Finite Group Databasebeta

← #11783912

Subgroups — #11783912

Order 1152.

725 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594954C211yesmaximal, characteristic
2C2×#63632C211yesmaximal, characteristic
3C3×#4932C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic
5Dic3×#208C211yesmaximal, characteristic, complemented
6C3×#4523C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#69430—31nomaximal
9#68729—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63952—22no—
18#63894C412yescomplemented
19C4×#624—21no—
20#63874—21no—
21#63844C412yescomplemented
22#63632C414yescomplemented
23C3×C3⋊#95—22no—
24#63570C414yescomplemented
25#63554—21no—
26Dic3×C3⋊C8—21no—
27#5522—31no—
28C4×#235—31no—
29C3×#376—31no—
30C2×#825—31no—
31Dic3×M16—31no—
32#4932D311yescharacteristic, complemented
33C2×#805—31no—
34C2×#805—31no—
35C2×#805—31no—
36C2×#805—61no—
37C4×#208—31no—
38C3×#339—31no—
39#4532—31no—
40#4523—31no—
41#4523D311yescharacteristic, complemented
42C22×C32×C4—21no—
43C22×C32×C4C2311yescharacteristic
44C2×#638—21no—
45#3828—21no—
46#3828—21no—
47#3828C2×C412yes—
48#3828C2×C412yes—
49C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×#634C2×C411yescharacteristic
52C22×C3×Dic3—21no—
53C22×C3×Dic3D412yes—
54C2×#624—22no—
55C32×C42—21no—
56C32×C42C2×C412yescomplemented
57#3748—21no—
58#3748C2×C412yescomplemented
59C2×C3⋊(C3⋊C8)—21no—
60C3×#217—21no—
61C3×C4⋊Dic3C2×C412yes—
62C3×C4×Dic3—21no—
63C3×C4×Dic3—21no—
64C3×C4×Dic3C2×C412yes—
65C3×C4×Dic3C2×C412yescomplemented
66C3×C4×Dic3D411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×#208—21no—
69C3×#208C2×C412yescomplemented
70C2×C3×C3⋊C8—21no—
71#3724—22no—
72#3722—22no—
73Dic32—22no—
74#1759—91noSylow
75C2×#235—31no—
76C2×#235—31no—
77C2×#235—61no—
78C2×C3×M16—31no—
79C3×#117—31no—
80C2×C3×C42—21no—
81C2×C3×C42—31no—
82C2×C3×C42—31no—
83C2×C3×C42C2×D311yescharacteristic
84C2×C3×C42C2×D311yescharacteristic
85C4×#67—62no—
86#926C2×D311yescharacteristic
87C2×C4×Dic3C2×D311yescharacteristic
88C2×C4×Dic3C2×D311yescharacteristic
89C2×#208—31no—
90C2×#208—31no—
91C2×#208—61no—
92C2×#208C2×D311yescharacteristic
93#893—32no—
94#887—32no—
95#67⋊C4—62no—
96C4×D12—32no—
97#872—61no—
98#872—61no—
99C42×D3—61no—
100C42×D3—61no—
101C4×Dic6—32no—
102C3×#95—62no—
103C3⋊#95—22no—
104#825—34no—
105#815—61no—
106C8×Dic3—61no—
107#805—34no—
108#805—34no—
109#805—34no—
110#805—64no—
111#803—61no—
112C4×C3⋊C8—61no—
113C23×C32C2×D411yescharacteristic
114C22×C3⋊D3—21no—
115C2×C32×C4—22no—
116C2×C32×C4—42no—
117C2×C32×C4C22×C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C2×C32×C4#4111yescharacteristic
123#638—22no—
124#638—22no—
125C2×C3⋊Dic3—21no—
126C4⋊(C3⋊D3)—21no—
127C4⋊(C3⋊D3)C4212yes—
128C4×C3⋊D3—22no—
129C4×C3⋊D3—22no—
130#634—21no—
131#634C4212yes—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—42no—
136C2×C3×Dic3C22⋊C412yes—
137C2×C3×Dic3C22⋊C412yes—
138#624—44no—
139C3⋊(C3⋊C8)—22no—
140C3×C3⋊C8—22no—
141C4×#41—91no—
142C2×#104—91no—
143C2×#104—91no—
144C4×M16—91no—
145#376—31no—
146#339—31no—
147#339—91no—
148C22×C3×C4—21no—
149C22×C3×C4—21no—
150C22×C3×C4—21no—
151C22×C3×C4—32no—
152C22×C3×C4—41no—
153C22×C3×C4—61no—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C2×#67—61no—
157C2×#67—61no—
158C2×#67—121no—
159C22×Dic3—21no—
160C22×Dic3#6712yes—
161#235—32no—
162#235—32no—
163#235—32no—
164#235—32no—
165#235—62no—
166#235—62no—
167#235—61no—
168#235—61no—
169#235—61no—
170#235—61no—
171#235—121no—
