Finite Group Databasebeta

← #11802988

Subgroups — #11802988

Order 1152.

1365 conjugacy classes of subgroups.

The subgroup lattice has 499 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×#63849C211yesmaximal, characteristic
4C3×#4936C211yesmaximal, characteristic, complemented
5C3×#4935C211yesmaximal, characteristic, complemented
6#10591378C214yesmaximal
7#10591359C211yesmaximal, characteristic, complemented
8#10591264C214yesmaximal, complemented
9#10591230C211yesmaximal, characteristic, complemented
10#74359—31nomaximal
11#74225—31nomaximal
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×#624C2212yes—
14C2×C32×C42C2211yescharacteristic
15C2×#3752C2212yes—
16C2×#3750C2212yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18#64081C418yescomplemented
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic3C2214yes—
24C2×#3724C2212yes—
25C2×#3724C2214yes—
26C2×#3722C2212yes—
27C2×Dic32C2212yes—
28#63900—24no—
29#63849—24no—
30C3×C3⋊#95C2214yes—
31#63579C2214yes—
32C2×#892—31no—
33C2×#892—31no—
34C2×D3×C4⋊C4—31no—
35C2×D3×C4⋊C4—31no—
36C2×#872—31no—
37C2×#872—31no—
38C2×#872—61no—
39C3×#384—31no—
40C3×#382—31no—
41#4989—34no—
42#4977—31no—
43#4977—31no—
44#4976—34no—
45#4975—31no—
46#4975—31no—
47#4936D311yescharacteristic, complemented
48#4935D311yescharacteristic, complemented
49#4668—34no—
50#4647—34no—
51C23×C3⋊D3C2311yescharacteristic
52C22×C32×C4C2312yes—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3C2312yes—
55C22×C3⋊Dic3C2311yescharacteristic
56C2×C4×C3⋊D3C2×C414yes—
57C2×C4×C3⋊D3D414yes—
58C2×C4×C3⋊D3Q814yes—
59C22×C3×Dic3C2312yes—
60C22×C3×Dic3C2312yes—
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C2×#624—24no—
64C2×#624—44no—
65C32×C42C2×C414yescomplemented
66#3752C2×C418yes—
67#3750C2×C418yescomplemented
68C4×C3⋊Dic3C2×C414yescomplemented
69C3×C4⋊Dic3—22no—
70C3×C4⋊Dic3—22no—
71C3×C4⋊Dic3—22no—
72C3×C4⋊Dic3—22no—
73C3×C4⋊Dic3—44no—
74#3724—24no—
75#3724—44no—
76#3722—24no—
77Dic32—24no—
78#2317—91noSylow
79C22×C4×D3—31no—
80C22×C4×D3—31no—
81C22×C4×D3—32no—
82C22×C4×D3—32no—
83C22×C4×D3—61no—
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—31no—
86C2×C3×C4⋊C4—31no—
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—34no—
89C2×C3×C42—21no—
90C2×C3×C42C2×D311yescharacteristic
91C2×C3×C42C2×D311yescharacteristic
92C2×(C2×D3)⋊C4—32no—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—62no—
97C2×C4⋊Dic3C2×D311yescharacteristic
98C2×C4⋊Dic3C2×D311yescharacteristic
99C2×C4⋊Dic3C2×D311yescharacteristic
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×C4⋊Dic3C2×D314yes—
102C2×Dic3⋊C4—32no—
103C2×Dic3⋊C4—32no—
104C2×Dic3⋊C4—32no—
105C2×Dic3⋊C4—32no—
106C2×Dic3⋊C4—34no—
107C2×Dic3⋊C4—34no—
108C2×Dic3⋊C4—62no—
109C2×C4×Dic3—31no—
