Finite Group Databasebeta

← #11878881

Subgroups — #11878881

Order 1152.

1152 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
1C2×#64153C211yesmaximal, characteristic
2#10596093C211yesmaximal, characteristic
3C32×#451C211yesmaximal, characteristic
4#10592927C211yesmaximal, characteristic
5#10592882C212yesmaximal, complemented
6#10592881C212yesmaximal, complemented
7#10592749C211yesmaximal, characteristic
8#10592494C212yesmaximal, complemented
9#10592491C212yesmaximal, complemented
10#10592438C211yesmaximal, characteristic
11#10592417C211yesmaximal, characteristic
12#80178—34nomaximal
13C22×C32×Q8C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C2×C32×Q16C2212yes—
16C32×C22⋊Q8C2211yescharacteristic
17Q8×C3⋊Dic3C2211yescharacteristic
18#64153—21no—
19#64153—21no—
20#64153C2212yes—
21#64153C2211yescharacteristic
22#64153C2212yes—
23C2×#3756C2212yes—
24C2×#3756C2212yes—
25#64133C2211yescharacteristic
26C2×#3750—21no—
27C2×#3750—21no—
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×#3746C2212yes—
30#64098—21no—
31#64097C2211yescharacteristic
32#64096—21no—
33#64096C2211yescharacteristic
34#64087—21no—
35#64086—21no—
36C32×#103C2212yes—
37C32×C22⋊C8C2211yescharacteristic
38#63662C2212yes—
39#63657C2211yescharacteristic
40#63643C2212yes—
41#63641C2212yes—
42C8×C3⋊Dic3C2212yes—
43#63637C2212yes—
44C2×#944—34no—
45#5622—34no—
46C3×#451D314yes—
47#5228—34no—
48#5183—38no—
49#5182—38no—
50#5050—34no—
51#4795—38no—
52#4792—38no—
53#4739—34no—
54#4718—34no—
55C2×C32×Q8—21no—
56C2×C32×Q8—42no—
57C2×C32×Q8C2312yes—
58C2×C32×Q8C2311yescharacteristic
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3—21no—
62C22×C3⋊Dic3D411yescharacteristic
63C22×C3⋊Dic3D411yescharacteristic
64C2×#634—21no—
65C2×#634—21no—
66C2×#634—42no—
67C2×#634C2311yescharacteristic
68C2×#634C2312yes—
69C32×Q16—42no—
70C2×C32×C8C2312yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2311yescharacteristic
73C32×C22⋊C4—21no—
74#3757—21no—
75#3756—42no—
76#3756—42no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3750—21no—
80#3750—21no—
81#3750—21no—
82#3750—21no—
83#3750—21no—
84#3750—22no—
85#3750—22no—
86#3750—22no—
87#3750—22no—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3—21no—
90C4×C3⋊Dic3D411yescharacteristic
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3C2311yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊(C3⋊C8)C2312yes—
95#3746—42no—
96#3209—91noSylow
97C22×C3×Q8C2×D314yes—
98C22×Dic6—34no—
99C2×C3×Q16C2×D318yes—
100C3×C22⋊Q8C2×D314yes—
101Q8×Dic3—34no—
102#944—38no—
103#944—34no—
104#944—38no—
105#944—64no—
106#944—64no—
107C2×#216—38no—
108C2×#216—38no—
109#924—34no—
110C2×Dic3⋊C4—64no—
111C2×Dic3⋊C4—64no—
112C2×C4×Dic3—34no—
113C2×Dic12—38no—
114#889—64no—
115#888—34no—
116#887—34no—
117#887—64no—
118#878—64no—
119#877—64no—
120C3×#103C2×D318yes—
121C3×C22⋊C8C2×D314yes—
