Finite Group Databasebeta

← #11786585

Subgroups — #11786585

Order 1152.

703 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic
2C3×#4995C211yesmaximal, characteristic, complemented
3#10591323C211yesmaximal, characteristic
4#10591139C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic
6#10589398C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#71647—31nomaximal
9#70674—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#893—21no—
18C3×#893—21no—
19C3×D3×C22⋊C4—22no—
20C3×C4×D12—21no—
21C3×C4×D12—21no—
22C2×(C2×D3)⋊Dic3—22no—
23C3×#808—21no—
24C3×#807—21no—
25#63576—21no—
26#63574—21no—
27#63558C414yescomplemented
28C3×#518—31no—
29#5521D311yescharacteristic
30C3×#428—31no—
31#5221—31no—
32C2×#833—31no—
33C2×#823—31no—
34#4995—31no—
35#4995D311yescharacteristic, complemented
36#4988—31no—
37#4964—31no—
38#4555—31no—
39#4532—31no—
40#4532—31no—
41#4532—31no—
42#4532—61no—
43C23×C3×D3D412yes—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C22×C3×Dic3—21no—
47C2×C3×D12—21no—
48C2×C3×D12—21no—
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12C2×C412yes—
52C2×C3×D12Q812yes—
53C2×C3×C4×D3—22no—
54C2×C3×C4×D3—22no—
55C32×C4⋊C4D411yescharacteristic
56C32×C4⋊C4D411yescharacteristic
57C32×C22⋊C4—21no—
58C32×C42—21no—
59C4×C3⋊Dic3—21no—
60C4×C3⋊Dic3—21no—
61#3748—21no—
62#3748C2×C412yescomplemented
63C2×C3⋊(C3⋊C8)—21no—
64C3×#217—21no—
65C3×(C2×D3)⋊C4—22no—
66C3×(C2×D3)⋊C4—22no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3D411yescharacteristic
70C3×C4⋊Dic3D411yescharacteristic
71C3×C4×Dic3—21no—
72C3×#208—21no—
73C3×#208C2×C412yescomplemented
74C2×C3×C3⋊C8—21no—
75(C2×D3)⋊Dic3—44no—
76#1856—91noSylow
77C22×C3×D4—31no—
78C22×D12C2×D311yescharacteristic
79C2×C3×M16—31no—
80C3×C4×D4—61no—
81C3×C4×D4—61no—
82C3×C4×D4—61no—
83C3×C4×D4—61no—
84C3×#117—21no—
85C3×#117—31no—
86C3×#117C2×D311yescharacteristic
87C3×#117C2×D311yescharacteristic
88C2×C3×C4⋊C4—31no—
89C2×C3×C22⋊C4—62no—
90C2×#217—62no—
91C2×(C2×D3)⋊C4—62no—
92#926C2×D311yescharacteristic
93C2×C4⋊Dic3C2×D311yescharacteristic
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#893—21no—
102#893—21no—
103D3×C22⋊C4—22no—
104C4×D12—21no—
105C4×D12—21no—
106C3×#107—61no—
107C3×#106—61no—
108#833—34no—
109#823—34no—
110#808—21no—
111#808—61no—
112#808—61no—
113#807—21no—
114#807—61no—
115#807—61no—
116C23×C32C2×D411yescharacteristic
117C22×C3×D3—22no—
118C22×C3×D3—22no—
119C22×C3×D3—42no—
120C22×C3×D3—42no—
121C22×C3×D3C4⋊C414yes—
122C2×C32×C4—21no—
123C2×C32×C4—21no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q811yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C3⋊Dic3—22no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3—41no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—42no—
136C2×C3×Dic3—41no—
137C3×D12—22no—
138C3×D12—22no—
139C3×D12—22no—
140C3×D12—22no—
141C3×C4×D3—82no—
142C3×C4×D3—82no—
143C3⋊(C3⋊C8)—22no—
144C3×C3⋊C8—22no—
145#518—31no—
146#428—31no—
147#428—91no—
148C2×#100—91no—
149#390—91no—
150#339—91no—
151#339—91no—
152C24×C3—32no—
153C23×D3#6712yes—
154C2×C3×D4—32no—
155C2×C3×D4—32no—
156C2×C3×D4—61no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C22×C3×C4—21no—
161C22×C3×C4—62no—
162C22×C3×C4—62no—
163C22×C3×C4—61no—
164C22×C3×C4C22×D311yescharacteristic
165C22×C3×C4C22×D311yescharacteristic
166C22×Dic3—21no—
167C22×Dic3—61no—
168C22×Dic3—61no—
169C22×Dic3—121no—
170C2×D12—21no—
171C2×D12—21no—
172C2×D12—21no—
173C2×D12—21no—
