Finite Group Databasebeta

← #11860013

Subgroups — #11860013

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 421 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic
2#10594954C212yesmaximal, complemented
3C3×#5106C211yesmaximal, characteristic, complemented
4C2×C3×C8×Dic3C211yesmaximal, characteristic, complemented
5#10591105C212yesmaximal, complemented
6#10590807C212yesmaximal, complemented
7#10590763C212yesmaximal, complemented
8#10590758C214yesmaximal, complemented
9#79165—31nomaximal
10C4×#904—31nomaximal
11C2×#3828C2212yes—
12C22×C32×C8C2211yescharacteristic
13C2×#3746C2211yescharacteristic
14#64113C418yescomplemented
15C2×#3745C2211yescharacteristic
16C2×#3744C2212yes—
17C3×#926C2212yes—
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20#63952—24no—
21#63894C2214yes—
22C4×#624—22no—
23#63874—22no—
24#63844C2214yes—
25C3×#818C2212yes—
26C3×#817C2212yes—
27C3×C8×Dic3C2212yes—
28C3×C8×Dic3C2212yes—
29#63567C2214yes—
30#63564C2214yes—
31C2×#904—31no—
32C2×#904—31no—
33C2×#904—61no—
34#5522—32no—
35C4×#235—32no—
36C3×#427—31no—
37C2×C3×C4×C8—31no—
38#5113—32no—
39#5106D311yescharacteristic, complemented
40C2×C8×Dic3D311yescharacteristic, complemented
41#5002—32no—
42#4873—32no—
43#4872—32no—
44#4852—34no—
45C4×Dic12—32no—
46C4×D24—32no—
47C4×#204—34no—
48C22×C32×C4C2311yescharacteristic
49C2×#638—22no—
50#3828—24no—
51#3828C2×C418yescomplemented
52C2×C4⋊(C3⋊D3)C2312yes—
53C2×C4×C3⋊D3—22no—
54C2×#634C2312yes—
55C22×C3×Dic3D412yes—
56C2×#624—24no—
57C2×C32×C8C2×C414yescomplemented
58C2×C32×C8C2311yescharacteristic
59C2×C32×C8C2311yescharacteristic
60#3746C2×C414yescomplemented
61#3745C2×C414yescomplemented
62#3744C2×C418yescomplemented
63C3×#217—22no—
64C3×C4⋊Dic3C2314yes—
65C3×C4×Dic3—22no—
66C3×C4×Dic3D411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3C2312yes—
69C2×C3×C3⋊C8—22no—
70C2×C3×C3⋊C8C2312yes—
71#3724—24no—
72#3722—24no—
73Dic32—24no—
74C4×#135—91noSylow
75C2×#235—32no—
76C2×#235—32no—
77C2×#235—62no—
78C22×C3×C8—21no—
79C22×C3×C8—31no—
80C22×C3×C8C2×D311yescharacteristic
81C22×C3×C8C2×D311yescharacteristic
82C3×#117—32no—
83C2×C3×C42—31no—
84C4×#67—64no—
85#926C2×D312yes—
86C2×C4×Dic3C2×D311yescharacteristic
87C22×C3⋊C8C2×D311yescharacteristic
88C2×Dic12—31no—
89C2×Dic12—31no—
90C2×Dic12—61no—
91#904—38no—
92#904—38no—
93#904—68no—
94C2×D24—31no—
95C2×D24—31no—
96C2×D24—61no—
97C2×#204—32no—
98C2×#204—32no—
99C2×#204—62no—
100#893—34no—
101#887—34no—
102#67⋊C4—64no—
103C4×D12—34no—
104#872—62no—
105#872—62no—
106C42×D3—62no—
107C42×D3—62no—
108C4×Dic6—34no—
109C3×#107—32no—
110C3×#106—32no—
111C3×C4×C8—32no—
112C3×C4×C8—32no—
113#821—34no—
114#818C2×D312yes—
115#817C2×D312yes—
116#816—34no—
117C8×Dic3C2×D312yes—
118C8×Dic3C2×D312yes—
119#810—34no—
120#809—34no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—22no—
123C2×C32×C4C22×C412yes—
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4#4112yes—
126C2×C32×C4C2411yescharacteristic
127#638—28no—
128C2×C3⋊Dic3—22no—
129C4⋊(C3⋊D3)—22no—
130C4⋊(C3⋊D3)C22×C414yes—
131C4×C3⋊D3—28no—
132#634—22no—
133#634C22×C414yes—
134C2×C3×Dic3—24no—
135C2×C3×Dic3—24no—
136C2×C3×Dic3C2×D412yes—
137C2×C3×Dic3C2×D412yes—
138#624—48no—
