Finite Group Databasebeta

← #11860896

Subgroups — #11860896

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64113C211yesmaximal, characteristic
2#10594990C212yesmaximal, complemented
3C2×C3×#818C211yesmaximal, characteristic, complemented
4C3×#5101C211yesmaximal, characteristic, complemented
5#10591106C212yesmaximal, complemented
6#10590807C212yesmaximal, complemented
7#10590773C214yesmaximal, complemented
8#10590763C212yesmaximal, complemented
9#79136—31nomaximal
10#78562—31nomaximal
11C2×#3828C2212yes—
12C22×C32×C8C2211yescharacteristic
13C2×#3746C2211yescharacteristic
14#64113C418yescomplemented
15C2×#3745C2211yescharacteristic
16C2×#3744C2212yes—
17C3×#926C2211yescharacteristic
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×#208C2211yescharacteristic
20#63952—24no—
21#63900—22no—
22#63894C2214yes—
23#63849—22no—
24#63844C2214yes—
25C3×#818C2212yes—
26C3×#818C2212yes—
27C3×#815C2212yes—
28C3×C8×Dic3C2212yes—
29#63567C2214yes—
30#63564C2214yes—
31C2×#904—31no—
32C2×#904—31no—
33C2×#904—61no—
34#5523—32no—
35#5504—32no—
36C2×C3×#107—31no—
37C3×#405—31no—
38#5133—32no—
39C2×#818D311yescharacteristic, complemented
40#5101D311yescharacteristic, complemented
41#4966—32no—
42#4889—34no—
43#4873—32no—
44#4872—32no—
45#4710—34no—
46C4×Dic12—32no—
47C4×D24—32no—
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×Dic3—22no—
56C2×#624—24no—
57C2×C32×C8C2×C414yescomplemented
58C2×C32×C8C2311yescharacteristic
59C2×C32×C8C2311yescharacteristic
60#3746C2×C414yescomplemented
61#3745C2×C414yescomplemented
62#3744C2×C418yescomplemented
63C3×#217D412yes—
64C3×C4⋊Dic3—22no—
65C3×C4⋊Dic3D411yescharacteristic
66C3×C4⋊Dic3D411yescharacteristic
67C3×C4⋊Dic3C2314yes—
68C3×C4×Dic3C2312yes—
69C3×#208—22no—
70C2×C3×C3⋊C8C2312yes—
71#3724—24no—
72#3722—24no—
73Dic32—24no—
74#2951—91noSylow
75C2×#235—32no—
76C2×#235—32no—
77C2×#235—62no—
78C2×C3×M16—31no—
79C22×C3×C8—21no—
80C22×C3×C8C2×D311yescharacteristic
81C22×C3×C8C2×D311yescharacteristic
82C3×#117—31no—
83C2×C3×C4⋊C4—32no—
84C4×#67—64no—
85#926C2×D311yescharacteristic
86C2×C4⋊Dic3C2×D312yes—
87C2×#208C2×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#892—62no—
102#892—62no—
103D3×C4⋊C4—62no—
104D3×C4⋊C4—62no—
105#887—34no—
106#67⋊C4—64no—
107C4×D12—34no—
108C4×Dic6—34no—
109C3×#107—32no—
110C3×#107—32no—
111C3×#97—32no—
112C3×C4×C8—32no—
113#821—34no—
114#818C2×D312yes—
115#818C2×D312yes—
116#816—34no—
117#815C2×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—82no—
136C2×C3×Dic3C2×D412yes—
137C2×C3×Dic3C2×D412yes—
138#624—84no—
139C32×C8C22×C412yes—
140C32×C8C22×C412yes—
141C3×C3⋊C8—22no—
142C2×#135—91no—
143#520—92no—
144#440—94no—
145C4×Q16—92no—
146C4×D8—92no—
147C2×#107—31no—
148#417—92no—
149#405—31no—
150C22×C3×C4—21no—
151C22×C3×C4—62no—
152C22×C3×C4C22×D311yescharacteristic
153C22×C3×C4C22×D311yescharacteristic
154C2×#67—62no—