174C2×D12Dic612yes—
175C2×D12C4×D312yes—
176C2×C4×D3—22no—
177C2×C4×D3—22no—
178C3×M16—32no—
179C3×M16—61no—
180C2×C3×C8—61no—
181C3×C4⋊C4—21no—
182C3×C4⋊C4—21no—
183C3×C4⋊C4—31no—
184C3×C4⋊C4—31no—
185C3×C4⋊C4—61no—
186C3×C4⋊C4—61no—
187C3×C4⋊C4#6711yescharacteristic
188C3×C4⋊C4#6711yescharacteristic
189C3×C4⋊C4#6711yescharacteristic
190C3×C4⋊C4#6711yescharacteristic
191C3×C22⋊C4—21no—
192C3×C22⋊C4—21no—
193C3×C22⋊C4—41no—
194C3×C22⋊C4—62no—
195C3×C22⋊C4—62no—
196C3×C22⋊C4—61no—
197C3×C42—21no—
198C3×C42—21no—
199C3×C42—41no—
200C3×C42—61no—
201#217—21no—
202#217—124no—
203(C2×D3)⋊C4—22no—
204(C2×D3)⋊C4—22no—
205(C2×D3)⋊C4—124no—
206C4⋊Dic3—21no—
207C4⋊Dic3—21no—
208C4⋊Dic3#6711yescharacteristic
209C4⋊Dic3#6711yescharacteristic
210C4×Dic3—21no—
211C4×Dic3—62no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C4×Dic3—121no—
217#208—21no—
218#208—32no—
219#208—32no—
220#208—62no—
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×C32C2×C4⋊C411yescharacteristic
232C22×C32#12011yescharacteristic
233C22×C32#12311yescharacteristic
234C2×C3×D3—24no—
235C2×C3×D3—42no—
236C2×C3×D3—42no—
237C2×C3×D3—44no—
238C2×C3×D3—82no—
239C32×C4—41no—
240C32×C4—41no—
241C32×C4C4×D411yescharacteristic
242C32×C4C4×D411yescharacteristic
243C32×C4C22⋊Q811yescharacteristic
244C32×C4C22⋊Q811yescharacteristic
245C3⋊Dic3—42no—
246C3×Dic3—41no—
247C3×Dic3—41no—
248C3×Dic3—81no—
249C22×D4—31no—
250C2×M16—31no—
251C2×M16—91no—
252C4×D4—61no—
253C4×D4—61no—
254C4×D4—61no—
255C4×D4—61no—
256#117—31no—
257#117D3211yescharacteristic
258C2×C4⋊C4—31no—
259C2×C22⋊C4—62no—
260C2×C22⋊C4—182no—
261C2×C42—91no—
262#107—61no—
263#107—181no—
264#106—61no—
265#106—181no—
266#100—94no—
267C23×C3—21no—
268C23×C3—34no—
269C23×C3—62no—
270C23×C3—62no—
271C23×C3—122no—
272C23×C3—122no—
273C23×C3D3×D411yescharacteristic
274C23×C3C2×#6711yescharacteristic
275C22×D3—22no—
276C22×D3—22no—
277C22×D3—42no—
278C22×D3—42no—
279C22×D3Dic3⋊C414yes—
280C3×D4—62no—
281C3×D4—62no—
282C3×D4—62no—
283C3×D4—62no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—41no—
295C2×C3×C4—41no—
296C2×C3×C4—61no—
297C2×C3×C4—61no—
298C2×C3×C4—122no—
299C2×C3×C4—121no—
300C2×C3×C4—242no—
301C2×C3×C4—242no—
302C2×C3×C4C2×Dic611yescharacteristic
303C2×C3×C4C2×C4×D311yescharacteristic
304C2×C3×C4C2×C4×D311yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4#23511yescharacteristic
307C2×C3×C4#23511yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×Q811yescharacteristic
310C2×C3×C4#23911yescharacteristic
311C2×C3×C4C2×#6711yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×C3×C4C2×#6711yescharacteristic
314C2×Dic3—21no—
315C2×Dic3—21no—
316C2×Dic3—42no—
317C2×Dic3—41no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—122no—
321C2×Dic3—122no—
322C2×Dic3—121no—
323C2×Dic3—121no—
324C2×Dic3—122no—
325C2×Dic3—121no—
326C2×Dic3—121no—
327D12—22no—
328D12—22no—
329D12—22no—
330D12—22no—
331C4×D3—82no—
332C4×D3—82no—
333C3×C8—62no—
334C3⋊C8—22no—
335C3⋊C8—62no—
336C3⋊C8—62no—
337C3⋊C8—122no—
338C2×C32—21no—
339C2×C32—21no—
340C2×C32#38511yescharacteristic
341C2×C32#45311yescharacteristic
342C2×C32#45511yescharacteristic
343C3×D3—44no—
344C24—32no—
345C2×D4—32no—
346C2×D4—32no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C22×C4—62no—
352C22×C4—62no—
353C22×C4—61no—
354C22×C4—181no—
355C22×C4C2×D3211yescharacteristic
356M16—32no—
357M16—61no—
358M16—92no—
359M16—181no—
360C2×C8—61no—
361C2×C8—181no—
362C4⋊C4—31no—
