Finite Group Databasebeta

← #11775725

Subgroups — #11775725

Order 1152.

498 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5691C211yesmaximal, characteristic
2#10590334C211yesmaximal, characteristic, complemented
3D3×#803C211yesmaximal, characteristic, complemented
4#10589409C211yesmaximal, characteristic, complemented
5C3×#4543C211yesmaximal, characteristic, complemented
6#10589086C211yesmaximal, characteristic, complemented
7#10589086C211yesmaximal, characteristic, complemented
8#71746—31nomaximal
9#68361—31nomaximal
10C32×#125C2211yescharacteristic
11C3×#898—21no—
12C3×#897C411yescharacteristic
13C3×#895C411yescharacteristic
14C3×#894—21no—
15C3×#893—21no—
16C3×#893C411yescharacteristic
17C3×#892—21no—
18C3×#887C411yescharacteristic
19C3×#875C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C2×#3711—21no—
22C2×D3×C3⋊C8—21no—
23#63630C2211yescharacteristic
24#63630C2211yescharacteristic
25C3×#803C2211yescharacteristic
26C3×#803C2211yescharacteristic
27#63554—21no—
28Dic3×C3⋊C8—21no—
29C3×#529—31no—
30#5691D311yescharacteristic
31C4×#208—31no—
32C2×#803—31no—
33#4707—31no—
34D3×#97—31no—
35C3×#330—31no—
36#4543—31no—
37#4543—31no—
38#4543—61no—
39#4543D311yescharacteristic, complemented
40#4540—31no—
41#4540—31no—
42#4464—31no—
43#4464—31no—
44C2×C3×D12—21no—
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3C2×C411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×C3×Dic6C2×C411yescharacteristic
51C32×C4⋊C4—21no—
52C32×C4⋊C4—21no—
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C4⋊C4C2×C411yescharacteristic
55C32×C42C2311yescharacteristic
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×C4⋊Dic3—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—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—24no—
73#1524—91noSylow
74C3×#126—61no—
75C3×#125—21no—
76C3×#125C2×D311yescharacteristic
77C3×#125C2×D311yescharacteristic
78C3×#124—31no—
79C3×#123—61no—
80C3×C22⋊Q8—31no—
81C3×#121—31no—
82C3×C4×Q8—31no—
83C3×C4×D4—31no—
84C3×C4×D4—61no—
85C3×#117—61no—
86C2×C3×C42—31no—
87C2×#208—61no—
88C22×C3⋊C8—61no—
89C2×ΓL(1,𝔽25)—61no—
90C2×D3×C8—61no—
91#898—21no—
92#897Dic311yescharacteristic
93#895Dic311yescharacteristic
94#894—21no—
95#893—21no—
96#893Dic311yescharacteristic
97#892—21no—
98#887Dic311yescharacteristic
99#875C2×D311yescharacteristic
100C42×D3C2×D311yescharacteristic
101C3×#97—31no—
102C3×#97—31no—
103#815—61no—
104C8×Dic3—61no—
105#803—31no—
106#803—31no—
107#803—31no—
108#803—31no—
109#803—61no—
110#803—61no—
111#803—61no—
112#803C2×D311yescharacteristic
113#803C2×D311yescharacteristic
114C4×C3⋊C8—61no—
115C22×C3×D3—21no—
116C22×C3×D3C22⋊C411yescharacteristic
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3×Dic3—21no—
123C2×C3×Dic3C22⋊C411yescharacteristic
124C2×C3×Dic3C22⋊C411yescharacteristic
125C2×C3×Dic3C22⋊C411yescharacteristic
126C3×D12—41no—
127C3×D12—42no—
128C3×C4×D3—22no—
129C3×C4×D3—22no—
130C3×C4×D3—41no—
131C3×C4×D3—42no—
132C3×Dic6—41no—
133C3⋊(C3⋊C8)—22no—
134C3⋊(C3⋊C8)—22no—
135C3×C3⋊C8—22no—
136C3×C3⋊C8—22no—
