Finite Group Databasebeta

← #11794039

Subgroups — #11794039

Order 1152.

972 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic
2C2×C32×#103C211yesmaximal, characteristic, complemented
3#10592928C211yesmaximal, characteristic, complemented
4C2×#63648C211yesmaximal, characteristic
5C2×#63641C211yesmaximal, characteristic, complemented
6#10592687C211yesmaximal, characteristic
7#10589395C211yesmaximal, characteristic, complemented
8#70280—34nomaximal
9C22×C32×Q8C2211yescharacteristic
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3755—22no—
14C2×#3755—22no—
15C2×#3755—22no—
16C2×#3752—21no—
17C2×#3752—21no—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C22×C3⋊(C3⋊C8)C2211yescharacteristic
21C32×#103—22no—
22#63658—21no—
23#63658—21no—
24#63648—22no—
25#63641—22no—
26C22×#215—34no—
27C2×C3×#103D314yescomplemented
28#5229—34no—
29C2×#821—34no—
30C2×Dic3⋊C8—34no—
31#4988—34no—
32#4529—34no—
33C23×C3⋊D3—21no—
34C2×C32×Q8—21no—
35C2×C32×Q8—21no—
36C2×C32×Q8—21no—
37C2×C32×Q8—21no—
38C2×C32×Q8—21no—
39C2×C32×Q8D412yes—
40C22×C32×C4—21no—
41C22×C32×C4—21no—
42C22×C32×C4C2311yescharacteristic
43C22×C3⋊Dic3—21no—
44C22×C3⋊Dic3D411yescharacteristic
45C22×C3⋊Dic3D411yescharacteristic
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)D412yes—
52C2×C32×C8—21no—
53C2×C32×C8—21no—
54C2×C32×C8—21no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57#3755—28no—
58#3752—42no—
59#3752—42no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4×C3⋊Dic3—21no—
63C4×C3⋊Dic3—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)D412yes—
67#2055—91noSylow
68C22×C3×Q8C2×D314yes—
69C22×D12—34no—
70C22×C3×C8C2×D314yes—
71C2×C3×C4⋊C4C2×D314yes—
72C2×#215—68no—
73C2×#215—68no—
74C2×#215—68no—
75C2×(C2×D3)⋊C4—64no—
76C2×(C2×D3)⋊C4—64no—
77C2×C4⋊Dic3—34no—
78C2×C4×Dic3—34no—
79C22×C3⋊C8—34no—
80C3×#103—28no—
81C3⋊#95—64no—
82C3⋊#95—64no—
83#821—68no—
84Dic3⋊C8—68no—
85C23×C32C2×D411yescharacteristic
86C22×C3⋊D3—22no—
87C22×C3⋊D3—41no—
88C22×C3⋊D3—41no—
89C22×C3⋊D3—41no—
90C22×C3⋊D3—41no—
91C22×C3⋊D3—41no—
92C22×C3⋊D3—41no—
93C32×Q8—22no—
94C32×Q8—22no—
95C32×Q8—41no—
96C32×Q8—41no—
97C2×C32×C4—22no—
98C2×C32×C4—41no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C3⋊Dic3—21no—
110C2×C3⋊Dic3—21no—
111C2×C3⋊Dic3—21no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—41no—
115C2×C3⋊Dic3—41no—
116C2×C3⋊Dic3—41no—
117C2×C3⋊Dic3SD1612yescomplemented
118C4⋊(C3⋊D3)—22no—
119C4⋊(C3⋊D3)—22no—
120C4⋊(C3⋊D3)—41no—
121C4⋊(C3⋊D3)—41no—
122C32×C8—41no—
123C3⋊(C3⋊C8)—22no—
124C22×SD16—91no—
125C2×C4⋊C8—91no—
126C2×#103C3⋊D311yescharacteristic, complemented
127C2×#102—91no—
128#391—91no—
129#390—91no—
130#340—91no—
131C23×D3—64no—
132C2×C3×Q8—24no—
133C2×C3×Q8—24no—
134C2×C3×Q8—24no—
135C2×C3×Q8—24no—
136C2×C3×Q8—24no—
137C2×C3×Q8#6718yes—
138C22×C3×C4—24no—
