Finite Group Databasebeta

← #11775130

Subgroups — #11775130

Order 1152.

708 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5627C211yesmaximal, characteristic
2D3×C3⋊#95C211yesmaximal, characteristic, complemented
3#10591154C211yesmaximal, characteristic, complemented
4#10589404C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic, complemented
7#10589149C211yesmaximal, characteristic, complemented
8#71708—31nomaximal
9#68334—31nomaximal
10C2×C3×#239C411yescharacteristic, complemented
11C22×C3×C4×D3C2211yescharacteristic
12C22×D3×Dic3—21no—
13C32×C22⋊Q8C2211yescharacteristic
14C3×#946C411yescharacteristic, complemented
15C3×#930C2211yescharacteristic
16C3×#895C411yescharacteristic, complemented
17C3×#894—21no—
18C3×#893—21no—
19C3×#892C411yescharacteristic, complemented
20C3×#882—21no—
21C3×#67⋊C4—21no—
22C2×#3711—21no—
23#63658C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27#63579—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29C3×#525—31no—
30#5627D311yescharacteristic
31C2×C3⋊#95—31no—
32#5207—31no—
33#4726—31no—
34D3×#95—31no—
35C3×#328—31no—
36#4538—31no—
37#4538—31no—
38#4538—61no—
39#4538D311yescharacteristic, complemented
40#4537—31no—
41#4537—31no—
42#4470—31no—
43#4451—31no—
44C23×C3×D3D411yescharacteristic
45C2×C32×Q8C2×C411yescharacteristic, complemented
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C3×#239—42no—
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12C2×C411yescharacteristic, complemented
55C2×C3×C4×D3—21no—
56C2×C3×C4×D3—42no—
57C2×C3×C4×D3C2×C411yescharacteristic
58C2×C3×C4×D3C2×C411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C2×C3×C4×D3D411yescharacteristic
61C2×D3×Dic3—24no—
62C2×D3×Dic3—42no—
63C2×D3×Dic3—42no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4C2×C411yescharacteristic, complemented
66C32×C22⋊C4—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C3×(C2×D3)⋊C4—21no—
69C3×(C2×D3)⋊C4—21no—
70C3×(C2×D3)⋊C4—21no—
71C3×(C2×D3)⋊C4—21no—
72C3×C4⋊Dic3C2×C411yescharacteristic, complemented
73C3×Dic3⋊C4—21no—
74C3×C4×Dic3—21no—
75C2×C3×C3⋊C8—21no—
76#3711—42no—
77#1504—91noSylow
78C2×C3×#41—31no—
79C23×C3×C4—31no—
80C23×Dic3—61no—
81C2×#239Dic311yescharacteristic, complemented
82C22×C4×D3—61no—
83C22×C4×D3C2×D311yescharacteristic
84C3×#123—61no—
85C3×C22⋊Q8—21no—
86C3×C22⋊Q8—31no—
87C3×C22⋊Q8C2×D311yescharacteristic
88C3×C22⋊Q8C2×D311yescharacteristic
89C3×#121—31no—
90C3×#121—31no—
91C3×#120—61no—
92C3×C4×D4—61no—
93C3×C4×D4—61no—
94C3×#117—31no—
95#946Dic311yescharacteristic, complemented
96#930C2×D311yescharacteristic
97C2×#208—61no—
98C2×ΓL(1,𝔽25)—61no—
99#895Dic311yescharacteristic, complemented
100#894—21no—
101#893—21no—
102#892Dic311yescharacteristic, complemented
103#882—21no—
104#67⋊C4—21no—
105C3×C22⋊C8—31no—
106C3×#95—31no—
107C3⋊#95—31no—
108C3⋊#95—31no—
109C3⋊#95—61no—
110C3⋊#95—61no—
111C3⋊#95—61no—
112C3⋊#95C2×D311yescharacteristic
113#830—31no—
114#830—31no—
115#830—61no—
116#830—61no—
117#830C2×D311yescharacteristic
118(C2×D3)⋊C8—61no—
119C23×C32C2×D411yescharacteristic
120C22×C3×D3—21no—
121C22×C3×D3—21no—