137#529—31no—
138C4×M16—91no—
139C2×#97—91no—
140#330—31no—
141#330—91no—
142#329—91no—
143#329—91no—
144C2×C3×Q8—31no—
145C2×C3×D4—31no—
146C2×C3×D4—61no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—61no—
151C2×D12—21no—
152C2×D12C2×Dic311yescharacteristic
153C2×C4×D3—21no—
154C2×C4×D3C2×Dic311yescharacteristic
155C2×C4×D3#6711yescharacteristic
156C2×C4×D3#6711yescharacteristic
157C2×Dic6C2×Dic311yescharacteristic
158C2×C3×C8—61no—
159C2×C3×C8—61no—
160C3×C4⋊C4—21no—
161C3×C4⋊C4—21no—
162C3×C4⋊C4—21no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—41no—
167C3×C4⋊C4—41no—
168C3×C4⋊C4—61no—
169C3×C4⋊C4—61no—
170C3×C4⋊C4C4×D311yescharacteristic
171C3×C4⋊C4C4×D311yescharacteristic
172C3×C4⋊C4C2×Dic311yescharacteristic
173C3×C4⋊C4C2×Dic311yescharacteristic
174C3×C22⋊C4—61no—
175C3×C22⋊C4—61no—
176C3×C22⋊C4—61no—
177C3×C22⋊C4—61no—
178C3×C22⋊C4—61no—
179C3×C42—21no—
180C3×C42—31no—
181C3×C42—31no—
182C3×C42—31no—
183C3×C42—61no—
184C3×C42C22×D311yescharacteristic
185C3×C42C22×D311yescharacteristic
186(C2×D3)⋊C4—21no—
187(C2×D3)⋊C4—21no—
188(C2×D3)⋊C4—21no—
189(C2×D3)⋊C4—21no—
190(C2×D3)⋊C4—21no—
191C4⋊Dic3—21no—
192Dic3⋊C4—21no—
193C4×Dic3—21no—
194C4×Dic3C2×Dic311yescharacteristic
195C4×Dic3#6711yescharacteristic
196C4×Dic3#6711yescharacteristic
197#208—64no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—64no—
201C2×C3⋊C8—61no—
202C2×C3⋊C8—61no—
203C2×C3⋊C8—61no—
204C2×C3⋊C8—61no—
205C2×C3⋊C8—121no—
206C2×C3⋊C8—121no—
207ΓL(1,𝔽25)—64no—
208D3×C8—64no—
209C22×C32C2×C22⋊C411yescharacteristic
210C2×C3×D3—21no—
211C2×C3×D3—21no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C2×C3×D3—41no—
215C2×C3×D3#10412yes—
216C32×C4—21no—
217C32×C4—21no—
218C32×C4—21no—
219C32×C4—41no—
220C32×C4—41no—
221C3×Dic3—21no—
222C3×Dic3—21no—
223C3×Dic3—41no—
224C3×Dic3#10412yes—
225C2×M16—181no—
226C22×C8—181no—
227#126—61no—
228#125D3211yescharacteristic
229#124—31no—
230#123—61no—
231C22⋊Q8—31no—
232#121—31no—
233C4×Q8—31no—
234C4×D4—31no—
235C4×D4—61no—
236#117—61no—
237C2×C42—31no—
238#97—31no—
239#97—31no—
240#97—91no—
241#97—91no—
242#97—181no—
243C4×C8—181no—
244C23×C3—31no—
245C23×C3—61no—
246C22×D3—21no—
247C22×D3#21711yescharacteristic
248C3×Q8—121no—
249C3×D4—121no—
250C3×D4—122no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
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—41no—
262C2×C3×C4—41no—
263C2×C3×C4—62no—
264C2×C3×C4—62no—
265C2×C3×C4—61no—
266C2×C3×C4—121no—
267C2×C3×C4—122no—
268C2×C3×C4C2×C4×D311yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4C22×Dic311yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273C2×C3×C4C2×#6711yescharacteristic
274C2×Dic3—21no—
275C2×Dic3#21711yescharacteristic
276C2×Dic3#21711yescharacteristic
277C2×Dic3#21711yescharacteristic
278D12—41no—
279D12—42no—
280C4×D3—22no—
281C4×D3—22no—
282C4×D3—41no—
283C4×D3—42no—
284Dic6—41no—
285C3×C8—62no—
286C3×C8—62no—
287C3⋊C8—22no—
288C3⋊C8—22no—
289C3⋊C8—62no—
290C3⋊C8—62no—
291C3⋊C8—62no—
292C3⋊C8—62no—
293C3⋊C8—122no—
294C3⋊C8—122no—
295C2×C32#41311yescharacteristic
