Finite Group Databasebeta

← #11860776

Subgroups — #11860776

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3744C211yesmaximal, characteristic
2#10594996C211yesmaximal, characteristic
3#10594828C211yesmaximal, characteristic, complemented
4C3×#5106C211yesmaximal, characteristic, complemented
5C3×#5101C211yesmaximal, characteristic, complemented
6#10591107C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic
8#10590773C214yesmaximal, complemented
9#10590758C214yesmaximal, complemented
10#79168—31nomaximal
11#78572—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×#634C2211yescharacteristic
14C22×C32×C8C2211yescharacteristic
15C2×#3744C418yescomplemented
16C2×#3744C2212yes—
17C2×#3744C2212yes—
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C3×#926C2211yescharacteristic
21C2×C3×#208C2211yescharacteristic
22#63974—22no—
23#63957—22no—
24#63894—22no—
25#63894C2214yes—
26#63844—22no—
27#63844C2214yescomplemented
28C3×#818C2212yescomplemented
29C3×#817C2212yescomplemented
30C3×#815C2212yescomplemented
31C3×C8×Dic3C2212yescomplemented
32#63567C2214yescomplemented
33#63564C2214yes—
34C22×#204—31no—
35C22×#204—31no—
36C22×#204—61no—
37#5521—31no—
38#5521—31no—
39#5516—31no—
40#5516—31no—
41C3×#427—31no—
42C3×#405—31no—
43#5131—31no—
44#5120—31no—
45#5106D311yescharacteristic, complemented
46#5101D311yescharacteristic, complemented
47#5004—31no—
48#5001—31no—
49#4889—34no—
50#4852—34no—
51#4710—34no—
52C4×#204—34no—
53C23×C3⋊D3—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)C2×C414yes—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×#634—21no—
61C2×#634—22no—
62C2×#634C2×C414yescomplemented
63C2×#634C2312yes—
64C2×#624—24no—
65C2×C32×C8C2×C414yescomplemented
66C2×C32×C8C2311yescharacteristic
67C2×C32×C8C2311yescharacteristic
68#3744C2×C418yescomplemented
69#3744C2×C418yescomplemented
70C3×#217—21no—
71C3×#217—21no—
72C3×#217D412yes—
73C3×C4⋊Dic3D412yes—
74C3×C4⋊Dic3C2312yes—
75C3×C4⋊Dic3C2312yes—
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C3×C4×Dic3C2312yes—
79C3×#208—22no—
80C2×C3×C3⋊C8C2312yes—
81#3724—24no—
82#3722—24no—
83Dic32—24no—
84#2949—91noSylow
85C22×D12—31no—
86C22×D12—31no—
87C22×D12—61no—
88C22×Dic6—31no—
89C22×Dic6—31no—
90C22×Dic6—61no—
91C2×C3×M16—31no—
92C22×C3×C8—21no—
93C22×C3×C8C2×D311yescharacteristic
94C22×C3×C8C2×D311yescharacteristic
95C3×#117—31no—
96C3×#117—31no—
97C3×#117—31no—
98#926C2×D311yescharacteristic
99#926C2×D311yescharacteristic
100#926C2×D311yescharacteristic
101C2×#208C2×D311yescharacteristic
102C2×#204—38no—
103C2×#204—38no—
104C2×#204—32no—
105C2×#204—32no—
106C2×#204—32no—
107C2×#204—32no—
108C2×#204—68no—
109C2×#204—62no—