363C4⋊C4—31no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4#62511yescharacteristic
367C4⋊C4#62511yescharacteristic
368C22⋊C4—21no—
369C22⋊C4—62no—
370C22⋊C4—62no—
371C22⋊C4—61no—
372C22⋊C4—364no—
373C42—21no—
374C42—61no—
375C42—181no—
376C42—181no—
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—21no—
383C22×C3—21no—
384C22×C3—41no—
385C22×C3—41no—
386C22×C3—64no—
387C22×C3—124no—
388C22×C3—122no—
389C22×C3—122no—
390C22×C3—242no—
391C22×C3D3×C4⋊C411yescharacteristic
392C22×C3#89411yescharacteristic
393C22×C3C2×Dic3⋊C411yescharacteristic
394C22×C3#92911yescharacteristic
395C22×C3#93711yescharacteristic
396C22×C3#95311yescharacteristic
397C2×D3—24no—
398C2×D3—42no—
399C2×D3—42no—
400C2×D3—44no—
401C2×D3—82no—
402C3×C4—21no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—21no—
406C3×C4—41no—
407C3×C4—41no—
408C3×C4—41no—
409C3×C4—41no—
410C3×C4—81no—
411C3×C4—81no—
412C3×C4—121no—
413C3×C4—121no—
414C3×C4—241no—
415C3×C4#89311yescharacteristic
416C3×C4#89611yescharacteristic
417C3×C4#92411yescharacteristic
418C3×C4#92411yescharacteristic
419C3×C4C4×#6711yescharacteristic
420C3×C4C4×#6711yescharacteristic
421C3×C4C4×#6711yescharacteristic
422C3×C4#94611yescharacteristic
423Dic3—41no—
424Dic3—41no—
425Dic3—81no—
426Dic3—122no—
427Dic3—122no—
428Dic3—124no—
429C32#185611yescharacteristic, complemented, Sylow
430C23—34no—
431C23—62no—
432C23—62no—
433C23—122no—
434C23—122no—
435C23D3×#6711yescharacteristic
436D4—62no—
437D4—62no—
438D4—62no—
439D4—62no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—122no—
445C2×C4—121no—
446C2×C4—182no—
447C2×C4—242no—
448C2×C4—242no—
449C2×C4—361no—
450C2×C4—361no—
451C2×C4D3×Dic611yescharacteristic
452C2×C4#379811yescharacteristic
453C2×C4#379911yescharacteristic
454C2×C4C4×D3211yescharacteristic
455C2×C4C2×#62511yescharacteristic
456C2×C4D3×#6711yescharacteristic
457C8—62no—
458C8—182no—
459C2×C3—21no—
460C2×C3—21no—
461C2×C3—21no—
462C2×C3—21no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—41no—
467C2×C3—41no—
468C2×C3—124no—
469C2×C3#498911yescharacteristic
470C2×C3#519811yescharacteristic
471C2×C3#520211yescharacteristic
472C2×C3#521011yescharacteristic
473C2×C3#524111yescharacteristic
474C2×C3#524211yescharacteristic
475D3—44no—
476C22—21no—
477C22—21no—
478C22—64no—
479C22—124no—
480C22—122no—
481C22—122no—
482C22—242no—
483C22#6385011yescharacteristic
484C22D3×Dic3⋊C411yescharacteristic
485C22#6397611yescharacteristic
486C4—41no—
487C4—41no—
488C4—121no—
489C4—121no—
490C4—241no—
491C4—362no—
492C4#6385111yescharacteristic
493C4#6385611yescharacteristic
494C4C4×#62511yescharacteristic
495C4#6390411yescharacteristic
496C3—21no—
497C3#7067411yescharacteristic, complemented
498C3#7164711yescharacteristic, complemented
499C2—21no—
500C2—21no—
501C2—124no—
502C2#1059127711yescharacteristic
503C2#1059166411yescharacteristic
504C2#1059166511yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC22×C32#120
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1856
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
4. #10591139C2semidirect
6. #10589398C2semidirect
7. #10589160C2semidirect
27. #63558C4semidirect
35. #4995D3semidirect
62. #3748C2×C4semidirect
73. C3×#208C2×C4semidirect
224. #208C4×D3semidirect
429. C32#1856semidirect
497. C3#70674semidirect
498. C3#71647semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
C3×#49952
#105913232
#105911392
C2×#635582
#105893982
#105891602
#716473
#706743