Finite Group Databasebeta

← #11776359

Subgroups — #11776359

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
1C3×D3×C4⋊Q8C211yesmaximal, characteristic
2#10590336C211yesmaximal, characteristic
3#10590248C211yesmaximal, characteristic
4#10589412C211yesmaximal, characteristic, complemented
5C3×#4546C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589095C211yesmaximal, characteristic, complemented
8#71774—31nomaximal
9#68483—31nomaximal
10C2×C3×D3×Q8C412yes—
11C32×C4⋊Q8C2211yescharacteristic
12C3×#944C412yes—
13C3×D3×C4⋊C4—21no—
14C3×D3×C4⋊C4—21no—
15C3×#888—21no—
16C3×#888—21no—
17C3×C42×D3C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C2×#3711—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—
27C2×C3×C4⋊Q8—31no—
28D3×C4⋊Q8D311yescharacteristic
29#4925—31no—
30#4924—31no—
31#4837—31no—
32#4833—31no—
33C3×#333—31no—
34#4546—31no—
35#4546—31no—
36#4546—31no—
37#4546—31no—
38#4546—61no—
39#4546D311yescharacteristic, complemented
40#4481—31no—
41#4481—31no—
42C2×C32×Q8C2×C412yes—
43C3×D3×Q8—44no—
44C2×C3×C4×D3—22no—
45C2×C3×C4×D3C2×C411yescharacteristic
46C2×C3×C4×D3D411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×Dic6—22no—
49C2×C3×Dic6C2×C412yes—
50C32×C4⋊C4—21no—
51C32×C4⋊C4—21no—
52C32×C42C2311yescharacteristic
53C2×C3⋊(C3⋊C8)—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×Dic3⋊C4—22no—
58C3×Dic3⋊C4—22no—
59C3×C4×Dic3C2×C411yescharacteristic
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3711—42no—
65#1548—91noSylow
66C22×C3×Q8—32no—
67C2×D3×Q8Dic312yes—
68C3×C4⋊Q8—21no—
69C3×C4⋊Q8—32no—
70C3×C4⋊Q8—31no—
71C3×C4⋊Q8—61no—
72C3×C4⋊Q8—61no—
73C3×C4⋊Q8C2×D311yescharacteristic
74C3×C4⋊Q8C2×D311yescharacteristic
75C2×C3×C4⋊C4—61no—
76C2×C3×C4⋊C4—61no—
77C2×C3×C42—31no—
78#944Dic312yes—
79C2×#208—61no—
80C2×ΓL(1,𝔽25)—61no—
81D3×C4⋊C4—21no—
82D3×C4⋊C4—21no—
83#888—21no—
84#888—21no—
85C42×D3C2×D311yescharacteristic
86#869C2×D311yescharacteristic
87C3×C4⋊C8—31no—
88C3×C4⋊C8—31no—
89#830—61no—
90(C2×D3)⋊C8—61no—
91Dic3⋊C8—61no—
92C8×Dic3—61no—
93C4⋊(C3⋊C8)—31no—
94C4⋊(C3⋊C8)—31no—
95C4⋊(C3⋊C8)—31no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—61no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)—61no—
100C4⋊(C3⋊C8)C2×D311yescharacteristic
101C4⋊(C3⋊C8)C2×D311yescharacteristic
102C4×C3⋊C8—61no—
103C22×C3×D3C22⋊C411yescharacteristic
104C32×Q8—42no—
105C2×C32×C4—22no—
106C2×C32×C4C22×C411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
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×D3—44no—
117C3×C4×D3SD1612yes—
118C3×C4×D3Q1612yes—
119C3×Dic6—44no—
120C3×Dic6—42no—
121C3⋊(C3⋊C8)—41no—
122C3⋊(C3⋊C8)—41no—
123C3×C3⋊C8—41no—
124C3×C3⋊C8—41no—
