Finite Group Databasebeta

← #11774469

Subgroups — #11774469

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
1#10593974C211yesmaximal, characteristic
2C3×D3×C4⋊C8C211yesmaximal, characteristic, complemented
3C4×#3711C211yesmaximal, characteristic, complemented
4#10589350C211yesmaximal, characteristic, complemented
5C3×#4483C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#70427—31nomaximal
9#68170—31nomaximal
10C4×#634C2211yescharacteristic
11C2×C3×D3×C8—21no—
12C3×C4×D12C2211yescharacteristic
13C3×C42×D3C2211yescharacteristic
14#63908C411yescharacteristic
15#63905—21no—
16C4×#625—21no—
17#63869C411yescharacteristic
18#63860C411yescharacteristic
19#63859—21no—
20#63857C411yescharacteristic
21#63855—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#5557—31no—
30#5479—31no—
31C2×C3×C4⋊C8—31no—
32C4×#208—31no—
33D3×C4⋊C8D311yescharacteristic, complemented
34C4×ΓL(1,𝔽25)—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4484—31no—
38#4484—31no—
39#4484—31no—
40#4484—61no—
41#4483—31no—
42#4483D311yescharacteristic, complemented
43#4456—31no—
44C2×#634C2×C411yescharacteristic
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3C2×C411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×#625—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54#3750—21no—
55C4×C3⋊Dic3—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3C2×C411yescharacteristic
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—
66Dic3⋊Dic3—21no—
67Dic3⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71(C2×D3)⋊Dic3—21no—
72#3711—24no—
73#1483—91noSylow
74C22×C3×C8—61no—
75C3×C4×D4—31no—
76C2×C3×C42—31no—
77#938—31no—
78#936—31no—
79#930—31no—
80#929—61no—
81C4×#67—61no—
82C4×#67—61no—
83#926—61no—
84#924—31no—
85C2×#208—61no—
86C2×ΓL(1,𝔽25)—61no—
87C2×D3×C8—21no—
88#897—31no—
89#890—31no—
90#883—61no—
91#879—61no—
92#876—61no—
93#875—31no—
94C4×D12C2×D311yescharacteristic
95#872—61no—
96C42×D3C2×D311yescharacteristic
97#870—31no—
98C4×Dic6—31no—
99C4×Dic6—31no—
100C4×Dic6—61no—
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—
121C2×C3⋊Dic3—21no—
122#634—21no—
123#634—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C3×D12—21no—
129C3×D12—21no—
130C3×C4×D3—22no—
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×C4×D3—21no—
135C3×C4×D3—41no—
136C3×C4×D3—41no—
137#625—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—91no—
146Q8⋊C8—91no—
147D4⋊C8—31no—
148D4⋊C8—91no—
149C2×C3×D4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—31no—
152C22×C3×C4—31no—
153C22×C3×C4—61no—
154C2×#67—61no—
155C2×#67—61no—
156C2×D12C4×D311yescharacteristic
157C2×C4×D3—21no—
158C2×C4×D3C4×D311yescharacteristic
159C2×C4×D3D1211yescharacteristic
160C2×C4×D3#6711yescharacteristic
161C2×Dic6—31no—
162C2×Dic6—31no—
163C2×Dic6—61no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—41no—
167C2×C3×C8—61no—
168C2×C3×C8—61no—
169C2×C3×C8—122no—
170C3×C4⋊C4—31no—
171C3×C22⋊C4—61no—
172C3×C42—21no—
173C3×C42—31no—
174C3×C42—31no—
175C3×C42—31no—
176C3×C42C22×D311yescharacteristic
177C3×C42C22×D311yescharacteristic
178#217—61no—
179#217—61no—
180#217—61no—
181#217—61no—
182(C2×D3)⋊C4—21no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187C4⋊Dic3—31no—
188C4⋊Dic3—31no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3C4×D311yescharacteristic
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—61no—
197Dic3⋊C4—61no—
198Dic3⋊C4—61no—
199Dic3⋊C4—121no—
200C4×Dic3—61no—
201C4×Dic3—61no—
202C4×Dic3—121no—
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—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#13111yescharacteristic
223C32×C4#13111yescharacteristic
224C32×C4AGL(1,ℤ/8)11yescharacteristic
225C32×C4#13711yescharacteristic
226C3⋊Dic3—41no—
227C3⋊Dic3—41no—
228C3×Dic3—21no—
229C3×Dic3—21no—
230C3×Dic3—21no—
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—91no—
241C4×D4—31no—
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—
252C23×C3—61no—
253C22×D3—21no—
254C22×D3(C2×D3)⋊C411yescharacteristic
255C3×D4—61no—
256C3×D4—61no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—31no—
