Finite Group Databasebeta

← #11776364

Subgroups — #11776364

Order 1152.

512 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#869C211yesmaximal, characteristic
2C3×#4837C211yesmaximal, characteristic
3#10590248C211yesmaximal, characteristic
4#10589347C211yesmaximal, characteristic, complemented
5C3×#4481C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589095C211yesmaximal, characteristic, complemented
8#70507—31nomaximal
9#68483—31nomaximal
10C2×D3×Dic6C412yes—
11#64078C2211yescharacteristic
12C2×C3×ΓL(1,𝔽25)—21no—
13C3×C42×D3C2211yescharacteristic
14C3×#869C2211yescharacteristic
15#63918—21no—
16#63918—21no—
17D3×C4⋊Dic3—21no—
18D3×C4⋊Dic3—21no—
19#63866C412yes—
20C32×C4⋊C8C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×Dic3⋊C8—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25(C2×D3)⋊(C3⋊C8)—21no—
26Dic3×C3⋊C8—21no—
27D3×C4⋊Q8—31no—
28C2×#869—31no—
29C3×#423—31no—
30#4925—31no—
31#4837D311yescharacteristic
32#4833—31no—
33C3×#333—31no—
34#4546—31no—
35#4481—31no—
36#4481—31no—
37#4481—31no—
38#4481—31no—
39#4481—31no—
40#4481—61no—
41#4481D311yescharacteristic, complemented
42C2×#634C2×C412yes—
43C2×C3×C4×D3C2×C411yescharacteristic
44C2×C3×C4×D3D411yescharacteristic
45C2×C3×C4×D3D411yescharacteristic
46C2×C3×Dic6C2×C412yes—
47C2×#627—22no—
48C2×D3×Dic3—22no—
49D3×Dic6—44no—
50C2×C32×C8—21no—
51C32×C42C2311yescharacteristic
52C4⋊(C3⋊Dic3)—21no—
53C4⋊(C3⋊Dic3)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4×Dic3C2×C411yescharacteristic
58C3×C4×Dic3D411yescharacteristic
59C3×C4×Dic3D411yescharacteristic
60C2×C3×C3⋊C8—21no—
61C2×C3×C3⋊C8—21no—
62C3×ΓL(1,𝔽25)—42no—
63Dic3⋊Dic3—22no—
64Dic3⋊Dic3—22no—
65#1548—91noSylow
66C2×D3×Q8—32no—
67C22×Dic6—32no—
68C2×C3×M16—61no—
69C3×C4⋊Q8—31no—
70C2×C3×C42—31no—
71#944—32no—
72C2×C4⋊Dic3—61no—
73C2×C4⋊Dic3—61no—
74C2×ΓL(1,𝔽25)—21no—
75D3×C4⋊C4—61no—
76D3×C4⋊C4—61no—
77#888—61no—
78#888—61no—
79C42×D3C2×D311yescharacteristic
80#869—32no—
81#869—31no—
82#869—31no—
83#869—61no—
84#869—61no—
85#869—61no—
86#869C2×D311yescharacteristic
87C3×C4⋊C8—21no—
88C3×C4⋊C8—31no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8—61no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93#830—61no—
94(C2×D3)⋊C8—61no—
95Dic3⋊C8—21no—
96C8×Dic3—61no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—61no—
100C4⋊(C3⋊C8)C2×D311yescharacteristic
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—61no—
103C22×C3×D3C22⋊C411yescharacteristic
104C2×C32×C4C22×C411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—22no—
108#634—42no—
109C2×C3×Dic3—22no—
110C2×C3×Dic3C22⋊C411yescharacteristic
111C2×C3×Dic3C22⋊C411yescharacteristic
112C2×C3×Dic3C22⋊C411yescharacteristic
113C3×C4×D3—21no—
114C3×C4×D3—21no—
115C3×C4×D3—22no—
116C3×C4×D3SD1612yes—
117C3×C4×D3Q1612yes—
118C3×Dic6—42no—
119#627—44no—
120D3×Dic3—44no—
121C32×C8—41no—
122C3⋊(C3⋊C8)—41no—
