Finite Group Databasebeta

← #11774007

Subgroups — #11774007

Order 1152.

599 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×#63905C211yesmaximal, characteristic
2C3×#4726C211yesmaximal, characteristic, complemented
3D3×#830C211yesmaximal, characteristic, complemented
4#10589335C211yesmaximal, characteristic, complemented
5C3×#4468C211yesmaximal, characteristic, complemented
6#10589148C211yesmaximal, characteristic, complemented
7#10589145C211yesmaximal, characteristic, complemented
8#69969—31nomaximal
9#68122—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×#625C411yescharacteristic
12C2×#3750C2211yescharacteristic
13C2×C3×(C2×D3)⋊C4C2211yescharacteristic
14C2×C3×ΓL(1,𝔽25)—21no—
15C2×Dic3⋊Dic3C411yescharacteristic
16C2×(C2×D3)⋊Dic3C411yescharacteristic
17C2×(C2×D3)⋊Dic3C411yescharacteristic
18#63905—21no—
19#63905—21no—
20#63905—21no—
21#63905—21no—
22C2×D3×C3⋊C8—21no—
23C32×C22⋊C8C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×#830C2211yescharacteristic
26C3×#830C2211yescharacteristic
27C3×(C2×D3)⋊C8—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29C2×#929—31no—
30C2×#883—31no—
31C3×#407—31no—
32C2×#830—31no—
33#4726D311yescharacteristic, complemented
34D3×C22⋊C8—31no—
35C3×#323—31no—
36#4525—31no—
37#4469—31no—
38#4469—31no—
39#4469—31no—
40#4469—31no—
41#4469—61no—
42#4468—31no—
43#4468D311yescharacteristic, complemented
44C23×C3×D3C2×C411yescharacteristic
45C23×C3×D3C2×C411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3C2×C411yescharacteristic
48C22×C3⋊Dic3C2×C411yescharacteristic
49C22×C3×Dic3C2×C411yescharacteristic
50C22×C3×Dic3C2×C411yescharacteristic
51C2×C3×C4×D3—42no—
52C2×C3×C4×D3D411yescharacteristic
53C2×C3×C4×D3D411yescharacteristic
54C2×C3×C4×D3D411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×#625—21no—
57C2×#625—21no—
58C2×#625—42no—
59C2×C32×C8—21no—
60#3750—21no—
61#3750—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×(C2×D3)⋊C4—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C3×ΓL(1,𝔽25)—42no—
68Dic3⋊Dic3—21no—
69Dic3⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72(C2×D3)⋊Dic3—21no—
73(C2×D3)⋊Dic3—21no—
74D3×C3⋊C8—42no—
75#1468—91noSylow
76C23×C3×C4—31no—
77C22×#67—31no—
78C22×#67—31no—
79C22×C4×D3C2×D311yescharacteristic
80C2×C3×M16—61no—
81C2×C3×C22⋊C4—31no—
82C2×#217—31no—
83C2×#217—31no—
84#929—61no—
85#929—61no—
86#929—61no—
87#929—61no—
88C2×(C2×D3)⋊C4—31no—
89C2×(C2×D3)⋊C4—31no—
90C2×(C2×D3)⋊C4C2×D311yescharacteristic
91C2×C4⋊Dic3—31no—
92C2×Dic3⋊C4—31no—
93C2×Dic3⋊C4—31no—
94C2×Dic3⋊C4—31no—
95C2×Dic3⋊C4—61no—
96C22×C3⋊C8—61no—
97C2×ΓL(1,𝔽25)—21no—
98C2×D3×C8—61no—
99#883—61no—
100#883—61no—
101#883—61no—
102#883—61no—
103C3×C22⋊C8—21no—
104C3×C22⋊C8—31no—
105C3×C22⋊C8—31no—
106C3×C22⋊C8—61no—
107C3×C22⋊C8C2×D311yescharacteristic
108C3×C22⋊C8C2×D311yescharacteristic
109#830—31no—
110#830—31no—
111#830—61no—
