Finite Group Databasebeta

← #11774478

Subgroups — #11774478

Order 1152.

503 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5580C211yesmaximal, characteristic
2C4×#3711C211yesmaximal, characteristic, complemented
3D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10589401C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589081C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71751—31nomaximal
9#68234—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C3×#947C411yescharacteristic
12C3×#946C411yescharacteristic
13C3×#898—21no—
14C3×#895C411yescharacteristic
15C3×#894—21no—
16C3×#890C411yescharacteristic
17C3×C4×D12—21no—
18C3×C4×D12C2211yescharacteristic
19C3×#872—21no—
20C3×C42×D3C2211yescharacteristic
21C2×#3711—21no—
22C2×D3×C3⋊C8—21no—
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C4×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27Dic3⋊(C3⋊C8)—21no—
28#63554—21no—
29C3×#529—31no—
30#5580D311yescharacteristic
31C2×C4⋊(C3⋊C8)—31no—
32C4×#208—31no—
33D3×C4⋊C8—31no—
34C4×ΓL(1,𝔽25)—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4535—31no—
38#4535—61no—
39#4535D311yescharacteristic, complemented
40D4⋊(C3⋊C8)—31no—
41D4⋊(C3⋊C8)—31no—
42#4483—31no—
43#4459—31no—
44C2×C32×Q8C2×C411yescharacteristic
45C2×C3×D12—21no—
46C2×C3×D12C2×C411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3C2×C411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×C3×C4×D3D411yescharacteristic
51C32×C4⋊C4—21no—
52C32×C4⋊C4C2×C411yescharacteristic
53C32×C42—21no—
54C32×C42C2311yescharacteristic
55C2×C3⋊(C3⋊C8)—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×(C2×D3)⋊C4—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3C2×C411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×Dic3⋊C4—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#3711—24no—
72D3×C3⋊C8—42no—
73#1483—91noSylow
74C3×#126—61no—
75C3×#125—31no—
76C3×#124—31no—
77C3×#123—61no—
78C3×C22⋊Q8—31no—
79C3×#121—31no—
80C3×C4×Q8—21no—
81C3×C4×Q8C2×D311yescharacteristic
82C3×C4×Q8C2×D311yescharacteristic
83C3×C4×D4—31no—
84C3×C4×D4—61no—
85C3×#117—61no—
86C2×C3×C42—31no—
87#947Dic311yescharacteristic
88#946Dic311yescharacteristic
89C2×#208—61no—
90C22×C3⋊C8—61no—
91C2×ΓL(1,𝔽25)—61no—
92C2×D3×C8—61no—
93#898—21no—
94#895Dic311yescharacteristic
95#894—21no—
96#890Dic311yescharacteristic
97C4×D12—21no—
98C4×D12C2×D311yescharacteristic
99#872—21no—
100C42×D3C2×D311yescharacteristic
101C3×C4⋊C8—31no—
102C3×C4×C8—31no—
103#815—61no—
104Dic3⋊C8—61no—
105C4⋊(C3⋊C8)—31no—
106C4⋊(C3⋊C8)—31no—
107C4⋊(C3⋊C8)—61no—
108C4⋊(C3⋊C8)—61no—
109C4⋊(C3⋊C8)C2×D311yescharacteristic
110#803—61no—
111C4×C3⋊C8—31no—
112C4×C3⋊C8—31no—
113C4×C3⋊C8—61no—
114C4×C3⋊C8C2×D311yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3C22⋊C411yescharacteristic
117C32×Q8—21no—
118C32×Q8—21no—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3×Dic3—21no—
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C3×D12—21no—
129C3×D12—21no—
130C3×D12—42no—
131C3×C4×D3—22no—
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×C4×D3—21no—
135C3×C4×D3—21no—
136C3×C4×D3—41no—
137C3×C4×D3—41no—
138C3⋊(C3⋊C8)—22no—
139C3⋊(C3⋊C8)—41no—
140C3×C3⋊C8—22no—
141C3×C3⋊C8—41no—
142#529—31no—
143C2×C4⋊C8—91no—
144C4×M16—91no—
