Finite Group Databasebeta

← #11878884

Subgroups — #11878884

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2#10596049C211yesmaximal, characteristic
3C32×#462C211yesmaximal, characteristic, complemented
4#10592885C212yesmaximal
5#10592882C212yesmaximal, complemented
6#10592789C211yesmaximal, characteristic, complemented
7#10592730C211yesmaximal, characteristic, complemented
8#10592548C211yesmaximal, characteristic, complemented
9#10592532C211yesmaximal, characteristic
10#10592508C212yesmaximal
11#10592491C212yesmaximal, complemented
12#80480—34nomaximal
13C2×Q8×C3⋊D3C2212yes—
14C2×C32×Q16C2212yes—
15C32×C4⋊Q8C2211yescharacteristic
16C32×C4×Q8C2211yescharacteristic
17#64155C2211yescharacteristic
18#64153C2212yes—
19#64153C2211yescharacteristic
20C2×#3756C2212yes—
21C2×#3756C2212yes—
22C2×#3746C2212yes—
23#64106C2211yescharacteristic
24#64105—21no—
25C4⋊C4×C3⋊D3—21no—
26C4⋊C4×C3⋊D3—21no—
27#64098—21no—
28#64097—21no—
29#64097—21no—
30#64097C2211yescharacteristic
31#64081—21no—
32C42×C3⋊D3C2211yescharacteristic
33#64078C2211yescharacteristic
34C4×#634—21no—
35C4×#634C2211yescharacteristic
36C32×C4⋊C8C2211yescharacteristic
37C32×#103C2212yes—
38#63662C2212yes—
39#63647C2212yes—
40#63643C2212yes—
41C8×C3⋊Dic3C2212yes—
42#63637C2212yes—
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
44D3×C4⋊Q8—34no—
45#5578—34no—
46C3×#462D314yescomplemented
47#5186—38no—
48#5183—38no—
49#5090—34no—
50#5031—34no—
51#4849—34no—
52#4833—34no—
53#4809—38no—
54#4792—38no—
55C2×C32×Q8C2312yes—
56C2×C32×Q8C2311yescharacteristic
57Q8×C3⋊D3—42no—
58Q8×C3⋊D3—42no—
59C2×C4×C3⋊D3—22no—
60C2×C4×C3⋊D3D411yescharacteristic
61C2×C4×C3⋊D3D411yescharacteristic
62C2×C4×C3⋊D3C2311yescharacteristic
63C2×#634—21no—
64C2×#634—22no—
65C2×#634C2311yescharacteristic
66C2×#634C2312yes—
67C32×Q16—42no—
68C2×C32×C8C2312yes—
69C32×C4⋊C4—21no—
70C32×C4⋊C4—21no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2311yescharacteristic
73C32×C42—21no—
74C32×C42C2311yescharacteristic
75#3756—42no—
76#3756—42no—
77#3752—21no—
78#3752—21no—
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—21no—
84#3750—21no—
85#3750—21no—
86#3750—21no—
87#3750—21no—
88#3750—22no—
89#3750—22no—
90C4×C3⋊Dic3—21no—
91C4×C3⋊Dic3D411yescharacteristic
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3C2311yescharacteristic
94C2×C3⋊(C3⋊C8)C2312yes—
95#3746—42no—
96#3209—91noSylow
97C2×D3×Q8—38no—
98C2×C3×Q16C2×D318yes—
99C3×C4⋊Q8C2×D314yes—
100C3×C4×Q8C2×D314yes—
101#946—34no—
102#944—34no—
103#944—38no—
104C2×#216—38no—
105C2×#216—38no—
106C2×Dic12—38no—
107#897—34no—
108#896—64no—
109D3×C4⋊C4—64no—
110D3×C4⋊C4—64no—
111#889—64no—
112#888—34no—
113#888—64no—
114#888—64no—
115#872—64no—
116C42×D3—34no—
117#869—34no—
118C4×Dic6—34no—
119C4×Dic6—64no—
120C3×C4⋊C8C2×D314yes—
121C3×#103C2×D318yes—
122#835—38no—
123(C2×D3)⋊C8—38no—
124#816—38no—
125C8×Dic3—38no—
