Finite Group Databasebeta

← #11786691

Subgroups — #11786691

Order 1152.

659 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5523C211yesmaximal, characteristic
2C3×#4995C211yesmaximal, characteristic, complemented
3#10591359C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic
5#10591087C211yesmaximal, characteristic
6#10589398C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#71664—31nomaximal
9#70680—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#892—21no—
18C3×D3×C4⋊C4—21no—
19C3×#67⋊C4—22no—
20C3×C4×D12—21no—
21C3×C4×Dic6—21no—
22C2×#3724—22no—
23C3×#808—21no—
24C3×#807—21no—
25#63568C414yescomplemented
26#63565—21no—
27#63562—21no—
28C3×#520—31no—
29#5523D311yescharacteristic
30C3×#428—31no—
31C2×#837—31no—
32#5232—31no—
33C2×#825—31no—
34#4995D311yescharacteristic, complemented
35#4975—31no—
36#4975—31no—
37#4966—31no—
38#4554—31no—
39#4532—31no—
40#4532—31no—
41#4532—61no—
42#4530—31no—
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C2×C3×#67—21no—
46C22×C3×Dic3—21no—
47C22×C3×Dic3D412yes—
48C3×#235—21no—
49C3×#235—21no—
50C3×#235C2×C412yes—
51C3×#235Q812yes—
52C2×C3×D12D411yescharacteristic
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—22no—
55C2×C3×Dic6D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C4⋊C4D411yescharacteristic
58C32×C22⋊C4—21no—
59C32×C42—21no—
60C4×C3⋊Dic3—21no—
61C4×C3⋊Dic3C2×C412yescomplemented
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×(C2×D3)⋊C4—22no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×Dic3⋊C4—22no—
71C3×C4×Dic3—22no—
72C3×#208—21no—
73C3×#208C2×C412yescomplemented
74C2×C3×C3⋊C8—21no—
75#3724—44no—
76#1859—91noSylow
77C2×C3×#41—31no—
78C2×#235C2×D311yescharacteristic
79C2×C3×M16—31no—
80C3×C4×Q8—61no—
81C3×C4×D4—61no—
82C3×C4×D4—62no—
83C3×#117—21no—
84C3×#117—61no—
85C3×#117C2×D311yescharacteristic
86C3×#117C2×D311yescharacteristic
87C2×C3×C4⋊C4—31no—
88C2×C3×C4⋊C4—31no—
89C2×C3×C4⋊C4—61no—
90C2×C4⋊Dic3C2×D311yescharacteristic
91C2×C4⋊Dic3C2×D311yescharacteristic
92C2×Dic3⋊C4—62no—
93C2×Dic3⋊C4—62no—
94C2×C4×Dic3—31no—
95C2×C4×Dic3—31no—
96C2×C4×Dic3—61no—
97C2×#208—31no—
98C2×#208—31no—
99C2×#208—61no—
100C2×#208C2×D311yescharacteristic
101#892—21no—
102D3×C4⋊C4—21no—
103#67⋊C4—22no—
104C4×D12—21no—
105C4×Dic6—21no—
106C3×#107—61no—
107C3×#106—61no—
108#837—34no—
109#835—61no—
110#832—61no—
111#825—34no—
112#810—61no—
113#809—61no—
114#808—21no—
115#807—21no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—21no—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×Q811yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C3⋊Dic3—22no—
127C2×C3⋊Dic3—22no—
128C2×C3⋊Dic3—22no—
129C3×#67—22no—
130C3×#67—22no—
131C2×C3×Dic3—21no—
132C2×C3×Dic3—22no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3—41no—
136C3×D12—21no—
137C3×D12C4⋊C412yescomplemented
138C3×C4×D3—22no—
139C3×C4×D3—22no—
140C3×C4×D3—82no—
141C3×Dic6—21no—
142C3×Dic6C4⋊C412yescomplemented
143C3⋊(C3⋊C8)—41no—
144C3×C3⋊C8—22no—
145#520—31no—
146#428—31no—
147C2×#104—91no—
148#417—91no—
149#384—91no—
150#343—91no—
151#339—91no—
152C3×#41—32no—
153C3×#41—32no—
154C3×#41—61no—
155C3×#41—61no—
156C2×C3×Q8—31no—
157C2×C3×D4—31no—
158C2×C3×D4—61no—
159C22×C3×C4—21no—
160C22×C3×C4—32no—
161C22×C3×C4—62no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C2×#67—21no—
167C22×Dic3—21no—
168C22×Dic3—61no—
169C22×Dic3—61no—
170C22×Dic3—121no—
171C22×Dic3#6712yes—
172#235—21no—
173#235—21no—
174#235Dic612yes—
175#235C4×D312yes—
176C2×D12#6711yescharacteristic
