Finite Group Databasebeta

← #11775063

Subgroups — #11775063

Order 1152.

627 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5477C211yesmaximal, characteristic
2#10592624C211yesmaximal, characteristic, complemented
3C3×C4×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#10589149C214yesmaximal, complemented
5#71811—31nomaximal
6#69469—31nomaximal
7C2×C3×#235—21no—
8C2×C32×C42C2211yescharacteristic
9C3×#930—21no—
10C3×#930C2212yes—
11C2×C3×C4⋊Dic3—21no—
12C2×C3×C4×Dic3—21no—
13C3×#875—21no—
14C3×#874C411yescharacteristic, complemented
15C3×C4×D12—21no—
16C3×C4×D12C412yescomplemented
17C3×#869C411yescharacteristic, complemented
18#63657C2212yes—
19C4⋊(C3⋊(C3⋊C8))—21no—
20C4×C3⋊(C3⋊C8)—21no—
21C3×C3⋊#95C2212yes—
22C3×#532—31no—
23#5477D311yescharacteristic
24C3×C4×C4⋊C4—31no—
25C4×C4⋊Dic3D311yescharacteristic, complemented
26#4925—31no—
27#4925—31no—
28#4925—61no—
29#4537—34no—
30#4451—34no—
31C22×C32×C4D411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4C2311yescharacteristic
34C2×C3×#67—22no—
35C22×C3×Dic3—22no—
36C3×#235—42no—
37C3×#235—42no—
38C2×C3×D12—21no—
39C2×C3×D12—21no—
40C2×C3×D12C2×C412yes—
41C2×C3×C4×D3—22no—
42C2×C3×Dic6—21no—
43C32×C42C2×C411yescharacteristic
44C32×C42C2×C411yescharacteristic
45C32×C42D411yescharacteristic
46C32×C42D411yescharacteristic
47C2×C3⋊(C3⋊C8)—22no—
48C3×(C2×D3)⋊C4—22no—
49C3×(C2×D3)⋊C4—22no—
50C3×C4⋊Dic3—24no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3C2×C412yes—
53C3×C4×Dic3—42no—
54#1502—91noSylow
55C2×C3×#41—61no—
56C2×#235—21no—
57C3×C4⋊Q8—31no—
58C3×#127—31no—
59C3×#124—61no—
60C3×#121—32no—
61C3×#121—61no—
62C3×C4×D4—32no—
63C3×C4×D4—61no—
64C2×C3×C4⋊C4—61no—
65C2×C3×C42—21no—
66C2×C3×C42—61no—
67C2×C3×C42C2×D311yescharacteristic
68C2×C3×C42C2×D311yescharacteristic
69#930—21no—
70#930C2×D312yes—
71C2×C4⋊Dic3—21no—
72C2×C4×Dic3—21no—
73#875—21no—
74#874Dic311yescharacteristic, complemented
75C4×D12—21no—
76C4×D12Dic312yescomplemented
77#869Dic311yescharacteristic, complemented
78C3×#95—32no—
79C3⋊#95C2×D312yes—
80#830—32no—
81#830—32no—
82#830—62no—
83C4⋊(C3⋊C8)—62no—
84C4⋊(C3⋊C8)—61no—
85C4⋊(C3⋊C8)—61no—
86C4×C3⋊C8—62no—
87C4×C3⋊C8—61no—
88C4×C3⋊C8—61no—
89C23×C32C2×D411yescharacteristic
90C22×C3×D3—22no—
91C2×C32×C4—22no—
92C2×C32×C4—41no—
93C2×C32×C4C22⋊C411yescharacteristic
94C2×C32×C4C22⋊C411yescharacteristic
95C2×C32×C4C22⋊C411yescharacteristic
96C2×C32×C4C22⋊C411yescharacteristic
97C2×C32×C4D812yes—
98C2×C32×C4SD1612yes—
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D411yescharacteristic
101C3×#67—42no—
102C3×#67—42no—
103C2×C3×Dic3—24no—
104C2×C3×Dic3—22no—
105C2×C3×Dic3—42no—
106C2×C3×Dic3—42no—
107C3×D12—42no—
108C3×D12—42no—
109C3×D12—42no—
110C3×C4×D3—44no—
111C3×Dic6—42no—
112C3⋊(C3⋊C8)—42no—
113#532—31no—
114#431—91no—
115C4×C4⋊C4—31no—
116#327—94no—
117C3×#41—122no—
118C3×#41—122no—
119C2×C3×Q8—61no—
120C2×C3×D4—32no—
121C2×C3×D4—62no—
122C2×C3×D4—61no—
123C2×C3×D4—61no—
124C22×C3×C4—21no—
125C22×C3×C4—21no—
126C22×C3×C4—21no—
127C22×C3×C4—62no—
128C22×C3×C4—62no—
129C22×C3×C4#6711yescharacteristic
130C22×C3×C4#6711yescharacteristic