122#835—38no—
123#830—34no—
124#816—38no—
125Dic3⋊C8—38no—
126C8×Dic3—38no—
127#810—38no—
128C23×C32C2×D411yescharacteristic
129C32×Q8—22no—
130C32×Q8—22no—
131C32×Q8—22no—
132C32×Q8—42no—
133C2×C32×C4—22no—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4—22no—
137C2×C32×C4—42no—
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2411yescharacteristic
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3—21no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—42no—
145C2×C3⋊Dic3Q1614yescomplemented
146C2×C3⋊Dic3C2×D411yescharacteristic
147C2×C3⋊Dic3C2×D411yescharacteristic
148C2×C3⋊Dic3C2×D411yescharacteristic
149C2×C3⋊Dic3C2×D411yescharacteristic
150#634—22no—
151#634—22no—
152#634—22no—
153#634—42no—
154#634—42no—
155C32×C8—22no—
156C3⋊(C3⋊C8)—22no—
157#533—91no—
158C2×C4⋊Q8—91no—
159#494—92no—
160#487—92no—
161#462—92no—
162#462—92no—
163#451—91no—
164#451—91no—
165#451—91no—
166#451C3⋊D311yescharacteristic
167#431—91no—
168C2×C3×Q8—24no—
169C2×C3×Q8—48no—
170C2×C3×Q8C22×D318yes—
171C2×C3×Q8C22×D314yes—
172C22×C3×C4—24no—
173C22×C3×C4C22×D314yes—
174C22×Dic3—34no—
175C22×Dic3—34no—
176C22×Dic3—64no—
177C2×Dic6—38no—
178C2×Dic6—34no—
179C2×Dic6—64no—
180C2×Dic6—64no—
181C2×Dic6—128no—
182C3×Q16—48no—
183C2×C3×C8C22×D318yes—
184C3×C4⋊C4—24no—
185C3×C4⋊C4C22×D314yes—
186C3×C22⋊C4—24no—
187#217—64no—
188#216—128no—
189#216—128no—
190C4⋊Dic3—34no—
191C4⋊Dic3—64no—
192Dic3⋊C4—64no—
193Dic3⋊C4—64no—
194Dic3⋊C4—64no—
195Dic3⋊C4—64no—
196Dic3⋊C4—68no—
197Dic3⋊C4—68no—
198Dic3⋊C4—68no—
199Dic3⋊C4—68no—
200Dic3⋊C4—64no—
201C4×Dic3—34no—
202C4×Dic3—34no—
203C4×Dic3—34no—
204C4×Dic3—34no—
205C4×Dic3—64no—
206C4×Dic3—64no—
207C2×C3⋊C8—38no—
208Dic12—128no—
209C22×C32—21no—
210C22×C32—21no—
211C22×C32C2×Q1612yes—
212C22×C32C22×D411yescharacteristic
213C32×C4—21no—
214C32×C4—42no—
215C32×C4—41no—
216C32×C4—41no—
217C32×C4H(5,𝔽2)12yes—
218C3⋊Dic3—21no—
219C3⋊Dic3—42no—
220C3⋊Dic3—41no—
221C3⋊Dic3—41no—
222C3⋊Dic3C2×Q1612yes—
223C3⋊Dic3C2×Q1612yes—
224C3⋊Dic3#13712yes—
225C22×Q8—91no—
226C22×Q8C2×C3⋊D311yescharacteristic
227C2×Q16—92no—
228C2×Q16—92no—
229C2×Q16—92no—
230C2×Q16C2×C3⋊D312yes—
231C4⋊Q8—91no—
232C4⋊Q8—92no—
233C4⋊Q8—92no—
234C4⋊Q8—91no—
235C4⋊Q8—181no—
236C4⋊Q8—181no—
237#125—181no—
238C22⋊Q8—91no—
239C22⋊Q8—181no—
240C22⋊Q8C2×C3⋊D311yescharacteristic
241C4×Q8—91no—
242C4×Q8—91no—
243C4×Q8—181no—
244#117—181no—
245C2×C4⋊C4—181no—
246C2×C4⋊C4—181no—
247C2×C42—91no—
248C4⋊C8—92no—
249#103—92no—
250#103—92no—
251#103—92no—
252#103C2×C3⋊D312yes—
253C22⋊C8—91no—
254C22⋊C8C2×C3⋊D311yescharacteristic
255C4×C8—92no—
256C23×C3D3×D414yes—
257C3×Q8—28no—
258C3×Q8—28no—
259C3×Q8—28no—
260C3×Q8—48no—
261C2×C3×C4—28no—
262C2×C3×C4—24no—
263C2×C3×C4—24no—
264C2×C3×C4—28no—
265C2×C3×C4—48no—
266C2×C3×C4D3×D414yes—
267C2×C3×C4C23×D314yes—
268C2×Dic3—316no—
269C2×Dic3—34no—
