Finite Group Databasebeta

← #11792573

Subgroups — #11792573

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×C32×Q16C211yesmaximal, characteristic, complemented
2C2×#64156C211yesmaximal, characteristic
3C22×#3755C211yesmaximal, characteristic
4#10592928C211yesmaximal, characteristic, complemented
5C2×#63662C211yesmaximal, characteristic, complemented
6C2×#63648C211yesmaximal, characteristic
7#10589416C211yesmaximal, characteristic, complemented
8#72072—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C32×Q8C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C32×Q16—22no—
13C2×C32×Q16—22no—
14C2×C32×Q16—22no—
15C22×C32×C8C2211yescharacteristic
16#64156—22no—
17#64156—22no—
18C2×#3755—22no—
19C2×#3755—22no—
20C2×#3755—22no—
21C2×#3752—22no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25#63662—22no—
26#63658—22no—
27#63648—22no—
28C22×C3×Q16D314yescomplemented
29C2×#947—34no—
30C22×#215—34no—
31#5229—34no—
32C2×#835—34no—
33C2×#821—34no—
34#4550—34no—
35C23×C3⋊D3—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8—21no—
39C2×C32×Q8—21no—
40C2×C32×Q8—21no—
41C2×C32×Q8—21no—
42C2×C32×Q8—21no—
43C2×C32×Q8—21no—
44C2×C32×Q8—21no—
45C2×C32×Q8—21no—
46C2×C32×Q8D412yes—
47C2×C32×Q8D412yes—
48C22×C32×C4—21no—
49C22×C32×C4—21no—
50C22×C32×C4C2311yescharacteristic
51C22×C3⋊Dic3—21no—
52C22×C3⋊Dic3D412yes—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)D412yes—
59C32×Q16—28no—
60C2×C32×C8—21no—
61C2×C32×C8—21no—
62C2×C32×C8D412yes—
63#3755—28no—
64#3752—28no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)D412yes—
72#2015—91noSylow
73C22×C3×Q8C2×D314yes—
74C22×C3×Q8C2×D314yes—
75C22×D12—34no—
76C2×C3×Q16—28no—
77C2×C3×Q16—28no—
78C2×C3×Q16—28no—
79C22×C3×C8C2×D314yes—
80#947—68no—
81#947—68no—
82C2×#215—68no—
83C2×#215—68no—
84C2×#215—68no—
85C2×(C2×D3)⋊C4—68no—
86C2×C4⋊Dic3—34no—
87C2×C4×Dic3—34no—
88C22×C3⋊C8—34no—
89#835—68no—
90C3⋊#95—68no—
91#821—68no—
92C23×C32C2×D411yescharacteristic
93C22×C3⋊D3—22no—
94C22×C3⋊D3—41no—
95C22×C3⋊D3—41no—
96C22×C3⋊D3—42no—
97C22×C3⋊D3—42no—
98C32×Q8—22no—
99C32×Q8—22no—
100C32×Q8—22no—
101C32×Q8—22no—
102C32×Q8—41no—
103C32×Q8—41no—
104C32×Q8—41no—
105C32×Q8—41no—
106C2×C32×C4—22no—
107C2×C32×C4—22no—
108C2×C32×C4—41no—
109C2×C32×C4—41no—
110C2×C32×C4—41no—
111C2×C32×C4—41no—
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—22no—
120C2×C3⋊Dic3—22no—
121C2×C3⋊Dic3—41no—
122C2×C3⋊Dic3—42no—
123C4⋊(C3⋊D3)—22no—
124C4⋊(C3⋊D3)—22no—
125C4⋊(C3⋊D3)—41no—
126C4⋊(C3⋊D3)—41no—
127C32×C8—22no—
128C3⋊(C3⋊C8)—22no—
129C22×Q16C3⋊D311yescharacteristic, complemented
130C22×SD16—91no—
131C2×#124—91no—
132C2×#103—91no—
133C2×#102—91no—
134#391—91no—
135#336—91no—
136C23×D3—64no—
137C2×C3×Q8—24no—
138C2×C3×Q8—24no—
139C2×C3×Q8—24no—
140C2×C3×Q8—24no—
141C2×C3×Q8—24no—
142C2×C3×Q8—24no—
143C2×C3×Q8—24no—
144C2×C3×Q8—24no—
145C2×C3×Q8—24no—
146C2×C3×Q8—24no—
147C2×C3×Q8#6718yes—
148C2×C3×Q8#6718yes—
149C22×C3×C4—24no—
150C22×C3×C4—24no—
151C22×C3×C4C22×D314yes—
152C22×Dic3—38no—
153C22×Dic3—64no—
154C2×D12—38no—
155C2×D12—64no—
156C2×D12—64no—
157C2×D12—64no—
158C2×D12—64no—
159C2×D12—64no—
160C3×Q16—232no—
161C2×C3×C8—24no—
162C2×C3×C8—24no—
163C2×C3×C8#6718yes—
164#215—632no—
165(C2×D3)⋊C4—632no—
166C4⋊Dic3—64no—
167C4⋊Dic3—64no—
168C4×Dic3—64no—
169C4×Dic3—64no—
170C2×C3⋊C8—38no—
171C2×C3⋊C8—64no—
172C2×C3⋊C8—64no—
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—42no—
185C32×C4#12011yescharacteristic
186C32×C4#12011yescharacteristic
187C32×C4#12111yescharacteristic
188C32×C4#12111yescharacteristic
189C3⋊Dic3—42no—
190C3⋊Dic3—81no—
191C22×Q8C2×C3⋊D311yescharacteristic
192C22×Q8C2×C3⋊D311yescharacteristic
193C22×D4—91no—
194C2×Q16—22no—
195C2×Q16—22no—
196C2×Q16—22no—
197C2×SD16—182no—