112#830—61no—
113#830C2×D311yescharacteristic
114#830C2×D311yescharacteristic
115(C2×D3)⋊C8—21no—
116(C2×D3)⋊C8—61no—
117C23×C32C22×C411yescharacteristic
118C22×C3×D3—21no—
119C22×C3×D3—21no—
120C22×C3×D3—22no—
121C22×C3×D3—21no—
122C22×C3×D3—21no—
123C22×C3×D3—21no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C22×C3×D3—41no—
127C22×C3×D3C22⋊C411yescharacteristic
128C22×C3×D3C22⋊C411yescharacteristic
129C2×C32×C4—41no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C3⋊Dic3—21no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—41no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—41no—
139C2×C3×Dic3—41no—
140C2×C3×Dic3C22⋊C411yescharacteristic
141C2×C3×Dic3C22⋊C411yescharacteristic
142C3×C4×D3—22no—
143C3×C4×D3—22no—
144C3×C4×D3—41no—
145C3×C4×D3—41no—
146#625—42no—
147#625—42no—
148C32×C8—41no—
149C3⋊(C3⋊C8)—41no—
150C3×C3⋊C8—41no—
151C3×C3⋊C8—41no—
152C2×#123—91no—
153#407—31no—
154C2×C22⋊C8—91no—
155#324—91no—
156#324—91no—
157#323—31no—
158#323—91no—
159C24×C3—31no—
160C24×C3—31no—
161C23×D3C4×D311yescharacteristic
162C23×D3C4×D311yescharacteristic
163C22×C3×C4—21no—
164C22×C3×C4—31no—
165C22×C3×C4—31no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4—31no—
169C22×C3×C4—31no—
170C22×C3×C4—122no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C2×#67—61no—
174C2×#67—61no—
175C2×#67—61no—
176C2×#67—61no—
177C2×#67—122no—
178C2×#67—122no—
179C22×Dic3—31no—
180C22×Dic3—31no—
181C22×Dic3—31no—
182C22×Dic3—31no—
183C22×Dic3—61no—
184C22×Dic3—61no—
185C22×Dic3C4×D311yescharacteristic
186C22×Dic3C4×D311yescharacteristic
187C2×C4×D3—42no—
188C2×C4×D3D1211yescharacteristic
189C2×C4×D3D1211yescharacteristic
190C2×C4×D3#6711yescharacteristic
191C2×C4×D3#6711yescharacteristic
192C3×M16—122no—
193C2×C3×C8—21no—
194C2×C3×C8—21no—
195C2×C3×C8—41no—
196C2×C3×C8—61no—
197C2×C3×C8—61no—
198C3×C22⋊C4—61no—
199C3×C22⋊C4—61no—
200#217—61no—
201#217—61no—
202#217—61no—
203#217—61no—
204(C2×D3)⋊C4—21no—
205(C2×D3)⋊C4—21no—
206(C2×D3)⋊C4—61no—
207(C2×D3)⋊C4—61no—
208(C2×D3)⋊C4—61no—
209(C2×D3)⋊C4—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212Dic3⋊C4—61no—
213Dic3⋊C4—61no—
214Dic3⋊C4—61no—
215Dic3⋊C4—61no—
216Dic3⋊C4—61no—
217Dic3⋊C4—61no—
218Dic3⋊C4—121no—
219Dic3⋊C4—121no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—121no—
225C2×C3⋊C8—122no—
226ΓL(1,𝔽25)—42no—
227D3×C8—122no—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32C2×C22⋊C411yescharacteristic
231C22×C32#13111yescharacteristic
232C22×C32#13111yescharacteristic
233C2×C3×D3—21no—
234C2×C3×D3—21no—
235C2×C3×D3—21no—
236C2×C3×D3—21no—
237C2×C3×D3—21no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240C2×C3×D3—41no—
241C2×C3×D3—41no—
242C2×C3×D3—41no—
243C2×C3×D3—81no—
244C2×C3×D3—81no—
245C2×C3×D3#9912yes—
246C32×C4—21no—
247C32×C4—21no—
248C3⋊Dic3—41no—
249C3⋊Dic3—41no—
250C3×Dic3—21no—
251C3×Dic3—21no—