126#810—38no—
127C4⋊(C3⋊C8)—34no—
128C22×C3⋊D3C2×D411yescharacteristic
129C32×Q8—21no—
130C32×Q8—22no—
131C32×Q8—21no—
132C32×Q8—22no—
133C2×C32×C4—21no—
134C2×C32×C4—22no—
135C2×C32×C4—21no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3C2×D411yescharacteristic
143C2×C3⋊Dic3C2×D411yescharacteristic
144C2×C3⋊Dic3C2×D411yescharacteristic
145C4×C3⋊D3—21no—
146C4×C3⋊D3—21no—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—44no—
149C4×C3⋊D3Q1614yescomplemented
150#634—21no—
151#634—22no—
152#634—21no—
153#634—22no—
154#634—44no—
155#634—42no—
156C32×C8—22no—
157C3⋊(C3⋊C8)—22no—
158#533—91no—
159C2×C4⋊Q8—91no—
160#494—92no—
161#487—92no—
162#462—91no—
163#462—91no—
164#462—91no—
165#462C3⋊D311yescharacteristic, complemented
166#451—92no—
167#451—92no—
168#431—91no—
169C2×C3×Q8C22×D318yes—
170C2×C3×Q8C22×D314yes—
171D3×Q8—128no—
172D3×Q8—128no—
173C2×C4×D3—34no—
174C2×C4×D3—34no—
175C2×C4×D3—34no—
176C2×C4×D3—68no—
177C2×Dic6—38no—
178C2×Dic6—34no—
179C2×Dic6—64no—
180C2×Dic6—68no—
181C3×Q16—48no—
182C2×C3×C8C22×D318yes—
183C3×C4⋊C4—24no—
184C3×C4⋊C4—24no—
185C3×C4⋊C4—24no—
186C3×C4⋊C4C22×D314yes—
187C3×C42—24no—
188C3×C42C22×D314yes—
189#216—128no—
190#216—128no—
191(C2×D3)⋊C4—64no—
192(C2×D3)⋊C4—64no—
193C4⋊Dic3—34no—
194C4⋊Dic3—64no—
195C4⋊Dic3—64no—
196C4⋊Dic3—64no—
197Dic3⋊C4—64no—
198Dic3⋊C4—64no—
199Dic3⋊C4—64no—
200Dic3⋊C4—64no—
201Dic3⋊C4—68no—
202Dic3⋊C4—68no—
203Dic3⋊C4—64no—
204C4×Dic3—34no—
205C4×Dic3—34no—
206C4×Dic3—34no—
207C4×Dic3—64no—
208C2×C3⋊C8—38no—
209Dic12—128no—
210C22×C32C22×D411yescharacteristic
211C2×C3⋊D3—21no—
212C2×C3⋊D3—21no—
213C2×C3⋊D3C2×Q1612yes—
214C32×C4—21no—
215C32×C4—42no—
216C32×C4—41no—
217C32×C4—41no—
218C32×C4C2×Q1612yes—
219C32×C4H(5,𝔽2)11yescharacteristic
220C32×C4H(5,𝔽2)11yescharacteristic
221C3⋊Dic3—21no—
222C3⋊Dic3—42no—
223C3⋊Dic3—41no—
224C3⋊Dic3—41no—
225C3⋊Dic3C2×Q1612yes—
226C3⋊Dic3#13712yes—
227C22×Q8—92no—
228C2×Q16—92no—
229C2×Q16—92no—
230C2×Q16—92no—
231C2×Q16C2×C3⋊D312yes—
232C4⋊Q8—91no—
233C4⋊Q8—92no—
234C4⋊Q8—91no—
235C4⋊Q8—91no—
236C4⋊Q8—181no—
237C4⋊Q8—181no—
238C4⋊Q8C2×C3⋊D311yescharacteristic
239#125—181no—
240C22⋊Q8—91no—
241C22⋊Q8—91no—
242C22⋊Q8—181no—
243C4×Q8—91no—
244C4×Q8—181no—
245C4×Q8C2×C3⋊D311yescharacteristic
246#117—181no—
247C2×C4⋊C4—181no—
248C2×C4⋊C4—181no—
249C2×C42—91no—
250C4⋊C8—91no—
251C4⋊C8C2×C3⋊D311yescharacteristic
252#103—92no—
253#103—92no—
254#103—92no—
255#103C2×C3⋊D312yes—
256C22⋊C8—92no—
257C4×C8—92no—
258C22×D3—34no—
259C3×Q8—24no—
260C3×Q8—28no—
261C3×Q8—24no—
262C3×Q8—28no—
263C2×C3×C4—24no—
264C2×C3×C4—28no—
265C2×C3×C4—24no—
266C2×C3×C4D3×D414yes—
267C2×C3×C4D3×D414yes—
268C2×C3×C4C23×D314yes—
269C2×Dic3—34no—
270C2×Dic3—34no—
271C2×Dic3—34no—
272C2×Dic3—64no—
273C2×Dic3—64no—
274C2×Dic3—68no—
275C4×D3—316no—
276C4×D3—68no—
277C4×D3—64no—
278C4×D3—64no—
279C4×D3—1216no—
280Dic6—64no—
281Dic6—68no—