261C2×C3×C4—31no—
262C2×C3×C4—31no—
263C2×C3×C4—62no—
264C2×C3×C4—61no—
265C2×C3×C4—61no—
266C2×C3×C4—61no—
267C2×C3×C4—61no—
268C2×C3×C4—61no—
269C2×C3×C4—121no—
270C2×C3×C4—121no—
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—
278#67—122no—
279C2×Dic3—21no—
280C2×Dic3—61no—
281C2×Dic3—61no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—121no—
285C2×Dic3—121no—
286C2×Dic3(C2×D3)⋊C411yescharacteristic
287C2×Dic3(C2×D3)⋊C411yescharacteristic
288C2×Dic3(C2×D3)⋊C411yescharacteristic
289D12—21no—
290D12—21no—
291C4×D3—22no—
292C4×D3—21no—
293C4×D3—21no—
294C4×D3—21no—
295C4×D3—21no—
296C4×D3—41no—
297C4×D3—41no—
298Dic6—62no—
299Dic6—61no—
300Dic6—61no—
301Dic6—61no—
302Dic6—61no—
303Dic6—121no—
304C3×C8—41no—
305C3×C8—41no—
306C3×C8—62no—
307C3×C8—81no—
308C3×C8—121no—
309C3⋊C8—22no—
310C3⋊C8—41no—
311C3⋊C8—62no—
312C3⋊C8—62no—
313C3⋊C8—122no—
314C2×C32#40811yescharacteristic
315C2×C32#41711yescharacteristic
316C2×C32C2×#10411yescharacteristic
317C3×D3—22no—
318C3×D3—81no—
319C2×Q8—91no—
320C2×D4—31no—
321C2×D4—181no—
322C22×C4—31no—
323C22×C4—31no—
324C22×C4—31no—
325C22×C4—61no—
326M16—184no—
327C2×C8—21no—
328C2×C8—61no—
329C2×C8—61no—
330C2×C8—122no—
331C2×C8—181no—
332C4⋊C4—31no—
333C4⋊C4—91no—
334C4⋊C4—181no—
335C4⋊C4—181no—
336C4⋊C4—181no—
337C4⋊C4—181no—
338C22⋊C4—61no—
339C22⋊C4—181no—
340C22⋊C4—181no—
341C22⋊C4—181no—
342C22⋊C4—181no—
343C42—31no—
344C42—31no—
345C42—31no—
346C42—181no—
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×(C2×D3)⋊C411yescharacteristic
357C2×D3—21no—
358C2×D3—21no—
359C2×D3—41no—
360C2×D3—41no—
361C2×D3—41no—
362C2×D3#82512yes—
363C3×C4—21no—
364C3×C4—21no—
365C3×C4—21no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—41no—
370C3×C4—61no—
371C3×C4—61no—
372C3×C4—61no—
373C3×C4—121no—
374C3×C4#90111yescharacteristic
375C3×C4#90111yescharacteristic
376C3×C4#90111yescharacteristic
377C3×C4#90711yescharacteristic
378C3×C4#91111yescharacteristic
379C3×C4#91511yescharacteristic
380C3×C4#93211yescharacteristic
381C3×C4#94211yescharacteristic
382Dic3—21no—
383Dic3—21no—
384Dic3—21no—
385Dic3—41no—
386Dic3—122no—
387Dic3—121no—
388Dic3—121no—
389Dic3—121no—
390Dic3—121no—
391Dic3—241no—
392C32#148311yescharacteristic, complemented, Sylow
393C23—31no—
394C23—61no—
395Q8—181no—
396Q8—181no—
397D4—61no—
398D4—61no—
399D4—362no—
400C2×C4—31no—
401C2×C4—31no—
402C2×C4—31no—
403C2×C4—62no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—121no—
410C2×C4—121no—
411C2×C4—181no—
412C2×C4—181no—
413C2×C4C4×D3211yescharacteristic
414C2×C4D3×D1211yescharacteristic
415C2×C4D3×#6711yescharacteristic
416C8—41no—
417C8—62no—
418C8—121no—
419C8—182no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—62no—
424C2×C3—241no—
425C2×C3#472711yescharacteristic
426C2×C3#477111yescharacteristic
427C2×C3D3×#10411yescharacteristic
428C2×C3#496611yescharacteristic
429C2×C3#511011yescharacteristic
430C2×C3C2×#82511yescharacteristic
431D3—22no—
432D3—81no—
433C22—32no—
434C22—61no—
435C22—61no—
436C22—121no—
437C22—121no—
438C22—121no—
439C22D3×(C2×D3)⋊C411yescharacteristic
440C4—21no—
441C4—61no—
442C4—61no—
443C4—61no—
444C4—121no—
445C4—361no—
446C4—361no—
447C4#6380311yescharacteristic
448C4#6380411yescharacteristic
449C4#6393211yescharacteristic
450C4#6394611yescharacteristic
451C3—21no—
452C3#6817011yescharacteristic, complemented
453C3#7042711yescharacteristic, complemented
454C2—62no—
455C2—241no—
456C2#1059060711yescharacteristic
457C2#1059095311yescharacteristic
458C2D3×#82511yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radical#63908C4
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. #10589350C2semidirect
5. C3×#4483C2semidirect
6. #10589085C2semidirect
7. #10589080C2semidirect
33. D3×C4⋊C8D3semidirect
42. #4483D3semidirect
392. C32#1483semidirect
452. C3#68170semidirect
453. C3#70427semidirect

Maximal subgroups

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

subgroupindex
#105939742
C3×D3×C4⋊C82
C4×#37112
#105893502
C3×#44832
#105890852
#105890802
#704273
#681703