252C3×Dic3—41no—
253C22×D4—91no—
254C23×C4—31no—
255C2×M16—61no—
256C22×C8—181no—
257#123—181no—
258#123—181no—
259#123—181no—
260#123—181no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—91no—
263C2×C22⋊C4—31no—
264C2×C22⋊C4—91no—
265C2×C22⋊C4—91no—
266C22⋊C8—31no—
267C22⋊C8—31no—
268C22⋊C8—61no—
269C22⋊C8—91no—
270C22⋊C8—181no—
271C22⋊C8D3211yescharacteristic
272C23×C3—21no—
273C23×C3—31no—
274C23×C3—31no—
275C23×C3—62no—
276C23×C3—61no—
277C23×C3—61no—
278C23×C3—61no—
279C23×C3—61no—
280C23×C3—61no—
281C23×C3—121no—
282C23×C3—121no—
283C23×C3—121no—
284C23×C3C2×C4×D311yescharacteristic
285C23×C3C2×C4×D311yescharacteristic
286C22×D3—21no—
287C22×D3—21no—
288C22×D3—22no—
289C22×D3—21no—
290C22×D3—21no—
291C22×D3—21no—
292C22×D3—41no—
293C22×D3—41no—
294C22×D3—41no—
295C22×D3(C2×D3)⋊C411yescharacteristic
296C22×D3(C2×D3)⋊C411yescharacteristic
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—31no—
300C2×C3×C4—31no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—61no—
306C2×C3×C4—81no—
307C2×C3×C4—121no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4C2×D1211yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4C2×#6711yescharacteristic
315#67—122no—
316#67—122no—
317#67—122no—
318#67—122no—
319C2×Dic3—21no—
320C2×Dic3—41no—
321C2×Dic3—41no—
322C2×Dic3—62no—
323C2×Dic3—61no—
324C2×Dic3—61no—
325C2×Dic3—61no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—61no—
329C2×Dic3—61no—
330C2×Dic3—61no—
331C2×Dic3—121no—
332C2×Dic3—121no—
333C2×Dic3—121no—
334C2×Dic3—121no—
335C2×Dic3—121no—
336C2×Dic3—241no—
337C2×Dic3(C2×D3)⋊C411yescharacteristic
338C2×Dic3(C2×D3)⋊C411yescharacteristic
339C4×D3—22no—
340C4×D3—22no—
341C4×D3—41no—
342C4×D3—41no—
343C3×C8—41no—
344C3×C8—41no—
345C3×C8—81no—
346C3×C8—121no—
347C3×C8—121no—
348C3⋊C8—41no—
349C3⋊C8—41no—
350C3⋊C8—121no—
351C3⋊C8—121no—
352C3⋊C8—241no—
353C2×C32—21no—
354C2×C32—21no—
355C2×C32#40811yescharacteristic
356C2×C32C2×#9911yescharacteristic
357C2×C32#41311yescharacteristic
358C3×D3—22no—
359C3×D3—41no—
360C3×D3—81no—
361C24—31no—
362C24—31no—
363C2×D4—181no—
364C2×D4—181no—
365C2×D4—362no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—31no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—31no—
372C22×C4—91no—
373C22×C4—91no—
374C22×C4—122no—
375C22×C4C2×D3211yescharacteristic
376M16—122no—
377C2×C8—21no—
378C2×C8—61no—
379C2×C8—61no—
380C2×C8—181no—
381C2×C8—362no—
382C4⋊C4—181no—
383C4⋊C4—181no—
384C4⋊C4—181no—
385C4⋊C4—181no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—181no—
389C22⋊C4—181no—
390C22⋊C4—181no—
391C22⋊C4—181no—
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—32no—
400C22×C3—41no—
401C22×C3—41no—
402C22×C3—61no—
403C22×C3—61no—
404C22×C3—61no—
405C22×C3—61no—
406C22×C3—61no—
407C22×C3—122no—
408C22×C3—122no—
409C22×C3—121no—
410C22×C3—121no—
411C22×C3—121no—
412C22×C3—241no—
413C22×C3—241no—