282Dic6—64no—
283Dic6—68no—
284Dic6—128no—
285Dic6—1216no—
286C3×C8—28no—
287C3⋊C8—68no—
288C2×C32#53511yescharacteristic
289C2×C32C22×Q1611yescharacteristic
290C2×C32C2×#13711yescharacteristic
291C3⋊D3—22no—
292C2×Q8—92no—
293C2×Q8—91no—
294C2×Q8—181no—
295C2×Q8—182no—
296C2×Q8—362no—
297C2×Q8—362no—
298C2×Q8C22×C3⋊D312yes—
299C2×Q8C22×C3⋊D311yescharacteristic
300C22×C4—91no—
301C22×C4—91no—
302C22×C4—91no—
303C22×C4—182no—
304Q16—42no—
305Q16—362no—
306Q16—362no—
307Q16—362no—
308C2×C8—92no—
309C2×C8C22×C3⋊D312yes—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—91no—
314C4⋊C4—182no—
315C4⋊C4—182no—
316C4⋊C4—181no—
317C4⋊C4—181no—
318C4⋊C4—181no—
319C4⋊C4—181no—
320C4⋊C4—181no—
321C4⋊C4—181no—
322C4⋊C4—181no—
323C4⋊C4—181no—
324C4⋊C4C22×C3⋊D311yescharacteristic
325C22⋊C4—181no—
326C22⋊C4—181no—
327C42—21no—
328C42—91no—
329C42—91no—
330C42—91no—
331C42—181no—
332C42C22×C3⋊D311yescharacteristic
333C22×C3C2×D3×D414yes—
334C2×D3—38no—
335C2×D3—64no—
336C2×D3—64no—
337C3×C4—24no—
338C3×C4—44no—
339C3×C4—48no—
340C3×C4—44no—
341C3×C4D3×Q1618yes—
342C3×C4#100414yes—
343C3×C4#100914yes—
344Dic3—38no—
345Dic3—38no—
346Dic3—64no—
347Dic3—124no—
348Dic3—128no—
349Dic3—124no—
350C32#320911yescharacteristic, complemented, Sylow
351C23—91no—
352Q8—21no—
353Q8—22no—
354Q8—21no—
355Q8—22no—
356Q8—181no—
357Q8—182no—
358Q8—181no—
359Q8—182no—
360Q8—362no—
361Q8—364no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—22no—
365C2×C4—91no—
366C2×C4—91no—
367C2×C4—94no—
368C2×C4—91no—
369C2×C4—182no—
370C2×C4—181no—
371C2×C4—181no—
372C2×C4—181no—
373C2×C4—181no—
374C2×C4—182no—
375C2×C4—364no—
376C2×C4D4×C3⋊D311yescharacteristic
377C2×C4D4×C3⋊D311yescharacteristic
378C2×C4C23×C3⋊D311yescharacteristic
379C8—22no—
380C8—182no—
381C2×C3#560714yes—
382C2×C3C2×D3×Q1614yes—
383C2×C3D3×#13714yes—
384D3—68no—
385C22—92no—
386C22—181no—
387C22—181no—
388C22C2×D4×C3⋊D311yescharacteristic
389C4—21no—
390C4—41no—
391C4—42no—
392C4—41no—
393C4—92no—
394C4—92no—
395C4—181no—
396C4—361no—
397C4—362no—
398C4—361no—
399C4Q16×C3⋊D312yes—
400C4#6436111yescharacteristic
401C4#6436611yescharacteristic
402C3#8048014yescomplemented
403C2—182no—
404C2#1059607811yescharacteristic
405C2C2×Q16×C3⋊D311yescharacteristic
406C2C3⋊D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#462C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#462C3⋊D3
hypocenterC32#3209
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. C32×#462C2semidirect
5. #10592882C2semidirect
6. #10592789C2semidirect
7. #10592730C2semidirect
8. #10592548C2semidirect
11. #10592491C2semidirect
46. C3×#462D3semidirect
149. C4×C3⋊D3Q16semidirect
165. #462C3⋊D3semidirect
350. C32#3209semidirect
402. C3#80480semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
#105960492
C32×#4622
#105928852
#105928822
#105927892
#105927302
#105925482
#105925322
#105925082
#105924912
#804803