Finite Group Databasebeta

← #11792591

Subgroups — #11792591

Order 1152.

1170 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3746C211yesmaximal, characteristic, complemented
2C22×#3744C211yesmaximal, characteristic
3C2×#64084C211yesmaximal, characteristic
4C2×#63648C211yesmaximal, characteristic
5C2×#63643C211yesmaximal, characteristic, complemented
6#10592628C211yesmaximal, characteristic, complemented
7C32×#336C211yesmaximal, characteristic, complemented
8#68677—34nomaximal
9C22×C4⋊(C3⋊D3)C2211yescharacteristic
10C22×#634C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13C22×C32×C8C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×#3752—22no—
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3746—22no—
18C2×#3746—22no—
19C2×#3746—22no—
20C2×#3744—22no—
21C2×#3744—22no—
22C2×#3744—22no—
23#64084—22no—
24#64084—22no—
25#63658—22no—
26#63648—22no—
27#63643—22no—
28C22×Dic12—34no—
29C22×#204—34no—
30C2×#875—34no—
31C2×#821—34no—
32C2×#816—34no—
33#4929—34no—
34C3×#336D314yescomplemented
35C23×C3⋊D3—21no—
36C22×C32×C4D412yes—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)D412yes—
47C2×#634—21no—
48C2×#634—21no—
49C2×#634—21no—
50C2×#634—21no—
51C2×#634—21no—
52C2×#634—21no—
53C2×#634—21no—
54C2×#634—21no—
55C2×#634—21no—
56C2×#634—21no—
57C2×#634D412yes—
58C2×#634D412yes—
59C2×C32×C8—21no—
60C2×C32×C8—21no—
61C2×C32×C8—21no—
62C2×C32×C8—21no—
63C2×C32×C8D412yes—
64C2×C32×C8D412yes—
65C32×C42—21no—
66C32×C42—21no—
67#3752—28no—
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)—21no—
70#3746—28no—
71#3744—28no—
72#2015—91noSylow
73C22×D12—34no—
74C22×Dic6—34no—
75C22×Dic6—34no—
76C22×C3×C8C2×D314yes—
77C22×C3×C8C2×D314yes—
78C2×C3×C42C2×D314yes—
79C2×(C2×D3)⋊C4—68no—
80C2×C4⋊Dic3—34no—
81C2×Dic12—68no—
82C2×Dic12—68no—
83C2×Dic12—68no—
84C2×#204—68no—
85C2×#204—68no—
86C2×#204—68no—
87#875—68no—
88#875—68no—
89C3⋊#95—68no—
90#821—68no—
91#816—68no—
92C23×C32C2×D411yescharacteristic
93C22×C3⋊D3—22no—
94C22×C3⋊D3—41no—
95C22×C3⋊D3—41no—
96C22×C3⋊D3—42no—
97C22×C3⋊D3—42no—
98C2×C32×C4—22no—
99C2×C32×C4—22no—
100C2×C32×C4—22no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C3⋊Dic3—22no—
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—41no—
111C2×C3⋊Dic3—41no—
112C2×C3⋊Dic3—41no—
113C2×C3⋊Dic3—41no—
114C2×C3⋊Dic3—42no—
115C4⋊(C3⋊D3)—22no—
116C4⋊(C3⋊D3)—22no—
117C4⋊(C3⋊D3)—41no—
118C4⋊(C3⋊D3)—41no—
119#634—22no—
120#634—22no—
121#634—22no—
122#634—22no—
123#634—41no—
124#634—41no—
125#634—41no—
126#634—41no—
127C32×C8—22no—
128C32×C8—22no—
129C22×Q16—91no—
130C22×SD16—91no—
131C2×#124—91no—
132C2×#103—91no—
133C2×#102—91no—
134#391—91no—
