Finite Group Databasebeta

← #11791407

Subgroups — #11791407

Order 1152.

769 conjugacy classes of subgroups.

The subgroup lattice has 419 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5477C211yesmaximal, characteristic
2C4×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
3C3×C4×#208C211yesmaximal, characteristic, complemented
4C2×#63568C214yesmaximal, complemented
5#71818—31nomaximal
6#69867—31nomaximal
7C2×C3×#235C2212yes—
8C2×C32×C42C2211yescharacteristic
9C2×C4⋊(C3⋊Dic3)—21no—
10C2×C4×C3⋊Dic3C2212yes—
11C3×#930—21no—
12C3×#930—21no—
13C2×C3×#208C2212yes—
14C3×#875C412yescomplemented
15C3×#874C411yescharacteristic, complemented
16C3×C4×D12—21no—
17C3×C4×D12—21no—
18C3×#869C411yescharacteristic, complemented
19#63658—21no—
20C3×#803—21no—
21C3×C4×C3⋊C8—21no—
22#63568—28no—
23C3×#532—31no—
24#5477D311yescharacteristic
25C3×C4×M16—31no—
26C2×#837—34no—
27C2×#825—34no—
28C4×C4⋊Dic3—31no—
29C4×C4⋊Dic3—31no—
30C4×C4⋊Dic3—61no—
31C4×#208D311yescharacteristic, complemented
32C22×C32×C4D411yescharacteristic
33C22×C32×C4D411yescharacteristic
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3—22no—
36C2×C3×#67—22no—
37C3×#235—24no—
38C3×#235—24no—
39C2×C3×D12—21no—
40C2×C3×D12—21no—
41C2×C3×D12C2×C412yes—
42C2×C3×C4×D3—22no—
43C2×C3×Dic6C2×C412yes—
44C32×C42C2×C411yescharacteristic
45C32×C42C2×C411yescharacteristic
46C32×C42D411yescharacteristic
47C32×C42D411yescharacteristic
48C4⋊(C3⋊Dic3)—24no—
49C4×C3⋊Dic3—24no—
50C3×(C2×D3)⋊C4—22no—
51C3×(C2×D3)⋊C4—22no—
52C3×C4⋊Dic3—21no—
53C3×C4⋊Dic3—21no—
54C3×#208—22no—
55C3×#208D414yescomplemented
56C2×C3×C3⋊C8—22no—
57#1980—91noSylow
58C2×C3×#41—32no—
59C2×#235C2×D312yes—
60C2×C3×M16—32no—
61C3×C4⋊Q8—31no—
62C3×#127—31no—
63C3×#124—32no—
64C3×#121—61no—
65C3×#121—61no—
66C3×C4×D4—61no—
67C3×C4×D4—61no—
68C2×C3×C42—21no—
69C2×C3×C42C2×D311yescharacteristic
70C2×C3×C42C2×D311yescharacteristic
71#930—21no—
72#930—21no—
73C2×C4⋊Dic3—62no—
74C2×C4⋊Dic3—61no—
75C2×C4⋊Dic3—61no—
76C2×C4×Dic3—32no—
77C2×C4×Dic3—32no—
78C2×C4×Dic3—62no—
79C2×#208C2×D312yes—
80#875Dic312yescomplemented
81#874Dic311yescharacteristic, complemented
82C4×D12—21no—
83C4×D12—21no—
84#869Dic311yescharacteristic, complemented
85C3×#97—61no—
86C3×C4×C8—61no—
87#837—68no—
88C3⋊#95—62no—
89C3⋊#95—61no—
90C3⋊#95—61no—
91#825—68no—
92#803—21no—
93C4×C3⋊C8—21no—
94C23×C32C2×D411yescharacteristic
95C22×C3×D3—22no—
96C2×C32×C4—22no—
97C2×C32×C4—41no—
98C2×C32×C4C22⋊C411yescharacteristic
99C2×C32×C4C22⋊C411yescharacteristic
100C2×C32×C4C22⋊C411yescharacteristic
101C2×C32×C4C22⋊C411yescharacteristic
102C2×C32×C4C22×C411yescharacteristic
103C2×C32×C4C2×D412yes—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4112yes—
106C2×C3⋊Dic3—24no—
107C2×C3⋊Dic3—42no—
108C2×C3⋊Dic3—42no—
109C3×#67—42no—
110C3×#67—42no—
111C2×C3×Dic3—22no—
112C3×D12—24no—
113C3×D12—42no—
114C3×D12—42no—
115C3×C4×D3—44no—
116C3×Dic6—24no—
117C3×C3⋊C8—24no—
118#532—31no—
119C2×#104—94no—
120C4×M16—31no—
121C4×C4⋊C4—91no—
122C3×#41—64no—
123C3×#41—64no—
124C2×C3×Q8—32no—
125C2×C3×D4—32no—
126C2×C3×D4—62no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—62no—
133C22×C3×C4D1211yescharacteristic
134C22×C3×C4D1211yescharacteristic
135C22×C3×C4#6711yescharacteristic
136C22×C3×C4#6711yescharacteristic
137C22×C3×C4C22×D311yescharacteristic