122C22×C3×D3—22no—
123C22×C3×D3—22no—
124C22×C3×D3—21no—
125C22×C3×D3C22⋊C411yescharacteristic
126C22×C3×D3C22⋊C411yescharacteristic
127C32×Q8—41no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4—41no—
131C2×C32×C4C22×C411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C3⋊Dic3—22no—
134C2×C3⋊Dic3—41no—
135C2×C3⋊Dic3—41no—
136C3×#67—41no—
137C3×#67—41no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C2×C3×Dic3—41no—
143C2×C3×Dic3C22⋊C411yescharacteristic
144C2×C3×Dic3C22⋊C411yescharacteristic
145C3×D12—41no—
146C3×D12—42no—
147C3×D12—42no—
148C3×C4×D3—22no—
149C3×C4×D3—22no—
150C3×C4×D3—41no—
151C3×C4×D3—41no—
152C3×C4×D3—42no—
153D3×Dic3—48no—
154C3⋊(C3⋊C8)—41no—
155C3×C3⋊C8—41no—
156#525—31no—
157#407—91no—
158C2×#95—91no—
159#328—31no—
160#328—91no—
161#327—91no—
162#327—91no—
163C24×C3—31no—
164C23×D3#6711yescharacteristic
165C3×#41—122no—
166C2×C3×Q8—21no—
167C2×C3×Q8C4×D311yescharacteristic, complemented
168C2×C3×Q8C2×Dic311yescharacteristic, complemented
169C2×C3×D4—31no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C22×C3×C4—21no—
174C22×C3×C4—31no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—31no—
178C22×C3×C4—31no—
179C22×C3×C4—61no—
180C22×C3×C4—61no—
181C22×C3×C4—122no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—21no—
185C22×Dic3—21no—
186C22×Dic3—64no—
187C22×Dic3—61no—
188C22×Dic3—61no—
189C22×Dic3—121no—
190C22×Dic3—122no—
191C22×Dic3—122no—
192C22×Dic3#6711yescharacteristic
193#239—42no—
194C2×D12—21no—
195C2×D12—21no—
196C2×D12C2×Dic311yescharacteristic, complemented
197C2×C4×D3—21no—
198C2×C4×D3—42no—
199C2×C4×D3—64no—
200C2×C4×D3—122no—
201C2×C4×D3—122no—
202C2×C4×D3C2×Dic311yescharacteristic
203C2×C4×D3C2×Dic311yescharacteristic
204C2×C4×D3#6711yescharacteristic
205C2×C4×D3#6711yescharacteristic
206C2×C3×C8—61no—
207C3×C4⋊C4—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—31no—
211C3×C4⋊C4—41no—
212C3×C4⋊C4—61no—
213C3×C4⋊C4C4×D311yescharacteristic, complemented
214C3×C4⋊C4C2×Dic311yescharacteristic, complemented
215C3×C22⋊C4—21no—
216C3×C22⋊C4—21no—
217C3×C22⋊C4—41no—
218C3×C22⋊C4—61no—
219C3×C22⋊C4—61no—
220C3×C22⋊C4—61no—
221C3×C22⋊C4—61no—
222C3×C42—61no—
223(C2×D3)⋊C4—21no—
224(C2×D3)⋊C4—21no—
225(C2×D3)⋊C4—21no—
226(C2×D3)⋊C4—21no—
227C4⋊Dic3C2×Dic311yescharacteristic, complemented
228Dic3⋊C4—21no—
229C4×Dic3—21no—
230#208—122no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—121no—
235ΓL(1,𝔽25)—122no—
236C22×C32—21no—
237C22×C32—21no—
238C22×C32C2×C22⋊C411yescharacteristic
239C22×C32AGL(1,ℤ/8)11yescharacteristic
240C22×C32#13711yescharacteristic
241C2×C3×D3—24no—
242C2×C3×D3—24no—
243C2×C3×D3—21no—
244C2×C3×D3—21no—
245C2×C3×D3—21no—
246C2×C3×D3—21no—
247C2×C3×D3—41no—
248C2×C3×D3—41no—
249C2×C3×D3—41no—
250C2×C3×D3#9912yes—
251C2×C3×D3#10412yes—
252C32×C4—21no—
253C32×C4—21no—
254C32×C4—41no—
255C32×C4—41no—
256C3⋊Dic3—42no—
257C3×Dic3—21no—
258C3×Dic3—21no—
259C3×Dic3—42no—
260C3×Dic3—41no—
261C2×#41—31no—
262C23×C4—31no—
263C23×C4—181no—
264C2×M16—181no—
265#123—61no—
266C22⋊Q8—31no—
267C22⋊Q8D3211yescharacteristic
268#121—31no—
