Finite Group Databasebeta

← #11784049

Subgroups — #11784049

Order 1152.

745 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×Dic6C211yesmaximal, characteristic
2C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
3C2×C3×#803C211yesmaximal, characteristic
4C2×#63566C212yesmaximal
5#10589164C212yesmaximal
6#71631—31nomaximal
7#69813—31nomaximal
8C22×C3×Dic6C2211yescharacteristic
9C2×C32×C42C2211yescharacteristic
10C2×C4⋊(C3⋊Dic3)C2212yes—
11C2×C4×C3⋊Dic3—21no—
12C2×C3×C4⋊Dic3C2211yescharacteristic
13C2×C3×Dic3⋊C4—21no—
14C2×C3×C4×Dic3—21no—
15C22×C3×C3⋊C8C2212yes—
16C3×C4×Dic6—22no—
17C3×C4×Dic6C414yescomplemented
18#63658—21no—
19C3×#803—22no—
20#63566C418yescomplemented
21C2×C3×C4×Q8—31no—
22C2×C4×Dic6D311yescharacteristic
23C2×C3×#97—31no—
24C2×#835—32no—
25C2×#816—32no—
26C4×C4⋊Dic3—31no—
27C4×C4⋊Dic3—31no—
28C4×C4⋊Dic3—61no—
29C2×#803D311yescharacteristic
30#4551—32no—
31#4529—32no—
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—22no—
36C22×C3×Dic3—21no—
37C22×C3×Dic3—21no—
38C2×C3×Dic6—21no—
39C2×C3×Dic6—22no—
40C2×C3×Dic6C2×C414yes—
41C2×C3×Dic6C2×C412yes—
42C32×C42C2×C412yes—
43C32×C42D412yes—
44C4⋊(C3⋊Dic3)—22no—
45C4⋊(C3⋊Dic3)C2×C414yes—
46C4×C3⋊Dic3—42no—
47C3×C4⋊Dic3—21no—
48C3×C4⋊Dic3C2×C412yes—
49C3×Dic3⋊C4—24no—
50C3×C4×Dic3—24no—
51C2×C3×C3⋊C8—22no—
52C2×C3×C3⋊C8—22no—
53C2×C3×C3⋊C8C2×C414yes—
54#1763—91noSylow
55C22×C3×Q8—31no—
56C22×Dic6C2×D311yescharacteristic
57C22×C3×C8—32no—
58C3×C4×Q8—34no—
59C3×C4×Q8—62no—
60C2×C3×C4⋊C4—31no—
61C2×C3×C4⋊C4—61no—
62C2×C3×C42—21no—
63C2×C3×C42—61no—
64C2×C3×C42C2×D311yescharacteristic
65C2×C3×C42C2×D311yescharacteristic
66C2×C4⋊Dic3—32no—
67C2×C4⋊Dic3—32no—
68C2×C4⋊Dic3—62no—
69C2×C4⋊Dic3C2×D311yescharacteristic
70C2×Dic3⋊C4—21no—
71C2×C4×Dic3—21no—
72C2×C4×Dic3—62no—
73C2×C4×Dic3—61no—
74C2×C4×Dic3—61no—
75C22×C3⋊C8C2×D312yes—
76C4×Dic6—22no—
77C4×Dic6Dic314yescomplemented
78C3×#97—62no—
79#835—38no—
80C3⋊#95—62no—
81C3⋊#95—61no—
82C3⋊#95—61no—
83#816—38no—
84#803—22no—
85C23×C32C2×D411yescharacteristic
86C2×C32×C4—21no—
87C2×C32×C4—21no—
88C2×C32×C4—22no—
89C2×C32×C4C22⋊C412yes—
90C2×C32×C4C22⋊C412yes—
91C2×C32×C4C22×C412yes—
92C2×C32×C4C22×C411yescharacteristic
93C2×C32×C4C2×D411yescharacteristic
94C2×C32×C4#4112yes—
95C2×C3⋊Dic3—24no—
96C2×C3⋊Dic3—42no—
97C2×C3⋊Dic3—42no—
98C2×C3×Dic3—22no—
99C2×C3×Dic3—24no—
100C2×C3×Dic3—22no—
101C2×C3×Dic3—41no—
102C2×C3×Dic3—41no—
103C3×Dic6—22no—
104C3×Dic6—24no—
105C3×Dic6C4214yescomplemented
106C3×C3⋊C8—24no—
107C2×C4×Q8—31no—
108C2×#103—92no—
109C2×#97—31no—
110C4×C4⋊C4—91no—
111#340—92no—
112C2×C3×Q8—34no—
113C2×C3×Q8—32no—
114C2×C3×Q8—62no—
115C2×C3×Q8—61no—
116C22×C3×C4—21no—
117C22×C3×C4—21no—
118C22×C3×C4—21no—
119C22×C3×C4—61no—
120C22×C3×C4—61no—
121C22×C3×C4D1211yescharacteristic
122C22×C3×C4D1211yescharacteristic
123C22×C3×C4#6711yescharacteristic
