Finite Group Databasebeta

← #11774467

Subgroups — #11774467

Order 1152.

509 conjugacy classes of subgroups.

The subgroup lattice has 465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593870C211yesmaximal, characteristic
2C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
3C4×#3711C211yesmaximal, characteristic, complemented
4#10589349C211yesmaximal, characteristic, complemented
5C3×#4484C211yesmaximal, characteristic, complemented
6#10589083C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#70427—31nomaximal
9#68234—31nomaximal
10C4×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×D3×C8—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—
22C2×#3711—21no—
23C32×C4⋊C8C2211yescharacteristic
24C4×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×Dic3⋊C8—21no—
26C3×C4⋊(C3⋊C8)C2211yescharacteristic
27C3×C4×C3⋊C8C2211yescharacteristic
28#63554—21no—
29#5580—31no—
30#5479—31no—
31C2×C3×C4⋊C8—31no—
32C4×#208—31no—
33D3×C4⋊C8D311yescharacteristic, complemented
34C4×ΓL(1,𝔽25)—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×D3×C8—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#3711—24no—
73#1483—91noSylow
74C22×C3×C8—61no—
75C3×C4×Q8—31no—
76C2×C3×C42—31no—
77#947—31no—
78#946—31no—
79#930—31no—
80#929—61no—
81C4×#67—61no—
82#924—31no—
83C2×#208—61no—
84C2×ΓL(1,𝔽25)—61no—
85C2×D3×C8—21no—
86#898—61no—
87#895—31no—
88#894—61no—
89#890—31no—
90#876—61no—
91#875—31no—
92C4×D12—31no—
93C4×D12—31no—
94C4×D12—61no—
95C4×D12—61no—
96#872—61no—
97#872—61no—
98C42×D3C2×D311yescharacteristic
99#870—31no—
100C4×Dic6C2×D311yescharacteristic
101C3×C4⋊C8—21no—
102C3×C4⋊C8—31no—
103C3×C4⋊C8—61no—
104C3×C4⋊C8C2×D311yescharacteristic
105C3×C4⋊C8C2×D311yescharacteristic
106C3×C4×C8—31no—
107#815—61no—
108Dic3⋊C8—21no—
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
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C3⋊Dic3—21no—
121C4⋊(C3⋊D3)—21no—
122C4⋊(C3⋊D3)—21no—
123C4×C3⋊D3—41no—
124C4×C3⋊D3—41no—
125C2×C3×Dic3—21no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3C22⋊C411yescharacteristic
128C2×C3×Dic3C22⋊C411yescharacteristic
129C2×C3×Dic3C22⋊C411yescharacteristic
130C3×C4×D3—22no—
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×C4×D3—21no—
135C3×Dic6—21no—
136C3×Dic6—21no—
137#626—42no—
138C32×C8—41no—
139C3⋊(C3⋊C8)—22no—
140C3×C3⋊C8—22no—
141C3×C3⋊C8—41no—
142#529—91no—
143C2×C4⋊C8—31no—
144C4×M16—91no—
145Q8⋊C8—31no—
146Q8⋊C8—91no—
147D4⋊C8—91no—
148D4⋊C8—91no—
149C2×C3×Q8—31no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C2×#67—61no—
154C2×D12—31no—
155C2×D12—31no—
156C2×D12—61no—
157C2×D12—61no—
158C2×C4×D3—61no—
159C2×C4×D3—61no—
160C2×C4×D3—121no—
161C2×C4×D3C4×D311yescharacteristic
162C2×C4×D3D1211yescharacteristic
163C2×C4×D3#6711yescharacteristic
164C2×Dic6C4×D311yescharacteristic
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—41no—
168C2×C3×C8—61no—
169C2×C3×C8—61no—
170C2×C3×C8—122no—
171C3×C4⋊C4—31no—
172C3×C4⋊C4—61no—