172#235—121no—
173C2×D12—31no—
174C2×D12—31no—
175C2×D12—61no—
176C2×C4×D3—61no—
177C2×C4×D3—61no—
178C2×C4×D3—62no—
179C2×C4×D3—62no—
180C2×C4×D3—121no—
181C2×Dic6—31no—
182C2×Dic6—31no—
183C2×Dic6—61no—
184C3×M16—32no—
185C3×M16—61no—
186C2×C3×C8—61no—
187C3×C4⋊C4—32no—
188C3×C22⋊C4—61no—
189C3×C42—21no—
190C3×C42—21no—
191C3×C42—22no—
192C3×C42—32no—
193C3×C42—31no—
194C3×C42—31no—
195C3×C42—32no—
196C3×C42—41no—
197C3×C42—61no—
198C3×C42—61no—
199C3×C42C4×D312yescomplemented
200C3×C42C4×D312yescomplemented
201#217—21no—
202(C2×D3)⋊C4—62no—
203(C2×D3)⋊C4—62no—
204C4⋊Dic3C4×D312yes—
205Dic3⋊C4—62no—
206Dic3⋊C4—62no—
207C4×Dic3—21no—
208C4×Dic3—21no—
209C4×Dic3—62no—
210C4×Dic3—62no—
211C4×Dic3C4×D312yes—
212C4×Dic3C4×D312yescomplemented
213C4×Dic3D1211yescharacteristic
214C4×Dic3D1211yescharacteristic
215#208—21no—
216#208—32no—
217#208—32no—
218#208—62no—
219#208—61no—
220#208—61no—
221#208—121no—
222#208C4×D312yescomplemented
223C2×C3⋊C8—21no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—121no—
227C22×C32—22no—
228C22×C32C2×C22⋊C411yescharacteristic
229C22×C32C4×D411yescharacteristic
230C22×C32C4×D411yescharacteristic
231C2×C3⋊D3—22no—
232C2×C3⋊D3—42no—
233C32×C4—42no—
234C32×C4C2×C4211yescharacteristic
235C32×C4#11711yescharacteristic
236C32×C4C4×D411yescharacteristic
237C32×C4C4×D411yescharacteristic
238C3⋊Dic3—22no—
239C3×Dic3—22no—
240C3×Dic3—22no—
241C3×Dic3—42no—
242C3×Dic3—42no—
243C2×#41—91no—
244C2×M16—31no—
245C2×M16—91no—
246C4×Q8—92no—
247C4×D4—92no—
248C4×D4—182no—
249#117—31no—
250#117—181no—
251C2×C42—31no—
252C2×C42—31no—
253C2×C42—181no—
254C2×C42D3211yescharacteristic
255#104—94no—
256#104—94no—
257#97—181no—
258C4×C8—181no—
259#95—62no—
260C23×C3—21no—
261C23×C3D3×D411yescharacteristic
262C23×C3C2×#6711yescharacteristic
263C22×D3—61no—
264C22×D3—61no—
265C22×D3—121no—
266C2×C3×C4—22no—
267C2×C3×C4—22no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—32no—
275C2×C3×C4—32no—
276C2×C3×C4—42no—
277C2×C3×C4—42no—
278C2×C3×C4—42no—
279C2×C3×C4—44no—
280C2×C3×C4—62no—
281C2×C3×C4—62no—
282C2×C3×C4—122no—
283C2×C3×C4—122no—
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4C2×C4×D311yescharacteristic
286C2×C3×C4C2×C4×D311yescharacteristic
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4C2×C4×D311yescharacteristic
290C2×C3×C4C2×D1211yescharacteristic
291C2×C3×C4#23511yescharacteristic
292C2×C3×C4#23511yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4#23711yescharacteristic
295C2×C3×C4#23911yescharacteristic
296#67—62no—
297#67—62no—
298#67—62no—
299#67—62no—
300#67—122no—
301#67—122no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—42no—
305C2×Dic3—42no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—121no—
309C2×Dic3(C2×D3)⋊C412yes—
310C2×Dic3(C2×D3)⋊C412yes—
311D12—32no—
312D12—32no—
313D12—62no—
314D12—61no—
315D12—61no—
316D12—121no—
317C4×D3—62no—
318C4×D3—62no—
319C4×D3—62no—
320C4×D3—62no—
321C4×D3—122no—
322C4×D3—122no—
323C4×D3—124no—
324C4×D3—124no—
325Dic6—32no—
326Dic6—32no—
327Dic6—62no—
328Dic6—61no—
329Dic6—61no—
330Dic6—121no—
331C3×C8—62no—
332C3⋊C8—22no—
333C3⋊C8—62no—
334C3⋊C8—62no—
335C3⋊C8—122no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32C4×C22⋊C411yescharacteristic
339C2×C32#42112yes—
340C3⋊D3—42no—
341#41—92no—
342#41—92no—
343#41—181no—
344#41—181no—
345C2×Q8—91no—
346C2×D4—91no—
347C2×D4—181no—
348C22×C4—21no—
349C22×C4—32no—
350C22×C4—61no—
351C22×C4—182no—
352C22×C4—181no—