145Q8⋊C8—31no—
146Q8⋊C8—91no—
147D4⋊C8—91no—
148D4⋊C8—91no—
149C2×C3×Q8—21no—
150C2×C3×Q8C4×D311yescharacteristic
151C2×C3×Q8C2×Dic311yescharacteristic
152C2×C3×D4—31no—
153C2×C3×D4—61no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—61no—
158C2×D12—21no—
159C2×D12C2×Dic311yescharacteristic
160C2×C4×D3—21no—
161C2×C4×D3C2×Dic311yescharacteristic
162C2×C4×D3#6711yescharacteristic
163C2×C4×D3#6711yescharacteristic
164C2×C3×C8—61no—
165C2×C3×C8—61no—
166C3×C4⋊C4—21no—
167C3×C4⋊C4—21no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4—31no—
170C3×C4⋊C4—41no—
171C3×C4⋊C4—61no—
172C3×C4⋊C4—61no—
173C3×C4⋊C4—61no—
174C3×C4⋊C4C4×D311yescharacteristic
175C3×C4⋊C4C2×Dic311yescharacteristic
176C3×C22⋊C4—61no—
177C3×C22⋊C4—61no—
178C3×C22⋊C4—61no—
179C3×C22⋊C4—61no—
180C3×C22⋊C4—61no—
181C3×C42—21no—
182C3×C42—21no—
183C3×C42—21no—
184C3×C42—31no—
185C3×C42—31no—
186C3×C42—31no—
187C3×C42—41no—
188C3×C42C22×D311yescharacteristic
189C3×C42C22×D311yescharacteristic
190(C2×D3)⋊C4—21no—
191(C2×D3)⋊C4—21no—
192(C2×D3)⋊C4—21no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—21no—
195C4⋊Dic3—21no—
196C4⋊Dic3C2×Dic311yescharacteristic
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199C4×Dic3C2×Dic311yescharacteristic
200C4×Dic3#6711yescharacteristic
201C4×Dic3#6711yescharacteristic
202#208—64no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210C2×C3⋊C8—121no—
211C2×C3⋊C8—122no—
212ΓL(1,𝔽25)—64no—
213D3×C8—122no—
214C22×C32C2×C22⋊C411yescharacteristic
215C2×C3×D3—21no—
216C2×C3×D3—21no—
217C2×C3×D3—41no—
218C2×C3×D3—41no—
219C2×C3×D3—41no—
220C2×C3×D3#10412yes—
221C32×C4—21no—
222C32×C4—41no—
223C32×C4—41no—
224C32×C4#13111yescharacteristic
225C32×C4#13111yescharacteristic
226C32×C4AGL(1,ℤ/8)11yescharacteristic
227C32×C4#13711yescharacteristic
228C3×Dic3—21no—
229C3×Dic3—21no—
230C3×Dic3—21no—
231C3×Dic3—41no—
232C2×M16—181no—
233C22×C8—181no—
234#126—61no—
235#125—31no—
236#124—31no—
237#123—61no—
238C22⋊Q8—31no—
239#121—31no—
240C4×Q8D3211yescharacteristic
241C4×D4—31no—
242C4×D4—61no—
243#117—61no—
244C2×C42—31no—
245C4⋊C8—31no—
246C4⋊C8—91no—
247C4⋊C8—181no—
248#97—181no—
249C4×C8—31no—
250C4×C8—91no—
251C23×C3—31no—
252C23×C3—61no—
253C22×D3—21no—
254C22×D3#21711yescharacteristic
255C3×Q8—22no—
256C3×Q8—21no—
257C3×Q8—21no—
258C3×Q8—21no—
259C3×Q8—21no—
260C3×Q8—41no—
261C3×D4—61no—
262C3×D4—61no—
263C3×D4—122no—
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—21no—
271C2×C3×C4—31no—
272C2×C3×C4—31no—
273C2×C3×C4—31no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—62no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4C22×Dic311yescharacteristic
288C2×C3×C4C2×#6711yescharacteristic
289C2×C3×C4C2×#6711yescharacteristic
290C2×Dic3—21no—
291C2×Dic3#21711yescharacteristic
292C2×Dic3#21711yescharacteristic
293C2×Dic3#21711yescharacteristic
294D12—21no—
295D12—21no—
296D12—42no—
297C4×D3—22no—
298C4×D3—21no—
299C4×D3—21no—
300C4×D3—21no—
301C4×D3—21no—
302C4×D3—41no—
303C4×D3—41no—
304C3×C8—62no—
305C3×C8—121no—
306C3⋊C8—22no—
307C3⋊C8—41no—
308C3⋊C8—62no—
309C3⋊C8—62no—
310C3⋊C8—122no—
311C3⋊C8—121no—
312C3⋊C8—121no—
313C3⋊C8—241no—
314C2×C32#40811yescharacteristic
315C2×C32#41711yescharacteristic
316C2×C32C2×#10411yescharacteristic
317C3×D3—22no—
