Finite Group Databasebeta

← #11774839

Subgroups — #11774839

Order 1152.

473 conjugacy classes of subgroups.

The subgroup lattice has 461 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593870C211yesmaximal, characteristic
2C3×#4837C211yesmaximal, characteristic, complemented
3#10590261C211yesmaximal, characteristic, complemented
4#10589349C211yesmaximal, characteristic, complemented
5C3×#4484C211yesmaximal, characteristic, complemented
6#10589083C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#70499—31nomaximal
9#68242—31nomaximal
10C4×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)—21no—
12C3×C42×D3C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63909C411yescharacteristic
15C4×#626—21no—
16#63874—21no—
17#63869C411yescharacteristic
18#63868—21no—
19#63864C411yescharacteristic
20#63856C411yescharacteristic
21#63850—21no—
22C32×C4⋊C8C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×Dic3⋊C8—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27Dic3⋊(C3⋊C8)—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29#5580—31no—
30#5479—31no—
31C3×#423—31no—
32#4925—31no—
33#4837D311yescharacteristic, complemented
34#4685—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4484—31no—
38#4484D311yescharacteristic, complemented
39#4483—31no—
40#4483—31no—
41#4483—31no—
42#4483—61no—
43#4459—31no—
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×C3×C4×D3C2×C411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×Dic6C2×C411yescharacteristic
50C2×#626—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53#3752—21no—
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55C2×C3⋊(C3⋊C8)—21no—
56C3×C4⋊Dic3C2×C411yescharacteristic
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C3×C4×Dic3C2×C411yescharacteristic
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C3×ΓL(1,𝔽25)—42no—
65#3724—21no—
66#3724—21no—
67Dic3⋊Dic3—21no—
68#3722—21no—
69#3722—21no—
70#3722—21no—
71(C2×D3)⋊Dic3—21no—
72#1495—91noSylow
73C2×C3×M16—61no—
74C3×C4×Q8—31no—
75C2×C3×C42—31no—
76#947—31no—
77#946—31no—
78#930—31no—
79#929—61no—
80C4×#67—61no—
81#924—31no—
82C2×ΓL(1,𝔽25)—21no—
83#898—61no—
84#895—31no—
85#894—61no—
86#890—31no—
87#876—61no—
88#875—31no—
89C4×D12—31no—
90C4×D12—31no—
91C4×D12—61no—
92C4×D12—61no—
93#872—61no—
94#872—61no—
95C42×D3C2×D311yescharacteristic
96#870—31no—
97C4×Dic6C2×D311yescharacteristic
98C3×C4⋊C8—21no—
99C3×C4⋊C8—31no—
100C3×C4⋊C8—61no—
101C3×C4⋊C8C2×D311yescharacteristic
102C3×C4⋊C8C2×D311yescharacteristic
103C3×C4×C8—31no—
104#830—61no—
105(C2×D3)⋊C8—61no—
106Dic3⋊C8—21no—
107Dic3⋊C8—61no—
108C4⋊(C3⋊C8)—61no—
109C4⋊(C3⋊C8)C2×D311yescharacteristic
110C4×C3⋊C8—31no—
111C4×C3⋊C8—31no—
112C4×C3⋊C8—61no—
113C4×C3⋊C8C2×D311yescharacteristic
114C22×C3⋊D3—21no—
115C22×C3×D3C22⋊C411yescharacteristic
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C3⋊Dic3—21no—
120C4⋊(C3⋊D3)—21no—
121C4⋊(C3⋊D3)—21no—
122C4×C3⋊D3—41no—
123C4×C3⋊D3—41no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C2×C3×Dic3C22⋊C411yescharacteristic
129C3×C4×D3—21no—
130C3×C4×D3—21no—
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133C3×C4×D3—41no—
134C3×Dic6—21no—
135C3×Dic6—21no—
136#626—42no—
137C32×C8—41no—
138C3⋊(C3⋊C8)—41no—
139C3×C3⋊C8—41no—