177C2×C4×D3—21no—
178C2×C4×D3—22no—
179C2×Dic6#6711yescharacteristic
180C3×M16—32no—
181C3×M16—61no—
182C2×C3×C8—61no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—62no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4—61no—
188C3×C4⋊C4—61no—
189C3×C4⋊C4—61no—
190C3×C4⋊C4#6711yescharacteristic
191C3×C4⋊C4#6711yescharacteristic
192C3×C4⋊C4#6711yescharacteristic
193C3×C4⋊C4#6711yescharacteristic
194C3×C22⋊C4—21no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—41no—
197C3×C22⋊C4—62no—
198C3×C42—21no—
199C3×C42—21no—
200C3×C42—41no—
201C3×C42—62no—
202(C2×D3)⋊C4—22no—
203C4⋊Dic3—21no—
204C4⋊Dic3—21no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207Dic3⋊C4—22no—
208Dic3⋊C4—124no—
209Dic3⋊C4—124no—
210C4×Dic3—22no—
211C4×Dic3—32no—
212C4×Dic3—32no—
213C4×Dic3—62no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—121no—
217#208—21no—
218#208—62no—
219#208—61no—
220#208—61no—
221#208—61no—
222#208—61no—
223#208—121no—
224#208C4×D312yescomplemented
225C2×C3⋊C8—21no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—121no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32C4×D411yescharacteristic
232C22×C32#12011yescharacteristic
233C22×C32C22⋊Q811yescharacteristic
234C2×C3×D3—22no—
235C2×C3×D3—41no—
236C2×C3×D3—41no—
237C32×C4—41no—
238C32×C4—41no—
239C32×C4C2×C4⋊C411yescharacteristic
240C32×C4C4×D411yescharacteristic
241C32×C4C22⋊Q811yescharacteristic
242C32×C4#12311yescharacteristic
243C3⋊Dic3—24no—
244C3×Dic3—22no—
245C3×Dic3—42no—
246C3×Dic3—81no—
247C2×#41—31no—
248C2×M16—31no—
249C2×M16—91no—
250C4×Q8—61no—
251C4×D4—61no—
252C4×D4—62no—
253#117—61no—
254#117D3211yescharacteristic
255C2×C4⋊C4—31no—
256C2×C4⋊C4—31no—
257C2×C4⋊C4—61no—
258C2×C4⋊C4—182no—
259C2×C42—91no—
260#107—61no—
261#106—61no—
262#104—94no—
263#103—181no—
264#102—181no—
265C23×C3—21no—
266C23×C3—61no—
267C23×C3D3×D411yescharacteristic
268C23×C3C2×#6711yescharacteristic
269C22×D3—21no—
270C3×Q8—32no—
271C3×Q8—61no—
272C3×D4—32no—
273C3×D4—62no—
274C3×D4—62no—
275C3×D4—61no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—41no—
287C2×C3×C4—41no—
288C2×C3×C4—61no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4—122no—
293C2×C3×C4—122no—
294C2×C3×C4—121no—
295C2×C3×C4—242no—
296C2×C3×C4C2×Dic611yescharacteristic
297C2×C3×C4C2×C4×D311yescharacteristic
298C2×C3×C4C2×C4×D311yescharacteristic
299C2×C3×C4#23511yescharacteristic
300C2×C3×C4#23511yescharacteristic
301C2×C3×C4#23511yescharacteristic
302C2×C3×C4D3×D411yescharacteristic
303C2×C3×C4D3×Q811yescharacteristic
304C2×C3×C4#23911yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306C2×C3×C4C2×#6711yescharacteristic
307C2×C3×C4C2×#6711yescharacteristic
308#67—22no—
309#67—22no—
310C2×Dic3—21no—
311C2×Dic3—22no—
312C2×Dic3—42no—
313C2×Dic3—42no—
314C2×Dic3—41no—
315C2×Dic3—62no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—62no—
321C2×Dic3—122no—
322C2×Dic3—122no—
323C2×Dic3—122no—
324D12—21no—
325D12Dic3⋊C412yescomplemented
326C4×D3—22no—
327C4×D3—22no—
328C4×D3—82no—
329Dic6—21no—
330Dic6Dic3⋊C412yescomplemented
331C3×C8—62no—
332C3⋊C8—22no—
333C3⋊C8—122no—
334C3⋊C8—121no—
335C3⋊C8—121no—
336C2×C32—21no—
337C2×C32—21no—
338C2×C32#38511yescharacteristic
339C2×C32#45311yescharacteristic
340C2×C32#45611yescharacteristic
341C3×D3—42no—
342#41—32no—
343#41—32no—
344#41—61no—
345#41—61no—
346C2×Q8—31no—
347C2×D4—31no—
348C2×D4—61no—
349C22×C4—32no—
350C22×C4—62no—
351C22×C4—61no—
352C22×C4—61no—
353C22×C4—181no—
354C22×C4C2×D3211yescharacteristic