353C22×C4C2×D3211yescharacteristic
354M16—32no—
355M16—61no—
356M16—92no—
357M16—181no—
358C2×C8—61no—
359C2×C8—181no—
360C4⋊C4—32no—
361C4⋊C4—182no—
362C22⋊C4—61no—
363C22⋊C4—182no—
364C42—21no—
365C42—32no—
366C42—31no—
367C42—31no—
368C42—32no—
369C42—61no—
370C42—61no—
371C42—182no—
372C42#62412yescomplemented
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—42no—
379C22×C3D3×C22⋊C411yescharacteristic
380C22×C3#67⋊C411yescharacteristic
381C22×C3#89311yescharacteristic
382C22×C3C2×(C2×D3)⋊C411yescharacteristic
383C22×C3C4×#6711yescharacteristic
384C22×C3C4×#6711yescharacteristic
385C2×D3—62no—
386C2×D3—62no—
387C2×D3—122no—
388C2×D3—122no—
389C2×D3—122no—
390C2×D3—242no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—21no—
394C3×C4—21no—
395C3×C4—42no—
396C3×C4—42no—
397C3×C4—44no—
398C3×C4—62no—
399C3×C4—62no—
400C3×C4—122no—
401C3×C4—122no—
402C3×C4C42×D311yescharacteristic
403C3×C4C42×D311yescharacteristic
404C3×C4#87211yescharacteristic
405C3×C4C4×D1211yescharacteristic
406C3×C4C4×D1211yescharacteristic
407C3×C4#67⋊C411yescharacteristic
408C3×C4#89211yescharacteristic
409C3×C4#89311yescharacteristic
410Dic3—22no—
411Dic3—22no—
412Dic3—42no—
413Dic3—42no—
414Dic3—62no—
415Dic3—62no—
416Dic3—122no—
417C32#175911yescharacteristic, complemented, Sylow
418C23—181no—
419C23D3×#6711yescharacteristic
420Q8—92no—
421Q8—181no—
422D4—92no—
423D4—182no—
424D4—182no—
425D4—181no—
426C2×C4—22no—
427C2×C4—32no—
428C2×C4—32no—
429C2×C4—42no—
430C2×C4—62no—
431C2×C4—62no—
432C2×C4—122no—
433C2×C4—122no—
434C2×C4—181no—
435C2×C4—182no—
436C2×C4—182no—
437C2×C4—364no—
438C2×C4#379911yescharacteristic
439C2×C4C4×D3211yescharacteristic
440C2×C4C4×D3211yescharacteristic
441C2×C4D3×D1211yescharacteristic
442C2×C4#380411yescharacteristic
443C2×C4C2×#62411yescharacteristic
444C8—62no—
445C8—182no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—22no—
452C2×C3—41no—
453C2×C3—41no—
454C2×C3#466611yescharacteristic
455C2×C3#482112yes—
456C2×C3C4×(C2×D3)⋊C411yescharacteristic
457C2×C3#500512yes—
458D3—122no—
459D3—122no—
460D3—242no—
461C22—22no—
462C22—182no—
463C22—362no—
464C22#6390411yescharacteristic
465C22D3×(C2×D3)⋊C411yescharacteristic
466C22#6395211yescharacteristic
467C4—42no—
468C4—62no—
469C4—62no—
470C4—122no—
471C4—122no—
472C4—182no—
473C4#6383611yescharacteristic
474C4#6388011yescharacteristic
475C4C4×#62411yescharacteristic
476C4#6389411yescharacteristic
477C3—21no—
478C3#6872911yescharacteristic, complemented
479C3#6943011yescharacteristic, complemented
480C2—21no—
481C2—21no—
482C2—362no—
483C2#1059039212yes—
484C2#1059123311yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1759
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C3×#4932C2semidirect
5. Dic3×#208C2semidirect
6. C3×#4523C2semidirect
7. #10589161C2semidirect
18. #63894C4semidirect
21. #63844C4semidirect
22. #63632C4semidirect
24. #63570C4semidirect
32. #4932D3semidirect
41. #4523D3semidirect
56. C32×C42C2×C4semidirect
58. #3748C2×C4semidirect
65. C3×C4×Dic3C2×C4semidirect
69. C3×#208C2×C4semidirect
199. C3×C42C4×D3semidirect
200. C3×C42C4×D3semidirect
212. C4×Dic3C4×D3semidirect
222. #208C4×D3semidirect
372. C42#624semidirect
417. C32#1759semidirect
478. C3#68729semidirect
479. C3#69430semidirect

Maximal subgroups

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

subgroupindex
#105949542
C2×#636322
C3×#49322
C2×#635702
Dic3×#2082
C3×#45232
#105891612
#694303
#687293