110C2×C4×Dic3—31no—
111C2×C4×Dic3—32no—
112C2×C4×Dic3—32no—
113C2×C4×Dic3—61no—
114#892—64no—
115#892—64no—
116D3×C4⋊C4—64no—
117D3×C4⋊C4—64no—
118#872—38no—
119#872—38no—
120#872—68no—
121C3×#95—34no—
122C3⋊#95—34no—
123C3⋊#95—34no—
124C3⋊#95C2×D314yes—
125C23×C32C2411yescharacteristic
126C22×C3⋊D3—22no—
127C22×C3⋊D3—22no—
128C22×C3⋊D3C22×C412yes—
129C22×C3⋊D3C2×D412yes—
130C22×C3⋊D3C2×Q812yes—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4C22×C414yes—
134C2×C32×C4C22×C412yes—
135C2×C32×C4C2×D412yes—
136C2×C32×C4C2×Q812yes—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3C22×C414yes—
140C2×C3⋊Dic3C22×C412yes—
141C2×C3⋊Dic3C2×D412yes—
142C2×C3⋊Dic3C2×Q812yes—
143C4×C3⋊D3C4⋊C4116yescomplemented
144C2×C3×Dic3—22no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—24no—
149C2×C3×Dic3—24no—
150C2×C3×Dic3—24no—
151C2×C3×Dic3—24no—
152#624—48no—
153C2×#117—91no—
154C2×#117—91no—
155C22×C4⋊C4—91no—
156#389—94no—
157#385—94no—
158#384—31no—
159#384—91no—
160#382—31no—
161#382—91no—
162C23×D3—31no—
163C23×D3—31no—
164C23×D3—61no—
165C22×C3×C4—21no—
166C22×C3×C4—22no—
167C22×C3×C4—32no—
168C22×C3×C4—32no—
169C22×C3×C4—32no—
170C22×C3×C4—32no—
171C22×C3×C4C22×D312yes—
172C22×C3×C4C22×D312yes—
173C22×C3×C4C22×D311yescharacteristic
174C22×C3×C4C22×D311yescharacteristic
175C22×Dic3—31no—
176C22×Dic3—31no—
177C22×Dic3—32no—
178C22×Dic3—32no—
179C22×Dic3—61no—
180C22×Dic3—62no—
181C22×Dic3C22×D312yes—
182C22×Dic3C22×D312yes—
183C22×Dic3C22×D312yes—
184C22×Dic3C22×D312yes—
185C2×C4×D3—34no—
186C2×C4×D3—34no—
187C2×C4×D3—34no—
188C2×C4×D3—34no—
189C2×C4×D3—34no—
190C2×C4×D3—34no—
191C2×C4×D3—64no—
192C2×C4×D3—64no—
193C2×C4×D3—64no—
194C2×C4×D3—64no—
195C2×C4×D3—64no—
196C2×C4×D3—124no—
197C2×C4×D3—124no—
198C3×C4⋊C4—62no—
199C3×C4⋊C4—62no—
200C3×C4⋊C4—62no—
201C3×C4⋊C4—62no—
202C3×C4⋊C4—124no—
203C3×C42—24no—
204C3×C42C4×D314yescomplemented
205C3×C42C4×D314yescomplemented
206(C2×D3)⋊C4—38no—
207(C2×D3)⋊C4—38no—
208(C2×D3)⋊C4—68no—
209(C2×D3)⋊C4—64no—
210(C2×D3)⋊C4—64no—
211C4⋊Dic3—22no—
212C4⋊Dic3—22no—
213C4⋊Dic3—22no—
214C4⋊Dic3—22no—
215C4⋊Dic3—44no—
216Dic3⋊C4—38no—
217Dic3⋊C4—38no—
218Dic3⋊C4—68no—
219Dic3⋊C4—64no—
220Dic3⋊C4—64no—
221Dic3⋊C4—124no—
222Dic3⋊C4—124no—
223C4×Dic3—34no—
224C4×Dic3—34no—
225C4×Dic3—64no—
226C4×Dic3—64no—
227C4×Dic3—64no—
228C22×C32C23×C411yescharacteristic
229C22×C32C22×D411yescharacteristic
230C22×C32C22×Q811yescharacteristic
231C22×C32H(5,𝔽2)12yes—
232C22×C322−1+412yes—
233C2×C3⋊D3—24no—
234C2×C3⋊D3—22no—
235C2×C3⋊D3—22no—
236C2×C3⋊D3—24no—
237C2×C3⋊D3C2×C4⋊C414yes—
238C32×C4—24no—
239C32×C4C2×C4⋊C414yes—
240C3⋊Dic3—24no—
241C3⋊Dic3C2×C4⋊C414yes—
242C3×Dic3—42no—
243C3×Dic3—42no—
244C3×Dic3—42no—
245C3×Dic3—42no—
246C23×C4—92no—