123C3×C3⋊C8—41no—
124C3×C3⋊C8—41no—
125C2×C4⋊Q8—91no—
126#431—91no—
127#423—31no—
128#333—31no—
129#333—91no—
130#333—91no—
131#333—91no—
132C2×C3×Q8—32no—
133C22×C3×C4—31no—
134C22×C3×C4—31no—
135C22×C3×C4—31no—
136C22×Dic3—62no—
137D3×Q8—124no—
138C2×C4×D3—62no—
139C2×C4×D3C4×D311yescharacteristic
140C2×C4×D3D1211yescharacteristic
141C2×C4×D3#6711yescharacteristic
142C2×Dic6—32no—
143C2×Dic6—32no—
144C2×Dic6—62no—
145C2×Dic6—62no—
146C2×Dic6—62no—
147C2×Dic6—124no—
148C2×Dic6C4×D312yes—
149C3×M16—122no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—41no—
153C2×C3×C8—61no—
154C2×C3×C8—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C42—21no—
158C3×C42—31no—
159C3×C42—31no—
160C3×C42—31no—
161C3×C42C22×D311yescharacteristic
162C3×C42C22×D311yescharacteristic
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
165C4⋊Dic3—62no—
166C4⋊Dic3—62no—
167C4⋊Dic3—61no—
168C4⋊Dic3—61no—
169C4⋊Dic3—61no—
170C4⋊Dic3—61no—
171C4⋊Dic3—121no—
172C4⋊Dic3—121no—
173Dic3⋊C4—62no—
174Dic3⋊C4—62no—
175C4×Dic3C4×D311yescharacteristic
176C4×Dic3D1211yescharacteristic
177C4×Dic3#6711yescharacteristic
178C2×C3⋊C8—21no—
179C2×C3⋊C8—21no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—121no—
183ΓL(1,𝔽25)—42no—
184C22×C32C2×C22⋊C411yescharacteristic
185C2×C3×D3—21no—
186C2×C3×D3—21no—
187C2×C3×D3#10312yes—
188C32×C4—21no—
189C32×C4C2×SD1611yescharacteristic
190C32×C4C2×Q1611yescharacteristic
191C32×C4#13711yescharacteristic
192C32×C4#13711yescharacteristic
193C3⋊Dic3—42no—
194C3×Dic3—21no—
195C3×Dic3—42no—
196C3×Dic3#10012yes—
197C3×Dic3#10312yes—
198C22×Q8—92no—
199C2×M16—61no—
200C4⋊Q8—31no—
201C4⋊Q8—92no—
202C4⋊Q8—91no—
203C4⋊Q8—181no—
204C4⋊Q8—181no—
205C2×C4⋊C4—181no—
206C2×C4⋊C4—181no—
207C2×C42—31no—
208C4⋊C8—31no—
209C4⋊C8—31no—
210C4⋊C8—61no—
211C4⋊C8—91no—
212C4⋊C8D3211yescharacteristic
213C22⋊C8—181no—
214C4×C8—181no—
215C23×C3—31no—
216C22×D3(C2×D3)⋊C411yescharacteristic
217C3×Q8—122no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—31no—
222C2×C3×C4—31no—
223C2×C3×C4—32no—
224C2×C3×C4—32no—
225C2×C3×C4—31no—
226C2×C3×C4—62no—
227C2×C3×C4—61no—
228C2×C3×C4—61no—
229C2×C3×C4—62no—
230C2×C3×C4C2×C4×D311yescharacteristic
231C2×C3×C4C2×C4×D311yescharacteristic
232C2×C3×C4C2×D1211yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4C2×#6711yescharacteristic
236C2×Dic3—22no—
237C2×Dic3—62no—
238C2×Dic3—62no—
239C2×Dic3—122no—
240C2×Dic3—124no—
241C2×Dic3(C2×D3)⋊C411yescharacteristic
242C2×Dic3(C2×D3)⋊C411yescharacteristic
243C2×Dic3(C2×D3)⋊C411yescharacteristic
244C4×D3—21no—
245C4×D3—21no—
246C4×D3—22no—
247C4×D3—124no—
248C4×D3#21412yes—
249C4×D3#21612yes—
250Dic6—42no—
251Dic6—124no—
252Dic6—124no—
253Dic6—122no—
254Dic6—122no—
255Dic6—242no—
256C3×C8—41no—
257C3×C8—41no—
258C3×C8—81no—
259C3×C8—121no—
260C3×C8—121no—
261C3⋊C8—41no—
262C3⋊C8—41no—
263C3⋊C8—121no—
264C3⋊C8—121no—