135#336C3⋊D311yescharacteristic, complemented
136C23×D3—64no—
137C22×C3×C4D1218yes—
138C22×C3×C4C22×D314yes—
139C22×Dic3—64no—
140C22×Dic3—64no—
141C22×Dic3—64no—
142C2×D12—38no—
143C2×D12—64no—
144C2×D12—64no—
145C2×D12—64no—
146C2×D12—64no—
147C2×D12—64no—
148C2×Dic6—38no—
149C2×Dic6—38no—
150C2×Dic6—64no—
151C2×Dic6—64no—
152C2×Dic6—64no—
153C2×Dic6—64no—
154C2×Dic6—64no—
155C2×Dic6—64no—
156C2×Dic6—64no—
157C2×Dic6—64no—
158C2×Dic6—64no—
159C2×Dic6—64no—
160C2×C3×C8—24no—
161C2×C3×C8—24no—
162C2×C3×C8—24no—
163C2×C3×C8—24no—
164C2×C3×C8D1218yes—
165C2×C3×C8D1218yes—
166C3×C42—24no—
167C3×C42—24no—
168(C2×D3)⋊C4—632no—
169C4⋊Dic3—64no—
170C4⋊Dic3—64no—
171Dic12—632no—
172#204—632no—
173C22×C32#12011yescharacteristic
174C22×C32#12111yescharacteristic
175C22×C32#12711yescharacteristic
176C22×C32#13512yes—
177C22×C32#13712yes—
178C2×C3⋊D3—42no—
179C2×C3⋊D3—44no—
180C2×C3⋊D3—82no—
181C2×C3⋊D3—81no—
182C2×C3⋊D3—81no—
183C32×C4—42no—
184C32×C4#12011yescharacteristic
185C32×C4#12011yescharacteristic
186C32×C4#12111yescharacteristic
187C32×C4#12111yescharacteristic
188C3⋊Dic3—42no—
189C3⋊Dic3—42no—
190C3⋊Dic3—81no—
191C22×Q8—91no—
192C22×Q8—91no—
193C22×D4—91no—
194C2×Q16—182no—
195C2×Q16—182no—
196C2×Q16—182no—
197C2×SD16—182no—
198C2×SD16—182no—
199C2×SD16—182no—
200C22×C8C2×C3⋊D311yescharacteristic
201C22×C8C2×C3⋊D311yescharacteristic
202#124—182no—
203#124—182no—
204C2×C4⋊C4—91no—
205C2×C22⋊C4—182no—
206C2×C42C2×C3⋊D311yescharacteristic
207#103—182no—
208#102—182no—
209#95—182no—
210C23×C3C2×D1214yes—
211C22×D3—68no—
212C22×D3—124no—
213C22×D3—124no—
214C22×D3—128no—
215C22×D3—128no—
216C2×C3×C4—28no—
217C2×C3×C4—28no—
218C2×C3×C4—28no—
219C2×C3×C4C2×D1214yes—
220C2×C3×C4C2×D1214yes—
221C2×C3×C4D3×D414yes—
222C2×C3×C4D3×D414yes—
223C2×C3×C4D3×D414yes—
224C2×C3×C4#23914yes—
225C2×Dic3—68no—
226C2×Dic3—68no—
227C2×Dic3—124no—
228C2×Dic3—124no—
229C2×Dic3—124no—
230C2×Dic3—124no—
231C2×Dic3—124no—
232C2×Dic3—128no—
233D12—68no—
234D12—68no—
235D12—124no—
236D12—124no—
237Dic6—68no—
238Dic6—68no—
239Dic6—68no—
240Dic6—68no—
241Dic6—124no—
242Dic6—124no—
243Dic6—124no—
244Dic6—124no—
245C3×C8—28no—
246C3×C8—28no—
247C2×C32#39211yescharacteristic
248C2×C32#45212yes—
249C2×C32#46412yes—
250C2×C32#49511yescharacteristic
251C2×C32#49711yescharacteristic
252C3⋊D3—82no—
253C24—181no—
254C2×Q8—92no—
255C2×Q8—92no—
256C2×Q8—181no—
257C2×Q8—181no—
258C2×Q8—181no—
259C2×Q8—181no—
260C2×Q8—181no—
261C2×Q8—181no—
262C2×Q8—181no—
263C2×Q8—181no—
264C2×Q8—181no—
265C2×Q8—181no—
266C2×D4—92no—
267C2×D4—181no—
268C2×D4—181no—
269C2×D4—181no—
270C2×D4—181no—
271C2×D4—181no—
272C22×C4—181no—
273C22×C4—181no—
274C22×C4—181no—
