Finite Group Databasebeta

← #11775278

Subgroups — #11775278

Order 1152.

524 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5624C211yesmaximal, characteristic
2#10591242C211yesmaximal, characteristic, complemented
3#10591063C211yesmaximal, characteristic, complemented
4#10589404C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic
7#10589149C211yesmaximal, characteristic
8#71755—31nomaximal
9#68311—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C3×#947C411yescharacteristic, complemented
12C3×Q8×Dic3C411yescharacteristic, complemented
13C3×#930C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C3×#898—21no—
16C3×#893C411yescharacteristic, complemented
17C3×#892—21no—
18C3×#890C411yescharacteristic, complemented
19C3×#886—21no—
20C3×#67⋊C4—21no—
21C2×Dic3⋊Dic3—21no—
22C2×Dic32—21no—
23#63658C2211yescharacteristic
24#63657C2211yescharacteristic
25C3×C3⋊#95C2211yescharacteristic
26C3×#830C2211yescharacteristic
27Dic3⋊(C3⋊C8)—21no—
28#63554—21no—
29C3×#529—31no—
30#5624D311yescharacteristic
31C4×C4⋊Dic3—31no—
32#4926—31no—
33#4719—31no—
34#4649—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—
44C2×C32×Q8C2×C411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4C2×C411yescharacteristic
55C32×C22⋊C4—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3C2×C411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3C2×C411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—24no—
72Dic32—42no—
73#1509—91noSylow
74C3×#126—61no—
75C3×#125—31no—
76C3×#124—31no—
77C3×#123—61no—
78C3×C22⋊Q8—21no—
79C3×C22⋊Q8C2×D311yescharacteristic
80C3×C22⋊Q8C2×D311yescharacteristic
81C3×#121—31no—
82C3×C4×Q8—31no—
83C3×C4×D4—31no—
84C3×C4×D4—61no—
85C3×#117—61no—
86C2×C3×C42—31no—
87#947Dic311yescharacteristic, complemented
88Q8×Dic3Dic311yescharacteristic, complemented
89#930C2×D311yescharacteristic
90C2×C4⋊Dic3—61no—
91C2×Dic3⋊C4—61no—
92C2×C4×Dic3—61no—
93C2×C4×Dic3—61no—
94C2×C4×Dic3C2×D311yescharacteristic
95#898—21no—
96#893Dic311yescharacteristic, complemented
97#892—21no—
98#890Dic311yescharacteristic, complemented
99#886—21no—
100#67⋊C4—21no—
101C3×C22⋊C8—31no—
102C3×#95—31no—
103C3⋊#95—31no—
104C3⋊#95—31no—
105C3⋊#95—61no—
106C3⋊#95C2×D311yescharacteristic
107#830—31no—
108#830—31no—
109#830—61no—
110#830C2×D311yescharacteristic
111#815—61no—
112Dic3⋊C8—61no—
113C4⋊(C3⋊C8)—61no—
114#803—61no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C32×Q8—41no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3—22no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C3×#67—41no—
127C3×#67—41no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3C22⋊C411yescharacteristic
138C2×C3×Dic3C22⋊C411yescharacteristic
139C3×D12—41no—
140C3×C4×D3—42no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—41no—
143#529—31no—
144#432—91no—
145C4×C4⋊C4—91no—
146#328—31no—
147#328—91no—
148#327—91no—
149#327—91no—
150C2×C3×Q8—21no—
151C2×C3×Q8C4×D311yescharacteristic
152C2×C3×Q8C2×Dic311yescharacteristic
153C2×C3×D4—31no—
154C2×C3×D4—61no—
155C22×C3×C4—21no—
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—61no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—21no—
163C22×Dic3—21no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—121no—
167C22×Dic3#6711yescharacteristic
168C22×Dic3#6711yescharacteristic
169C2×D12C2×Dic311yescharacteristic
170C2×C4×D3—21no—
171C2×C3×C8—61no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—41no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4C4×D311yescharacteristic
181C3×C4⋊C4C2×Dic311yescharacteristic
182C3×C22⋊C4—21no—
183C3×C22⋊C4—21no—
184C3×C22⋊C4—41no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C22⋊C4—61no—
189C3×C42—31no—
190C3×C42—31no—
191C3×C42—31no—
192C3×C42—31no—
193C3×C42—61no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—21no—
197(C2×D3)⋊C4—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—21no—
200C4⋊Dic3—64no—
201C4⋊Dic3C2×Dic311yescharacteristic
202Dic3⋊C4—21no—
203Dic3⋊C4—64no—
204C4×Dic3—21no—
205C4×Dic3—122no—
206C4×Dic3—122no—
207C4×Dic3C2×Dic311yescharacteristic
208C4×Dic3C2×Dic311yescharacteristic
209C4×Dic3#6711yescharacteristic
210C4×Dic3#6711yescharacteristic
211C2×C3⋊C8—21no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—121no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32C2×C22⋊C411yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C22×C32#13711yescharacteristic
220C2×C3×D3—41no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C32×C4—21no—
224C32×C4—21no—
225C32×C4—41no—
226C32×C4—41no—
227C3⋊Dic3—42no—
228C3×Dic3—21no—
229C3×Dic3—21no—
230C3×Dic3—21no—
231C3×Dic3—42no—
232C3×Dic3—41no—
233C3×Dic3#10412yes—
234#126—61no—
235#125—31no—
236#124—31no—
237#123—61no—
238C22⋊Q8D3211yescharacteristic
239#121—31no—
240C4×Q8—31no—
241C4×D4—31no—