155C2×#67—62no—
156C2×#67—122no—
157C22×Dic3—22no—
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—
175C3×M16—62no—
176C2×C3×C8—24no—
177C2×C3×C8—21no—
178C2×C3×C8—21no—
179C2×C3×C8—32no—
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—31no—
187C3×C4⋊C4—31no—
188C3×C4⋊C4—34no—
189C3×C4⋊C4—62no—
190C3×C22⋊C4—32no—
191C3×C42—32no—
192#217D1212yes—
193(C2×D3)⋊C4—64no—
194(C2×D3)⋊C4—64no—
195C4⋊Dic3—22no—
196C4⋊Dic3D1211yescharacteristic
197C4⋊Dic3D1211yescharacteristic
198C4⋊Dic3C22×D314yes—
199Dic3⋊C4—64no—
200Dic3⋊C4—64no—
201C4×Dic3—64no—
202C4×Dic3—64no—
203C4×Dic3C22×D312yes—
204#208—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—21no—
216C22×C32—21no—
217C22×C32C4×D412yes—
218C22×C32C22×D411yescharacteristic
219C2×C3⋊D3—24no—
220C2×C3⋊D3—42no—
221C2×C3⋊D3—42no—
222C32×C4C4×D412yes—
223C32×C4C23×C411yescharacteristic
224C32×C4C2×#4111yescharacteristic
225C3⋊Dic3—24no—
226C3×Dic3—22no—
227C3×Dic3—22no—
228C3×Dic3—44no—
229C2×#41—92no—
230#135—98no—
231C2×Q16—91no—
232C2×SD16—92no—
233C2×D8—91no—
234C2×M16—31no—
235C22×C8D3211yescharacteristic
236C4×Q8—94no—
237C4×D4—94no—
238C4×D4—184no—
239#117—31no—
240#117—182no—
241C2×C4⋊C4—32no—
242C2×C4⋊C4—182no—
243#107—32no—
244#107—32no—
245#103—94no—
246#102—94no—
247#97—32no—
248C4×C8—32no—
249C23×C3—21no—
250C23×C3C2×D1211yescharacteristic
251C23×C3D3×D411yescharacteristic
252C22×D3—62no—
253C22×D3—62no—
254C22×D3—122no—
255C2×C3×C4—21no—
256C2×C3×C4—22no—
257C2×C3×C4—21no—
258C2×C3×C4—22no—
259C2×C3×C4—32no—
260C2×C3×C4—32no—
261C2×C3×C4—64no—
262C2×C3×C4—242no—
263C2×C3×C4C2×C4×D312yes—
264C2×C3×C4C2×C4×D312yes—
265C2×C3×C4C2×D1211yescharacteristic
266C2×C3×C4#23512yes—
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4#23912yes—
269C2×C3×C4C23×D311yescharacteristic
270C2×C3×C4C23×D311yescharacteristic
271#67—68no—
272#67—68no—
273#67—128no—
274C2×Dic3—24no—
275C2×Dic3—62no—
276C2×Dic3—62no—
277C2×Dic3—82no—
278C2×Dic3—122no—
279C2×Dic3C2×D1212yes—
280C2×Dic3C2×D1212yes—
281D12—34no—
282D12—34no—
283D12—64no—
284D12—62no—
285D12—62no—
286D12—122no—
287C4×D3—68no—
288C4×D3—68no—
289C4×D3—128no—
290C4×D3—244no—
291C4×D3—244no—
292Dic6—34no—
293Dic6—34no—
294Dic6—64no—
295Dic6—62no—
296Dic6—62no—
297Dic6—122no—
298C3×C8—22no—
299C3×C8—22no—
300C3×C8—62no—
301C3×C8C2×C4×D312yes—
302C3×C8C2×C4×D312yes—
303C3×C8C2×C4×D312yes—
304C3×C8C2×C4×D312yes—
305C3⋊C8—22no—
306C2×C32—22no—
307C2×C32C2×C4×D411yescharacteristic
308C2×C32#57611yescharacteristic
309C2×C32#57811yescharacteristic
310C3⋊D3—44no—
311#41—98no—
312#41—184no—
313C2×Q8—92no—
314C2×D4—92no—
315C2×D4—182no—
316C22×C4—62no—
317C22×C4—184no—
318C22×C4—182no—
319C22×C4C2×D3211yescharacteristic
320Q16—94no—
321SD16—98no—
322D8—94no—
323M16—62no—
324C2×C8—32no—
325C2×C8#62414yescomplemented
326C2×C8C2×D3211yescharacteristic
327C2×C8C2×D3211yescharacteristic
328C4⋊C4—31no—