124C22×C3×C4#6711yescharacteristic
125C22×C3×C4C22×D311yescharacteristic
126C22×C3×C4C22×D311yescharacteristic
127C22×Dic3—21no—
128C22×Dic3—21no—
129C22×Dic3—64no—
130C22×Dic3—62no—
131C22×Dic3—62no—
132C2×Dic6—22no—
133C2×Dic6—21no—
134C2×Dic6C4×D314yes—
135C2×Dic6C2×Dic312yes—
136C2×C3×C8—34no—
137C2×C3×C8—62no—
138C2×C3×C8—62no—
139C3×C4⋊C4—32no—
140C3×C4⋊C4—64no—
141C3×C4⋊C4—61no—
142C3×C42—22no—
143C3×C42—22no—
144C3×C42—64no—
145C3×C42C4×D312yes—
146C3×C42C2×Dic312yes—
147C3×C42#6712yes—
148C3×C42#6712yes—
149C4⋊Dic3—21no—
150C4⋊Dic3—34no—
151C4⋊Dic3—34no—
152C4⋊Dic3—64no—
153C4⋊Dic3—64no—
154C4⋊Dic3—62no—
155C4⋊Dic3—62no—
156C4⋊Dic3C2×Dic312yes—
157Dic3⋊C4—24no—
158C4×Dic3—24no—
159C4×Dic3—124no—
160C4×Dic3—122no—
161C4×Dic3—122no—
162C2×C3⋊C8—22no—
163C2×C3⋊C8—22no—
164C2×C3⋊C8C4×D314yes—
165C22×C32C2×C22⋊C411yescharacteristic
166C22×C32C4×D412yes—
167C22×C32AGL(1,ℤ/8)11yescharacteristic
168C22×C32#13712yes—
169C22×C32#13711yescharacteristic
170C32×C4—22no—
171C32×C4—22no—
172C32×C4C2×C4211yescharacteristic
173C32×C4#11711yescharacteristic
174C32×C4C4×D412yes—
175C3⋊Dic3—44no—
176C3×Dic3—24no—
177C3×Dic3—42no—
178C22×Q8—31no—
179C22×C8—32no—
180C4×Q8—34no—
181C4×Q8—62no—
182C2×C4⋊C4—31no—
183C2×C4⋊C4—61no—
184C2×C4⋊C4—92no—
185C2×C42—61no—
186C2×C42—181no—
187C2×C42D3211yescharacteristic
188#103—98no—
189#97—62no—
190#95—181no—
191C23×C3—21no—
192C23×C3C2×D1211yescharacteristic
193C23×C3C2×#6711yescharacteristic
194C3×Q8—34no—
195C3×Q8—62no—
196C3×Q8—64no—
197C2×C3×C4—22no—
198C2×C3×C4—22no—
199C2×C3×C4—21no—
200C2×C3×C4—21no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—22no—
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—42no—
212C2×C3×C4—64no—
213C2×C3×C4—62no—
214C2×C3×C4—62no—
215C2×C3×C4—121no—
216C2×C3×C4—121no—
217C2×C3×C4(C2×D3)⋊C412yes—
218C2×C3×C4(C2×D3)⋊C412yes—
219C2×C3×C4#21712yes—
220C2×C3×C4#21712yes—
221C2×C3×C4C2×C4×D312yes—
222C2×C3×C4C2×C4×D312yes—
223C2×C3×C4C2×C4×D311yescharacteristic
224C2×C3×C4#23512yes—
225C2×C3×C4#23512yes—
226C2×C3×C4C22×Dic311yescharacteristic
227C2×C3×C4C2×#6711yescharacteristic
228C2×C3×C4C2×#6711yescharacteristic
229C2×Dic3—24no—
230C2×Dic3—22no—
231C2×Dic3—22no—
232C2×Dic3—41no—
233C2×Dic3—41no—
234C2×Dic3—68no—
235C2×Dic3—64no—
236C2×Dic3—64no—
237C2×Dic3—124no—
238C2×Dic3—124no—
239C2×Dic3—122no—
240C2×Dic3—122no—
241C2×Dic3—122no—
242C2×Dic3—122no—
243Dic6—22no—
244Dic6—24no—
245Dic6C4×Dic314yescomplemented
246C3×C8—64no—
247C3⋊C8—24no—
248C2×C32C4×C22⋊C411yescharacteristic
249C2×C32#41711yescharacteristic
250C2×C32#41911yescharacteristic
251C2×C32#44012yes—
252C2×C32#44112yes—
253C2×Q8—34no—
254C2×Q8—32no—
255C2×Q8—62no—
256C2×Q8—61no—
257C22×C4—61no—
258C22×C4—61no—
259C22×C4—182no—
260C22×C4#62611yescharacteristic
261C22×C4#62611yescharacteristic
262C22×C4C2×D3211yescharacteristic
263C2×C8—34no—
264C2×C8—62no—