270C2×Dic3—34no—
271C2×Dic3—34no—
272C2×Dic3—34no—
273C2×Dic3—68no—
274C2×Dic3—64no—
275C2×Dic3—64no—
276C2×Dic3—68no—
277C2×Dic3—128no—
278Dic6—68no—
279Dic6—68no—
280Dic6—68no—
281Dic6—128no—
282Dic6—128no—
283C3×C8—28no—
284C3⋊C8—68no—
285C2×C32—22no—
286C2×C32#53511yescharacteristic
287C2×C32C22×Q1611yescharacteristic
288C2×C32C2×#13711yescharacteristic
289C2×Q8—21no—
290C2×Q8—42no—
291C2×Q8—92no—
292C2×Q8—91no—
293C2×Q8—181no—
294C2×Q8—181no—
295C2×Q8—362no—
296C2×Q8C22×C3⋊D312yes—
297C2×Q8C22×C3⋊D311yescharacteristic
298C22×C4—21no—
299C22×C4—91no—
300C22×C4—91no—
301C22×C4—181no—
302C22×C4C22×C3⋊D311yescharacteristic
303Q16—42no—
304Q16—362no—
305Q16—362no—
306Q16—362no—
307C2×C8—92no—
308C2×C8C22×C3⋊D312yes—
309C4⋊C4—21no—
310C4⋊C4—91no—
311C4⋊C4—182no—
312C4⋊C4—182no—
313C4⋊C4—182no—
314C4⋊C4—182no—
315C4⋊C4—181no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4C22×C3⋊D311yescharacteristic
322C22⋊C4—21no—
323C22⋊C4—181no—
324C42—91no—
325C42—91no—
326C42—91no—
327C42—91no—
328C42—181no—
329C42—181no—
330C22×C3—24no—
331C22×C3—24no—
332C22×C3D3×Q1618yes—
333C22×C3C2×D3×D414yes—
334C3×C4—24no—
335C3×C4—44no—
336C3×C4—48no—
337C3×C4—44no—
338C3×C4#100418yes—
339Dic3—38no—
340Dic3—38no—
341Dic3—38no—
342Dic3—64no—
343Dic3—124no—
344Dic3—128no—
345Dic3—124no—
346C32#320911yescharacteristic, complemented, Sylow
347C23D4×C3⋊D311yescharacteristic
348Q8—22no—
349Q8—22no—
350Q8—22no—
351Q8—42no—
352Q8—182no—
353Q8—182no—
354Q8—182no—
355Q8—362no—
356Q8—362no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—22no—
361C2×C4—42no—
362C2×C4—91no—
363C2×C4—91no—
364C2×C4—91no—
365C2×C4—94no—
366C2×C4—91no—
367C2×C4—182no—
368C2×C4—181no—
369C2×C4—181no—
370C2×C4—182no—
371C2×C4—362no—
372C2×C4D4×C3⋊D311yescharacteristic
373C2×C4C23×C3⋊D311yescharacteristic
374C8—22no—
375C8—182no—
376C2×C3—28no—
377C2×C3#559214yes—
378C2×C3C2×D3×Q1614yes—
379C2×C3D3×#13714yes—
380C22—21no—
381C22—21no—
382C22Q16×C3⋊D312yes—
383C22C2×D4×C3⋊D311yescharacteristic
384C4—21no—
385C4—41no—
386C4—42no—
387C4—41no—
388C4—92no—
389C4—92no—
390C4—92no—
391C4—181no—
392C4—361no—
393C4—362no—
394C4—361no—
395C4#6436112yes—
396C3#8017814yescomplemented
397C2—22no—
398C2#1059606311yescharacteristic
399C2C2×Q16×C3⋊D311yescharacteristic
400C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#451C2
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
hypercenter#451C3⋊D3
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
5. #10592882C2semidirect
6. #10592881C2semidirect
8. #10592494C2semidirect
9. #10592491C2semidirect
145. C2×C3⋊Dic3Q16semidirect
346. C32#3209semidirect
396. C3#80178semidirect

Maximal subgroups

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

subgroupindex
C2×#641532
#105960932
C32×#4512
#105929272
#105928822
#105928812
#105927492
#105924942
#105924912
#105924382
#105924172
#801783