329C4⋊C4—31no—
330C4⋊C4—34no—
331C4⋊C4—62no—
332C4⋊C4—184no—
333C22⋊C4—32no—
334C22⋊C4—184no—
335C42—32no—
336C42—184no—
337C22×C3—21no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—22no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3C4×D1212yes—
346C22×C3#89312yes—
347C22×C3C22×D1211yescharacteristic
348C22×C3C2×D3×D411yescharacteristic
349C2×D3—64no—
350C2×D3—64no—
351C2×D3—124no—
352C2×D3—122no—
353C2×D3—122no—
354C2×D3—122no—
355C2×D3—122no—
356C2×D3—242no—
357C2×D3—242no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—22no—
361C3×C4—62no—
362C3×C4—62no—
363C3×C4—124no—
364C3×C4C4×D1212yes—
365C3×C4#89312yes—
366C3×C4C22×C4×D311yescharacteristic
367C3×C4C22×C4×D311yescharacteristic
368C3×C4C2×#23511yescharacteristic
369C3×C4C2×#23911yescharacteristic
370Dic3—22no—
371Dic3—22no—
372Dic3—44no—
373Dic3—64no—
374Dic3—64no—
375Dic3—124no—
376C32#295111yescharacteristic, complemented, Sylow
377C23—182no—
378C23D3×D1211yescharacteristic
379Q8—94no—
380Q8—182no—
381D4—94no—
382D4—188no—
383D4—182no—
384C2×C4—32no—
385C2×C4—32no—
386C2×C4—64no—
387C2×C4—182no—
388C2×C4—188no—
389C2×C4—242no—
390C2×C4—724no—
391C2×C4#379912yes—
392C2×C4D3×D1211yescharacteristic
393C2×C4C2×#62412yes—
394C2×C4C22×D3211yescharacteristic
395C8—62no—
396C8C2×#62412yes—
397C8C2×#62412yes—
398C2×C3—22no—
399C2×C3—22no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—42no—
404C2×C3C2×C4×D1211yescharacteristic
405C2×C3C2×#89311yescharacteristic
406C2×C3#575211yescharacteristic
407C2×C3#575311yescharacteristic
408C2×C3#575711yescharacteristic
409C2×C3#576611yescharacteristic
410D3—124no—
411D3—124no—
412D3—244no—
413C22—21no—
414C22—21no—
415C22—184no—
416C22—362no—
417C22—362no—
418C22#6389412yes—
419C22C2×D3×D1211yescharacteristic
420C4—62no—
421C4—62no—
422C4—124no—
423C4—184no—
424C4#6389412yes—
425C4C2×#379911yescharacteristic
426C4C22×#62411yescharacteristic
427C3—21no—
428C3#7856211yescharacteristic, complemented
429C3#7913611yescharacteristic, complemented
430C2—22no—
431C2—364no—
432C2#1059467811yescharacteristic
433C2#1059469111yescharacteristic
434C2C2×#6389411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×#64113C2
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2951
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594990C2semidirect
3. C2×C3×#818C2semidirect
4. C3×#5101C2semidirect
5. #10591106C2semidirect
6. #10590807C2semidirect
7. #10590773C2semidirect
8. #10590763C2semidirect
14. #64113C4semidirect
39. C2×#818D3semidirect
40. #5101D3semidirect
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
325. C2×C8#624semidirect
376. C32#2951semidirect
428. C3#78562semidirect
429. C3#79136semidirect

Maximal subgroups

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

subgroupindex
C2×#641132
#105949902
C2×C3×#8182
C3×#51012
#105911062
#105908072
#105907732
#105907632
#791363
#785623