139C22×C3×C4—24no—
140C22×C3×C4C22×D314yes—
141C22×Dic3—34no—
142C22×Dic3—34no—
143C22×Dic3—64no—
144C2×D12—38no—
145C2×D12—64no—
146C2×D12—64no—
147C2×D12—64no—
148C2×D12—64no—
149C2×D12—64no—
150C2×C3×C8—24no—
151C2×C3×C8—24no—
152C2×C3×C8—24no—
153C3×C4⋊C4—24no—
154C3×C4⋊C4—24no—
155#215—632no—
156(C2×D3)⋊C4—128no—
157(C2×D3)⋊C4—128no—
158C4⋊Dic3—64no—
159C4⋊Dic3—64no—
160C4×Dic3—64no—
161C4×Dic3—64no—
162C2×C3⋊C8—38no—
163C2×C3⋊C8—64no—
164C2×C3⋊C8—64no—
165C22×C32#12111yescharacteristic
166C22×C32#12111yescharacteristic
167C22×C32#12111yescharacteristic
168C22×C32C2×SD1611yescharacteristic
169C22×C32#13511yescharacteristic
170C22×C32AGL(1,ℤ/8)11yescharacteristic
171C22×C32#13711yescharacteristic
172C2×C3⋊D3—42no—
173C2×C3⋊D3—42no—
174C2×C3⋊D3—42no—
175C2×C3⋊D3—81no—
176C2×C3⋊D3—81no—
177C2×C3⋊D3—81no—
178C2×C3⋊D3—81no—
179C32×C4—42no—
180C32×C4—81no—
181C32×C4#12011yescharacteristic
182C32×C4#12311yescharacteristic
183C32×C4#12311yescharacteristic
184C32×C4#12411yescharacteristic
185C3⋊Dic3—22no—
186C3⋊Dic3—41no—
187C3⋊Dic3—81no—
188C22×Q8C2×C3⋊D311yescharacteristic
189C22×D4—91no—
190C2×SD16—182no—
191C2×SD16—182no—
192C2×SD16—182no—
193C22×C8—91no—
194C22×C8C2×C3⋊D311yescharacteristic
195C2×C4⋊C4—91no—
196C2×C4⋊C4C2×C3⋊D311yescharacteristic
197C2×C22⋊C4—181no—
198C2×C22⋊C4—181no—
199C2×C42—91no—
200C4⋊C8—182no—
201#103—22no—
202#102—182no—
203#95—181no—
204#95—181no—
205C23×C3D3×D414yes—
206C22×D3—68no—
207C22×D3—124no—
208C22×D3—124no—
209C22×D3—124no—
210C22×D3—124no—
211C22×D3—124no—
212C22×D3—124no—
213C3×Q8—28no—
214C3×Q8—28no—
215C3×Q8—44no—
216C3×Q8—44no—
217C2×C3×C4—28no—
218C2×C3×C4—44no—
219C2×C3×C4—44no—
220C2×C3×C4—44no—
221C2×C3×C4—44no—
222C2×C3×C4—44no—
223C2×C3×C4#23514yes—
224C2×C3×C4#23514yes—
225C2×C3×C4D3×D414yes—
226C2×C3×C4D3×D414yes—
227C2×C3×C4#23714yes—
228C2×C3×C4C2×#6714yes—
229C2×Dic3—38no—
230C2×Dic3—64no—
231C2×Dic3—64no—
232C2×Dic3—64no—
233C2×Dic3—64no—
234C2×Dic3—64no—
235C2×Dic3—124no—
236C2×Dic3—124no—
237C2×Dic3—124no—
238D12—68no—
239D12—68no—
240D12—124no—
241D12—124no—
242C3×C8—44no—
243C3⋊C8—68no—
244C2×C32#39411yescharacteristic
245C2×C32#46011yescharacteristic
246C2×C32#46111yescharacteristic
247C2×C32#46311yescharacteristic
248C2×C32#46411yescharacteristic
249C2×C32#46511yescharacteristic
250C2×C32#46811yescharacteristic
251C3⋊D3—82no—
252C24—181no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—21no—
258C2×Q8#63812yes—
259C2×D4—92no—
260C2×D4—181no—
261C2×D4—181no—
262C2×D4—181no—
263C2×D4—181no—
264C2×D4—181no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—91no—
268C22×C4—91no—
269C22×C4—181no—
270C22×C4C22×C3⋊D311yescharacteristic
271SD16—188no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—92no—
276C2×C8—181no—
277C2×C8—181no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—181no—