110C2×#204—62no—
111#893—34no—
112#893—62no—
113#887—34no—
114#887—62no—
115D3×C22⋊C4—62no—
116D3×C22⋊C4—62no—
117#877—62no—
118#877—62no—
119C4×D12—34no—
120C4×D12—62no—
121C4×Dic6—34no—
122C4×Dic6—62no—
123C3×#107—32no—
124C3×#106—32no—
125C3×#97—32no—
126C3×C4×C8—32no—
127#821—34no—
128#818C2×D312yescomplemented
129#817C2×D312yescomplemented
130#816—34no—
131#815C2×D312yescomplemented
132C8×Dic3C2×D312yescomplemented
133#810—34no—
134#809—34no—
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—24no—
138C22×C3⋊D3—82no—
139C2×C32×C4C22×C412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4112yes—
142C2×C32×C4C2411yescharacteristic
143C2×C3⋊Dic3—24no—
144C2×C3⋊Dic3—22no—
145C4⋊(C3⋊D3)—24no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)C22×C414yes—
148#634—24no—
149#634—22no—
150#634C22×C414yes—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3C2×D414yes—
154#624—84no—
155C32×C8C22×C412yes—
156C32×C8C22×C412yes—
157C3×C3⋊C8—22no—
158C22×SD16—91no—
159#519—91no—
160#518—91no—
161#440—94no—
162C4×SD16—94no—
163#427—31no—
164#419—91no—
165#418—91no—
166#405—31no—
167C23×D3—61no—
168C23×D3—61no—
169C23×D3—121no—
170C22×C3×C4—21no—
171C22×C3×C4C22×D311yescharacteristic
172C22×C3×C4C22×D311yescharacteristic
173C22×Dic3—61no—
174C22×Dic3—61no—
175C22×Dic3—121no—
176C2×D12—34no—
177C2×D12—34no—
178C2×D12—32no—
179C2×D12—32no—
180C2×D12—64no—
181C2×D12—62no—
182C2×D12—61no—
183C2×D12—62no—
184C2×D12—61no—
185C2×D12—62no—
186C2×D12—122no—
187C2×D12—121no—
188C2×C4×D3—64no—
189C2×C4×D3—64no—
190C2×Dic6—34no—
191C2×Dic6—34no—
192C2×Dic6—32no—
193C2×Dic6—32no—
194C2×Dic6—64no—
195C2×Dic6—62no—
196C2×Dic6—61no—
197C2×Dic6—62no—
198C2×Dic6—61no—
199C2×Dic6—62no—
200C2×Dic6—122no—
201C2×Dic6—121no—
202C3×M16—62no—
203C2×C3×C8—24no—
204C2×C3×C8—21no—
205C2×C3×C8—21no—
206C2×C3×C8—32no—
207C2×C3×C8C4×D314yescomplemented
208C2×C3×C8C4×D314yescomplemented
209C2×C3×C8C22×D311yescharacteristic
210C2×C3×C8C22×D311yescharacteristic
211C2×C3×C8C22×D311yescharacteristic
212C2×C3×C8C22×D311yescharacteristic
213C3×C4⋊C4—32no—
214C3×C4⋊C4—32no—
215C3×C4⋊C4—32no—
216C3×C22⋊C4—32no—
217C3×C22⋊C4—61no—
218C3×C22⋊C4—61no—
219C3×C42—32no—
220C3×C42—61no—
221C3×C42—61no—
222#217—21no—
223#217—21no—
224#217D1212yes—
225(C2×D3)⋊C4—64no—
226(C2×D3)⋊C4—64no—
227C4⋊Dic3D1212yes—
228C4⋊Dic3C22×D312yes—
229C4⋊Dic3C22×D312yes—
230Dic3⋊C4—64no—
231Dic3⋊C4—64no—
232C4×Dic3—21no—
233C4×Dic3—21no—
234C4×Dic3—64no—
235C4×Dic3—64no—
236C4×Dic3C22×D312yes—
237#208—22no—
238C2×C3⋊C8C22×D312yes—
239#204—38no—
240#204—38no—
241#204—38no—
242#204—38no—
243#204—68no—
244#204—68no—
245C22×C32—22no—
246C22×C32C4×D412yes—
247C22×C32C22×D411yescharacteristic