275C22×C4C4⋊(C3⋊D3)12yes—
276C22×C4C22×C3⋊D311yescharacteristic
277Q16—188no—
278SD16—188no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8C4⋊(C3⋊D3)12yes—
284C2×C8C4⋊(C3⋊D3)12yes—
285C4⋊C4—181no—
286C4⋊C4—181no—
287C22⋊C4—188no—
288C42—21no—
289C42—21no—
290C22×C3#87414yes—
291C22×C3#88214yes—
292C22×C3#89514yes—
293C22×C3#90418yes—
294C22×C3#90918yes—
295C2×D3—128no—
296C2×D3—1216no—
297C2×D3—244no—
298C2×D3—244no—
299C2×D3—248no—
300C3×C4—48no—
301C3×C4#88214yes—
302C3×C4#88214yes—
303C3×C4#89514yes—
304C3×C4#89514yes—
305Dic3—128no—
306Dic3—128no—
307Dic3—244no—
308C32#201511yescharacteristic, complemented, Sylow
309C23—182no—
310C23—361no—
311C23—361no—
312C23—362no—
313C23—362no—
314C23C2×C4⋊(C3⋊D3)11yescharacteristic
315Q8—182no—
316Q8—182no—
317Q8—182no—
318Q8—182no—
319Q8—361no—
320Q8—361no—
321Q8—361no—
322Q8—361no—
323D4—182no—
324D4—182no—
325D4—361no—
326D4—361no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—182no—
331C2×C4—182no—
332C2×C4—361no—
333C2×C4—361no—
334C2×C4—361no—
335C2×C4—361no—
336C2×C4—361no—
337C2×C4—362no—
338C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
339C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
340C2×C4D4×C3⋊D311yescharacteristic
341C2×C4D4×C3⋊D311yescharacteristic
342C2×C4D4×C3⋊D311yescharacteristic
343C2×C4#383211yescharacteristic
344C8—22no—
345C8—22no—
346C2×C3#467114yes—
347C2×C3#469614yes—
348C2×C3#471514yes—
349C2×C3#473318yes—
350C2×C3#484518yes—
351D3—248no—
352C22—362no—
353C22—364no—
354C22—722no—
355C22—721no—
356C22—721no—
357C22#6408311yescharacteristic
358C22#6409111yescharacteristic
359C22#6410411yescharacteristic
360C22#6411312yes—
361C22#6411812yes—
362C4—42no—
363C4—362no—
364C4—362no—
365C4—721no—
366C4#6409111yescharacteristic
367C4#6409111yescharacteristic
368C4#6410411yescharacteristic
369C4#6410411yescharacteristic
370C3#6867714yescomplemented
371C2—722no—
372C2#1059237011yescharacteristic
373C2#1059239511yescharacteristic
374C2#1059241411yescharacteristic
375C2#1059243212yes—
376C2#1059254412yes—
subgroupG/H
centerC23C2×C4⋊(C3⋊D3)
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC32×#336C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#336C3⋊D3
hypocenterC32#2015
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
1. C22×#3746C2semidirect
5. C2×#63643C2semidirect
6. #10592628C2semidirect
7. C32×#336C2semidirect
34. C3×#336D3semidirect
135. #336C3⋊D3semidirect
308. C32#2015semidirect
370. C3#68677semidirect

Maximal subgroups

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

subgroupindex
C22×#37462
C22×#37442
C2×#640842
C2×#636482
C2×#636432
#105926282
C32×#3362
#686773