Finite Group Databasebeta

← #11776145

Subgroups — #11776145

Order 1152.

544 conjugacy classes of subgroups.

The subgroup lattice has 421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5725C211yesmaximal, characteristic
2D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
3#10590248C211yesmaximal, characteristic, complemented
4#10589413C211yesmaximal, characteristic, complemented
5C3×#4547C211yesmaximal, characteristic, complemented
6#10589090C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71804—31nomaximal
9#68417—31nomaximal
10C2×C3×#239—21no—
11C32×C4⋊Q8C2211yescharacteristic
12C3×#947—21no—
13C3×#895—21no—
14C3×#895C412yes—
15C3×#893—21no—
16C3×#893C412yes—
17C3×#874C2211yescharacteristic
18C3×C42×D3C2211yescharacteristic
19C2×D3×C3⋊C8—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24Dic3⋊(C3⋊C8)—21no—
25(C2×D3)⋊(C3⋊C8)—21no—
26Dic3×C3⋊C8—21no—
27C3×#532—31no—
28#5725D311yescharacteristic
29#4925—31no—
30C2×C4⋊(C3⋊C8)—31no—
31#4833—31no—
32D3×C4⋊C8—31no—
33C3×#332—31no—
34#4547—31no—
35#4547—31no—
36#4547—61no—
37#4547D311yescharacteristic, complemented
38#4544—31no—
39#4544—31no—
40#4485—31no—
41#4485—31no—
42C2×C32×Q8—21no—
43C3×#239—42no—
44C3×#239—42no—
45C2×C3×D12—22no—
46C2×C3×D12—21no—
47C2×C3×D12—21no—
48C2×C3×D12C2×C412yes—
49C2×C3×C4×D3—22no—
50C2×C3×C4×D3C2×C411yescharacteristic
51C2×C3×C4×D3D411yescharacteristic
52C2×C3×C4×D3D411yescharacteristic
53C32×C4⋊C4—21no—
54C32×C4⋊C4C2×C412yes—
55C32×C42C2311yescharacteristic
56C2×C3⋊(C3⋊C8)—21no—
57C2×C3⋊(C3⋊C8)—21no—
58C3×(C2×D3)⋊C4—22no—
59C3×(C2×D3)⋊C4—22no—
60C3×C4×Dic3C2×C411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C3×C4×Dic3D411yescharacteristic
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65D3×C3⋊C8—42no—
66#1540—91noSylow
67C2×C3×#41—61no—
68C2×#239—21no—
69C3×C4⋊Q8—21no—
70C3×C4⋊Q8C2×D311yescharacteristic
71C3×C4⋊Q8C2×D311yescharacteristic
72C3×#127—31no—
73C3×#124—61no—
74C3×#121—32no—
75C3×#121—61no—
76C3×C4×D4—32no—
77C3×C4×D4—61no—
78C2×C3×C42—31no—
79#947—21no—
80C22×C3⋊C8—61no—
81C2×D3×C8—61no—
82#895—21no—
83#895Dic312yes—
84#893—21no—
85#893Dic312yes—
86#874C2×D311yescharacteristic
87C42×D3C2×D311yescharacteristic
88C3×C4⋊C8—31no—
89C3×C4⋊C8—31no—
90#830—61no—
91(C2×D3)⋊C8—61no—
92Dic3⋊C8—61no—
93C8×Dic3—61no—
94C4⋊(C3⋊C8)—31no—
95C4⋊(C3⋊C8)—31no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)—61no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4⋊(C3⋊C8)C2×D311yescharacteristic
103C4×C3⋊C8—61no—
104C22×C3×D3—22no—
105C22×C3×D3C22⋊C411yescharacteristic
106C32×Q8—41no—
107C32×Q8—41no—
108C2×C32×C4—22no—
109C2×C32×C4C22×C411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3×Dic3C22⋊C411yescharacteristic
113C2×C3×Dic3C22⋊C411yescharacteristic
114C2×C3×Dic3C22⋊C411yescharacteristic
115C3×D12—42no—
116C3×D12—44no—
117C3×D12—41no—
118C3×D12—41no—
119C3×D12—41no—
120C3×D12—41no—
121C3×C4×D3—21no—
122C3×C4×D3—21no—
123C3×C4×D3—41no—
124C3×C4×D3—44no—
125C3×C4×D3D812yes—
126C3×C4×D3SD1612yes—
127C3⋊(C3⋊C8)—41no—
128C3⋊(C3⋊C8)—41no—
129C3×C3⋊C8—41no—
130C3×C3⋊C8—41no—
131#532—31no—
132#431—91no—