247C23×C4—91no—
248#117—98no—
249#117—184no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—31no—
253C2×C4⋊C4—31no—
254C2×C4⋊C4—34no—
255C2×C4⋊C4—92no—
256C2×C4⋊C4—92no—
257C2×C4⋊C4—94no—
258C2×C4⋊C4—184no—
259C2×C22⋊C4—92no—
260C2×C22⋊C4—92no—
261C2×C42—91no—
262C2×C42—92no—
263C2×C42D3211yescharacteristic
264#95—34no—
265#95—94no—
266C23×C3—21no—
267C23×C3C23×D311yescharacteristic
268C23×C3C23×D311yescharacteristic
269C22×D3—32no—
270C22×D3—32no—
271C22×D3—32no—
272C22×D3—32no—
273C22×D3—32no—
274C22×D3—32no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—62no—
278C22×D3—62no—
279C22×D3—62no—
280C22×D3—62no—
281C22×D3—62no—
282C22×D3—122no—
283C22×D3—122no—
284C2×C3×C4—22no—
285C2×C3×C4—22no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—24no—
292C2×C3×C4—42no—
293C2×C3×C4—42no—
294C2×C3×C4—62no—
295C2×C3×C4—62no—
296C2×C3×C4—62no—
297C2×C3×C4—62no—
298C2×C3×C4—64no—
299C2×C3×C4—64no—
300C2×C3×C4—64no—
301C2×C3×C4—64no—
302C2×C3×C4C2×C4×D314yes—
303C2×C3×C4C2×C4×D314yes—
304C2×C3×C4C2×C4×D312yes—
305C2×C3×C4C2×C4×D312yes—
306C2×C3×C4D3×D412yes—
307C2×C3×C4D3×D412yes—
308C2×C3×C4D3×Q812yes—
309C2×C3×C4D3×Q812yes—
310C2×Dic3—22no—
311C2×Dic3—22no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—24no—
315C2×Dic3—24no—
316C2×Dic3—24no—
317C2×Dic3—24no—
318C2×Dic3—32no—
319C2×Dic3—32no—
320C2×Dic3—32no—
321C2×Dic3—32no—
322C2×Dic3—32no—
323C2×Dic3—32no—
324C2×Dic3—34no—
325C2×Dic3—34no—
326C2×Dic3—62no—
327C2×Dic3—62no—
328C2×Dic3—62no—
329C2×Dic3—64no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334C2×Dic3—122no—
335C2×Dic3—122no—
336C4×D3—316no—
337C4×D3—316no—
338C4×D3—616no—
339C4×D3—128no—
340C4×D3—128no—
341C2×C32C22×C4⋊C411yescharacteristic
342C2×C32#52012yes—
343C2×C32#53511yescharacteristic
344C2×C32#53611yescharacteristic
345C2×C32#54412yes—
346C3⋊D3—24no—
347C24—91no—
348C22×C4—32no—
349C22×C4—32no—
350C22×C4—32no—
351C22×C4—32no—
352C22×C4—91no—
353C22×C4—94no—
354C22×C4—94no—
355C22×C4—94no—
356C22×C4—92no—
357C22×C4—184no—
358C22×C4—364no—
359C22×C4C2×D3212yes—
360C22×C4C2×D3211yescharacteristic
361C4⋊C4—62no—
362C4⋊C4—62no—
363C4⋊C4—62no—
364C4⋊C4—62no—
365C4⋊C4—98no—
366C4⋊C4—124no—
367C4⋊C4—184no—
368C4⋊C4—364no—
369C22⋊C4—98no—
370C22⋊C4—184no—
371C42—94no—
372C42—184no—
373C42#62414yescomplemented
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—22no—
378C22×C3—21no—
379C22×C3C22×C4×D311yescharacteristic
380C22×C3C22×C4×D311yescharacteristic
381C22×C3C2×D3×D411yescharacteristic
382C22×C3C2×D3×D411yescharacteristic
383C22×C3#100412yes—
384C22×C3C2×D3×Q811yescharacteristic
385C22×C3C2×D3×Q811yescharacteristic
386C22×C3#100712yes—
387C22×C3#100912yes—
388C22×C3#101012yes—
389C2×D3—34no—
390C2×D3—34no—
391C2×D3—64no—
392C2×D3—62no—