318C3×D3—81no—
319C2×Q8D3×Dic311yescharacteristic
320C2×D4—31no—
321C2×D4—61no—
322C22×C4—31no—
323C22×C4—31no—
324C22×C4—31no—
325C22×C4—61no—
326M16—184no—
327C2×C8—61no—
328C2×C8—61no—
329C2×C8—181no—
330C2×C8—181no—
331C2×C8—362no—
332C4⋊C4—21no—
333C4⋊C4—31no—
334C4⋊C4—61no—
335C4⋊C4—61no—
336C4⋊C4—61no—
337C4⋊C4D3×Dic311yescharacteristic
338C22⋊C4—61no—
339C22⋊C4—61no—
340C22⋊C4—61no—
341C22⋊C4—61no—
342C22⋊C4—61no—
343C42—21no—
344C42—31no—
345C42—31no—
346C42—31no—
347C42C2×D3211yescharacteristic
348C22×C3—21no—
349C22×C3—32no—
350C22×C3—61no—
351C22×C3—61no—
352C22×C3—121no—
353C22×C3—121no—
354C22×C3—121no—
355C22×C3D3×C22⋊C411yescharacteristic
356C22×C3C2×#21711yescharacteristic
357C2×D3—21no—
358C2×D3—21no—
359C2×D3—41no—
360C2×D3—41no—
361C2×D3—41no—
362C2×D3#83712yes—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—41no—
370C3×C4—42no—
371C3×C4—41no—
372C3×C4—41no—
373C3×C4—41no—
374C3×C4—41no—
375C3×C4—61no—
376C3×C4—61no—
377C3×C4—61no—
378C3×C4—81no—
379C3×C4—121no—
380C3×C4#90111yescharacteristic
381C3×C4#90711yescharacteristic
382C3×C4#91411yescharacteristic
383C3×C4#91811yescharacteristic
384C3×C4#94811yescharacteristic
385C3×C4#94811yescharacteristic
386C3×C4#94911yescharacteristic
387C3×C4#95111yescharacteristic
388Dic3—21no—
389Dic3—21no—
390Dic3—21no—
391Dic3—41no—
392C32#148311yescharacteristic, complemented, Sylow
393C23—31no—
394C23—61no—
395Q8—21no—
396Q8—21no—
397D4—61no—
398D4—61no—
399D4—122no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—31no—
403C2×C4—31no—
404C2×C4—31no—
405C2×C4—62no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—121no—
412C2×C4—121no—
413C2×C4C2×D3×Dic311yescharacteristic
414C2×C4D3×#6711yescharacteristic
415C2×C4D3×#6711yescharacteristic
416C8—62no—
417C8—121no—
418C8—182no—
419C8—361no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—62no—
424C2×C3—241no—
425C2×C3#472711yescharacteristic
426C2×C3#480311yescharacteristic
427C2×C3D3×#10411yescharacteristic
428C2×C3#523211yescharacteristic
429C2×C3#523411yescharacteristic
430C2×C3C2×#83711yescharacteristic
431D3—22no—
432D3—81no—
433C22—32no—
434C22—61no—
435C22—61no—
436C22—121no—
437C22—121no—
438C22—121no—
439C22D3×#21711yescharacteristic
440C4—21no—
441C4—41no—
442C4—41no—
443C4—61no—
444C4—61no—
445C4—61no—
446C4—121no—
447C4#6381411yescharacteristic
448C4#6381511yescharacteristic
449C4#6393911yescharacteristic
450C4#6394311yescharacteristic
451C3—21no—
452C3#6823411yescharacteristic, complemented
453C3#7175111yescharacteristic, complemented
454C2—62no—
455C2—241no—
456C2#1059114511yescharacteristic
457C2#1059155011yescharacteristic
458C2D3×#83711yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#895C4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1483
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C4×#3711C2semidirect
3. D3×C4⋊(C3⋊C8)C2semidirect
4. #10589401C2semidirect
5. C3×#4535C2semidirect
6. #10589081C2semidirect
7. #10589080C2semidirect
39. #4535D3semidirect
392. C32#1483semidirect
452. C3#68234semidirect
453. C3#71751semidirect

Maximal subgroups

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

subgroupindex
C3×#55802
C4×#37112
D3×C4⋊(C3⋊C8)2
#105894012
C3×#45352
#105890812
#105890802
#717513
#682343