265C2×C8—62no—
266C4⋊C4—32no—
267C4⋊C4—64no—
268C4⋊C4—61no—
269C4⋊C4—94no—
270C4⋊C4—182no—
271C42—64no—
272C42—362no—
273C42D3×Dic312yes—
274C42#62512yes—
275C22×C3—21no—
276C22×C3—21no—
277C22×C3—22no—
278C22×C3—22no—
279C22×C3—21no—
280C22×C3C4×D1212yes—
281C22×C3#90811yescharacteristic
282C22×C3#90911yescharacteristic
283C22×C3#90912yes—
284C22×C3C2×(C2×D3)⋊C411yescharacteristic
285C22×C3C4×#6712yes—
286C22×C3#94212yes—
287C22×C3#94911yescharacteristic
288C22×C3#95111yescharacteristic
289C22×C3C2×#21711yescharacteristic
290C3×C4—24no—
291C3×C4—22no—
292C3×C4—22no—
293C3×C4—22no—
294C3×C4—22no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—22no—
298C3×C4—42no—
299C3×C4—64no—
300C3×C4—122no—
301C3×C4C42×D311yescharacteristic
302C3×C4#87211yescharacteristic
303C3×C4C2×C4×Dic311yescharacteristic
304C3×C4#92611yescharacteristic
305C3×C4C4×#6712yes—
306C3×C4C4×#6712yes—
307Dic3—24no—
308Dic3—42no—
309Dic3—128no—
310Dic3—124no—
311Dic3—124no—
312C32#176311yescharacteristic, complemented, Sylow
313C23C2×#62611yescharacteristic
314Q8—34no—
315Q8—62no—
316Q8—64no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—64no—
321C2×C4—62no—
322C2×C4—62no—
323C2×C4—121no—
324C2×C4—121no—
325C2×C4—184no—
326C2×C4—362no—
327C2×C4—362no—
328C2×C4(C2×D3)⋊Dic312yes—
329C2×C4(C2×D3)⋊Dic312yes—
330C2×C4#379812yes—
331C2×C4C4×D3212yes—
332C2×C4C2×D3×Dic311yescharacteristic
333C2×C4C2×#62511yescharacteristic
334C8—64no—
335C2×C3—21no—
336C2×C3—21no—
337C2×C3—21no—
338C2×C3—22no—
339C2×C3—22no—
340C2×C3#471012yes—
341C2×C3#471612yes—
342C2×C3C4×(C2×D3)⋊C411yescharacteristic
343C2×C3#502612yes—
344C2×C3#503012yes—
345C2×C3#512011yescharacteristic
346C2×C3#513311yescharacteristic
347C2×C3C4×#21711yescharacteristic
348C2×C3#522511yescharacteristic
349C2×C3#523211yescharacteristic
350C22#6382511yescharacteristic
351C22#6383111yescharacteristic
352C22#6383312yes—
353C22C4×#62612yes—
354C22C2×(C2×D3)⋊Dic311yescharacteristic
355C4—22no—
356C4—22no—
357C4—64no—
358C4—122no—
359C4—364no—
360C4#6385511yescharacteristic
361C4C4×D3×Dic311yescharacteristic
362C4C4×#62512yes—
363C3—21no—
364C3#6981311yescharacteristic, complemented
365C3#7163111yescharacteristic, complemented
366C2#1059036212yes—
367C2#1059038312yes—
368C2#1059108811yescharacteristic
369C2#1059110011yescharacteristic
370C2C4×(C2×D3)⋊Dic311yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socle, prime radicalC23×C32C2×D4
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1763
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
17. C3×C4×Dic6C4semidirect
20. #63566C4semidirect
77. C4×Dic6Dic3semidirect
105. C3×Dic6C42semidirect
245. Dic6C4×Dic3semidirect
312. C32#1763semidirect
364. C3#69813semidirect
365. C3#71631semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×Dic62
C4×C4⋊(C3⋊Dic3)2
C2×C3×#8032
C2×#635662
#105891642
#716313
#698133