248C2×C3⋊D3—24no—
249C2×C3⋊D3—44no—
250C2×C3⋊D3—84no—
251C32×C4C4×D412yes—
252C32×C4C23×C411yescharacteristic
253C32×C4C2×#4111yescharacteristic
254C3⋊Dic3—24no—
255C3×Dic3—24no—
256C3×Dic3—42no—
257C3×Dic3—42no—
258C22×Q8—91no—
259C22×D4—91no—
260C2×SD16—98no—
261C2×SD16—92no—
262C2×SD16—92no—
263C2×M16—31no—
264C22×C8D3211yescharacteristic
265C4×Q8—94no—
266C4×Q8—182no—
267C4×D4—94no—
268C4×D4—182no—
269#117—31no—
270#117—31no—
271#117—31no—
272#117—182no—
273C2×C22⋊C4—182no—
274#107—32no—
275#106—32no—
276#103—94no—
277#102—94no—
278#97—32no—
279C4×C8—32no—
280C23×C3—21no—
281C23×C3C2×D1211yescharacteristic
282C23×C3D3×D411yescharacteristic
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—64no—
286C22×D3—64no—
287C22×D3—122no—
288C22×D3—124no—
289C22×D3—242no—
290C22×D3—242no—
291C22×D3—244no—
292C2×C3×C4—21no—
293C2×C3×C4—22no—
294C2×C3×C4—21no—
295C2×C3×C4—22no—
296C2×C3×C4—34no—
297C2×C3×C4—62no—
298C2×C3×C4—62no—
299C2×C3×C4C2×C4×D312yes—
300C2×C3×C4C2×C4×D312yes—
301C2×C3×C4C2×D1211yescharacteristic
302C2×C3×C4#23512yes—
303C2×C3×C4D3×D411yescharacteristic
304C2×C3×C4#23912yes—
305C2×C3×C4C23×D311yescharacteristic
306C2×C3×C4C23×D311yescharacteristic
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—64no—
310C2×Dic3—64no—
311C2×Dic3—62no—
312C2×Dic3—62no—
313C2×Dic3—122no—
314C2×Dic3—124no—
315C2×Dic3C2×D1214yes—
316D12—34no—
317D12—34no—
318D12—64no—
319D12—64no—
320D12—64no—
321D12—62no—
322D12—62no—
323D12—122no—
324D12—124no—
325C4×D3—244no—
326C4×D3—244no—
327Dic6—34no—
328Dic6—34no—
329Dic6—64no—
330Dic6—64no—
331Dic6—64no—
332Dic6—62no—
333Dic6—62no—
334Dic6—122no—
335Dic6—124no—
336C3×C8—22no—
337C3×C8—22no—
338C3×C8—62no—
339C3×C8C2×C4×D312yes—
340C3×C8C2×C4×D312yes—
341C3×C8C2×C4×D312yes—
342C3×C8C2×C4×D312yes—
343C3⋊C8—22no—
344C2×C32—22no—
345C2×C32C2×C4×D411yescharacteristic
346C2×C32#57712yes—
347C3⋊D3—44no—
348C24—181no—
349C2×Q8—92no—
350C2×Q8—94no—
351C2×Q8—182no—
352C2×Q8—181no—
353C2×D4—92no—
354C2×D4—94no—
355C2×D4—182no—
356C2×D4—181no—
357C22×C4—184no—
358C22×C4—181no—
359C22×C4C2×D3211yescharacteristic
360SD16—98no—
361SD16—98no—
362M16—62no—
363C2×C8—32no—
364C2×C8#62414yescomplemented
365C2×C8C2×D3211yescharacteristic
366C2×C8C2×D3211yescharacteristic
367C4⋊C4—32no—
368C4⋊C4—32no—
369C4⋊C4—32no—
370C4⋊C4—184no—
371C22⋊C4—32no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C22⋊C4—184no—
375C42—32no—
376C42—61no—
377C42—61no—
378C42—184no—
379C22×C3—24no—
380C22×C3—22no—
381C22×C3—22no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3C4×D1212yes—
385C22×C3#89312yes—
386C22×C3C22×D1211yescharacteristic
387C22×C3C2×D3×D411yescharacteristic
388C2×D3—64no—