269#121—31no—
270#120—61no—
271C4×D4—61no—
272C4×D4—61no—
273#117—31no—
274C22⋊C8—31no—
275C22⋊C8—91no—
276C22⋊C8—181no—
277#95—31no—
278#95—91no—
279#95—181no—
280C23×C3—21no—
281C23×C3—31no—
282C23×C3—31no—
283C23×C3—62no—
284C23×C3—62no—
285C23×C3—61no—
286C23×C3—61no—
287C23×C3—61no—
288C23×C3D3×D411yescharacteristic
289C23×C3C2×#6711yescharacteristic
290C22×D3—21no—
291C22×D3—21no—
292C22×D3—22no—
293C22×D3—22no—
294C22×D3—21no—
295C22×D3#21711yescharacteristic
296C22×D3#21711yescharacteristic
297C3×Q8—41no—
298C3×Q8—41no—
299C3×Q8—81no—
300C3×D4—121no—
301C3×D4—122no—
302C3×D4—122no—
303C3×D4—121no—
304C3×D4—121no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—31no—
312C2×C3×C4—31no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—62no—
320C2×C3×C4—61no—
321C2×C3×C4—81no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4—122no—
325C2×C3×C4—121no—
326C2×C3×C4—121no—
327C2×C3×C4—121no—
328C2×C3×C4C2×C4×D311yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4C22×Dic311yescharacteristic
331C2×C3×C4C2×#6711yescharacteristic
332#67—41no—
333#67—41no—
334C2×Dic3—22no—
335C2×Dic3—21no—
336C2×Dic3—41no—
337C2×Dic3—41no—
338C2×Dic3—41no—
339C2×Dic3—62no—
340C2×Dic3—62no—
341C2×Dic3—122no—
342C2×Dic3—128no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3—121no—
346C2×Dic3—121no—
347C2×Dic3—241no—
348C2×Dic3—241no—
349C2×Dic3#21711yescharacteristic
350C2×Dic3#21711yescharacteristic
351D12—41no—
352D12—42no—
353D12—42no—
354C4×D3—22no—
355C4×D3—22no—
356C4×D3—41no—
357C4×D3—41no—
358C4×D3—42no—
359C4×D3—128no—
360C3×C8—121no—
361C3⋊C8—41no—
362C3⋊C8—121no—
363C3⋊C8—121no—
364C3⋊C8—241no—
365C2×C32—21no—
366C2×C32—21no—
367C2×C32C2×#9911yescharacteristic
368C2×C32#41711yescharacteristic
369C2×C32C2×#10411yescharacteristic
370C3×D3—22no—
371C3×D3—22no—
372C3×D3—81no—
373C24—31no—
374#41—122no—
375C2×Q8D3×Dic311yescharacteristic, complemented
376C2×D4—31no—
377C2×D4—61no—
378C2×D4—61no—
379C2×D4—61no—
380C22×C4—31no—
381C22×C4—31no—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—61no—
386C22×C4—61no—
387C22×C4—122no—
388C22×C4—184no—
389C22×C4—181no—
390C22×C4—362no—
391C22×C4—362no—
392C22×C4C2×D3211yescharacteristic
393M16—362no—
394C2×C8—61no—
395C2×C8—181no—
396C4⋊C4—21no—
397C4⋊C4—31no—
398C4⋊C4—61no—
399C4⋊C4D3×Dic311yescharacteristic, complemented
400C22⋊C4—21no—
401C22⋊C4—61no—
402C22⋊C4—61no—
403C22⋊C4—61no—
404C22⋊C4—61no—
405C42—61no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—32no—
414C22×C3—32no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—64no—
418C22×C3—64no—
419C22×C3—61no—
420C22×C3—61no—
421C22×C3—61no—
422C22×C3—61no—
423C22×C3—121no—
424C22×C3—121no—
425C22×C3—121no—
426C22×C3D3×C22⋊C411yescharacteristic
427C22×C3#91411yescharacteristic
428C22×C3#91811yescharacteristic
429C22×C3#94911yescharacteristic
430C22×C3#95111yescharacteristic
431C22×C3C2×#21711yescharacteristic
432C2×D3—24no—
433C2×D3—24no—
434C2×D3—21no—
435C2×D3—21no—
436C2×D3—21no—
437C2×D3—21no—
438C2×D3—41no—
439C2×D3—41no—
440C2×D3—41no—
441C2×D3#83412yes—
442C2×D3#83712yes—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4—41no—