140C3×C3⋊C8—41no—
141#529—91no—
142#431—91no—
143#423—31no—
144Q8⋊C8—31no—
145Q8⋊C8—91no—
146D4⋊C8—91no—
147D4⋊C8—91no—
148C2×C3×Q8—31no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C2×#67—61no—
153C2×D12—31no—
154C2×D12—31no—
155C2×D12—61no—
156C2×D12—61no—
157C2×C4×D3—61no—
158C2×C4×D3—61no—
159C2×C4×D3—121no—
160C2×C4×D3C4×D311yescharacteristic
161C2×C4×D3D1211yescharacteristic
162C2×C4×D3#6711yescharacteristic
163C2×Dic6C4×D311yescharacteristic
164C3×M16—122no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—41no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C3×C4⋊C4—31no—
171C3×C4⋊C4—61no—
172C3×C42—21no—
173C3×C42—31no—
174C3×C42—31no—
175C3×C42—31no—
176C3×C42—61no—
177C3×C42C22×D311yescharacteristic
178C3×C42C22×D311yescharacteristic
179#217—61no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189(C2×D3)⋊C4—121no—
190C4⋊Dic3—31no—
191C4⋊Dic3—31no—
192C4⋊Dic3—61no—
193C4⋊Dic3—61no—
194C4⋊Dic3C4×D311yescharacteristic
195Dic3⋊C4—21no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201C4×Dic3—21no—
202C4×Dic3C4×D311yescharacteristic
203C4×Dic3D1211yescharacteristic
204C4×Dic3#6711yescharacteristic
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—121no—
210ΓL(1,𝔽25)—42no—
211C22×C32C2×C22⋊C411yescharacteristic
212C2×C3⋊D3—41no—
213C2×C3⋊D3—41no—
214C2×C3⋊D3—41no—
215C2×C3×D3—21no—
216C2×C3×D3—21no—
217C2×C3×D3—21no—
218C32×C4—21no—
219C32×C4#13111yescharacteristic
220C32×C4#13111yescharacteristic
221C32×C4AGL(1,ℤ/8)11yescharacteristic
222C32×C4#13711yescharacteristic
223C3⋊Dic3—41no—
224C3×Dic3—21no—
225C3×Dic3—21no—
226C3×Dic3—21no—
227C3×Dic3—41no—
228C3×Dic3—41no—
229C2×M16—61no—
230#126—181no—
231#125—91no—
232#124—91no—
233#123—181no—
234C22⋊Q8—91no—
235#121—91no—
236C4×Q8—31no—
237C4×D4—91no—
238C4×D4—181no—
239#117—181no—
240C2×C42—31no—
241C4⋊C8—31no—
242C4⋊C8—61no—
243C4⋊C8—181no—
244C4⋊C8D3211yescharacteristic
245C22⋊C8—181no—
246C4×C8—31no—
247C4×C8—91no—
248C23×C3—31no—
249C22×D3—61no—
250C22×D3—61no—
251C22×D3—121no—
252C22×D3(C2×D3)⋊C411yescharacteristic
253C3×Q8—61no—
254C3×Q8—61no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—31no—
259C2×C3×C4—31no—
260C2×C3×C4—31no—
261C2×C3×C4—61no—
262C2×C3×C4—61no—
263C2×C3×C4—61no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—121no—
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×D1211yescharacteristic
271C2×C3×C4D3×D411yescharacteristic
272C2×C3×C4D3×D411yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274#67—122no—
275C2×Dic3—21no—
276C2×Dic3—21no—
277C2×Dic3—61no—
278C2×Dic3—61no—
279C2×Dic3—121no—
280C2×Dic3(C2×D3)⋊C411yescharacteristic
281C2×Dic3(C2×D3)⋊C411yescharacteristic
282C2×Dic3(C2×D3)⋊C411yescharacteristic
283D12—62no—
284D12—61no—
285D12—61no—
286D12—61no—
287D12—61no—
288D12—121no—
289D12—122no—
290C4×D3—21no—
291C4×D3—21no—
292C4×D3—21no—
293C4×D3—21no—
294C4×D3—41no—
295C4×D3—121no—
296C4×D3—121no—
297C4×D3—121no—
298C4×D3—121no—
299C4×D3—241no—
300C4×D3—241no—
301Dic6—21no—
302Dic6—21no—
303C3×C8—41no—
304C3×C8—41no—
305C3×C8—81no—
306C3×C8—121no—
307C3×C8—121no—
308C3⋊C8—41no—
309C3⋊C8—41no—
310C3⋊C8—121no—
311C3⋊C8—121no—
312C3⋊C8—122no—
313C2×C32#40811yescharacteristic
314C2×C32#41711yescharacteristic
315C2×C32#42111yescharacteristic
316C3⋊D3—81no—