414C22×C3D3×C22⋊C411yescharacteristic
415C22×C3#90111yescharacteristic
416C22×C3#90711yescharacteristic
417C22×C3#90711yescharacteristic
418C22×C3#90711yescharacteristic
419C22×C3C2×(C2×D3)⋊C411yescharacteristic
420C2×D3—21no—
421C2×D3—21no—
422C2×D3—21no—
423C2×D3—21no—
424C2×D3—21no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C2×D3—81no—
431C2×D3—81no—
432C2×D3#80612yes—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—61no—
440C3×C4—61no—
441C3×C4—121no—
442Dic3—21no—
443Dic3—21no—
444Dic3—41no—
445Dic3—122no—
446Dic3—121no—
447Dic3—121no—
448Dic3—121no—
449Dic3—121no—
450Dic3—241no—
451C32#146811yescharacteristic, complemented, Sylow
452C23—31no—
453C23—31no—
454C23—62no—
455C23—61no—
456C23—61no—
457C23—61no—
458C23—61no—
459C23—61no—
460C23—121no—
461C23—121no—
462C23—121no—
463C23C4×D3211yescharacteristic
464D4—362no—
465D4—362no—
466C2×C4—31no—
467C2×C4—31no—
468C2×C4—41no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—61no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—121no—
475C2×C4—121no—
476C2×C4—181no—
477C2×C4—181no—
478C2×C4—181no—
479C2×C4—181no—
480C2×C4—361no—
481C2×C4D3×D1211yescharacteristic
482C2×C4D3×#6711yescharacteristic
483C8—41no—
484C8—121no—
485C8—121no—
486C8—361no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—41no—
495C2×C3—41no—
496C2×C3—62no—
497C2×C3—121no—
498C2×C3—241no—
499C2×C3#472711yescharacteristic
500C2×C3D3×#9911yescharacteristic
501C2×C3#474511yescharacteristic
502C2×C3C2×#80611yescharacteristic
503C2×C3#512911yescharacteristic
504C2×C3#513211yescharacteristic
505D3—22no—
506D3—41no—
507D3—81no—
508C22—21no—
509C22—21no—
510C22—32no—
511C22—61no—
512C22—61no—
513C22—61no—
514C22—61no—
515C22—61no—
516C22—122no—
517C22—122no—
518C22—121no—
519C22—121no—
520C22—121no—
521C22—241no—
522C22—241no—
523C22#6380411yescharacteristic
524C22#6380511yescharacteristic
525C22D3×(C2×D3)⋊C411yescharacteristic
526C4—21no—
527C4—21no—
528C4—61no—
529C4—61no—
530C4—121no—
531C4—361no—
532C4—361no—
533C3—21no—
534C3#6812211yescharacteristic, complemented
535C3#6996911yescharacteristic, complemented
536C2—21no—
537C2—21no—
538C2—62no—
539C2—121no—
540C2—241no—
541C2D3×#80611yescharacteristic
542C2#1059095511yescharacteristic
543C2#1059100611yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×#625C4
cosocleC22×C32×C4C23
hypercenterC22⋊C8D32
hypocenterC32#1468
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4726C2semidirect
3. D3×#830C2semidirect
4. #10589335C2semidirect
5. C3×#4468C2semidirect
6. #10589148C2semidirect
7. #10589145C2semidirect
33. #4726D3semidirect
43. #4468D3semidirect
451. C32#1468semidirect
534. C3#68122semidirect
535. C3#69969semidirect

Maximal subgroups

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

subgroupindex
C2×#639052
C3×#47262
D3×#8302
#105893352
C3×#44682
#105891482
#105891452
#699693
#681223