131C22×C3×C4#6711yescharacteristic
132C22×C3×C4#6711yescharacteristic
133C22×C3×C4C22×D311yescharacteristic
134C22×C3×C4C22×D311yescharacteristic
135C2×#67—22no—
136C22×Dic3—22no—
137#235—42no—
138#235—42no—
139C2×D12—21no—
140C2×D12—21no—
141C2×D12C2×Dic312yes—
142C2×C4×D3—22no—
143C2×Dic6—21no—
144C3×C4⋊C4—32no—
145C3×C4⋊C4—64no—
146C3×C4⋊C4—61no—
147C3×C22⋊C4—62no—
148C3×C22⋊C4—62no—
149C3×C42—21no—
150C3×C42—21no—
151C3×C42—21no—
152C3×C42—21no—
153C3×C42—122no—
154C3×C42C4×D311yescharacteristic
155C3×C42C4×D311yescharacteristic
156C3×C42D1211yescharacteristic
157C3×C42D1211yescharacteristic
158C3×C42C2×Dic311yescharacteristic
159C3×C42C2×Dic311yescharacteristic
160C3×C42#6711yescharacteristic
161C3×C42#6711yescharacteristic
162(C2×D3)⋊C4—22no—
163(C2×D3)⋊C4—22no—
164C4⋊Dic3—24no—
165C4⋊Dic3—21no—
166C4⋊Dic3C2×Dic312yes—
167C4×Dic3—42no—
168C2×C3⋊C8—64no—
169C2×C3⋊C8—62no—
170C2×C3⋊C8—62no—
171C22×C32—21no—
172C22×C32—21no—
173C22×C32C2×C22⋊C411yescharacteristic
174C22×C32C2×D811yescharacteristic
175C22×C32C2×SD1611yescharacteristic
176C2×C3×D3—42no—
177C2×C3×D3—42no—
178C2×C3×D3—42no—
179C32×C4—21no—
180C32×C4—21no—
181C32×C4—21no—
182C32×C4#10212yes—
183C32×C4#10212yes—
184C32×C4#10412yes—
185C3×Dic3—44no—
186C3×Dic3—42no—
187C2×#41—61no—
188C4⋊Q8—31no—
189#127—31no—
190#124—61no—
191#121—32no—
192#121—61no—
193C4×D4—32no—
194C4×D4—61no—
195C2×C4⋊C4—61no—
196C2×C42—61no—
197C2×C42D3211yescharacteristic
198C4⋊C8—181no—
199C22⋊C8—92no—
200C4×C8—181no—
201#95—32no—
202C23×C3—21no—
203C23×C3—62no—
204C23×C3C2×#6711yescharacteristic
205C23×C3C2×#6711yescharacteristic
206C22×D3—22no—
207C3×Q8—122no—
208C3×D4—122no—
209C3×D4—122no—
210C3×D4—122no—
211C3×D4—122no—
212C3×D4—122no—
213C2×C3×C4—22no—
214C2×C3×C4—22no—
215C2×C3×C4—22no—
216C2×C3×C4—22no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—42no—
224C2×C3×C4—41no—
225C2×C3×C4—41no—
226C2×C3×C4—42no—
227C2×C3×C4—64no—
228C2×C3×C4—62no—
229C2×C3×C4—122no—
230C2×C3×C4—122no—
231C2×C3×C4—124no—
232C2×C3×C4(C2×D3)⋊C411yescharacteristic
233C2×C3×C4(C2×D3)⋊C411yescharacteristic
234C2×C3×C4(C2×D3)⋊C411yescharacteristic
235C2×C3×C4(C2×D3)⋊C411yescharacteristic
236C2×C3×C4#21312yes—
237C2×C3×C4#21312yes—
238C2×C3×C4#21412yes—
239C2×C3×C4#21512yes—
240C2×C3×C4#21711yescharacteristic
241C2×C3×C4#21711yescharacteristic
242C2×C3×C4#21711yescharacteristic
243C2×C3×C4#21711yescharacteristic
244C2×C3×C4C2×C4×D311yescharacteristic
245C2×C3×C4C2×D1211yescharacteristic
246C2×C3×C4C22×Dic311yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248#67—42no—
249#67—42no—
250C2×Dic3—24no—
251C2×Dic3—22no—
252C2×Dic3—42no—
253C2×Dic3—42no—
254D12—42no—
255D12—42no—
256D12—42no—
257C4×D3—44no—
258Dic6—42no—
259C3⋊C8—124no—
260C3⋊C8—122no—
261C3⋊C8—122no—
262C2×C32—21no—
263C2×C32—21no—
264C2×C32#41011yescharacteristic
265C2×C32C2×#10211yescharacteristic
266C2×C32C2×#10411yescharacteristic
267C3×D3—82no—
268#41—122no—
269#41—122no—
270C2×Q8—61no—
271C2×D4—32no—
272C2×D4—62no—
273C2×D4—61no—
274C2×D4—61no—
275C22×C4—62no—
276C22×C4—62no—
277C22×C4#62511yescharacteristic