242C4×D4—61no—
243#117—61no—
244C2×C4⋊C4—181no—
245C2×C42—31no—
246C2×C42—181no—
247C4⋊C8—181no—
248C22⋊C8—31no—
249C22⋊C8—91no—
250#97—181no—
251#95—31no—
252#95—91no—
253C23×C3—21no—
254C23×C3—61no—
255C23×C3D3×D411yescharacteristic
256C23×C3C2×#6711yescharacteristic
257C22×D3—21no—
258C3×Q8—41no—
259C3×Q8—41no—
260C3×Q8—81no—
261C3×D4—121no—
262C3×D4—121no—
263C3×D4—121no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—31no—
273C2×C3×C4—31no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—62no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—62no—
282C2×C3×C4—61no—
283C2×C3×C4—81no—
284C2×C3×C4—122no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4C22×Dic311yescharacteristic
290C2×C3×C4C2×#6711yescharacteristic
291#67—41no—
292#67—41no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—22no—
296C2×Dic3—22no—
297C2×Dic3—21no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—62no—
301C2×Dic3—62no—
302C2×Dic3—122no—
303C2×Dic3—121no—
304C2×Dic3—121no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—241no—
308C2×Dic3—241no—
309C2×Dic3#21711yescharacteristic
310C2×Dic3#21711yescharacteristic
311C2×Dic3#21711yescharacteristic
312C2×Dic3#21711yescharacteristic
313D12—41no—
314C4×D3—42no—
315C3×C8—121no—
316C3⋊C8—41no—
317C3⋊C8—121no—
318C3⋊C8—121no—
319C3⋊C8—241no—
320C2×C32—21no—
321C2×C32—21no—
322C2×C32#41011yescharacteristic
323C2×C32#41711yescharacteristic
324C2×C32C2×#10411yescharacteristic
325C3×D3—81no—
326C2×Q8D3×Dic311yescharacteristic
327C2×D4—31no—
328C2×D4—61no—
329C22×C4—31no—
330C22×C4—31no—
331C22×C4—61no—
332C22×C4—61no—
333C22×C4—181no—
334C22×C4C2×D3211yescharacteristic
335C2×C8—61no—
336C2×C8—181no—
337C4⋊C4—21no—
338C4⋊C4—31no—
339C4⋊C4—61no—
340C4⋊C4—61no—
341C4⋊C4—61no—
342C4⋊C4—184no—
343C4⋊C4D3×Dic311yescharacteristic
344C22⋊C4—21no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C22⋊C4—61no—
349C42—31no—
350C42—31no—
351C42—31no—
352C42—31no—
353C42—61no—
354C42—362no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—121no—
365C22×C3—121no—
366C22×C3—121no—
367C22×C3D3×C22⋊C411yescharacteristic
368C22×C3#91411yescharacteristic
369C22×C3#91811yescharacteristic
370C22×C3#94911yescharacteristic
371C22×C3#95111yescharacteristic
372C22×C3C2×#21711yescharacteristic
373C2×D3—41no—
374C2×D3—41no—
375C2×D3—41no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—32no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—41no—
386C3×C4—41no—
387C3×C4—61no—
388C3×C4—61no—
389C3×C4—61no—
390C3×C4—81no—
391C3×C4—81no—
392C3×C4—122no—
393C3×C4—121no—
394Dic3—21no—
395Dic3—21no—
396Dic3—21no—
397Dic3—42no—
398Dic3—41no—
399Dic3—122no—
400Dic3—122no—
401Dic3—242no—
402Dic3#83712yes—
403C32#150911yescharacteristic, complemented, Sylow
404C23—61no—
405C23D3×#6711yescharacteristic
406Q8—41no—
407D4—121no—
408D4—121no—
409D4—121no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—31no—
415C2×C4—31no—
416C2×C4—41no—
417C2×C4—62no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—62no—
421C2×C4—61no—
422C2×C4—122no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—182no—
426C2×C4—361no—
427C2×C4—361no—
428C2×C4C2×D3×Dic311yescharacteristic
429C2×C4D3×#6711yescharacteristic
430C8—121no—
431C8—361no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—241no—
442C2×C3#474011yescharacteristic
443C2×C3#480311yescharacteristic
444C2×C3D3×#10411yescharacteristic
445C2×C3#523211yescharacteristic
446C2×C3C2×#83711yescharacteristic
447C2×C3#524011yescharacteristic
448D3—81no—
449C22—21no—
450C22—21no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22#6393911yescharacteristic
455C22#6394311yescharacteristic
456C22D3×#21711yescharacteristic
457C4—21no—
458C4—21no—
459C4—32no—
460C4—41no—
461C4—41no—
462C4—61no—
463C4—61no—
464C4—61no—
465C4—122no—
466C4—121no—
467C4—362no—
468C3—21no—
469C3#6831111yescharacteristic, complemented
470C3#7175511yescharacteristic, complemented
471C2—21no—
472C2—21no—
473C2—241no—
474C2#1059152811yescharacteristic
475C2#1059155011yescharacteristic
476C2D3×#83711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C22
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1509
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. #10591242C2semidirect
3. #10591063C2semidirect
4. #10589404C2semidirect
5. C3×#4538C2semidirect
11. C3×#947C4semidirect
12. C3×Q8×Dic3C4semidirect
16. C3×#893C4semidirect
18. C3×#890C4semidirect
39. #4538D3semidirect
87. #947Dic3semidirect
88. Q8×Dic3Dic3semidirect
96. #893Dic3semidirect
98. #890Dic3semidirect
403. C32#1509semidirect
469. C3#68311semidirect
470. C3#71755semidirect

Maximal subgroups

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

subgroupindex
C3×#56242
#105912422
#105910632
#105894042
C3×#45382
#105891502
#105891492
#717553
#683113