138C22×C3×C4C22×D311yescharacteristic
139C2×#67—22no—
140C22×Dic3—64no—
141C22×Dic3—62no—
142C22×Dic3—62no—
143#235—24no—
144#235—24no—
145C2×D12—21no—
146C2×D12—21no—
147C2×D12C2×Dic312yes—
148C2×C4×D3—22no—
149C2×Dic6C2×Dic312yes—
150C3×M16—34no—
151C3×M16—62no—
152C2×C3×C8—62no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C22⋊C4—62no—
156C3×C22⋊C4—62no—
157C3×C42—21no—
158C3×C42—21no—
159C3×C42—21no—
160C3×C42—21no—
161C3×C42C4×D311yescharacteristic
162C3×C42C4×D311yescharacteristic
163C3×C42C2×Dic311yescharacteristic
164C3×C42C2×Dic311yescharacteristic
165C3×C42#6711yescharacteristic
166C3×C42#6711yescharacteristic
167C3×C42#6711yescharacteristic
168C3×C42#6711yescharacteristic
169(C2×D3)⋊C4—22no—
170(C2×D3)⋊C4—22no—
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—68no—
174C4⋊Dic3—64no—
175C4⋊Dic3—64no—
176C4×Dic3—64no—
177C4×Dic3—64no—
178C4×Dic3—124no—
179#208—22no—
180#208D1214yescomplemented
181C2×C3⋊C8—22no—
182C22×C32—21no—
183C22×C32—21no—
184C22×C32C2×C22⋊C411yescharacteristic
185C22×C32#12411yescharacteristic
186C22×C32#12711yescharacteristic
187C2×C3×D3—42no—
188C2×C3×D3—42no—
189C2×C3×D3—42no—
190C32×C4—21no—
191C32×C4—21no—
192C32×C4—21no—
193C32×C4#10412yescomplemented
194C32×C4C4×D412yes—
195C32×C4#12112yes—
196C3⋊Dic3—44no—
197C3×Dic3—42no—
198C2×#41—32no—
199C2×M16—32no—
200C4⋊Q8—31no—
201#127—31no—
202#124—32no—
203#121—61no—
204#121—61no—
205C4×D4—61no—
206C4×D4—61no—
207C2×C4⋊C4—181no—
208C2×C42—92no—
209C2×C42D3211yescharacteristic
210#104—188no—
211#97—61no—
212C4×C8—61no—
213#95—181no—
214C23×C3—21no—
215C23×C3—62no—
216C23×C3C2×D1211yescharacteristic
217C23×C3C2×#6711yescharacteristic
218C22×D3—22no—
219C3×Q8—64no—
220C3×D4—64no—
221C3×D4—122no—
222C3×D4—122no—
223C3×D4—122no—
224C3×D4—122no—
225C2×C3×C4—24no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—22no—
233C2×C3×C4—22no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—42no—
239C2×C3×C4—62no—
240C2×C3×C4—124no—
241C2×C3×C4(C2×D3)⋊C411yescharacteristic
242C2×C3×C4(C2×D3)⋊C411yescharacteristic
243C2×C3×C4(C2×D3)⋊C411yescharacteristic
244C2×C3×C4(C2×D3)⋊C411yescharacteristic
245C2×C3×C4#21711yescharacteristic
246C2×C3×C4#21711yescharacteristic
247C2×C3×C4#21711yescharacteristic
248C2×C3×C4#21711yescharacteristic
249C2×C3×C4C2×C4×D311yescharacteristic
250C2×C3×C4C2×D1212yes—
251C2×C3×C4#23512yes—
252C2×C3×C4D3×D412yes—
253C2×C3×C4#23712yes—
254C2×C3×C4C22×Dic311yescharacteristic
255C2×C3×C4C2×#6711yescharacteristic
256C2×C3×C4C2×#6711yescharacteristic
257#67—42no—
258#67—42no—
259C2×Dic3—22no—
260C2×Dic3—68no—
261C2×Dic3—64no—
262C2×Dic3—64no—
263C2×Dic3—124no—
264C2×Dic3—124no—
265C2×Dic3—122no—
266C2×Dic3—122no—
267C2×Dic3—122no—
268C2×Dic3—122no—
269D12—24no—
270D12—42no—
271D12—42no—
272C4×D3—44no—
273Dic6—24no—
274C3×C8—64no—
275C3⋊C8—24no—
276C2×C32—21no—
277C2×C32—21no—
278C2×C32#39011yescharacteristic
279C2×C32C2×#10411yescharacteristic
280C2×C32#42111yescharacteristic
281C3×D3—82no—
282#41—64no—
283#41—64no—
284C2×Q8—32no—
285C2×D4—32no—
286C2×D4—62no—
287C2×D4—61no—
288C2×D4—61no—
289C22×C4—62no—
290C22×C4—182no—
291C22×C4#62611yescharacteristic
292C22×C4#62611yescharacteristic
293C22×C4C2×D3211yescharacteristic
294M16—34no—
295M16—62no—
296C2×C8—62no—
297C4⋊C4—61no—
298C4⋊C4—61no—
299C4⋊C4—184no—
300C22⋊C4—62no—
301C22⋊C4—62no—