173C3×C42—21no—
174C3×C42—31no—
175C3×C42—31no—
176C3×C42—31no—
177C3×C42—61no—
178C3×C42C22×D311yescharacteristic
179C3×C42C22×D311yescharacteristic
180#217—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—61no—
190(C2×D3)⋊C4—121no—
191C4⋊Dic3—31no—
192C4⋊Dic3—31no—
193C4⋊Dic3—61no—
194C4⋊Dic3—61no—
195C4⋊Dic3C4×D311yescharacteristic
196Dic3⋊C4—21no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—61no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202C4×Dic3—21no—
203C4×Dic3C4×D311yescharacteristic
204C4×Dic3D1211yescharacteristic
205C4×Dic3#6711yescharacteristic
206#208—64no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—121no—
212ΓL(1,𝔽25)—64no—
213D3×C8—42no—
214C22×C32C2×C22⋊C411yescharacteristic
215C2×C3⋊D3—41no—
216C2×C3⋊D3—41no—
217C2×C3⋊D3—41no—
218C2×C3×D3—21no—
219C2×C3×D3—21no—
220C2×C3×D3#10412yes—
221C32×C4—21no—
222C32×C4#13111yescharacteristic
223C32×C4#13111yescharacteristic
224C32×C4AGL(1,ℤ/8)11yescharacteristic
225C32×C4#13711yescharacteristic
226C3⋊Dic3—41no—
227C3×Dic3—21no—
228C3×Dic3—21no—
229C3×Dic3—21no—
230C3×Dic3—41no—
231C3×Dic3—41no—
232C2×M16—181no—
233C22×C8—61no—
234#126—181no—
235#125—91no—
236#124—91no—
237#123—181no—
238C22⋊Q8—91no—
239#121—91no—
240C4×Q8—31no—
241C4×D4—91no—
242C4×D4—181no—
243#117—181no—
244C2×C42—31no—
245C4⋊C8—31no—
246C4⋊C8—61no—
247C4⋊C8D3211yescharacteristic
248#97—181no—
249C4×C8—31no—
250C4×C8—91no—
251C23×C3—31no—
252C22×D3—61no—
253C22×D3—61no—
254C22×D3—121no—
255C22×D3(C2×D3)⋊C411yescharacteristic
256C3×Q8—61no—
257C3×Q8—61no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—31no—
262C2×C3×C4—31no—
263C2×C3×C4—31no—
264C2×C3×C4—62no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—61no—
270C2×C3×C4—61no—
271C2×C3×C4C2×C4×D311yescharacteristic
272C2×C3×C4C2×C4×D311yescharacteristic
273C2×C3×C4C2×D1211yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4C2×#6711yescharacteristic
277#67—122no—
278C2×Dic3—21no—
279C2×Dic3—21no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—121no—
283C2×Dic3(C2×D3)⋊C411yescharacteristic
284C2×Dic3(C2×D3)⋊C411yescharacteristic
285C2×Dic3(C2×D3)⋊C411yescharacteristic
286D12—62no—
287D12—61no—
288D12—61no—
289D12—61no—
290D12—61no—
291D12—121no—
292D12—122no—
293C4×D3—22no—
294C4×D3—21no—
295C4×D3—21no—
296C4×D3—21no—
297C4×D3—21no—
298C4×D3—121no—
299C4×D3—121no—
300C4×D3—121no—
301C4×D3—121no—
302C4×D3—241no—
303C4×D3—241no—
304Dic6—21no—
305Dic6—21no—
306C3×C8—41no—
307C3×C8—41no—
308C3×C8—62no—
309C3×C8—81no—
310C3×C8—121no—
311C3⋊C8—22no—
312C3⋊C8—41no—
313C3⋊C8—62no—
314C3⋊C8—62no—
315C3⋊C8—122no—
316C2×C32#40811yescharacteristic
317C2×C32#41711yescharacteristic
318C2×C32C2×#10411yescharacteristic
319C3⋊D3—81no—
320C3×D3—22no—
321C2×Q8—31no—
322C2×D4—91no—
323C2×D4—181no—
324C22×C4—31no—
325C22×C4—31no—
326C22×C4—31no—
327C22×C4—181no—
328M16—184no—
329C2×C8—21no—
330C2×C8—61no—
331C2×C8—61no—
332C2×C8—122no—
333C2×C8—181no—
334C4⋊C4—31no—
335C4⋊C4—61no—
336C4⋊C4—91no—