296C2×C32C2×#10411yescharacteristic
297C2×C32C2×#10411yescharacteristic
298C3×D3—22no—
299C3×D3—81no—
300C2×Q8—31no—
301C2×D4—31no—
302C2×D4—61no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—61no—
307M16—184no—
308C2×C8—61no—
309C2×C8—61no—
310C2×C8—184no—
311C2×C8—181no—
312C2×C8—181no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4D3×Dic311yescharacteristic
318C4⋊C4D3×Dic311yescharacteristic
319C22⋊C4—61no—
320C22⋊C4—61no—
321C22⋊C4—61no—
322C22⋊C4—61no—
323C22⋊C4—61no—
324C42—31no—
325C42—31no—
326C42—31no—
327C42—61no—
328C42C2×D3211yescharacteristic
329C22×C3—21no—
330C22×C3—32no—
331C22×C3—61no—
332C22×C3—61no—
333C22×C3—121no—
334C22×C3—121no—
335C22×C3—121no—
336C22×C3D3×C22⋊C411yescharacteristic
337C22×C3C2×#21711yescharacteristic
338C2×D3—21no—
339C2×D3—21no—
340C2×D3—41no—
341C2×D3—41no—
342C2×D3—41no—
343C2×D3#83712yes—
344C3×C4—21no—
345C3×C4—21no—
346C3×C4—21no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—21no—
350C3×C4—32no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—41no—
354C3×C4—41no—
355C3×C4—41no—
356C3×C4—41no—
357C3×C4—41no—
358C3×C4—61no—
359C3×C4—61no—
360C3×C4—81no—
361C3×C4—81no—
362C3×C4—121no—
363Dic3—21no—
364Dic3—21no—
365Dic3—41no—
366Dic3#83712yes—
367C32#152411yescharacteristic, complemented, Sylow
368C23—31no—
369C23—61no—
370Q8—121no—
371D4—121no—
372D4—122no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—31no—
376C2×C4—31no—
377C2×C4—31no—
378C2×C4—62no—
379C2×C4—62no—
380C2×C4—61no—
381C2×C4—121no—
382C2×C4—122no—
383C2×C4C2×D3×Dic311yescharacteristic
384C2×C4D3×#6711yescharacteristic
385C2×C4D3×#6711yescharacteristic
386C8—62no—
387C8—62no—
388C8—182no—
389C8—182no—
390C2×C3—21no—
391C2×C3—21no—
392C2×C3—21no—
393C2×C3—62no—
394C2×C3—241no—
395C2×C3#475111yescharacteristic
396C2×C3D3×#10411yescharacteristic
397C2×C3D3×#10411yescharacteristic
398C2×C3C2×#83711yescharacteristic
399C2×C3C2×#83711yescharacteristic
400C2×C3#523711yescharacteristic
401D3—22no—
402D3—81no—
403C22—32no—
404C22—61no—
405C22—61no—
406C22—121no—
407C22—121no—
408C22—121no—
409C22D3×#21711yescharacteristic
410C4—21no—
411C4—21no—
412C4—21no—
413C4—32no—
414C4—41no—
415C4—41no—
416C4—61no—
417C4—61no—
418C4—121no—
419C3—21no—
420C3#6836111yescharacteristic, complemented
421C3#7174611yescharacteristic, complemented
422C2—62no—
423C2—241no—
424C2#1059163711yescharacteristic
425C2D3×#83711yescharacteristic
426C2D3×#83711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×#125C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#895C4
cosocleC32×C42C23
hypercenter#125D32
hypocenterC32#1524
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. #10590334C2semidirect
3. D3×#803C2semidirect
4. #10589409C2semidirect
5. C3×#4543C2semidirect
6. #10589086C2semidirect
7. #10589086C2semidirect
39. #4543D3semidirect
367. C32#1524semidirect
420. C3#68361semidirect
421. C3#71746semidirect

Maximal subgroups

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

subgroupindex
C3×#56912
#105903342
D3×#8032
#105894092
C3×#45432
#105890862
#717463
#683613