302C42—184no—
303C42D3×Dic311yescharacteristic
304C42D3×Dic311yescharacteristic
305C42#62511yescharacteristic
306C42#62511yescharacteristic
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—21no—
310C22×C3—21no—
311C22×C3—21no—
312C22×C3—21no—
313C22×C3—21no—
314C22×C3—21no—
315C22×C3—21no—
316C22×C3—122no—
317C22×C3—122no—
318C22×C3—122no—
319C22×C3#87411yescharacteristic
320C22×C3#87511yescharacteristic
321C22×C3C2×(C2×D3)⋊C411yescharacteristic
322C22×C3#93611yescharacteristic
323C22×C3#94011yescharacteristic
324C22×C3C2×#21711yescharacteristic
325C2×D3—42no—
326C2×D3—42no—
327C2×D3—42no—
328C3×C4—22no—
329C3×C4—21no—
330C3×C4—21no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—22no—
336C3×C4—22no—
337C3×C4—22no—
338C3×C4—41no—
339C3×C4—41no—
340C3×C4—122no—
341C3×C4#82512yescomplemented
342C3×C4#83712yescomplemented
343C3×C4C4×D1212yes—
344C3×C4#93012yes—
345C3×C4D4×Dic312yes—
346C3×C4#93812yes—
347Dic3—42no—
348Dic3—128no—
349Dic3—124no—
350Dic3—124no—
351C32#198011yescharacteristic, complemented, Sylow
352C23—62no—
353C23C2×#62611yescharacteristic
354Q8—64no—
355D4—64no—
356D4—122no—
357D4—122no—
358D4—122no—
359D4—122no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—62no—
363C2×C4—124no—
364C2×C4—184no—
365C2×C4—362no—
366C2×C4—362no—
367C2×C4(C2×D3)⋊Dic311yescharacteristic
368C2×C4(C2×D3)⋊Dic311yescharacteristic
369C2×C4(C2×D3)⋊Dic311yescharacteristic
370C2×C4(C2×D3)⋊Dic311yescharacteristic
371C2×C4#379512yes—
372C2×C4D3×D1212yes—
373C2×C4C2×D3×Dic311yescharacteristic
374C2×C4C2×#62511yescharacteristic
375C8—64no—
376C2×C3—22no—
377C2×C3—22no—
378C2×C3—21no—
379C2×C3—21no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—21no—
383C2×C3—21no—
384C2×C3—21no—
385C2×C3—242no—
386C2×C3#493911yescharacteristic
387C2×C3C2×#82511yescharacteristic
388C2×C3#513911yescharacteristic
389C2×C3#522111yescharacteristic
390C2×C3C2×#83711yescharacteristic
391C2×C3#523611yescharacteristic
392D3—82no—
393C22—21no—
394C22—21no—
395C22—122no—
396C22—122no—
397C22—122no—
398C22#6386011yescharacteristic
399C22#6391111yescharacteristic
400C22C2×(C2×D3)⋊Dic311yescharacteristic
401C4—21no—
402C4—21no—
403C4—21no—
404C4—122no—
405C4—364no—
406C4#6356812yescomplemented
407C4Dic3×D1212yes—
408C4#6390812yes—
409C3—21no—
410C3#6986711yescharacteristic, complemented
411C3#7181811yescharacteristic, complemented
412C2—21no—
413C2—21no—
414C2—242no—
415C2C2×#6356811yescharacteristic
416C2#1059111011yescharacteristic
417C2#1059131811yescharacteristic
subgroupG/H
centerC2×C4C2×#625
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5477C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1980
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊(C3⋊Dic3)C2semidirect
3. C3×C4×#208C2semidirect
4. C2×#63568C2semidirect
14. C3×#875C4semidirect
15. C3×#874C4semidirect
18. C3×#869C4semidirect
31. C4×#208D3semidirect
55. C3×#208D4semidirect
80. #875Dic3semidirect
81. #874Dic3semidirect
84. #869Dic3semidirect
180. #208D12semidirect
193. C32×C4#104semidirect
341. C3×C4#825semidirect
342. C3×C4#837semidirect
351. C32#1980semidirect
406. C4#63568semidirect
410. C3#69867semidirect
411. C3#71818semidirect

Maximal subgroups

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

subgroupindex
C3×#54772
C4×C4⋊(C3⋊Dic3)2
C3×C4×#2082
C2×#635682
#718183
#698673