198C2×SD16—182no—
199C2×SD16—182no—
200C22×C8—91no—
201C22×C8C2×C3⋊D311yescharacteristic
202#124—182no—
203#124—182no—
204C2×C4⋊C4—91no—
205C2×C22⋊C4—182no—
206C2×C42—91no—
207#103—182no—
208#102—182no—
209#95—182no—
210C23×C3D3×D414yes—
211C22×D3—68no—
212C22×D3—128no—
213C22×D3—128no—
214C22×D3—124no—
215C22×D3—124no—
216C3×Q8—28no—
217C3×Q8—28no—
218C3×Q8—28no—
219C3×Q8—28no—
220C3×Q8—44no—
221C3×Q8—44no—
222C3×Q8—44no—
223C3×Q8—44no—
224C2×C3×C4—28no—
225C2×C3×C4—28no—
226C2×C3×C4—44no—
227C2×C3×C4—44no—
228C2×C3×C4—44no—
229C2×C3×C4—44no—
230C2×C3×C4D3×D414yes—
231C2×C3×C4D3×D414yes—
232C2×C3×C4#23714yes—
233C2×C3×C4C2×#6714yes—
234C2×C3×C4C2×#6714yes—
235C2×C3×C4C2×#6714yes—
236C2×Dic3—68no—
237C2×Dic3—68no—
238C2×Dic3—68no—
239C2×Dic3—128no—
240C2×Dic3—124no—
241D12—68no—
242D12—68no—
243D12—124no—
244D12—124no—
245C3×C8—28no—
246C3⋊C8—68no—
247C2×C32#39211yescharacteristic
248C2×C32#45212yes—
249C2×C32#46412yes—
250C2×C32#49511yescharacteristic
251C2×C32#49711yescharacteristic
252C3⋊D3—82no—
253C24—181no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—21no—
264C2×Q8#63812yes—
265C2×Q8#63812yes—
266C2×D4—92no—
267C2×D4—181no—
268C2×D4—181no—
269C2×D4—181no—
270C2×D4—181no—
271C2×D4—181no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—92no—
275C22×C4—181no—
276C22×C4C22×C3⋊D311yescharacteristic
277Q16—28no—
278SD16—188no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—92no—
282C2×C8—181no—
283C2×C8—181no—
284C2×C8#63812yes—
285C4⋊C4—181no—
286C4⋊C4—181no—
287C22⋊C4—188no—
288C42—181no—
289C42—181no—
290C22×C3#91818yes—
291C22×C3#91918yes—
292C22×C3#93714yes—
293C22×C3#93914yes—
294C22×C3#94014yes—
295C2×D3—1216no—
296C2×D3—128no—
297C2×D3—248no—
298C2×D3—244no—
299C2×D3—244no—
300C3×C4—48no—
301C3×C4—48no—
302C3×C4#93714yes—
303C3×C4#93814yes—
304C3×C4#93914yes—
305C3×C4#95314yes—
306Dic3—128no—
307Dic3—244no—
308C32#201511yescharacteristic, complemented, Sylow
309C23—182no—
310C23—362no—
311C23—362no—
312C23—361no—
313C23—361no—
314C23D4×C3⋊D311yescharacteristic
315Q8—22no—
316Q8—22no—
317Q8—22no—
318Q8—22no—
319Q8—41no—
320Q8—41no—
321Q8—41no—
322Q8—41no—
323D4—182no—
324D4—182no—
325D4—361no—
326D4—361no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—362no—
337C2×C4—361no—
338C2×C4D4×C3⋊D311yescharacteristic
339C2×C4D4×C3⋊D311yescharacteristic
340C2×C4#383011yescharacteristic
341C2×C4C2×#63811yescharacteristic
342C2×C4C2×#63811yescharacteristic
343C2×C4C2×#63811yescharacteristic
344C8—22no—
345C8—182no—
346C2×C3#518518yes—
347C2×C3#518718yes—
348C2×C3#519014yes—
349C2×C3#519114yes—
350C2×C3#522314yes—
351D3—248no—
352C22—364no—
353C22—362no—
354C22—722no—
355C22—721no—
356C22—721no—
357C22#6412712yes—
358C22#6412812yes—
359C22#6414611yescharacteristic
360C22#6414811yescharacteristic
361C22#6414911yescharacteristic
362C4—42no—
363C4—42no—
364C4—362no—
365C4—721no—
366C4#6414611yescharacteristic
367C4#6414711yescharacteristic
368C4#6414811yescharacteristic
369C4#6416211yescharacteristic
370C3#7207214yescomplemented
371C2—722no—
372C2#1059288412yes—
373C2#1059288612yes—
374C2#1059288911yescharacteristic
375C2#1059289011yescharacteristic
376C2#1059292211yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC22×C32×Q16C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×Q16C3⋊D3
hypocenterC32#2015
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
1. C22×C32×Q16C2semidirect
4. #10592928C2semidirect
5. C2×#63662C2semidirect
7. #10589416C2semidirect
28. C22×C3×Q16D3semidirect
129. C22×Q16C3⋊D3semidirect
308. C32#2015semidirect
370. C3#72072semidirect

Maximal subgroups

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

subgroupindex
C22×C32×Q162
C2×#641562
C22×#37552
#105929282
C2×#636622
C2×#636482
#105894162
#720723