389C2×D3—64no—
390C2×D3—124no—
391C2×D3—124no—
392C2×D3—124no—
393C2×D3—244no—
394C2×D3—244no—
395C2×D3—244no—
396C2×D3—248no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—22no—
400C3×C4—64no—
401C3×C4—122no—
402C3×C4—122no—
403C3×C4C4×D1212yes—
404C3×C4#89312yes—
405C3×C4C22×C4×D311yescharacteristic
406C3×C4C22×C4×D311yescharacteristic
407C3×C4C2×#23511yescharacteristic
408C3×C4C2×#23911yescharacteristic
409Dic3—24no—
410Dic3—42no—
411Dic3—42no—
412Dic3—64no—
413Dic3—64no—
414Dic3—124no—
415C32#294911yescharacteristic, complemented, Sylow
416C23—182no—
417C23—184no—
418C23—722no—
419C23D3×D1211yescharacteristic
420Q8—94no—
421Q8—182no—
422Q8—184no—
423D4—94no—
424D4—182no—
425D4—184no—
426C2×C4—34no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—182no—
430C2×C4—184no—
431C2×C4—724no—
432C2×C4#379912yes—
433C2×C4D3×D1211yescharacteristic
434C2×C4C2×#62412yes—
435C2×C4C22×D3211yescharacteristic
436C8—62no—
437C8C2×#62412yes—
438C8C2×#62412yes—
439C2×C3—24no—
440C2×C3—22no—
441C2×C3—22no—
442C2×C3—21no—
443C2×C3—22no—
444C2×C3C2×C4×D1211yescharacteristic
445C2×C3C2×#89311yescharacteristic
446C2×C3#575112yes—
447C2×C3#577012yes—
448D3—124no—
449D3—124no—
450D3—244no—
451C22—22no—
452C22—184no—
453C22—364no—
454C22—724no—
455C22#6389412yes—
456C22C2×D3×D1211yescharacteristic
457C4—64no—
458C4—122no—
459C4—122no—
460C4—184no—
461C4#6389412yes—
462C4C2×#379911yescharacteristic
463C4C22×#62411yescharacteristic
464C3—21no—
465C3#7857211yescharacteristic, complemented
466C3#7916811yescharacteristic, complemented
467C2—22no—
468C2—364no—
469C2#1059467912yes—
470C2C2×#6389411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2949
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
3. #10594828C2semidirect
4. C3×#5106C2semidirect
5. C3×#5101C2semidirect
6. #10591107C2semidirect
8. #10590773C2semidirect
9. #10590758C2semidirect
15. C2×#3744C4semidirect
27. #63844C22semidirect
28. C3×#818C22semidirect
29. C3×#817C22semidirect
30. C3×#815C22semidirect
31. C3×C8×Dic3C22semidirect
32. #63567C22semidirect
45. #5106D3semidirect
46. #5101D3semidirect
62. C2×#634C2×C4semidirect
65. C2×C32×C8C2×C4semidirect
68. #3744C2×C4semidirect
69. #3744C2×C4semidirect
128. #818C2×D3semidirect
129. #817C2×D3semidirect
131. #815C2×D3semidirect
132. C8×Dic3C2×D3semidirect
207. C2×C3×C8C4×D3semidirect
208. C2×C3×C8C4×D3semidirect
364. C2×C8#624semidirect
415. C32#2949semidirect
465. C3#78572semidirect
466. C3#79168semidirect

Maximal subgroups

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

subgroupindex
C22×#37442
#105949962
#105948282
C3×#51062
C3×#51012
#105911072
#105910962
#105907732
#105907582
#791683
#785723