317C3×D3—41no—
318C2×Q8—31no—
319C2×D4—91no—
320C2×D4—181no—
321C22×C4—31no—
322C22×C4—31no—
323C22×C4—31no—
324C22×C4—181no—
325M16—122no—
326C2×C8—21no—
327C2×C8—61no—
328C2×C8—61no—
329C2×C8—181no—
330C4⋊C4—31no—
331C4⋊C4—61no—
332C4⋊C4—91no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C4⋊C4—181no—
336C22⋊C4—181no—
337C22⋊C4—181no—
338C22⋊C4—181no—
339C22⋊C4—181no—
340C22⋊C4—181no—
341C42—31no—
342C42—31no—
343C42—31no—
344C42—61no—
345C42C2×D3211yescharacteristic
346C22×C3—21no—
347C22×C3—61no—
348C22×C3—61no—
349C22×C3—61no—
350C22×C3D3×C22⋊C411yescharacteristic
351C22×C3C2×(C2×D3)⋊C411yescharacteristic
352C2×D3—21no—
353C2×D3—21no—
354C2×D3—21no—
355C2×D3—122no—
356C2×D3—121no—
357C2×D3—121no—
358C2×D3—121no—
359C2×D3—121no—
360C2×D3—121no—
361C2×D3—121no—
362C2×D3—241no—
363C2×D3—241no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—41no—
371C3×C4—61no—
372C3×C4—61no—
373C3×C4—61no—
374C3×C4—121no—
375C3×C4—121no—
376C3×C4#90111yescharacteristic
377C3×C4#90711yescharacteristic
378C3×C4#90711yescharacteristic
379C3×C4#90711yescharacteristic
380C3×C4#91411yescharacteristic
381C3×C4#91811yescharacteristic
382C3×C4#93211yescharacteristic
383C3×C4#94211yescharacteristic
384Dic3—21no—
385Dic3—21no—
386Dic3—21no—
387Dic3—41no—
388Dic3—41no—
389Dic3—121no—
390Dic3—121no—
391Dic3—241no—
392C32#149511yescharacteristic, complemented, Sylow
393C23—31no—
394C23—181no—
395Q8—61no—
396Q8—61no—
397D4—181no—
398D4—181no—
399D4—362no—
400C2×C4—31no—
401C2×C4—31no—
402C2×C4—31no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—121no—
410C2×C4—181no—
411C2×C4—361no—
412C2×C4—361no—
413C2×C4C4×D3211yescharacteristic
414C2×C4D3×D1211yescharacteristic
415C2×C4D3×#6711yescharacteristic
416C8—41no—
417C8—121no—
418C8—121no—
419C8—361no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—121no—
424C2×C3#472711yescharacteristic
425C2×C3#480311yescharacteristic
426C2×C3#482111yescharacteristic
427C2×C3#496611yescharacteristic
428C2×C3#512911yescharacteristic
429C2×C3#513911yescharacteristic
430D3—41no—
431D3—242no—
432D3—241no—
433D3—241no—
434C22—61no—
435C22—61no—
436C22—61no—
437C22—361no—
438C22—361no—
439C22—361no—
440C22D3×(C2×D3)⋊C411yescharacteristic
441C4—21no—
442C4—61no—
443C4—61no—
444C4—61no—
445C4—121no—
446C4—121no—
447C4—361no—
448C4#6380411yescharacteristic
449C4#6380511yescharacteristic
450C4#6393411yescharacteristic
451C4#6394811yescharacteristic
452C3—21no—
453C3#6824211yescharacteristic, complemented
454C3#7049911yescharacteristic, complemented
455C2—121no—
456C2—721no—
457C2#1059060911yescharacteristic
458C2#1059095511yescharacteristic
459C2#1059100511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#63909C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1495
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×#4837C2semidirect
3. #10590261C2semidirect
4. #10589349C2semidirect
5. C3×#4484C2semidirect
6. #10589083C2semidirect
7. #10589082C2semidirect
33. #4837D3semidirect
38. #4484D3semidirect
392. C32#1495semidirect
453. C3#68242semidirect
454. C3#70499semidirect

Maximal subgroups

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

subgroupindex
#105938702
C3×#48372
#105902612
#105893492
C3×#44842
#105890832
#105890822
#704993
#682423