133C2×C4⋊C8—91no—
134#332—31no—
135#332—91no—
136#331—91no—
137#331—91no—
138C3×#41—122no—
139C3×#41—122no—
140C2×C3×Q8—21no—
141C2×C3×Q8—21no—
142C2×C3×Q8—41no—
143C2×C3×D4—32no—
144C2×C3×D4—62no—
145C2×C3×D4—61no—
146C2×C3×D4—61no—
147C22×C3×C4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—62no—
151#239—42no—
152#239—42no—
153C2×D12—22no—
154C2×D12—21no—
155C2×D12—21no—
156C2×D12C2×Dic312yes—
157C2×C4×D3—22no—
158C2×C4×D3C2×Dic311yescharacteristic
159C2×C4×D3#6711yescharacteristic
160C2×C4×D3#6711yescharacteristic
161C2×C3×C8—61no—
162C2×C3×C8—61no—
163C3×C4⋊C4—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4—22no—
166C3×C4⋊C4—41no—
167C3×C4⋊C4C4×D312yes—
168C3×C4⋊C4C2×Dic312yes—
169C3×C22⋊C4—62no—
170C3×C22⋊C4—62no—
171C3×C42—21no—
172C3×C42—31no—
173C3×C42—31no—
174C3×C42—31no—
175C3×C42C22×D311yescharacteristic
176C3×C42C22×D311yescharacteristic
177(C2×D3)⋊C4—22no—
178(C2×D3)⋊C4—22no—
179C4×Dic3C2×Dic311yescharacteristic
180C4×Dic3#6711yescharacteristic
181C4×Dic3#6711yescharacteristic
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188C2×C3⋊C8—121no—
189C2×C3⋊C8—121no—
190C2×C3⋊C8—122no—
191D3×C8—122no—
192C22×C32C2×C22⋊C411yescharacteristic
193C2×C3×D3—21no—
194C2×C3×D3—21no—
195C2×C3×D3—42no—
196C2×C3×D3—42no—
197C2×C3×D3—42no—
198C2×C3×D3#10212yes—
199C32×C4—21no—
200C32×C4—42no—
201C32×C4C2×D811yescharacteristic
202C32×C4C2×SD1611yescharacteristic
203C32×C4#13511yescharacteristic
204C32×C4#13511yescharacteristic
205C3×Dic3—21no—
206C3×Dic3—21no—
207C3×Dic3#10212yes—
208C2×#41—61no—
209C22×C8—181no—
210C4⋊Q8D3211yescharacteristic
211#127—31no—
212#124—61no—
213#121—32no—
214#121—61no—
215C4×D4—32no—
216C4×D4—61no—
217C2×C42—31no—
218C4⋊C8—31no—
219C4⋊C8—31no—
220C4⋊C8—91no—
221C4⋊C8—91no—
222C4⋊C8—181no—
223C22⋊C8—181no—
224C4×C8—181no—
225C23×C3—31no—
226C23×C3—62no—
227C22×D3—22no—
228C22×D3#21711yescharacteristic
229C3×Q8—41no—
230C3×Q8—41no—
231C3×Q8—41no—
232C3×Q8—41no—
233C3×Q8—81no—
234C3×Q8—81no—
235C3×D4—122no—
236C3×D4—124no—
237C3×D4—121no—
238C3×D4—121no—
239C3×D4—121no—
240C3×D4—121no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—21no—
246C2×C3×C4—31no—
247C2×C3×C4—32no—
248C2×C3×C4—32no—
249C2×C3×C4—31no—
250C2×C3×C4—31no—
251C2×C3×C4—42no—
252C2×C3×C4—61no—
253C2×C3×C4—61no—
254C2×C3×C4—121no—
255C2×C3×C4—124no—
256C2×C3×C4C2×C4×D311yescharacteristic
257C2×C3×C4D3×D411yescharacteristic
258C2×C3×C4D3×D411yescharacteristic
259C2×C3×C4C22×Dic311yescharacteristic
260C2×C3×C4C2×#6711yescharacteristic
261C2×C3×C4C2×#6711yescharacteristic
262C2×Dic3#21711yescharacteristic
263C2×Dic3#21711yescharacteristic
264C2×Dic3#21711yescharacteristic
265D12—42no—
266D12—44no—
267D12—41no—
268D12—41no—
269D12—41no—
270D12—41no—
271C4×D3—21no—
272C4×D3—21no—
273C4×D3—41no—
274C4×D3—44no—
275C4×D3#21312yes—
276C4×D3#21412yes—
277C3×C8—121no—
278C3×C8—121no—
279C3⋊C8—41no—
280C3⋊C8—41no—
281C3⋊C8—121no—
282C3⋊C8—121no—
283C3⋊C8—121no—
284C3⋊C8—121no—
285C3⋊C8—241no—
286C3⋊C8—241no—
287C2×C32#41311yescharacteristic
288C2×C32C2×#10211yescharacteristic
289C2×C32#41611yescharacteristic