139C32×C8C22×C412yes—
140C32×C8C22×C412yes—
141C3×C3⋊C8—22no—
142C2×#135—91no—
143C4×#41—92no—
144C4×Q16—92no—
145C4×SD16—94no—
146C4×D8—92no—
147#427—31no—
148#416—92no—
149C2×C4×C8—31no—
150C22×C3×C4—21no—
151C22×C3×C4—32no—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C2×#67—62no—
155C2×#67—62no—
156C2×#67—122no—
157C22×Dic3D1212yes—
158#235—38no—
159#235—38no—
160#235—68no—
161#235—64no—
162#235—64no—
163#235—124no—
164C2×D12—32no—
165C2×D12—32no—
166C2×D12—62no—
167C2×C4×D3—62no—
168C2×C4×D3—62no—
169C2×C4×D3—64no—
170C2×C4×D3—64no—
171C2×C4×D3—122no—
172C2×Dic6—32no—
173C2×Dic6—32no—
174C2×Dic6—62no—
175C2×C3×C8—24no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—32no—
179C2×C3×C8—62no—
180C2×C3×C8C4×D314yescomplemented
181C2×C3×C8C4×D314yescomplemented
182C2×C3×C8C22×D311yescharacteristic
183C2×C3×C8C22×D311yescharacteristic
184C2×C3×C8C22×D311yescharacteristic
185C2×C3×C8C22×D311yescharacteristic
186C3×C4⋊C4—34no—
187C3×C22⋊C4—62no—
188C3×C42—31no—
189C3×C42—31no—
190C3×C42—32no—
191C3×C42—62no—
192#217—22no—
193(C2×D3)⋊C4—64no—
194(C2×D3)⋊C4—64no—
195C4⋊Dic3C22×D314yes—
196Dic3⋊C4—64no—
197Dic3⋊C4—64no—
198C4×Dic3—22no—
199C4×Dic3—64no—
200C4×Dic3—64no—
201C4×Dic3D1211yescharacteristic
202C4×Dic3D1211yescharacteristic
203C4×Dic3C22×D312yes—
204C2×C3⋊C8—22no—
205C2×C3⋊C8C22×D312yes—
206Dic12—34no—
207Dic12—34no—
208Dic12—64no—
209D24—34no—
210D24—34no—
211D24—64no—
212#204—38no—
213#204—38no—
214#204—68no—
215C22×C32—22no—
216C22×C32C4×D412yes—
217C22×C32C22×D411yescharacteristic
218C2×C3⋊D3—24no—
219C2×C3⋊D3—44no—
220C32×C4C4×D412yes—
221C32×C4C23×C411yescharacteristic
222C32×C4C2×#4111yescharacteristic
223C3⋊Dic3—24no—
224C3×Dic3—22no—
225C3×Dic3—44no—
226C3×Dic3#13514yescomplemented
227C2×#41—92no—
228#135—98no—
229C2×Q16—91no—
230C2×SD16—92no—
231C2×D8—91no—
232C22×C8—31no—
233C22×C8D3211yescharacteristic
234C4×Q8—94no—
235C4×D4—94no—
236C4×D4—184no—
237#117—32no—
238#117—182no—
239C2×C42—31no—
240C2×C42—182no—
241#107—32no—
242#106—32no—
243#103—94no—
244#102—94no—
245C4×C8—32no—
246C4×C8—32no—
247C23×C3—21no—
248C23×C3C2×D1211yescharacteristic
249C23×C3D3×D411yescharacteristic
250C22×D3—62no—
251C22×D3—62no—
252C22×D3—122no—
253C2×C3×C4—21no—
254C2×C3×C4—22no—
255C2×C3×C4—21no—
256C2×C3×C4—22no—
257C2×C3×C4—32no—
258C2×C3×C4—32no—
259C2×C3×C4—64no—
260C2×C3×C4—64no—
261C2×C3×C4C2×C4×D312yes—
262C2×C3×C4C2×C4×D312yes—
263C2×C3×C4C2×D1211yescharacteristic
264C2×C3×C4#23512yes—
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4#23912yes—
267C2×C3×C4C23×D311yescharacteristic
268C2×C3×C4C23×D311yescharacteristic
269#67—68no—
270#67—68no—
271#67—128no—
272C2×Dic3—24no—
273C2×Dic3—24no—
274C2×Dic3—62no—
275C2×Dic3—62no—
276C2×Dic3—122no—
277C2×Dic3C2×D1212yes—
278C2×Dic3C2×D1212yes—
279D12—34no—
280D12—34no—
281D12—64no—
282D12—62no—
283D12—62no—
284D12—122no—
285C4×D3—68no—
286C4×D3—68no—
287C4×D3—128no—
288C4×D3—128no—
289C4×D3—128no—
290Dic6—34no—
291Dic6—34no—
292Dic6—64no—
293Dic6—62no—
294Dic6—62no—
295Dic6—122no—
296C3×C8—22no—
297C3×C8—22no—
298C3×C8—62no—
299C3×C8C2×C4×D312yes—
300C3×C8C2×C4×D312yes—
301C3×C8C2×C4×D312yes—
302C3×C8C2×C4×D312yes—
303C3⋊C8—22no—