278C22×C4#62511yescharacteristic
279C22×C4C2×D3211yescharacteristic
280C2×C8—182no—
281C4⋊C4—32no—
282C4⋊C4—64no—
283C4⋊C4—61no—
284C22⋊C4—62no—
285C22⋊C4—62no—
286C42—122no—
287C42D3×Dic311yescharacteristic
288C42D3×Dic311yescharacteristic
289C42#62611yescharacteristic
290C42#62611yescharacteristic
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—122no—
301C22×C3—122no—
302C22×C3—122no—
303C22×C3C2×(C2×D3)⋊C411yescharacteristic
304C22×C3C2×#21311yescharacteristic
305C22×C3C2×#21311yescharacteristic
306C22×C3C2×#21411yescharacteristic
307C22×C3C2×#21511yescharacteristic
308C22×C3C2×#21711yescharacteristic
309C2×D3—42no—
310C2×D3—42no—
311C2×D3—42no—
312C3×C4—22no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—22no—
320C3×C4—22no—
321C3×C4—22no—
322C3×C4—41no—
323C3×C4—41no—
324C3×C4—124no—
325C3×C4—122no—
326C3×C4#80512yes—
327C3×C4#80912yes—
328C3×C4#80912yes—
329C3×C4#83212yes—
330C3×C4#83212yes—
331C3×C4#83712yes—
332Dic3—44no—
333Dic3—42no—
334C32#150211yescharacteristic, complemented, Sylow
335C23—62no—
336C23C2×#62511yescharacteristic
337Q8—122no—
338D4—122no—
339D4—122no—
340D4—122no—
341D4—122no—
342D4—122no—
343C2×C4—22no—
344C2×C4—41no—
345C2×C4—64no—
346C2×C4—62no—
347C2×C4—122no—
348C2×C4—122no—
349C2×C4—124no—
350C2×C4#371312yes—
351C2×C4#371512yes—
352C2×C4(C2×D3)⋊Dic311yescharacteristic
353C2×C4(C2×D3)⋊Dic311yescharacteristic
354C2×C4(C2×D3)⋊Dic311yescharacteristic
355C2×C4(C2×D3)⋊Dic311yescharacteristic
356C2×C4C2×D3×Dic311yescharacteristic
357C2×C4C2×#62611yescharacteristic
358C8—362no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—41no—
367C2×C3—41no—
368C2×C3—242no—
369C2×C3C2×#80511yescharacteristic
370C2×C3C2×#80911yescharacteristic
371C2×C3#500611yescharacteristic
372C2×C3C2×#83211yescharacteristic
373C2×C3C2×#83711yescharacteristic
374C2×C3#524011yescharacteristic
375D3—82no—
376C22—21no—
377C22—21no—
378C22—122no—
379C22—122no—
380C22—122no—
381C22C2×#371311yescharacteristic
382C22C2×#371511yescharacteristic
383C22C2×(C2×D3)⋊Dic311yescharacteristic
384C4—21no—
385C4—21no—
386C4—21no—
387C4—124no—
388C4—122no—
389C4#6356212yes—
390C4#6356212yes—
391C4#6356912yes—
392C3—21no—
393C3#6946911yescharacteristic, complemented
394C3#7181111yescharacteristic, complemented
395C2—21no—
396C2—21no—
397C2—242no—
398C2C2×#6356211yescharacteristic
399C2C2×#6356911yescharacteristic
400C2#1059123111yescharacteristic
subgroupG/H
centerC2×C4(C2×D3)⋊Dic3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5477C2
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1502
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #10592624C2semidirect
3. C3×C4×C4⋊Dic3C2semidirect
4. #10589149C2semidirect
14. C3×#874C4semidirect
16. C3×C4×D12C4semidirect
17. C3×#869C4semidirect
25. C4×C4⋊Dic3D3semidirect
74. #874Dic3semidirect
76. C4×D12Dic3semidirect
77. #869Dic3semidirect
334. C32#1502semidirect
393. C3#69469semidirect
394. C3#71811semidirect

Maximal subgroups

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

subgroupindex
C3×#54772
#105926242
C3×C4×C4⋊Dic32
#105891492
#718113
#694693