290C3×D3—22no—
291C3×D3—82no—
292#41—122no—
293#41—122no—
294C2×Q8—21no—
295C2×D4—32no—
296C2×D4—62no—
297C2×D4—61no—
298C2×D4—61no—
299C22×C4—31no—
300C22×C4—31no—
301C22×C4—31no—
302C22×C4—62no—
303C2×C8—61no—
304C2×C8—61no—
305C2×C8—181no—
306C2×C8—181no—
307C2×C8—362no—
308C4⋊C4—21no—
309C4⋊C4D3×Dic312yes—
310C22⋊C4—62no—
311C22⋊C4—62no—
312C42—31no—
313C42—31no—
314C42—31no—
315C42C2×D3211yescharacteristic
316C22×C3—21no—
317C22×C3—32no—
318C22×C3—61no—
319C22×C3—61no—
320C22×C3—122no—
321C22×C3—122no—
322C22×C3—122no—
323C22×C3D3×C22⋊C411yescharacteristic
324C22×C3C2×#21711yescharacteristic
325C2×D3—21no—
326C2×D3—21no—
327C2×D3—42no—
328C2×D3—42no—
329C2×D3—42no—
330C2×D3#83212yes—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—21no—
336C3×C4—21no—
337C3×C4—32no—
338C3×C4—41no—
339C3×C4—42no—
340C3×C4—42no—
341C3×C4—61no—
342C3×C4—61no—
343C3×C4—82no—
344C3×C4D3×D811yescharacteristic
345C3×C4D3×SD1611yescharacteristic
346C3×C4#91611yescharacteristic
347C3×C4#91911yescharacteristic
348C3×C4C2×#21311yescharacteristic
349C3×C4C2×#21411yescharacteristic
350C3×C4#95011yescharacteristic
351C3×C4#95011yescharacteristic
352Dic3—21no—
353Dic3—21no—
354Dic3#83212yes—
355C32#154011yescharacteristic, complemented, Sylow
356C23—31no—
357C23—62no—
358Q8—41no—
359Q8—41no—
360D4—122no—
361D4—124no—
362D4—121no—
363D4—121no—
364D4—121no—
365D4—121no—
366C2×C4—22no—
367C2×C4—31no—
368C2×C4—32no—
369C2×C4—32no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—121no—
375C2×C4—124no—
376C2×C4C2×D3×Dic311yescharacteristic
377C2×C4D3×#6711yescharacteristic
378C2×C4D3×#6711yescharacteristic
379C8—121no—
380C8—121no—
381C8—361no—
382C8—361no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—21no—
386C2×C3—62no—
387C2×C3—242no—
388C2×C3#475111yescharacteristic
389C2×C3D3×#10211yescharacteristic
390C2×C3#480411yescharacteristic
391C2×C3C2×#83211yescharacteristic
392C2×C3#523311yescharacteristic
393C2×C3#523711yescharacteristic
394D3—22no—
395D3—82no—
396C22—32no—
397C22—61no—
398C22—61no—
399C22—122no—
400C22—122no—
401C22—122no—
402C22D3×#21711yescharacteristic
403C4—21no—
404C4—32no—
405C4—42no—
406C4—61no—
407C4—61no—
408C4D3×#21311yescharacteristic
409C4D3×#21411yescharacteristic
410C4#6394711yescharacteristic
411C4#6394911yescharacteristic
412C3—21no—
413C3#6841711yescharacteristic, complemented
414C3#7180411yescharacteristic, complemented
415C2—62no—
416C2—242no—
417C2D3×#83211yescharacteristic
418C2#1059155611yescharacteristic
419C2#1059163711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5725C2
cosocleC32×C42C23
hypercenterC4⋊Q8D32
hypocenterC32#1540
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. D3×C4⋊(C3⋊C8)C2semidirect
3. #10590248C2semidirect
4. #10589413C2semidirect
5. C3×#4547C2semidirect
6. #10589090C2semidirect
7. #10589090C2semidirect
37. #4547D3semidirect
355. C32#1540semidirect
413. C3#68417semidirect
414. C3#71804semidirect

Maximal subgroups

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

subgroupindex
C3×#57252
D3×C4⋊(C3⋊C8)2
#105902482
#105894132
C3×#45472
#105890902
#718043
#684173