304C2×C32—22no—
305C2×C32C2×C4×D411yescharacteristic
306C2×C32C2×#13512yes—
307C3⋊D3—44no—
308#41—98no—
309#41—184no—
310C2×Q8—92no—
311C2×D4—92no—
312C2×D4—182no—
313C22×C4—32no—
314C22×C4—184no—
315C22×C4—182no—
316C22×C4C2×D3211yescharacteristic
317Q16—94no—
318SD16—98no—
319D8—94no—
320C2×C8—32no—
321C2×C8—62no—
322C2×C8#62414yescomplemented
323C2×C8C2×D3211yescharacteristic
324C2×C8C2×D3211yescharacteristic
325C4⋊C4—34no—
326C4⋊C4—184no—
327C22⋊C4—62no—
328C22⋊C4—184no—
329C42—32no—
330C42—31no—
331C42—31no—
332C42—62no—
333C42—184no—
334C22×C3—22no—
335C22×C3—22no—
336C22×C3—21no—
337C22×C3—22no—
338C22×C3—42no—
339C22×C3C4×D1212yes—
340C22×C3#89312yes—
341C22×C3C22×D1211yescharacteristic
342C22×C3C2×D3×D411yescharacteristic
343C2×D3—64no—
344C2×D3—64no—
345C2×D3—124no—
346C2×D3—124no—
347C2×D3—124no—
348C2×D3—244no—
349C3×C4—21no—
350C3×C4—21no—
351C3×C4—22no—
352C3×C4—34no—
353C3×C4—62no—
354C3×C4—124no—
355C3×C4C4×D1212yes—
356C3×C4#89312yes—
357C3×C4C22×C4×D311yescharacteristic
358C3×C4C22×C4×D311yescharacteristic
359C3×C4C2×#23511yescharacteristic
360C3×C4C2×#23911yescharacteristic
361Dic3—22no—
362Dic3—44no—
363Dic3—64no—
364Dic3—64no—
365Dic3—124no—
366Dic3#90414yescomplemented
367C32C4×#13511yescharacteristic, complemented, Sylow
368C23—182no—
369C23D3×D1211yescharacteristic
370Q8—94no—
371Q8—182no—
372D4—94no—
373D4—188no—
374D4—182no—
375C2×C4—32no—
376C2×C4—32no—
377C2×C4—64no—
378C2×C4—64no—
379C2×C4—182no—
380C2×C4—188no—
381C2×C4—368no—
382C2×C4#379912yes—
383C2×C4D3×D1211yescharacteristic
384C2×C4C2×#62412yes—
385C2×C4C22×D3211yescharacteristic
386C8—62no—
387C8C2×#62412yes—
388C8C2×#62412yes—
389C2×C3—22no—
390C2×C3—22no—
391C2×C3—21no—
392C2×C3—22no—
393C2×C3—42no—
394C2×C3C2×C4×D1211yescharacteristic
395C2×C3C2×#89311yescharacteristic
396C2×C3C2×#90412yes—
397C2×C3D3×#13512yes—
398D3—124no—
399D3—124no—
400D3—244no—
401C22—22no—
402C22—184no—
403C22—364no—
404C22#6389412yes—
405C22C2×D3×D1211yescharacteristic
406C4—34no—
407C4—62no—
408C4—124no—
409C4—184no—
410C4#6389412yes—
411C4C2×#379911yescharacteristic
412C4C22×#62411yescharacteristic
413C3—21no—
414C3C4×#90411yescharacteristic, complemented
415C3#7916511yescharacteristic, complemented
416C2—22no—
417C2—364no—
418C2D3×#90412yes—
419C2C2×#6389411yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×#64113C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32C4×#135
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594954C2semidirect
3. C3×#5106C2semidirect
4. C2×C3×C8×Dic3C2semidirect
5. #10591105C2semidirect
6. #10590807C2semidirect
7. #10590763C2semidirect
8. #10590758C2semidirect
14. #64113C4semidirect
39. #5106D3semidirect
40. C2×C8×Dic3D3semidirect
51. #3828C2×C4semidirect
57. C2×C32×C8C2×C4semidirect
60. #3746C2×C4semidirect
61. #3745C2×C4semidirect
62. #3744C2×C4semidirect
180. C2×C3×C8C4×D3semidirect
181. C2×C3×C8C4×D3semidirect
226. C3×Dic3#135semidirect
322. C2×C8#624semidirect
366. Dic3#904semidirect
367. C32C4×#135semidirect
414. C3C4×#904semidirect
415. C3#79165semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
#105949542
C3×#51062
C2×C3×C8×Dic32
#105911052
#105908072
#105907632
#105907582
#791653
C4×#9043