125C2×C4⋊Q8—31no—
126#431—91no—
127#423—91no—
128#333—31no—
129#333—91no—
130#333—91no—
131#333—91no—
132C2×C3×Q8—22no—
133C2×C3×Q8—32no—
134C2×C3×Q8—62no—
135C2×C3×Q8—124no—
136C2×C3×Q8C4×D312yes—
137C2×C3×Q8C2×Dic312yes—
138C22×C3×C4—31no—
139C22×C3×C4—31no—
140C22×C3×C4—31no—
141C22×C3×C4—62no—
142D3×Q8—44no—
143C2×C4×D3—22no—
144C2×C4×D3C2×Dic311yescharacteristic
145C2×C4×D3#6711yescharacteristic
146C2×C4×D3#6711yescharacteristic
147C2×Dic6—22no—
148C2×Dic6C2×Dic312yes—
149C2×C3×C8—61no—
150C2×C3×C8—61no—
151C3×C4⋊C4—21no—
152C3×C4⋊C4—21no—
153C3×C4⋊C4—21no—
154C3×C4⋊C4—21no—
155C3×C4⋊C4—41no—
156C3×C4⋊C4—41no—
157C3×C4⋊C4—62no—
158C3×C4⋊C4—62no—
159C3×C4⋊C4—61no—
160C3×C4⋊C4—61no—
161C3×C42—21no—
162C3×C42—31no—
163C3×C42—31no—
164C3×C42—31no—
165C3×C42C22×D311yescharacteristic
166C3×C42C22×D311yescharacteristic
167C4⋊Dic3—21no—
168C4⋊Dic3—21no—
169Dic3⋊C4—22no—
170Dic3⋊C4—22no—
171C4×Dic3C2×Dic311yescharacteristic
172C4×Dic3#6711yescharacteristic
173C4×Dic3#6711yescharacteristic
174#208—122no—
175C2×C3⋊C8—21no—
176C2×C3⋊C8—21no—
177C2×C3⋊C8—61no—
178C2×C3⋊C8—61no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—121no—
182C2×C3⋊C8—121no—
183ΓL(1,𝔽25)—122no—
184C22×C32C2×C22⋊C411yescharacteristic
185C2×C3×D3—21no—
186C2×C3×D3—21no—
187C2×C3×D3#10312yes—
188C32×C4—21no—
189C32×C4—42no—
190C32×C4C2×SD1611yescharacteristic
191C32×C4C2×Q1611yescharacteristic
192C32×C4#13711yescharacteristic
193C32×C4#13711yescharacteristic
194C3×Dic3—21no—
195C3×Dic3—42no—
196C3×Dic3#10012yes—
197C3×Dic3#10312yes—
198C22×Q8—32no—
199C2×M16—181no—
200C4⋊Q8—32no—
201C4⋊Q8—31no—
202C4⋊Q8—61no—
203C4⋊Q8—61no—
204C4⋊Q8D3211yescharacteristic
205C2×C4⋊C4—61no—
206C2×C4⋊C4—61no—
207C2×C42—31no—
208C4⋊C8—31no—
209C4⋊C8—31no—
210C4⋊C8—91no—
211C4⋊C8—91no—
212C4⋊C8—181no—
213C22⋊C8—181no—
214C4×C8—181no—
215C23×C3—31no—
216C22×D3#21711yescharacteristic
217C3×Q8—42no—
218C3×Q8—42no—
219C3×Q8—82no—
220C3×Q8—122no—
221C3×Q8—124no—
222C2×C3×C4—22no—
223C2×C3×C4—22no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—32no—
230C2×C3×C4—32no—
231C2×C3×C4—31no—
232C2×C3×C4—42no—
233C2×C3×C4—62no—
234C2×C3×C4—61no—
235C2×C3×C4—61no—
236C2×C3×C4—62no—
237C2×C3×C4—124no—
238C2×C3×C4C2×C4×D311yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4C22×Dic311yescharacteristic
242C2×C3×C4C2×#6711yescharacteristic
243C2×C3×C4C2×#6711yescharacteristic
244C2×Dic3—22no—
245C2×Dic3#21711yescharacteristic
246C2×Dic3#21711yescharacteristic
247C2×Dic3#21711yescharacteristic
248C4×D3—21no—
249C4×D3—21no—
250C4×D3—22no—
251C4×D3—44no—
252C4×D3#21512yes—
253C4×D3#21612yes—
254Dic6—44no—
255Dic6—42no—
256C3×C8—121no—
257C3×C8—121no—
258C3⋊C8—41no—
259C3⋊C8—41no—
