacteristic
374C2×C32#53611yescharacteristic
375C2×C32#53612yes—
376C3×D3—24no—
377C24—31no—
378C2×Q8—34no—
379C2×Q8—62no—
380C2×Q8—62no—
381C2×Q8—98no—
382C2×Q8—94no—
383C2×Q8—184no—
384C2×Q8—184no—
385C2×Q8—1832no—
386C2×Q8—182no—
387C2×Q8—182no—
388C22×C4—31no—
389C22×C4—34no—
390C22×C4—34no—
391C22×C4—34no—
392C22×C4—32no—
393C22×C4—32no—
394C22×C4—32no—
395C22×C4—98no—
396C22×C4—92no—
397C22×C4—92no—
398C22×C4—184no—
399C22×C4—184no—
400C22×C4C2×D3212yes—
401C22×C4C2×D3211yescharacteristic
402C4⋊C4—64no—
403C4⋊C4—62no—
404C4⋊C4—182no—
405C22⋊C4—64no—
406C22⋊C4—184no—
407C42—22no—
408C42—62no—
409C42—184no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—34no—
416C22×C3—62no—
417C22×C3—62no—
418C22×C3—64no—
419C22×C3—64no—
420C22×C3C22×C4×D311yescharacteristic
421C22×C3C22×C4×D311yescharacteristic
422C22×C3C22×D1211yescharacteristic
423C22×C3C2×D3×D411yescharacteristic
424C22×C3C2×D3×D411yescharacteristic
425C22×C3#100712yes—
426C22×C3#101012yes—
427C22×C3#101012yes—
428C22×C3#101012yes—
429C22×C3C22×#6711yescharacteristic
430C2×D3—24no—
431C2×D3—22no—
432C2×D3—22no—
433C2×D3—24no—
434C2×D3C2×(C2×D3)⋊C414yes—
435C3×C4—24no—
436C3×C4—34no—
437C3×C4—44no—
438C3×C4—42no—
439C3×C4—42no—
440C3×C4—64no—
441C3×C4—122no—
442C3×C4—122no—
443C3×C4D3×C22⋊C414yes—
444C3×C4C2×(C2×D3)⋊C414yes—
445Dic3—24no—
446Dic3—42no—
447Dic3—42no—
448Dic3—64no—
449Dic3—64no—
450Dic3—124no—
451Dic3—122no—
452Dic3—122no—
453Dic3—242no—
454Dic3C2×(C2×D3)⋊C414yes—
455C32#231011yescharacteristic, complemented, Sylow
456C23—32no—
457C23—32no—
458C23—32no—
459C23—62no—
460C23—62no—
461C23C22×D3211yescharacteristic
462Q8—68no—
463Q8—1816no—
464Q8—188no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—32no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—316no—
472C2×C4—34no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—64no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—94no—
481C2×C4—1816no—
482C2×C4—182no—
483C2×C4—182no—
484C2×C4—184no—
485C2×C4—182no—
486C2×C4C4×D3212yes—
487C2×C4D3×D1212yes—
488C2×C4D3×#6712yes—
489C2×C3—22no—
490C2×C3—22no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—64no—
495C2×C3C2×D3×C22⋊C411yescharacteristic
496C2×C3#551612yes—
497C2×C3#552611yescharacteristic
498C2×C3#552611yescharacteristic
499C2×C3#557212yes—
500C2×C3#562812yes—
501C2×C3#567511yescharacteristic
502C2×C3#572411yescharacteristic
503C2×C3C22×(C2×D3)⋊C411yescharacteristic
504C2×C3#582512yes—
505D3—24no—
506C22—34no—
507C22—64no—
508C22—64no—
509C22—62no—
510C22—62no—
511C22#6429712yes—
512C22#6429812yes—
513C22C2×C4×D3211yescharacteristic
514C22C2×D3×D1211yescharacteristic
515C22C2×D3×#6711yescharacteristic
516C4—34no—
517C4—42no—
518C4—64no—
519C4—122no—
520C4—122no—
521C4—184no—
522C4—362no—
523C4D3×(C2×D3)⋊C414yes—
524C3—21no—
525C3#7661011yescharacteristic, complemented
526C3#8223011yescharacteristic, complemented
527C2—64no—
528C2#1059388512yes—
529C2#1059389311yescharacteristic
530C2#1059389411yescharacteristic
531C2#1059488412yes—
532C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2310
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10592628C2semidirect
5. C3×#4929C2semidirect
7. #10591235C2semidirect
8. #10591220C2semidirect
9. #10591213C2semidirect
19. C2×D3×Dic6C4semidirect
50. #4929D3semidirect
455. C32#2310semidirect
525. C3#76610semidirect
526. C3#82230semidirect

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C2×C3×#8722
C2×#638412
#105926282
C3×#49292
#105913622
#105912352
#105912202
#105912132
#822303
#766103