450C3×C4—41no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—61no—
454C3×C4—61no—
455C3×C4—81no—
456C3×C4—81no—
457C3×C4—122no—
458C3×C4—121no—
459Dic3—21no—
460Dic3—21no—
461Dic3—42no—
462Dic3—41no—
463Dic3—122no—
464Dic3—122no—
465Dic3—242no—
466C32#150411yescharacteristic, complemented, Sylow
467C23—31no—
468C23—31no—
469C23—62no—
470C23—62no—
471C23—61no—
472C23—61no—
473C23—61no—
474C23D3×#6711yescharacteristic
475Q8—41no—
476D4—121no—
477D4—122no—
478D4—122no—
479D4—121no—
480D4—121no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—31no—
484C2×C4—31no—
485C2×C4—41no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—61no—
490C2×C4—121no—
491C2×C4—121no—
492C2×C4—122no—
493C2×C4—121no—
494C2×C4—121no—
495C2×C4—121no—
496C2×C4—182no—
497C2×C4—368no—
498C2×C4—361no—
499C2×C4—361no—
500C2×C4C2×D3×Dic311yescharacteristic
501C2×C4D3×#6711yescharacteristic
502C8—121no—
503C8—361no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—41no—
512C2×C3—41no—
513C2×C3—62no—
514C2×C3—62no—
515C2×C3—241no—
516C2×C3D3×#9911yescharacteristic
517C2×C3#480311yescharacteristic
518C2×C3D3×#10411yescharacteristic
519C2×C3C2×#83411yescharacteristic
520C2×C3#523211yescharacteristic
521C2×C3C2×#83711yescharacteristic
522D3—22no—
523D3—22no—
524D3—81no—
525C22—21no—
526C22—21no—
527C22—32no—
528C22—32no—
529C22—64no—
530C22—64no—
531C22—61no—
532C22—61no—
533C22—61no—
534C22—61no—
535C22—121no—
536C22—121no—
537C22—121no—
538C22#6393911yescharacteristic
539C22#6394311yescharacteristic
540C22D3×#21711yescharacteristic
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—61no—
546C4—61no—
547C4—122no—
548C4—121no—
549C4—362no—
550C3—21no—
551C3#6833411yescharacteristic, complemented
552C3#7170811yescharacteristic, complemented
553C2—21no—
554C2—21no—
555C2—62no—
556C2—62no—
557C2—241no—
558C2D3×#83411yescharacteristic
559C2#1059155011yescharacteristic
560C2D3×#83711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5627C2
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1504
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. D3×C3⋊#95C2semidirect
3. #10591154C2semidirect
4. #10589404C2semidirect
5. C3×#4538C2semidirect
6. #10589150C2semidirect
7. #10589149C2semidirect
10. C2×C3×#239C4semidirect
14. C3×#946C4semidirect
16. C3×#895C4semidirect
19. C3×#892C4semidirect
39. #4538D3semidirect
45. C2×C32×Q8C2×C4semidirect
54. C2×C3×D12C2×C4semidirect
65. C32×C4⋊C4C2×C4semidirect
72. C3×C4⋊Dic3C2×C4semidirect
81. C2×#239Dic3semidirect
95. #946Dic3semidirect
99. #895Dic3semidirect
102. #892Dic3semidirect
167. C2×C3×Q8C4×D3semidirect
168. C2×C3×Q8C2×Dic3semidirect
196. C2×D12C2×Dic3semidirect
213. C3×C4⋊C4C4×D3semidirect
214. C3×C4⋊C4C2×Dic3semidirect
227. C4⋊Dic3C2×Dic3semidirect
375. C2×Q8D3×Dic3semidirect
399. C4⋊C4D3×Dic3semidirect
466. C32#1504semidirect
551. C3#68334semidirect
552. C3#71708semidirect

Maximal subgroups

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

subgroupindex
C3×#56272
D3×C3⋊#952
#105911542
#105894042
C3×#45382
#105891502
#105891492
#717083
#683343