260C3⋊C8—121no—
261C3⋊C8—121no—
262C3⋊C8—121no—
263C3⋊C8—121no—
264C3⋊C8—241no—
265C3⋊C8—241no—
266C2×C32C2×#10011yescharacteristic
267C2×C32C2×#10311yescharacteristic
268C2×C32#41911yescharacteristic
269C3×D3—22no—
270C2×Q8—32no—
271C2×Q8—62no—
272C2×Q8—124no—
273C2×Q8D3×Dic312yes—
274C22×C4—31no—
275C22×C4—31no—
276C22×C4—31no—
277C22×C4—62no—
278M16—362no—
279C2×C8—61no—
280C2×C8—61no—
281C2×C8—181no—
282C2×C8—181no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—62no—
286C4⋊C4—62no—
287C4⋊C4—61no—
288C4⋊C4—61no—
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×#21711yescharacteristic
299C2×D3—21no—
300C2×D3—21no—
301C2×D3#83512yes—
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—42no—
312C3×C4—42no—
313C3×C4—61no—
314C3×C4—82no—
315C3×C4—122no—
316C3×C4D3×SD1611yescharacteristic
317C3×C4#91511yescharacteristic
318C3×C4D3×Q1611yescharacteristic
319C3×C4#91811yescharacteristic
320C3×C4C2×#21511yescharacteristic
321C3×C4#94211yescharacteristic
322C3×C4#94211yescharacteristic
323C3×C4C2×#21611yescharacteristic
324Dic3—21no—
325Dic3—42no—
326Dic3#83312yes—
327Dic3#83512yes—
328C32#154811yescharacteristic, complemented, Sylow
329C23—31no—
330Q8—42no—
331Q8—122no—
332Q8—124no—
333C2×C4—22no—
334C2×C4—31no—
335C2×C4—31no—
336C2×C4—32no—
337C2×C4—32no—
338C2×C4—31no—
339C2×C4—62no—
340C2×C4—61no—
341C2×C4—61no—
342C2×C4—62no—
343C2×C4—124no—
344C2×C4C2×D3×Dic311yescharacteristic
345C2×C4D3×#6711yescharacteristic
346C2×C4D3×#6711yescharacteristic
347C8—121no—
348C8—121no—
349C8—361no—
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×#83311yescharacteristic
359C2×C3C2×#83511yescharacteristic
360C2×C3#522511yescharacteristic
361D3—22no—
362C22—32no—
363C22—61no—
364C22—61no—
365C22D3×#21711yescharacteristic
366C4—21no—
367C4—32no—
368C4—32no—
369C4—42no—
370C4—61no—
371C4—122no—
372C4D3×#21511yescharacteristic
373C4D3×#21611yescharacteristic
374C4#6394611yescharacteristic
375C4#6394811yescharacteristic
376C3—21no—
377C3#6848311yescharacteristic, complemented
378C3#7177411yescharacteristic, complemented
379C2—62no—
380C2D3×#83311yescharacteristic
381C2D3×#83511yescharacteristic
382C2#1059155711yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenterC4⋊Q8D32
hypocenterC32#1548
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
4. #10589412C2semidirect
5. C3×#4546C2semidirect
6. #10589095C2semidirect
7. #10589095C2semidirect
39. #4546D3semidirect
328. C32#1548semidirect
377. C3#68483semidirect
378. C3#71774semidirect

Maximal subgroups

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

subgroupindex
C3×D3×C4⋊Q82
#105903362
#105902482
#105894122
C3×#45462
#105890952
#717743
#684833