281C4⋊C4—181no—
282C22⋊C4—362no—
283C22⋊C4—362no—
284C42—181no—
285C42—181no—
286C22×C3#88414yes—
287C22×C3#88414yes—
288C22×C3D3×SD1614yes—
289C22×C3#91414yes—
290C22×C3#91814yes—
291C22×C3#91914yes—
292C22×C3#93914yes—
293C2×D3—128no—
294C2×D3—128no—
295C2×D3—128no—
296C2×D3—244no—
297C2×D3—244no—
298C2×D3—244no—
299C2×D3—244no—
300C3×C4—48no—
301C3×C4—84no—
302C3×C4#88314yes—
303C3×C4#88514yes—
304C3×C4#92914yes—
305C3×C4#93714yes—
306Dic3—68no—
307Dic3—124no—
308Dic3—244no—
309C32#205511yescharacteristic, complemented, Sylow
310C23—182no—
311C23—361no—
312C23—361no—
313C23—361no—
314C23—361no—
315C23—361no—
316C23—361no—
317C23D4×C3⋊D311yescharacteristic
318Q8—22no—
319Q8—22no—
320Q8—41no—
321Q8—41no—
322D4—182no—
323D4—182no—
324D4—361no—
325D4—361no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—92no—
333C2×C4—181no—
334C2×C4—181no—
335C2×C4—181no—
336C2×C4—181no—
337C2×C4—181no—
338C2×C4—361no—
339C2×C4—361no—
340C2×C4—361no—
341C2×C4#382811yescharacteristic
342C2×C4#382811yescharacteristic
343C2×C4D4×C3⋊D311yescharacteristic
344C2×C4D4×C3⋊D311yescharacteristic
345C2×C4#383011yescharacteristic
346C2×C4C2×#63811yescharacteristic
347C8—41no—
348C8—182no—
349C2×C3#480714yes—
350C2×C3#481214yes—
351C2×C3#481814yes—
352C2×C3#481914yes—
353C2×C3#495914yes—
354C2×C3#516314yes—
355C2×C3#518514yes—
356D3—248no—
357C22—362no—
358C22—362no—
359C22—362no—
360C22—721no—
361C22—721no—
362C22—721no—
363C22—721no—
364C22#6409311yescharacteristic
365C22#6409311yescharacteristic
366C22SD16×C3⋊D311yescharacteristic
367C22#6412311yescharacteristic
368C22#6412711yescharacteristic
369C22#6412811yescharacteristic
370C22#6414811yescharacteristic
371C4—42no—
372C4—81no—
373C4—182no—
374C4—361no—
375C4—721no—
376C4#6409211yescharacteristic
377C4#6409411yescharacteristic
378C4#6413811yescharacteristic
379C4#6414611yescharacteristic
380C3#7028014yescomplemented
381C2—722no—
382C2#1059250611yescharacteristic
383C2#1059251111yescharacteristic
384C2#1059251711yescharacteristic
385C2#1059251811yescharacteristic
386C2#1059265811yescharacteristic
387C2#1059286211yescharacteristic
388C2#1059288411yescharacteristic
subgroupG/H
centerC23D4×C3⋊D3
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C22×C3⋊D3
FittingC2×C32×#103C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×#103C3⋊D3
hypocenterC32#2055
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×C32×#103C2semidirect
3. #10592928C2semidirect
5. C2×#63641C2semidirect
7. #10589395C2semidirect
27. C2×C3×#103D3semidirect
117. C2×C3⋊Dic3SD16semidirect
126. C2×#103C3⋊D3semidirect
309. C32#2055semidirect
380. C3#70280semidirect

Maximal subgroups

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

subgroupindex
C22×#37552
C2×C32×#1032
#105929282
C2×#636482
C2×#636412
#105926872
#105893952
#702803