355M16—32no—
356M16—61no—
357M16—181no—
358M16—181no—
359C2×C8—61no—
360C2×C8—181no—
361C4⋊C4—62no—
362C4⋊C4—61no—
363C4⋊C4—61no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—364no—
367C4⋊C4#62511yescharacteristic
368C4⋊C4#62511yescharacteristic
369C22⋊C4—21no—
370C22⋊C4—62no—
371C42—21no—
372C42—62no—
373C42—92no—
374C42—181no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—62no—
385C22×C3—121no—
386C22×C3—121no—
387C22×C3#89311yescharacteristic
388C22×C3#89611yescharacteristic
389C22×C3#92411yescharacteristic
390C22×C3C4×#6711yescharacteristic
391C22×C3#93711yescharacteristic
392C22×C3#95311yescharacteristic
393C2×D3—22no—
394C2×D3—41no—
395C2×D3—41no—
396C3×C4—21no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—41no—
401C3×C4—41no—
402C3×C4—41no—
403C3×C4—41no—
404C3×C4—62no—
405C3×C4—81no—
406C3×C4—81no—
407C3×C4—122no—
408C3×C4—241no—
409C3×C4D3×C4⋊C411yescharacteristic
410C3×C4#89411yescharacteristic
411C3×C4C2×Dic3⋊C411yescharacteristic
412C3×C4#92411yescharacteristic
413C3×C4C4×#6711yescharacteristic
414C3×C4C4×#6711yescharacteristic
415C3×C4#92911yescharacteristic
416C3×C4#94611yescharacteristic
417Dic3—22no—
418Dic3—42no—
419Dic3—64no—
420Dic3—64no—
421Dic3—81no—
422Dic3—124no—
423C32#185911yescharacteristic, complemented, Sylow
424C23—61no—
425C23D3×#6711yescharacteristic
426Q8—32no—
427Q8—61no—
428D4—32no—
429D4—62no—
430D4—62no—
431D4—61no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—61no—
435C2×C4—62no—
436C2×C4—62no—
437C2×C4—62no—
438C2×C4—122no—
439C2×C4—122no—
440C2×C4—121no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4—182no—
444C2×C4—242no—
445C2×C4D3×Dic611yescharacteristic
446C2×C4#379811yescharacteristic
447C2×C4#379911yescharacteristic
448C2×C4C4×D3211yescharacteristic
449C2×C4C2×#62511yescharacteristic
450C2×C4D3×#6711yescharacteristic
451C8—62no—
452C8—361no—
453C2×C3—21no—
454C2×C3—21no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—41no—
461C2×C3—41no—
462C2×C3—122no—
463C2×C3#498911yescharacteristic
464C2×C3#519811yescharacteristic
465C2×C3#520511yescharacteristic
466C2×C3#521011yescharacteristic
467C2×C3#524111yescharacteristic
468C2×C3#524611yescharacteristic
469D3—42no—
470C22—21no—
471C22—21no—
472C22—62no—
473C22—121no—
474C22—121no—
475C22#6385111yescharacteristic
476C22#6390411yescharacteristic
477C22#6397611yescharacteristic
478C4—41no—
479C4—41no—
480C4—62no—
481C4—122no—
482C4—184no—
483C4—241no—
484C4#6385011yescharacteristic
485C4#6385611yescharacteristic
486C4D3×Dic3⋊C411yescharacteristic
487C4C4×#62511yescharacteristic
488C3—21no—
489C3#7068011yescharacteristic, complemented
490C3#7166411yescharacteristic, complemented
491C2—21no—
492C2—21no—
493C2—122no—
494C2#1059127711yescharacteristic
495C2#1059166511yescharacteristic
496C2#1059168711yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1859
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#4995C2semidirect
3. #10591359C2semidirect
6. #10589398C2semidirect
7. #10589167C2semidirect
25. #63568C4semidirect
34. #4995D3semidirect
61. C4×C3⋊Dic3C2×C4semidirect
73. C3×#208C2×C4semidirect
137. C3×D12C4⋊C4semidirect
142. C3×Dic6C4⋊C4semidirect
224. #208C4×D3semidirect
325. D12Dic3⋊C4semidirect
330. Dic6Dic3⋊C4semidirect
423. C32#1859semidirect
489. C3#70680semidirect
490. C3#71664semidirect

Maximal subgroups

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

subgroupindex
C3×#55232
C3×#49952
#105913592
C2×#635682
#105910872
#105893982
#105891672
#716643
#706803