265C3⋊C8—241no—
266C2×C32C2×#10011yescharacteristic
267C2×C32C2×#10311yescharacteristic
268C2×C32#41911yescharacteristic
269C3×D3—22no—
270C2×Q8—32no—
271C2×Q8—92no—
272C2×Q8—182no—
273C2×Q8—364no—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—31no—
277C22×C4—182no—
278M16—122no—
279C2×C8—21no—
280C2×C8—61no—
281C2×C8—61no—
282C2×C8—181no—
283C4⋊C4—61no—
284C4⋊C4—61no—
285C4⋊C4—182no—
286C4⋊C4—182no—
287C4⋊C4—181no—
288C4⋊C4—181no—
289C42—31no—
290C42—31no—
291C42—31no—
292C42C2×D3211yescharacteristic
293C22×C3—21no—
294C22×C3—32no—
295C22×C3—61no—
296C22×C3—61no—
297C22×C3D3×C22⋊C411yescharacteristic
298C22×C3C2×(C2×D3)⋊C411yescharacteristic
299C2×D3—21no—
300C2×D3—21no—
301C2×D3#81012yes—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—32no—
309C3×C4—32no—
310C3×C4—41no—
311C3×C4—61no—
312C3×C4—122no—
313C3×C4#90911yescharacteristic
314C3×C4#90911yescharacteristic
315C3×C4D3×SD1611yescharacteristic
316C3×C4#91511yescharacteristic
317C3×C4D3×Q1611yescharacteristic
318C3×C4#91811yescharacteristic
319C3×C4C2×#21411yescharacteristic
320C3×C4C2×#21611yescharacteristic
321Dic3—21no—
322Dic3—42no—
323Dic3—122no—
324Dic3—122no—
325Dic3—242no—
326Dic3#81012yes—
327Dic3#82312yes—
328C32#154811yescharacteristic, complemented, Sylow
329C23—31no—
330Q8—122no—
331Q8—362no—
332Q8—364no—
333C2×C4—31no—
334C2×C4—31no—
335C2×C4—32no—
336C2×C4—32no—
337C2×C4—31no—
338C2×C4—62no—
339C2×C4—61no—
340C2×C4—61no—
341C2×C4—62no—
342C2×C4—182no—
343C2×C4—364no—
344C2×C4C4×D3211yescharacteristic
345C2×C4D3×D1211yescharacteristic
346C2×C4D3×#6711yescharacteristic
347C8—41no—
348C8—121no—
349C8—121no—
350C8—361no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—62no—
355C2×C3D3×#10011yescharacteristic
356C2×C3D3×#10311yescharacteristic
357C2×C3#480211yescharacteristic
358C2×C3C2×#81011yescharacteristic
359C2×C3#512011yescharacteristic
360C2×C3C2×#82311yescharacteristic
361D3—22no—
362C22—32no—
363C22—61no—
364C22—61no—
365C22D3×(C2×D3)⋊C411yescharacteristic
366C4—21no—
367C4—32no—
368C4—32no—
369C4—61no—
370C4—122no—
371C4—362no—
372C4#6380011yescharacteristic
373C4#6380111yescharacteristic
374C4D3×#21411yescharacteristic
375C4D3×#21611yescharacteristic
376C3—21no—
377C3#6848311yescharacteristic, complemented
378C3#7050711yescharacteristic, complemented
379C2—62no—
380C2D3×#81011yescharacteristic
381C2#1059094811yescharacteristic
382C2D3×#82311yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1548
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #10589347C2semidirect
5. C3×#4481C2semidirect
6. #10589096C2semidirect
7. #10589095C2semidirect
41. #4481D3semidirect
328. C32#1548semidirect
377. C3#68483semidirect
378. C3#70507semidirect

Maximal subgroups

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

subgroupindex
D3×#8692
C3×#48372
#105902482
#105893472
C3×#44812
#105890962
#105890952
#705073
#684833