337C4⋊C4—181no—
338C4⋊C4—181no—
339C4⋊C4—181no—
340C22⋊C4—181no—
341C22⋊C4—181no—
342C22⋊C4—181no—
343C22⋊C4—181no—
344C22⋊C4—181no—
345C42—31no—
346C42—31no—
347C42—31no—
348C42—61no—
349C42C2×D3211yescharacteristic
350C22×C3—21no—
351C22×C3—32no—
352C22×C3—61no—
353C22×C3—61no—
354C22×C3D3×C22⋊C411yescharacteristic
355C22×C3C2×(C2×D3)⋊C411yescharacteristic
356C2×D3—21no—
357C2×D3—21no—
358C2×D3—122no—
359C2×D3—121no—
360C2×D3—121no—
361C2×D3—121no—
362C2×D3—121no—
363C2×D3—121no—
364C2×D3—121no—
365C2×D3—241no—
366C2×D3—241no—
367C2×D3#82512yes—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—41no—
375C3×C4—61no—
376C3×C4—61no—
377C3×C4—61no—
378C3×C4—121no—
379C3×C4—121no—
380C3×C4#90111yescharacteristic
381C3×C4#90111yescharacteristic
382C3×C4#90111yescharacteristic
383C3×C4#90711yescharacteristic
384C3×C4#91411yescharacteristic
385C3×C4#91811yescharacteristic
386C3×C4#93211yescharacteristic
387C3×C4#94211yescharacteristic
388Dic3—21no—
389Dic3—21no—
390Dic3—21no—
391Dic3—41no—
392Dic3—41no—
393Dic3—121no—
394Dic3—121no—
395Dic3—241no—
396C32#148311yescharacteristic, complemented, Sylow
397C23—31no—
398C23—181no—
399Q8—61no—
400Q8—61no—
401D4—181no—
402D4—181no—
403D4—362no—
404C2×C4—31no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—62no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—181no—
415C2×C4—361no—
416C2×C4—361no—
417C2×C4C4×D3211yescharacteristic
418C2×C4D3×D1211yescharacteristic
419C2×C4D3×#6711yescharacteristic
420C8—41no—
421C8—62no—
422C8—121no—
423C8—182no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—62no—
428C2×C3#472711yescharacteristic
429C2×C3#480311yescharacteristic
430C2×C3D3×#10411yescharacteristic
431C2×C3#496611yescharacteristic
432C2×C3#511011yescharacteristic
433C2×C3C2×#82511yescharacteristic
434D3—22no—
435D3—242no—
436D3—241no—
437D3—241no—
438C22—32no—
439C22—61no—
440C22—61no—
441C22—361no—
442C22—361no—
443C22—361no—
444C22D3×(C2×D3)⋊C411yescharacteristic
445C4—21no—
446C4—61no—
447C4—61no—
448C4—61no—
449C4—121no—
450C4—121no—
451C4—361no—
452C4#6380311yescharacteristic
453C4#6380411yescharacteristic
454C4#6393411yescharacteristic
455C4#6394811yescharacteristic
456C3—21no—
457C3#6823411yescharacteristic, complemented
458C3#7042711yescharacteristic, complemented
459C2—62no—
460C2—721no—
461C2#1059060911yescharacteristic
462C2#1059095311yescharacteristic
463C2D3×#82511yescharacteristic
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#1483
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×D3×C4⋊C8C2semidirect
3. C4×#3711C2semidirect
4. #10589349C2semidirect
5. C3×#4484C2semidirect
6. #10589083C2semidirect
7. #10589082C2semidirect
33. D3×C4⋊C8D3semidirect
38. #4484D3semidirect
396. C32#1483semidirect
457. C3#68234semidirect
458. C3#70427semidirect

Maximal subgroups

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

subgroupindex
#105938702
C3×D3×C4⋊C82
C4×#37112
#105893492
C3×#44842
#105890832
#105890822
#704273
#682343