393C2×D3—62no—
394C2×D3—64no—
395C2×D3—62no—
396C2×D3—62no—
397C2×D3—64no—
398C2×D3—64no—
399C2×D3—64no—
400C2×D3—124no—
401C2×D3—122no—
402C2×D3—124no—
403C2×D3—122no—
404C3×C4—24no—
405C3×C4—24no—
406C3×C4—24no—
407C3×C4—44no—
408C3×C4—122no—
409C3×C4—122no—
410C3×C4—122no—
411C3×C4—122no—
412C3×C4D3×C4⋊C414yes—
413C3×C4D3×C4⋊C414yes—
414Dic3—34no—
415Dic3—34no—
416Dic3—42no—
417Dic3—42no—
418Dic3—42no—
419Dic3—42no—
420Dic3—64no—
421Dic3—64no—
422Dic3—64no—
423Dic3—124no—
424C32#231711yescharacteristic, complemented, Sylow
425C23—92no—
426C23—92no—
427C23—92no—
428C23—182no—
429C23—182no—
430C23C22×D3211yescharacteristic
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—64no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—64no—
439C2×C4—64no—
440C2×C4—64no—
441C2×C4—92no—
442C2×C4—92no—
443C2×C4—92no—
444C2×C4—916no—
445C2×C4—94no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—368no—
449C2×C4#379712yes—
450C2×C4#380212yes—
451C2×C4C2×#62414yes—
452C2×C4C2×#62412yes—
453C2×C3—22no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—22no—
457C2×C3—21no—
458C2×C3C2×D3×C4⋊C411yescharacteristic
459C2×C3C2×D3×C4⋊C411yescharacteristic
460C2×C3#550412yes—
461C2×C3#552312yes—
462C2×C3#567411yescharacteristic
463C2×C3#567511yescharacteristic
464C2×C3#568912yes—
465C2×C3#571511yescharacteristic
466C2×C3#572411yescharacteristic
467C2×C3#572912yes—
468D3—64no—
469D3—64no—
470D3—124no—
471C22—94no—
472C22—184no—
473C22—182no—
474C22—184no—
475C22—182no—
476C22#6429712yes—
477C22C2×#379711yescharacteristic
478C22C2×#380211yescharacteristic
479C22#6430712yes—
480C22C22×#62411yescharacteristic
481C4—24no—
482C4—94no—
483C4—122no—
484C4—122no—
485C4—122no—
486C4—122no—
487C4—184no—
488C4#6390014yes—
489C3—21no—
490C3#7422511yescharacteristic, complemented
491C3#7435911yescharacteristic, complemented
492C2—184no—
493C2#1059385512yes—
494C2#1059390811yescharacteristic
495C2#1059401011yescharacteristic
496C2C2×#6390011yescharacteristic
497C2#1059499012yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C42D32
hypocenterC32#2317
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. C3×#4936C2semidirect
5. C3×#4935C2semidirect
7. #10591359C2semidirect
8. #10591264C2semidirect
9. #10591230C2semidirect
18. #64081C4semidirect
47. #4936D3semidirect
48. #4935D3semidirect
65. C32×C42C2×C4semidirect
67. #3750C2×C4semidirect
68. C4×C3⋊Dic3C2×C4semidirect
143. C4×C3⋊D3C4⋊C4semidirect
204. C3×C42C4×D3semidirect
205. C3×C42C4×D3semidirect
373. C42#624semidirect
424. C32#2317semidirect
490. C3#74225semidirect
491. C3#74359semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C2×#639002
C2×#638492
C3×#49362
C3×#49352
#105913782
#105913592
#105912642
#105912302
#743593
#742253